form-5.0.1/0000755000175100017510000000000015217035744006233 5form-5.0.1/scripts/0000755000175100017510000000000015217035744007722 5form-5.0.1/scripts/run-latex2html.sh0000755000175100017510000000212215217035721013057 #!/bin/bash # # @file run-latex2html.sh # # Usage: # run-latex2html.sh main.tex # set -euo pipefail if [ $# -ne 1 ]; then echo "Usage: $(basename "$0") main.tex" >&2 exit 1 fi MAIN_PATH=$1 MAIN_TEX=$(basename "$MAIN_PATH") MAIN_DIR=$(dirname "$MAIN_PATH") case $MAIN_TEX in *.tex) MAIN=$(basename "$MAIN_TEX" .tex) ;; *) MAIN_PATH=$MAIN_PATH.tex MAIN=$MAIN_TEX MAIN_TEX=$MAIN.tex ;; esac MAIN_DIR=$MAIN_DIR/$MAIN if [ -z "${LATEX2HTML+x}" ] || [ -z "$LATEX2HTML" ]; then LATEX2HTML=latex2html fi # https://stackoverflow.com/a/43919044 a="/$0"; a="${a%/*}"; a="${a:-.}"; a="${a##/}/"; BINDIR=$(cd "$a"; pwd) LATEX2HTML_INIT=$BINDIR/.latex2html-init "$LATEX2HTML" -init_file "$LATEX2HTML_INIT" "$MAIN_PATH" fix_html() { # (1) HREF="main.html#SECTION..." -> HREF="#SECTION..." # (2) workaround for latex2html < v2025 # See: https://github.com/latex2html/latex2html/commit/b77ee98 sed "s/$2.html#/#/g" "$1" | sed 's/&̈#305;/\ï/g' >"$1.tmp" mv "$1.tmp" "$1" } fix_html "$MAIN_DIR/index.html" "$MAIN" fix_html "$MAIN_DIR/$MAIN.html" "$MAIN" form-5.0.1/scripts/.latex2html-init0000644000175100017510000000061215217035721012662 $ADDRESS = '' . 'This document was generated using the ' . "LaTeX2HTML" . " translator Version $TEX2HTMLVERSION." . ''; $DO_INCLUDE = 'float'; # https://github.com/vermaseren/form/issues/442 $DVIPSOPT = ' -E'; $INFO = 0; $MAX_SPLIT_DEPTH = 0; $NO_FOOTNODE = 1; $NO_NAVIGATION = 1; $SHORT_INDEX = 1; $SHOW_SECTION_NUMBERS = 1; 1; form-5.0.1/README.md0000644000175100017510000000617715217035721007440 FORM ==== [![Test](https://github.com/form-dev/form/actions/workflows/test.yml/badge.svg?branch=master)](https://github.com/form-dev/form/actions/workflows/test.yml) [![Coverage Status](https://coveralls.io/repos/github/form-dev/form/badge.svg?branch=master)](https://coveralls.io/github/form-dev/form?branch=master) FORM is a Symbolic Manipulation System. It reads symbolic expressions from files and executes symbolic/algebraic transformations upon them. The answers are returned in a textual mathematical representation. As its landmark feature, the size of the considered expressions in FORM is only limited by the available disk space and not by the available RAM. FORM has been essential for many state-of-the-art computations in High Energy Physics. FORM's original author is Jos Vermaseren of NIKHEF, the Dutch institute for subatomic physics. Other people that have made contributions can be found in the file "[AUTHORS](AUTHORS)". Quick examples -------------- The following FORM program repeatedly matches the power of a variable `x` in the expression `E`, as long as the power is more than 1 and creates two new terms with lower power: ```form Symbol x,n; Local E = x^10; repeat id x^n?{>1} = x^(n-1) + x^(n-2); Print; .end ``` and yields `E = 34 + 55*x`. The following FORM program matches the function `f` that has any arguments before encountering an `x` and any arguments after, and switches them around: ```form CFunction f; Symbol x; Local E = f(1,2,x,3,4); id f(?a,x,?b) = f(?b,?a); Print; .end ``` and yields `E = f(3,4,1,2)`. FORM can match many more complicated patterns and has many more features, as documented in the [additional information](#additional-information). Build instructions ------------ Before building FORM, it is advised to install the optional dependencies `gmp`, `mpfr`, `zstd`, `zlib` and `flint` for better performance. To use arbitrary-precision floating-point arithmetic, both `gmp` and `mpfr` are required; if either is unavailable it will not be enabled. To quickly build FORM, install the `autoconf` and `automake` packages. Then, after cloning the repository, run: ```sh autoreconf -i ./configure make make install ``` For more advanced build options, see the file "[INSTALL](INSTALL)". Additional information ---------------------- The latest release notes are available on the [Wiki](https://github.com/form-dev/form/wiki/Release-Notes-FORM-5.0.0); the latest reference manual can be found [here](https://form-dev.github.io/form-docs/stable/manual/), and the Form Cookbook can be found [here](https://github.com/form-dev/form/wiki/FORM-Cookbook). More background information, a collection of FORM programs, and a number of courses can be found on the official [FORM website](http://www.nikhef.nl/~form) and on the [Wiki](https://github.com/form-dev/form/wiki). Information about copying and licensing of this software can be found in the file "[COPYING](COPYING)". Bugs and remarks ---------------- For reporting bugs, asking questions, giving remarks and suggestions, we welcome you to use the [Issue Tracker](https://github.com/form-dev/form/issues) or [Discussion Forum](https://github.com/form-dev/form/discussions). form-5.0.1/m4/0000755000175100017510000000000015217035744006553 5form-5.0.1/m4/ax_check_compile_flag.m40000644000175100017510000000641115217035721013200 # =========================================================================== # http://www.gnu.org/software/autoconf-archive/ax_check_compile_flag.html # =========================================================================== # # SYNOPSIS # # AX_CHECK_COMPILE_FLAG(FLAG, [ACTION-SUCCESS], [ACTION-FAILURE], [EXTRA-FLAGS], [INPUT]) # # DESCRIPTION # # Check whether the given FLAG works with the current language's compiler # or gives an error. 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"$ac_site_file" \ || { { printf "%s\n" "$as_me:${as_lineno-$LINENO}: error: in \`$ac_pwd':" >&5 printf "%s\n" "$as_me: error: in \`$ac_pwd':" >&2;} as_fn_error $? "failed to load site script $ac_site_file See \`config.log' for more details" "$LINENO" 5; } fi done if test -r "$cache_file"; then # Some versions of bash will fail to source /dev/null (special files # actually), so we avoid doing that. DJGPP emulates it as a regular file. if test /dev/null != "$cache_file" && test -f "$cache_file"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: loading cache $cache_file" >&5 printf "%s\n" "$as_me: loading cache $cache_file" >&6;} case $cache_file in [\\/]* | ?:[\\/]* ) . "$cache_file";; *) . "./$cache_file";; esac fi else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: creating cache $cache_file" >&5 printf "%s\n" "$as_me: creating cache $cache_file" >&6;} >$cache_file fi # Test code for whether the C compiler supports C89 (global declarations) ac_c_conftest_c89_globals=' /* Does the compiler advertise C89 conformance? Do not test the value of __STDC__, because some compilers set it to 0 while being otherwise adequately conformant. */ #if !defined __STDC__ # error "Compiler does not advertise C89 conformance" #endif #include #include struct stat; /* Most of the following tests are stolen from RCS 5.7 src/conf.sh. */ struct buf { int x; }; struct buf * (*rcsopen) (struct buf *, struct stat *, int); static char *e (p, i) char **p; int i; { return p[i]; } static char *f (char * (*g) (char **, int), char **p, ...) { char *s; va_list v; va_start (v,p); s = g (p, va_arg (v,int)); va_end (v); return s; } /* OSF 4.0 Compaq cc is some sort of almost-ANSI by default. It has function prototypes and stuff, but not \xHH hex character constants. These do not provoke an error unfortunately, instead are silently treated as an "x". The following induces an error, until -std is added to get proper ANSI mode. Curiously \x00 != x always comes out true, for an array size at least. It is necessary to write \x00 == 0 to get something that is true only with -std. */ int osf4_cc_array ['\''\x00'\'' == 0 ? 1 : -1]; /* IBM C 6 for AIX is almost-ANSI by default, but it replaces macro parameters inside strings and character constants. */ #define FOO(x) '\''x'\'' int xlc6_cc_array[FOO(a) == '\''x'\'' ? 1 : -1]; int test (int i, double x); struct s1 {int (*f) (int a);}; struct s2 {int (*f) (double a);}; int pairnames (int, char **, int *(*)(struct buf *, struct stat *, int), int, int);' # Test code for whether the C compiler supports C89 (body of main). ac_c_conftest_c89_main=' ok |= (argc == 0 || f (e, argv, 0) != argv[0] || f (e, argv, 1) != argv[1]); ' # Test code for whether the C compiler supports C99 (global declarations) ac_c_conftest_c99_globals=' // Does the compiler advertise C99 conformance? #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L # error "Compiler does not advertise C99 conformance" #endif #include extern int puts (const char *); extern int printf (const char *, ...); extern int dprintf (int, const char *, ...); extern void *malloc (size_t); // Check varargs macros. These examples are taken from C99 6.10.3.5. // dprintf is used instead of fprintf to avoid needing to declare // FILE and stderr. #define debug(...) dprintf (2, __VA_ARGS__) #define showlist(...) puts (#__VA_ARGS__) #define report(test,...) ((test) ? puts (#test) : printf (__VA_ARGS__)) static void test_varargs_macros (void) { int x = 1234; int y = 5678; debug ("Flag"); debug ("X = %d\n", x); showlist (The first, second, and third items.); report (x>y, "x is %d but y is %d", x, y); } // Check long long types. #define BIG64 18446744073709551615ull #define BIG32 4294967295ul #define BIG_OK (BIG64 / BIG32 == 4294967297ull && BIG64 % BIG32 == 0) #if !BIG_OK #error "your preprocessor is broken" #endif #if BIG_OK #else #error "your preprocessor is broken" #endif static long long int bignum = -9223372036854775807LL; static unsigned long long int ubignum = BIG64; struct incomplete_array { int datasize; double data[]; }; struct named_init { int number; const wchar_t *name; double average; }; typedef const char *ccp; static inline int test_restrict (ccp restrict text) { // See if C++-style comments work. // Iterate through items via the restricted pointer. // Also check for declarations in for loops. for (unsigned int i = 0; *(text+i) != '\''\0'\''; ++i) continue; return 0; } // Check varargs and va_copy. static bool test_varargs (const char *format, ...) { va_list args; va_start (args, format); va_list args_copy; va_copy (args_copy, args); const char *str = ""; int number = 0; float fnumber = 0; while (*format) { switch (*format++) { case '\''s'\'': // string str = va_arg (args_copy, const char *); break; case '\''d'\'': // int number = va_arg (args_copy, int); break; case '\''f'\'': // float fnumber = va_arg (args_copy, double); break; default: break; } } va_end (args_copy); va_end (args); return *str && number && fnumber; } ' # Test code for whether the C compiler supports C99 (body of main). ac_c_conftest_c99_main=' // Check bool. _Bool success = false; success |= (argc != 0); // Check restrict. if (test_restrict ("String literal") == 0) success = true; char *restrict newvar = "Another string"; // Check varargs. success &= test_varargs ("s, d'\'' f .", "string", 65, 34.234); test_varargs_macros (); // Check flexible array members. struct incomplete_array *ia = malloc (sizeof (struct incomplete_array) + (sizeof (double) * 10)); ia->datasize = 10; for (int i = 0; i < ia->datasize; ++i) ia->data[i] = i * 1.234; // Check named initializers. struct named_init ni = { .number = 34, .name = L"Test wide string", .average = 543.34343, }; ni.number = 58; int dynamic_array[ni.number]; dynamic_array[0] = argv[0][0]; dynamic_array[ni.number - 1] = 543; // work around unused variable warnings ok |= (!success || bignum == 0LL || ubignum == 0uLL || newvar[0] == '\''x'\'' || dynamic_array[ni.number - 1] != 543); ' # Test code for whether the C compiler supports C11 (global declarations) ac_c_conftest_c11_globals=' // Does the compiler advertise C11 conformance? #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 201112L # error "Compiler does not advertise C11 conformance" #endif // Check _Alignas. char _Alignas (double) aligned_as_double; char _Alignas (0) no_special_alignment; extern char aligned_as_int; char _Alignas (0) _Alignas (int) aligned_as_int; // Check _Alignof. enum { int_alignment = _Alignof (int), int_array_alignment = _Alignof (int[100]), char_alignment = _Alignof (char) }; _Static_assert (0 < -_Alignof (int), "_Alignof is signed"); // Check _Noreturn. int _Noreturn does_not_return (void) { for (;;) continue; } // Check _Static_assert. struct test_static_assert { int x; _Static_assert (sizeof (int) <= sizeof (long int), "_Static_assert does not work in struct"); long int y; }; // Check UTF-8 literals. #define u8 syntax error! char const utf8_literal[] = u8"happens to be ASCII" "another string"; // Check duplicate typedefs. typedef long *long_ptr; typedef long int *long_ptr; typedef long_ptr long_ptr; // Anonymous structures and unions -- taken from C11 6.7.2.1 Example 1. struct anonymous { union { struct { int i; int j; }; struct { int k; long int l; } w; }; int m; } v1; ' # Test code for whether the C compiler supports C11 (body of main). ac_c_conftest_c11_main=' _Static_assert ((offsetof (struct anonymous, i) == offsetof (struct anonymous, w.k)), "Anonymous union alignment botch"); v1.i = 2; v1.w.k = 5; ok |= v1.i != 5; ' # Test code for whether the C compiler supports C11 (complete). ac_c_conftest_c11_program="${ac_c_conftest_c89_globals} ${ac_c_conftest_c99_globals} ${ac_c_conftest_c11_globals} int main (int argc, char **argv) { int ok = 0; ${ac_c_conftest_c89_main} ${ac_c_conftest_c99_main} ${ac_c_conftest_c11_main} return ok; } " # Test code for whether the C compiler supports C99 (complete). ac_c_conftest_c99_program="${ac_c_conftest_c89_globals} ${ac_c_conftest_c99_globals} int main (int argc, char **argv) { int ok = 0; ${ac_c_conftest_c89_main} ${ac_c_conftest_c99_main} return ok; } " # Test code for whether the C compiler supports C89 (complete). ac_c_conftest_c89_program="${ac_c_conftest_c89_globals} int main (int argc, char **argv) { int ok = 0; ${ac_c_conftest_c89_main} return ok; } " # Test code for whether the C++ compiler supports C++98 (global declarations) ac_cxx_conftest_cxx98_globals=' // Does the compiler advertise C++98 conformance? #if !defined __cplusplus || __cplusplus < 199711L # error "Compiler does not advertise C++98 conformance" #endif // These inclusions are to reject old compilers that // lack the unsuffixed header files. #include #include // and are *not* freestanding headers in C++98. extern void assert (int); namespace std { extern int strcmp (const char *, const char *); } // Namespaces, exceptions, and templates were all added after "C++ 2.0". using std::exception; using std::strcmp; namespace { void test_exception_syntax() { try { throw "test"; } catch (const char *s) { // Extra parentheses suppress a warning when building autoconf itself, // due to lint rules shared with more typical C programs. assert (!(strcmp) (s, "test")); } } template struct test_template { T const val; explicit test_template(T t) : val(t) {} template T add(U u) { return static_cast(u) + val; } }; } // anonymous namespace ' # Test code for whether the C++ compiler supports C++98 (body of main) ac_cxx_conftest_cxx98_main=' assert (argc); assert (! argv[0]); { test_exception_syntax (); test_template tt (2.0); assert (tt.add (4) == 6.0); assert (true && !false); } ' # Test code for whether the C++ compiler supports C++11 (global declarations) ac_cxx_conftest_cxx11_globals=' // Does the compiler advertise C++ 2011 conformance? #if !defined __cplusplus || __cplusplus < 201103L # error "Compiler does not advertise C++11 conformance" #endif namespace cxx11test { constexpr int get_val() { return 20; } struct testinit { int i; double d; }; class delegate { public: delegate(int n) : n(n) {} delegate(): delegate(2354) {} virtual int getval() { return this->n; }; protected: int n; }; class overridden : public delegate { public: overridden(int n): delegate(n) {} virtual int getval() override final { return this->n * 2; } }; class nocopy { public: nocopy(int i): i(i) {} nocopy() = default; nocopy(const nocopy&) = delete; nocopy & operator=(const nocopy&) = delete; private: int i; }; // for testing lambda expressions template Ret eval(Fn f, Ret v) { return f(v); } // for testing variadic templates and trailing return types template auto sum(V first) -> V { return first; } template auto sum(V first, Args... rest) -> V { return first + sum(rest...); } } ' # Test code for whether the C++ compiler supports C++11 (body of main) ac_cxx_conftest_cxx11_main=' { // Test auto and decltype auto a1 = 6538; auto a2 = 48573953.4; auto a3 = "String literal"; int total = 0; for (auto i = a3; *i; ++i) { total += *i; } decltype(a2) a4 = 34895.034; } { // Test constexpr short sa[cxx11test::get_val()] = { 0 }; } { // Test initializer lists cxx11test::testinit il = { 4323, 435234.23544 }; } { // Test range-based for int array[] = {9, 7, 13, 15, 4, 18, 12, 10, 5, 3, 14, 19, 17, 8, 6, 20, 16, 2, 11, 1}; for (auto &x : array) { x += 23; } } { // Test lambda expressions using cxx11test::eval; assert (eval ([](int x) { return x*2; }, 21) == 42); double d = 2.0; assert (eval ([&](double x) { return d += x; }, 3.0) == 5.0); assert (d == 5.0); assert (eval ([=](double x) mutable { return d += x; }, 4.0) == 9.0); assert (d == 5.0); } { // Test use of variadic templates using cxx11test::sum; auto a = sum(1); auto b = sum(1, 2); auto c = sum(1.0, 2.0, 3.0); } { // Test constructor delegation cxx11test::delegate d1; cxx11test::delegate d2(); cxx11test::delegate d3(45); } { // Test override and final cxx11test::overridden o1(55464); } { // Test nullptr char *c = nullptr; } { // Test template brackets test_template<::test_template> v(test_template(12)); 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"no acceptable egrep could be found in $PATH$PATH_SEPARATOR/usr/xpg4/bin" "$LINENO" 5 fi else ac_cv_path_EGREP=$EGREP fi fi fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ac_cv_path_EGREP" >&5 printf "%s\n" "$ac_cv_path_EGREP" >&6; } EGREP="$ac_cv_path_EGREP" printf "%s\n" "#define TIME_WITH_SYS_TIME 1" >>confdefs.h ac_fn_c_check_header_compile "$LINENO" "fcntl.h" "ac_cv_header_fcntl_h" "$ac_includes_default" if test "x$ac_cv_header_fcntl_h" = xyes then : printf "%s\n" "#define HAVE_FCNTL_H 1" >>confdefs.h fi ac_fn_c_check_header_compile "$LINENO" "limits.h" "ac_cv_header_limits_h" "$ac_includes_default" if test "x$ac_cv_header_limits_h" = xyes then : printf "%s\n" "#define HAVE_LIMITS_H 1" >>confdefs.h fi ac_fn_c_check_header_compile "$LINENO" "sys/file.h" "ac_cv_header_sys_file_h" "$ac_includes_default" if test "x$ac_cv_header_sys_file_h" = xyes then : printf "%s\n" "#define HAVE_SYS_FILE_H 1" >>confdefs.h fi ac_ext=cpp ac_cpp='$CXXCPP $CPPFLAGS' ac_compile='$CXX -c $CXXFLAGS $CPPFLAGS conftest.$ac_ext >&5' ac_link='$CXX -o conftest$ac_exeext $CXXFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_cxx_compiler_gnu ac_fn_cxx_check_header_compile "$LINENO" "unordered_map" "ac_cv_header_unordered_map" "$ac_includes_default" if test "x$ac_cv_header_unordered_map" = xyes then : printf "%s\n" "#define HAVE_UNORDERED_MAP 1" >>confdefs.h fi ac_fn_cxx_check_header_compile "$LINENO" "tr1/unordered_map" "ac_cv_header_tr1_unordered_map" "$ac_includes_default" if test "x$ac_cv_header_tr1_unordered_map" = xyes then : printf "%s\n" "#define HAVE_TR1_UNORDERED_MAP 1" >>confdefs.h fi ac_fn_cxx_check_header_compile "$LINENO" "boost/unordered_map.hpp" "ac_cv_header_boost_unordered_map_hpp" "$ac_includes_default" if test "x$ac_cv_header_boost_unordered_map_hpp" = xyes then : printf "%s\n" "#define HAVE_BOOST_UNORDERED_MAP_HPP 1" >>confdefs.h fi ac_fn_cxx_check_header_compile "$LINENO" "unordered_set" "ac_cv_header_unordered_set" "$ac_includes_default" if test "x$ac_cv_header_unordered_set" = xyes then : printf "%s\n" "#define HAVE_UNORDERED_SET 1" >>confdefs.h fi ac_fn_cxx_check_header_compile "$LINENO" "tr1/unordered_set" "ac_cv_header_tr1_unordered_set" "$ac_includes_default" if test "x$ac_cv_header_tr1_unordered_set" = xyes then : printf "%s\n" "#define HAVE_TR1_UNORDERED_SET 1" >>confdefs.h fi ac_fn_cxx_check_header_compile "$LINENO" "boost/unordered_set.hpp" "ac_cv_header_boost_unordered_set_hpp" "$ac_includes_default" if test "x$ac_cv_header_boost_unordered_set_hpp" = xyes then : printf "%s\n" "#define HAVE_BOOST_UNORDERED_SET_HPP 1" >>confdefs.h fi ac_ext=c ac_cpp='$CPP $CPPFLAGS' ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_c_compiler_gnu # Checks for builtin functions ok=no if test $ok != yes then : { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking __builtin_popcount" >&5 printf %s "checking __builtin_popcount... " >&6; } cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ int main (void) { int x = __builtin_popcount((unsigned int)(-1)); ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO" then : ok=yes; printf "%s\n" "#define HAVE_BUILTIN_POPCOUNT 1" >>confdefs.h fi rm -f core conftest.err conftest.$ac_objext conftest.beam \ conftest$ac_exeext conftest.$ac_ext { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ok" >&5 printf "%s\n" "$ok" >&6; } fi if test $ok != yes then : { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking __popcnt" >&5 printf %s "checking __popcnt... " >&6; } cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include int main (void) { unsigned int x = __popcnt((unsigned int)(-1)); ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO" then : ok=yes; printf "%s\n" "#define HAVE_POPCNT 1" >>confdefs.h fi rm -f core conftest.err conftest.$ac_objext conftest.beam \ conftest$ac_exeext conftest.$ac_ext { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ok" >&5 printf "%s\n" "$ok" >&6; } fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking __attribute__((noreturn))" >&5 printf %s "checking __attribute__((noreturn))... " >&6; } cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ extern void fatal() __attribute__((noreturn)); int main (void) { return 0; ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO" then : printf "%s\n" "#define NORETURN __attribute__((noreturn))" >>confdefs.h { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: yes" >&5 printf "%s\n" "yes" >&6; } else $as_nop printf "%s\n" "#define NORETURN /**/" >>confdefs.h { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi rm -f core conftest.err conftest.$ac_objext conftest.beam \ conftest$ac_exeext conftest.$ac_ext # Check for inline { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for inline" >&5 printf %s "checking for inline... " >&6; } if test ${ac_cv_c_inline+y} then : printf %s "(cached) " >&6 else $as_nop ac_cv_c_inline=no for ac_kw in inline __inline__ __inline; do cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #ifndef __cplusplus typedef int foo_t; static $ac_kw foo_t static_foo (void) {return 0; } $ac_kw foo_t foo (void) {return 0; } #endif _ACEOF if ac_fn_c_try_compile "$LINENO" then : ac_cv_c_inline=$ac_kw fi rm -f core conftest.err conftest.$ac_objext conftest.beam conftest.$ac_ext test "$ac_cv_c_inline" != no && break done fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ac_cv_c_inline" >&5 printf "%s\n" "$ac_cv_c_inline" >&6; } case $ac_cv_c_inline in inline | yes) ;; *) case $ac_cv_c_inline in no) ac_val=;; *) ac_val=$ac_cv_c_inline;; esac cat >>confdefs.h <<_ACEOF #ifndef __cplusplus #define inline $ac_val #endif _ACEOF ;; esac # Sets _FILE_OFFSET_BITS if possible # Check whether --enable-largefile was given. if test ${enable_largefile+y} then : enableval=$enable_largefile; fi if test "$enable_largefile" != no; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for special C compiler options needed for large files" >&5 printf %s "checking for special C compiler options needed for large files... " >&6; } if test ${ac_cv_sys_largefile_CC+y} then : printf %s "(cached) " >&6 else $as_nop ac_cv_sys_largefile_CC=no if test "$GCC" != yes; then ac_save_CC=$CC while :; do # IRIX 6.2 and later do not support large files by default, # so use the C compiler's -n32 option if that helps. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include /* Check that off_t can represent 2**63 - 1 correctly. We can't simply define LARGE_OFF_T to be 9223372036854775807, since some C++ compilers masquerading as C compilers incorrectly reject 9223372036854775807. */ #define LARGE_OFF_T (((off_t) 1 << 31 << 31) - 1 + ((off_t) 1 << 31 << 31)) int off_t_is_large[(LARGE_OFF_T % 2147483629 == 721 && LARGE_OFF_T % 2147483647 == 1) ? 1 : -1]; int main (void) { ; return 0; } _ACEOF if ac_fn_c_try_compile "$LINENO" then : break fi rm -f core conftest.err conftest.$ac_objext conftest.beam CC="$CC -n32" if ac_fn_c_try_compile "$LINENO" then : ac_cv_sys_largefile_CC=' -n32'; break fi rm -f core conftest.err conftest.$ac_objext conftest.beam break done CC=$ac_save_CC rm -f conftest.$ac_ext fi fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ac_cv_sys_largefile_CC" >&5 printf "%s\n" "$ac_cv_sys_largefile_CC" >&6; } if test "$ac_cv_sys_largefile_CC" != no; then CC=$CC$ac_cv_sys_largefile_CC fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for _FILE_OFFSET_BITS value needed for large files" >&5 printf %s "checking for _FILE_OFFSET_BITS value needed for large files... " >&6; } if test ${ac_cv_sys_file_offset_bits+y} then : printf %s "(cached) " >&6 else $as_nop while :; do cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include /* Check that off_t can represent 2**63 - 1 correctly. We can't simply define LARGE_OFF_T to be 9223372036854775807, since some C++ compilers masquerading as C compilers incorrectly reject 9223372036854775807. */ #define LARGE_OFF_T (((off_t) 1 << 31 << 31) - 1 + ((off_t) 1 << 31 << 31)) int off_t_is_large[(LARGE_OFF_T % 2147483629 == 721 && LARGE_OFF_T % 2147483647 == 1) ? 1 : -1]; int main (void) { ; return 0; } _ACEOF if ac_fn_c_try_compile "$LINENO" then : ac_cv_sys_file_offset_bits=no; break fi rm -f core conftest.err conftest.$ac_objext conftest.beam conftest.$ac_ext cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #define _FILE_OFFSET_BITS 64 #include /* Check that off_t can represent 2**63 - 1 correctly. We can't simply define LARGE_OFF_T to be 9223372036854775807, since some C++ compilers masquerading as C compilers incorrectly reject 9223372036854775807. */ #define LARGE_OFF_T (((off_t) 1 << 31 << 31) - 1 + ((off_t) 1 << 31 << 31)) int off_t_is_large[(LARGE_OFF_T % 2147483629 == 721 && LARGE_OFF_T % 2147483647 == 1) ? 1 : -1]; int main (void) { ; return 0; } _ACEOF if ac_fn_c_try_compile "$LINENO" then : ac_cv_sys_file_offset_bits=64; break fi rm -f core conftest.err conftest.$ac_objext conftest.beam conftest.$ac_ext ac_cv_sys_file_offset_bits=unknown break done fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ac_cv_sys_file_offset_bits" >&5 printf "%s\n" "$ac_cv_sys_file_offset_bits" >&6; } case $ac_cv_sys_file_offset_bits in #( no | unknown) ;; *) printf "%s\n" "#define _FILE_OFFSET_BITS $ac_cv_sys_file_offset_bits" >>confdefs.h ;; esac rm -rf conftest* if test $ac_cv_sys_file_offset_bits = unknown; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for _LARGE_FILES value needed for large files" >&5 printf %s "checking for _LARGE_FILES value needed for large files... " >&6; } if test ${ac_cv_sys_large_files+y} then : printf %s "(cached) " >&6 else $as_nop while :; do cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include /* Check that off_t can represent 2**63 - 1 correctly. We can't simply define LARGE_OFF_T to be 9223372036854775807, since some C++ compilers masquerading as C compilers incorrectly reject 9223372036854775807. */ #define LARGE_OFF_T (((off_t) 1 << 31 << 31) - 1 + ((off_t) 1 << 31 << 31)) int off_t_is_large[(LARGE_OFF_T % 2147483629 == 721 && LARGE_OFF_T % 2147483647 == 1) ? 1 : -1]; int main (void) { ; return 0; } _ACEOF if ac_fn_c_try_compile "$LINENO" then : ac_cv_sys_large_files=no; break fi rm -f core conftest.err conftest.$ac_objext conftest.beam conftest.$ac_ext cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #define _LARGE_FILES 1 #include /* Check that off_t can represent 2**63 - 1 correctly. We can't simply define LARGE_OFF_T to be 9223372036854775807, since some C++ compilers masquerading as C compilers incorrectly reject 9223372036854775807. */ #define LARGE_OFF_T (((off_t) 1 << 31 << 31) - 1 + ((off_t) 1 << 31 << 31)) int off_t_is_large[(LARGE_OFF_T % 2147483629 == 721 && LARGE_OFF_T % 2147483647 == 1) ? 1 : -1]; int main (void) { ; return 0; } _ACEOF if ac_fn_c_try_compile "$LINENO" then : ac_cv_sys_large_files=1; break fi rm -f core conftest.err conftest.$ac_objext conftest.beam conftest.$ac_ext ac_cv_sys_large_files=unknown break done fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ac_cv_sys_large_files" >&5 printf "%s\n" "$ac_cv_sys_large_files" >&6; } case $ac_cv_sys_large_files in #( no | unknown) ;; *) printf "%s\n" "#define _LARGE_FILES $ac_cv_sys_large_files" >>confdefs.h ;; esac rm -rf conftest* fi fi # POSIX or Windows API # Check whether --with-api was given. if test ${with_api+y} then : withval=$with_api; if test "x$withval" != xposix && test "x$withval" != xwindows then : { { printf "%s\n" "$as_me:${as_lineno-$LINENO}: error: in \`$ac_pwd':" >&5 printf "%s\n" "$as_me: error: in \`$ac_pwd':" >&2;} as_fn_error $? "Invalid argument for API. Use --with-api=posix or --with-api=windows See \`config.log' for more details" "$LINENO" 5; } fi else $as_nop with_api=posix fi if test "x$with_api" = xposix then : print_api=POSIX for ac_header in unistd.h do : ac_fn_c_check_header_compile "$LINENO" "unistd.h" "ac_cv_header_unistd_h" "$ac_includes_default" if test "x$ac_cv_header_unistd_h" = xyes then : printf "%s\n" "#define HAVE_UNISTD_H 1" >>confdefs.h else $as_nop { { printf "%s\n" "$as_me:${as_lineno-$LINENO}: error: in \`$ac_pwd':" >&5 printf "%s\n" "$as_me: error: in \`$ac_pwd':" >&2;} as_fn_error $? "unistd.h is not found See \`config.log' for more details" "$LINENO" 5; } fi done printf "%s\n" "#define UNIX /**/" >>confdefs.h fi if test "x$with_api" = xwindows then : print_api=Windows for ac_header in windows.h do : ac_fn_c_check_header_compile "$LINENO" "windows.h" "ac_cv_header_windows_h" "$ac_includes_default" if test "x$ac_cv_header_windows_h" = xyes then : printf "%s\n" "#define HAVE_WINDOWS_H 1" >>confdefs.h else $as_nop { { printf "%s\n" "$as_me:${as_lineno-$LINENO}: error: in \`$ac_pwd':" >&5 printf "%s\n" "$as_me: error: in \`$ac_pwd':" >&2;} as_fn_error $? "windows.h is not found See \`config.log' for more details" "$LINENO" 5; } fi done printf "%s\n" "#define WINDOWS /**/" >>confdefs.h fi if test "x$with_api" = xposix; then ONUNIX_TRUE= ONUNIX_FALSE='#' else ONUNIX_TRUE='#' ONUNIX_FALSE= fi if test "x$with_api" = xwindows; then ONWINDOWS_TRUE= ONWINDOWS_FALSE='#' else ONWINDOWS_TRUE='#' ONWINDOWS_FALSE= fi # Check for gmp # Check whether --with-gmp was given. if test ${with_gmp+y} then : withval=$with_gmp; if test "x$withval" != xyes && test "x$withval" != xno && test "x$withval" != xcheck then : with_gmp=yes CPPFLAGS="$CPPFLAGS -I$withval/include" LDFLAGS="$LDFLAGS -L$withval/lib" fi else $as_nop with_gmp=check fi if test "x$with_gmp" != xno then : flag=: if $flag then : ac_fn_c_check_header_compile "$LINENO" "gmp.h" "ac_cv_header_gmp_h" "$ac_includes_default" if test "x$ac_cv_header_gmp_h" = xyes then : else $as_nop flag=false fi fi if $flag then : { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for __gmpz_init in -lgmp" >&5 printf %s "checking for __gmpz_init in -lgmp... " >&6; } if test ${ac_cv_lib_gmp___gmpz_init+y} then : printf %s "(cached) " >&6 else $as_nop ac_check_lib_save_LIBS=$LIBS LIBS="-lgmp $LIBS" cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ /* Override any GCC internal prototype to avoid an error. Use char because int might match the return type of a GCC builtin and then its argument prototype would still apply. */ char __gmpz_init (); int main (void) { return __gmpz_init (); ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO" then : ac_cv_lib_gmp___gmpz_init=yes else $as_nop ac_cv_lib_gmp___gmpz_init=no fi rm -f core conftest.err conftest.$ac_objext conftest.beam \ conftest$ac_exeext conftest.$ac_ext LIBS=$ac_check_lib_save_LIBS fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ac_cv_lib_gmp___gmpz_init" >&5 printf "%s\n" "$ac_cv_lib_gmp___gmpz_init" >&6; } if test "x$ac_cv_lib_gmp___gmpz_init" = xyes then : LIBS="-lgmp $LIBS" else $as_nop flag=false fi fi if $flag then : printf "%s\n" "#define WITHGMP /**/" >>confdefs.h with_gmp=yes else $as_nop if test "x$with_gmp" = xyes then : { { printf "%s\n" "$as_me:${as_lineno-$LINENO}: error: in \`$ac_pwd':" >&5 printf "%s\n" "$as_me: error: in \`$ac_pwd':" >&2;} as_fn_error $? "test for GMP failed. Give --without-gmp if you want to compile without GMP See \`config.log' for more details" "$LINENO" 5; } fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: GMP is not available" >&5 printf "%s\n" "$as_me: GMP is not available" >&6;} with_gmp=no fi fi # Check for mpfr # Check whether --with-mpfr was given. if test ${with_mpfr+y} then : withval=$with_mpfr; if test "x$withval" != xyes && test "x$withval" != xno && test "x$withval" != xcheck then : with_mpfr=yes CPPFLAGS="$CPPFLAGS -I$withval/include" LDFLAGS="$LDFLAGS -L$withval/lib" fi else $as_nop with_mpfr=check fi if test "x$with_mpfr" != xno then : flag=: if $flag then : ac_fn_c_check_header_compile "$LINENO" "mpfr.h" "ac_cv_header_mpfr_h" "$ac_includes_default" if test "x$ac_cv_header_mpfr_h" = xyes then : else $as_nop flag=false fi fi if $flag then : { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for mpfr_init2 in -lmpfr" >&5 printf %s "checking for mpfr_init2 in -lmpfr... " >&6; } if test ${ac_cv_lib_mpfr_mpfr_init2+y} then : printf %s "(cached) " >&6 else $as_nop ac_check_lib_save_LIBS=$LIBS LIBS="-lmpfr $LIBS" cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ /* Override any GCC internal prototype to avoid an error. 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"test for parform failed. Give --disable-parform if you do not need to build parform See \`config.log' for more details" "$LINENO" 5; } fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: building parform has been disabled" >&5 printf "%s\n" "$as_me: building parform has been disabled" >&6;} if test "x$enable_debug" = xyes then : { printf "%s\n" "$as_me:${as_lineno-$LINENO}: building parvorm has been disabled" >&5 printf "%s\n" "$as_me: building parvorm has been disabled" >&6;} fi enable_parform=no fi fi build_parform=$enable_parform if test "x$enable_parform" = xyes && test "x$enable_debug" = xyes then : build_parvorm=yes else $as_nop build_parvorm=no fi if test "x$build_parform" = xyes; then BUILD_PARFORM_TRUE= BUILD_PARFORM_FALSE='#' else BUILD_PARFORM_TRUE='#' BUILD_PARFORM_FALSE= fi if test "x$build_parvorm" = xyes; then BUILD_PARVORM_TRUE= BUILD_PARVORM_FALSE='#' else BUILD_PARVORM_TRUE='#' BUILD_PARVORM_FALSE= fi if test "x$MPICXX" != x && test "x$cxxstd_flag" != x; then MPICXX="$MPICXX $cxxstd_flag" fi if test "x$build_form" = xyes || test "x$build_tform" = xyes || test "x$build_parform" = xyes || test "x$build_vorm" = xyes || test "x$build_tvorm" = xyes || test "x$build_parvorm" = xyes then : build_any=yes else $as_nop build_any=no fi # Check for float if test "x$enable_float" != xno then : if test "x$with_gmp" = xyes && test "x$with_mpfr" = xyes then : enable_float=yes else $as_nop if test "x$enable_float" = xyes && test "x$build_any" = xyes then : { { printf "%s\n" "$as_me:${as_lineno-$LINENO}: error: in \`$ac_pwd':" >&5 printf "%s\n" "$as_me: error: in \`$ac_pwd':" >&2;} as_fn_error $? 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Give --disable-sanitize if you want to compile without sanitizer See \`config.log' for more details" "$LINENO" 5; } fi if test "x$enable_sanitize" != xno; then DEBUGCOMPILEFLAGS="$DEBUGCOMPILEFLAGS -fsanitize=$enable_sanitize" fi elif test "x$vendor" = xintel; then DEBUGCOMPILEFLAGS='-g3 -Wall -O0' if test "x$enable_coverage" != xno; then enable_coverage=unavailable fi if test "x$enable_sanitize" != xno; then enable_sanitize=unavailable fi else DEBUGCOMPILEFLAGS=-g if test "x$enable_coverage" != xno; then enable_coverage=unavailable fi if test "x$enable_sanitize" != xno; then enable_sanitize=unavailable fi fi fi my_test_DEBUGLINKFLAGS=${DEBUGLINKFLAGS+set} if test "$my_test_DEBUGLINKFLAGS" != set && test "x$enable_debug" = xyes; then DEBUGLINKFLAGS=-rdynamic if test "x$vendor" = xgnu; then # Coverage option. if test "x$enable_coverage" = xyes; then DEBUGLINKFLAGS="$DEBUGLINKFLAGS -coverage" fi # Sanitizer option. if test "x$enable_sanitize" != xno; then # Workaround for https://bugs.launchpad.net/ubuntu/+source/gcc-defaults/+bug/1650186 ok=no save_CFLAGS=$CFLAGS save_LDFLAGS=$LDFLAGS CFLAGS="$CFLAGS -fsanitize=$enable_sanitize" cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ int main (void) { ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO" then : ok=yes fi rm -f core conftest.err conftest.$ac_objext conftest.beam \ conftest$ac_exeext conftest.$ac_ext if test "x$ok" != xyes; then LDFLAGS="$LDFLAGS -fuse-ld=gold" cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ int main (void) { ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO" then : ok=yes fi rm -f core conftest.err conftest.$ac_objext conftest.beam \ conftest$ac_exeext conftest.$ac_ext if test "x$ok" = xyes; then DEBUGLINKFLAGS="$DEBUGLINKFLAGS -fuse-ld=gold" fi fi CFLAGS=$save_CFLAGS LDFLAGS=$save_LDFLAGS fi fi fi # Check for doxygen # Extract the first word of "doxygen", so it can be a program name with args. set dummy doxygen; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_DOXYGEN+y} then : printf %s "(cached) " >&6 else $as_nop case $DOXYGEN in [\\/]* | ?:[\\/]*) ac_cv_path_DOXYGEN="$DOXYGEN" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_DOXYGEN="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_DOXYGEN" && ac_cv_path_DOXYGEN="""" ;; esac fi DOXYGEN=$ac_cv_path_DOXYGEN if test -n "$DOXYGEN"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $DOXYGEN" >&5 printf "%s\n" "$DOXYGEN" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi if test "x$DOXYGEN" != x; then CONFIG_DOXYGEN_TRUE= CONFIG_DOXYGEN_FALSE='#' else CONFIG_DOXYGEN_TRUE='#' CONFIG_DOXYGEN_FALSE= fi # Check for LaTeX programs # Extract the first word of "latex", so it can be a program name with args. set dummy latex; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_LATEX+y} then : printf %s "(cached) " >&6 else $as_nop case $LATEX in [\\/]* | ?:[\\/]*) ac_cv_path_LATEX="$LATEX" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_LATEX="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_LATEX" && ac_cv_path_LATEX="""" ;; esac fi LATEX=$ac_cv_path_LATEX if test -n "$LATEX"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $LATEX" >&5 printf "%s\n" "$LATEX" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi # Extract the first word of "pdflatex", so it can be a program name with args. set dummy pdflatex; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_PDFLATEX+y} then : printf %s "(cached) " >&6 else $as_nop case $PDFLATEX in [\\/]* | ?:[\\/]*) ac_cv_path_PDFLATEX="$PDFLATEX" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_PDFLATEX="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_PDFLATEX" && ac_cv_path_PDFLATEX="""" ;; esac fi PDFLATEX=$ac_cv_path_PDFLATEX if test -n "$PDFLATEX"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $PDFLATEX" >&5 printf "%s\n" "$PDFLATEX" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi # Extract the first word of "dvips", so it can be a program name with args. set dummy dvips; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_DVIPS+y} then : printf %s "(cached) " >&6 else $as_nop case $DVIPS in [\\/]* | ?:[\\/]*) ac_cv_path_DVIPS="$DVIPS" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_DVIPS="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_DVIPS" && ac_cv_path_DVIPS="""" ;; esac fi DVIPS=$ac_cv_path_DVIPS if test -n "$DVIPS"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $DVIPS" >&5 printf "%s\n" "$DVIPS" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi # Extract the first word of "makeindex", so it can be a program name with args. set dummy makeindex; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_MAKEINDEX+y} then : printf %s "(cached) " >&6 else $as_nop case $MAKEINDEX in [\\/]* | ?:[\\/]*) ac_cv_path_MAKEINDEX="$MAKEINDEX" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_MAKEINDEX="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_MAKEINDEX" && ac_cv_path_MAKEINDEX="""" ;; esac fi MAKEINDEX=$ac_cv_path_MAKEINDEX if test -n "$MAKEINDEX"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $MAKEINDEX" >&5 printf "%s\n" "$MAKEINDEX" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi # Extract the first word of "htlatex", so it can be a program name with args. set dummy htlatex; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_HTLATEX+y} then : printf %s "(cached) " >&6 else $as_nop case $HTLATEX in [\\/]* | ?:[\\/]*) ac_cv_path_HTLATEX="$HTLATEX" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_HTLATEX="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_HTLATEX" && ac_cv_path_HTLATEX="""" ;; esac fi HTLATEX=$ac_cv_path_HTLATEX if test -n "$HTLATEX"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $HTLATEX" >&5 printf "%s\n" "$HTLATEX" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi # Extract the first word of "latex2html", so it can be a program name with args. set dummy latex2html; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_LATEX2HTML+y} then : printf %s "(cached) " >&6 else $as_nop case $LATEX2HTML in [\\/]* | ?:[\\/]*) ac_cv_path_LATEX2HTML="$LATEX2HTML" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_LATEX2HTML="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_LATEX2HTML" && ac_cv_path_LATEX2HTML="""" ;; esac fi LATEX2HTML=$ac_cv_path_LATEX2HTML if test -n "$LATEX2HTML"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $LATEX2HTML" >&5 printf "%s\n" "$LATEX2HTML" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi if test "x$LATEX" != x; then CONFIG_TEX_TRUE= CONFIG_TEX_FALSE='#' else CONFIG_TEX_TRUE='#' CONFIG_TEX_FALSE= fi if test "x$LATEX" != x && test "x$DVIPS" != x; then CONFIG_PS_TRUE= CONFIG_PS_FALSE='#' else CONFIG_PS_TRUE='#' CONFIG_PS_FALSE= fi if test "x$PDFLATEX" != x; then CONFIG_PDF_TRUE= CONFIG_PDF_FALSE='#' else CONFIG_PDF_TRUE='#' CONFIG_PDF_FALSE= fi if test "x$MAKEINDEX" != x; then CONFIG_MAKEINDEX_TRUE= CONFIG_MAKEINDEX_FALSE='#' else CONFIG_MAKEINDEX_TRUE='#' CONFIG_MAKEINDEX_FALSE= fi if test "x$HTLATEX" != x; then CONFIG_HTLATEX_TRUE= CONFIG_HTLATEX_FALSE='#' else CONFIG_HTLATEX_TRUE='#' CONFIG_HTLATEX_FALSE= fi if test "x$LATEX2HTML" != x; then CONFIG_LATEX2HTML_TRUE= CONFIG_LATEX2HTML_FALSE='#' else CONFIG_LATEX2HTML_TRUE='#' CONFIG_LATEX2HTML_FALSE= fi # Check for Ruby >= 2.0 and test/unit. # Extract the first word of "ruby", so it can be a program name with args. set dummy ruby; ac_word=$2 { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 printf %s "checking for $ac_word... " >&6; } if test ${ac_cv_path_RUBY+y} then : printf %s "(cached) " >&6 else $as_nop case $RUBY in [\\/]* | ?:[\\/]*) ac_cv_path_RUBY="$RUBY" # Let the user override the test with a path. ;; *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS case $as_dir in #((( '') as_dir=./ ;; */) ;; *) as_dir=$as_dir/ ;; esac for ac_exec_ext in '' $ac_executable_extensions; do if as_fn_executable_p "$as_dir$ac_word$ac_exec_ext"; then ac_cv_path_RUBY="$as_dir$ac_word$ac_exec_ext" printf "%s\n" "$as_me:${as_lineno-$LINENO}: found $as_dir$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_path_RUBY" && ac_cv_path_RUBY="""" ;; esac fi RUBY=$ac_cv_path_RUBY if test -n "$RUBY"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $RUBY" >&5 printf "%s\n" "$RUBY" >&6; } else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 printf "%s\n" "no" >&6; } fi ok=yes test "x$RUBY" = x && ok=no if test "x$ok" = xyes; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking whether ruby >= 2.0" >&5 printf %s "checking whether ruby >= 2.0... " >&6; } $RUBY -e 'exit(1) if RUBY_VERSION < "2.0.0"' >/dev/null 2>&1 || ok=no { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ok" >&5 printf "%s\n" "$ok" >&6; } fi if test "x$ok" = xyes; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for ruby test/unit" >&5 printf %s "checking for ruby test/unit... " >&6; } { cat >conftest.rb </dev/null 2>&1 || ok=no require 'test/unit' EOF { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $ok" >&5 printf "%s\n" "$ok" >&6; } fi with_ruby_test=$ok if test "x$with_ruby_test" = xyes; then CONFIG_RUBY_TRUE= CONFIG_RUBY_FALSE='#' else CONFIG_RUBY_TRUE='#' CONFIG_RUBY_FALSE= fi ac_config_files="$ac_config_files Makefile sources/Makefile doc/Makefile doc/manual/Makefile doc/manual/manual.tex doc/devref/Makefile doc/devref/devref.tex doc/doxygen/Makefile doc/doxygen/DoxyfileHTML doc/doxygen/DoxyfileLATEX doc/doxygen/DoxyfilePDFLATEX check/Makefile" cat >confcache <<\_ACEOF # This file is a shell script that caches the results of configure # tests run on this system so they can be shared between configure # scripts and configure runs, see configure's option --config-cache. # It is not useful on other systems. If it contains results you don't # want to keep, you may remove or edit it. # # config.status only pays attention to the cache file if you give it # the --recheck option to rerun configure. # # `ac_cv_env_foo' variables (set or unset) will be overridden when # loading this file, other *unset* `ac_cv_foo' will be assigned the # following values. _ACEOF # The following way of writing the cache mishandles newlines in values, # but we know of no workaround that is simple, portable, and efficient. # So, we kill variables containing newlines. # Ultrix sh set writes to stderr and can't be redirected directly, # and sets the high bit in the cache file unless we assign to the vars. ( for ac_var in `(set) 2>&1 | sed -n 's/^\([a-zA-Z_][a-zA-Z0-9_]*\)=.*/\1/p'`; do eval ac_val=\$$ac_var case $ac_val in #( *${as_nl}*) case $ac_var in #( *_cv_*) { printf "%s\n" "$as_me:${as_lineno-$LINENO}: WARNING: cache variable $ac_var contains a newline" >&5 printf "%s\n" "$as_me: WARNING: cache variable $ac_var contains a newline" >&2;} ;; esac case $ac_var in #( _ | IFS | as_nl) ;; #( BASH_ARGV | BASH_SOURCE) eval $ac_var= ;; #( *) { eval $ac_var=; unset $ac_var;} ;; esac ;; esac done (set) 2>&1 | case $as_nl`(ac_space=' '; set) 2>&1` in #( *${as_nl}ac_space=\ *) # `set' does not quote correctly, so add quotes: double-quote # substitution turns \\\\ into \\, and sed turns \\ into \. sed -n \ "s/'/'\\\\''/g; s/^\\([_$as_cr_alnum]*_cv_[_$as_cr_alnum]*\\)=\\(.*\\)/\\1='\\2'/p" ;; #( *) # `set' quotes correctly as required by POSIX, so do not add quotes. sed -n "/^[_$as_cr_alnum]*_cv_[_$as_cr_alnum]*=/p" ;; esac | sort ) | sed ' /^ac_cv_env_/b end t clear :clear s/^\([^=]*\)=\(.*[{}].*\)$/test ${\1+y} || &/ t end s/^\([^=]*\)=\(.*\)$/\1=${\1=\2}/ :end' >>confcache if diff "$cache_file" confcache >/dev/null 2>&1; then :; else if test -w "$cache_file"; then if test "x$cache_file" != "x/dev/null"; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: updating cache $cache_file" >&5 printf "%s\n" "$as_me: updating cache $cache_file" >&6;} if test ! -f "$cache_file" || test -h "$cache_file"; then cat confcache >"$cache_file" else case $cache_file in #( */* | ?:*) mv -f confcache "$cache_file"$$ && mv -f "$cache_file"$$ "$cache_file" ;; #( *) mv -f confcache "$cache_file" ;; esac fi fi else { printf "%s\n" "$as_me:${as_lineno-$LINENO}: not updating unwritable cache $cache_file" >&5 printf "%s\n" "$as_me: not updating unwritable cache $cache_file" >&6;} fi fi rm -f confcache test "x$prefix" = xNONE && prefix=$ac_default_prefix # Let make expand exec_prefix. test "x$exec_prefix" = xNONE && exec_prefix='${prefix}' DEFS=-DHAVE_CONFIG_H ac_libobjs= ac_ltlibobjs= U= for ac_i in : $LIBOBJS; do test "x$ac_i" = x: && continue # 1. Remove the extension, and $U if already installed. ac_script='s/\$U\././;s/\.o$//;s/\.obj$//' ac_i=`printf "%s\n" "$ac_i" | sed "$ac_script"` # 2. Prepend LIBOBJDIR. When used with automake>=1.10 LIBOBJDIR # will be set to the directory where LIBOBJS objects are built. as_fn_append ac_libobjs " \${LIBOBJDIR}$ac_i\$U.$ac_objext" as_fn_append ac_ltlibobjs " \${LIBOBJDIR}$ac_i"'$U.lo' done LIBOBJS=$ac_libobjs LTLIBOBJS=$ac_ltlibobjs { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking that generated files are newer than configure" >&5 printf %s "checking that generated files are newer than configure... " >&6; } if test -n "$am_sleep_pid"; then # Hide warnings about reused PIDs. wait $am_sleep_pid 2>/dev/null fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: done" >&5 printf "%s\n" "done" >&6; } if test -n "$EXEEXT"; then am__EXEEXT_TRUE= am__EXEEXT_FALSE='#' else am__EXEEXT_TRUE='#' am__EXEEXT_FALSE= fi if test -z "${FIXED_VERSION_TRUE}" && test -z "${FIXED_VERSION_FALSE}"; then as_fn_error $? "conditional \"FIXED_VERSION\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${AMDEP_TRUE}" && test -z "${AMDEP_FALSE}"; then as_fn_error $? "conditional \"AMDEP\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${am__fastdepCC_TRUE}" && test -z "${am__fastdepCC_FALSE}"; then as_fn_error $? "conditional \"am__fastdepCC\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${am__fastdepCXX_TRUE}" && test -z "${am__fastdepCXX_FALSE}"; then as_fn_error $? "conditional \"am__fastdepCXX\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${ONUNIX_TRUE}" && test -z "${ONUNIX_FALSE}"; then as_fn_error $? "conditional \"ONUNIX\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${ONWINDOWS_TRUE}" && test -z "${ONWINDOWS_FALSE}"; then as_fn_error $? "conditional \"ONWINDOWS\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${WITHZSTD_TRUE}" && test -z "${WITHZSTD_FALSE}"; then as_fn_error $? "conditional \"WITHZSTD\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${WITHFLINT_TRUE}" && test -z "${WITHFLINT_FALSE}"; then as_fn_error $? "conditional \"WITHFLINT\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${BUILD_FORM_TRUE}" && test -z "${BUILD_FORM_FALSE}"; then as_fn_error $? "conditional \"BUILD_FORM\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${BUILD_VORM_TRUE}" && test -z "${BUILD_VORM_FALSE}"; then as_fn_error $? "conditional \"BUILD_VORM\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${BUILD_TFORM_TRUE}" && test -z "${BUILD_TFORM_FALSE}"; then as_fn_error $? "conditional \"BUILD_TFORM\" was never defined. Usually this means the macro was only invoked conditionally." "$LINENO" 5 fi if test -z "${BUILD_TVORM_TRUE}" && test -z "${BUILD_TVORM_FALSE}"; then as_fn_error $? "conditional \"BUILD_TVORM\" was never defined. Usually this means the macro was only invoked conditionally." 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Type 'make' to build all." echo echo "Type 'make install' to install the executables in" echo " $outputdir" echo "and the man page in" echo " $manoutputdir" echo if test "x$with_ruby_test" = xyes; then echo "Type 'make check' to run automatic tests." else echo "Automatic tests are not available." fi echo echo "Available documentation:" atleastone=no if test "x$DOXYGEN" != x; then atleastone=yes str=' doxygen ( html ' if test "x$MAKEINDEX" != x; then if test "x$LATEX" != x; then str=$str'dvi ' if test "x$DVIPS" != x; then str=$str'ps ' fi fi if test "x$PDFLATEX" != x; then str=$str'pdf ' fi fi str=$str')' echo "$str" fi if test "x$LATEX" != x || test "x$PDFLATEX" != x; then atleastone=yes str=' manual ( ' if test "x$HTLATEX" != x; then str=$str'html ' fi if test "x$LATEX" != x; then str=$str'dvi ' if test "x$DVIPS" != x; then str=$str'ps ' fi fi if test "x$PDFLATEX" != x; then str=$str'pdf ' fi str=$str')' echo "$str" fi if test $atleastone = no; then echo " " else echo echo "Type 'make ' in the directories doc/manual or" echo "doc/doxygen to generate the respective documentation with" echo "the specified format." fi echo echo "#########################################################" echo form-5.0.1/AUTHORS0000644000175100017510000000130015217035721007210 Over the years the following people have made contributions to the code of FORM (in alphabetical order) Joshua Davies Rafael L. Delgado Denny Fliegner Markus Frank Florian Herren Stephen Jones Toshiaki Kaneko Jan Kuipers Florian Lorkowski Vitaly Magerya Andreas Maier Coenraad Marinissen Andrei Onyshenko Irina Pushkina Maximilian Reininghaus Thomas Reiter Albert Retey Ben Ruijl Misha Tentyukov Takahiro Ueda Jos Vermaseren Jens Vollinga Much support has come from Hans Staudenmaier and Hans Kuehn in Karlsruhe, the late Eric Wassenaar and Ton Damen at Nikhef and all the directors of Nikhef during the period that FORM was developed. form-5.0.1/configure.ac0000644000175100017510000012522715217035721010445 # Get the version from # (1) .version file available in a tarball, or # (2) the latest tag in the repository. m4_define([FORM_VERSION], m4_esyscmd_s([ if test -f .version; then cat .version else scripts/git-version-gen.sh -C . -v || { # As a fallback, try for form3.h. major_version=`grep MAJORVERSION sources/form3.h | sed -e 's/ *#define *MAJORVERSION *//'` minor_version=`grep MINORVERSION sources/form3.h | sed -e 's/ *#define *MINORVERSION *//'` patch_version=`grep PATCHVERSION sources/form3.h | sed -e 's/ *#define *PATCHVERSION *//'` if test "x$major_version" != x && test "x$minor_version" != x && test "x$patch_version" != x; then # Make the version files. echo "$major_version.$minor_version.$patch_version" >.version echo "#define REPO_MAJOR_VERSION $major_version" >sources/version.h.in echo "#define REPO_MINOR_VERSION $minor_version" >>sources/version.h.in echo "#define REPO_PATCH_VERSION $patch_version" >>sources/version.h.in echo '\\def\\repomajorversion'"{$major_version}" >doc/manual/version.tex.in echo '\\def\\repominorversion'"{$minor_version}" >>doc/manual/version.tex.in echo '\\def\\repopatchversion'"{$patch_version}" >>doc/manual/version.tex.in cp doc/manual/version.tex.in doc/devref/version.tex.in touch doc/doxygen/version.sh.in fi cat <&2 ======================================================================== Failed to determine the revision of the source code. The reason may be - this is neither a source distribution (containing the configure script) nor a cloned Git repository, - this is a shallow clone and no version tags are reachable, - some required utilities (e.g., git) are missing. Source distributions and some binaries can be found in: http://www.nikhef.nl/~form/maindir/binaries/binaries.html https://github.com/form-dev/form/releases The latest source code can be cloned by: git clone https://github.com/form-dev/form.git END test -f .version && cat <&2 You can continue the build, but binaries will not contain the revision information. 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then echo " flint" atleastone=yes fi if test "x$with_gmp" = xyes; then echo " gmp" atleastone=yes fi if test "x$with_mpfr" = xyes; then echo " mpfr" atleastone=yes fi if test "x$with_zlib" = xyes; then echo " zlib" atleastone=yes fi if test "x$with_zstd" = xyes; then echo " zstd" atleastone=yes fi if test $atleastone = no; then echo " " fi echo echo "Optionally enabled features:" atleastone=no if test "x$enable_backtrace" = xyes; then echo " backtrace" atleastone=yes fi if test $atleastone = no; then echo " " fi echo echo "The following executables can be compiled:" atleastone=no if test "x$build_form" = xyes; then opts= if test "x$enable_native" = xyes; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}native" fi if test "x$STATIC_LDFLAGS" != x; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}statically linked" fi if test "x$enable_profile" = xgprof; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}gprof" fi if test "x$enable_profile" = xgperftools; 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then opts="${opts}, " fi opts="${opts}gperftools" fi if test "x$opts" != x; then opts=" (${opts})" fi echo " tform multi-threaded version$opts" atleastone=yes fi if test "x$build_tvorm" = xyes; then opts= if test "x$enable_coverage" = xyes; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}gcov" fi if test "x$enable_sanitize" != xno; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}sanitize=$enable_sanitize" fi if test "x$opts" != x; then opts=" (${opts})" fi echo " tvorm multi-threaded debugging version$opts" atleastone=yes fi if test "x$build_parform" = xyes; then opts= if test "x$enable_native" = xyes; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}native" fi if test "x$MPI_STATIC_LDFLAGS" != x; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}statically linked" fi if test "x$enable_profile" = xgprof; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}gprof" fi if test "x$enable_profile" = xgperftools; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}gperftools" fi if test "x$opts" != x; then opts=" (${opts})" fi echo " parform parallel version using MPI$opts" atleastone=yes fi if test "x$build_parvorm" = xyes; then opts= if test "x$enable_coverage" = xyes; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}gcov" fi if test "x$enable_sanitize" != xno; then if test "x$opts" != x; then opts="${opts}, " fi opts="${opts}sanitize=$enable_sanitize" fi if test "x$opts" != x; then opts=" (${opts})" fi echo " parvorm parallel debugging version using MPI$opts" atleastone=yes fi if test $atleastone = no; then echo " " fi if test "x$thread_clock_ok" = xno; then s="none" if test "x$build_tform" = xyes && test "x$build_tvorm" = xyes; then s="tform and tvorm" elif test "x$build_tform" = xyes; then s="tform" elif test "x$build_tvorm" = xyes; then s="tvorm" fi if test "x$s" != xnone; then echo echo "***CAUTION*** $s may have clock" echo "problems which make that each worker registers" echo "the complete time used by all workers and the master." fi fi echo echo "Type 'make ' in the source directory to" echo "build a specific version. Type 'make' to build all." echo echo "Type 'make install' to install the executables in" echo " $outputdir" echo "and the man page in" echo " $manoutputdir" echo if test "x$with_ruby_test" = xyes; then echo "Type 'make check' to run automatic tests." else echo "Automatic tests are not available." fi echo echo "Available documentation:" atleastone=no if test "x$DOXYGEN" != x; then atleastone=yes str=' doxygen ( html ' if test "x$MAKEINDEX" != x; then if test "x$LATEX" != x; then str=$str'dvi ' if test "x$DVIPS" != x; then str=$str'ps ' fi fi if test "x$PDFLATEX" != x; then str=$str'pdf ' fi fi str=$str')' echo "$str" fi if test "x$LATEX" != x || test "x$PDFLATEX" != x; then atleastone=yes str=' manual ( ' if test "x$HTLATEX" != x; then str=$str'html ' fi if test "x$LATEX" != x; then str=$str'dvi ' if test "x$DVIPS" != x; then str=$str'ps ' fi fi if test "x$PDFLATEX" != x; then str=$str'pdf ' fi str=$str')' echo "$str" fi if test $atleastone = no; then echo " " else echo echo "Type 'make ' in the directories doc/manual or" echo "doc/doxygen to generate the respective documentation with" echo "the specified format." fi echo echo "#########################################################" echo form-5.0.1/Makefile.am0000644000175100017510000000054215217035721010203 SUBDIRS = doc sources check EXTRA_DIST = README.md scripts/.latex2html-init scripts/run-latex2html.sh dist-hook: $(DISTHOOK_VERSION) if FIXED_VERSION DISTHOOK_VERSION = \ cp "$(srcdir)/.version" "$(distdir)/.version" else DISTHOOK_VERSION = \ $(SHELL) "$(top_srcdir)/scripts/git-version-gen.sh" -C "$(srcdir)" -v -o "$(distdir)/.version" endif form-5.0.1/COPYING0000644000175100017510000010451315217035721007205 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. 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The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such. 14. Revised Versions of this License. The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License "or any later version" applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version. 15. Disclaimer of Warranty. THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. 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Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . form-5.0.1/extern/0000755000175100017510000000000015217035744007540 5form-5.0.1/extern/zstd/0000755000175100017510000000000015217035744010524 5form-5.0.1/extern/zstd/zlibWrapper/0000755000175100017510000000000015217035744013025 5form-5.0.1/extern/zstd/zlibWrapper/gzlib.c0000644000175100017510000004152015217035741014217 /* gzlib.c contains minimal changes required to be compiled with zlibWrapper: * - gz_statep was converted to union to work with -Wstrict-aliasing=1 */ /* gzlib.c -- zlib functions common to reading and writing gzip files * Copyright (C) 2004-2017 Mark Adler * For conditions of distribution and use, see https://www.zlib.net/zlib_license.html */ #include "gzguts.h" #if defined(_WIN32) && !defined(__BORLANDC__) && !defined(__MINGW32__) # define LSEEK _lseeki64 #else #if defined(_LARGEFILE64_SOURCE) && _LFS64_LARGEFILE-0 # define LSEEK lseek64 #else # define LSEEK lseek #endif #endif /* Local functions */ local void gz_reset _Z_OF((gz_statep)); local gzFile gz_open _Z_OF((const void *, int, const char *)); #if defined UNDER_CE /* Map the Windows error number in ERROR to a locale-dependent error message string and return a pointer to it. Typically, the values for ERROR come from GetLastError. The string pointed to shall not be modified by the application, but may be overwritten by a subsequent call to gz_strwinerror The gz_strwinerror function does not change the current setting of GetLastError. */ char ZLIB_INTERNAL *gz_strwinerror(DWORD error) { static char buf[1024]; wchar_t *msgbuf; DWORD lasterr = GetLastError(); DWORD chars = FormatMessage(FORMAT_MESSAGE_FROM_SYSTEM | FORMAT_MESSAGE_ALLOCATE_BUFFER, NULL, error, 0, /* Default language */ (LPVOID)&msgbuf, 0, NULL); if (chars != 0) { /* If there is an \r\n appended, zap it. */ if (chars >= 2 && msgbuf[chars - 2] == '\r' && msgbuf[chars - 1] == '\n') { chars -= 2; msgbuf[chars] = 0; } if (chars > sizeof (buf) - 1) { chars = sizeof (buf) - 1; msgbuf[chars] = 0; } wcstombs(buf, msgbuf, chars + 1); LocalFree(msgbuf); } else { sprintf(buf, "unknown win32 error (%ld)", error); } SetLastError(lasterr); return buf; } #endif /* UNDER_CE */ /* Reset gzip file state */ local void gz_reset(gz_statep state) { state.state->x.have = 0; /* no output data available */ if (state.state->mode == GZ_READ) { /* for reading ... */ state.state->eof = 0; /* not at end of file */ state.state->past = 0; /* have not read past end yet */ state.state->how = LOOK; /* look for gzip header */ } state.state->seek = 0; /* no seek request pending */ gz_error(state, Z_OK, NULL); /* clear error */ state.state->x.pos = 0; /* no uncompressed data yet */ state.state->strm.avail_in = 0; /* no input data yet */ } /* Open a gzip file either by name or file descriptor. */ local gzFile gz_open(const void *path, int fd, const char *mode) { gz_statep state; z_size_t len; int oflag; #ifdef O_CLOEXEC int cloexec = 0; #endif #ifdef O_EXCL int exclusive = 0; #endif /* check input */ if (path == NULL) return NULL; /* allocate gzFile structure to return */ state.state = (gz_state*)malloc(sizeof(gz_state)); if (state.state == NULL) return NULL; state.state->size = 0; /* no buffers allocated yet */ state.state->want = GZBUFSIZE; /* requested buffer size */ state.state->msg = NULL; /* no error message yet */ /* interpret mode */ state.state->mode = GZ_NONE; state.state->level = Z_DEFAULT_COMPRESSION; state.state->strategy = Z_DEFAULT_STRATEGY; state.state->direct = 0; while (*mode) { if (*mode >= '0' && *mode <= '9') state.state->level = *mode - '0'; else switch (*mode) { case 'r': state.state->mode = GZ_READ; break; #ifndef NO_GZCOMPRESS case 'w': state.state->mode = GZ_WRITE; break; case 'a': state.state->mode = GZ_APPEND; break; #endif case '+': /* can't read and write at the same time */ free(state.state); return NULL; case 'b': /* ignore -- will request binary anyway */ break; #ifdef O_CLOEXEC case 'e': cloexec = 1; break; #endif #ifdef O_EXCL case 'x': exclusive = 1; break; #endif case 'f': state.state->strategy = Z_FILTERED; break; case 'h': state.state->strategy = Z_HUFFMAN_ONLY; break; case 'R': state.state->strategy = Z_RLE; break; case 'F': state.state->strategy = Z_FIXED; break; case 'T': state.state->direct = 1; break; default: /* could consider as an error, but just ignore */ ; } mode++; } /* must provide an "r", "w", or "a" */ if (state.state->mode == GZ_NONE) { free(state.state); return NULL; } /* can't force transparent read */ if (state.state->mode == GZ_READ) { if (state.state->direct) { free(state.state); return NULL; } state.state->direct = 1; /* for empty file */ } /* save the path name for error messages */ #ifdef WIDECHAR if (fd == -2) { len = wcstombs(NULL, path, 0); if (len == (z_size_t)-1) len = 0; } else #endif len = strlen((const char *)path); state.state->path = (char *)malloc(len + 1); if (state.state->path == NULL) { free(state.state); return NULL; } #ifdef WIDECHAR if (fd == -2) if (len) wcstombs(state.state->path, path, len + 1); else *(state.state->path) = 0; else #endif #if !defined(NO_snprintf) && !defined(NO_vsnprintf) (void)snprintf(state.state->path, len + 1, "%s", (const char *)path); #else strcpy(state.state->path, (const char*)path); #endif /* compute the flags for open() */ oflag = #ifdef O_LARGEFILE O_LARGEFILE | #endif #ifdef O_BINARY O_BINARY | #endif #ifdef O_CLOEXEC (cloexec ? O_CLOEXEC : 0) | #endif (state.state->mode == GZ_READ ? O_RDONLY : (O_WRONLY | O_CREAT | #ifdef O_EXCL (exclusive ? O_EXCL : 0) | #endif (state.state->mode == GZ_WRITE ? O_TRUNC : O_APPEND))); /* open the file with the appropriate flags (or just use fd) */ state.state->fd = fd > -1 ? fd : ( #ifdef WIDECHAR fd == -2 ? _wopen(path, oflag, 0666) : #endif open((const char *)path, oflag, 0666)); if (state.state->fd == -1) { free(state.state->path); free(state.state); return NULL; } if (state.state->mode == GZ_APPEND) { LSEEK(state.state->fd, 0, SEEK_END); /* so gzoffset() is correct */ state.state->mode = GZ_WRITE; /* simplify later checks */ } /* save the current position for rewinding (only if reading) */ if (state.state->mode == GZ_READ) { state.state->start = LSEEK(state.state->fd, 0, SEEK_CUR); if (state.state->start == -1) state.state->start = 0; } /* initialize stream */ gz_reset(state); /* return stream */ return state.file; } /* -- see zlib.h -- */ gzFile ZEXPORT gzopen(const char *path, const char *mode) { return gz_open(path, -1, mode); } /* -- see zlib.h -- */ gzFile ZEXPORT gzopen64(const char *path, const char *mode) { return gz_open(path, -1, mode); } /* -- see zlib.h -- */ gzFile ZEXPORT gzdopen(int fd, const char *mode) { char *path; /* identifier for error messages */ gzFile gz; if (fd == -1 || (path = (char *)malloc(7 + 3 * sizeof(int))) == NULL) return NULL; #if !defined(NO_snprintf) && !defined(NO_vsnprintf) (void)snprintf(path, 7 + 3 * sizeof(int), "", fd); #else sprintf(path, "", fd); /* for debugging */ #endif gz = gz_open(path, fd, mode); free(path); return gz; } /* -- see zlib.h -- */ #ifdef WIDECHAR gzFile ZEXPORT gzopen_w(const wchar_t *path, const char *mode) { return gz_open(path, -2, mode); } #endif /* -- see zlib.h -- */ int ZEXPORT gzbuffer(gzFile file, unsigned size) { gz_statep state; /* get internal structure and check integrity */ if (file == NULL) return -1; state.file = file; if (state.state->mode != GZ_READ && state.state->mode != GZ_WRITE) return -1; /* make sure we haven't already allocated memory */ if (state.state->size != 0) return -1; /* check and set requested size */ if ((size << 1) < size) return -1; /* need to be able to double it */ if (size < 2) size = 2; /* need two bytes to check magic header */ state.state->want = size; return 0; } /* -- see zlib.h -- */ int ZEXPORT gzrewind(gzFile file) { gz_statep state; /* get internal structure */ if (file == NULL) return -1; state.file = file; /* check that we're reading and that there's no error */ if (state.state->mode != GZ_READ || (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR)) return -1; /* back up and start over */ if (LSEEK(state.state->fd, state.state->start, SEEK_SET) == -1) return -1; gz_reset(state); return 0; } /* -- see zlib.h -- */ z_off64_t ZEXPORT gzseek64(gzFile file, z_off64_t offset, int whence) { unsigned n; z_off64_t ret; gz_statep state; /* get internal structure and check integrity */ if (file == NULL) return -1; state.file = file; if (state.state->mode != GZ_READ && state.state->mode != GZ_WRITE) return -1; /* check that there's no error */ if (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR) return -1; /* can only seek from start or relative to current position */ if (whence != SEEK_SET && whence != SEEK_CUR) return -1; /* normalize offset to a SEEK_CUR specification */ if (whence == SEEK_SET) offset -= state.state->x.pos; else if (state.state->seek) offset += state.state->skip; state.state->seek = 0; /* if within raw area while reading, just go there */ if (state.state->mode == GZ_READ && state.state->how == COPY && state.state->x.pos + offset >= 0) { ret = LSEEK(state.state->fd, offset - state.state->x.have, SEEK_CUR); if (ret == -1) return -1; state.state->x.have = 0; state.state->eof = 0; state.state->past = 0; state.state->seek = 0; gz_error(state, Z_OK, NULL); state.state->strm.avail_in = 0; state.state->x.pos += offset; return state.state->x.pos; } /* calculate skip amount, rewinding if needed for back seek when reading */ if (offset < 0) { if (state.state->mode != GZ_READ) /* writing -- can't go backwards */ return -1; offset += state.state->x.pos; if (offset < 0) /* before start of file! */ return -1; if (gzrewind(file) == -1) /* rewind, then skip to offset */ return -1; } /* if reading, skip what's in output buffer (one less gzgetc() check) */ if (state.state->mode == GZ_READ) { n = GT_OFF(state.state->x.have) || (z_off64_t)state.state->x.have > offset ? (unsigned)offset : state.state->x.have; state.state->x.have -= n; state.state->x.next += n; state.state->x.pos += n; offset -= n; } /* request skip (if not zero) */ if (offset) { state.state->seek = 1; state.state->skip = offset; } return state.state->x.pos + offset; } /* -- see zlib.h -- */ z_off_t ZEXPORT gzseek(gzFile file, z_off_t offset, int whence) { z_off64_t ret; ret = gzseek64(file, (z_off64_t)offset, whence); return ret == (z_off_t)ret ? (z_off_t)ret : -1; } /* -- see zlib.h -- */ z_off64_t ZEXPORT gztell64(gzFile file) { gz_statep state; /* get internal structure and check integrity */ if (file == NULL) return -1; state.file = file; if (state.state->mode != GZ_READ && state.state->mode != GZ_WRITE) return -1; /* return position */ return state.state->x.pos + (state.state->seek ? state.state->skip : 0); } /* -- see zlib.h -- */ z_off_t ZEXPORT gztell(gzFile file) { z_off64_t ret; ret = gztell64(file); return ret == (z_off_t)ret ? (z_off_t)ret : -1; } /* -- see zlib.h -- */ z_off64_t ZEXPORT gzoffset64(gzFile file) { z_off64_t offset; gz_statep state; /* get internal structure and check integrity */ if (file == NULL) return -1; state.file = file; if (state.state->mode != GZ_READ && state.state->mode != GZ_WRITE) return -1; /* compute and return effective offset in file */ offset = LSEEK(state.state->fd, 0, SEEK_CUR); if (offset == -1) return -1; if (state.state->mode == GZ_READ) /* reading */ offset -= state.state->strm.avail_in; /* don't count buffered input */ return offset; } /* -- see zlib.h -- */ z_off_t ZEXPORT gzoffset(gzFile file) { z_off64_t ret; ret = gzoffset64(file); return ret == (z_off_t)ret ? (z_off_t)ret : -1; } /* -- see zlib.h -- */ int ZEXPORT gzeof(gzFile file) { gz_statep state; /* get internal structure and check integrity */ if (file == NULL) return 0; state.file = file; if (state.state->mode != GZ_READ && state.state->mode != GZ_WRITE) return 0; /* return end-of-file state */ return state.state->mode == GZ_READ ? state.state->past : 0; } /* -- see zlib.h -- */ const char * ZEXPORT gzerror(gzFile file, int *errnum) { gz_statep state; /* get internal structure and check integrity */ if (file == NULL) return NULL; state.file = file; if (state.state->mode != GZ_READ && state.state->mode != GZ_WRITE) return NULL; /* return error information */ if (errnum != NULL) *errnum = state.state->err; return state.state->err == Z_MEM_ERROR ? "out of memory" : (state.state->msg == NULL ? "" : state.state->msg); } /* -- see zlib.h -- */ void ZEXPORT gzclearerr(gzFile file) { gz_statep state; /* get internal structure and check integrity */ if (file == NULL) return; state.file = file; if (state.state->mode != GZ_READ && state.state->mode != GZ_WRITE) return; /* clear error and end-of-file */ if (state.state->mode == GZ_READ) { state.state->eof = 0; state.state->past = 0; } gz_error(state, Z_OK, NULL); } /* Create an error message in allocated memory and set state.state->err and state.state->msg accordingly. Free any previous error message already there. Do not try to free or allocate space if the error is Z_MEM_ERROR (out of memory). Simply save the error message as a static string. If there is an allocation failure constructing the error message, then convert the error to out of memory. */ void ZLIB_INTERNAL gz_error(gz_statep state, int err, const char *msg) { /* free previously allocated message and clear */ if (state.state->msg != NULL) { if (state.state->err != Z_MEM_ERROR) free(state.state->msg); state.state->msg = NULL; } /* if fatal, set state.state->x.have to 0 so that the gzgetc() macro fails */ if (err != Z_OK && err != Z_BUF_ERROR) state.state->x.have = 0; /* set error code, and if no message, then done */ state.state->err = err; if (msg == NULL) return; /* for an out of memory error, return literal string when requested */ if (err == Z_MEM_ERROR) return; /* construct error message with path */ if ((state.state->msg = (char *)malloc(strlen(state.state->path) + strlen(msg) + 3)) == NULL) { state.state->err = Z_MEM_ERROR; return; } #if !defined(NO_snprintf) && !defined(NO_vsnprintf) (void)snprintf(state.state->msg, strlen(state.state->path) + strlen(msg) + 3, "%s%s%s", state.state->path, ": ", msg); #else strcpy(state.state->msg, state.state->path); strcat(state.state->msg, ": "); strcat(state.state->msg, msg); #endif } #ifndef INT_MAX /* portably return maximum value for an int (when limits.h presumed not available) -- we need to do this to cover cases where 2's complement not used, since C standard permits 1's complement and sign-bit representations, otherwise we could just use ((unsigned)-1) >> 1 */ unsigned ZLIB_INTERNAL gz_intmax() { unsigned p, q; p = 1; do { q = p; p <<= 1; p++; } while (p > q); return q >> 1; } #endif form-5.0.1/extern/zstd/zlibWrapper/gzguts.h0000644000175100017510000001600215217035741014435 /* gzguts.h contains minimal changes required to be compiled with zlibWrapper: * - #include "zlib.h" was changed to #include "zstd_zlibwrapper.h" * - gz_statep was converted to union to work with -Wstrict-aliasing=1 */ /* gzguts.h -- zlib internal header definitions for gz* operations * Copyright (C) 2004, 2005, 2010, 2011, 2012, 2013, 2016 Mark Adler * For conditions of distribution and use, see https://www.zlib.net/zlib_license.html */ #ifdef _LARGEFILE64_SOURCE # ifndef _LARGEFILE_SOURCE # define _LARGEFILE_SOURCE 1 # endif # ifdef _FILE_OFFSET_BITS # undef _FILE_OFFSET_BITS # endif #endif #ifdef HAVE_HIDDEN # define ZLIB_INTERNAL __attribute__((visibility ("hidden"))) #else # define ZLIB_INTERNAL #endif #include #include "zstd_zlibwrapper.h" #include "gzcompatibility.h" #ifdef STDC # include # include # include #endif #ifndef _POSIX_SOURCE # define _POSIX_SOURCE #endif #include #ifdef _WIN32 # include #else # include #endif #if defined(__TURBOC__) || defined(_MSC_VER) || defined(_WIN32) # include #endif #if defined(_WIN32) # define WIDECHAR #endif #ifdef WINAPI_FAMILY # define open _open # define read _read # define write _write # define close _close #endif #ifdef NO_DEFLATE /* for compatibility with old definition */ # define NO_GZCOMPRESS #endif #if defined(STDC99) || (defined(__TURBOC__) && __TURBOC__ >= 0x550) # ifndef HAVE_VSNPRINTF # define HAVE_VSNPRINTF # endif #endif #if defined(__CYGWIN__) # ifndef HAVE_VSNPRINTF # define HAVE_VSNPRINTF # endif #endif #if defined(MSDOS) && defined(__BORLANDC__) && (BORLANDC > 0x410) # ifndef HAVE_VSNPRINTF # define HAVE_VSNPRINTF # endif #endif #ifndef HAVE_VSNPRINTF # ifdef MSDOS /* vsnprintf may exist on some MS-DOS compilers (DJGPP?), but for now we just assume it doesn't. */ # define NO_vsnprintf # endif # ifdef __TURBOC__ # define NO_vsnprintf # endif # ifdef WIN32 /* In Win32, vsnprintf is available as the "non-ANSI" _vsnprintf. */ # if !defined(vsnprintf) && !defined(NO_vsnprintf) # if !defined(_MSC_VER) || ( defined(_MSC_VER) && _MSC_VER < 1500 ) # define vsnprintf _vsnprintf # endif # endif # endif # ifdef __SASC # define NO_vsnprintf # endif # ifdef VMS # define NO_vsnprintf # endif # ifdef __OS400__ # define NO_vsnprintf # endif # ifdef __MVS__ # define NO_vsnprintf # endif #endif /* unlike snprintf (which is required in C99), _snprintf does not guarantee null termination of the result -- however this is only used in gzlib.c where the result is assured to fit in the space provided */ #if defined(_MSC_VER) && _MSC_VER < 1900 # define snprintf _snprintf #endif #ifndef local # define local static #endif /* since "static" is used to mean two completely different things in C, we define "local" for the non-static meaning of "static", for readability (compile with -Dlocal if your debugger can't find static symbols) */ /* gz* functions always use library allocation functions */ #ifndef STDC extern voidp malloc _Z_OF((uInt size)); extern void free _Z_OF((voidpf ptr)); #endif /* get errno and strerror definition */ #if defined UNDER_CE # include # define zstrerror() gz_strwinerror((DWORD)GetLastError()) #else # ifndef NO_STRERROR # include # define zstrerror() strerror(errno) # else # define zstrerror() "stdio error (consult errno)" # endif #endif /* provide prototypes for these when building zlib without LFS */ #if !defined(_LARGEFILE64_SOURCE) || _LFS64_LARGEFILE-0 == 0 ZEXTERN gzFile ZEXPORT gzopen64 _Z_OF((const char *, const char *)); ZEXTERN z_off64_t ZEXPORT gzseek64 _Z_OF((gzFile, z_off64_t, int)); ZEXTERN z_off64_t ZEXPORT gztell64 _Z_OF((gzFile)); ZEXTERN z_off64_t ZEXPORT gzoffset64 _Z_OF((gzFile)); #endif /* default memLevel */ #if MAX_MEM_LEVEL >= 8 # define DEF_MEM_LEVEL 8 #else # define DEF_MEM_LEVEL MAX_MEM_LEVEL #endif /* default i/o buffer size -- double this for output when reading (this and twice this must be able to fit in an unsigned type) */ #define GZBUFSIZE 8192 /* gzip modes, also provide a little integrity check on the passed structure */ #define GZ_NONE 0 #define GZ_READ 7247 #define GZ_WRITE 31153 #define GZ_APPEND 1 /* mode set to GZ_WRITE after the file is opened */ /* values for gz_state how */ #define LOOK 0 /* look for a gzip header */ #define COPY 1 /* copy input directly */ #define GZIP 2 /* decompress a gzip stream */ /* internal gzip file state data structure */ typedef struct { /* exposed contents for gzgetc() macro */ struct gzFile_s x; /* "x" for exposed */ /* x.have: number of bytes available at x.next */ /* x.next: next output data to deliver or write */ /* x.pos: current position in uncompressed data */ /* used for both reading and writing */ int mode; /* see gzip modes above */ int fd; /* file descriptor */ char *path; /* path or fd for error messages */ unsigned size; /* buffer size, zero if not allocated yet */ unsigned want; /* requested buffer size, default is GZBUFSIZE */ unsigned char *in; /* input buffer (double-sized when writing) */ unsigned char *out; /* output buffer (double-sized when reading) */ int direct; /* 0 if processing gzip, 1 if transparent */ /* just for reading */ int how; /* 0: get header, 1: copy, 2: decompress */ z_off64_t start; /* where the gzip data started, for rewinding */ int eof; /* true if end of input file reached */ int past; /* true if read requested past end */ /* just for writing */ int level; /* compression level */ int strategy; /* compression strategy */ /* seek request */ z_off64_t skip; /* amount to skip (already rewound if backwards) */ int seek; /* true if seek request pending */ /* error information */ int err; /* error code */ char *msg; /* error message */ /* zlib inflate or deflate stream */ z_stream strm; /* stream structure in-place (not a pointer) */ } gz_state; typedef union { gz_state FAR *state; gzFile file; } gz_statep; /* shared functions */ void ZLIB_INTERNAL gz_error _Z_OF((gz_statep, int, const char *)); #if defined UNDER_CE char ZLIB_INTERNAL *gz_strwinerror _Z_OF((DWORD error)); #endif /* GT_OFF(x), where x is an unsigned value, is true if x > maximum z_off64_t value -- needed when comparing unsigned to z_off64_t, which is signed (possible z_off64_t types off_t, off64_t, and long are all signed) */ #ifdef INT_MAX # define GT_OFF(x) (sizeof(int) == sizeof(z_off64_t) && (x) > INT_MAX) #else unsigned ZLIB_INTERNAL gz_intmax _Z_OF((void)); # define GT_OFF(x) (sizeof(int) == sizeof(z_off64_t) && (x) > gz_intmax()) #endif form-5.0.1/extern/zstd/zlibWrapper/zstd_zlibwrapper.c0000644000175100017510000012411415217035741016516 /* * Copyright (c) Meta Platforms, Inc. and affiliates. * All rights reserved. * * This source code is licensed under both the BSD-style license (found in the * LICENSE file in the root directory of this source tree) and the GPLv2 (found * in the COPYING file in the root directory of this source tree). * You may select, at your option, one of the above-listed licenses. */ /* === Tuning parameters === */ #ifndef ZWRAP_USE_ZSTD #define ZWRAP_USE_ZSTD 0 #endif /* === Dependencies === */ #include #include /* vsprintf */ #include /* va_list, for z_gzprintf */ #include #define NO_DUMMY_DECL #define ZLIB_CONST #include /* without #define Z_PREFIX */ #include "zstd_zlibwrapper.h" #define ZSTD_STATIC_LINKING_ONLY /* ZSTD_isFrame, ZSTD_MAGICNUMBER, ZSTD_customMem */ #include "zstd.h" /* === Constants === */ #define Z_INFLATE_SYNC 8 #define ZLIB_HEADERSIZE 4 #define ZSTD_HEADERSIZE ZSTD_FRAMEHEADERSIZE_MIN(ZSTD_f_zstd1) #define ZWRAP_DEFAULT_CLEVEL 3 /* Z_DEFAULT_COMPRESSION is translated to ZWRAP_DEFAULT_CLEVEL for zstd */ /* === Debug === */ #define LOG_WRAPPERC(...) /* fprintf(stderr, __VA_ARGS__) */ #define LOG_WRAPPERD(...) /* fprintf(stderr, __VA_ARGS__) */ #define FINISH_WITH_GZ_ERR(msg) { (void)msg; return Z_STREAM_ERROR; } #define FINISH_WITH_NULL_ERR(msg) { (void)msg; return NULL; } /* === Utility === */ #define MIN(x,y) ((x) < (y) ? (x) : (y)) static unsigned ZWRAP_isLittleEndian(void) { const union { unsigned u; char c[4]; } one = { 1 }; /* don't use static : performance detrimental */ return one.c[0]; } #ifndef __has_builtin # define __has_builtin(x) 0 #endif static unsigned ZWRAP_swap32(unsigned in) { #if defined(_MSC_VER) /* Visual Studio */ return _byteswap_ulong(in); #elif (defined (__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 403)) \ || (defined(__clang__) && __has_builtin(__builtin_bswap32)) return __builtin_bswap32(in); #else return ((in << 24) & 0xff000000 ) | ((in << 8) & 0x00ff0000 ) | ((in >> 8) & 0x0000ff00 ) | ((in >> 24) & 0x000000ff ); #endif } static unsigned ZWRAP_readLE32(const void* ptr) { unsigned value; memcpy(&value, ptr, sizeof(value)); if (ZWRAP_isLittleEndian()) return value; else return ZWRAP_swap32(value); } /* === Wrapper === */ static int g_ZWRAP_useZSTDcompression = ZWRAP_USE_ZSTD; /* 0 = don't use ZSTD */ void ZWRAP_useZSTDcompression(int turn_on) { g_ZWRAP_useZSTDcompression = turn_on; } int ZWRAP_isUsingZSTDcompression(void) { return g_ZWRAP_useZSTDcompression; } static ZWRAP_decompress_type g_ZWRAPdecompressionType = ZWRAP_AUTO; void ZWRAP_setDecompressionType(ZWRAP_decompress_type type) { g_ZWRAPdecompressionType = type; } ZWRAP_decompress_type ZWRAP_getDecompressionType(void) { return g_ZWRAPdecompressionType; } const char * zstdVersion(void) { return ZSTD_VERSION_STRING; } ZEXTERN const char * ZEXPORT z_zlibVersion _Z_OF((void)) { return zlibVersion(); } static void* ZWRAP_allocFunction(void* opaque, size_t size) { z_streamp strm = (z_streamp) opaque; void* address = strm->zalloc(strm->opaque, 1, (uInt)size); /* LOG_WRAPPERC("ZWRAP alloc %p, %d \n", address, (int)size); */ return address; } static void ZWRAP_freeFunction(void* opaque, void* address) { z_streamp strm = (z_streamp) opaque; strm->zfree(strm->opaque, address); /* if (address) LOG_WRAPPERC("ZWRAP free %p \n", address); */ } static void* ZWRAP_customMalloc(size_t size, ZSTD_customMem customMem) { if (customMem.customAlloc) return customMem.customAlloc(customMem.opaque, size); return malloc(size); } static void* ZWRAP_customCalloc(size_t size, ZSTD_customMem customMem) { if (customMem.customAlloc) { /* calloc implemented as malloc+memset; * not as efficient as calloc, but next best guess for custom malloc */ void* const ptr = customMem.customAlloc(customMem.opaque, size); memset(ptr, 0, size); return ptr; } return calloc(1, size); } static void ZWRAP_customFree(void* ptr, ZSTD_customMem customMem) { if (ptr!=NULL) { if (customMem.customFree) customMem.customFree(customMem.opaque, ptr); else free(ptr); } } /* === Compression === */ typedef enum { ZWRAP_useInit, ZWRAP_useReset, ZWRAP_streamEnd } ZWRAP_state_t; typedef struct { ZSTD_CStream* zbc; int compressionLevel; int streamEnd; /* a flag to signal the end of a stream */ unsigned long long totalInBytes; /* we need it as strm->total_in can be reset by user */ ZSTD_customMem customMem; z_stream allocFunc; /* copy of zalloc, zfree, opaque */ ZSTD_inBuffer inBuffer; ZSTD_outBuffer outBuffer; ZWRAP_state_t comprState; unsigned long long pledgedSrcSize; } ZWRAP_CCtx; /* typedef ZWRAP_CCtx internal_state; */ static size_t ZWRAP_freeCCtx(ZWRAP_CCtx* zwc) { if (zwc==NULL) return 0; /* support free on NULL */ ZSTD_freeCStream(zwc->zbc); ZWRAP_customFree(zwc, zwc->customMem); return 0; } static ZWRAP_CCtx* ZWRAP_createCCtx(z_streamp strm) { ZWRAP_CCtx* zwc; ZSTD_customMem customMem = { NULL, NULL, NULL }; if (strm->zalloc && strm->zfree) { customMem.customAlloc = ZWRAP_allocFunction; customMem.customFree = ZWRAP_freeFunction; } customMem.opaque = strm; zwc = (ZWRAP_CCtx*)ZWRAP_customCalloc(sizeof(ZWRAP_CCtx), customMem); if (zwc == NULL) return NULL; zwc->allocFunc = *strm; customMem.opaque = &zwc->allocFunc; zwc->customMem = customMem; return zwc; } static int ZWRAP_initializeCStream(ZWRAP_CCtx* zwc, const void* dict, size_t dictSize, unsigned long long pledgedSrcSize) { LOG_WRAPPERC("- ZWRAP_initializeCStream=%p\n", zwc); if (zwc == NULL || zwc->zbc == NULL) return Z_STREAM_ERROR; if (!pledgedSrcSize) pledgedSrcSize = zwc->pledgedSrcSize; { unsigned initErr = 0; ZSTD_parameters const params = ZSTD_getParams(zwc->compressionLevel, pledgedSrcSize, dictSize); ZSTD_CCtx_params* cctxParams = ZSTD_createCCtxParams(); if (!cctxParams) return Z_STREAM_ERROR; LOG_WRAPPERC("pledgedSrcSize=%d windowLog=%d chainLog=%d hashLog=%d searchLog=%d minMatch=%d strategy=%d\n", (int)pledgedSrcSize, params.cParams.windowLog, params.cParams.chainLog, params.cParams.hashLog, params.cParams.searchLog, params.cParams.minMatch, params.cParams.strategy); initErr |= ZSTD_isError(ZSTD_CCtx_reset(zwc->zbc, ZSTD_reset_session_only)); initErr |= ZSTD_isError(ZSTD_CCtxParams_init_advanced(cctxParams, params)); initErr |= ZSTD_isError(ZSTD_CCtx_setParametersUsingCCtxParams(zwc->zbc, cctxParams)); initErr |= ZSTD_isError(ZSTD_CCtx_setPledgedSrcSize(zwc->zbc, pledgedSrcSize)); initErr |= ZSTD_isError(ZSTD_CCtx_loadDictionary(zwc->zbc, dict, dictSize)); ZSTD_freeCCtxParams(cctxParams); if (initErr) return Z_STREAM_ERROR; } return Z_OK; } static int ZWRAPC_finishWithError(ZWRAP_CCtx* zwc, z_streamp strm, int error) { LOG_WRAPPERC("- ZWRAPC_finishWithError=%d\n", error); if (zwc) ZWRAP_freeCCtx(zwc); if (strm) strm->state = NULL; return (error) ? error : Z_STREAM_ERROR; } static int ZWRAPC_finishWithErrorMsg(z_streamp strm, char* message) { ZWRAP_CCtx* zwc = (ZWRAP_CCtx*) strm->state; strm->msg = message; if (zwc == NULL) return Z_STREAM_ERROR; return ZWRAPC_finishWithError(zwc, strm, 0); } int ZWRAP_setPledgedSrcSize(z_streamp strm, unsigned long long pledgedSrcSize) { ZWRAP_CCtx* zwc = (ZWRAP_CCtx*) strm->state; if (zwc == NULL) return Z_STREAM_ERROR; zwc->pledgedSrcSize = pledgedSrcSize; zwc->comprState = ZWRAP_useInit; return Z_OK; } static struct internal_state* convert_into_sis(void* ptr) { return (struct internal_state*) ptr; } ZEXTERN int ZEXPORT z_deflateInit_ _Z_OF((z_streamp strm, int level, const char *version, int stream_size)) { ZWRAP_CCtx* zwc; LOG_WRAPPERC("- deflateInit level=%d\n", level); if (!g_ZWRAP_useZSTDcompression) { return deflateInit_((strm), (level), version, stream_size); } zwc = ZWRAP_createCCtx(strm); if (zwc == NULL) return Z_MEM_ERROR; if (level == Z_DEFAULT_COMPRESSION) level = ZWRAP_DEFAULT_CLEVEL; zwc->streamEnd = 0; zwc->totalInBytes = 0; zwc->compressionLevel = level; strm->state = convert_into_sis(zwc); /* use state which in not used by user */ strm->total_in = 0; strm->total_out = 0; strm->adler = 0; return Z_OK; } ZEXTERN int ZEXPORT z_deflateInit2_ _Z_OF((z_streamp strm, int level, int method, int windowBits, int memLevel, int strategy, const char *version, int stream_size)) { if (!g_ZWRAP_useZSTDcompression) return deflateInit2_(strm, level, method, windowBits, memLevel, strategy, version, stream_size); return z_deflateInit_ (strm, level, version, stream_size); } int ZWRAP_deflateReset_keepDict(z_streamp strm) { LOG_WRAPPERC("- ZWRAP_deflateReset_keepDict\n"); if (!g_ZWRAP_useZSTDcompression) return deflateReset(strm); { ZWRAP_CCtx* zwc = (ZWRAP_CCtx*) strm->state; if (zwc) { zwc->streamEnd = 0; zwc->totalInBytes = 0; } } strm->total_in = 0; strm->total_out = 0; strm->adler = 0; return Z_OK; } ZEXTERN int ZEXPORT z_deflateReset _Z_OF((z_streamp strm)) { LOG_WRAPPERC("- deflateReset\n"); if (!g_ZWRAP_useZSTDcompression) return deflateReset(strm); ZWRAP_deflateReset_keepDict(strm); { ZWRAP_CCtx* zwc = (ZWRAP_CCtx*) strm->state; if (zwc) zwc->comprState = ZWRAP_useInit; } return Z_OK; } ZEXTERN int ZEXPORT z_deflateSetDictionary _Z_OF((z_streamp strm, const Bytef *dictionary, uInt dictLength)) { if (!g_ZWRAP_useZSTDcompression) { LOG_WRAPPERC("- deflateSetDictionary\n"); return deflateSetDictionary(strm, dictionary, dictLength); } { ZWRAP_CCtx* zwc = (ZWRAP_CCtx*) strm->state; LOG_WRAPPERC("- deflateSetDictionary level=%d\n", (int)zwc->compressionLevel); if (!zwc) return Z_STREAM_ERROR; if (zwc->zbc == NULL) { zwc->zbc = ZSTD_createCStream_advanced(zwc->customMem); if (zwc->zbc == NULL) return ZWRAPC_finishWithError(zwc, strm, 0); } { int res = ZWRAP_initializeCStream(zwc, dictionary, dictLength, ZSTD_CONTENTSIZE_UNKNOWN); if (res != Z_OK) return ZWRAPC_finishWithError(zwc, strm, res); } zwc->comprState = ZWRAP_useReset; } return Z_OK; } ZEXTERN int ZEXPORT z_deflate _Z_OF((z_streamp strm, int flush)) { ZWRAP_CCtx* zwc; if (!g_ZWRAP_useZSTDcompression) { LOG_WRAPPERC("- deflate1 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out); return deflate(strm, flush); } zwc = (ZWRAP_CCtx*) strm->state; if (zwc == NULL) { LOG_WRAPPERC("zwc == NULL\n"); return Z_STREAM_ERROR; } if (zwc->zbc == NULL) { zwc->zbc = ZSTD_createCStream_advanced(zwc->customMem); if (zwc->zbc == NULL) return ZWRAPC_finishWithError(zwc, strm, 0); { int const initErr = ZWRAP_initializeCStream(zwc, NULL, 0, (flush == Z_FINISH) ? strm->avail_in : ZSTD_CONTENTSIZE_UNKNOWN); if (initErr != Z_OK) return ZWRAPC_finishWithError(zwc, strm, initErr); } if (flush != Z_FINISH) zwc->comprState = ZWRAP_useReset; } else { if (zwc->totalInBytes == 0) { if (zwc->comprState == ZWRAP_useReset) { size_t resetErr = ZSTD_CCtx_reset(zwc->zbc, ZSTD_reset_session_only); if (ZSTD_isError(resetErr)) { LOG_WRAPPERC("ERROR: ZSTD_CCtx_reset errorCode=%s\n", ZSTD_getErrorName(resetErr)); return ZWRAPC_finishWithError(zwc, strm, 0); } resetErr = ZSTD_CCtx_setPledgedSrcSize(zwc->zbc, (flush == Z_FINISH) ? strm->avail_in : zwc->pledgedSrcSize); if (ZSTD_isError(resetErr)) { LOG_WRAPPERC("ERROR: ZSTD_CCtx_setPledgedSrcSize errorCode=%s\n", ZSTD_getErrorName(resetErr)); return ZWRAPC_finishWithError(zwc, strm, 0); } } else { int const res = ZWRAP_initializeCStream(zwc, NULL, 0, (flush == Z_FINISH) ? strm->avail_in : ZSTD_CONTENTSIZE_UNKNOWN); if (res != Z_OK) return ZWRAPC_finishWithError(zwc, strm, res); if (flush != Z_FINISH) zwc->comprState = ZWRAP_useReset; } } /* (zwc->totalInBytes == 0) */ } /* ! (zwc->zbc == NULL) */ LOG_WRAPPERC("- deflate2 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out); if (strm->avail_in > 0) { zwc->inBuffer.src = strm->next_in; zwc->inBuffer.size = strm->avail_in; zwc->inBuffer.pos = 0; zwc->outBuffer.dst = strm->next_out; zwc->outBuffer.size = strm->avail_out; zwc->outBuffer.pos = 0; { size_t const cErr = ZSTD_compressStream(zwc->zbc, &zwc->outBuffer, &zwc->inBuffer); LOG_WRAPPERC("deflate ZSTD_compressStream srcSize=%d dstCapacity=%d\n", (int)zwc->inBuffer.size, (int)zwc->outBuffer.size); if (ZSTD_isError(cErr)) return ZWRAPC_finishWithError(zwc, strm, 0); } strm->next_out += zwc->outBuffer.pos; strm->total_out += zwc->outBuffer.pos; strm->avail_out -= zwc->outBuffer.pos; strm->total_in += zwc->inBuffer.pos; zwc->totalInBytes += zwc->inBuffer.pos; strm->next_in += zwc->inBuffer.pos; strm->avail_in -= zwc->inBuffer.pos; } if (flush == Z_FULL_FLUSH #if ZLIB_VERNUM >= 0x1240 || flush == Z_TREES #endif || flush == Z_BLOCK) return ZWRAPC_finishWithErrorMsg(strm, "Z_FULL_FLUSH, Z_BLOCK and Z_TREES are not supported!"); if (flush == Z_FINISH) { size_t bytesLeft; if (zwc->streamEnd) return Z_STREAM_END; zwc->outBuffer.dst = strm->next_out; zwc->outBuffer.size = strm->avail_out; zwc->outBuffer.pos = 0; bytesLeft = ZSTD_endStream(zwc->zbc, &zwc->outBuffer); LOG_WRAPPERC("deflate ZSTD_endStream dstCapacity=%d bytesLeft=%d\n", (int)strm->avail_out, (int)bytesLeft); if (ZSTD_isError(bytesLeft)) return ZWRAPC_finishWithError(zwc, strm, 0); strm->next_out += zwc->outBuffer.pos; strm->total_out += zwc->outBuffer.pos; strm->avail_out -= zwc->outBuffer.pos; if (bytesLeft == 0) { zwc->streamEnd = 1; LOG_WRAPPERC("Z_STREAM_END2 strm->total_in=%d strm->avail_out=%d strm->total_out=%d\n", (int)strm->total_in, (int)strm->avail_out, (int)strm->total_out); return Z_STREAM_END; } } else if (flush == Z_SYNC_FLUSH || flush == Z_PARTIAL_FLUSH) { size_t bytesLeft; zwc->outBuffer.dst = strm->next_out; zwc->outBuffer.size = strm->avail_out; zwc->outBuffer.pos = 0; bytesLeft = ZSTD_flushStream(zwc->zbc, &zwc->outBuffer); LOG_WRAPPERC("deflate ZSTD_flushStream dstCapacity=%d bytesLeft=%d\n", (int)strm->avail_out, (int)bytesLeft); if (ZSTD_isError(bytesLeft)) return ZWRAPC_finishWithError(zwc, strm, 0); strm->next_out += zwc->outBuffer.pos; strm->total_out += zwc->outBuffer.pos; strm->avail_out -= zwc->outBuffer.pos; } LOG_WRAPPERC("- deflate3 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out); return Z_OK; } ZEXTERN int ZEXPORT z_deflateEnd _Z_OF((z_streamp strm)) { if (!g_ZWRAP_useZSTDcompression) { LOG_WRAPPERC("- deflateEnd\n"); return deflateEnd(strm); } LOG_WRAPPERC("- deflateEnd total_in=%d total_out=%d\n", (int)(strm->total_in), (int)(strm->total_out)); { size_t errorCode; ZWRAP_CCtx* zwc = (ZWRAP_CCtx*) strm->state; if (zwc == NULL) return Z_OK; /* structures are already freed */ strm->state = NULL; errorCode = ZWRAP_freeCCtx(zwc); if (ZSTD_isError(errorCode)) return Z_STREAM_ERROR; } return Z_OK; } ZEXTERN uLong ZEXPORT z_deflateBound _Z_OF((z_streamp strm, uLong sourceLen)) { if (!g_ZWRAP_useZSTDcompression) return deflateBound(strm, sourceLen); return ZSTD_compressBound(sourceLen); } ZEXTERN int ZEXPORT z_deflateParams _Z_OF((z_streamp strm, int level, int strategy)) { if (!g_ZWRAP_useZSTDcompression) { LOG_WRAPPERC("- deflateParams level=%d strategy=%d\n", level, strategy); return deflateParams(strm, level, strategy); } return Z_OK; } /* === Decompression === */ typedef enum { ZWRAP_ZLIB_STREAM, ZWRAP_ZSTD_STREAM, ZWRAP_UNKNOWN_STREAM } ZWRAP_stream_type; typedef struct { ZSTD_DStream* zbd; char headerBuf[16]; /* must be >= ZSTD_frameHeaderSize_min */ int errorCount; unsigned long long totalInBytes; /* we need it as strm->total_in can be reset by user */ ZWRAP_state_t decompState; ZSTD_inBuffer inBuffer; ZSTD_outBuffer outBuffer; /* zlib params */ int stream_size; char *version; int windowBits; ZSTD_customMem customMem; z_stream allocFunc; /* just to copy zalloc, zfree, opaque */ } ZWRAP_DCtx; static void ZWRAP_initDCtx(ZWRAP_DCtx* zwd) { zwd->errorCount = 0; zwd->outBuffer.pos = 0; zwd->outBuffer.size = 0; } static ZWRAP_DCtx* ZWRAP_createDCtx(z_streamp strm) { ZWRAP_DCtx* zwd; ZSTD_customMem customMem = { NULL, NULL, NULL }; if (strm->zalloc && strm->zfree) { customMem.customAlloc = ZWRAP_allocFunction; customMem.customFree = ZWRAP_freeFunction; } customMem.opaque = strm; zwd = (ZWRAP_DCtx*)ZWRAP_customCalloc(sizeof(ZWRAP_DCtx), customMem); if (zwd == NULL) return NULL; zwd->allocFunc = *strm; customMem.opaque = &zwd->allocFunc; zwd->customMem = customMem; ZWRAP_initDCtx(zwd); return zwd; } static size_t ZWRAP_freeDCtx(ZWRAP_DCtx* zwd) { if (zwd==NULL) return 0; /* support free on null */ ZSTD_freeDStream(zwd->zbd); ZWRAP_customFree(zwd->version, zwd->customMem); ZWRAP_customFree(zwd, zwd->customMem); return 0; } int ZWRAP_isUsingZSTDdecompression(z_streamp strm) { if (strm == NULL) return 0; return (strm->reserved == ZWRAP_ZSTD_STREAM); } static int ZWRAPD_finishWithError(ZWRAP_DCtx* zwd, z_streamp strm, int error) { LOG_WRAPPERD("- ZWRAPD_finishWithError=%d\n", error); ZWRAP_freeDCtx(zwd); strm->state = NULL; return (error) ? error : Z_STREAM_ERROR; } static int ZWRAPD_finishWithErrorMsg(z_streamp strm, char* message) { ZWRAP_DCtx* const zwd = (ZWRAP_DCtx*) strm->state; strm->msg = message; if (zwd == NULL) return Z_STREAM_ERROR; return ZWRAPD_finishWithError(zwd, strm, 0); } ZEXTERN int ZEXPORT z_inflateInit_ _Z_OF((z_streamp strm, const char* version, int stream_size)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB) { strm->reserved = ZWRAP_ZLIB_STREAM; return inflateInit(strm); } { ZWRAP_DCtx* const zwd = ZWRAP_createDCtx(strm); LOG_WRAPPERD("- inflateInit\n"); if (zwd == NULL) return ZWRAPD_finishWithError(zwd, strm, 0); zwd->version = (char*)ZWRAP_customMalloc(strlen(version)+1, zwd->customMem); if (zwd->version == NULL) return ZWRAPD_finishWithError(zwd, strm, 0); strcpy(zwd->version, version); zwd->stream_size = stream_size; zwd->totalInBytes = 0; strm->state = convert_into_sis(zwd); strm->total_in = 0; strm->total_out = 0; strm->reserved = ZWRAP_UNKNOWN_STREAM; strm->adler = 0; } return Z_OK; } ZEXTERN int ZEXPORT z_inflateInit2_ _Z_OF((z_streamp strm, int windowBits, const char *version, int stream_size)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB) { return inflateInit2_(strm, windowBits, version, stream_size); } { int const ret = z_inflateInit_ (strm, version, stream_size); LOG_WRAPPERD("- inflateInit2 windowBits=%d\n", windowBits); if (ret == Z_OK) { ZWRAP_DCtx* const zwd = (ZWRAP_DCtx*)strm->state; if (zwd == NULL) return Z_STREAM_ERROR; zwd->windowBits = windowBits; } return ret; } } int ZWRAP_inflateReset_keepDict(z_streamp strm) { LOG_WRAPPERD("- ZWRAP_inflateReset_keepDict\n"); if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateReset(strm); { ZWRAP_DCtx* const zwd = (ZWRAP_DCtx*) strm->state; if (zwd == NULL) return Z_STREAM_ERROR; ZWRAP_initDCtx(zwd); zwd->decompState = ZWRAP_useReset; zwd->totalInBytes = 0; } strm->total_in = 0; strm->total_out = 0; return Z_OK; } ZEXTERN int ZEXPORT z_inflateReset _Z_OF((z_streamp strm)) { LOG_WRAPPERD("- inflateReset\n"); if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateReset(strm); { int const ret = ZWRAP_inflateReset_keepDict(strm); if (ret != Z_OK) return ret; } { ZWRAP_DCtx* const zwd = (ZWRAP_DCtx*) strm->state; if (zwd == NULL) return Z_STREAM_ERROR; zwd->decompState = ZWRAP_useInit; } return Z_OK; } #if ZLIB_VERNUM >= 0x1240 ZEXTERN int ZEXPORT z_inflateReset2 _Z_OF((z_streamp strm, int windowBits)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateReset2(strm, windowBits); { int const ret = z_inflateReset (strm); if (ret == Z_OK) { ZWRAP_DCtx* const zwd = (ZWRAP_DCtx*)strm->state; if (zwd == NULL) return Z_STREAM_ERROR; zwd->windowBits = windowBits; } return ret; } } #endif ZEXTERN int ZEXPORT z_inflateSetDictionary _Z_OF((z_streamp strm, const Bytef *dictionary, uInt dictLength)) { LOG_WRAPPERD("- inflateSetDictionary\n"); if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateSetDictionary(strm, dictionary, dictLength); { ZWRAP_DCtx* const zwd = (ZWRAP_DCtx*) strm->state; if (zwd == NULL || zwd->zbd == NULL) return Z_STREAM_ERROR; { size_t const resetErr = ZSTD_DCtx_reset(zwd->zbd, ZSTD_reset_session_only); if (ZSTD_isError(resetErr)) return ZWRAPD_finishWithError(zwd, strm, 0); } { size_t const loadErr = ZSTD_DCtx_loadDictionary(zwd->zbd, dictionary, dictLength); if (ZSTD_isError(loadErr)) return ZWRAPD_finishWithError(zwd, strm, 0); } zwd->decompState = ZWRAP_useReset; if (zwd->totalInBytes == ZSTD_HEADERSIZE) { zwd->inBuffer.src = zwd->headerBuf; zwd->inBuffer.size = zwd->totalInBytes; zwd->inBuffer.pos = 0; zwd->outBuffer.dst = strm->next_out; zwd->outBuffer.size = 0; zwd->outBuffer.pos = 0; { size_t const errorCode = ZSTD_decompressStream(zwd->zbd, &zwd->outBuffer, &zwd->inBuffer); LOG_WRAPPERD("inflateSetDictionary ZSTD_decompressStream errorCode=%d srcSize=%d dstCapacity=%d\n", (int)errorCode, (int)zwd->inBuffer.size, (int)zwd->outBuffer.size); if (zwd->inBuffer.pos < zwd->outBuffer.size || ZSTD_isError(errorCode)) { LOG_WRAPPERD("ERROR: ZSTD_decompressStream %s\n", ZSTD_getErrorName(errorCode)); return ZWRAPD_finishWithError(zwd, strm, 0); } } } } return Z_OK; } ZEXTERN int ZEXPORT z_inflate _Z_OF((z_streamp strm, int flush)) { ZWRAP_DCtx* zwd; if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) { int const result = inflate(strm, flush); LOG_WRAPPERD("- inflate2 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d res=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out, result); return result; } if (strm->avail_in <= 0) return Z_OK; zwd = (ZWRAP_DCtx*) strm->state; LOG_WRAPPERD("- inflate1 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out); if (zwd == NULL) return Z_STREAM_ERROR; if (zwd->decompState == ZWRAP_streamEnd) return Z_STREAM_END; if (zwd->totalInBytes < ZLIB_HEADERSIZE) { if (zwd->totalInBytes == 0 && strm->avail_in >= ZLIB_HEADERSIZE) { if (ZWRAP_readLE32(strm->next_in) != ZSTD_MAGICNUMBER) { { int const initErr = (zwd->windowBits) ? inflateInit2_(strm, zwd->windowBits, zwd->version, zwd->stream_size) : inflateInit_(strm, zwd->version, zwd->stream_size); LOG_WRAPPERD("ZLIB inflateInit errorCode=%d\n", initErr); if (initErr != Z_OK) return ZWRAPD_finishWithError(zwd, strm, initErr); } strm->reserved = ZWRAP_ZLIB_STREAM; { size_t const freeErr = ZWRAP_freeDCtx(zwd); if (ZSTD_isError(freeErr)) goto error; } { int const result = (flush == Z_INFLATE_SYNC) ? inflateSync(strm) : inflate(strm, flush); LOG_WRAPPERD("- inflate3 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d res=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out, res); return result; } } } else { /* ! (zwd->totalInBytes == 0 && strm->avail_in >= ZLIB_HEADERSIZE) */ size_t const srcSize = MIN(strm->avail_in, ZLIB_HEADERSIZE - zwd->totalInBytes); memcpy(zwd->headerBuf+zwd->totalInBytes, strm->next_in, srcSize); strm->total_in += srcSize; zwd->totalInBytes += srcSize; strm->next_in += srcSize; strm->avail_in -= srcSize; if (zwd->totalInBytes < ZLIB_HEADERSIZE) return Z_OK; if (ZWRAP_readLE32(zwd->headerBuf) != ZSTD_MAGICNUMBER) { z_stream strm2; strm2.next_in = strm->next_in; strm2.avail_in = strm->avail_in; strm2.next_out = strm->next_out; strm2.avail_out = strm->avail_out; { int const initErr = (zwd->windowBits) ? inflateInit2_(strm, zwd->windowBits, zwd->version, zwd->stream_size) : inflateInit_(strm, zwd->version, zwd->stream_size); LOG_WRAPPERD("ZLIB inflateInit errorCode=%d\n", initErr); if (initErr != Z_OK) return ZWRAPD_finishWithError(zwd, strm, initErr); } /* inflate header */ strm->next_in = (unsigned char*)zwd->headerBuf; strm->avail_in = ZLIB_HEADERSIZE; strm->avail_out = 0; { int const dErr = inflate(strm, Z_NO_FLUSH); LOG_WRAPPERD("ZLIB inflate errorCode=%d strm->avail_in=%d\n", dErr, (int)strm->avail_in); if (dErr != Z_OK) return ZWRAPD_finishWithError(zwd, strm, dErr); } if (strm->avail_in > 0) goto error; strm->next_in = strm2.next_in; strm->avail_in = strm2.avail_in; strm->next_out = strm2.next_out; strm->avail_out = strm2.avail_out; strm->reserved = ZWRAP_ZLIB_STREAM; /* mark as zlib stream */ { size_t const freeErr = ZWRAP_freeDCtx(zwd); if (ZSTD_isError(freeErr)) goto error; } { int const result = (flush == Z_INFLATE_SYNC) ? inflateSync(strm) : inflate(strm, flush); LOG_WRAPPERD("- inflate2 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d res=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out, res); return result; } } } /* if ! (zwd->totalInBytes == 0 && strm->avail_in >= ZLIB_HEADERSIZE) */ } /* (zwd->totalInBytes < ZLIB_HEADERSIZE) */ strm->reserved = ZWRAP_ZSTD_STREAM; /* mark as zstd steam */ if (flush == Z_INFLATE_SYNC) { strm->msg = "inflateSync is not supported!"; goto error; } if (!zwd->zbd) { zwd->zbd = ZSTD_createDStream_advanced(zwd->customMem); if (zwd->zbd == NULL) { LOG_WRAPPERD("ERROR: ZSTD_createDStream_advanced\n"); goto error; } zwd->decompState = ZWRAP_useInit; } if (zwd->totalInBytes < ZSTD_HEADERSIZE) { if (zwd->totalInBytes == 0 && strm->avail_in >= ZSTD_HEADERSIZE) { if (zwd->decompState == ZWRAP_useInit) { size_t const initErr = ZSTD_initDStream(zwd->zbd); if (ZSTD_isError(initErr)) { LOG_WRAPPERD("ERROR: ZSTD_initDStream errorCode=%s\n", ZSTD_getErrorName(initErr)); goto error; } } else { size_t const resetErr = ZSTD_DCtx_reset(zwd->zbd, ZSTD_reset_session_only); if (ZSTD_isError(resetErr)) goto error; } } else { size_t const srcSize = MIN(strm->avail_in, ZSTD_HEADERSIZE - zwd->totalInBytes); memcpy(zwd->headerBuf+zwd->totalInBytes, strm->next_in, srcSize); strm->total_in += srcSize; zwd->totalInBytes += srcSize; strm->next_in += srcSize; strm->avail_in -= srcSize; if (zwd->totalInBytes < ZSTD_HEADERSIZE) return Z_OK; if (zwd->decompState == ZWRAP_useInit) { size_t const initErr = ZSTD_initDStream(zwd->zbd); if (ZSTD_isError(initErr)) { LOG_WRAPPERD("ERROR: ZSTD_initDStream errorCode=%s\n", ZSTD_getErrorName(initErr)); goto error; } } else { size_t const resetErr = ZSTD_DCtx_reset(zwd->zbd, ZSTD_reset_session_only); if (ZSTD_isError(resetErr)) goto error; } zwd->inBuffer.src = zwd->headerBuf; zwd->inBuffer.size = ZSTD_HEADERSIZE; zwd->inBuffer.pos = 0; zwd->outBuffer.dst = strm->next_out; zwd->outBuffer.size = 0; zwd->outBuffer.pos = 0; { size_t const dErr = ZSTD_decompressStream(zwd->zbd, &zwd->outBuffer, &zwd->inBuffer); LOG_WRAPPERD("inflate ZSTD_decompressStream1 errorCode=%d srcSize=%d dstCapacity=%d\n", (int)dErr, (int)zwd->inBuffer.size, (int)zwd->outBuffer.size); if (ZSTD_isError(dErr)) { LOG_WRAPPERD("ERROR: ZSTD_decompressStream1 %s\n", ZSTD_getErrorName(dErr)); goto error; } } if (zwd->inBuffer.pos != zwd->inBuffer.size) goto error; /* not consumed */ } } /* (zwd->totalInBytes < ZSTD_HEADERSIZE) */ zwd->inBuffer.src = strm->next_in; zwd->inBuffer.size = strm->avail_in; zwd->inBuffer.pos = 0; zwd->outBuffer.dst = strm->next_out; zwd->outBuffer.size = strm->avail_out; zwd->outBuffer.pos = 0; { size_t const dErr = ZSTD_decompressStream(zwd->zbd, &zwd->outBuffer, &zwd->inBuffer); LOG_WRAPPERD("inflate ZSTD_decompressStream2 errorCode=%d srcSize=%d dstCapacity=%d\n", (int)dErr, (int)strm->avail_in, (int)strm->avail_out); if (ZSTD_isError(dErr)) { zwd->errorCount++; LOG_WRAPPERD("ERROR: ZSTD_decompressStream2 %s zwd->errorCount=%d\n", ZSTD_getErrorName(dErr), zwd->errorCount); if (zwd->errorCount<=1) return Z_NEED_DICT; else goto error; } LOG_WRAPPERD("inflate inBuffer.pos=%d inBuffer.size=%d outBuffer.pos=%d outBuffer.size=%d o\n", (int)zwd->inBuffer.pos, (int)zwd->inBuffer.size, (int)zwd->outBuffer.pos, (int)zwd->outBuffer.size); strm->next_out += zwd->outBuffer.pos; strm->total_out += zwd->outBuffer.pos; strm->avail_out -= zwd->outBuffer.pos; strm->total_in += zwd->inBuffer.pos; zwd->totalInBytes += zwd->inBuffer.pos; strm->next_in += zwd->inBuffer.pos; strm->avail_in -= zwd->inBuffer.pos; if (dErr == 0) { LOG_WRAPPERD("inflate Z_STREAM_END1 avail_in=%d avail_out=%d total_in=%d total_out=%d\n", (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out); zwd->decompState = ZWRAP_streamEnd; return Z_STREAM_END; } } /* dErr lifetime */ LOG_WRAPPERD("- inflate2 flush=%d avail_in=%d avail_out=%d total_in=%d total_out=%d res=%d\n", (int)flush, (int)strm->avail_in, (int)strm->avail_out, (int)strm->total_in, (int)strm->total_out, Z_OK); return Z_OK; error: return ZWRAPD_finishWithError(zwd, strm, 0); } ZEXTERN int ZEXPORT z_inflateEnd _Z_OF((z_streamp strm)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateEnd(strm); LOG_WRAPPERD("- inflateEnd total_in=%d total_out=%d\n", (int)(strm->total_in), (int)(strm->total_out)); { ZWRAP_DCtx* const zwd = (ZWRAP_DCtx*) strm->state; if (zwd == NULL) return Z_OK; /* structures are already freed */ { size_t const freeErr = ZWRAP_freeDCtx(zwd); if (ZSTD_isError(freeErr)) return Z_STREAM_ERROR; } strm->state = NULL; } return Z_OK; } ZEXTERN int ZEXPORT z_inflateSync _Z_OF((z_streamp strm)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) { return inflateSync(strm); } return z_inflate(strm, Z_INFLATE_SYNC); } /* Advanced compression functions */ ZEXTERN int ZEXPORT z_deflateCopy _Z_OF((z_streamp dest, z_streamp source)) { if (!g_ZWRAP_useZSTDcompression) return deflateCopy(dest, source); return ZWRAPC_finishWithErrorMsg(source, "deflateCopy is not supported!"); } ZEXTERN int ZEXPORT z_deflateTune _Z_OF((z_streamp strm, int good_length, int max_lazy, int nice_length, int max_chain)) { if (!g_ZWRAP_useZSTDcompression) return deflateTune(strm, good_length, max_lazy, nice_length, max_chain); return ZWRAPC_finishWithErrorMsg(strm, "deflateTune is not supported!"); } #if ZLIB_VERNUM >= 0x1260 ZEXTERN int ZEXPORT z_deflatePending _Z_OF((z_streamp strm, unsigned *pending, int *bits)) { if (!g_ZWRAP_useZSTDcompression) return deflatePending(strm, pending, bits); return ZWRAPC_finishWithErrorMsg(strm, "deflatePending is not supported!"); } #endif ZEXTERN int ZEXPORT z_deflatePrime _Z_OF((z_streamp strm, int bits, int value)) { if (!g_ZWRAP_useZSTDcompression) return deflatePrime(strm, bits, value); return ZWRAPC_finishWithErrorMsg(strm, "deflatePrime is not supported!"); } ZEXTERN int ZEXPORT z_deflateSetHeader _Z_OF((z_streamp strm, gz_headerp head)) { if (!g_ZWRAP_useZSTDcompression) return deflateSetHeader(strm, head); return ZWRAPC_finishWithErrorMsg(strm, "deflateSetHeader is not supported!"); } /* Advanced decompression functions */ #if ZLIB_VERNUM >= 0x1280 ZEXTERN int ZEXPORT z_inflateGetDictionary _Z_OF((z_streamp strm, Bytef *dictionary, uInt *dictLength)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateGetDictionary(strm, dictionary, dictLength); return ZWRAPD_finishWithErrorMsg(strm, "inflateGetDictionary is not supported!"); } #endif ZEXTERN int ZEXPORT z_inflateCopy _Z_OF((z_streamp dest, z_streamp source)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !source->reserved) return inflateCopy(dest, source); return ZWRAPD_finishWithErrorMsg(source, "inflateCopy is not supported!"); } #if ZLIB_VERNUM >= 0x1240 ZEXTERN long ZEXPORT z_inflateMark _Z_OF((z_streamp strm)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateMark(strm); return ZWRAPD_finishWithErrorMsg(strm, "inflateMark is not supported!"); } #endif ZEXTERN int ZEXPORT z_inflatePrime _Z_OF((z_streamp strm, int bits, int value)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflatePrime(strm, bits, value); return ZWRAPD_finishWithErrorMsg(strm, "inflatePrime is not supported!"); } ZEXTERN int ZEXPORT z_inflateGetHeader _Z_OF((z_streamp strm, gz_headerp head)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateGetHeader(strm, head); return ZWRAPD_finishWithErrorMsg(strm, "inflateGetHeader is not supported!"); } ZEXTERN int ZEXPORT z_inflateBackInit_ _Z_OF((z_streamp strm, int windowBits, unsigned char FAR *window, const char *version, int stream_size)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateBackInit_(strm, windowBits, window, version, stream_size); return ZWRAPD_finishWithErrorMsg(strm, "inflateBackInit is not supported!"); } ZEXTERN int ZEXPORT z_inflateBack _Z_OF((z_streamp strm, in_func in, void FAR *in_desc, out_func out, void FAR *out_desc)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateBack(strm, in, in_desc, out, out_desc); return ZWRAPD_finishWithErrorMsg(strm, "inflateBack is not supported!"); } ZEXTERN int ZEXPORT z_inflateBackEnd _Z_OF((z_streamp strm)) { if (g_ZWRAPdecompressionType == ZWRAP_FORCE_ZLIB || !strm->reserved) return inflateBackEnd(strm); return ZWRAPD_finishWithErrorMsg(strm, "inflateBackEnd is not supported!"); } ZEXTERN uLong ZEXPORT z_zlibCompileFlags _Z_OF((void)) { return zlibCompileFlags(); } /* === utility functions === */ #ifndef Z_SOLO ZEXTERN int ZEXPORT z_compress _Z_OF((Bytef *dest, uLongf *destLen, const Bytef *source, uLong sourceLen)) { if (!g_ZWRAP_useZSTDcompression) return compress(dest, destLen, source, sourceLen); { size_t dstCapacity = *destLen; size_t const cSize = ZSTD_compress(dest, dstCapacity, source, sourceLen, ZWRAP_DEFAULT_CLEVEL); LOG_WRAPPERD("z_compress sourceLen=%d dstCapacity=%d\n", (int)sourceLen, (int)dstCapacity); if (ZSTD_isError(cSize)) return Z_STREAM_ERROR; *destLen = cSize; } return Z_OK; } ZEXTERN int ZEXPORT z_compress2 _Z_OF((Bytef *dest, uLongf *destLen, const Bytef *source, uLong sourceLen, int level)) { if (!g_ZWRAP_useZSTDcompression) return compress2(dest, destLen, source, sourceLen, level); { size_t dstCapacity = *destLen; size_t const cSize = ZSTD_compress(dest, dstCapacity, source, sourceLen, level); if (ZSTD_isError(cSize)) return Z_STREAM_ERROR; *destLen = cSize; } return Z_OK; } ZEXTERN uLong ZEXPORT z_compressBound _Z_OF((uLong sourceLen)) { if (!g_ZWRAP_useZSTDcompression) return compressBound(sourceLen); return ZSTD_compressBound(sourceLen); } ZEXTERN int ZEXPORT z_uncompress _Z_OF((Bytef *dest, uLongf *destLen, const Bytef *source, uLong sourceLen)) { if (!ZSTD_isFrame(source, sourceLen)) return uncompress(dest, destLen, source, sourceLen); { size_t dstCapacity = *destLen; size_t const dSize = ZSTD_decompress(dest, dstCapacity, source, sourceLen); if (ZSTD_isError(dSize)) return Z_STREAM_ERROR; *destLen = dSize; } return Z_OK; } #endif /* !Z_SOLO */ /* checksum functions */ ZEXTERN uLong ZEXPORT z_adler32 _Z_OF((uLong adler, const Bytef *buf, uInt len)) { return adler32(adler, buf, len); } ZEXTERN uLong ZEXPORT z_crc32 _Z_OF((uLong crc, const Bytef *buf, uInt len)) { return crc32(crc, buf, len); } #if ZLIB_VERNUM >= 0x12B0 ZEXTERN uLong ZEXPORT z_adler32_z _Z_OF((uLong adler, const Bytef *buf, z_size_t len)) { return adler32_z(adler, buf, len); } ZEXTERN uLong ZEXPORT z_crc32_z _Z_OF((uLong crc, const Bytef *buf, z_size_t len)) { return crc32_z(crc, buf, len); } #endif #if ZLIB_VERNUM >= 0x1270 ZEXTERN const z_crc_t FAR * ZEXPORT z_get_crc_table _Z_OF((void)) { return get_crc_table(); } #endif /* Error function */ ZEXTERN const char * ZEXPORT z_zError _Z_OF((int err)) { /* Just use zlib Error function */ return zError(err); } form-5.0.1/extern/zstd/zlibWrapper/gzcompatibility.h0000644000175100017510000000351615217035741016332 /* * Copyright (c) Meta Platforms, Inc. and affiliates. * All rights reserved. * * This source code is licensed under both the BSD-style license (found in the * LICENSE file in the root directory of this source tree) and the GPLv2 (found * in the COPYING file in the root directory of this source tree). * You may select, at your option, one of the above-listed licenses. */ #if ZLIB_VERNUM <= 0x1240 ZEXTERN int ZEXPORT gzclose_r _Z_OF((gzFile file)); ZEXTERN int ZEXPORT gzclose_w _Z_OF((gzFile file)); ZEXTERN int ZEXPORT gzbuffer _Z_OF((gzFile file, unsigned size)); ZEXTERN z_off_t ZEXPORT gzoffset _Z_OF((gzFile file)); #if !defined(_WIN32) && defined(Z_LARGE64) # define z_off64_t off64_t #else # if defined(_WIN32) && !defined(__GNUC__) && !defined(Z_SOLO) # define z_off64_t __int64 # else # define z_off64_t z_off_t # endif #endif #endif #if ZLIB_VERNUM <= 0x1250 struct gzFile_s { unsigned have; unsigned char *next; z_off64_t pos; }; #endif #if ZLIB_VERNUM <= 0x1270 #if defined(_WIN32) && !defined(Z_SOLO) # include /* for wchar_t */ ZEXTERN gzFile ZEXPORT gzopen_w _Z_OF((const wchar_t *path, const char *mode)); #endif #endif #if ZLIB_VERNUM < 0x12B0 #ifdef Z_SOLO typedef unsigned long z_size_t; #else # define z_longlong long long # if defined(NO_SIZE_T) typedef unsigned NO_SIZE_T z_size_t; # elif defined(STDC) # include typedef size_t z_size_t; # else typedef unsigned long z_size_t; # endif # undef z_longlong #endif ZEXTERN z_size_t ZEXPORT gzfread _Z_OF((voidp buf, z_size_t size, z_size_t nitems, gzFile file)); ZEXTERN z_size_t ZEXPORT gzfwrite _Z_OF((voidpc buf, z_size_t size, z_size_t nitems, gzFile file)); #endif form-5.0.1/extern/zstd/zlibWrapper/gzread.c0000644000175100017510000005276215217035741014376 /* gzread.c contains minimal changes required to be compiled with zlibWrapper: * - gz_statep was converted to union to work with -Wstrict-aliasing=1 */ /* gzread.c -- zlib functions for reading gzip files * Copyright (C) 2004, 2005, 2010, 2011, 2012, 2013, 2016 Mark Adler * For conditions of distribution and use, see https://www.zlib.net/zlib_license.html */ #include "gzguts.h" /* fix for Visual Studio, which doesn't support ssize_t type. * see https://github.com/facebook/zstd/issues/1800#issuecomment-545945050 */ #if defined(_MSC_VER) && !defined(ssize_t) # include typedef SSIZE_T ssize_t; #endif /* Local functions */ local int gz_load _Z_OF((gz_statep, unsigned char *, unsigned, unsigned *)); local int gz_avail _Z_OF((gz_statep)); local int gz_look _Z_OF((gz_statep)); local int gz_decomp _Z_OF((gz_statep)); local int gz_fetch _Z_OF((gz_statep)); local int gz_skip _Z_OF((gz_statep, z_off64_t)); local z_size_t gz_read _Z_OF((gz_statep, voidp, z_size_t)); /* Use read() to load a buffer -- return -1 on error, otherwise 0. Read from state.state->fd, and update state.state->eof, state.state->err, and state.state->msg as appropriate. This function needs to loop on read(), since read() is not guaranteed to read the number of bytes requested, depending on the type of descriptor. */ local int gz_load(gz_statep state, unsigned char *buf, unsigned len, unsigned *have) { ssize_t ret; unsigned get, max = ((unsigned)-1 >> 2) + 1; *have = 0; do { get = len - *have; if (get > max) get = max; ret = read(state.state->fd, buf + *have, get); if (ret <= 0) break; *have += (unsigned)ret; } while (*have < len); if (ret < 0) { gz_error(state, Z_ERRNO, zstrerror()); return -1; } if (ret == 0) state.state->eof = 1; return 0; } /* Load up input buffer and set eof flag if last data loaded -- return -1 on error, 0 otherwise. Note that the eof flag is set when the end of the input file is reached, even though there may be unused data in the buffer. Once that data has been used, no more attempts will be made to read the file. If strm->avail_in != 0, then the current data is moved to the beginning of the input buffer, and then the remainder of the buffer is loaded with the available data from the input file. */ local int gz_avail(gz_statep state) { unsigned got; z_streamp strm = &(state.state->strm); if (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR) return -1; if (state.state->eof == 0) { if (strm->avail_in) { /* copy what's there to the start */ unsigned char *p = state.state->in; unsigned const char *q = strm->next_in; unsigned n = strm->avail_in; do { *p++ = *q++; } while (--n); } if (gz_load(state, state.state->in + strm->avail_in, state.state->size - strm->avail_in, &got) == -1) return -1; strm->avail_in += got; strm->next_in = state.state->in; } return 0; } /* Look for gzip header, set up for inflate or copy. state.state->x.have must be 0. If this is the first time in, allocate required memory. state.state->how will be left unchanged if there is no more input data available, will be set to COPY if there is no gzip header and direct copying will be performed, or it will be set to GZIP for decompression. If direct copying, then leftover input data from the input buffer will be copied to the output buffer. In that case, all further file reads will be directly to either the output buffer or a user buffer. If decompressing, the inflate state will be initialized. gz_look() will return 0 on success or -1 on failure. */ local int gz_look(gz_statep state) { z_streamp strm = &(state.state->strm); /* allocate read buffers and inflate memory */ if (state.state->size == 0) { /* allocate buffers */ state.state->in = (unsigned char *)malloc(state.state->want); state.state->out = (unsigned char *)malloc(state.state->want << 1); if (state.state->in == NULL || state.state->out == NULL) { free(state.state->out); free(state.state->in); gz_error(state, Z_MEM_ERROR, "out of memory"); return -1; } state.state->size = state.state->want; /* allocate inflate memory */ state.state->strm.zalloc = Z_NULL; state.state->strm.zfree = Z_NULL; state.state->strm.opaque = Z_NULL; state.state->strm.avail_in = 0; state.state->strm.next_in = Z_NULL; if (inflateInit2(&(state.state->strm), 15 + 16) != Z_OK) { /* gunzip */ free(state.state->out); free(state.state->in); state.state->size = 0; gz_error(state, Z_MEM_ERROR, "out of memory"); return -1; } } /* get at least the magic bytes in the input buffer */ if (strm->avail_in < 2) { if (gz_avail(state) == -1) return -1; if (strm->avail_in == 0) return 0; } /* look for gzip magic bytes -- if there, do gzip decoding (note: there is a logical dilemma here when considering the case of a partially written gzip file, to wit, if a single 31 byte is written, then we cannot tell whether this is a single-byte file, or just a partially written gzip file -- for here we assume that if a gzip file is being written, then the header will be written in a single operation, so that reading a single byte is sufficient indication that it is not a gzip file) */ if (strm->avail_in > 1 && ((strm->next_in[0] == 31 && strm->next_in[1] == 139) /* gz header */ || (strm->next_in[0] == 40 && strm->next_in[1] == 181))) { /* zstd header */ inflateReset(strm); state.state->how = GZIP; state.state->direct = 0; return 0; } /* no gzip header -- if we were decoding gzip before, then this is trailing garbage. Ignore the trailing garbage and finish. */ if (state.state->direct == 0) { strm->avail_in = 0; state.state->eof = 1; state.state->x.have = 0; return 0; } /* doing raw i/o, copy any leftover input to output -- this assumes that the output buffer is larger than the input buffer, which also assures space for gzungetc() */ state.state->x.next = state.state->out; if (strm->avail_in) { memcpy(state.state->x.next, strm->next_in, strm->avail_in); state.state->x.have = strm->avail_in; strm->avail_in = 0; } state.state->how = COPY; state.state->direct = 1; return 0; } /* Decompress from input to the provided next_out and avail_out in the state. On return, state.state->x.have and state.state->x.next point to the just decompressed data. If the gzip stream completes, state.state->how is reset to LOOK to look for the next gzip stream or raw data, once state.state->x.have is depleted. Returns 0 on success, -1 on failure. */ local int gz_decomp(gz_statep state) { int ret = Z_OK; unsigned had; z_streamp strm = &(state.state->strm); /* fill output buffer up to end of deflate stream */ had = strm->avail_out; do { /* get more input for inflate() */ if (strm->avail_in == 0 && gz_avail(state) == -1) return -1; if (strm->avail_in == 0) { gz_error(state, Z_BUF_ERROR, "unexpected end of file"); break; } /* decompress and handle errors */ ret = inflate(strm, Z_NO_FLUSH); if (ret == Z_STREAM_ERROR || ret == Z_NEED_DICT) { gz_error(state, Z_STREAM_ERROR, "internal error: inflate stream corrupt"); return -1; } if (ret == Z_MEM_ERROR) { gz_error(state, Z_MEM_ERROR, "out of memory"); return -1; } if (ret == Z_DATA_ERROR) { /* deflate stream invalid */ gz_error(state, Z_DATA_ERROR, strm->msg == NULL ? "compressed data error" : strm->msg); return -1; } } while (strm->avail_out && ret != Z_STREAM_END); /* update available output */ state.state->x.have = had - strm->avail_out; state.state->x.next = strm->next_out - state.state->x.have; /* if the gzip stream completed successfully, look for another */ if (ret == Z_STREAM_END) state.state->how = LOOK; /* good decompression */ return 0; } /* Fetch data and put it in the output buffer. Assumes state.state->x.have is 0. Data is either copied from the input file or decompressed from the input file depending on state.state->how. If state.state->how is LOOK, then a gzip header is looked for to determine whether to copy or decompress. Returns -1 on error, otherwise 0. gz_fetch() will leave state.state->how as COPY or GZIP unless the end of the input file has been reached and all data has been processed. */ local int gz_fetch(gz_statep state) { z_streamp strm = &(state.state->strm); do { switch(state.state->how) { case LOOK: /* -> LOOK, COPY (only if never GZIP), or GZIP */ if (gz_look(state) == -1) return -1; if (state.state->how == LOOK) return 0; break; case COPY: /* -> COPY */ if (gz_load(state, state.state->out, state.state->size << 1, &(state.state->x.have)) == -1) return -1; state.state->x.next = state.state->out; return 0; case GZIP: /* -> GZIP or LOOK (if end of gzip stream) */ strm->avail_out = state.state->size << 1; strm->next_out = state.state->out; if (gz_decomp(state) == -1) return -1; } } while (state.state->x.have == 0 && (!state.state->eof || strm->avail_in)); return 0; } /* Skip len uncompressed bytes of output. Return -1 on error, 0 on success. */ local int gz_skip(gz_statep state, z_off64_t len) { unsigned n; /* skip over len bytes or reach end-of-file, whichever comes first */ while (len) /* skip over whatever is in output buffer */ if (state.state->x.have) { n = GT_OFF(state.state->x.have) || (z_off64_t)state.state->x.have > len ? (unsigned)len : state.state->x.have; state.state->x.have -= n; state.state->x.next += n; state.state->x.pos += n; len -= n; } /* output buffer empty -- return if we're at the end of the input */ else if (state.state->eof && state.state->strm.avail_in == 0) break; /* need more data to skip -- load up output buffer */ else { /* get more output, looking for header if required */ if (gz_fetch(state) == -1) return -1; } return 0; } /* Read len bytes into buf from file, or less than len up to the end of the input. Return the number of bytes read. If zero is returned, either the end of file was reached, or there was an error. state.state->err must be consulted in that case to determine which. */ local z_size_t gz_read(gz_statep state, voidp buf, z_size_t len) { z_size_t got; unsigned n; /* if len is zero, avoid unnecessary operations */ if (len == 0) return 0; /* process a skip request */ if (state.state->seek) { state.state->seek = 0; if (gz_skip(state, state.state->skip) == -1) return 0; } /* get len bytes to buf, or less than len if at the end */ got = 0; do { /* set n to the maximum amount of len that fits in an unsigned int */ n = -1; if (n > len) n = (unsigned)len; /* first just try copying data from the output buffer */ if (state.state->x.have) { if (state.state->x.have < n) n = state.state->x.have; memcpy(buf, state.state->x.next, n); state.state->x.next += n; state.state->x.have -= n; } /* output buffer empty -- return if we're at the end of the input */ else if (state.state->eof && state.state->strm.avail_in == 0) { state.state->past = 1; /* tried to read past end */ break; } /* need output data -- for small len or new stream load up our output buffer */ else if (state.state->how == LOOK || n < (state.state->size << 1)) { /* get more output, looking for header if required */ if (gz_fetch(state) == -1) return 0; continue; /* no progress yet -- go back to copy above */ /* the copy above assures that we will leave with space in the output buffer, allowing at least one gzungetc() to succeed */ } /* large len -- read directly into user buffer */ else if (state.state->how == COPY) { /* read directly */ if (gz_load(state, (unsigned char *)buf, n, &n) == -1) return 0; } /* large len -- decompress directly into user buffer */ else { /* state.state->how == GZIP */ state.state->strm.avail_out = n; state.state->strm.next_out = (unsigned char *)buf; if (gz_decomp(state) == -1) return 0; n = state.state->x.have; state.state->x.have = 0; } /* update progress */ len -= n; buf = (char *)buf + n; got += n; state.state->x.pos += n; } while (len); /* return number of bytes read into user buffer */ return got; } /* -- see zlib.h -- */ int ZEXPORT gzread(gzFile file, voidp buf, unsigned len) { gz_statep state; /* get internal structure */ if (file == NULL) return -1; state.file = file; /* check that we're reading and that there's no (serious) error */ if (state.state->mode != GZ_READ || (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR)) return -1; /* since an int is returned, make sure len fits in one, otherwise return with an error (this avoids a flaw in the interface) */ if ((int)len < 0) { gz_error(state, Z_STREAM_ERROR, "request does not fit in an int"); return -1; } /* read len or fewer bytes to buf */ len = (unsigned)gz_read(state, buf, len); /* check for an error */ if (len == 0 && state.state->err != Z_OK && state.state->err != Z_BUF_ERROR) return -1; /* return the number of bytes read (this is assured to fit in an int) */ return (int)len; } /* -- see zlib.h -- */ z_size_t ZEXPORT gzfread(voidp buf, z_size_t size, z_size_t nitems, gzFile file) { z_size_t len; gz_statep state; /* get internal structure */ if (file == NULL) return 0; state.file = file; /* check that we're reading and that there's no (serious) error */ if (state.state->mode != GZ_READ || (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR)) return 0; /* compute bytes to read -- error on overflow */ len = nitems * size; if (size && len / size != nitems) { gz_error(state, Z_STREAM_ERROR, "request does not fit in a size_t"); return 0; } /* read len or fewer bytes to buf, return the number of full items read */ return len ? gz_read(state, buf, len) / size : 0; } /* -- see zlib.h -- */ #if ZLIB_VERNUM >= 0x1261 #ifdef Z_PREFIX_SET # undef z_gzgetc #else # undef gzgetc #endif #endif #if ZLIB_VERNUM == 0x1260 # undef gzgetc #endif #if ZLIB_VERNUM <= 0x1250 ZEXTERN int ZEXPORT gzgetc _Z_OF((gzFile file)); ZEXTERN int ZEXPORT gzgetc_ _Z_OF((gzFile file)); #endif int ZEXPORT gzgetc(gzFile file) { int ret; unsigned char buf[1]; gz_statep state; /* get internal structure */ if (file == NULL) return -1; state.file = file; /* check that we're reading and that there's no (serious) error */ if (state.state->mode != GZ_READ || (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR)) return -1; /* try output buffer (no need to check for skip request) */ if (state.state->x.have) { state.state->x.have--; state.state->x.pos++; return *(state.state->x.next)++; } /* nothing there -- try gz_read() */ ret = (int)gz_read(state, buf, 1); return ret < 1 ? -1 : buf[0]; } int ZEXPORT gzgetc_(gzFile file) { return gzgetc(file); } /* -- see zlib.h -- */ int ZEXPORT gzungetc(int c, gzFile file) { gz_statep state; /* get internal structure */ if (file == NULL) return -1; state.file = file; /* check that we're reading and that there's no (serious) error */ if (state.state->mode != GZ_READ || (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR)) return -1; /* process a skip request */ if (state.state->seek) { state.state->seek = 0; if (gz_skip(state, state.state->skip) == -1) return -1; } /* can't push EOF */ if (c < 0) return -1; /* if output buffer empty, put byte at end (allows more pushing) */ if (state.state->x.have == 0) { state.state->x.have = 1; state.state->x.next = state.state->out + (state.state->size << 1) - 1; state.state->x.next[0] = (unsigned char)c; state.state->x.pos--; state.state->past = 0; return c; } /* if no room, give up (must have already done a gzungetc()) */ if (state.state->x.have == (state.state->size << 1)) { gz_error(state, Z_DATA_ERROR, "out of room to push characters"); return -1; } /* slide output data if needed and insert byte before existing data */ if (state.state->x.next == state.state->out) { unsigned char *src = state.state->out + state.state->x.have; unsigned char *dest = state.state->out + (state.state->size << 1); while (src > state.state->out) *--dest = *--src; state.state->x.next = dest; } state.state->x.have++; state.state->x.next--; state.state->x.next[0] = (unsigned char)c; state.state->x.pos--; state.state->past = 0; return c; } /* -- see zlib.h -- */ char * ZEXPORT gzgets(gzFile file, char *buf, int len) { unsigned left, n; char *str; unsigned char *eol; gz_statep state; /* check parameters and get internal structure */ if (file == NULL || buf == NULL || len < 1) return NULL; state.file = file; /* check that we're reading and that there's no (serious) error */ if (state.state->mode != GZ_READ || (state.state->err != Z_OK && state.state->err != Z_BUF_ERROR)) return NULL; /* process a skip request */ if (state.state->seek) { state.state->seek = 0; if (gz_skip(state, state.state->skip) == -1) return NULL; } /* copy output bytes up to new line or len - 1, whichever comes first -- append a terminating zero to the string (we don't check for a zero in the contents, let the user worry about that) */ str = buf; left = (unsigned)len - 1; if (left) do { /* assure that something is in the output buffer */ if (state.state->x.have == 0 && gz_fetch(state) == -1) return NULL; /* error */ if (state.state->x.have == 0) { /* end of file */ state.state->past = 1; /* read past end */ break; /* return what we have */ } /* look for end-of-line in current output buffer */ n = state.state->x.have > left ? left : state.state->x.have; eol = (unsigned char *)memchr(state.state->x.next, '\n', n); if (eol != NULL) n = (unsigned)(eol - state.state->x.next) + 1; /* copy through end-of-line, or remainder if not found */ memcpy(buf, state.state->x.next, n); state.state->x.have -= n; state.state->x.next += n; state.state->x.pos += n; left -= n; buf += n; } while (left && eol == NULL); /* return terminated string, or if nothing, end of file */ if (buf == str) return NULL; buf[0] = 0; return str; } /* -- see zlib.h -- */ int ZEXPORT gzdirect(gzFile file) { gz_statep state; /* get internal structure */ if (file == NULL) return 0; state.file = file; /* if the state is not known, but we can find out, then do so (this is mainly for right after a gzopen() or gzdopen()) */ if (state.state->mode == GZ_READ && state.state->how == LOOK && state.state->x.have == 0) (void)gz_look(state); /* return 1 if transparent, 0 if processing a gzip stream */ return state.state->direct; } /* -- see zlib.h -- */ int ZEXPORT gzclose_r(gzFile file) { int ret, err; gz_statep state; /* get internal structure */ if (file == NULL) return Z_STREAM_ERROR; state.file = file; /* check that we're reading */ if (state.state->mode != GZ_READ) return Z_STREAM_ERROR; /* free memory and close file */ if (state.state->size) { inflateEnd(&(state.state->strm)); free(state.state->out); free(state.state->in); } err = state.state->err == Z_BUF_ERROR ? Z_BUF_ERROR : Z_OK; gz_error(state, Z_OK, NULL); free(state.state->path); ret = close(state.state->fd); free(state.state); return ret ? Z_ERRNO : err; } form-5.0.1/extern/zstd/zlibWrapper/gzclose.c0000644000175100017510000000151015217035741014551 /* gzclose.c contains minimal changes required to be compiled with zlibWrapper: * - gz_statep was converted to union to work with -Wstrict-aliasing=1 */ /* gzclose.c -- zlib gzclose() function * Copyright (C) 2004, 2010 Mark Adler * For conditions of distribution and use, see https://www.zlib.net/zlib_license.html */ #include "gzguts.h" /* gzclose() is in a separate file so that it is linked in only if it is used. That way the other gzclose functions can be used instead to avoid linking in unneeded compression or decompression routines. */ int ZEXPORT gzclose(gzFile file) { #ifndef NO_GZCOMPRESS gz_statep state; if (file == NULL) return Z_STREAM_ERROR; state.file = file; return state.state->mode == GZ_READ ? gzclose_r(file) : gzclose_w(file); #else return gzclose_r(file); #endif } form-5.0.1/extern/zstd/zlibWrapper/zstd_zlibwrapper.h0000644000175100017510000000713015217035741016521 /* * Copyright (c) Meta Platforms, Inc. and affiliates. * All rights reserved. * * This source code is licensed under both the BSD-style license (found in the * LICENSE file in the root directory of this source tree) and the GPLv2 (found * in the COPYING file in the root directory of this source tree). * You may select, at your option, one of the above-listed licenses. */ #ifndef ZSTD_ZLIBWRAPPER_H #define ZSTD_ZLIBWRAPPER_H #define ZLIB_CONST #define Z_PREFIX #define ZLIB_INTERNAL /* disables gz*64 functions but fixes zlib 1.2.4 with Z_PREFIX */ #include #if !defined(z_const) #define z_const #endif #if !defined(_Z_OF) #define _Z_OF OF #endif #if defined (__cplusplus) extern "C" { #endif /* returns a string with version of zstd library */ const char * zstdVersion(void); /*** COMPRESSION ***/ /* ZWRAP_useZSTDcompression() enables/disables zstd compression during runtime. By default zstd compression is disabled. To enable zstd compression please use one of the methods: - compilation with the additional option -DZWRAP_USE_ZSTD=1 - using '#define ZWRAP_USE_ZSTD 1' in source code before '#include "zstd_zlibwrapper.h"' - calling ZWRAP_useZSTDcompression(1) All above-mentioned methods will enable zstd compression for all threads. Be aware that ZWRAP_useZSTDcompression() is not thread-safe and may lead to a race condition. */ void ZWRAP_useZSTDcompression(int turn_on); /* checks if zstd compression is turned on */ int ZWRAP_isUsingZSTDcompression(void); /* Changes a pledged source size for a given compression stream. It will change ZSTD compression parameters what may improve compression speed and/or ratio. The function should be called just after deflateInit() or deflateReset() and before deflate() or deflateSetDictionary(). It's only helpful when data is compressed in blocks. There will be no change in case of deflateInit() or deflateReset() immediately followed by deflate(strm, Z_FINISH) as this case is automatically detected. */ int ZWRAP_setPledgedSrcSize(z_streamp strm, unsigned long long pledgedSrcSize); /* Similar to deflateReset but preserves dictionary set using deflateSetDictionary. It should improve compression speed because there will be less calls to deflateSetDictionary When using zlib compression this method redirects to deflateReset. */ int ZWRAP_deflateReset_keepDict(z_streamp strm); /*** DECOMPRESSION ***/ typedef enum { ZWRAP_FORCE_ZLIB, ZWRAP_AUTO } ZWRAP_decompress_type; /* ZWRAP_setDecompressionType() enables/disables automatic recognition of zstd/zlib compressed data during runtime. By default auto-detection of zstd and zlib streams in enabled (ZWRAP_AUTO). Forcing zlib decompression with ZWRAP_setDecompressionType(ZWRAP_FORCE_ZLIB) slightly improves decompression speed of zlib-encoded streams. Be aware that ZWRAP_setDecompressionType() is not thread-safe and may lead to a race condition. */ void ZWRAP_setDecompressionType(ZWRAP_decompress_type type); /* checks zstd decompression type */ ZWRAP_decompress_type ZWRAP_getDecompressionType(void); /* Checks if zstd decompression is used for a given stream. If will return 1 only when inflate() was called and zstd header was detected. */ int ZWRAP_isUsingZSTDdecompression(z_streamp strm); /* Similar to inflateReset but preserves dictionary set using inflateSetDictionary. inflate() will return Z_NEED_DICT only for the first time what will improve decompression speed. For zlib streams this method redirects to inflateReset. */ int ZWRAP_inflateReset_keepDict(z_streamp strm); #if defined (__cplusplus) } #endif #endif /* ZSTD_ZLIBWRAPPER_H */ form-5.0.1/extern/zstd/zlibWrapper/gzwrite.c0000644000175100017510000004737515217035741014621 /* gzwrite.c contains minimal changes required to be compiled with zlibWrapper: * - gz_statep was converted to union to work with -Wstrict-aliasing=1 */ /* gzwrite.c -- zlib functions for writing gzip files * Copyright (C) 2004-2017 Mark Adler * For conditions of distribution and use, see https://www.zlib.net/zlib_license.html */ #include #include "gzguts.h" /* Local functions */ local int gz_init _Z_OF((gz_statep)); local int gz_comp _Z_OF((gz_statep, int)); local int gz_zero _Z_OF((gz_statep, z_off64_t)); local z_size_t gz_write _Z_OF((gz_statep, voidpc, z_size_t)); /* Initialize state for writing a gzip file. Mark initialization by setting state.state->size to non-zero. Return -1 on a memory allocation failure, or 0 on success. */ local int gz_init(gz_statep state) { int ret; z_streamp strm = &(state.state->strm); /* allocate input buffer (double size for gzprintf) */ state.state->in = (unsigned char*)malloc(state.state->want << 1); if (state.state->in == NULL) { gz_error(state, Z_MEM_ERROR, "out of memory"); return -1; } /* only need output buffer and deflate state if compressing */ if (!state.state->direct) { /* allocate output buffer */ state.state->out = (unsigned char*)malloc(state.state->want); if (state.state->out == NULL) { free(state.state->in); gz_error(state, Z_MEM_ERROR, "out of memory"); return -1; } /* allocate deflate memory, set up for gzip compression */ strm->zalloc = Z_NULL; strm->zfree = Z_NULL; strm->opaque = Z_NULL; ret = deflateInit2(strm, state.state->level, Z_DEFLATED, MAX_WBITS + 16, DEF_MEM_LEVEL, state.state->strategy); if (ret != Z_OK) { free(state.state->out); free(state.state->in); gz_error(state, Z_MEM_ERROR, "out of memory"); return -1; } strm->next_in = NULL; } /* mark state as initialized */ state.state->size = state.state->want; /* initialize write buffer if compressing */ if (!state.state->direct) { strm->avail_out = state.state->size; strm->next_out = state.state->out; state.state->x.next = strm->next_out; } return 0; } /* Compress whatever is at avail_in and next_in and write to the output file. Return -1 if there is an error writing to the output file or if gz_init() fails to allocate memory, otherwise 0. flush is assumed to be a valid deflate() flush value. If flush is Z_FINISH, then the deflate() state is reset to start a new gzip stream. If gz->direct is true, then simply write to the output file without compressing, and ignore flush. */ local int gz_comp(gz_statep state, int flush) { int ret, writ; unsigned have, put, max = ((unsigned)-1 >> 2) + 1; z_streamp strm = &(state.state->strm); /* allocate memory if this is the first time through */ if (state.state->size == 0 && gz_init(state) == -1) return -1; /* write directly if requested */ if (state.state->direct) { while (strm->avail_in) { put = strm->avail_in > max ? max : strm->avail_in; writ = (int)write(state.state->fd, strm->next_in, put); if (writ < 0) { gz_error(state, Z_ERRNO, zstrerror()); return -1; } strm->avail_in -= (unsigned)writ; strm->next_in += writ; } return 0; } /* run deflate() on provided input until it produces no more output */ ret = Z_OK; do { /* write out current buffer contents if full, or if flushing, but if doing Z_FINISH then don't write until we get to Z_STREAM_END */ if (strm->avail_out == 0 || (flush != Z_NO_FLUSH && (flush != Z_FINISH || ret == Z_STREAM_END))) { while (strm->next_out > state.state->x.next) { put = strm->next_out - state.state->x.next > (int)max ? max : (unsigned)(strm->next_out - state.state->x.next); writ = (int)write(state.state->fd, state.state->x.next, put); if (writ < 0) { gz_error(state, Z_ERRNO, zstrerror()); return -1; } state.state->x.next += writ; } if (strm->avail_out == 0) { strm->avail_out = state.state->size; strm->next_out = state.state->out; state.state->x.next = state.state->out; } } /* compress */ have = strm->avail_out; ret = deflate(strm, flush); if (ret == Z_STREAM_ERROR) { gz_error(state, Z_STREAM_ERROR, "internal error: deflate stream corrupt"); return -1; } have -= strm->avail_out; } while (have); /* if that completed a deflate stream, allow another to start */ if (flush == Z_FINISH) deflateReset(strm); /* all done, no errors */ return 0; } /* Compress len zeros to output. Return -1 on a write error or memory allocation failure by gz_comp(), or 0 on success. */ local int gz_zero(gz_statep state, z_off64_t len) { int first; unsigned n; z_streamp strm = &(state.state->strm); /* consume whatever's left in the input buffer */ if (strm->avail_in && gz_comp(state, Z_NO_FLUSH) == -1) return -1; /* compress len zeros (len guaranteed > 0) */ first = 1; while (len) { n = GT_OFF(state.state->size) || (z_off64_t)state.state->size > len ? (unsigned)len : state.state->size; if (first) { memset(state.state->in, 0, n); first = 0; } strm->avail_in = n; strm->next_in = state.state->in; state.state->x.pos += n; if (gz_comp(state, Z_NO_FLUSH) == -1) return -1; len -= n; } return 0; } /* Write len bytes from buf to file. Return the number of bytes written. If the returned value is less than len, then there was an error. */ local z_size_t gz_write(gz_statep state, voidpc buf, z_size_t len) { z_size_t put = len; /* if len is zero, avoid unnecessary operations */ if (len == 0) return 0; /* allocate memory if this is the first time through */ if (state.state->size == 0 && gz_init(state) == -1) return 0; /* check for seek request */ if (state.state->seek) { state.state->seek = 0; if (gz_zero(state, state.state->skip) == -1) return 0; } /* for small len, copy to input buffer, otherwise compress directly */ if (len < state.state->size) { /* copy to input buffer, compress when full */ do { z_size_t have, copy; if (state.state->strm.avail_in == 0) state.state->strm.next_in = state.state->in; have = (unsigned)((state.state->strm.next_in + state.state->strm.avail_in) - state.state->in); copy = state.state->size - have; if (copy > len) copy = len; memcpy(state.state->in + have, buf, copy); state.state->strm.avail_in += copy; state.state->x.pos += copy; buf = (const char *)buf + copy; len -= copy; if (len && gz_comp(state, Z_NO_FLUSH) == -1) return 0; } while (len); } else { /* consume whatever's left in the input buffer */ if (state.state->strm.avail_in && gz_comp(state, Z_NO_FLUSH) == -1) return 0; /* directly compress user buffer to file */ state.state->strm.next_in = (z_const Bytef *)buf; do { z_size_t n = (unsigned)-1; if (n > len) n = len; state.state->strm.avail_in = (uInt)n; state.state->x.pos += n; if (gz_comp(state, Z_NO_FLUSH) == -1) return 0; len -= n; } while (len); } /* input was all buffered or compressed */ return put; } /* -- see zlib.h -- */ int ZEXPORT gzwrite(gzFile file, voidpc buf, unsigned len) { gz_statep state; /* get internal structure */ if (file == NULL) return 0; state.file = file; /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return 0; /* since an int is returned, make sure len fits in one, otherwise return with an error (this avoids a flaw in the interface) */ if ((int)len < 0) { gz_error(state, Z_DATA_ERROR, "requested length does not fit in int"); return 0; } /* write len bytes from buf (the return value will fit in an int) */ return (int)gz_write(state, buf, len); } /* -- see zlib.h -- */ z_size_t ZEXPORT gzfwrite(voidpc buf, z_size_t size, z_size_t nitems, gzFile file) { z_size_t len; gz_statep state; /* get internal structure */ assert(size != 0); if (file == NULL) return 0; state.file = file; /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return 0; /* compute bytes to read -- error on overflow */ len = nitems * size; if (size && (len / size != nitems)) { gz_error(state, Z_STREAM_ERROR, "request does not fit in a size_t"); return 0; } /* write len bytes to buf, return the number of full items written */ return len ? gz_write(state, buf, len) / size : 0; } /* -- see zlib.h -- */ int ZEXPORT gzputc(gzFile file, int c) { unsigned have; unsigned char buf[1]; gz_statep state; z_streamp strm; /* get internal structure */ if (file == NULL) return -1; state.file = file; strm = &(state.state->strm); /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return -1; /* check for seek request */ if (state.state->seek) { state.state->seek = 0; if (gz_zero(state, state.state->skip) == -1) return -1; } /* try writing to input buffer for speed (state.state->size == 0 if buffer not initialized) */ if (state.state->size) { if (strm->avail_in == 0) strm->next_in = state.state->in; have = (unsigned)((strm->next_in + strm->avail_in) - state.state->in); if (have < state.state->size) { state.state->in[have] = (unsigned char)c; strm->avail_in++; state.state->x.pos++; return c & 0xff; } } /* no room in buffer or not initialized, use gz_write() */ buf[0] = (unsigned char)c; if (gz_write(state, buf, 1) != 1) return -1; return c & 0xff; } /* -- see zlib.h -- */ int ZEXPORT gzputs(gzFile file, const char *str) { int ret; z_size_t len; gz_statep state; /* get internal structure */ if (file == NULL) return -1; state.file = file; /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return -1; /* write string */ len = strlen(str); ret = (int)gz_write(state, str, len); return ret == 0 && len != 0 ? -1 : ret; } #if defined(STDC) || defined(Z_HAVE_STDARG_H) #include /* -- see zlib.h -- */ int ZEXPORTVA gzvprintf(gzFile file, const char *format, va_list va) { int len; unsigned left; char *next; gz_statep state; z_streamp strm; /* get internal structure */ if (file == NULL) return Z_STREAM_ERROR; state.file = file; strm = &(state.state->strm); /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return Z_STREAM_ERROR; /* make sure we have some buffer space */ if (state.state->size == 0 && gz_init(state) == -1) return state.state->err; /* check for seek request */ if (state.state->seek) { state.state->seek = 0; if (gz_zero(state, state.state->skip) == -1) return state.state->err; } /* do the printf() into the input buffer, put length in len -- the input buffer is double-sized just for this function, so there is guaranteed to be state.state->size bytes available after the current contents */ if (strm->avail_in == 0) strm->next_in = state.state->in; next = (char *)(state.state->in + (strm->next_in - state.state->in) + strm->avail_in); next[state.state->size - 1] = 0; #ifdef NO_vsnprintf # ifdef HAS_vsprintf_void (void)vsprintf(next, format, va); for (len = 0; len < state.state->size; len++) if (next[len] == 0) break; # else len = vsprintf(next, format, va); # endif #else # ifdef HAS_vsnprintf_void (void)vsnprintf(next, state.state->size, format, va); len = strlen(next); # else len = vsnprintf(next, state.state->size, format, va); # endif #endif /* check that printf() results fit in buffer */ if (len == 0 || (unsigned)len >= state.state->size || next[state.state->size - 1] != 0) return 0; /* update buffer and position, compress first half if past that */ strm->avail_in += (unsigned)len; state.state->x.pos += len; if (strm->avail_in >= state.state->size) { left = strm->avail_in - state.state->size; strm->avail_in = state.state->size; if (gz_comp(state, Z_NO_FLUSH) == -1) return state.state->err; memcpy(state.state->in, state.state->in + state.state->size, left); strm->next_in = state.state->in; strm->avail_in = left; } return len; } int ZEXPORTVA gzprintf(gzFile file, const char *format, ...) { va_list va; int ret; va_start(va, format); ret = gzvprintf(file, format, va); va_end(va); return ret; } #else /* !STDC && !Z_HAVE_STDARG_H */ /* -- see zlib.h -- */ int ZEXPORTVA gzprintf(gzFile file, const char *format, int a1, int a2, int a3, int a4, int a5, int a6, int a7, int a8, int a9, int a10, int a11, int a12, int a13, int a14, int a15, int a16, int a17, int a18, int a19, int a20) { unsigned len, left; char *next; gz_statep state; z_streamp strm; /* get internal structure */ if (file == NULL) return Z_STREAM_ERROR; state = (gz_statep)file; strm = &(state.state->strm); /* check that can really pass pointer in ints */ if (sizeof(int) != sizeof(void *)) return Z_STREAM_ERROR; /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return Z_STREAM_ERROR; /* make sure we have some buffer space */ if (state.state->size == 0 && gz_init(state) == -1) return state.state->error; /* check for seek request */ if (state.state->seek) { state.state->seek = 0; if (gz_zero(state, state.state->skip) == -1) return state.state->error; } /* do the printf() into the input buffer, put length in len -- the input buffer is double-sized just for this function, so there is guaranteed to be state.state->size bytes available after the current contents */ if (strm->avail_in == 0) strm->next_in = state.state->in; next = (char *)(strm->next_in + strm->avail_in); next[state.state->size - 1] = 0; #ifdef NO_snprintf # ifdef HAS_sprintf_void sprintf(next, format, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20); for (len = 0; len < size; len++) if (next[len] == 0) break; # else len = sprintf(next, format, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20); # endif #else # ifdef HAS_snprintf_void snprintf(next, state.state->size, format, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20); len = strlen(next); # else len = snprintf(next, state.state->size, format, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20); # endif #endif /* check that printf() results fit in buffer */ if (len == 0 || len >= state.state->size || next[state.state->size - 1] != 0) return 0; /* update buffer and position, compress first half if past that */ strm->avail_in += len; state.state->x.pos += len; if (strm->avail_in >= state.state->size) { left = strm->avail_in - state.state->size; strm->avail_in = state.state->size; if (gz_comp(state, Z_NO_FLUSH) == -1) return state.state->err; memcpy(state.state->in, state.state->in + state.state->size, left); strm->next_in = state.state->in; strm->avail_in = left; } return (int)len; } #endif /* -- see zlib.h -- */ int ZEXPORT gzflush(gzFile file, int flush) { gz_statep state; /* get internal structure */ if (file == NULL) return Z_STREAM_ERROR; state.file = file; /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return Z_STREAM_ERROR; /* check flush parameter */ if (flush < 0 || flush > Z_FINISH) return Z_STREAM_ERROR; /* check for seek request */ if (state.state->seek) { state.state->seek = 0; if (gz_zero(state, state.state->skip) == -1) return state.state->err; } /* compress remaining data with requested flush */ (void)gz_comp(state, flush); return state.state->err; } /* -- see zlib.h -- */ int ZEXPORT gzsetparams(gzFile file, int level, int strategy) { gz_statep state; z_streamp strm; /* get internal structure */ if (file == NULL) return Z_STREAM_ERROR; state.file = file; strm = &(state.state->strm); /* check that we're writing and that there's no error */ if (state.state->mode != GZ_WRITE || state.state->err != Z_OK) return Z_STREAM_ERROR; /* if no change is requested, then do nothing */ if (level == state.state->level && strategy == state.state->strategy) return Z_OK; /* check for seek request */ if (state.state->seek) { state.state->seek = 0; if (gz_zero(state, state.state->skip) == -1) return state.state->err; } /* change compression parameters for subsequent input */ if (state.state->size) { /* flush previous input with previous parameters before changing */ if (strm->avail_in && gz_comp(state, Z_BLOCK) == -1) return state.state->err; deflateParams(strm, level, strategy); } state.state->level = level; state.state->strategy = strategy; return Z_OK; } /* -- see zlib.h -- */ int ZEXPORT gzclose_w(gzFile file) { int ret = Z_OK; gz_statep state; /* get internal structure */ if (file == NULL) return Z_STREAM_ERROR; state.file = file; /* check that we're writing */ if (state.state->mode != GZ_WRITE) return Z_STREAM_ERROR; /* check for seek request */ if (state.state->seek) { state.state->seek = 0; if (gz_zero(state, state.state->skip) == -1) ret = state.state->err; } /* flush, free memory, and close file */ if (gz_comp(state, Z_FINISH) == -1) ret = state.state->err; if (state.state->size) { if (!state.state->direct) { (void)deflateEnd(&(state.state->strm)); free(state.state->out); } free(state.state->in); } gz_error(state, Z_OK, NULL); free(state.state->path); if (close(state.state->fd) == -1) ret = Z_ERRNO; free(state.state); return ret; } form-5.0.1/build-aux/0000755000175100017510000000000015217035744010125 5form-5.0.1/build-aux/install-sh0000755000175100017510000003577615217035732012070 #!/bin/sh # install - install a program, script, or datafile scriptversion=2020-11-14.01; # UTC # This originates from X11R5 (mit/util/scripts/install.sh), which was # later released in X11R6 (xc/config/util/install.sh) with the # following copyright and license. # # Copyright (C) 1994 X Consortium # # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to # deal in the Software without restriction, including without limitation the # rights to use, copy, modify, merge, publish, distribute, sublicense, and/or # sell copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included in # all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE # X CONSORTIUM BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN # AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNEC- # TION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. # # Except as contained in this notice, the name of the X Consortium shall not # be used in advertising or otherwise to promote the sale, use or other deal- # ings in this Software without prior written authorization from the X Consor- # tium. # # # FSF changes to this file are in the public domain. # # Calling this script install-sh is preferred over install.sh, to prevent # 'make' implicit rules from creating a file called install from it # when there is no Makefile. # # This script is compatible with the BSD install script, but was written # from scratch. tab=' ' nl=' ' IFS=" $tab$nl" # Set DOITPROG to "echo" to test this script. doit=${DOITPROG-} doit_exec=${doit:-exec} # Put in absolute file names if you don't have them in your path; # or use environment vars. chgrpprog=${CHGRPPROG-chgrp} chmodprog=${CHMODPROG-chmod} chownprog=${CHOWNPROG-chown} cmpprog=${CMPPROG-cmp} cpprog=${CPPROG-cp} mkdirprog=${MKDIRPROG-mkdir} mvprog=${MVPROG-mv} rmprog=${RMPROG-rm} stripprog=${STRIPPROG-strip} posix_mkdir= # Desired mode of installed file. mode=0755 # Create dirs (including intermediate dirs) using mode 755. # This is like GNU 'install' as of coreutils 8.32 (2020). mkdir_umask=22 backupsuffix= chgrpcmd= chmodcmd=$chmodprog chowncmd= mvcmd=$mvprog rmcmd="$rmprog -f" stripcmd= src= dst= dir_arg= dst_arg= copy_on_change=false is_target_a_directory=possibly usage="\ Usage: $0 [OPTION]... [-T] SRCFILE DSTFILE or: $0 [OPTION]... SRCFILES... DIRECTORY or: $0 [OPTION]... -t DIRECTORY SRCFILES... or: $0 [OPTION]... -d DIRECTORIES... In the 1st form, copy SRCFILE to DSTFILE. In the 2nd and 3rd, copy all SRCFILES to DIRECTORY. In the 4th, create DIRECTORIES. Options: --help display this help and exit. --version display version info and exit. -c (ignored) -C install only if different (preserve data modification time) -d create directories instead of installing files. -g GROUP $chgrpprog installed files to GROUP. -m MODE $chmodprog installed files to MODE. -o USER $chownprog installed files to USER. -p pass -p to $cpprog. -s $stripprog installed files. -S SUFFIX attempt to back up existing files, with suffix SUFFIX. -t DIRECTORY install into DIRECTORY. -T report an error if DSTFILE is a directory. Environment variables override the default commands: CHGRPPROG CHMODPROG CHOWNPROG CMPPROG CPPROG MKDIRPROG MVPROG RMPROG STRIPPROG By default, rm is invoked with -f; when overridden with RMPROG, it's up to you to specify -f if you want it. If -S is not specified, no backups are attempted. Email bug reports to bug-automake@gnu.org. Automake home page: https://www.gnu.org/software/automake/ " while test $# -ne 0; do case $1 in -c) ;; -C) copy_on_change=true;; -d) dir_arg=true;; -g) chgrpcmd="$chgrpprog $2" shift;; --help) echo "$usage"; exit $?;; -m) mode=$2 case $mode in *' '* | *"$tab"* | *"$nl"* | *'*'* | *'?'* | *'['*) echo "$0: invalid mode: $mode" >&2 exit 1;; esac shift;; -o) chowncmd="$chownprog $2" shift;; -p) cpprog="$cpprog -p";; -s) stripcmd=$stripprog;; -S) backupsuffix="$2" shift;; -t) is_target_a_directory=always dst_arg=$2 # Protect names problematic for 'test' and other utilities. case $dst_arg in -* | [=\(\)!]) dst_arg=./$dst_arg;; esac shift;; -T) is_target_a_directory=never;; --version) echo "$0 $scriptversion"; exit $?;; --) shift break;; -*) echo "$0: invalid option: $1" >&2 exit 1;; *) break;; esac shift done # We allow the use of options -d and -T together, by making -d # take the precedence; this is for compatibility with GNU install. if test -n "$dir_arg"; then if test -n "$dst_arg"; then echo "$0: target directory not allowed when installing a directory." >&2 exit 1 fi fi if test $# -ne 0 && test -z "$dir_arg$dst_arg"; then # When -d is used, all remaining arguments are directories to create. # When -t is used, the destination is already specified. # Otherwise, the last argument is the destination. 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(umask $mkdir_umask && eval "\$doit_exec \$mkdirprog $prefixes") || test -d "$dstdir" || exit 1 obsolete_mkdir_used=true fi fi fi if test -n "$dir_arg"; then { test -z "$chowncmd" || $doit $chowncmd "$dst"; } && { test -z "$chgrpcmd" || $doit $chgrpcmd "$dst"; } && { test "$obsolete_mkdir_used$chowncmd$chgrpcmd" = false || test -z "$chmodcmd" || $doit $chmodcmd $mode "$dst"; } || exit 1 else # Make a couple of temp file names in the proper directory. dsttmp=${dstdirslash}_inst.$$_ rmtmp=${dstdirslash}_rm.$$_ # Trap to clean up those temp files at exit. trap 'ret=$?; rm -f "$dsttmp" "$rmtmp" && exit $ret' 0 # Copy the file name to the temp name. (umask $cp_umask && { test -z "$stripcmd" || { # Create $dsttmp read-write so that cp doesn't create it read-only, # which would cause strip to fail. if test -z "$doit"; then : >"$dsttmp" # No need to fork-exec 'touch'. else $doit touch "$dsttmp" fi } } && $doit_exec $cpprog "$src" "$dsttmp") && # and set any options; do chmod last to preserve setuid bits. # # If any of these fail, we abort the whole thing. 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Don't worry if it fails, # e.g., if mv doesn't support -f. if test -n "$backupsuffix" && test -f "$dst"; then $doit $mvcmd -f "$dst" "$dst$backupsuffix" 2>/dev/null fi # Rename the file to the real destination. $doit $mvcmd -f "$dsttmp" "$dst" 2>/dev/null || # The rename failed, perhaps because mv can't rename something else # to itself, or perhaps because mv is so ancient that it does not # support -f. { # Now remove or move aside any old file at destination location. # We try this two ways since rm can't unlink itself on some # systems and the destination file might be busy for other # reasons. In this case, the final cleanup might fail but the new # file should still install successfully. { test ! -f "$dst" || $doit $rmcmd "$dst" 2>/dev/null || { $doit $mvcmd -f "$dst" "$rmtmp" 2>/dev/null && { $doit $rmcmd "$rmtmp" 2>/dev/null; :; } } || { echo "$0: cannot unlink or rename $dst" >&2 (exit 1); exit 1 } } && # Now rename the file to the real destination. $doit $mvcmd "$dsttmp" "$dst" } fi || exit 1 trap '' 0 fi done # Local variables: # eval: (add-hook 'before-save-hook 'time-stamp) # time-stamp-start: "scriptversion=" # time-stamp-format: "%:y-%02m-%02d.%02H" # time-stamp-time-zone: "UTC0" # time-stamp-end: "; # UTC" # End: form-5.0.1/build-aux/depcomp0000755000175100017510000005602015217035732011422 #! /bin/sh # depcomp - compile a program generating dependencies as side-effects scriptversion=2018-03-07.03; # UTC # Copyright (C) 1999-2021 Free Software Foundation, Inc. # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2, or (at your option) # any later version. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # You should have received a copy of the GNU General Public License # along with this program. If not, see . # As a special exception to the GNU General Public License, if you # distribute this file as part of a program that contains a # configuration script generated by Autoconf, you may include it under # the same distribution terms that you use for the rest of that program. # Originally written by Alexandre Oliva . case $1 in '') echo "$0: No command. Try '$0 --help' for more information." 1>&2 exit 1; ;; -h | --h*) cat <<\EOF Usage: depcomp [--help] [--version] PROGRAM [ARGS] Run PROGRAMS ARGS to compile a file, generating dependencies as side-effects. Environment variables: depmode Dependency tracking mode. source Source file read by 'PROGRAMS ARGS'. object Object file output by 'PROGRAMS ARGS'. DEPDIR directory where to store dependencies. depfile Dependency file to output. tmpdepfile Temporary file to use when outputting dependencies. libtool Whether libtool is used (yes/no). Report bugs to . EOF exit $? ;; -v | --v*) echo "depcomp $scriptversion" exit $? ;; esac # Get the directory component of the given path, and save it in the # global variables '$dir'. Note that this directory component will # be either empty or ending with a '/' character. This is deliberate. set_dir_from () { case $1 in */*) dir=`echo "$1" | sed -e 's|/[^/]*$|/|'`;; *) dir=;; esac } # Get the suffix-stripped basename of the given path, and save it the # global variable '$base'. set_base_from () { base=`echo "$1" | sed -e 's|^.*/||' -e 's/\.[^.]*$//'` } # If no dependency file was actually created by the compiler invocation, # we still have to create a dummy depfile, to avoid errors with the # Makefile "include basename.Plo" scheme. make_dummy_depfile () { echo "#dummy" > "$depfile" } # Factor out some common post-processing of the generated depfile. # Requires the auxiliary global variable '$tmpdepfile' to be set. aix_post_process_depfile () { # If the compiler actually managed to produce a dependency file, # post-process it. if test -f "$tmpdepfile"; then # Each line is of the form 'foo.o: dependency.h'. # Do two passes, one to just change these to # $object: dependency.h # and one to simply output # dependency.h: # which is needed to avoid the deleted-header problem. { sed -e "s,^.*\.[$lower]*:,$object:," < "$tmpdepfile" sed -e "s,^.*\.[$lower]*:[$tab ]*,," -e 's,$,:,' < "$tmpdepfile" } > "$depfile" rm -f "$tmpdepfile" else make_dummy_depfile fi } # A tabulation character. tab=' ' # A newline character. nl=' ' # Character ranges might be problematic outside the C locale. # These definitions help. upper=ABCDEFGHIJKLMNOPQRSTUVWXYZ lower=abcdefghijklmnopqrstuvwxyz digits=0123456789 alpha=${upper}${lower} if test -z "$depmode" || test -z "$source" || test -z "$object"; then echo "depcomp: Variables source, object and depmode must be set" 1>&2 exit 1 fi # Dependencies for sub/bar.o or sub/bar.obj go into sub/.deps/bar.Po. depfile=${depfile-`echo "$object" | sed 's|[^\\/]*$|'${DEPDIR-.deps}'/&|;s|\.\([^.]*\)$|.P\1|;s|Pobj$|Po|'`} tmpdepfile=${tmpdepfile-`echo "$depfile" | sed 's/\.\([^.]*\)$/.T\1/'`} rm -f "$tmpdepfile" # Avoid interferences from the environment. gccflag= dashmflag= # Some modes work just like other modes, but use different flags. We # parameterize here, but still list the modes in the big case below, # to make depend.m4 easier to write. Note that we *cannot* use a case # here, because this file can only contain one case statement. if test "$depmode" = hp; then # HP compiler uses -M and no extra arg. gccflag=-M depmode=gcc fi if test "$depmode" = dashXmstdout; then # This is just like dashmstdout with a different argument. dashmflag=-xM depmode=dashmstdout fi cygpath_u="cygpath -u -f -" if test "$depmode" = msvcmsys; then # This is just like msvisualcpp but w/o cygpath translation. # Just convert the backslash-escaped backslashes to single forward # slashes to satisfy depend.m4 cygpath_u='sed s,\\\\,/,g' depmode=msvisualcpp fi if test "$depmode" = msvc7msys; then # This is just like msvc7 but w/o cygpath translation. # Just convert the backslash-escaped backslashes to single forward # slashes to satisfy depend.m4 cygpath_u='sed s,\\\\,/,g' depmode=msvc7 fi if test "$depmode" = xlc; then # IBM C/C++ Compilers xlc/xlC can output gcc-like dependency information. gccflag=-qmakedep=gcc,-MF depmode=gcc fi case "$depmode" in gcc3) ## gcc 3 implements dependency tracking that does exactly what ## we want. Yay! Note: for some reason libtool 1.4 doesn't like ## it if -MD -MP comes after the -MF stuff. Hmm. ## Unfortunately, FreeBSD c89 acceptance of flags depends upon ## the command line argument order; so add the flags where they ## appear in depend2.am. Note that the slowdown incurred here ## affects only configure: in makefiles, %FASTDEP% shortcuts this. for arg do case $arg in -c) set fnord "$@" -MT "$object" -MD -MP -MF "$tmpdepfile" "$arg" ;; *) set fnord "$@" "$arg" ;; esac shift # fnord shift # $arg done "$@" stat=$? if test $stat -ne 0; then rm -f "$tmpdepfile" exit $stat fi mv "$tmpdepfile" "$depfile" ;; gcc) ## Note that this doesn't just cater to obsosete pre-3.x GCC compilers. ## but also to in-use compilers like IMB xlc/xlC and the HP C compiler. ## (see the conditional assignment to $gccflag above). ## There are various ways to get dependency output from gcc. Here's ## why we pick this rather obscure method: ## - Don't want to use -MD because we'd like the dependencies to end ## up in a subdir. Having to rename by hand is ugly. ## (We might end up doing this anyway to support other compilers.) ## - The DEPENDENCIES_OUTPUT environment variable makes gcc act like ## -MM, not -M (despite what the docs say). Also, it might not be ## supported by the other compilers which use the 'gcc' depmode. ## - Using -M directly means running the compiler twice (even worse ## than renaming). if test -z "$gccflag"; then gccflag=-MD, fi "$@" -Wp,"$gccflag$tmpdepfile" stat=$? if test $stat -ne 0; then rm -f "$tmpdepfile" exit $stat fi rm -f "$depfile" echo "$object : \\" > "$depfile" # The second -e expression handles DOS-style file names with drive # letters. sed -e 's/^[^:]*: / /' \ -e 's/^['$alpha']:\/[^:]*: / /' < "$tmpdepfile" >> "$depfile" ## This next piece of magic avoids the "deleted header file" problem. ## The problem is that when a header file which appears in a .P file ## is deleted, the dependency causes make to die (because there is ## typically no way to rebuild the header). We avoid this by adding ## dummy dependencies for each header file. Too bad gcc doesn't do ## this for us directly. ## Some versions of gcc put a space before the ':'. On the theory ## that the space means something, we add a space to the output as ## well. hp depmode also adds that space, but also prefixes the VPATH ## to the object. Take care to not repeat it in the output. ## Some versions of the HPUX 10.20 sed can't process this invocation ## correctly. Breaking it into two sed invocations is a workaround. tr ' ' "$nl" < "$tmpdepfile" \ | sed -e 's/^\\$//' -e '/^$/d' -e "s|.*$object$||" -e '/:$/d' \ | sed -e 's/$/ :/' >> "$depfile" rm -f "$tmpdepfile" ;; hp) # This case exists only to let depend.m4 do its work. It works by # looking at the text of this script. This case will never be run, # since it is checked for above. exit 1 ;; sgi) if test "$libtool" = yes; then "$@" "-Wp,-MDupdate,$tmpdepfile" else "$@" -MDupdate "$tmpdepfile" fi stat=$? if test $stat -ne 0; then rm -f "$tmpdepfile" exit $stat fi rm -f "$depfile" if test -f "$tmpdepfile"; then # yes, the sourcefile depend on other files echo "$object : \\" > "$depfile" # Clip off the initial element (the dependent). Don't try to be # clever and replace this with sed code, as IRIX sed won't handle # lines with more than a fixed number of characters (4096 in # IRIX 6.2 sed, 8192 in IRIX 6.5). We also remove comment lines; # the IRIX cc adds comments like '#:fec' to the end of the # dependency line. tr ' ' "$nl" < "$tmpdepfile" \ | sed -e 's/^.*\.o://' -e 's/#.*$//' -e '/^$/ d' \ | tr "$nl" ' ' >> "$depfile" echo >> "$depfile" # The second pass generates a dummy entry for each header file. tr ' ' "$nl" < "$tmpdepfile" \ | sed -e 's/^.*\.o://' -e 's/#.*$//' -e '/^$/ d' -e 's/$/:/' \ >> "$depfile" else make_dummy_depfile fi rm -f "$tmpdepfile" ;; xlc) # This case exists only to let depend.m4 do its work. It works by # looking at the text of this script. This case will never be run, # since it is checked for above. exit 1 ;; aix) # The C for AIX Compiler uses -M and outputs the dependencies # in a .u file. In older versions, this file always lives in the # current directory. Also, the AIX compiler puts '$object:' at the # start of each line; $object doesn't have directory information. # Version 6 uses the directory in both cases. set_dir_from "$object" set_base_from "$object" if test "$libtool" = yes; then tmpdepfile1=$dir$base.u tmpdepfile2=$base.u tmpdepfile3=$dir.libs/$base.u "$@" -Wc,-M else tmpdepfile1=$dir$base.u tmpdepfile2=$dir$base.u tmpdepfile3=$dir$base.u "$@" -M fi stat=$? if test $stat -ne 0; then rm -f "$tmpdepfile1" "$tmpdepfile2" "$tmpdepfile3" exit $stat fi for tmpdepfile in "$tmpdepfile1" "$tmpdepfile2" "$tmpdepfile3" do test -f "$tmpdepfile" && break done aix_post_process_depfile ;; tcc) # tcc (Tiny C Compiler) understand '-MD -MF file' since version 0.9.26 # FIXME: That version still under development at the moment of writing. # Make that this statement remains true also for stable, released # versions. # It will wrap lines (doesn't matter whether long or short) with a # trailing '\', as in: # # foo.o : \ # foo.c \ # foo.h \ # # It will put a trailing '\' even on the last line, and will use leading # spaces rather than leading tabs (at least since its commit 0394caf7 # "Emit spaces for -MD"). "$@" -MD -MF "$tmpdepfile" stat=$? if test $stat -ne 0; then rm -f "$tmpdepfile" exit $stat fi rm -f "$depfile" # Each non-empty line is of the form 'foo.o : \' or ' dep.h \'. # We have to change lines of the first kind to '$object: \'. sed -e "s|.*:|$object :|" < "$tmpdepfile" > "$depfile" # And for each line of the second kind, we have to emit a 'dep.h:' # dummy dependency, to avoid the deleted-header problem. sed -n -e 's|^ *\(.*\) *\\$|\1:|p' < "$tmpdepfile" >> "$depfile" rm -f "$tmpdepfile" ;; ## The order of this option in the case statement is important, since the ## shell code in configure will try each of these formats in the order ## listed in this file. A plain '-MD' option would be understood by many ## compilers, so we must ensure this comes after the gcc and icc options. pgcc) # Portland's C compiler understands '-MD'. # Will always output deps to 'file.d' where file is the root name of the # source file under compilation, even if file resides in a subdirectory. # The object file name does not affect the name of the '.d' file. # pgcc 10.2 will output # foo.o: sub/foo.c sub/foo.h # and will wrap long lines using '\' : # foo.o: sub/foo.c ... \ # sub/foo.h ... \ # ... set_dir_from "$object" # Use the source, not the object, to determine the base name, since # that's sadly what pgcc will do too. set_base_from "$source" tmpdepfile=$base.d # For projects that build the same source file twice into different object # files, the pgcc approach of using the *source* file root name can cause # problems in parallel builds. Use a locking strategy to avoid stomping on # the same $tmpdepfile. lockdir=$base.d-lock trap " echo '$0: caught signal, cleaning up...' >&2 rmdir '$lockdir' exit 1 " 1 2 13 15 numtries=100 i=$numtries while test $i -gt 0; do # mkdir is a portable test-and-set. if mkdir "$lockdir" 2>/dev/null; then # This process acquired the lock. "$@" -MD stat=$? # Release the lock. rmdir "$lockdir" break else # If the lock is being held by a different process, wait # until the winning process is done or we timeout. while test -d "$lockdir" && test $i -gt 0; do sleep 1 i=`expr $i - 1` done fi i=`expr $i - 1` done trap - 1 2 13 15 if test $i -le 0; then echo "$0: failed to acquire lock after $numtries attempts" >&2 echo "$0: check lockdir '$lockdir'" >&2 exit 1 fi if test $stat -ne 0; then rm -f "$tmpdepfile" exit $stat fi rm -f "$depfile" # Each line is of the form `foo.o: dependent.h', # or `foo.o: dep1.h dep2.h \', or ` dep3.h dep4.h \'. # Do two passes, one to just change these to # `$object: dependent.h' and one to simply `dependent.h:'. sed "s,^[^:]*:,$object :," < "$tmpdepfile" > "$depfile" # Some versions of the HPUX 10.20 sed can't process this invocation # correctly. Breaking it into two sed invocations is a workaround. sed 's,^[^:]*: \(.*\)$,\1,;s/^\\$//;/^$/d;/:$/d' < "$tmpdepfile" \ | sed -e 's/$/ :/' >> "$depfile" rm -f "$tmpdepfile" ;; hp2) # The "hp" stanza above does not work with aCC (C++) and HP's ia64 # compilers, which have integrated preprocessors. 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But MiNT is downward compatible to TOS, so this should # be no problem. atarist[e]:*MiNT:*:* | atarist[e]:*mint:*:* | atarist[e]:*TOS:*:*) GUESS=m68k-atari-mint$UNAME_RELEASE ;; atari*:*MiNT:*:* | atari*:*mint:*:* | atarist[e]:*TOS:*:*) GUESS=m68k-atari-mint$UNAME_RELEASE ;; *falcon*:*MiNT:*:* | *falcon*:*mint:*:* | *falcon*:*TOS:*:*) GUESS=m68k-atari-mint$UNAME_RELEASE ;; milan*:*MiNT:*:* | milan*:*mint:*:* | *milan*:*TOS:*:*) GUESS=m68k-milan-mint$UNAME_RELEASE ;; hades*:*MiNT:*:* | hades*:*mint:*:* | *hades*:*TOS:*:*) GUESS=m68k-hades-mint$UNAME_RELEASE ;; *:*MiNT:*:* | *:*mint:*:* | *:*TOS:*:*) GUESS=m68k-unknown-mint$UNAME_RELEASE ;; m68k:machten:*:*) GUESS=m68k-apple-machten$UNAME_RELEASE ;; powerpc:machten:*:*) GUESS=powerpc-apple-machten$UNAME_RELEASE ;; RISC*:Mach:*:*) GUESS=mips-dec-mach_bsd4.3 ;; RISC*:ULTRIX:*:*) GUESS=mips-dec-ultrix$UNAME_RELEASE ;; VAX*:ULTRIX*:*:*) GUESS=vax-dec-ultrix$UNAME_RELEASE ;; 2020:CLIX:*:* | 2430:CLIX:*:*) GUESS=clipper-intergraph-clix$UNAME_RELEASE ;; mips:*:*:UMIPS | mips:*:*:RISCos) set_cc_for_build sed 's/^ //' << EOF > "$dummy.c" #ifdef __cplusplus #include /* for printf() prototype */ int main (int argc, char *argv[]) { #else int main (argc, argv) int argc; char *argv[]; { #endif #if defined (host_mips) && defined (MIPSEB) #if defined (SYSTYPE_SYSV) printf ("mips-mips-riscos%ssysv\\n", argv[1]); exit (0); #endif #if defined (SYSTYPE_SVR4) printf ("mips-mips-riscos%ssvr4\\n", argv[1]); exit (0); #endif #if defined (SYSTYPE_BSD43) || defined(SYSTYPE_BSD) printf ("mips-mips-riscos%sbsd\\n", argv[1]); exit (0); #endif #endif exit (-1); } EOF $CC_FOR_BUILD -o "$dummy" "$dummy.c" && dummyarg=`echo "$UNAME_RELEASE" | sed -n 's/\([0-9]*\).*/\1/p'` && SYSTEM_NAME=`"$dummy" "$dummyarg"` && { echo "$SYSTEM_NAME"; exit; } GUESS=mips-mips-riscos$UNAME_RELEASE ;; Motorola:PowerMAX_OS:*:*) GUESS=powerpc-motorola-powermax ;; Motorola:*:4.3:PL8-*) GUESS=powerpc-harris-powermax ;; Night_Hawk:*:*:PowerMAX_OS | Synergy:PowerMAX_OS:*:*) GUESS=powerpc-harris-powermax ;; Night_Hawk:Power_UNIX:*:*) GUESS=powerpc-harris-powerunix ;; m88k:CX/UX:7*:*) GUESS=m88k-harris-cxux7 ;; m88k:*:4*:R4*) GUESS=m88k-motorola-sysv4 ;; m88k:*:3*:R3*) GUESS=m88k-motorola-sysv3 ;; AViiON:dgux:*:*) # DG/UX returns AViiON for all architectures UNAME_PROCESSOR=`/usr/bin/uname -p` if test "$UNAME_PROCESSOR" = mc88100 || test "$UNAME_PROCESSOR" = mc88110 then if test "$TARGET_BINARY_INTERFACE"x = m88kdguxelfx || \ test "$TARGET_BINARY_INTERFACE"x = x then GUESS=m88k-dg-dgux$UNAME_RELEASE else GUESS=m88k-dg-dguxbcs$UNAME_RELEASE fi else GUESS=i586-dg-dgux$UNAME_RELEASE fi ;; M88*:DolphinOS:*:*) # DolphinOS (SVR3) GUESS=m88k-dolphin-sysv3 ;; M88*:*:R3*:*) # Delta 88k system running SVR3 GUESS=m88k-motorola-sysv3 ;; XD88*:*:*:*) # Tektronix XD88 system running UTekV (SVR3) GUESS=m88k-tektronix-sysv3 ;; Tek43[0-9][0-9]:UTek:*:*) # Tektronix 4300 system running UTek (BSD) GUESS=m68k-tektronix-bsd ;; *:IRIX*:*:*) IRIX_REL=`echo "$UNAME_RELEASE" | sed -e 's/-/_/g'` GUESS=mips-sgi-irix$IRIX_REL ;; ????????:AIX?:[12].1:2) # AIX 2.2.1 or AIX 2.1.1 is RT/PC AIX. GUESS=romp-ibm-aix # uname -m gives an 8 hex-code CPU id ;; # Note that: echo "'`uname -s`'" gives 'AIX ' i*86:AIX:*:*) GUESS=i386-ibm-aix ;; ia64:AIX:*:*) if test -x /usr/bin/oslevel ; then IBM_REV=`/usr/bin/oslevel` else IBM_REV=$UNAME_VERSION.$UNAME_RELEASE fi GUESS=$UNAME_MACHINE-ibm-aix$IBM_REV ;; *:AIX:2:3) if grep bos325 /usr/include/stdio.h >/dev/null 2>&1; then set_cc_for_build sed 's/^ //' << EOF > "$dummy.c" #include main() { if (!__power_pc()) exit(1); puts("powerpc-ibm-aix3.2.5"); exit(0); } EOF if $CC_FOR_BUILD -o "$dummy" "$dummy.c" && SYSTEM_NAME=`"$dummy"` then GUESS=$SYSTEM_NAME else GUESS=rs6000-ibm-aix3.2.5 fi elif grep bos324 /usr/include/stdio.h >/dev/null 2>&1; then GUESS=rs6000-ibm-aix3.2.4 else GUESS=rs6000-ibm-aix3.2 fi ;; *:AIX:*:[4567]) IBM_CPU_ID=`/usr/sbin/lsdev -C -c processor -S available | sed 1q | awk '{ print $1 }'` if /usr/sbin/lsattr -El "$IBM_CPU_ID" | grep ' POWER' >/dev/null 2>&1; then IBM_ARCH=rs6000 else IBM_ARCH=powerpc fi if test -x /usr/bin/lslpp ; then IBM_REV=`/usr/bin/lslpp -Lqc bos.rte.libc | \ awk -F: '{ print $3 }' | sed s/[0-9]*$/0/` else IBM_REV=$UNAME_VERSION.$UNAME_RELEASE fi GUESS=$IBM_ARCH-ibm-aix$IBM_REV ;; *:AIX:*:*) GUESS=rs6000-ibm-aix ;; ibmrt:4.4BSD:*|romp-ibm:4.4BSD:*) GUESS=romp-ibm-bsd4.4 ;; ibmrt:*BSD:*|romp-ibm:BSD:*) # covers RT/PC BSD and GUESS=romp-ibm-bsd$UNAME_RELEASE # 4.3 with uname added to ;; # report: romp-ibm BSD 4.3 *:BOSX:*:*) GUESS=rs6000-bull-bosx ;; DPX/2?00:B.O.S.:*:*) GUESS=m68k-bull-sysv3 ;; 9000/[34]??:4.3bsd:1.*:*) GUESS=m68k-hp-bsd ;; hp300:4.4BSD:*:* | 9000/[34]??:4.3bsd:2.*:*) GUESS=m68k-hp-bsd4.4 ;; 9000/[34678]??:HP-UX:*:*) HPUX_REV=`echo "$UNAME_RELEASE" | sed -e 's/[^.]*.[0B]*//'` case $UNAME_MACHINE in 9000/31?) HP_ARCH=m68000 ;; 9000/[34]??) HP_ARCH=m68k ;; 9000/[678][0-9][0-9]) if test -x /usr/bin/getconf; then sc_cpu_version=`/usr/bin/getconf SC_CPU_VERSION 2>/dev/null` sc_kernel_bits=`/usr/bin/getconf SC_KERNEL_BITS 2>/dev/null` case $sc_cpu_version in 523) HP_ARCH=hppa1.0 ;; # CPU_PA_RISC1_0 528) HP_ARCH=hppa1.1 ;; # CPU_PA_RISC1_1 532) # CPU_PA_RISC2_0 case $sc_kernel_bits in 32) HP_ARCH=hppa2.0n ;; 64) HP_ARCH=hppa2.0w ;; '') HP_ARCH=hppa2.0 ;; # HP-UX 10.20 esac ;; esac fi if test "$HP_ARCH" = ""; then set_cc_for_build sed 's/^ //' << EOF > "$dummy.c" #define _HPUX_SOURCE #include #include int main () { #if defined(_SC_KERNEL_BITS) long bits = sysconf(_SC_KERNEL_BITS); #endif long cpu = sysconf (_SC_CPU_VERSION); switch (cpu) { case CPU_PA_RISC1_0: puts ("hppa1.0"); break; case CPU_PA_RISC1_1: puts ("hppa1.1"); break; case CPU_PA_RISC2_0: #if defined(_SC_KERNEL_BITS) switch (bits) { case 64: puts ("hppa2.0w"); break; case 32: puts ("hppa2.0n"); break; default: puts ("hppa2.0"); break; } break; #else /* !defined(_SC_KERNEL_BITS) */ puts ("hppa2.0"); break; #endif default: puts ("hppa1.0"); break; } exit (0); } EOF (CCOPTS="" $CC_FOR_BUILD -o "$dummy" "$dummy.c" 2>/dev/null) && HP_ARCH=`"$dummy"` test -z "$HP_ARCH" && HP_ARCH=hppa fi ;; esac if test "$HP_ARCH" = hppa2.0w then set_cc_for_build # hppa2.0w-hp-hpux* has a 64-bit kernel and a compiler generating # 32-bit code. hppa64-hp-hpux* has the same kernel and a compiler # generating 64-bit code. GNU and HP use different nomenclature: # # $ CC_FOR_BUILD=cc ./config.guess # => hppa2.0w-hp-hpux11.23 # $ CC_FOR_BUILD="cc +DA2.0w" ./config.guess # => hppa64-hp-hpux11.23 if echo __LP64__ | (CCOPTS="" $CC_FOR_BUILD -E - 2>/dev/null) | grep -q __LP64__ then HP_ARCH=hppa2.0w else HP_ARCH=hppa64 fi fi GUESS=$HP_ARCH-hp-hpux$HPUX_REV ;; ia64:HP-UX:*:*) HPUX_REV=`echo "$UNAME_RELEASE" | sed -e 's/[^.]*.[0B]*//'` GUESS=ia64-hp-hpux$HPUX_REV ;; 3050*:HI-UX:*:*) set_cc_for_build sed 's/^ //' << EOF > "$dummy.c" #include int main () { long cpu = sysconf (_SC_CPU_VERSION); /* The order matters, because CPU_IS_HP_MC68K erroneously returns true for CPU_PA_RISC1_0. CPU_IS_PA_RISC returns correct results, however. */ if (CPU_IS_PA_RISC (cpu)) { switch (cpu) { case CPU_PA_RISC1_0: puts ("hppa1.0-hitachi-hiuxwe2"); break; case CPU_PA_RISC1_1: puts ("hppa1.1-hitachi-hiuxwe2"); break; case CPU_PA_RISC2_0: puts ("hppa2.0-hitachi-hiuxwe2"); break; default: puts ("hppa-hitachi-hiuxwe2"); break; } } else if (CPU_IS_HP_MC68K (cpu)) puts ("m68k-hitachi-hiuxwe2"); else puts ("unknown-hitachi-hiuxwe2"); exit (0); } EOF $CC_FOR_BUILD -o "$dummy" "$dummy.c" && SYSTEM_NAME=`"$dummy"` && { echo "$SYSTEM_NAME"; exit; } GUESS=unknown-hitachi-hiuxwe2 ;; 9000/7??:4.3bsd:*:* | 9000/8?[79]:4.3bsd:*:*) GUESS=hppa1.1-hp-bsd ;; 9000/8??:4.3bsd:*:*) GUESS=hppa1.0-hp-bsd ;; *9??*:MPE/iX:*:* | *3000*:MPE/iX:*:*) GUESS=hppa1.0-hp-mpeix ;; hp7??:OSF1:*:* | hp8?[79]:OSF1:*:*) GUESS=hppa1.1-hp-osf ;; hp8??:OSF1:*:*) GUESS=hppa1.0-hp-osf ;; i*86:OSF1:*:*) if test -x /usr/sbin/sysversion ; then GUESS=$UNAME_MACHINE-unknown-osf1mk else GUESS=$UNAME_MACHINE-unknown-osf1 fi ;; parisc*:Lites*:*:*) GUESS=hppa1.1-hp-lites ;; C1*:ConvexOS:*:* | convex:ConvexOS:C1*:*) GUESS=c1-convex-bsd ;; C2*:ConvexOS:*:* | convex:ConvexOS:C2*:*) if getsysinfo -f scalar_acc then echo c32-convex-bsd else echo c2-convex-bsd fi exit ;; C34*:ConvexOS:*:* | convex:ConvexOS:C34*:*) GUESS=c34-convex-bsd ;; C38*:ConvexOS:*:* | convex:ConvexOS:C38*:*) GUESS=c38-convex-bsd ;; C4*:ConvexOS:*:* | convex:ConvexOS:C4*:*) GUESS=c4-convex-bsd ;; CRAY*Y-MP:*:*:*) CRAY_REL=`echo "$UNAME_RELEASE" | sed -e 's/\.[^.]*$/.X/'` GUESS=ymp-cray-unicos$CRAY_REL ;; CRAY*[A-Z]90:*:*:*) echo "$UNAME_MACHINE"-cray-unicos"$UNAME_RELEASE" \ | sed -e 's/CRAY.*\([A-Z]90\)/\1/' \ -e y/ABCDEFGHIJKLMNOPQRSTUVWXYZ/abcdefghijklmnopqrstuvwxyz/ \ -e 's/\.[^.]*$/.X/' exit ;; CRAY*TS:*:*:*) CRAY_REL=`echo "$UNAME_RELEASE" | sed -e 's/\.[^.]*$/.X/'` GUESS=t90-cray-unicos$CRAY_REL ;; CRAY*T3E:*:*:*) CRAY_REL=`echo "$UNAME_RELEASE" | sed -e 's/\.[^.]*$/.X/'` GUESS=alphaev5-cray-unicosmk$CRAY_REL ;; CRAY*SV1:*:*:*) CRAY_REL=`echo "$UNAME_RELEASE" | sed -e 's/\.[^.]*$/.X/'` GUESS=sv1-cray-unicos$CRAY_REL ;; *:UNICOS/mp:*:*) CRAY_REL=`echo "$UNAME_RELEASE" | sed -e 's/\.[^.]*$/.X/'` GUESS=craynv-cray-unicosmp$CRAY_REL ;; F30[01]:UNIX_System_V:*:* | F700:UNIX_System_V:*:*) FUJITSU_PROC=`uname -m | tr ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz` FUJITSU_SYS=`uname -p | tr ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz | sed -e 's/\///'` FUJITSU_REL=`echo "$UNAME_RELEASE" | sed -e 's/ /_/'` GUESS=${FUJITSU_PROC}-fujitsu-${FUJITSU_SYS}${FUJITSU_REL} ;; 5000:UNIX_System_V:4.*:*) FUJITSU_SYS=`uname -p | tr ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz | sed -e 's/\///'` FUJITSU_REL=`echo "$UNAME_RELEASE" | tr ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz | sed -e 's/ /_/'` GUESS=sparc-fujitsu-${FUJITSU_SYS}${FUJITSU_REL} ;; i*86:BSD/386:*:* | i*86:BSD/OS:*:* | *:Ascend\ Embedded/OS:*:*) GUESS=$UNAME_MACHINE-pc-bsdi$UNAME_RELEASE ;; sparc*:BSD/OS:*:*) GUESS=sparc-unknown-bsdi$UNAME_RELEASE ;; *:BSD/OS:*:*) GUESS=$UNAME_MACHINE-unknown-bsdi$UNAME_RELEASE ;; arm:FreeBSD:*:*) UNAME_PROCESSOR=`uname -p` set_cc_for_build if echo __ARM_PCS_VFP | $CC_FOR_BUILD -E - 2>/dev/null \ | grep -q __ARM_PCS_VFP then FREEBSD_REL=`echo "$UNAME_RELEASE" | sed -e 's/[-(].*//'` GUESS=$UNAME_PROCESSOR-unknown-freebsd$FREEBSD_REL-gnueabi else FREEBSD_REL=`echo "$UNAME_RELEASE" | sed -e 's/[-(].*//'` GUESS=$UNAME_PROCESSOR-unknown-freebsd$FREEBSD_REL-gnueabihf fi ;; *:FreeBSD:*:*) UNAME_PROCESSOR=`/usr/bin/uname -p` case $UNAME_PROCESSOR in amd64) UNAME_PROCESSOR=x86_64 ;; i386) UNAME_PROCESSOR=i586 ;; esac FREEBSD_REL=`echo "$UNAME_RELEASE" | sed -e 's/[-(].*//'` GUESS=$UNAME_PROCESSOR-unknown-freebsd$FREEBSD_REL ;; i*:CYGWIN*:*) GUESS=$UNAME_MACHINE-pc-cygwin ;; *:MINGW64*:*) GUESS=$UNAME_MACHINE-pc-mingw64 ;; *:MINGW*:*) GUESS=$UNAME_MACHINE-pc-mingw32 ;; *:MSYS*:*) GUESS=$UNAME_MACHINE-pc-msys ;; i*:PW*:*) GUESS=$UNAME_MACHINE-pc-pw32 ;; *:SerenityOS:*:*) GUESS=$UNAME_MACHINE-pc-serenity ;; *:Interix*:*) case $UNAME_MACHINE in x86) GUESS=i586-pc-interix$UNAME_RELEASE ;; authenticamd | genuineintel | EM64T) GUESS=x86_64-unknown-interix$UNAME_RELEASE ;; IA64) GUESS=ia64-unknown-interix$UNAME_RELEASE ;; esac ;; i*:UWIN*:*) GUESS=$UNAME_MACHINE-pc-uwin ;; amd64:CYGWIN*:*:* | x86_64:CYGWIN*:*:*) GUESS=x86_64-pc-cygwin ;; prep*:SunOS:5.*:*) SUN_REL=`echo "$UNAME_RELEASE" | sed -e 's/[^.]*//'` GUESS=powerpcle-unknown-solaris2$SUN_REL ;; *:GNU:*:*) # the GNU system GNU_ARCH=`echo "$UNAME_MACHINE" | sed -e 's,[-/].*$,,'` GNU_REL=`echo "$UNAME_RELEASE" | sed -e 's,/.*$,,'` GUESS=$GNU_ARCH-unknown-$LIBC$GNU_REL ;; *:GNU/*:*:*) # other systems with GNU libc and userland GNU_SYS=`echo "$UNAME_SYSTEM" | sed 's,^[^/]*/,,' | tr "[:upper:]" "[:lower:]"` GNU_REL=`echo "$UNAME_RELEASE" | sed -e 's/[-(].*//'` GUESS=$UNAME_MACHINE-unknown-$GNU_SYS$GNU_REL-$LIBC ;; *:Minix:*:*) GUESS=$UNAME_MACHINE-unknown-minix ;; aarch64:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; aarch64_be:Linux:*:*) UNAME_MACHINE=aarch64_be GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; alpha:Linux:*:*) case `sed -n '/^cpu model/s/^.*: \(.*\)/\1/p' /proc/cpuinfo 2>/dev/null` in EV5) UNAME_MACHINE=alphaev5 ;; EV56) UNAME_MACHINE=alphaev56 ;; PCA56) UNAME_MACHINE=alphapca56 ;; PCA57) UNAME_MACHINE=alphapca56 ;; EV6) UNAME_MACHINE=alphaev6 ;; EV67) UNAME_MACHINE=alphaev67 ;; EV68*) UNAME_MACHINE=alphaev68 ;; esac objdump --private-headers /bin/sh | grep -q ld.so.1 if test "$?" = 0 ; then LIBC=gnulibc1 ; fi GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; arc:Linux:*:* | arceb:Linux:*:* | arc32:Linux:*:* | arc64:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; arm*:Linux:*:*) set_cc_for_build if echo __ARM_EABI__ | $CC_FOR_BUILD -E - 2>/dev/null \ | grep -q __ARM_EABI__ then GUESS=$UNAME_MACHINE-unknown-linux-$LIBC else if echo __ARM_PCS_VFP | $CC_FOR_BUILD -E - 2>/dev/null \ | grep -q __ARM_PCS_VFP then GUESS=$UNAME_MACHINE-unknown-linux-${LIBC}eabi else GUESS=$UNAME_MACHINE-unknown-linux-${LIBC}eabihf fi fi ;; avr32*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; cris:Linux:*:*) GUESS=$UNAME_MACHINE-axis-linux-$LIBC ;; crisv32:Linux:*:*) GUESS=$UNAME_MACHINE-axis-linux-$LIBC ;; e2k:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; frv:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; hexagon:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; i*86:Linux:*:*) GUESS=$UNAME_MACHINE-pc-linux-$LIBC ;; ia64:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; k1om:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; loongarch32:Linux:*:* | loongarch64:Linux:*:* | loongarchx32:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; m32r*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; m68*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; mips:Linux:*:* | mips64:Linux:*:*) set_cc_for_build IS_GLIBC=0 test x"${LIBC}" = xgnu && IS_GLIBC=1 sed 's/^ //' << EOF > "$dummy.c" #undef CPU #undef mips #undef mipsel #undef mips64 #undef mips64el #if ${IS_GLIBC} && defined(_ABI64) LIBCABI=gnuabi64 #else #if ${IS_GLIBC} && defined(_ABIN32) LIBCABI=gnuabin32 #else LIBCABI=${LIBC} #endif #endif #if ${IS_GLIBC} && defined(__mips64) && defined(__mips_isa_rev) && __mips_isa_rev>=6 CPU=mipsisa64r6 #else #if ${IS_GLIBC} && !defined(__mips64) && defined(__mips_isa_rev) && __mips_isa_rev>=6 CPU=mipsisa32r6 #else #if defined(__mips64) CPU=mips64 #else CPU=mips #endif #endif #endif #if defined(__MIPSEL__) || defined(__MIPSEL) || defined(_MIPSEL) || defined(MIPSEL) MIPS_ENDIAN=el #else #if defined(__MIPSEB__) || defined(__MIPSEB) || defined(_MIPSEB) || defined(MIPSEB) MIPS_ENDIAN= #else MIPS_ENDIAN= #endif #endif EOF cc_set_vars=`$CC_FOR_BUILD -E "$dummy.c" 2>/dev/null | grep '^CPU\|^MIPS_ENDIAN\|^LIBCABI'` eval "$cc_set_vars" test "x$CPU" != x && { echo "$CPU${MIPS_ENDIAN}-unknown-linux-$LIBCABI"; exit; } ;; mips64el:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; openrisc*:Linux:*:*) GUESS=or1k-unknown-linux-$LIBC ;; or32:Linux:*:* | or1k*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; padre:Linux:*:*) GUESS=sparc-unknown-linux-$LIBC ;; parisc64:Linux:*:* | hppa64:Linux:*:*) GUESS=hppa64-unknown-linux-$LIBC ;; parisc:Linux:*:* | hppa:Linux:*:*) # Look for CPU level case `grep '^cpu[^a-z]*:' /proc/cpuinfo 2>/dev/null | cut -d' ' -f2` in PA7*) GUESS=hppa1.1-unknown-linux-$LIBC ;; PA8*) GUESS=hppa2.0-unknown-linux-$LIBC ;; *) GUESS=hppa-unknown-linux-$LIBC ;; esac ;; ppc64:Linux:*:*) GUESS=powerpc64-unknown-linux-$LIBC ;; ppc:Linux:*:*) GUESS=powerpc-unknown-linux-$LIBC ;; ppc64le:Linux:*:*) GUESS=powerpc64le-unknown-linux-$LIBC ;; ppcle:Linux:*:*) GUESS=powerpcle-unknown-linux-$LIBC ;; riscv32:Linux:*:* | riscv32be:Linux:*:* | riscv64:Linux:*:* | riscv64be:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; s390:Linux:*:* | s390x:Linux:*:*) GUESS=$UNAME_MACHINE-ibm-linux-$LIBC ;; sh64*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; sh*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; sparc:Linux:*:* | sparc64:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; tile*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; vax:Linux:*:*) GUESS=$UNAME_MACHINE-dec-linux-$LIBC ;; x86_64:Linux:*:*) set_cc_for_build LIBCABI=$LIBC if test "$CC_FOR_BUILD" != no_compiler_found; then if (echo '#ifdef __ILP32__'; echo IS_X32; echo '#endif') | \ (CCOPTS="" $CC_FOR_BUILD -E - 2>/dev/null) | \ grep IS_X32 >/dev/null then LIBCABI=${LIBC}x32 fi fi GUESS=$UNAME_MACHINE-pc-linux-$LIBCABI ;; xtensa*:Linux:*:*) GUESS=$UNAME_MACHINE-unknown-linux-$LIBC ;; i*86:DYNIX/ptx:4*:*) # ptx 4.0 does uname -s correctly, with DYNIX/ptx in there. # earlier versions are messed up and put the nodename in both # sysname and nodename. GUESS=i386-sequent-sysv4 ;; i*86:UNIX_SV:4.2MP:2.*) # Unixware is an offshoot of SVR4, but it has its own version # number series starting with 2... # I am not positive that other SVR4 systems won't match this, # I just have to hope. -- rms. # Use sysv4.2uw... so that sysv4* matches it. GUESS=$UNAME_MACHINE-pc-sysv4.2uw$UNAME_VERSION ;; i*86:OS/2:*:*) # If we were able to find `uname', then EMX Unix compatibility # is probably installed. GUESS=$UNAME_MACHINE-pc-os2-emx ;; i*86:XTS-300:*:STOP) GUESS=$UNAME_MACHINE-unknown-stop ;; i*86:atheos:*:*) GUESS=$UNAME_MACHINE-unknown-atheos ;; i*86:syllable:*:*) GUESS=$UNAME_MACHINE-pc-syllable ;; i*86:LynxOS:2.*:* | i*86:LynxOS:3.[01]*:* | i*86:LynxOS:4.[02]*:*) GUESS=i386-unknown-lynxos$UNAME_RELEASE ;; i*86:*DOS:*:*) GUESS=$UNAME_MACHINE-pc-msdosdjgpp ;; i*86:*:4.*:*) UNAME_REL=`echo "$UNAME_RELEASE" | sed 's/\/MP$//'` if grep Novell /usr/include/link.h >/dev/null 2>/dev/null; then GUESS=$UNAME_MACHINE-univel-sysv$UNAME_REL else GUESS=$UNAME_MACHINE-pc-sysv$UNAME_REL fi ;; i*86:*:5:[678]*) # UnixWare 7.x, OpenUNIX and OpenServer 6. case `/bin/uname -X | grep "^Machine"` in *486*) UNAME_MACHINE=i486 ;; *Pentium) UNAME_MACHINE=i586 ;; *Pent*|*Celeron) UNAME_MACHINE=i686 ;; esac GUESS=$UNAME_MACHINE-unknown-sysv${UNAME_RELEASE}${UNAME_SYSTEM}${UNAME_VERSION} ;; i*86:*:3.2:*) if test -f /usr/options/cb.name; then UNAME_REL=`sed -n 's/.*Version //p' /dev/null >/dev/null ; then UNAME_REL=`(/bin/uname -X|grep Release|sed -e 's/.*= //')` (/bin/uname -X|grep i80486 >/dev/null) && UNAME_MACHINE=i486 (/bin/uname -X|grep '^Machine.*Pentium' >/dev/null) \ && UNAME_MACHINE=i586 (/bin/uname -X|grep '^Machine.*Pent *II' >/dev/null) \ && UNAME_MACHINE=i686 (/bin/uname -X|grep '^Machine.*Pentium Pro' >/dev/null) \ && UNAME_MACHINE=i686 GUESS=$UNAME_MACHINE-pc-sco$UNAME_REL else GUESS=$UNAME_MACHINE-pc-sysv32 fi ;; pc:*:*:*) # Left here for compatibility: # uname -m prints for DJGPP always 'pc', but it prints nothing about # the processor, so we play safe by assuming i586. # Note: whatever this is, it MUST be the same as what config.sub # prints for the "djgpp" host, or else GDB configure will decide that # this is a cross-build. GUESS=i586-pc-msdosdjgpp ;; Intel:Mach:3*:*) GUESS=i386-pc-mach3 ;; paragon:*:*:*) GUESS=i860-intel-osf1 ;; i860:*:4.*:*) # i860-SVR4 if grep Stardent /usr/include/sys/uadmin.h >/dev/null 2>&1 ; then GUESS=i860-stardent-sysv$UNAME_RELEASE # Stardent Vistra i860-SVR4 else # Add other i860-SVR4 vendors below as they are discovered. GUESS=i860-unknown-sysv$UNAME_RELEASE # Unknown i860-SVR4 fi ;; mini*:CTIX:SYS*5:*) # "miniframe" GUESS=m68010-convergent-sysv ;; mc68k:UNIX:SYSTEM5:3.51m) GUESS=m68k-convergent-sysv ;; M680?0:D-NIX:5.3:*) GUESS=m68k-diab-dnix ;; M68*:*:R3V[5678]*:*) test -r /sysV68 && { echo 'm68k-motorola-sysv'; exit; } ;; 3[345]??:*:4.0:3.0 | 3[34]??A:*:4.0:3.0 | 3[34]??,*:*:4.0:3.0 | 3[34]??/*:*:4.0:3.0 | 4400:*:4.0:3.0 | 4850:*:4.0:3.0 | SKA40:*:4.0:3.0 | SDS2:*:4.0:3.0 | SHG2:*:4.0:3.0 | S7501*:*:4.0:3.0) OS_REL='' test -r /etc/.relid \ && OS_REL=.`sed -n 's/[^ ]* [^ ]* \([0-9][0-9]\).*/\1/p' < /etc/.relid` /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4.3"$OS_REL"; exit; } /bin/uname -p 2>/dev/null | /bin/grep entium >/dev/null \ && { echo i586-ncr-sysv4.3"$OS_REL"; exit; } ;; 3[34]??:*:4.0:* | 3[34]??,*:*:4.0:*) /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4; exit; } ;; NCR*:*:4.2:* | MPRAS*:*:4.2:*) OS_REL='.3' test -r /etc/.relid \ && OS_REL=.`sed -n 's/[^ ]* [^ ]* \([0-9][0-9]\).*/\1/p' < /etc/.relid` /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4.3"$OS_REL"; exit; } /bin/uname -p 2>/dev/null | /bin/grep entium >/dev/null \ && { echo i586-ncr-sysv4.3"$OS_REL"; exit; } /bin/uname -p 2>/dev/null | /bin/grep pteron >/dev/null \ && { echo i586-ncr-sysv4.3"$OS_REL"; exit; } ;; m68*:LynxOS:2.*:* | m68*:LynxOS:3.0*:*) GUESS=m68k-unknown-lynxos$UNAME_RELEASE ;; mc68030:UNIX_System_V:4.*:*) GUESS=m68k-atari-sysv4 ;; TSUNAMI:LynxOS:2.*:*) GUESS=sparc-unknown-lynxos$UNAME_RELEASE ;; rs6000:LynxOS:2.*:*) GUESS=rs6000-unknown-lynxos$UNAME_RELEASE ;; PowerPC:LynxOS:2.*:* | PowerPC:LynxOS:3.[01]*:* | PowerPC:LynxOS:4.[02]*:*) GUESS=powerpc-unknown-lynxos$UNAME_RELEASE ;; SM[BE]S:UNIX_SV:*:*) GUESS=mips-dde-sysv$UNAME_RELEASE ;; RM*:ReliantUNIX-*:*:*) GUESS=mips-sni-sysv4 ;; RM*:SINIX-*:*:*) GUESS=mips-sni-sysv4 ;; *:SINIX-*:*:*) if uname -p 2>/dev/null >/dev/null ; then UNAME_MACHINE=`(uname -p) 2>/dev/null` GUESS=$UNAME_MACHINE-sni-sysv4 else GUESS=ns32k-sni-sysv fi ;; PENTIUM:*:4.0*:*) # Unisys `ClearPath HMP IX 4000' SVR4/MP effort # says GUESS=i586-unisys-sysv4 ;; *:UNIX_System_V:4*:FTX*) # From Gerald Hewes . # How about differentiating between stratus architectures? -djm GUESS=hppa1.1-stratus-sysv4 ;; *:*:*:FTX*) # From seanf@swdc.stratus.com. GUESS=i860-stratus-sysv4 ;; i*86:VOS:*:*) # From Paul.Green@stratus.com. GUESS=$UNAME_MACHINE-stratus-vos ;; *:VOS:*:*) # From Paul.Green@stratus.com. GUESS=hppa1.1-stratus-vos ;; mc68*:A/UX:*:*) GUESS=m68k-apple-aux$UNAME_RELEASE ;; news*:NEWS-OS:6*:*) GUESS=mips-sony-newsos6 ;; R[34]000:*System_V*:*:* | R4000:UNIX_SYSV:*:* | R*000:UNIX_SV:*:*) if test -d /usr/nec; then GUESS=mips-nec-sysv$UNAME_RELEASE else GUESS=mips-unknown-sysv$UNAME_RELEASE fi ;; BeBox:BeOS:*:*) # BeOS running on hardware made by Be, PPC only. GUESS=powerpc-be-beos ;; BeMac:BeOS:*:*) # BeOS running on Mac or Mac clone, PPC only. GUESS=powerpc-apple-beos ;; BePC:BeOS:*:*) # BeOS running on Intel PC compatible. GUESS=i586-pc-beos ;; BePC:Haiku:*:*) # Haiku running on Intel PC compatible. GUESS=i586-pc-haiku ;; x86_64:Haiku:*:*) GUESS=x86_64-unknown-haiku ;; SX-4:SUPER-UX:*:*) GUESS=sx4-nec-superux$UNAME_RELEASE ;; SX-5:SUPER-UX:*:*) GUESS=sx5-nec-superux$UNAME_RELEASE ;; SX-6:SUPER-UX:*:*) GUESS=sx6-nec-superux$UNAME_RELEASE ;; SX-7:SUPER-UX:*:*) GUESS=sx7-nec-superux$UNAME_RELEASE ;; SX-8:SUPER-UX:*:*) GUESS=sx8-nec-superux$UNAME_RELEASE ;; SX-8R:SUPER-UX:*:*) GUESS=sx8r-nec-superux$UNAME_RELEASE ;; SX-ACE:SUPER-UX:*:*) GUESS=sxace-nec-superux$UNAME_RELEASE ;; Power*:Rhapsody:*:*) GUESS=powerpc-apple-rhapsody$UNAME_RELEASE ;; *:Rhapsody:*:*) GUESS=$UNAME_MACHINE-apple-rhapsody$UNAME_RELEASE ;; arm64:Darwin:*:*) GUESS=aarch64-apple-darwin$UNAME_RELEASE ;; *:Darwin:*:*) UNAME_PROCESSOR=`uname -p` case $UNAME_PROCESSOR in unknown) UNAME_PROCESSOR=powerpc ;; esac if command -v xcode-select > /dev/null 2> /dev/null && \ ! xcode-select --print-path > /dev/null 2> /dev/null ; then # Avoid executing cc if there is no toolchain installed as # cc will be a stub that puts up a graphical alert # prompting the user to install developer tools. CC_FOR_BUILD=no_compiler_found else set_cc_for_build fi if test "$CC_FOR_BUILD" != no_compiler_found; then if (echo '#ifdef __LP64__'; echo IS_64BIT_ARCH; echo '#endif') | \ (CCOPTS="" $CC_FOR_BUILD -E - 2>/dev/null) | \ grep IS_64BIT_ARCH >/dev/null then case $UNAME_PROCESSOR in i386) UNAME_PROCESSOR=x86_64 ;; powerpc) UNAME_PROCESSOR=powerpc64 ;; esac fi # On 10.4-10.6 one might compile for PowerPC via gcc -arch ppc if (echo '#ifdef __POWERPC__'; echo IS_PPC; echo '#endif') | \ (CCOPTS="" $CC_FOR_BUILD -E - 2>/dev/null) | \ grep IS_PPC >/dev/null then UNAME_PROCESSOR=powerpc fi elif test "$UNAME_PROCESSOR" = i386 ; then # uname -m returns i386 or x86_64 UNAME_PROCESSOR=$UNAME_MACHINE fi GUESS=$UNAME_PROCESSOR-apple-darwin$UNAME_RELEASE ;; *:procnto*:*:* | *:QNX:[0123456789]*:*) UNAME_PROCESSOR=`uname -p` if test "$UNAME_PROCESSOR" = x86; then UNAME_PROCESSOR=i386 UNAME_MACHINE=pc fi GUESS=$UNAME_PROCESSOR-$UNAME_MACHINE-nto-qnx$UNAME_RELEASE ;; *:QNX:*:4*) GUESS=i386-pc-qnx ;; NEO-*:NONSTOP_KERNEL:*:*) GUESS=neo-tandem-nsk$UNAME_RELEASE ;; NSE-*:NONSTOP_KERNEL:*:*) GUESS=nse-tandem-nsk$UNAME_RELEASE ;; NSR-*:NONSTOP_KERNEL:*:*) GUESS=nsr-tandem-nsk$UNAME_RELEASE ;; NSV-*:NONSTOP_KERNEL:*:*) GUESS=nsv-tandem-nsk$UNAME_RELEASE ;; NSX-*:NONSTOP_KERNEL:*:*) GUESS=nsx-tandem-nsk$UNAME_RELEASE ;; *:NonStop-UX:*:*) GUESS=mips-compaq-nonstopux ;; BS2000:POSIX*:*:*) GUESS=bs2000-siemens-sysv ;; DS/*:UNIX_System_V:*:*) GUESS=$UNAME_MACHINE-$UNAME_SYSTEM-$UNAME_RELEASE ;; *:Plan9:*:*) # "uname -m" is not consistent, so use $cputype instead. 386 # is converted to i386 for consistency with other x86 # operating systems. if test "${cputype-}" = 386; then UNAME_MACHINE=i386 elif test "x${cputype-}" != x; then UNAME_MACHINE=$cputype fi GUESS=$UNAME_MACHINE-unknown-plan9 ;; *:TOPS-10:*:*) GUESS=pdp10-unknown-tops10 ;; *:TENEX:*:*) GUESS=pdp10-unknown-tenex ;; KS10:TOPS-20:*:* | KL10:TOPS-20:*:* | TYPE4:TOPS-20:*:*) GUESS=pdp10-dec-tops20 ;; XKL-1:TOPS-20:*:* | TYPE5:TOPS-20:*:*) GUESS=pdp10-xkl-tops20 ;; *:TOPS-20:*:*) GUESS=pdp10-unknown-tops20 ;; *:ITS:*:*) GUESS=pdp10-unknown-its ;; SEI:*:*:SEIUX) GUESS=mips-sei-seiux$UNAME_RELEASE ;; *:DragonFly:*:*) DRAGONFLY_REL=`echo "$UNAME_RELEASE" | sed -e 's/[-(].*//'` GUESS=$UNAME_MACHINE-unknown-dragonfly$DRAGONFLY_REL ;; *:*VMS:*:*) UNAME_MACHINE=`(uname -p) 2>/dev/null` case $UNAME_MACHINE in A*) GUESS=alpha-dec-vms ;; I*) GUESS=ia64-dec-vms ;; V*) GUESS=vax-dec-vms ;; esac ;; *:XENIX:*:SysV) GUESS=i386-pc-xenix ;; i*86:skyos:*:*) SKYOS_REL=`echo "$UNAME_RELEASE" | sed -e 's/ .*$//'` GUESS=$UNAME_MACHINE-pc-skyos$SKYOS_REL ;; i*86:rdos:*:*) GUESS=$UNAME_MACHINE-pc-rdos ;; i*86:Fiwix:*:*) GUESS=$UNAME_MACHINE-pc-fiwix ;; *:AROS:*:*) GUESS=$UNAME_MACHINE-unknown-aros ;; x86_64:VMkernel:*:*) GUESS=$UNAME_MACHINE-unknown-esx ;; amd64:Isilon\ OneFS:*:*) GUESS=x86_64-unknown-onefs ;; *:Unleashed:*:*) GUESS=$UNAME_MACHINE-unknown-unleashed$UNAME_RELEASE ;; esac # Do we have a guess based on uname results? if test "x$GUESS" != x; then echo "$GUESS" exit fi # No uname command or uname output not recognized. set_cc_for_build cat > "$dummy.c" < #include #endif #if defined(ultrix) || defined(_ultrix) || defined(__ultrix) || defined(__ultrix__) #if defined (vax) || defined (__vax) || defined (__vax__) || defined(mips) || defined(__mips) || defined(__mips__) || defined(MIPS) || defined(__MIPS__) #include #if defined(_SIZE_T_) || defined(SIGLOST) #include #endif #endif #endif main () { #if defined (sony) #if defined (MIPSEB) /* BFD wants "bsd" instead of "newsos". Perhaps BFD should be changed, I don't know.... */ printf ("mips-sony-bsd\n"); exit (0); #else #include printf ("m68k-sony-newsos%s\n", #ifdef NEWSOS4 "4" #else "" #endif ); exit (0); #endif #endif #if defined (NeXT) #if !defined (__ARCHITECTURE__) #define __ARCHITECTURE__ "m68k" #endif int version; version=`(hostinfo | sed -n 's/.*NeXT Mach \([0-9]*\).*/\1/p') 2>/dev/null`; if (version < 4) printf ("%s-next-nextstep%d\n", __ARCHITECTURE__, version); else printf ("%s-next-openstep%d\n", __ARCHITECTURE__, version); exit (0); #endif #if defined (MULTIMAX) || defined (n16) #if defined (UMAXV) printf ("ns32k-encore-sysv\n"); exit (0); #else #if defined (CMU) printf ("ns32k-encore-mach\n"); exit (0); #else printf ("ns32k-encore-bsd\n"); exit (0); #endif #endif #endif #if defined (__386BSD__) printf ("i386-pc-bsd\n"); exit (0); #endif #if defined (sequent) #if defined (i386) printf ("i386-sequent-dynix\n"); exit (0); #endif #if defined (ns32000) printf ("ns32k-sequent-dynix\n"); exit (0); #endif #endif #if defined (_SEQUENT_) struct utsname un; uname(&un); if (strncmp(un.version, "V2", 2) == 0) { printf ("i386-sequent-ptx2\n"); exit (0); } if (strncmp(un.version, "V1", 2) == 0) { /* XXX is V1 correct? */ printf ("i386-sequent-ptx1\n"); exit (0); } printf ("i386-sequent-ptx\n"); exit (0); #endif #if defined (vax) #if !defined (ultrix) #include #if defined (BSD) #if BSD == 43 printf ("vax-dec-bsd4.3\n"); exit (0); #else #if BSD == 199006 printf ("vax-dec-bsd4.3reno\n"); exit (0); #else printf ("vax-dec-bsd\n"); exit (0); #endif #endif #else printf ("vax-dec-bsd\n"); exit (0); #endif #else #if defined(_SIZE_T_) || defined(SIGLOST) struct utsname un; uname (&un); printf ("vax-dec-ultrix%s\n", un.release); exit (0); #else printf ("vax-dec-ultrix\n"); exit (0); #endif #endif #endif #if defined(ultrix) || defined(_ultrix) || defined(__ultrix) || defined(__ultrix__) #if defined(mips) || defined(__mips) || defined(__mips__) || defined(MIPS) || defined(__MIPS__) #if defined(_SIZE_T_) || defined(SIGLOST) struct utsname *un; uname (&un); printf ("mips-dec-ultrix%s\n", un.release); exit (0); #else printf ("mips-dec-ultrix\n"); exit (0); #endif #endif #endif #if defined (alliant) && defined (i860) printf ("i860-alliant-bsd\n"); exit (0); #endif exit (1); } EOF $CC_FOR_BUILD -o "$dummy" "$dummy.c" 2>/dev/null && SYSTEM_NAME=`"$dummy"` && { echo "$SYSTEM_NAME"; exit; } # Apollos put the system type in the environment. test -d /usr/apollo && { echo "$ISP-apollo-$SYSTYPE"; exit; } echo "$0: unable to guess system type" >&2 case $UNAME_MACHINE:$UNAME_SYSTEM in mips:Linux | mips64:Linux) # If we got here on MIPS GNU/Linux, output extra information. cat >&2 <&2 <&2 </dev/null || echo unknown` uname -r = `(uname -r) 2>/dev/null || echo unknown` uname -s = `(uname -s) 2>/dev/null || echo unknown` uname -v = `(uname -v) 2>/dev/null || echo unknown` /usr/bin/uname -p = `(/usr/bin/uname -p) 2>/dev/null` /bin/uname -X = `(/bin/uname -X) 2>/dev/null` hostinfo = `(hostinfo) 2>/dev/null` /bin/universe = `(/bin/universe) 2>/dev/null` /usr/bin/arch -k = `(/usr/bin/arch -k) 2>/dev/null` /bin/arch = `(/bin/arch) 2>/dev/null` /usr/bin/oslevel = `(/usr/bin/oslevel) 2>/dev/null` /usr/convex/getsysinfo = `(/usr/convex/getsysinfo) 2>/dev/null` UNAME_MACHINE = "$UNAME_MACHINE" UNAME_RELEASE = "$UNAME_RELEASE" UNAME_SYSTEM = "$UNAME_SYSTEM" UNAME_VERSION = "$UNAME_VERSION" EOF fi exit 1 # Local variables: # eval: (add-hook 'before-save-hook 'time-stamp) # time-stamp-start: "timestamp='" # time-stamp-format: "%:y-%02m-%02d" # time-stamp-end: "'" # End: form-5.0.1/build-aux/compile0000755000175100017510000001635015217035732011425 #! /bin/sh # Wrapper for compilers which do not understand '-c -o'. scriptversion=2018-03-07.03; # UTC # Copyright (C) 1999-2021 Free Software Foundation, Inc. # Written by Tom Tromey . # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2, or (at your option) # any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # As a special exception to the GNU General Public License, if you # distribute this file as part of a program that contains a # configuration script generated by Autoconf, you may include it under # the same distribution terms that you use for the rest of that program. # This file is maintained in Automake, please report # bugs to or send patches to # . nl=' ' # We need space, tab and new line, in precisely that order. Quoting is # there to prevent tools from complaining about whitespace usage. IFS=" "" $nl" file_conv= # func_file_conv build_file lazy # Convert a $build file to $host form and store it in $file # Currently only supports Windows hosts. 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Try '$0 --help' for more information." 1>&2 exit 1; ;; -h | --h*) cat <<\EOF Usage: compile [--help] [--version] PROGRAM [ARGS] Wrapper for compilers which do not understand '-c -o'. Remove '-o dest.o' from ARGS, run PROGRAM with the remaining arguments, and rename the output as expected. If you are trying to build a whole package this is not the right script to run: please start by reading the file 'INSTALL'. Report bugs to . 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Check the 'README' file, it" echo "often tells you about the needed prerequisites for installing" echo "this package. You may also peek at any GNU archive site, in" echo "case some other package contains this missing '$1' program." ;; esac } give_advice "$1" | sed -e '1s/^/WARNING: /' \ -e '2,$s/^/ /' >&2 # Propagate the correct exit status (expected to be 127 for a program # not found, 63 for a program that failed due to version mismatch). exit $st # Local variables: # eval: (add-hook 'before-save-hook 'time-stamp) # time-stamp-start: "scriptversion=" # time-stamp-format: "%:y-%02m-%02d.%02H" # time-stamp-time-zone: "UTC0" # time-stamp-end: "; # UTC" # End: form-5.0.1/check/0000755000175100017510000000000015217035744007310 5form-5.0.1/check/examples.frm0000644000175100017510000020373415217035721011560 * Tests using the examples in the manual * * Some assertions here check for trivial, secondary things like runtime * information or layout. Usually, this should be avoided. But since we are here * not only testing FORM but also the code examples in the manual, this extra * strictness makes sometimes sense. * In the manual the example code has been given a comment that says it is used * here. Therefore, if you change something here, consider applying the * appropriate changes also in the manual. #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ Var_Symbols_1 : s x(:10),y; L F=y^7; id y=x+x^2; print; .end assert succeeded? assert bytesize("F") == 27 * wordsize assert result("F") =~ expr("x^7 + 7*x^8 + 21*x^9 + 35*x^10") *--#] Var_Symbols_1 : *--#[ Var_Sets_1 : Symbols a1,a2,a3,b1,b2,b3,x,n; CFunctions g1,g2,g3,g; Local expr = g(a1)+g(a2)+g(a3)+g(x); id,g(x?{a1,a2,a3}[n]) = {g1,g2,g3}[n]({b1,b2,b3}[n]); print; .end assert succeeded? assert result("expr") =~ expr("g1(b1) + g2(b2) + g3(b3) + g(x)") *--#] Var_Sets_1 : *--#[ Var_Dummy_indices_1 : i mu,nu; f f1,f2; L F=f1(mu)*f2(mu)+f1(nu)*f2(nu); sum mu; sum nu; print; .end assert succeeded? assert result("F") =~ expr("2*f1(N1_?)*f2(N1_?)") *--#] Var_Dummy_indices_1 : *--#[ Var_Dummy_indices_2 : Index mu,nu; CFunctions f,g; Vectors p,q; Local F = (f(mu)*g(mu))^2; sum mu; id f(nu?) = p(nu); id g(nu?) = q(nu); print; .end assert succeeded? assert result("F") =~ expr("p.p*q.q") *--#] Var_Dummy_indices_2 : *--#[ Var_Dummy_indices_3 : Index mu,nu; Symbol x; CFunctions f,g; Vectors p,q; Local F = x^2; repeat; id,once,x = f(mu)*g(mu); sum mu; endrepeat; id f(nu?) = p(nu); id g(nu?) = q(nu); print; .end assert succeeded? assert result("F") =~ expr("p.q^2") *--#] Var_Dummy_indices_3 : *--#[ Var_Dummy_indices_4 : Indices mu,nu; CFunctions f; L F = f(mu,nu)*f(nu,mu); sum mu, nu; Print; .sort Indices rho,si; Vectors p1,p2,p3,v; Tensor g; Local G = e_(mu,nu,rho,si)*g(mu,nu,p1,v)*g(rho,si,p2,v); sum mu,nu,rho,si; Multiply F^3; id v = e_(p1,p2,p3,?); print; .end assert succeeded? assert result("G") =~ expr("f(N1_?,N2_?)*f(N2_?,N1_?)*f(N3_?,N4_?)*f(N4_?,N3_?)*f(N5_?,N6_?)*f(N6_?,N5_?) *g(N7_?,N8_?,p1,N9_?)*g(N10_?,N11_?,p2,N12_?)*e_(p1,p2,p3,N9_?)*e_(p1,p2,p3,N12_?)*e_(N7_?,N8_?,N10_?,N11_?)") *--#] Var_Dummy_indices_4 : *--#[ Var_Extra_Symbols_1 : * NOTE: removed "Generated on `DATE_'" Vector p,q,p1,p2; CFunction f; CFunction Dot,InvDot; Symbol x,x1,x2; Set pdot:p,q; Off Statistics; Local F = x+x^2+1/x+1/x^2+f(x1)+f(x2)*p.q*x+f(x2)/p.q^2; id p1?pdot.p2?pdot = Dot(p1,p2); id 1/p1?pdot.p2?pdot = InvDot(p1,p2); Print; .sort ExtraSymbols,array,Y; Format DOUBLEFORTRAN; ToPolynomial; Print; .sort #write " SUBROUTINE sub(Y)" #write "*" #write "* Compute the extra symbols." #write "*" #write " REAL*8 Y(`EXTRASYMBOLS_')" #write " REAL*8 Dot,InvDot" #write " Dot(p1,p2)=p1(1)*p2(1)-p1(2)*p2(2)-p1(3)*p2(3)\ -p1(4)*p2(4)" #write " InvDot(p1,p2)=1.D0/(Dot(p1,p2))" #write "*" #write "* We still have to add definitions here." #write "* And we have to import all the variables." #write "*" #write "%X" #write "*" #write " RETURN" #write " END" ExtraSymbols,underscore,Z; Format Normal; Format 80; Print; .sort FromPolynomial; Print; .end assert succeeded? if !threaded? # In TFORM, the output can differ. assert stdout =~ exact_pattern(<<'EOF') F = x^-2 + x^-1 + x + x^2 + f(x1) + f(x2)*Dot(p,q)*x + f(x2)*InvDot(p,q)^2; ExtraSymbols,array,Y; Format DOUBLEFORTRAN; ToPolynomial; Print; .sort F = & Y(1) + Y(1)**2 + Y(2) + Y(5)**2*Y(3) + x + x*Y(4)*Y(3) + x**2 #write " SUBROUTINE sub(Y)" #write "*" #write "* Compute the extra symbols." #write "*" #write " REAL*8 Y(`EXTRASYMBOLS_')" #write " REAL*8 Dot,InvDot" #write " Dot(p1,p2)=p1(1)*p2(1)-p1(2)*p2(2)-p1(3)*p2(3)\ -p1(4)*p2(4)" #write " InvDot(p1,p2)=1.D0/(Dot(p1,p2))" #write "*" #write "* We still have to add definitions here." #write "* And we have to import all the variables." #write "*" #write "%X" #write "*" #write " RETURN" #write " END" ExtraSymbols,underscore,Z; Format Normal; Format 80; Print; .sort F = Z1_ + Z1_^2 + Z2_ + Z5_^2*Z3_ + x + x*Z4_*Z3_ + x^2; FromPolynomial; Print; .end F = x^-2 + x^-1 + x + x^2 + f(x1) + f(x2)*Dot(p,q)*x + f(x2)*InvDot(p,q)^2; EOF assert file("sub.f") == <<-'EOF' SUBROUTINE sub(Y) * * Compute the extra symbols. * REAL*8 Y(5) REAL*8 Dot,InvDot Dot(p1,p2)=p1(1)*p2(1)-p1(2)*p2(2)-p1(3)*p2(3)-p1(4)*p2(4) InvDot(p1,p2)=1.D0/(Dot(p1,p2)) * * We still have to add definitions here. * And we have to import all the variables. * Y(1)=x**(-1) Y(2)=f(x1) Y(3)=f(x2) Y(4)=Dot(p,q) Y(5)=InvDot(p,q) * RETURN END EOF end *--#] Var_Extra_Symbols_1 : *--#[ Pre_call_1 : #define a "1" #define bc2 "x" #define bc3 "y" #define b "c`~a'" #procedure hop(c,?d); #redefine a "3" #message This is the call: `c',`?d' #endprocedure #redefine a "2" #message This is b: `b' #call hop(`b`!b''`!b'`b'`!b'`b',`~a',`b',`a') .end assert succeeded? assert stdout =~ /#message This is b: `b'\n~~~This is b: c2\n/ assert stdout =~ /#call hop\(`b`!b''`!b'`b'`!b'`b',`~a',`b',`a'\)\n~~~This is the call: xc2c3c2c3,3,c3,2\n/ *--#] Pre_call_1 : *--#[ Pre_define_1 : #define c "3" #define var1(a,b) "(`~a'+`~b'+`c')" #define var2(a,b) "(`~a'+`~b'+`~c')" #redefine c "4" Local F1 = `var1(1,2)'; Local F2 = `var2(1,2)'; Print; .end assert succeeded? assert result("F1") =~ expr("6") assert result("F2") =~ expr("7") *--#] Pre_define_1 : *--#[ Pre_preout_1 : #PreOut ON S a1,...,a4; L F = (a1+...+a4)^2; id a4 = -a1; .end assert succeeded? assert stdout =~ exact_pattern(<<-EOF #PreOut ON S a1,...,a4; S,a1,a2,a3,a4 L F = (a1+...+a4)^2; L,F=(a1+a2+a3+a4)^2 id a4 = -a1; id,a4=-a1 .end EOF ) *--#] Pre_preout_1 : *--#[ Pre_write_1 : Symbols a,b; L F = a+b; #$a1 = a+b; #$a2 = (a+b)^2; #$a3 = $a1^3; #write " One power: %$\\n Two powers: %$\\n Three powers: %$\n%s"\ ,$a1,$a2,$a3," The end" .end assert succeeded? assert stdout =~ exact_pattern(<<-EOF One power: b+a Two powers: b^2+2*a*b+a^2 Three powers: b^3+3*a*b^2+3*a^2*b+a^3 The end .end EOF ) *--#] Pre_write_1 : *--#[ Pre_write_2 : * TODO: change the result in the manual. S x1,...,x10; L MyExpression = (x1+...+x10)^4; .sort Format Fortran; #write " FUNCTION fun(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)" #write " REAL x1,x2,x3,x4,x5,x6,x7,x8,x9,x10" #write " fun = %e",MyExpression(fun) #write " RETURN" #write " END" .end assert succeeded? assert file("fun.f") == <<-EOF FUNCTION fun(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10) REAL x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 fun = x10**4 + 4*x9*x10**3 + 6*x9**2*x10**2 + 4*x9**3*x10 + x9**4 & + 4*x8*x10**3 + 12*x8*x9*x10**2 + 12*x8*x9**2*x10 + 4*x8*x9**3 & + 6*x8**2*x10**2 + 12*x8**2*x9*x10 + 6*x8**2*x9**2 + 4*x8**3* & x10 + 4*x8**3*x9 + x8**4 + 4*x7*x10**3 + 12*x7*x9*x10**2 + 12*x7 & *x9**2*x10 + 4*x7*x9**3 + 12*x7*x8*x10**2 + 24*x7*x8*x9*x10 + 12 & *x7*x8*x9**2 + 12*x7*x8**2*x10 + 12*x7*x8**2*x9 + 4*x7*x8**3 + 6 & *x7**2*x10**2 + 12*x7**2*x9*x10 + 6*x7**2*x9**2 + 12*x7**2*x8* & x10 + 12*x7**2*x8*x9 + 6*x7**2*x8**2 + 4*x7**3*x10 + 4*x7**3*x9 & + 4*x7**3*x8 + x7**4 + 4*x6*x10**3 + 12*x6*x9*x10**2 + 12*x6* & x9**2*x10 + 4*x6*x9**3 + 12*x6*x8*x10**2 + 24*x6*x8*x9*x10 + 12* & x6*x8*x9**2 + 12*x6*x8**2*x10 + 12*x6*x8**2*x9 + 4*x6*x8**3 + 12 & *x6*x7*x10**2 + 24*x6*x7*x9*x10 + 12*x6*x7*x9**2 + 24*x6*x7*x8* & x10 + 24*x6*x7*x8*x9 + 12*x6*x7*x8**2 + 12*x6*x7**2*x10 + 12*x6* & x7**2*x9 + 12*x6*x7**2*x8 + 4*x6*x7**3 + 6*x6**2*x10**2 + 12* & x6**2*x9*x10 + 6*x6**2*x9**2 + 12*x6**2*x8*x10 + 12*x6**2*x8*x9 & + 6*x6**2*x8**2 fun = fun + 12*x6**2*x7*x10 + 12*x6**2*x7*x9 + 12*x6**2*x7*x8 + 6 & *x6**2*x7**2 + 4*x6**3*x10 + 4*x6**3*x9 + 4*x6**3*x8 + 4*x6**3* & x7 + x6**4 + 4*x5*x10**3 + 12*x5*x9*x10**2 + 12*x5*x9**2*x10 + 4 & *x5*x9**3 + 12*x5*x8*x10**2 + 24*x5*x8*x9*x10 + 12*x5*x8*x9**2 & + 12*x5*x8**2*x10 + 12*x5*x8**2*x9 + 4*x5*x8**3 + 12*x5*x7* & x10**2 + 24*x5*x7*x9*x10 + 12*x5*x7*x9**2 + 24*x5*x7*x8*x10 + 24 & *x5*x7*x8*x9 + 12*x5*x7*x8**2 + 12*x5*x7**2*x10 + 12*x5*x7**2*x9 & + 12*x5*x7**2*x8 + 4*x5*x7**3 + 12*x5*x6*x10**2 + 24*x5*x6*x9* & x10 + 12*x5*x6*x9**2 + 24*x5*x6*x8*x10 + 24*x5*x6*x8*x9 + 12*x5* & x6*x8**2 + 24*x5*x6*x7*x10 + 24*x5*x6*x7*x9 + 24*x5*x6*x7*x8 + & 12*x5*x6*x7**2 + 12*x5*x6**2*x10 + 12*x5*x6**2*x9 + 12*x5*x6**2* & x8 + 12*x5*x6**2*x7 + 4*x5*x6**3 + 6*x5**2*x10**2 + 12*x5**2*x9* & x10 + 6*x5**2*x9**2 + 12*x5**2*x8*x10 + 12*x5**2*x8*x9 + 6*x5**2 & *x8**2 + 12*x5**2*x7*x10 + 12*x5**2*x7*x9 + 12*x5**2*x7*x8 + 6* & x5**2*x7**2 + 12*x5**2*x6*x10 + 12*x5**2*x6*x9 + 12*x5**2*x6*x8 & + 12*x5**2*x6*x7 fun = fun + 6*x5**2*x6**2 + 4*x5**3*x10 + 4*x5**3*x9 + 4*x5**3*x8 & + 4*x5**3*x7 + 4*x5**3*x6 + x5**4 + 4*x4*x10**3 + 12*x4*x9* & x10**2 + 12*x4*x9**2*x10 + 4*x4*x9**3 + 12*x4*x8*x10**2 + 24*x4* & x8*x9*x10 + 12*x4*x8*x9**2 + 12*x4*x8**2*x10 + 12*x4*x8**2*x9 + & 4*x4*x8**3 + 12*x4*x7*x10**2 + 24*x4*x7*x9*x10 + 12*x4*x7*x9**2 & + 24*x4*x7*x8*x10 + 24*x4*x7*x8*x9 + 12*x4*x7*x8**2 + 12*x4* & x7**2*x10 + 12*x4*x7**2*x9 + 12*x4*x7**2*x8 + 4*x4*x7**3 + 12*x4 & *x6*x10**2 + 24*x4*x6*x9*x10 + 12*x4*x6*x9**2 + 24*x4*x6*x8*x10 & + 24*x4*x6*x8*x9 + 12*x4*x6*x8**2 + 24*x4*x6*x7*x10 + 24*x4*x6* & x7*x9 + 24*x4*x6*x7*x8 + 12*x4*x6*x7**2 + 12*x4*x6**2*x10 + 12* & x4*x6**2*x9 + 12*x4*x6**2*x8 + 12*x4*x6**2*x7 + 4*x4*x6**3 + 12* & x4*x5*x10**2 + 24*x4*x5*x9*x10 + 12*x4*x5*x9**2 + 24*x4*x5*x8* & x10 + 24*x4*x5*x8*x9 + 12*x4*x5*x8**2 + 24*x4*x5*x7*x10 + 24*x4* & x5*x7*x9 + 24*x4*x5*x7*x8 + 12*x4*x5*x7**2 + 24*x4*x5*x6*x10 + & 24*x4*x5*x6*x9 + 24*x4*x5*x6*x8 + 24*x4*x5*x6*x7 + 12*x4*x5* & x6**2 fun = fun + 12*x4*x5**2*x10 + 12*x4*x5**2*x9 + 12*x4*x5**2*x8 + & 12*x4*x5**2*x7 + 12*x4*x5**2*x6 + 4*x4*x5**3 + 6*x4**2*x10**2 + & 12*x4**2*x9*x10 + 6*x4**2*x9**2 + 12*x4**2*x8*x10 + 12*x4**2*x8* & x9 + 6*x4**2*x8**2 + 12*x4**2*x7*x10 + 12*x4**2*x7*x9 + 12*x4**2 & *x7*x8 + 6*x4**2*x7**2 + 12*x4**2*x6*x10 + 12*x4**2*x6*x9 + 12* & x4**2*x6*x8 + 12*x4**2*x6*x7 + 6*x4**2*x6**2 + 12*x4**2*x5*x10 & + 12*x4**2*x5*x9 + 12*x4**2*x5*x8 + 12*x4**2*x5*x7 + 12*x4**2* & x5*x6 + 6*x4**2*x5**2 + 4*x4**3*x10 + 4*x4**3*x9 + 4*x4**3*x8 + & 4*x4**3*x7 + 4*x4**3*x6 + 4*x4**3*x5 + x4**4 + 4*x3*x10**3 + 12* & x3*x9*x10**2 + 12*x3*x9**2*x10 + 4*x3*x9**3 + 12*x3*x8*x10**2 + & 24*x3*x8*x9*x10 + 12*x3*x8*x9**2 + 12*x3*x8**2*x10 + 12*x3*x8**2 & *x9 + 4*x3*x8**3 + 12*x3*x7*x10**2 + 24*x3*x7*x9*x10 + 12*x3*x7* & x9**2 + 24*x3*x7*x8*x10 + 24*x3*x7*x8*x9 + 12*x3*x7*x8**2 + 12* & x3*x7**2*x10 + 12*x3*x7**2*x9 + 12*x3*x7**2*x8 + 4*x3*x7**3 + 12 & *x3*x6*x10**2 + 24*x3*x6*x9*x10 + 12*x3*x6*x9**2 + 24*x3*x6*x8* & x10 fun = fun + 24*x3*x6*x8*x9 + 12*x3*x6*x8**2 + 24*x3*x6*x7*x10 + & 24*x3*x6*x7*x9 + 24*x3*x6*x7*x8 + 12*x3*x6*x7**2 + 12*x3*x6**2* & x10 + 12*x3*x6**2*x9 + 12*x3*x6**2*x8 + 12*x3*x6**2*x7 + 4*x3* & x6**3 + 12*x3*x5*x10**2 + 24*x3*x5*x9*x10 + 12*x3*x5*x9**2 + 24* & x3*x5*x8*x10 + 24*x3*x5*x8*x9 + 12*x3*x5*x8**2 + 24*x3*x5*x7*x10 & + 24*x3*x5*x7*x9 + 24*x3*x5*x7*x8 + 12*x3*x5*x7**2 + 24*x3*x5* & x6*x10 + 24*x3*x5*x6*x9 + 24*x3*x5*x6*x8 + 24*x3*x5*x6*x7 + 12* & x3*x5*x6**2 + 12*x3*x5**2*x10 + 12*x3*x5**2*x9 + 12*x3*x5**2*x8 & + 12*x3*x5**2*x7 + 12*x3*x5**2*x6 + 4*x3*x5**3 + 12*x3*x4* & x10**2 + 24*x3*x4*x9*x10 + 12*x3*x4*x9**2 + 24*x3*x4*x8*x10 + 24 & *x3*x4*x8*x9 + 12*x3*x4*x8**2 + 24*x3*x4*x7*x10 + 24*x3*x4*x7*x9 & + 24*x3*x4*x7*x8 + 12*x3*x4*x7**2 + 24*x3*x4*x6*x10 + 24*x3*x4* & x6*x9 + 24*x3*x4*x6*x8 + 24*x3*x4*x6*x7 + 12*x3*x4*x6**2 + 24*x3 & *x4*x5*x10 + 24*x3*x4*x5*x9 + 24*x3*x4*x5*x8 + 24*x3*x4*x5*x7 + & 24*x3*x4*x5*x6 + 12*x3*x4*x5**2 + 12*x3*x4**2*x10 + 12*x3*x4**2* & x9 fun = fun + 12*x3*x4**2*x8 + 12*x3*x4**2*x7 + 12*x3*x4**2*x6 + 12 & *x3*x4**2*x5 + 4*x3*x4**3 + 6*x3**2*x10**2 + 12*x3**2*x9*x10 + 6 & *x3**2*x9**2 + 12*x3**2*x8*x10 + 12*x3**2*x8*x9 + 6*x3**2*x8**2 & + 12*x3**2*x7*x10 + 12*x3**2*x7*x9 + 12*x3**2*x7*x8 + 6*x3**2* & x7**2 + 12*x3**2*x6*x10 + 12*x3**2*x6*x9 + 12*x3**2*x6*x8 + 12* & x3**2*x6*x7 + 6*x3**2*x6**2 + 12*x3**2*x5*x10 + 12*x3**2*x5*x9 & + 12*x3**2*x5*x8 + 12*x3**2*x5*x7 + 12*x3**2*x5*x6 + 6*x3**2* & x5**2 + 12*x3**2*x4*x10 + 12*x3**2*x4*x9 + 12*x3**2*x4*x8 + 12* & x3**2*x4*x7 + 12*x3**2*x4*x6 + 12*x3**2*x4*x5 + 6*x3**2*x4**2 + & 4*x3**3*x10 + 4*x3**3*x9 + 4*x3**3*x8 + 4*x3**3*x7 + 4*x3**3*x6 & + 4*x3**3*x5 + 4*x3**3*x4 + x3**4 + 4*x2*x10**3 + 12*x2*x9* & x10**2 + 12*x2*x9**2*x10 + 4*x2*x9**3 + 12*x2*x8*x10**2 + 24*x2* & x8*x9*x10 + 12*x2*x8*x9**2 + 12*x2*x8**2*x10 + 12*x2*x8**2*x9 + & 4*x2*x8**3 + 12*x2*x7*x10**2 + 24*x2*x7*x9*x10 + 12*x2*x7*x9**2 & + 24*x2*x7*x8*x10 + 24*x2*x7*x8*x9 + 12*x2*x7*x8**2 + 12*x2* & x7**2*x10 fun = fun + 12*x2*x7**2*x9 + 12*x2*x7**2*x8 + 4*x2*x7**3 + 12*x2* & x6*x10**2 + 24*x2*x6*x9*x10 + 12*x2*x6*x9**2 + 24*x2*x6*x8*x10 & + 24*x2*x6*x8*x9 + 12*x2*x6*x8**2 + 24*x2*x6*x7*x10 + 24*x2*x6* & x7*x9 + 24*x2*x6*x7*x8 + 12*x2*x6*x7**2 + 12*x2*x6**2*x10 + 12* & x2*x6**2*x9 + 12*x2*x6**2*x8 + 12*x2*x6**2*x7 + 4*x2*x6**3 + 12* & x2*x5*x10**2 + 24*x2*x5*x9*x10 + 12*x2*x5*x9**2 + 24*x2*x5*x8* & x10 + 24*x2*x5*x8*x9 + 12*x2*x5*x8**2 + 24*x2*x5*x7*x10 + 24*x2* & x5*x7*x9 + 24*x2*x5*x7*x8 + 12*x2*x5*x7**2 + 24*x2*x5*x6*x10 + & 24*x2*x5*x6*x9 + 24*x2*x5*x6*x8 + 24*x2*x5*x6*x7 + 12*x2*x5* & x6**2 + 12*x2*x5**2*x10 + 12*x2*x5**2*x9 + 12*x2*x5**2*x8 + 12* & x2*x5**2*x7 + 12*x2*x5**2*x6 + 4*x2*x5**3 + 12*x2*x4*x10**2 + 24 & *x2*x4*x9*x10 + 12*x2*x4*x9**2 + 24*x2*x4*x8*x10 + 24*x2*x4*x8* & x9 + 12*x2*x4*x8**2 + 24*x2*x4*x7*x10 + 24*x2*x4*x7*x9 + 24*x2* & x4*x7*x8 + 12*x2*x4*x7**2 + 24*x2*x4*x6*x10 + 24*x2*x4*x6*x9 + & 24*x2*x4*x6*x8 + 24*x2*x4*x6*x7 + 12*x2*x4*x6**2 + 24*x2*x4*x5* & x10 fun = fun + 24*x2*x4*x5*x9 + 24*x2*x4*x5*x8 + 24*x2*x4*x5*x7 + 24 & *x2*x4*x5*x6 + 12*x2*x4*x5**2 + 12*x2*x4**2*x10 + 12*x2*x4**2*x9 & + 12*x2*x4**2*x8 + 12*x2*x4**2*x7 + 12*x2*x4**2*x6 + 12*x2* & x4**2*x5 + 4*x2*x4**3 + 12*x2*x3*x10**2 + 24*x2*x3*x9*x10 + 12* & x2*x3*x9**2 + 24*x2*x3*x8*x10 + 24*x2*x3*x8*x9 + 12*x2*x3*x8**2 & + 24*x2*x3*x7*x10 + 24*x2*x3*x7*x9 + 24*x2*x3*x7*x8 + 12*x2*x3* & x7**2 + 24*x2*x3*x6*x10 + 24*x2*x3*x6*x9 + 24*x2*x3*x6*x8 + 24* & x2*x3*x6*x7 + 12*x2*x3*x6**2 + 24*x2*x3*x5*x10 + 24*x2*x3*x5*x9 & + 24*x2*x3*x5*x8 + 24*x2*x3*x5*x7 + 24*x2*x3*x5*x6 + 12*x2*x3* & x5**2 + 24*x2*x3*x4*x10 + 24*x2*x3*x4*x9 + 24*x2*x3*x4*x8 + 24* & x2*x3*x4*x7 + 24*x2*x3*x4*x6 + 24*x2*x3*x4*x5 + 12*x2*x3*x4**2 & + 12*x2*x3**2*x10 + 12*x2*x3**2*x9 + 12*x2*x3**2*x8 + 12*x2* & x3**2*x7 + 12*x2*x3**2*x6 + 12*x2*x3**2*x5 + 12*x2*x3**2*x4 + 4* & x2*x3**3 + 6*x2**2*x10**2 + 12*x2**2*x9*x10 + 6*x2**2*x9**2 + 12 & *x2**2*x8*x10 + 12*x2**2*x8*x9 + 6*x2**2*x8**2 + 12*x2**2*x7*x10 & + 12*x2**2*x7*x9 fun = fun + 12*x2**2*x7*x8 + 6*x2**2*x7**2 + 12*x2**2*x6*x10 + 12 & *x2**2*x6*x9 + 12*x2**2*x6*x8 + 12*x2**2*x6*x7 + 6*x2**2*x6**2 & + 12*x2**2*x5*x10 + 12*x2**2*x5*x9 + 12*x2**2*x5*x8 + 12*x2**2* & x5*x7 + 12*x2**2*x5*x6 + 6*x2**2*x5**2 + 12*x2**2*x4*x10 + 12* & x2**2*x4*x9 + 12*x2**2*x4*x8 + 12*x2**2*x4*x7 + 12*x2**2*x4*x6 & + 12*x2**2*x4*x5 + 6*x2**2*x4**2 + 12*x2**2*x3*x10 + 12*x2**2* & x3*x9 + 12*x2**2*x3*x8 + 12*x2**2*x3*x7 + 12*x2**2*x3*x6 + 12* & x2**2*x3*x5 + 12*x2**2*x3*x4 + 6*x2**2*x3**2 + 4*x2**3*x10 + 4* & x2**3*x9 + 4*x2**3*x8 + 4*x2**3*x7 + 4*x2**3*x6 + 4*x2**3*x5 + 4 & *x2**3*x4 + 4*x2**3*x3 + x2**4 + 4*x1*x10**3 + 12*x1*x9*x10**2 & + 12*x1*x9**2*x10 + 4*x1*x9**3 + 12*x1*x8*x10**2 + 24*x1*x8*x9* & x10 + 12*x1*x8*x9**2 + 12*x1*x8**2*x10 + 12*x1*x8**2*x9 + 4*x1* & x8**3 + 12*x1*x7*x10**2 + 24*x1*x7*x9*x10 + 12*x1*x7*x9**2 + 24* & x1*x7*x8*x10 + 24*x1*x7*x8*x9 + 12*x1*x7*x8**2 + 12*x1*x7**2*x10 & + 12*x1*x7**2*x9 + 12*x1*x7**2*x8 + 4*x1*x7**3 + 12*x1*x6* & x10**2 fun = fun + 24*x1*x6*x9*x10 + 12*x1*x6*x9**2 + 24*x1*x6*x8*x10 + & 24*x1*x6*x8*x9 + 12*x1*x6*x8**2 + 24*x1*x6*x7*x10 + 24*x1*x6*x7* & x9 + 24*x1*x6*x7*x8 + 12*x1*x6*x7**2 + 12*x1*x6**2*x10 + 12*x1* & x6**2*x9 + 12*x1*x6**2*x8 + 12*x1*x6**2*x7 + 4*x1*x6**3 + 12*x1* & x5*x10**2 + 24*x1*x5*x9*x10 + 12*x1*x5*x9**2 + 24*x1*x5*x8*x10 & + 24*x1*x5*x8*x9 + 12*x1*x5*x8**2 + 24*x1*x5*x7*x10 + 24*x1*x5* & x7*x9 + 24*x1*x5*x7*x8 + 12*x1*x5*x7**2 + 24*x1*x5*x6*x10 + 24* & x1*x5*x6*x9 + 24*x1*x5*x6*x8 + 24*x1*x5*x6*x7 + 12*x1*x5*x6**2 & + 12*x1*x5**2*x10 + 12*x1*x5**2*x9 + 12*x1*x5**2*x8 + 12*x1* & x5**2*x7 + 12*x1*x5**2*x6 + 4*x1*x5**3 + 12*x1*x4*x10**2 + 24*x1 & *x4*x9*x10 + 12*x1*x4*x9**2 + 24*x1*x4*x8*x10 + 24*x1*x4*x8*x9 & + 12*x1*x4*x8**2 + 24*x1*x4*x7*x10 + 24*x1*x4*x7*x9 + 24*x1*x4* & x7*x8 + 12*x1*x4*x7**2 + 24*x1*x4*x6*x10 + 24*x1*x4*x6*x9 + 24* & x1*x4*x6*x8 + 24*x1*x4*x6*x7 + 12*x1*x4*x6**2 + 24*x1*x4*x5*x10 & + 24*x1*x4*x5*x9 + 24*x1*x4*x5*x8 + 24*x1*x4*x5*x7 + 24*x1*x4* & x5*x6 fun = fun + 12*x1*x4*x5**2 + 12*x1*x4**2*x10 + 12*x1*x4**2*x9 + & 12*x1*x4**2*x8 + 12*x1*x4**2*x7 + 12*x1*x4**2*x6 + 12*x1*x4**2* & x5 + 4*x1*x4**3 + 12*x1*x3*x10**2 + 24*x1*x3*x9*x10 + 12*x1*x3* & x9**2 + 24*x1*x3*x8*x10 + 24*x1*x3*x8*x9 + 12*x1*x3*x8**2 + 24* & x1*x3*x7*x10 + 24*x1*x3*x7*x9 + 24*x1*x3*x7*x8 + 12*x1*x3*x7**2 & + 24*x1*x3*x6*x10 + 24*x1*x3*x6*x9 + 24*x1*x3*x6*x8 + 24*x1*x3* & x6*x7 + 12*x1*x3*x6**2 + 24*x1*x3*x5*x10 + 24*x1*x3*x5*x9 + 24* & x1*x3*x5*x8 + 24*x1*x3*x5*x7 + 24*x1*x3*x5*x6 + 12*x1*x3*x5**2 & + 24*x1*x3*x4*x10 + 24*x1*x3*x4*x9 + 24*x1*x3*x4*x8 + 24*x1*x3* & x4*x7 + 24*x1*x3*x4*x6 + 24*x1*x3*x4*x5 + 12*x1*x3*x4**2 + 12*x1 & *x3**2*x10 + 12*x1*x3**2*x9 + 12*x1*x3**2*x8 + 12*x1*x3**2*x7 + & 12*x1*x3**2*x6 + 12*x1*x3**2*x5 + 12*x1*x3**2*x4 + 4*x1*x3**3 + & 12*x1*x2*x10**2 + 24*x1*x2*x9*x10 + 12*x1*x2*x9**2 + 24*x1*x2*x8 & *x10 + 24*x1*x2*x8*x9 + 12*x1*x2*x8**2 + 24*x1*x2*x7*x10 + 24*x1 & *x2*x7*x9 + 24*x1*x2*x7*x8 + 12*x1*x2*x7**2 + 24*x1*x2*x6*x10 + & 24*x1*x2*x6*x9 fun = fun + 24*x1*x2*x6*x8 + 24*x1*x2*x6*x7 + 12*x1*x2*x6**2 + 24 & *x1*x2*x5*x10 + 24*x1*x2*x5*x9 + 24*x1*x2*x5*x8 + 24*x1*x2*x5*x7 & + 24*x1*x2*x5*x6 + 12*x1*x2*x5**2 + 24*x1*x2*x4*x10 + 24*x1*x2* & x4*x9 + 24*x1*x2*x4*x8 + 24*x1*x2*x4*x7 + 24*x1*x2*x4*x6 + 24*x1 & *x2*x4*x5 + 12*x1*x2*x4**2 + 24*x1*x2*x3*x10 + 24*x1*x2*x3*x9 + & 24*x1*x2*x3*x8 + 24*x1*x2*x3*x7 + 24*x1*x2*x3*x6 + 24*x1*x2*x3* & x5 + 24*x1*x2*x3*x4 + 12*x1*x2*x3**2 + 12*x1*x2**2*x10 + 12*x1* & x2**2*x9 + 12*x1*x2**2*x8 + 12*x1*x2**2*x7 + 12*x1*x2**2*x6 + 12 & *x1*x2**2*x5 + 12*x1*x2**2*x4 + 12*x1*x2**2*x3 + 4*x1*x2**3 + 6* & x1**2*x10**2 + 12*x1**2*x9*x10 + 6*x1**2*x9**2 + 12*x1**2*x8*x10 & + 12*x1**2*x8*x9 + 6*x1**2*x8**2 + 12*x1**2*x7*x10 + 12*x1**2* & x7*x9 + 12*x1**2*x7*x8 + 6*x1**2*x7**2 + 12*x1**2*x6*x10 + 12* & x1**2*x6*x9 + 12*x1**2*x6*x8 + 12*x1**2*x6*x7 + 6*x1**2*x6**2 + & 12*x1**2*x5*x10 + 12*x1**2*x5*x9 + 12*x1**2*x5*x8 + 12*x1**2*x5* & x7 + 12*x1**2*x5*x6 + 6*x1**2*x5**2 + 12*x1**2*x4*x10 + 12*x1**2 & *x4*x9 fun = fun + 12*x1**2*x4*x8 + 12*x1**2*x4*x7 + 12*x1**2*x4*x6 + 12 & *x1**2*x4*x5 + 6*x1**2*x4**2 + 12*x1**2*x3*x10 + 12*x1**2*x3*x9 & + 12*x1**2*x3*x8 + 12*x1**2*x3*x7 + 12*x1**2*x3*x6 + 12*x1**2* & x3*x5 + 12*x1**2*x3*x4 + 6*x1**2*x3**2 + 12*x1**2*x2*x10 + 12* & x1**2*x2*x9 + 12*x1**2*x2*x8 + 12*x1**2*x2*x7 + 12*x1**2*x2*x6 & + 12*x1**2*x2*x5 + 12*x1**2*x2*x4 + 12*x1**2*x2*x3 + 6*x1**2* & x2**2 + 4*x1**3*x10 + 4*x1**3*x9 + 4*x1**3*x8 + 4*x1**3*x7 + 4* & x1**3*x6 + 4*x1**3*x5 + 4*x1**3*x4 + 4*x1**3*x3 + 4*x1**3*x2 + & x1**4 RETURN END EOF *--#] Pre_write_2 : *--#[ DolVars_1 : S x,a,b; Off statistics; L F = (a+b)^4+a*(a+x)^3; .sort #$a = 0; if ( count(x,1) > $a ) $a = count_(x,1); Print " >> After %t the maximum power of x is %$",$a; ModuleOption noparallel; * suppresses noparallel warning #write " ># $a = `$a'" .sort #write " ># $a = `$a'" .end assert succeeded? assert stdout =~ Regexp.new(<<-EOF ># \\$a = 0 \.sort >> .+0 >> .+0 >> .+0 >> .+0 >> .+0 >> .+1 >> .+2 >> .+3 #write " ># \\$a = `\\$a'" ># \\$a = 3 EOF ) *--#] DolVars_1 : *--#[ DolVarsParallel_1 : S a1,...,a10; L F = (a1+...+a10)^3; .sort #$c = 0; Print +f "<%w> %t"; Multiply,(a1+...+a10); $c = $c+1; ModuleOption,sum,$c; .sort #message $c = `$c' #$max = 0; #$min = 10; if ( count(a1,1) > $max ) $max = count_(a1,1); if ( count(a4,1) < $min ) $min = count_(a4,1); ModuleOption,maximum,$max; ModuleOption,minimum,$min; .sort #message $max = `$max' #message $min = `$min' .end assert succeeded? if serial? assert stdout =~ /\s+\.sort\n(<>\ \ \+\ \S+\n){220}\n/ else assert stdout =~ /\s+\.sort\n(<\d+>\ \ \+\ \S+\n){220}\n/ end assert stdout =~ /~~~\$c = 2200/ assert stdout =~ /~~~\$max = 4/ assert stdout =~ /~~~\$min = 0/ *--#] DolVarsParallel_1 : *--#[ Sta_Also_1 : Symbols x,y,cosphi,sinphi; Local F = x+y; id x = cosphi*x-sinphi*y; also y = sinphi*x+cosphi*y; Print; .end assert succeeded? assert result("F") =~ expr("- y*sinphi + y*cosphi + x*sinphi + x*cosphi") *--#] Sta_Also_1 : *--#[ Sta_Antibracket_1 : Symbols x, y; Local F = (1+x+x^2)*(1+y+y^2); AntiBracket y; Print; .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') F = + x * ( 1 + y + y^2 ) + x^2 * ( 1 + y + y^2 ) + 1 + y + y^2; EOF *--#] Sta_Antibracket_1 : *--#[ Sta_Antiputinside_1 : Symbols x, y, z; Cfunction f; Local F = 10 + x + y^2 + y*z; Antiputinside f,x; Print; .end assert succeeded? assert result("F") =~ expr(" f(y*z) + f(y^2) + f(1)*x + f(10) ") *--#] Sta_Antiputinside_1 : *--#[ Sta_ArgImplode_1 : CF Z1, ..., Z4; S x, a, b; L s = a * (Z1(0,0,0,1,0,0,-1) - Z2(0,0,0,1,0,0,-1)) + b * (Z3(-2,8,-1,-1) - Z4(-2,8,-1,-1)); ArgImplode Z1; repeat id Z2(?a,0,x?!{0,0},?b) = Z2(?a,x+sig_(x),?b); ArgExplode Z3; repeat id Z4(?a,x?!{1,0,-1},?b) = Z4(?a,0,x-sig_(x),?b); id Z2(?a) = Z1(?a); id Z4(?a) = Z3(?a); Print; .end assert succeeded? assert result("s") =~ expr("0") *--#] Sta_ArgImplode_1 : *--#[ Sta_Argtoextrasymbol_1 : Symbols x, y; Cfunction f; Local F = f(x + 1); Local F1 = f(y,x + 1); Argtoextrasymbol; Print; .end assert succeeded? assert result("F") =~ expr("f(Z1_)") assert result("F1") =~ expr("f(Z2_,Z1_)") *--#] Sta_Argtoextrasymbol_1 : *--#[ Sta_Argument_1 : Symbols x, y, z; CFunction f; Local F = f(x + 2*y + z^2); Argument; Identify y = x; Endargument; Print; .end assert succeeded? assert result("F") =~ expr(" f(z^2 + 3*x) ") *--#] Sta_Argument_1 : *--#[ Sta_Argument_2 : Symbols x,y; CFunction f, f1, f2, f3; Local F = f(x,x,x,x) + f1(x,x,x,x) + f2(x,x) + f3(x); Argument 2,f,1,{f,f1},3,4; Identify x = y; Endargument; Print; .end assert succeeded? assert result("F") =~ expr(" f(y,y,y,y) + f1(x,y,y,y) + f2(x,y) + f3(x) ") *--#] Sta_Argument_2 : *--#[ Sta_Bracket_1 : Symbols x, y; Local F = (1+x+x^2)*(1+y+y^2); Bracket y; Print; .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') F = + y * ( 1 + x + x^2 ) + y^2 * ( 1 + x + x^2 ) + 1 + x + x^2; EOF *--#] Sta_Bracket_1 : *--#[ Sta_Chainin_1 : Function f; Symbol x,y,z; Local F = f(x)*f(y)*f(z); ChainIn f; Print; .end assert succeeded? assert result("F") =~ expr(" f(x,y,z) ") *--#] Sta_Chainin_1 : *--#[ Sta_Chainout_1 : Function f; Symbol x,y,z; Local F = f(x,y,z); ChainOut f; Print; .end assert succeeded? assert result("F") =~ expr(" f(x)*f(y)*f(z) ") *--#] Sta_Chainout_1 : *--#[ Sta_Collect_1 : S a,b,c; CF cfun; L F = a*(b^2+c) + a^2*(b+6) + b^3 + c*b + 12; B a; .sort Collect cfun; P; .end assert succeeded? assert result("F") =~ expr(" cfun(6 + b)*a^2 + cfun(12 + b*c + b^3) + cfun(c + b^2)*a ") *--#] Sta_Collect_1 : *--#[ Sta_CommuteInSet_1 : I i1,...,i10; F A1,...,A10; CommuteInSet{A1,A3,A5},{A1,g_},{A1,A1}; L F = A5*A1*A5*A1*A5*A2*A3*A5*A1*A5*A3*A1; L G = g_(2,i1)*g_(2,i2,i3)*A1(i2)*g_(1,i4)*g_(1,5_,i5,i6) *A1(i1)*A1(i3)*g5_(1)*A3(i5)*A3(i4)*g5_(1); Print +f +s; .end assert succeeded? assert result("F") =~ expr(" + A1*A1*A5*A5*A5*A2*A1*A1*A3*A3*A5*A5 ") assert result("G") =~ expr(" + g_(1,i4,i5,i6)*g_(2,i1,i2,i3)*A1(i1)*A1(i2)*A1(i3)* A3(i5)*A3(i4)*g_(1,5_) ") *--#] Sta_CommuteInSet_1 : *--#[ Sta_Commute_1 : CFunction f,g; Symbol x; Local F = f(x)*g(x) + g(x)*f(x); Print; .end assert succeeded? assert result("F") =~ expr(" 2*f(x)*g(x) ") *--#] Sta_Commute_1 : *--#[ Sta_Denominators_1 : Symbols x, y; Cfunction rat, den; PolyRatFun rat; Local F = 1/(x+y); Denominators den; Identify den(x?) = rat(1,x); Print; .end assert succeeded? assert result("F") =~ expr(" rat(1,x + y) ") *--#] Sta_Denominators_1 : *--#[ Sta_Discard_1 : Symbols x; Local F = x^3 + x^4 + x^5 + x^6; if ( count(x,1) > 5 ) Discard; Print; .end assert succeeded? assert result("F") =~ expr(" x^3 + x^4 + x^5 ") *--#] Sta_Discard_1 : *--#[ Sta_Do_1 : Symbol x,y; CFunction f; LocalFactorized F = (1+y)*(2+y)*(3+y)*(4+y)*(5+y); .sort #$nf = numfactors_(F); Local G = +...+; Do $i = 1,$nf; Identify,only x^$i = f(F[factor_^$i]); Enddo; Print; ModuleOption local $i; .end assert succeeded? assert stdout =~ exact_pattern(" F = ( 1 + y ) * ( 2 + y ) * ( 3 + y ) * ( 4 + y ) * ( 5 + y ); ") assert result("G") =~ expr(" f(1 + y) + f(2 + y) + f(3 + y) + f(4 + y) + f(5 + y) ") *--#] Sta_Do_1 : *--#[ Sta_Drop_1 : Local F1 = 1; Local F2 = 2; Local F3 = 3; .sort Drop; Ndrop F1; Print; .end assert succeeded? assert result("F1") =~ expr("1") *--#] Sta_Drop_1 : *--#[ Sta_DropCoefficient_1 : Symbols x; Local F = 1 + 10*x + 20*x^2; DropCoefficient; Print; .end assert succeeded? assert result("F") =~ expr(" 1 + x + x^2 ") *--#] Sta_DropCoefficient_1 *--#[ Sta_DropCoefficient_2 : Symbols x; Cfunction f; Local F = f(1 + 5*x + 10*x^2); Argument; DropCoefficient; Endargument; Print; .end assert succeeded? assert result("F") =~ expr(" f(1 + x + x^2) ") *--#] Sta_DropCoefficient_2 *--#[ Sta_DropSymbols_1 : Symbols x, y, z; Local F = 1 + x + x^2 + z^3 + 2^2*y^4; Dropsymbols; Print; .end assert succeeded? assert result("F") =~ expr(" 8 ") *--#] Sta_Dropsymbols_1 *--#[ Sta_FactArg_1 : *TODO: OldFactArg is needed for the result in the manual. On OldFactArg; Symbols a,b,c; CFunctions f,f1,f2,f3; Local F = f(-3*a*b)+f(3*a*b) +f1(-3*a*b)+f1(3*a*b) +f2(-3*a*b)+f2(3*a*b) +f3(-3*a*b)+f3(3*a*b); FactArg,f; Factarg,(0),f1; Factarg,(1),f2; Factarg,(-1),f3; Print; .end assert succeeded? assert result("F") =~ expr(" f(a,b,-1,3) + f(a,b,3) + 2*f1(a*b) + f2(a*b,-1,3) + f2(a*b,3) + f3(a*b,-3) + f3(a*b,3) ") *--#] Sta_FactArg_1 : *--#[ Sta_Factorize_1 : Symbols x; Local F = x^3 + 3*x^2 + 3*x + 1; Factorize; Print; .end assert succeeded? assert result("F") =~ expr(" ( 1 + x ) * ( 1 + x ) * ( 1 + x ) ") *--#] Sta_Factorize_1 : *--#[ Sta_Fill_1 : Table B(1:1); Local dummy = 1; .sort Fill B(1) = dummy; Drop dummy; .sort * The next line is disabled to prevent a segmentation fault. * Local F = B(1); Print; .end #pend_if windows? assert finished? assert warning? *--#] Sta_Fill_1 : *--#[ Sta_Fill_2 : Table B(1:1); Local dummy = 1; .sort Fill B(1) = dummy; .sort Local F = B(1); Print; .sort Drop; .sort Local dummy = 2; .sort Local F = B(1); Print; .end # RHS expressions in Fill doesn't work in ParFORM. (#17) # Anyway, the user is warned even in the sequential FORM, and should avoid it. #pend_if mpi? assert finished? assert warning? assert return_value == 0 assert result("F", 0) =~ expr("1") assert result("F", 1) =~ expr("2") *--#] Sta_Fill_2 : *--#[ Sta_Fill_3 : Table B(1:1); Local dummy = 1; .sort #$value = dummy; Fill B(1) = `$value'; Drop dummy; .sort Local F = B(1); Print; .end assert succeeded? assert result("F") =~ expr("1") *--#] Sta_Fill_3 : *--#[ Sta_Fill_4 : Table B(1:1); Local u = 2; Local dummy = 1; .sort Fill B(1) = dummy; Drop dummy; .sort Local v = 5; Local F = B(1); Print; .end # RHS expressions in Fill doesn't work in ParFORM. (#17) # Anyway, the user is warned even in the sequential FORM, and should avoid it. #pend_if mpi? assert finished? assert warning? assert return_value == 0 assert result("F") =~ expr("5") *--#] Sta_Fill_4 : *--#[ Sta_Identify_1 : Vector Q,p1,...,p5,q1,...,q5; Cfunction V(s),replace; Format 60; * This is a t1 topology: L F = V(Q,p1,p4)*V(p1,p2,p5)* V(p2,p3,Q)*V(p3,p4,p5); $t = term_; id,all,$t*replace_(,...,) = $t*replace(,...,); Print +s; ModuleOption local $t; * allow parallel execution .end assert succeeded? assert result("F") =~ expr(" + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p1,q1,p2,q2,p3,q3,p4,q4,p5,q5) + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p2,q1,p1,q2,p4,q3,p3,q4,p5,q5) + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p3,q1,p4,q2,p1,q3,p2,q4,p5,q5) + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p4,q1,p3,q2,p2,q3,p1,q4,p5,q5) ") *--#] Sta_Identify_1 : *--#[ Sta_Keep_1 : CF f,g; I i1; S x,y,z; L F = f(i1,x)*(g(i1,y)+g(i1,z)); B f; .sort Keep Brackets; sum i1; Print; .end assert succeeded? assert result("F") =~ expr("f(N1_?,x)*g(i1,y)+f(N1_?,x)*g(i1,z)") *--#] Sta_Keep_1 : *--#[ Sta_LFactorized_1 : Symbols x,y,z; LocalFactorized F1 = 3*(x+y)*(y+z)*((x+z)*(2*x+1)); LocalFactorized F2 = 3*(x+y)*(y+z)+((x+z)*(2*x+1)); Print; .end assert succeeded? assert result("F1") =~ expr(" ( 3 ) * ( y + x ) * ( z + y ) * ( z + x + 2*x*z + 2*x^2 ) ") assert result("F2") =~ expr(" ( z + 3*y*z + 3*y^2 + x + 5*x*z + 3*x*y + 2*x^2 ) ") *--#] Sta_LFactorized_1 : *--#[ Sta_MakeInteger_1 : S a,b,c; CF f; L F = f(22/3*a+14/5*b+18/7*c); MakeInteger,f; Print +f; .end assert succeeded? assert result("F") =~ expr("2/105*f(135*c + 147*b + 385*a)") *--#] Sta_MakeInteger_1 : *--#[ Sta_PolyFun_1 : Symbol x,y; CF acc; PolyFun acc; Local F = 3*x^2*acc(1+y+y^2)+2*x^2*acc(1-y+y^2); Print; .end assert succeeded? assert result("F") =~ expr("x^2 * acc(5 + y + 5*y^2)") *--#] Sta_PolyFun_1 : *--#[ Sta_PolyRatFun_1 : S x,y; CF acc; PolyRatFun acc; Local F = 3*x^2*acc(1+y+y^2,1-y)+2*x^2*acc(1-y+y^2,1+y); P; .end assert succeeded? assert result("F") =~ expr("x^2*acc(-y^3-10*y^2-2*y-5,y^2-1)") *--#] Sta_PolyRatFun_1 : *--#[ Sta_PushPopHide_1 : Local F1 = 1; .sort PushHide; Local F2 = 1; * This statement does not affect F1: Multiply 2; .sort PushHide; Local F3 = 1; * This statement does not affect F1,F2: Multiply 2; .sort PopHide; * This statement does not affect F1: Multiply 2; .sort PopHide; * This statement affects all expressions: Multiply 2; Print; .end assert succeeded? assert result("F1") =~ expr("2") assert result("F2") =~ expr("8") assert result("F3") =~ expr("8") *--#] Sta_PushPopHide_1 : *--#[ Sta_PushPopHide_2 : Local F1 = 1; .sort PushHide; Multiply 2; .sort PopHide; .sort PopHide; .end assert compile_error?("PopHide statement without corresponding PushHide statement") *--#] Sta_PushPopHide_2 : *--#[ Sta_Print_1 : Symbols a,b,c; Local F = 3*a+2*b; Print "> %T"; id a = b+c; Print ">> %t"; Print; .end assert succeeded? assert stdout =~ exact_pattern(<<-'EOF' > 3*a >> + 3*b >> + 3*c > 2*b >> + 2*b EOF ) assert result("F") =~ expr("3*c + 5*b") *--#] Sta_Print_1 : *--#[ Sta_Putinside_1 : Symbols x, y, z; Cfunction f; Local F = 1 + x + 2*x + y^2+ z^3; Putinside f,x; Print; .end assert succeeded? assert result("F") =~ expr(" f(2*x) + f(x) + f(1) + f(1)*z^3 + f(1)*y^2") *--#] Sta_Putinside_1 : *--#[ Sta_Repeat_1 : Symbols x, y, z; CFunction f, g; Local F = f(x)*g(y)*g(z); Repeat; Identify f(?a)*g(?b) = f(?a,?b); Endrepeat; Print; .end assert succeeded? assert result("F") =~ expr("f(x,y,z)") *--#] Sta_Repeat_1 : *--#[ Sta_ReplaceLoop_1 : *TODO: change the result in the manual. Functions f(antisymmetric),ff(cyclesymmetric); Indices i1,...,i8; Local F = f(i1,i4,i2)*f(i5,i2,i3)*f(i3,i1,i6)*f(i4,i7,i8); ReplaceLoop f,arg=3,loop=3,out=ff; P; .end assert succeeded? assert result("F") =~ expr("- ff(i4,i5,i6)*f(i4,i7,i8)") *--#] Sta_ReplaceLoop_1 : *--#[ Sta_ReplaceLoop_2 : *TODO: change the result in the manual. Functions f(antisymmetric),ff(cyclesymmetric); Indices i1,...,i9; Local F = f(i1,i4,i2)*f(i5,i2,i3)*f(i3,i1,i6)*f(i4,i7,i8) *f(i6,i7,i8); ReplaceLoop f,arg=3,loop=all,out=ff; P; .end assert succeeded? assert result("F") =~ expr("- f(i1,i2,i4)*f(i2,i3,i5)*f(i1,i3,i6)*ff(i4,i6)") *--#] Sta_ReplaceLoop_2 : *--#[ Sta_Shuffle_1 : CF f,ff,g; S a,b,c,d,x1,x2; Local F1 = ff*f(a,b)*f(c,d); Local F2 = g(a,b)*g(c,d); repeat id f(x1?,?a)*f(x2?,?b)*ff(?c) = +f(?a)*f(x2,?b)*ff(?c,x1) +f(x1,?a)*f(?b)*ff(?c,x2); id f(?a)*f(?b)*ff(?c) = f(?c,?a,?b); shuffle,g; Print; .end assert succeeded? assert result("F1") =~ expr("f(a,b,c,d)+f(a,c,b,d)+f(a,c,d,b)+f(c,a,b,d)+f(c,a,d,b)+f(c,d,a,b)") assert result("F2") =~ expr("g(a,b,c,d)+g(a,c,b,d)+g(a,c,d,b)+g(c,a,b,d)+g(c,a,d,b)+g(c,d,a,b)") *--#] Sta_Shuffle_1 : *--#[ Sta_Setexitflag_1 : CFunction f; Symbol x; Local test = +...+; Identify f(x?even_) = x; If (Match(f(x?))); Print "Error: unreplaced f: %t"; SetExitFlag; EndIf; .sort Print; .end # For now, this hangs in ParFORM and is not valgrind clean for tform #pend_if mpi? || ( valgrind? && threaded? ) assert succeeded? assert stdout =~ exact_pattern(" Error: unreplaced f: + f(1) Error: unreplaced f: + f(3) Error: unreplaced f: + f(5) ") *--#] Sta_Setexitflag_1 : *--#[ Sta_Splitarg_1 : CFunction f; Symbol a,b,c,d; Local test = f(a+b-5*c*d); SplitArg f; Print; .end assert succeeded? assert result("test") =~ expr("f( - 5*c*d,b,a)") *--#] Sta_Splitarg_1 : *--#[ Sta_Splitarg_2 : CFunction f,g,h; Symbol x,y; Local test = f(2 + 3*x + 4*x^2) + g(2 + 3*x + 4*x^2) + h(x + x*y + x^2*y); SplitArg (x) f; SplitArg (x^2) g; SplitArg (x*y) h; Print; .end assert succeeded? assert result("test") =~ expr("f(2 + 4*x^2,3*x) + g(2 + 3*x,4*x^2) + h(x + x^2*y,x*y)") *--#] Sta_Splitarg_2 : *--#[ Sta_Splitarg_3 : CFunction f; Symbol x,y; Local test = f(2 + 3*x + 4*x^2 + 5*x*y + 6*y); SplitArg ((x)) f; Print; .end assert succeeded? assert result("test") =~ expr("f(2 + 6*y,3*x,5*x*y,4*x^2)") *--#] Sta_Splitarg_3 : *--#[ Sta_Splitfirstarg_1 : CFunction f; Symbol x; Local test = f(1 + x + x^2 + x^3); SplitFirstArg f; Print; .end assert succeeded? assert result("test") =~ expr("f(x + x^2 + x^3,1)") *--#] Sta_Splitfirstarg_1 : *--#[ Sta_Splitlastarg_1 : CFunction f; Symbol x; Local test = f(1 + x + x^2 + x^3); SplitLastArg f; Print; .end assert succeeded? assert result("test") =~ expr("f(1 + x + x^2,x^3)") *--#] Sta_Splitlastarg_1 : *--#[ Sta_Stuffle_1 : CF S,R; Symbols N,n; L F = S(R(1,-3),N)*S(R(-5,1),N); id S(R(?a),n?)*S(R(?b),n?) = S(?a)*S(?b)*R(n); Stuffle,S-; id S(?a)*R(n?) = S(R(?a),n); Print +s; .end assert succeeded? assert result("F") =~ expr(<<-'EOF' + S(R(-6,-4),N) - S(R(-6,-3,1),N) - S(R(-6,1,-3),N) - S(R(-5,1,-4),N) + S(R(-5,1,-3,1),N) + 2*S(R(-5,1,1,-3),N) - S(R(-5,2,-3),N) - S(R(1,-5,-4),N) + S(R(1,-5,-3,1),N) + S(R(1,-5,1,-3),N) + S(R(1,-3,-5,1),N) - S(R(1,8,1),N) EOF ) *--#] Sta_Stuffle_1 : *--#[ Sta_Sum_1 : CFunction f; Index mu,nu; Local test1 = f(mu,mu); Local test2 = f(mu,nu); Local test3 = f(mu,nu)*f(mu,nu); Sum mu,0,1,2, nu,0,1,2; Print; .end assert succeeded? assert result("test1") =~ expr("f(0,0) + f(1,1) + f(2,2)") assert result("test2") =~ expr("f(0,0) + f(0,1) + f(0,2) + f(1,0) + f(1,1) + f(1,2) + f(2,0) + f(2,1) + f(2,2)") assert result("test3") =~ expr("f(0,0)^2 + f(0,1)^2 + f(0,2)^2 + f(1,0)^2 + f(1,1)^2 + f(1,2)^2 + f(2,0)^2 + f(2,1)^2 + f(2,2)^2") *--#] Sta_Sum_1 : *--#[ Sta_Sum_2 : CFunction f,g; Index mu,nu; Local test1 = f(mu,nu)*g(mu,nu); Local test2 = f(N2_?,N1_?)*g(N2_?,N1_?); Sum mu,nu; Print; .end assert succeeded? assert result("test1") =~ expr("f(N1_?,N2_?)*g(N1_?,N2_?)") assert result("test2") =~ expr("f(N1_?,N2_?)*g(N1_?,N2_?)") *--#] Sta_Sum_2 : *--#[ Sta_Sum_3 : CFunction f,g; Index mu,nu; Local test = f(mu,nu)*g(mu,nu); Sum mu, nu,0,1,2; Print; .end assert succeeded? assert result("test") =~ expr("f(N1_?,0)*g(N1_?,0) + f(N1_?,1)*g(N1_?,1) + f(N1_?,2)*g(N1_?,2)") *--#] Sta_Sum_3 : *--#[ Sta_Term_1 : CFunction f; Symbol x; Local test = f(10); Term; Repeat Identify f(x?{>1}) = f(x-1) + f(x-2); EndTerm; Print; .end assert succeeded? assert result("test") =~ expr("34*f(0) + 55*f(1)") *--#] Sta_Term_1 : *--#[ Sta_ToTensor_1 : *NOTE: "functions" option is needed. Vector p,p1,p2; Function f; Index mu; Tensor tt,t; Local F = p.p1^2*f(p,p1)*p(mu)*tt(p1,p,p2,p); ToTensor functions, p,t; Print; .end assert succeeded? assert result("F") =~ expr(" f(N1_?,p1)*tt(p1,N2_?,p2,N3_?)*t(p1,p1,mu,N1_?,N2_?,N3_?) ") *--#] Sta_ToTensor_1 : *--#[ Sta_ToVector_1 : Tensor t1,t2; Vector v1,v2; Index mu1,mu2,mu3; Local test = t1(mu1,mu2,mu3) + t2(mu1,mu2,mu3); ToVector t1,v1; ToVector v2,t2; Print; .end assert succeeded? assert result("test") =~ expr("v1(mu1)*v1(mu2)*v1(mu3) + v2(mu1)*v2(mu2)*v2(mu3)") *--#] Sta_ToVector_1 : *--#[ Sta_Transform_1 : Symbol x,x1,x2; CF H,H1; Off Statistics; L F = H(3,4,2,6,1,1,1,2); Transform,H,explode(1,last), replace(1,last)=(0,1,1,0), encode(1,last):base=2; Print; .end assert succeeded? assert result("F") =~ expr("H(907202)") *--#] Sta_Transform_1 : *--#[ Sta_Transform_2 : Symbol x,x1,x2; CF H,H1; Off Statistics; L F = H(3,4,2,6,1,1,1,2); repeat id H(?a,x?!{0,1},?b) = H(?a,0,x-1,?b); Print; .sort Multiply H1; repeat id H(x?,?a)*H1(?b) = H(?a)*H1(?b,1-x); id H1(?a)*H = H(?a); Print; .sort repeat id H(x1?,x2?,?a) = H(2*x1+x2,?a); Print; .end assert succeeded? assert result("F") =~ expr("H(907202)") *--#] Sta_Transform_2 : *--#[ Sta_Transform_3 : Symbol a; Vector p; CFunction f1,f2; Local test = f1(0,1) + f2(2,a) + f2(2,p); Transform f1 replace(1,last)=(0,1,1,0); * This will not affect f2(2,p) because xarg_ does not match vectors: Transform f2 replace(1,last)=(xarg_,2*xarg_+1); Print; .end assert succeeded? assert result("test") =~ expr("f1(1,0) + f2(5,1 + 2*a) + f2(5,p)") *--#] Sta_Transform_3 : *--#[ Sta_Transform_4 : CFunction f2,f3; Local test = f2(1,1,0,1) + f3(1,1,0,1); Transform f2 encode(1,last):base=2; Transform f3 encode(1,last):base=3; Print; .end assert succeeded? assert result("test") =~ expr("f2(13) + f3(37)") *--#] Sta_Transform_4 : *--#[ Sta_Transform_5 : CFunction f2,f3,F2,F3; Local test = f2(13) + f2(100) + f3(37) + F2(13) + F3(37); Transform f2 decode(1,5):base=2; Transform f3 decode(1,5):base=3; Transform F2 decode(5,1):base=2; Transform F3 decode(5,1):base=3; Print; .end assert succeeded? assert result("test") =~ expr("f2(0,1,1,0,1) + f2(100) + f3(0,1,1,0,1) + F2(1,0,1,1,0) + F3(1,0,1,1,0)") *--#] Sta_Transform_5 : *--#[ Sta_Transform_6 : CFunction f; Symbol a; Local test = f(0,0,1,0,a,0,0,0,-1); Transform f implode(1,last); Print; .end assert succeeded? assert result("test") =~ expr("f(3,2*a,-4)") *--#] Sta_Transform_6 : *--#[ Sta_Transform_7 : CFunction f; Symbol a; Local test = f(3,2*a,-4); Transform f explode(1,last); Print; .end assert succeeded? assert result("test") =~ expr("f(0,0,1,0,a,0,0,0,-1)") *--#] Sta_Transform_7 : *--#[ Sta_Transform_8 : CFunction f,cyc; Symbol a1,...,a7; Local test = f(a1,a2,a3,a4,a5,a6,a7)*cyc(2,6); Identify cyc(?a$cyc) = 1; Transform f permute(1,3,5)($cyc); ModuleOption local $cyc; Print; .end assert succeeded? assert result("test") =~ expr("f(a3,a6,a5,a4,a1,a2,a7)") *--#] Sta_Transform_8 : *--#[ Sta_Transform_9 : CFunction f; Local test = f(1,...,10); Transform f reverse(3,7); Print; .end assert succeeded? assert result("test") =~ expr("f(1,2,7,6,5,4,3,8,9,10)") *--#] Sta_Transform_9 : *--#[ Sta_Transform_10 : CFunction f,g; Function h,i; Symbol x; Vector p; Index mu; Local test = f(100,g(1),g(2)^2,x,x^2,mu,p,p.p,1/p.p,h*i,i*h); Identify f(?a) = f(?a,?a); Transform f dedup(1,last); Print; .end assert succeeded? assert result("test") =~ expr("f(100,g(1),g(2)^2,x,x^2,mu,p,p.p,p.p^-1,h*i,i*h)") *--#] Sta_Transform_10 : *--#[ Sta_Transform_11 : CFunction f,g,h; Local test = f(1,...,9) + g(1,...,9) + h(1,...,9); Transform f cycle(3,7)=-1; Transform g permute(3,...,7); Transform h cycle(3,7)=+2; Print; .end assert succeeded? assert result("test") =~ expr("f(1,2,4,5,6,7,3,8,9) + g(1,2,4,5,6,7,3,8,9) + h(1,2,6,7,3,4,5,8,9)") *--#] Sta_Transform_11 : *--#[ Sta_Transform_11b : CFunction h; Local test = h(1,...,9); Transform h cycle(3,7)=2; Print; .end assert compile_error?("Cycle in a Transform statement should be followed by =+/-number/$") *--#] Sta_Transform_11b : *--#[ Sta_Transform_12 : CFunction f; Symbol y,n; Local test = f(0) + f(1) + f(0,1) + f(0,0,1) + f(0,1,1) + f(0,0) + f(1,0) + f(1,1) + f(1,0,0) + f(0,1,0) + f(1,0,1); Transform f islyndon(1,last)=(y,n); Print; .end assert succeeded? assert result("test") =~ expr("f(0)*y + f(0,0)*n + f(0,0,1)*y + f(0,1)*y + f(0,1,0)*n + f(0,1,1)*y + f(1)*y + f(1,0)*n + f(1,0,0)*n + f(1,0,1)*n + f(1,1)*n") *--#] Sta_Transform_12 : *--#[ Sta_Transform_13 : CFunction f; Symbol y,n; Local test = f(0) + f(1) + f(0,1) + f(0,0,1) + f(0,1,1) + f(0,0) + f(1,0) + f(1,1) + f(1,0,0) + f(0,1,0) + f(1,0,1); Transform f tolyndon(1,last)=(y,n); Print; .end assert succeeded? assert result("test") =~ expr("f(0)*y + f(0,0)*n + 3*f(0,0,1)*y + 2*f(0,1)*y + 2*f(0,1,1)*y + f(1)*y + f(1,1)*n") *--#] Sta_Transform_13 : *--#[ Sta_Transform_14 : CFunction f; Symbol x; Local test = f(,...,); Transform f addargs(1,last); Print; .end assert succeeded? assert result("test") =~ expr("f(x + x^2 + x^3 + x^4 + x^5)") *--#] Sta_Transform_14 : *--#[ Sta_Transform_15 : CFunction f; Symbol x; Local test = f(,...,); Transform f mulargs(1,last); Print; .end assert succeeded? assert result("test") =~ expr("f(x^15)") *--#] Sta_Transform_15 : *--#[ Sta_Transform_16 : CFunction f,g; Symbol x; Local test = f(1,...,5) + g(1,...,5); Transform f dropargs(2,4); Transform g dropargs(1,last); Print; .end assert succeeded? assert result("test") =~ expr("f(1,5) + g") *--#] Sta_Transform_16 : *--#[ Sta_Transform_17 : CFunction f,g; Symbol x; Local test = f(1,...,5) + g(1,...,5); Transform f selectargs(2,4); Transform g selectargs(1,last); Print; .end assert succeeded? assert result("test") =~ expr("f(2,3,4) + g(1,2,3,4,5)") *--#] Sta_Transform_17 : *--#[ Sta_TryReplace_1 : Symbol x,y,z; Local test = x+z; * These will replace x by y but not z by y, because z * comes before y in the default sort ordering: TryReplace x,y; TryReplace z,y; Print; .end assert succeeded? assert result("test") =~ expr("z+y") *--#] Sta_TryReplace_1 : *--#[ Sta_While_1 : Symbol x,y,z; Local Fx = (1+x)^6; Local Fy = (1+y)^6; Local Fz = (1+z)^6; While (Count(x,1) > 3); Multiply 1/x; EndWhile; Repeat; If (Count(y,1) > 3); Multiply 1/y; EndIf; EndRepeat; While (Count(z,1) > 3) Multiply 1/z; Print; .end assert succeeded? assert result("Fx") =~ expr("1 + 6*x + 15*x^2 + 42*x^3"); assert result("Fy") =~ expr("1 + 6*y + 15*y^2 + 42*y^3"); assert result("Fz") =~ expr("1 + 6*z + 15*z^2 + 42*z^3"); *--#] Sta_While_1 : *--#[ Fun_distrib_1 : Symbols x1,...,x4; CFunctions f,f1,f2; Local F = f(x1,...,x4); id f(?a) = distrib_(-1,2,f1,f2,?a); Print +s; .end assert succeeded? assert result("F") =~ expr(" + f1(x1,x2)*f2(x3,x4) - f1(x1,x3)*f2(x2,x4) + f1(x1,x4)*f2(x2,x3) + f1(x2,x3)*f2(x1,x4) - f1(x2,x4)*f2(x1,x3) + f1(x3,x4)*f2(x1,x2) ") *--#] Fun_distrib_1 : *--#[ Fun_exteuclidean_1 : Symbols x1,x2,x3,x4; Local F = exteuclidean_(54,84); Print; .sort id exteuclidean_(x1?,x2?,x3?,x4?) = x1*x3+x2*x4; Print; .end assert succeeded? assert result("F", 0) =~ expr("exteuclidean_(54,84,-3,2)") assert result("F", 1) =~ expr("6") *--#] Fun_exteuclidean_1 : *--#[ Fun_exteuclidean_2 : Symbols x1,x2,x3,x4,a,b; Local F = exteuclidean_(97,101); Print; .sort id exteuclidean_(x1?,x2?,x3?,x4?) = x1*x3+x2*x4 +a*mod2_(1/97,101)+b*mod2_(1/101,97); Print; .end assert succeeded? assert result("F", 0) =~ expr("exteuclidean_(97,101,25,-24)") assert result("F", 1) =~ expr("1 - 24*b + 25*a") *--#] Fun_exteuclidean_2 : *--#[ Fun_makerational_1 : #$m = prime_(1); #write <> "The prime number is %$",$m L F = MakeRational_(12345678,$m); Print; .sort Modulus `$m'; Print; .end assert succeeded? if wordsize == 2 assert stdout =~ /The prime number is 32719/ assert result("F", 0) =~ expr("127/37") assert result("F", 1) =~ expr("10615") elsif wordsize == 4 assert stdout =~ /The prime number is 2147483587/ assert result("F", 0) =~ expr("9719/38790") assert result("F", 1) =~ expr("12345678") end *--#] Fun_makerational_1 : *--#[ Fun_perm_1 : CFunction f; Symbols x1,...,x3; Local F = perm_(f,x1,x2,x3); Print +s; .end assert succeeded? assert result("F") =~ expr(""" + f(x1,x2,x3) + f(x1,x3,x2) + f(x2,x1,x3) + f(x2,x3,x1) + f(x3,x1,x2) + f(x3,x2,x1) """) *--#] Fun_perm_1 : *--#[ Fun_prime_1 : Symbols x1,x2,x3,x4; ON highfirst; Local F = x1*prime_(1)+x2*prime_(2) +x3*prime_(3)+x4*prime_(4); Print; .end assert succeeded? if wordsize == 2 assert result("F") =~ expr("32719*x1 + 32717*x2 + 32713*x3 + 32707*x4") elsif wordsize == 4 assert result("F") =~ expr("2147483587*x1 + 2147483579*x2 + 2147483563*x3 + 2147483549*x4") end *--#] Fun_prime_1 : *--#[ Fun_putfirst_1 : S a,a1,...,a10; CF f,g; L F = g(a,a1,...,a10); id g(?a) = putfirst_(f,4,?a); Print; .end assert succeeded? assert result("F") =~ expr(" f(a3,a,a1,a2,a4,a5,a6,a7,a8,a9,a10) ") *--#] Fun_putfirst_1 : *--#[ Fun_ranperm_1 : Function f; Symbols x1,...,x5; Local F = ranperm_(f,1,2,3,4,5,6) +ranperm_(f,x1,x2,x3+x1,x4,x5); Print +s; .end assert succeeded? # We can't predict the results! *--#] Fun_ranperm_1 : *--#[ Fun_sump_1 : Symbol i,x; Local F = sump_(i,0,5,x/i); Print; .end assert succeeded? assert result("F") =~ expr("1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5") *--#] Fun_sump_1 : *--#[ Brackets_1 : Symbols a,b,c,x; L F = a*x^2+b*x+c; B x; .sort L Discriminant = F[x]^2-4*F[x^2]*F[1]; Print; .end assert succeeded? assert result("Discriminant") =~ pattern("b^2-4*a*c"); *--#] Brackets_1 : *--#[ PolyandFact_1 : Symbol x,y; CFunction rat; PolyRatFun rat; L F = rat(x+y,x-y)+rat(x-y,x+y); Print; .end assert succeeded? assert result("F") =~ expr("rat(2*x^2 + 2*y^2,x^2 - y^2)") *--#] PolyandFact_1 : *--#[ PolyandFact_2 : * TODO: change the result in the manual. Symbol x,y; CFunction f1,f2; Local F = f1(x^4-y^4)+f2(3*y^4-3*x^4); FactArg,f1,f2; Print; .end assert succeeded? assert result("F") =~ expr("f1(-1,y - x,y + x,y^2 + x^2) + f2(3,y - x,y + x,y^2 + x^2)") *--#] PolyandFact_2 : *--#[ PolyandFact_3 : * TODO: change the the first result in the manual. Symbol x,y; CFunction f1,f2; Local F = f2(3*y^4-3*x^4); FactArg,f2; Print; .sort ChainOut,f2; id f2(x?number_) = x; Print; .end assert succeeded? assert result("F", 0) =~ expr("f2(3,y - x,y + x,y^2 + x^2)") assert result("F", 1) =~ expr("3*f2(y-x)*f2(y+x)*f2(y^2+x^2)") *--#] PolyandFact_3 : *--#[ PolyandFact_4 : Symbol x,y; Local F = x^4-y^4; Print; .sort Print; Factorize F; .end assert succeeded? assert result("F", 0) =~ expr("-y^4+x^4") assert result("F", 1) =~ expr("(-1)*(y-x)*(y+x)*(y^2+x^2)") *--#] PolyandFact_4 : *--#[ PolyandFact_5 : * TODO: change the the result of F2 in the manual. Symbol x,y; Local F1 = x^4-y^4; Local F2 = 0; Local F3 = 1; Local F4 = x^4-y^4; Print; Factorize F1,F2,F3; .sort #do i = 1,4 #$n`i' = numfactors_(F`i'); #message expression F`i' has `$n`i'' factors #enddo .end assert succeeded? assert result("F1") =~ expr("(-1)*(y-x)*(y+x)*(y^2+x^2)") assert result("F2") =~ expr("(0)") assert result("F3") =~ expr("(1)") assert result("F4") =~ expr("-y^4+x^4") assert stdout =~ /~~~expression F1 has 4 factors/ assert stdout =~ /~~~expression F2 has 1 factors/ assert stdout =~ /~~~expression F3 has 1 factors/ assert stdout =~ /~~~expression F4 has 0 factors/ *--#] PolyandFact_5 : *--#[ PolyandFact_6 : Symbol x,y; Local F = x^4-y^4; Factorize F; .sort #$n = numfactors_(F); #do i = 1,`$n' Local F`i' = F[factor_^`i']; #enddo Print; .end assert succeeded? assert result("F") =~ expr("(-1)*(y-x)*(y+x)*(y^2+x^2)") assert result("F1") =~ expr("-1") assert result("F2") =~ expr("y-x") assert result("F3") =~ expr("y+x") assert result("F4") =~ expr("y^2+x^2") *--#] PolyandFact_6 : *--#[ PolyandFact_7 : Symbol x,y; LocalFactorize E = -(x+1)*(x+2)*((x+3)*(x+4)); Print; .end assert succeeded? assert result("E") =~ expr(" ( - 1 ) * ( 1 + x ) * ( 2 + x ) * ( 12 + 7*x + x^2 ) ") *--#] PolyandFact_7 : *--#[ PolyandFact_8 : Symbol x,y; LocalFactorize E = -(x+1)*(x+2)*((x+3)*(x+4)); Local F = -(x+1)*(x+2)*((x+3)*(x+4)); Print; .sort LF G = (x-1)*(x+2)^2*E^2*F^2; Print G; .end assert succeeded? assert result("E") =~ expr(" (-1) *(1+x) *(2+x) *(12+7*x+x^2) ") assert result("F") =~ expr(" -24-50*x-35*x^2-10*x^3-x^4 ") assert result("G") =~ expr(" (-1+x) *(2+x) *(2+x) *(-1) *(1+x) *(2+x) *(12+7*x+x^2) *(-1) *(1+x) *(2+x) *(12+7*x+x^2) *(-24-50*x-35*x^2-10*x^3-x^4) *(-24-50*x-35*x^2-10*x^3-x^4) ") *--#] PolyandFact_8 : *--#[ PolyandFact_9 : Symbol x,y; LocalFactorize E = -(x+1)*(x+2)*((x+3)*(x+4)); Local F = -(x+1)*(x+2)*((x+3)*(x+4)); .sort LF G = (x-1)*(x+2)^2*E^2*F^2; Print G; Factorize G; .end assert succeeded? assert result("G") =~ expr(" (-1+x) *(1+x) *(1+x) *(1+x) *(1+x) *(2+x) *(2+x) *(2+x) *(2+x) *(2+x) *(2+x) *(3+x) *(3+x) *(3+x) *(3+x) *(4+x) *(4+x) *(4+x) *(4+x) ") *--#] PolyandFact_9 : *--#[ PolyandFact_10 : Symbol x,y; LocalFactorize E = -0*(x+1)*(x+2)*0*((x+3)*(x+4)); Print; .end assert succeeded? assert result("E") =~ expr(" (-1) *(0) *(1+x) *(2+x) *(0) *(12+7*x+x^2) ") *--#] PolyandFact_10 : *--#[ PolyandFact_11 : Symbol x,y; Format Nospaces; LocalFactorize E = -0*3*(x+1)*(x+2)/2*0*((x+3)*(x+4)); Print; .sort Print; Factorize(keepzero) E; .end assert succeeded? assert result("E", 0) =~ expr(" (-1) *(0) *(3) *(1+x) *(2+x) *(1/2) *(0) *(12+7*x+x^2) ") assert result("E", 1) =~ expr(" (0) *(-3/2) *(1+x) *(2+x) *(3+x) *(4+x) ") *--#] PolyandFact_11 : *--#[ PolyandFact_12 : Symbol x,y; LFactorized F = (x+1)*(x+y)*(y+1); Print; .sort Print; Bracket x; UnFactorize F; .end assert succeeded? assert result("F", 0) =~ expr(" (1+x) *(y+x) *(1+y) ") assert result("F", 1) =~ expr(" +x*(1+2*y+y^2) +x^2*(1+y) +y+y^2 ") *--#] PolyandFact_12 : *--#[ PolyandFact_13 : Symbol x,y; LFactorized F = (x+1)*(x+y)*(y+1); Print; .sort #$num = numfactors_(F); Local G = *...*; Bracket x; Print; .end assert succeeded? assert result("F", 0) =~ expr(" (1+x) *(y+x) *(1+y) ") assert result("F", 1) =~ expr(" (1+x) *(y+x) *(1+y) ") assert result("G") =~ expr(" +x*(1+2*y+y^2) +x^2*(1+y) +y+y^2 ") *--#] PolyandFact_13 : *--#[ PolyandFact_14 : Symbol x,y; CFunction f; Off Statistics; #$a = x^4-y^4; Local F = f(x^4-y^4)+f(x^6-y^6); Print; .sort #factdollar $a; #do i = 1,`$a[0]' #write <> "Factor `i' of `$a' is `$a[`i']'" #enddo id f(x?$b) = f(x); FactDollar $b; do $i = 1,$b[0]; Print "Factor %$ of %$ is %$",$i,$b,$b[$i]; enddo; Print; ModuleOption noparallel; * suppresses noparallel warning .end assert succeeded? assert result("F", 0) =~ expr(" f(-y^4+x^4)+f(-y^6+x^6) ") assert result("F", 1) =~ expr(" f(-y^4+x^4)+f(-y^6+x^6) ") assert stdout =~ exact_pattern(" Factor 1 of -y^4+x^4 is -1 #enddo Factor 2 of -y^4+x^4 is y-x Factor 3 of -y^4+x^4 is y+x Factor 4 of -y^4+x^4 is y^2+x^2 id f(x?$b) = f(x); ") assert stdout =~ exact_pattern(" Factor 1 of - y^4 + x^4 is - 1 Factor 2 of - y^4 + x^4 is y - x Factor 3 of - y^4 + x^4 is y + x Factor 4 of - y^4 + x^4 is y^2 + x^2 Factor 1 of - y^6 + x^6 is - 1 Factor 2 of - y^6 + x^6 is y - x Factor 3 of - y^6 + x^6 is y + x Factor 4 of - y^6 + x^6 is y^2 - x*y + x^2 Factor 5 of - y^6 + x^6 is y^2 + x*y + x^2 ") *--#] PolyandFact_14 : *--#[ PolyandFact_15 : Symbol x,y; CFunction f; Format Nospaces; #$a = x^4-y^4; #factdollar $a; Local F = f(numfactors_($a)) +f(<$a[1]>,...,<$a[`$a[0]']>); Print; .end assert succeeded? assert result("F", 0) =~ expr(" f(-1,y-x,y+x,y^2+x^2)+f(4) ") *--#] PolyandFact_15 : *--#[ PolyandFact_16 : Symbol x,y; Format NoSpaces; On ShortStats; Local F1 = x^60-1; Local F2 = y^60-x^60; Factorize F1,F2; Print; .end if wordsize < 4 # ERROR: polynomials too large (> WORDSIZE) else assert succeeded? assert result("F1") =~ expr(" (-1+x) *(1-x+x^2) *(1-x+x^2-x^3+x^4) *(1-x+x^3-x^4+x^5-x^7+x^8) *(1+x) *(1+x+x^2) *(1+x+x^2+x^3+x^4) *(1+x-x^3-x^4-x^5+x^7+x^8) *(1-x^2+x^4) *(1-x^2+x^4-x^6+x^8) *(1+x^2) *(1+x^2-x^6-x^8-x^10+x^14+x^16) ") assert result("F2") =~ expr(" (y-x) *(y+x) *(y^2-x*y+x^2) *(y^4-x*y^3+x^2*y^2-x^3*y+x^4) *(y^4+x*y^3+x^2*y^2+x^3*y+x^4) *(y^2+x*y+x^2) *(y^2+x^2) *(y^8-x*y^7+x^3*y^5-x^4*y^4+x^5*y^3-x^7*y+x^8) *(y^8+x*y^7-x^3*y^5-x^4*y^4-x^5*y^3+x^7*y+x^8) *(y^8-x^2*y^6+x^4*y^4-x^6*y^2+x^8) *(y^4-x^2*y^2+x^4) *(y^16+x^2*y^14-x^6*y^10-x^8*y^8-x^10*y^6+x^14*y^2+x^16) ") end *--#] PolyandFact_16 : *--#[ PolyandFact_17 : Symbols a,b; LF F = (a+b)^2; multiply 2; Print; .end assert succeeded? assert result("F") =~ expr(" ( 2*b + 2*a ) * ( 2*b + 2*a ) ") *--#] PolyandFact_17 : *--#[ PolyandFact_18 : Symbols a,b; LF F = (a+b)^2; .sort LF F = 2*F; Print; .end assert succeeded? assert result("F") =~ expr(" ( 2 ) * ( b + a ) * ( b + a ) ") *--#] PolyandFact_18 : *--#[ OutputOptimization_1 : CF f; S a,b,c; L H = f(a)+f(b)+(a+b+c)^2; L G = f(c)+(a+b+c)^3; Format O2; Print +f; .sort ExtraSymbols,array,w; Format Fortran; #optimize G #write " REAL*8 w(`optimmaxvar_')" #write "%O" #write " G = %e",G #clearoptimize .sort #optimize H #write " REAL*8 w(`optimmaxvar_')" #write "%O" #write " H = %e",H .end assert succeeded? if serial? # TFORM may optimize the expressions in a different way. assert file("outg.f") == <<-'EOF' REAL*8 w(4) w(1)=f(c) w(2)=c**2 w(3)=3*c + b w(3)=b*w(3) w(3)=3*w(2) + w(3) w(3)=b*w(3) w(4)=2*c + b w(4)=b*w(4) w(2)=w(2) + w(4) w(4)=c + b w(4)=3*w(4) + a w(4)=a*w(4) w(2)=3*w(2) + w(4) w(2)=a*w(2) w(4)=c**3 G = w(1) + w(2) + w(3) + w(4) EOF assert file("outh.f") == <<-'EOF' REAL*8 w(5) w(1)=f(a) w(2)=f(b) w(3)=c**2 w(4)=2*c + b w(4)=b*w(4) w(5)=c + b w(5)=2*w(5) + a w(5)=a*w(5) H = w(1) + w(2) + w(3) + w(4) + w(5) EOF end *--#] OutputOptimization_1 : *--#[ Dictionaries_1 : Symbols x1,y2,z3,N; Indices mu,nu,ro,si; Tensor tens; CFunction S,R,f; ExtraSymbols array w; #OpenDictionary test #add x1: "x_1" #add y2: "y^{(2)}" #add z3: "{\cal Z}" #add *: " " #add S(R(1),N): "S_1(N)" #add S(R(2),N): "S_2(N)" #add S(R(1,1),N): "S_{1,1}(N)" #add f: "\ln" #add mu: "\mu" #add nu: "\nu" #add ro: "\rho" #add si: "\sigma" #add tens: "T" #CloseDictionary Local F = x1*y2*z3 + S(R(1),N) + S(R(1,1),N) + S(R(2),N) + tens(mu,nu,ro,si) + f(x1+1); #usedictionary test Print +s; .end assert succeeded? assert result("F") =~ expr(" + x_1 y^2 {\\cal Z} + T(\\mu,\\nu,\\rho,\\sigma) + S_1(N) + S_{1,1}(N) + S_2(N) + \\ln(1 + x_1) ") *--#] Dictionaries_1 : *--#[ Dictionaries_2 : Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "TWO" #add 5: "FIVE" #add 7: "SEVEN" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers Print; .end assert succeeded? assert stdout =~ exact_pattern(" F = & 1/SEVEN*x + 1/TWO*x**2 + x**3 + FIVE/4*x**4 + x**5 + 1/TWO*x**6 & + 1/SEVEN*x**7 + 1.D0/56.D0*x**8 ") *--#] Dictionaries_2 : *--#[ Dictionaries_3 : Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "TWO" #add 5: "FIVE" #add 7: "SEVEN" #add 1/2: "HALF" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers Print; .end assert succeeded? assert stdout =~ exact_pattern(" F = & 1/SEVEN*x + HALF*x**2 + x**3 + FIVE/4*x**4 + x**5 + HALF*x**6 + & 1/SEVEN*x**7 + 1.D0/56.D0*x**8 ") *--#] Dictionaries_3 : *--#[ Dictionaries_4 : Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "TWO" #add 5: "FIVE" #add 7: "SEVEN" #add 1/2: "HALF" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers (warnings) Print; .end assert succeeded? assert stdout =~ exact_pattern(" F = & 1/SEVEN*x + HALF*x**2 + x**3 + FIVE/4*x**4 + x**5 + HALF*x**6 + >>>>>>>>Could not translate coefficient with dictionary numbers<<<<<<<<< <<< & 1/SEVEN*x**7 + 1.D0/56.D0*x**8 ") *--#] Dictionaries_4 : *--#[ Dictionaries_5 : Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "cd2" #add 5: "cd5" #add 7: "cd7" #add 56: "cd56" #add 1/2: "c1d2" #add 5/4: "c5d4" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers (warnings) Print; .end assert succeeded? assert stdout =~ exact_pattern(" F = & 1/cd7*x + c1d2*x**2 + x**3 + c5d4*x**4 + x**5 + c1d2*x**6 + 1/ & cd7*x**7 + 1/cd56*x**8 ") *--#] Dictionaries_5 : *--#[ Dictionaries_6 : Symbol x; CFunction f; #OpenDictionary ranges #add (1,2): "w(%#)" #add (3): "ww(%#)" #add (4,6): "www(%@)" #CloseDictionary Local F = +...+; ToPolynomial; Print; .sort #UseDictionary ranges Print; .end assert succeeded? assert result("F", 0) =~ expr(" x*Z1_ + x^2*Z2_ + x^3*Z3_ + x^4*Z4_ + x^5*Z5_ + x^6*Z6_ ") assert result("F", 1) =~ expr(" x*w(1) + x^2*w(2) + x^3*ww(3) + x^4*www(1) + x^5*www(2) + x^6*www(3) ") *--#] Dictionaries_6 : *--#[ DiracAlgebra_1 : * * Symmetric trace of a gamma5 and 12 regular matrices * I m1,...,m12; F G5,g1,g2; L F = G5(m1,...,m12); id G5(?a) = distrib_(-1,4,g1,g2,?a); id g1(?a) = e_(?a); id g2(?a) = g_(1,?a); tracen,1; .end assert succeeded? assert stdout =~ /Generated terms = 51975$/ assert stdout =~ /Terms in output = 51975$/ assert bytesize("F") == 459582 * wordsize *--#] DiracAlgebra_1 : *--#[ DiracAlgebra_2 : * * Regular trace of a gamma5 and 12 regular matrices * I m1,...,m12; L F = g_(1,5_,m1,...,m12); trace4,1; .end assert succeeded? assert @stdout =~ /Generated terms = 1053$/ assert @stdout =~ /Terms in output = 1029$/ assert bytesize("F") == 10142 * wordsize *--#] DiracAlgebra_2 : *--#[ NotesMetric_1 : Indices m1,m2,m3,n1,n2,n3,i1,i2,i3; Cfunction eta(symmetric),e(antisymmetric); Off Statistics; * * We have our own Levi-Civita tensor e * Local F = e(m1,m2,m3)*e(m1,m2,m3); * * We write the contraction as * id e(m1?,m2?,m3?)*e(n1?,n2?,n3?) = e_(m1,m2,m3)*e_(i1,i2,i3)* eta(n1,i1)*eta(n2,i2)*eta(n3,i3); * * Now we can use the internal workings of the contract: * Contract; Print +s; .sort; * * For specifying a metric we need individual components: * Sum i1,1,2,3; Sum i2,1,2,3; Sum i3,1,2,3; Print +s; .sort; * * And now we can provide the metric tensor * id eta(1,1) = 1; id eta(2,2) = 1; id eta(3,3) = -1; id eta(1,2) = 0; id eta(1,3) = 0; id eta(2,3) = 0; Print +s; .end assert succeeded? assert result("F",0) =~ expr(<<-EOF + eta(i1,i1)*eta(i2,i2)*eta(i3,i3) - eta(i1,i1)*eta(i2,i3)^2 - eta(i1,i2)^2*eta(i3,i3) + 2*eta(i1,i2)*eta(i1,i3)*eta(i2,i3) - eta(i1,i3)^2*eta(i2,i2) EOF ) assert result("F",1) =~ expr(<<-EOF + 6*eta(1,1)*eta(2,2)*eta(3,3) - 6*eta(1,1)*eta(2,3)^2 - 6*eta(1,2)^2*eta(3,3) + 12*eta(1,2)*eta(1,3)*eta(2,3) - 6*eta(1,3)^2*eta(2,2) EOF ) assert result("F") =~ expr("-6") *--#] NotesMetric_1 : *--#[ NotesMetric_2 : Indices i1,i2,i3; FixIndex 1:1,2:1,3:-1; Off Statistics; * Local F = e_(i1,i2,i3)*e_(i1,i2,i3); Sum i1,1,2,3; Sum i2,1,2,3; Sum i3,1,2,3; Print +s; .sort Contract; Print +s; .end assert succeeded? assert result("F",0) =~ expr("+6*e_(1,2,3)*e_(1,2,3)") assert result("F") =~ expr("-6") *--#] NotesMetric_2 : *--#[ NotesMetric_3 : Indices i1=0,i2=0,i3=0; FixIndex 1:1,2:1,3:-1; Off Statistics; * Local F = e_(i1,i2,i3)*e_(i1,i2,i3); Contract; Print +s; .sort Sum i1,1,2,3; Sum i2,1,2,3; Sum i3,1,2,3; Print +s; .end assert succeeded? assert result("F",0) =~ expr(<<-EOF + d_(i1,i1)*d_(i2,i2)*d_(i3,i3) - d_(i1,i1)*d_(i2,i3)*d_(i2,i3) - d_(i1,i2)*d_(i1,i2)*d_(i3,i3) + 2*d_(i1,i2)*d_(i1,i3)*d_(i2,i3) - d_(i1,i3)*d_(i1,i3)*d_(i2,i2) EOF ) assert result("F") =~ expr("-6") *--#] NotesMetric_3 : *--#[ ExtComm_1 : symbol a,b; #external "n1" cat -u #external "n2" cat -u * cat simply repeats its input. The default prompt is an * empty line. So we use "\n\n" here -- one "\n" is to finish * the line, and the next "\n" is the prompt: #toexternal "(a+b)^2\n\n" #setexternal `n1' * For this channel the prompt will be "READY\n": #toexternal "(a+b)^3\nREADY\n" #setexternal `n2' * Set the default prompt: #prompt Local aPLUSbTO2= #fromexternal ; #setexternal `n1' #prompt READY Local aPLUSbTO3= #fromexternal ; #rmexternal `n1' #rmexternal `n2' Print; .end #require unix? # This gives Valgrind errors (3 memory leaks) on Travis CI # (osx-gcc-valgrind-parvorm), but cleanly works on Linux with mpich 3.2. # Might be an OS- or implementation-specific bug. # Update (22 Sep 2017): Now I see even for Linux (both on Travis CI and # a desktop PC) each child process leads to 1 memory leak. Best to skip this # test for Valgrind. #pend_if valgrind? assert succeeded? assert result("aPLUSbTO2") =~ expr("b^2 + 2*a*b + a^2") assert result("aPLUSbTO3") =~ expr("b^3 + 3*a*b^2 + 3*a^2*b + a^3") *--#] ExtComm_1 : form-5.0.1/check/diagrams/0000755000175100017510000000000015217035744011077 5form-5.0.1/check/diagrams/diagrams.h0000644000175100017510000007501115217035721012756 ** * Enable verbose output. * *#define FormDiagramsVerbose ** * Enable cache read and write. * *#define FormDiagramsCacheRead *#define FormDiagramsCacheWrite ** * Skip cache existence check. * *#define FormDiagramsCacheSkipCheck ** * Specify the cache directory. * *#define FormDiagramsCacheDir "CACHE_DIRECTORY_PATH" ** * Terminate with a non-zero status if any validation check fails. * *#define FormDiagramsRaiseError ** * Override options used by DoComparison(). * * For example, to generate the cache if it does not exist, one can set it * via the -D option or the environment variable: * FormDiagramsOptionOverrides=cacheread,cachewrite,nocacheskipcheck,raiseerror * *#define FormDiagramsOptionOverrides #ifndef `FormDiagramsCacheDir' #define FormDiagramsCacheDir "./.diagrams_cache" #endif #ifdef `TESTFILEDIR' #redefine FormDiagramsCacheDir "`TESTFILEDIR'/.diagrams_cache" #endif #define MaxLegs "9" #define MaxPropagators "19" #define CurrentModel "" #define Bosons "" #define AntiParticles "" #define QgrafStyleFile "qgraf.sty" #define QgrafModelFile "qgraf.mdl" #define QgrafInputFile "qgraf.dat" #define QgrafOutputFile "qgraf.out" #define FeynGraphTemplateFile "feyngraph.jinja" #define FeynGraphInputFile "feyngraph.toml" #define FeynGraphOutputFile "diagrams.out" #define QgrafVersion "" #define FeynGraphVersion "" Format nospaces; Format 255; * Note that the momentum convention is that all momenta are incoming. * - Incoming particles are assigned momenta p1, p2, ... * - Outgoing particles are assigned momenta -q1, -q2, ... * - Internal particles are assigned momenta k1, k2, ... S n1,n2,x1,x2; CF topo,node,counter,coeff,vx,vxs(symmetric),acc,replace; V p1,...,p`MaxLegs',q1,...,q`MaxLegs',k1,...,k`MaxPropagators',l1,...,l`MaxPropagators'; Set kk:k1,...,k`MaxPropagators'; Set ll:l1,...,l`MaxPropagators'; #OpenDictionary wildmom #do i = 1, `MaxPropagators' #add k`i': "k`i'?$k`i'" #enddo #CloseDictionary #do i = 1, `MaxPropagators' #$k`i' = 0; #enddo Model TEMP; Particle f1; Particle f2; EndModel; *--#[ SetupPhi3Model : SetupPhi3Model() ** * Prepares the PHI3 model. * #procedure SetupPhi3Model() #define filename "`QgrafModelFile'" #create <`filename'> #write <`filename'> "[phi,phi,+]" #write <`filename'> "[phi,phi,phi]" #close <`filename'> Model PHI3; Particle phi,1; Vertex phi,phi,phi:g; EndModel; #redefine CurrentModel "PHI3" #redefine Bosons "phi" #redefine AntiParticles "" #endprocedure *--#] SetupPhi3Model : *--#[ SetupPhi4Model : SetupPhi4Model() ** * Prepares the PHI4 model. * #procedure SetupPhi4Model() #define filename "`QgrafModelFile'" #create <`filename'> #write <`filename'> "[phi,phi,+]" #write <`filename'> "[phi,phi,phi,phi]" #close <`filename'> Model PHI4; Particle phi,1; Vertex phi,phi,phi,phi:g^2; EndModel; #redefine CurrentModel "PHI4" #redefine Bosons "phi" #redefine AntiParticles "" #endprocedure *--#] SetupPhi4Model : *--#[ SetupPhi34Model : SetupPhi34Model() ** * Prepares the PHI34 model. * #procedure SetupPhi34Model() #define filename "`QgrafModelFile'" #create <`filename'> #write <`filename'> "[phi,phi,+]" #write <`filename'> "[phi,phi,phi]" #write <`filename'> "[phi,phi,phi,phi]" #close <`filename'> Model PHI34; Particle phi,1; Vertex phi,phi,phi:g; Vertex phi,phi,phi,phi:g^2; EndModel; #redefine CurrentModel "PHI34" #redefine Bosons "phi" #redefine AntiParticles "" #endprocedure *--#] SetupPhi4Model : *--#[ SetupQcdModel : SetupQcdModel() ** * Prepares the QCD model. * #procedure SetupQcdModel() #define filename "`QgrafModelFile'" #create <`filename'> #write <`filename'> "[qua,QUA,-]" #write <`filename'> "[glu,glu,+]" #write <`filename'> "[gho,GHO,-]" #write <`filename'> "[QUA,qua,glu]" #write <`filename'> "[glu,glu,glu]" #write <`filename'> "[glu,glu,glu,glu]" #write <`filename'> "[GHO,gho,glu]" #close <`filename'> Model QCD; Particle qua,QUA,-2; Particle gho,GHO,-1; Particle glu,+3; Vertex QUA,qua,glu:g; Vertex GHO,gho,glu:g; Vertex glu,glu,glu:g; Vertex glu,glu,glu,glu:g^2; EndModel; #redefine CurrentModel "QCD" #redefine Bosons "glu" #redefine AntiParticles "QUA,GHO" #endprocedure *--#] SetupQcdModel : *--#[ SetupQcdbModel : SetupQcdbModel() ** * Prepares the QCD model with the background field. * #procedure SetupQcdbModel() #define filename "`QgrafModelFile'" #create <`filename'> #write <`filename'> "[qua,QUA,-]" #write <`filename'> "[glu,glu,+]" #write <`filename'> "[gho,GHO,-]" #write <`filename'> "[back,back,+,external]" #write <`filename'> "[QUA,qua,glu]" #write <`filename'> "[GHO,gho,glu]" #write <`filename'> "[glu,glu,glu]" #write <`filename'> "[glu,glu,glu,glu]" #write <`filename'> "[QUA,qua,back]" #write <`filename'> "[GHO,gho,back]" #write <`filename'> "[GHO,gho,back,glu]" #write <`filename'> "[back,glu,glu]" #write <`filename'> "[back,glu,glu,glu]" #close <`filename'> Model QCDB; Particle qua,QUA,-2; Particle gho,GHO,-1; Particle glu,+3; Particle back,+3,external; Vertex QUA,qua,glu:g; Vertex GHO,gho,glu:g; Vertex glu,glu,glu:g; Vertex glu,glu,glu,glu:g^2; Vertex QUA,qua,back:g; Vertex GHO,gho,back:g; Vertex GHO,gho,back,glu:g^2; Vertex back,glu,glu:g; Vertex back,glu,glu,glu:g^2; EndModel; #redefine CurrentModel "QCDB" #redefine Bosons "glu,back" #redefine AntiParticles "QUA,GHO" #endprocedure *--#] SetupQcdbModel : *--#[ MakeDiagrams : MakeDiagrams(numIn,numOut) ** * Manipulates diagrams for further manipulation. * * Parameters * ---------- * numIn: positive integer * The number of incoming particles. * numOut: positive integer * The number of outgoing particles. * * Example Input * ------------- * topo_(1) * *node_(1,1,QUA(-p1)) * *node_(2,1,qua(-q1)) * *node_(3,g,QUA(k2),qua(p1),glu(k1)) * *node_(4,g,QUA(q1),qua(-k2),glu(-k1)) * * vx(QUA(-2),qua(1),glu(2)) * *vx(QUA(1),qua(-1),glu(2)) * * Example Output * -------------- * node(QUA(q1),qua(-k2),glu(-k1)) * *node(QUA(k2),qua(p1),glu(k1)) * #procedure MakeDiagrams(numIn,numOut) * for diagrams_ multiply replace_(topo_,dummy_); id node_(n1?,n2?,?a) = node_(?a); id node_(f1?(p1?)) = 1; multiply replace_(node_,node); * for QGRAF * Incoming fields have indices -1, -3, -5, ..., - 2j+1, ... * Outgoing fields have indices -2, -4, -6, ..., - 2j, ... * See the manual of QGRAF section 5.1 "The indices". #do i = 1, `numIn' repeat id vx(?a,f1?(1-2*`i'),?b) = vx(?a,f1(p`i'),?b); #enddo #do i = 1, `numOut' repeat id vx(?a,f1?(-2*`i'),?b) = vx(?a,f1(q`i'),?b); #enddo repeat id vx(?a,f1?(-1),?b) = vx(?a,f1(p1),?b); repeat id vx(?a,f1?(-2),?b) = vx(?a,f1(q1),?b); multiply counter(1); repeat id vx(?a,f1?(n1?),?b) * vx(?c,f2?(n1?),?d) * counter(n2?) = vx(?a,f1(kk[n2]),?b) * vx(?c,f2(-kk[n2]),?d) * counter(n2+1); repeat id vx(?a,f1?(n1?),?b,f2?(n1?),?c) * counter(n2?) = vx(?a,f1(kk[n2]),?b,f2(-kk[n2]),?c) * counter(n2+1); multiply replace_(counter,dummy_); multiply replace_(vx,node); #ifdef `FormDiagramsVerbose' P +sss; #endif .sort:mkdiag; #endprocedure *--#] MakeDiagrams : *--#[ CanonicalizeDiagrams : CanonicalizeDiagrams() ** * Canonicalizes diagrams. * * This procedure attaches a unique topology ID and reassigns * the loop momenta k1, k2, ... in a canonical way. * * Example Input * ------------- * node(QUA(q1),qua(-k2),glu(-k1)) * *node(QUA(k2),qua(p1),glu(k1)) * * Example Output * -------------- * topo(1) * *node(QUA(q1),qua(-k1),glu(k2)) * *node(QUA(k1),qua(p1),glu(-k2)) * #procedure CanonicalizeDiagrams() #define numactiveexprs "`numactiveexprs_'" #define activeexprnames "`activeexprnames_'" * Label each term uniquely. #$counter = 0; #define i "0" #do e = {`activeexprnames',} #ifdef `e' #redefine i "{`i'+1}" #$counter`i' = 0; inexpression `e'; $counter`i' = $counter`i' + 1; $counter = $counter`i'; multiply counter($counter`i'); goto end; endinexpression; #endif #enddo #undefine i label end; * Save the current numerical coefficient. putinside coeff,xarg_; B node; ModuleOption maximum, $counter; #do i = 1, `numactiveexprs' ModuleOption local, $counter`i'; #enddo Moduleoption inparallel; .sort:canondiag-1; * Extract vertex structure into acc(vxs(v1,...)*...). Keep Brackets; id node(?a) = node(?a) * vxs(?a); argument vxs; id f1?(p1?) = p1; endargument; multiply acc(1); multiply replace_(vxs,vx); id vx(?a) = acc(vxs(?a)); repeat id acc(x1?) * acc(x2?) = acc(x1 * x2); B acc; .sort:canondiag-2; #do e = {`activeexprnames',} #ifdef `e' CreateSpectator [`e'.spec], "`e'.`PID_'.spec"; #endif #enddo #$numtopo = 0; #do loop = 1, 1 * Find a new topology. Keep Brackets; #$found = 0; if ($found == 0); if (match(acc(x1?$x1))); $found = 1; $numtopo = $numtopo + 1; $topo = $x1; inside $x1; $numv = count_(vxs,1); endinside; endif; endif; B acc; ModuleOption noparallel; .sort:canondiag-3-{`$numtopo'+1}; #if `$found' * Try to match the topology with the current term in all possible ways. Keep Brackets; #$found = 0; $replaced = 0; argument acc; #UseDictionary wildmom($) if ((count(vxs,1) == `$numv') && match(`$topo')); #CloseDictionary $found = 1; $replaced = 1; $t = term_; inside $t; id all, $topo * replace_(,...,) = $topo * *...*; multiply replace_(vxs,dummy_); id replace(-k1?vector_,k2?) = replace(k1,-k2); chainin replace; multiply replace_(,...,); endinside; multiply replace_(vxs,dummy_); multiply topo(`$numtopo'); multiply $t; endif; endargument; if ($replaced); id acc(x1?) = x1; endif; ModuleOption maximum, $found; ModuleOption local, $t, $replaced, <$k1>,...,<$k`MaxPropagators'>; .sort:canondiag-4-`$numtopo'; #if `$found' * Perform all the generated replacements. #redefine loop "0" id ifnomatch-> notreplaced, replace(?a) = replace_(?a); #do e = {`activeexprnames',} #ifdef `e' inexpression `e'; tospectator [`e'.spec]; endinexpression; #endif #enddo label notreplaced; B acc; .sort:canondiag-5-`$numtopo'; #endif #endif #enddo * Restore expressions from the spectators. #do e = {`activeexprnames',} #ifdef `e' CopySpectator [`e'.copy] = [`e'.spec]; #exchange `e',[`e'.copy] #endif #enddo .sort:canondiag-6; #do e = {`activeexprnames',} #ifdef `e' Drop [`e'.copy]; EmptySpectator [`e'.spec]; #endif #enddo * Drop duplicate terms (keep the first one). #define maxunrolling "100" #define unrolling #define i "0" #do k = 1, `$counter' #if {`k'+`maxunrolling'-1} <= `$counter' #redefine unrolling "`maxunrolling'" #else #redefine unrolling "{`$counter'-`k'+1}" #endif #do j = 0, {`unrolling'-1} if (match(counter({`k'+`j'}))); #redefine i "0" #do e = {`activeexprnames',} #ifdef `e' #redefine i "{`i'+1}" #$found`i'x`j' = 0; inexpression `e'; if ($found`i'x`j'); discard; else; $found`i'x`j' = 1; multiply replace_(counter,dummy_); tospectator [`e'.spec]; endif; endinexpression; #endif #enddo endif; #enddo #do i = 1, `numactiveexprs' #do j = 0, {`unrolling'-1} ModuleOption local, $found`i'x`j'; #enddo #enddo ModuleOption inparallel; .sort:canondiag-7-`k'; #redefine k "{`k'+`unrolling'-1}" #enddo #undefine i #if `$counter' == 0 .sort:canondiag-7; #endif * Restore expressions from the spectators. #do e = {`activeexprnames',} #ifdef `e' CopySpectator [`e'.copy] = [`e'.spec]; #exchange `e',[`e'.copy] #endif #enddo .sort:canondiag-8; #do e = {`activeexprnames',} #ifdef `e' Drop [`e'.copy]; RemoveSpectator [`e'.spec]; #endif #enddo * Restore the coefficient. dropcoefficient; id coeff(x1?) = x1; * Reorder identical boson fields at each vertex to align the momenta. #do b = {`Bosons',} #ifdef `b' * Assume that they appear in adjacent positions. repeat id node(?a,`b'(?b),`b'(?c),?d) = node(?a,`b'(?b,?c),?d); multiply replace_(`b',vxs); multiply replace_(vxs,`b'); repeat id node(?a,`b'(p1?,p2?,?b),?c) = node(?a,`b'(p1),`b'(p2,?b),?c); #endif #enddo * Align the loop momenta with the flow of particles. #ifdef `AntiParticles' #do i = 1, `MaxPropagators' if (match(node(?a,f1?{`AntiParticles'}(-k`i'),?b))); multiply replace_(k`i',-k`i'); endif; #enddo #endif .sort:canondiag-9; #endprocedure *--#] CanonicalizeDiagrams : *--#[ CompareDiagrams : CompareDiagrams(F1,F2,F0) ** * Compares diagrams in two expressions. * * The common diagrams are extracted from F1 and F2, and stored in F0. * Diagrams must consist of "topo" and "node" functions. * * Parameters * ---------- * F1, F2: expression [in/out] * The expressions to be compared. Common diagrams will be removed from * these expressions. * F0: expression [out] * The extracted common diagrams. * #procedure CompareDiagrams(F1,F2,F0) #call CanonicalizeDiagrams() B+ topo,node; .sort:compdiag-1; Keep Brackets; L `F0' = 0 #do t = `F1'; #$t = `t'; #inside $t; dropcoefficient; #endinside; #$t1 = `F1'[`$t']; #$t2 = `F2'[`$t']; #$tt = $t1 - $t2; #if termsin($tt) == 0 + (`t') #endif #enddo ; .sort:compdiag-2; L `F1' = `F1' - `F0'; L `F2' = `F2' - `F0'; #ifdef `FormDiagramsVerbose' P +sss; #endif .sort:compdiag-3; #endprocedure *--#] CompareDiagrams : *--#[ DoComparison : DoComparison(other,model,options...) ** * Performs comparison. * * Example * ------- * #call DoComparison(qgraf,qcd,in=qua,out=qua,loops=1,form_options=ONEPI_,FLOOP_,qgraf_options=onepi,floop) * #procedure DoComparison(other,model,?a) #define DiagramGenerator "`tolower_(`other')'" #switch `DiagramGenerator' #case qgraf #define DiagramGeneratorName "QGRAF" #redefine DiagramGeneratorVersion "`~QgrafVersion'" #break #case feyngraph #define DiagramGeneratorName "FeynGraph" #redefine DiagramGeneratorVersion "feyngraph `~FeynGraphVersion'" #break #default #message error: unknown diagram generator: `other' #terminate #endswitch #define in "" #define out "" #define loops "" #define formoptions "" #define qgrafoptions "" #define feyngraphoptions "" #define options "" #define next "" #do a = {`?a',} #ifdef `a' #if "`keepleft_(`a',3)'" == "in=" #redefine next "in" #redefine a "`takeleft_(`a',3)'" #elseif "`keepleft_(`a',4)'" == "out=" #redefine next "out" #redefine a "`takeleft_(`a',4)'" #elseif "`keepleft_(`a',6)'" == "loops=" #redefine next "loops" #redefine a "`takeleft_(`a',6)'" #elseif "`keepleft_(`a',13)'" == "form_options=" #redefine next "formoptions" #redefine a "`takeleft_(`a',13)'" #elseif "`keepleft_(`a',14)'" == "qgraf_options=" #redefine next "qgrafoptions" #redefine a "`takeleft_(`a',14)'" #elseif "`keepleft_(`a',18)'" == "feyngraph_options=" #redefine next "feyngraphoptions" #redefine a "`takeleft_(`a',18)'" #elseif "`keepleft_(`a',8)'" == "options=" #redefine next "options" #redefine a "`takeleft_(`a',8)'" #endif #ifdef `a' #ifdef `next' #ifdef ``next'' #redefine `next' "``next'',`a'" #else #redefine `next' "`a'" #endif #endif #endif #endif #enddo #ifdef `FormDiagramsOptionOverrides' #define options "`options',`FormDiagramsOptionOverrides'" #endif #ifdef `options' #do a = {`options',} #ifdef `a' #switch `tolower_(`a')' #case verbose #define FormDiagramsVerbose #break #case noverbose #define FormDiagramsVerbose "" #break #case cacheread #define FormDiagramsCacheRead #break #case nocacheread #define FormDiagramsCacheRead "" #break #case cachewrite #define FormDiagramsCacheWrite #break #case nocachewrite #define FormDiagramsCacheWrite "" #break #case cacheskipcheck #define FormDiagramsCacheSkipCheck #break #case nocacheskipcheck #define FormDiagramsCacheSkipCheck "" #break #case forcecacheread #define FormDiagramsCacheRead #define FormDiagramsCacheSkipCheck #break #case raiseerror #define FormDiagramsRaiseError #break #case noraiseerror #define FormDiagramsRaiseError "" #break #default #message warning: unknown option: `a' #terminate #endswitch #endif #enddo #endif #define numIn "0" #define numOut "0" #do a = {`in',} #ifdef `a' #redefine numIn "{`numIn'+1}" #endif #enddo #do a = {`out',} #ifdef `a' #redefine numOut "{`numOut'+1}" #endif #enddo #define momenta "" #do i = 1, `numIn' #redefine momenta "`momenta',p`i'" #enddo #do i = 1, `numOut' #redefine momenta "`momenta',q`i'" #enddo * Construct the cache key. #define opt1 "`formoptions'" #define opt2 "``DiagramGenerator'options'" #define val1 "" #define val2 "" #do i = 1, 2 #do a = {`opt`i'',} #ifdef `a' #if `i' == 1 #redefine a "`tolower_(`a')'" #if "`keepright_(`a',1)'" == "_" #redefine a "`takeright_(`a',1)'" #endif #elseif (`i' == 2) && "`DiagramGenerator'" == "feyngraph" #if "`keepright_(`a',12)'" == "self_loops=0" #redefine a "`takeright_(`a',12)'selfloops0" #elseif "`keepright_(`a',16)'" == "opi_components=1" #redefine a "`takeright_(`a',16)'opicomponents1" #endif #endif #redefine val`i' "`val`i''`a'" #endif #enddo #ifdef `val`i'' #else #redefine val`i' "none" #endif #enddo #if "`val1'" == "`val2'" #redefine val2 "" #endif #define cachekey "`DiagramGenerator'_`model'" #do b = {in,out,loops,val1,val2} #redefine cachekey "`cachekey'_" #do a = {``b'',} #ifdef `a' #redefine cachekey "`cachekey'`a'" #endif #enddo #if "`keepright_(`cachekey',1)'" == "_" #redefine cachekey "`takeright_(`cachekey',1)'" #endif #enddo * Cache file names. #define cachefile "`FormDiagramsCacheDir'/`cachekey'.dat" #define cachetmpfile "`cachekey'.dat.`PID_'.tmp" #define cachetmpfile2 "`FormDiagramsCacheDir'/`cachekey'.dat2.`PID_'.tmp" * Set up the model. #call Setup`toupper_(`keepleft_(`model',1)')'`takeleft_(`model',1)'Model() * Generate diagrams. #ifdef `formoptions' #define optionvalue "0" #do a = {`formoptions',} #ifdef `a' #redefine optionvalue "`optionvalue'+``a''" #endif #enddo #redefine formoptions "`optionvalue'" #else #redefine formoptions "0" #endif L F1 = diagrams_(`CurrentModel',{`in'},{`out'},{`momenta'},kk,`loops',`formoptions'); #ifdef `FormDiagramsVerbose' P +sss; #endif .sort:gen-diag; #$nF1 = termsin_(F1); * Check if the cache exists. #ifdef `FormDiagramsCacheRead' #ifdef `FormDiagramsCacheSkipCheck' #$cacheexists = 1; #else #$cacheexists = #pipe if [ -f "`cachefile'" ]; then echo 1; else echo 0; fi ; #endif #else #$cacheexists = 0; #endif #if `$cacheexists' == 1 * If the cache exists, then compare the generated diagrams with the cache, * which has already been confirmed to be consistent with the other generator. #message Read cache file: `cachefile' Skip; L F2 = #include `cachefile' ; .sort:load-cache-1; #$nF2 = termsin_(F2); Drop; L oldF1 = F1; L oldF2 = F2; .sort:load-cache-2; Drop; L F0 = 0; L F1 = oldF1 - oldF2; L F2 = - F1; .sort:load-cache-3; #else * Otherwise, we must perform a full comparison. #ifdef `FormDiagramsCacheWrite' * Output the generated diagrams into a temporary file. .sort:save-tmp; #write <`cachetmpfile'> " %+E", F1 #close <`cachetmpfile'> #endif Skip; L F2 = #switch `DiagramGenerator' #case qgraf #call SetupQgrafFormStyle #call RunQgraf(in=`in',out=`out',loops=`loops',options=`qgrafoptions') #break #case feyngraph #call SetupFeynGraphTemplate #call RunFeynGraph(in=`in',out=`out',loops=`loops',options=`feyngraphoptions') #break #endswitch ; #ifdef `FormDiagramsVerbose' P +sss; #endif .sort:run-`DiagramGenerator'; #$nF2 = termsin_(F2); #call MakeDiagrams(`numIn',`numOut') #call CompareDiagrams(F1,F2,F0) #ifdef `FormDiagramsCacheWrite' * If the generated diagrams are consistent with those by the other generator * then write the cache file. #if (`ZERO_F1' == 1) && (`ZERO_F2' == 1) #message Write cache file: `cachefile' #system mkdir -p "`FormDiagramsCacheDir'" #system echo "* Compared with `DiagramGeneratorVersion'" >"`cachetmpfile2'" #system echo "* Number of diagrams: FORM: `$nF1', `DiagramGeneratorName': `$nF2'" >>"`cachetmpfile2'" * awk filter for normalizing leading spaces. #system awk " /topo_/ { if (NR > 1) print \"\" sub(/^ */, \" \") printf \"%s\", \$0 next } { sub(/^ */, \"\") printf \"%s\", \$0 } END { print \"\" } " "`cachetmpfile'" >>"`cachetmpfile2'" #system mv "`cachetmpfile2'" "`cachefile'" #endif #remove <`cachetmpfile'> #endif #endif #define ok #ifdef `TESTCASE' #if "`cachekey'" == "`TESTCASE'" #message INFO: cachekey matches the test case: `cachekey' #else #message WARNING: cachekey does not match the test case: `cachekey' vs. `TESTCASE' #redefine ok "" #endif #endif #if (`ZERO_F1' == 1) && (`ZERO_F2' == 1) #message INFO: Diagrams generated by FORM and `DiagramGeneratorName' match (`$nF1' terms). #else #if `$nF1' != `$nF2' #message ERROR: Diagrams generated by FORM and `DiagramGeneratorName' do not match (`$nF1' terms vs. `$nF2' terms). #else #message ERROR: Diagrams generated by FORM and `DiagramGeneratorName' do not match. #endif #redefine ok "" #endif #ifdef `FormDiagramsRaiseError' #ifdef `ok' #else #terminate #endif #endif #endprocedure *--#] DoComparison : *--#[ RunQgraf : RunQgraf(options...) ** * Runs QGRAF and reads its output. * * Example * ------- * #call SetupQcdModel() * #call SetupQgrafFormStyle() * L F = * #call RunQgraf(in=qua,out=qua,loops=1,options=nosnail) * ; * * Example Output * -------------- * F = * vx(QUA(-2),qua(1),glu(2))*vx(QUA(1),qua(-1),glu(2)); * #procedure RunQgraf(?a) #define in "" #define out "" #define loops "" #define loopmomentum "" #define options "" #define next "options" #do a = {`?a',} #ifdef `a' #if "`keepleft_(`a',3)'" == "in=" #redefine next "in" #redefine a "`takeleft_(`a',3)'" #elseif "`keepleft_(`a',4)'" == "out=" #redefine next "out" #redefine a "`takeleft_(`a',4)'" #elseif "`keepleft_(`a',6)'" == "loops=" #redefine next "loops" #redefine a "`takeleft_(`a',6)'" #elseif "`keepleft_(`a',14)'" == "loop_momentum=" #redefine next "loopmomentum" #redefine a "`takeleft_(`a',14)'" #elseif "`keepleft_(`a',8)'" == "options=" #redefine next "options" #redefine a "`takeleft_(`a',8)'" #endif #ifdef `a' #ifdef ``next'' #redefine `next' "``next'',`a'" #else #redefine `next' "`a'" #endif #endif #endif #enddo #ifndef `loopmomentum' #redefine loopmomentum "k" #endif #remove <`QgrafOutputFile'> #define filename "`QgrafInputFile'" #create <`filename'> #write <`filename'> "output = \'`QgrafOutputFile'\';" #write <`filename'> "style = \'`QgrafStyleFile'\';" #write <`filename'> "model = \'`QgrafModelFile'\';" #write <`filename'> "in = `in';" #write <`filename'> "out = `out';" #write <`filename'> "loops = `loops';" #write <`filename'> "loop_momentum = `loopmomentum';" #write <`filename'> "options = `options';" #close <`filename'> #system qgraf #ifdef `FormDiagramsVerbose' #system cat `QgrafOutputFile' #endif #include `QgrafOutputFile' #endprocedure *--#] RunQgraf : *--#[ SetupQgrafFormStyle : SetupQgrafFormStyle() ** * Prepares the QGRAF style file for FORM. * #procedure SetupQgrafFormStyle() #define filename "`QgrafStyleFile'" #create <`filename'> #write <`filename'> "" #write <`filename'> "*" #write <`filename'> "* file generated by " #write <`filename'> "*" #write <`filename'> "* *" #write <`filename'> "*" #write <`filename'> "#redefine QgrafVersion \"\"" #write <`filename'> "*" #write <`filename'> "" #write <`filename'> "*--#[[ d:" #write <`filename'> " " #write <`filename'> " *vx((),)" #write <`filename'> "" #write <`filename'> "*--#]] d: " #write <`filename'> "" #write <`filename'> "*" #write <`filename'> "* end" #write <`filename'> "*" #write <`filename'> "" #close <`filename'> #endprocedure *--#] SetupQgrafFormStyle : *--#[ RunFeynGraph : RunFeynGraph(options...) ** * Runs FeynGraph and reads its output. * * Example * ------- * #call SetupQcdModel() * #call SetupFeynGraphTemplate() * L F = * #call RunFeynGraph(in=qua,out=qua,loops=1,options=self_loops=0) * ; * * Example Output * -------------- * F = * vx(QUA(-2),qua(3),glu(2))*vx(QUA(3),qua(-1),glu(2)); * #procedure RunFeynGraph(?a) #define in "" #define out "" #define loops "" #define loopmomentum "" #define options "" #define next "options" #do a = {`?a',} #ifdef `a' #if "`keepleft_(`a',3)'" == "in=" #redefine next "in" #redefine a "`takeleft_(`a',3)'" #elseif "`keepleft_(`a',4)'" == "out=" #redefine next "out" #redefine a "`takeleft_(`a',4)'" #elseif "`keepleft_(`a',6)'" == "loops=" #redefine next "loops" #redefine a "`takeleft_(`a',6)'" #elseif "`keepleft_(`a',14)'" == "loop_momentum=" #redefine next "loopmomentum" #redefine a "`takeleft_(`a',14)'" #elseif "`keepleft_(`a',8)'" == "options=" #redefine next "options" #redefine a "`takeleft_(`a',8)'" #endif #ifdef `a' #ifdef ``next'' #redefine `next' "``next'',`a'" #else #redefine `next' "`a'" #endif #endif #endif #enddo #ifndef `loopmomentum' #redefine loopmomentum "k" #endif #remove <`FeynGraphOutputFile'> #define filename "`FeynGraphInputFile'" #create <`filename'> #write <`filename'> "template = \"`FeynGraphTemplateFile'\"" #write <`filename'> "[process]" #write <`filename'> "in = [%" #do a = {`in',} #ifdef `a' #write <`filename'> "\"`a'\", %" #endif #enddo #write <`filename'> "]" #write <`filename'> "out = [%" #do a = {`out',} #ifdef `a' #write <`filename'> "\"`a'\", %" #endif #enddo #write <`filename'> "]" #write <`filename'> "loops = `loops'" #write <`filename'> "model = \"`QgrafModelFile'\"" #write <`filename'> "momenta = [%" #define i "1" #do a = {`in',} #ifdef `a' #write <`filename'> "\"p`i++'\", %" #endif #enddo #redefine i "1" #do a = {`out',} #ifdef `a' #write <`filename'> "\"q`i++'\", %" #endif #enddo #do i = 1, `loops' #write <`filename'> "\"k`i'\", %" #enddo #write <`filename'> "]" #write <`filename'> "[filter]" #do a = {`options',} #ifdef `a' #switch `a' #case onshell #write <`filename'> "`a' = true" #break #default #write <`filename'> "`a'" #endswitch #endif #enddo #close <`filename'> #system feyngraph `FeynGraphInputFile' #pipe echo \#redefine FeynGraphVersion \"$(feyngraph --version)\" #ifdef `FormDiagramsVerbose' #system cat `FeynGraphOutputFile' #endif #include `FeynGraphOutputFile' #endprocedure *--#] RunFeynGraph : *--#[ SetupFeynGraphTemplate : SetupFeynGraphTemplate() ** * Prepares the FeynGraph template file for FORM. * #procedure SetupFeynGraphTemplate() #define filename "`FeynGraphTemplateFile'" #create <`filename'> #write <`filename'> "{\%- for diag in diagrams -\%}" #write <`filename'> " {\%- set n_in = diag.n_in() -\%}" #write <`filename'> " {\%- set n_ext = diag.n_ext() -\%}" #write <`filename'> "*--#[[ d{{ loop.index }}:" #write <`filename'> " {{ \"+\" ~ diag.sign() if diag.sign() >= 0 else diag.sign() -}}" #write <`filename'> " {{ \"/\" ~ diag.symmetry_factor() if diag.symmetry_factor() != 1 else \"\" }}" #write <`filename'> "{\%- for vertex in diag.vertices() \%}" #write <`filename'> " *vx(" #write <`filename'> "{\%- for par in vertex.particles_ordered() -\%}" #write <`filename'> " {\%- set j = vertex.propagators_ordered()[loop.index0].id() -\%}" #write <`filename'> " {\%- if j < n_in -\%}" #write <`filename'> " {\%- set j = - 2 * j - 1 -\%}" #write <`filename'> " {\%- elif j < n_ext -\%}" #write <`filename'> " {\%- set j = - 2 * (j - n_in + 1) -\%}" #write <`filename'> " {\%- endif -\%}" #write <`filename'> " {{ par.name() }}({{ j }})" #write <`filename'> " {\%- if not loop.last -\%},{\%- endif -\%}" #write <`filename'> "{\%- endfor -\%}" #write <`filename'> ")" #write <`filename'> "{\%- endfor \%}" #write <`filename'> "*--#]] d{{ loop.index }}: " #write <`filename'> "{\% endfor \%}" #close <`filename'> #endprocedure *--#] SetupFeynGraphTemplate : * vim: ft=form et ts=8 sts=2 sw=2 fdm=marker fmr=#[,#] fdc=4 form-5.0.1/check/check.rb0000755000175100017510000014662115217035721010642 #!/bin/sh # frozen_string_literal: true # See bbatsov/rubocop#3326 # rubocop:disable all exec ruby "-S" "-x" "$0" "$@" #! ruby # rubocop:enable all # Check the Ruby version. if RUBY_VERSION < "2.0.0" warn("ruby 2.0 required for the test suite") exit(1) end require "fileutils" require "io/console/size" require "open3" require "optparse" require "ostruct" require "rbconfig" require "set" require "thread" require "tmpdir" # Show an error message and exit. def fatal(message, file = nil, lineno = nil) if !file.nil? && !lineno.nil? $stderr.puts("#{file}:#{lineno}: error: #{message}") elsif !file.nil? $stderr.puts("#{file}: error: #{message}") else $stderr.puts("error: #{message}") end exit(1) end # Show a warning message. def warn(message, file = nil, lineno = nil) if !file.nil? && !lineno.nil? $stderr.puts("#{file}:#{lineno}: warning: #{message}") elsif !file.nil? $stderr.puts("#{file}: warning: #{message}") else $stderr.puts("warning: #{message}") end end # Get a string from the given environment variable. def read_env_str(key, default_value) value = default_value if ENV.key?(key) value = ENV[key] end value end # Get a positive integer from the given environment variable. def read_env_positive_int(key, default_value) if default_value <= 0 raise ArgumentError, "invalid default_value: #{default_value}" end value = default_value if ENV.key?(key) begin value = Integer(ENV[key]) raise ArgumentError if value <= 0 rescue ArgumentError, TypeError warn("environment variable ignored: #{key} is not positive integer: #{ENV[key]}") value = default_value end end value end # Get the total size of the physical memory available on the host machine. def total_physical_memory platform = RbConfig::CONFIG["host_os"].downcase case when platform.include?("linux") File.foreach("/proc/meminfo") do |line| m = line.match(/\bMemTotal\b\D+(\d+)/) return m[1].to_i * 1024 if m end when platform.include?("darwin") return `sysctl -n hw.memsize`.to_i when platform.include?("mingw") || platform.include?("mswin") return `powershell -NoProfile -Command "(Get-CimInstance Win32_ComputerSystem).TotalPhysicalMemory"`.to_i end nil end # The default prefix for the root temporary directory. See TempDir.root. TMPDIR_PREFIX = "form_check_" # The default extra options for mpirun. DEFAULT_MPIRUN_OPTS = read_env_str("FORM_CHECK_MPIRUN_OPTS", nil) # The default extra options for valgrind. DEFAULT_VALGRIND_OPTS = read_env_str("FORM_CHECK_VALGRIND_OPTS", nil) # The default maximal running time in seconds of FORM jobs before they get terminated. DEFAULT_TIMEOUT = read_env_positive_int("FORM_CHECK_DEFAULT_TIMEOUT", 10) # The factor multiplied to DEFAULT_TIMEOUT when Valgrind is used. VALGRIND_TIME_DILATION = read_env_positive_int("FORM_CHECK_VALGRIND_TIME_DILATION", 30) # The default directory for searching test cases. TESTDIR = File.dirname(__FILE__) # Routines for temporary directories. class TempDir @root = nil # Return the root temporary directory name. def self.root if @root.nil? @root = Dir.mktmpdir(TMPDIR_PREFIX) end @root end # Create a temporary directory under the root temporary directory, and return # the directory name. def self.mktmpdir(prefix) Dir.mktmpdir(prefix, root) end # Clean up the all temporary directory. def self.cleanup return if @root.nil? # The first try. FileUtils.rm_rf(@root) # Wait up to 5 seconds. 50.times do # If the directory still remains, try to remove it after 0.1 seconds. if !FileTest.directory?(@root) return end sleep(0.1) FileUtils.rm_rf(@root) end # Failed. if FileTest.directory?(@root) warn("failed to delete the temporary directory '#{@root}'") end @root = nil end # We need to register the cleanup function before loading test/unit. at_exit { TempDir.cleanup } end # Register a function before loading test/unit. at_exit { defined?(output_detailed_statistics) && output_detailed_statistics } # We use test/unit, which is now not in the standard library. begin require "test/unit" rescue LoadError warn("test/unit required for the test suite") exit(1) end # Try a monkey patch to call output_detailed_statistics() before the test suite summary. begin require "test/unit/ui/console/testrunner" module Test module Unit module UI module Console class TestRunner alias old_output_statistics output_statistics alias _old_output output alias _old_output_summary_marker output_summary_marker def output_statistics(*args, **kwargs, &block) if need_output_detailed_statistics? output_summary_marker output_detailed_statistics(method(:output)) output_summary_marker end old_output_statistics(*args, **kwargs, &block) end end end end end end rescue NameError, LoadError # do nothing end # Find the path to a program. def which(name) result = nil if name != File.basename(name) # Convert the relative path to the absolute path. result = File.expand_path(name) else # Search from $PATH. ENV["PATH"].split(File::PATH_SEPARATOR).each do |path| candidate = File.join(path, name) if File.executable?(candidate) result = File.expand_path(candidate) break end end end result = name if result.nil? # Fallback. result end # Puts a message using ANSI color codes if available. def puts_colored(output, something, color_name) c = _make_color(output, color_name) if !c.nil? something = format("%s%s%s", c[0], something, c[1]) end output.puts(something) end def _make_color(output, name) if _guess_color_availability_for(output) begin require "test/unit/color-scheme" return [ Test::Unit::ColorScheme.default[name].escape_sequence, Test::Unit::Color.new("reset").escape_sequence ] rescue NameError, LoadError # do nothing end end nil end def _guess_color_availability_for(output) return true if ENV["GITHUB_ACTIONS"] == "true" return false unless output.tty? return true if RUBY_PLATFORM =~ /mswin|mingw/ term = ENV.fetch("TERM", nil) return true if term && term =~ /(?:term|screen)(?:-(?:256)?color)?\z/ if defined?(Test::Unit::UI::Console::TestRunner::TERM_COLOR_SUPPORT) && Test::Unit::UI::Console::TestRunner::TERM_COLOR_SUPPORT return true end return true if ENV["EMACS"] == "t" false end # To be mixed-in all FORM tests. module FormTest # Interplay with globals. @cfg = nil @tests = nil def self.cfg=(val) @cfg = val end def self.cfg @cfg end def self.tests=(val) @tests = val end def self.tests @tests end def info FormTest.tests.classes_info[self.class.name] end # Accessors to the configuration. def timeout FormTest.cfg.timeout end def ncpu FormTest.cfg.ncpu end def serial? FormTest.cfg.serial? end def threaded? FormTest.cfg.threaded? end def mpi? FormTest.cfg.mpi? end def flint? FormTest.cfg.flint? end def valgrind? if FormTest.cfg.fake_valgrind.nil? !FormTest.cfg.valgrind.nil? else FormTest.cfg.fake_valgrind end end def wordsize FormTest.cfg.wordsize end # Host environment. def cygwin? RbConfig::CONFIG["host_os"] =~ /cygwin/i end def mac? RbConfig::CONFIG["host_os"] =~ /darwin|mac os/i end def linux? RbConfig::CONFIG["host_os"] =~ /linux/i end def unix? cygwin? || mac? || linux? || RbConfig::CONFIG["host_os"] =~ /solaris|bsd/i end def windows? # NOTE: "cygwin" is intentionally excluded. RbConfig::CONFIG["host_os"] =~ /mswin|msys|mingw|bccwin|wince|emc/i end def travis? ENV["TRAVIS"] == "true" end def github? ENV["GITHUB_ACTIONS"] == "true" end # Total memory in bytes. -1 if undetermined. def total_memory @@total_memory_mutex.synchronize do if @@cached_total_memory.nil? result = total_physical_memory if result.nil? @@cached_total_memory = -1 else @@cached_total_memory = result end if result.nil? || result <= 0 warn("failed to determine total physical memory") end end @@cached_total_memory end end @@cached_total_memory = nil @@total_memory_mutex = Mutex.new def reveal_newlines(str) if FormTest.cfg.show_newlines str.gsub("\r", "").gsub("\n", "\n") else str end end # Override methods in Test::Unit::TestCase. def setup super @tmpdir = nil @filename = nil end def teardown cleanup_files super end # Set up the working directory and put FORM files. def setup_files cleanup_files @tmpdir = TempDir.mktmpdir("#{self.class.name}_") nfiles.times do |i| File.write(File.join(@tmpdir, "#{i + 1}.frm"), info.sources[i]) end end # Delete the working directory. def cleanup_files if !@tmpdir.nil? FileUtils.rm_rf(@tmpdir) end @tmpdir = nil end # Called from derived classes' test_* methods. def do_test(&block) if !requires info.status = "OMITTED" if defined?(omit) omit(requires_str, &block) elsif defined?(skip) skip(requires_str) end return end if !FormTest.cfg.full && pendings info.status = "SKIPPED" if defined?(pend) pend(pendings_str) do assert(false) yield end elsif defined?(skip) skip(requires_str) end return end FormTest.cfg.retries.times do |t| setup_files prepare @stdout = "" @stderr = "" old_formpath = ENV.fetch("FORMPATH", nil) begin ENV["FORM"] = FormTest.cfg.form_cmd ENV["FORMPATH"] = add_path(old_formpath, File.dirname(info.full_filename)) ENV["TESTFILE"] = info.full_filename ENV["TESTFILEDIR"] = File.dirname(info.full_filename) ENV["TESTCASE"] = info.classname ENV["TESTTMPDIR"] = @tmpdir nfiles.times do |i| @filename = "#{i + 1}.frm" execute("#{ulimits}#{FormTest.cfg.form_cmd} #{@filename}") if !finished? info.status = "TIMEOUT" assert(false, "timeout (= #{timeout} sec) in #{@filename} of #{info.desc}") end if return_value != 0 break end end # On Windows, we convert newline characters in stdout/stderr into # the Unix-style newline characters used in our test cases. @raw_stdout = @stdout @raw_stderr = @stderr if windows? @stdout = @stdout.gsub("\r\n", "\n") @stderr = @stderr.gsub("\r\n", "\n") end # MesPrint inevitably inserts newline characters when a line exceeds # its length limit. To verify error/warning messages, here we remove # newline characters that seem to be part of continuation lines # (this simple implementation also removes newline characters that are # not due to MesPrint). @cleaned_stdout = @stdout.gsub(/\R(?= ?\S)(?!\S+ Line \d+)/, "") yield # NOTE: Here we catch all exceptions, though it is a very bad style. This # is because, in Ruby 1.9, test/unit is implemented based on # minitest and MiniTest::Assertion is not a subclass of # StandardError. rescue Exception => e # rubocop:disable Lint/RescueException if info.status == "TIMEOUT" && t < FormTest.cfg.retries - 1 warn("timeout (= #{timeout} sec) in #{@filename} of #{info.desc}, retry") info.status = nil info.times = nil next end $stderr.puts $stderr.puts("=" * 79) puts_colored($stderr, "#{info.desc} FAILED", "failure") $stderr.puts("=" * 79) $stderr.puts(reveal_newlines(@raw_stdout)) $stderr.puts("=" * 79) $stderr.puts if info.status.nil? if (defined?(MiniTest::Assertion) && e.is_a?(MiniTest::Assertion)) || (defined?(Test::Unit::AssertionFailedError) && e.is_a?(Test::Unit::AssertionFailedError)) info.status = "FAILED" else info.status = "ERROR" end end raise e else if FormTest.cfg.verbose $stderr.puts $stderr.puts("=" * 79) $stderr.puts("#{info.desc} SUCCEEDED") $stderr.puts("=" * 79) $stderr.puts(reveal_newlines(@raw_stdout)) $stderr.puts("=" * 79) $stderr.puts end info.status = "OK" ensure ENV["FORMPATH"] = old_formpath end break end end # Execute a FORM job. def execute(cmdline) if FormTest.cfg.verbose $stderr.puts("Command: #{cmdline}") end @finished = false @exit_status = nil t0 = Time.now begin result = execute_impl(cmdline, timeout, @tmpdir) @finished = result[:finished_in_time] @exit_status = result[:exit_status] # We print both stdout and stderr when a test fails. An easy way to # implement this is to copy messages in stderr to those in stdout, # namely, use the combined output. Unfortunately their orders # (how stdout and stderr are merged) may not be preserved. # Note that we exclude the Valgrind warnings "Warning: set address range perms: ..." # which can happen when the program allocates big memory chunks. out = result[:combined_lines] out = out.reject { |l| l =~ /Warning: set address range perms/ } @stdout += out.join @stderr += result[:stderr_lines].join ensure t1 = Time.now dt = t1 - t0 if info.times.nil? info.times = [] end info.times.push(dt) end end def execute_impl(cmd, timeout, chdir) stdout_lines = [] stderr_lines = [] combined_lines = [] exit_status = nil finished_in_time = false mutex = Mutex.new Open3.popen3(cmd, chdir: chdir) do |stdin, stdout, stderr, wait_thr| stdin.close stdout_thread = Thread.new do while (line = stdout.gets) stdout_lines << line mutex.synchronize { combined_lines << line } end end stderr_thread = Thread.new do while (line = stderr.gets) stderr_lines << line mutex.synchronize { combined_lines << line } end end if wait_thr.join(timeout) finished_in_time = true exit_status = wait_thr.value.exitstatus stdout_thread.join stderr_thread.join else Process.kill("KILL", wait_thr.pid) wait_thr.join mutex.synchronize do stdout_thread.kill stderr_thread.kill end end end { stdout_lines: stdout_lines, stderr_lines: stderr_lines, combined_lines: combined_lines, exit_status: exit_status, finished_in_time: finished_in_time } end # Default assertions. def default_check if return_value != 0 assert(false, "nonzero return value (= #{return_value}) from #{@filename} of #{info.desc}") elsif warning? assert(false, "warning in #{@filename} of #{info.desc}") else assert(true) end end # Methods to be overridden in derived classes. # The number of FORM files attached to the test. def nfiles 1 end # The required condition. The test will be skipped if the condition does not # hold. def requires true end # The string representation for the required condition. def requires_str "true" end # The pending condition. The test will be skipped if the condition holds. def pendings false end # The string representation for the pending condition. def pendings_str "false" end # The method to be called before the test. def prepare # Can be overridden in child classes. end # The sequence of ulimit commands to set the resource usage limits. def ulimits "" end # Test-result functions. # The exit status as a number def return_value @exit_status end # The verbatim result keeping line breaks and whitespaces. # Must be in the default output format. def exact_result(exprname, index = -1) matches = @stdout.scan(/^[ \t]+#{Regexp.escape(exprname)}\s*=(.+?);/m) return matches[index].first if !matches.empty? && !matches[index].nil? "" end # The result on one line with multiple whitespaces reduced to one. # Must be in the default output format. def result(exprname, index = -1) r = exact_result(exprname, index) return r.gsub(/\s+/, "") if !r.nil? "" end # The number of terms in the given expression. # Must be in the default statistics format. def nterms(exprname, index = -1) matches = @stdout.scan(/^[ \t]+#{exprname}\s*Terms in output\s*=\s*(\d+).*?Bytes used\s*=\s*\d+/m) return matches[index].first.to_i if !matches.empty? && !matches[index].nil? -1 end # The size in byte. # Must be in the default statistics format. def bytesize(exprname, index = -1) matches = @stdout.scan(/^[ \t]+#{exprname}\s*Terms in output\s*=\s*\d+.*?Bytes used\s*=\s*(\d+)/m) return matches[index].first.to_i if !matches.empty? && !matches[index].nil? -1 end # The file contents as a string (in the working directory). def file(filename) begin File.open(File.join(@tmpdir, filename), "r") do |f| result = f.read # On Windows, we convert newline characters in the file into # the Unix-style newline characters used in our test cases. if windows? result = result.gsub("\r\n", "\n") end return result end rescue StandardError warn("failed to read '#{filename}'") end "" end # Same as file(filename). def read(filename) file filename end # Write to a file (in the working directory). def write(filename, text) fname = File.join(@tmpdir, filename) FileUtils.mkdir_p(File.dirname(fname)) File.write(fname, text) end # The working directory for the test. def workdir @tmpdir end # The standard output of the FORM job as a string. def stdout @stdout end # The standard error of the FORM job as a string. def stderr @stderr end # Test-result functions to be used in assertions. # true if the FORM job finished in timeout. def finished? @finished end # true if the FORM job put warning messages. def warning?(expected_message = nil) if expected_message.nil? @stdout.include?("Warning:") else @cleaned_stdout =~ Regexp.new("Warning: .*#{Regexp.escape(expected_message)}") end end # true if the FORM job put preprocessor errors. def preprocess_error?(expected_message = nil) if expected_message.nil? @stdout =~ /(^|\R)\S+ Line \d+ ==>/ else @cleaned_stdout =~ Regexp.new("(^|\\R)\\S+ Line \\d+ ==> .*#{Regexp.escape(expected_message)}") end end # true if the FORM job put compile-time errors. def compile_error?(expected_message = nil) if expected_message.nil? @stdout =~ /(^|\R)\S+ Line \d+ -->/ else @cleaned_stdout =~ Regexp.new("(^|\\R)\\S+ Line \\d+ --> .*#{Regexp.escape(expected_message)}") end end # true if the FORM job put run-time errors. # NOTE: indeed this implementation detects abnormal terminations # via "Terminate()", which also happens for preprocessor/compiler errors. def runtime_error?(expected_message = nil) if serial? result = @stdout =~ /Program terminating at \S+ Line \d+ -->/ elsif threaded? result = @stdout =~ /Program terminating in thread \d+ at \S+ Line \d+ -->/ elsif mpi? result = @stdout =~ /Program terminating in process \d+ at \S+ Line \d+ -->/ end if expected_message.nil? result else # NOTE: it just tests if the output contains the expected message, # which is probably put before "Terminate()" is called. result && @cleaned_stdout =~ Regexp.new(Regexp.escape(expected_message)) end end # true if the FORM job completed without any warnings/errors and # the exit code was 0. def succeeded? if finished? && !warning? && !preprocess_error? && !compile_error? && !runtime_error? && return_value == 0 if FormTest.cfg.valgrind.nil? if @stderr.empty? return true end @stdout += "!!! stderr is not empty" return false end # Check for Valgrind errors. ok = !@stderr.include?("Invalid read") && !@stderr.include?("Invalid write") && !@stderr.include?("Invalid free") && !@stderr.include?("Mismatched free") && !@stderr.include?("Use of uninitialised value") && !@stderr.include?("Conditional jump or move depends on uninitialised value") && !@stderr.include?("points to unaddressable byte") && !@stderr.include?("points to uninitialised byte") && !@stderr.include?("contains uninitialised byte") && !@stderr.include?("Source and destination overlap in memcpy") && !@stderr.include?("has a fishy") && @stderr !~ /definitely lost: [1-9]/ && @stderr !~ /indirectly lost: [1-9]/ && @stderr !~ /possibly lost: [1-9]/ if !ok @stdout += "!!! Valgrind test failed" end return ok end false end # Utility functions for pattern matching. # A pattern from the given string with escaping any special characters. def exact_pattern(str) san_str = Regexp.quote(str) Regexp.new(san_str) end # The same as #exact_pattern but ignores whitespaces. def pattern(str) san_str = Regexp.quote(str.gsub(/\s+/, "")) Regexp.new(san_str) end # Same as #pattern but matches only with the whole expression. # Assumes the default output format. def expr(str) san_str = Regexp.quote(str.gsub(/\s+/, "")) Regexp.new("^#{san_str}$") end end # Information of a test case. class TestInfo def initialize @classname = nil @full_filename = nil @where = nil # where the test is defined @foldname = nil # fold name of the test @enabled = nil # enabled or not @sources = [] # FORM sources @time_dilation = nil @status = nil # status @times = nil # elapsed time (array) end attr_accessor :classname, :full_filename, :where, :foldname, :enabled, :sources, :time_dilation, :status, :times # Return the description of the test. def desc "#{@foldname} (#{@where})" end end # List of test cases. class TestCases def initialize @files = [] # Ruby files @classes = [] # test class names (unsorted) @classes_info = {} # TestInfo objects, key: Ruby class name @name_patterns = [] @exclude_patterns = [] end attr_reader :classes_info attr_accessor :name_patterns, :exclude_patterns # Return a list containing info objects for enabled tests. def classes_info_list infos = [] @classes.each do |c| info = @classes_info["Test_#{c}"] if info.enabled infos.push(info) end end infos end # Convert a .frm file to a .rb file and load it. def make_ruby_file(filename, fold_markers = nil) # Handle fold markers. if fold_markers.nil? fold_open_pattern = /^\*..#\[/ fold_open_with_name_pattern = /^\*..#\[\s*([^:]*)/ fold_close_pattern = /^\*..#\]/ fold_close_with_name_pattern = /^\*..#\]\s*([^:]*)/ else fold_open_marker = Regexp.escape(fold_markers[:open]) fold_close_marker = Regexp.escape(fold_markers[:close]) fold_open_pattern = /^#{fold_open_marker}/ fold_open_with_name_pattern = /^#{fold_open_marker}\s*([^:]*)/ fold_close_pattern = /^#{fold_close_marker}/ fold_close_with_name_pattern = /^#{fold_close_marker}\s*([^:]*)/ end # Check existing files. full_filename = File.expand_path(filename) inname = File.basename(filename) outname = "#{File.basename(filename, '.frm')}.rb" if @files.include?(outname) fatal("duplicate output file name", inname) end @files.push(outname) outname = File.join(TempDir.root, outname) File.open(filename, "r") do |infile| File.open(outname, "w") do |outfile| lineno = 0 level = 0 classname = nil info = nil block = nil blockno = 0 fileno = 0 skipping = false heredoc = nil requires = nil pendings = nil prepares = nil ulimits = nil time_dilation = nil infile.each_line do |line| line.chop! lineno += 1 if level == 0 case line when fold_open_with_name_pattern # fold open: start a class fold = $1.strip if fold.empty? fatal("empty fold", inname, lineno) end classname = canonical_name(fold) info = TestInfo.new @classes.push(classname) @classes_info["Test_#{classname}"] = info info.classname = classname info.full_filename = full_filename info.where = "#{inname}:#{lineno}" info.foldname = fold info.enabled = test_enabled?(classname) level += 1 block = "" blockno = 0 fileno = 0 skipping = !info.enabled heredoc = nil requires = nil pendings = nil prepares = nil ulimits = nil time_dilation = nil if skipping line = "" else line = "class Test_#{classname} < Test::Unit::TestCase; include FormTest" end when fold_close_pattern # unexpected fold close fatal("unexpected fold close", inname, lineno) else # as commentary line = "" end elsif heredoc.nil? && line =~ fold_close_with_name_pattern && level == 1 # fold close: end of the class fold = $1.strip foldname = info.foldname if !fold.empty? && fold != foldname warn("unmatched fold '#{fold}', which should be '#{foldname}'", inname, lineno) end line = "" if !skipping if fileno == 0 # no .end blockno.times do outfile.write("\n") end block += ".end\n" fileno += 1 info.sources.push(block) line += "def test_#{classname}; do_test { default_check } end; " else outfile.write("def test_#{classname}; do_test {\n" + block) line = "} end; " end line += "def nfiles; #{fileno} end; " if fileno != 1 if !requires.nil? requires = requires.map { |s| "(#{s})" }.join(" && ") line += "def requires; #{requires} end; " line += "def requires_str; %(#{requires}) end; " end if !pendings.nil? pendings = pendings.map { |s| "(#{s})" }.join(" || ") line += "def pendings; #{pendings} end; " line += "def pendings_str; %(#{pendings}) end; " end if !prepares.nil? prepares = prepares.join("; ") line += "def prepare; #{prepares} end; " end if !ulimits.nil? ulimits.map! { |s| "ulimit #{s}; " } ulimits = ulimits.join line += "def ulimits; %(#{ulimits}) end; " end if !time_dilation.nil? line += "def timeout; super() * #{time_dilation} end;" end line += "end" end level = 0 classname = nil info = nil elsif heredoc.nil? && line =~ /^\s*\.end/ # .end if skipping line = "" else blockno += 1 if fileno > 0 # previous .end blockno.times do outfile.write("\n") end block += "#{line}\n" fileno += 1 info.sources.push(block) block = "" blockno = 0 line = nil # later end elsif heredoc.nil? && line =~ /^\s*#\s*require\s+(.*)/ # #require line = "" if requires.nil? requires = [] end requires << $1 elsif heredoc.nil? && line =~ /^\s*#\s*pend_if\s+(.*)/ # #pend_if line = "" if pendings.nil? pendings = [] end pendings << $1 elsif heredoc.nil? && line =~ /^\s*#\s*prepare\s+(.*)/ # #prepare line = "" if prepares.nil? prepares = [] end prepares << $1 elsif heredoc.nil? && line =~ /^\s*#\s*ulimit\s+(.*)/ # #ulimit # Example: #ulimit -v 4_000_000 line = "" if ulimits.nil? ulimits = [] end ulimits << $1.gsub(/(?<=\d)_(?=\d)/, "") # remove decimal marks (underscores) elsif heredoc.nil? && line =~ /^\s*#\s*time_dilation\s+(.*)/ # #time_dilation line = "" if !time_dilation.nil? fatal("attempted to set time_dilation twice", inname, lineno) end time_dilation = $1.to_f if time_dilation <= 0 fatal("invalid time_dilation", inname, lineno) end info.time_dilation = time_dilation elsif heredoc.nil? && line =~ /^\*\s*#\s*(require|prepare|pend_if|ulimit|time_dilation)\s+(.*)/ # *#, commented out in the FORM way line = "" else if heredoc.nil? if line =~ fold_open_pattern # fold open level += 1 elsif line =~ fold_close_with_name_pattern # fold close level -= 1 elsif line =~ /<= 1 fatal("expected fold close", inname, lineno) end end end require outname end # true if the test is enabled def test_enabled?(name) # construct regular expressions (wildcards: '*' and '?') @name_patterns.length.times do |i| if !@name_patterns[i].is_a?(Regexp) s = @name_patterns[i].to_s.gsub("*", ".*").tr("?", ".") s = "^#{s}$" @name_patterns[i] = Regexp.new(s) end end @exclude_patterns.length.times do |i| if !@exclude_patterns[i].is_a?(Regexp) s = @exclude_patterns[i].to_s.gsub("*", ".*").tr("?", ".") s = "^#{s}$" @exclude_patterns[i] = Regexp.new(s) end end # check --name NAME ok = true if !@name_patterns.empty? ok = false @name_patterns.each do |pat| if name =~ pat ok = true break end end end if !ok return false end # check --exclude NAME if !@exclude_patterns.empty? @exclude_patterns.each do |pat| if name =~ pat ok = false break end end end ok end # Return a class name that is valid and unique. def canonical_name(name) prefix = name.gsub(/[^a-zA-Z0-9_]/, "_") s = prefix i = 0 loop do if !@classes.include?(s) break end i += 1 s = "#{prefix}_#{i}" end s end # Delete a test. def delete(classname) @classes.delete(classname) @classes_info.delete("Test_#{classname}") # It seems difficult to delete a class. # Instead, remove the test method. klass = Object.const_get(:"Test_#{classname}") klass.send(:remove_method, :"test_#{classname}") end end # FORM configuration. class FormConfig def initialize(form, mpirun, mpirun_opts, valgrind, valgrind_opts, fake_valgrind, wordsize, ncpu, timeout, retries, stat, full, verbose, show_newlines) @form = form @mpirun = mpirun @mpirun_opts = mpirun_opts @valgrind = valgrind @valgrind_opts = valgrind_opts @fake_valgrind = fake_valgrind @ncpu = ncpu @timeout = timeout @retries = retries @stat = stat @full = full @verbose = verbose @show_newlines = show_newlines @form_bin = nil @mpirun_bin = nil @valgrind_bin = nil @valgrind_supp = nil @head = nil @is_serial = nil @is_threaded = nil @is_mpi = nil @has_flint = nil @wordsize = wordsize @form_cmd = nil end attr_reader :form, :mpirun, :mpirun_opts, :valgrind, :valgrind_opts, :fake_valgrind, :ncpu, :timeout, :retries, :stat, :full, :verbose, :show_newlines, :form_bin, :mpirun_bin, :valgrind_bin, :valgrind_supp, :head, :wordsize, :form_cmd def serial? @is_serial end def threaded? @is_threaded end def mpi? @is_mpi end def flint? @has_flint end def check_bin(name, bin) # Check if the executable is available. if File.executable?(bin) return end if name == bin fatal("executable '#{name}' not found") else fatal("executable '#{name}' ('#{bin}') not found") end end def check # Check if FORM is available. @form_bin = which(@form) check_bin(@form, @form_bin) # Check if Valgrind is available. if !@valgrind.nil? @valgrind_bin = which(@valgrind) check_bin(@valgrind, @valgrind_bin) end # Check the FORM version. tmpdir = TempDir.mktmpdir("ver_") begin frmname = File.join(tmpdir, "ver.frm") File.write(frmname, <<-TEST_FRM) #- Off finalstats; .end TEST_FRM @head = "" out, _status = Open3.capture2e("#{@form_bin} #{frmname}") out.split("\n").each do |output_line| if output_line =~ /FORM/ @head = output_line break end end case @head when /^FORM/ @is_serial = true @is_threaded = false @is_mpi = false when /^TFORM/ @is_serial = false @is_threaded = true @is_mpi = false when /^ParFORM/ @is_serial = false @is_threaded = false @is_mpi = true else system("#{form_bin} #{frmname}") fatal("failed to get the version of '#{@form}'") end # Check if Flint is available. # Use form -vv which contains either "+flint=VERSION" or "-flint". feature_out, _status = Open3.capture2e(@form_bin, "-vv") if feature_out =~ /(?:^|\s)\+flint(?:=|\s|$)/ @has_flint = true elsif feature_out =~ /(?:^|\s)-flint(?:\s|$)/ @has_flint = false else warn("failed to determine FLINT support of '#{@form}'") @has_flint = false end # Check the wordsize. # Method 1: from the output header. # Method 2: 2^64 = 0 (mod 2^64) => 64-bit machine => sizeof(WORD) = 4, etc. wordsize1 = nil wordsize2 = nil if @head =~ /FORM[^(]*\([^)]*\)\s*(\d+)-bits/ wordsize1 = $1.to_i / 16 end frmname2 = File.join(tmpdir, "ws.frm") File.write(frmname2, <<-TEST_FRM) #do w={2,4,8} #message wordtest,`w',{2^(`w'*16-1)},{2^(`w'*16)} #enddo .end TEST_FRM out, _err, status = Open3.capture3("#{@form_bin} #{frmname2}") if status.success? out.split("\n").each do |output_line| if output_line =~ /~~~wordtest,(\d+),(-?\d+),(-?\d+)/ w = $1.to_i x = $2.to_i y = $3.to_i if x != 0 && y == 0 wordsize2 = w break end end end end if !@wordsize.nil? if !wordsize1.nil? && @wordsize != wordsize1 warn("--wordsize=#{@wordsize} specified but the header of '#{@form}' indicates the wordsize = #{wordsize1}") end if !wordsize2.nil? && @wordsize != wordsize2 warn("--wordsize=#{@wordsize} specified but the preprocessor calculator of '#{@form}' determined wordsize = #{wordsize2}") end end if @wordsize.nil? if !wordsize1.nil? && !wordsize2.nil? && wordsize1 != wordsize2 warn("the header of '#{@form}' indicates the wordsize = #{wordsize1} but the preprocessor calculator determined wordsize = #{wordsize2}") elsif !wordsize1.nil? @wordsize = wordsize1 else @wordsize = wordsize2 end end if @wordsize.nil? warn("failed to get the wordsize of '#{@form}'") warn("assuming wordsize = 4") @wordsize = 4 end # Prepare for mpirun if @is_mpi @mpirun_bin = which(@mpirun) check_bin(@mpirun, @mpirun_bin) # Open MPI is known to be not Valgrind-clean. Try to suppress some # errors. Unfortunately, it would be insufficient. supp = File.expand_path(File.join(File.dirname(@mpirun_bin), "..", "share", "openmpi", "openmpi-valgrind.supp")) if File.exist?(supp) @valgrind_supp = supp end end # Construct the command. cmdlist = [] if @is_mpi cmdlist << @mpirun_bin << "-np" << @ncpu.to_s if !@mpirun_opts.nil? cmdlist << @mpirun_opts end end if !@valgrind_bin.nil? cmdlist << @valgrind_bin cmdlist << "--leak-check=full" if !@valgrind_supp.nil? cmdlist << "--suppressions=#{@valgrind_supp}" end if !@valgrind_opts.nil? cmdlist << @valgrind_opts end end cmdlist << @form_bin if @is_threaded cmdlist << "-w#{@ncpu}" end @form_cmd = cmdlist.join(" ") # Check the output header. out, err, status = Open3.capture3("#{@form_cmd} #{frmname}") if status.success? form_version_line = out.split("\n").first if form_version_line.nil? warn("failed to get the actual version of FORM") else @head = form_version_line end else system("#{@form_cmd} #{frmname}") fatal("failed to execute '#{@form_cmd}'") end if !@valgrind.nil? # Include Valgrind version information. valgrind_version_line = err.split("\n").select { |line| line.include?("Valgrind") }.first if valgrind_version_line.nil? warn("failed to get the version of Valgrind") else @head += "\n#{valgrind_version_line}" end end ensure FileUtils.rm_rf(tmpdir) end end end # Return paths obtained by `oldpath` + `newpath`. def add_path(oldpath, newpath) newpath = File.expand_path(newpath) if oldpath.nil? return newpath end "#{newpath}#{File::PATH_SEPARATOR}#{oldpath}" end # Parse `TEST=...`. def parse_def(pat) if pat =~ /^TEST=(.*)/ return $1 end nil end # Parse GROUPID/GROUPCOUNT def parse_group(group) if group =~ %r{^(\d+)/(\d+)$} group_id = $1.to_i group_count = $2.to_i if group_count <= 0 fatal("group count must be positive: '#{group}'") end if group_id <= 0 || group_id > group_count fatal("group id out of range: '#{group}'") end return group_id, group_count end fatal("unrecognized group specification: '#{group}'") end # Search for the `file`. def search_file(file, opts) f = file return f if File.exist?(f) if !opts.dir.nil? f = File.join(opts.dir, file) return f if File.exist?(f) end if !TESTDIR.nil? f = File.join(TESTDIR, file) return f if File.exist?(f) end fatal("file '#{file}' not found") end # Search for the `dir`. def search_dir(dir, opts) d = dir return d if File.directory?(d) if !opts.dir.nil? d = File.join(opts.dir, dir) return d if File.directory?(d) end if !TESTDIR.nil? d = File.join(TESTDIR, dir) return d if File.directory?(d) end fatal("directory '#{dir}' not found") end def main # Parse options. opts = OpenStruct.new opts.list = false opts.path = nil opts.form = "form" opts.mpirun = "mpirun" opts.mpirun_opts = nil opts.ncpu = 4 opts.timeout = nil opts.retries = 1 opts.stat = false opts.full = false opts.enable_valgrind = false opts.valgrind = "valgrind" opts.valgrind_opts = nil opts.fake_valgrind = nil opts.wordsize = nil opts.dir = nil opts.name_patterns = [] opts.exclude_patterns = [] opts.group_id = nil opts.group_count = nil opts.files = [] opts.verbose = false opts.show_newlines = false parser = OptionParser.new parser.banner = "Usage: #{File.basename($0)} [options] [--] [binname] [files|tests..]" parser.on("-h", "--help", "Show this help and exit") { puts(parser); exit } parser.on("-l", "--list", "List all tests and exit") { opts.list = true } parser.on("--path PATH", "Use PATH for executables") { |path| opts.path = add_path(opts.path, path) } parser.on("--form BIN", "Use BIN as FORM executable") { |bin| opts.form = bin } parser.on("--mpirun BIN", "Use BIN as mpirun executable") { |bin| opts.mpirun = bin } parser.on("--mpirun-opts OPTS", "Pass command line options OPTS to mpirun") { |s| opts.mpirun_opts = s } parser.on("-w", "--ncpu N", "Use N CPUs") { |n| opts.ncpu = n.to_i } parser.on("-t", "--timeout N", "Timeout N in seconds") { |n| opts.timeout = n.to_i } parser.on("-r", "--retries N", "Retry up to N times when timeout") { |n| opts.retries = n.to_i } parser.on("-s", "--stat", "Print detailed statistics") { opts.stat = true } parser.on("-f", "--full", "Full test, ignoring pending") { opts.full = true } parser.on("--enable-valgrind", "Enable Valgrind") { opts.enable_valgrind = true } parser.on("--fake-valgrind", "Pretend to run under Valgrind") { opts.fake_valgrind = true } parser.on("--fake-no-valgrind", "Pretend not to run under Valgrind") { opts.fake_valgrind = false } parser.on("--valgrind BIN", "Use BIN as Valgrind executable") { |bin| opts.enable_valgrind = true; opts.valgrind = bin } parser.on("--valgrind-opts OPTS", "Pass command line options OPTS to valgrind") { |s| opts.valgrind_opts = s } parser.on("--wordsize N", "Set the word size") { |n| opts.wordsize = n.to_i } parser.on("-C", "--directory DIR", "Directory for test cases") { |dir| opts.dir = search_dir(dir, opts) } parser.on("-n", "--name NAME", "Run tests matching NAME") { |pat| opts.name_patterns << pat } parser.on("-x", "--exclude NAME", "Do not run tests matching NAME") { |pat| opts.exclude_patterns << pat } parser.on("-g", "--group GROUPID/GROUPCOUNT", "Split tests and run only one group") { |group| opts.group_id, opts.group_count = parse_group(group) } parser.on("--fold-markers OPEN,CLOSE", "Set fold markers") { |open_close| a = open_close.split(",", 2); opts.fold_markers = { open: a[0], close: a[1] } } parser.on("-v", "--verbose", "Enable verbose output") { opts.verbose = true } parser.on("--show-newlines", "Show newline characters") { opts.show_newlines = true } parser.on("-D TEST=NAME", "Alternative way to run tests NAME") { |pat| opts.name_patterns << parse_def(pat) } begin parser.parse!(ARGV) rescue OptionParser::ParseError => e $stderr.puts(e.backtrace.first + ": #{e.message} (#{e.class})") e.backtrace[1..-1].each { |m| $stderr.puts("\tfrom #{m}") } puts(parser) exit(1) end # Parse other arguments. while !ARGV.empty? if ARGV[0] =~ /\.frm$/ opts.files << search_file(ARGV[0], opts) elsif ARGV[0] =~ /valgrind/ opts.enable_valgrind = true opts.valgrind = ARGV[0] elsif ARGV[0] =~ /mpirun/ || ARGV[0] =~ /mpiexec/ opts.mpirun = ARGV[0] elsif ARGV[0] =~ /form/ || ARGV[0] =~ /vorm/ || File.executable?(ARGV[0]) opts.form = ARGV[0] elsif File.exist?(ARGV[0]) opts.files << ARGV[0] else opts.name_patterns << ARGV[0] end ARGV.shift end # Make test cases. FormTest.tests = TestCases.new FormTest.tests.name_patterns = opts.name_patterns FormTest.tests.exclude_patterns = opts.exclude_patterns if opts.files.empty? Dir.glob(File.join(opts.dir.nil? ? TESTDIR : opts.dir, "*.frm")).sort.each do |file| opts.files << search_file(file, opts) end end opts.files.uniq.sort.each do |file| FormTest.tests.make_ruby_file(file, opts.fold_markers) end # Split tests into groups and run only one group. if opts.group_id infos = FormTest.tests.classes_info_list total = infos.length divided = total / opts.group_count reminder = total - divided * opts.group_count test_nos = [] n = 0 (1..opts.group_count).each do |i| (1..divided).each do if i == opts.group_id test_nos.push(n) end n += 1 end if i <= reminder if i == opts.group_id test_nos.push(n) end n += 1 end end infos = FormTest.tests.classes_info_list infos.each_with_index do |info, i| if !test_nos.include?(i) FormTest.tests.delete(info.classname) end end end # --list option. if opts.list infos = FormTest.tests.classes_info_list infos.each do |info| puts("#{info.foldname} (#{info.where})") end puts("#{infos.length} tests") exit end # --path option. if !opts.path.nil? ENV["PATH"] = add_path(ENV.fetch("PATH", nil), opts.path) end # Default mpirun_opts. if opts.mpirun_opts.nil? opts.mpirun_opts = DEFAULT_MPIRUN_OPTS end # Default valgrind_opts. if opts.valgrind_opts.nil? opts.valgrind_opts = DEFAULT_VALGRIND_OPTS end # Default timeout. if opts.timeout.nil? opts.timeout = DEFAULT_TIMEOUT # Running Valgrind can be really slow. if opts.enable_valgrind opts.timeout *= VALGRIND_TIME_DILATION end end # Initialize the FORM configuration. FormTest.cfg = FormConfig.new(opts.form, opts.mpirun, opts.mpirun_opts, opts.enable_valgrind ? opts.valgrind : nil, opts.valgrind_opts, opts.fake_valgrind, opts.wordsize, opts.ncpu, [opts.timeout, 1].max, [opts.retries, 1].max, opts.stat, opts.full, opts.verbose, opts.show_newlines) FormTest.cfg.check puts("Check #{FormTest.cfg.form_bin}") puts(FormTest.cfg.head) end def need_output_detailed_statistics? # Check if already done. $output_detailed_statistics_done ||= false return false if $output_detailed_statistics_done # Check if --stat enabled. return false if FormTest.cfg.nil? || !FormTest.cfg.stat # Check if enabled test cases exist. return false if FormTest.tests.classes_info_list.empty? true end def output_detailed_statistics(output = nil) return if !need_output_detailed_statistics? $output_detailed_statistics_done = true # method to output output ||= method(:puts) # Print detailed statistics. term_width = IO.console_size[1] infos = FormTest.tests.classes_info_list max_foldname_width = infos.map { |info| info.foldname.length }.max max_where_width = infos.map { |info| info.where.length }.max + 2 status_width = 7 time_width = 13 bar_width = term_width - max_foldname_width - max_where_width - status_width - time_width - 5 if bar_width < 12 bar_width = 12 elsif bar_width > 40 bar_width = 40 end infos.each do |info| (0..(info.sources.length - 1)).each do |i| t = 0 if !info.times.nil? && i < info.times.length t = info.times[i] end timeout = FormTest.cfg.timeout if !info.time_dilation.nil? timeout *= info.time_dilation end if i == 0 s = format("%s %s %s %s%s", lpad(info.foldname, max_foldname_width), lpad("(#{info.where})", max_where_width), lpad(info.status.nil? ? "UNKNOWN" : info.status, status_width), bar_str(t, timeout, bar_width), format_time(t, timeout)) else s = format("%s %s %s %s%s", lpad("", max_foldname_width), lpad("", max_where_width), lpad("", status_width), bar_str(t, timeout, bar_width), format_time(t, timeout)) end color_key = case info.status when "FAILED", "TIMEOUT" then "failure" when "SKIPPED" then "pending" when "OMITTED" then "omission" end if !color_key.nil? begin output.call(s, color(color_key)) rescue StandardError output.call(s) end else output.call(s) end end end output.call("Default timeout: #{FormTest.cfg.timeout}s") true end # Return the string with padding to left. def lpad(str, len) if str.length > len str[0..(len - 1)] elsif str.length < len str + " " * (len - str.length) else str end end # Return a string for a bar chart. def bar_str(value, max_value, bar_width) bar_body_width = bar_width - 2 bar = " " * bar_width bar[0] = "|" bar[bar_width - 1] = "|" pos = (Float(value) / max_value * bar_body_width).round if pos < 0 pos = 0 elsif pos > bar_body_width pos = bar_body_width end if pos >= 1 (1..pos).each do |i| bar[i] = "#" end end bar end # Format an elapsed time. def format_time(time, max_time) overflow = time > max_time if overflow t = max_time else t = time end t = Float(t) h = Integer(t / 3600) t %= 3600 m = Integer(t / 60) t %= 60 s = Integer(t) t %= 1 ms = Integer(t * 1000) format("%s%02d:%02d:%02d.%03d", overflow ? ">" : " ", h, m, s, ms) end if $0 == __FILE__ main end form-5.0.1/check/formunit/0000755000175100017510000000000015217035744011153 5form-5.0.1/check/formunit/fu.frm0000644000175100017510000000345115217035721012211 #- * Print an estimate for form units per hour on the current machine. * The definition of 1 form unit is: * * 1fu = performing a trace with 14 Dirac's gamma matrices 3600 times. * * This program is based on aap1000.frm. * * Caveat: the number obtained by this program may (strongly) depend on the * number of CPUs, buffer sizes as well as other environmental conditions. * Parallel versions can have relatively large overheads for such simple tasks. * MPI implementations tend to use busy-wait on blocking operations, which * suppresses the number. Moreover, here we use the CPU time instead of the real * time. *--#[ Fuph : #ifndef `N' #define N "192" #endif #define NUM "14" #ifdef `QUIET' Off stats; #endif #procedure FormatFloat(x,str,n) #$x = `x'; #do i=0,`n' #$i = integer_($x); #$x = ($x - $i) * 10; #if `i' == 0 #redefine `str' "`$i'." #else #redefine `str' "``str''`$i'" #endif #enddo #endprocedure I m1,...,m`NUM'; S x,j; CF f; #$t0 = `timer_'; L FF = sum_(j,1,`N',f(j)); .sort id f(x?) = 1; multiply g_(1,m1,...,m`NUM'); trace4,1; .sort Drop; #$t = (`timer_' - `$t0') / 1000; #$fu = `N' / 3600; #$fuph = $fu / $t * 3600; #define t #call FormatFloat($t,t,3) #define fu #call FormatFloat($fu,fu,6) #define fuph #call FormatFloat($fuph,fuph,2) Format 120; #if `NTHREADS_' >= 2 #write " `fu' form units in `t' seconds (total cpu time) with {`NTHREADS_'-1} workers" #write " corresponding to `fuph' form units per hour per core" #elseif `NPARALLELTASKS_' >= 2 #write " `fu' form units in `t' seconds (total cpu time) with `NPARALLELTASKS_' processes" #write " corresponding to `fuph' form units per hour per core" #else #write " `fu' form units in `t' seconds (cpu time)" #write " corresponding to `fuph' form units per hour" #endif *--#] Fuph : .end form-5.0.1/check/README.md0000644000175100017510000002362215217035721010507 # FORM Test Suite This directory contains a collection of test cases that can be used for verifying the behaviour of FORM. It also has a script to run the test cases and check the results. ## Prerequisites The test runner script is written in [Ruby](https://www.ruby-lang.org/) and requires Ruby 2.0 or later. The script uses the library commonly referred to as `test/unit`. In some Linux distributions, it is installed together with Ruby, while some distributions may have it as an optional package, or one may need to manually install [test-unit](http://test-unit.github.io/test-unit/en/) via the `gem` command. ## Usage ### From the build system To use the test suite from the automatic build system (see also the [INSTALL](../INSTALL) file), run the following command: ```bash # in the root build directory make check ``` which tests the executables (release versions) compiled by the build system. ### Testing in standalone mode Alternatively, one can run the test runner script directly: ```bash # in the "check" directory ./check.rb ``` By default, this runs tests with the `form` executable found in `$PATH`. To test another executable, specify its path as a command-line argument: ```bash ./check.rb /path/to/form ``` One can also specify a TFORM (or ParFORM) executable in this way. TFORM and ParFORM will be run with 4 CPUs (can be changed by the `--cpu N` option). By default, all test cases in all FORM files (`*.frm`) found in the `check` directory (not in subdirectories) are used. To select test cases or FORM files to run, specify their names as command-line arguments. For example: ```bash ./check.rb Issue8 ./check.rb 'divmod_*' ./check.rb examples.frm ``` For more advanced options, refer to the help message using the `--help` option. ## Writing tests ### Where to add test cases? Currently, the standard test set (run by default) includes: - `examples.frm`: Examples provided in the manual. - `features.frm`: Test cases for newly added features. - `fixes.frm`: Test cases for bug fixes. - `user.frm`: Test cases contributed by users. Each test case in these files should finish in a short time: the timeout is set to 10 seconds. Bigger tests that take more time are put in subdirectories (e.g., `extra`) and should be specified by command-line options when the test suite is invoked: ```bash ./check.rb -C extra # Extra library files must be available in FORMPATH. ``` ### Structure of a test case A test case is given as a fold in a FORM file. The following is a simple example: ``` *--#[ Test1 : S x; L F = (1+x)^2; P; .end assert succeeded? assert result("F") =~ expr("1 + 2*x + x^2") *--#] Test1 : ``` The fold name `Test1` gives the name of the test case, which should be unique. The part before `.end` is a normal FORM program. After `.end`, one can write a Ruby program to check the results. The `assert` method checks whether its argument evaluates to `true`. In this example: - The first assertion verifies `succeeded?`, which returns `true` if the FORM finishes successfully. - The second assertion checks the printed result of the expression `F` by a regular expression matching (`=~`). - On the left-hand side, `result("F")` returns the (lastly) printed output for the expression `F` as a string. - On the right-hand side, `expr("...")` creates a regular expression by removing white spaces in its argument. Since `expr()` removes all white spaces, one can include new lines in the argument. For example: ``` *--#[ Test2 : S x; L F = (1+x)^2; P +s; .end assert succeeded? assert result("F") =~ expr(" + 1 + 2*x + x^2 ") *--#] Test2 : ``` which is convenient to copy and paste a long output from a terminal. Two or more FORM programs, separated by `.end`, can be put in a test case. The part after the last `.end` is considered as a Ruby program. For example: ``` *--#[ Test3 : S x; G F = (1+x)^2; P; .store Save out.sav; .end Load out.sav; L G = F; P; .end assert succeeded? assert result("F") =~ expr("1 + 2*x + x^2") assert result("G") =~ expr("1 + 2*x + x^2") *--#] Test3 : ``` Some test cases need to run only under specific conditions. In such cases, one can use special instructions starting with `#`. For example: ``` *--#[ Test4 : S x; L F = #pipe echo "(1+x)^2" ; P; .end #require unix? assert succeeded? assert result("F") =~ expr("1 + 2*x + x^2") *--#] Test4 : ``` In this example, `#require unix?` ensures that the test runs only on Unix, where `#pipe` is expected to work. ### Available environment variables The following environment variables are accessible in FORM test cases via preprocessor variables. - `FORM` Path to the currently used FORM executable, possibly with additional command-line options. Example: `/home/form-dev/form/build/sources/tvorm -w4` - `TESTFILE` Path to the FORM test file. Example: `/home/form-dev/form/check/examples.frm` - `TESTFILEDIR` Path to the directory containing the FORM test file. This path is prepended to the `FORMPATH` environment variable. Example: `/home/form-dev/form/check` - `TESTCASE` Name of the current test case. Example: `Var_Symbols_1` - `TESTTMPDIR` Path to the temporary directory used as the current working directory. Example: `/tmp/form_check_20251121-426943-de5rmj/Test_Var_Symbols_1_20251121-426943-cczq26` ### Available methods The following methods are available in Ruby test programs. #### Execution configuration - `timeout → integer or float` Timeout duration in seconds. - `ncpu → integer` Number of assigned CPUs. - `total_memory → integer` Total physical memory available in bytes. - `serial? → bool` `true` if FORM is the serial version, otherwise `false`. - `threaded? → bool` `true` if FORM is the multithreaded version (TFORM), otherwise `false`. - `mpi? → bool` `true` if FORM is the MPI version (ParFORM), otherwise `false`. - `flint? → bool` `true` if FORM was built with FLINT support, otherwise `false`. - `valgrind? → bool` `true` if FORM is running under Valgrind, otherwise `false`. - `wordsize → integer` Word size in bytes used by FORM (`4` on 64-bit systems). - `cygwin? → bool` `true` if running on Cygwin, otherwise `false`. - `mac? → bool` `true` if running on macOS, otherwise `false`. - `linux? → bool` `true` if running on Linux, otherwise `false`. - `unix? → bool` `true` if running on Unix, otherwise `false`. - `windows? → bool` `true` if running on Windows, otherwise `false`. - `travis? → bool` `true` if running on Travis CI, otherwise `false`. - `github? → bool` `true` if running on GitHub Actions, otherwise `false`. #### Job status - `return_value → integer` Exit status of the FORM job. - `finished? → bool` `true` if the FORM job finished within the timeout, otherwise `false`. - `succeeded? → bool` `true` if the FORM job finished without any problems, otherwise `false`. - `warning? → bool` `true` if the FORM job issued a warning, otherwise `false`. - `warning?(expected_message : string) → bool` `true` if the FORM job issued the expected warning, otherwise `false`. The following methods are similar to `warning?`, but they check for preprocessor errors, compile-time errors, and run-time errors, respectively: - `preprocess_error? → bool` `preprocess_error?(expected_message : string) → bool` - `compile_error? → bool` `compile_error?(expected_message : string) → bool` - `runtime_error? → bool` `runtime_error?(expected_message : string) → bool` #### Standard streams - `stdout → string` Standard output of the FORM job. - `stderr → string` Standard error of the FORM job. #### Expressions The following methods assume the default format for printing expressions: - `result(expr_name : string) → string` The last printed output of the specified expression. - `result(expr_name : string, index : integer) → string` The printed output of the specified expression at the given index (zero-based). - `exact_result(expr_name : string) → string` `exact_result(expr_name : string, index : integer) → string` Similar to `result`, but returns the exact output, preserving line breaks and whitespaces. The following methods assume the default format for statistics: - `nterms(expr_name : string) → integer` `nterms(expr_name : string, index : integer) → integer` The number of terms as reported in the statistics for the specified expression. - `bytesize(expr_name : string) → integer` `bytesize(expr_name : string, index : integer) → integer` The size in bytes as reported in the statistics for the specified expression. #### Helper methods - `exact_pattern(str : string) → regexp` Regular expression constructed from the given text with escaping any special characters. - `pattern(str : string) → regexp` Similar to `exact_pattern`, but ignores whitespaces. - `expr(str : string) → regexp` Similar to `pattern`, but matches only with the whole expression. - `file(filename : string) → string` `read(filename : string) → string` Text in the specified file. - `write(filename : string, text : string) → nil` Writes a text into the specified file. ### Available instructions `check.rb` recognises the following instructions. - `#require ` Ensures that the test is executed only if the specified `` is met. - `#pend_if ` Marks the test as pending if the specified `` is met. - `#prepare ` Executes the given `` before running the test. For example: ``` #prepare write "foo.prc", "#procedure foo\n#message foo\n#endprocedure" ``` - `#ulimit ` Sets the resource limits. This is done via the `ulimit` command. For example: ``` #require linux? #ulimit -v 8_000_000 ``` This sets the maximum amount of virtual memory available to 8,000,000 KiB (~ 8GB). - `#time_dilation ` Multiplies the timeout by the specified `` factor. For example: ``` #time_dilation 2.0 ``` form-5.0.1/check/coverage.frm0000644000175100017510000004711715217035721011536 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ cov_dollar : #- Off stats; #$Pzero = 2-1-1; #$Pone = 1; #$Ptwo = `$Pone'+$Pone+$Pzero+`$Pzero'; #if `$Pone' == `$Ptwo' #terminate #endif #if (`$Pone' > `$Ptwo') || (`$Pone' >= `$Ptwo') #terminate #endif #if (`$Ptwo' < `$Pone') || (`$Ptwo' <= `$Pone') #terminate #endif Symbol x,y; Local test = (`$Pone'*x+y)^`$Ptwo'; .sort #$Ptest = test; $test = test; ModuleOption,local $test; Print; .end assert succeeded? *--#] cov_dollar : *--#[ cov_if : Symbol x(:100),y,z; CFunction f,g(symmetric),h; Vector p,q; Tensor T,G(symmetric); Index mu,i1,...,i8; Set hset: h; Local test = x * ( + z^2 + z^3 + f(x) + f(y) + f(y)*x + p(mu) + p + p.q + T(p)*z + f(p) + g(p) + h(p) + g(i1,i2)*g(i1,i2) + g(i1,i2)*g(i1,i3) + g(i1,i2,i3)*g(i1,i2,i3) + *...**g(i8,i1) + G(i1,i2)*G(i1,i2) + G(i1,i2)*G(i1,i3) + G(i1,i2,i3)*G(i1,i2,i3) + *...**G(i8,i1) ); Local test2 = x; .sort #$one = 1; #$two = 2; #$pdotq = p.q; #if ( (maxpowerof(x) > 100) || (minpowerof(x) > -100) ) Multiply z; #endif #if ( termsin(test) == 15 ) Multiply 2; #endif #if ( exists(test3) ) Multiply 1000; #endif #if (isfactorized(test2) == 0) If (Expression(test2)); Identify x = 100; EndIf; #endif If (Match(f(x?)*x?)); Identify x = 1; EndIf; If (Count(z,1) == 3); Identify x = 1; ElseIf (Count(z,1) == $two); Identify x = 2; EndIf; If (Count(p+v,1) == 1); Identify x = 1; EndIf; If (Count(p+d,1) == 1); Identify x = 2; EndIf; If (Count(p+f,1) == 1); Identify x = 3; EndIf; If (Count(p+?{f,g},1) == 1); Identify x = 4; EndIf; If (Count(p+?hset,1) == 1); Identify x = 5; EndIf; If (Occurs(p.q)); Multiply 6; EndIf; If (Match($pdotq)); Multiply 6; EndIf; If (Occurs(f) || Match(g(p))); Multiply 2; Identify x = 2; EndIf; If ( (Coefficient == MultipleOf(3)) && (Count(z,1) == $one) ); Multiply z; EndIf; If (FindLoop(g, arguments=2, loopsize=2)); Identify x = 2; EndIf; If (FindLoop(g, arguments=3, loopsize=2)); Identify x = 3; EndIf; If (FindLoop(g, arguments=3, loopsize<3, include=i3)); Multiply 4; EndIf; If (FindLoop(g, arguments=2, loopsize=8)); Multiply 5; EndIf; If (FindLoop(G, arguments=2, loopsize=2)); Identify x = 2; EndIf; If (FindLoop(G, arguments=3, loopsize=2)); Identify x = 3; EndIf; If (FindLoop(G, arguments=3, loopsize<3, include=i3)); Multiply 4; EndIf; If (FindLoop(G, arguments=2, loopsize=8)); Multiply 5; EndIf; If ($two); Multiply 2; EndIf; If (1 >= $two); Multiply 1000; EndIf; If (1 < 2); Multiply 2; EndIf; If (1 <= 2); Multiply 2; EndIf; If (1 > 2); Multiply 1000; EndIf; If (1 >= 2); Multiply 1000; EndIf; If (0); Multiply 1000; EndIf; Print; .end assert succeeded? assert result("test") =~ expr("16*z^2 + 8*z^3 + 576*p.q + 8*p(mu) + 8*p + 16*f(x) + 96*f(y) + 64*f(p) + 64*g(p) + 16*g(i1,i2)^2 + 8*g(i1,i2)*g(i1,i3)*x + 40*g(i1,i2)*g(i1,i8)*g(i2,i3)*g(i3,i4)*g(i4,i5)*g(i5,i6)*g(i6,i7)*g(i7,i8)*x + 96*g(i1,i2,i3)^2 + 40*h(p) + 24*T(p)*z^2 + 96*G(i1,i2,i3)*G(i1,i2,i3) + 16*G(i1,i2)*G(i1,i2) + 8*G(i1,i2)*G(i1,i3)*x + 40*G(i1,i2)*G(i1,i8)*G(i2,i3)*G(i3,i4)*G(i4,i5)*G(i5,i6)*G(i6,i7)*G(i7,i8)*x") assert result("test2") =~ expr("800") *--#] cov_if : *--#[ cov_factorin_ : CFunction f; Symbol x1,x2,x3; Vector p,q; Index mu; Local F = 10*x1*p.q*p(mu)*f(x1)*(x1+x2+x3/3); Local F2 = 10*x1*p.q*p(mu)*f(x1)*(x1+x2+x3/3); #$f = 10*x1*p.q*p(mu)*f(x1)*(x1+x2+x3/3); .sort Drop F2; Local G = factorin_(F); Local G2 = factorin_(F2); Local g = factorin_($f); Print; .end assert succeeded? assert result("G") =~ expr("10/3*f(x1)*p(mu)*p.q*x1") assert result("G2") =~ expr("10/3*f(x1)*p(mu)*p.q*x1") assert result("g") =~ expr("10/3*f(x1)*p(mu)*p.q*x1") *--#] cov_factorin_ : *--#[ cov_hideskip : #: scratchsize 1 #: hidesize 1 Symbol x,y,z; Local f = (1+x+y+z)^70; Local g = (1+x+y+z)^70; .sort Hide f; Skip g; Identify x = 2; Identify y = 2; Identify z = 2; .sort UnHide f; Identify x = 1; Identify y = 1; Identify z = 1; Print; .end assert succeeded? assert result("f") =~ expr("1393796574908163946345982392040522594123776") assert result("g") =~ expr("1393796574908163946345982392040522594123776") *--#] cov_hideskip : *--#[ cov_identify_once : #- Symbol n,m,x,y; Vector p,q,r,s; CFunction f,g; Set two:2; #$two = 2; Local testS = + x*f(1) + x*f(2) + x^2*f(2) + x^2*f(3) + x^-1*f(-1) + x^-1*f(0) ; Local testDP = + p.q*f(1) + p.q*f(2) + p.q^2*f(2) + p.q^2*f(3) + p.q^-1*f(-1) + p.q^-1*f(0) ; * Arrange so the later patterns could match more than once: Identify x^n? = x^n * y^n; Identify p.q^n? = p.q^n * r.s^n; Identify,once x? = x * g(1); Identify,once x?^2 = x^2 * g(2); Identify,once x?^n?two = x^n * g(3); Identify,once x?^$two = x^$two * g(4); Identify,once x?^n?!two = x^n * g(5); Identify,once f(n?)*x?^n? = f(n)*x^n * g(6); Identify,once f(m?!{n?})*x?^n?!{m?} = f(m)*x^n * g(7); Identify,once p?.q? = p.q * g(1); Identify,once p?.q?^2 = p.q^2 * g(2); Identify,once p?.q?^n?two = p.q^n * g(3); Identify,once p?.q?^$two = p.q^$two * g(4); Identify,once p?.q?^n?!two = p.q^n * g(5); Identify,once f(n?)*p?.q?^n? = f(n)*p.q^n * g(6); Identify,once f(m?!{n?})*p?.q?^n?!{m?} = f(m)*p.q^n * g(7); Print; .end assert succeeded? assert result("testS") =~ expr(" f(-1)*g(5)*g(6)*x^-1*y^-1 + f(0)*g(5)*g(6)*g(7)*x^-1*y^-1 + 2*f(1)*g(1)* g(5)*g(6)*x*y + 2*f(2)*g(1)*g(2)*g(3)*g(4)*g(6)*x^2*y^2 "); assert result("testDP") =~ expr(" f(-1)*g(5)*g(6)*p.q^-1*r.s^-1 + f(0)*g(5)*g(6)*g(7)*p.q^-1*r.s^-1 + f(1) *g(1)*g(4)*g(5)*g(6)*g(7)*p.q^2*r.s + f(2)*g(1)*g(2)*g(3)*g(4)*g(5)*g(6) *g(7)*p.q^3*r.s^2 + f(2)*g(1)*g(4)*g(5)*g(6)*g(7)*p.q^2*r.s + f(3)*g(1)* g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*p.q^3*r.s^2 "); *--#] cov_identify_once : *--#[ cov_identify_only : #- Symbol n,m,x; Vector p,q; CFunction f,g; Vector v; Index mu,nu; Set two:2; #$two = 2; Local test = + x + x^2 + x^-1 + x*f(1) + x*f(2) + x^2*f(2) + x^2*f(3) + x^-1*f(-1) + x^-1*f(0) ; * Generate some combinations Identify x^n? = (1+x^n) * (1+p.q^n) * (1 + (mu+nu)*v(mu)); .sort Identify,only x = x * g(1); Identify,only x^2 = x^2 * g(2); Identify,only x^n?two = x^2 * g(3); Identify,only x^$two = x^$two * g(4); Identify,only x?^2 = x^2 * g(5); Identify,only x?^n?two = x^n * g(6); Identify,only x?^$two = x^$two * g(7); Identify,only x?^n?!two = x^n * g(8); Identify,only f(n?)*x^n? = f(n)*x^n * g(9); Identify,only f(n?)*x?^n? = f(n)*x^n * g(10); Identify,only f(m?!{n?})*x^n?!{m?} = f(m)*x^n * g(11); Identify,only f(m?!{n?})*x?^n?!{m?} = f(m)*x^n * g(12); Identify,only p.q = p.q * g(13); Identify,only p.q^2 = p.q^2 * g(14); Identify,only p.q^n?two = p.q^2 * g(15); Identify,only p.q^$two = p.q^$two * g(16); Identify,only p.q?^2 = p.q^2 * g(17); Identify,only p?.q?^2 = p.q^2 * g(18); Identify,only p?.q?^2 = p.q^2 * g(19); Identify,only p.q?^n?two = p.q^n * g(20); Identify,only p.q?^$two = p.q^$two * g(21); Identify,only p.q?^n?!two = p.q^n * g(22); Identify,only f(n?)*p.q^n? = f(n)*p.q^n * g(23); Identify,only f(n?)*p.q?^n? = f(n)*p.q^n * g(24); Identify,only f(n?)*p?.q?^n? = f(n)*p.q^n * g(25); Identify,only f(m?!{n?})*p.q^n?!{m?} = f(m)*p.q^n * g(26); Identify,only f(m?!{n?})*p.q?^n?!{m?} = f(m)*p.q^n * g(27); Identify,only f(m?!{n?})*p?.q?^n?!{m?} = f(m)*p.q^n * g(28); Identify,only mu?*v?(mu?)*f(n?)*p.q^n? = mu*v(mu)*f(n)*p.q^n * g(29); Identify,only mu?*v?(mu?)*f(n?)*p.q?^n? = mu*v(mu)*f(n)*p.q^n * g(30); Identify,only mu?*v?(mu?)*f(n?)*p?.q?^n? = mu*v(mu)*f(n)*p.q^n * g(31); Identify,only mu?*v?(mu?)*f(m?!{n?})*p.q^n?!{m?} = mu*v(mu)*f(m)*p.q^n * g(32); Identify,only mu?*v?(mu?)*f(m?!{n?})*p.q?^n?!{m?} = mu*v(mu)*f(m)*p.q^n * g(33); Identify,only mu?*v?(mu?)*f(m?!{n?})*p?.q?^n?!{m?} = mu*v(mu)*f(m)*p.q^n * g(34); Identify,only nu?!{mu?}*v?(mu?!{nu?})*f(n?)*p.q^n? = nu*v(mu)*f(n)*p.q^n * g(35); Identify,only nu?!{mu?}*v?(mu?!{nu?})*f(n?)*p.q?^n? = nu*v(mu)*f(n)*p.q^n * g(36); Identify,only nu?!{mu?}*v?(mu?!{nu?})*f(n?)*p?.q?^n? = nu*v(mu)*f(n)*p.q^n * g(37); Identify,only nu?!{mu?}*v?(mu?!{nu?})*f(m?!{n?})*p.q^n?!{m?} = nu*v(mu)*f(m)*p.q^n * g(38); Identify,only nu?!{mu?}*v?(mu?!{nu?})*f(m?!{n?})*p.q?^n?!{m?} = nu*v(mu)*f(m)*p.q^n * g(39); Identify,only nu?!{mu?}*v?(mu?!{nu?})*f(m?!{n?})*p?.q?^n?!{m?} = nu*v(mu)*f(m)*p.q^n * g(40); Print; .end assert succeeded? assert result("test") =~ expr(" 3 + 3*mu*v(mu) + 3*nu*v(mu) + f(-1)*g(8)*g(9)*g(10)*g(22)*g(23)*g(24)*g( 25)*p.q^-1*x^-1 + f(-1)*g(8)*g(9)*g(10)*g(22)*g(23)*g(24)*g(25)*g(29)*g( 30)*g(31)*mu*v(mu)*p.q^-1*x^-1 + f(-1)*g(8)*g(9)*g(10)*g(22)*g(23)*g(24) *g(25)*g(35)*g(36)*g(37)*nu*v(mu)*p.q^-1*x^-1 + f(-1)*g(8)*g(9)*g(10)*g( 26)*x^-1 + f(-1)*g(8)*g(9)*g(10)*g(26)*g(32)*mu*v(mu)*x^-1 + f(-1)*g(8)* g(9)*g(10)*g(26)*g(38)*nu*v(mu)*x^-1 + f(-1)*g(11)*g(22)*g(23)*g(24)*g( 25)*p.q^-1 + f(-1)*g(11)*g(22)*g(23)*g(24)*g(25)*g(29)*g(30)*g(31)*mu* v(mu)*p.q^-1 + f(-1)*g(11)*g(22)*g(23)*g(24)*g(25)*g(35)*g(36)*g(37)*nu* v(mu)*p.q^-1 + f(-1)*g(11)*g(26) + f(-1)*g(11)*g(26)*g(32)*mu*v(mu) + f( -1)*g(11)*g(26)*g(38)*nu*v(mu) + f(0)*g(8)*g(11)*g(12)*g(22)*g(26)*g(27) *g(28)*p.q^-1*x^-1 + f(0)*g(8)*g(11)*g(12)*g(22)*g(26)*g(27)*g(28)*g(32) *g(33)*g(34)*mu*v(mu)*p.q^-1*x^-1 + f(0)*g(8)*g(11)*g(12)*g(22)*g(26)*g( 27)*g(28)*g(38)*g(39)*g(40)*nu*v(mu)*p.q^-1*x^-1 + f(0)*g(8)*g(11)*g(12) *g(23)*x^-1 + f(0)*g(8)*g(11)*g(12)*g(23)*g(29)*mu*v(mu)*x^-1 + f(0)*g(8 )*g(11)*g(12)*g(23)*g(35)*nu*v(mu)*x^-1 + f(0)*g(9)*g(22)*g(26)*g(27)*g( 28)*p.q^-1 + f(0)*g(9)*g(22)*g(26)*g(27)*g(28)*g(32)*g(33)*g(34)*mu* v(mu)*p.q^-1 + f(0)*g(9)*g(22)*g(26)*g(27)*g(28)*g(38)*g(39)*g(40)*nu* v(mu)*p.q^-1 + f(0)*g(9)*g(23) + f(0)*g(9)*g(23)*g(29)*mu*v(mu) + f(0)* g(9)*g(23)*g(35)*nu*v(mu) + f(1)*g(1)*g(8)*g(9)*g(10)*g(13)*g(21)*g(26)* g(27)*g(28)*p.q^2*x + f(1)*g(1)*g(8)*g(9)*g(10)*g(13)*g(21)*g(26)*g(27)* g(28)*g(32)*g(33)*g(34)*mu*v(mu)*p.q^2*x + f(1)*g(1)*g(8)*g(9)*g(10)*g( 13)*g(21)*g(26)*g(27)*g(28)*g(38)*g(39)*g(40)*nu*v(mu)*p.q^2*x + f(1)*g( 1)*g(8)*g(9)*g(10)*g(26)*x + f(1)*g(1)*g(8)*g(9)*g(10)*g(26)*g(32)*mu* v(mu)*x + f(1)*g(1)*g(8)*g(9)*g(10)*g(26)*g(38)*nu*v(mu)*x + f(1)*g(11)* g(13)*g(21)*g(26)*g(27)*g(28)*p.q^2 + f(1)*g(11)*g(13)*g(21)*g(26)*g(27) *g(28)*g(32)*g(33)*g(34)*mu*v(mu)*p.q^2 + f(1)*g(11)*g(13)*g(21)*g(26)* g(27)*g(28)*g(38)*g(39)*g(40)*nu*v(mu)*p.q^2 + f(1)*g(11)*g(26) + f(1)* g(11)*g(26)*g(32)*mu*v(mu) + f(1)*g(11)*g(26)*g(38)*nu*v(mu) + f(2)*g(1) *g(8)*g(11)*g(12)*g(13)*g(21)*g(23)*g(24)*g(25)*p.q^2*x + f(2)*g(1)*g(8) *g(11)*g(12)*g(13)*g(21)*g(23)*g(24)*g(25)*g(29)*g(30)*g(31)*mu*v(mu)* p.q^2*x + f(2)*g(1)*g(8)*g(11)*g(12)*g(13)*g(21)*g(23)*g(24)*g(25)*g(35) *g(36)*g(37)*nu*v(mu)*p.q^2*x + f(2)*g(1)*g(8)*g(11)*g(12)*g(26)*x + f(2 )*g(1)*g(8)*g(11)*g(12)*g(26)*g(32)*mu*v(mu)*x + f(2)*g(1)*g(8)*g(11)*g( 12)*g(26)*g(38)*nu*v(mu)*x + f(2)*g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(9)*g( 10)*g(14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*g(23)*g(24)*g(25)*p.q^2* x^2 + f(2)*g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(9)*g(10)*g(14)*g(15)*g(16)*g( 17)*g(18)*g(19)*g(20)*g(23)*g(24)*g(25)*g(29)*g(30)*g(31)*mu*v(mu)*p.q^2 *x^2 + f(2)*g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(9)*g(10)*g(14)*g(15)*g(16)* g(17)*g(18)*g(19)*g(20)*g(23)*g(24)*g(25)*g(35)*g(36)*g(37)*nu*v(mu)* p.q^2*x^2 + f(2)*g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(9)*g(10)*g(26)*x^2 + f( 2)*g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(9)*g(10)*g(26)*g(32)*mu*v(mu)*x^2 + f(2)*g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(9)*g(10)*g(26)*g(38)*nu*v(mu)*x^2 + f(2)*g(11)*g(13)*g(21)*g(23)*g(24)*g(25)*p.q^2 + f(2)*g(11)*g(13)*g( 21)*g(23)*g(24)*g(25)*g(29)*g(30)*g(31)*mu*v(mu)*p.q^2 + f(2)*g(11)*g(13 )*g(21)*g(23)*g(24)*g(25)*g(35)*g(36)*g(37)*nu*v(mu)*p.q^2 + f(2)*g(11)* g(14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*g(23)*g(24)*g(25)*p.q^2 + f(2) *g(11)*g(14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*g(23)*g(24)*g(25)*g(29) *g(30)*g(31)*mu*v(mu)*p.q^2 + f(2)*g(11)*g(14)*g(15)*g(16)*g(17)*g(18)* g(19)*g(20)*g(23)*g(24)*g(25)*g(35)*g(36)*g(37)*nu*v(mu)*p.q^2 + 2*f(2)* g(11)*g(26) + 2*f(2)*g(11)*g(26)*g(32)*mu*v(mu) + 2*f(2)*g(11)*g(26)*g( 38)*nu*v(mu) + f(3)*g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(11)*g(12)*g(14)*g(15 )*g(16)*g(17)*g(18)*g(19)*g(20)*g(26)*g(27)*g(28)*p.q^2*x^2 + f(3)*g(2)* g(3)*g(4)*g(5)*g(6)*g(7)*g(11)*g(12)*g(14)*g(15)*g(16)*g(17)*g(18)*g(19) *g(20)*g(26)*g(27)*g(28)*g(32)*g(33)*g(34)*mu*v(mu)*p.q^2*x^2 + f(3)*g(2 )*g(3)*g(4)*g(5)*g(6)*g(7)*g(11)*g(12)*g(14)*g(15)*g(16)*g(17)*g(18)*g( 19)*g(20)*g(26)*g(27)*g(28)*g(38)*g(39)*g(40)*nu*v(mu)*p.q^2*x^2 + f(3)* g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(11)*g(12)*g(26)*x^2 + f(3)*g(2)*g(3)*g(4 )*g(5)*g(6)*g(7)*g(11)*g(12)*g(26)*g(32)*mu*v(mu)*x^2 + f(3)*g(2)*g(3)* g(4)*g(5)*g(6)*g(7)*g(11)*g(12)*g(26)*g(38)*nu*v(mu)*x^2 + f(3)*g(11)*g( 14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*g(26)*g(27)*g(28)*p.q^2 + f(3)* g(11)*g(14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*g(26)*g(27)*g(28)*g(32)* g(33)*g(34)*mu*v(mu)*p.q^2 + f(3)*g(11)*g(14)*g(15)*g(16)*g(17)*g(18)*g( 19)*g(20)*g(26)*g(27)*g(28)*g(38)*g(39)*g(40)*nu*v(mu)*p.q^2 + f(3)*g(11 )*g(26) + f(3)*g(11)*g(26)*g(32)*mu*v(mu) + f(3)*g(11)*g(26)*g(38)*nu* v(mu) + g(1)*g(8)*x + g(1)*g(8)*mu*v(mu)*x + g(1)*g(8)*nu*v(mu)*x + g(1) *g(8)*g(13)*g(21)*p.q^2*x + g(1)*g(8)*g(13)*g(21)*mu*v(mu)*p.q^2*x + g(1 )*g(8)*g(13)*g(21)*nu*v(mu)*p.q^2*x + g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*x^2 + g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*mu*v(mu)*x^2 + g(2)*g(3)*g(4)*g(5)*g(6) *g(7)*nu*v(mu)*x^2 + g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(14)*g(15)*g(16)*g( 17)*g(18)*g(19)*g(20)*p.q^2*x^2 + g(2)*g(3)*g(4)*g(5)*g(6)*g(7)*g(14)*g( 15)*g(16)*g(17)*g(18)*g(19)*g(20)*mu*v(mu)*p.q^2*x^2 + g(2)*g(3)*g(4)*g( 5)*g(6)*g(7)*g(14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*nu*v(mu)*p.q^2* x^2 + g(8)*x^-1 + g(8)*mu*v(mu)*x^-1 + g(8)*nu*v(mu)*x^-1 + g(8)*g(22)* p.q^-1*x^-1 + g(8)*g(22)*mu*v(mu)*p.q^-1*x^-1 + g(8)*g(22)*nu*v(mu)* p.q^-1*x^-1 + g(13)*g(21)*p.q^2 + g(13)*g(21)*mu*v(mu)*p.q^2 + g(13)*g( 21)*nu*v(mu)*p.q^2 + g(14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*p.q^2 + g(14)*g(15)*g(16)*g(17)*g(18)*g(19)*g(20)*mu*v(mu)*p.q^2 + g(14)*g(15)* g(16)*g(17)*g(18)*g(19)*g(20)*nu*v(mu)*p.q^2 + g(22)*p.q^-1 + g(22)*mu* v(mu)*p.q^-1 + g(22)*nu*v(mu)*p.q^-1 "); *--#] cov_identify_only : *--#[ cov_saveload : Symbol x; Function f; CFunction g; Index mu; Vector p,q; Tensor T; Global F = (1+x)^20 + f(1) + g(2) + p.q + p(mu) + T(q) + T(mu) + e_(p,q); .store Save test.sav F; .end Load test.sav; Local G = F; .sort Delete storage; Identify x = 1; Print; .end assert succeeded? assert result("G") =~ expr("1048576 + p.q + p(mu) + e_(p,q) + g(2) + T(q) + T(mu) + f(1)") *--#] cov_saveload : *--#[ cov_symm : * pattern matching of functions with symmtry properties Indices x1,x2,x3,x4,x5; CFunction fs(symmetric), fas(antisymmetric), fcs(cyclesymmetric); Function gs(symmetric), gas(antisymmetric), gcs(cyclesymmetric); CTensor Ts(symmetric), Tas(antisymmetric), Tcs(cyclesymmetric); Tensor Us(symmetric), Uas(antisymmetric), Ucs(cyclesymmetric); Local test = + fs(1,2,3,4,5) + fas(1,2,3,4,5) + fcs(1,2,3,4,5) + gs(1,2,3,4,5) + gas(1,2,3,4,5) + gcs(1,2,3,4,5) + Ts(1,2,3,4,5) + Tas(1,2,3,4,5) + Tcs(1,2,3,4,5) + Us(1,2,3,4,5) + Uas(1,2,3,4,5) + Ucs(1,2,3,4,5) ; Identify fs(x1?,x2?,4,3,x5?) = fs; Identify fas(x1?,x2?,4,3,x5?) = - fas; Identify fcs(5,1,x3?,x4?,x5?) = fcs; Identify gs(x1?,x2?,4,3,x5?) = gs; Identify gas(x1?,x2?,4,3,x5?) = - gas; Identify gcs(5,1,x3?,x4?,x5?) = gcs; Identify Ts(x1?,x2?,4,3,x5?) = Ts; Identify Tas(x1?,x2?,4,3,x5?) = - Tas; Identify Tcs(5,1,x3?,x4?,x5?) = Tcs; Identify Us(x1?,x2?,4,3,x5?) = Us; Identify Uas(x1?,x2?,4,3,x5?) = - Uas; Identify Ucs(5,1,x3?,x4?,x5?) = Ucs; Print; .end assert succeeded? assert result("test") =~ expr("fs + fas + fcs + Ts + Tas + Tcs + Us + Uas + Ucs + gs + gas + gcs") *--#] cov_symm : *--#[ cov_tablebase_1 : CTable,sparse f(1); #do i = 1,10 Fill f(`i') = `i'; #enddo .sort TableBase "test.tbl" create; TableBase "test.tbl" addto f; .end TableBase "test.tbl" open; Tablebase "test.tbl" load; .sort Local test = +...+; TestUse; .sort TableBase "test.tbl" use; Apply; Print; .end #pend_if mpi? assert succeeded? assert result("test") =~ expr("55 + f(11)") *--#] cov_tablebase_1 : *--#[ cov_tablebase_2 : CTable,sparse f(1); #do i = 1,10 Fill f(`i') = `i'; #enddo .sort TableBase "test2.tbl" create; TableBase "test2.tbl" addto f; .end TableBase "test2.tbl" open; Tablebase "test2.tbl" enter; .sort Local test = +...+; Apply; Print; .end #pend_if mpi? assert succeeded? assert result("test") =~ expr("55 + f(11)") *--#] cov_tablebase_2 : *--#[ cov_tablebase_3 : CTable,sparse f(1); #do i = 1,10 Fill f(`i') = `i'; #enddo .sort TableBase "test3.tbl" create; TableBase "test3.tbl" addto f; .end TableBase "test3.tbl" open; Tablebase "test3.tbl" audit; .end #pend_if mpi? assert succeeded? assert stdout =~ exact_pattern(<<'EOF') Table,sparse,f(1) f(1) f(2) f(3) f(4) f(5) f(6) f(7) f(8) f(9) f(10) .end EOF *--#] cov_tablebase_3 : *--#[ cov_transform : CFunction Z,f,g,h,i; Symbol inf,x,y,y1,y2,n1,n2; Set funs: f,g; #$one = 1; #$two = 2; Local test1 = f(1,2,3,4) + g(1,2,3,4) + h(1,2,3,4) + i(1,2,3,4); Local test2 = f(1,2,3,4); Local test3 = f(1,2,3,4,5,6,7); Local test4 = f(1,2,3,4); Local test5 = f(1,2,3,4) + g(1,2,3,4); Local test6 = f(1) + f(1,1) + f(1,2) + f(2,1) + f(1,3,2) + f(2,3,1); Local test7 = test6; Local test8 = + g(1)*f(1,1,1) + g(2)*f(-1,1,1) + g(3)*f(2,1,1) + g(4)*f(1,-2,1) + g(5)*f(-1,-1,-1) * Check against HarmonicSums.m - ( + g(1)*Z(1, 1, 1, inf) - g(2)*Z(-1, -1, 1, inf) + g(3)*Z(2, 1, 1, inf) + g(4)*(-Z(1, -2, -1, inf)) - g(5)*Z(-1, 1, 1, inf) ) ; Local test9 = test8; InExpression test1; Transform funs addargs($one,last); Transform {h,i}, mulargs($one,last); EndInExpression; InExpression test2; Transform f explode(1,last); Identify f(?a) = f(?a)*g(nargs_(?a)); Identify g(y?$len) = 1; Transform f encode(1,last):base=$two; Transform f decode(1,$len):base=2, implode(1,last); EndInExpression; InExpression test3; Transform f permute($one,3,5)($two,6); EndInExpression; InExpression test4; Transform f reverse($two,last); EndInExpression; InExpression test5; Transform f cycle($two,last)=+1; Transform g cycle(2,last)=-$one; EndInExpression; InExpression test6; Transform f islyndon(1,last)=(y1,n1); Transform f islyndon<(1,last)=(y1,n1); Transform f islyndon-(1,last)=(y1,n1); Transform f islyndon>(1,last)=(y2,n2); Transform f islyndon+(1,last)=(y2,n2); EndInExpression; InExpression test7; Transform f tolyndon(1,last)=(y1,n1); Transform f tolyndon<(1,last)=(y1,n1); Transform f tolyndon-(1,last)=(y1,n1); Transform f tolyndon>(1,last)=(y2,n2); Transform f tolyndon+(1,last)=(y2,n2); EndInExpression; InExpression test8; Transform f HtoZ(1,last); Identify f(?a) = Z(?a,inf); EndInExpression; InExpression test9; Transform Z ZtoH(1,last-1); Identify Z(?a,inf) = f(?a); EndInExpression; ModuleOption local $len; Print; .end assert succeeded? assert result("test1") =~ expr("f(10) + g(10) + h(24) + i(24)") assert result("test2") =~ expr("f(1,2,3,4)") assert result("test3") =~ expr("f(3,6,5,4,1,2,7)") assert result("test4") =~ expr("f(1,4,3,2)") assert result("test5") =~ expr("f(1,4,2,3) + g(1,3,4,2)") assert result("test6") =~ expr("f(1)*y1^3*y2^2 + f(1,1)*n1^3*n2^2 + f(1,2)*y1^3*n2^2 + f(1,3,2)*y1^3*n2^2 + f(2,1)*y2^2*n1^3 + f(2,3,1)*n1^3*n2^2") assert result("test7") =~ expr("f(1)*y1^3*y2^2 + f(1,1)*n1^3*n2^2 + 2*f(2,1)*y1^3*y2^2 + f(3,1,2)*y1^3*y2^2 + f(3,2,1)*y1^3*y2^2") assert result("test8") =~ expr("0") assert result("test9") =~ expr("0") *--#] cov_transform : form-5.0.1/check/features.frm0000644000175100017510000026741215217035721011563 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ divmod_1 : * Test div_, rem_ functions for monic univariate polynomials #- S x1; L F1 = (x1+1)^2; L F2 = (x1+1); .sort L F3 = div_(F1,F2); L F4 = rem_(F1,F2); P; .end assert succeeded? assert result("F3") =~ expr("1 + x1") assert result("F4") =~ expr("0") *--#] divmod_1 : *--#[ divmod_2 : * Test div_, rem_ functions for non-monic univariate polynomials with remainder #- S x1; L F1 = (2*x1+1)^2+3*x1+5; L F2 = (2*x1+1); .sort L F3 = div_(F1,F2); L F4 = rem_(F1,F2); P; .end assert succeeded? assert result("F3") =~ expr("5/2 + 2*x1") assert result("F4") =~ expr("7/2") *--#] divmod_2 : *--#[ divmod_3 : * Test div_, rem_ functions for non-monic multivariate polynomials without remainder #- S x1,x2; L F1 = (2*x1*x2+1*x1)^2; L F2 = (2*x1*x2+1*x1); .sort L F3 = div_(F1,F2); L F4 = rem_(F1,F2); P; .end assert succeeded? assert result("F3") =~ expr("x1 + 2*x1*x2") assert result("F4") =~ expr("0") *--#] divmod_3 : *--#[ divmod_4 : * Test div_, rem_ functions for non-monic multivariate polynomials with remainder #- S x1,x2,x3; L F1 = -7*x1*x2^9*x3+5*x1*x2^10*x3-3*x1^2*x2^3*x3^2+35*x1^2*x2^4*x3^4 -42*x1^2*x2^5*x3^2-25*x1^2*x2^5*x3^4+30*x1^2*x2^6*x3^2-8*x1^4*x2^5*x3^3+40*x1^5*x3^6 -48*x1^5*x2*x3^4+3*x1^6*x2^2*x3; L F2 = x1*x2^5-5*x1^2*x3^3+6*x1^2*x2*x3; L F3 = div_(F1,F2); L F4 = rem_(F1,F2); P; .end assert succeeded? assert result("F3") =~ expr(" - 25/72*x3^5 + 12969970703125/2742118830047232*x3^30 - 5/12*x2*x3^3 + 2593994140625/457019805007872*x2*x3^28 - 1/2*x2^2*x3 + 518798828125/ 76169967501312*x2^2*x3^26 + 103759765625/12694994583552*x2^3*x3^24 - 7* x2^4*x3 + 20751953125/2115832430592*x2^4*x3^22 + 5*x2^5*x3 + 29052734375/ 2821109907456*x2^5*x3^20 + 830078125/78364164096*x2^6*x3^18 + 830078125/ 78364164096*x2^7*x3^16 + 33203125/3265173504*x2^8*x3^14 + 6640625/ 725594112*x2^9*x3^12 + 5703125/725594112*x2^10*x3^10 + 765625/120932352* x2^11*x3^8 + 15625/3359232*x2^12*x3^6 + 625/209952*x2^13*x3^4 + 875/ 559872*x2^14*x3^2 + 25/46656*x2^15 - 20751953125/2821109907456*x1*x3^23 - 4150390625/470184984576*x1*x2*x3^21 - 830078125/78364164096*x1*x2^2* x3^19 - 166015625/13060694016*x1*x2^3*x3^17 - 33203125/2176782336*x1* x2^4*x3^15 - 11328125/725594112*x1*x2^5*x3^13 - 78125/5038848*x1*x2^6* x3^11 - 296875/20155392*x1*x2^7*x3^9 - 21875/1679616*x1*x2^8*x3^7 - 625/ 62208*x1*x2^9*x3^5 - 625/93312*x1*x2^10*x3^3 - 25/7776*x1*x2^11*x3 + 9765625/725594112*x1^2*x3^16 + 1953125/120932352*x1^2*x2*x3^14 + 390625/ 20155392*x1^2*x2^2*x3^12 + 78125/3359232*x1^2*x2^3*x3^10 + 15625/559872* x1^2*x2^4*x3^8 + 625/23328*x1^2*x2^5*x3^6 + 125/5184*x1^2*x2^6*x3^4 + 25/ 1296*x1^2*x2^7*x3^2 + 5/432*x1^2*x2^8 - 8*x1^3*x3^3 - 3125/93312*x1^3* x3^9 - 625/15552*x1^3*x2*x3^7 - 125/2592*x1^3*x2^2*x3^5 - 25/432*x1^3* x2^3*x3^3 - 5/72*x1^3*x2^4*x3 + 5/12*x1^4*x3^2 + 1/2*x1^4*x2 ") assert result("F4") =~ expr(" 25/72*x1*x2^5*x3^5 - 12969970703125/2742118830047232*x1*x2^5*x3^30 + 5/ 12*x1*x2^6*x3^3 - 2593994140625/457019805007872*x1*x2^6*x3^28 + 1/2*x1* x2^7*x3 - 518798828125/76169967501312*x1*x2^7*x3^26 - 103759765625/ 12694994583552*x1*x2^8*x3^24 - 20751953125/2115832430592*x1*x2^9*x3^22 - 29052734375/2821109907456*x1*x2^10*x3^20 - 830078125/78364164096*x1* x2^11*x3^18 - 830078125/78364164096*x1*x2^12*x3^16 - 33203125/3265173504 *x1*x2^13*x3^14 - 6640625/725594112*x1*x2^14*x3^12 - 5703125/725594112* x1*x2^15*x3^10 - 765625/120932352*x1*x2^16*x3^8 - 15625/3359232*x1*x2^17 *x3^6 - 625/209952*x1*x2^18*x3^4 - 875/559872*x1*x2^19*x3^2 - 25/46656* x1*x2^20 - 125/72*x1^2*x3^8 + 64849853515625/2742118830047232*x1^2*x3^33 - 103759765625/2821109907456*x1^3*x3^26 - 5/432*x1^3*x2^13 + 48828125/ 725594112*x1^4*x3^19 - 15625/93312*x1^5*x3^12 - 1/2*x1^5*x2^6 + 25/12* x1^6*x3^5 ") *--#] divmod_4 : *--#[ moebius_1 : S i,x; L F = sum_(i,1,200,moebius_(i)*x^i); P; .end:result; assert succeeded? # Sum[MoebiusMu[i] x^i, {i, 1, 200}] // InputForm assert result("F") =~ expr(" x - x^2 - x^3 - x^5 + x^6 - x^7 + x^10 - x^11 - x^13 + x^14 + x^15 - x^17 - x^19 + x^21 + x^22 - x^23 + x^26 - x^29 - x^30 - x^31 + x^33 + x^34 + x^35 - x^37 + x^38 + x^39 - x^41 - x^42 - x^43 + x^46 - x^47 + x^51 - x^53 + x^55 + x^57 + x^58 - x^59 - x^61 + x^62 + x^65 - x^66 - x^67 + x^69 - x^70 - x^71 - x^73 + x^74 + x^77 - x^78 - x^79 + x^82 - x^83 + x^85 + x^86 + x^87 - x^89 + x^91 + x^93 + x^94 + x^95 - x^97 - x^101 - x^102 - x^103 - x^105 + x^106 - x^107 - x^109 - x^110 + x^111 - x^113 - x^114 + x^115 + x^118 + x^119 + x^122 + x^123 - x^127 + x^129 - x^130 - x^131 + x^133 + x^134 - x^137 - x^138 - x^139 + x^141 + x^142 + x^143 + x^145 + x^146 - x^149 - x^151 - x^154 + x^155 - x^157 + x^158 + x^159 + x^161 - x^163 - x^165 + x^166 - x^167 - x^170 - x^173 - x^174 + x^177 + x^178 - x^179 - x^181 - x^182 + x^183 + x^185 - x^186 + x^187 - x^190 - x^191 - x^193 + x^194 - x^195 - x^197 - x^199 ") *--#] moebius_1 : *--#[ moebius_2 : S x,x1,x2; CF f1,f2; L F = 1; multiply +...+; multiply +...+; id x1 = x; id x2 = x^20; .sort S n; id f1(n?) = moebius_(10000+n); .sort id f2(n?) = moebius_(20000+n); P; .end:result; assert succeeded? # Sum[MoebiusMu[10000 + i] MoebiusMu[20000 + j] x^(i + 20 * j), {i, 1, 10}, {j, 1, 10}] // InputForm assert result("F") =~ expr(" -x^21 + x^22 - x^23 - x^25 - x^26 + x^27 + x^29 + x^30 - x^41 + x^42 - x^43 - x^45 - x^46 + x^47 + x^49 + x^50 + x^61 - x^62 + x^63 + x^65 + x^66 - x^67 - x^69 - x^70 + x^101 - x^102 + x^103 + x^105 + x^106 - x^107 - x^109 - x^110 - x^121 + x^122 - x^123 - x^125 - x^126 + x^127 + x^129 + x^130 - x^181 + x^182 - x^183 - x^185 - x^186 + x^187 + x^189 + x^190 - x^201 + x^202 - x^203 - x^205 - x^206 + x^207 + x^209 + x^210 ") *--#] moebius_2 : *--#[ moebius_3 : * corner cases, see #430 #do i=1,9 L F`i' = moebius_(2^15-`i'); #enddo #do i=1,9 L G`i' = moebius_(2^31-`i'); #enddo P; .end #time_dilation 4.0 # memory usage is so intense #pend_if serial? && total_memory < 8_000_000_000 #pend_if threaded? && total_memory < 20_000_000_000 #pend_if mpi? && total_memory < 20_000_000_000 # too heavy on GitHub (often fails) #pend_if github? && valgrind? assert succeeded? if wordsize >= 2 assert result("F1") =~ expr("-1") assert result("F2") =~ expr("1") assert result("F3") =~ expr("1") assert result("F4") =~ expr("0") assert result("F5") =~ expr("-1") assert result("F6") =~ expr("1") assert result("F7") =~ expr("0") assert result("F8") =~ expr("0") assert result("F9") =~ expr("-1") end if wordsize >= 4 assert result("G1") =~ expr("-1") assert result("G2") =~ expr("0") assert result("G3") =~ expr("-1") assert result("G4") =~ expr("0") assert result("G5") =~ expr("1") assert result("G6") =~ expr("-1") assert result("G7") =~ expr("1") assert result("G8") =~ expr("0") assert result("G9") =~ expr("-1") end *--#] moebius_3 : *--#[ partitions_ : * Test partitions function #- V p1,p2,p3,p4,p5,p6; CF f1,f2,f3; L F1 = partitions_(3,f1,2,f1,2,f1,2,p1,p2,p3,p4,p5,p6) - dd_(p1,p2,p3,p4,p5,p6); L F2 = partitions_(0,f1,2,p1,p2,p3,p4,p5,p6) - dd_(p1,p2,p3,p4,p5,p6); L F3 = partitions_(4,f1,2,f1,2,f2,1,f3,1,p1,p1,p1,p1,p1,p1) - 90*f1(p1,p1)^2*f2(p1)*f3(p1); L F4 = partitions_(2,f1,2,f2,0,p1,p2,p3,p4,p5,p6) - distrib_(1,2,f1,f2,p1,p2,p3,p4,p5,p6); id p1?.p2? = f1(p1,p2); * for dd_ P; .end assert succeeded? assert result("F1") =~ expr("0") assert result("F2") =~ expr("0") assert result("F3") =~ expr("0") assert result("F4") =~ expr("0") *--#] partitions_ : *--#[ AppendPath_unix : #include foo/foo1.h * foo/bar/p1.prc #call p1 P; .end #:path foo:bar #include foo1.h * foo/bar/p2.prc #call p2 P; .end #:path foo:bar #include foo2.h * bar/p1.prc #call p1 P; .end #require unix? #prepare write "foo/foo1.h", "#prependpath bar\n" #prepare write "foo/foo2.h", "#appendpath bar\n" #prepare write "foo/bar/p1.prc", "#procedure p1()\nL F=1234;\n#endprocedure\n" #prepare write "foo/bar/p2.prc", "#procedure p2()\nL G=5678;\n#endprocedure\n" #prepare write "bar/p1.prc", "#procedure p1()\nL H=9012;\n#endprocedure\n" assert succeeded? assert result("F") =~ expr("1234") assert result("G") =~ expr("5678") assert result("H") =~ expr("9012") *--#] AppendPath_unix : *--#[ AppendPath_windows : #include foo\foo1.h * foo/bar/p1.prc #call p1 P; .end #:path foo;bar #include foo1.h * foo/bar/p2.prc #call p2 P; .end #:path foo;bar #include foo2.h * bar/p1.prc #call p1 P; .end #require windows? #prepare write "foo/foo1.h", "#prependpath bar\n" #prepare write "foo/foo2.h", "#appendpath bar\n" #prepare write "foo/bar/p1.prc", "#procedure p1()\nL F=1234;\n#endprocedure\n" #prepare write "foo/bar/p2.prc", "#procedure p2()\nL G=5678;\n#endprocedure\n" #prepare write "bar/p1.prc", "#procedure p1()\nL H=9012;\n#endprocedure\n" assert succeeded? assert result("F") =~ expr("1234") assert result("G") =~ expr("5678") assert result("H") =~ expr("9012") *--#] AppendPath_windows : *--#[ TimeoutAfter_1 : #procedure problematicprocedure * Do nothing. #endprocedure #timeoutafter 1000 #call problematicprocedure #timeoutafter 0 .end #require unix? assert succeeded? *--#] TimeoutAfter_1 : *--#[ TimeoutAfter_2 : #procedure problematicprocedure * Infinite loop. #do i=1,1 #redefine i "0" #enddo #endprocedure #timeoutafter 1 #call problematicprocedure #timeoutafter 0 .end #require unix? # Sometimes, FORM can terminate without printing the error message, so don't # assert anything. We only test whether this hits the test suite timeout limit, # or not. TODO in principle this can be considered to be a bug, to be looked at # in the future. *--#] TimeoutAfter_2 : *--#[ dedup : * Test deduplication #- Auto S n; Auto V p; CF f1,f2,f3,f,g; T t1,t2,t3; L F1 = #do i = 1,20 +ranperm_(f,,...,) #enddo ; L F2 = f1(1,2,3,p,1,1,2,2,p); L F3 = f2(1,2,3,p,1,1,2,2,p); L F4 = f3(1,2,3,p,1,1,2,2,p); L F5 = t1(1,2,3,p,1,1,2,2,p); L F6 = t2(1,2,3,p,1,1,2,2,p); L F7 = t3(1,2,3,p,1,1,2,2,p); L F8 = f1(1,2,1,100000000,n^4,100,n^4,n^5,-10000,p1.p2,p6,p1.p2); id f(?a) = f(?a)*g(?a); transform f,dedup(1,last); repeat id g(?a,p?,?b,p?,?c) = g(?a,p,?b,?c); id f(?a)*g(?a) = 0; * Test functions transform f1,dedup(1,last); transform f2,dedup(3,last); transform f3,dedup(1,5); * Test tensors transform t1,dedup(1,last); transform t2,dedup(3,last); transform t3,dedup(1,5); P; .end assert succeeded? assert result("F1") =~ expr("0") assert result("F2") =~ expr("f1(1,2,3,p)") assert result("F3") =~ expr("f2(1,2,3,p,1,2)") assert result("F4") =~ expr("f3(1,2,3,p,1,2,2,p)") assert result("F5") =~ expr("t1(1,2,3,p)") assert result("F6") =~ expr("t2(1,2,3,p,1,2)") assert result("F7") =~ expr("t3(1,2,3,p,1,2,2,p)") assert result("F8") =~ expr("f1(1,2,100000000,n^4,100,n^5,-10000,p1.p2,p6)") *--#] dedup : *--#[ CoToTensor : V p1,p2,q1,q2,nosquare; Set pp:p1,p2; CF f; T Q1,functions; #$q1 = q1; #$Q1 = Q1; L F0 = f(q1,q2) * p1.q1 * p2.q1 * q1.q1 * q1.q2; #do i={1,...,7,11,...,17,51,61,71,72} L F`i' = F0; #enddo inexpression F1; totensor q1,Q1; endinexpression; inexpression F2; totensor nosquare,q1,Q1; endinexpression; inexpression F3; totensor functions,q1,Q1; endinexpression; inexpression F4; totensor nosquare,functions,q1,Q1; endinexpression; inexpression F5; totensor !pp,q1,Q1; endinexpression; inexpression F6; totensor !{p1},q1,Q1; endinexpression; inexpression F7; totensor nosquare,functions,!pp,q1,Q1; endinexpression; inexpression F11; totensor $q1,Q1; endinexpression; inexpression F12; totensor q1,$Q1; endinexpression; inexpression F13; totensor $q1,$Q1; endinexpression; inexpression F14; totensor Q1,q1; endinexpression; inexpression F15; totensor $Q1,q1; endinexpression; inexpression F16; totensor Q1,$q1; endinexpression; inexpression F17; totensor $Q1,$q1; endinexpression; inexpression F51; totensor !{p1,p2},q1,Q1; endinexpression; inexpression F61; totensor !p1,q1,Q1; endinexpression; inexpression F71; multiply replace_(q1,nosquare); totensor nosquare,functions; endinexpression; inexpression F72; multiply replace_(q1,nosquare); totensor nosquare,functions,nosquare,functions; endinexpression; P; .end assert succeeded? assert result("F0") =~ expr("f(q1,q2)*p1.q1*p2.q1*q1.q1*q1.q2") assert result("F1") =~ expr("f(q1,q2)*Q1(p1,p2,q2,N1_?,N1_?)") assert result("F2") =~ expr("f(q1,q2)*Q1(p1,p2,q2)*q1.q1") assert result("F3") =~ expr("f(N1_?,q2)*Q1(p1,p2,q2,N1_?,N2_?,N2_?)") assert result("F4") =~ expr("f(N1_?,q2)*Q1(p1,p2,q2,N1_?)*q1.q1") assert result("F5") =~ expr("f(q1,q2)*Q1(q2,N1_?,N1_?)*p1.q1*p2.q1") assert result("F6") =~ expr("f(q1,q2)*Q1(p2,q2,N1_?,N1_?)*p1.q1") assert result("F7") =~ expr("f(N1_?,q2)*Q1(q2,N1_?)*p1.q1*p2.q1*q1.q1") assert result("F1") == result("F11") assert result("F1") == result("F12") assert result("F1") == result("F13") assert result("F1") == result("F14") assert result("F1") == result("F15") assert result("F1") == result("F16") assert result("F1") == result("F17") assert result("F5") == result("F51") assert result("F6") == result("F61") assert result("F71") =~ expr("f(nosquare,q2)*functions(p1,p2,q2,N1_?,N1_?)") assert result("F72") =~ expr("f(N1_?,q2)*functions(p1,p2,q2,N1_?)*nosquare.nosquare") *--#] CoToTensor : *--#[ Format_allfloat : * See also Issue #216. #- Off stats; S x; L F = x - x^2 + 2*x^3 + 1/2*x^4 - 2/3*x^5; .sort #message (0) normal #write " F = %E;", F .sort #message (1) Fortran Format Fortran; #write " F = %E;", F .sort * TODO: this combination doesn't work correctly, though no one may use * single-precision Fortran seriously. * * #message Fortran,allfloat * Format Fortran; * Format allfloat; * #write " F = %E;", F * .sort #message (2) DoubleFortran Format DoubleFortran; #write " F = %E;", F .sort #message (3) DoubleFortran,allfloat Format DoubleFortran; Format allfloat; #write " F = %E;", F .sort #message (4) QuadrupleFortran Format QuadrupleFortran; #write " F = %E;", F .sort #message (5) QuadrupleFortran,allfloat Format QuadrupleFortran; Format allfloat; #write " F = %E;", F .sort #message (6) Fortran90,.0_wp Format Fortran90,.0_wp; * forcibly allfloat #write " F = %E;", F .end assert succeeded? assert result("F", 0) =~ expr("x - x^2 + 2*x^3 + 1/2*x^4 - 2/3*x^5") assert result("F", 1) =~ expr("x - x**2 + 2*x**3 + 1./2.*x**4 - 2./3.*x**5") assert result("F", 2) =~ expr("x - x**2 + 2*x**3 + 1.D0/2.D0*x**4 - 2.D0/3.D0*x**5") assert result("F", 3) =~ expr("x - x**2 + 2.D0*x**3 + 1.D0/2.D0*x**4 - 2.D0/3.D0*x**5") assert result("F", 4) =~ expr("x - x**2 + 2*x**3 + 1.Q0/2.Q0*x**4 - 2.Q0/3.Q0*x**5") assert result("F", 5) =~ expr("x - x**2 + 2.Q0*x**3 + 1.Q0/2.Q0*x**4 - 2.Q0/3.Q0*x**5") assert result("F", 6) =~ expr("x - x**2 + 2.0_wp*x**3 + 1.0_wp/2.0_wp*x**4 - 2.0_wp/3.0_wp*x**5") *--#] Format_allfloat : *--#[ Format_noreset_linelen : #- Off stats; Auto S x; L F = (x1+...+x5)^3; .sort #message (0) normal,80 #write " F = %E;", F .sort #message (1) Fortran,72 Format Fortran; #write " F = %E;", F .sort #message (2) C,50 Format 50; Format C; #write " F = %E;", F .sort #message (3) Fortran,50 Format Fortran; #write " F = %E;", F .end assert succeeded? assert result("F", 0) =~ expr(" x5^3 + 3*x4*x5^2 + 3*x4^2*x5 + x4^3 + 3*x3*x5^2 + 6*x3*x4*x5 + 3*x3*x4^2 + 3*x3^2*x5 + 3*x3^2*x4 + x3^3 + 3*x2*x5^2 + 6*x2*x4*x5 + 3*x2*x4^2 + 6 *x2*x3*x5 + 6*x2*x3*x4 + 3*x2*x3^2 + 3*x2^2*x5 + 3*x2^2*x4 + 3*x2^2*x3 + x2^3 + 3*x1*x5^2 + 6*x1*x4*x5 + 3*x1*x4^2 + 6*x1*x3*x5 + 6*x1*x3*x4 + 3*x1*x3^2 + 6*x1*x2*x5 + 6*x1*x2*x4 + 6*x1*x2*x3 + 3*x1*x2^2 + 3*x1^2 *x5 + 3*x1^2*x4 + 3*x1^2*x3 + 3*x1^2*x2 + x1^3 ") assert result("F", 1) =~ expr(" x5**3 + 3*x4*x5**2 + 3*x4**2*x5 + x4**3 + 3*x3*x5**2 + 6*x3*x4*x5 & + 3*x3*x4**2 + 3*x3**2*x5 + 3*x3**2*x4 + x3**3 + 3*x2*x5**2 + 6 & *x2*x4*x5 + 3*x2*x4**2 + 6*x2*x3*x5 + 6*x2*x3*x4 + 3*x2*x3**2 + & 3*x2**2*x5 + 3*x2**2*x4 + 3*x2**2*x3 + x2**3 + 3*x1*x5**2 + 6*x1 & *x4*x5 + 3*x1*x4**2 + 6*x1*x3*x5 + 6*x1*x3*x4 + 3*x1*x3**2 + 6* & x1*x2*x5 + 6*x1*x2*x4 + 6*x1*x2*x3 + 3*x1*x2**2 + 3*x1**2*x5 + 3 & *x1**2*x4 + 3*x1**2*x3 + 3*x1**2*x2 + x1**3 ") assert result("F", 2) =~ expr(" pow(x5,3) + 3*x4*pow(x5,2) + 3*pow(x4,2)*x5 + pow(x4,3) + 3*x3*pow(x5,2) + 6*x3*x4*x5 + 3*x3*pow(x4,2) + 3*pow(x3,2)*x5 + 3*pow( x3,2)*x4 + pow(x3,3) + 3*x2*pow(x5,2) + 6* x2*x4*x5 + 3*x2*pow(x4,2) + 6*x2*x3*x5 + 6* x2*x3*x4 + 3*x2*pow(x3,2) + 3*pow(x2,2)*x5 + 3*pow(x2,2)*x4 + 3*pow(x2,2)*x3 + pow( x2,3) + 3*x1*pow(x5,2) + 6*x1*x4*x5 + 3*x1* pow(x4,2) + 6*x1*x3*x5 + 6*x1*x3*x4 + 3*x1* pow(x3,2) + 6*x1*x2*x5 + 6*x1*x2*x4 + 6*x1* x2*x3 + 3*x1*pow(x2,2) + 3*pow(x1,2)*x5 + 3 *pow(x1,2)*x4 + 3*pow(x1,2)*x3 + 3*pow( x1,2)*x2 + pow(x1,3) ") assert result("F", 3) =~ expr(" x5**3 + 3*x4*x5**2 + 3*x4**2*x5 + x4**3 + 3* & x3*x5**2 + 6*x3*x4*x5 + 3*x3*x4**2 + 3* & x3**2*x5 + 3*x3**2*x4 + x3**3 + 3*x2*x5**2 & + 6*x2*x4*x5 + 3*x2*x4**2 + 6*x2*x3*x5 + & 6*x2*x3*x4 + 3*x2*x3**2 + 3*x2**2*x5 + 3* & x2**2*x4 + 3*x2**2*x3 + x2**3 + 3*x1*x5**2 & + 6*x1*x4*x5 + 3*x1*x4**2 + 6*x1*x3*x5 + & 6*x1*x3*x4 + 3*x1*x3**2 + 6*x1*x2*x5 + 6* & x1*x2*x4 + 6*x1*x2*x3 + 3*x1*x2**2 + 3* & x1**2*x5 + 3*x1**2*x4 + 3*x1**2*x3 + 3* & x1**2*x2 + x1**3 ") *--#] Format_noreset_linelen : *--#[ Float_1 : #- * Example from the FORM Workshop (Madrid 2023) slides, also in the manual. #StartFloat 500b,MZV=15 Local F1 = -mzv_(8,1,1,5) +29056868/39414375*mzv_(2)^6*mzv_(3) -47576/40425*mzv_(2)^5*mzv_(5) -163291/18375*mzv_(2)^4*mzv_(7) -4/105*mzv_(2)^3*mzv_(3)^3 -450797/11025*mzv_(2)^3*mzv_(9) +7/5*mzv_(2)^2*mzv_(3)^2*mzv_(5) +16/25*mzv_(2)^2*mzv_(3)*mzv_(5,3) +454049/1400*mzv_(2)^2*mzv_(11) -16/25*mzv_(2)^2*mzv_(5,3,3) +3*mzv_(2)*mzv_(3)^2*mzv_(7) +61/14*mzv_(2)*mzv_(3)*mzv_(5)^2 +2/7*mzv_(2)*mzv_(3)*mzv_(7,3) +2172853/420*mzv_(2)*mzv_(13) -2/7*mzv_(2)*mzv_(7,3,3) +1/7*mzv_(2)*mzv_(5,5,3) -33/4*mzv_(3)^2*mzv_(9) -133/6*mzv_(3)*mzv_(5)*mzv_(7) -25/9*mzv_(3)*mzv_(9,3) -244/105*mzv_(5)^3 -359/105*mzv_(5)*mzv_(7,3) +3/10*mzv_(7)*mzv_(5,3) +89/18*mzv_(9,3,3) +569/105*mzv_(7,3,5); L F2 = mzv_(15); Evaluate mzv_; Print; .sort Skip F1,F2; Local X = F1/F2; ToRational; Print; .sort #EndFloat Local G1 = F1; Local G2 = F2; Print G1,G2; .end #pend_if wordsize == 2 assert succeeded? assert result("X") =~ expr("229903169/25200") assert stdout =~ exact_pattern(<<'EOF') F1 = 9.1234206877960755900164875575406726239325002222490534540605137258846994\ 916348297032751308227224952419629422497720599224543719959652966613231560\ 6913926e+03; EOF assert stdout =~ exact_pattern(<<'EOF') F2 = 1.0000305882363070204935517285106450625876279487068581775065699328933322\ 671563422795730723343470175484943669684442492832530297757588781904321794\ 40477e+00; EOF assert stdout =~ exact_pattern(<<'EOF') G1 = float_(10,10,1,225649930152063087544280124519603661924016376904153173222\ 961313295752588365049496190204609112667217257624737508104376810254484309\ 3830597279756558899541412586941038636793415360118); EOF assert stdout =~ exact_pattern(<<'EOF') G2 = float_(10,10,1,247337966873870703631573653423368526098272821023387457752\ 643030990710929556575503489173572446024607642191456056189912528713904095\ 704444384800390830056125051897088334731440434); EOF *--#] Float_1 : *--#[ evaluate_symbol : #- #StartFloat 64b Symbol a,b; Local PI0 = a*b; Local PI1 = pi_; Local PI2 = pi_*3; Local PI3 = pi_*sqrt_(3); Local PI4 = pi_*pi_*pi_; Local PI5 = a*pi_*b; Local PI6 = sqrt_(pi_); Local EE1 = ee_; Local EE2 = pi_*ee_; Local EM1 = em_; ToFloat; Evaluate; Print; .end #pend_if wordsize == 2 assert result("PI0") =~ expr("1.0e+00*a*b") assert result("PI1") =~ expr("3.141592653589793238e+00") assert result("PI2") =~ expr("9.424777960769379715e+00") assert result("PI3") =~ expr("5.441398092702653552e+00") assert result("PI4") =~ expr("3.100627668029982018e+01") assert result("PI5") =~ expr("3.141592653589793238e+00*a*b") assert result("PI6") =~ expr("1.772453850905516027e+00") assert result("EE1") =~ expr("2.718281828459045235e+00") assert result("EE2") =~ expr("8.539734222673567065e+00") assert result("EM1") =~ expr("5.772156649015328606e-01") *--#] evaluate_symbol : *--#[ evaluate_symbol_pi : #- #StartFloat 128b Local PI = pi_; Local EE = ee_; Local EM = em_; ToFloat; Evaluate pi_; Print; .end #pend_if wordsize == 2 assert result("PI") =~ expr("3.1415926535897932384626433832795028842e+00") assert result("EE") =~ expr("1.0e+00*ee_") assert result("EM") =~ expr("1.0e+00*em_") *--#] evaluate_symbol_pi : *--#[ evaluate_symbol_ee : #- #StartFloat 160b Local PI = pi_; Local EE = ee_; Local EM = em_; ToFloat; Evaluate ee_; Print; .end #pend_if wordsize == 2 assert result("PI") =~ expr("1.0e+00*pi_") assert result("EE") =~ expr("2.7182818284590452353602874713526624977572470937e+00") assert result("EM") =~ expr("1.0e+00*em_") *--#] evaluate_symbol_ee : *--#[ evaluate_symbol_em : #- #StartFloat 192b Local PI = pi_; Local EE = ee_; Local EM = em_; ToFloat; Evaluate em_; Print; .end #pend_if wordsize == 2 assert result("PI") =~ expr("1.0e+00*pi_") assert result("EE") =~ expr("1.0e+00*ee_") assert result("EM") =~ expr("5.77215664901532860606512090082402431042159335939923598806e-01") *--#] evaluate_symbol_em : *--#[ evaluate_mzv_2 : #- L F = mzv_(2); .sort Hide; #do digits=1,10 #StartFloat `digits'd,MZV=2 Local F`digits' = F; Evaluate mzv_; Print; .sort Hide; #endfloat #enddo * The following checks that a new StartFloat without a previous * EndFloat causes no problems. #do digits=11,20 #StartFloat `digits'd,MZV=2 Local F`digits' = F; Evaluate mzv_; Print; .sort Hide; #enddo .end #pend_if wordsize == 2 assert result("F1") =~ expr("2e+00") assert result("F2") =~ expr("1.6e+00") assert result("F3") =~ expr("1.64e+00") assert result("F4") =~ expr("1.645e+00") assert result("F5") =~ expr("1.6449e+00") assert result("F6") =~ expr("1.64493e+00") assert result("F7") =~ expr("1.644934e+00") assert result("F8") =~ expr("1.6449341e+00") assert result("F9") =~ expr("1.64493407e+00") assert result("F10") =~ expr("1.644934067e+00") assert result("F11") =~ expr("1.6449340668e+00") assert result("F12") =~ expr("1.64493406685e+00") assert result("F13") =~ expr("1.644934066848e+00") assert result("F14") =~ expr("1.6449340668482e+00") assert result("F15") =~ expr("1.64493406684823e+00") assert result("F16") =~ expr("1.644934066848226e+00") assert result("F17") =~ expr("1.6449340668482264e+00") assert result("F18") =~ expr("1.64493406684822644e+00") assert result("F19") =~ expr("1.644934066848226436e+00") assert result("F20") =~ expr("1.6449340668482264365e+00") *--#] evaluate_mzv_2 : *--#[ evaluate_all_mzv_2-6 : #- Symbol a,n,x,jj; CFunction mzv; #do weight=2,6 L F`weight' = x^`weight'*mzv(); #enddo * Generate all possible arguments repeat id x^n?{>0}*mzv(?a) = sum_(jj,1,n, x^(n-jj)*mzv(?a,jj)); * Only keep convergent MZVs id mzv(1,?a) = 0; .sort Hide; #do weight=2,6 #StartFloat 74b,MZV=`weight' Local MZV`weight' = F`weight'; id mzv(?a) = mzv(?a)*mzv_(?a); Evaluate mzv_; Print +s; .sort Hide; #endfloat #enddo .end #pend_if wordsize == 2 assert succeeded? assert result("MZV2") =~ expr(" + 1.644934066848226436472e+00*mzv(2) ") assert result("MZV3") =~ expr(" + 1.2020569031595942854e+00*mzv(2,1) + 1.2020569031595942854e+00*mzv(3) ") assert result("MZV4") =~ expr(" + 1.082323233711138191516e+00*mzv(2,1,1) + 8.11742425283353643637e-01*mzv(2,2) + 2.70580808427784547879e-01*mzv(3,1) + 1.082323233711138191516e+00*mzv(4) ") assert result("MZV5") =~ expr(" + 1.036927755143369926331e+00*mzv(2,1,1,1) + 7.11566197550572432097e-01*mzv(2,1,2) + 2.288103976033537597687e-01*mzv(2,2,1) + 7.11566197550572432097e-01*mzv(2,3) + 9.655115998944373446565e-02*mzv(3,1,1) + 2.288103976033537597687e-01*mzv(3,2) + 9.655115998944373446565e-02*mzv(4,1) + 1.036927755143369926331e+00*mzv(5) ") assert result("MZV6") =~ expr(" + 1.017343061984449139715e+00*mzv(2,1,1,1,1) + 6.745239140339681404916e-01*mzv(2,1,1,2) + 2.137988682245925470996e-01*mzv(2,1,2,1) + 6.183495605712693078956e-01*mzv(2,1,3) + 8.848338245436871429433e-02*mzv(2,2,1,1) + 1.907518241220842136965e-01*mzv(2,2,2) + 7.922139756520716599903e-02*mzv(2,3,1) + 6.745239140339681404916e-01*mzv(2,4) + 4.053689727151973782905e-02*mzv(3,1,1,1) + 7.922139756520716599903e-02*mzv(3,1,2) + 3.230902899166988169841e-02*mzv(3,2,1) + 2.137988682245925470996e-01*mzv(3,3) + 1.748985316901140442593e-02*mzv(4,1,1) + 8.848338245436871429433e-02*mzv(4,2) + 4.053689727151973782905e-02*mzv(5,1) + 1.017343061984449139715e+00*mzv(6) ") *--#] evaluate_all_mzv_2-6 : *--#[ evaluate_all_euler_1-4 : Symbol a,n,x,jj; CFunction euler; #do weight=1,6 L F`weight' = x^`weight'*euler(); #enddo * Generate all possible arguments repeat id x^n?{>0}*euler(?a) = sum_(jj,1,n, x^(n-jj)*euler(?a,-jj))+sum_(jj,1,n, x^(n-jj)*euler(?a,jj)); * Only keep convergent sums id euler(1,?a) = 0; .sort Hide; #do weight=1,4 #StartFloat 74b,MZV=`weight' Local EULER`weight' = F`weight'; id euler(?a) = euler(?a)*euler_(?a); Evaluate euler_; Print +s; .sort Hide; #endfloat #enddo .end #pend_if wordsize == 2 assert succeeded? assert result("EULER1") =~ expr(" - 6.931471805599453094172e-01*euler(-1) ") assert result("EULER2") =~ expr(" - 8.224670334241132182362e-01*euler(-2) - 5.822405264650125059027e-01*euler(-1,-1) + 2.402265069591007123336e-01*euler(-1,1) + 1.644934066848226436472e+00*euler(2) ") assert result("EULER3") =~ expr(" - 9.015426773696957140498e-01*euler(-3) - 2.430703516700615775627e-01*euler(-2,-1) + 1.50257112894949285675e-01*euler(-2,1) - 3.888958461681063290997e-01*euler(-1,-2) + 2.140723708667062274342e-01*euler(-1,-1,-1) - 5.372131936080402009406e-01*euler(-1,-1,1) + 9.475300423012770572183e-02*euler(-1,1,-1) - 5.550410866482157995314e-02*euler(-1,1,1) + 2.695764795315278073874e-01*euler(-1,2) - 5.082152128046848508121e-01*euler(2,-1) + 1.2020569031595942854e+00*euler(2,1) + 1.2020569031595942854e+00*euler(3) ") assert result("EULER4") =~ expr(" - 9.470328294972459175765e-01*euler(-4) - 1.17875999650509326841e-01*euler(-3,-1) + 8.778567156865530203659e-02*euler(-3,1) - 2.029356063208384109093e-01*euler(-2,-2) + 5.465305273826365205925e-02*euler(-2,-1,-1) - 9.309712599176857714371e-02*euler(-2,-1,1) + 3.41591261665139137232e-02*euler(-2,1,-1) - 2.375236632261848595145e-02*euler(-2,1,1) + 1.626546673974200807756e-01*euler(-2,2) - 3.395454690873598695907e-01*euler(-1,-3) + 6.936803430285457740076e-02*euler(-1,-2,-1) - 1.1285749644390297273e-01*euler(-1,-2,1) + 2.410220753003005639135e-01*euler(-1,-1,-2) + 8.798553701050896029994e-02*euler(-1,-1,-1,-1) - 5.091676406429263452417e-02*euler(-1,-1,-1,1) + 2.02865795179889634385e-01*euler(-1,-1,1,-1) - 5.174790616738993863308e-01*euler(-1,-1,1,1) - 3.522826783975370883778e-01*euler(-1,-1,2) + 7.734090056675821939211e-02*euler(-1,1,-2) - 2.327506608672756416438e-02*euler(-1,1,-1,-1) + 4.075823915930925192076e-02*euler(-1,1,-1,1) - 1.413423721499000878947e-02*euler(-1,1,1,-1) + 9.618129107628477161979e-03*euler(-1,1,1,1) - 6.053489317192111168615e-02*euler(-1,1,2) + 4.551222386652609668434e-02*euler(-1,2,-1) - 3.289319519435604132636e-02*euler(-1,2,1) + 2.866757544385383102356e-01*euler(-1,3) - 5.685258800390969025941e-01*euler(2,-2) - 1.935553538130652468834e-01*euler(2,-1,-1) + 1.141234274160608451268e-01*euler(2,-1,1) - 4.336923770489551966887e-01*euler(2,1,-1) + 1.082323233711138191516e+00*euler(2,1,1) + 8.11742425283353643637e-01*euler(2,2) - 1.728452782389843861048e-01*euler(3,-1) + 2.70580808427784547879e-01*euler(3,1) + 1.082323233711138191516e+00*euler(4) ") *--#] evaluate_all_euler_1-4 : *--#[ evaluate_all_mzvhalf_1-6 : Symbol a,n,x,jj; CFunction mzvhalf; #do weight=1,6 L F`weight' = x^`weight'*mzvhalf(); #enddo * Generate all possible arguments repeat id x^n?{>0}*mzvhalf(?a) = sum_(jj,1,n, x^(n-jj)*mzvhalf(?a,jj)); .sort Hide; #do weight=1,6 #StartFloat 74b, MZV = `weight' Local MZVHALF`weight' = F`weight'; id mzvhalf(?a) = mzvhalf(?a)*mzvhalf_(?a); Evaluate mzvhalf_; Print +s; .sort Hide; #endfloat #enddo .end #pend_if wordsize == 2 assert succeeded? assert result("MZVHALF1") =~ expr(" +6.931471805599453094172e-01*mzvhalf(1) ") assert result("MZVHALF2") =~ expr(" +2.402265069591007123336e-01*mzvhalf(1,1) + 5.822405264650125059027e-01*mzvhalf(2) ") assert result("MZVHALF3") =~ expr(" +5.550410866482157995314e-02*mzvhalf(1,1,1) + 2.140723708667062274342e-01*mzvhalf(1,2) + 9.475300423012770572182e-02*mzvhalf(2,1) + 5.372131936080402009406e-01*mzvhalf(3) ") assert result("MZVHALF4") =~ expr(" +9.618129107628477161979e-03*mzvhalf(1,1,1,1) + 5.091676406429263452417e-02*mzvhalf(1,1,2) + 2.327506608672756416438e-02*mzvhalf(1,2,1) + 2.02865795179889634385e-01*mzvhalf(1,3) + 1.413423721499000878947e-02*mzvhalf(2,1,1) + 8.798553701050896029994e-02*mzvhalf(2,2) + 4.075823915930925192076e-02*mzvhalf(3,1) + 5.174790616738993863308e-01*mzvhalf(4) ") assert result("MZVHALF5") =~ expr(" +1.333355814642844342341e-03*mzvhalf(1,1,1,1,1) + 8.977079866463296833435e-03*mzvhalf(1,1,1,2) + 4.180785927505245511698e-03*mzvhalf(1,1,2,1) + 4.888837363087644124842e-02*mzvhalf(1,1,3) + 2.590491526783706529017e-03*mzvhalf(1,2,1,1) + 2.202353039232048705332e-02*mzvhalf(1,2,2) + 1.040778815345923684362e-02*mzvhalf(1,3,1) + 1.977851218733276555108e-01*mzvhalf(1,4) + 1.801653787038017905577e-03*mzvhalf(2,1,1,1) + 1.326622979787512352052e-02*mzvhalf(2,1,2) + 6.215468460408135423935e-03*mzvhalf(2,2,1) + 8.496239975196462665687e-02*mzvhalf(2,3) + 3.876067314665263762197e-03*mzvhalf(3,1,1) + 3.888005884184390429248e-02*mzvhalf(3,2) + 1.853078606546661304236e-02*mzvhalf(4,1) + 5.084005792422687074591e-01*mzvhalf(5) ") assert result("MZVHALF6") =~ expr(" +1.540353039338160995444e-04*mzvhalf(1,1,1,1,1,1) + 1.258876902820489070556e-03*mzvhalf(1,1,1,1,2) + 5.934649939092641274313e-04*mzvhalf(1,1,1,2,1) + 8.687699837464924332492e-03*mzvhalf(1,1,1,3) + 3.725016654823881497105e-04*mzvhalf(1,1,2,1,1) + 3.999767838591861292463e-03*mzvhalf(1,1,2,2) + 1.911985496708273694742e-03*mzvhalf(1,1,3,1) + 4.795057789712260825139e-02*mzvhalf(1,1,4) + 2.626471417724444826556e-04*mzvhalf(1,2,1,1,1) + 2.463136250615208192292e-03*mzvhalf(1,2,1,2) + 1.169869909499536413856e-03*mzvhalf(1,2,2,1) + 2.145129727375666323602e-02*mzvhalf(1,2,3) + 7.400960371731285392346e-04*mzvhalf(1,3,1,1) + 1.004682297311360973229e-02*mzvhalf(1,3,2) + 4.847461771043371713843e-03*mzvhalf(1,4,1) + 1.953981544864645991443e-01*mzvhalf(1,5) + 1.97232820211621153726e-04*mzvhalf(2,1,1,1,1) + 1.706168769515668670888e-03*mzvhalf(2,1,1,2) + 8.069036109476304022076e-04*mzvhalf(2,1,2,1) + 1.287224686067429263904e-02*mzvhalf(2,1,3) + 5.081857692654553033744e-04*mzvhalf(2,2,1,1) + 5.968128689077008853625e-03*mzvhalf(2,2,2) + 2.863764078749510138598e-03*mzvhalf(2,3,1) + 8.355552124728128937156e-02*mzvhalf(2,4) + 3.596008310955505224866e-04*mzvhalf(3,1,1,1) + 3.701399425949438029416e-03*mzvhalf(3,1,2) + 1.765926326069690097067e-03*mzvhalf(3,2,1) + 3.801462469797616251775e-02*mzvhalf(3,3) + 1.122469979658377667375e-03*mzvhalf(4,1,1) + 1.798212154990578314126e-02*mzvhalf(4,2) + 8.723003057596888427165e-03*mzvhalf(5,1) + 5.0409539780398855069e-01*mzvhalf(6) ") *--#] evaluate_all_mzvhalf_1-6 : *--#[ evaluate_sin : #StartFloat 24d Symbol n; CFunction sin; Local SIN = sum_(n,4,27,sin(2*pi_*n/24)*sin_(2*pi_*n/24))+sin(4*pi_/13)*sin_(4*pi_/13)+sin(-1.2*pi_/13)*sin_(-1.2*pi_/13); Evaluate sin_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("SIN") =~ expr(" + 8.22983865893656394579617e-01*sin(4/13*pi_) + 8.66025403784438646763723e-01*sin(1/3*pi_) + 9.65925826289068286749743e-01*sin(5/12*pi_) + 1.0e+00*sin(1/2*pi_) + 9.65925826289068286749743e-01*sin(7/12*pi_) + 8.66025403784438646763723e-01*sin(2/3*pi_) + 7.07106781186547524400844e-01*sin(3/4*pi_) + 5.0e-01*sin(5/6*pi_) + 2.58819045102520762348899e-01*sin(11/12*pi_) - 2.58819045102520762348899e-01*sin(13/12*pi_) - 5.0e-01*sin(7/6*pi_) - 7.07106781186547524400844e-01*sin(5/4*pi_) - 8.66025403784438646763723e-01*sin(4/3*pi_) - 9.65925826289068286749743e-01*sin(17/12*pi_) - 1.0e+00*sin(3/2*pi_) - 9.65925826289068286749743e-01*sin(19/12*pi_) - 8.66025403784438646763723e-01*sin(5/3*pi_) - 7.07106781186547524400844e-01*sin(7/4*pi_) - 5.0e-01*sin(11/6*pi_) - 2.58819045102520762348899e-01*sin(23/12*pi_) + 2.58819045102520762348899e-01*sin(25/12*pi_) + 5.0e-01*sin(13/6*pi_) + 7.07106781186547524400844e-01*sin(9/4*pi_) - 2.8594567839868926206474e-01*sin( - 9.23076923076923076923077e-02*pi_ ) ") *--#] evaluate_sin : *--#[ evaluate_cos : #StartFloat 24d Symbol n; CFunction cos; Local COS = sum_(n,4,27,cos(2*pi_*n/24)*cos_(2*pi_*n/24))+cos(-2^32*pi_/3)*cos_(-2^32*pi_/3)+cos(4*pi_/13)*cos_(4*pi_/13)+cos(-1.2*pi_/13)*cos_(-1.2*pi_/13)+cos(2^32*pi_/(2^32+1))*cos_(2^32*pi_/(2^32+1)); Evaluate cos_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("COS") =~ expr(" - 5.0e-01*cos( - 4294967296/3*pi_) + 5.68064746731155802511808e-01*cos(4/13*pi_) + 5.0e-01*cos(1/3*pi_) + 2.58819045102520762348899e-01*cos(5/12*pi_) - 2.58819045102520762348899e-01*cos(7/12*pi_) - 5.0e-01*cos(2/3*pi_) - 7.07106781186547524400844e-01*cos(3/4*pi_) - 8.66025403784438646763723e-01*cos(5/6*pi_) - 9.65925826289068286749743e-01*cos(11/12*pi_) - 9.99999999999999999732484e-01*cos(4294967296/4294967297*pi_) - 9.65925826289068286749743e-01*cos(13/12*pi_) - 8.66025403784438646763723e-01*cos(7/6*pi_) - 7.07106781186547524400844e-01*cos(5/4*pi_) - 5.0e-01*cos(4/3*pi_) - 2.58819045102520762348899e-01*cos(17/12*pi_) + 2.58819045102520762348899e-01*cos(19/12*pi_) + 5.0e-01*cos(5/3*pi_) + 7.07106781186547524400844e-01*cos(7/4*pi_) + 8.66025403784438646763723e-01*cos(11/6*pi_) + 9.65925826289068286749743e-01*cos(23/12*pi_) + 1.0e+00*cos(2*pi_) + 9.65925826289068286749743e-01*cos(25/12*pi_) + 8.66025403784438646763723e-01*cos(13/6*pi_) + 7.07106781186547524400844e-01*cos(9/4*pi_) + 9.58245829109166210690747e-01*cos( - 9.23076923076923076923077e-02* pi_) - 1.0e+00*cos(pi_) ") *--#] evaluate_cos : *--#[ evaluate_tan : #StartFloat 24d Symbol n; CFunction tan; Local TAN = sum_(n,4,27,tan(2*pi_*n/24)*tan_(2*pi_*n/24))+tan(4*pi_/13)*tan_(4*pi_/13)+tan(-1.2*pi_/13)*tan_(-1.2*pi_/13); Evaluate tan_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("TAN") =~ expr(" + tan_(1/2*pi_)*tan(1/2*pi_) + tan_(3/2*pi_)*tan(3/2*pi_) + 1.44875011278097222958133e+00*tan(4/13*pi_) + 1.73205080756887729352745e+00*tan(1/3*pi_) + 3.73205080756887729352745e+00*tan(5/12*pi_) - 3.73205080756887729352745e+00*tan(7/12*pi_) - 1.73205080756887729352745e+00*tan(2/3*pi_) + 1.0e+00*tan(3/4*pi_) - 5.77350269189625764509149e-01*tan(5/6*pi_) - 2.67949192431122706472554e-01*tan(11/12*pi_) + 2.67949192431122706472554e-01*tan(13/12*pi_) + 5.77350269189625764509149e-01*tan(7/6*pi_) + 1.0e+00*tan(5/4*pi_) + 1.73205080756887729352745e+00*tan(4/3*pi_) + 3.73205080756887729352745e+00*tan(17/12*pi_) - 3.73205080756887729352745e+00*tan(19/12*pi_) - 1.73205080756887729352745e+00*tan(5/3*pi_) + 1.0e+00*tan(7/4*pi_) - 5.77350269189625764509149e-01*tan(11/6*pi_) - 2.67949192431122706472554e-01*tan(23/12*pi_) + 2.67949192431122706472554e-01*tan(25/12*pi_) + 5.77350269189625764509149e-01*tan(13/6*pi_) + 1.0e+00*tan(9/4*pi_) - 2.9840534621947567190308e-01*tan( - 9.23076923076923076923077e-02*pi_ ) ") *--#] evaluate_tan : *--#[ evaluate_asin : #StartFloat 82b CFunction asin; Local ASIN = asin(0)*asin_(0)+2*asin(-1.0)*asin_(-1.0)/pi_+2*asin(1)*asin_(1)/pi_+asin(-0.7356)*asin_(-0.7356)+asin(4/13)*asin_(4/13)+asin(-3/2)*asin_(-3/2)+asin(5)*asin_(5); Evaluate asin_, pi_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("ASIN") =~ expr(" + asin_( - 3/2)*asin( - 3/2) + asin_(5)*asin(5) + 3.12766721941544958213894e-01*asin(4/13) - 8.26551974047654326578014e-01*asin( - 7.356e-01) - 1.0e+00*asin( - 1.0e+00) + 1.0e+00*asin(1) ") *--#] evaluate_asin : *--#[ evaluate_acos : #StartFloat 82b CFunction acos; Local ACOS = 2*acos(0)*acos_(0)/pi_+acos(-1.0)*acos_(-1.0)/pi_+acos(1)*acos_(1)+acos(-0.7356)*acos_(-0.7356)+acos(4/13)*acos_(4/13)+acos(-3/2)*acos_(-3/2)+acos(5)*acos_(5); Evaluate acos_, pi_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("ACOS") =~ expr(" + acos_( - 3/2)*acos( - 3/2) + acos_(5)*acos(5) + 1.25802960485335166101743e+00*acos(4/13) + 2.39734830084255094580934e+00*acos( - 7.356e-01) + 1.0e+00*acos( - 1.0e+00) + 1.0e+00*acos(0) ") *--#] evaluate_acos : *--#[ evaluate_atan : #StartFloat 82b CFunction atan; Local ATAN = atan(0)*atan_(0)+atan(-1.0)*atan_(-1.0)+atan(1)*atan_(1)+atan(-0.7356)*atan_(-0.7356)+atan(4/13)*atan_(4/13)+2*atan(-10^20)*atan_(-10^20)/pi_+2*atan(10^20)*atan_(10^20)/pi_; Evaluate atan_, pi_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("ATAN") =~ expr(" - 9.99999999999999999993634e-01*atan( - 100000000000000000000) + 2.98498931586179277935128e-01*atan(4/13) + 9.99999999999999999993634e-01*atan(100000000000000000000) - 6.34221230827067632052843e-01*atan( - 7.356e-01) - 7.85398163397448309615661e-01*atan( - 1.0e+00) + 7.85398163397448309615661e-01*atan(1) ") *--#] evaluate_atan : *--#[ evaluate_atan2 : #Startfloat 21d CFunction atan2; Local ATAN2 = atan2(0,0)*atan2_(0,0) +atan2(0,24)*atan2_(0,24) +atan2(24/13,0)*atan2_(24/13,0) +atan2(3,-1.45)*atan2_(3,-1.45) +atan2(0.54321,-1.2345)*atan2_(0.54321,-1.2345) +atan2(5.4321,-45/11)*atan2_(5.4321,-45/11); Evaluate; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("ATAN2") =~ expr(" + 1.57079632679489661923e+00*atan2(24/13,0) + 2.72706541948852419832e+00*atan2(5.4321e-01, - 1.2345e+00) + 2.21627784862167698618e+00*atan2(5.4321e+00, - 45/11) + 2.02102192305561165724e+00*atan2(3, - 1.45e+00) ") *--#] evaluate_atan2 : *--#[ evaluate_sqrt : #Startfloat 21d CFunction sqrt; Local SQRT = sqrt(0)*sqrt_(0)+sqrt(1)*sqrt_(1)+sqrt(1.456789)*sqrt_(1.456789)+sqrt(25/7)*sqrt_(25/7)+sqrt(-1)*sqrt_(-1)+sqrt(5932)*sqrt_(5932); Evaluate sqrt_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("SQRT") =~ expr(" + sqrt_(-1)*sqrt(-1) + 1.88982236504613613607e+00*sqrt(25/7) + 1.20697514473165519284e+00*sqrt(1.456789e+00) + 1.0e+00*sqrt(1) + 7.70194780558788258528e+01*sqrt(5932) ") *--#] evaluate_sqrt : *--#[ evaluate_ln : #Startfloat 60b CFunction ln; Local LN = ln(1)*ln_(1)+ln(0)*ln_(0)+ln(ee_)*ln_(ee_)+ln(2.71828)*ln_(2.71828)+ln(2/3)*ln_(2/3)+ln(-5)*ln_(-5); Evaluate ln_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("LN") =~ expr(" + ln_(ee_)*ln(ee_) + ln_(-5)*ln(-5) + ln_(0)*ln(0) - 4.05465108108164382e-01*ln(2/3) + 9.99999327347282003e-01*ln(2.71828e+00) ") *--#] evaluate_ln : *--#[ evaluate_eexp : #Startfloat 84b CFunction exp; Local EXP = exp(0)*eexp_(0)+exp(1)*eexp_(1)+exp(-10)*eexp_(-10)+exp(2/11)*eexp_(2/11)+exp(36124.5)*eexp_(36124.5); Evaluate; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("EXP") =~ expr(" + 1.199396102035385909645662e+00*exp(2/11) + 4.688258114961839863324201e+15688*exp(3.61245e+04) + 4.539992976248485153559152e-05*exp(-10) + 1.0e+00*exp(0) + 2.718281828459045235360287e+00*exp(1) ") *--#] evaluate_eexp : *--#[ evaluate_li2 : #Startfloat 18d CFunction li2; Local LI2 = li2(0)*li2_(0)+li2(1)*li2_(1)+li2(-1)*li2_(-1)+li2(1/2)*li2_(1/2)+li2(1.4)*li2_(1.4)+li2(-10)*li2_(-10); Evaluate li2_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("LI2") =~ expr(" + li2_(1.4e+00)*li2(1.4e+00) + li2_(-10)*li2(-10) + 5.82240526465012506e-01*li2(1/2) - 8.22467033424113218e-01*li2(-1) + 1.64493406684822644e+00*li2(1) ") *--#] evaluate_li2 : *--#[ evaluate_gamma : #Startfloat 131b CFunction gamma; Local GAMMA = gamma(-754)*gamma_(-754)+gamma(-1)*gamma_(-1)+gamma(0)*gamma_(0)+gamma(1)*gamma_(1)+gamma(563)*gamma_(563)*invfac_(562)+gamma(-3/2)*gamma_(-3/2)+gamma(3.456)*gamma_(3.456); Evaluate gamma_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("GAMMA") =~ expr(" + gamma_(-754)*gamma(-754) + gamma_(-1)*gamma(-1) + gamma_(0)*gamma(0) + 2.3632718012073547030642233111215269104e+00*gamma( - 3/2) + 3.1669090330100746768222387336126462899e+00*gamma(3.456e+00) + 1.0e+00*gamma(1) + 1.0e+00*gamma(563) ") *--#] evaluate_gamma : *--#[ evaluate_agm : #Startfloat 33b CFunction agm,f; Local AGM = agm(24,6)*agm_(24,6)+agm(24,0)*agm_(24,0)+agm(0,6)*agm_(0,6)+agm(24,-1)*agm_(24,-1)+agm(-1,6)*agm_(-1,6)+agm(0,-1)*agm_(0,-1)+agm(-1,0)*agm_(-1,0); Evaluate agm_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("AGM") =~ expr(" + agm_(-1,6)*agm(-1,6) + agm_(24,-1)*agm(24,-1) + 1.34581715e+01*agm(24,6) ") *--#] evaluate_agm : *--#[ evaluate_sinh : #Startfloat 96b CFunction sinh; Local SINH = sinh(0)*sinh_(0)+sinh(1.0)*sinh_(1.0)+sinh(ln_(2))*sinh_(ln_(2))+sinh(-ln_(2))*sinh_(-ln_(2)); Argument sinh_; Evaluate; Endargument; Evaluate sinh_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("SINH") =~ expr(" - 7.5e-01*sinh( - ln_(2)) + 7.5e-01*sinh(ln_(2)) + 1.175201193643801456882381851e+00*sinh(1.0e+00) ") *--#] evaluate_sinh : *--#[ evaluate_cosh : #Startfloat 96b CFunction cosh; Local COSH = cosh(0)*cosh_(0)+cosh(1.0)*cosh_(1.0)+cosh(-1.0)*cosh_(-1.0)+cosh(ln_(2))*cosh_(ln_(2))+cosh(-ln_(2))*cosh_(-ln_(2)); Argument cosh_; Evaluate; Endargument; Evaluate cosh_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("COSH") =~ expr(" + 1.25e+00*cosh( - ln_(2)) + 1.25e+00*cosh(ln_(2)) + 1.543080634815243778477905621e+00*cosh( - 1.0e+00) + 1.543080634815243778477905621e+00*cosh(1.0e+00) + 1.0e+00*cosh(0) ") *--#] evaluate_cosh : *--#[ evaluate_tanh : #Startfloat 96b CFunction tanh; Local TANH = tanh(0)*tanh_(0)+tanh(1.0)*tanh_(1.0)+tanh(-1.0)*tanh_(-1.0)+tanh(ln_(2))*tanh_(ln_(2))+tanh(-ln_(2))*tanh_(-ln_(2)); Argument tanh_; Evaluate; Endargument; Evaluate tanh_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("TANH") =~ expr(" - 6.0e-01*tanh( - ln_(2)) + 6.0e-01*tanh(ln_(2)) - 7.615941559557648881194582826e-01*tanh( - 1.0e+00) + 7.615941559557648881194582826e-01*tanh(1.0e+00) ") *--#] evaluate_tanh : *--#[ evaluate_asinh : #Startfloat 21d CFunction asinh; Local ASINH = asinh(0)*asinh_(0)+asinh(1.0)*asinh_(1.0)+asinh(-1)*asinh_(-1); Evaluate asinh_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("ASINH") =~ expr(" + 8.81373587019543025233e-01*asinh(1.0e+00) - 8.81373587019543025233e-01*asinh(-1) ") *--#] evaluate_asinh : *--#[ evaluate_acosh : #Startfloat 21d CFunction acosh; Local ACOSH = acosh(0)*acosh_(0)+acosh(1.0)*acosh_(1.0)+acosh(-1)*acosh_(-1)+acosh(24/7)*acosh_(24/7); Evaluate acosh_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("ACOSH") =~ expr(" + acosh_(-1)*acosh(-1) + acosh_(0)*acosh(0) + 1.90331107830883818521e+00*acosh(24/7) ") *--#] evaluate_acosh : *--#[ evaluate_atanh : #Startfloat 21d CFunction atanh; Local ATANH = atanh(0)*atanh_(0)+atanh(1.0)*atanh_(1.0)+atanh(-1)*atanh_(-1)+atanh(24/7)*atanh_(24/7)+atanh(1/9)*atanh_(1/9)+atanh(-.54321)*atanh_(-.54321); Evaluate atanh_; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("ATANH") =~ expr(" + atanh_(24/7)*atanh(24/7) + atanh_(1.0e+00)*atanh(1.0e+00) + atanh_(-1)*atanh(-1) + 1.11571775657104877883e-01*atanh(1/9) - 6.08698087464190136361e-01*atanh( - 5.4321e-01) ") *--#] evaluate_atanh : *--#[ torat : #- #StartFloat 16d Symbol a,b,jj; Local F1 = 0.0 -10^-20*a +1023/1024*a^2 -17/1024*a^3 +3602879701896397/2^55*a^4 -10^20*a^5 +17*a^6 ; Local F2 = sum_(jj,1,16,(355/113+10^-jj)*a^jj); Local F3 = 0.3*a^1+0.33*a^2+0.333*a^3+0.3333*a^4+0.33333*a^5+0.333333*a^6+0.3333333*a^7+0.33333333*a^8+0.333333333*a^9+0.3333333333*a^10+0.33333333333*a^11+0.333333333333*a^12+0.3333333333333*a^13+0.33333333333333*a^14+0.333333333333333*a^15+0.3333333333333333*a^16; ToFloat; .sort ToRat; .sort #StartFloat 50d Local F4 = 10e-20; ToRat; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert result("F1") =~ expr("+ 1023/1024*a^2 - 17/1024*a^3 + 1/10*a^4 - 100000000000000000000*a^5 + 17*a^6") assert result("F2") =~ expr("+ 3663/1130*a + 35613/11300*a^2 + 355113/113000*a^3 + 3550113/1130000*a^4 + 35500113/11300000*a^5 + 355000113/113000000*a^6 + 2205176720676/701929469027*a^7 + 5798543718053/1845733628322*a^8 + 4781671236789/1522053097423*a^9 + 492368235747/156725663768*a^10 + 355/113*a^11 + 355/113*a^12 + 355/113*a^13 + 355/113*a^14 + 355/113*a^15 + 355/113*a^16") assert result("F3") =~ expr(" + 3/10*a + 33/100*a^2 + 333/1000*a^3 + 3333/10000*a^4 + 33333/100000*a^5 + 333333/1000000*a^6 + 3333333/10000000*a^7 + 33333333/100000000*a^8 + 1/3*a^9 + 1/3*a^10 + 1/3*a^11 + 1/3*a^12 + 1/3*a^13 + 1/3*a^14 + 1/3*a^15 + 1/3*a^16") assert result("F4") =~ expr("+ 1/10000000000000000000") *--#] torat : *--#[ strictrounding_1 : #StartFloat 6d CFunction f; Local F1 = 1.23456789e-4+f(1.0)+f(1.0000001); Print; .sort Skip F1; Local F2 = F1; StrictRounding 4d; Argument f; StrictRounding; EndArgument; Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F1") =~ expr("1.23457e-04 + f(1.0e+00) + f(1.0e+00)") assert result("F2") =~ expr("1.235e-04 + 2*f(1.0e+00)") *--#] strictrounding_1 : *--#[ strictrounding_2 : #StartFloat 20b CFunction f; Local F = 1.1e-4; StrictRounding 5b; .sort #EndFloat #StartFloat 40d Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F") =~ expr("1.10626220703125e-04") *--#] strictrounding_2 : *--#[ strictrounding_error: #- StrictRounding; #StartFloat 10d StrictRounding 5; StrictRounding d5; StrictRounding 5 d; .end #pend_if wordsize == 2 assert runtime_error?("Illegal attempt for strict rounding without activating floating point numbers.") assert runtime_error?("Forgotten #startfloat instruction?") assert runtime_error?("Illegal argument(s) in StrictRounding statement: ''") assert runtime_error?("Illegal argument(s) in StrictRounding statement: 'd5'") assert runtime_error?("Illegal argument(s) in StrictRounding statement: ',d'") *--#] strictrounding_error : *--#[ chop : #StartFloat 15d #StartFloat 15d Symbol x; Local F1 = 4.7*x-1.0e-10*x^2+.2e-10*x^3-0.00005*x^4+x^5/1000000; Local F2 = 4.7*x-1.0e-10*x^2+.2e-10*x^3-0.00005*x^4+x^5/1000000; Local F3 = 4.7*x-1.0e-10*x^2+.2e-10*x^3-0.00005*x^4+x^5/1000000; Local F4 = 4.7*x-1.0e-10*x^2+.2e-10*x^3-0.00005*x^4+x^5/1000000; Local F5 = 4.7*x-1.0e-10*x^2+.2e-10*x^3-0.00005*x^4+x^5/1000000; Print; .sort Skip; NSkip F1; Chop 1.0e-10; .sort Skip; NSkip F2; Chop 1/10000; .sort Skip; NSkip F3; Chop 7; .sort Skip; NSkip F4; Chop 10^-6; .sort Skip; NSkip F5; Chop 10^6; .sort Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F1") =~ expr("4.7e+00*x - 1.0e-10*x^2 - 5.0e-05*x^4 + 1/1000000*x^5") assert result("F2") =~ expr("4.7e+00*x + 1/1000000*x^5") assert result("F3") =~ expr("1/1000000*x^5") assert result("F4") =~ expr("4.7e+00*x - 5.0e-05*x^4 + 1/1000000*x^5") assert result("F5") =~ expr("1/1000000*x^5") *--#] chop : *--#[ chop_error : Chop 10; #StartFloat 10d Chop; Chop 1/0; Chop 1e-10a; .end #pend_if wordsize == 2 assert compile_error?("Illegal attempt to chop a float_ without activating floating point numbers.") assert compile_error?("Forgotten #startfloat instruction?") assert compile_error?("Chop needs a number (float, rational or power) as an argument.") assert compile_error?("Division by zero in chop statement.") assert compile_error?("Illegal argument(s) in Chop statement: 'a'.") *--#] chop_error : *--#[ pattern_float : #- Off Statistics; #StartFloat 10d #message StartFloat Symbol a,x1,...,x4; CFunction f,g; Vector p; Local F = 1.0-2.0*a+3.0*f-4.0*p.p+5.0*p; id 1.0 = 5; id f?(?a) = g(?a); id float_(?a) = g(?a); id float_(x1?,x2?,x3?,x4?) = g(x1,x2,x3,x4); Print; .sort #endfloat #message endfloat id float_(2,3,1,340282366920938463463374607431768211456) = 5; id f?(?a) = g(?a); id float_(?a) = g(?a); id float_(x1?,x2?,x3?,x4?) = g(x1,x2,x3,x4); Print +s; .end #pend_if wordsize == 2 assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~StartFloat F = - 2.0e+00*a - 4.0e+00*p.p + 5.0e+00*p + 1.0e+00 + 3.0e+00*g; ~~~endfloat F = - a*float_(2,3,1,680564733841876926926749214863536422912) - p.p*float_(2,3,1,1361129467683753853853498429727072845824) + p*float_(2,3,1,1701411834604692317316873037158841057280) + float_(2,3,1,340282366920938463463374607431768211456) + g*float_(2,3,1,1020847100762815390390123822295304634368) ; EOF *--#] pattern_float : *--#[ transform_float : #- CFunction f; Off Statistics; #StartFloat 10d #message StartFloat Local F = 1.0*f(1,2,3); Transform replace(1,last)=(xarg_,2*xarg_+1); Print; .sort #endfloat #message endfloat Transform mulargs(1,last); Print; .end #pend_if wordsize == 2 assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~StartFloat F = 1.0e+00*f(3,5,7); ~~~endfloat F = f(105)*float_(2,3,1,340282366920938463463374607431768211456); EOF *--#] transform_float : *--#[ transform_float_error : #- CFunction f,g; Off Statistics; #StartFloat 10d Local F = 1.0*f(1,2,3)*g(3,2,1); Transform float_, reverse(1,last); Transform {float_,f}, addargs(1,last); Print; .sort #endfloat Transform float_, dropargs(1,last); Transform {float_,f}, selectargs(1,2); Print; .end #pend_if wordsize == 2 assert runtime_error?("Illegal use of a transform statement and float_") assert runtime_error?("Illegal use of a transform statement and float_") assert runtime_error?("Illegal use of a transform statement and float_") assert runtime_error?("Illegal use of a transform statement and float_") *--#] transform_float_error : *--#[ argument_float : #StartFloat 24d CFunction f; Symbol a,b,c,d; #StartFloat 24d Local F = 1.0 -2.0*f(a+5*b-3*c)+f(3.14*a*b); Normalize; MakeInteger; Argument; Multiply 10*d; EndArgument; SplitArg; FactArg; Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F") =~ expr("1.0e+00 + f(a,b,d,3.14e+01) + 2.0e+00*f(30,c,d,-50,b,d,-10,a,d)") *--#] argument_float : *--#[ AddWithFloat : * This tests AddWithFloat in float.c #StartFloat 10d Symbol x1,...,x4; Local F = (x1+1.0*x2+x3+1.0*x4)^5; id x1 = 1-x2-x3-x4; Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F") =~ expr("1 + 0.0e+00*x4 + 0.0e+00*x4^2 + 0.0e+00*x4^3 + 0.0e+00*x4^4 + 0.0e+00* x4^5 + 0.0e+00*x3*x4 + 0.0e+00*x3*x4^2 + 0.0e+00*x3*x4^3 + 0.0e+00*x3* x4^4 + 0.0e+00*x3^2*x4 + 0.0e+00*x3^2*x4^2 + 0.0e+00*x3^2*x4^3 + 0.0e+00 *x3^3*x4 + 0.0e+00*x3^3*x4^2 + 0.0e+00*x3^4*x4 + 0.0e+00*x2 + 0.0e+00*x2 *x4 + 0.0e+00*x2*x4^2 + 0.0e+00*x2*x4^3 + 0.0e+00*x2*x4^4 + 0.0e+00*x2* x3 + 0.0e+00*x2*x3*x4 + 0.0e+00*x2*x3*x4^2 + 0.0e+00*x2*x3*x4^3 + 0.0e+00*x2*x3^2 + 0.0e+00*x2*x3^2*x4 + 0.0e+00*x2*x3^2*x4^2 + 0.0e+00*x2 *x3^3 + 0.0e+00*x2*x3^3*x4 + 0.0e+00*x2*x3^4 + 0.0e+00*x2^2 + 0.0e+00* x2^2*x4 + 0.0e+00*x2^2*x4^2 + 0.0e+00*x2^2*x4^3 + 0.0e+00*x2^2*x3 + 0.0e+00*x2^2*x3*x4 + 0.0e+00*x2^2*x3*x4^2 + 0.0e+00*x2^2*x3^2 + 0.0e+00* x2^2*x3^2*x4 + 0.0e+00*x2^2*x3^3 + 0.0e+00*x2^3 + 0.0e+00*x2^3*x4 + 0.0e+00*x2^3*x4^2 + 0.0e+00*x2^3*x3 + 0.0e+00*x2^3*x3*x4 + 0.0e+00*x2^3* x3^2 + 0.0e+00*x2^4 + 0.0e+00*x2^4*x4 + 0.0e+00*x2^4*x3 + 0.0e+00*x2^5") *--#] AddWithFloat : *--#[ float_extremes : #StartFloat 10d CFunction f; #do i = 0,62 Local F`i' = 1.`i'e{2^`i'}*f({2^`i'}); Local G`i' = 1.`i'e{-2^`i'}*f({2^`i'}); #enddo Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F0") =~ expr("1.0e+01*f(1)") assert result("G0") =~ expr("1.0e-01*f(1)") assert result("F1") =~ expr("1.1e+02*f(2)") assert result("G1") =~ expr("1.1e-02*f(2)") assert result("F2") =~ expr("1.2e+04*f(4)") assert result("G2") =~ expr("1.2e-04*f(4)") assert result("F3") =~ expr("1.3e+08*f(8)") assert result("G3") =~ expr("1.3e-08*f(8)") assert result("F4") =~ expr("1.4e+16*f(16)") assert result("G4") =~ expr("1.4e-16*f(16)") assert result("F5") =~ expr("1.5e+32*f(32)") assert result("G5") =~ expr("1.5e-32*f(32)") assert result("F6") =~ expr("1.6e+64*f(64)") assert result("G6") =~ expr("1.6e-64*f(64)") assert result("F7") =~ expr("1.7e+128*f(128)") assert result("G7") =~ expr("1.7e-128*f(128)") assert result("F8") =~ expr("1.8e+256*f(256)") assert result("G8") =~ expr("1.8e-256*f(256)") assert result("F9") =~ expr("1.9e+512*f(512)") assert result("G9") =~ expr("1.9e-512*f(512)") assert result("F10") =~ expr("1.1e+1024*f(1024)") assert result("G10") =~ expr("1.1e-1024*f(1024)") assert result("F11") =~ expr("1.11e+2048*f(2048)") assert result("G11") =~ expr("1.11e-2048*f(2048)") assert result("F12") =~ expr("1.12e+4096*f(4096)") assert result("G12") =~ expr("1.12e-4096*f(4096)") assert result("F13") =~ expr("1.13e+8192*f(8192)") assert result("G13") =~ expr("1.13e-8192*f(8192)") assert result("F14") =~ expr("1.14e+16384*f(16384)") assert result("G14") =~ expr("1.14e-16384*f(16384)") assert result("F15") =~ expr("1.15e+32768*f(32768)") assert result("G15") =~ expr("1.15e-32768*f(32768)") assert result("F16") =~ expr("1.16e+65536*f(65536)") assert result("G16") =~ expr("1.16e-65536*f(65536)") assert result("F17") =~ expr("1.17e+131072*f(131072)") assert result("G17") =~ expr("1.17e-131072*f(131072)") assert result("F18") =~ expr("1.18e+262144*f(262144)") assert result("G18") =~ expr("1.18e-262144*f(262144)") assert result("F19") =~ expr("1.19e+524288*f(524288)") assert result("G19") =~ expr("1.19e-524288*f(524288)") assert result("F20") =~ expr("1.2e+1048576*f(1048576)") assert result("G20") =~ expr("1.2e-1048576*f(1048576)") assert result("F21") =~ expr("1.21e+2097152*f(2097152)") assert result("G21") =~ expr("1.21e-2097152*f(2097152)") assert result("F22") =~ expr("1.22e+4194304*f(4194304)") assert result("G22") =~ expr("1.22e-4194304*f(4194304)") assert result("F23") =~ expr("1.23e+8388608*f(8388608)") assert result("G23") =~ expr("1.23e-8388608*f(8388608)") assert result("F24") =~ expr("1.24e+16777216*f(16777216)") assert result("G24") =~ expr("1.24e-16777216*f(16777216)") assert result("F25") =~ expr("1.25e+33554432*f(33554432)") assert result("G25") =~ expr("1.25e-33554432*f(33554432)") assert result("F26") =~ expr("1.26e+67108864*f(67108864)") assert result("G26") =~ expr("1.26e-67108864*f(67108864)") assert result("F27") =~ expr("1.27e+134217728*f(134217728)") assert result("G27") =~ expr("1.27e-134217728*f(134217728)") assert result("F28") =~ expr("1.28e+268435456*f(268435456)") assert result("G28") =~ expr("1.28e-268435456*f(268435456)") assert result("F29") =~ expr("1.29e+536870912*f(536870912)") assert result("G29") =~ expr("1.29e-536870912*f(536870912)") assert result("F30") =~ expr("1.3e+1073741824*f(1073741824)") assert result("G30") =~ expr("1.3e-1073741824*f(1073741824)") assert result("F31") =~ expr("1.31e+2147483648*f(2147483648)") assert result("G31") =~ expr("1.31e-2147483648*f(2147483648)") assert result("F32") =~ expr("1.32e+4294967296*f(4294967296)") assert result("G32") =~ expr("1.32e-4294967296*f(4294967296)") assert result("F33") =~ expr("1.33e+8589934592*f(8589934592)") assert result("G33") =~ expr("1.33e-8589934592*f(8589934592)") assert result("F34") =~ expr("1.34e+17179869184*f(17179869184)") assert result("G34") =~ expr("1.34e-17179869184*f(17179869184)") assert result("F35") =~ expr("1.35e+34359738368*f(34359738368)") assert result("G35") =~ expr("1.35e-34359738368*f(34359738368)") assert result("F36") =~ expr("1.36e+68719476736*f(68719476736)") assert result("G36") =~ expr("1.36e-68719476736*f(68719476736)") assert result("F37") =~ expr("1.37e+137438953472*f(137438953472)") assert result("G37") =~ expr("1.37e-137438953472*f(137438953472)") assert result("F38") =~ expr("1.38e+274877906944*f(274877906944)") assert result("G38") =~ expr("1.38e-274877906944*f(274877906944)") assert result("F39") =~ expr("1.39e+549755813888*f(549755813888)") assert result("G39") =~ expr("1.39e-549755813888*f(549755813888)") assert result("F40") =~ expr("1.4e+1099511627776*f(1099511627776)") assert result("G40") =~ expr("1.4e-1099511627776*f(1099511627776)") assert result("F41") =~ expr("1.41e+2199023255552*f(2199023255552)") assert result("G41") =~ expr("1.41e-2199023255552*f(2199023255552)") assert result("F42") =~ expr("1.42e+4398046511104*f(4398046511104)") assert result("G42") =~ expr("1.42e-4398046511104*f(4398046511104)") assert result("F43") =~ expr("1.43e+8796093022208*f(8796093022208)") assert result("G43") =~ expr("1.43e-8796093022208*f(8796093022208)") assert result("F44") =~ expr("1.44e+17592186044416*f(17592186044416)") assert result("G44") =~ expr("1.44e-17592186044416*f(17592186044416)") assert result("F45") =~ expr("1.45e+35184372088832*f(35184372088832)") assert result("G45") =~ expr("1.45e-35184372088832*f(35184372088832)") assert result("F46") =~ expr("1.46e+70368744177664*f(70368744177664)") assert result("G46") =~ expr("1.46e-70368744177664*f(70368744177664)") assert result("F47") =~ expr("1.47e+140737488355328*f(140737488355328)") assert result("G47") =~ expr("1.47e-140737488355328*f(140737488355328)") assert result("F48") =~ expr("1.48e+281474976710656*f(281474976710656)") assert result("G48") =~ expr("1.48e-281474976710656*f(281474976710656)") assert result("F49") =~ expr("1.49e+562949953421312*f(562949953421312)") assert result("G49") =~ expr("1.49e-562949953421312*f(562949953421312)") assert result("F50") =~ expr("1.5e+1125899906842624*f(1125899906842624)") assert result("G50") =~ expr("1.5e-1125899906842624*f(1125899906842624)") assert result("F51") =~ expr("1.51e+2251799813685248*f(2251799813685248)") assert result("G51") =~ expr("1.51e-2251799813685248*f(2251799813685248)") assert result("F52") =~ expr("1.52e+4503599627370496*f(4503599627370496)") assert result("G52") =~ expr("1.52e-4503599627370496*f(4503599627370496)") assert result("F53") =~ expr("1.53e+9007199254740992*f(9007199254740992)") assert result("G53") =~ expr("1.53e-9007199254740992*f(9007199254740992)") assert result("F54") =~ expr("1.54e+18014398509481984*f(18014398509481984)") assert result("G54") =~ expr("1.54e-18014398509481984*f(18014398509481984)") assert result("F55") =~ expr("1.55e+36028797018963968*f(36028797018963968)") assert result("G55") =~ expr("1.55e-36028797018963968*f(36028797018963968)") assert result("F56") =~ expr("1.56e+72057594037927936*f(72057594037927936)") assert result("G56") =~ expr("1.56e-72057594037927936*f(72057594037927936)") assert result("F57") =~ expr("1.57e+144115188075855872*f(144115188075855872)") assert result("G57") =~ expr("1.57e-144115188075855872*f(144115188075855872)") assert result("F58") =~ expr("1.58e+288230376151711744*f(288230376151711744)") assert result("G58") =~ expr("1.58e-288230376151711744*f(288230376151711744)") assert result("F59") =~ expr("1.59e+576460752303423488*f(576460752303423488)") assert result("G59") =~ expr("1.59e-576460752303423488*f(576460752303423488)") assert result("F60") =~ expr("1.6e+1152921504606846976*f(1152921504606846976)") assert result("G60") =~ expr("1.6e-1152921504606846976*f(1152921504606846976)") assert result("F61") =~ expr("1.61e+2305843009213693952*f(2305843009213693952)") assert result("G61") =~ expr("1.61e-2305843009213693952*f(2305843009213693952)") assert result("F62") =~ expr("1.62e+4611686018427387904*f(4611686018427387904)") assert result("G62") =~ expr("1.62e-4611686018427387904*f(4611686018427387904)") *--#] float_extremes : *--#[ MergeWithFloat : * This tests MergeWithFloat in float.c #: termsinsmall 16 On fewerstats 1; #StartFloat 10d Auto Symbol x; * This tests most cases of MergeWithFloat Local F = (x1+1.0*x2+x3+1.0*x4)^5; id x1 = 1-x2-x3-x4; .sort * This tests a corncer case of MergeWithFloat Local G = x1+...+x15+1.0*x16+2^320*x16; Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F") =~ expr("1 + 0.0e+00*x4 + 0.0e+00*x4^2 + 0.0e+00*x4^3 + 0.0e+00*x4^4 + 0.0e+00* x4^5 + 0.0e+00*x3*x4 + 0.0e+00*x3*x4^2 + 0.0e+00*x3*x4^3 + 0.0e+00*x3* x4^4 + 0.0e+00*x3^2*x4 + 0.0e+00*x3^2*x4^2 + 0.0e+00*x3^2*x4^3 + 0.0e+00 *x3^3*x4 + 0.0e+00*x3^3*x4^2 + 0.0e+00*x3^4*x4 + 0.0e+00*x2 + 0.0e+00*x2 *x4 + 0.0e+00*x2*x4^2 + 0.0e+00*x2*x4^3 + 0.0e+00*x2*x4^4 + 0.0e+00*x2* x3 + 0.0e+00*x2*x3*x4 + 0.0e+00*x2*x3*x4^2 + 0.0e+00*x2*x3*x4^3 + 0.0e+00*x2*x3^2 + 0.0e+00*x2*x3^2*x4 + 0.0e+00*x2*x3^2*x4^2 + 0.0e+00*x2 *x3^3 + 0.0e+00*x2*x3^3*x4 + 0.0e+00*x2*x3^4 + 0.0e+00*x2^2 + 0.0e+00* x2^2*x4 + 0.0e+00*x2^2*x4^2 + 0.0e+00*x2^2*x4^3 + 0.0e+00*x2^2*x3 + 0.0e+00*x2^2*x3*x4 + 0.0e+00*x2^2*x3*x4^2 + 0.0e+00*x2^2*x3^2 + 0.0e+00* x2^2*x3^2*x4 + 0.0e+00*x2^2*x3^3 + 0.0e+00*x2^3 + 0.0e+00*x2^3*x4 + 0.0e+00*x2^3*x4^2 + 0.0e+00*x2^3*x3 + 0.0e+00*x2^3*x3*x4 + 0.0e+00*x2^3* x3^2 + 0.0e+00*x2^4 + 0.0e+00*x2^4*x4 + 0.0e+00*x2^4*x3 + 0.0e+00*x2^5") assert result("G") =~ expr(" 2.135987036e+96*x16 + x15 + x14 + x13 + x12 + x11 + x10 + x9 + x8 + x7 + x6 + x5 + x4 + x3 + x2 + x1") *--#] MergeWithFloat : *--#[ float_zero : #StartFloat 10d CFunction f; Local FloatZero = f(0.0,0.0-123,000.000000,0.0e-13,.0e+4,0e1,0.,0.e+2,0e-10); Print; .end #pend_if wordsize == 2 assert succeeded? assert result("FloatZero") =~ expr("f(0.0e+00, - 1.23e+02,0.0e+00,0.0e+00,0.0e+00,0.0e+00,0.0e+00,0.0e+00, 0.0e+00)") *--#] float_zero : *--#[ float_error : Local F = 1.0; Evaluate; ToFloat; ToRat; .sort #StartFloat 10d Evaluate x; .sort CFunction x; Evaluate x; ToFloat y; ToRat z; .end #pend_if wordsize == 2 assert compile_error?("The floating point system has not been started: .0") assert compile_error?("Illegal character at this position: .0") assert compile_error?("Illegal position for 0") assert compile_error?("Illegal attempt to evaluate a function without activating floating point numbers.") assert compile_error?("Forgotten #startfloat instruction?") assert compile_error?("Illegal attempt to convert to float_ without activating floating point numbers.") assert compile_error?("Forgotten #startfloat instruction?") assert compile_error?("Illegal attempt to convert from float_ without activating floating point numbers.") assert compile_error?("Forgotten #startfloat instruction?") assert compile_error?("should be a built in function that can be evaluated numerically.") assert compile_error?("should be a built in function that can be evaluated numerically.") assert compile_error?("Illegal argument(s) in ToFloat statement: 'y'") assert compile_error?("Illegal argument(s) in ToRat statement: 'z'") *--#] float_error : *--#[ format_and_floats : #- Off Statistics; #Startfloat 10d Symbol x,y; Local test = + 1 + 3*x + 3/4*x^2 + (2^y-1)*x^3 + (2^y)*x^4 + 1/(2^y-1)*x^5 + 1/(2^y)*x^6 + 3/(2^y-1)*x^7 + 3/(2^y)*x^8 + (2^y)/(2^y-1)*x^9 + (2^y-1)/(2^y)*x^10 + (2^y)/(2^y+1)*x^11 ; .sort Drop; Local test31 = replace_(y,31)*test; Local test32 = replace_(y,32)*test; ToFloat; #message Raw Format FloatPrecision off; Print +s; .sort #message Mathematica Format FloatPrecision 5d; Format mathematica; Print +s; .sort #message Maple Format FloatPrecision 20b; Format maple; Print +s; .sort #message C Format FloatPrecision; Format c; Print +s; .sort #message Fortran Format Fortran; Print +s; .sort #message Doublefortran Format Doublefortran; Print +s; .sort #message Quadfortran Format Quadfortran; Print +s; .sort #message Fortran90 Format Fortran90; Print +s; .sort #message Fortran90_ki Format Fortran90,_ki; Print +s; .end #pend_if wordsize == 2 assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~Raw test31 = + x*float_(2,3,1,1020847100762815390390123822295304634368) + x^2*float_(2,2,0,255211775190703847597530955573826158592) + x^3*float_(2,1,1,2147483647) + x^4*float_(2,3,1,730750818665451459101842416358141509827966271488) + x^5*float_(2,2,0,158456325102315651516285845520) + x^6*float_(2,2,0,158456325028528675187087900672) + x^7*float_(2,2,0,475368975306946954548857536560) + x^8*float_(2,2,0,475368975085586025561263702016) + x^9*float_(2,3,1,340282367079394788565690258948054056976) + x^10*float_(2,1,0,18446744065119617024) + x^11*float_(2,2,0,340282366762482138508632908505158778895) + float_(2,3,1,340282366920938463463374607431768211456) ; test32 = + x*float_(2,3,1,1020847100762815390390123822295304634368) + x^2*float_(2,2,0,255211775190703847597530955573826158592) + x^3*float_(2,1,1,4294967295) + x^4*float_(2,3,1,1461501637330902918203684832716283019655932542976) + x^5*float_(2,2,0,79228162532711081671548469249) + x^6*float_(2,2,0,79228162514264337593543950336) + x^7*float_(2,2,0,237684487598133245014645407747) + x^8*float_(2,2,0,237684487542793012780631851008) + x^9*float_(2,3,1,340282367000166625996085689103316680705) + x^10*float_(2,1,0,18446744069414584320) + x^11*float_(2,2,0,340282366841710300967557013907638845440) + float_(2,3,1,340282366920938463463374607431768211456) ; ~~~Mathematica test31 = ( + 3.0*^+00*x + 7.5*^-01*x^2 + 2.1475*^+09*x^3 + 2.1475*^+09*x^4 + 4.6566*^-10*x^5 + 4.6566*^-10*x^6 + 1.397*^-09*x^7 + 1.397*^-09*x^8 + 1.0*^+00*x^9 + 1.0*^+00*x^10 + 1.0*^+00*x^11 + 1.0*^+00 ); test32 = ( + 3.0*^+00*x + 7.5*^-01*x^2 + 4.295*^+09*x^3 + 4.295*^+09*x^4 + 2.3283*^-10*x^5 + 2.3283*^-10*x^6 + 6.9849*^-10*x^7 + 6.9849*^-10*x^8 + 1.0*^+00*x^9 + 1.0*^+00*x^10 + 1.0*^+00*x^11 + 1.0*^+00 ); ~~~Maple test31 = + 3.0e+00*x + 7.5e-01*x^2 + 2.14748e+09*x^3 + 2.14748e+09*x^4 + 4.65661e-10*x^5 + 4.65661e-10*x^6 + 1.39698e-09*x^7 + 1.39698e-09*x^8 + 1.0e+00*x^9 + 1.0e+00*x^10 + 1.0e+00*x^11 + 1.0e+00 ; test32 = + 3.0e+00*x + 7.5e-01*x^2 + 4.29497e+09*x^3 + 4.29497e+09*x^4 + 2.32831e-10*x^5 + 2.32831e-10*x^6 + 6.98492e-10*x^7 + 6.98492e-10*x^8 + 1.0e+00*x^9 + 1.0e+00*x^10 + 1.0e+00*x^11 + 1.0e+00 ; ~~~C test31 = + 3.0e+00*x + 7.5e-01*pow(x,2) + 2.147483647e+09*pow(x,3) + 2.147483648e+09*pow(x,4) + 4.656612875e-10*pow(x,5) + 4.656612873e-10*pow(x,6) + 1.396983863e-09*pow(x,7) + 1.396983862e-09*pow(x,8) + 1.0e+00*pow(x,9) + 9.999999995e-01*pow(x,10) + 9.999999995e-01*pow(x,11) + 1.0e+00 ; test32 = + 3.0e+00*x + 7.5e-01*pow(x,2) + 4.294967295e+09*pow(x,3) + 4.294967296e+09*pow(x,4) + 2.328306437e-10*pow(x,5) + 2.328306437e-10*pow(x,6) + 6.984919311e-10*pow(x,7) + 6.98491931e-10*pow(x,8) + 1.0e+00*pow(x,9) + 9.999999998e-01*pow(x,10) + 9.999999998e-01*pow(x,11) + 1.0e+00 ; ~~~Fortran test31 = + 3.0E+00*x & + 7.5E-01*x**2 & + 2.147483647E+09*x**3 & + 2.147483648E+09*x**4 & + 4.656612875E-10*x**5 & + 4.656612873E-10*x**6 & + 1.396983863E-09*x**7 & + 1.396983862E-09*x**8 & + 1.0E+00*x**9 & + 9.999999995E-01*x**10 & + 9.999999995E-01*x**11 & + 1.0E+00 & test32 = + 3.0E+00*x & + 7.5E-01*x**2 & + 4.294967295E+09*x**3 & + 4.294967296E+09*x**4 & + 2.328306437E-10*x**5 & + 2.328306437E-10*x**6 & + 6.984919311E-10*x**7 & + 6.98491931E-10*x**8 & + 1.0E+00*x**9 & + 9.999999998E-01*x**10 & + 9.999999998E-01*x**11 & + 1.0E+00 & ~~~Doublefortran test31 = + 3.0D+00*x & + 7.5D-01*x**2 & + 2.147483647D+09*x**3 & + 2.147483648D+09*x**4 & + 4.656612875D-10*x**5 & + 4.656612873D-10*x**6 & + 1.396983863D-09*x**7 & + 1.396983862D-09*x**8 & + 1.0D+00*x**9 & + 9.999999995D-01*x**10 & + 9.999999995D-01*x**11 & + 1.0D+00 & test32 = + 3.0D+00*x & + 7.5D-01*x**2 & + 4.294967295D+09*x**3 & + 4.294967296D+09*x**4 & + 2.328306437D-10*x**5 & + 2.328306437D-10*x**6 & + 6.984919311D-10*x**7 & + 6.98491931D-10*x**8 & + 1.0D+00*x**9 & + 9.999999998D-01*x**10 & + 9.999999998D-01*x**11 & + 1.0D+00 & ~~~Quadfortran test31 = + 3.0Q+00*x & + 7.5Q-01*x**2 & + 2.147483647Q+09*x**3 & + 2.147483648Q+09*x**4 & + 4.656612875Q-10*x**5 & + 4.656612873Q-10*x**6 & + 1.396983863Q-09*x**7 & + 1.396983862Q-09*x**8 & + 1.0Q+00*x**9 & + 9.999999995Q-01*x**10 & + 9.999999995Q-01*x**11 & + 1.0Q+00 & test32 = + 3.0Q+00*x & + 7.5Q-01*x**2 & + 4.294967295Q+09*x**3 & + 4.294967296Q+09*x**4 & + 2.328306437Q-10*x**5 & + 2.328306437Q-10*x**6 & + 6.984919311Q-10*x**7 & + 6.98491931Q-10*x**8 & + 1.0Q+00*x**9 & + 9.999999998Q-01*x**10 & + 9.999999998Q-01*x**11 & + 1.0Q+00 & ~~~Fortran90 test31 = + 3.0E+00*x & + 7.5E-01*x**2 & + 2.147483647E+09*x**3 & + 2.147483648E+09*x**4 & + 4.656612875E-10*x**5 & + 4.656612873E-10*x**6 & + 1.396983863E-09*x**7 & + 1.396983862E-09*x**8 & + 1.0E+00*x**9 & + 9.999999995E-01*x**10 & + 9.999999995E-01*x**11 & + 1.0E+00 & test32 = + 3.0E+00*x & + 7.5E-01*x**2 & + 4.294967295E+09*x**3 & + 4.294967296E+09*x**4 & + 2.328306437E-10*x**5 & + 2.328306437E-10*x**6 & + 6.984919311E-10*x**7 & + 6.98491931E-10*x**8 & + 1.0E+00*x**9 & + 9.999999998E-01*x**10 & + 9.999999998E-01*x**11 & + 1.0E+00 & ~~~Fortran90_ki test31 = + 3.0E+00_ki*x & + 7.5E-01_ki*x**2 & + 2.147483647E+09_ki*x**3 & + 2.147483648E+09_ki*x**4 & + 4.656612875E-10_ki*x**5 & + 4.656612873E-10_ki*x**6 & + 1.396983863E-09_ki*x**7 & + 1.396983862E-09_ki*x**8 & + 1.0E+00_ki*x**9 & + 9.999999995E-01_ki*x**10 & + 9.999999995E-01_ki*x**11 & + 1.0E+00_ki & test32 = + 3.0E+00_ki*x & + 7.5E-01_ki*x**2 & + 4.294967295E+09_ki*x**3 & + 4.294967296E+09_ki*x**4 & + 2.328306437E-10_ki*x**5 & + 2.328306437E-10_ki*x**6 & + 6.984919311E-10_ki*x**7 & + 6.98491931E-10_ki*x**8 & + 1.0E+00_ki*x**9 & + 9.999999998E-01_ki*x**10 & + 9.999999998E-01_ki*x**11 & + 1.0E+00_ki & EOF *--#] format_and_floats : *--#[ startfloat_error : #Startfloat 100bd,MZV = 10 .end #pend_if wordsize == 2 assert runtime_error?("Illegal parameter in #StartFloat: 100bd,MZV = 10") *--#] startfloat_error : *--#[ mzv_error_1: #StartFloat 10d, MZV=2 Local F = mzv_(2,1); Evaluate mzv_; .end #pend_if wordsize == 2 assert runtime_error?("Error: Weight of Euler/MZV sum greater than 2.") assert runtime_error?("Please increase the maximum weight in #startfloat.") *--#] mzv_error_1 : *--#[ mzv_error_2: #StartFloat 10d, MZV=3 Local F = mzv_(1,2); Evaluate mzv_; .end #pend_if wordsize == 2 assert runtime_error?("Divergent MZV in CalculateMZV") *--#] mzv_error_2 : *--#[ mzv_error_3: #StartFloat 10d, MZV=3 Local F = mzv_(-2,1); Evaluate mzv_; .end #pend_if wordsize == 2 assert runtime_error?("Illegal index[0] in CalculateMZV: -2") *--#] mzv_error_3 : *--#[ mzv_error_4: #StartFloat 10d, MZV=3 Local F = mzvhalf_(2,-1); Evaluate mzvhalf_; .end #pend_if wordsize == 2 assert runtime_error?("Illegal index[1] in CalculateMZVhalf: -1") *--#] mzv_error_4 : *--#[ mzv_error_5: #StartFloat 10d, MZV=3 Local F = euler_(1,-2); Evaluate euler_; .end #pend_if wordsize == 2 assert runtime_error?("Divergent Euler sum in CalculateEuler") *--#] mzv_error_5 : *--#[ humanstats : #- On humanstats; Symbol x; Local test1 = (1+x)^499; Local test2 = (1+x)^500; Local test3 = (1+x)^1000; .end # In 32bit FORM, the "Bytes used" numbers are different #pend_if wordsize != 4 assert succeeded? assert stdout =~ exact_pattern("Generated terms = 500 ( <1 K )") assert stdout =~ exact_pattern("Terms in output = 500 ( <1 K )") assert stdout =~ exact_pattern("Bytes used = 54420 ( 54 KiB)") assert stdout =~ exact_pattern("Generated terms = 501 ( 1 K )") assert stdout =~ exact_pattern("Terms in output = 501 ( 1 K )") assert stdout =~ exact_pattern("Bytes used = 54644 ( 55 KiB)") assert stdout =~ exact_pattern("Generated terms = 1001 ( 1 K )") assert stdout =~ exact_pattern("Terms in output = 1001 ( 1 K )") assert stdout =~ exact_pattern("Bytes used = 199172 (199 KiB)") *--#] humanstats : *--#[ ModuleOption_dollar_order : $a = 0; ModuleOption sum,$a; $b = 0; ModuleOption maximum,$b; $c = 0; ModuleOption minimum,$c; $d = 0; ModuleOption local,$d; discard; .end assert succeeded? *--#] ModuleOption_dollar_order : *--#[ ModuleOption_dollar_warnings_1 : $a = 0; ModuleOption local,$a; ModuleOption local,$a; .end assert succeeded? *--#] ModuleOption_dollar_warnings_1 : *--#[ ModuleOption_dollar_warnings_2 : ModuleOption local,$a; $b = 0; ModuleOption local,$b; ModuleOption sum,$b; .end assert return_value == 0 assert warning?("Undefined $-variable in module option; option ignored: $a") assert warning?("Conflicting module options for $-variable; later option ignored: $b") *--#] ModuleOption_dollar_warnings_2 : *--#[ Issue49 : * Add mul_ function for polynomial multiplications Symbols x,y,z; #$p = (1+x+y+z)^4; #$q = $p+1; #$r = mul_($p,$q); L r1 = $r; L r2 = $p^2 + $p; .sort Drop; L Zero = r1 - r2; P; .end assert succeeded? assert result("Zero") =~ expr("0") *--#] Issue49 : *--#[ Issue72 : * "Setups: PATHVALUE not yet implemented" #:incdir foo #:path * foo/p1.prc #call p1() P; .end #:incdir #:path foo/bar * foo/bar/p1.prc #call p1() P; .end #prepare write "foo/p1.prc", "#procedure p1()\nL F=12345;\n#endprocedure\n" #prepare write "foo/bar/p1.prc", "#procedure p1()\nL G=123456;\n#endprocedure\n" assert succeeded? assert result("F") =~ expr("12345") assert result("G") =~ expr("123456") *--#] Issue72 : *--#[ Issue84 : * Set to match with a vector V p,p1,...,p6; CF f,g,h; L F = f(p1,-p1,p2,-p2); id,all,f(?a,-p?vector_,?b) = f(?a,p,?b)*g(p); Print +s; .end assert succeeded? assert result("F") =~ expr(" + f(p1,p1,p2,-p2)*g(p1) + f(p1,-p1,p2,p2)*g(p2) ") *--#] Issue84 : *--#[ Issue86_1 : * Feature request: take/drop n-th argument of list * [with zero-dimensional tables] CF f; S x,n,n1,n2; * Get [1,1]. nargs >= 1. Table first(f?(x?,?a)); Fill first = f(x); * Get [last,last]. nargs >= 1. Table last(f?(?a,x?)); Fill last = f(x); * Get [2,last]. nargs >= 1. Table rest(f?(x?,?a)); Fill rest = f(?a); * Get [1,last-1]. nargs >= 1. Table most(f?(?a,x?)); Fill most = f(?a); * Join two functions. Table join(f?(?a),f?(?b)); Fill join = f(?a,?b); * Rotate left by n. nargs >= 1. Table roll(n?int_,f?(?a)); Fill roll = + delta_(n) * f(?a) + thetap_(n) * roll(n-1,join(rest(f(?a)),first(f(?a)))) + thetap_(-n) * roll(n+1,join(last(f(?a)),most(f(?a)))) ; * Get [1,n]. 1 <= n <= nargs. Table firstn(n?pos_,f?(?a)); Table firstnimpl(n?pos0_,f?(?a),f?(x?,?b)); Fill firstn = firstnimpl(n,f,f(?a,dum_)); Fill firstnimpl = + delta_(n) * f(?a) + thetap_(n) * firstnimpl(n-1,f(?a,x),f(?b)) ; * Get the n-th argument. 1 <= n <= nargs. Table take(n?pos_,f?(?a)); Fill take = first(roll(n-1,f(?a))); * Drop the n-th argument. 1 <= n <= nargs. Table drop(n?pos_,f?(?a)); Fill drop = roll(1-n,most(roll(n,f(?a)))); * Get [n1,n2]. Negative indices count from the end. 1 <= n1 <= n2 <= nargs. Table slice(n1?!{0,},n2?!{0,},f?(?a)); Fill slice = + thetap_(n1) * thetap_(n2) * firstn(n2-n1+1,roll(n1-1,f(?a))) + thetap_(n1) * thetap_(-n2) * slice(n1,nargs_(?a)+n2+1,f(?a)) + thetap_(-n1) * thetap_(n2) * slice(nargs_(?a)+n1+1,n2,f(?a)) + thetap_(-n1) * thetap_(-n2) * slice(nargs_(?a)+n1+1,nargs_(?a)+n2+1,f(?a)) ; L F0 = f(1,...,9); L F1 = first(F0); L F2 = last(F0); L F3 = rest(F0); L F4 = most(F0); L F5 = roll(0,F0); L F6 = roll(2,F0); L F7 = roll(-2,F0); L F8 = firstn(3,F0); L F9 = take(3,F0); L F10 = drop(3,F0); L F11 = slice(3,3,F0); L F12 = slice(3,6,F0); L F13 = slice(3,-4,F0); L F14 = slice(-7,6,F0); L F15 = slice(-7,-4,F0); P; .end assert succeeded? assert result("F0") =~ expr("f(1,2,3,4,5,6,7,8,9)") assert result("F1") =~ expr("f(1)") assert result("F2") =~ expr("f(9)") assert result("F3") =~ expr("f(2,3,4,5,6,7,8,9)") assert result("F4") =~ expr("f(1,2,3,4,5,6,7,8)") assert result("F5") =~ expr("f(1,2,3,4,5,6,7,8,9)") assert result("F6") =~ expr("f(3,4,5,6,7,8,9,1,2)") assert result("F7") =~ expr("f(8,9,1,2,3,4,5,6,7)") assert result("F8") =~ expr("f(1,2,3)") assert result("F9") =~ expr("f(3)") assert result("F10") =~ expr("f(1,2,4,5,6,7,8,9)") assert result("F11") =~ expr("f(3)") assert result("F12") =~ expr("f(3,4,5,6)") assert result("F13") =~ expr("f(3,4,5,6)") assert result("F14") =~ expr("f(3,4,5,6)") assert result("F15") =~ expr("f(3,4,5,6)") *--#] Issue86_1 : *--#[ Issue86_2 : * [with the Translate statement] CF f; L F0 = f(1,2,3,4,5,6,7,8,9); #do i=1,4 #do j=1,8 L F`i'`j' = F0; #enddo #enddo $n1 = 3; $n2 = 5; $n3 = 4; #procedure Test(F,trans) inexpression `F'1; transform,f,`trans'(3,5); endinexpression; inexpression `F'2; transform,f,`trans'(3,$n2); endinexpression; inexpression `F'3; transform,f,`trans'(3,last-4); endinexpression; inexpression `F'4; transform,f,`trans'(3,last-$n3); endinexpression; inexpression `F'5; transform,f,`trans'($n1,5); endinexpression; inexpression `F'6; transform,f,`trans'($n1,$n2); endinexpression; inexpression `F'7; transform,f,`trans'($n1,last-4); endinexpression; inexpression `F'8; transform,f,`trans'($n1,last-$n3); endinexpression; #endprocedure #call Test(F1,dropargs) #call Test(F2,selectargs) #call Test(F3,addargs) #call Test(F4,mulargs) P; ModuleOption local, $n1,$n2,$n3; .end assert succeeded? assert result("F0") =~ expr("f(1,2,3,4,5,6,7,8,9)") assert result("F11") =~ expr("f(1,2,6,7,8,9)") assert result("F21") =~ expr("f(3,4,5)") assert result("F31") =~ expr("f(1,2,12,6,7,8,9)") assert result("F41") =~ expr("f(1,2,60,6,7,8,9)") assert result("F12") == result("F11") assert result("F13") == result("F11") assert result("F14") == result("F11") assert result("F15") == result("F11") assert result("F16") == result("F11") assert result("F17") == result("F11") assert result("F18") == result("F11") assert result("F22") == result("F21") assert result("F23") == result("F21") assert result("F24") == result("F21") assert result("F25") == result("F21") assert result("F26") == result("F21") assert result("F27") == result("F21") assert result("F28") == result("F21") assert result("F32") == result("F31") assert result("F33") == result("F31") assert result("F34") == result("F31") assert result("F35") == result("F31") assert result("F36") == result("F31") assert result("F37") == result("F31") assert result("F38") == result("F31") assert result("F42") == result("F41") assert result("F43") == result("F41") assert result("F44") == result("F41") assert result("F45") == result("F41") assert result("F46") == result("F41") assert result("F47") == result("F41") assert result("F48") == result("F41") *--#] Issue86_2 : *--#[ Issue87 : * Feature request: (anti)bracketing w.r.t. a set s a, b, c, d; set ab: a, b; L test = (a + b)*(c + d); b ab; print +s; .end assert succeeded? assert result("test") =~ expr(" + b * ( + d + c ) + a * ( + d + c ) ") *--#] Issue87 : *--#[ Issue135_1 : * "Assign instructions cannot occur inside statements" without inside statements L F = #do i=1,10 #$x = `i'; + `$x' #enddo ; P; .end assert succeeded? assert result("F") =~ expr("55") *--#] Issue135_1 : *--#[ Issue135_2 : S a1,...,a10; L F = #do i = 1,10 #$x = `i'*a`i' +2; +`$x' #enddo ; P; .end assert succeeded? assert result("F") =~ expr(" 20 + 10*a10 + 9*a9 + 8*a8 + 7*a7 + 6*a6 + 5*a5 + 4*a4 + 3*a3 + 2*a2 + a1 ") *--#] Issue135_2 : *--#[ Issue135_3 : S a1,...,a10,x; CF f; CTable sparse,tab(1); #do i=1,10 Fill tab(`i') = f(`i'*a`i') + 2; #enddo L F = #do i = 1,10 #$tmp = tab(`i'); #inside $tmp id f(x?) = x; #endinside + (`$tmp') #enddo ; P; .end assert succeeded? assert result("F") =~ expr(" 20 + 10*a10 + 9*a9 + 8*a8 + 7*a7 + 6*a6 + 5*a5 + 4*a4 + 3*a3 + 2*a2 + a1 ") *--#] Issue135_3 : *--#[ Issue137_1 : * New command: ArgToExtraSymbol (,ToNumber) S a,b; CF f; L F = f(1) + f(a) + f(b) + f(a+b); ArgToExtraSymbol f; P; .end assert succeeded? assert result("F") =~ expr("f(Z4_) + f(Z3_) + f(Z2_) + f(Z1_)") *--#] Issue137_1 : *--#[ Issue137_2 : S a,b; CF f; L F = f(1) + f(a) + f(b) + f(a+b); ArgToExtraSymbol,ToNumber,f; P; .end assert succeeded? assert result("F") =~ expr("f(1) + f(2) + f(3) + f(4)") *--#] Issue137_2 : *--#[ Issue137_3 : CF f; S s; I i; V v; * Fast notation. L F = f(0) + f(1) + f(-1) + f(s) + f(i) + f(v) + f(-v) + f(f); argtoextrasymbol; P; .end assert succeeded? assert result("F") =~ expr(" f(Z8_) + f(Z7_) + f(Z6_) + f(Z5_) + f(Z4_) + f(Z3_) + f(Z2_) + f(Z1_) ") *--#] Issue137_3 : *--#[ Issue137_4 : #:threadbucketsize 10 #:processbucketsize 10 CF f; Auto S x; * NOTE: Large N gives another problem with ParFORM (#141). #define N "500" L F0 = #do i=1,`N' + f(1+x`i') * f(1+x{`i'+100}) * f(1+x{`i'+200}) #enddo ; .sort Hide; L F1 = F0; .sort * If all workers fail to share an unique mapping in a consistent way, * the following code gives a non-zero result or a crash. argtoextrasymbol; .sort argument; frompolynomial; endargument; .sort Drop; L ZERO = F1 - F0; P; .end assert succeeded? assert result("ZERO") =~ expr("0") *--#] Issue137_4 : *--#[ Issue175_1 : * Loop over currently active expressions #175 L FF = 1; L [FF|a,b] = 1; L [FF,[GG]] = 1; #do e={`activeexprnames_'} L `e' = `e' + 1; #enddo L N = `numactiveexprs_'; P; .end assert succeeded? assert result("FF") =~ expr("2") assert result("[FF|a,b]") =~ expr("2") assert result("[FF,[GG]]") =~ expr("2") assert result("N") =~ expr("3") *--#] Issue175_1 : *--#[ Issue175_2 : L F1 = 1; L F2 = 1; L F3 = 1; L F1 = 1; * redefine in the same module! *.sort ;* workaround #message `numactiveexprs_' #message `activeexprnames_' #do e={`activeexprnames_'} L `e' = `e' + 1; #enddo P; .end assert succeeded? assert result("F1") =~ expr("2") assert result("F2") =~ expr("2") assert result("F3") =~ expr("2") *--#] Issue175_2 : *--#[ Issue175_3 : L F1 = 1; L F2 = 1; L F3 = 1; .sort L F1 = 1; * replace an existing expression! *.sort ;* workaround #message `numactiveexprs_' #message `activeexprnames_' #do e={`activeexprnames_'} L `e' = `e' + 1; #enddo P; .end assert succeeded? assert result("F1") =~ expr("2") assert result("F2") =~ expr("2") assert result("F3") =~ expr("2") *--#] Issue175_3 : *--#[ Issue175_4 : CF F1,F2,F3; L [F1(1,1,1,1)] = F1(1,1,1,1); L [F2(-1,1,1,1)] = F2(-1,1,1,1); .sort * Redefine. Local [F1(1,1,1,1)] = F1(1,1,1,1); .sort #message `numactiveexprs_' #message `activeexprnames_' #do e={`activeexprnames_'} L `e' = `e' + 1; #enddo P; .end assert succeeded? assert result("[F1(1,1,1,1)]") =~ expr("1 + F1(1,1,1,1)") assert result("[F2(-1,1,1,1)]") =~ expr("1 + F2(-1,1,1,1)") *--#] Issue175_4 : *--#[ Issue187 : * What is the fastest equivalent of Foreach in FORM? * distrib_ generates combinations in lexicographical order (in the given * arguments.) S x1,...,x5; CF f; L F = f(x2,x5,x3,x1,x4); #$counter = 0; id f(?a$a) = 1; term; multiply distrib_(1,3,f,dummy_,$a); $counter = $counter + 1; id f(?a) = f($counter,?a); endterm; P +s; ModuleOption noparallel; .end assert succeeded? assert result("F") =~ expr(" + f(1,x2,x5,x3) + f(2,x2,x5,x1) + f(3,x2,x5,x4) + f(4,x2,x3,x1) + f(5,x2,x3,x4) + f(6,x2,x1,x4) + f(7,x5,x3,x1) + f(8,x5,x3,x4) + f(9,x5,x1,x4) + f(10,x3,x1,x4) ") *--#] Issue187 : *--#[ Issue243_1 : * #continuedo? NF f; L F = 1; #do i=1,5 #if `i' == 3 #continuedo #endif multiply right, f(`i'); #enddo chainin f; P; .end assert succeeded? assert result("F") =~ expr("f(1,2,4,5)") *--#] Issue243_1 : *--#[ Issue243_2 : NF f; L F = 1; #define i "9" #do i=1,2 #do i=1,3 #do i=1,8 #if `i' == 3 #continuedo 2 #endif multiply right, f(`i'); #enddo multiply right, f(-`i'); #enddo multiply right, f(-`i'); #enddo multiply right, f(`i'); chainin f; P; .end assert succeeded? assert result("F") =~ expr("f(1,2,1,2,1,2,-1,1,2,1,2,1,2,-2,9)") *--#] Issue243_2 : *--#[ Issue243_3 : NF f; L F = 1; #do i=1,3 #do i=1,2 #continuedo 0 multiply right, f(`i'); #enddo #enddo chainin f; P; .end assert succeeded? assert result("F") =~ expr("f(1,2,1,2,1,2)") *--#] Issue243_3 : *--#[ Issue243_e1 : #continuedo .end assert preprocess_error?("#continuedo without #do") *--#] Issue243_e1 : *--#[ Issue243_e2 : #do i=1,3 #continuedo -1 #enddo .end assert preprocess_error?("Improper syntax of #continuedo instruction") *--#] Issue243_e2 : *--#[ Issue243_e3 : #do i=1,3 #continuedo 1a #enddo .end assert preprocess_error?("Improper syntax of #continuedo instruction") *--#] Issue243_e3 : *--#[ Issue243_e4 : #do i=1,3 #continuedo 2 #enddo .end assert preprocess_error?("Too many loop levels requested in #continuedo instruction") *--#] Issue243_e4 : *--#[ Issue243_e5 : #procedure foo #continuedo #endprocedure #do i=1,3 #call foo #enddo .end assert preprocess_error?("Trying to jump out of a procedure with a #continuedo instruction") *--#] Issue243_e5 : *--#[ Issue243_e6 : #procedure foo #continuedo 2 #endprocedure #do i=1,3 #do j=1,3 #call foo #enddo #enddo .end assert preprocess_error?("Trying to jump out of a procedure with a #continuedo instruction") *--#] Issue243_e6 : *--#[ Issue392_ContinuationLines_1 : #: ContinuationLines 1 * Setting ContinuationLines to 0 should remove continuation line limit. auto symbol x; local ex = (xabcdefg + xhijklmnop)^100; .sort format C; #write "%e" ex .end assert succeeded? assert file("out.c") =~ /[_] [+]= / *--#] Issue392_ContinuationLines_1 : *--#[ Issue392_ContinuationLines_0 : #: ContinuationLines 0 * Setting ContinuationLines to 0 should remove continuation line limit. auto symbol x; local ex = (xabcdefg + xhijklmnop)^100; .sort format C; #write "%e" ex .end assert succeeded? assert !(file("out.c") =~ /[_] [+]= /) *--#] Issue392_ContinuationLines_0 : *--#[ Sortrealloc_1 : On sortreallocate; Symbol x,y; Local F = (x+y)^10; .sort Identify x = - y; .sort Print +s; .end assert succeeded? assert result("F") =~ expr("0"); *--#] Sortrealloc_1 : *--#[ Sortrealloc_2 : Symbol x,y; Local F = (x+y)^10; .sort #sortreallocate Identify x = - y; .sort Print +s; .end assert succeeded? assert result("F") =~ expr("0"); *--#] Sortrealloc_2 : *--#[ TempSortDir_unix : #: TempSortDir bad/path Local test = 1; .end #require unix? assert runtime_error? *--#] TempSortDir_unix : *--#[ TempSortDir_windows : #: TempSortDir bad_path Local test = 1; .end #require windows? assert runtime_error? *--#] TempSortDir_windows : *--#[ ZeroUnchanged : #- #procedure exprinfo #message Module `CMODULE_': #do e = {`activeexprnames_'} #if `ZERO_`e'' #message zero `e': `ZERO_`e'' #endif #if `UNCHANGED_`e'' #message unchanged `e': `UNCHANGED_`e'' #endif #enddo #if `ZERO_' #message All zero: `ZERO_' #endif #if `UNCHANGED_' #message All unchanged: `UNCHANGED_' #endif #message #endprocedure Off stats; Symbol x,y; Local test1 = x; Local test2 = y; Local test3 = 1; .sort:1; #call exprinfo Identify x = 0; .sort:2; #call exprinfo Identify y = 0; .sort:3; #call exprinfo .sort:4; #call exprinfo Multiply 0; .sort:5; #message Here, test3 is incorrectly flagged as unchanged: #call exprinfo Print; .end assert succeeded? assert result("test1") =~ expr("0") assert result("test2") =~ expr("0") assert result("test3") =~ expr("0") assert stdout =~ exact_pattern(<<'EOF') ~~~Module 2: ~~~ ~~~Module 3: ~~~zero test1: 1 ~~~unchanged test2: 1 ~~~unchanged test3: 1 ~~~ ~~~Module 4: ~~~zero test1: 1 ~~~unchanged test1: 1 ~~~zero test2: 1 ~~~unchanged test3: 1 ~~~ ~~~Module 5: ~~~zero test1: 1 ~~~unchanged test1: 1 ~~~zero test2: 1 ~~~unchanged test2: 1 ~~~unchanged test3: 1 ~~~All unchanged: 1 ~~~ ~~~Here, test3 is incorrectly flagged as unchanged: ~~~Module 6: ~~~zero test1: 1 ~~~unchanged test1: 1 ~~~zero test2: 1 ~~~unchanged test2: 1 ~~~zero test3: 1 ~~~unchanged test3: 1 ~~~All zero: 1 ~~~All unchanged: 1 ~~~ EOF *--#] ZeroUnchanged : *--#[ tablebase_ro_1 : Table,sparse,no1fill(1); Fill no1fill(1) = 1; Fill no1fill(2) = 2; Fill no1fill(3) = 3; TableBase "no1.tbl" create; TableBase "no1.tbl" addto no1fill; .end Table,sparse,no2fill(1); Fill no2fill(1) = 1; Fill no2fill(2) = 2; Fill no2fill(3) = 3; .sort TableBase "no1.tbl" open,readonly; TableBase "no1.tbl" addto no2fill; .end assert runtime_error?('Tablebase with the name no1.tbl opened in read only mode') *--#] tablebase_ro_1 : *--#[ tablebase_ro_2 : TableBase "no212.tbl" open, readonly; .end assert runtime_error?('Trying to open non-existent TableBase in readonly mode: no212.tbl') *--#] tablebase_ro_2 : *--#[ diagrams_err_1 : Model PHI3; Particle phi,1; Vertex phi,phi,phi:1; EndModel; .end assert runtime_error?('Invalid coupling constant in vertex statement.') *--#] diagrams_err_1 : *--#[ diagrams_err_2 : Model PHI3; Particle phi,1; Vertex phi,phi,phi:g^-1; EndModel; .end assert runtime_error?('Invalid negative power of coupling constant.') *--#] diagrams_err_2 : *--#[ diagrams_err_3 : Vector q1,q2,p1,p2; Model PHI3; Particle phi,1; Vertex phi,phi,phi:g; EndModel; Local test = diagrams_(PHI3,{phi},{phi},{},{p1,p2},1,0); .end assert runtime_error?('Insufficient external momenta in diagrams_') *--#] diagrams_err_3 : *--#[ diagrams_err_4 : Vector q1,q2,p1,p2; Model PHI3; Particle phi,1; Vertex phi,phi,phi:g; EndModel; Local test = diagrams_(PHI3,{phi},{phi},{q1,q2},{},1,0); .end assert runtime_error?('Insufficient internal momenta in diagrams_') *--#] diagrams_err_4 : *--#[ diagrams_err_5 : Vector q1,q2,p1,p2; Model PHI3; Particle phi,1; Vertex phi,phi,phi:g; EndModel; Local test = diagrams_(PHI3,{phi},{phi},{q1,-q2},{p1,p2},1,0); .end assert runtime_error?('Invalid negative external momentum in diagrams_: -q2') *--#] diagrams_err_5 : *--#[ diagrams_err_6 : Vector q1,q2,p1,p2; Model PHI3; Particle phi,1; Vertex phi,phi,phi:g; EndModel; Local test = diagrams_(PHI3,{phi},{phi},{q1,q2},{-p1,p2},1,0); .end assert runtime_error?('Invalid negative internal momentum in diagrams_: -p1') *--#] diagrams_err_6 : *--#[ diagrams_err_7 : Vector q1,q2,p1,p2; Model PHI3; Particle phi,1; Vertex phi,phi,phi:g; EndModel; Local test = diagrams_(PHI3,{phi},{phi},{q1,q1},{p1,p2},1,0); .end assert runtime_error?('Invalid repeated momentum in diagrams_: q1') *--#] diagrams_err_7 : *--#[ diagrams_err_8 : Vector q1,q2,p1,p2; Model PHI3; Particle phi,1; Vertex phi,phi,phi:g; EndModel; Local test = diagrams_(PHI3,{phi},{phi},{q1,q2},{q1,p2},1,0); .end assert runtime_error?('Invalid repeated momentum in diagrams_: q1') *--#] diagrams_err_8 : form-5.0.1/check/polynomial.frm0000644000175100017510000007364415217035721012132 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end * Tests of the polynomial routines, with flint and poly *--#[ polynomial_prc : #- #ifndef `NVARS' #define NVARS "2" #endif Off statistics; Symbol y1,...,y`NVARS'; CFunction tmp,prf,fa; #procedure genpoly(NPOLYS,NVARS,NEGPOW,MAXPOW,MAXCOEFF,NTERMS) * Generate random polynomials for input * Make sure we include some special cases #$p1 = 0; #$p2 = 1; #$p3 = -1; #$p4 = 1/19; #$p5 = -1/19; #do i = 6,`NPOLYS' #$TERMS = random_(`NTERMS'); #$p`i' = #do t = 1,`$TERMS' * "tmp" wrapper stops the generation of two terms each * iter, since random_ is evaluated after bracket expansion + tmp(random_(2*`MAXCOEFF')-`MAXCOEFF') #do v = 1,`NVARS' * y`v'^(random_(`NEGPOW'+`MAXPOW'+1)-1-`NEGPOW') #enddo #enddo ; #enddo #inside <$p1>,...,<$p`NPOLYS'> Identify tmp(y1?) = y1; #endinside *#do i = 1,`NPOLYS' * #message p`i' = `$p`i'' *#enddo #endprocedure * testijaik: a common factor between arguments #procedure testijaik(op,imin,imax,jmin,jmax,kmin,kmax) #reset timer On flint; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `k' >= `j' Local flint`op'p`i'p`j'p`k' = `op'_($p`i'*$p`j',$p`i'*$p`k'); #endif #enddo #enddo #enddo ModuleOption inparallel; .sort #message `op': flint runtime: `TIMER_' #reset timer Off flint; Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `k' >= `j' Local poly`op'p`i'p`j'p`k' = `op'_($p`i'*$p`j',$p`i'*$p`k'); #endif #enddo #enddo #enddo ModuleOption inparallel; .sort #message `op': poly runtime: `TIMER_' Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `k' >= `j' Local diff`op'p`i'p`j'p`k' = flint`op'p`i'p`j'p`k' - poly`op'p`i'p`j'p`k'; #if `op' == gcd Local diff2`op'p`i'p`j'p`k' = flint`op'p`i'p`j'p`k' + poly`op'p`i'p`j'p`k'; #endif #endif #enddo #enddo #enddo ModuleOption inparallel; .sort #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `k' >= `j' #if `op' == gcd #if (`ZERO_diff`op'p`i'p`j'p`k'' == 0) && (`ZERO_diff2`op'p`i'p`j'p`k'' == 1) #message Warning: sign difference in `op' p`i'p`j'p`k' #elseif (`ZERO_diff`op'p`i'p`j'p`k'' == 0) && (`ZERO_diff2`op'p`i'p`j'p`k'' == 0) #message Error: difference in `op' p`i'p`j'p`k' Print +s flint`op'p`i'p`j'p`k'; Print +s poly`op'p`i'p`j'p`k'; Print +s diff`op'p`i'p`j'p`k'; .sort #terminate #endif #else #if `ZERO_diff`op'p`i'p`j'p`k'' == 0 #message Error: difference in `op' p`i'p`j'p`k' Print flint`op'p`i'p`j'p`k'; Print poly`op'p`i'p`j'p`k'; Print diff`op'p`i'p`j'p`k'; .sort #terminate #endif #endif #endif #enddo #enddo #enddo Drop; .sort #message `op': OK #endprocedure * testiaj #procedure testiaj(op,imin,imax,jmin,jmax) #reset timer On flint; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' Local flint`op'p`i'p`j' = `op'_($p`i',$p`j'); #endif #enddo #enddo ModuleOption inparallel; .sort #message `op': flint runtime: `TIMER_' #reset timer Off flint; Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' Local poly`op'p`i'p`j' = `op'_($p`i',$p`j'); #endif #enddo #enddo ModuleOption inparallel; .sort #message `op': poly runtime: `TIMER_' Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' Local diff`op'p`i'p`j' = flint`op'p`i'p`j' - poly`op'p`i'p`j'; #endif #enddo #enddo ModuleOption inparallel; .sort #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' #if `ZERO_diff`op'p`i'p`j'' == 0 #message Error: difference in `op' p`i'p`j' Print flint`op'p`i'p`j'; Print poly`op'p`i'p`j'; Print diff`op'p`i'p`j'; .sort #terminate #endif #endif #enddo #enddo Drop; .sort #message `op': OK #endprocedure * testijaj: the second arg divides the first #procedure testijaj(op,imin,imax,jmin,jmax) #reset timer On flint; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' Local flint`op'p`i'p`j' = `op'_($p`i'*$p`j',$p`j'); #endif #enddo #enddo ModuleOption inparallel; .sort #message `op': flint runtime: `TIMER_' #reset timer Off flint; Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' Local poly`op'p`i'p`j' = `op'_($p`i'*$p`j',$p`j'); #endif #enddo #enddo ModuleOption inparallel; .sort #message `op': poly runtime: `TIMER_' Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' Local diff`op'p`i'p`j' = flint`op'p`i'p`j' - poly`op'p`i'p`j'; #endif #enddo #enddo ModuleOption inparallel; .sort #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' #if `ZERO_diff`op'p`i'p`j'' == 0 #message Error: difference in `op' p`i'p`j' Print flint`op'p`i'p`j'; Print poly`op'p`i'p`j'; Print diff`op'p`i'p`j'; .sort #terminate #endif #endif #enddo #enddo Drop; .sort #message `op': OK #endprocedure * testijak: the second arg usually has higher degree than the first #procedure testijak(op,imin,imax,jmin,jmax,kmin,kmax) #reset timer On flint; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `j' >= `i' Local flint`op'p`i'p`j'p`k' = `op'_($p`i'*$p`j',$p`k'); #endif #enddo #enddo #enddo ModuleOption inparallel; .sort #message `op': flint runtime: `TIMER_' #reset timer Off flint; Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `j' >= `i' Local poly`op'p`i'p`j'p`k' = `op'_($p`i'*$p`j',$p`k'); #endif #enddo #enddo #enddo ModuleOption inparallel; .sort #message `op': poly runtime: `TIMER_' Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `j' >= `i' Local diff`op'p`i'p`j'p`k' = flint`op'p`i'p`j'p`k' - poly`op'p`i'p`j'p`k'; #endif #enddo #enddo #enddo ModuleOption inparallel; .sort #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #if `j' >= `i' #if `ZERO_diff`op'p`i'p`j'p`k'' == 0 #message Error: difference in `op' p`i'p`j'p`k' Print flint`op'p`i'p`j'p`k'; Print poly`op'p`i'p`j'p`k'; Print diff`op'p`i'p`j'p`k'; .sort #terminate #endif #endif #enddo #enddo #enddo Drop; .sort #message `op': OK #endprocedure * Here it is hard to compare flint and poly, since FORM caches the factorization. * For now, check at least that nothing crashes and valgrind is clean. #procedure testfactij(imin,imax,jmin,jmax) #reset timer On flint; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' Local flintp`i'p`j' = fa($p`i'*$p`j'); #endif #enddo #enddo FactArg fa; ModuleOption inparallel; .sort #message factarg: flint runtime: `TIMER_' Drop; .sort #message factarg: OK #endprocedure #procedure testfactdolij(imin,imax,jmin,jmax) #reset timer On flint; #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' #$flintp`i'p`j' = $p`i'*$p`j'; #factdollar $flintp`i'p`j' #endif #enddo #enddo .sort #message factdollar: flint runtime: `TIMER_' #reset timer Off flint; .sort #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' #$polyp`i'p`j' = $p`i'*$p`j'; #factdollar $polyp`i'p`j' #endif #enddo #enddo .sort #message factdollar: poly runtime: `TIMER_' #do i = `imin',`imax' #do j = `jmin',`jmax' #if `j' >= `i' #if `$flintp`i'p`j'[0]' != `$polyp`i'p`j'[0]' #message Error: factor count difference in factdollar p`i'p`j' #message $flintp`i'`j'[0] = `$flintp`i'p`j'[0]' #message $polyp`i'p`j'[0] = `$polyp`i'p`j'[0]' #terminate #endif #do f = 1,`$flintp`i'p`j'[0]' #$diffp`i'p`j' = (`$flintp`i'p`j'[`f']') - (`$polyp`i'p`j'[`f']'); #if `$diffp`i'p`j'' != 0 #message Error: factor difference in factdollar p`i'p`j' f`f' #message $flintp`i'`j'[`f'] = `$flintp`i'p`j'[`f']' #message $polyp`i'p`j'[`f'] = `$polyp`i'p`j'[`f']' #terminate #endif #enddo #endif #enddo #enddo #message factdollar: OK #endprocedure #procedure testprf(op,imin,imax,jmin,jmax,kmin,kmax,lmin,lmax) #reset timer On flint; PolyRatFun prf; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #do l = `lmin',`lmax' #if `j' >= `i' #if `l' >= `i' Local flintprf`op'p`i'p`j'p`k'p`l' = #if `op' == norm + prf($p`i'*$p`j',$p`k') * prf($p`k',$p`i'*$p`l') #elseif `op' == add + prf($p`i'*$p`j',$p`k') + prf($p`k',$p`i'*$p`l') #endif ; #endif #endif #enddo #enddo #enddo #enddo ModuleOption inparallel; .sort #message prf `op': flint runtime: `TIMER_' #reset timer Off flint; PolyRatFun prf; Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #do l = `lmin',`lmax' #if `j' >= `i' #if `l' >= `i' Local polyprf`op'p`i'p`j'p`k'p`l' = #if `op' == norm + prf($p`i'*$p`j',$p`k') * prf($p`k',$p`i'*$p`l') #elseif `op' == add + prf($p`i'*$p`j',$p`k') + prf($p`k',$p`i'*$p`l') #endif ; #endif #endif #enddo #enddo #enddo #enddo ModuleOption inparallel; .sort #message prf `op': poly runtime: `TIMER_' PolyRatFun; Hide; #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #do l = `lmin',`lmax' #if `j' >= `i' #if `l' >= `i' Local diffprf`op'p`i'p`j'p`k'p`l' = + flintprf`op'p`i'p`j'p`k'p`l' - polyprf`op'p`i'p`j'p`k'p`l' ; #endif #endif #enddo #enddo #enddo #enddo ModuleOption inparallel; .sort #do i = `imin',`imax' #do j = `jmin',`jmax' #do k = `kmin',`kmax' #do l = `lmin',`lmax' #if `j' >= `i' #if `l' >= `i' #if `ZERO_diffprf`op'p`i'p`j'p`k'p`l'' == 0 #message Error: difference in prf `op' p`i'p`j'p`k'p`l' Print flintprf`op'p`i'p`j'p`k'p`l'; Print polyprf`op'p`i'p`j'p`k'p`l'; Print diffprf`op'p`i'p`j'p`k'p`l'; .sort #terminate #endif #endif #endif #enddo #enddo #enddo #enddo Drop; .sort #message prf `op': OK #endprocedure #procedure testinv(x3min,x3max,x1min,x1max) #reset timer On flint; #do x3 = `x3min',`x3max' #do x1 = `x1min',`x1max' * Construct an x2 which produces an inverse without crashing FORM #$arg2 = $p`x1'*$p`x3'-1; * Avoid 0 for second arg: #if `$arg2' == 0 Local flintinvp`x3'p`x1' = 0; #else Local flintinvp`x3'p`x1' = inverse_($p`x1',`$arg2'); #endif #enddo #enddo ModuleOption inparallel; .sort #message inverse: flint runtime: `TIMER_' #reset timer Off flint; Hide; #do x3 = `x3min',`x3max' #do x1 = `x1min',`x1max' * Construct an x2 which produces an inverse without crashing FORM #$arg2 = $p`x1'*$p`x3'-1; * Avoid 0 for second arg: #if `$arg2' == 0 Local polyinvp`x3'p`x1' = 0; #else Local polyinvp`x3'p`x1' = inverse_($p`x1',`$arg2'); #endif #enddo #enddo ModuleOption inparallel; .sort #message inverse: poly runtime: `TIMER_' Hide; #do x3 = `x3min',`x3max' #do x1 = `x1min',`x1max' Local diffinvp`x3'p`x1' = flintinvp`x3'p`x1' - polyinvp`x3'p`x1'; #enddo #enddo ModuleOption inparallel; .sort #do x3 = `x3min',`x3max' #do x1 = `x1min',`x1max' #if `ZERO_diffinvp`x3'p`x1'' == 0 #message Error: difference in inv p`x3'p`x1' Print flintinvp`x3'p`x1'; Print polyinvp`x3'p`x1'; Print diffinvp`x3'p`x1'; .sort #endif #enddo #enddo Drop; .sort #message inv: OK #endprocedure *--#] polynomial_prc : *--#[ polynomial_gcd_nvar_1 : #- #define NPOLYS "12" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijaik(gcd,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("gcd: OK") *--#] polynomial_gcd_nvar_1 : *--#[ polynomial_gcd_nvar_2 : #- #define NPOLYS "10" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijaik(gcd,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("gcd: OK") *--#] polynomial_gcd_nvar_2 : *--#[ polynomial_gcd_nvar_5 : #- #define NPOLYS "8" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "9" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijaik(gcd,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("gcd: OK") *--#] polynomial_gcd_nvar_5 : *--#[ polynomial_mul_nvar_1 : #- #define NPOLYS "60" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "40" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testiaj(mul,2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("mul: OK") *--#] polynomial_mul_nvar_1 : *--#[ polynomial_mul_nvar_2 : #- #define NPOLYS "30" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "40" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testiaj(mul,2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("mul: OK") *--#] polynomial_mul_nvar_2 : *--#[ polynomial_mul_nvar_5 : #- #define NPOLYS "20" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "40" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testiaj(mul,2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("mul: OK") *--#] polynomial_mul_nvar_5 : *--#[ polynomial_div_nvar_1 : #- #define NPOLYS "60" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "40" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijaj(div,2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("div: OK") *--#] polynomial_div_nvar_1 : *--#[ polynomial_div_nvar_2 : #- #define NPOLYS "30" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "35" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijaj(div,2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("div: OK") *--#] polynomial_div_nvar_2 : *--#[ polynomial_div_nvar_5 : #- #define NPOLYS "20" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "35" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijaj(div,2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("div: OK") *--#] polynomial_div_nvar_5 : *--#[ polynomial_rem_nvar_1 : #- #define NPOLYS "16" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijak(rem,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("rem: OK") *--#] polynomial_rem_nvar_1 : *--#[ polynomial_rem_nvar_2 : #- #define NPOLYS "12" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "10" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijak(rem,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("rem: OK") *--#] polynomial_rem_nvar_2 : *--#[ polynomial_rem_nvar_5 : #- #define NPOLYS "8" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "10" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testijak(rem,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("rem: OK") *--#] polynomial_rem_nvar_5 : *--#[ polynomial_factarg_nvar_1 : #- #define NPOLYS "25" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testfactij(2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 # This takes too long when running without FLINT under lcov. Skip if valgrind, and hence lcov. #pend_if valgrind? # This needs longer if running without flint. #time_dilation 2.0 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("factarg: OK") *--#] polynomial_factarg_nvar_1 : *--#[ polynomial_factarg_nvar_2 : #- #define NPOLYS "15" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testfactij(2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 # This takes too long when running without FLINT under lcov. Skip if valgrind, and hence lcov. #pend_if valgrind? # This needs longer if running without flint. #time_dilation 3.0 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("factarg: OK") *--#] polynomial_factarg_nvar_2 : *--#[ polynomial_factarg_nvar_5 : #- #define NPOLYS "10" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "10" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testfactij(2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 # This takes too long when running without FLINT under lcov. Skip if valgrind, and hence lcov. # This one is not valgrind clean for flint < 3.2.1 ! #pend_if valgrind? # This needs longer if running without flint. #time_dilation 3.0 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("factarg: OK") *--#] polynomial_factarg_nvar_5 : *--#[ polynomial_factdol_nvar_1 : #- #define NPOLYS "25" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "14" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testfactdolij(2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 # This takes too long when running without FLINT under lcov. Skip if valgrind, and hence lcov. #pend_if valgrind? # This needs longer if running without flint. #time_dilation 2.0 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("factdollar: OK") *--#] polynomial_factdol_nvar_1 : *--#[ polynomial_factdol_nvar_2 : #- #define NPOLYS "15" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "14" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testfactdolij(2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 # This takes too long when running without FLINT under lcov. Skip if valgrind, and hence lcov. #pend_if valgrind? # This needs longer if running without flint. #time_dilation 2.0 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("factdollar: OK") *--#] polynomial_factdol_nvar_2 : *--#[ polynomial_factdol_nvar_5 : #- #define NPOLYS "10" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "9" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testfactdolij(2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 # This takes too long when running without FLINT under lcov. Skip if valgrind, and hence lcov. #pend_if valgrind? # This needs longer if running without flint. #time_dilation 2.0 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("factdollar: OK") *--#] polynomial_factdol_nvar_5 : *--#[ polynomial_prf_norm_nvar_1 : #- #define NPOLYS "8" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testprf(norm,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("prf norm: OK") *--#] polynomial_prf_norm_nvar_1 : *--#[ polynomial_prf_norm_nvar_2 : #- #define NPOLYS "8" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testprf(norm,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("prf norm: OK") *--#] polynomial_prf_norm_nvar_2 : *--#[ polynomial_prf_norm_nvar_5 : #- #define NPOLYS "7" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "9" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testprf(norm,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("prf norm: OK") *--#] polynomial_prf_norm_nvar_5 : *--#[ polynomial_prf_add_nvar_1 : #- #define NPOLYS "8" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testprf(add,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("prf add: OK") *--#] polynomial_prf_add_nvar_1 : *--#[ polynomial_prf_add_nvar_2 : #- #define NPOLYS "8" #define NVARS "2" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testprf(add,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("prf add: OK") *--#] polynomial_prf_add_nvar_2 : *--#[ polynomial_prf_add_nvar_5 : #- #define NPOLYS "7" #define NVARS "5" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "8" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testprf(add,2,`NPOLYS',2,`NPOLYS',2,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("prf add: OK") *--#] polynomial_prf_add_nvar_5 : *--#[ polynomial_inverse_nvar_1 : #- #define NPOLYS "20" #define NVARS "1" #define NEGPOW "0" #define MAXPOW "10" #define MAXCOEFF "100" #define NTERMS "15" #include polynomial.frm # polynomial_prc #call genpoly(`NPOLYS',`NVARS',`NEGPOW',`MAXPOW',`MAXCOEFF',`NTERMS') #call testinv(1,`NPOLYS',2,`NPOLYS') .end #pend_if wordsize == 2 assert succeeded? || warning?("FORM was not built with FLINT support.") assert stdout =~ exact_pattern("inv: OK") *--#] polynomial_inverse_nvar_1 : *--#[ polynomial_extra_1 : * Assorted additional tests, to fully cover flintinterface.cc with just this test set Symbol w,x,y,z; CFunction f,g,prf; * Negative powers and fast-notation symbols Local test1 = prf(1/x + y + z,w); Local test2 = prf(1/x + x + 1,x); * Zero conversion #$zero = 0; Local test3 = mul_($zero,1); * GCD which must fit in a term: I don't think this is reachable *Local test4 = f(gcd_((x+1)^2,(x+1)*(x-1))); *Local test5 = f(gcd_((x+1)^2,(x+1)*(y-1))); * Long integer conversion with different limb counts Local test6 = + g(1)*prf(y+2^32-1,1) + g(2)*prf(y+2^64-1,1) + g(3)*prf(y+2^96-1,1) + g(4)*prf(y+2^128-1,1) + g(5)*prf(y+2^160-1,1); * Output coeff has longer denominator than numerator: Local test7 = mul_(1+x,1/2^64+x) + mul_(y+x,y/2^64+x); * Result is 0 Local test8 = prf(1+x,1) + prf(-1-x,1); Local test9 = prf(y+x,1) + prf(-y-x,1); * Result is fast notation Local test10 = prf(x+1,2) + prf(x-1,2); Local test11 = prf(x+y,2) + prf(x-y,2); * Copy non-prf term data, absorb coefficient Local test12 = prf(x+1,1) + prf(x-1,1)*(f(1)*g(1)*x*3/2); Local test13 = prf(x+y,1) + prf(x-y,1)*(f(1)*g(1)*x*3/2); .sort PolyRatFun prf; Print; .end assert succeeded? assert result("test1") =~ expr("prf(x*y + x*z + 1,w*x)") assert result("test2") =~ expr("prf(x^2 + x + 1,x^2)") assert result("test3") =~ expr("0") # assert result("test4") =~ expr("f(1 + x)*prf(1,1)") # assert result("test5") =~ expr("f(1 + x)*prf(1,1)") # assert result("test6") =~ expr("g(1)*prf(y + 4294967295,1) + g(2)*prf(y + 18446744073709551615,1) + g(3)*prf(y + 79228162514264337593543950335,1) + g(4)*prf(y + 340282366920938\463463374607431768211455,1) + g(5)*prf(y + 14615016373309029182036848327\16283019655932542975,1);") assert result("test7") =~ expr("y^2*prf(1,18446744073709551616) + x*prf(18446744073709551617,18446744073709551616) + x*y*prf(18446744073709551617,18446744073709551616) + x^2*prf(2,1) + prf(1,18446744073709551616)") assert result("test8") =~ expr("0") assert result("test9") =~ expr("0") assert result("test10") =~ expr("prf(x,1)") assert result("test11") =~ expr("prf(x,1)") assert result("test12") =~ expr("f(1)*g(1)*x*prf(3*x - 3,2) + prf(x + 1,1)") assert result("test13") =~ expr("f(1)*g(1)*x*prf(3*x - 3*y,2) + prf(x + y,1)") *--#] polynomial_extra_1 : *--#[ polynomial_error_1 : CFunction f,prf; PolyRatFun prf; Local test = prf(f(1),1); .end assert runtime_error? assert stdout =~ exact_pattern("ERROR: polynomials and polyratfuns must contain symbols only") *--#] polynomial_error_1 : *--#[ polynomial_error_2 : CFunction f,prf; PolyRatFun prf; * Fast notation version Local test = prf(f,1); .end assert runtime_error? assert stdout =~ exact_pattern("ERROR: polynomials and polyratfuns must contain symbols only") *--#] polynomial_error_2 : *--#[ polynomial_error_3 : Symbol x; Local test = inverse_(x+1,x+1); .end assert runtime_error? assert stdout =~ exact_pattern("flint::inverse_poly error: inverse does not exist") || stdout =~ exact_pattern("ERROR: polynomial inverse does not exist") *--#] polynomial_error_3 : *--#[ polynomial_error_4 : CFunction prf; PolyRatFun prf; Local test = prf; .end assert runtime_error? assert stdout =~ exact_pattern("ERROR: PolyRatFun cannot have zero arguments") *--#] polynomial_error_4 : *--#[ polynomial_error_5 : CFunction prf; PolyRatFun prf; Local test = prf(1,2,3); Print; .end assert runtime_error? assert stdout =~ exact_pattern("ERROR: PolyRatFun cannot have more than two arguments") *--#] polynomial_error_5 : *--#[ polynomial_error_6 : CFunction prf; Symbol x,y; PolyRatFun prf; Local test = prf(x,y,3); Print; .end assert runtime_error? assert stdout =~ exact_pattern("ERROR: PolyRatFun cannot have more than two arguments") *--#] polynomial_error_6 : *--#[ polynomial_error_7 : #- #: MaxTermSize 200 CFunction prf; Symbol x; PolyRatFun prf; #define N "3" * This one goes wrong in flint::ratfun_normalize rather than to_argument_poly Local test = prf((x+1)^`N',(x+2)^`N')*prf((x^`N'-1)^`N',(x^`N'-2)^`N'); Print; .end assert runtime_error? assert stdout =~ exact_pattern("flint::ratfun_normalize: output exceeds MaxTermSize") || stdout =~ exact_pattern("ERROR: PolyRatFun doesn't fit in a term") *--#] polynomial_error_7 : *--#[ polynomial_error_8 : #: MaxTermSize 200 CFunction prf; Symbol x; PolyRatFun prf; #define N "4" Local test = prf((x+1)^`N',(x+2)^`N')*prf((x^`N'-1)^`N',(x^`N'-2)^`N'); Print; .end assert runtime_error? assert stdout =~ exact_pattern("flint::to_argument_poly: output exceeds MaxTermSize") || stdout =~ exact_pattern("ERROR: PolyRatFun doesn't fit in a term") *--#] polynomial_error_8 : *--#[ polynomial_error_9 : #: MaxTermSize 241 CFunction prf; Symbol x; PolyRatFun prf; #define N "5" * This one goes wrong before properly starting to write the second argument Local test = prf((x+1)^`N',(x+2)^`N')*prf((x^`N'-1)^`N',(x^`N'-2)^`N'); Print; .end assert runtime_error? assert stdout =~ exact_pattern("flint::to_argument_poly: output exceeds MaxTermSize") || stdout =~ exact_pattern("ERROR: PolyRatFun doesn't fit in a term") *--#] polynomial_error_9 : *--#[ polynomial_error_10 : #: MaxTermSize 322 CFunction prf; Symbol x,y; PolyRatFun prf; #define N "3" * This one goes wrong in flint::ratfun_normalize rather than to_argument_mpoly Local test = prf((x+y)^`N',(x+2*y)^`N')*prf((x^`N'-y)^`N',(x^`N'-2*y)^`N'); Print; .end assert runtime_error? assert stdout =~ exact_pattern("flint::ratfun_normalize: output exceeds MaxTermSize") || stdout =~ exact_pattern("ERROR: PolyRatFun doesn't fit in a term") *--#] polynomial_error_10 : *--#[ polynomial_error_11 : #: MaxTermSize 200 CFunction prf; Symbol x,y; PolyRatFun prf; #define N "3" Local test = prf((x+y)^`N',(x+2*y)^`N')*prf((x^`N'-y)^`N',(x^`N'-2*y)^`N'); Print; .end assert runtime_error? assert stdout =~ exact_pattern("flint::to_argument_mpoly: output exceeds MaxTermSize") || stdout =~ exact_pattern("ERROR: PolyRatFun doesn't fit in a term") *--#] polynomial_error_11 : *--#[ polynomial_error_12 : #: MaxTermSize 283 CFunction prf; Symbol x,y,z; PolyRatFun prf; #define N "2" * This one goes wrong before properly starting to write the second argument Local test = prf((x+y+z)^`N',(x+2*y)^`N')*prf((x^`N'-y-z)^`N',(x^`N'-2*y)^`N'); Print; .end assert runtime_error? assert stdout =~ exact_pattern("flint::to_argument_mpoly: output exceeds MaxTermSize") || stdout =~ exact_pattern("ERROR: PolyRatFun doesn't fit in a term") *--#] polynomial_error_12 : form-5.0.1/check/user.frm0000644000175100017510000140612015217035721010713 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ jodavies_include : * Paste denexpand.prc * Expand a "den" function DEN in the variable EP. This is useful in cases * where we have isolated the dependence on the EP symbol, and cannot merge * everything into a common PolyRatFun without exceeding MaxTermSize. * Den is expanded, and the resulting EP-independent coefficients are merged * into a PolyRatFun PRF as we go. This should most likely be the same name * as an existing PolyRatFun of EP-independent variables in the input. Symbol denexpn,denexpm,denexpo,denexpi,denexpj; CFunction denexpnum,denexpcollect,denexpprftmp; .sort #procedure denexpand(DEN,EP,DEPTH,PRF) #message denexpand.prc: expanding `DEN' for small `EP', depth `DEPTH' * Make sure the sorting mode is highfirst, to work around Issue 336 * https://github.com/vermaseren/form/issues/336 On highfirst; * PolyRatFun should be disabled initially PolyRatFun; * Check for multi-argument DEN, this is not expected input If (Match(`DEN'(denexpn?,denexpm?)) > 0); Print "denexpand.prc: Error: unexpected multi-argument `DEN': %t"; Exit; EndIf; * Check PRF doesn't contain the expansion symbol: Argument `PRF'; If (Count(`EP',1) != 0); Print "denexpand.prc: Error: unexpected `EP' in `PRF': %t"; Exit; EndIf; EndArgument; * Extract any poles in EP: FactArg `DEN'; ChainOut `DEN'; Identify `DEN'(`EP') = 1/`EP'; * Discard terms which are already beyond DEPTH, now that we are sure DEN contains no poles in EP: If (Count(`EP',1) > `DEPTH') Discard; * Discard EP powers within DEN, if they will produce terms beyond DEPTH. * Account for external negative powers: $denexptermEPmax = - count_(`EP',1) + `DEPTH'; Argument `DEN'; If (Count(`EP',1) > $denexptermEPmax) Discard; EndArgument; * Bring DENs to a unique form: FactArg `DEN'; ChainOut `DEN'; Normalize,^-1 `DEN'; Identify `DEN'(1) = 1; * Record the highest order EP pole #$denexpMinEPpole = 0; If (Count(`EP',1) < $denexpMinEPpole) $denexpMinEPpole = count_(`EP',1); * Collect together the relevant terms AntiBracket `DEN',`EP',`PRF'; ModuleOption,local $denexptermEPmax; ModuleOption,minimum $denexpMinEPpole; .sort:DE prep; * WORKAROUND (Issue 332) #if {-`$denexpMinEPpole'+`DEPTH'} <= 0 #message denexpand.prc: setting power limit denexpEP(:1); Symbol denexpEP(:1); #else #message denexpand.prc: setting power limit denexpEP(:{-`$denexpMinEPpole'+`DEPTH'}); Symbol denexpEP(:{-`$denexpMinEPpole'+`DEPTH'}); #endif PolyRatFun `PRF'; Collect denexpcollect; * This sort is necessary to work around Issue 336 ? .sort:DE coll; #ifdef `DENEXPANDVERBOSE' #$term = 1; Print "Starting Term %$ in thread %w ...", $term; $term = $term + 1; #endif * Fully compute each coefficient inside a Term environment. Since we used AntiBracket * above, the resulting series expansion will never merge with the other terms. Term; * Open the Collect, so that the PolyRatFuns will properly merge. They do not do so, * if we were to attempt the expansion inside the argument of denexpcollect. Identify denexpcollect(denexpn?) = denexpn; * Convert to power-limited EP symbol for speed, but only external powers and inside * the function we are expanding. The symbol might appear in tags, etc. Identify `EP' = denexpEP; Identify 1/`EP' = 1/denexpEP; Argument `DEN'; Multiply replace_(`EP', denexpEP); EndArgument; * Change DEN notation SplitArg ((denexpEP)) `DEN'; Transform `DEN' addargs(2,last); * A single-argument DEN has no EP dependence and can already be merged with PRF. Typically * this doesn't happen, but it depends how the input was prepared. Identify `DEN'(denexpj?) = `PRF'(1,denexpj); * Loop through the powers of denexpEP which should appear in the output, and fully compute each in turn. #do denexpPow = `$denexpMinEPpole',`DEPTH' Repeat; If (Count(denexpEP,1) == `denexpPow'); * Expand one DEN by one power, then simplify Identify,Once `DEN'(denexpn?,denexpm?) = `PRF'(1,denexpn) - `PRF'(1,denexpn)*denexpnum(denexpm/denexpEP)*denexpEP*`DEN'(denexpn,denexpm); * Now extract possible denexpEP dependence, without fully expanding denexpnum: Repeat; SplitArg ((denexpEP)) denexpnum; Identify denexpnum(denexpEP) = denexpEP; Identify denexpnum(denexpn?) = `PRF'(denexpn,1); Transform denexpnum addargs(2,last); Identify denexpnum(denexpn?,denexpm?) = `PRF'(denexpn,1) + denexpEP*denexpnum(denexpm/denexpEP); EndRepeat; EndIf; EndRepeat; * Before starting the next power, remove terms in the DEN which would produce denexpEP powers beyond DEPTH $denexptermEPmax = - count_(denexpEP,1) + `DEPTH'; Argument `DEN'; If (Count(denexpEP,1) > $denexptermEPmax) Discard; EndArgument; Identify `DEN'(denexpn?,0) = `PRF'(1,denexpn); Sort; #enddo EndTerm; * Replace original EP symbol Multiply replace_(denexpEP,`EP'); #ifdef `DENEXPANDVERBOSE' ModuleOption,local $term; #endif ModuleOption,local $denexptermEPmax; .sort:DE exp; #printtimes * End with PolyRatFun disabled again PolyRatFun; #endprocedure * Paste coefftools.h Symbol coefftx,coeffty; * Convert assumed previous PolyRatFun p (PolyRatFun should now be disabled) * into products of num and den factors n and d. #procedure prf2numden(prf,num,den) #message coefftools.h: prf2numden(`prf',`num',`den') Identify `prf'(coefftx?,coeffty?) = `num'(coefftx)*`den'(coeffty); FactArg `num'; FactArg `den'; ChainOut `num'; ChainOut `den'; Identify `num'(coefftx?number_) = coefftx; Identify `den'(coeffty?number_) = 1/coeffty; #endprocedure * Convert products of num and den factors n and d into a PolyRatFun p. * If there are many such factors it is usually faster to loop over moving * them into the PolyRatFun one at a time. #procedure numden2prf(num,den,prf) #message coefftools.h: numden2prf(`num',`den',`prf') * Check for functions inside num, den, which will cause a crash: #$termprint = 0; Argument `num'; If (Match(`num'?(?a))); $termprint = 1; EndIf; EndArgument; Argument `den'; If (Match(`num'?(?a))); $termprint = 1; EndIf; EndArgument; If ($termprint == 1); Print "numden2prf: found a function inside `num' or `den': %t"; Exit; EndIf; #do coeffti = 1,1 #$coeffti = 1; * #message coefftools.h: numden2prf loop... * Identify,once `num'(coefftx?) = `prf'(coefftx,1); * Identify,once `den'(coeffty?) = `prf'(1,coeffty); Identify `num'(coefftx?) = `prf'(coefftx,1); Identify `den'(coeffty?) = `prf'(1,coeffty); If (Count(`num',1,`den',1) > 0) $coeffti = 0; ModuleOption,minimum $coeffti; ModuleOption,local $termprint; .sort(PolyRatFun=`prf') #redefine coeffti "`$coeffti'" #printtimes #enddo PolyRatFun; * Look for bug Issue 336. It is recommended to always use highfirst sort mode to avoid this. If (Match(`prf'(coefftx?,0)) > 0); Print "coefftools.h: numden2prf(`num',`den',`prf'): error: division by zero in: %t"; Exit; EndIf; .sort #endprocedure * Extract S dependence from a numerator function n, which may contain a large sum of terms. * For eg, #call extractfromnum(ep) will convert num(1+ep*x+ep*y) into 1 + ep*num(x+y). #procedure extractfromnum(num,S) #message coefftools.h: extractfromnum(`num',`S') Repeat; SplitArg ((`S')) `num'; * issue-269 workaround, see also https://arxiv.org/abs/math-ph/0010025 Identify `num'(`S') = `S'; Transform `num' addargs(2,last); Identify `num'(coefftx?,coeffty?) = `num'(coefftx) + `S'*`num'(coeffty/`S'); FactArg `num'; ChainOut `num'; Identify `num'(coefftx?number_) = coefftx; * For cases which contained nested num, which already factorized the coefficients of S: Repeat Identify `num'(`num'(coefftx?)) = `num'(coefftx); * The below leads to horrible performance with lots of expansion followed by re-factorization * in the code above. I don't remember why I introduced these lines in the first place, instead * to the line above. * Argument `num'; * If (Count(`S',1) == 0) Repeat Identify `num'(coefftx?) = coefftx; * EndArgument; EndRepeat; #endprocedure * It is sometimes useful to rename denominator functions den as deniso, if they * contain dependence on a particular symbol S. * For eg, #call isolateden(den,ep,denep) will convert den(x+y)*den(ep*x+y) into * den(x+y)*denep(ep*x+y). #procedure isolateden(den,S,deniso) #message coefftools.h: isolateden(`den',`S',`deniso') FactArg `den'; ChainOut `den'; Identify `den'(coefftx?number_) = 1/coefftx; SplitArg ((`S')) `den'; Transform `den' addargs(2,last); Identify `den'(`S') = 1/`S'; Identify `den'(coefftx?,coeffty?) = `deniso'(coefftx+coeffty); #endprocedure * Try to factorize the specified list of variables, putting them into products of * numerator function num. ?S may contain num itself, but should not contain den. * Try to cancel against any existing den functions. #procedure mergeterms(num,den,?S) AntiBracket `?S'; .sort #message coefftools.h: mergeterms(`num',`den',`?S') Collect `num'; Argument `num'; Repeat Identify `num'(coefftx?) = coefftx; If (Count(`den',1) > 0); Print "coefftools.h: mergeterms: `num' should not contain `den' in input: %t"; EndIf; EndArgument; FactArg `num'; ChainOut `num'; Identify `num'(coefftx?number_) = coefftx; Normalize `num'; Normalize^-1 `den'; Identify `num'(coefftx?)*`den'(coefftx?) = 1; #endprocedure *--#] jodavies_include : *--#[ jodavies_denexpand : #- Off Statistics; On Highfirst; #include- user.frm # jodavies_include #define NUMTESTS "28" AutoDeclare Symbol n,m; Symbol ep; CFunction prf,den,denep,num,prfexpden; #do EXPDEPTH = {-1,0,1,5} Drop; .sort Local test1 = prf((n0+ep*n1+ep^2*n2+ep^3*n3),(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test2 = prf((n0+ep*n1+ep^2*n2+ep^3*n3),ep*(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test3 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3),(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test4 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3),ep*(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test5 = prf((n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test6 = prf((n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),ep*(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test7 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test8 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),ep*(m0+ep*m1+ep^2*m2+ep^3*m3)); Local test9 = prf((n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),(m0+ep*m1+ep^2*m2+ep^3*m3+ep^4*m4+ep^5*m5+ep^6*m6)); Local test10 = prf((n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),ep*(m0+ep*m1+ep^2*m2+ep^3*m3+ep^4*m4+ep^5*m5+ep^6*m6)); Local test11 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),(m0+ep*m1+ep^2*m2+ep^3*m3+ep^4*m4+ep^5*m5+ep^6*m6)); Local test12 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3+ep^4*n4+ep^5*n5+ep^6*n6),ep*(m0+ep*m1+ep^2*m2+ep^3*m3+ep^4*m4+ep^5*m5+ep^6*m6)); Local test13 = prf((n0+ep*n1+ep^2*n2+ep^3*n3),(ep*m0+ep*m1+ep^2*m2+ep^3*m3)); Local test14 = prf((n0+ep*n1+ep^2*n2+ep^3*n3),ep*(ep*m0+ep*m1+ep^2*m2+ep^3*m3)); Local test15 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3),(ep*m0+ep*m1+ep^2*m2+ep^3*m3)); Local test16 = prf(ep*(n0+ep*n1+ep^2*n2+ep^3*n3),ep*(ep*m0+ep*m1+ep^2*m2+ep^3*m3)); Local test17 = prf(1,1+ep); Local test18 = prf(1,ep^5*(1+ep)); Local test19 = prf(1,ep^5*(1+2*ep)); Local test20 = prf(1,1); Local test21 = prf(1,1+ep)+prf(-1,1)+prf(ep,1+ep); Local test22 = prf(1,ep); Local test23 = prf(ep,ep); Local test24 = prf(0,ep); Local test25 = prf(0,1); Local test26 = prf(ep^6,1); Local test27 = prf(ep^7,ep); * This test breaks if the internal power limit is set to zero: Local test28 = prf(1,m0+m1+ep*(m0+m1)); * Format for denexpand #call prf2numden(prf,num,den) #call extractfromnum(num,ep) #call isolateden(den,ep,denep) #call numden2prf(num,den,prf) .sort #call denexpand(denep,ep,`EXPDEPTH',prf) Local result1 = n0*prfexpden(m0) + ep*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^2*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^3*(-(m1^3*n0) + 2*m0*m1*m2*n0 - m0^2*m3*n0 + m0*m1^2*n1 - m0^2*m2*n1 - m0^2*m1*n2 + m0^3*n3)*prfexpden(m0)^4 + ep^4*(m1^4*n0 - 3*m0*m1^2*m2*n0 + m0^2*m2^2*n0 + 2*m0^2*m1*m3*n0 - m0*m1^3*n1 + 2*m0^2*m1*m2*n1 - m0^3*m3*n1 + m0^2*m1^2*n2 - m0^3*m2*n2 - m0^3*m1*n3)*prfexpden(m0)^5 + ep^5*(-(m1^5*n0) + 4*m0*m1^3*m2*n0 - 3*m0^2*m1*m2^2*n0 - 3*m0^2*m1^2*m3*n0 + 2*m0^3*m2*m3*n0 + m0*m1^4*n1 - 3*m0^2*m1^2*m2*n1 + m0^3*m2^2*n1 + 2*m0^3*m1*m3*n1 - m0^2*m1^3*n2 + 2*m0^3*m1*m2*n2 - m0^4*m3*n2 + m0^3*m1^2*n3 - m0^4*m2*n3)*prfexpden(m0)^6; Local result2 = n0*prfexpden(ep)*prfexpden(m0) + (-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^2*(n3*prfexpden(m0) - m1*n2*prfexpden(m0)^2 + (m1^2 - m0*m2)*n1*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n0*prfexpden(m0)^4) + ep^3*(-(m1*n3*prfexpden(m0)^2) + (m1^2 - m0*m2)*n2*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n1*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3)*n0*prfexpden(m0)^5) + ep^4*((m1^2 - m0*m2)*n3*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n2*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3)*n1*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3)*n0*prfexpden(m0)^6) + ep^5*((-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n3*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3)*n2*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3)*n1*prfexpden(m0)^6 + (m1^6 - 5*m0*m1^4*m2 + 6*m0^2*m1^2*m2^2 - m0^3*m2^3 + 4*m0^2*m1^3*m3 - 6*m0^3*m1*m2*m3 + m0^4*m3^2)*n0*prfexpden(m0)^7); Local result3 = ep*n0*prfexpden(m0) + ep^2*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^3*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^4*(-(m1^3*n0) + 2*m0*m1*m2*n0 - m0^2*m3*n0 + m0*m1^2*n1 - m0^2*m2*n1 - m0^2*m1*n2 + m0^3*n3)*prfexpden(m0)^4 + ep^5*(m1^4*n0 - 3*m0*m1^2*m2*n0 + m0^2*m2^2*n0 + 2*m0^2*m1*m3*n0 - m0*m1^3*n1 + 2*m0^2*m1*m2*n1 - m0^3*m3*n1 + m0^2*m1^2*n2 - m0^3*m2*n2 - m0^3*m1*n3)*prfexpden(m0)^5; Local result4 = n0*prfexpden(m0) + ep*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^2*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^3*(-(m1^3*n0) + 2*m0*m1*m2*n0 - m0^2*m3*n0 + m0*m1^2*n1 - m0^2*m2*n1 - m0^2*m1*n2 + m0^3*n3)*prfexpden(m0)^4 + ep^4*(m1^4*n0 - 3*m0*m1^2*m2*n0 + m0^2*m2^2*n0 + 2*m0^2*m1*m3*n0 - m0*m1^3*n1 + 2*m0^2*m1*m2*n1 - m0^3*m3*n1 + m0^2*m1^2*n2 - m0^3*m2*n2 - m0^3*m1*n3)*prfexpden(m0)^5 + ep^5*(-(m1^5*n0) + 4*m0*m1^3*m2*n0 - 3*m0^2*m1*m2^2*n0 - 3*m0^2*m1^2*m3*n0 + 2*m0^3*m2*m3*n0 + m0*m1^4*n1 - 3*m0^2*m1^2*m2*n1 + m0^3*m2^2*n1 + 2*m0^3*m1*m3*n1 - m0^2*m1^3*n2 + 2*m0^3*m1*m2*n2 - m0^4*m3*n2 + m0^3*m1^2*n3 - m0^4*m2*n3)*prfexpden(m0)^6; Local result5 = n0*prfexpden(m0) + ep*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^2*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^3*(-(m1^3*n0) + 2*m0*m1*m2*n0 - m0^2*m3*n0 + m0*m1^2*n1 - m0^2*m2*n1 - m0^2*m1*n2 + m0^3*n3)*prfexpden(m0)^4 + ep^4*(m1^4*n0 - 3*m0*m1^2*m2*n0 + m0^2*m2^2*n0 + 2*m0^2*m1*m3*n0 - m0*m1^3*n1 + 2*m0^2*m1*m2*n1 - m0^3*m3*n1 + m0^2*m1^2*n2 - m0^3*m2*n2 - m0^3*m1*n3 + m0^4*n4)*prfexpden(m0)^5 + ep^5*(-(m1^5*n0) + 4*m0*m1^3*m2*n0 - 3*m0^2*m1*m2^2*n0 - 3*m0^2*m1^2*m3*n0 + 2*m0^3*m2*m3*n0 + m0*m1^4*n1 - 3*m0^2*m1^2*m2*n1 + m0^3*m2^2*n1 + 2*m0^3*m1*m3*n1 - m0^2*m1^3*n2 + 2*m0^3*m1*m2*n2 - m0^4*m3*n2 + m0^3*m1^2*n3 - m0^4*m2*n3 - m0^4*m1*n4 + m0^5*n5)*prfexpden(m0)^6; Local result6 = n0*prfexpden(ep)*prfexpden(m0) + (-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^2*(n3*prfexpden(m0) - m1*n2*prfexpden(m0)^2 + (m1^2 - m0*m2)*n1*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n0*prfexpden(m0)^4) + ep^3*(n4*prfexpden(m0) - m1*n3*prfexpden(m0)^2 + (m1^2 - m0*m2)*n2*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n1*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3)*n0*prfexpden(m0)^5) + ep^4*(n5*prfexpden(m0) - m1*n4*prfexpden(m0)^2 + (m1^2 - m0*m2)*n3*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n2*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3)*n1*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3)*n0*prfexpden(m0)^6) + ep^5*(n6*prfexpden(m0) - m1*n5*prfexpden(m0)^2 + (m1^2 - m0*m2)*n4*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n3*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3)*n2*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3)*n1*prfexpden(m0)^6 + (m1^6 - 5*m0*m1^4*m2 + 6*m0^2*m1^2*m2^2 - m0^3*m2^3 + 4*m0^2*m1^3*m3 - 6*m0^3*m1*m2*m3 + m0^4*m3^2)*n0*prfexpden(m0)^7); Local result7 = ep*n0*prfexpden(m0) + ep^2*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^3*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^4*(-(m1^3*n0) + 2*m0*m1*m2*n0 - m0^2*m3*n0 + m0*m1^2*n1 - m0^2*m2*n1 - m0^2*m1*n2 + m0^3*n3)*prfexpden(m0)^4 + ep^5*(m1^4*n0 - 3*m0*m1^2*m2*n0 + m0^2*m2^2*n0 + 2*m0^2*m1*m3*n0 - m0*m1^3*n1 + 2*m0^2*m1*m2*n1 - m0^3*m3*n1 + m0^2*m1^2*n2 - m0^3*m2*n2 - m0^3*m1*n3 + m0^4*n4)*prfexpden(m0)^5; Local result8 = n0*prfexpden(m0) + ep*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^2*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^3*(-(m1^3*n0) + 2*m0*m1*m2*n0 - m0^2*m3*n0 + m0*m1^2*n1 - m0^2*m2*n1 - m0^2*m1*n2 + m0^3*n3)*prfexpden(m0)^4 + ep^4*(m1^4*n0 - 3*m0*m1^2*m2*n0 + m0^2*m2^2*n0 + 2*m0^2*m1*m3*n0 - m0*m1^3*n1 + 2*m0^2*m1*m2*n1 - m0^3*m3*n1 + m0^2*m1^2*n2 - m0^3*m2*n2 - m0^3*m1*n3 + m0^4*n4)*prfexpden(m0)^5 + ep^5*(-(m1^5*n0) + 4*m0*m1^3*m2*n0 - 3*m0^2*m1*m2^2*n0 - 3*m0^2*m1^2*m3*n0 + 2*m0^3*m2*m3*n0 + m0*m1^4*n1 - 3*m0^2*m1^2*m2*n1 + m0^3*m2^2*n1 + 2*m0^3*m1*m3*n1 - m0^2*m1^3*n2 + 2*m0^3*m1*m2*n2 - m0^4*m3*n2 + m0^3*m1^2*n3 - m0^4*m2*n3 - m0^4*m1*n4 + m0^5*n5)*prfexpden(m0)^6; Local result9 = n0*prfexpden(m0) + ep*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^2*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^3*(n3*prfexpden(m0) - m1*n2*prfexpden(m0)^2 + (m1^2 - m0*m2)*n1*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n0*prfexpden(m0)^4) + ep^4*(n4*prfexpden(m0) - m1*n3*prfexpden(m0)^2 + (m1^2 - m0*m2)*n2*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n1*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3 - m0^3*m4)*n0*prfexpden(m0)^5) + ep^5*(n5*prfexpden(m0) - m1*n4*prfexpden(m0)^2 + (m1^2 - m0*m2)*n3*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n2*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3 - m0^3*m4)*n1*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3 + 2*m0^3*m1*m4 - m0^4*m5)*n0*prfexpden(m0)^6); Local result10 = n0*prfexpden(ep)*prfexpden(m0) + (-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^2*(n3*prfexpden(m0) - m1*n2*prfexpden(m0)^2 + (m1^2 - m0*m2)*n1*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n0*prfexpden(m0)^4) + ep^3*(n4*prfexpden(m0) - m1*n3*prfexpden(m0)^2 + (m1^2 - m0*m2)*n2*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n1*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3 - m0^3*m4)*n0*prfexpden(m0)^5) + ep^4*(n5*prfexpden(m0) - m1*n4*prfexpden(m0)^2 + (m1^2 - m0*m2)*n3*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n2*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3 - m0^3*m4)*n1*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3 + 2*m0^3*m1*m4 - m0^4*m5)*n0*prfexpden(m0)^6) + ep^5*(n6*prfexpden(m0) - m1*n5*prfexpden(m0)^2 + (m1^2 - m0*m2)*n4*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n3*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3 - m0^3*m4)*n2*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3 + 2*m0^3*m1*m4 - m0^4*m5)*n1*prfexpden(m0)^6 + (m1^6 - 5*m0*m1^4*m2 + 6*m0^2*m1^2*m2^2 - m0^3*m2^3 + 4*m0^2*m1^3*m3 - 6*m0^3*m1*m2*m3 + m0^4*m3^2 - 3*m0^3*m1^2*m4 + 2*m0^4*m2*m4 + 2*m0^4*m1*m5 - m0^5*m6)*n0*prfexpden(m0)^7); Local result11 = ep*n0*prfexpden(m0) + ep^2*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^3*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^4*(-(m1^3*n0) + 2*m0*m1*m2*n0 - m0^2*m3*n0 + m0*m1^2*n1 - m0^2*m2*n1 - m0^2*m1*n2 + m0^3*n3)*prfexpden(m0)^4 + ep^5*(m1^4*n0 - 3*m0*m1^2*m2*n0 + m0^2*m2^2*n0 + 2*m0^2*m1*m3*n0 - m0^3*m4*n0 - m0*m1^3*n1 + 2*m0^2*m1*m2*n1 - m0^3*m3*n1 + m0^2*m1^2*n2 - m0^3*m2*n2 - m0^3*m1*n3 + m0^4*n4)*prfexpden(m0)^5; Local result12 = n0*prfexpden(m0) + ep*(-(m1*n0) + m0*n1)*prfexpden(m0)^2 + ep^2*(m1^2*n0 - m0*m2*n0 - m0*m1*n1 + m0^2*n2)*prfexpden(m0)^3 + ep^3*(n3*prfexpden(m0) - m1*n2*prfexpden(m0)^2 + (m1^2 - m0*m2)*n1*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n0*prfexpden(m0)^4) + ep^4*(n4*prfexpden(m0) - m1*n3*prfexpden(m0)^2 + (m1^2 - m0*m2)*n2*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n1*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3 - m0^3*m4)*n0*prfexpden(m0)^5) + ep^5*(n5*prfexpden(m0) - m1*n4*prfexpden(m0)^2 + (m1^2 - m0*m2)*n3*prfexpden(m0)^3 + (-m1^3 + 2*m0*m1*m2 - m0^2*m3)*n2*prfexpden(m0)^4 + (m1^4 - 3*m0*m1^2*m2 + m0^2*m2^2 + 2*m0^2*m1*m3 - m0^3*m4)*n1*prfexpden(m0)^5 + (-m1^5 + 4*m0*m1^3*m2 - 3*m0^2*m1*m2^2 - 3*m0^2*m1^2*m3 + 2*m0^3*m2*m3 + 2*m0^3*m1*m4 - m0^4*m5)*n0*prfexpden(m0)^6); Local result13 = n1*prfexpden(m0 + m1) + n0*prfexpden(ep)*prfexpden(m0 + m1) - m2*n0*prfexpden(m0 + m1)^2 + ep*(n2*prfexpden(m0 + m1) - m2*n1*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n0*prfexpden(m0 + m1)^3) + ep^2*(n3*prfexpden(m0 + m1) - m2*n2*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n1*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n0*prfexpden(m0 + m1)^4) + ep^3*(-(m2*n3*prfexpden(m0 + m1)^2) + (m2^2 - m0*m3 - m1*m3)*n2*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n1*prfexpden(m0 + m1)^4 + n0*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4)) + ep^4*((m2^2 - m0*m3 - m1*m3)*n3*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n2*prfexpden(m0 + m1)^4 + n1*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n0*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5)) + ep^5*((-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n3*prfexpden(m0 + m1)^4 + n2*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n1*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5) + n0*prfexpden(m0 + m1)*(-(m3^3*prfexpden(m0 + m1)^3) + 6*m2^2*m3^2*prfexpden(m0 + m1)^4 - 5*m2^4*m3*prfexpden(m0 + m1)^5 + m2^6*prfexpden(m0 + m1)^6)); Local result14 = n2*prfexpden(m0 + m1) + n0*prfexpden(ep)^2*prfexpden(m0 + m1) - m2*n1*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n0*prfexpden(m0 + m1)^3 + prfexpden(ep)*(n1*prfexpden(m0 + m1) - m2*n0*prfexpden(m0 + m1)^2) + ep*(n3*prfexpden(m0 + m1) - m2*n2*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n1*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n0*prfexpden(m0 + m1)^4) + ep^2*(-(m2*n3*prfexpden(m0 + m1)^2) + (m2^2 - m0*m3 - m1*m3)*n2*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n1*prfexpden(m0 + m1)^4 + n0*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4)) + ep^3*((m2^2 - m0*m3 - m1*m3)*n3*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n2*prfexpden(m0 + m1)^4 + n1*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n0*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5)) + ep^4*((-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n3*prfexpden(m0 + m1)^4 + n2*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n1*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5) + n0*prfexpden(m0 + m1)*(-(m3^3*prfexpden(m0 + m1)^3) + 6*m2^2*m3^2*prfexpden(m0 + m1)^4 - 5*m2^4*m3*prfexpden(m0 + m1)^5 + m2^6*prfexpden(m0 + m1)^6)) + ep^5*(n3*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n2*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5) + n1*prfexpden(m0 + m1)*(-(m3^3*prfexpden(m0 + m1)^3) + 6*m2^2*m3^2*prfexpden(m0 + m1)^4 - 5*m2^4*m3*prfexpden(m0 + m1)^5 + m2^6*prfexpden(m0 + m1)^6) + n0*prfexpden(m0 + m1)*(4*m2*m3^3*prfexpden(m0 + m1)^4 - 10*m2^3*m3^2*prfexpden(m0 + m1)^5 + 6*m2^5*m3*prfexpden(m0 + m1)^6 - m2^7*prfexpden(m0 + m1)^7)); Local result15 = n0*prfexpden(m0 + m1) + ep*(n1*prfexpden(m0 + m1) - m2*n0*prfexpden(m0 + m1)^2) + ep^2*(n2*prfexpden(m0 + m1) - m2*n1*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n0*prfexpden(m0 + m1)^3) + ep^3*(n3*prfexpden(m0 + m1) - m2*n2*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n1*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n0*prfexpden(m0 + m1)^4) + ep^4*(-(m2*n3*prfexpden(m0 + m1)^2) + (m2^2 - m0*m3 - m1*m3)*n2*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n1*prfexpden(m0 + m1)^4 + n0*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4)) + ep^5*((m2^2 - m0*m3 - m1*m3)*n3*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n2*prfexpden(m0 + m1)^4 + n1*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n0*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5)); Local result16 = n1*prfexpden(m0 + m1) + n0*prfexpden(ep)*prfexpden(m0 + m1) - m2*n0*prfexpden(m0 + m1)^2 + ep*(n2*prfexpden(m0 + m1) - m2*n1*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n0*prfexpden(m0 + m1)^3) + ep^2*(n3*prfexpden(m0 + m1) - m2*n2*prfexpden(m0 + m1)^2 + (m2^2 - m0*m3 - m1*m3)*n1*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n0*prfexpden(m0 + m1)^4) + ep^3*(-(m2*n3*prfexpden(m0 + m1)^2) + (m2^2 - m0*m3 - m1*m3)*n2*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n1*prfexpden(m0 + m1)^4 + n0*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4)) + ep^4*((m2^2 - m0*m3 - m1*m3)*n3*prfexpden(m0 + m1)^3 + (-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n2*prfexpden(m0 + m1)^4 + n1*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n0*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5)) + ep^5*((-m2^3 + 2*m0*m2*m3 + 2*m1*m2*m3)*n3*prfexpden(m0 + m1)^4 + n2*prfexpden(m0 + m1)*(m3^2*prfexpden(m0 + m1)^2 - 3*m2^2*m3*prfexpden(m0 + m1)^3 + m2^4*prfexpden(m0 + m1)^4) + n1*prfexpden(m0 + m1)*(-3*m2*m3^2*prfexpden(m0 + m1)^3 + 4*m2^3*m3*prfexpden(m0 + m1)^4 - m2^5*prfexpden(m0 + m1)^5) + n0*prfexpden(m0 + m1)*(-(m3^3*prfexpden(m0 + m1)^3) + 6*m2^2*m3^2*prfexpden(m0 + m1)^4 - 5*m2^4*m3*prfexpden(m0 + m1)^5 + m2^6*prfexpden(m0 + m1)^6)); Local result17 = 1 - ep + ep^2 - ep^3 + ep^4 - ep^5; Local result18 = -1 + ep - ep^2 + ep^3 - ep^4 + ep^5 + prfexpden(ep) - prfexpden(ep)^2 + prfexpden(ep)^3 - prfexpden(ep)^4 + prfexpden(ep)^5; Local result19 = -32 + 64*ep - 128*ep^2 + 256*ep^3 - 512*ep^4 + 1024*ep^5 + 16*prfexpden(ep) - 8*prfexpden(ep)^2 + 4*prfexpden(ep)^3 - 2*prfexpden(ep)^4 + prfexpden(ep)^5; Local result20 = 1; Local result21 = 0; Local result22 = ep^-1; Local result23 = 1; Local result24 = 0; Local result25 = 0; Local result26 = 0; Local result27 = 0; Local result28 = prfexpden(m0 + m1) - ep*prfexpden(m0 + m1) + ep^2*prfexpden(m0 + m1) - ep^3*prfexpden(m0 + m1) + ep^4*prfexpden(m0 + m1) - ep^5*prfexpden(m0 + m1); .sort InExpression result1,...,result`NUMTESTS'; Identify prfexpden(ep) = 1/ep; If (Count(ep,1) > `EXPDEPTH') Discard; EndInExpression; .sort PolyRatFun prf; Drop; * Compare #do i = 1,`NUMTESTS' Local diff`i' = test`i' - result`i'; #enddo * Normalize notation between FORM and Mathematica results Identify prfexpden(n?) = prf(1,n); #do i = 0,10 Identify n`i' = prf(n`i',1); Identify m`i' = prf(m`i',1); #enddo .sort #do i = 1,`NUMTESTS' #if `ZERO_diff`i'' == 0 #message Error in test`i' EXPDEPTH `EXPDEPTH' #terminate #endif #enddo #enddo .end # This causes a strange valgrind leak error, see #507 #pend_if valgrind? assert succeeded? *--#] jodavies_denexpand : *--#[ jodavies_prf_1 : #- Off Statistics; Off ThreadStats; * PolyRatFun-heavy test based on mbox1l reduction from calc. * LiteRed propagators defined as {M`j'^2-sp[p1+q1+q2], M`j'^2-sp[p1], M`j'^2-sp[p1+q2], M`j'^2-sp[p1+q1+q2+q3]}, * with SPs sp[q1,q1]=0;sp[q2,q2]=0;sp[q3,q3]=q33;sp[q1,q2]=q12;sp[q1,q3]=q13;sp[q2,q3]=q23; * q1 --------------- q3 * | 1 | * 3| |4 * | 2 | * q2 --------------- -q1-q2-q3 * Procedures cut from lrTopoTools.h #procedure lrttMergeIndices(NAME) Repeat; Identify `NAME'(?a)*`NAME'(?b) = `NAME'(L,?a,L,?b); Repeat Identify `NAME'(?a,L,n1?,?b,L,n2?,?c) = `NAME'(?a,n1+n2,L,?b,L,?c); Identify `NAME'(?a,L,L) = `NAME'(?a); EndRepeat; #endprocedure #procedure lrttKin2Prf #do i = 1,`NUMEXTMOM' #do j = `i',`NUMEXTMOM' Identify q`i'`j'^n1? = prf(q`i'`j'^n1,1); #enddo #enddo #endprocedure #define j "1" #define NUMEXTMOM "3" * Without this mode, MaxTermSize requirement gets out of hand very quickly #define MBOX1Lq33EQq44 "1" Symbol L,n1,n2,n3,n4; Symbol ep,q11,q12,q13,q22,q23,q33,M`j'; CFunction prf,tmpprf; CFunction mbox1l,mbox1lm`j'm; * 3,2,2,2 needs a 200K MaxTermSize. Explodes extremely quickly for any harder integrals. Local test = mbox1l(2,1,1,1); .sort PolyRatFun prf; #do red = 1,1 #message mbox1l: reduction loop... Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg0_,n3?neg_,n4?{,>1}) = mbox1l(n1,-1+n2,2+n3,-1+n4)*prf(-q13^3-n3*q13^3-q13^2*q23-n3*q13^2*q23,q13^2*q33-n4*q13^2*q33+2*q13*q23*q33-2*n4*q13*q23*q33+q23^2*q33-n4*q23^2*q33-2*q12*q33^2+2*n4*q12*q33^2)+mbox1l(1+n1,n2,1+n3,-2+n4)*prf(2*M`j'^2*n1*q13+2*M`j'^2*n1*q33-2*n1*q13*q33-n1*q33^2,-2*M`j'^2*q33+2*M`j'^2*n4*q33)+mbox1l(1+n1,n2,1+n3,-1+n4)*prf(6*M`j'^2*n1*q13+4*M`j'^2*n1*q33-2*n1*q13*q33-n1*q33^2,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(2*n2*q12*q13^2+2*n2*q13^3+2*n2*q12*q13*q23+4*n2*q13^2*q23+2*n2*q13*q23^2-2*n2*q12^2*q33-3*n2*q12*q13*q33+n2*q13^2*q33-n2*q12*q23*q33+2*n2*q13*q23*q33+n2*q23^2*q33-2*n2*q12*q33^2,q13^2*q33-n4*q13^2*q33+2*q13*q23*q33-2*n4*q13*q23*q33+q23^2*q33-n4*q23^2*q33-2*q12*q33^2+2*n4*q12*q33^2)+mbox1l(-1+n1,n2,2+n3,-1+n4)*prf(q12*q13^2+n3*q12*q13^2+2*q13^3+2*n3*q13^3+q12*q13*q23+n3*q12*q13*q23+3*q13^2*q23+3*n3*q13^2*q23+q13*q23^2+n3*q13*q23^2-3*q12*q13*q33-3*n3*q12*q13*q33+q13^2*q33+n3*q13^2*q33+q12*q23*q33+n3*q12*q23*q33+2*q13*q23*q33+2*n3*q13*q23*q33+q23^2*q33+n3*q23^2*q33-2*q12*q33^2-2*n3*q12*q33^2,q13^2*q33-n4*q13^2*q33+2*q13*q23*q33-2*n4*q13*q23*q33+q23^2*q33-n4*q23^2*q33-2*q12*q33^2+2*n4*q12*q33^2)+mbox1l(n1,1+n2,1+n3,-2+n4)*prf(-4*M`j'^2*n2*q12*q13^2-2*M`j'^2*n2*q13^3-4*M`j'^2*n2*q12*q13*q23-4*M`j'^2*n2*q13^2*q23-2*M`j'^2*n2*q13*q23^2+4*M`j'^2*n2*q12^2*q33+4*M`j'^2*n2*q12*q13*q33-2*M`j'^2*n2*q13^2*q33+2*n2*q13^3*q33-4*M`j'^2*n2*q13*q23*q33+4*n2*q13^2*q23*q33-2*M`j'^2*n2*q23^2*q33+2*n2*q13*q23^2*q33+4*M`j'^2*n2*q12*q33^2-4*n2*q12*q13*q33^2+n2*q13^2*q33^2+2*n2*q13*q23*q33^2+n2*q23^2*q33^2-2*n2*q12*q33^3,2*M`j'^2*q13^2*q33-2*M`j'^2*n4*q13^2*q33+4*M`j'^2*q13*q23*q33-4*M`j'^2*n4*q13*q23*q33+2*M`j'^2*q23^2*q33-2*M`j'^2*n4*q23^2*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n4*q12*q33^2)+mbox1l(n1,n2,2+n3,-2+n4)*prf(-2*M`j'^2*q12*q13^2-2*M`j'^2*n3*q12*q13^2-2*M`j'^2*q13^3-2*M`j'^2*n3*q13^3-2*M`j'^2*q12*q13*q23-2*M`j'^2*n3*q12*q13*q23-4*M`j'^2*q13^2*q23-4*M`j'^2*n3*q13^2*q23-2*M`j'^2*q13*q23^2-2*M`j'^2*n3*q13*q23^2+4*M`j'^2*q12*q13*q33+4*M`j'^2*n3*q12*q13*q33-2*M`j'^2*q13^2*q33-2*M`j'^2*n3*q13^2*q33+2*q13^3*q33+2*n3*q13^3*q33-4*M`j'^2*q13*q23*q33-4*M`j'^2*n3*q13*q23*q33+4*q13^2*q23*q33+4*n3*q13^2*q23*q33-2*M`j'^2*q23^2*q33-2*M`j'^2*n3*q23^2*q33+2*q13*q23^2*q33+2*n3*q13*q23^2*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n3*q12*q33^2-4*q12*q13*q33^2-4*n3*q12*q13*q33^2+q13^2*q33^2+n3*q13^2*q33^2+2*q13*q23*q33^2+2*n3*q13*q23*q33^2+q23^2*q33^2+n3*q23^2*q33^2-2*q12*q33^3-2*n3*q12*q33^3,2*M`j'^2*q13^2*q33-2*M`j'^2*n4*q13^2*q33+4*M`j'^2*q13*q23*q33-4*M`j'^2*n4*q13*q23*q33+2*M`j'^2*q23^2*q33-2*M`j'^2*n4*q23^2*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n4*q12*q33^2)+mbox1l(n1,n2,1+n3,-1+n4)*(tmpprf(ep,1)*prf(4*q13^3*q33+8*q13^2*q23*q33+4*q13*q23^2*q33-8*q12*q13*q33^2+2*q13^2*q33^2+4*q13*q23*q33^2+2*q23^2*q33^2-4*q12*q33^3,2*M`j'^2*q13^2*q33-2*M`j'^2*n4*q13^2*q33+4*M`j'^2*q13*q23*q33-4*M`j'^2*n4*q13*q23*q33+2*M`j'^2*q23^2*q33-2*M`j'^2*n4*q23^2*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n4*q12*q33^2)+prf(2*M`j'^2*n1*q13^3-2*M`j'^2*n2*q13^3+4*M`j'^2*n1*q13^2*q23-4*M`j'^2*n2*q13^2*q23+2*M`j'^2*n1*q13*q23^2-2*M`j'^2*n2*q13*q23^2+2*M`j'^2*q12*q13*q33-4*M`j'^2*n1*q12*q13*q33+2*M`j'^2*n2*q12*q13*q33+2*M`j'^2*n3*q12*q13*q33+2*M`j'^2*q13^2*q33+2*M`j'^2*n1*q13^2*q33-2*M`j'^2*n4*q13^2*q33-10*q13^3*q33+2*n1*q13^3*q33+2*n2*q13^3*q33+2*n3*q13^3*q33+4*n4*q13^3*q33-2*M`j'^2*q12*q23*q33+2*M`j'^2*n2*q12*q23*q33-2*M`j'^2*n3*q12*q23*q33+4*M`j'^2*q13*q23*q33+4*M`j'^2*n1*q13*q23*q33-4*M`j'^2*n4*q13*q23*q33-20*q13^2*q23*q33+4*n1*q13^2*q23*q33+4*n2*q13^2*q23*q33+4*n3*q13^2*q23*q33+8*n4*q13^2*q23*q33+2*M`j'^2*q23^2*q33+2*M`j'^2*n1*q23^2*q33-2*M`j'^2*n4*q23^2*q33-10*q13*q23^2*q33+2*n1*q13*q23^2*q33+2*n2*q13*q23^2*q33+2*n3*q13*q23^2*q33+4*n4*q13*q23^2*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n1*q12*q33^2+4*M`j'^2*n4*q12*q33^2+20*q12*q13*q33^2-4*n1*q12*q13*q33^2-4*n2*q12*q13*q33^2-4*n3*q12*q13*q33^2-8*n4*q12*q13*q33^2-5*q13^2*q33^2+n1*q13^2*q33^2+n2*q13^2*q33^2+n3*q13^2*q33^2+2*n4*q13^2*q33^2-10*q13*q23*q33^2+2*n1*q13*q23*q33^2+2*n2*q13*q23*q33^2+2*n3*q13*q23*q33^2+4*n4*q13*q23*q33^2-5*q23^2*q33^2+n1*q23^2*q33^2+n2*q23^2*q33^2+n3*q23^2*q33^2+2*n4*q23^2*q33^2+10*q12*q33^3-2*n1*q12*q33^3-2*n2*q12*q33^3-2*n3*q12*q33^3-4*n4*q12*q33^3,2*M`j'^2*q13^2*q33-2*M`j'^2*n4*q13^2*q33+4*M`j'^2*q13*q23*q33-4*M`j'^2*n4*q13*q23*q33+2*M`j'^2*q23^2*q33-2*M`j'^2*n4*q23^2*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n4*q12*q33^2))+mbox1l(n1,1+n2,1+n3,-1+n4)*prf(-4*M`j'^2*n2*q12*q13^3-4*M`j'^2*n2*q13^4-8*M`j'^2*n2*q12*q13^2*q23-12*M`j'^2*n2*q13^3*q23-4*M`j'^2*n2*q12*q13*q23^2-12*M`j'^2*n2*q13^2*q23^2-4*M`j'^2*n2*q13*q23^3+4*M`j'^2*n2*q12^2*q13*q33+4*M`j'^2*n2*q12*q13^2*q33-10*M`j'^2*n2*q13^3*q33+4*n2*q12*q13^3*q33+4*n2*q13^4*q33+4*M`j'^2*n2*q12^2*q23*q33+4*M`j'^2*n2*q12*q13*q23*q33-24*M`j'^2*n2*q13^2*q23*q33+8*n2*q12*q13^2*q23*q33+12*n2*q13^3*q23*q33-18*M`j'^2*n2*q13*q23^2*q33+4*n2*q12*q13*q23^2*q33+12*n2*q13^2*q23^2*q33-4*M`j'^2*n2*q23^3*q33+4*n2*q13*q23^3*q33+4*M`j'^2*n2*q12^2*q33^2+20*M`j'^2*n2*q12*q13*q33^2-8*n2*q12^2*q13*q33^2-4*M`j'^2*n2*q13^2*q33^2-6*n2*q12*q13^2*q33^2+4*n2*q13^3*q33^2+8*M`j'^2*n2*q12*q23*q33^2-8*M`j'^2*n2*q13*q23*q33^2-4*n2*q12*q13*q23*q33^2+10*n2*q13^2*q23*q33^2-4*M`j'^2*n2*q23^2*q33^2+2*n2*q12*q23^2*q33^2+8*n2*q13*q23^2*q33^2+2*n2*q23^3*q33^2+8*M`j'^2*n2*q12*q33^3-4*n2*q12^2*q33^3-8*n2*q12*q13*q33^3+n2*q13^2*q33^3-4*n2*q12*q23*q33^3+2*n2*q13*q23*q33^3+n2*q23^2*q33^3-2*n2*q12*q33^4,2*M`j'^2*q13^2*q33-2*M`j'^2*n4*q13^2*q33+4*M`j'^2*q13*q23*q33-4*M`j'^2*n4*q13*q23*q33+2*M`j'^2*q23^2*q33-2*M`j'^2*n4*q23^2*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n4*q12*q33^2)+mbox1l(n1,n2,2+n3,-1+n4)*prf(-4*M`j'^2*q12*q13^3-4*M`j'^2*n3*q12*q13^3-4*M`j'^2*q13^4-4*M`j'^2*n3*q13^4-4*M`j'^2*q12*q13^2*q23-4*M`j'^2*n3*q12*q13^2*q23-8*M`j'^2*q13^3*q23-8*M`j'^2*n3*q13^3*q23-4*M`j'^2*q13^2*q23^2-4*M`j'^2*n3*q13^2*q23^2+6*M`j'^2*q12*q13^2*q33+6*M`j'^2*n3*q12*q13^2*q33-10*M`j'^2*q13^3*q33-10*M`j'^2*n3*q13^3*q33+4*q13^4*q33+4*n3*q13^4*q33-2*M`j'^2*q12*q13*q23*q33-2*M`j'^2*n3*q12*q13*q23*q33-20*M`j'^2*q13^2*q23*q33-20*M`j'^2*n3*q13^2*q23*q33+8*q13^3*q23*q33+8*n3*q13^3*q23*q33-10*M`j'^2*q13*q23^2*q33-10*M`j'^2*n3*q13*q23^2*q33+4*q13^2*q23^2*q33+4*n3*q13^2*q23^2*q33+20*M`j'^2*q12*q13*q33^2+20*M`j'^2*n3*q12*q13*q33^2-4*M`j'^2*q13^2*q33^2-4*M`j'^2*n3*q13^2*q33^2-8*q12*q13^2*q33^2-8*n3*q12*q13^2*q33^2+4*q13^3*q33^2+4*n3*q13^3*q33^2-8*M`j'^2*q13*q23*q33^2-8*M`j'^2*n3*q13*q23*q33^2+8*q13^2*q23*q33^2+8*n3*q13^2*q23*q33^2-4*M`j'^2*q23^2*q33^2-4*M`j'^2*n3*q23^2*q33^2+4*q13*q23^2*q33^2+4*n3*q13*q23^2*q33^2+8*M`j'^2*q12*q33^3+8*M`j'^2*n3*q12*q33^3-8*q12*q13*q33^3-8*n3*q12*q13*q33^3+q13^2*q33^3+n3*q13^2*q33^3+2*q13*q23*q33^3+2*n3*q13*q23*q33^3+q23^2*q33^3+n3*q23^2*q33^3-2*q12*q33^4-2*n3*q12*q33^4,2*M`j'^2*q13^2*q33-2*M`j'^2*n4*q13^2*q33+4*M`j'^2*q13*q23*q33-4*M`j'^2*n4*q13*q23*q33+2*M`j'^2*q23^2*q33-2*M`j'^2*n4*q23^2*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n4*q12*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg_,n3?neg0_,n4?{,>1}) = mbox1l(n1,n2,1+n3,-1+n4)*prf(n3*q13,-q33+n4*q33)+mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-2*q12-2*n2*q12-2*q13-2*n2*q13-2*q23-2*n2*q23-q33-n2*q33,-q33+n4*q33)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(-(n3*q12)-2*n3*q13-n3*q23-n3*q33,-q33+n4*q33)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(2*M`j'^2*n1*q13+2*M`j'^2*n1*q23+2*M`j'^2*n1*q33-2*n1*q12*q33-2*n1*q13*q33-2*n1*q23*q33-n1*q33^2,-2*M`j'^2*q33+2*M`j'^2*n4*q33)+mbox1l(1+n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n1*q12+6*M`j'^2*n1*q13+6*M`j'^2*n1*q23+4*M`j'^2*n1*q33-2*n1*q12*q33-2*n1*q13*q33-2*n1*q23*q33-n1*q33^2,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(n1,2+n2,n3,-2+n4)*prf(4*M`j'^2*q12+4*M`j'^2*n2*q12+2*M`j'^2*q13+2*M`j'^2*n2*q13+2*M`j'^2*q23+2*M`j'^2*n2*q23+2*M`j'^2*q33+2*M`j'^2*n2*q33-2*q12*q33-2*n2*q12*q33-2*q13*q33-2*n2*q13*q33-2*q23*q33-2*n2*q23*q33-q33^2-n2*q33^2,-2*M`j'^2*q33+2*M`j'^2*n4*q33)+mbox1l(n1,1+n2,1+n3,-2+n4)*prf(2*M`j'^2*n3*q12+2*M`j'^2*n3*q13+2*M`j'^2*n3*q23+2*M`j'^2*n3*q33-2*n3*q12*q33-2*n3*q13*q33-2*n3*q23*q33-n3*q33^2,-2*M`j'^2*q33+2*M`j'^2*n4*q33)+mbox1l(n1,1+n2,n3,-1+n4)*(tmpprf(ep,1)*prf(-4*q12*q33-4*q13*q33-4*q23*q33-2*q33^2,-2*M`j'^2*q33+2*M`j'^2*n4*q33)+prf(2*M`j'^2*q13-2*M`j'^2*n1*q13+2*M`j'^2*n2*q13+2*M`j'^2*q23-2*M`j'^2*n1*q23+2*M`j'^2*n2*q23-2*M`j'^2*q33-2*M`j'^2*n1*q33+2*M`j'^2*n4*q33+10*q12*q33-2*n1*q12*q33-2*n2*q12*q33-2*n3*q12*q33-4*n4*q12*q33+10*q13*q33-2*n1*q13*q33-2*n2*q13*q33-2*n3*q13*q33-4*n4*q13*q33+10*q23*q33-2*n1*q23*q33-2*n2*q23*q33-2*n3*q23*q33-4*n4*q23*q33+5*q33^2-n1*q33^2-n2*q33^2-n3*q33^2-2*n4*q33^2,-2*M`j'^2*q33+2*M`j'^2*n4*q33))+mbox1l(n1,2+n2,n3,-1+n4)*prf(4*M`j'^2*q12*q13+4*M`j'^2*n2*q12*q13+4*M`j'^2*q13^2+4*M`j'^2*n2*q13^2+4*M`j'^2*q12*q23+4*M`j'^2*n2*q12*q23+8*M`j'^2*q13*q23+8*M`j'^2*n2*q13*q23+4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2+8*M`j'^2*q12*q33+8*M`j'^2*n2*q12*q33-4*q12^2*q33-4*n2*q12^2*q33+10*M`j'^2*q13*q33+10*M`j'^2*n2*q13*q33-8*q12*q13*q33-8*n2*q12*q13*q33-4*q13^2*q33-4*n2*q13^2*q33+10*M`j'^2*q23*q33+10*M`j'^2*n2*q23*q33-8*q12*q23*q33-8*n2*q12*q23*q33-8*q13*q23*q33-8*n2*q13*q23*q33-4*q23^2*q33-4*n2*q23^2*q33+4*M`j'^2*q33^2+4*M`j'^2*n2*q33^2-4*q12*q33^2-4*n2*q12*q33^2-4*q13*q33^2-4*n2*q13*q33^2-4*q23*q33^2-4*n2*q23*q33^2-q33^3-n2*q33^3,-2*M`j'^2*q33+2*M`j'^2*n4*q33)+mbox1l(n1,1+n2,1+n3,-1+n4)*prf(4*M`j'^2*n3*q12*q13+4*M`j'^2*n3*q13^2+4*M`j'^2*n3*q13*q23+6*M`j'^2*n3*q12*q33+10*M`j'^2*n3*q13*q33-4*n3*q12*q13*q33-4*n3*q13^2*q33+6*M`j'^2*n3*q23*q33-4*n3*q13*q23*q33+4*M`j'^2*n3*q33^2-2*n3*q12*q33^2-4*n3*q13*q33^2-2*n3*q23*q33^2-n3*q33^3,-2*M`j'^2*q33+2*M`j'^2*n4*q33); Identify,ifmatch->jump mbox1l(n1?neg_,n2?neg0_,n3?neg0_,n4?{,>1}) = mbox1l(n1,1+n2,n3,-1+n4)*prf(-n2,-1+n4)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-n3,-1+n4)+mbox1l(2+n1,n2,n3,-2+n4)*prf(2*M`j'^2+2*M`j'^2*n1-q33-n1*q33,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(2*M`j'^2*n2-n2*q33,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(1+n1,n2,1+n3,-2+n4)*prf(2*M`j'^2*n3-n3*q33,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(1+n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(-q33,-M`j'^2+M`j'^2*n4)+prf(-4*M`j'^2-2*M`j'^2*n1+2*M`j'^2*n4+5*q33-n1*q33-n2*q33-n3*q33-2*n4*q33,-2*M`j'^2+2*M`j'^2*n4))+mbox1l(2+n1,n2,n3,-1+n4)*prf(4*M`j'^2*q33+4*M`j'^2*n1*q33-q33^2-n1*q33^2,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(1+n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n2*q13+4*M`j'^2*n2*q23+4*M`j'^2*n2*q33-2*n2*q12*q33-2*n2*q13*q33-2*n2*q23*q33-n2*q33^2,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(1+n1,n2,1+n3,-1+n4)*prf(4*M`j'^2*n3*q13+4*M`j'^2*n3*q33-2*n3*q13*q33-n3*q33^2,-2*M`j'^2+2*M`j'^2*n4); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg0_,n3?neg0_,n4?{,>1}) = mbox1l(1+n1,n2,n3,-2+n4)*prf(n1,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(n1,1+n2,n3,-2+n4)*prf(n2,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(n1,n2,1+n3,-2+n4)*prf(n3,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(1,-M`j'^2+M`j'^2*n4)+prf(-6+n1+n2+n3+2*n4,-2*M`j'^2+2*M`j'^2*n4))+mbox1l(1+n1,n2,n3,-1+n4)*prf(-2*M`j'^2*n1+n1*q33,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(n1,1+n2,n3,-1+n4)*prf(-2*M`j'^2*n2+2*n2*q12+2*n2*q13+2*n2*q23+n2*q33,-2*M`j'^2+2*M`j'^2*n4)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3+2*n3*q13+n3*q33,-2*M`j'^2+2*M`j'^2*n4); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg0_,n3?neg_,n4?pos_) = mbox1l(n1,n2,1+n3,n4)*prf(-q13,1)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-q13,q33)+mbox1l(-1+n1,n2,2+n3,-1+n4)*prf(q12*q13^2+n3*q12*q13^2+q13^3+n3*q13^3+q12*q13*q23+n3*q12*q13*q23+2*q13^2*q23+2*n3*q13^2*q23+q13*q23^2+n3*q13*q23^2-q12*q13*q33-n3*q12*q13*q33,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(q13^3+n3*q13^3+q13^2*q23+n3*q13^2*q23+q13^2*q33+n3*q13^2*q33,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(2*n2*q12*q13^2+n2*q13^3+2*n2*q12*q13*q23+2*n2*q13^2*q23+n2*q13*q23^2-2*n2*q12^2*q33-n2*q12*q13*q33-n2*q12*q23*q33,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-2+n1,1+n2,1+n3,n4)*prf(-2*n2*q12*q13^2-2*n2*q13^3-2*n2*q12*q13*q23-4*n2*q13^2*q23-2*n2*q13*q23^2+2*n2*q12^2*q33+2*n2*q12*q13*q33-n2*q13^2*q33+2*n2*q12*q23*q33-n2*q13*q23*q33+n2*q12*q33^2,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,n2,1+n3,n4)*prf(q13^3-n1*q13^3+n2*q13^3+2*q13^2*q23-2*n1*q13^2*q23+2*n2*q13^2*q23+q13*q23^2-n1*q13*q23^2+n2*q13*q23^2-3*q12*q13*q33+2*n1*q12*q13*q33-n2*q12*q13*q33-n3*q12*q13*q33+q13^2*q33-n1*q13^2*q33+n2*q13^2*q33+q12*q23*q33-n2*q12*q23*q33+n3*q12*q23*q33+3*q13*q23*q33-2*n1*q13*q23*q33+n2*q13*q23*q33+n3*q13*q23*q33+2*q23^2*q33-n1*q23^2*q33+n3*q23^2*q33-3*q12*q33^2+2*n1*q12*q33^2-n2*q12*q33^2-n3*q12*q33^2,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-2+n1,n2,2+n3,n4)*prf(-(q12*q13^2)-n3*q12*q13^2-2*q13^3-2*n3*q13^3-q12*q13*q23-n3*q12*q13*q23-3*q13^2*q23-3*n3*q13^2*q23-q13*q23^2-n3*q13*q23^2+2*q12*q13*q33+2*n3*q12*q13*q33-q13^2*q33-n3*q13^2*q33-q12*q23*q33-n3*q12*q23*q33-q13*q23*q33-n3*q13*q23*q33-q23^2*q33-n3*q23^2*q33+q12*q33^2+n3*q12*q33^2,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,n2,2+n3,n4)*prf(2*q12*q13^3+2*n3*q12*q13^3+2*q13^4+2*n3*q13^4+2*q12*q13^2*q23+2*n3*q12*q13^2*q23+4*q13^3*q23+4*n3*q13^3*q23+2*q13^2*q23^2+2*n3*q13^2*q23^2-q12*q13^2*q33-n3*q12*q13^2*q33+q13^3*q33+n3*q13^3*q33+q12*q13*q23*q33+n3*q12*q13*q23*q33+2*q13^2*q23*q33+2*n3*q13^2*q23*q33+q13*q23^2*q33+n3*q13*q23^2*q33-q12*q13*q33^2-n3*q12*q13*q33^2,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,1+n2,1+n3,n4)*prf(2*n2*q12*q13^3+2*n2*q13^4+4*n2*q12*q13^2*q23+6*n2*q13^3*q23+2*n2*q12*q13*q23^2+6*n2*q13^2*q23^2+2*n2*q13*q23^3-2*n2*q12^2*q13*q33-2*n2*q12*q13^2*q33+n2*q13^3*q33-2*n2*q12^2*q23*q33-4*n2*q12*q13*q23*q33+2*n2*q13^2*q23*q33-2*n2*q12*q23^2*q33+n2*q13*q23^2*q33-n2*q12*q13*q33^2-n2*q12*q23*q33^2,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg_,n3?neg0_,n4?pos_) = mbox1l(n1,1+n2,n3,-1+n4)*prf(-q13-q23,q33)+mbox1l(n1,1+n2,n3,n4)*prf(-2*q12-q13-q23,1)+mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-2*q12-2*n2*q12-q13-n2*q13-q23-n2*q23,-q33+n1*q33)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(-(n3*q12)-n3*q13-n3*q23,-q33+n1*q33)+mbox1l(-1+n1,1+n2,n3,n4)*prf(-2*q13+n1*q13-n2*q13-2*q23+n1*q23-n2*q23-2*q33+n1*q33-n2*q33,-q33+n1*q33)+mbox1l(-2+n1,2+n2,n3,n4)*prf(2*q12+2*n2*q12+2*q13+2*n2*q13+2*q23+2*n2*q23+q33+n2*q33,-q33+n1*q33)+mbox1l(-1+n1,n2,1+n3,n4)*prf(-(n3*q13)-n3*q33,-q33+n1*q33)+mbox1l(-2+n1,1+n2,1+n3,n4)*prf(n3*q12+2*n3*q13+n3*q23+n3*q33,-q33+n1*q33)+mbox1l(-1+n1,2+n2,n3,n4)*prf(-2*q12*q13-2*n2*q12*q13-2*q13^2-2*n2*q13^2-2*q12*q23-2*n2*q12*q23-4*q13*q23-4*n2*q13*q23-2*q23^2-2*n2*q23^2-q13*q33-n2*q13*q33-q23*q33-n2*q23*q33,-q33+n1*q33)+mbox1l(-1+n1,1+n2,1+n3,n4)*prf(-2*n3*q12*q13-2*n3*q13^2-2*n3*q13*q23-n3*q12*q33-n3*q13*q33-n3*q23*q33,-q33+n1*q33); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg0_,n3?neg_,n4?pos_) = mbox1l(n1,-1+n2,2+n3,-1+n4)*prf(q12*q13+n3*q12*q13,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,-2+n2,2+n3,n4)*prf(q13^2+n3*q13^2,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-(q12*q13)+q12*q23,-q13^2-2*q13*q23-q23^2+2*q12*q33)+mbox1l(-1+n1,n2,1+n3,n4)*prf(-(q12*q13)+q12*q23+q13*q23+q23^2-q12*q33,q13^2+2*q13*q23+q23^2-2*q12*q33)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(-(q12*q13)-n3*q12*q13+q13*q23+n3*q13*q23-q12*q33-n3*q12*q33,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,-1+n2,1+n3,n4)*prf(-2*q13^2+n2*q13^2-n3*q13^2-2*q13*q23+n2*q13*q23-n3*q13*q23+2*q12*q33-n2*q12*q33+n3*q12*q33,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,-1+n2,2+n3,n4)*prf(2*q12*q13^2+2*n3*q12*q13^2+q12*q13*q33+n3*q12*q13*q33,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,n2,1+n3,n4)*prf(-2*q12*q13^2-2*q12*q13*q23+2*q12^2*q33-q12*q13*q33+q12*q23*q33,-q13^2-2*q13*q23-q23^2+2*q12*q33); Identify,ifmatch->jump mbox1l(n1?neg_,0,0,1) = tmpprf(1,-2+2*ep+n1)*mbox1l(1+n1,0,0,0)*prf(-n1,1)+mbox1l(1+n1,0,0,1)*(tmpprf(ep,-2+2*ep+n1)*prf(-2*q33,1)+tmpprf(1,-2+2*ep+n1)*prf(q33-2*n1*q33,1))+tmpprf(1,-2+2*ep+n1)*mbox1l(2+n1,0,0,0)*prf(2*M`j'^2+2*M`j'^2*n1-q33-n1*q33,1)+tmpprf(1,-2+2*ep+n1)*mbox1l(2+n1,0,0,1)*prf(4*M`j'^2*q33+4*M`j'^2*n1*q33-q33^2-n1*q33^2,1); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg_,n3?pos_,n4?{,>1}) = mbox1l(1+n1,1+n2,n3,-2+n4)*prf(-2*M`j'^2*n1*q12-2*M`j'^2*n1*q23,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,1+n3,-2+n4)*prf(-2*M`j'^2*n3*q12-2*M`j'^2*n3*q23,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(1+n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n1*q12*q13+4*M`j'^2*n1*q13*q23,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-q12^2-n2*q12^2-2*q12*q23-2*n2*q12*q23-q23^2-n2*q23^2,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(n1,2+n2,n3,-2+n4)*prf(-4*M`j'^2*q12^2-4*M`j'^2*n2*q12^2+2*M`j'^2*q12*q13+2*M`j'^2*n2*q12*q13+2*q12^2*q13+2*n2*q12^2*q13-4*M`j'^2*q12*q23-4*M`j'^2*n2*q12*q23+2*M`j'^2*q13*q23+2*M`j'^2*n2*q13*q23+2*q12*q13*q23+2*n2*q12*q13*q23+q12^2*q33+n2*q12^2*q33+q12*q23*q33+n2*q12*q23*q33,8*M`j'^2*q13^2-8*M`j'^2*n4*q13^2-4*q13^3+4*n4*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n4*q13*q33-4*q13^2*q33+4*n4*q13^2*q33-q13*q33^2+n4*q13*q33^2)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-6*M`j'^2*q12-8*M`j'^2*q13+4*q12*q13+4*q13^2-6*M`j'^2*q23+4*q13*q23-4*M`j'^2*q33+2*q12*q33+4*q13*q33+2*q23*q33+q33^2,-8*M`j'^2*q13+4*q13^2-4*M`j'^2*q33+4*q13*q33+q33^2)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(-6*M`j'^2*n1*q12*q13+4*n1*q12*q13^2+2*M`j'^2*n1*q13*q23-4*M`j'^2*n1*q12*q33+4*n1*q12*q13*q33+n1*q12*q33^2,8*M`j'^2*q13^2-8*M`j'^2*n4*q13^2-4*q13^3+4*n4*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n4*q13*q33-4*q13^2*q33+4*n4*q13^2*q33-q13*q33^2+n4*q13*q33^2)+mbox1l(n1,2+n2,-1+n3,-1+n4)*prf(6*M`j'^2*q12*q13+6*M`j'^2*n2*q12*q13-2*q12*q13^2-2*n2*q12*q13^2-4*M`j'^2*q12*q23-4*M`j'^2*n2*q12*q23-2*M`j'^2*q13*q23-2*M`j'^2*n2*q13*q23+2*q12*q13*q23+2*n2*q12*q13*q23+2*q13^2*q23+2*n2*q13^2*q23-4*M`j'^2*q23^2-4*M`j'^2*n2*q23^2+2*q13*q23^2+2*n2*q13*q23^2+4*M`j'^2*q12*q33+4*M`j'^2*n2*q12*q33-3*q12*q13*q33-3*n2*q12*q13*q33+q12*q23*q33+n2*q12*q23*q33+q13*q23*q33+n2*q13*q23*q33+q23^2*q33+n2*q23^2*q33-q12*q33^2-n2*q12*q33^2,8*M`j'^2*q13^2-8*M`j'^2*n4*q13^2-4*q13^3+4*n4*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n4*q13*q33-4*q13^2*q33+4*n4*q13^2*q33-q13*q33^2+n4*q13*q33^2)+mbox1l(n1,1+n2,n3,-1+n4)*(tmpprf(ep,1)*prf(4*q12*q13^2+4*q13^2*q23+2*q12*q13*q33+2*q13*q23*q33,8*M`j'^2*q13^2-8*M`j'^2*n4*q13^2-4*q13^3+4*n4*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n4*q13*q33-4*q13^2*q33+4*n4*q13^2*q33-q13*q33^2+n4*q13*q33^2)+prf(-14*M`j'^2*q12*q13+4*M`j'^2*n1*q12*q13-8*M`j'^2*n2*q12*q13-2*M`j'^2*n3*q12*q13+6*M`j'^2*n4*q12*q13-2*q12*q13^2+6*n2*q12*q13^2+4*n3*q12*q13^2-6*M`j'^2*q13*q23-4*M`j'^2*n1*q13*q23-2*M`j'^2*n3*q13*q23+6*M`j'^2*n4*q13*q23-6*q13^2*q23+4*n1*q13^2*q23+2*n2*q13^2*q23+4*n3*q13^2*q23-4*M`j'^2*q12*q33+4*M`j'^2*n1*q12*q33-4*M`j'^2*n2*q12*q33+q12*q13*q33-2*n1*q12*q13*q33+5*n2*q12*q13*q33+2*n3*q12*q13*q33-3*q13*q23*q33+2*n1*q13*q23*q33+n2*q13*q23*q33+2*n3*q13*q23*q33+q12*q33^2-n1*q12*q33^2+n2*q12*q33^2,8*M`j'^2*q13^2-8*M`j'^2*n4*q13^2-4*q13^3+4*n4*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n4*q13*q33-4*q13^2*q33+4*n4*q13^2*q33-q13*q33^2+n4*q13*q33^2))+mbox1l(n1,2+n2,n3,-1+n4)*prf(-4*M`j'^2*q12^2*q13-4*M`j'^2*n2*q12^2*q13+4*q12^2*q13^2+4*n2*q12^2*q13^2+4*q12*q13^2*q23+4*n2*q12*q13^2*q23+4*M`j'^2*q13*q23^2+4*M`j'^2*n2*q13*q23^2-4*M`j'^2*q12^2*q33-4*M`j'^2*n2*q12^2*q33+4*q12^2*q13*q33+4*n2*q12^2*q13*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33+4*q12*q13*q23*q33+4*n2*q12*q13*q23*q33+q12^2*q33^2+n2*q12^2*q33^2+q12*q23*q33^2+n2*q12*q23*q33^2,8*M`j'^2*q13^2-8*M`j'^2*n4*q13^2-4*q13^3+4*n4*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n4*q13*q33-4*q13^2*q33+4*n4*q13^2*q33-q13*q33^2+n4*q13*q33^2); Identify,ifmatch->jump mbox1l(n1?neg_,n2?neg0_,n3?pos_,n4?{,>1}) = mbox1l(1+n1,n2,1+n3,-2+n4)*prf(2*M`j'^2*n3*q13,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(2+n1,n2,-1+n3,-1+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(2+n1,n2,n3,-2+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(2+n1,n2,n3,-1+n4)*prf(-4*M`j'^2*q13^2-4*M`j'^2*n1*q13^2,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,n3,-1+n4)*prf(n2*q12+n2*q23,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(-4*M`j'^2*n2*q12+2*M`j'^2*n2*q13+2*n2*q12*q13+n2*q12*q33,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(1+n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(-4*q13^2-2*q13*q33,8*M`j'^2*q13-8*M`j'^2*n4*q13-4*q13^2+4*n4*q13^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q13*q33+4*n4*q13*q33-q33^2+n4*q33^2)+prf(10*M`j'^2*q13+4*M`j'^2*n1*q13+2*M`j'^2*n3*q13-6*M`j'^2*n4*q13+4*q13^2-4*n1*q13^2-2*n2*q13^2-4*n3*q13^2+2*q13*q33-2*n1*q13*q33-n2*q13*q33-2*n3*q13*q33,8*M`j'^2*q13-8*M`j'^2*n4*q13-4*q13^2+4*n4*q13^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q13*q33+4*n4*q13*q33-q33^2+n4*q33^2))+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(-2*M`j'^2*n2*q13+2*n2*q13^2-4*M`j'^2*n2*q23+2*n2*q13*q23+n2*q13*q33+n2*q23*q33,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(1+n1,n2,-1+n3,n4)*prf(2*M`j'^2*q13+4*M`j'^2*q33-2*q13*q33-q33^2,8*M`j'^2*q13-4*q13^2+4*M`j'^2*q33-4*q13*q33-q33^2)+mbox1l(1+n1,1+n2,n3,-1+n4)*prf(-4*M`j'^2*n2*q12*q13+4*n2*q12*q13^2+4*M`j'^2*n2*q13*q23-4*M`j'^2*n2*q12*q33+4*n2*q12*q13*q33+n2*q12*q33^2,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg_,n3?{,>1},n4?pos_) = mbox1l(n1,1+n2,n3,-1+n4)*prf(-2*M`j'^2*q12-2*M`j'^2*q23,8*M`j'^2*q13-4*q13^2+4*M`j'^2*q33-4*q13*q33-q33^2)+mbox1l(n1,1+n2,-2+n3,1+n4)*prf(-2*M`j'^2*n4*q12-2*M`j'^2*n4*q23,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(-1+n1,2+n2,-1+n3,n4)*prf(-(q12^2*q13)-n2*q12^2*q13-2*q12*q13*q23-2*n2*q12*q13*q23-q13*q23^2-n2*q13*q23^2-q12^2*q33-n2*q12^2*q33-2*q12*q23*q33-2*n2*q12*q23*q33-q23^2*q33-n2*q23^2*q33,-2*q13^3+2*n3*q13^3-q13^2*q33+n3*q13^2*q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(-6*M`j'^2*n1*q12*q13+4*n1*q12*q13^2+2*M`j'^2*n1*q13*q23-4*M`j'^2*n1*q12*q33+4*n1*q12*q13*q33+n1*q12*q33^2,8*M`j'^2*q13^2-8*M`j'^2*n3*q13^2-4*q13^3+4*n3*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n3*q13*q33-4*q13^2*q33+4*n3*q13^2*q33-q13*q33^2+n3*q13*q33^2)+mbox1l(n1,2+n2,-1+n3,-1+n4)*prf(-4*M`j'^2*q12^2*q13-4*M`j'^2*n2*q12^2*q13+2*M`j'^2*q12*q13^2+2*M`j'^2*n2*q12*q13^2+2*q12^2*q13^2+2*n2*q12^2*q13^2-4*M`j'^2*q12*q13*q23-4*M`j'^2*n2*q12*q13*q23+2*M`j'^2*q13^2*q23+2*M`j'^2*n2*q13^2*q23+2*q12*q13^2*q23+2*n2*q12*q13^2*q23-4*M`j'^2*q12^2*q33-4*M`j'^2*n2*q12^2*q33+3*q12^2*q13*q33+3*n2*q12^2*q13*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33+3*q12*q13*q23*q33+3*n2*q12*q13*q23*q33+q12^2*q33^2+n2*q12^2*q33^2+q12*q23*q33^2+n2*q12*q23*q33^2,8*M`j'^2*q13^3-8*M`j'^2*n3*q13^3-4*q13^4+4*n3*q13^4+4*M`j'^2*q13^2*q33-4*M`j'^2*n3*q13^2*q33-4*q13^3*q33+4*n3*q13^3*q33-q13^2*q33^2+n3*q13^2*q33^2)+mbox1l(1+n1,1+n2,-1+n3,n4)*prf(-4*M`j'^2*n1*q12*q13^2-4*M`j'^2*n1*q13^2*q23-8*M`j'^2*n1*q12*q13*q33+4*n1*q12*q13^2*q33-4*M`j'^2*n1*q12*q33^2+4*n1*q12*q13*q33^2+n1*q12*q33^3,8*M`j'^2*q13^2-8*M`j'^2*n3*q13^2-4*q13^3+4*n3*q13^3+4*M`j'^2*q13*q33-4*M`j'^2*n3*q13*q33-4*q13^2*q33+4*n3*q13^2*q33-q13*q33^2+n3*q13*q33^2)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(2*M`j'^2*n1*q12*q13^2+2*M`j'^2*n1*q13^2*q23-4*M`j'^2*n1*q12*q13*q33+2*n1*q12*q13^2*q33+4*M`j'^2*n1*q13*q23*q33-2*n1*q13^2*q23*q33-4*M`j'^2*n1*q12*q33^2+3*n1*q12*q13*q33^2-n1*q13*q23*q33^2+n1*q12*q33^3,8*M`j'^2*q13^3-8*M`j'^2*n3*q13^3-4*q13^4+4*n3*q13^4+4*M`j'^2*q13^2*q33-4*M`j'^2*n3*q13^2*q33-4*q13^3*q33+4*n3*q13^3*q33-q13^2*q33^2+n3*q13^2*q33^2)+mbox1l(n1,2+n2,-2+n3,n4)*prf(-2*M`j'^2*q12*q13^2-2*M`j'^2*n2*q12*q13^2-8*M`j'^2*q13^3-8*M`j'^2*n2*q13^3+2*q12*q13^3+2*n2*q12*q13^3+4*q13^4+4*n2*q13^4-4*M`j'^2*q12*q13*q23-4*M`j'^2*n2*q12*q13*q23-10*M`j'^2*q13^2*q23-10*M`j'^2*n2*q13^2*q23+2*q12*q13^2*q23+2*n2*q12*q13^2*q23+6*q13^3*q23+6*n2*q13^3*q23-4*M`j'^2*q13*q23^2-4*M`j'^2*n2*q13*q23^2+2*q13^2*q23^2+2*n2*q13^2*q23^2+8*M`j'^2*q12*q13*q33+8*M`j'^2*n2*q12*q13*q33-4*M`j'^2*q13^2*q33-4*M`j'^2*n2*q13^2*q33-3*q12*q13^2*q33-3*n2*q12*q13^2*q33+4*q13^3*q33+4*n2*q13^3*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33-4*M`j'^2*q13*q23*q33-4*M`j'^2*n2*q13*q23*q33+3*q12*q13*q23*q33+3*n2*q12*q13*q23*q33+5*q13^2*q23*q33+5*n2*q13^2*q23*q33-4*M`j'^2*q23^2*q33-4*M`j'^2*n2*q23^2*q33+3*q13*q23^2*q33+3*n2*q13*q23^2*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n2*q12*q33^2-4*q12*q13*q33^2-4*n2*q12*q13*q33^2+q13^2*q33^2+n2*q13^2*q33^2+q12*q23*q33^2+n2*q12*q23*q33^2+q13*q23*q33^2+n2*q13*q23*q33^2+q23^2*q33^2+n2*q23^2*q33^2-q12*q33^3-n2*q12*q33^3,8*M`j'^2*q13^3-8*M`j'^2*n3*q13^3-4*q13^4+4*n3*q13^4+4*M`j'^2*q13^2*q33-4*M`j'^2*n3*q13^2*q33-4*q13^3*q33+4*n3*q13^3*q33-q13^2*q33^2+n3*q13^2*q33^2)+mbox1l(n1,1+n2,-1+n3,n4)*(tmpprf(ep,1)*prf(4*q12*q13^3+4*q13^3*q23+2*q12*q13^2*q33+2*q13^2*q23*q33,8*M`j'^2*q13^3-8*M`j'^2*n3*q13^3-4*q13^4+4*n3*q13^4+4*M`j'^2*q13^2*q33-4*M`j'^2*n3*q13^2*q33-4*q13^3*q33+4*n3*q13^3*q33-q13^2*q33^2+n3*q13^2*q33^2)+prf(2*M`j'^2*q12*q13^2+4*M`j'^2*n1*q12*q13^2-2*M`j'^2*n3*q12*q13^2-2*M`j'^2*n4*q12*q13^2+16*M`j'^2*q13^3+8*M`j'^2*n2*q13^3-8*M`j'^2*n3*q13^3-10*q12*q13^3+2*n2*q12*q13^3+4*n3*q12*q13^3+4*n4*q12*q13^3-8*q13^4-4*n2*q13^4+4*n3*q13^4+10*M`j'^2*q13^2*q23-4*M`j'^2*n1*q13^2*q23+8*M`j'^2*n2*q13^2*q23-2*M`j'^2*n3*q13^2*q23-2*M`j'^2*n4*q13^2*q23-14*q13^3*q23+4*n1*q13^3*q23-2*n2*q13^3*q23+4*n3*q13^3*q23+4*n4*q13^3*q23-8*M`j'^2*q12*q13*q33+8*M`j'^2*n1*q12*q13*q33-8*M`j'^2*n2*q12*q13*q33+8*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-4*M`j'^2*n3*q13^2*q33-q12*q13^2*q33-4*n1*q12*q13^2*q33+5*n2*q12*q13^2*q33+2*n3*q12*q13^2*q33+2*n4*q12*q13^2*q33-8*q13^3*q33-4*n2*q13^3*q33+4*n3*q13^3*q33+4*M`j'^2*q13*q23*q33-4*M`j'^2*n1*q13*q23*q33+4*M`j'^2*n2*q13*q23*q33-9*q13^2*q23*q33+4*n1*q13^2*q23*q33-3*n2*q13^2*q23*q33+2*n3*q13^2*q23*q33+2*n4*q13^2*q23*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n1*q12*q33^2-4*M`j'^2*n2*q12*q33^2+4*q12*q13*q33^2-4*n1*q12*q13*q33^2+4*n2*q12*q13*q33^2-2*q13^2*q33^2-n2*q13^2*q33^2+n3*q13^2*q33^2-q13*q23*q33^2+n1*q13*q23*q33^2-n2*q13*q23*q33^2+q12*q33^3-n1*q12*q33^3+n2*q12*q33^3,8*M`j'^2*q13^3-8*M`j'^2*n3*q13^3-4*q13^4+4*n3*q13^4+4*M`j'^2*q13^2*q33-4*M`j'^2*n3*q13^2*q33-4*q13^3*q33+4*n3*q13^3*q33-q13^2*q33^2+n3*q13^2*q33^2))+mbox1l(n1,2+n2,-1+n3,n4)*prf(-4*M`j'^2*q12^2*q13^2-4*M`j'^2*n2*q12^2*q13^2+4*q12^2*q13^3+4*n2*q12^2*q13^3+4*q12*q13^3*q23+4*n2*q12*q13^3*q23+4*M`j'^2*q13^2*q23^2+4*M`j'^2*n2*q13^2*q23^2-12*M`j'^2*q12^2*q13*q33-12*M`j'^2*n2*q12^2*q13*q33+8*q12^2*q13^2*q33+8*n2*q12^2*q13^2*q33-12*M`j'^2*q12*q13*q23*q33-12*M`j'^2*n2*q12*q13*q23*q33+8*q12*q13^2*q23*q33+8*n2*q12*q13^2*q23*q33-4*M`j'^2*q12^2*q33^2-4*M`j'^2*n2*q12^2*q33^2+5*q12^2*q13*q33^2+5*n2*q12^2*q13*q33^2-4*M`j'^2*q12*q23*q33^2-4*M`j'^2*n2*q12*q23*q33^2+5*q12*q13*q23*q33^2+5*n2*q12*q13*q23*q33^2+q12^2*q33^3+n2*q12^2*q33^3+q12*q23*q33^3+n2*q12*q23*q33^3,8*M`j'^2*q13^3-8*M`j'^2*n3*q13^3-4*q13^4+4*n3*q13^4+4*M`j'^2*q13^2*q33-4*M`j'^2*n3*q13^2*q33-4*q13^3*q33+4*n3*q13^3*q33-q13^2*q33^2+n3*q13^2*q33^2); Identify,ifmatch->jump mbox1l(n1?neg_,n2?neg0_,n3?{,>1},n4?pos_) = mbox1l(1+n1,n2,n3,-1+n4)*prf(2*M`j'^2*q13,8*M`j'^2*q13-4*q13^2+4*M`j'^2*q33-4*q13*q33-q33^2)+mbox1l(1+n1,n2,-2+n3,1+n4)*prf(2*M`j'^2*n4*q13,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(2+n1,n2,-1+n3,-1+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(2+n1,n2,-1+n3,n4)*prf(-4*M`j'^2*q13^2-4*M`j'^2*n1*q13^2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-(n2*q12)-2*n2*q13-n2*q23-n2*q33,-2*q13+2*n3*q13-q33+n3*q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(4*M`j'^2*n2*q12+2*M`j'^2*n2*q13-2*n2*q12*q13-n2*q12*q33,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(2+n1,n2,-2+n3,n4)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13+4*M`j'^2*q33+4*M`j'^2*n1*q33-2*q13*q33-2*n1*q13*q33-q33^2-n1*q33^2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(6*M`j'^2*n2*q13-2*n2*q13^2+4*M`j'^2*n2*q23-2*n2*q13*q23+4*M`j'^2*n2*q33-3*n2*q13*q33-n2*q23*q33-n2*q33^2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(1+n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(4*q13^2+2*q13*q33,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+prf(-10*M`j'^2*q13-4*M`j'^2*n1*q13+6*M`j'^2*n3*q13-2*M`j'^2*n4*q13-4*q13^2+4*n1*q13^2+2*n2*q13^2+4*n4*q13^2-8*M`j'^2*q33-4*M`j'^2*n1*q33+4*M`j'^2*n3*q33+2*q13*q33+4*n1*q13*q33+n2*q13*q33-2*n3*q13*q33+2*n4*q13*q33+2*q33^2+n1*q33^2-n3*q33^2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2))+mbox1l(1+n1,1+n2,-1+n3,n4)*prf(-4*M`j'^2*n2*q12*q13+4*n2*q12*q13^2+4*M`j'^2*n2*q13*q23-4*M`j'^2*n2*q12*q33+4*n2*q12*q13*q33+n2*q12*q33^2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg0_,n3?pos_,n4?{,>1}) = mbox1l(1+n1,n2,n3,-2+n4)*prf(2*M`j'^2*n1,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,n3,-2+n4)*prf(2*M`j'^2*n2,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,1+n3,-2+n4)*prf(2*M`j'^2*n3,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(1+n1,n2,n3,-1+n4)*prf(-4*M`j'^2*n1*q13,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n2*q12+4*M`j'^2*n2*q23,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,-1+n3,n4)*prf(-2*M`j'^2+2*q13+q33,8*M`j'^2*q13-4*q13^2+4*M`j'^2*q33-4*q13*q33-q33^2)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-2*M`j'^2*n1+2*n1*q13+n1*q33,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(-2*M`j'^2*n2+2*n2*q13+n2*q33,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(4*q13+2*q33,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)+prf(-2*M`j'^2-2*M`j'^2*n3+2*M`j'^2*n4-10*q13+2*n1*q13+2*n2*q13+4*n3*q13+2*n4*q13-5*q33+n1*q33+n2*q33+2*n3*q33+n4*q33,-8*M`j'^2*q13+8*M`j'^2*n4*q13+4*q13^2-4*n4*q13^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q13*q33-4*n4*q13*q33+q33^2-n4*q33^2)); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg0_,n3?{,>1},n4?pos_) = mbox1l(1+n1,n2,-2+n3,n4)*prf(2*M`j'^2*n1,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(n1,1+n2,-2+n3,n4)*prf(2*M`j'^2*n2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(n1,n2,-2+n3,1+n4)*prf(2*M`j'^2*n4,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(n1,n2,n3,-1+n4)*prf(-2*M`j'^2+2*q13+q33,8*M`j'^2*q13-4*q13^2+4*M`j'^2*q33-4*q13*q33-q33^2)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-2*M`j'^2*n1+2*n1*q13+n1*q33,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(-2*M`j'^2*n2+2*n2*q13+n2*q33,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(4*q13+2*q33,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+prf(-2*M`j'^2+2*M`j'^2*n3-2*M`j'^2*n4-10*q13+2*n1*q13+2*n2*q13+2*n3*q13+4*n4*q13-5*q33+n1*q33+n2*q33+n3*q33+2*n4*q33,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2))+mbox1l(1+n1,n2,-1+n3,n4)*prf(-4*M`j'^2*n1*q13-4*M`j'^2*n1*q33+2*n1*q13*q33+n1*q33^2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-4*M`j'^2*n2*q12-8*M`j'^2*n2*q13+4*n2*q12*q13+4*n2*q13^2-4*M`j'^2*n2*q23+4*n2*q13*q23-4*M`j'^2*n2*q33+2*n2*q12*q33+4*n2*q13*q33+2*n2*q23*q33+n2*q33^2,-8*M`j'^2*q13+8*M`j'^2*n3*q13+4*q13^2-4*n3*q13^2-4*M`j'^2*q33+4*M`j'^2*n3*q33+4*q13*q33-4*n3*q13*q33+q33^2-n3*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?neg_,n3?pos_,n4?pos_) = mbox1l(n1,1+n2,n3,-1+n4)*prf(-q12,q13)+mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-q12^2-n2*q12^2-q12*q23-n2*q12*q23,-q13^2+n1*q13^2)+mbox1l(-2+n1,2+n2,n3,n4)*prf(q12^2+n2*q12^2+2*q12*q23+2*n2*q12*q23+q23^2+n2*q23^2,-q13^2+n1*q13^2)+mbox1l(n1,1+n2,n3,n4)*prf(-2*q12*q13-q12*q33,q13)+mbox1l(n1,1+n2,-1+n3,n4)*prf(q13^2+q13*q23-q12*q33,q13^2)+mbox1l(-1+n1,1+n2,n3,n4)*prf(-2*q12*q13+n1*q12*q13-n2*q12*q13+2*q13*q23-n1*q13*q23+n2*q13*q23-2*q12*q33+n1*q12*q33-n2*q12*q33,-q13^2+n1*q13^2)+mbox1l(-1+n1,2+n2,-1+n3,n4)*prf(q12*q13+n2*q12*q13-q12*q23-n2*q12*q23-q13*q23-n2*q13*q23-q23^2-n2*q23^2+q12*q33+n2*q12*q33,-q13^2+n1*q13^2)+mbox1l(-1+n1,2+n2,n3,n4)*prf(-2*q12^2*q13-2*n2*q12^2*q13-2*q12*q13*q23-2*n2*q12*q13*q23-q12^2*q33-n2*q12^2*q33-q12*q23*q33-n2*q12*q23*q33,-q13^2+n1*q13^2); Identify,ifmatch->jump mbox1l(n1?neg_,0,1,1) = tmpprf(1,-1+2*ep+n1)*mbox1l(n1,0,0,2)*prf(-2*M`j'^2,2*q13+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,0,0,1)*prf(-2*M`j'^2*n1,2*q13+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,0,0,2)*prf(2*M`j'^2*q13,2*q13+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,0,2,0)*prf(2*M`j'^2*q13,2*q13+q33)+mbox1l(1+n1,0,1,1)*(tmpprf(ep,-1+2*ep+n1)*prf(2*q13,1)+tmpprf(1,-1+2*ep+n1)*prf(2*n1*q13,1))+tmpprf(1,-1+2*ep+n1)*mbox1l(2+n1,0,1,0)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13,2*q13+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(2+n1,0,1,1)*prf(-4*M`j'^2*q13^2-4*M`j'^2*n1*q13^2,2*q13+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(n1,0,2,0)*prf(2*M`j'^2-2*q13-q33,2*q13+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,0,1,0)*prf(2*M`j'^2*n1-2*n1*q13-n1*q33,2*q13+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(2+n1,0,0,1)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13+4*M`j'^2*q33+4*M`j'^2*n1*q33-2*q13*q33-2*n1*q13*q33-q33^2-n1*q33^2,2*q13+q33); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?neg_,n4?{,>1}) = mbox1l(n1,1+n2,1+n3,-2+n4)*prf(2*M`j'^2*n2*q12+2*M`j'^2*n2*q23,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(-1+n1,n2,2+n3,-1+n4)*prf(2*q12^3+2*n3*q12^3+q12^2*q13+n3*q12^2*q13+5*q12^2*q23+5*n3*q12^2*q23+2*q12*q13*q23+2*n3*q12*q13*q23+4*q12*q23^2+4*n3*q12*q23^2+q13*q23^2+n3*q13*q23^2+q23^3+n3*q23^3,2*q12*q13^2-2*n4*q12*q13^2+2*q13^3-2*n4*q13^3+4*q12*q13*q23-4*n4*q12*q13*q23+6*q13^2*q23-6*n4*q13^2*q23+2*q12*q23^2-2*n4*q12*q23^2+6*q13*q23^2-6*n4*q13*q23^2+2*q23^3-2*n4*q23^3-4*q12^2*q33+4*n4*q12^2*q33-4*q12*q13*q33+4*n4*q12*q13*q33+q13^2*q33-n4*q13^2*q33-4*q12*q23*q33+4*n4*q12*q23*q33+2*q13*q23*q33-2*n4*q13*q23*q33+q23^2*q33-n4*q23^2*q33-2*q12*q33^2+2*n4*q12*q33^2)+mbox1l(n1,n2,2+n3,-2+n4)*prf(8*M`j'^2*q12^3+8*M`j'^2*n3*q12^3-4*q12^4-4*n3*q12^4+4*M`j'^2*q12^2*q13+4*M`j'^2*n3*q12^2*q13-6*q12^3*q13-6*n3*q12^3*q13+2*M`j'^2*q12*q13^2+2*M`j'^2*n3*q12*q13^2-2*q12^2*q13^2-2*n3*q12^2*q13^2+12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-10*q12^3*q23-10*n3*q12^3*q23+8*M`j'^2*q12*q13*q23+8*M`j'^2*n3*q12*q13*q23-10*q12^2*q13*q23-10*n3*q12^2*q13*q23+2*M`j'^2*q13^2*q23+2*M`j'^2*n3*q13^2*q23-2*q12*q13^2*q23-2*n3*q12*q13^2*q23+6*M`j'^2*q12*q23^2+6*M`j'^2*n3*q12*q23^2-8*q12^2*q23^2-8*n3*q12^2*q23^2+4*M`j'^2*q13*q23^2+4*M`j'^2*n3*q13*q23^2-4*q12*q13*q23^2-4*n3*q12*q13*q23^2+2*M`j'^2*q23^3+2*M`j'^2*n3*q23^3-2*q12*q23^3-2*n3*q12*q23^3-4*M`j'^2*q12^2*q33-4*M`j'^2*n3*q12^2*q33-2*q12^3*q33-2*n3*q12^3*q33-q12^2*q13*q33-n3*q12^2*q13*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n3*q12*q23*q33-3*q12^2*q23*q33-3*n3*q12^2*q23*q33-q12*q13*q23*q33-n3*q12*q13*q23*q33-q12*q23^2*q33-n3*q12*q23^2*q33,-8*M`j'^2*q12*q13^2+8*M`j'^2*n4*q12*q13^2+4*q12^2*q13^2-4*n4*q12^2*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n4*q13^3+8*q12*q13^3-8*n4*q12*q13^3+4*q13^4-4*n4*q13^4-16*M`j'^2*q12*q13*q23+16*M`j'^2*n4*q12*q13*q23+8*q12^2*q13*q23-8*n4*q12^2*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n4*q13^2*q23+24*q12*q13^2*q23-24*n4*q12*q13^2*q23+16*q13^3*q23-16*n4*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n4*q12*q23^2+4*q12^2*q23^2-4*n4*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n4*q13*q23^2+24*q12*q13*q23^2-24*n4*q12*q13*q23^2+24*q13^2*q23^2-24*n4*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n4*q23^3+8*q12*q23^3-8*n4*q12*q23^3+16*q13*q23^3-16*n4*q13*q23^3+4*q23^4-4*n4*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n4*q12^2*q33-8*q12^3*q33+8*n4*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n4*q12*q13*q33-16*q12^2*q13*q33+16*n4*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+4*q13^3*q33-4*n4*q13^3*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n4*q12*q23*q33-16*q12^2*q23*q33+16*n4*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33+12*q13^2*q23*q33-12*n4*q13^2*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+12*q13*q23^2*q33-12*n4*q13*q23^2*q33+4*q23^3*q33-4*n4*q23^3*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n4*q12*q33^2-8*q12^2*q33^2+8*n4*q12^2*q33^2-8*q12*q13*q33^2+8*n4*q12*q13*q33^2+q13^2*q33^2-n4*q13^2*q33^2-8*q12*q23*q33^2+8*n4*q12*q23*q33^2+2*q13*q23*q33^2-2*n4*q13*q23*q33^2+q23^2*q33^2-n4*q23^2*q33^2-2*q12*q33^3+2*n4*q12*q33^3)+mbox1l(n1,-1+n2,1+n3,n4)*prf(-2*M`j'^2*q12-8*M`j'^2*q13+4*q12*q13+4*q13^2-2*M`j'^2*q23+4*q13*q23-4*M`j'^2*q33+2*q12*q33+4*q13*q33+2*q23*q33+q33^2,-8*M`j'^2*q12+4*q12^2-8*M`j'^2*q13+8*q12*q13+4*q13^2-8*M`j'^2*q23+8*q12*q23+8*q13*q23+4*q23^2-4*M`j'^2*q33+4*q12*q33+4*q13*q33+4*q23*q33+q33^2)+mbox1l(1+n1,n2,1+n3,-2+n4)*prf(-8*M`j'^2*n1*q12^2*q13+4*n1*q12^3*q13+2*M`j'^2*n1*q12*q13^2+4*n1*q12^2*q13^2+8*M`j'^2*n1*q12^2*q23-4*n1*q12^3*q23+12*M`j'^2*n1*q12*q13*q23-4*n1*q12^2*q13*q23+2*M`j'^2*n1*q13^2*q23-4*n1*q12*q13^2*q23+10*M`j'^2*n1*q12*q23^2-8*n1*q12^2*q23^2+4*M`j'^2*n1*q13*q23^2-8*n1*q12*q13*q23^2+2*M`j'^2*n1*q23^3-4*n1*q12*q23^3-12*M`j'^2*n1*q12^2*q33+4*n1*q12^3*q33+6*n1*q12^2*q13*q33-4*M`j'^2*n1*q12*q23*q33+2*n1*q12^2*q23*q33-2*n1*q12*q13*q23*q33-2*n1*q12*q23^2*q33+2*n1*q12^2*q33^2,-8*M`j'^2*q12*q13^2+8*M`j'^2*n4*q12*q13^2+4*q12^2*q13^2-4*n4*q12^2*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n4*q13^3+8*q12*q13^3-8*n4*q12*q13^3+4*q13^4-4*n4*q13^4-16*M`j'^2*q12*q13*q23+16*M`j'^2*n4*q12*q13*q23+8*q12^2*q13*q23-8*n4*q12^2*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n4*q13^2*q23+24*q12*q13^2*q23-24*n4*q12*q13^2*q23+16*q13^3*q23-16*n4*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n4*q12*q23^2+4*q12^2*q23^2-4*n4*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n4*q13*q23^2+24*q12*q13*q23^2-24*n4*q12*q13*q23^2+24*q13^2*q23^2-24*n4*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n4*q23^3+8*q12*q23^3-8*n4*q12*q23^3+16*q13*q23^3-16*n4*q13*q23^3+4*q23^4-4*n4*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n4*q12^2*q33-8*q12^3*q33+8*n4*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n4*q12*q13*q33-16*q12^2*q13*q33+16*n4*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*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6*q13^3*q23-16*n4*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n4*q12*q23^2+4*q12^2*q23^2-4*n4*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n4*q13*q23^2+24*q12*q13*q23^2-24*n4*q12*q13*q23^2+24*q13^2*q23^2-24*n4*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n4*q23^3+8*q12*q23^3-8*n4*q12*q23^3+16*q13*q23^3-16*n4*q13*q23^3+4*q23^4-4*n4*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n4*q12^2*q33-8*q12^3*q33+8*n4*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n4*q12*q13*q33-16*q12^2*q13*q33+16*n4*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+4*q13^3*q33-4*n4*q13^3*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n4*q12*q23*q33-16*q12^2*q23*q33+16*n4*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33+12*q13^2*q23*q33-12*n4*q13^2*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+12*q13*q23^2*q33-12*n4*q13*q23^2*q33+4*q23^3*q33-4*n4*q23^3*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n4*q12*q33^2-8*q12^2*q33^2+8*n4*q12^2*q33^2-8*q12*q13*q33^2+8*n4*q12*q13*q33^2+q13^2*q33^2-n4*q13^2*q33^2-8*q12*q23*q33^2+8*n4*q12*q23*q33^2+2*q13*q23*q33^2-2*n4*q13*q23*q33^2+q23^2*q33^2-n4*q23^2*q33^2-2*q12*q33^3+2*n4*q12*q33^3); Identify,ifmatch->jump mbox1l(n1?neg_,n2?pos_,n3?neg0_,n4?{,>1}) = mbox1l(2+n1,-1+n2,n3,-1+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13+2*M`j'^2*q23+2*M`j'^2*n1*q23,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(2*M`j'^2*n2*q13+2*M`j'^2*n2*q23,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-(n3*q12)-n3*q23,-2*q12+2*n4*q12-2*q13+2*n4*q13-2*q23+2*n4*q23-q33+n4*q33)+mbox1l(2+n1,n2,n3,-2+n4)*prf(-8*M`j'^2*q12-8*M`j'^2*n1*q12+4*q12^2+4*n1*q12^2-2*M`j'^2*q13-2*M`j'^2*n1*q13+4*q12*q13+4*n1*q12*q13-2*M`j'^2*q23-2*M`j'^2*n1*q23+4*q12*q23+4*n1*q12*q23+2*q12*q33+2*n1*q12*q33,8*M`j'^2*q12-8*M`j'^2*n4*q12-4*q12^2+4*n4*q12^2+8*M`j'^2*q13-8*M`j'^2*n4*q13-8*q12*q13+8*n4*q12*q13-4*q13^2+4*n4*q13^2+8*M`j'^2*q23-8*M`j'^2*n4*q23-8*q12*q23+8*n4*q12*q23-8*q13*q23+8*n4*q13*q23-4*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q12*q33+4*n4*q12*q33-4*q13*q33+4*n4*q13*q33-4*q23*q33+4*n4*q23*q33-q33^2+n4*q33^2)+mbox1l(1+n1,n2,1+n3,-2+n4)*prf(-4*M`j'^2*n3*q12+2*n3*q12^2-2*M`j'^2*n3*q13+2*n3*q12*q13-2*M`j'^2*n3*q23+2*n3*q12*q23+n3*q12*q33,8*M`j'^2*q12-8*M`j'^2*n4*q12-4*q12^2+4*n4*q12^2+8*M`j'^2*q13-8*M`j'^2*n4*q13-8*q12*q13+8*n4*q12*q13-4*q13^2+4*n4*q13^2+8*M`j'^2*q23-8*M`j'^2*n4*q23-8*q12*q23+8*n4*q12*q23-8*q13*q23+8*n4*q13*q23-4*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q12*q33+4*n4*q12*q33-4*q13*q33+4*n4*q13*q33-4*q23*q33+4*n4*q23*q33-q33^2+n4*q33^2)+mbox1l(1+n1,-1+n2,1+n3,-1+n4)*prf(2*M`j'^2*n3*q13-2*n3*q12*q13-2*n3*q13^2-2*M`j'^2*n3*q23-2*n3*q13*q23-n3*q13*q33,8*M`j'^2*q12-8*M`j'^2*n4*q12-4*q12^2+4*n4*q12^2+8*M`j'^2*q13-8*M`j'^2*n4*q13-8*q12*q13+8*n4*q12*q13-4*q13^2+4*n4*q13^2+8*M`j'^2*q23-8*M`j'^2*n4*q23-8*q12*q23+8*n4*q12*q23-8*q13*q23+8*n4*q13*q23-4*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q12*q33+4*n4*q12*q33-4*q13*q33+4*n4*q13*q33-4*q23*q33+4*n4*q23*q33-q33^2+n4*q33^2)+mbox1l(1+n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(-4*q12*q13-4*q13^2-4*q12*q23-8*q13*q23-4*q23^2-2*q13*q33-2*q23*q33,8*M`j'^2*q12-8*M`j'^2*n4*q12-4*q12^2+4*n4*q12^2+8*M`j'^2*q13-8*M`j'^2*n4*q13-8*q12*q13+8*n4*q12*q13-4*q13^2+4*n4*q13^2+8*M`j'^2*q23-8*M`j'^2*n4*q23-8*q12*q23+8*n4*q12*q23-8*q13*q23+8*n4*q13*q23-4*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q12*q33+4*n4*q12*q33-4*q13*q33+4*n4*q13*q33-4*q23*q33+4*n4*q23*q33-q33^2+n4*q33^2)+prf(16*M`j'^2*q12+8*M`j'^2*n1*q12-8*M`j'^2*n4*q12-8*q12^2-4*n1*q12^2+4*n4*q12^2+10*M`j'^2*q13+4*M`j'^2*n1*q13+2*M`j'^2*n2*q13-6*M`j'^2*n4*q13-4*q12*q13-8*n1*q12*q13-4*n2*q12*q13-2*n3*q12*q13+4*n4*q12*q13+4*q13^2-4*n1*q13^2-4*n2*q13^2-2*n3*q13^2+10*M`j'^2*q23+4*M`j'^2*n1*q23+2*M`j'^2*n2*q23-6*M`j'^2*n4*q23-4*q12*q23-8*n1*q12*q23-4*n2*q12*q23-2*n3*q12*q23+4*n4*q12*q23+8*q13*q23-8*n1*q13*q23-8*n2*q13*q23-4*n3*q13*q23+4*q23^2-4*n1*q23^2-4*n2*q23^2-2*n3*q23^2-4*q12*q33-2*n1*q12*q33+2*n4*q12*q33+2*q13*q33-2*n1*q13*q33-2*n2*q13*q33-n3*q13*q33+2*q23*q33-2*n1*q23*q33-2*n2*q23*q33-n3*q23*q33,8*M`j'^2*q12-8*M`j'^2*n4*q12-4*q12^2+4*n4*q12^2+8*M`j'^2*q13-8*M`j'^2*n4*q13-8*q12*q13+8*n4*q12*q13-4*q13^2+4*n4*q13^2+8*M`j'^2*q23-8*M`j'^2*n4*q23-8*q12*q23+8*n4*q12*q23-8*q13*q23+8*n4*q13*q23-4*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q12*q33+4*n4*q12*q33-4*q13*q33+4*n4*q13*q33-4*q23*q33+4*n4*q23*q33-q33^2+n4*q33^2))+mbox1l(1+n1,-1+n2,n3,n4)*prf(-2*M`j'^2*q13-2*M`j'^2*q23-4*M`j'^2*q33+2*q12*q33+2*q13*q33+2*q23*q33+q33^2,-8*M`j'^2*q12+4*q12^2-8*M`j'^2*q13+8*q12*q13+4*q13^2-8*M`j'^2*q23+8*q12*q23+8*q13*q23+4*q23^2-4*M`j'^2*q33+4*q12*q33+4*q13*q33+4*q23*q33+q33^2)+mbox1l(2+n1,n2,n3,-1+n4)*prf(4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2+8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23+4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2-8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33+4*q12^2*q33+4*n1*q12^2*q33+4*q12*q13*q33+4*n1*q12*q13*q33+4*q12*q23*q33+4*n1*q12*q23*q33+2*q12*q33^2+2*n1*q12*q33^2,8*M`j'^2*q12-8*M`j'^2*n4*q12-4*q12^2+4*n4*q12^2+8*M`j'^2*q13-8*M`j'^2*n4*q13-8*q12*q13+8*n4*q12*q13-4*q13^2+4*n4*q13^2+8*M`j'^2*q23-8*M`j'^2*n4*q23-8*q12*q23+8*n4*q12*q23-8*q13*q23+8*n4*q13*q23-4*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q12*q33+4*n4*q12*q33-4*q13*q33+4*n4*q13*q33-4*q23*q33+4*n4*q23*q33-q33^2+n4*q33^2)+mbox1l(1+n1,n2,1+n3,-1+n4)*prf(-4*M`j'^2*n3*q12*q13+4*n3*q12^2*q13+4*n3*q12*q13^2+4*M`j'^2*n3*q12*q23+4*M`j'^2*n3*q13*q23+4*n3*q12*q13*q23+4*M`j'^2*n3*q23^2-4*M`j'^2*n3*q12*q33+2*n3*q12^2*q33+4*n3*q12*q13*q33+2*n3*q12*q23*q33+n3*q12*q33^2,8*M`j'^2*q12-8*M`j'^2*n4*q12-4*q12^2+4*n4*q12^2+8*M`j'^2*q13-8*M`j'^2*n4*q13-8*q12*q13+8*n4*q12*q13-4*q13^2+4*n4*q13^2+8*M`j'^2*q23-8*M`j'^2*n4*q23-8*q12*q23+8*n4*q12*q23-8*q13*q23+8*n4*q13*q23-4*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n4*q33-4*q12*q33+4*n4*q12*q33-4*q13*q33+4*n4*q13*q33-4*q23*q33+4*n4*q23*q33-q33^2+n4*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?{,>1},n3?neg_,n4?pos_) = mbox1l(n1,n2,1+n3,-1+n4)*prf(2*M`j'^2*q12+2*M`j'^2*q23,8*M`j'^2*q12-4*q12^2+8*M`j'^2*q13-8*q12*q13-4*q13^2+8*M`j'^2*q23-8*q12*q23-8*q13*q23-4*q23^2+4*M`j'^2*q33-4*q12*q33-4*q13*q33-4*q23*q33-q33^2)+mbox1l(n1,-2+n2,1+n3,1+n4)*prf(2*M`j'^2*n4*q12+2*M`j'^2*n4*q23,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(q12^2*q13+n3*q12^2*q13+q12^2*q23+n3*q12^2*q23+2*q12*q13*q23+2*n3*q12*q13*q23+2*q12*q23^2+2*n3*q12*q23^2+q13*q23^2+n3*q13*q23^2+q23^3+n3*q23^3+q12^2*q33+n3*q12^2*q33+2*q12*q23*q33+2*n3*q12*q23*q33+q23^2*q33+n3*q23^2*q33,2*q12*q13^2-2*n2*q12*q13^2+2*q13^3-2*n2*q13^3+4*q12*q13*q23-4*n2*q12*q13*q23+6*q13^2*q23-6*n2*q13^2*q23+2*q12*q23^2-2*n2*q12*q23^2+6*q13*q23^2-6*n2*q13*q23^2+2*q23^3-2*n2*q23^3-4*q12^2*q33+4*n2*q12^2*q33-4*q12*q13*q33+4*n2*q12*q13*q33+q13^2*q33-n2*q13^2*q33-4*q12*q23*q33+4*n2*q12*q23*q33+2*q13*q23*q33-2*n2*q13*q23*q33+q23^2*q33-n2*q23^2*q33-2*q12*q33^2+2*n2*q12*q33^2)+mbox1l(1+n1,-1+n2,1+n3,-1+n4)*prf(-6*M`j'^2*n1*q12*q13^2+4*n1*q12^2*q13^2+4*n1*q12*q13^3-4*M`j'^2*n1*q12*q13*q23+4*n1*q12^2*q13*q23+2*M`j'^2*n1*q13^2*q23+8*n1*q12*q13^2*q23+2*M`j'^2*n1*q12*q23^2+4*M`j'^2*n1*q13*q23^2+4*n1*q12*q13*q23^2+2*M`j'^2*n1*q23^3+4*M`j'^2*n1*q12^2*q33-4*n1*q12^3*q33-4*M`j'^2*n1*q12*q13*q33-2*n1*q12^2*q13*q33+4*n1*q12*q13^2*q33-6*n1*q12^2*q23*q33+2*n1*q12*q13*q23*q33-2*n1*q12*q23^2*q33-2*n1*q12^2*q33^2+n1*q12*q13*q33^2-n1*q12*q23*q33^2,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2+4*q12^2*q13^2-4*n2*q12^2*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3+8*q12*q13^3-8*n2*q12*q13^3+4*q13^4-4*n2*q13^4-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23+8*q12^2*q13*q23-8*n2*q12^2*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23+24*q12*q13^2*q23-24*n2*q12*q13^2*q23+16*q13^3*q23-16*n2*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2+4*q12^2*q23^2-4*n2*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2+24*q12*q13*q23^2-24*n2*q12*q13*q23^2+24*q13^2*q23^2-24*n2*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+8*q12*q23^3-8*n2*q12*q23^3+16*q13*q23^3-16*n2*q13*q23^3+4*q23^4-4*n2*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-4*q12*q13^2*q33+4*n2*q12*q13^2*q33+4*q13^3*q33-4*n2*q13^3*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-8*q12*q13*q23*q33+8*n2*q12*q13*q23*q33+12*q13^2*q23*q33-12*n2*q13^2*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-4*q12*q23^2*q33+4*n2*q12*q23^2*q33+12*q13*q23^2*q33-12*n2*q13*q23^2*q33+4*q23^3*q33-4*n2*q23^3*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2+q13^2*q33^2-n2*q13^2*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2+2*q13*q23*q33^2-2*n2*q13*q23*q33^2+q23^2*q33^2-n2*q23^2*q33^2-2*q12*q33^3+2*n2*q12*q33^3)+mbox1l(n1,-1+n2,2+n3,-1+n4)*prf(4*M`j'^2*q12^2*q13+4*M`j'^2*n3*q12^2*q13-2*q12^3*q13-2*n3*q12^3*q13+2*M`j'^2*q12*q13^2+2*M`j'^2*n3*q12*q13^2-2*q12^2*q13^2-2*n3*q12^2*q13^2+4*M`j'^2*q12^2*q23+4*M`j'^2*n3*q12^2*q23-2*q12^3*q23-2*n3*q12^3*q23+8*M`j'^2*q12*q13*q23+8*M`j'^2*n3*q12*q13*q23-6*q12^2*q13*q23-6*n3*q12^2*q13*q23+2*M`j'^2*q13^2*q23+2*M`j'^2*n3*q13^2*q23-2*q12*q13^2*q23-2*n3*q12*q13^2*q23+6*M`j'^2*q12*q23^2+6*M`j'^2*n3*q12*q23^2-4*q12^2*q23^2-4*n3*q12^2*q23^2+4*M`j'^2*q13*q23^2+4*M`j'^2*n3*q13*q23^2-4*q12*q13*q23^2-4*n3*q12*q13*q23^2+2*M`j'^2*q23^3+2*M`j'^2*n3*q23^3-2*q12*q23^3-2*n3*q12*q23^3-2*q12^3*q33-2*n3*q12^3*q33-3*q12^2*q13*q33-3*n3*q12^2*q13*q33-5*q12^2*q23*q33-5*n3*q12^2*q23*q33-3*q12*q13*q23*q33-3*n3*q12*q13*q23*q33-3*q12*q23^2*q33-3*n3*q12*q23^2*q33-q12^2*q33^2-n3*q12^2*q33^2-q12*q23*q33^2-n3*q12*q23*q33^2,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2+4*q12^2*q13^2-4*n2*q12^2*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3+8*q12*q13^3-8*n2*q12*q13^3+4*q13^4-4*n2*q13^4-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23+8*q12^2*q13*q23-8*n2*q12^2*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23+24*q12*q13^2*q23-24*n2*q12*q13^2*q23+16*q13^3*q23-16*n2*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2+4*q12^2*q23^2-4*n2*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2+24*q12*q13*q23^2-24*n2*q12*q13*q23^2+24*q13^2*q23^2-24*n2*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+8*q12*q23^3-8*n2*q12*q23^3+16*q13*q23^3-16*n2*q13*q23^3+4*q23^4-4*n2*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-4*q12*q13^2*q33+4*n2*q12*q13^2*q33+4*q13^3*q33-4*n2*q13^3*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q3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2*q13*q23*q33-n3*q12*q13*q23*q33-7*q13^2*q23*q33-7*n3*q13^2*q23*q33+4*M`j'^2*q23^2*q33+4*M`j'^2*n3*q23^2*q33-4*q12*q23^2*q33-4*n3*q12*q23^2*q33-5*q13*q23^2*q33-5*n3*q13*q23^2*q33-2*q23^3*q33-2*n3*q23^3*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n3*q12*q33^2+2*q12^2*q33^2+2*n3*q12^2*q33^2+4*q12*q13*q33^2+4*n3*q12*q13*q33^2-q13^2*q33^2-n3*q13^2*q33^2+q12*q23*q33^2+n3*q12*q23*q33^2-q13*q23*q33^2-n3*q13*q23*q33^2-q23^2*q33^2-n3*q23^2*q33^2+q12*q33^3+n3*q12*q33^3,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2+4*q12^2*q13^2-4*n2*q12^2*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3+8*q12*q13^3-8*n2*q12*q13^3+4*q13^4-4*n2*q13^4-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23+8*q12^2*q13*q23-8*n2*q12^2*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23+24*q12*q13^2*q23-24*n2*q12*q13^2*q23+16*q13^3*q23-16*n2*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2+4*q12^2*q23^2-4*n2*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2+24*q12*q13*q23^2-24*n2*q12*q13*q23^2+24*q13^2*q23^2-24*n2*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+8*q12*q23^3-8*n2*q12*q23^3+16*q13*q23^3-16*n2*q13*q23^3+4*q23^4-4*n2*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-4*q12*q13^2*q33+4*n2*q12*q13^2*q33+4*q13^3*q33-4*n2*q13^3*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-8*q12*q13*q23*q33+8*n2*q12*q13*q23*q33+12*q13^2*q23*q33-12*n2*q13^2*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-4*q12*q23^2*q33+4*n2*q12*q23^2*q33+12*q13*q23^2*q33-12*n2*q13*q23^2*q33+4*q23^3*q33-4*n2*q23^3*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2+q13^2*q33^2-n2*q13^2*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2+2*q13*q23*q33^2-2*n2*q13*q23*q33^2+q23^2*q33^2-n2*q23^2*q33^2-2*q12*q33^3+2*n2*q12*q33^3)+mbox1l(1+n1,-1+n2,1+n3,n4)*prf(-4*M`j'^2*n1*q12*q13^3-12*M`j'^2*n1*q12*q13^2*q23-4*M`j'^2*n1*q13^3*q23-12*M`j'^2*n1*q12*q13*q23^2-12*M`j'^2*n1*q13^2*q23^2-4*M`j'^2*n1*q12*q23^3-12*M`j'^2*n1*q13*q23^3-4*M`j'^2*n1*q23^4+4*n1*q12^3*q13*q33-8*M`j'^2*n1*q12*q13^2*q33+8*n1*q12^2*q13^2*q33+4*n1*q12*q13^3*q33+16*M`j'^2*n1*q12^2*q23*q33-4*n1*q12^3*q23*q33+8*M`j'^2*n1*q12*q13*q23*q33+4*n1*q12*q13^2*q23*q33+16*M`j'^2*n1*q12*q23^2*q33-8*n1*q12^2*q23^2*q33-4*n1*q12*q13*q23^2*q33-4*n1*q12*q23^3*q33-4*M`j'^2*n1*q12*q13*q33^2+4*n1*q12^2*q13*q33^2+4*n1*q12*q13^2*q33^2+4*M`j'^2*n1*q12*q23*q33^2-4*n1*q12^2*q23*q33^2-4*n1*q12*q23^2*q33^2+n1*q12*q13*q33^3-n1*q12*q23*q33^3,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2+4*q12^2*q13^2-4*n2*q12^2*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3+8*q12*q13^3-8*n2*q12*q13^3+4*q13^4-4*n2*q13^4-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23+8*q12^2*q13*q23-8*n2*q12^2*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23+24*q12*q13^2*q23-24*n2*q12*q13^2*q23+16*q13^3*q23-16*n2*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2+4*q12^2*q23^2-4*n2*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2+24*q12*q13*q23^2-24*n2*q12*q13*q23^2+24*q13^2*q23^2-24*n2*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+8*q12*q23^3-8*n2*q12*q23^3+16*q13*q23^3-16*n2*q13*q23^3+4*q23^4-4*n2*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-4*q12*q13^2*q33+4*n2*q12*q13^2*q33+4*q13^3*q33-4*n2*q13^3*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-8*q12*q13*q23*q33+8*n2*q12*q13*q23*q33+12*q13^2*q23*q33-12*n2*q13^2*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-4*q12*q23^2*q33+4*n2*q12*q23^2*q33+12*q13*q23^2*q33-12*n2*q13*q23^2*q33+4*q23^3*q33-4*n2*q23^3*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2+q13^2*q33^2-n2*q13^2*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2+2*q13*q23*q33^2-2*n2*q13*q23*q33^2+q23^2*q33^2-n2*q23^2*q33^2-2*q12*q33^3+2*n2*q12*q33^3)+mbox1l(n1,-1+n2,2+n3,n4)*prf(4*M`j'^2*q12^2*q13^2+4*M`j'^2*n3*q12^2*q13^2-4*q12^3*q13^2-4*n3*q12^3*q13^2-4*q12^2*q13^3-4*n3*q12^2*q13^3-4*q12^3*q13*q23-4*n3*q12^3*q13*q23-12*q12^2*q13^2*q23-12*n3*q12^2*q13^2*q23-4*q12*q13^3*q23-4*n3*q12*q13^3*q23-4*M`j'^2*q12^2*q23^2-4*M`j'^2*n3*q12^2*q23^2-8*M`j'^2*q12*q13*q23^2-8*M`j'^2*n3*q12*q13*q23^2-8*q12^2*q13*q23^2-8*n3*q12^2*q13*q23^2-4*M`j'^2*q13^2*q23^2-4*M`j'^2*n3*q13^2*q23^2-8*q12*q13^2*q23^2-8*n3*q12*q13^2*q23^2-8*M`j'^2*q12*q23^3-8*M`j'^2*n3*q12*q23^3-8*M`j'^2*q13*q23^3-8*M`j'^2*n3*q13*q23^3-4*q12*q13*q23^3-4*n3*q12*q13*q23^3-4*M`j'^2*q23^4-4*M`j'^2*n3*q23^4+8*M`j'^2*q12^3*q33+8*M`j'^2*n3*q12^3*q33+12*M`j'^2*q12^2*q13*q33+12*M`j'^2*n3*q12^2*q13*q33-6*q12^3*q13*q33-6*n3*q12^3*q13*q33-8*q12^2*q13^2*q33-8*n3*q12^2*q13^2*q33+20*M`j'^2*q12^2*q23*q33+20*M`j'^2*n3*q12^2*q23*q33-2*q12^3*q23*q33-2*n3*q12^3*q23*q33+12*M`j'^2*q12*q13*q23*q33+12*M`j'^2*n3*q12*q13*q23*q33-16*q12^2*q13*q23*q33-16*n3*q12^2*q13*q23*q33-8*q12*q13^2*q23*q33-8*n3*q12*q13^2*q23*q33+12*M`j'^2*q12*q23^2*q33+12*M`j'^2*n3*q12*q23^2*q33-4*q12^2*q23^2*q33-4*n3*q12^2*q23^2*q33-10*q12*q13*q23^2*q33-10*n3*q12*q13*q23^2*q33-2*q12*q23^3*q33-2*n3*q12*q23^3*q33+4*M`j'^2*q12^2*q33^2+4*M`j'^2*n3*q12^2*q33^2-2*q12^3*q33^2-2*n3*q12^3*q33^2-5*q12^2*q13*q33^2-5*n3*q12^2*q13*q33^2+4*M`j'^2*q12*q23*q33^2+4*M`j'^2*n3*q12*q23*q33^2-5*q12^2*q23*q33^2-5*n3*q12^2*q23*q33^2-5*q12*q13*q23*q33^2-5*n3*q12*q13*q23*q33^2-3*q12*q23^2*q33^2-3*n3*q12*q23^2*q33^2-q12^2*q33^3-n3*q12^2*q33^3-q12*q23*q33^3-n3*q12*q23*q33^3,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2+4*q12^2*q13^2-4*n2*q12^2*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3+8*q12*q13^3-8*n2*q12*q13^3+4*q13^4-4*n2*q13^4-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23+8*q12^2*q13*q23-8*n2*q12^2*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23+24*q12*q13^2*q23-24*n2*q12*q13^2*q23+16*q13^3*q23-16*n2*q13^3*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2+4*q12^2*q23^2-4*n2*q12^2*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2+24*q12*q13*q23^2-24*n2*q12*q13*q23^2+24*q13^2*q23^2-24*n2*q13^2*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+8*q12*q23^3-8*n2*q12*q23^3+16*q13*q23^3-16*n2*q13*q23^3+4*q23^4-4*n2*q23^4+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-4*q12*q13^2*q33+4*n2*q12*q13^2*q33+4*q13^3*q33-4*n2*q13^3*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-8*q12*q13*q23*q33+8*n2*q12*q13*q23*q33+12*q13^2*q23*q33-12*n2*q13^2*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-4*q12*q23^2*q33+4*n2*q12*q23^2*q33+12*q13*q23^2*q33-12*n2*q13*q23^2*q33+4*q23^3*q33-4*n2*q23^3*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2+q13^2*q33^2-n2*q13^2*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2+2*q13*q23*q33^2-2*n2*q13*q23*q33^2+q23^2*q33^2-n2*q23^2*q33^2-2*q12*q33^3+2*n2*q12*q33^3); Identify,ifmatch->jump mbox1l(n1?neg_,n2?{,>1},n3?neg0_,n4?pos_) = mbox1l(2+n1,-1+n2,n3,-1+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13+2*M`j'^2*q23+2*M`j'^2*n1*q23,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(1+n1,-2+n2,n3,1+n4)*prf(2*M`j'^2*n4*q13+2*M`j'^2*n4*q23,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(n1,-1+n2,1+n3,n4)*prf(-(n3*q12)-2*n3*q13-n3*q23-n3*q33,-2*q12+2*n2*q12-2*q13+2*n2*q13-2*q23+2*n2*q23-q33+n2*q33)+mbox1l(1+n1,n2,n3,-1+n4)*prf(-8*M`j'^2*q12+4*q12^2-2*M`j'^2*q13+4*q12*q13-2*M`j'^2*q23+4*q12*q23+2*q12*q33,-8*M`j'^2*q12+4*q12^2-8*M`j'^2*q13+8*q12*q13+4*q13^2-8*M`j'^2*q23+8*q12*q23+8*q13*q23+4*q23^2-4*M`j'^2*q33+4*q12*q33+4*q13*q33+4*q23*q33+q33^2)+mbox1l(1+n1,-1+n2,1+n3,-1+n4)*prf(-4*M`j'^2*n3*q12+2*n3*q12^2-2*M`j'^2*n3*q13+2*n3*q12*q13-2*M`j'^2*n3*q23+2*n3*q12*q23+n3*q12*q33,8*M`j'^2*q12-8*M`j'^2*n2*q12-4*q12^2+4*n2*q12^2+8*M`j'^2*q13-8*M`j'^2*n2*q13-8*q12*q13+8*n2*q12*q13-4*q13^2+4*n2*q13^2+8*M`j'^2*q23-8*M`j'^2*n2*q23-8*q12*q23+8*n2*q12*q23-8*q13*q23+8*n2*q13*q23-4*q23^2+4*n2*q23^2+4*M`j'^2*q33-4*M`j'^2*n2*q33-4*q12*q33+4*n2*q12*q33-4*q13*q33+4*n2*q13*q33-4*q23*q33+4*n2*q23*q33-q33^2+n2*q33^2)+mbox1l(2+n1,-2+n2,n3,n4)*prf(-2*M`j'^2*q13-2*M`j'^2*n1*q13-2*M`j'^2*q23-2*M`j'^2*n1*q23-4*M`j'^2*q33-4*M`j'^2*n1*q33+2*q12*q33+2*n1*q12*q33+2*q13*q33+2*n1*q13*q33+2*q23*q33+2*n1*q23*q33+q33^2+n1*q33^2,8*M`j'^2*q12-8*M`j'^2*n2*q12-4*q12^2+4*n2*q12^2+8*M`j'^2*q13-8*M`j'^2*n2*q13-8*q12*q13+8*n2*q12*q13-4*q13^2+4*n2*q13^2+8*M`j'^2*q23-8*M`j'^2*n2*q23-8*q12*q23+8*n2*q12*q23-8*q13*q23+8*n2*q13*q23-4*q23^2+4*n2*q23^2+4*M`j'^2*q33-4*M`j'^2*n2*q33-4*q12*q33+4*n2*q12*q33-4*q13*q33+4*n2*q13*q33-4*q23*q33+4*n2*q23*q33-q33^2+n2*q33^2)+mbox1l(1+n1,-1+n2,n3,n4)*(tmpprf(ep,1)*prf(-4*q12*q13-4*q13^2-4*q12*q23-8*q13*q23-4*q23^2-2*q13*q33-2*q23*q33,8*M`j'^2*q12-8*M`j'^2*n2*q12-4*q12^2+4*n2*q12^2+8*M`j'^2*q13-8*M`j'^2*n2*q13-8*q12*q13+8*n2*q12*q13-4*q13^2+4*n2*q13^2+8*M`j'^2*q23-8*M`j'^2*n2*q23-8*q12*q23+8*n2*q12*q23-8*q13*q23+8*n2*q13*q23-4*q23^2+4*n2*q23^2+4*M`j'^2*q33-4*M`j'^2*n2*q33-4*q12*q33+4*n2*q12*q33-4*q13*q33+4*n2*q13*q33-4*q23*q33+4*n2*q23*q33-q33^2+n2*q33^2)+prf(10*M`j'^2*q13+4*M`j'^2*n1*q13-6*M`j'^2*n2*q13+2*M`j'^2*n4*q13+4*q12*q13-4*n1*q12*q13-2*n3*q12*q13-4*n4*q12*q13+4*q13^2-4*n1*q13^2-2*n3*q13^2-4*n4*q13^2+10*M`j'^2*q23+4*M`j'^2*n1*q23-6*M`j'^2*n2*q23+2*M`j'^2*n4*q23+4*q12*q23-4*n1*q12*q23-2*n3*q12*q23-4*n4*q12*q23+8*q13*q23-8*n1*q13*q23-4*n3*q13*q23-8*n4*q13*q23+4*q23^2-4*n1*q23^2-2*n3*q23^2-4*n4*q23^2+8*M`j'^2*q33+4*M`j'^2*n1*q33-4*M`j'^2*n2*q33-4*q12*q33-2*n1*q12*q33+2*n2*q12*q33-2*q13*q33-4*n1*q13*q33+2*n2*q13*q33-n3*q13*q33-2*n4*q13*q33-2*q23*q33-4*n1*q23*q33+2*n2*q23*q33-n3*q23*q33-2*n4*q23*q33-2*q33^2-n1*q33^2+n2*q33^2,8*M`j'^2*q12-8*M`j'^2*n2*q12-4*q12^2+4*n2*q12^2+8*M`j'^2*q13-8*M`j'^2*n2*q13-8*q12*q13+8*n2*q12*q13-4*q13^2+4*n2*q13^2+8*M`j'^2*q23-8*M`j'^2*n2*q23-8*q12*q23+8*n2*q12*q23-8*q13*q23+8*n2*q13*q23-4*q23^2+4*n2*q23^2+4*M`j'^2*q33-4*M`j'^2*n2*q33-4*q12*q33+4*n2*q12*q33-4*q13*q33+4*n2*q13*q33-4*q23*q33+4*n2*q23*q33-q33^2+n2*q33^2))+mbox1l(1+n1,-2+n2,1+n3,n4)*prf(-6*M`j'^2*n3*q13+2*n3*q12*q13+2*n3*q13^2-2*M`j'^2*n3*q23+2*n3*q13*q23-4*M`j'^2*n3*q33+2*n3*q12*q33+3*n3*q13*q33+2*n3*q23*q33+n3*q33^2,8*M`j'^2*q12-8*M`j'^2*n2*q12-4*q12^2+4*n2*q12^2+8*M`j'^2*q13-8*M`j'^2*n2*q13-8*q12*q13+8*n2*q12*q13-4*q13^2+4*n2*q13^2+8*M`j'^2*q23-8*M`j'^2*n2*q23-8*q12*q23+8*n2*q12*q23-8*q13*q23+8*n2*q13*q23-4*q23^2+4*n2*q23^2+4*M`j'^2*q33-4*M`j'^2*n2*q33-4*q12*q33+4*n2*q12*q33-4*q13*q33+4*n2*q13*q33-4*q23*q33+4*n2*q23*q33-q33^2+n2*q33^2)+mbox1l(2+n1,-1+n2,n3,n4)*prf(4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2+8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23+4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2-8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33+4*q12^2*q33+4*n1*q12^2*q33+4*q12*q13*q33+4*n1*q12*q13*q33+4*q12*q23*q33+4*n1*q12*q23*q33+2*q12*q33^2+2*n1*q12*q33^2,8*M`j'^2*q12-8*M`j'^2*n2*q12-4*q12^2+4*n2*q12^2+8*M`j'^2*q13-8*M`j'^2*n2*q13-8*q12*q13+8*n2*q12*q13-4*q13^2+4*n2*q13^2+8*M`j'^2*q23-8*M`j'^2*n2*q23-8*q12*q23+8*n2*q12*q23-8*q13*q23+8*n2*q13*q23-4*q23^2+4*n2*q23^2+4*M`j'^2*q33-4*M`j'^2*n2*q33-4*q12*q33+4*n2*q12*q33-4*q13*q33+4*n2*q13*q33-4*q23*q33+4*n2*q23*q33-q33^2+n2*q33^2)+mbox1l(1+n1,-1+n2,1+n3,n4)*prf(-4*M`j'^2*n3*q12*q13+4*n3*q12^2*q13+4*n3*q12*q13^2+4*M`j'^2*n3*q12*q23+4*M`j'^2*n3*q13*q23+4*n3*q12*q13*q23+4*M`j'^2*n3*q23^2-4*M`j'^2*n3*q12*q33+2*n3*q12^2*q33+4*n3*q12*q13*q33+2*n3*q12*q23*q33+n3*q12*q33^2,8*M`j'^2*q12-8*M`j'^2*n2*q12-4*q12^2+4*n2*q12^2+8*M`j'^2*q13-8*M`j'^2*n2*q13-8*q12*q13+8*n2*q12*q13-4*q13^2+4*n2*q13^2+8*M`j'^2*q23-8*M`j'^2*n2*q23-8*q12*q23+8*n2*q12*q23-8*q13*q23+8*n2*q13*q23-4*q23^2+4*n2*q23^2+4*M`j'^2*q33-4*M`j'^2*n2*q33-4*q12*q33+4*n2*q12*q33-4*q13*q33+4*n2*q13*q33-4*q23*q33+4*n2*q23*q33-q33^2+n2*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?neg0_,n4?{,>1}) = mbox1l(1+n1,n2,n3,-2+n4)*prf(2*M`j'^2*n1,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,n3,-2+n4)*prf(2*M`j'^2*n2,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,1+n3,-2+n4)*prf(2*M`j'^2*n3,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-4*M`j'^2*n3*q12-4*M`j'^2*n3*q23,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(n1,-1+n2,n3,n4)*prf(-2*M`j'^2+2*q12+2*q13+2*q23+q33,8*M`j'^2*q12-4*q12^2+8*M`j'^2*q13-8*q12*q13-4*q13^2+8*M`j'^2*q23-8*q12*q23-8*q13*q23-4*q23^2+4*M`j'^2*q33-4*q12*q33-4*q13*q33-4*q23*q33-q33^2)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(-2*M`j'^2*n1+2*n1*q12+2*n1*q13+2*n1*q23+n1*q33,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3+2*n3*q12+2*n3*q13+2*n3*q23+n3*q33,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(4*q12+4*q13+4*q23+2*q33,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2)+prf(-2*M`j'^2-2*M`j'^2*n2+2*M`j'^2*n4-10*q12+2*n1*q12+4*n2*q12+2*n3*q12+2*n4*q12-10*q13+2*n1*q13+4*n2*q13+2*n3*q13+2*n4*q13-10*q23+2*n1*q23+4*n2*q23+2*n3*q23+2*n4*q23-5*q33+n1*q33+2*n2*q33+n3*q33+n4*q33,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2))+mbox1l(1+n1,n2,n3,-1+n4)*prf(-8*M`j'^2*n1*q12+4*n1*q12^2-4*M`j'^2*n1*q13+4*n1*q12*q13-4*M`j'^2*n1*q23+4*n1*q12*q23+2*n1*q12*q33,-8*M`j'^2*q12+8*M`j'^2*n4*q12+4*q12^2-4*n4*q12^2-8*M`j'^2*q13+8*M`j'^2*n4*q13+8*q12*q13-8*n4*q12*q13+4*q13^2-4*n4*q13^2-8*M`j'^2*q23+8*M`j'^2*n4*q23+8*q12*q23-8*n4*q12*q23+8*q13*q23-8*n4*q13*q23+4*q23^2-4*n4*q23^2-4*M`j'^2*q33+4*M`j'^2*n4*q33+4*q12*q33-4*n4*q12*q33+4*q13*q33-4*n4*q13*q33+4*q23*q33-4*n4*q23*q33+q33^2-n4*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?{,>1},n3?neg0_,n4?pos_) = mbox1l(1+n1,-2+n2,n3,n4)*prf(2*M`j'^2*n1,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(n1,-2+n2,1+n3,n4)*prf(2*M`j'^2*n3,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(n1,-2+n2,n3,1+n4)*prf(2*M`j'^2*n4,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(n1,n2,n3,-1+n4)*prf(-2*M`j'^2+2*q12+2*q13+2*q23+q33,8*M`j'^2*q12-4*q12^2+8*M`j'^2*q13-8*q12*q13-4*q13^2+8*M`j'^2*q23-8*q12*q23-8*q13*q23-4*q23^2+4*M`j'^2*q33-4*q12*q33-4*q13*q33-4*q23*q33-q33^2)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(-2*M`j'^2*n1+2*n1*q12+2*n1*q13+2*n1*q23+n1*q33,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3+2*n3*q12+2*n3*q13+2*n3*q23+n3*q33,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(n1,-1+n2,n3,n4)*(tmpprf(ep,1)*prf(4*q12+4*q13+4*q23+2*q33,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+prf(-2*M`j'^2+2*M`j'^2*n2-2*M`j'^2*n4-10*q12+2*n1*q12+2*n2*q12+2*n3*q12+4*n4*q12-10*q13+2*n1*q13+2*n2*q13+2*n3*q13+4*n4*q13-10*q23+2*n1*q23+2*n2*q23+2*n3*q23+4*n4*q23-5*q33+n1*q33+n2*q33+n3*q33+2*n4*q33,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2))+mbox1l(1+n1,-1+n2,n3,n4)*prf(-4*M`j'^2*n1*q13-4*M`j'^2*n1*q23-4*M`j'^2*n1*q33+2*n1*q12*q33+2*n1*q13*q33+2*n1*q23*q33+n1*q33^2,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2)+mbox1l(n1,-1+n2,1+n3,n4)*prf(-4*M`j'^2*n3*q12-8*M`j'^2*n3*q13+4*n3*q12*q13+4*n3*q13^2-4*M`j'^2*n3*q23+4*n3*q13*q23-4*M`j'^2*n3*q33+2*n3*q12*q33+4*n3*q13*q33+2*n3*q23*q33+n3*q33^2,-8*M`j'^2*q12+8*M`j'^2*n2*q12+4*q12^2-4*n2*q12^2-8*M`j'^2*q13+8*M`j'^2*n2*q13+8*q12*q13-8*n2*q12*q13+4*q13^2-4*n2*q13^2-8*M`j'^2*q23+8*M`j'^2*n2*q23+8*q12*q23-8*n2*q12*q23+8*q13*q23-8*n2*q13*q23+4*q23^2-4*n2*q23^2-4*M`j'^2*q33+4*M`j'^2*n2*q33+4*q12*q33-4*n2*q12*q33+4*q13*q33-4*n2*q13*q33+4*q23*q33-4*n2*q23*q33+q33^2-n2*q33^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?neg_,n4?pos_) = mbox1l(n1,n2,1+n3,-1+n4)*prf(-(q12*q13)+q12*q23,-q13^2-2*q13*q23-q23^2+2*q12*q33)+mbox1l(-1+n1,n2,2+n3,-1+n4)*prf(-q12^2-n3*q12^2-q12*q23-n3*q12*q23,-q13^2+n1*q13^2-2*q13*q23+2*n1*q13*q23-q23^2+n1*q23^2+2*q12*q33-2*n1*q12*q33)+mbox1l(-2+n1,n2,2+n3,n4)*prf(q12^2+n3*q12^2+2*q12*q23+2*n3*q12*q23+q23^2+n3*q23^2,-q13^2+n1*q13^2-2*q13*q23+2*n1*q13*q23-q23^2+n1*q23^2+2*q12*q33-2*n1*q12*q33)+mbox1l(n1,-1+n2,1+n3,n4)*prf(q13^2+q13*q23-q12*q33,q13^2+2*q13*q23+q23^2-2*q12*q33)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(-(q12*q13)-n3*q12*q13+q13*q23+n3*q13*q23-q12*q33-n3*q12*q33,-q13^2+n1*q13^2-2*q13*q23+2*n1*q13*q23-q23^2+n1*q23^2+2*q12*q33-2*n1*q12*q33)+mbox1l(-1+n1,n2,1+n3,n4)*prf(2*q12*q13-n1*q12*q13+n3*q12*q13-2*q12*q23+n1*q12*q23-n3*q12*q23-2*q13*q23+n1*q13*q23-n3*q13*q23-2*q23^2+n1*q23^2-n3*q23^2+2*q12*q33-n1*q12*q33+n3*q12*q33,-q13^2+n1*q13^2-2*q13*q23+2*n1*q13*q23-q23^2+n1*q23^2+2*q12*q33-2*n1*q12*q33)+mbox1l(n1,n2,1+n3,n4)*prf(-2*q12*q13^2-2*q12*q13*q23+2*q12^2*q33-q12*q13*q33+q12*q23*q33,-q13^2-2*q13*q23-q23^2+2*q12*q33)+mbox1l(-1+n1,n2,2+n3,n4)*prf(-2*q12^2*q13-2*n3*q12^2*q13-2*q12*q13*q23-2*n3*q12*q13*q23-q12^2*q33-n3*q12^2*q33-q12*q23*q33-n3*q12*q23*q33,-q13^2+n1*q13^2-2*q13*q23+2*n1*q13*q23-q23^2+n1*q23^2+2*q12*q33-2*n1*q12*q33); Identify,ifmatch->jump mbox1l(n1?neg_,1,0,1) = tmpprf(1,-1+2*ep+n1)*mbox1l(n1,0,0,2)*prf(-2*M`j'^2,2*q12+2*q13+2*q23+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,0,0,1)*prf(-2*M`j'^2*n1,2*q12+2*q13+2*q23+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,0,0,2)*prf(2*M`j'^2*q13+2*M`j'^2*q23,2*q12+2*q13+2*q23+q33)+mbox1l(1+n1,1,0,1)*(tmpprf(ep,-1+2*ep+n1)*prf(2*q13+2*q23,1)+tmpprf(1,-1+2*ep+n1)*prf(2*n1*q13+2*n1*q23,1))+tmpprf(1,-1+2*ep+n1)*mbox1l(2+n1,1,0,0)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13+2*M`j'^2*q23+2*M`j'^2*n1*q23,2*q12+2*q13+2*q23+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(n1,2,0,0)*prf(2*M`j'^2-2*q12-2*q13-2*q23-q33,2*q12+2*q13+2*q23+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,1,0,0)*prf(2*M`j'^2*n1-2*n1*q12-2*n1*q13-2*n1*q23-n1*q33,2*q12+2*q13+2*q23+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(1+n1,2,0,0)*prf(8*M`j'^2*q12-4*q12^2+2*M`j'^2*q13-4*q12*q13+2*M`j'^2*q23-4*q12*q23-2*q12*q33,2*q12+2*q13+2*q23+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(2+n1,0,0,1)*prf(2*M`j'^2*q13+2*M`j'^2*n1*q13+2*M`j'^2*q23+2*M`j'^2*n1*q23+4*M`j'^2*q33+4*M`j'^2*n1*q33-2*q12*q33-2*n1*q12*q33-2*q13*q33-2*n1*q13*q33-2*q23*q33-2*n1*q23*q33-q33^2-n1*q33^2,2*q12+2*q13+2*q23+q33)+tmpprf(1,-1+2*ep+n1)*mbox1l(2+n1,1,0,1)*prf(-4*M`j'^2*q13^2-4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23-8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2-4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33+8*M`j'^2*n1*q12*q33-4*q12^2*q33-4*n1*q12^2*q33-4*q12*q13*q33-4*n1*q12*q13*q33-4*q12*q23*q33-4*n1*q12*q23*q33-2*q12*q33^2-2*n1*q12*q33^2,2*q12+2*q13+2*q23+q33); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?{,>1},n4?neg_) = mbox1l(1+n1,-1+n2,-1+n3,1+n4)*prf(n1*q13,-q12+n3*q12)+mbox1l(-1+n1,1+n2,-1+n3,1+n4)*prf(-(n2*q12)-n2*q23,-q12+n3*q12)+mbox1l(1+n1,n2,-1+n3,1+n4)*prf(4*n1*q13+n1*q33,-1+n3)+mbox1l(n1,1+n2,-1+n3,1+n4)*prf(-2*n2*q12+2*n2*q13-2*n2*q23+n2*q33,-1+n3)+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(q13+n4*q13+q33+n4*q33,-q12+n3*q12)+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(-q12-n4*q12+2*q13+2*n4*q13-q23-n4*q23+q33+n4*q33,-q12+n3*q12)+mbox1l(1+n1,n2,-2+n3,1+n4)*prf(2*M`j'^2*n1*q12-4*M`j'^2*n1*q13-2*n1*q12*q13-n1*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,1+n2,-2+n3,1+n4)*prf(2*M`j'^2*n2*q12-2*n2*q12*q13+4*M`j'^2*n2*q23-n2*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-2+n3,2+n4)*prf(2*M`j'^2*q12+2*M`j'^2*n4*q12-4*M`j'^2*q13-4*M`j'^2*n4*q13-2*q12*q13-2*n4*q12*q13-4*M`j'^2*q33-4*M`j'^2*n4*q33-q12*q33-n4*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-1+n3,1+n4)*(tmpprf(ep,1)*prf(-4*q12*q13-2*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+prf(-2*M`j'^2*q12-2*M`j'^2*n1*q12+2*M`j'^2*n3*q12-2*M`j'^2*q13+2*M`j'^2*n1*q13-2*M`j'^2*n4*q13+10*q12*q13-2*n1*q12*q13-2*n2*q12*q13-4*n3*q12*q13-2*n4*q12*q13+2*M`j'^2*q23-2*M`j'^2*n2*q23+2*M`j'^2*n4*q23+5*q12*q33-n1*q12*q33-n2*q12*q33-2*n3*q12*q33-n4*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12))+mbox1l(n1,n2,-1+n3,2+n4)*prf(12*M`j'^2*q12*q13+12*M`j'^2*n4*q12*q13-4*M`j'^2*q13^2-4*M`j'^2*n4*q13^2-4*q12*q13^2-4*n4*q12*q13^2+4*M`j'^2*q13*q23+4*M`j'^2*n4*q13*q23+6*M`j'^2*q12*q33+6*M`j'^2*n4*q12*q33-2*M`j'^2*q13*q33-2*M`j'^2*n4*q13*q33-4*q12*q13*q33-4*n4*q12*q13*q33+2*M`j'^2*q23*q33+2*M`j'^2*n4*q23*q33-q12*q33^2-n4*q12*q33^2,-2*M`j'^2*q12+2*M`j'^2*n3*q12); Identify,ifmatch->jump mbox1l(n1?neg_,n2?pos_,n3?{,>1},n4?neg0_) = mbox1l(2+n1,n2,-2+n3,n4)*prf(1+n1,-1+n3)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-n2,-1+n3)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(n2,-1+n3)+mbox1l(1+n1,n2,-1+n3,n4)*prf(-2-n1+n3,-1+n3)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-n4,-1+n3)+mbox1l(1+n1,n2,-2+n3,1+n4)*prf(n4,-1+n3)+mbox1l(1+n1,1+n2,-1+n3,n4)*prf(-2*n2*q12,-1+n3)+mbox1l(1+n1,n2,-1+n3,1+n4)*prf(2*n4*q13,-1+n3); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?{,>1},n3?pos_,n4?neg_) = mbox1l(1+n1,-1+n2,-1+n3,1+n4)*prf(n1*q13,-q12+n2*q12)+mbox1l(n1,-1+n2,n3,1+n4)*prf(q13-n1*q13+n4*q13,-q12+n2*q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-q23,q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(q12+q23,q12)+mbox1l(n1,n2,n3,1+n4)*prf(-2*q13-q33,1)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-2*q13-2*n4*q13-q33-n4*q33,-q12+n2*q12)+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(q13+n4*q13+q33+n4*q33,-q12+n2*q12)+mbox1l(n1,-1+n2,n3,2+n4)*prf(2*q13^2+2*n4*q13^2+q13*q33+n4*q13*q33,-q12+n2*q12); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?{,>1},n4?neg0_) = mbox1l(1+n1,n2,-1+n3,n4)*prf(-n1,-1+n3)+mbox1l(1+n1,n2,-2+n3,n4)*prf(n1,-2*M`j'^2+2*M`j'^2*n3)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-n2,-1+n3)+mbox1l(n1,1+n2,-2+n3,n4)*prf(n2,-2*M`j'^2+2*M`j'^2*n3)+mbox1l(n1,n2,-2+n3,1+n4)*prf(n4,-2*M`j'^2+2*M`j'^2*n3)+mbox1l(n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(1,-M`j'^2+M`j'^2*n3)+prf(-6+n1+n2+2*n3+n4,-2*M`j'^2+2*M`j'^2*n3))+mbox1l(n1,n2,-1+n3,1+n4)*prf(-2*M`j'^2*n4+2*n4*q13+n4*q33,-2*M`j'^2+2*M`j'^2*n3); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?{,>1},n4?neg0_) = mbox1l(1+n1,n2,-1+n3,n4)*prf(-n1,-1+n3)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(n1,-1+n3)+mbox1l(n1,2+n2,-2+n3,n4)*prf(1+n2,-1+n3)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-2-n2+n3,-1+n3)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-n4,-1+n3)+mbox1l(n1,1+n2,-2+n3,1+n4)*prf(n4,-1+n3)+mbox1l(1+n1,1+n2,-1+n3,n4)*prf(-2*n1*q12,-1+n3)+mbox1l(n1,1+n2,-1+n3,1+n4)*prf(-2*n4*q12-2*n4*q23,-1+n3); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?pos_,n4?neg_) = mbox1l(n1,-1+n2,n3,1+n4)*prf(-q13,q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(q13,q12)+mbox1l(-1+n1,1+n2,-1+n3,1+n4)*prf(-(n2*q23),-q12+n1*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-2*q12+n1*q12-n4*q12-q23+n2*q23-n4*q23,-q12+n1*q12)+mbox1l(-2+n1,n2,n3,2+n4)*prf(q12+n4*q12+q23+n4*q23,-q12+n1*q12)+mbox1l(n1,n2,n3,1+n4)*prf(-2*q13-q33,1)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-q13-n4*q13-q33-n4*q33,-q12+n1*q12)+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(q13+n4*q13+q33+n4*q33,-q12+n1*q12)+mbox1l(-1+n1,n2,n3,2+n4)*prf(-2*q12*q13-2*n4*q12*q13-2*q13*q23-2*n4*q13*q23-q12*q33-n4*q12*q33-q23*q33-n4*q23*q33,-q12+n1*q12); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?pos_,n4?neg0_) = mbox1l(1+n1,n2,-1+n3,n4)*prf(n1,n1-n2)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-n2,n1-n2)+mbox1l(n1,-1+n2,n3,1+n4)*prf(-(n4*q13),n1*q12-n2*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-(n4*q12)-n4*q23,n1*q12-n2*q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(n4*q12+n4*q13+n4*q23,n1*q12-n2*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?neg_,n4?{,>1}) = mbox1l(1+n1,n2,1+n3,-2+n4)*prf(-2*M`j'^2*n1*q13,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,-1+n2,2+n3,-1+n4)*prf(-q13^3-n3*q13^3-q13^2*q23-n3*q13^2*q23,q13^2*q33-n4*q13^2*q33+2*q13*q23*q33-2*n4*q13*q23*q33+q23^2*q33-n4*q23^2*q33-2*q12*q33^2+2*n4*q12*q33^2)+mbox1l(n1,n2,2+n3,-2+n4)*prf(-4*M`j'^2*q12*q13^2-4*M`j'^2*n3*q12*q13^2+2*M`j'^2*q13^3+2*M`j'^2*n3*q13^3-4*M`j'^2*q12*q13*q23-4*M`j'^2*n3*q12*q13*q23+4*M`j'^2*q13^2*q23+4*M`j'^2*n3*q13^2*q23+2*M`j'^2*q13*q23^2+2*M`j'^2*n3*q13*q23^2-4*M`j'^2*q12*q13*q33-4*M`j'^2*n3*q12*q13*q33+q12*q13^2*q33+n3*q12*q13^2*q33+q12*q13*q23*q33+n3*q12*q13*q23*q33,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3)+mbox1l(-1+n1,n2,1+n3,n4)*prf(6*M`j'^2*q13+4*M`j'^2*q33-2*q13*q33-q33^2,4*M`j'^2*q33-q33^2)+mbox1l(n1,1+n2,1+n3,-2+n4)*prf(-8*M`j'^2*n2*q12*q13^2+2*M`j'^2*n2*q13^3-8*M`j'^2*n2*q12*q13*q23+4*M`j'^2*n2*q13^2*q23+2*M`j'^2*n2*q13*q23^2+8*M`j'^2*n2*q12^2*q33-4*M`j'^2*n2*q12*q13*q33+2*n2*q12*q13^2*q33+2*n2*q12*q13*q23*q33-2*n2*q12^2*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(8*M`j'^2*n2*q12*q13^2+2*M`j'^2*n2*q13^3+8*M`j'^2*n2*q12*q13*q23+4*M`j'^2*n2*q13^2*q23+2*M`j'^2*n2*q13*q23^2-8*M`j'^2*n2*q12^2*q33-2*n2*q12*q13^2*q33-4*M`j'^2*n2*q12*q23*q33-2*n2*q12*q13*q23*q33+2*n2*q12^2*q33^2-n2*q12*q13*q33^2+n2*q12*q23*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3)+mbox1l(-1+n1,n2,2+n3,-1+n4)*prf(4*M`j'^2*q12*q13^2+4*M`j'^2*n3*q12*q13^2+2*M`j'^2*q13^3+2*M`j'^2*n3*q13^3+4*M`j'^2*q12*q13*q23+4*M`j'^2*n3*q12*q13*q23-2*M`j'^2*q13*q23^2-2*M`j'^2*n3*q13*q23^2-q12*q13^2*q33-n3*q12*q13^2*q33+4*M`j'^2*q12*q23*q33+4*M`j'^2*n3*q12*q23*q33-q12*q13*q23*q33-n3*q12*q13*q23*q33+q13^2*q23*q33+n3*q13^2*q23*q33+q13*q23^2*q33+n3*q13*q23^2*q33-q12*q13*q33^2-n3*q12*q13*q33^2-q12*q23*q33^2-n3*q12*q23*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3)+mbox1l(n1,n2,1+n3,-1+n4)*(tmpprf(ep,1)*prf(2*q13^3*q33+4*q13^2*q23*q33+2*q13*q23^2*q33-4*q12*q13*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3)+prf(-6*M`j'^2*q13^3-2*M`j'^2*n1*q13^3-4*M`j'^2*n2*q13^3+6*M`j'^2*n4*q13^3-12*M`j'^2*q13^2*q23-4*M`j'^2*n1*q13^2*q23-8*M`j'^2*n2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-6*M`j'^2*q13*q23^2-2*M`j'^2*n1*q13*q23^2-4*M`j'^2*n2*q13*q23^2+6*M`j'^2*n4*q13*q23^2+16*M`j'^2*q12*q13*q33+4*M`j'^2*n1*q12*q13*q33+4*M`j'^2*n2*q12*q13*q33+4*M`j'^2*n3*q12*q13*q33-12*M`j'^2*n4*q12*q13*q33-3*q13^3*q33+2*n1*q13^3*q33+2*n2*q13^3*q33+n3*q13^3*q33-4*M`j'^2*q12*q23*q33+4*M`j'^2*n2*q12*q23*q33-4*M`j'^2*n3*q12*q23*q33-6*q13^2*q23*q33+4*n1*q13^2*q23*q33+4*n2*q13^2*q23*q33+2*n3*q13^2*q23*q33-3*q13*q23^2*q33+2*n1*q13*q23^2*q33+2*n2*q13*q23^2*q33+n3*q13*q23^2*q33+5*q12*q13*q33^2-4*n1*q12*q13*q33^2-3*n2*q12*q13*q33^2-3*n3*q12*q13*q33^2+q12*q23*q33^2-n2*q12*q23*q33^2+n3*q12*q23*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3))+mbox1l(n1,n2,2+n3,-1+n4)*prf(-8*M`j'^2*q12*q13^3-8*M`j'^2*n3*q12*q13^3+4*M`j'^2*q13^4+4*M`j'^2*n3*q13^4-8*M`j'^2*q12*q13^2*q23-8*M`j'^2*n3*q12*q13^2*q23+8*M`j'^2*q13^3*q23+8*M`j'^2*n3*q13^3*q23+4*M`j'^2*q13^2*q23^2+4*M`j'^2*n3*q13^2*q23^2-12*M`j'^2*q12*q13^2*q33-12*M`j'^2*n3*q12*q13^2*q33+2*q12*q13^3*q33+2*n3*q12*q13^3*q33-4*M`j'^2*q12*q13*q23*q33-4*M`j'^2*n3*q12*q13*q23*q33+2*q12*q13^2*q23*q33+2*n3*q12*q13^2*q23*q33+q12*q13^2*q33^2+n3*q12*q13^2*q33^2+q12*q13*q23*q33^2+n3*q12*q13*q23*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3)+mbox1l(n1,1+n2,1+n3,-1+n4)*prf(-8*M`j'^2*n2*q12*q13^3+4*M`j'^2*n2*q13^4-16*M`j'^2*n2*q12*q13^2*q23+12*M`j'^2*n2*q13^3*q23-8*M`j'^2*n2*q12*q13*q23^2+12*M`j'^2*n2*q13^2*q23^2+4*M`j'^2*n2*q13*q23^3+8*M`j'^2*n2*q12^2*q13*q33-16*M`j'^2*n2*q12*q13^2*q33+4*n2*q12*q13^3*q33+8*M`j'^2*n2*q12^2*q23*q33-16*M`j'^2*n2*q12*q13*q23*q33+8*n2*q12*q13^2*q23*q33+4*n2*q12*q13*q23^2*q33+8*M`j'^2*n2*q12^2*q33^2-6*n2*q12^2*q13*q33^2+2*n2*q12*q13^2*q33^2-2*n2*q12^2*q23*q33^2+2*n2*q12*q13*q23*q33^2-2*n2*q12^2*q33^3,4*M`j'^2*q13^2*q33-4*M`j'^2*n4*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n4*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n4*q12*q33^2-q13^2*q33^2+n4*q13^2*q33^2-2*q13*q23*q33^2+2*n4*q13*q23*q33^2-q23^2*q33^2+n4*q23^2*q33^2+2*q12*q33^3-2*n4*q12*q33^3); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg_,n3?neg0_,n4?{,>1}) = mbox1l(n1,n2,1+n3,-1+n4)*prf(n3*q13,-q33+n4*q33)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(-4*M`j'^2*n1*q12-2*M`j'^2*n1*q13-2*M`j'^2*n1*q23,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-4*M`j'^2*q12-4*M`j'^2*n2*q12-2*M`j'^2*q13-2*M`j'^2*n2*q13-2*M`j'^2*q23-2*M`j'^2*n2*q23,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,2+n2,n3,-2+n4)*prf(4*M`j'^2*q12+4*M`j'^2*n2*q12-2*M`j'^2*q13-2*M`j'^2*n2*q13-2*M`j'^2*q23-2*M`j'^2*n2*q23-2*q12*q33-2*n2*q12*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,1+n3,-2+n4)*prf(-2*M`j'^2*n3*q13-2*M`j'^2*n3*q23-n3*q12*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3*q13+2*M`j'^2*n3*q23-n3*q12*q33-n3*q23*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,n3,-1+n4)*(tmpprf(ep,1)*prf(-4*q12*q33-2*q13*q33-2*q23*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+prf(4*M`j'^2*q12+4*M`j'^2*n1*q12-4*M`j'^2*n4*q12+10*M`j'^2*q13+2*M`j'^2*n1*q13+4*M`j'^2*n2*q13-6*M`j'^2*n4*q13+10*M`j'^2*q23+2*M`j'^2*n1*q23+4*M`j'^2*n2*q23-6*M`j'^2*n4*q23+8*q12*q33-4*n1*q12*q33-2*n2*q12*q33-2*n3*q12*q33-2*n4*q12*q33+2*q13*q33-2*n1*q13*q33-2*n2*q13*q33-n3*q13*q33+2*q23*q33-2*n1*q23*q33-2*n2*q23*q33-n3*q23*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2))+mbox1l(-1+n1,1+n2,n3,n4)*prf(4*M`j'^2*q12+6*M`j'^2*q13+6*M`j'^2*q23+4*M`j'^2*q33-2*q12*q33-2*q13*q33-2*q23*q33-q33^2,4*M`j'^2*q33-q33^2)+mbox1l(n1,2+n2,n3,-1+n4)*prf(-4*M`j'^2*q13^2-4*M`j'^2*n2*q13^2-8*M`j'^2*q13*q23-8*M`j'^2*n2*q13*q23-4*M`j'^2*q23^2-4*M`j'^2*n2*q23^2+8*M`j'^2*q12*q33+8*M`j'^2*n2*q12*q33-4*q12^2*q33-4*n2*q12^2*q33-4*q12*q13*q33-4*n2*q12*q13*q33-4*q12*q23*q33-4*n2*q12*q23*q33-2*q12*q33^2-2*n2*q12*q33^2,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,1+n3,-1+n4)*prf(-4*M`j'^2*n3*q13^2-4*M`j'^2*n3*q13*q23+4*M`j'^2*n3*q12*q33-2*n3*q12*q13*q33-n3*q12*q33^2,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?neg0_,n3?neg_,n4?pos_) = mbox1l(n1,n2,1+n3,-1+n4)*prf(-2*M`j'^2*q13,4*M`j'^2*q33-q33^2)+mbox1l(-2+n1,n2,1+n3,1+n4)*prf(-2*M`j'^2*n4*q13,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(q13^3+n3*q13^3+q13^2*q23+n3*q13^2*q23+q13^2*q33+n3*q13^2*q33,q13^2*q33-n1*q13^2*q33+2*q13*q23*q33-2*n1*q13*q23*q33+q23^2*q33-n1*q23^2*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,n2,2+n3,-1+n4)*prf(4*M`j'^2*q12*q13^2+4*M`j'^2*n3*q12*q13^2+2*M`j'^2*q13^3+2*M`j'^2*n3*q13^3+4*M`j'^2*q12*q13*q23+4*M`j'^2*n3*q12*q13*q23+4*M`j'^2*q13^2*q23+4*M`j'^2*n3*q13^2*q23+2*M`j'^2*q13*q23^2+2*M`j'^2*n3*q13*q23^2-q12*q13^2*q33-n3*q12*q13^2*q33-q12*q13*q23*q33-n3*q12*q13*q23*q33-q12*q13*q33^2-n3*q12*q13*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(8*M`j'^2*n2*q12*q13^2+2*M`j'^2*n2*q13^3+8*M`j'^2*n2*q12*q13*q23+4*M`j'^2*n2*q13^2*q23+2*M`j'^2*n2*q13*q23^2-8*M`j'^2*n2*q12^2*q33-2*n2*q12*q13^2*q33-4*M`j'^2*n2*q12*q23*q33-2*n2*q12*q13*q23*q33+2*n2*q12^2*q33^2-n2*q12*q13*q33^2+n2*q12*q23*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3)+mbox1l(-2+n1,1+n2,1+n3,n4)*prf(-8*M`j'^2*n2*q12*q13^2-6*M`j'^2*n2*q13^3-8*M`j'^2*n2*q12*q13*q23-12*M`j'^2*n2*q13^2*q23-6*M`j'^2*n2*q13*q23^2+8*M`j'^2*n2*q12^2*q33+4*M`j'^2*n2*q12*q13*q33-4*M`j'^2*n2*q13^2*q33+2*n2*q12*q13^2*q33+2*n2*q13^3*q33+8*M`j'^2*n2*q12*q23*q33-4*M`j'^2*n2*q13*q23*q33+2*n2*q12*q13*q23*q33+4*n2*q13^2*q23*q33+2*n2*q13*q23^2*q33+4*M`j'^2*n2*q12*q33^2-2*n2*q12^2*q33^2-2*n2*q12*q13*q33^2+n2*q13^2*q33^2-2*n2*q12*q23*q33^2+n2*q13*q23*q33^2-n2*q12*q33^3,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3)+mbox1l(-2+n1,n2,2+n3,n4)*prf(-4*M`j'^2*q12*q13^2-4*M`j'^2*n3*q12*q13^2-6*M`j'^2*q13^3-6*M`j'^2*n3*q13^3-4*M`j'^2*q12*q13*q23-4*M`j'^2*n3*q12*q13*q23-8*M`j'^2*q13^2*q23-8*M`j'^2*n3*q13^2*q23-2*M`j'^2*q13*q23^2-2*M`j'^2*n3*q13*q23^2+4*M`j'^2*q12*q13*q33+4*M`j'^2*n3*q12*q13*q33-4*M`j'^2*q13^2*q33-4*M`j'^2*n3*q13^2*q33+q12*q13^2*q33+n3*q12*q13^2*q33+2*q13^3*q33+2*n3*q13^3*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n3*q12*q23*q33-4*M`j'^2*q13*q23*q33-4*M`j'^2*n3*q13*q23*q33+q12*q13*q23*q33+n3*q12*q13*q23*q33+3*q13^2*q23*q33+3*n3*q13^2*q23*q33-4*M`j'^2*q23^2*q33-4*M`j'^2*n3*q23^2*q33+q13*q23^2*q33+n3*q13*q23^2*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n3*q12*q33^2-2*q12*q13*q33^2-2*n3*q12*q13*q33^2+q13^2*q33^2+n3*q13^2*q33^2+q12*q23*q33^2+n3*q12*q23*q33^2+q13*q23*q33^2+n3*q13*q23*q33^2+q23^2*q33^2+n3*q23^2*q33^2-q12*q33^3-n3*q12*q33^3,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3)+mbox1l(-1+n1,n2,1+n3,n4)*(tmpprf(ep,1)*prf(2*q13^3*q33+4*q13^2*q23*q33+2*q13*q23^2*q33-4*q12*q13*q33^2,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3)+prf(2*M`j'^2*q13^3-2*M`j'^2*n1*q13^3+4*M`j'^2*n2*q13^3-2*M`j'^2*n4*q13^3+4*M`j'^2*q13^2*q23-4*M`j'^2*n1*q13^2*q23+8*M`j'^2*n2*q13^2*q23-4*M`j'^2*n4*q13^2*q23+2*M`j'^2*q13*q23^2-2*M`j'^2*n1*q13*q23^2+4*M`j'^2*n2*q13*q23^2-2*M`j'^2*n4*q13*q23^2-8*M`j'^2*q12*q13*q33+4*M`j'^2*n1*q12*q13*q33-4*M`j'^2*n2*q12*q13*q33-4*M`j'^2*n3*q12*q13*q33+4*M`j'^2*n4*q12*q13*q33+4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+4*M`j'^2*n2*q13^2*q33-5*q13^3*q33+2*n1*q13^3*q33+n3*q13^3*q33+2*n4*q13^3*q33+4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33+4*M`j'^2*n3*q12*q23*q33+12*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*n2*q13*q23*q33+4*M`j'^2*n3*q13*q23*q33-10*q13^2*q23*q33+4*n1*q13^2*q23*q33+2*n3*q13^2*q23*q33+4*n4*q13^2*q23*q33+8*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33+4*M`j'^2*n3*q23^2*q33-5*q13*q23^2*q33+2*n1*q13*q23^2*q33+n3*q13*q23^2*q33+2*n4*q13*q23^2*q33-12*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-4*M`j'^2*n2*q12*q33^2-4*M`j'^2*n3*q12*q33^2+11*q12*q13*q33^2-4*n1*q12*q13*q33^2-n2*q12*q13*q33^2-n3*q12*q13*q33^2-4*n4*q12*q13*q33^2-q13^2*q33^2+n1*q13^2*q33^2-n2*q13^2*q33^2-q12*q23*q33^2+n2*q12*q23*q33^2-n3*q12*q23*q33^2-3*q13*q23*q33^2+2*n1*q13*q23*q33^2-n2*q13*q23*q33^2-n3*q13*q23*q33^2-2*q23^2*q33^2+n1*q23^2*q33^2-n3*q23^2*q33^2+3*q12*q33^3-2*n1*q12*q33^3+n2*q12*q33^3+n3*q12*q33^3,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3))+mbox1l(-1+n1,n2,2+n3,n4)*prf(8*M`j'^2*q12*q13^3+8*M`j'^2*n3*q12*q13^3+4*M`j'^2*q13^4+4*M`j'^2*n3*q13^4+8*M`j'^2*q12*q13^2*q23+8*M`j'^2*n3*q12*q13^2*q23+8*M`j'^2*q13^3*q23+8*M`j'^2*n3*q13^3*q23+4*M`j'^2*q13^2*q23^2+4*M`j'^2*n3*q13^2*q23^2+4*M`j'^2*q12*q13^2*q33+4*M`j'^2*n3*q12*q13^2*q33-2*q12*q13^3*q33-2*n3*q12*q13^3*q33+4*M`j'^2*q12*q13*q23*q33+4*M`j'^2*n3*q12*q13*q23*q33-2*q12*q13^2*q23*q33-2*n3*q12*q13^2*q23*q33+4*M`j'^2*q12*q13*q33^2+4*M`j'^2*n3*q12*q13*q33^2-3*q12*q13^2*q33^2-3*n3*q12*q13^2*q33^2-q12*q13*q23*q33^2-n3*q12*q13*q23*q33^2-q12*q13*q33^3-n3*q12*q13*q33^3,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3)+mbox1l(-1+n1,1+n2,1+n3,n4)*prf(8*M`j'^2*n2*q12*q13^3+4*M`j'^2*n2*q13^4+16*M`j'^2*n2*q12*q13^2*q23+12*M`j'^2*n2*q13^3*q23+8*M`j'^2*n2*q12*q13*q23^2+12*M`j'^2*n2*q13^2*q23^2+4*M`j'^2*n2*q13*q23^3-8*M`j'^2*n2*q12^2*q13*q33-8*M`j'^2*n2*q12^2*q23*q33-8*M`j'^2*n2*q12*q13*q23*q33-8*M`j'^2*n2*q12*q23^2*q33+4*M`j'^2*n2*q12*q13*q33^2-2*n2*q12^2*q13*q33^2-2*n2*q12*q13^2*q33^2-4*M`j'^2*n2*q12*q23*q33^2+2*n2*q12^2*q23*q33^2+2*n2*q12*q23^2*q33^2-n2*q12*q13*q33^3+n2*q12*q23*q33^3,4*M`j'^2*q13^2*q33-4*M`j'^2*n1*q13^2*q33+8*M`j'^2*q13*q23*q33-8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q23^2*q33-4*M`j'^2*n1*q23^2*q33-8*M`j'^2*q12*q33^2+8*M`j'^2*n1*q12*q33^2-q13^2*q33^2+n1*q13^2*q33^2-2*q13*q23*q33^2+2*n1*q13*q23*q33^2-q23^2*q33^2+n1*q23^2*q33^2+2*q12*q33^3-2*n1*q12*q33^3); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?neg_,n3?neg0_,n4?pos_) = mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-4*M`j'^2*q12-4*M`j'^2*n2*q12-2*M`j'^2*q13-2*M`j'^2*n2*q13-2*M`j'^2*q23-2*M`j'^2*n2*q23,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-2+n1,1+n2,n3,1+n4)*prf(-4*M`j'^2*n4*q12-2*M`j'^2*n4*q13-2*M`j'^2*n4*q23,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,n2,1+n3,n4)*prf(-(n3*q13)-n3*q33,-q33+n1*q33)+mbox1l(n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*q12-2*M`j'^2*q13-2*M`j'^2*q23-2*q12*q33,4*M`j'^2*q33-q33^2)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3*q13-2*M`j'^2*n3*q23-n3*q12*q33,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-2+n1,2+n2,n3,n4)*prf(4*M`j'^2*q12+4*M`j'^2*n2*q12+6*M`j'^2*q13+6*M`j'^2*n2*q13+6*M`j'^2*q23+6*M`j'^2*n2*q23+4*M`j'^2*q33+4*M`j'^2*n2*q33-2*q12*q33-2*n2*q12*q33-2*q13*q33-2*n2*q13*q33-2*q23*q33-2*n2*q23*q33-q33^2-n2*q33^2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,1+n2,n3,n4)*(tmpprf(ep,1)*prf(-4*q12*q33-2*q13*q33-2*q23*q33,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+prf(4*M`j'^2*q12-4*M`j'^2*n1*q12+4*M`j'^2*n4*q12-6*M`j'^2*q13+2*M`j'^2*n1*q13-4*M`j'^2*n2*q13+2*M`j'^2*n4*q13-6*M`j'^2*q23+2*M`j'^2*n1*q23-4*M`j'^2*n2*q23+2*M`j'^2*n4*q23-8*M`j'^2*q33+4*M`j'^2*n1*q33-4*M`j'^2*n2*q33+8*q12*q33-2*n1*q12*q33-2*n2*q12*q33-2*n3*q12*q33-4*n4*q12*q33+6*q13*q33-2*n1*q13*q33-n3*q13*q33-2*n4*q13*q33+6*q23*q33-2*n1*q23*q33-n3*q23*q33-2*n4*q23*q33+2*q33^2-n1*q33^2+n2*q33^2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2))+mbox1l(-2+n1,1+n2,1+n3,n4)*prf(6*M`j'^2*n3*q13+2*M`j'^2*n3*q23+4*M`j'^2*n3*q33-n3*q12*q33-2*n3*q13*q33-n3*q23*q33-n3*q33^2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,2+n2,n3,n4)*prf(-4*M`j'^2*q13^2-4*M`j'^2*n2*q13^2-8*M`j'^2*q13*q23-8*M`j'^2*n2*q13*q23-4*M`j'^2*q23^2-4*M`j'^2*n2*q23^2+8*M`j'^2*q12*q33+8*M`j'^2*n2*q12*q33-4*q12^2*q33-4*n2*q12^2*q33-4*q12*q13*q33-4*n2*q12*q13*q33-4*q12*q23*q33-4*n2*q12*q23*q33-2*q12*q33^2-2*n2*q12*q33^2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,1+n2,1+n3,n4)*prf(-4*M`j'^2*n3*q13^2-4*M`j'^2*n3*q13*q23+4*M`j'^2*n3*q12*q33-2*n3*q12*q13*q33-n3*q12*q33^2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?neg0_,n4?{,>1}) = mbox1l(1+n1,n2,n3,-2+n4)*prf(2*M`j'^2*n1,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,1+n2,n3,-2+n4)*prf(2*M`j'^2*n2,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,1+n3,-2+n4)*prf(2*M`j'^2*n3,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,1+n3,-1+n4)*prf(4*M`j'^2*n3*q13,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(-1+n1,n2,n3,n4)*prf(-2*M`j'^2+q33,4*M`j'^2*q33-q33^2)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(-2*M`j'^2*n2+n2*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(-1+n1,n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3+n3*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2)+mbox1l(n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(2,-4*M`j'^2+4*M`j'^2*n4+q33-n4*q33)+prf(-2*M`j'^2-2*M`j'^2*n1+2*M`j'^2*n4-5*q33+2*n1*q33+n2*q33+n3*q33+n4*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2))+mbox1l(n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n2*q13+4*M`j'^2*n2*q23+2*n2*q12*q33,-4*M`j'^2*q33+4*M`j'^2*n4*q33+q33^2-n4*q33^2); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?neg0_,n3?neg0_,n4?pos_) = mbox1l(-2+n1,1+n2,n3,n4)*prf(2*M`j'^2*n2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-2+n1,n2,1+n3,n4)*prf(2*M`j'^2*n3,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-2+n1,n2,n3,1+n4)*prf(2*M`j'^2*n4,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(n1,n2,n3,-1+n4)*prf(-2*M`j'^2+q33,4*M`j'^2*q33-q33^2)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(-2*M`j'^2*n2+n2*q33,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3+n3*q33,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,n2,n3,n4)*(tmpprf(ep,1)*prf(2,-4*M`j'^2+4*M`j'^2*n1+q33-n1*q33)+prf(-2*M`j'^2+2*M`j'^2*n1-2*M`j'^2*n4-5*q33+n1*q33+n2*q33+n3*q33+2*n4*q33,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2))+mbox1l(-1+n1,1+n2,n3,n4)*prf(-4*M`j'^2*n2*q13-4*M`j'^2*n2*q23-4*M`j'^2*n2*q33+2*n2*q12*q33+2*n2*q13*q33+2*n2*q23*q33+n2*q33^2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2)+mbox1l(-1+n1,n2,1+n3,n4)*prf(-4*M`j'^2*n3*q13-4*M`j'^2*n3*q33+2*n3*q13*q33+n3*q33^2,-4*M`j'^2*q33+4*M`j'^2*n1*q33+q33^2-n1*q33^2); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?neg_,n4?pos_) = mbox1l(n1,-1+n2,2+n3,-1+n4)*prf(q12*q13+n3*q12*q13,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,-2+n2,2+n3,n4)*prf(q13^2+n3*q13^2,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-(q12*q13)+q12*q23,-q13^2-2*q13*q23-q23^2+2*q12*q33)+mbox1l(-1+n1,n2,1+n3,n4)*prf(-(q12*q13)+q12*q23+q13*q23+q23^2-q12*q33,q13^2+2*q13*q23+q23^2-2*q12*q33)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(-(q12*q13)-n3*q12*q13+q13*q23+n3*q13*q23-q12*q33-n3*q12*q33,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,-1+n2,1+n3,n4)*prf(-2*q13^2+n2*q13^2-n3*q13^2-2*q13*q23+n2*q13*q23-n3*q13*q23+2*q12*q33-n2*q12*q33+n3*q12*q33,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,-1+n2,2+n3,n4)*prf(2*q12*q13^2+2*n3*q12*q13^2+q12*q13*q33+n3*q12*q13*q33,-q13^2+n2*q13^2-2*q13*q23+2*n2*q13*q23-q23^2+n2*q23^2+2*q12*q33-2*n2*q12*q33)+mbox1l(n1,n2,1+n3,n4)*prf(-2*q12*q13^2-2*q12*q13*q23+2*q12^2*q33-q12*q13*q33+q12*q23*q33,-q13^2-2*q13*q23-q23^2+2*q12*q33); Identify,ifmatch->jump mbox1l(1,n2?neg_,0,1) = tmpprf(1,-1+2*ep+n2)*mbox1l(0,n2,0,2)*prf(-2*M`j'^2,q33)+tmpprf(1,-1+2*ep+n2)*mbox1l(0,1+n2,0,1)*prf(-2*M`j'^2*n2,q33)+tmpprf(1,-1+2*ep+n2)*mbox1l(0,1+n2,0,2)*prf(-4*M`j'^2*q12-2*M`j'^2*q13-2*M`j'^2*q23,q33)+mbox1l(1,1+n2,0,1)*(tmpprf(ep,-1+2*ep+n2)*prf(-4*q12-2*q13-2*q23,1)+tmpprf(1,-1+2*ep+n2)*prf(-4*n2*q12-2*n2*q13-2*n2*q23,1))+tmpprf(1,-1+2*ep+n2)*mbox1l(1,2+n2,0,0)*prf(-4*M`j'^2*q12-4*M`j'^2*n2*q12-2*M`j'^2*q13-2*M`j'^2*n2*q13-2*M`j'^2*q23-2*M`j'^2*n2*q23,q33)+tmpprf(1,-1+2*ep+n2)*mbox1l(2,n2,0,0)*prf(2*M`j'^2-q33,q33)+tmpprf(1,-1+2*ep+n2)*mbox1l(1,1+n2,0,0)*prf(2*M`j'^2*n2-n2*q33,q33)+tmpprf(1,-1+2*ep+n2)*mbox1l(2,1+n2,0,0)*prf(4*M`j'^2*q12-2*M`j'^2*q13-2*M`j'^2*q23-2*q12*q33,q33)+tmpprf(1,-1+2*ep+n2)*mbox1l(0,2+n2,0,1)*prf(4*M`j'^2*q12+4*M`j'^2*n2*q12+6*M`j'^2*q13+6*M`j'^2*n2*q13+6*M`j'^2*q23+6*M`j'^2*n2*q23+4*M`j'^2*q33+4*M`j'^2*n2*q33-2*q12*q33-2*n2*q12*q33-2*q13*q33-2*n2*q13*q33-2*q23*q33-2*n2*q23*q33-q33^2-n2*q33^2,q33)+tmpprf(1,-1+2*ep+n2)*mbox1l(1,2+n2,0,1)*prf(-4*M`j'^2*q13^2-4*M`j'^2*n2*q13^2-8*M`j'^2*q13*q23-8*M`j'^2*n2*q13*q23-4*M`j'^2*q23^2-4*M`j'^2*n2*q23^2+8*M`j'^2*q12*q33+8*M`j'^2*n2*q12*q33-4*q12^2*q33-4*n2*q12^2*q33-4*q12*q13*q33-4*n2*q12*q13*q33-4*q12*q23*q33-4*n2*q12*q23*q33-2*q12*q33^2-2*n2*q12*q33^2,q33); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?{,>1},n4?neg_) = mbox1l(1+n1,-1+n2,-1+n3,1+n4)*prf(n1*q13,-q12+n3*q12)+mbox1l(-1+n1,1+n2,-1+n3,1+n4)*prf(-(n2*q12)-n2*q23,-q12+n3*q12)+mbox1l(1+n1,n2,-1+n3,1+n4)*prf(4*n1*q13+n1*q33,-1+n3)+mbox1l(n1,1+n2,-1+n3,1+n4)*prf(-2*n2*q12+2*n2*q13-2*n2*q23+n2*q33,-1+n3)+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(q13+n4*q13+q33+n4*q33,-q12+n3*q12)+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(-q12-n4*q12+2*q13+2*n4*q13-q23-n4*q23+q33+n4*q33,-q12+n3*q12)+mbox1l(1+n1,n2,-2+n3,1+n4)*prf(2*M`j'^2*n1*q12-4*M`j'^2*n1*q13-2*n1*q12*q13-n1*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,1+n2,-2+n3,1+n4)*prf(2*M`j'^2*n2*q12-2*n2*q12*q13+4*M`j'^2*n2*q23-n2*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-2+n3,2+n4)*prf(2*M`j'^2*q12+2*M`j'^2*n4*q12-4*M`j'^2*q13-4*M`j'^2*n4*q13-2*q12*q13-2*n4*q12*q13-4*M`j'^2*q33-4*M`j'^2*n4*q33-q12*q33-n4*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-1+n3,1+n4)*(tmpprf(ep,1)*prf(-4*q12*q13-2*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+prf(-2*M`j'^2*q12-2*M`j'^2*n1*q12+2*M`j'^2*n3*q12-2*M`j'^2*q13+2*M`j'^2*n1*q13-2*M`j'^2*n4*q13+10*q12*q13-2*n1*q12*q13-2*n2*q12*q13-4*n3*q12*q13-2*n4*q12*q13+2*M`j'^2*q23-2*M`j'^2*n2*q23+2*M`j'^2*n4*q23+5*q12*q33-n1*q12*q33-n2*q12*q33-2*n3*q12*q33-n4*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12))+mbox1l(n1,n2,-1+n3,2+n4)*prf(12*M`j'^2*q12*q13+12*M`j'^2*n4*q12*q13-4*M`j'^2*q13^2-4*M`j'^2*n4*q13^2-4*q12*q13^2-4*n4*q12*q13^2+4*M`j'^2*q13*q23+4*M`j'^2*n4*q13*q23+6*M`j'^2*q12*q33+6*M`j'^2*n4*q12*q33-2*M`j'^2*q13*q33-2*M`j'^2*n4*q13*q33-4*q12*q13*q33-4*n4*q12*q13*q33+2*M`j'^2*q23*q33+2*M`j'^2*n4*q23*q33-q12*q33^2-n4*q12*q33^2,-2*M`j'^2*q12+2*M`j'^2*n3*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg_,n3?{,>1},n4?neg0_) = mbox1l(1+n1,n2,-1+n3,n4)*prf(-n1,-1+n3)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(n1,-1+n3)+mbox1l(n1,2+n2,-2+n3,n4)*prf(1+n2,-1+n3)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-2-n2+n3,-1+n3)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-n4,-1+n3)+mbox1l(n1,1+n2,-2+n3,1+n4)*prf(n4,-1+n3)+mbox1l(1+n1,1+n2,-1+n3,n4)*prf(-2*n1*q12,-1+n3)+mbox1l(n1,1+n2,-1+n3,1+n4)*prf(-2*n4*q12-2*n4*q23,-1+n3); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?neg0_,n3?pos_,n4?neg_) = mbox1l(n1,-1+n2,n3,1+n4)*prf(-q13,q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(q13,q12)+mbox1l(-1+n1,1+n2,-1+n3,1+n4)*prf(-(n2*q23),-q12+n1*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-2*q12+n1*q12-n4*q12-q23+n2*q23-n4*q23,-q12+n1*q12)+mbox1l(-2+n1,n2,n3,2+n4)*prf(q12+n4*q12+q23+n4*q23,-q12+n1*q12)+mbox1l(n1,n2,n3,1+n4)*prf(-2*q13-q33,1)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-q13-n4*q13-q33-n4*q33,-q12+n1*q12)+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(q13+n4*q13+q33+n4*q33,-q12+n1*q12)+mbox1l(-1+n1,n2,n3,2+n4)*prf(-2*q12*q13-2*n4*q12*q13-2*q13*q23-2*n4*q13*q23-q12*q33-n4*q12*q33-q23*q33-n4*q23*q33,-q12+n1*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?{,>1},n4?neg0_) = mbox1l(1+n1,n2,-1+n3,n4)*prf(-n1,-1+n3)+mbox1l(1+n1,n2,-2+n3,n4)*prf(n1,-2*M`j'^2+2*M`j'^2*n3)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-n2,-1+n3)+mbox1l(n1,1+n2,-2+n3,n4)*prf(n2,-2*M`j'^2+2*M`j'^2*n3)+mbox1l(n1,n2,-2+n3,1+n4)*prf(n4,-2*M`j'^2+2*M`j'^2*n3)+mbox1l(n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(1,-M`j'^2+M`j'^2*n3)+prf(-6+n1+n2+2*n3+n4,-2*M`j'^2+2*M`j'^2*n3))+mbox1l(n1,n2,-1+n3,1+n4)*prf(-2*M`j'^2*n4+2*n4*q13+n4*q33,-2*M`j'^2+2*M`j'^2*n3); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?{,>1},n4?neg0_) = mbox1l(2+n1,n2,-2+n3,n4)*prf(1+n1,-1+n3)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-n2,-1+n3)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(n2,-1+n3)+mbox1l(1+n1,n2,-1+n3,n4)*prf(-2-n1+n3,-1+n3)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-n4,-1+n3)+mbox1l(1+n1,n2,-2+n3,1+n4)*prf(n4,-1+n3)+mbox1l(1+n1,1+n2,-1+n3,n4)*prf(-2*n2*q12,-1+n3)+mbox1l(1+n1,n2,-1+n3,1+n4)*prf(2*n4*q13,-1+n3); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?pos_,n4?neg_) = mbox1l(1+n1,-1+n2,-1+n3,1+n4)*prf(n1*q13,-q12+n2*q12)+mbox1l(n1,-1+n2,n3,1+n4)*prf(q13-n1*q13+n4*q13,-q12+n2*q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-q23,q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(q12+q23,q12)+mbox1l(n1,n2,n3,1+n4)*prf(-2*q13-q33,1)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-2*q13-2*n4*q13-q33-n4*q33,-q12+n2*q12)+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(q13+n4*q13+q33+n4*q33,-q12+n2*q12)+mbox1l(n1,-1+n2,n3,2+n4)*prf(2*q13^2+2*n4*q13^2+q13*q33+n4*q13*q33,-q12+n2*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?pos_,n4?neg0_) = mbox1l(1+n1,n2,-1+n3,n4)*prf(n1,n1-n2)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-n2,n1-n2)+mbox1l(n1,-1+n2,n3,1+n4)*prf(-(n4*q13),n1*q12-n2*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-(n4*q12)-n4*q23,n1*q12-n2*q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(n4*q12+n4*q13+n4*q23,n1*q12-n2*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?neg0_,n4?neg_) = mbox1l(1+n1,-2+n2,n3,1+n4)*prf(-(M`j'^2*n1*q13)-M`j'^2*n1*q23-M`j'^2*n1*q33,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-2+n2,1+n3,1+n4)*prf(-(M`j'^2*n3*q13)-M`j'^2*n3*q23-M`j'^2*n3*q33,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-1+n2,1+n3,1+n4)*prf(M`j'^2*n3*q13+M`j'^2*n3*q23+M`j'^2*n3*q33,-2*M`j'^2+2*M`j'^2*n2+q12-n2*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(4*M`j'^2*q12-2*q12^2+3*M`j'^2*q13-2*q12*q13+3*M`j'^2*q23-2*q12*q23+M`j'^2*q33-q12*q33,4*M`j'^2*q12-2*q12^2)+mbox1l(-1+n1,-1+n2,1+n3,1+n4)*prf(3*M`j'^2*n3*q13-2*n3*q12*q13-M`j'^2*n3*q23+M`j'^2*n3*q33-n3*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-1+n2,n3,1+n4)*(tmpprf(ep,1)*prf(-2*q12*q13-2*q12*q23-2*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+prf(7*M`j'^2*q13+M`j'^2*n1*q13-3*M`j'^2*n2*q13-2*M`j'^2*n3*q13+4*M`j'^2*n4*q13+q12*q13-2*n1*q12*q13-3*n4*q12*q13+3*M`j'^2*q23+M`j'^2*n1*q23-3*M`j'^2*n2*q23+2*M`j'^2*n3*q23+3*q12*q23-2*n1*q12*q23-2*n3*q12*q23-n4*q12*q23+M`j'^2*q33+M`j'^2*n1*q33-M`j'^2*n2*q33+4*q12*q33-2*n1*q12*q33-n2*q12*q33-n3*q12*q33-n4*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2))+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(-q13^2-n4*q13^2-2*q13*q23-2*n4*q13*q23-q23^2-n4*q23^2+2*q12*q33+2*n4*q12*q33,-2*q12^2+2*n2*q12^2)+mbox1l(n1,-2+n2,n3,2+n4)*prf(-(M`j'^2*q12*q13)-M`j'^2*n4*q12*q13+2*M`j'^2*q13^2+2*M`j'^2*n4*q13^2-q12*q13^2-n4*q12*q13^2-M`j'^2*q12*q23-M`j'^2*n4*q12*q23+2*M`j'^2*q13*q23+2*M`j'^2*n4*q13*q23-q12*q13*q23-n4*q12*q13*q23-M`j'^2*q12*q33-M`j'^2*n4*q12*q33,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2+2*q12^3-2*n2*q12^3)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-3*M`j'^2*q12*q13-3*M`j'^2*n4*q12*q13+q12^2*q13+n4*q12^2*q13+M`j'^2*q12*q23+M`j'^2*n4*q12*q23-q12^2*q23-n4*q12^2*q23+2*M`j'^2*q13*q23+2*M`j'^2*n4*q13*q23-q12*q13*q23-n4*q12*q13*q23+2*M`j'^2*q23^2+2*M`j'^2*n4*q23^2-q12*q23^2-n4*q12*q23^2-3*M`j'^2*q12*q33-3*M`j'^2*n4*q12*q33+q12^2*q33+n4*q12^2*q33,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2+2*q12^3-2*n2*q12^3)+mbox1l(n1,-1+n2,n3,2+n4)*prf(2*M`j'^2*q13^2+2*M`j'^2*n4*q13^2-2*q12*q13^2-2*n4*q12*q13^2-2*q12*q13*q23-2*n4*q12*q13*q23-2*M`j'^2*q23^2-2*M`j'^2*n4*q23^2+2*M`j'^2*q13*q33+2*M`j'^2*n4*q13*q33-3*q12*q13*q33-3*n4*q12*q13*q33-2*M`j'^2*q23*q33-2*M`j'^2*n4*q23*q33-q12*q23*q33-n4*q12*q23*q33-q12*q33^2-n4*q12*q33^2,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2); Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?neg_,n4?neg0_) = mbox1l(-1+n1,n2,1+n3,n4)*prf(M`j'^2,4*M`j'^2-2*q12)+mbox1l(1+n1,-2+n2,1+n3,n4)*prf(M`j'^2*n1,-4*M`j'^2+4*M`j'^2*n2+2*q12-2*n2*q12)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(M`j'^2+M`j'^2*n3,-4*M`j'^2+4*M`j'^2*n2+2*q12-2*n2*q12)+mbox1l(n1,-2+n2,2+n3,n4)*prf(M`j'^2+M`j'^2*n3,-4*M`j'^2+4*M`j'^2*n2+2*q12-2*n2*q12)+mbox1l(n1,-1+n2,2+n3,n4)*prf(-(M`j'^2*q12)-M`j'^2*n3*q12,-2*M`j'^2+2*M`j'^2*n2+q12-n2*q12)+mbox1l(n1,-1+n2,1+n3,n4)*(tmpprf(ep,1)*prf(q12,-2*M`j'^2+2*M`j'^2*n2+q12-n2*q12)+prf(-5*M`j'^2-M`j'^2*n1+3*M`j'^2*n2-2*M`j'^2*n3-2*q12+2*n1*q12+2*n3*q12+n4*q12,-4*M`j'^2+4*M`j'^2*n2+2*q12-2*n2*q12))+mbox1l(n1,-2+n2,1+n3,1+n4)*prf(M`j'^2*n4*q12-2*M`j'^2*n4*q13+n4*q12*q13,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-1+n2,n3,1+n4)*prf(n4*q13+n4*q23,-2*q12+2*n2*q12)+mbox1l(-1+n1,-1+n2,1+n3,1+n4)*prf(-(M`j'^2*n4*q12)+n4*q12^2-2*M`j'^2*n4*q23+n4*q12*q23,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-1+n2,1+n3,1+n4)*prf(-2*M`j'^2*n4*q13+2*n4*q12*q13+2*M`j'^2*n4*q23+n4*q12*q33,-4*M`j'^2+4*M`j'^2*n2+2*q12-2*n2*q12); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?neg0_,n4?neg_) = mbox1l(-2+n1,1+n2,n3,1+n4)*prf(-(M`j'^2*n2*q13)-M`j'^2*n2*q23-M`j'^2*n2*q33,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(-2+n1,n2,1+n3,1+n4)*prf(-(M`j'^2*n3*q13)-M`j'^2*n3*q23-M`j'^2*n3*q33,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(-1+n1,n2,1+n3,1+n4)*prf(M`j'^2*n3*q13+M`j'^2*n3*q23+M`j'^2*n3*q33,-2*M`j'^2+2*M`j'^2*n1+q12-n1*q12)+mbox1l(n1,-1+n2,n3,1+n4)*prf(-(M`j'^2*q13)-M`j'^2*q23+M`j'^2*q33-q12*q33,4*M`j'^2*q12-2*q12^2)+mbox1l(-1+n1,-1+n2,1+n3,1+n4)*prf(3*M`j'^2*n3*q13-2*n3*q12*q13-M`j'^2*n3*q23+M`j'^2*n3*q33-n3*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(-1+n1,n2,n3,1+n4)*(tmpprf(ep,1)*prf(-2*q12*q13-2*q12*q23-2*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+prf(-8*M`j'^2*q12+4*M`j'^2*n1*q12-4*M`j'^2*n4*q12+4*q12^2-2*n1*q12^2+2*n4*q12^2-M`j'^2*q13+M`j'^2*n1*q13+M`j'^2*n2*q13-2*M`j'^2*n3*q13+5*q12*q13-2*n1*q12*q13-2*n2*q12*q13-n4*q12*q13-5*M`j'^2*q23+M`j'^2*n1*q23+M`j'^2*n2*q23+2*M`j'^2*n3*q23-4*M`j'^2*n4*q23+7*q12*q23-2*n1*q12*q23-2*n2*q12*q23-2*n3*q12*q23+n4*q12*q23+M`j'^2*q33-M`j'^2*n1*q33+M`j'^2*n2*q33+4*q12*q33-n1*q12*q33-2*n2*q12*q33-n3*q12*q33-n4*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2))+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(-q13^2-n4*q13^2-2*q13*q23-2*n4*q13*q23-q23^2-n4*q23^2+2*q12*q33+2*n4*q12*q33,-2*q12^2+2*n1*q12^2)+mbox1l(-2+n1,n2,n3,2+n4)*prf(4*M`j'^2*q12^2+4*M`j'^2*n4*q12^2-2*q12^3-2*n4*q12^3+M`j'^2*q12*q13+M`j'^2*n4*q12*q13-q12^2*q13-n4*q12^2*q13+5*M`j'^2*q12*q23+5*M`j'^2*n4*q12*q23-3*q12^2*q23-3*n4*q12^2*q23+2*M`j'^2*q13*q23+2*M`j'^2*n4*q13*q23-q12*q13*q23-n4*q12*q13*q23+2*M`j'^2*q23^2+2*M`j'^2*n4*q23^2-q12*q23^2-n4*q12*q23^2-M`j'^2*q12*q33-M`j'^2*n4*q12*q33,-4*M`j'^2*q12^2+4*M`j'^2*n1*q12^2+2*q12^3-2*n1*q12^3)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-(M`j'^2*q12*q13)-M`j'^2*n4*q12*q13+2*M`j'^2*q13^2+2*M`j'^2*n4*q13^2-q12*q13^2-n4*q12*q13^2-M`j'^2*q12*q23-M`j'^2*n4*q12*q23+2*M`j'^2*q13*q23+2*M`j'^2*n4*q13*q23-q12*q13*q23-n4*q12*q13*q23-3*M`j'^2*q12*q33-3*M`j'^2*n4*q12*q33+q12^2*q33+n4*q12^2*q33,-4*M`j'^2*q12^2+4*M`j'^2*n1*q12^2+2*q12^3-2*n1*q12^3)+mbox1l(-1+n1,n2,n3,2+n4)*prf(2*M`j'^2*q13^2+2*M`j'^2*n4*q13^2-2*q12*q13^2-2*n4*q12*q13^2-2*q12*q13*q23-2*n4*q12*q13*q23-2*M`j'^2*q23^2-2*M`j'^2*n4*q23^2+2*M`j'^2*q13*q33+2*M`j'^2*n4*q13*q33-3*q12*q13*q33-3*n4*q12*q13*q33-2*M`j'^2*q23*q33-2*M`j'^2*n4*q23*q33-q12*q23*q33-n4*q12*q23*q33-q12*q33^2-n4*q12*q33^2,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?neg_,n4?neg0_) = mbox1l(n1,-1+n2,1+n3,n4)*prf(M`j'^2,4*M`j'^2-2*q12)+mbox1l(-2+n1,1+n2,1+n3,n4)*prf(M`j'^2*n2,-4*M`j'^2+4*M`j'^2*n1+2*q12-2*n1*q12)+mbox1l(-2+n1,n2,2+n3,n4)*prf(M`j'^2+M`j'^2*n3,-4*M`j'^2+4*M`j'^2*n1+2*q12-2*n1*q12)+mbox1l(-1+n1,-1+n2,2+n3,n4)*prf(M`j'^2+M`j'^2*n3,-4*M`j'^2+4*M`j'^2*n1+2*q12-2*n1*q12)+mbox1l(-1+n1,n2,2+n3,n4)*prf(-(M`j'^2*q12)-M`j'^2*n3*q12,-2*M`j'^2+2*M`j'^2*n1+q12-n1*q12)+mbox1l(-1+n1,n2,1+n3,n4)*(tmpprf(ep,1)*prf(q12,-2*M`j'^2+2*M`j'^2*n1+q12-n1*q12)+prf(-5*M`j'^2+3*M`j'^2*n1-M`j'^2*n2-2*M`j'^2*n3-2*q12+2*n2*q12+2*n3*q12+n4*q12,-4*M`j'^2+4*M`j'^2*n1+2*q12-2*n1*q12))+mbox1l(-1+n1,-1+n2,1+n3,1+n4)*prf(-(M`j'^2*n4*q12)-2*M`j'^2*n4*q13+n4*q12*q13,4*M`j'^2*q12-4*M`j'^2*n1*q12-2*q12^2+2*n1*q12^2)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-2*n4*q12-n4*q13-n4*q23,-2*q12+2*n1*q12)+mbox1l(-2+n1,n2,1+n3,1+n4)*prf(-3*M`j'^2*n4*q12+n4*q12^2-2*M`j'^2*n4*q23+n4*q12*q23,4*M`j'^2*q12-4*M`j'^2*n1*q12-2*q12^2+2*n1*q12^2)+mbox1l(-1+n1,n2,1+n3,1+n4)*prf(-2*M`j'^2*n4*q13+2*n4*q12*q13+2*M`j'^2*n4*q23+n4*q12*q33,-4*M`j'^2+4*M`j'^2*n1+2*q12-2*n1*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?neg0_,n4?neg0_) = mbox1l(1+n1,-2+n2,n3,n4)*prf(M`j'^2*n1,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-1+n2,1+n3,n4)*prf(-(M`j'^2*n3),-2*M`j'^2+2*M`j'^2*n2+q12-n2*q12)+mbox1l(n1,-2+n2,1+n3,n4)*prf(M`j'^2*n3,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-2+n2,n3,1+n4)*prf(M`j'^2*n4,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(-1+n1,n2,n3,n4)*prf(-M`j'^2+q12,4*M`j'^2*q12-2*q12^2)+mbox1l(-1+n1,-1+n2,1+n3,n4)*prf(-(M`j'^2*n3)+n3*q12,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(-1+n1,-1+n2,n3,1+n4)*prf(-(M`j'^2*n4)+n4*q12,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2)+mbox1l(n1,-1+n2,n3,n4)*(tmpprf(ep,1)*prf(1,-2*M`j'^2+2*M`j'^2*n2+q12-n2*q12)+prf(-M`j'^2-M`j'^2*n1+M`j'^2*n2-5*q12+2*n1*q12+n2*q12+n3*q12+n4*q12,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2))+mbox1l(n1,-1+n2,n3,1+n4)*prf(2*M`j'^2*n4*q13+2*M`j'^2*n4*q23+n4*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n2*q12+2*q12^2-2*n2*q12^2); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?neg0_,n4?neg0_) = mbox1l(-2+n1,1+n2,n3,n4)*prf(M`j'^2*n2,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(-1+n1,n2,1+n3,n4)*prf(-(M`j'^2*n3),-2*M`j'^2+2*M`j'^2*n1+q12-n1*q12)+mbox1l(-2+n1,n2,1+n3,n4)*prf(M`j'^2*n3,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(-2+n1,n2,n3,1+n4)*prf(M`j'^2*n4,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(n1,-1+n2,n3,n4)*prf(-M`j'^2+q12,4*M`j'^2*q12-2*q12^2)+mbox1l(-1+n1,-1+n2,1+n3,n4)*prf(-(M`j'^2*n3)+n3*q12,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(-1+n1,-1+n2,n3,1+n4)*prf(-(M`j'^2*n4)+n4*q12,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2)+mbox1l(-1+n1,n2,n3,n4)*(tmpprf(ep,1)*prf(1,-2*M`j'^2+2*M`j'^2*n1+q12-n1*q12)+prf(-M`j'^2+M`j'^2*n1-M`j'^2*n2-5*q12+n1*q12+2*n2*q12+n3*q12+n4*q12,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2))+mbox1l(-1+n1,n2,n3,1+n4)*prf(-4*M`j'^2*n4*q12+2*n4*q12^2-2*M`j'^2*n4*q13+2*n4*q12*q13-2*M`j'^2*n4*q23+2*n4*q12*q23+n4*q12*q33,-4*M`j'^2*q12+4*M`j'^2*n1*q12+2*q12^2-2*n1*q12^2); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?neg0_,n4?neg_) = mbox1l(n1,-1+n2,n3,1+n4)*prf(-q13,q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(q12+q23,q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-2*q13+n3*q13-n4*q13+2*q23-n3*q23+n4*q23,-q12+n3*q12)+mbox1l(n1,n2,n3,1+n4)*prf(-2*q13-q33,1)+mbox1l(n1,n2,-2+n3,2+n4)*prf(q13^2+n4*q13^2+2*q13*q23+2*n4*q13*q23+q23^2+n4*q23^2-2*q12*q33-2*n4*q12*q33,-q12^2+n3*q12^2)+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(-q13^2-n4*q13^2-q13*q23-n4*q13*q23+q12*q33+n4*q12*q33,-q12^2+n3*q12^2)+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(q12*q13+n4*q12*q13-q12*q23-n4*q12*q23-q13*q23-n4*q13*q23-q23^2-n4*q23^2+q12*q33+n4*q12*q33,-q12^2+n3*q12^2)+mbox1l(n1,n2,-1+n3,2+n4)*prf(-2*q13^2-2*n4*q13^2-2*q13*q23-2*n4*q13*q23+2*q12*q33+2*n4*q12*q33-q13*q33-n4*q13*q33+q23*q33+n4*q23*q33,-q12+n3*q12); Identify,ifmatch->jump mbox1l(1,1,n3?neg_,0) = tmpprf(1,-1+2*ep+n3)*mbox1l(0,2,n3,0)*prf(-M`j'^2,q12)+tmpprf(1,-1+2*ep+n3)*mbox1l(0,2,1+n3,0)*prf(M`j'^2,1)+tmpprf(1,-1+2*ep+n3)*mbox1l(2,0,1+n3,0)*prf(M`j'^2,1)+tmpprf(1,-1+2*ep+n3)*mbox1l(0,1,1+n3,0)*prf(-(M`j'^2*n3),q12)+tmpprf(1,-1+2*ep+n3)*mbox1l(0,1,2+n3,0)*prf(M`j'^2+M`j'^2*n3,1)+tmpprf(1,-1+2*ep+n3)*mbox1l(1,0,2+n3,0)*prf(M`j'^2+M`j'^2*n3,1)+tmpprf(1,-1+2*ep+n3)*mbox1l(2,0,n3,0)*prf(M`j'^2-q12,q12)+mbox1l(1,1,1+n3,0)*(tmpprf(ep,-1+2*ep+n3)*prf(2*q12,1)+tmpprf(1,-1+2*ep+n3)*prf(2*n3*q12,1))+tmpprf(1,-1+2*ep+n3)*mbox1l(1,0,1+n3,0)*prf(M`j'^2*n3-n3*q12,q12)+tmpprf(1,-1+2*ep+n3)*mbox1l(1,1,2+n3,0)*prf(-2*M`j'^2*q12-2*M`j'^2*n3*q12,1); Identify,ifmatch->jump mbox1l(n1?neg_,n2?pos_,n3?pos_,n4?{,>1}) = mbox1l(1+n1,-1+n2,1+n3,-1+n4)*prf(-(n3*q13),-q12+n4*q12-q23+n4*q23)+mbox1l(2+n1,n2,n3,-2+n4)*prf(2*q12*q13+2*n1*q12*q13,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,n2,-1+n3,n4)*prf(q33,2*q13+q33)+mbox1l(2+n1,-1+n2,n3,-1+n4)*prf(-(q13*q33)-n1*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(2+n1,n2,-1+n3,-1+n4)*prf(q12*q33+n1*q12*q33+q13*q33+n1*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n2*q13^2+2*n2*q13*q23-n2*q12*q33+n2*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,n2,n3,-1+n4)*prf(-4*q12*q13-2*n1*q12*q13+2*n4*q12*q13-2*n2*q13^2+2*n3*q13^2-2*q13*q23-2*n2*q13*q23+2*n4*q13*q23-q12*q33-n1*q12*q33+n2*q12*q33-n2*q13*q33+n3*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33); Identify,ifmatch->jump mbox1l(n1?neg_,n2?pos_,n3?{,>1},n4?pos_) = mbox1l(1+n1,n2,n3,-1+n4)*prf(2*q12^2+2*q12*q13+2*q12*q23+q12*q33,2*q12^2+4*q12*q23+2*q23^2)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n2*q12*q13+n2*q12*q33,-2*q12^2+2*n3*q12^2-4*q12*q23+4*n3*q12*q23-2*q23^2+2*n3*q23^2)+mbox1l(1+n1,n2,-2+n3,1+n4)*prf(2*n4*q12^2+2*n4*q12*q13+2*n4*q12*q23+n4*q12*q33,-2*q12^2+2*n3*q12^2-4*q12*q23+4*n3*q12*q23-2*q23^2+2*n3*q23^2)+mbox1l(2+n1,n2,-1+n3,-1+n4)*prf(-4*M`j'^2*q12^3-4*M`j'^2*n1*q12^3-8*M`j'^2*q12^2*q13-8*M`j'^2*n1*q12^2*q13+4*q12^3*q13+4*n1*q12^3*q13+4*q12^2*q13^2+4*n1*q12^2*q13^2+4*q12^2*q13*q23+4*n1*q12^2*q13*q23+4*M`j'^2*q12*q23^2+4*M`j'^2*n1*q12*q23^2-2*M`j'^2*q12^2*q33-2*M`j'^2*n1*q12^2*q33+2*q12^3*q33+2*n1*q12^3*q33+4*q12^2*q13*q33+4*n1*q12^2*q13*q33+2*M`j'^2*q12*q23*q33+2*M`j'^2*n1*q12*q23*q33+2*q12^2*q23*q33+2*n1*q12^2*q23*q33+q12^2*q33^2+n1*q12^2*q33^2,-4*M`j'^2*q12^3+4*M`j'^2*n3*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n3*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n3*q23^3)+mbox1l(1+n1,-1+n2,n3,n4)*prf(12*M`j'^2*q12^2*q13+16*M`j'^2*q12*q13^2-8*q12^2*q13^2-8*q12*q13^3+8*M`j'^2*q12*q13*q23-8*q12*q13^2*q23-4*M`j'^2*q13*q23^2+8*M`j'^2*q12^2*q33+16*M`j'^2*q12*q13*q33-8*q12^2*q13*q33-12*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*q12*q13*q23*q33+4*M`j'^2*q12*q33^2-2*q12^2*q33^2-6*q12*q13*q33^2-2*q12*q23*q33^2-q12*q33^3,4*M`j'^2*q12^3+12*M`j'^2*q12^2*q23+12*M`j'^2*q12*q23^2+4*M`j'^2*q23^3)+mbox1l(2+n1,-1+n2,-1+n3,n4)*prf(4*M`j'^2*q12^2*q13+4*M`j'^2*n1*q12^2*q13+4*M`j'^2*q12*q13^2+4*M`j'^2*n1*q12*q13^2-4*q12^2*q13^2-4*n1*q12^2*q13^2-4*q12*q13^3-4*n1*q12*q13^3-4*M`j'^2*q13^2*q23-4*M`j'^2*n1*q13^2*q23-4*q12*q13^2*q23-4*n1*q12*q13^2*q23-4*M`j'^2*q13*q23^2-4*M`j'^2*n1*q13*q23^2+8*M`j'^2*q12^2*q33+8*M`j'^2*n1*q12^2*q33+12*M`j'^2*q12*q13*q33+12*M`j'^2*n1*q12*q13*q33-6*q12^2*q13*q33-6*n1*q12^2*q13*q33-8*q12*q13^2*q33-8*n1*q12*q13^2*q33+8*M`j'^2*q12*q23*q33+8*M`j'^2*n1*q12*q23*q33-6*q12*q13*q23*q33-6*n1*q12*q13*q23*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n1*q12*q33^2-2*q12^2*q33^2-2*n1*q12^2*q33^2-5*q12*q13*q33^2-5*n1*q12*q13*q33^2-2*q12*q23*q33^2-2*n1*q12*q23*q33^2-q12*q33^3-n1*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n3*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n3*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n3*q23^3)+mbox1l(2+n1,n2,-2+n3,n4)*prf(4*M`j'^2*q12^3+4*M`j'^2*n1*q12^3-4*M`j'^2*q12*q13^2-4*M`j'^2*n1*q12*q13^2+4*q12^2*q13^2+4*n1*q12^2*q13^2+4*q12*q13^3+4*n1*q12*q13^3+4*M`j'^2*q12^2*q23+4*M`j'^2*n1*q12^2*q23+4*q12^2*q13*q23+4*n1*q12^2*q13*q23+4*M`j'^2*q13^2*q23+4*M`j'^2*n1*q13^2*q23+8*q12*q13^2*q23+8*n1*q12*q13^2*q23+4*M`j'^2*q12*q23^2+4*M`j'^2*n1*q12*q23^2+8*M`j'^2*q13*q23^2+8*M`j'^2*n1*q13*q23^2+4*q12*q13*q23^2+4*n1*q12*q13*q23^2+4*M`j'^2*q23^3+4*M`j'^2*n1*q23^3-10*M`j'^2*q12^2*q33-10*M`j'^2*n1*q12^2*q33-12*M`j'^2*q12*q13*q33-12*M`j'^2*n1*q12*q13*q33+6*q12^2*q13*q33+6*n1*q12^2*q13*q33+8*q12*q13^2*q33+8*n1*q12*q13^2*q33-14*M`j'^2*q12*q23*q33-14*M`j'^2*n1*q12*q23*q33+2*q12^2*q23*q33+2*n1*q12^2*q23*q33+10*q12*q13*q23*q33+10*n1*q12*q13*q23*q33+2*q12*q23^2*q33+2*n1*q12*q23^2*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n1*q12*q33^2+2*q12^2*q33^2+2*n1*q12^2*q33^2+5*q12*q13*q33^2+5*n1*q12*q13*q33^2+3*q12*q23*q33^2+3*n1*q12*q23*q33^2+q12*q33^3+n1*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n3*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n3*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n3*q23^3)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(-4*M`j'^2*n2*q12^3-20*M`j'^2*n2*q12^2*q13+8*n2*q12^3*q13-16*M`j'^2*n2*q12*q13^2+16*n2*q12^2*q13^2+8*n2*q12*q13^3-8*M`j'^2*n2*q12^2*q23-20*M`j'^2*n2*q12*q13*q23+16*n2*q12^2*q13*q23+16*n2*q12*q13^2*q23-4*M`j'^2*n2*q12*q23^2+8*n2*q12*q13*q23^2-10*M`j'^2*n2*q12^2*q33+4*n2*q12^3*q33-16*M`j'^2*n2*q12*q13*q33+16*n2*q12^2*q13*q33+12*n2*q12*q13^2*q33-10*M`j'^2*n2*q12*q23*q33+8*n2*q12^2*q23*q33+16*n2*q12*q13*q23*q33+4*n2*q12*q23^2*q33-4*M`j'^2*n2*q12*q33^2+4*n2*q12^2*q33^2+6*n2*q12*q13*q33^2+4*n2*q12*q23*q33^2+n2*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n3*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n3*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n3*q23^3)+mbox1l(1+n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(8*q12^3*q13+8*q12^2*q13^2+16*q12^2*q13*q23+8*q12*q13^2*q23+8*q12*q13*q23^2+4*q12^3*q33+8*q12^2*q13*q33+8*q12^2*q23*q33+8*q12*q13*q23*q33+4*q12*q23^2*q33+2*q12^2*q33^2+2*q12*q23*q33^2,-4*M`j'^2*q12^3+4*M`j'^2*n3*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n3*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n3*q23^3)+prf(4*M`j'^2*n2*q12^3-4*M`j'^2*n4*q12^3+20*M`j'^2*q12^2*q13+4*M`j'^2*n1*q12^2*q13+16*M`j'^2*n2*q12^2*q13-16*M`j'^2*n3*q12^2*q13-4*M`j'^2*n4*q12^2*q13-20*q12^3*q13+4*n1*q12^3*q13+8*n3*q12^3*q13+8*n4*q12^3*q13+16*M`j'^2*q12*q13^2+16*M`j'^2*n2*q12*q13^2-16*M`j'^2*n3*q12*q13^2-28*q12^2*q13^2+4*n1*q12^2*q13^2-8*n2*q12^2*q13^2+16*n3*q12^2*q13^2+8*n4*q12^2*q13^2-8*q12*q13^3-8*n2*q12*q13^3+8*n3*q12*q13^3-8*M`j'^2*q12^2*q23-4*M`j'^2*n1*q12^2*q23+8*M`j'^2*n2*q12^2*q23+4*M`j'^2*n3*q12^2*q23-8*M`j'^2*n4*q12^2*q23+12*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-12*M`j'^2*n3*q12*q13*q23-4*M`j'^2*n4*q12*q13*q23-40*q12^2*q13*q23+8*n1*q12^2*q13*q23+16*n3*q12^2*q13*q23+16*n4*q12^2*q13*q23-28*q12*q13^2*q23+4*n1*q12*q13^2*q23-8*n2*q12*q13^2*q23+16*n3*q12*q13^2*q23+8*n4*q12*q13^2*q23-16*M`j'^2*q12*q23^2-8*M`j'^2*n1*q12*q23^2+4*M`j'^2*n2*q12*q23^2+8*M`j'^2*n3*q12*q23^2-4*M`j'^2*n4*q12*q23^2-8*M`j'^2*q13*q23^2-4*M`j'^2*n1*q13*q23^2+4*M`j'^2*n3*q13*q23^2-20*q12*q13*q23^2+4*n1*q12*q13*q23^2+8*n3*q12*q13*q23^2+8*n4*q12*q13*q23^2-8*M`j'^2*q23^3-4*M`j'^2*n1*q23^3+4*M`j'^2*n3*q23^3+14*M`j'^2*q12^2*q33+4*M`j'^2*n1*q12^2*q33+8*M`j'^2*n2*q12^2*q33-10*M`j'^2*n3*q12^2*q33-2*M`j'^2*n4*q12^2*q33-10*q12^3*q33+2*n1*q12^3*q33+4*n3*q12^3*q33+4*n4*q12^3*q33+16*M`j'^2*q12*q13*q33+16*M`j'^2*n2*q12*q13*q33-16*M`j'^2*n3*q12*q13*q33-28*q12^2*q13*q33+4*n1*q12^2*q13*q33-8*n2*q12^2*q13*q33+16*n3*q12^2*q13*q33+8*n4*q12^2*q13*q33-12*q12*q13^2*q33-12*n2*q12*q13^2*q33+12*n3*q12*q13^2*q33+14*M`j'^2*q12*q23*q33+4*M`j'^2*n1*q12*q23*q33+8*M`j'^2*n2*q12*q23*q33-10*M`j'^2*n3*q12*q23*q33-2*M`j'^2*n4*q12*q23*q33-20*q12^2*q23*q33+4*n1*q12^2*q23*q33+8*n3*q12^2*q23*q33+8*n4*q12^2*q23*q33-28*q12*q13*q23*q33+4*n1*q12*q13*q23*q33-8*n2*q12*q13*q23*q33+16*n3*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-10*q12*q23^2*q33+2*n1*q12*q23^2*q33+4*n3*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n2*q12*q33^2-4*M`j'^2*n3*q12*q33^2-7*q12^2*q33^2+n1*q12^2*q33^2-2*n2*q12^2*q33^2+4*n3*q12^2*q33^2+2*n4*q12^2*q33^2-6*q12*q13*q33^2-6*n2*q12*q13*q33^2+6*n3*q12*q13*q33^2-7*q12*q23*q33^2+n1*q12*q23*q33^2-2*n2*q12*q23*q33^2+4*n3*q12*q23*q33^2+2*n4*q12*q23*q33^2-q12*q33^3-n2*q12*q33^3+n3*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n3*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n3*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n3*q23^3))+mbox1l(2+n1,n2,-1+n3,n4)*prf(-8*q12^3*q13^2-8*n1*q12^3*q13^2-8*q12^2*q13^3-8*n1*q12^2*q13^3-16*M`j'^2*q12^2*q13*q23-16*M`j'^2*n1*q12^2*q13*q23-16*M`j'^2*q12*q13^2*q23-16*M`j'^2*n1*q12*q13^2*q23-8*q12^2*q13^2*q23-8*n1*q12^2*q13^2*q23-16*M`j'^2*q12*q13*q23^2-16*M`j'^2*n1*q12*q13*q23^2+8*M`j'^2*q12^3*q33+8*M`j'^2*n1*q12^3*q33+8*M`j'^2*q12^2*q13*q33+8*M`j'^2*n1*q12^2*q13*q33-8*q12^3*q13*q33-8*n1*q12^3*q13*q33-12*q12^2*q13^2*q33-12*n1*q12^2*q13^2*q33+8*M`j'^2*q12^2*q23*q33+8*M`j'^2*n1*q12^2*q23*q33-8*M`j'^2*q12*q13*q23*q33-8*M`j'^2*n1*q12*q13*q23*q33-8*q12^2*q13*q23*q33-8*n1*q12^2*q13*q23*q33+4*M`j'^2*q12^2*q33^2+4*M`j'^2*n1*q12^2*q33^2-2*q12^3*q33^2-2*n1*q12^3*q33^2-6*q12^2*q13*q33^2-6*n1*q12^2*q13*q33^2-2*q12^2*q23*q33^2-2*n1*q12^2*q23*q33^2-q12^2*q33^3-n1*q12^2*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n3*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n3*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n3*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n3*q23^3); Identify,ifmatch->jump mbox1l(n1?neg_,n2?{,>1},n3?pos_,n4?pos_) = mbox1l(1+n1,n2,n3,-1+n4)*prf(2*q12^2-2*q12*q13+2*q12*q23-q12*q33,2*q12^2+4*q12*q23+2*q23^2)+mbox1l(1+n1,-1+n2,1+n3,-1+n4)*prf(-2*n3*q12*q13-n3*q12*q33,-2*q12^2+2*n2*q12^2-4*q12*q23+4*n2*q12*q23-2*q23^2+2*n2*q23^2)+mbox1l(1+n1,-1+n2,-1+n3,1+n4)*prf(-2*n4*q12*q13-n4*q12*q33,-2*q12^2+2*n2*q12^2-4*q12*q23+4*n2*q12*q23-2*q23^2+2*n2*q23^2)+mbox1l(2+n1,-1+n2,n3,-1+n4)*prf(8*M`j'^2*q12^2*q13+8*M`j'^2*n1*q12^2*q13-4*q12^2*q13^2-4*n1*q12^2*q13^2+2*M`j'^2*q12^2*q33+2*M`j'^2*n1*q12^2*q33-4*q12^2*q13*q33-4*n1*q12^2*q13*q33-2*M`j'^2*q12*q23*q33-2*M`j'^2*n1*q12*q23*q33-q12^2*q33^2-n1*q12^2*q33^2,-4*M`j'^2*q12^3+4*M`j'^2*n2*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n2*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n2*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3)+mbox1l(1+n1,n2,-1+n3,n4)*prf(8*M`j'^2*q12^2*q13+16*M`j'^2*q12*q13^2-8*q12^2*q13^2-8*q12*q13^3+4*M`j'^2*q12^2*q23+12*M`j'^2*q12*q13*q23-8*q12*q13^2*q23+8*M`j'^2*q12*q23^2+4*M`j'^2*q13*q23^2+4*M`j'^2*q23^3+2*M`j'^2*q12^2*q33+16*M`j'^2*q12*q13*q33-8*q12^2*q13*q33-12*q12*q13^2*q33+2*M`j'^2*q12*q23*q33-8*q12*q13*q23*q33+4*M`j'^2*q12*q33^2-2*q12^2*q33^2-6*q12*q13*q33^2-2*q12*q23*q33^2-q12*q33^3,4*M`j'^2*q12^3+12*M`j'^2*q12^2*q23+12*M`j'^2*q12*q23^2+4*M`j'^2*q23^3)+mbox1l(2+n1,-1+n2,-1+n3,n4)*prf(-4*M`j'^2*q12^2*q13-4*M`j'^2*n1*q12^2*q13+4*M`j'^2*q12*q13^2+4*M`j'^2*n1*q12*q13^2-4*q12*q13^3-4*n1*q12*q13^3-4*M`j'^2*q13^2*q23-4*M`j'^2*n1*q13^2*q23-4*q12*q13^2*q23-4*n1*q12*q13^2*q23-4*M`j'^2*q13*q23^2-4*M`j'^2*n1*q13*q23^2+2*M`j'^2*q12^2*q33+2*M`j'^2*n1*q12^2*q33+12*M`j'^2*q12*q13*q33+12*M`j'^2*n1*q12*q13*q33-8*q12*q13^2*q33-8*n1*q12*q13^2*q33+6*M`j'^2*q12*q23*q33+6*M`j'^2*n1*q12*q23*q33-4*q12*q13*q23*q33-4*n1*q12*q13*q23*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n1*q12*q33^2-5*q12*q13*q33^2-5*n1*q12*q13*q33^2-q12*q23*q33^2-n1*q12*q23*q33^2-q12*q33^3-n1*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n2*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n2*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n2*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3)+mbox1l(2+n1,-2+n2,n3,n4)*prf(-4*M`j'^2*q12*q13^2-4*M`j'^2*n1*q12*q13^2+4*q12*q13^3+4*n1*q12*q13^3+4*M`j'^2*q13^2*q23+4*M`j'^2*n1*q13^2*q23-12*M`j'^2*q12*q13*q33-12*M`j'^2*n1*q12*q13*q33+8*q12*q13^2*q33+8*n1*q12*q13^2*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n1*q12*q33^2+5*q12*q13*q33^2+5*n1*q12*q13*q33^2+q12*q33^3+n1*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n2*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n2*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n2*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3)+mbox1l(1+n1,-1+n2,n3,n4)*(tmpprf(ep,1)*prf(-8*q12^2*q13^2-8*q12*q13^2*q23-8*q12^2*q13*q33-8*q12*q13*q23*q33-2*q12^2*q33^2-2*q12*q23*q33^2,-4*M`j'^2*q12^3+4*M`j'^2*n2*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n2*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n2*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3)+prf(-4*M`j'^2*n1*q12^2*q13-4*M`j'^2*n2*q12^2*q13+4*M`j'^2*n3*q12^2*q13+4*M`j'^2*n4*q12^2*q13+16*M`j'^2*q12*q13^2-16*M`j'^2*n2*q12*q13^2+16*M`j'^2*n3*q12*q13^2+12*q12^2*q13^2-4*n1*q12^2*q13^2-8*n3*q12^2*q13^2-8*n4*q12^2*q13^2-8*q12*q13^3+8*n2*q12*q13^3-8*n3*q12*q13^3+8*M`j'^2*q12*q13*q23-8*M`j'^2*n2*q12*q13*q23+4*M`j'^2*n3*q12*q13*q23+4*M`j'^2*n4*q12*q13*q23+12*q12*q13^2*q23-4*n1*q12*q13^2*q23-8*n3*q12*q13^2*q23-8*n4*q12*q13^2*q23+8*M`j'^2*q13*q23^2+4*M`j'^2*n1*q13*q23^2-4*M`j'^2*n2*q13*q23^2-4*M`j'^2*q12^2*q33-4*M`j'^2*n1*q12^2*q33+2*M`j'^2*n3*q12^2*q33+2*M`j'^2*n4*q12^2*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33+16*M`j'^2*n3*q12*q13*q33+12*q12^2*q13*q33-4*n1*q12^2*q13*q33-8*n3*q12^2*q13*q33-8*n4*q12^2*q13*q33-12*q12*q13^2*q33+12*n2*q12*q13^2*q33-12*n3*q12*q13^2*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n1*q12*q23*q33+2*M`j'^2*n3*q12*q23*q33+2*M`j'^2*n4*q12*q23*q33+12*q12*q13*q23*q33-4*n1*q12*q13*q23*q33-8*n3*q12*q13*q23*q33-8*n4*q12*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n2*q12*q33^2+4*M`j'^2*n3*q12*q33^2+3*q12^2*q33^2-n1*q12^2*q33^2-2*n3*q12^2*q33^2-2*n4*q12^2*q33^2-6*q12*q13*q33^2+6*n2*q12*q13*q33^2-6*n3*q12*q13*q33^2+3*q12*q23*q33^2-n1*q12*q23*q33^2-2*n3*q12*q23*q33^2-2*n4*q12*q23*q33^2-q12*q33^3+n2*q12*q33^3-n3*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n2*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n2*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n2*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3))+mbox1l(1+n1,-2+n2,1+n3,n4)*prf(-16*M`j'^2*n3*q12*q13^2+8*n3*q12*q13^3-16*M`j'^2*n3*q12*q13*q33+12*n3*q12*q13^2*q33-4*M`j'^2*n3*q12*q33^2+6*n3*q12*q13*q33^2+n3*q12*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n2*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n2*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n2*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3)+mbox1l(2+n1,-1+n2,n3,n4)*prf(8*q12^2*q13^3+8*n1*q12^2*q13^3+16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n1*q12*q13^2*q23-8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n1*q12^2*q13*q33+12*q12^2*q13^2*q33+12*n1*q12^2*q13^2*q33+8*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n1*q12*q13*q23*q33-4*M`j'^2*q12^2*q33^2-4*M`j'^2*n1*q12^2*q33^2+6*q12^2*q13*q33^2+6*n1*q12^2*q13*q33^2+q12^2*q33^3+n1*q12^2*q33^3,-4*M`j'^2*q12^3+4*M`j'^2*n2*q12^3-12*M`j'^2*q12^2*q23+12*M`j'^2*n2*q12^2*q23-12*M`j'^2*q12*q23^2+12*M`j'^2*n2*q12*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?pos_,n4?{,>1}) = mbox1l(n1,n2,-1+n3,n4)*prf(1,-2*q13-q33)+mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-n3,-q12+n4*q12-q23+n4*q23)+mbox1l(1+n1,n2,n3,-1+n4)*prf(-(n1*q12),-q12+n4*q12-q23+n4*q23)+mbox1l(1+n1,n2,n3,-2+n4)*prf(n1*q12,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(-(n1*q13)-n1*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-(n1*q12)+n1*q13+n1*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(n2*q12+2*n2*q13+n2*q23+n2*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(n1,n2,n3,-1+n4)*prf(-q12-n2*q12+n4*q12-2*n2*q13+2*n3*q13-q23-n2*q23+n4*q23-n2*q33+n3*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?{,>1},n4?pos_) = mbox1l(n1,n2,n3,-1+n4)*prf(1,2*q12+2*q23)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(n2,-2*q12+2*n3*q12-2*q23+2*n3*q23)+mbox1l(n1,n2,-2+n3,1+n4)*prf(2*n4*q12+2*n4*q13+2*n4*q23+n4*q33,-4*q12*q13+4*n3*q12*q13-4*q13*q23+4*n3*q13*q23-2*q12*q33+2*n3*q12*q33-2*q23*q33+2*n3*q23*q33)+mbox1l(n1,-1+n2,n3,n4)*prf(4*M`j'^2*q12+8*M`j'^2*q13-4*q12*q13-4*q13^2+4*M`j'^2*q23-4*q13*q23+4*M`j'^2*q33-2*q12*q33-4*q13*q33-2*q23*q33-q33^2,4*M`j'^2*q12^2+8*M`j'^2*q12*q23+4*M`j'^2*q23^2)+mbox1l(1+n1,n2,-1+n3,n4)*prf(4*M`j'^2*n1*q12*q13-4*n1*q12^2*q13-4*n1*q12*q13^2-4*M`j'^2*n1*q12*q23-4*M`j'^2*n1*q13*q23-4*n1*q12*q13*q23-4*M`j'^2*n1*q23^2+4*M`j'^2*n1*q12*q33-2*n1*q12^2*q33-4*n1*q12*q13*q33-2*n1*q12*q23*q33-n1*q12*q33^2,-4*M`j'^2*q12^2+4*M`j'^2*n3*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n3*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n3*q23^2)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-4*M`j'^2*n1*q12^2-4*M`j'^2*n1*q12*q13+4*n1*q12^2*q13+4*n1*q12*q13^2-4*M`j'^2*n1*q12*q23+4*M`j'^2*n1*q13*q23+4*n1*q12*q13*q23-2*M`j'^2*n1*q12*q33+2*n1*q12^2*q33+4*n1*q12*q13*q33+2*M`j'^2*n1*q23*q33+2*n1*q12*q23*q33+n1*q12*q33^2,-8*M`j'^2*q12^2*q13+8*M`j'^2*n3*q12^2*q13-16*M`j'^2*q12*q13*q23+16*M`j'^2*n3*q12*q13*q23-8*M`j'^2*q13*q23^2+8*M`j'^2*n3*q13*q23^2-4*M`j'^2*q12^2*q33+4*M`j'^2*n3*q12^2*q33-8*M`j'^2*q12*q23*q33+8*M`j'^2*n3*q12*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n3*q23^2*q33)+mbox1l(1+n1,-1+n2,-1+n3,n4)*prf(4*M`j'^2*n1*q12*q13+8*M`j'^2*n1*q13^2-4*n1*q12*q13^2-4*n1*q13^3+4*M`j'^2*n1*q13*q23-4*n1*q13^2*q23+4*M`j'^2*n1*q12*q33+12*M`j'^2*n1*q13*q33-6*n1*q12*q13*q33-8*n1*q13^2*q33+4*M`j'^2*n1*q23*q33-6*n1*q13*q23*q33+4*M`j'^2*n1*q33^2-2*n1*q12*q33^2-5*n1*q13*q33^2-2*n1*q23*q33^2-n1*q33^3,-8*M`j'^2*q12^2*q13+8*M`j'^2*n3*q12^2*q13-16*M`j'^2*q12*q13*q23+16*M`j'^2*n3*q12*q13*q23-8*M`j'^2*q13*q23^2+8*M`j'^2*n3*q13*q23^2-4*M`j'^2*q12^2*q33+4*M`j'^2*n3*q12^2*q33-8*M`j'^2*q12*q23*q33+8*M`j'^2*n3*q12*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n3*q23^2*q33)+mbox1l(1+n1,n2,-2+n3,n4)*prf(4*M`j'^2*n1*q12^2-8*M`j'^2*n1*q13^2+4*n1*q12*q13^2+4*n1*q13^3+4*M`j'^2*n1*q12*q23-8*M`j'^2*n1*q13*q23+4*n1*q12*q13*q23+8*n1*q13^2*q23+4*n1*q13*q23^2-2*M`j'^2*n1*q12*q33-12*M`j'^2*n1*q13*q33+6*n1*q12*q13*q33+8*n1*q13^2*q33-6*M`j'^2*n1*q23*q33+2*n1*q12*q23*q33+10*n1*q13*q23*q33+2*n1*q23^2*q33-4*M`j'^2*n1*q33^2+2*n1*q12*q33^2+5*n1*q13*q33^2+3*n1*q23*q33^2+n1*q33^3,-8*M`j'^2*q12^2*q13+8*M`j'^2*n3*q12^2*q13-16*M`j'^2*q12*q13*q23+16*M`j'^2*n3*q12*q13*q23-8*M`j'^2*q13*q23^2+8*M`j'^2*n3*q13*q23^2-4*M`j'^2*q12^2*q33+4*M`j'^2*n3*q12^2*q33-8*M`j'^2*q12*q23*q33+8*M`j'^2*n3*q12*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n3*q23^2*q33)+mbox1l(n1,1+n2,-2+n3,n4)*prf(-4*M`j'^2*n2*q12^2-20*M`j'^2*n2*q12*q13+8*n2*q12^2*q13-16*M`j'^2*n2*q13^2+16*n2*q12*q13^2+8*n2*q13^3-8*M`j'^2*n2*q12*q23-20*M`j'^2*n2*q13*q23+16*n2*q12*q13*q23+16*n2*q13^2*q23-4*M`j'^2*n2*q23^2+8*n2*q13*q23^2-10*M`j'^2*n2*q12*q33+4*n2*q12^2*q33-16*M`j'^2*n2*q13*q33+16*n2*q12*q13*q33+12*n2*q13^2*q33-10*M`j'^2*n2*q23*q33+8*n2*q12*q23*q33+16*n2*q13*q23*q33+4*n2*q23^2*q33-4*M`j'^2*n2*q33^2+4*n2*q12*q33^2+6*n2*q13*q33^2+4*n2*q23*q33^2+n2*q33^3,-8*M`j'^2*q12^2*q13+8*M`j'^2*n3*q12^2*q13-16*M`j'^2*q12*q13*q23+16*M`j'^2*n3*q12*q13*q23-8*M`j'^2*q13*q23^2+8*M`j'^2*n3*q13*q23^2-4*M`j'^2*q12^2*q33+4*M`j'^2*n3*q12^2*q33-8*M`j'^2*q12*q23*q33+8*M`j'^2*n3*q12*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n3*q23^2*q33)+mbox1l(n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(8*q12^2*q13+8*q12*q13^2+16*q12*q13*q23+8*q13^2*q23+8*q13*q23^2+4*q12^2*q33+8*q12*q13*q33+8*q12*q23*q33+8*q13*q23*q33+4*q23^2*q33+2*q12*q33^2+2*q23*q33^2,-8*M`j'^2*q12^2*q13+8*M`j'^2*n3*q12^2*q13-16*M`j'^2*q12*q13*q23+16*M`j'^2*n3*q12*q13*q23-8*M`j'^2*q13*q23^2+8*M`j'^2*n3*q13*q23^2-4*M`j'^2*q12^2*q33+4*M`j'^2*n3*q12^2*q33-8*M`j'^2*q12*q23*q33+8*M`j'^2*n3*q12*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n3*q23^2*q33)+prf(4*M`j'^2*n2*q12^2-4*M`j'^2*n4*q12^2+12*M`j'^2*q12*q13+16*M`j'^2*n2*q12*q13-12*M`j'^2*n3*q12*q13-4*M`j'^2*n4*q12*q13-24*q12^2*q13+4*n1*q12^2*q13+8*n3*q12^2*q13+8*n4*q12^2*q13+16*M`j'^2*q13^2+16*M`j'^2*n2*q13^2-16*M`j'^2*n3*q13^2-32*q12*q13^2+4*n1*q12*q13^2-8*n2*q12*q13^2+16*n3*q12*q13^2+8*n4*q12*q13^2-8*q13^3-8*n2*q13^3+8*n3*q13^3+8*M`j'^2*n2*q12*q23-8*M`j'^2*n4*q12*q23+12*M`j'^2*q13*q23+16*M`j'^2*n2*q13*q23-12*M`j'^2*n3*q13*q23-4*M`j'^2*n4*q13*q23-48*q12*q13*q23+8*n1*q12*q13*q23+16*n3*q12*q13*q23+16*n4*q12*q13*q23-32*q13^2*q23+4*n1*q13^2*q23-8*n2*q13^2*q23+16*n3*q13^2*q23+8*n4*q13^2*q23+4*M`j'^2*n2*q23^2-4*M`j'^2*n4*q23^2-24*q13*q23^2+4*n1*q13*q23^2+8*n3*q13*q23^2+8*n4*q13*q23^2+6*M`j'^2*q12*q33+8*M`j'^2*n2*q12*q33-6*M`j'^2*n3*q12*q33-2*M`j'^2*n4*q12*q33-12*q12^2*q33+2*n1*q12^2*q33+4*n3*q12^2*q33+4*n4*q12^2*q33+16*M`j'^2*q13*q33+16*M`j'^2*n2*q13*q33-16*M`j'^2*n3*q13*q33-32*q12*q13*q33+4*n1*q12*q13*q33-8*n2*q12*q13*q33+16*n3*q12*q13*q33+8*n4*q12*q13*q33-12*q13^2*q33-12*n2*q13^2*q33+12*n3*q13^2*q33+6*M`j'^2*q23*q33+8*M`j'^2*n2*q23*q33-6*M`j'^2*n3*q23*q33-2*M`j'^2*n4*q23*q33-24*q12*q23*q33+4*n1*q12*q23*q33+8*n3*q12*q23*q33+8*n4*q12*q23*q33-32*q13*q23*q33+4*n1*q13*q23*q33-8*n2*q13*q23*q33+16*n3*q13*q23*q33+8*n4*q13*q23*q33-12*q23^2*q33+2*n1*q23^2*q33+4*n3*q23^2*q33+4*n4*q23^2*q33+4*M`j'^2*q33^2+4*M`j'^2*n2*q33^2-4*M`j'^2*n3*q33^2-8*q12*q33^2+n1*q12*q33^2-2*n2*q12*q33^2+4*n3*q12*q33^2+2*n4*q12*q33^2-6*q13*q33^2-6*n2*q13*q33^2+6*n3*q13*q33^2-8*q23*q33^2+n1*q23*q33^2-2*n2*q23*q33^2+4*n3*q23*q33^2+2*n4*q23*q33^2-q33^3-n2*q33^3+n3*q33^3,-8*M`j'^2*q12^2*q13+8*M`j'^2*n3*q12^2*q13-16*M`j'^2*q12*q13*q23+16*M`j'^2*n3*q12*q13*q23-8*M`j'^2*q13*q23^2+8*M`j'^2*n3*q13*q23^2-4*M`j'^2*q12^2*q33+4*M`j'^2*n3*q12^2*q33-8*M`j'^2*q12*q23*q33+8*M`j'^2*n3*q12*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n3*q23^2*q33)); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?{,>1},n3?pos_,n4?pos_) = mbox1l(n1,n2,n3,-1+n4)*prf(-1,2*q12+2*q23)+mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-n3,-2*q12+2*n2*q12-2*q23+2*n2*q23)+mbox1l(n1,-1+n2,-1+n3,1+n4)*prf(-n4,-2*q12+2*n2*q12-2*q23+2*n2*q23)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(2*M`j'^2*n1*q12-2*n1*q12*q13-2*M`j'^2*n1*q23-n1*q12*q33,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n2*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2)+mbox1l(n1,n2,-1+n3,n4)*prf(6*M`j'^2*q12+8*M`j'^2*q13-4*q12*q13-4*q13^2+6*M`j'^2*q23-4*q13*q23+4*M`j'^2*q33-2*q12*q33-4*q13*q33-2*q23*q33-q33^2,4*M`j'^2*q12^2+8*M`j'^2*q12*q23+4*M`j'^2*q23^2)+mbox1l(1+n1,-1+n2,-1+n3,n4)*prf(-2*M`j'^2*n1*q12+4*M`j'^2*n1*q13-2*n1*q13^2+2*M`j'^2*n1*q23-2*n1*q13*q23+4*M`j'^2*n1*q33-3*n1*q13*q33-n1*q23*q33-n1*q33^2,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n2*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2)+mbox1l(1+n1,-2+n2,n3,n4)*prf(-4*M`j'^2*n1*q13+2*n1*q13^2-4*M`j'^2*n1*q33+3*n1*q13*q33+n1*q33^2,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n2*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2)+mbox1l(n1,-1+n2,n3,n4)*(tmpprf(ep,1)*prf(-4*q12*q13-4*q13*q23-2*q12*q33-2*q23*q33,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n2*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2)+prf(4*M`j'^2*q12-4*M`j'^2*n2*q12+2*M`j'^2*n3*q12+2*M`j'^2*n4*q12+8*M`j'^2*q13-8*M`j'^2*n2*q13+8*M`j'^2*n3*q13+8*q12*q13-2*n1*q12*q13-4*n3*q12*q13-4*n4*q12*q13-4*q13^2+4*n2*q13^2-4*n3*q13^2+4*M`j'^2*q23-4*M`j'^2*n2*q23+2*M`j'^2*n3*q23+2*M`j'^2*n4*q23+8*q13*q23-2*n1*q13*q23-4*n3*q13*q23-4*n4*q13*q23+4*M`j'^2*q33-4*M`j'^2*n2*q33+4*M`j'^2*n3*q33+4*q12*q33-n1*q12*q33-2*n3*q12*q33-2*n4*q12*q33-4*q13*q33+4*n2*q13*q33-4*n3*q13*q33+4*q23*q33-n1*q23*q33-2*n3*q23*q33-2*n4*q23*q33-q33^2+n2*q33^2-n3*q33^2,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n2*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2))+mbox1l(n1,-2+n2,1+n3,n4)*prf(-8*M`j'^2*n3*q13+4*n3*q13^2-4*M`j'^2*n3*q33+4*n3*q13*q33+n3*q33^2,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n2*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2)+mbox1l(1+n1,-1+n2,n3,n4)*prf(-4*M`j'^2*n1*q12*q13+4*n1*q12*q13^2+4*M`j'^2*n1*q13*q23-4*M`j'^2*n1*q12*q33+4*n1*q12*q13*q33+n1*q12*q33^2,-4*M`j'^2*q12^2+4*M`j'^2*n2*q12^2-8*M`j'^2*q12*q23+8*M`j'^2*n2*q12*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2); Identify,ifmatch->jump mbox1l(n1?neg0_,n2?pos_,n3?pos_,n4?{,>1}) = mbox1l(n1,n2,1+n3,-1+n4)*prf(n3,-1+n4)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(-2*n1*q12,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(1+n1,n2,n3,-1+n4)*prf(n1*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(n1,1+n2,-1+n3,n4)*prf(2*q12+2*q13+2*q23+q33,2*q13+q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n1*q12-n1*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(n1,2+n2,-1+n3,-1+n4)*prf(-2*q12-2*n2*q12-2*q13-2*n2*q13-2*q23-2*n2*q23-q33-n2*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(n1,1+n2,n3,-1+n4)*prf(4*q12+2*n2*q12-2*n4*q12+2*q13+2*n2*q13-2*n3*q13+4*q23+2*n2*q23-2*n4*q23+q33+n2*q33-n3*q33,-2*q13+2*n4*q13-q33+n4*q33); Identify,ifmatch->jump mbox1l(n1?neg_,1,1,1) = tmpprf(1,2*ep+n1)*mbox1l(n1,1,0,2)*prf(-2*M`j'^2,2*q13+q33)+tmpprf(1,2*ep+n1)*mbox1l(n1,1,2,0)*prf(-2*M`j'^2,2*q13+q33)+tmpprf(1,2*ep+n1)*mbox1l(n1,2,1,0)*prf(-2*M`j'^2,2*q13+q33)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,1,0,2)*prf(2*M`j'^2*q12,q12+q23)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,1,2,0)*prf(2*M`j'^2*q12,q12+q23)+tmpprf(1,2*ep+n1)*mbox1l(n1,0,2,1)*prf(-4*M`j'^2+2*q13+q33,q12+q23)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,2,1,0)*prf(-4*M`j'^2*q12^2+4*M`j'^2*q12*q13-4*M`j'^2*q12*q23+2*M`j'^2*q12*q33,2*q12*q13+2*q13*q23+q12*q33+q23*q33)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,1,1,0)*prf(2*M`j'^2*n1*q12-2*n1*q12*q13-2*M`j'^2*n1*q23-n1*q12*q33,2*q12*q13+2*q13*q23+q12*q33+q23*q33)+mbox1l(1+n1,1,1,1)*(tmpprf(ep,2*ep+n1)*prf(4*q12*q13+2*q12*q33,q12+q23)+tmpprf(1,2*ep+n1)*prf(2*q12*q13+4*n1*q12*q13+q12*q33+2*n1*q12*q33,q12+q23))+tmpprf(1,2*ep+n1)*mbox1l(n1,2,0,1)*prf(6*M`j'^2*q12+8*M`j'^2*q13-4*q12*q13-4*q13^2+6*M`j'^2*q23-4*q13*q23+4*M`j'^2*q33-2*q12*q33-4*q13*q33-2*q23*q33-q33^2,2*q12*q13+2*q13*q23+q12*q33+q23*q33)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,1,0,1)*prf(-2*M`j'^2*n1*q12+4*M`j'^2*n1*q13-2*n1*q13^2+2*M`j'^2*n1*q23-2*n1*q13*q23+4*M`j'^2*n1*q33-3*n1*q13*q33-n1*q23*q33-n1*q33^2,2*q12*q13+2*q13*q23+q12*q33+q23*q33)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,0,1,1)*prf(-4*M`j'^2*n1*q13+2*n1*q13^2-4*M`j'^2*n1*q33+3*n1*q13*q33+n1*q33^2,2*q12*q13+2*q13*q23+q12*q33+q23*q33)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,0,2,1)*prf(8*M`j'^2*q12*q13-4*q12*q13^2+4*M`j'^2*q12*q33-4*q12*q13*q33-q12*q33^2,q12^2+2*q12*q23+q23^2)+tmpprf(1,2*ep+n1)*mbox1l(2+n1,1,1,1)*prf(-4*q12^2*q13^2-4*n1*q12^2*q13^2-8*M`j'^2*q12*q13*q23-8*M`j'^2*n1*q12*q13*q23+4*M`j'^2*q12^2*q33+4*M`j'^2*n1*q12^2*q33-4*q12^2*q13*q33-4*n1*q12^2*q13*q33-q12^2*q33^2-n1*q12^2*q33^2,q12^2+2*q12*q23+q23^2)+tmpprf(1,2*ep+n1)*mbox1l(2+n1,1,1,0)*prf(-8*M`j'^2*q12^2*q13-8*M`j'^2*n1*q12^2*q13+4*q12^2*q13^2+4*n1*q12^2*q13^2-2*M`j'^2*q12^2*q33-2*M`j'^2*n1*q12^2*q33+4*q12^2*q13*q33+4*n1*q12^2*q13*q33+2*M`j'^2*q12*q23*q33+2*M`j'^2*n1*q12*q23*q33+q12^2*q33^2+n1*q12^2*q33^2,2*q12^2*q13+4*q12*q13*q23+2*q13*q23^2+q12^2*q33+2*q12*q23*q33+q23^2*q33)+tmpprf(1,2*ep+n1)*mbox1l(1+n1,2,0,1)*prf(-8*M`j'^2*q12^2*q13-16*M`j'^2*q12*q13^2+8*q12^2*q13^2+8*q12*q13^3-4*M`j'^2*q12^2*q23-12*M`j'^2*q12*q13*q23+8*q12*q13^2*q23-8*M`j'^2*q12*q23^2-4*M`j'^2*q13*q23^2-4*M`j'^2*q23^3-2*M`j'^2*q12^2*q33-16*M`j'^2*q12*q13*q33+8*q12^2*q13*q33+12*q12*q13^2*q33-2*M`j'^2*q12*q23*q33+8*q12*q13*q23*q33-4*M`j'^2*q12*q33^2+2*q12^2*q33^2+6*q12*q13*q33^2+2*q12*q23*q33^2+q12*q33^3,2*q12^2*q13+4*q12*q13*q23+2*q13*q23^2+q12^2*q33+2*q12*q23*q33+q23^2*q33)+tmpprf(1,2*ep+n1)*mbox1l(2+n1,0,1,1)*prf(4*M`j'^2*q12*q13^2+4*M`j'^2*n1*q12*q13^2-4*q12*q13^3-4*n1*q12*q13^3-4*M`j'^2*q13^2*q23-4*M`j'^2*n1*q13^2*q23+12*M`j'^2*q12*q13*q33+12*M`j'^2*n1*q12*q13*q33-8*q12*q13^2*q33-8*n1*q12*q13^2*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n1*q12*q33^2-5*q12*q13*q33^2-5*n1*q12*q13*q33^2-q12*q33^3-n1*q12*q33^3,2*q12^2*q13+4*q12*q13*q23+2*q13*q23^2+q12^2*q33+2*q12*q23*q33+q23^2*q33)+tmpprf(1,2*ep+n1)*mbox1l(2+n1,1,0,1)*prf(4*M`j'^2*q12^2*q13+4*M`j'^2*n1*q12^2*q13-4*M`j'^2*q12*q13^2-4*M`j'^2*n1*q12*q13^2+4*q12*q13^3+4*n1*q12*q13^3+4*M`j'^2*q13^2*q23+4*M`j'^2*n1*q13^2*q23+4*q12*q13^2*q23+4*n1*q12*q13^2*q23+4*M`j'^2*q13*q23^2+4*M`j'^2*n1*q13*q23^2-2*M`j'^2*q12^2*q33-2*M`j'^2*n1*q12^2*q33-12*M`j'^2*q12*q13*q33-12*M`j'^2*n1*q12*q13*q33+8*q12*q13^2*q33+8*n1*q12*q13^2*q33-6*M`j'^2*q12*q23*q33-6*M`j'^2*n1*q12*q23*q33+4*q12*q13*q23*q33+4*n1*q12*q13*q23*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n1*q12*q33^2+5*q12*q13*q33^2+5*n1*q12*q13*q33^2+q12*q23*q33^2+n1*q12*q23*q33^2+q12*q33^3+n1*q12*q33^3,2*q12^2*q13+4*q12*q13*q23+2*q13*q23^2+q12^2*q33+2*q12*q23*q33+q23^2*q33); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg_,n3?pos_,n4?{,>1}) = mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(-(n3*q12)-n3*q23,-q13+n4*q13)+mbox1l(n1,2+n2,n3,-2+n4)*prf(2*q12^2+2*n2*q12^2+2*q12*q23+2*n2*q12*q23,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(n1,1+n2,-1+n3,n4)*prf(2*q12+2*q13+2*q23+q33,2*q13+q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n1*q12*q13+2*n1*q12*q33+n1*q23*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-2*q12^2-2*n2*q12^2-2*q12*q13-2*n2*q12*q13-4*q12*q23-4*n2*q12*q23-2*q13*q23-2*n2*q13*q23-2*q23^2-2*n2*q23^2-q12*q33-n2*q12*q33-q23*q33-n2*q23*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(n1,2+n2,-1+n3,-1+n4)*prf(2*q12*q23+2*n2*q12*q23+2*q13*q23+2*n2*q13*q23+2*q23^2+2*n2*q23^2+q23*q33+n2*q23*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(n1,1+n2,n3,-1+n4)*prf(4*q12*q13-2*n1*q12*q13+2*n2*q12*q13+2*n3*q12*q13-2*n4*q12*q13+2*q13*q23+2*n3*q13*q23-2*n4*q13*q23+q12*q33-2*n1*q12*q33+n2*q12*q33+n3*q12*q33-n1*q23*q33+n3*q23*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg_,n3?{,>1},n4?pos_) = mbox1l(n1,1+n2,n3,-1+n4)*prf(q12*q33,2*q13^2)+mbox1l(n1,1+n2,-2+n3,1+n4)*prf(n4*q12*q33,-2*q13^2+2*n3*q13^2)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n1*q12*q13+n1*q12*q33,-2*q13^2+2*n3*q13^2)+mbox1l(n1,2+n2,-1+n3,-1+n4)*prf(4*M`j'^2*q12^2*q13+4*M`j'^2*n2*q12^2*q13+4*M`j'^2*q12*q13*q23+4*M`j'^2*n2*q12*q13*q23+4*M`j'^2*q12^2*q33+4*M`j'^2*n2*q12^2*q33+2*M`j'^2*q12*q13*q33+2*M`j'^2*n2*q12*q13*q33-2*q12^2*q13*q33-2*n2*q12^2*q13*q33-q12^2*q33^2-n2*q12^2*q33^2,-4*M`j'^2*q13^3+4*M`j'^2*n3*q13^3)+mbox1l(-1+n1,1+n2,n3,n4)*prf(-4*M`j'^2*q12*q13^2-4*M`j'^2*q13^2*q23-8*M`j'^2*q12*q13*q33+4*q12*q13^2*q33-4*M`j'^2*q12*q33^2+4*q12*q13*q33^2+q12*q33^3,4*M`j'^2*q13^3)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(6*M`j'^2*n1*q12*q13*q33+4*M`j'^2*n1*q12*q33^2-2*n1*q12*q13*q33^2-n1*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n3*q13^3)+mbox1l(n1,2+n2,-2+n3,n4)*prf(4*M`j'^2*q12*q13^2+4*M`j'^2*n2*q12*q13^2+4*M`j'^2*q13^3+4*M`j'^2*n2*q13^3+4*M`j'^2*q12*q13*q23+4*M`j'^2*n2*q12*q13*q23+8*M`j'^2*q13^2*q23+8*M`j'^2*n2*q13^2*q23+4*M`j'^2*q13*q23^2+4*M`j'^2*n2*q13*q23^2+2*M`j'^2*q12*q13*q33+2*M`j'^2*n2*q12*q13*q33-2*q12*q13^2*q33-2*n2*q12*q13^2*q33+4*M`j'^2*q12*q23*q33+4*M`j'^2*n2*q12*q23*q33-2*q12*q13*q23*q33-2*n2*q12*q13*q23*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n2*q12*q33^2-3*q12*q13*q33^2-3*n2*q12*q13*q33^2-q12*q23*q33^2-n2*q12*q23*q33^2-q12*q33^3-n2*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n3*q13^3)+mbox1l(-1+n1,2+n2,-1+n3,n4)*prf(-4*M`j'^2*q12^2*q13-4*M`j'^2*n2*q12^2*q13-4*M`j'^2*q12*q13^2-4*M`j'^2*n2*q12*q13^2-8*M`j'^2*q12*q13*q23-8*M`j'^2*n2*q12*q13*q23-4*M`j'^2*q13^2*q23-4*M`j'^2*n2*q13^2*q23-4*M`j'^2*q13*q23^2-4*M`j'^2*n2*q13*q23^2-4*M`j'^2*q12^2*q33-4*M`j'^2*n2*q12^2*q33-8*M`j'^2*q12*q13*q33-8*M`j'^2*n2*q12*q13*q33+2*q12^2*q13*q33+2*n2*q12^2*q13*q33+4*q12*q13^2*q33+4*n2*q12*q13^2*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33+2*q12*q13*q23*q33+2*n2*q12*q13*q23*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n2*q12*q33^2+q12^2*q33^2+n2*q12^2*q33^2+4*q12*q13*q33^2+4*n2*q12*q13*q33^2+q12*q23*q33^2+n2*q12*q23*q33^2+q12*q33^3+n2*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n3*q13^3)+mbox1l(n1,1+n2,-1+n3,n4)*(tmpprf(ep,1)*prf(4*q12*q13^2*q33+2*q12*q13*q33^2,-4*M`j'^2*q13^3+4*M`j'^2*n3*q13^3)+prf(-4*M`j'^2*q12*q13^2-4*M`j'^2*n1*q12*q13^2+4*M`j'^2*n3*q12*q13^2-8*M`j'^2*q13^3-4*M`j'^2*n2*q13^3+4*M`j'^2*n3*q13^3-8*M`j'^2*q13^2*q23-4*M`j'^2*n2*q13^2*q23+4*M`j'^2*n3*q13^2*q23-2*M`j'^2*q12*q13*q33-8*M`j'^2*n1*q12*q13*q33+4*M`j'^2*n2*q12*q13*q33+6*M`j'^2*n3*q12*q13*q33-2*M`j'^2*n4*q12*q13*q33-6*q12*q13^2*q33+4*n1*q12*q13^2*q33+2*n2*q12*q13^2*q33+4*n4*q12*q13^2*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n1*q12*q33^2+4*M`j'^2*n3*q12*q33^2-q12*q13*q33^2+4*n1*q12*q13*q33^2+n2*q12*q13*q33^2-2*n3*q12*q13*q33^2+2*n4*q12*q13*q33^2+q12*q33^3+n1*q12*q33^3-n3*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n3*q13^3))+mbox1l(n1,2+n2,-1+n3,n4)*prf(4*q12^2*q13^2*q33+4*n2*q12^2*q13^2*q33+8*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n2*q12*q13*q23*q33-4*M`j'^2*q12^2*q33^2-4*M`j'^2*n2*q12^2*q33^2+4*q12^2*q13*q33^2+4*n2*q12^2*q13*q33^2+q12^2*q33^3+n2*q12^2*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n3*q13^3); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?neg_,n3?pos_,n4?pos_) = mbox1l(n1,1+n2,n3,-1+n4)*prf(-4*q12*q13-q12*q33,2*q13^2)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(-2*n3*q12*q13-n3*q12*q33,-2*q13^2+2*n1*q13^2)+mbox1l(-1+n1,1+n2,-1+n3,1+n4)*prf(-2*n4*q12*q13-n4*q12*q33,-2*q13^2+2*n1*q13^2)+mbox1l(-1+n1,2+n2,n3,-1+n4)*prf(-12*M`j'^2*q12^2*q13-12*M`j'^2*n2*q12^2*q13-4*M`j'^2*q12*q13^2-4*M`j'^2*n2*q12*q13^2+4*q12^2*q13^2+4*n2*q12^2*q13^2-4*M`j'^2*q12*q13*q23-4*M`j'^2*n2*q12*q13*q23-4*M`j'^2*q12^2*q33-4*M`j'^2*n2*q12^2*q33-2*M`j'^2*q12*q13*q33-2*M`j'^2*n2*q12*q13*q33+4*q12^2*q13*q33+4*n2*q12^2*q13*q33+q12^2*q33^2+n2*q12^2*q33^2,-4*M`j'^2*q13^3+4*M`j'^2*n1*q13^3)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-4*M`j'^2*q12*q13^2+4*M`j'^2*q13^3+4*M`j'^2*q13^2*q23-14*M`j'^2*q12*q13*q33+4*q12*q13^2*q33-4*M`j'^2*q12*q33^2+4*q12*q13*q33^2+q12*q33^3,4*M`j'^2*q13^3)+mbox1l(-2+n1,2+n2,n3,n4)*prf(12*M`j'^2*q12^2*q13+12*M`j'^2*n2*q12^2*q13+16*M`j'^2*q12*q13^2+16*M`j'^2*n2*q12*q13^2-4*q12^2*q13^2-4*n2*q12^2*q13^2-8*q12*q13^3-8*n2*q12*q13^3+16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-4*q12*q13^2*q23-4*n2*q12*q13^2*q23+4*M`j'^2*q13*q23^2+4*M`j'^2*n2*q13*q23^2+4*M`j'^2*q12^2*q33+4*M`j'^2*n2*q12^2*q33+16*M`j'^2*q12*q13*q33+16*M`j'^2*n2*q12*q13*q33-4*q12^2*q13*q33-4*n2*q12^2*q13*q33-12*q12*q13^2*q33-12*n2*q12*q13^2*q33+4*M`j'^2*q12*q23*q33+4*M`j'^2*n2*q12*q23*q33-4*q12*q13*q23*q33-4*n2*q12*q13*q23*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n2*q12*q33^2-q12^2*q33^2-n2*q12^2*q33^2-6*q12*q13*q33^2-6*n2*q12*q13*q33^2-q12*q23*q33^2-n2*q12*q23*q33^2-q12*q33^3-n2*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n1*q13^3)+mbox1l(-1+n1,2+n2,-1+n3,n4)*prf(-8*M`j'^2*q12*q13^2-8*M`j'^2*n2*q12*q13^2+4*q12*q13^3+4*n2*q12*q13^3-12*M`j'^2*q12*q13*q23-12*M`j'^2*n2*q12*q13*q23-4*M`j'^2*q13^2*q23-4*M`j'^2*n2*q13^2*q23+4*q12*q13^2*q23+4*n2*q12*q13^2*q23-4*M`j'^2*q13*q23^2-4*M`j'^2*n2*q13*q23^2-10*M`j'^2*q12*q13*q33-10*M`j'^2*n2*q12*q13*q33+8*q12*q13^2*q33+8*n2*q12*q13^2*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33+4*q12*q13*q23*q33+4*n2*q12*q13*q23*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n2*q12*q33^2+5*q12*q13*q33^2+5*n2*q12*q13*q33^2+q12*q23*q33^2+n2*q12*q23*q33^2+q12*q33^3+n2*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n1*q13^3)+mbox1l(-2+n1,1+n2,1+n3,n4)*prf(16*M`j'^2*n3*q12*q13^2-8*n3*q12*q13^3+16*M`j'^2*n3*q12*q13*q33-12*n3*q12*q13^2*q33+4*M`j'^2*n3*q12*q33^2-6*n3*q12*q13*q33^2-n3*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n1*q13^3)+mbox1l(-1+n1,1+n2,n3,n4)*(tmpprf(ep,1)*prf(-8*q12*q13^3-8*q12*q13^2*q33-2*q12*q13*q33^2,-4*M`j'^2*q13^3+4*M`j'^2*n1*q13^3)+prf(-16*M`j'^2*q12*q13^2+12*M`j'^2*n1*q12*q13^2-4*M`j'^2*n2*q12*q13^2-12*M`j'^2*n3*q12*q13^2+4*M`j'^2*n4*q12*q13^2+20*q12*q13^3-8*n1*q12*q13^3-4*n2*q12*q13^3-8*n4*q12*q13^3+8*M`j'^2*q13^2*q23-4*M`j'^2*n1*q13^2*q23+4*M`j'^2*n2*q13^2*q23-20*M`j'^2*q12*q13*q33+16*M`j'^2*n1*q12*q13*q33-4*M`j'^2*n2*q12*q13*q33-14*M`j'^2*n3*q12*q13*q33+2*M`j'^2*n4*q12*q13*q33+24*q12*q13^2*q33-12*n1*q12*q13^2*q33-4*n2*q12*q13^2*q33+4*n3*q12*q13^2*q33-8*n4*q12*q13^2*q33-4*M`j'^2*q12*q33^2+4*M`j'^2*n1*q12*q33^2-4*M`j'^2*n3*q12*q33^2+9*q12*q13*q33^2-6*n1*q12*q13*q33^2-n2*q12*q13*q33^2+4*n3*q12*q13*q33^2-2*n4*q12*q13*q33^2+q12*q33^3-n1*q12*q33^3+n3*q12*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n1*q13^3))+mbox1l(-1+n1,2+n2,n3,n4)*prf(-8*q12^2*q13^3-8*n2*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23-16*M`j'^2*n2*q12*q13^2*q23+8*M`j'^2*q12^2*q13*q33+8*M`j'^2*n2*q12^2*q13*q33-12*q12^2*q13^2*q33-12*n2*q12^2*q13^2*q33-8*M`j'^2*q12*q13*q23*q33-8*M`j'^2*n2*q12*q13*q23*q33+4*M`j'^2*q12^2*q33^2+4*M`j'^2*n2*q12^2*q33^2-6*q12^2*q13*q33^2-6*n2*q12^2*q13*q33^2-q12^2*q33^3-n2*q12^2*q33^3,-4*M`j'^2*q13^3+4*M`j'^2*n1*q13^3); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?pos_,n4?{,>1}) = mbox1l(n1,n2,-1+n3,n4)*prf(1,-2*q13-q33)+mbox1l(-1+n1,n2,1+n3,-1+n4)*prf(n3,-q13+n4*q13)+mbox1l(n1,1+n2,n3,-2+n4)*prf(-(n2*q12),-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(n1,1+n2,n3,-1+n4)*prf(n2*q12,-q13+n4*q13)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-(n1*q13)-n1*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(-2*n2*q13-n2*q23-n2*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(n2*q12+2*n2*q13+n2*q23+n2*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33)+mbox1l(n1,n2,n3,-1+n4)*prf(-q13+n1*q13-2*n3*q13+n4*q13+n1*q33-n3*q33,-2*q13^2+2*n4*q13^2-q13*q33+n4*q13*q33); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?{,>1},n4?pos_) = mbox1l(n1,n2,n3,-1+n4)*prf(-1,2*q13)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-n1,-2*q13+2*n3*q13)+mbox1l(n1,n2,-2+n3,1+n4)*prf(-(n4*q33),-4*q13^2+4*n3*q13^2-2*q13*q33+2*n3*q13*q33)+mbox1l(-1+n1,n2,n3,n4)*prf(4*M`j'^2*q13+4*M`j'^2*q33-2*q13*q33-q33^2,4*M`j'^2*q13^2)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-4*M`j'^2*n2*q13^2-4*M`j'^2*n2*q13*q23+4*M`j'^2*n2*q12*q33-2*n2*q12*q13*q33-n2*q12*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n3*q13^2)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(-4*M`j'^2*n2*q12*q13-4*M`j'^2*n2*q13^2-4*M`j'^2*n2*q12*q33-2*M`j'^2*n2*q13*q33+2*n2*q12*q13*q33+n2*q12*q33^2,-8*M`j'^2*q13^3+8*M`j'^2*n3*q13^3-4*M`j'^2*q13^2*q33+4*M`j'^2*n3*q13^2*q33)+mbox1l(1+n1,n2,-2+n3,n4)*prf(-6*M`j'^2*n1*q13*q33-4*M`j'^2*n1*q33^2+2*n1*q13*q33^2+n1*q33^3,-8*M`j'^2*q13^3+8*M`j'^2*n3*q13^3-4*M`j'^2*q13^2*q33+4*M`j'^2*n3*q13^2*q33)+mbox1l(-1+n1,1+n2,-1+n3,n4)*prf(4*M`j'^2*n2*q12*q13+8*M`j'^2*n2*q13^2+4*M`j'^2*n2*q13*q23+4*M`j'^2*n2*q12*q33+12*M`j'^2*n2*q13*q33-2*n2*q12*q13*q33-4*n2*q13^2*q33+4*M`j'^2*n2*q23*q33-2*n2*q13*q23*q33+4*M`j'^2*n2*q33^2-n2*q12*q33^2-4*n2*q13*q33^2-n2*q23*q33^2-n2*q33^3,-8*M`j'^2*q13^3+8*M`j'^2*n3*q13^3-4*M`j'^2*q13^2*q33+4*M`j'^2*n3*q13^2*q33)+mbox1l(n1,1+n2,-2+n3,n4)*prf(-4*M`j'^2*n2*q13^2-4*M`j'^2*n2*q13*q23-10*M`j'^2*n2*q13*q33+2*n2*q13^2*q33-4*M`j'^2*n2*q23*q33+2*n2*q13*q23*q33-4*M`j'^2*n2*q33^2+3*n2*q13*q33^2+n2*q23*q33^2+n2*q33^3,-8*M`j'^2*q13^3+8*M`j'^2*n3*q13^3-4*M`j'^2*q13^2*q33+4*M`j'^2*n3*q13^2*q33)+mbox1l(n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(-4*q13^2*q33-2*q13*q33^2,-8*M`j'^2*q13^3+8*M`j'^2*n3*q13^3-4*M`j'^2*q13^2*q33+4*M`j'^2*n3*q13^2*q33)+prf(4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-4*M`j'^2*n3*q13^2+10*M`j'^2*q13*q33+8*M`j'^2*n1*q13*q33-10*M`j'^2*n3*q13*q33+2*M`j'^2*n4*q13*q33+8*q13^2*q33-4*n1*q13^2*q33-2*n2*q13^2*q33-4*n4*q13^2*q33+4*M`j'^2*q33^2+4*M`j'^2*n1*q33^2-4*M`j'^2*n3*q33^2+2*q13*q33^2-4*n1*q13*q33^2-n2*q13*q33^2+2*n3*q13*q33^2-2*n4*q13*q33^2-q33^3-n1*q33^3+n3*q33^3,-8*M`j'^2*q13^3+8*M`j'^2*n3*q13^3-4*M`j'^2*q13^2*q33+4*M`j'^2*n3*q13^2*q33)); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?neg0_,n3?pos_,n4?pos_) = mbox1l(n1,n2,n3,-1+n4)*prf(1,2*q13)+mbox1l(-1+n1,n2,1+n3,-1+n4)*prf(n3,-2*q13+2*n1*q13)+mbox1l(-1+n1,n2,-1+n3,1+n4)*prf(n4,-2*q13+2*n1*q13)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n2*q12+2*M`j'^2*n2*q13-2*n2*q12*q13-n2*q12*q33,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2)+mbox1l(n1,n2,-1+n3,n4)*prf(2*M`j'^2*q13+4*M`j'^2*q33-2*q13*q33-q33^2,4*M`j'^2*q13^2)+mbox1l(-1+n1,1+n2,-1+n3,n4)*prf(6*M`j'^2*n2*q13-2*n2*q13^2+4*M`j'^2*n2*q23-2*n2*q13*q23+4*M`j'^2*n2*q33-3*n2*q13*q33-n2*q23*q33-n2*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2)+mbox1l(-2+n1,1+n2,n3,n4)*prf(-4*M`j'^2*n2*q12-8*M`j'^2*n2*q13+2*n2*q12*q13+4*n2*q13^2-4*M`j'^2*n2*q23+2*n2*q13*q23-4*M`j'^2*n2*q33+n2*q12*q33+4*n2*q13*q33+n2*q23*q33+n2*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2)+mbox1l(-1+n1,n2,n3,n4)*(tmpprf(ep,1)*prf(4*q13^2+2*q13*q33,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2)+prf(4*M`j'^2*q13-4*M`j'^2*n1*q13+6*M`j'^2*n3*q13-2*M`j'^2*n4*q13-12*q13^2+4*n1*q13^2+2*n2*q13^2+4*n4*q13^2+4*M`j'^2*q33-4*M`j'^2*n1*q33+4*M`j'^2*n3*q33-8*q13*q33+4*n1*q13*q33+n2*q13*q33-2*n3*q13*q33+2*n4*q13*q33-q33^2+n1*q33^2-n3*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2))+mbox1l(-2+n1,n2,1+n3,n4)*prf(-8*M`j'^2*n3*q13+4*n3*q13^2-4*M`j'^2*n3*q33+4*n3*q13*q33+n3*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2)+mbox1l(-1+n1,1+n2,n3,n4)*prf(-4*M`j'^2*n2*q12*q13+4*n2*q12*q13^2+4*M`j'^2*n2*q13*q23-4*M`j'^2*n2*q12*q33+4*n2*q12*q13*q33+n2*q12*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2); Identify,ifmatch->jump mbox1l(n1?pos_,n2?neg0_,n3?pos_,n4?{,>1}) = mbox1l(n1,n2,1+n3,-1+n4)*prf(n3,-1+n4)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(-2*n2*q12,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(1+n1,n2,-1+n3,n4)*prf(q33,2*q13+q33)+mbox1l(2+n1,n2,-1+n3,-1+n4)*prf(-q33-n1*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(-2*n2*q13-2*n2*q23-n2*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(n1,1+n2,n3,-1+n4)*prf(2*n2*q12+2*n2*q13+2*n2*q23+n2*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(1+n1,n2,n3,-1+n4)*prf(-2*q13-2*n3*q13+2*n4*q13+q33+n1*q33-n3*q33,-2*q13+2*n4*q13-q33+n4*q33); Identify,ifmatch->jump mbox1l(1,n2?neg_,1,1) = tmpprf(1,2*ep+n2)*mbox1l(1,n2,0,2)*prf(-2*M`j'^2,2*q13+q33)+tmpprf(1,2*ep+n2)*mbox1l(1,n2,2,0)*prf(-2*M`j'^2,2*q13+q33)+tmpprf(1,2*ep+n2)*mbox1l(2,n2,1,0)*prf(-2*M`j'^2,2*q13+q33)+tmpprf(1,2*ep+n2)*mbox1l(1,1+n2,0,2)*prf(-2*M`j'^2*q12,q13)+tmpprf(1,2*ep+n2)*mbox1l(1,1+n2,2,0)*prf(-2*M`j'^2*q12,q13)+tmpprf(1,2*ep+n2)*mbox1l(0,n2,2,1)*prf(4*M`j'^2-2*q13-q33,q13)+tmpprf(1,2*ep+n2)*mbox1l(2,1+n2,1,0)*prf(-8*M`j'^2*q12*q13-2*M`j'^2*q12*q33,2*q13^2+q13*q33)+mbox1l(1,1+n2,1,1)*(tmpprf(ep,2*ep+n2)*prf(-4*q12*q13-2*q12*q33,q13)+tmpprf(1,2*ep+n2)*prf(-2*q12*q13-4*n2*q12*q13-q12*q33-2*n2*q12*q33,q13))+tmpprf(1,2*ep+n2)*mbox1l(1,1+n2,1,0)*prf(-4*M`j'^2*n2*q12-2*M`j'^2*n2*q13+2*n2*q12*q13+n2*q12*q33,2*q13^2+q13*q33)+tmpprf(1,2*ep+n2)*mbox1l(2,n2,0,1)*prf(-2*M`j'^2*q13-4*M`j'^2*q33+2*q13*q33+q33^2,2*q13^2+q13*q33)+tmpprf(1,2*ep+n2)*mbox1l(0,1+n2,1,1)*prf(4*M`j'^2*n2*q12+8*M`j'^2*n2*q13-2*n2*q12*q13-4*n2*q13^2+4*M`j'^2*n2*q23-2*n2*q13*q23+4*M`j'^2*n2*q33-n2*q12*q33-4*n2*q13*q33-n2*q23*q33-n2*q33^2,2*q13^2+q13*q33)+tmpprf(1,2*ep+n2)*mbox1l(1,1+n2,0,1)*prf(-6*M`j'^2*n2*q13+2*n2*q13^2-4*M`j'^2*n2*q23+2*n2*q13*q23-4*M`j'^2*n2*q33+3*n2*q13*q33+n2*q23*q33+n2*q33^2,2*q13^2+q13*q33)+tmpprf(1,2*ep+n2)*mbox1l(0,1+n2,2,1)*prf(8*M`j'^2*q12*q13-4*q12*q13^2+4*M`j'^2*q12*q33-4*q12*q13*q33-q12*q33^2,q13^2)+tmpprf(1,2*ep+n2)*mbox1l(1,2+n2,1,1)*prf(-4*q12^2*q13^2-4*n2*q12^2*q13^2-8*M`j'^2*q12*q13*q23-8*M`j'^2*n2*q12*q13*q23+4*M`j'^2*q12^2*q33+4*M`j'^2*n2*q12^2*q33-4*q12^2*q13*q33-4*n2*q12^2*q13*q33-q12^2*q33^2-n2*q12^2*q33^2,q13^2)+tmpprf(1,2*ep+n2)*mbox1l(1,2+n2,1,0)*prf(-12*M`j'^2*q12^2*q13-12*M`j'^2*n2*q12^2*q13-4*M`j'^2*q12*q13^2-4*M`j'^2*n2*q12*q13^2+4*q12^2*q13^2+4*n2*q12^2*q13^2-4*M`j'^2*q12*q13*q23-4*M`j'^2*n2*q12*q13*q23-4*M`j'^2*q12^2*q33-4*M`j'^2*n2*q12^2*q33-2*M`j'^2*q12*q13*q33-2*M`j'^2*n2*q12*q13*q33+4*q12^2*q13*q33+4*n2*q12^2*q13*q33+q12^2*q33^2+n2*q12^2*q33^2,2*q13^3+q13^2*q33)+tmpprf(1,2*ep+n2)*mbox1l(2,1+n2,0,1)*prf(-4*M`j'^2*q12*q13^2+4*M`j'^2*q13^3+4*M`j'^2*q13^2*q23-14*M`j'^2*q12*q13*q33+4*q12*q13^2*q33-4*M`j'^2*q12*q33^2+4*q12*q13*q33^2+q12*q33^3,2*q13^3+q13^2*q33)+tmpprf(1,2*ep+n2)*mbox1l(0,2+n2,1,1)*prf(12*M`j'^2*q12^2*q13+12*M`j'^2*n2*q12^2*q13+16*M`j'^2*q12*q13^2+16*M`j'^2*n2*q12*q13^2-4*q12^2*q13^2-4*n2*q12^2*q13^2-8*q12*q13^3-8*n2*q12*q13^3+16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-4*q12*q13^2*q23-4*n2*q12*q13^2*q23+4*M`j'^2*q13*q23^2+4*M`j'^2*n2*q13*q23^2+4*M`j'^2*q12^2*q33+4*M`j'^2*n2*q12^2*q33+16*M`j'^2*q12*q13*q33+16*M`j'^2*n2*q12*q13*q33-4*q12^2*q13*q33-4*n2*q12^2*q13*q33-12*q12*q13^2*q33-12*n2*q12*q13^2*q33+4*M`j'^2*q12*q23*q33+4*M`j'^2*n2*q12*q23*q33-4*q12*q13*q23*q33-4*n2*q12*q13*q23*q33+4*M`j'^2*q12*q33^2+4*M`j'^2*n2*q12*q33^2-q12^2*q33^2-n2*q12^2*q33^2-6*q12*q13*q33^2-6*n2*q12*q13*q33^2-q12*q23*q33^2-n2*q12*q23*q33^2-q12*q33^3-n2*q12*q33^3,2*q13^3+q13^2*q33)+tmpprf(1,2*ep+n2)*mbox1l(1,2+n2,0,1)*prf(-8*M`j'^2*q12*q13^2-8*M`j'^2*n2*q12*q13^2+4*q12*q13^3+4*n2*q12*q13^3-12*M`j'^2*q12*q13*q23-12*M`j'^2*n2*q12*q13*q23-4*M`j'^2*q13^2*q23-4*M`j'^2*n2*q13^2*q23+4*q12*q13^2*q23+4*n2*q12*q13^2*q23-4*M`j'^2*q13*q23^2-4*M`j'^2*n2*q13*q23^2-10*M`j'^2*q12*q13*q33-10*M`j'^2*n2*q12*q13*q33+8*q12*q13^2*q33+8*n2*q12*q13^2*q33-4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33+4*q12*q13*q23*q33+4*n2*q12*q13*q23*q33-4*M`j'^2*q12*q33^2-4*M`j'^2*n2*q12*q33^2+5*q12*q13*q33^2+5*n2*q12*q13*q33^2+q12*q23*q33^2+n2*q12*q23*q33^2+q12*q33^3+n2*q12*q33^3,2*q13^3+q13^2*q33); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?neg_,n4?{,>1}) = mbox1l(n1,n2,2+n3,-2+n4)*prf(-2*M`j'^2*q12^2*q13^2-2*M`j'^2*n3*q12^2*q13^2+2*q12^3*q13^2+2*n3*q12^3*q13^2+2*q12^3*q13*q23+2*n3*q12^3*q13*q23+2*M`j'^2*q12^2*q23^2+2*M`j'^2*n3*q12^2*q23^2-2*M`j'^2*q12^2*q13*q33-2*M`j'^2*n3*q12^2*q13*q33+3*q12^3*q13*q33+3*n3*q12^3*q13*q33+2*M`j'^2*q12^2*q23*q33+2*M`j'^2*n3*q12^2*q23*q33+q12^3*q23*q33+n3*q12^3*q23*q33+q12^3*q33^2+n3*q12^3*q33^2,-2*M`j'^2*q13^4+2*M`j'^2*n4*q13^4-8*M`j'^2*q13^3*q23+8*M`j'^2*n4*q13^3*q23-12*M`j'^2*q13^2*q23^2+12*M`j'^2*n4*q13^2*q23^2-8*M`j'^2*q13*q23^3+8*M`j'^2*n4*q13*q23^3-2*M`j'^2*q23^4+2*M`j'^2*n4*q23^4+8*M`j'^2*q12*q13^2*q33-8*M`j'^2*n4*q12*q13^2*q33-2*q12^2*q13^2*q33+2*n4*q12^2*q13^2*q33-2*q12*q13^3*q33+2*n4*q12*q13^3*q33+16*M`j'^2*q12*q13*q23*q33-16*M`j'^2*n4*q12*q13*q23*q33-4*q12^2*q13*q23*q33+4*n4*q12^2*q13*q23*q33-6*q12*q13^2*q23*q33+6*n4*q12*q13^2*q23*q33+8*M`j'^2*q12*q23^2*q33-8*M`j'^2*n4*q12*q23^2*q33-2*q12^2*q23^2*q33+2*n4*q12^2*q23^2*q33-6*q12*q13*q23^2*q33+6*n4*q12*q13*q23^2*q33-2*q12*q23^3*q33+2*n4*q12*q23^3*q33-8*M`j'^2*q12^2*q33^2+8*M`j'^2*n4*q12^2*q33^2+4*q12^3*q33^2-4*n4*q12^3*q33^2+4*q12^2*q13*q33^2-4*n4*q12^2*q13*q33^2-q12*q13^2*q33^2+n4*q12*q13^2*q33^2+4*q12^2*q23*q33^2-4*n4*q12^2*q23*q33^2-2*q12*q13*q23*q33^2+2*n4*q12*q13*q23*q33^2-q12*q23^2*q33^2+n4*q12*q23^2*q33^2+2*q12^2*q33^3-2*n4*q12^2*q33^3)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(8*M`j'^2*n2*q12^2*q13^2-4*n2*q12^3*q13^2+2*M`j'^2*n2*q12*q13^3-4*n2*q12^2*q13^3+8*M`j'^2*n2*q12^2*q13*q23-4*n2*q12^3*q13*q23+6*M`j'^2*n2*q12*q13^2*q23-8*n2*q12^2*q13^2*q23+2*M`j'^2*n2*q13^3*q23+6*M`j'^2*n2*q12*q13*q23^2-4*n2*q12^2*q13*q23^2+6*M`j'^2*n2*q13^2*q23^2+2*M`j'^2*n2*q12*q23^3+6*M`j'^2*n2*q13*q23^3+2*M`j'^2*n2*q23^4-8*M`j'^2*n2*q12^3*q33+4*n2*q12^4*q33+4*M`j'^2*n2*q12^2*q13*q33-6*n2*q12^2*q13^2*q33-12*M`j'^2*n2*q12^2*q23*q33+8*n2*q12^3*q23*q33-8*M`j'^2*n2*q12*q13*q23*q33+2*n2*q12*q13^2*q23*q33-8*M`j'^2*n2*q12*q23^2*q33+6*n2*q12^2*q23^2*q33+4*n2*q12*q13*q23^2*q33+2*n2*q12*q23^3*q33+4*M`j'^2*n2*q12^2*q33^2-4*n2*q12^2*q13*q33^2+n2*q12*q13*q23*q33^2+n2*q12*q23^2*q33^2-n2*q12^2*q33^3,-2*M`j'^2*q13^4+2*M`j'^2*n4*q13^4-8*M`j'^2*q13^3*q23+8*M`j'^2*n4*q13^3*q23-12*M`j'^2*q13^2*q23^2+12*M`j'^2*n4*q13^2*q23^2-8*M`j'^2*q13*q23^3+8*M`j'^2*n4*q13*q23^3-2*M`j'^2*q23^4+2*M`j'^2*n4*q23^4+8*M`j'^2*q12*q13^2*q33-8*M`j'^2*n4*q12*q13^2*q33-2*q12^2*q13^2*q33+2*n4*q12^2*q13^2*q33-2*q12*q13^3*q33+2*n4*q12*q13^3*q33+16*M`j'^2*q12*q13*q23*q33-16*M`j'^2*n4*q12*q13*q23*q33-4*q12^2*q13*q23*q33+4*n4*q12^2*q13*q23*q33-6*q12*q13^2*q23*q33+6*n4*q12*q13^2*q23*q33+8*M`j'^2*q12*q23^2*q33-8*M`j'^2*n4*q12*q23^2*q33-2*q12^2*q23^2*q33+2*n4*q12^2*q23^2*q33-6*q12*q13*q23^2*q33+6*n4*q12*q13*q23^2*q33-2*q12*q23^3*q33+2*n4*q12*q23^3*q33-8*M`j'^2*q12^2*q33^2+8*M`j'^2*n4*q12^2*q33^2+4*q12^3*q33^2-4*n4*q12^3*q33^2+4*q12^2*q13*q33^2-4*n4*q12^2*q13*q33^2-q12*q13^2*q33^2+n4*q12*q13^2*q33^2+4*q12^2*q23*q33^2-4*n4*q12^2*q23*q33^2-2*q12*q13*q23*q33^2+2*n4*q12*q13*q23*q33^2-q12*q23^2*q33^2+n4*q12*q23^2*q33^2+2*q12^2*q33^3-2*n4*q12^2*q33^3)+mbox1l(1+n1,n2,1+n3,-2+n4)*prf(8*M`j'^2*n1*q12^2*q13^3+12*M`j'^2*n1*q12^2*q13^2*q23-4*M`j'^2*n1*q12*q13^3*q23-12*M`j'^2*n1*q12*q13^2*q23^2-4*M`j'^2*n1*q12^2*q23^3-12*M`j'^2*n1*q12*q13*q23^3-4*M`j'^2*n1*q12*q23^4-12*M`j'^2*n1*q12^3*q13*q33+4*n1*q12^4*q13*q33+10*M`j'^2*n1*q12^2*q13^2*q33+4*n1*q12^3*q13^2*q33+4*M`j'^2*n1*q12^3*q23*q33-4*n1*q12^4*q23*q33+20*M`j'^2*n1*q12^2*q13*q23*q33-4*n1*q12^3*q13*q23*q33-4*n1*q12^2*q13^2*q23*q33+10*M`j'^2*n1*q12^2*q23^2*q33-8*n1*q12^3*q23^2*q33-8*n1*q12^2*q13*q23^2*q33-4*n1*q12^2*q23^3*q33-12*M`j'^2*n1*q12^3*q33^2+4*n1*q12^4*q33^2+2*M`j'^2*n1*q12^2*q13*q33^2+6*n1*q12^3*q13*q33^2-2*M`j'^2*n1*q12^2*q23*q33^2+2*n1*q12^3*q23*q33^2-2*n1*q12^2*q13*q23*q33^2-2*n1*q12^2*q23^2*q33^2+2*n1*q12^3*q33^3,4*M`j'^2*q12*q13^4-4*M`j'^2*n4*q12*q13^4+4*M`j'^2*q13^5-4*M`j'^2*n4*q13^5+16*M`j'^2*q12*q13^3*q23-16*M`j'^2*n4*q12*q13^3*q23+20*M`j'^2*q13^4*q23-20*M`j'^2*n4*q13^4*q23+24*M`j'^2*q12*q13^2*q23^2-24*M`j'^2*n4*q12*q13^2*q23^2+40*M`j'^2*q13^3*q23^2-40*M`j'^2*n4*q13^3*q23^2+16*M`j'^2*q12*q13*q23^3-16*M`j'^2*n4*q12*q13*q23^3+40*M`j'^2*q13^2*q23^3-40*M`j'^2*n4*q13^2*q23^3+4*M`j'^2*q12*q23^4-4*M`j'^2*n4*q12*q23^4+20*M`j'^2*q13*q23^4-20*M`j'^2*n4*q13*q23^4+4*M`j'^2*q23^5-4*M`j'^2*n4*q23^5-16*M`j'^2*q12^2*q13^2*q33+16*M`j'^2*n4*q12^2*q13^2*q33+4*q12^3*q13^2*q33-4*n4*q12^3*q13^2*q33-16*M`j'^2*q12*q13^3*q33+16*M`j'^2*n4*q12*q13^3*q33+8*q12^2*q13^3*q33-8*n4*q12^2*q13^3*q33+2*M`j'^2*q13^4*q33-2*M`j'^2*n4*q13^4*q33+4*q12*q13^4*q33-4*n4*q12*q13^4*q33-32*M`j'^2*q12^2*q13*q23*q33+32*M`j'^2*n4*q12^2*q13*q23*q33+8*q12^3*q13*q23*q33-8*n4*q12^3*q13*q23*q33-48*M`j'^2*q12*q13^2*q23*q33+48*M`j'^2*n4*q12*q13^2*q23*q33+24*q12^2*q13^2*q23*q33-24*n4*q12^2*q13^2*q23*q33+8*M`j'^2*q13^3*q23*q33-8*M`j'^2*n4*q13^3*q23*q33+16*q12*q13^3*q23*q33-16*n4*q12*q13^3*q23*q33-16*M`j'^2*q12^2*q23^2*q33+16*M`j'^2*n4*q12^2*q23^2*q33+4*q12^3*q23^2*q33-4*n4*q12^3*q23^2*q33-48*M`j'^2*q12*q13*q23^2*q33+48*M`j'^2*n4*q12*q13*q23^2*q33+24*q12^2*q13*q23^2*q33-24*n4*q12^2*q13*q23^2*q33+12*M`j'^2*q13^2*q23^2*q33-12*M`j'^2*n4*q13^2*q23^2*q33+24*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Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?neg_,n4?pos_) = 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12^2*q13*q23*q33+64*M`j'^2*n2*q12^2*q13*q23*q33+16*q12^3*q13*q23*q33-16*n2*q12^3*q13*q23*q33-96*M`j'^2*q12*q13^2*q23*q33+96*M`j'^2*n2*q12*q13^2*q23*q33+48*q12^2*q13^2*q23*q33-48*n2*q12^2*q13^2*q23*q33+16*M`j'^2*q13^3*q23*q33-16*M`j'^2*n2*q13^3*q23*q33+32*q12*q13^3*q23*q33-32*n2*q12*q13^3*q23*q33-32*M`j'^2*q12^2*q23^2*q33+32*M`j'^2*n2*q12^2*q23^2*q33+8*q12^3*q23^2*q33-8*n2*q12^3*q23^2*q33-96*M`j'^2*q12*q13*q23^2*q33+96*M`j'^2*n2*q12*q13*q23^2*q33+48*q12^2*q13*q23^2*q33-48*n2*q12^2*q13*q23^2*q33+24*M`j'^2*q13^2*q23^2*q33-24*M`j'^2*n2*q13^2*q23^2*q33+48*q12*q13^2*q23^2*q33-48*n2*q12*q13^2*q23^2*q33-32*M`j'^2*q12*q23^3*q33+32*M`j'^2*n2*q12*q23^3*q33+16*q12^2*q23^3*q33-16*n2*q12^2*q23^3*q33+16*M`j'^2*q13*q23^3*q33-16*M`j'^2*n2*q13*q23^3*q33+32*q12*q13*q23^3*q33-32*n2*q12*q13*q23^3*q33+4*M`j'^2*q23^4*q33-4*M`j'^2*n2*q23^4*q33+8*q12*q23^4*q33-8*n2*q12*q23^4*q33+32*M`j'^2*q12^3*q33^2-32*M`j'^2*n2*q12^3*q33^2-16*q12^4*q33^2+16*n2*q12^4*q33^2+32*M`j'^2*q12^2*q13*q33^2-32*M`j'^2*n2*q12^2*q13*q33^2-32*q12^3*q13*q33^2+32*n2*q12^3*q13*q33^2-16*M`j'^2*q12*q13^2*q33^2+16*M`j'^2*n2*q12*q13^2*q33^2-8*q12^2*q13^2*q33^2+8*n2*q12^2*q13^2*q33^2+8*q12*q13^3*q33^2-8*n2*q12*q13^3*q33^2+32*M`j'^2*q12^2*q23*q33^2-32*M`j'^2*n2*q12^2*q23*q33^2-32*q12^3*q23*q33^2+32*n2*q12^3*q23*q33^2-32*M`j'^2*q12*q13*q23*q33^2+32*M`j'^2*n2*q12*q13*q23*q33^2-16*q12^2*q13*q23*q33^2+16*n2*q12^2*q13*q23*q33^2+24*q12*q13^2*q23*q33^2-24*n2*q12*q13^2*q23*q33^2-16*M`j'^2*q12*q23^2*q33^2+16*M`j'^2*n2*q12*q23^2*q33^2-8*q12^2*q23^2*q33^2+8*n2*q12^2*q23^2*q33^2+24*q12*q13*q23^2*q33^2-24*n2*q12*q13*q23^2*q33^2+8*q12*q23^3*q33^2-8*n2*q12*q23^3*q33^2+16*M`j'^2*q12^2*q33^3-16*M`j'^2*n2*q12^2*q33^3-16*q12^3*q33^3+16*n2*q12^3*q33^3-16*q12^2*q13*q33^3+16*n2*q12^2*q13*q33^3+2*q12*q13^2*q33^3-2*n2*q12*q13^2*q33^3-16*q12^2*q23*q33^3+16*n2*q12^2*q23*q33^3+4*q12*q13*q23*q33^3-4*n2*q12*q13*q23*q33^3+2*q12*q23^2*q33^3-2*n2*q12*q23^2*q33^3-4*q12^2*q33^4+4*n2*q12^2*q33^4); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?neg_,n4?pos_) = mbox1l(-1+n1,-1+n2,1+n3,1+n4)*prf(2*M`j'^2*n4*q12*q13^3+4*M`j'^2*n4*q12*q13^2*q23+2*M`j'^2*n4*q12*q13*q23^2-2*M`j'^2*n4*q12^2*q13*q33+M`j'^2*n4*q12*q13^2*q33-2*M`j'^2*n4*q12^2*q23*q33-M`j'^2*n4*q12*q23^2*q33,-2*M`j'^2*q13^4+2*M`j'^2*n1*q13^4-8*M`j'^2*q13^3*q23+8*M`j'^2*n1*q13^3*q23-12*M`j'^2*q13^2*q23^2+12*M`j'^2*n1*q13^2*q23^2-8*M`j'^2*q13*q23^3+8*M`j'^2*n1*q13*q23^3-2*M`j'^2*q23^4+2*M`j'^2*n1*q23^4+8*M`j'^2*q12*q13^2*q33-8*M`j'^2*n1*q12*q13^2*q33-2*q12^2*q13^2*q33+2*n1*q12^2*q13^2*q33-2*q12*q13^3*q33+2*n1*q12*q13^3*q33+16*M`j'^2*q12*q13*q23*q33-16*M`j'^2*n1*q12*q13*q23*q33-4*q12^2*q13*q23*q33+4*n1*q12^2*q13*q23*q33-6*q12*q13^2*q23*q33+6*n1*q12*q13^2*q23*q33+8*M`j'^2*q12*q23^2*q33-8*M`j'^2*n1*q12*q23^2*q33-2*q12^2*q23^2*q33+2*n1*q12^2*q23^2*q33-6*q12*q13*q23^2*q33+6*n1*q12*q13*q23^2*q33-2*q12*q23^3*q33+2*n1*q12*q23^3*q33-8*M`j'^2*q12^2*q33^2+8*M`j'^2*n1*q12^2*q33^2+4*q12^3*q33^2-4*n1*q12^3*q33^2+4*q12^2*q13*q33^2-4*n1*q12^2*q13*q33^2-q12*q13^2*q33^2+n1*q12*q13^2*q33^2+4*q12^2*q23*q33^2-4*n1*q12^2*q23*q33^2-2*q12*q13*q23*q33^2+2*n1*q12*q13*q23*q33^2-q12*q23^2*q33^2+n1*q12*q23^2*q33^2+2*q12^2*q33^3-2*n1*q12^2*q33^3)+mbox1l(n1,n2,1+n3,-1+n4)*prf(4*M`j'^2*q12*q13^3+6*M`j'^2*q12*q13^2*q23-2*M`j'^2*q12*q23^3-6*M`j'^2*q12^2*q13*q33+2*q12^3*q13*q33+M`j'^2*q12*q13^2*q33+2*q12^2*q13^2*q33+2*M`j'^2*q12^2*q23*q33-2*q12^3*q23*q33-M`j'^2*q12*q23^2*q33-2*q12^2*q23^2*q33+q12^2*q13*q33^2-q12^2*q23*q33^2,2*M`j'^2*q13^4+8*M`j'^2*q13^3*q23+12*M`j'^2*q13^2*q23^2+8*M`j'^2*q13*q23^3+2*M`j'^2*q23^4-8*M`j'^2*q12*q13^2*q33+2*q12^2*q13^2*q33+2*q12*q13^3*q33-16*M`j'^2*q12*q13*q23*q33+4*q12^2*q13*q23*q33+6*q12*q13^2*q23*q33-8*M`j'^2*q12*q23^2*q33+2*q12^2*q23^2*q33+6*q12*q13*q23^2*q33+2*q12*q23^3*q33+8*M`j'^2*q12^2*q33^2-4*q12^3*q33^2-4*q12^2*q13*q33^2+q12*q13^2*q33^2-4*q12^2*q23*q33^2+2*q12*q13*q23*q33^2+q12*q23^2*q33^2-2*q12^2*q33^3)+mbox1l(-1+n1,1+n2,1+n3,-1+n4)*prf(8*M`j'^2*n2*q12^2*q13^2-4*n2*q12^3*q13^2+2*M`j'^2*n2*q12*q13^3-4*n2*q12^2*q13^3+8*M`j'^2*n2*q12^2*q13*q23-4*n2*q12^3*q13*q23+4*M`j'^2*n2*q12*q13^2*q23-8*n2*q12^2*q13^2*q23+2*M`j'^2*n2*q12*q13*q23^2-4*n2*q12^2*q13*q23^2-8*M`j'^2*n2*q12^3*q33+4*n2*q12^4*q33+2*M`j'^2*n2*q12^2*q13*q33+2*n2*q12^3*q13*q33+M`j'^2*n2*q12*q13^2*q33-4*n2*q12^2*q13^2*q33-6*M`j'^2*n2*q12^2*q23*q33+6*n2*q12^3*q23*q33-2*n2*q12^2*q13*q23*q33-M`j'^2*n2*q12*q23^2*q33+2*n2*q12^2*q23^2*q33+2*n2*q12^3*q33^2-n2*q12^2*q13*q33^2+n2*q12^2*q23*q33^2,-2*M`j'^2*q13^4+2*M`j'^2*n1*q13^4-8*M`j'^2*q13^3*q23+8*M`j'^2*n1*q13^3*q23-12*M`j'^2*q13^2*q23^2+12*M`j'^2*n1*q13^2*q23^2-8*M`j'^2*q13*q23^3+8*M`j'^2*n1*q13*q23^3-2*M`j'^2*q23^4+2*M`j'^2*n1*q23^4+8*M`j'^2*q12*q13^2*q33-8*M`j'^2*n1*q12*q13^2*q33-2*q12^2*q13^2*q33+2*n1*q12^2*q13^2*q33-2*q12*q13^3*q33+2*n1*q12*q13^3*q33+16*M`j'^2*q12*q13*q23*q33-16*M`j'^2*n1*q12*q13*q23*q33-4*q12^2*q13*q23*q33+4*n1*q12^2*q13*q23*q33-6*q12*q13^2*q23*q33+6*n1*q12*q13^2*q23*q33+8*M`j'^2*q12*q23^2*q33-8*M`j'^2*n1*q12*q23^2*q33-2*q12^2*q23^2*q33+2*n1*q12^2*q23^2*q33-6*q12*q13*q23^2*q33+6*n1*q12*q13*q23^2*q33-2*q12*q23^3*q33+2*n1*q12*q23^3*q33-8*M`j'^2*q12^2*q33^2+8*M`j'^2*n1*q12^2*q33^2+4*q12^3*q33^2-4*n1*q12^3*q33^2+4*q12^2*q13*q33^2-4*n1*q12^2*q13*q33^2-q12*q13^2*q33^2+n1*q12*q13^2*q33^2+4*q12^2*q23*q33^2-4*n1*q12^2*q23*q33^2-2*q12*q13*q23*q33^2+2*n1*q12*q13*q23*q33^2-q12*q23^2*q33^2+n1*q12*q23^2*q33^2+2*q12^2*q33^3-2*n1*q12^2*q33^3)+mbox1l(-1+n1,n2,2+n3,-1+n4)*prf(4*M`j'^2*q12^2*q13^2+4*M`j'^2*n3*q12^2*q13^2-4*q12^3*q13^2-4*n3*q12^3*q13^2+4*M`j'^2*q12*q13^3+4*M`j'^2*n3*q12*q13^3-4*q12^2*q13^3-4*n3*q12^2*q13^3-4*q12^3*q13*q23-4*n3*q12^3*q13*q23+4*M`j'^2*q12*q13^2*q23+4*M`j'^2*n3*q12*q13^2*q23-8*q12^2*q13^2*q23-8*n3*q12^2*q13^2*q23-4*M`j'^2*q12^2*q23^2-4*M`j'^2*n3*q12^2*q23^2-4*M`j'^2*q12*q13*q23^2-4*M`j'^2*n3*q12*q13*q23^2-4*q12^2*q13*q23^2-4*n3*q12^2*q13*q23^2-4*M`j'^2*q12*q23^3-4*M`j'^2*n3*q12*q23^3-2*q12^3*q13*q33-2*n3*q12^3*q13*q33+2*M`j'^2*q12*q13^2*q33+2*M`j'^2*n3*q12*q13^2*q33-4*q12^2*q13^2*q33-4*n3*q12^2*q13^2*q33-2*q12^3*q23*q33-2*n3*q12^3*q23*q33-6*q12^2*q13*q23*q33-6*n3*q12^2*q13*q23*q33-2*M`j'^2*q12*q23^2*q33-2*M`j'^2*n3*q12*q23^2*q33-2*q12^2*q23^2*q33-2*n3*q12^2*q23^2*q33-q12^2*q13*q33^2-n3*q12^2*q13*q33^2-q12^2*q23*q33^2-n3*q12^2*q23*q33^2,-4*M`j'^2*q13^4+4*M`j'^2*n1*q13^4-16*M`j'^2*q13^3*q23+16*M`j'^2*n1*q13^3*q23-24*M`j'^2*q13^2*q23^2+24*M`j'^2*n1*q13^2*q23^2-16*M`j'^2*q13*q23^3+16*M`j'^2*n1*q13*q23^3-4*M`j'^2*q23^4+4*M`j'^2*n1*q23^4+16*M`j'^2*q12*q13^2*q33-16*M`j'^2*n1*q12*q13^2*q33-4*q12^2*q13^2*q33+4*n1*q12^2*q13^2*q33-4*q12*q13^3*q33+4*n1*q12*q13^3*q33+32*M`j'^2*q12*q13*q23*q33-32*M`j'^2*n1*q12*q13*q23*q33-8*q12^2*q13*q23*q33+8*n1*q12^2*q13*q23*q33-12*q12*q13^2*q23*q33+12*n1*q12*q13^2*q23*q33+16*M`j'^2*q12*q23^2*q33-16*M`j'^2*n1*q12*q23^2*q33-4*q12^2*q23^2*q33+4*n1*q12^2*q23^2*q33-12*q12*q13*q23^2*q33+12*n1*q12*q13*q23^2*q33-4*q12*q23^3*q33+4*n1*q12*q23^3*q33-16*M`j'^2*q12^2*q33^2+16*M`j'^2*n1*q12^2*q33^2+8*q12^3*q33^2-8*n1*q12^3*q33^2+8*q12^2*q13*q33^2-8*n1*q12^2*q13*q33^2-2*q12*q13^2*q33^2+2*n1*q12*q13^2*q33^2+8*q12^2*q23*q33^2-8*n1*q12^2*q23*q33^2-4*q12*q13*q23*q33^2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^2*q23*q33^3,-4*M`j'^2*q13^4+4*M`j'^2*n1*q13^4-16*M`j'^2*q13^3*q23+16*M`j'^2*n1*q13^3*q23-24*M`j'^2*q13^2*q23^2+24*M`j'^2*n1*q13^2*q23^2-16*M`j'^2*q13*q23^3+16*M`j'^2*n1*q13*q23^3-4*M`j'^2*q23^4+4*M`j'^2*n1*q23^4+16*M`j'^2*q12*q13^2*q33-16*M`j'^2*n1*q12*q13^2*q33-4*q12^2*q13^2*q33+4*n1*q12^2*q13^2*q33-4*q12*q13^3*q33+4*n1*q12*q13^3*q33+32*M`j'^2*q12*q13*q23*q33-32*M`j'^2*n1*q12*q13*q23*q33-8*q12^2*q13*q23*q33+8*n1*q12^2*q13*q23*q33-12*q12*q13^2*q23*q33+12*n1*q12*q13^2*q23*q33+16*M`j'^2*q12*q23^2*q33-16*M`j'^2*n1*q12*q23^2*q33-4*q12^2*q23^2*q33+4*n1*q12^2*q23^2*q33-12*q12*q13*q23^2*q33+12*n1*q12*q13*q23^2*q33-4*q12*q23^3*q33+4*n1*q12*q23^3*q33-16*M`j'^2*q12^2*q33^2+16*M`j'^2*n1*q12^2*q33^2+8*q12^3*q33^2-8*n1*q12^3*q33^2+8*q12^2*q13*q33^2-8*n1*q12^2*q13*q33^2-2*q12*q13^2*q33^2+2*n1*q12*q13^2*q33^2+8*q12^2*q23*q33^2-8*n1*q12^2*q23*q33^2-4*q12*q13*q23*q33^2+4*n1*q12*q13*q23*q33^2-2*q12*q23^2*q33^2+2*n1*q12*q23^2*q33^2+4*q12^2*q33^3-4*n1*q12^2*q33^3); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?neg0_,n4?{,>1}) = mbox1l(n1,n2,1+n3,-2+n4)*prf(-2*M`j'^2*n3*q12+n3*q12^2,-2*M`j'^2*q13^2+2*M`j'^2*n4*q13^2-4*M`j'^2*q13*q23+4*M`j'^2*n4*q13*q23-2*M`j'^2*q23^2+2*M`j'^2*n4*q23^2+4*M`j'^2*q12*q33-4*M`j'^2*n4*q12*q33-2*q12^2*q33+2*n4*q12^2*q33-2*q12*q13*q33+2*n4*q12*q13*q33-2*q12*q23*q33+2*n4*q12*q23*q33-q12*q33^2+n4*q12*q33^2)+mbox1l(1+n1,n2,n3,-2+n4)*prf(-2*M`j'^2*n1*q12*q13-2*M`j'^2*n1*q12*q23-2*M`j'^2*n1*q12*q33,-4*M`j'^2*q12*q13^2+4*M`j'^2*n4*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n4*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n4*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n4*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n4*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n4*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n4*q12^2*q33-4*q12^3*q33+4*n4*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-8*q12^2*q13*q33+8*n4*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n4*q12*q23*q33-8*q12^2*q23*q33+8*n4*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-4*q12^2*q33^2+4*n4*q12^2*q33^2-4*q12*q13*q33^2+4*n4*q12*q13*q33^2-4*q12*q23*q33^2+4*n4*q12*q23*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n2*q12-2*n2*q12^2+2*M`j'^2*n2*q13-2*n2*q12*q13+2*M`j'^2*n2*q23-2*n2*q12*q23-n2*q12*q33,-2*M`j'^2*q13^2+2*M`j'^2*n4*q13^2-4*M`j'^2*q13*q23+4*M`j'^2*n4*q13*q23-2*M`j'^2*q23^2+2*M`j'^2*n4*q23^2+4*M`j'^2*q12*q33-4*M`j'^2*n4*q12*q33-2*q12^2*q33+2*n4*q12^2*q33-2*q12*q13*q33+2*n4*q12*q13*q33-2*q12*q23*q33+2*n4*q12*q23*q33-q12*q33^2+n4*q12*q33^2)+mbox1l(n1,1+n2,n3,-2+n4)*prf(-8*M`j'^2*n2*q12^2+4*n2*q12^3-6*M`j'^2*n2*q12*q13+4*n2*q12^2*q13-6*M`j'^2*n2*q12*q23+4*n2*q12^2*q23-2*M`j'^2*n2*q12*q33+2*n2*q12^2*q33,-4*M`j'^2*q12*q13^2+4*M`j'^2*n4*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n4*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n4*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n4*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n4*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n4*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n4*q12^2*q33-4*q12^3*q33+4*n4*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-8*q12^2*q13*q33+8*n4*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n4*q12*q23*q33-8*q12^2*q23*q33+8*n4*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-4*q12^2*q33^2+4*n4*q12^2*q33^2-4*q12*q13*q33^2+4*n4*q12*q13*q33^2-4*q12*q23*q33^2+4*n4*q12*q23*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3*q12*q13+2*n3*q12^2*q13+2*M`j'^2*n3*q12*q23+n3*q12^2*q33,-2*M`j'^2*q13^2+2*M`j'^2*n4*q13^2-4*M`j'^2*q13*q23+4*M`j'^2*n4*q13*q23-2*M`j'^2*q23^2+2*M`j'^2*n4*q23^2+4*M`j'^2*q12*q33-4*M`j'^2*n4*q12*q33-2*q12^2*q33+2*n4*q12^2*q33-2*q12*q13*q33+2*n4*q12*q13*q33-2*q12*q23*q33+2*n4*q12*q23*q33-q12*q33^2+n4*q12*q33^2)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(-2*M`j'^2*n1*q12*q13-2*M`j'^2*n1*q13^2-2*M`j'^2*n1*q12*q23-4*M`j'^2*n1*q13*q23-2*M`j'^2*n1*q23^2-2*M`j'^2*n1*q12*q33-2*M`j'^2*n1*q13*q33-2*M`j'^2*n1*q23*q33,-4*M`j'^2*q12*q13^2+4*M`j'^2*n4*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n4*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n4*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n4*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n4*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n4*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n4*q12^2*q33-4*q12^3*q33+4*n4*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-8*q12^2*q13*q33+8*n4*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n4*q12*q23*q33-8*q12^2*q23*q33+8*n4*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-4*q12^2*q33^2+4*n4*q12^2*q33^2-4*q12*q13*q33^2+4*n4*q12*q13*q33^2-4*q12*q23*q33^2+4*n4*q12*q23*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-6*M`j'^2*n3*q12*q13+2*n3*q12^2*q13-4*M`j'^2*n3*q13^2+2*n3*q12*q13^2-2*M`j'^2*n3*q12*q23-6*M`j'^2*n3*q13*q23+2*n3*q12*q13*q23-2*M`j'^2*n3*q23^2-2*M`j'^2*n3*q12*q33-2*M`j'^2*n3*q13*q33+n3*q12*q13*q33-2*M`j'^2*n3*q23*q33,-4*M`j'^2*q12*q13^2+4*M`j'^2*n4*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n4*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n4*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n4*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n4*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n4*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n4*q12^2*q33-4*q12^3*q33+4*n4*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-8*q12^2*q13*q33+8*n4*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n4*q12*q23*q33-8*q12^2*q23*q33+8*n4*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-4*q12^2*q33^2+4*n4*q12^2*q33^2-4*q12*q13*q33^2+4*n4*q12*q13*q33^2-4*q12*q23*q33^2+4*n4*q12*q23*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,-1+n2,n3,n4)*prf(-2*M`j'^2*q12*q13-2*M`j'^2*q13^2-2*M`j'^2*q12*q23-4*M`j'^2*q13*q23-2*M`j'^2*q23^2+2*M`j'^2*q12*q33-2*q12^2*q33-2*q12*q13*q33-2*q12*q23*q33-q12*q33^2,4*M`j'^2*q12*q13^2+4*M`j'^2*q13^3+8*M`j'^2*q12*q13*q23+12*M`j'^2*q13^2*q23+4*M`j'^2*q12*q23^2+12*M`j'^2*q13*q23^2+4*M`j'^2*q23^3-8*M`j'^2*q12^2*q33+4*q12^3*q33-8*M`j'^2*q12*q13*q33+8*q12^2*q13*q33+2*M`j'^2*q13^2*q33+4*q12*q13^2*q33-8*M`j'^2*q12*q23*q33+8*q12^2*q23*q33+4*M`j'^2*q13*q23*q33+8*q12*q13*q23*q33+2*M`j'^2*q23^2*q33+4*q12*q23^2*q33-4*M`j'^2*q12*q33^2+4*q12^2*q33^2+4*q12*q13*q33^2+4*q12*q23*q33^2+q12*q33^3)+mbox1l(-1+n1,n2,1+n3,-1+n4)*prf(4*M`j'^2*n3*q12^2-2*n3*q12^3+10*M`j'^2*n3*q12*q13-6*n3*q12^2*q13+4*M`j'^2*n3*q13^2-4*n3*q12*q13^2+6*M`j'^2*n3*q12*q23-4*n3*q12^2*q23+6*M`j'^2*n3*q13*q23-6*n3*q12*q13*q23+2*M`j'^2*n3*q23^2-2*n3*q12*q23^2+4*M`j'^2*n3*q12*q33-3*n3*q12^2*q33+2*M`j'^2*n3*q13*q33-4*n3*q12*q13*q33+2*M`j'^2*n3*q23*q33-3*n3*q12*q23*q33-n3*q12*q33^2,-4*M`j'^2*q12*q13^2+4*M`j'^2*n4*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n4*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n4*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n4*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n4*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n4*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n4*q12^2*q33-4*q12^3*q33+4*n4*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-8*q12^2*q13*q33+8*n4*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n4*q12*q23*q33-8*q12^2*q23*q33+8*n4*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-4*q12^2*q33^2+4*n4*q12^2*q33^2-4*q12*q13*q33^2+4*n4*q12*q13*q33^2-4*q12*q23*q33^2+4*n4*q12*q23*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(-4*q12^2*q13-4*q12*q13^2-4*q12^2*q23-8*q12*q13*q23-4*q12*q23^2-4*q12^2*q33-6*q12*q13*q33-6*q12*q23*q33-2*q12*q33^2,-4*M`j'^2*q12*q13^2+4*M`j'^2*n4*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n4*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n4*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n4*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n4*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n4*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n4*q12^2*q33-4*q12^3*q33+4*n4*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-8*q12^2*q13*q33+8*n4*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n4*q12*q23*q33-8*q12^2*q23*q33+8*n4*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-4*q12^2*q33^2+4*n4*q12^2*q33^2-4*q12*q13*q33^2+4*n4*q12*q13*q33^2-4*q12*q23*q33^2+4*n4*q12*q23*q33^2-q12*q33^3+n4*q12*q33^3)+prf(-2*M`j'^2*q12*q13+4*M`j'^2*n1*q12*q13-6*M`j'^2*n2*q12*q13+2*M`j'^2*n4*q12*q13+12*q12^2*q13-4*n1*q12^2*q13-2*n3*q12^2*q13-4*n4*q12^2*q13-2*M`j'^2*q13^2+2*M`j'^2*n1*q13^2-4*M`j'^2*n2*q13^2+2*M`j'^2*n4*q13^2+12*q12*q13^2-4*n1*q12*q13^2-2*n3*q12*q13^2-4*n4*q12*q13^2-2*M`j'^2*q12*q23+4*M`j'^2*n1*q12*q23-6*M`j'^2*n2*q12*q23+2*M`j'^2*n4*q12*q23+12*q12^2*q23-4*n1*q12^2*q23-2*n3*q12^2*q23-4*n4*q12^2*q23-4*M`j'^2*q13*q23+4*M`j'^2*n1*q13*q23-8*M`j'^2*n2*q13*q23+4*M`j'^2*n4*q13*q23+24*q12*q13*q23-8*n1*q12*q13*q23-4*n3*q12*q13*q23-8*n4*q12*q13*q23-2*M`j'^2*q23^2+2*M`j'^2*n1*q23^2-4*M`j'^2*n2*q23^2+2*M`j'^2*n4*q23^2+12*q12*q23^2-4*n1*q12*q23^2-2*n3*q12*q23^2-4*n4*q12*q23^2+2*M`j'^2*q12*q33+4*M`j'^2*n1*q12*q33-2*M`j'^2*n2*q12*q33-2*M`j'^2*n4*q12*q33+10*q12^2*q33-4*n1*q12^2*q33-2*n2*q12^2*q33-2*n3*q12^2*q33-2*n4*q12^2*q33+2*M`j'^2*n1*q13*q33-2*M`j'^2*n2*q13*q33+16*q12*q13*q33-6*n1*q12*q13*q33-2*n2*q12*q13*q33-3*n3*q12*q13*q33-4*n4*q12*q13*q33+2*M`j'^2*n1*q23*q33-2*M`j'^2*n2*q23*q33+16*q12*q23*q33-6*n1*q12*q23*q33-2*n2*q12*q23*q33-3*n3*q12*q23*q33-4*n4*q12*q23*q33+5*q12*q33^2-2*n1*q12*q33^2-n2*q12*q33^2-n3*q12*q33^2-n4*q12*q33^2,-4*M`j'^2*q12*q13^2+4*M`j'^2*n4*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n4*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n4*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n4*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n4*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n4*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n4*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n4*q12^2*q33-4*q12^3*q33+4*n4*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-8*q12^2*q13*q33+8*n4*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n4*q13^2*q33-4*q12*q13^2*q33+4*n4*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n4*q12*q23*q33-8*q12^2*q23*q33+8*n4*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n4*q13*q23*q33-8*q12*q13*q23*q33+8*n4*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n4*q23^2*q33-4*q12*q23^2*q33+4*n4*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-4*q12^2*q33^2+4*n4*q12^2*q33^2-4*q12*q13*q33^2+4*n4*q12*q13*q33^2-4*q12*q23*q33^2+4*n4*q12*q23*q33^2-q12*q33^3+n4*q12*q33^3)); Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?neg0_,n4?pos_) = mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3*q13-2*M`j'^2*n3*q23-n3*q12*q33,-4*M`j'^2*q13^2+4*M`j'^2*n2*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n2*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n2*q12*q33-4*q12^2*q33+4*n2*q12^2*q33-4*q12*q13*q33+4*n2*q12*q13*q33-4*q12*q23*q33+4*n2*q12*q23*q33-2*q12*q33^2+2*n2*q12*q33^2)+mbox1l(n1,n2,n3,-1+n4)*prf(-4*M`j'^2*q12*q13-2*M`j'^2*q13^2-4*M`j'^2*q12*q23-4*M`j'^2*q13*q23-2*M`j'^2*q23^2-2*M`j'^2*q12*q33-M`j'^2*q13*q33-M`j'^2*q23*q33,4*M`j'^2*q12*q13^2+4*M`j'^2*q13^3+8*M`j'^2*q12*q13*q23+12*M`j'^2*q13^2*q23+4*M`j'^2*q12*q23^2+12*M`j'^2*q13*q23^2+4*M`j'^2*q23^3-8*M`j'^2*q12^2*q33+4*q12^3*q33-8*M`j'^2*q12*q13*q33+8*q12^2*q13*q33+2*M`j'^2*q13^2*q33+4*q12*q13^2*q33-8*M`j'^2*q12*q23*q33+8*q12^2*q23*q33+4*M`j'^2*q13*q23*q33+8*q12*q13*q23*q33+2*M`j'^2*q23^2*q33+4*q12*q23^2*q33-4*M`j'^2*q12*q33^2+4*q12^2*q33^2+4*q12*q13*q33^2+4*q12*q23*q33^2+q12*q33^3)+mbox1l(n1,-2+n2,n3,1+n4)*prf(-2*M`j'^2*n4*q12*q33-M`j'^2*n4*q13*q33-M`j'^2*n4*q23*q33,-4*M`j'^2*q12*q13^2+4*M`j'^2*n2*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n2*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n2*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n2*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n2*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n2*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n2*q12^2*q33-4*q12^3*q33+4*n2*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n2*q12*q13*q33-8*q12^2*q13*q33+8*n2*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n2*q13^2*q33-4*q12*q13^2*q33+4*n2*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n2*q12*q23*q33-8*q12^2*q23*q33+8*n2*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n2*q13*q23*q33-8*q12*q13*q23*q33+8*n2*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n2*q23^2*q33-4*q12*q23^2*q33+4*n2*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n2*q12*q33^2-4*q12^2*q33^2+4*n2*q12^2*q33^2-4*q12*q13*q33^2+4*n2*q12*q13*q33^2-4*q12*q23*q33^2+4*n2*q12*q23*q33^2-q12*q33^3+n2*q12*q33^3)+mbox1l(-1+n1,n2,n3,n4)*prf(4*M`j'^2*q13+4*M`j'^2*q23+4*M`j'^2*q33-2*q12*q33-2*q13*q33-2*q23*q33-q33^2,4*M`j'^2*q13^2+8*M`j'^2*q13*q23+4*M`j'^2*q23^2-8*M`j'^2*q12*q33+4*q12^2*q33+4*q12*q13*q33+4*q12*q23*q33+2*q12*q33^2)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(-2*M`j'^2*n1*q13^2-4*M`j'^2*n1*q13*q23-2*M`j'^2*n1*q23^2+2*M`j'^2*n1*q12*q33-2*n1*q12^2*q33-M`j'^2*n1*q13*q33-2*n1*q12*q13*q33-M`j'^2*n1*q23*q33-2*n1*q12*q23*q33-n1*q12*q33^2,-4*M`j'^2*q12*q13^2+4*M`j'^2*n2*q12*q13^2-4*M`j'^2*q13^3+4*M`j'^2*n2*q13^3-8*M`j'^2*q12*q13*q23+8*M`j'^2*n2*q12*q13*q23-12*M`j'^2*q13^2*q23+12*M`j'^2*n2*q13^2*q23-4*M`j'^2*q12*q23^2+4*M`j'^2*n2*q12*q23^2-12*M`j'^2*q13*q23^2+12*M`j'^2*n2*q13*q23^2-4*M`j'^2*q23^3+4*M`j'^2*n2*q23^3+8*M`j'^2*q12^2*q33-8*M`j'^2*n2*q12^2*q33-4*q12^3*q33+4*n2*q12^3*q33+8*M`j'^2*q12*q13*q33-8*M`j'^2*n2*q12*q13*q33-8*q12^2*q13*q33+8*n2*q12^2*q13*q33-2*M`j'^2*q13^2*q33+2*M`j'^2*n2*q13^2*q33-4*q12*q13^2*q33+4*n2*q12*q13^2*q33+8*M`j'^2*q12*q23*q33-8*M`j'^2*n2*q12*q23*q33-8*q12^2*q23*q33+8*n2*q12^2*q23*q33-4*M`j'^2*q13*q23*q33+4*M`j'^2*n2*q13*q23*q33-8*q12*q13*q23*q33+8*n2*q12*q13*q23*q33-2*M`j'^2*q23^2*q33+2*M`j'^2*n2*q23^2*q33-4*q12*q23^2*q33+4*n2*q12*q23^2*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n2*q12*q33^2-4*q12^2*q33^2+4*n2*q12^2*q33^2-4*q12*q13*q33^2+4*n2*q12*q13*q33^2-4*q12*q23*q33^2+4*n2*q12*q23*q33^2-q12*q33^3+n2*q12*q33^3)+mbox1l(n1,-1+n2,1+n3,n4)*prf(-4*M`j'^2*n3*q13^2-4*M`j'^2*n3*q13*q23+4*M`j'^2*n3*q12*q33-2*n3*q12*q13*q33-n3*q12*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n2*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n2*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n2*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n2*q12*q33-4*q12^2*q33+4*n2*q12^2*q33-4*q12*q13*q33+4*n2*q12*q13*q33-4*q12*q23*q33+4*n2*q12*q23*q33-2*q12*q33^2+2*n2*q12*q33^2)+mbox1l(1+n1,-2+n2,n3,n4)*prf(-4*M`j'^2*n1*q12*q33-6*M`j'^2*n1*q13*q33-6*M`j'^2*n1*q23*q33-4*M`j'^2*n1*q33^2+2*n1*q12*q33^2+2*n1*q13*q33^2+2*n1*q23*q33^2+n1*q33^3,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-8*q12*q13^2*q33+8*n2*q12*q13^2*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-16*q12*q13*q23*q33+16*n2*q12*q13*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-8*q12*q23^2*q33+8*n2*q12*q23^2*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2-2*q12*q33^3+2*n2*q12*q33^3)+mbox1l(n1,-1+n2,n3,n4)*(tmpprf(ep,1)*prf(-8*q12^2*q33-12*q12*q13*q33-4*q13^2*q33-12*q12*q23*q33-8*q13*q23*q33-4*q23^2*q33-4*q12*q33^2-2*q13*q33^2-2*q23*q33^2,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-8*q12*q13^2*q33+8*n2*q12*q13^2*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-16*q12*q13*q23*q33+16*n2*q12*q13*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-8*q12*q23^2*q33+8*n2*q12*q23^2*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2-2*q12*q33^3+2*n2*q12*q33^3)+prf(4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-4*M`j'^2*n2*q13^2+8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-8*M`j'^2*n2*q13*q23+4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2-4*M`j'^2*n2*q23^2+4*M`j'^2*q12*q33-4*M`j'^2*n2*q12*q33+4*M`j'^2*n4*q12*q33+20*q12^2*q33-4*n1*q12^2*q33-4*n2*q12^2*q33-4*n3*q12^2*q33-8*n4*q12^2*q33+10*M`j'^2*q13*q33+8*M`j'^2*n1*q13*q33-10*M`j'^2*n2*q13*q33+2*M`j'^2*n4*q13*q33+28*q12*q13*q33-8*n1*q12*q13*q33-4*n2*q12*q13*q33-6*n3*q12*q13*q33-12*n4*q12*q13*q33+8*q13^2*q33-4*n1*q13^2*q33-2*n3*q13^2*q33-4*n4*q13^2*q33+10*M`j'^2*q23*q33+8*M`j'^2*n1*q23*q33-10*M`j'^2*n2*q23*q33+2*M`j'^2*n4*q23*q33+28*q12*q23*q33-8*n1*q12*q23*q33-4*n2*q12*q23*q33-6*n3*q12*q23*q33-12*n4*q12*q23*q33+16*q13*q23*q33-8*n1*q13*q23*q33-4*n3*q13*q23*q33-8*n4*q13*q23*q33+8*q23^2*q33-4*n1*q23^2*q33-2*n3*q23^2*q33-4*n4*q23^2*q33+4*M`j'^2*q33^2+4*M`j'^2*n1*q33^2-4*M`j'^2*n2*q33^2+8*q12*q33^2-4*n1*q12*q33^2-2*n3*q12*q33^2-4*n4*q12*q33^2+2*q13*q33^2-4*n1*q13*q33^2+2*n2*q13*q33^2-n3*q13*q33^2-2*n4*q13*q33^2+2*q23*q33^2-4*n1*q23*q33^2+2*n2*q23*q33^2-n3*q23*q33^2-2*n4*q23*q33^2-q33^3-n1*q33^3+n2*q33^3,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-8*q12*q13^2*q33+8*n2*q12*q13^2*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-16*q12*q13*q23*q33+16*n2*q12*q13*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-8*q12*q23^2*q33+8*n2*q12*q23^2*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2-2*q12*q33^3+2*n2*q12*q33^3))+mbox1l(-1+n1,-1+n2,1+n3,n4)*prf(4*M`j'^2*n3*q12*q13+8*M`j'^2*n3*q13^2+4*M`j'^2*n3*q12*q23+12*M`j'^2*n3*q13*q23+4*M`j'^2*n3*q23^2+4*M`j'^2*n3*q12*q33-2*n3*q12^2*q33+12*M`j'^2*n3*q13*q33-6*n3*q12*q13*q33-4*n3*q13^2*q33+8*M`j'^2*n3*q23*q33-4*n3*q12*q23*q33-6*n3*q13*q23*q33-2*n3*q23^2*q33+4*M`j'^2*n3*q33^2-3*n3*q12*q33^2-4*n3*q13*q33^2-3*n3*q23*q33^2-n3*q33^3,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-8*q12*q13^2*q33+8*n2*q12*q13^2*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-16*q12*q13*q23*q33+16*n2*q12*q13*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-8*q12*q23^2*q33+8*n2*q12*q23^2*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2-2*q12*q33^3+2*n2*q12*q33^3)+mbox1l(n1,-2+n2,1+n3,n4)*prf(-4*M`j'^2*n3*q13^2-4*M`j'^2*n3*q13*q23-4*M`j'^2*n3*q12*q33-10*M`j'^2*n3*q13*q33+2*n3*q12*q13*q33+2*n3*q13^2*q33-6*M`j'^2*n3*q23*q33+2*n3*q13*q23*q33-4*M`j'^2*n3*q33^2+2*n3*q12*q33^2+3*n3*q13*q33^2+2*n3*q23*q33^2+n3*q33^3,-8*M`j'^2*q12*q13^2+8*M`j'^2*n2*q12*q13^2-8*M`j'^2*q13^3+8*M`j'^2*n2*q13^3-16*M`j'^2*q12*q13*q23+16*M`j'^2*n2*q12*q13*q23-24*M`j'^2*q13^2*q23+24*M`j'^2*n2*q13^2*q23-8*M`j'^2*q12*q23^2+8*M`j'^2*n2*q12*q23^2-24*M`j'^2*q13*q23^2+24*M`j'^2*n2*q13*q23^2-8*M`j'^2*q23^3+8*M`j'^2*n2*q23^3+16*M`j'^2*q12^2*q33-16*M`j'^2*n2*q12^2*q33-8*q12^3*q33+8*n2*q12^3*q33+16*M`j'^2*q12*q13*q33-16*M`j'^2*n2*q12*q13*q33-16*q12^2*q13*q33+16*n2*q12^2*q13*q33-4*M`j'^2*q13^2*q33+4*M`j'^2*n2*q13^2*q33-8*q12*q13^2*q33+8*n2*q12*q13^2*q33+16*M`j'^2*q12*q23*q33-16*M`j'^2*n2*q12*q23*q33-16*q12^2*q23*q33+16*n2*q12^2*q23*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n2*q13*q23*q33-16*q12*q13*q23*q33+16*n2*q12*q13*q23*q33-4*M`j'^2*q23^2*q33+4*M`j'^2*n2*q23^2*q33-8*q12*q23^2*q33+8*n2*q12*q23^2*q33+8*M`j'^2*q12*q33^2-8*M`j'^2*n2*q12*q33^2-8*q12^2*q33^2+8*n2*q12^2*q33^2-8*q12*q13*q33^2+8*n2*q12*q13*q33^2-8*q12*q23*q33^2+8*n2*q12*q23*q33^2-2*q12*q33^3+2*n2*q12*q33^3); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?neg0_,n4?pos_) = mbox1l(n1,n2,n3,-1+n4)*prf(M`j'^2*q13+M`j'^2*q23,2*M`j'^2*q13^2+4*M`j'^2*q13*q23+2*M`j'^2*q23^2-4*M`j'^2*q12*q33+2*q12^2*q33+2*q12*q13*q33+2*q12*q23*q33+q12*q33^2)+mbox1l(-1+n1,-1+n2,n3,1+n4)*prf(M`j'^2*n4*q13+M`j'^2*n4*q23,-2*M`j'^2*q13^2+2*M`j'^2*n1*q13^2-4*M`j'^2*q13*q23+4*M`j'^2*n1*q13*q23-2*M`j'^2*q23^2+2*M`j'^2*n1*q23^2+4*M`j'^2*q12*q33-4*M`j'^2*n1*q12*q33-2*q12^2*q33+2*n1*q12^2*q33-2*q12*q13*q33+2*n1*q12*q13*q33-2*q12*q23*q33+2*n1*q12*q23*q33-q12*q33^2+n1*q12*q33^2)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(4*M`j'^2*n2*q12-2*n2*q12^2+M`j'^2*n2*q13-2*n2*q12*q13+M`j'^2*n2*q23-2*n2*q12*q23-n2*q12*q33,-2*M`j'^2*q13^2+2*M`j'^2*n1*q13^2-4*M`j'^2*q13*q23+4*M`j'^2*n1*q13*q23-2*M`j'^2*q23^2+2*M`j'^2*n1*q23^2+4*M`j'^2*q12*q33-4*M`j'^2*n1*q12*q33-2*q12^2*q33+2*n1*q12^2*q33-2*q12*q13*q33+2*n1*q12*q13*q33-2*q12*q23*q33+2*n1*q12*q23*q33-q12*q33^2+n1*q12*q33^2)+mbox1l(-1+n1,n2,1+n3,-1+n4)*prf(4*M`j'^2*n3*q12-2*n3*q12^2+2*M`j'^2*n3*q13-2*n3*q12*q13+2*M`j'^2*n3*q23-2*n3*q12*q23-n3*q12*q33,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33-4*q12^2*q33+4*n1*q12^2*q33-4*q12*q13*q33+4*n1*q12*q13*q33-4*q12*q23*q33+4*n1*q12*q23*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(n1,-1+n2,n3,n4)*prf(2*M`j'^2*q13+2*M`j'^2*q23+4*M`j'^2*q33-2*q12*q33-2*q13*q33-2*q23*q33-q33^2,4*M`j'^2*q13^2+8*M`j'^2*q13*q23+4*M`j'^2*q23^2-8*M`j'^2*q12*q33+4*q12^2*q33+4*q12*q13*q33+4*q12*q23*q33+2*q12*q33^2)+mbox1l(-1+n1,n2,n3,n4)*(tmpprf(ep,1)*prf(4*q12*q13+4*q13^2+4*q12*q23+8*q13*q23+4*q23^2+2*q13*q33+2*q23*q33,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33-4*q12^2*q33+4*n1*q12^2*q33-4*q12*q13*q33+4*n1*q12*q13*q33-4*q12*q23*q33+4*n1*q12*q23*q33-2*q12*q33^2+2*n1*q12*q33^2)+prf(4*M`j'^2*q13-4*M`j'^2*n1*q13+6*M`j'^2*n2*q13-2*M`j'^2*n4*q13-12*q12*q13+4*n1*q12*q13+2*n3*q12*q13+4*n4*q12*q13-12*q13^2+4*n1*q13^2+2*n3*q13^2+4*n4*q13^2+4*M`j'^2*q23-4*M`j'^2*n1*q23+6*M`j'^2*n2*q23-2*M`j'^2*n4*q23-12*q12*q23+4*n1*q12*q23+2*n3*q12*q23+4*n4*q12*q23-24*q13*q23+8*n1*q13*q23+4*n3*q13*q23+8*n4*q13*q23-12*q23^2+4*n1*q23^2+2*n3*q23^2+4*n4*q23^2+4*M`j'^2*q33-4*M`j'^2*n1*q33+4*M`j'^2*n2*q33-2*q12*q33+2*n1*q12*q33-2*n2*q12*q33-8*q13*q33+4*n1*q13*q33-2*n2*q13*q33+n3*q13*q33+2*n4*q13*q33-8*q23*q33+4*n1*q23*q33-2*n2*q23*q33+n3*q23*q33+2*n4*q23*q33-q33^2+n1*q33^2-n2*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33-4*q12^2*q33+4*n1*q12^2*q33-4*q12*q13*q33+4*n1*q12*q13*q33-4*q12*q23*q33+4*n1*q12*q23*q33-2*q12*q33^2+2*n1*q12*q33^2))+mbox1l(-2+n1,1+n2,n3,n4)*prf(-8*M`j'^2*n2*q12+4*n2*q12^2-8*M`j'^2*n2*q13+8*n2*q12*q13+4*n2*q13^2-8*M`j'^2*n2*q23+8*n2*q12*q23+8*n2*q13*q23+4*n2*q23^2-4*M`j'^2*n2*q33+4*n2*q12*q33+4*n2*q13*q33+4*n2*q23*q33+n2*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33-4*q12^2*q33+4*n1*q12^2*q33-4*q12*q13*q33+4*n1*q12*q13*q33-4*q12*q23*q33+4*n1*q12*q23*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,-1+n2,1+n3,n4)*prf(6*M`j'^2*n3*q13-2*n3*q12*q13-2*n3*q13^2+2*M`j'^2*n3*q23-2*n3*q13*q23+4*M`j'^2*n3*q33-2*n3*q12*q33-3*n3*q13*q33-2*n3*q23*q33-n3*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33-4*q12^2*q33+4*n1*q12^2*q33-4*q12*q13*q33+4*n1*q12*q13*q33-4*q12*q23*q33+4*n1*q12*q23*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-2+n1,n2,1+n3,n4)*prf(-4*M`j'^2*n3*q12+2*n3*q12^2-8*M`j'^2*n3*q13+6*n3*q12*q13+4*n3*q13^2-4*M`j'^2*n3*q23+4*n3*q12*q23+6*n3*q13*q23+2*n3*q23^2-4*M`j'^2*n3*q33+3*n3*q12*q33+4*n3*q13*q33+3*n3*q23*q33+n3*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33-4*q12^2*q33+4*n1*q12^2*q33-4*q12*q13*q33+4*n1*q12*q13*q33-4*q12*q23*q33+4*n1*q12*q23*q33-2*q12*q33^2+2*n1*q12*q33^2)+mbox1l(-1+n1,n2,1+n3,n4)*prf(4*M`j'^2*n3*q12*q13-4*n3*q12^2*q13-4*n3*q12*q13^2-4*M`j'^2*n3*q12*q23-4*M`j'^2*n3*q13*q23-4*n3*q12*q13*q23-4*M`j'^2*n3*q23^2+4*M`j'^2*n3*q12*q33-2*n3*q12^2*q33-4*n3*q12*q13*q33-2*n3*q12*q23*q33-n3*q12*q33^2,-4*M`j'^2*q13^2+4*M`j'^2*n1*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23-4*M`j'^2*q23^2+4*M`j'^2*n1*q23^2+8*M`j'^2*q12*q33-8*M`j'^2*n1*q12*q33-4*q12^2*q33+4*n1*q12^2*q33-4*q12*q13*q33+4*n1*q12*q13*q33-4*q12*q23*q33+4*n1*q12*q23*q33-2*q12*q33^2+2*n1*q12*q33^2); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?neg0_,n4?{,>1}) = mbox1l(n1,1+n2,n3,-1+n4)*prf(n2,-1+n4)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(-2*n2*q12,-2*q12+2*n4*q12-2*q13+2*n4*q13-2*q23+2*n4*q23-q33+n4*q33)+mbox1l(2+n1,n2,n3,-2+n4)*prf(2*q12+2*n1*q12,-2*q12+2*n4*q12-2*q13+2*n4*q13-2*q23+2*n4*q23-q33+n4*q33)+mbox1l(1+n1,-1+n2,n3,n4)*prf(q33,2*q12+2*q13+2*q23+q33)+mbox1l(2+n1,-1+n2,n3,-1+n4)*prf(-q33-n1*q33,-2*q12+2*n4*q12-2*q13+2*n4*q13-2*q23+2*n4*q23-q33+n4*q33)+mbox1l(1+n1,n2,n3,-1+n4)*prf(-4*q12-2*n1*q12+2*n4*q12-2*q13-2*n2*q13+2*n4*q13-2*q23-2*n2*q23+2*n4*q23+q33+n1*q33-n2*q33,-2*q12+2*n4*q12-2*q13+2*n4*q13-2*q23+2*n4*q23-q33+n4*q33)+mbox1l(1+n1,-1+n2,1+n3,-1+n4)*prf(-2*n3*q13-n3*q33,-2*q12+2*n4*q12-2*q13+2*n4*q13-2*q23+2*n4*q23-q33+n4*q33)+mbox1l(n1,n2,1+n3,-1+n4)*prf(2*n3*q13+n3*q33,-2*q12+2*n4*q12-2*q13+2*n4*q13-2*q23+2*n4*q23-q33+n4*q33); Identify,ifmatch->jump mbox1l(1,1,n3?neg_,1) = tmpprf(1,2*ep+n3)*mbox1l(1,0,n3,2)*prf(-2*M`j'^2,2*q12+2*q13+2*q23+q33)+tmpprf(1,2*ep+n3)*mbox1l(2,1,n3,0)*prf(-2*M`j'^2,2*q12+2*q13+2*q23+q33)+tmpprf(1,2*ep+n3)*mbox1l(0,2,n3,1)*prf(4*M`j'^2-2*q12-2*q13-2*q23-q33,q13+q23)+tmpprf(1,2*ep+n3)*mbox1l(1,2,n3,0)*prf(-8*M`j'^2*q12+4*q12^2-2*M`j'^2*q13+4*q12*q13-2*M`j'^2*q23+4*q12*q23+2*q12*q33,2*q12*q13+2*q13^2+2*q12*q23+4*q13*q23+2*q23^2+q13*q33+q23*q33)+tmpprf(1,2*ep+n3)*mbox1l(1,1,1+n3,0)*prf(-4*M`j'^2*n3*q12+2*n3*q12^2-2*M`j'^2*n3*q13+2*n3*q12*q13-2*M`j'^2*n3*q23+2*n3*q12*q23+n3*q12*q33,2*q12*q13+2*q13^2+2*q12*q23+4*q13*q23+2*q23^2+q13*q33+q23*q33)+tmpprf(1,2*ep+n3)*mbox1l(1,1,2+n3,0)*prf(2*M`j'^2*q12*q13+2*M`j'^2*n3*q12*q13-2*q12^2*q13-2*n3*q12^2*q13-2*M`j'^2*q12*q23-2*M`j'^2*n3*q12*q23-q12^2*q33-n3*q12^2*q33,q13^2+2*q13*q23+q23^2-2*q12*q33)+tmpprf(1,2*ep+n3)*mbox1l(1,0,1+n3,2)*prf(-4*M`j'^2*q12*q13^2-4*M`j'^2*q12*q13*q23+4*M`j'^2*q12^2*q33-2*M`j'^2*q12*q13*q33+2*M`j'^2*q12*q23*q33,-2*q12*q13^2-2*q13^3-4*q12*q13*q23-6*q13^2*q23-2*q12*q23^2-6*q13*q23^2-2*q23^3+4*q12^2*q33+4*q12*q13*q33-q13^2*q33+4*q12*q23*q33-2*q13*q23*q33-q23^2*q33+2*q12*q33^2)+mbox1l(1,1,1+n3,1)*(tmpprf(ep,2*ep+n3)*prf(4*q12*q13^2+4*q12*q13*q23-4*q12^2*q33+2*q12*q13*q33-2*q12*q23*q33,q13^2+2*q13*q23+q23^2-2*q12*q33)+tmpprf(1,2*ep+n3)*prf(2*q12*q13^2+4*n3*q12*q13^2+2*q12*q13*q23+4*n3*q12*q13*q23-2*q12^2*q33-4*n3*q12^2*q33+q12*q13*q33+2*n3*q12*q13*q33-q12*q23*q33-2*n3*q12*q23*q33,q13^2+2*q13*q23+q23^2-2*q12*q33))+tmpprf(1,2*ep+n3)*mbox1l(2,0,n3,1)*prf(-2*M`j'^2*q13-2*M`j'^2*q23-4*M`j'^2*q33+2*q12*q33+2*q13*q33+2*q23*q33+q33^2,2*q12*q13+2*q13^2+2*q12*q23+4*q13*q23+2*q23^2+q13*q33+q23*q33)+tmpprf(1,2*ep+n3)*mbox1l(0,1,1+n3,1)*prf(4*M`j'^2*n3*q12-2*n3*q12^2+8*M`j'^2*n3*q13-6*n3*q12*q13-4*n3*q13^2+4*M`j'^2*n3*q23-4*n3*q12*q23-6*n3*q13*q23-2*n3*q23^2+4*M`j'^2*n3*q33-3*n3*q12*q33-4*n3*q13*q33-3*n3*q23*q33-n3*q33^2,2*q12*q13+2*q13^2+2*q12*q23+4*q13*q23+2*q23^2+q13*q33+q23*q33)+tmpprf(1,2*ep+n3)*mbox1l(1,0,1+n3,1)*prf(-6*M`j'^2*n3*q13+2*n3*q12*q13+2*n3*q13^2-2*M`j'^2*n3*q23+2*n3*q13*q23-4*M`j'^2*n3*q33+2*n3*q12*q33+3*n3*q13*q33+2*n3*q23*q33+n3*q33^2,2*q12*q13+2*q13^2+2*q12*q23+4*q13*q23+2*q23^2+q13*q33+q23*q33)+tmpprf(1,2*ep+n3)*mbox1l(1,1,2+n3,1)*prf(-4*q12^2*q13^2-4*n3*q12^2*q13^2-8*M`j'^2*q12*q13*q23-8*M`j'^2*n3*q12*q13*q23+4*M`j'^2*q12^2*q33+4*M`j'^2*n3*q12^2*q33-4*q12^2*q13*q33-4*n3*q12^2*q13*q33-q12^2*q33^2-n3*q12^2*q33^2,q13^2+2*q13*q23+q23^2-2*q12*q33)+tmpprf(1,2*ep+n3)*mbox1l(0,2,1+n3,1)*prf(-8*M`j'^2*q12*q13^2+4*q12^2*q13^2+4*q12*q13^3-8*M`j'^2*q12*q13*q23+4*q12^2*q13*q23+8*q12*q13^2*q23+4*q12*q13*q23^2+8*M`j'^2*q12^2*q33-4*q12^3*q33-4*M`j'^2*q12*q13*q33-2*q12^2*q13*q33+4*q12*q13^2*q33+4*M`j'^2*q12*q23*q33-6*q12^2*q23*q33+2*q12*q13*q23*q33-2*q12*q23^2*q33-2*q12^2*q33^2+q12*q13*q33^2-q12*q23*q33^2,q13^3+3*q13^2*q23+3*q13*q23^2+q23^3-2*q12*q13*q33-2*q12*q23*q33)+tmpprf(1,2*ep+n3)*mbox1l(2,1,1+n3,0)*prf(8*M`j'^2*q12*q13^3+12*M`j'^2*q12*q13^2*q23-4*M`j'^2*q12*q23^3-12*M`j'^2*q12^2*q13*q33+4*q12^3*q13*q33+2*M`j'^2*q12*q13^2*q33+4*q12^2*q13^2*q33+4*M`j'^2*q12^2*q23*q33-4*q12^3*q23*q33-2*M`j'^2*q12*q23^2*q33-4*q12^2*q23^2*q33+2*q12^2*q13*q33^2-2*q12^2*q23*q33^2,2*q12*q13^3+2*q13^4+6*q12*q13^2*q23+8*q13^3*q23+6*q12*q13*q23^2+12*q13^2*q23^2+2*q12*q23^3+8*q13*q23^3+2*q23^4-4*q12^2*q13*q33-4*q12*q13^2*q33+q13^3*q33-4*q12^2*q23*q33-8*q12*q13*q23*q33+3*q13^2*q23*q33-4*q12*q23^2*q33+3*q13*q23^2*q33+q23^3*q33-2*q12*q13*q33^2-2*q12*q23*q33^2)+tmpprf(1,2*ep+n3)*mbox1l(1,2,1+n3,0)*prf(16*M`j'^2*q12^2*q13^2-8*q12^3*q13^2+4*M`j'^2*q12*q13^3-8*q12^2*q13^3+16*M`j'^2*q12^2*q13*q23-8*q12^3*q13*q23+8*M`j'^2*q12*q13^2*q23-16*q12^2*q13^2*q23+4*M`j'^2*q12*q13*q23^2-8*q12^2*q13*q23^2-16*M`j'^2*q12^3*q33+8*q12^4*q33+4*M`j'^2*q12^2*q13*q33+4*q12^3*q13*q33+2*M`j'^2*q12*q13^2*q33-8*q12^2*q13^2*q33-12*M`j'^2*q12^2*q23*q33+12*q12^3*q23*q33-4*q12^2*q13*q23*q33-2*M`j'^2*q12*q23^2*q33+4*q12^2*q23^2*q33+4*q12^3*q33^2-2*q12^2*q13*q33^2+2*q12^2*q23*q33^2,2*q12*q13^3+2*q13^4+6*q12*q13^2*q23+8*q13^3*q23+6*q12*q13*q23^2+12*q13^2*q23^2+2*q12*q23^3+8*q13*q23^3+2*q23^4-4*q12^2*q13*q33-4*q12*q13^2*q33+q13^3*q33-4*q12^2*q23*q33-8*q12*q13*q23*q33+3*q13^2*q23*q33-4*q12*q23^2*q33+3*q13*q23^2*q33+q23^3*q33-2*q12*q13*q33^2-2*q12*q23*q33^2)+tmpprf(1,2*ep+n3)*mbox1l(2,0,1+n3,1)*prf(4*M`j'^2*q12*q13^3+4*M`j'^2*q13^4+8*M`j'^2*q12*q13^2*q23+12*M`j'^2*q13^3*q23+4*M`j'^2*q12*q13*q23^2+12*M`j'^2*q13^2*q23^2+4*M`j'^2*q13*q23^3-4*M`j'^2*q12^2*q13*q33-2*M`j'^2*q12*q13^2*q33-4*M`j'^2*q12^2*q23*q33-8*M`j'^2*q12*q13*q23*q33-6*M`j'^2*q12*q23^2*q33+4*M`j'^2*q12*q13*q33^2-2*q12^2*q13*q33^2-2*q12*q13^2*q33^2-4*M`j'^2*q12*q23*q33^2+2*q12^2*q23*q33^2+2*q12*q23^2*q33^2-q12*q13*q33^3+q12*q23*q33^3,2*q12*q13^3+2*q13^4+6*q12*q13^2*q23+8*q13^3*q23+6*q12*q13*q23^2+12*q13^2*q23^2+2*q12*q23^3+8*q13*q23^3+2*q23^4-4*q12^2*q13*q33-4*q12*q13^2*q33+q13^3*q33-4*q12^2*q23*q33-8*q12*q13*q23*q33+3*q13^2*q23*q33-4*q12*q23^2*q33+3*q13*q23^2*q33+q23^3*q33-2*q12*q13*q33^2-2*q12*q23*q33^2)+tmpprf(1,2*ep+n3)*mbox1l(0,1,2+n3,1)*prf(-4*M`j'^2*q12^2*q13^2-4*M`j'^2*n3*q12^2*q13^2+4*q12^3*q13^2+4*n3*q12^3*q13^2-16*M`j'^2*q12*q13^3-16*M`j'^2*n3*q12*q13^3+12*q12^2*q13^3+12*n3*q12^2*q13^3+8*q12*q13^4+8*n3*q12*q13^4+4*q12^3*q13*q23+4*n3*q12^3*q13*q23-16*M`j'^2*q12*q13^2*q23-16*M`j'^2*n3*q12*q13^2*q23+20*q12^2*q13^2*q23+20*n3*q12^2*q13^2*q23+20*q12*q13^3*q23+20*n3*q12*q13^3*q23+4*M`j'^2*q12^2*q23^2+4*M`j'^2*n3*q12^2*q23^2+8*M`j'^2*q12*q13*q23^2+8*M`j'^2*n3*q12*q13*q23^2+8*q12^2*q13*q23^2+8*n3*q12^2*q13*q23^2+4*M`j'^2*q13^2*q23^2+4*M`j'^2*n3*q13^2*q23^2+16*q12*q13^2*q23^2+16*n3*q12*q13^2*q23^2+8*M`j'^2*q12*q23^3+8*M`j'^2*n3*q12*q23^3+8*M`j'^2*q13*q23^3+8*M`j'^2*n3*q13*q23^3+4*q12*q13*q23^3+4*n3*q12*q13*q23^3+4*M`j'^2*q23^4+4*M`j'^2*n3*q23^4+12*M`j'^2*q12^2*q13*q33+12*M`j'^2*n3*q12^2*q13*q33-6*q12^3*q13*q33-6*n3*q12^3*q13*q33-16*M`j'^2*q12*q13^2*q33-16*M`j'^2*n3*q12*q13^2*q33+4*q12^2*q13^2*q33+4*n3*q12^2*q13^2*q33+12*q12*q13^3*q33+12*n3*q12*q13^3*q33-4*M`j'^2*q12^2*q23*q33-4*M`j'^2*n3*q12^2*q23*q33+2*q12^3*q23*q33+2*n3*q12^3*q23*q33-4*M`j'^2*q12*q13*q23*q33-4*M`j'^2*n3*q12*q13*q23*q33+16*q12*q13^2*q23*q33+16*n3*q12*q13^2*q23*q33-4*M`j'^2*q12*q23^2*q33-4*M`j'^2*n3*q12*q23^2*q33+4*q12^2*q23^2*q33+4*n3*q12^2*q23^2*q33+6*q12*q13*q23^2*q33+6*n3*q12*q13*q23^2*q33+2*q12*q23^3*q33+2*n3*q12*q23^3*q33+8*M`j'^2*q12^2*q33^2+8*M`j'^2*n3*q12^2*q33^2-4*q12^3*q33^2-4*n3*q12^3*q33^2-4*M`j'^2*q12*q13*q33^2-4*M`j'^2*n3*q12*q13*q33^2-5*q12^2*q13*q33^2-5*n3*q12^2*q13*q33^2+6*q12*q13^2*q33^2+6*n3*q12*q13^2*q33^2+4*M`j'^2*q12*q23*q33^2+4*M`j'^2*n3*q12*q23*q33^2-5*q12^2*q23*q33^2-5*n3*q12^2*q23*q33^2+q12*q13*q23*q33^2+n3*q12*q13*q23*q33^2-q12*q23^2*q33^2-n3*q12*q23^2*q33^2-2*q12^2*q33^3-2*n3*q12^2*q33^3+q12*q13*q33^3+n3*q12*q13*q33^3-q12*q23*q33^3-n3*q12*q23*q33^3,2*q12*q13^3+2*q13^4+6*q12*q13^2*q23+8*q13^3*q23+6*q12*q13*q23^2+12*q13^2*q23^2+2*q12*q23^3+8*q13*q23^3+2*q23^4-4*q12^2*q13*q33-4*q12*q13^2*q33+q13^3*q33-4*q12^2*q23*q33-8*q12*q13*q23*q33+3*q13^2*q23*q33-4*q12*q23^2*q33+3*q13*q23^2*q33+q23^3*q33-2*q12*q13*q33^2-2*q12*q23*q33^2)+tmpprf(1,2*ep+n3)*mbox1l(1,0,2+n3,1)*prf(8*M`j'^2*q12*q13^3+8*M`j'^2*n3*q12*q13^3-4*q12^2*q13^3-4*n3*q12^2*q13^3-4*q12*q13^4-4*n3*q12*q13^4+8*M`j'^2*q12*q13^2*q23+8*M`j'^2*n3*q12*q13^2*q23-4*q12^2*q13^2*q23-4*n3*q12^2*q13^2*q23+4*M`j'^2*q13^3*q23+4*M`j'^2*n3*q13^3*q23-8*q12*q13^3*q23-8*n3*q12*q13^3*q23+8*M`j'^2*q13^2*q23^2+8*M`j'^2*n3*q13^2*q23^2-4*q12*q13^2*q23^2-4*n3*q12*q13^2*q23^2+4*M`j'^2*q13*q23^3+4*M`j'^2*n3*q13*q23^3-4*M`j'^2*q12^2*q13*q33-4*M`j'^2*n3*q12^2*q13*q33+10*M`j'^2*q12*q13^2*q33+10*M`j'^2*n3*q12*q13^2*q33-6*q12^2*q13^2*q33-6*n3*q12^2*q13^2*q33-8*q12*q13^3*q33-8*n3*q12*q13^3*q33-4*M`j'^2*q12^2*q23*q33-4*M`j'^2*n3*q12^2*q23*q33-12*M`j'^2*q12*q13*q23*q33-12*M`j'^2*n3*q12*q13*q23*q33+2*q12^2*q13*q23*q33+2*n3*q12^2*q13*q23*q33-6*q12*q13^2*q23*q33-6*n3*q12*q13^2*q23*q33-6*M`j'^2*q12*q23^2*q33-6*M`j'^2*n3*q12*q23^2*q33+2*q12*q13*q23^2*q33+2*n3*q12*q13*q23^2*q33+4*M`j'^2*q12*q13*q33^2+4*M`j'^2*n3*q12*q13*q33^2-2*q12^2*q13*q33^2-2*n3*q12^2*q13*q33^2-5*q12*q13^2*q33^2-5*n3*q12*q13^2*q33^2-4*M`j'^2*q12*q23*q33^2-4*M`j'^2*n3*q12*q23*q33^2+2*q12^2*q23*q33^2+2*n3*q12^2*q23*q33^2+q12*q13*q23*q33^2+n3*q12*q13*q23*q33^2+2*q12*q23^2*q33^2+2*n3*q12*q23^2*q33^2-q12*q13*q33^3-n3*q12*q13*q33^3+q12*q23*q33^3+n3*q12*q23*q33^3,2*q12*q13^3+2*q13^4+6*q12*q13^2*q23+8*q13^3*q23+6*q12*q13*q23^2+12*q13^2*q23^2+2*q12*q23^3+8*q13*q23^3+2*q23^4-4*q12^2*q13*q33-4*q12*q13^2*q33+q13^3*q33-4*q12^2*q23*q33-8*q12*q13*q23*q33+3*q13^2*q23*q33-4*q12*q23^2*q33+3*q13*q23^2*q33+q23^3*q33-2*q12*q13*q33^2-2*q12*q23*q33^2); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?{,>1},n4?neg_) = mbox1l(n1,-1+n2,n3,1+n4)*prf(-4*q13-q33,2*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(2*q12-2*q13+2*q23-q33,2*q12)+mbox1l(1+n1,-1+n2,-1+n3,1+n4)*prf(-2*n1*q13-n1*q33,-2*q12+2*n3*q12)+mbox1l(-1+n1,1+n2,-1+n3,1+n4)*prf(-2*n2*q13-n2*q33,-2*q12+2*n3*q12)+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(-2*q13-2*n4*q13+q33+n4*q33,-2*q12+2*n3*q12)+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(2*q13+2*n4*q13+q33+n4*q33,-2*q12+2*n3*q12)+mbox1l(1+n1,n2,-2+n3,1+n4)*prf(2*M`j'^2*n1*q13-2*n1*q12*q13-2*M`j'^2*n1*q23+2*M`j'^2*n1*q33-n1*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,1+n2,-2+n3,1+n4)*prf(6*M`j'^2*n2*q13-2*n2*q12*q13+2*M`j'^2*n2*q23+2*M`j'^2*n2*q33-n2*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-2+n3,2+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n4*q13-2*q12*q13-2*n4*q12*q13-2*M`j'^2*q23-2*M`j'^2*n4*q23-2*M`j'^2*q33-2*M`j'^2*n4*q33-q12*q33-n4*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-1+n3,1+n4)*(tmpprf(ep,1)*prf(-4*q12*q13-2*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+prf(-8*M`j'^2*q13-4*M`j'^2*n2*q13+6*M`j'^2*n3*q13-2*M`j'^2*n4*q13+10*q12*q13-2*n1*q12*q13-2*n2*q12*q13-4*n3*q12*q13-2*n4*q12*q13+4*M`j'^2*q23+2*M`j'^2*n1*q23-2*M`j'^2*n2*q23-2*M`j'^2*n3*q23+2*M`j'^2*n4*q23-2*M`j'^2*q33-M`j'^2*n1*q33-M`j'^2*n2*q33+2*M`j'^2*n3*q33+5*q12*q33-n1*q12*q33-n2*q12*q33-2*n3*q12*q33-n4*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12))+mbox1l(n1,n2,-1+n3,2+n4)*prf(-4*q12*q13^2-4*n4*q12*q13^2-8*M`j'^2*q13*q23-8*M`j'^2*n4*q13*q23+4*M`j'^2*q12*q33+4*M`j'^2*n4*q12*q33-4*q12*q13*q33-4*n4*q12*q13*q33-q12*q33^2-n4*q12*q33^2,-2*M`j'^2*q12+2*M`j'^2*n3*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?pos_,n4?neg_) = mbox1l(n1,n2,-1+n3,1+n4)*prf(-2*q13-2*q23-q33,2*q12)+mbox1l(1+n1,-1+n2,-1+n3,1+n4)*prf(-(n1*q33),-2*q12+2*n2*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(2*q12+2*q13+2*q23+q33,2*q12)+mbox1l(n1,-1+n2,n3,1+n4)*prf(2*q13-2*n3*q13+2*n4*q13+n1*q33-n3*q33,-2*q12+2*n2*q12)+mbox1l(-1+n1,-1+n2,1+n3,1+n4)*prf(2*n3*q13+n3*q33,-2*q12+2*n2*q12)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-2*q13-2*n4*q13-q33-n4*q33,-2*q12+2*n2*q12)+mbox1l(n1,-1+n2,-1+n3,2+n4)*prf(q33+n4*q33,-2*q12+2*n2*q12); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?pos_,n4?neg_) = mbox1l(-2+n1,n2,n3,2+n4)*prf(q12+n4*q12+q23+n4*q23,-q12+n1*q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(-q33,2*q12)+mbox1l(n1,-1+n2,n3,1+n4)*prf(q33,2*q12)+mbox1l(-1+n1,1+n2,-1+n3,1+n4)*prf(-2*n2*q13-2*n2*q23-n2*q33,-2*q12+2*n1*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-4*q12+2*n1*q12-2*n4*q12+2*n2*q13-2*n3*q13-2*q23+2*n2*q23-2*n4*q23+n2*q33-n3*q33,-2*q12+2*n1*q12)+mbox1l(-1+n1,-1+n2,1+n3,1+n4)*prf(2*n3*q13+n3*q33,-2*q12+2*n1*q12)+mbox1l(-1+n1,-1+n2,n3,2+n4)*prf(-q33-n4*q33,-2*q12+2*n1*q12)+mbox1l(-1+n1,n2,-1+n3,2+n4)*prf(q33+n4*q33,-2*q12+2*n1*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?{,>1},n4?neg0_) = mbox1l(-1+n1,n2,n3,n4)*prf(1,2*q12)+mbox1l(n1,-1+n2,n3,n4)*prf(1,2*q12)+mbox1l(1+n1,-1+n2,-1+n3,n4)*prf(n1,-2*q12+2*n3*q12)+mbox1l(-1+n1,1+n2,-1+n3,n4)*prf(n2,-2*q12+2*n3*q12)+mbox1l(-1+n1,n2,-1+n3,1+n4)*prf(n4,-2*q12+2*n3*q12)+mbox1l(n1,-1+n2,-1+n3,1+n4)*prf(n4,-2*q12+2*n3*q12)+mbox1l(1+n1,n2,-2+n3,n4)*prf(-2*M`j'^2*n1+n1*q12,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,1+n2,-2+n3,n4)*prf(-2*M`j'^2*n2+n2*q12,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-2+n3,1+n4)*prf(-2*M`j'^2*n4+n4*q12,-2*M`j'^2*q12+2*M`j'^2*n3*q12)+mbox1l(n1,n2,-1+n3,n4)*(tmpprf(ep,1)*prf(1,-M`j'^2+M`j'^2*n3)+prf(2*M`j'^2+M`j'^2*n1+M`j'^2*n2-2*M`j'^2*n3-6*q12+n1*q12+n2*q12+2*n3*q12+n4*q12,-2*M`j'^2*q12+2*M`j'^2*n3*q12))+mbox1l(n1,n2,-1+n3,1+n4)*prf(-2*M`j'^2*n4*q13+2*n4*q12*q13+2*M`j'^2*n4*q23+n4*q12*q33,-2*M`j'^2*q12+2*M`j'^2*n3*q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?pos_,n4?neg0_) = mbox1l(-1+n1,n2,n3,n4)*prf(-1,2*q12)+mbox1l(n1,n2,-1+n3,n4)*prf(1,2*q12)+mbox1l(1+n1,-1+n2,-1+n3,n4)*prf(n1,-2*q12+2*n2*q12)+mbox1l(-1+n1,-1+n2,1+n3,n4)*prf(-n3,-2*q12+2*n2*q12)+mbox1l(n1,-1+n2,n3,n4)*prf(-n1+n3,-2*q12+2*n2*q12)+mbox1l(-1+n1,-1+n2,n3,1+n4)*prf(-n4,-2*q12+2*n2*q12)+mbox1l(n1,-1+n2,-1+n3,1+n4)*prf(n4,-2*q12+2*n2*q12)+mbox1l(n1,-1+n2,n3,1+n4)*prf(n4*q13,-q12+n2*q12); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?pos_,n4?neg0_) = mbox1l(n1,-1+n2,n3,n4)*prf(-1,2*q12)+mbox1l(n1,n2,-1+n3,n4)*prf(1,2*q12)+mbox1l(-1+n1,1+n2,-1+n3,n4)*prf(n2,-2*q12+2*n1*q12)+mbox1l(-1+n1,-1+n2,1+n3,n4)*prf(-n3,-2*q12+2*n1*q12)+mbox1l(-1+n1,n2,n3,n4)*prf(-n2+n3,-2*q12+2*n1*q12)+mbox1l(-1+n1,-1+n2,n3,1+n4)*prf(-n4,-2*q12+2*n1*q12)+mbox1l(-1+n1,n2,-1+n3,1+n4)*prf(n4,-2*q12+2*n1*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-(n4*q12)-n4*q23,-q12+n1*q12); If (Match(mbox1l(n1?!{n2?},n2?!{n1?},n3?,n4?))); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?pos_,n4?neg0_) = mbox1l(1+n1,n2,-1+n3,n4)*prf(n1,n1-n2)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-n2,n1-n2)+mbox1l(n1,-1+n2,n3,1+n4)*prf(-(n4*q13),n1*q12-n2*q12)+mbox1l(-1+n1,n2,n3,1+n4)*prf(-(n4*q12)-n4*q23,n1*q12-n2*q12)+mbox1l(n1,n2,-1+n3,1+n4)*prf(n4*q12+n4*q13+n4*q23,n1*q12-n2*q12); EndIf; Identify,ifmatch->jump mbox1l(1,1,1,n4?neg_) = tmpprf(1,2*ep+n4)*mbox1l(0,1,2,n4)*prf(-M`j'^2,q12)+tmpprf(1,2*ep+n4)*mbox1l(0,2,1,n4)*prf(-M`j'^2,q12)+tmpprf(1,2*ep+n4)*mbox1l(1,0,2,n4)*prf(-M`j'^2,q12)+tmpprf(1,2*ep+n4)*mbox1l(2,0,1,n4)*prf(-M`j'^2,q12)+tmpprf(1,2*ep+n4)*mbox1l(0,1,1,1+n4)*prf(-(M`j'^2*n4),q12)+tmpprf(1,2*ep+n4)*mbox1l(1,0,1,1+n4)*prf(-(M`j'^2*n4),q12)+tmpprf(1,2*ep+n4)*mbox1l(1,2,0,n4)*prf(2*M`j'^2-q12,q12)+tmpprf(1,2*ep+n4)*mbox1l(2,1,0,n4)*prf(2*M`j'^2-q12,q12)+tmpprf(1,2*ep+n4)*mbox1l(1,1,0,1+n4)*prf(2*M`j'^2*n4-n4*q12,q12)+tmpprf(1,2*ep+n4)*mbox1l(1,0,2,1+n4)*prf(-4*M`j'^2*q13-M`j'^2*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(0,2,1,1+n4)*prf(-2*M`j'^2*q13-M`j'^2*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(2,0,1,1+n4)*prf(-2*M`j'^2*q13-M`j'^2*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(0,1,2,1+n4)*prf(2*M`j'^2*q12-2*M`j'^2*q13+2*M`j'^2*q23-M`j'^2*q33,q12)+mbox1l(1,1,1,1+n4)*(tmpprf(ep,2*ep+n4)*prf(-4*q13-2*q33,1)+tmpprf(1,2*ep+n4)*prf(-2*q13-4*n4*q13-q33-2*n4*q33,1))+tmpprf(1,2*ep+n4)*mbox1l(1,0,1,2+n4)*prf(-2*M`j'^2*q13-2*M`j'^2*n4*q13+M`j'^2*q33+M`j'^2*n4*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(0,1,1,2+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n4*q13+M`j'^2*q33+M`j'^2*n4*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(2,1,0,1+n4)*prf(2*M`j'^2*q13-2*q12*q13-2*M`j'^2*q23+2*M`j'^2*q33-q12*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(1,2,0,1+n4)*prf(6*M`j'^2*q13-2*q12*q13+2*M`j'^2*q23+2*M`j'^2*q33-q12*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(1,1,0,2+n4)*prf(2*M`j'^2*q13+2*M`j'^2*n4*q13-2*q12*q13-2*n4*q12*q13-2*M`j'^2*q23-2*M`j'^2*n4*q23-2*M`j'^2*q33-2*M`j'^2*n4*q33-q12*q33-n4*q12*q33,q12)+tmpprf(1,2*ep+n4)*mbox1l(1,1,1,2+n4)*prf(-4*q12*q13^2-4*n4*q12*q13^2-8*M`j'^2*q13*q23-8*M`j'^2*n4*q13*q23+4*M`j'^2*q12*q33+4*M`j'^2*n4*q12*q33-4*q12*q13*q33-4*n4*q12*q13*q33-q12*q33^2-n4*q12*q33^2,q12); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?pos_,n4?{,>1}) = mbox1l(n1,n2,1+n3,-2+n4)*prf(-2*M`j'^2*n3*q12,-4*q12*q13^2+4*n4*q12*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n4*q13*q23+4*M`j'^2*q12*q33-4*M`j'^2*n4*q12*q33-4*q12*q13*q33+4*n4*q12*q13*q33-q12*q33^2+n4*q12*q33^2)+mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-8*M`j'^2*n3*q13,-4*q12*q13^2+4*n4*q12*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n4*q13*q23+4*M`j'^2*q12*q33-4*M`j'^2*n4*q12*q33-4*q12*q13*q33+4*n4*q12*q13*q33-q12*q33^2+n4*q12*q33^2)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(-4*M`j'^2*n2*q12^2-8*M`j'^2*n2*q12*q23-4*M`j'^2*n2*q23^2,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(1+n1,n2,n3,-2+n4)*prf(8*M`j'^2*n1*q12*q13-2*M`j'^2*n1*q12*q33,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,1+n2,n3,-2+n4)*prf(4*M`j'^2*n2*q12^2-4*M`j'^2*n2*q12*q13+4*M`j'^2*n2*q12*q23-2*M`j'^2*n2*q12*q33,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(-4*M`j'^2*n1*q13^2-8*M`j'^2*n1*q13*q33,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,n2,-1+n3,n4)*prf(-4*M`j'^2*q12*q13-4*q12*q13^2-8*M`j'^2*q13*q23+2*M`j'^2*q12*q33-4*q12*q13*q33-q12*q33^2,8*q12*q13^3+16*M`j'^2*q13^2*q23-8*M`j'^2*q12*q13*q33+12*q12*q13^2*q33+8*M`j'^2*q13*q23*q33-4*M`j'^2*q12*q33^2+6*q12*q13*q33^2+q12*q33^3)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-4*M`j'^2*n1*q12*q13+4*M`j'^2*n1*q13^2-4*n1*q12*q13^2-4*M`j'^2*n1*q13*q23+6*M`j'^2*n1*q12*q33+8*M`j'^2*n1*q13*q33-4*n1*q12*q13*q33-n1*q12*q33^2,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(8*M`j'^2*n2*q12*q13+16*M`j'^2*n2*q13^2-4*n2*q12*q13^2+4*M`j'^2*n2*q12*q23+12*M`j'^2*n2*q13*q23+4*M`j'^2*n2*q23^2-2*M`j'^2*n2*q12*q33+8*M`j'^2*n2*q13*q33-4*n2*q12*q13*q33-n2*q12*q33^2,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)+mbox1l(n1,n2,n3,-1+n4)*(tmpprf(ep,1)*prf(-8*q12*q13^2-8*q12*q13*q33-2*q12*q33^2,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)+prf(-4*M`j'^2*q12*q13-4*M`j'^2*n1*q12*q13-4*M`j'^2*n2*q12*q13+4*M`j'^2*n3*q12*q13+4*M`j'^2*n4*q12*q13-16*M`j'^2*n2*q13^2+16*M`j'^2*n3*q13^2+20*q12*q13^2-4*n1*q12*q13^2-4*n2*q12*q13^2-8*n3*q12*q13^2-4*n4*q12*q13^2-8*M`j'^2*q13*q23+4*M`j'^2*n1*q13*q23-12*M`j'^2*n2*q13*q23+8*M`j'^2*n4*q13*q23+2*M`j'^2*q12*q33-4*M`j'^2*n1*q12*q33+4*M`j'^2*n2*q12*q33+2*M`j'^2*n3*q12*q33-2*M`j'^2*n4*q12*q33-8*M`j'^2*n2*q13*q33+8*M`j'^2*n3*q13*q33+20*q12*q13*q33-4*n1*q12*q13*q33-4*n2*q12*q13*q33-8*n3*q12*q13*q33-4*n4*q12*q13*q33+5*q12*q33^2-n1*q12*q33^2-n2*q12*q33^2-2*n3*q12*q33^2-n4*q12*q33^2,-8*q12*q13^3+8*n4*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n4*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n4*q12*q13*q33-12*q12*q13^2*q33+12*n4*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n4*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n4*q12*q33^2-6*q12*q13*q33^2+6*n4*q12*q13*q33^2-q12*q33^3+n4*q12*q33^3)); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?{,>1},n4?pos_) = mbox1l(n1,n2,n3,-1+n4)*prf(2*M`j'^2*q13-2*q12*q13-2*M`j'^2*q23-q12*q33,4*q12*q13^2+8*M`j'^2*q13*q23-4*M`j'^2*q12*q33+4*q12*q13*q33+q12*q33^2)+mbox1l(n1,n2,-2+n3,1+n4)*prf(4*M`j'^2*n4*q13^2+4*M`j'^2*n4*q13*q23-4*M`j'^2*n4*q12*q33+2*M`j'^2*n4*q13*q33-2*M`j'^2*n4*q23*q33,-8*q12*q13^3+8*n3*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n3*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n3*q12*q13*q33-12*q12*q13^2*q33+12*n3*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n3*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n3*q12*q33^2-6*q12*q13*q33^2+6*n3*q12*q13*q33^2-q12*q33^3+n3*q12*q33^3)+mbox1l(n1,1+n2,-1+n3,-1+n4)*prf(-4*M`j'^2*n2*q12*q13+4*n2*q12^2*q13+4*M`j'^2*n2*q13^2+4*M`j'^2*n2*q12*q23+4*n2*q12*q13*q23+4*M`j'^2*n2*q23^2-4*M`j'^2*n2*q12*q33+2*n2*q12^2*q33+2*M`j'^2*n2*q13*q33-2*M`j'^2*n2*q23*q33+2*n2*q12*q23*q33,-8*q12*q13^3+8*n3*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n3*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n3*q12*q13*q33-12*q12*q13^2*q33+12*n3*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n3*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n3*q12*q33^2-6*q12*q13*q33^2+6*n3*q12*q13*q33^2-q12*q33^3+n3*q12*q33^3)+mbox1l(n1,-1+n2,n3,n4)*prf(8*M`j'^2*q13^2-4*q12*q13^2-4*q13^3-4*q13^2*q23-4*M`j'^2*q12*q33+4*M`j'^2*q13*q33-4*q13^2*q33-4*M`j'^2*q23*q33+q12*q33^2-q13*q33^2+q23*q33^2,4*q12^2*q13^2+8*M`j'^2*q12*q13*q23+4*q12*q13^2*q23+8*M`j'^2*q13*q23^2-4*M`j'^2*q12^2*q33+4*q12^2*q13*q33-4*M`j'^2*q12*q23*q33+4*q12*q13*q23*q33+q12^2*q33^2+q12*q23*q33^2)+mbox1l(1+n1,n2,-1+n3,-1+n4)*prf(-8*M`j'^2*n1*q12*q13^2+4*n1*q12^2*q13^2+8*n1*q12*q13^3+8*M`j'^2*n1*q13^2*q23+4*n1*q12*q13^2*q23+4*M`j'^2*n1*q12^2*q33-6*M`j'^2*n1*q12*q13*q33-2*n1*q12^2*q13*q33+8*n1*q12*q13^2*q33+2*M`j'^2*n1*q12*q23*q33+2*M`j'^2*n1*q13*q23*q33-2*n1*q12*q13*q23*q33-2*M`j'^2*n1*q23^2*q33-2*n1*q12^2*q33^2+2*n1*q12*q13*q33^2-2*n1*q12*q23*q33^2,-8*q12^2*q13^3+8*n3*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n3*q12*q13^2*q23-8*q12*q13^3*q23+8*n3*q12*q13^3*q23-16*M`j'^2*q13^2*q23^2+16*M`j'^2*n3*q13^2*q23^2+8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n3*q12^2*q13*q33-12*q12^2*q13^2*q33+12*n3*q12^2*q13^2*q33-12*q12*q13^2*q23*q33+12*n3*q12*q13^2*q23*q33-8*M`j'^2*q13*q23^2*q33+8*M`j'^2*n3*q13*q23^2*q33+4*M`j'^2*q12^2*q33^2-4*M`j'^2*n3*q12^2*q33^2-6*q12^2*q13*q33^2+6*n3*q12^2*q13*q33^2+4*M`j'^2*q12*q23*q33^2-4*M`j'^2*n3*q12*q23*q33^2-6*q12*q13*q23*q33^2+6*n3*q12*q13*q23*q33^2-q12^2*q33^3+n3*q12^2*q33^3-q12*q23*q33^3+n3*q12*q23*q33^3)+mbox1l(-1+n1,1+n2,-1+n3,n4)*prf(4*M`j'^2*n2*q12^2*q13-4*n2*q12^3*q13-4*n2*q12^2*q13^2-4*M`j'^2*n2*q12^2*q23-8*n2*q12^2*q13*q23-4*n2*q12*q13^2*q23-8*M`j'^2*n2*q12*q23^2-4*M`j'^2*n2*q13*q23^2-4*n2*q12*q13*q23^2-4*M`j'^2*n2*q23^3+4*M`j'^2*n2*q12^2*q33-2*n2*q12^3*q33-4*n2*q12^2*q13*q33+4*M`j'^2*n2*q12*q23*q33-4*n2*q12^2*q23*q33-4*n2*q12*q13*q23*q33-2*n2*q12*q23^2*q33-n2*q12^2*q33^2-n2*q12*q23*q33^2,-8*q12^2*q13^3+8*n3*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n3*q12*q13^2*q23+8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n3*q12^2*q13*q33-12*q12^2*q13^2*q33+12*n3*q12^2*q13^2*q33-8*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n3*q12*q13*q23*q33+4*M`j'^2*q12^2*q33^2-4*M`j'^2*n3*q12^2*q33^2-6*q12^2*q13*q33^2+6*n3*q12^2*q13*q33^2-q12^2*q33^3+n3*q12^2*q33^3)+mbox1l(1+n1,n2,-2+n3,n4)*prf(4*M`j'^2*n1*q12^2*q13^2-4*M`j'^2*n1*q12*q13^3+4*M`j'^2*n1*q12^2*q13*q23-4*M`j'^2*n1*q12*q13^2*q23-4*M`j'^2*n1*q13^3*q23-8*M`j'^2*n1*q13^2*q23^2-4*M`j'^2*n1*q13*q23^3-4*M`j'^2*n1*q12^3*q33+2*M`j'^2*n1*q12^2*q13*q33+4*n1*q12^3*q13*q33-8*M`j'^2*n1*q12*q13^2*q33+6*n1*q12^2*q13^2*q33+4*n1*q12*q13^3*q33+2*M`j'^2*n1*q12^2*q23*q33+10*M`j'^2*n1*q12*q13*q23*q33+2*n1*q12^2*q13*q23*q33+2*n1*q12*q13^2*q23*q33+6*M`j'^2*n1*q12*q23^2*q33-2*n1*q12*q13*q23^2*q33+2*n1*q12^3*q33^2-4*M`j'^2*n1*q12*q13*q33^2+3*n1*q12^2*q13*q33^2+4*n1*q12*q13^2*q33^2+4*M`j'^2*n1*q12*q23*q33^2+n1*q12^2*q23*q33^2-n1*q12*q13*q23*q33^2-n1*q12*q23^2*q33^2+n1*q12*q13*q33^3-n1*q12*q23*q33^3,-8*q12^3*q13^3+8*n3*q12^3*q13^3-16*M`j'^2*q12^2*q13^2*q23+16*M`j'^2*n3*q12^2*q13^2*q23-8*q12^2*q13^3*q23+8*n3*q12^2*q13^3*q23-16*M`j'^2*q12*q13^2*q23^2+16*M`j'^2*n3*q12*q13^2*q23^2+8*M`j'^2*q12^3*q13*q33-8*M`j'^2*n3*q12^3*q13*q33-12*q12^3*q13^2*q33+12*n3*q12^3*q13^2*q33-12*q12^2*q13^2*q23*q33+12*n3*q12^2*q13^2*q23*q33-8*M`j'^2*q12*q13*q23^2*q33+8*M`j'^2*n3*q12*q13*q23^2*q33+4*M`j'^2*q12^3*q33^2-4*M`j'^2*n3*q12^3*q33^2-6*q12^3*q13*q33^2+6*n3*q12^3*q13*q33^2+4*M`j'^2*q12^2*q23*q33^2-4*M`j'^2*n3*q12^2*q23*q33^2-6*q12^2*q13*q23*q33^2+6*n3*q12^2*q13*q23*q33^2-q12^3*q33^3+n3*q12^3*q33^3-q12^2*q23*q33^3+n3*q12^2*q23*q33^3)+mbox1l(1+n1,-1+n2,-1+n3,n4)*prf(4*M`j'^2*n1*q12*q13^3+4*M`j'^2*n1*q12*q13^2*q23+4*M`j'^2*n1*q13^3*q23+4*M`j'^2*n1*q13^2*q23^2-4*M`j'^2*n1*q12^2*q13*q33+8*M`j'^2*n1*q12*q13^2*q33-2*n1*q12^2*q13^2*q33-4*n1*q12*q13^3*q33-4*M`j'^2*n1*q12*q13*q23*q33-2*n1*q12*q13^2*q23*q33-4*M`j'^2*n1*q12^2*q33^2+4*M`j'^2*n1*q12*q13*q33^2+n1*q12^2*q13*q33^2-4*n1*q12*q13^2*q33^2-4*M`j'^2*n1*q12*q23*q33^2+n1*q12*q13*q23*q33^2+n1*q12^2*q33^3-n1*q12*q13*q33^3+n1*q12*q23*q33^3,-8*q12^3*q13^3+8*n3*q12^3*q13^3-16*M`j'^2*q12^2*q13^2*q23+16*M`j'^2*n3*q12^2*q13^2*q23-8*q12^2*q13^3*q23+8*n3*q12^2*q13^3*q23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q12*q13^2*q23*q33+12*n3*q12*q13^2*q23*q33+8*n4*q12*q13^2*q23*q33-2*M`j'^2*q12*q23^2*q33-4*M`j'^2*n1*q12*q23^2*q33+2*M`j'^2*n3*q12*q23^2*q33+2*M`j'^2*n4*q12*q23^2*q33+2*n1*q12*q13*q23^2*q33-2*n2*q12*q13*q23^2*q33-4*M`j'^2*q12^2*q33^2+4*M`j'^2*n1*q12^2*q33^2-8*M`j'^2*n2*q12^2*q33^2+4*M`j'^2*n3*q12^2*q33^2+11*q12^3*q33^2-4*n1*q12^3*q33^2+n2*q12^3*q33^2-3*n3*q12^3*q33^2-4*n4*q12^3*q33^2+4*M`j'^2*q12*q13*q33^2+4*M`j'^2*n2*q12*q13*q33^2-4*M`j'^2*n3*q12*q13*q33^2-4*q12^2*q13*q33^2-4*n1*q12^2*q13*q33^2+7*n2*q12^2*q13*q33^2+2*n4*q12^2*q13*q33^2-6*q12*q13^2*q33^2-6*n2*q12*q13^2*q33^2+6*n3*q12*q13^2*q33^2-4*M`j'^2*q12*q23*q33^2-4*M`j'^2*n2*q12*q23*q33^2+4*M`j'^2*n3*q12*q23*q33^2+17*q12^2*q23*q33^2-5*n1*q12^2*q23*q33^2+n2*q12^2*q23*q33^2-5*n3*q12^2*q23*q33^2-6*n4*q12^2*q23*q33^2-4*q12*q13*q23*q33^2+2*n1*q12*q13*q23*q33^2+n2*q12*q13*q23*q33^2+2*n4*q12*q13*q23*q33^2+6*q12*q23^2*q33^2-n1*q12*q23^2*q33^2-2*n3*q12*q23^2*q33^2-2*n4*q12*q23^2*q33^2+q12^2*q33^3-n1*q12^2*q33^3+2*n2*q12^2*q33^3-n3*q12^2*q33^3-q12*q13*q33^3-n2*q12*q13*q33^3+n3*q12*q13*q33^3+q12*q23*q33^3+n2*q12*q23*q33^3-n3*q12*q23*q33^3,-8*q12^3*q13^3+8*n3*q12^3*q13^3-16*M`j'^2*q12^2*q13^2*q23+16*M`j'^2*n3*q12^2*q13^2*q23-8*q12^2*q13^3*q23+8*n3*q12^2*q13^3*q23-16*M`j'^2*q12*q13^2*q23^2+16*M`j'^2*n3*q12*q13^2*q23^2+8*M`j'^2*q12^3*q13*q33-8*M`j'^2*n3*q12^3*q13*q33-12*q12^3*q13^2*q33+12*n3*q12^3*q13^2*q33-12*q12^2*q13^2*q23*q33+12*n3*q12^2*q13^2*q23*q33-8*M`j'^2*q12*q13*q23^2*q33+8*M`j'^2*n3*q12*q13*q23^2*q33+4*M`j'^2*q12^3*q33^2-4*M`j'^2*n3*q12^3*q33^2-6*q12^3*q13*q33^2+6*n3*q12^3*q13*q33^2+4*M`j'^2*q12^2*q23*q33^2-4*M`j'^2*n3*q12^2*q23*q33^2-6*q12^2*q13*q23*q33^2+6*n3*q12^2*q13*q23*q33^2-q12^3*q33^3+n3*q12^3*q33^3-q12^2*q23*q33^3+n3*q12^2*q23*q33^3)); Identify,ifmatch->jump mbox1l(n1?pos_,n2?{,>1},n3?pos_,n4?pos_) = mbox1l(n1,-1+n2,1+n3,-1+n4)*prf(-2*M`j'^2*n3*q13,-4*q12*q13^2+4*n2*q12*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n2*q13*q23+4*M`j'^2*q12*q33-4*M`j'^2*n2*q12*q33-4*q12*q13*q33+4*n2*q12*q13*q33-q12*q33^2+n2*q12*q33^2)+mbox1l(n1,-1+n2,-1+n3,1+n4)*prf(-2*M`j'^2*n4*q13,-4*q12*q13^2+4*n2*q12*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n2*q13*q23+4*M`j'^2*q12*q33-4*M`j'^2*n2*q12*q33-4*q12*q13*q33+4*n2*q12*q13*q33-q12*q33^2+n2*q12*q33^2)+mbox1l(n1,n2,n3,-1+n4)*prf(4*M`j'^2*q12*q13-4*M`j'^2*q13^2-4*q12*q13^2-4*M`j'^2*q13*q23+4*M`j'^2*q12*q33-2*M`j'^2*q13*q33-4*q12*q13*q33-q12*q33^2,8*q12*q13^3+16*M`j'^2*q13^2*q23-8*M`j'^2*q12*q13*q33+12*q12*q13^2*q33+8*M`j'^2*q13*q23*q33-4*M`j'^2*q12*q33^2+6*q12*q13*q33^2+q12*q33^3)+mbox1l(n1,-2+n2,1+n3,n4)*prf(-8*M`j'^2*n3*q13^2+4*n3*q13^3-4*M`j'^2*n3*q13*q33+4*n3*q13^2*q33+n3*q13*q33^2,-4*q12^2*q13^2+4*n2*q12^2*q13^2-8*M`j'^2*q12*q13*q23+8*M`j'^2*n2*q12*q13*q23-4*q12*q13^2*q23+4*n2*q12*q13^2*q23-8*M`j'^2*q13*q23^2+8*M`j'^2*n2*q13*q23^2+4*M`j'^2*q12^2*q33-4*M`j'^2*n2*q12^2*q33-4*q12^2*q13*q33+4*n2*q12^2*q13*q33+4*M`j'^2*q12*q23*q33-4*M`j'^2*n2*q12*q23*q33-4*q12*q13*q23*q33+4*n2*q12*q13*q23*q33-q12^2*q33^2+n2*q12^2*q33^2-q12*q23*q33^2+n2*q12*q23*q33^2)+mbox1l(1+n1,-1+n2,n3,-1+n4)*prf(8*M`j'^2*n1*q12*q13^2-8*n1*q12*q13^3-8*M`j'^2*n1*q13^2*q23+6*M`j'^2*n1*q12*q13*q33-8*n1*q12*q13^2*q33-2*M`j'^2*n1*q13*q23*q33-2*n1*q12*q13*q33^2,-8*q12^2*q13^3+8*n2*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n2*q12*q13^2*q23-8*q12*q13^3*q23+8*n2*q12*q13^3*q23-16*M`j'^2*q13^2*q23^2+16*M`j'^2*n2*q13^2*q23^2+8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n2*q12^2*q13*q33-12*q12^2*q13^2*q33+12*n2*q12^2*q13^2*q33-12*q12*q13^2*q23*q33+12*n2*q12*q13^2*q23*q33-8*M`j'^2*q13*q23^2*q33+8*M`j'^2*n2*q13*q23^2*q33+4*M`j'^2*q12^2*q33^2-4*M`j'^2*n2*q12^2*q33^2-6*q12^2*q13*q33^2+6*n2*q12^2*q13*q33^2+4*M`j'^2*q12*q23*q33^2-4*M`j'^2*n2*q12*q23*q33^2-6*q12*q13*q23*q33^2+6*n2*q12*q13*q23*q33^2-q12^2*q33^3+n2*q12^2*q33^3-q12*q23*q33^3+n2*q12*q23*q33^3)+mbox1l(-1+n1,n2,n3,n4)*prf(-4*M`j'^2*q12^2*q13+4*q12^2*q13^2+4*q12*q13^2*q23+4*M`j'^2*q13*q23^2-4*M`j'^2*q12^2*q33+4*q12^2*q13*q33-4*M`j'^2*q12*q23*q33+4*q12*q13*q23*q33+q12^2*q33^2+q12*q23*q33^2,8*q12^2*q13^3+16*M`j'^2*q12*q13^2*q23-8*M`j'^2*q12^2*q13*q33+12*q12^2*q13^2*q33+8*M`j'^2*q12*q13*q23*q33-4*M`j'^2*q12^2*q33^2+6*q12^2*q13*q33^2+q12^2*q33^3)+mbox1l(n1,n2,-1+n3,n4)*prf(8*M`j'^2*q12^2*q13^2+16*M`j'^2*q12*q13^3-4*q12^2*q13^3-8*q12*q13^4+4*M`j'^2*q12^2*q13*q23+20*M`j'^2*q12*q13^2*q23-4*q12^2*q13^2*q23-12*q12*q13^3*q23-4*M`j'^2*q13^2*q23^2-4*q12*q13^2*q23^2-4*M`j'^2*q13*q23^3-2*M`j'^2*q12^2*q13*q33+16*M`j'^2*q12*q13^2*q33-12*q12*q13^3*q33+4*M`j'^2*q12^2*q23*q33+14*M`j'^2*q12*q13*q23*q33-4*q12^2*q13*q23*q33-12*q12*q13^2*q23*q33+4*M`j'^2*q12*q23^2*q33-4*q12*q13*q23^2*q33-4*M`j'^2*q12^2*q33^2+4*M`j'^2*q12*q13*q33^2+3*q12^2*q13*q33^2-6*q12*q13^2*q33^2-q12^2*q23*q33^2-3*q12*q13*q23*q33^2-q12*q23^2*q33^2+q12^2*q33^3-q12*q13*q33^3,8*q12^3*q13^3+16*M`j'^2*q12^2*q13^2*q23+8*q12^2*q13^3*q23+16*M`j'^2*q12*q13^2*q23^2-8*M`j'^2*q12^3*q13*q33+12*q12^3*q13^2*q33+12*q12^2*q13^2*q23*q33+8*M`j'^2*q12*q13*q23^2*q33-4*M`j'^2*q12^3*q33^2+6*q12^3*q13*q33^2-4*M`j'^2*q12^2*q23*q33^2+6*q12^2*q13*q23*q33^2+q12^3*q33^3+q12^2*q23*q33^3)+mbox1l(1+n1,-1+n2,-1+n3,n4)*prf(-4*M`j'^2*n1*q12^2*q13^2+4*M`j'^2*n1*q12*q13^3+4*M`j'^2*n1*q13^3*q23+4*M`j'^2*n1*q13^2*q23^2+2*M`j'^2*n1*q12^2*q13*q33+8*M`j'^2*n1*q12*q13^2*q33-4*n1*q12^2*q13^2*q33-4*n1*q12*q13^3*q33-6*M`j'^2*n1*q12*q13*q23*q33+4*M`j'^2*n1*q12^2*q33^2+4*M`j'^2*n1*q12*q13*q33^2-4*n1*q12^2*q13*q33^2-4*n1*q12*q13^2*q33^2-n1*q12^2*q33^3-n1*q12*q13*q33^3,-8*q12^3*q13^3+8*n2*q12^3*q13^3-16*M`j'^2*q12^2*q13^2*q23+16*M`j'^2*n2*q12^2*q13^2*q23-8*q12^2*q13^3*q23+8*n2*q12^2*q13^3*q23-16*M`j'^2*q12*q13^2*q23^2+16*M`j'^2*n2*q12*q13^2*q23^2+8*M`j'^2*q12^3*q13*q33-8*M`j'^2*n2*q12^3*q13*q33-12*q12^3*q13^2*q33+12*n2*q12^3*q13^2*q33-12*q12^2*q13^2*q23*q33+12*n2*q12^2*q13^2*q23*q33-8*M`j'^2*q12*q13*q23^2*q33+8*M`j'^2*n2*q12*q13*q23^2*q33+4*M`j'^2*q12^3*q33^2-4*M`j'^2*n2*q12^3*q33^2-6*q12^3*q13*q33^2+6*n2*q12^3*q13*q33^2+4*M`j'^2*q12^2*q23*q33^2-4*M`j'^2*n2*q12^2*q23*q33^2-6*q12^2*q13*q23*q33^2+6*n2*q12^2*q13*q23*q33^2-q12^3*q33^3+n2*q12^3*q33^3-q12^2*q23*q33^3+n2*q12^2*q23*q33^3)+mbox1l(1+n1,-2+n2,n3,n4)*prf(-4*M`j'^2*n1*q12*q13^3-4*M`j'^2*n1*q13^3*q23-8*M`j'^2*n1*q12*q13^2*q33+4*n1*q12*q13^3*q33-4*M`j'^2*n1*q12*q13*q33^2+4*n1*q12*q13^2*q33^2+n1*q12*q13*q33^3,-8*q12^3*q13^3+8*n2*q12^3*q13^3-16*M`j'^2*q12^2*q13^2*q23+16*M`j'^2*n2*q12^2*q13^2*q23-8*q12^2*q13^3*q23+8*n2*q12^2*q13^3*q23-16*M`j'^2*q12*q13^2*q23^2+16*M`j'^2*n2*q12*q13^2*q23^2+8*M`j'^2*q12^3*q13*q33-8*M`j'^2*n2*q12^3*q13*q33-12*q12^3*q13^2*q33+12*n2*q12^3*q13^2*q33-12*q12^2*q13^2*q23*q33+12*n2*q12^2*q13^2*q23*q33-8*M`j'^2*q12*q13*q23^2*q33+8*M`j'^2*n2*q12*q13*q23^2*q33+4*M`j'^2*q12^3*q33^2-4*M`j'^2*n2*q12^3*q33^2-6*q12^3*q13*q33^2+6*n2*q12^3*q13*q33^2+4*M`j'^2*q12^2*q23*q33^2-4*M`j'^2*n2*q12^2*q23*q33^2-6*q12^2*q13*q23*q33^2+6*n2*q12^2*q13*q23*q33^2-q12^3*q33^3+n2*q12^3*q33^3-q12^2*q23*q33^3+n2*q12^2*q23*q33^3)+mbox1l(n1,-1+n2,n3,n4)*(tmpprf(ep,1)*prf(-8*q12^2*q13^3-8*q12*q13^3*q23-8*q12^2*q13^2*q33-8*q12*q13^2*q23*q33-2*q12^2*q13*q33^2-2*q12*q13*q23*q33^2,-8*q12^3*q13^3+8*n2*q12^3*q13^3-16*M`j'^2*q12^2*q13^2*q23+16*M`j'^2*n2*q12^2*q13^2*q23-8*q12^2*q13^3*q23+8*n2*q12^2*q13^3*q23-16*M`j'^2*q12*q13^2*q23^2+16*M`j'^2*n2*q12*q13^2*q23^2+8*M`j'^2*q12^3*q13*q33-8*M`j'^2*n2*q12^3*q13*q33-12*q12^3*q13^2*q33+12*n2*q12^3*q13^2*q33-12*q12^2*q13^2*q23*q33+12*n2*q12^2*q13^2*q23*q33-8*M`j'^2*q12*q13*q23^2*q33+8*M`j'^2*n2*q12*q13*q23^2*q33+4*M`j'^2*q12^3*q33^2-4*M`j'^2*n2*q12^3*q33^2-6*q12^3*q13*q33^2+6*n2*q12^3*q13*q33^2+4*M`j'^2*q12^2*q23*q33^2-4*M`j'^2*n2*q12^2*q23*q33^2-6*q12^2*q13*q23*q33^2+6*n2*q12^2*q13*q23*q33^2-q12^3*q33^3+n2*q12^3*q33^3-q12^2*q23*q33^3+n2*q12^2*q23*q33^3)+prf(4*M`j'^2*q12^2*q13^2-4*M`j'^2*n1*q12^2*q13^2-4*M`j'^2*n2*q12^2*q13^2+4*M`j'^2*n3*q12^2*q13^2+4*M`j'^2*n4*q12^2*q13^2+16*M`j'^2*q12*q13^3-16*M`j'^2*n2*q12*q13^3+16*M`j'^2*n3*q12*q13^3+20*q12^2*q13^3-4*n2*q12^2*q13^3-8*n3*q12^2*q13^3-8*n4*q12^2*q13^3-8*q12*q13^4+8*n2*q12*q13^4-8*n3*q12*q13^4+16*M`j'^2*q12*q13^2*q23+8*M`j'^2*n1*q12*q13^2*q23-16*M`j'^2*n2*q12*q13^2*q23+4*M`j'^2*n3*q12*q13^2*q23+4*M`j'^2*n4*q12*q13^2*q23+12*q12*q13^3*q23-8*n1*q12*q13^3*q23+4*n2*q12*q13^3*q23-8*n3*q12*q13^3*q23-8*n4*q12*q13^3*q23-4*M`j'^2*q13^2*q23^2-4*M`j'^2*n1*q13^2*q23^2+4*M`j'^2*n2*q13^2*q23^2-4*M`j'^2*q12^2*q13*q33-8*M`j'^2*n1*q12^2*q13*q33+4*M`j'^2*n2*q12^2*q13*q33+2*M`j'^2*n3*q12^2*q13*q33+2*M`j'^2*n4*q12^2*q13*q33+16*M`j'^2*q12*q13^2*q33-16*M`j'^2*n2*q12*q13^2*q33+16*M`j'^2*n3*q12*q13^2*q33+24*q12^2*q13^2*q33+4*n1*q12^2*q13^2*q33-8*n2*q12^2*q13^2*q33-8*n3*q12^2*q13^2*q33-8*n4*q12^2*q13^2*q33-12*q12*q13^3*q33+12*n2*q12*q13^3*q33-12*n3*q12*q13^3*q33+12*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n1*q12*q13*q23*q33-12*M`j'^2*n2*q12*q13*q23*q33+2*M`j'^2*n3*q12*q13*q23*q33+2*M`j'^2*n4*q12*q13*q23*q33+12*q12*q13^2*q23*q33-8*n1*q12*q13^2*q23*q33+4*n2*q12*q13^2*q23*q33-8*n3*q12*q13^2*q23*q33-8*n4*q12*q13^2*q23*q33-4*M`j'^2*q12^2*q33^2-4*M`j'^2*n1*q12^2*q33^2+4*M`j'^2*n2*q12^2*q33^2+4*M`j'^2*q12*q13*q33^2-4*M`j'^2*n2*q12*q13*q33^2+4*M`j'^2*n3*q12*q13*q33^2+9*q12^2*q13*q33^2+4*n1*q12^2*q13*q33^2-5*n2*q12^2*q13*q33^2-2*n3*q12^2*q13*q33^2-2*n4*q12^2*q13*q33^2-6*q12*q13^2*q33^2+6*n2*q12*q13^2*q33^2-6*n3*q12*q13^2*q33^2+3*q12*q13*q23*q33^2-2*n1*q12*q13*q23*q33^2+n2*q12*q13*q23*q33^2-2*n3*q12*q13*q23*q33^2-2*n4*q12*q13*q23*q33^2+q12^2*q33^3+n1*q12^2*q33^3-n2*q12^2*q33^3-q12*q13*q33^3+n2*q12*q13*q33^3-n3*q12*q13*q33^3,-8*q12^3*q13^3+8*n2*q12^3*q13^3-16*M`j'^2*q12^2*q13^2*q23+16*M`j'^2*n2*q12^2*q13^2*q23-8*q12^2*q13^3*q23+8*n2*q12^2*q13^3*q23-16*M`j'^2*q12*q13^2*q23^2+16*M`j'^2*n2*q12*q13^2*q23^2+8*M`j'^2*q12^3*q13*q33-8*M`j'^2*n2*q12^3*q13*q33-12*q12^3*q13^2*q33+12*n2*q12^3*q13^2*q33-12*q12^2*q13^2*q23*q33+12*n2*q12^2*q13^2*q23*q33-8*M`j'^2*q12*q13*q23^2*q33+8*M`j'^2*n2*q12*q13*q23^2*q33+4*M`j'^2*q12^3*q33^2-4*M`j'^2*n2*q12^3*q33^2-6*q12^3*q13*q33^2+6*n2*q12^3*q13*q33^2+4*M`j'^2*q12^2*q23*q33^2-4*M`j'^2*n2*q12^2*q23*q33^2-6*q12^2*q13*q23*q33^2+6*n2*q12^2*q13*q23*q33^2-q12^3*q33^3+n2*q12^3*q33^3-q12^2*q23*q33^3+n2*q12^2*q23*q33^3)); Identify,ifmatch->jump mbox1l(n1?{,>1},n2?pos_,n3?pos_,n4?pos_) = mbox1l(-1+n1,n2,1+n3,-1+n4)*prf(2*M`j'^2*n3*q12+2*M`j'^2*n3*q23,-4*q12*q13^2+4*n1*q12*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23+4*M`j'^2*q12*q33-4*M`j'^2*n1*q12*q33-4*q12*q13*q33+4*n1*q12*q13*q33-q12*q33^2+n1*q12*q33^2)+mbox1l(-1+n1,n2,-1+n3,1+n4)*prf(2*M`j'^2*n4*q12+2*M`j'^2*n4*q23,-4*q12*q13^2+4*n1*q12*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23+4*M`j'^2*q12*q33-4*M`j'^2*n1*q12*q33-4*q12*q13*q33+4*n1*q12*q13*q33-q12*q33^2+n1*q12*q33^2)+mbox1l(-2+n1,1+n2,n3,n4)*prf(4*M`j'^2*n2*q12^3+12*M`j'^2*n2*q12^2*q23+12*M`j'^2*n2*q12*q23^2+4*M`j'^2*n2*q23^3,-8*q12^2*q13^3+8*n1*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n1*q12*q13^2*q23+8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n1*q12^2*q13*q33-12*q12^2*q13^2*q33+12*n1*q12^2*q13^2*q33-8*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n1*q12*q13*q23*q33+4*M`j'^2*q12^2*q33^2-4*M`j'^2*n1*q12^2*q33^2-6*q12^2*q13*q33^2+6*n1*q12^2*q13*q33^2-q12^2*q33^3+n1*q12^2*q33^3)+mbox1l(-1+n1,1+n2,n3,-1+n4)*prf(-4*M`j'^2*n2*q12^2+4*M`j'^2*n2*q12*q13-8*M`j'^2*n2*q12*q23+4*M`j'^2*n2*q13*q23-4*M`j'^2*n2*q23^2+2*M`j'^2*n2*q12*q33+2*M`j'^2*n2*q23*q33,-8*q12*q13^3+8*n1*q12*q13^3-16*M`j'^2*q13^2*q23+16*M`j'^2*n1*q13^2*q23+8*M`j'^2*q12*q13*q33-8*M`j'^2*n1*q12*q13*q33-12*q12*q13^2*q33+12*n1*q12*q13^2*q33-8*M`j'^2*q13*q23*q33+8*M`j'^2*n1*q13*q23*q33+4*M`j'^2*q12*q33^2-4*M`j'^2*n1*q12*q33^2-6*q12*q13*q33^2+6*n1*q12*q13*q33^2-q12*q33^3+n1*q12*q33^3)+mbox1l(-1+n1,-1+n2,1+n3,n4)*prf(8*M`j'^2*n3*q13-4*n3*q13^2+4*M`j'^2*n3*q33-4*n3*q13*q33-n3*q33^2,-4*q12*q13^2+4*n1*q12*q13^2-8*M`j'^2*q13*q23+8*M`j'^2*n1*q13*q23+4*M`j'^2*q12*q33-4*M`j'^2*n1*q12*q33-4*q12*q13*q33+4*n1*q12*q13*q33-q12*q33^2+n1*q12*q33^2)+mbox1l(n1,n2,n3,-1+n4)*prf(-8*M`j'^2*q12*q13+4*q12*q13^2-2*M`j'^2*q12*q33+4*q12*q13*q33+2*M`j'^2*q23*q33+q12*q33^2,8*q12*q13^3+16*M`j'^2*q13^2*q23-8*M`j'^2*q12*q13*q33+12*q12*q13^2*q33+8*M`j'^2*q13*q23*q33-4*M`j'^2*q12*q33^2+6*q12*q13*q33^2+q12*q33^3)+mbox1l(n1,-1+n2,n3,n4)*prf(4*M`j'^2*q12*q13^2-4*q12*q13^3-4*M`j'^2*q13^2*q23+12*M`j'^2*q12*q13*q33-8*q12*q13^2*q33+4*M`j'^2*q12*q33^2-5*q12*q13*q33^2-q12*q33^3,8*q12^2*q13^3+16*M`j'^2*q12*q13^2*q23-8*M`j'^2*q12^2*q13*q33+12*q12^2*q13^2*q33+8*M`j'^2*q12*q13*q23*q33-4*M`j'^2*q12^2*q33^2+6*q12^2*q13*q33^2+q12^2*q33^3)+mbox1l(n1,n2,-1+n3,n4)*prf(4*M`j'^2*q12^2*q13-4*M`j'^2*q12*q13^2+4*q12*q13^3+4*M`j'^2*q13^2*q23+4*q12*q13^2*q23+4*M`j'^2*q13*q23^2-2*M`j'^2*q12^2*q33-12*M`j'^2*q12*q13*q33+8*q12*q13^2*q33-6*M`j'^2*q12*q23*q33+4*q12*q13*q23*q33-4*M`j'^2*q12*q33^2+5*q12*q13*q33^2+q12*q23*q33^2+q12*q33^3,8*q12^2*q13^3+16*M`j'^2*q12*q13^2*q23-8*M`j'^2*q12^2*q13*q33+12*q12^2*q13^2*q33+8*M`j'^2*q12*q13*q23*q33-4*M`j'^2*q12^2*q33^2+6*q12^2*q13*q33^2+q12^2*q33^3)+mbox1l(-1+n1,1+n2,-1+n3,n4)*prf(-8*M`j'^2*n2*q12^2*q13-16*M`j'^2*n2*q12*q13^2+8*n2*q12^2*q13^2+8*n2*q12*q13^3-4*M`j'^2*n2*q12^2*q23-12*M`j'^2*n2*q12*q13*q23+8*n2*q12*q13^2*q23-8*M`j'^2*n2*q12*q23^2-4*M`j'^2*n2*q13*q23^2-4*M`j'^2*n2*q23^3-2*M`j'^2*n2*q12^2*q33-16*M`j'^2*n2*q12*q13*q33+8*n2*q12^2*q13*q33+12*n2*q12*q13^2*q33-2*M`j'^2*n2*q12*q23*q33+8*n2*q12*q13*q23*q33-4*M`j'^2*n2*q12*q33^2+2*n2*q12^2*q33^2+6*n2*q12*q13*q33^2+2*n2*q12*q23*q33^2+n2*q12*q33^3,-8*q12^2*q13^3+8*n1*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n1*q12*q13^2*q23+8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n1*q12^2*q13*q33-12*q12^2*q13^2*q33+12*n1*q12^2*q13^2*q33-8*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n1*q12*q13*q23*q33+4*M`j'^2*q12^2*q33^2-4*M`j'^2*n1*q12^2*q33^2-6*q12^2*q13*q33^2+6*n1*q12^2*q13*q33^2-q12^2*q33^3+n1*q12^2*q33^3)+mbox1l(-1+n1,n2,n3,n4)*(tmpprf(ep,1)*prf(8*q12^2*q13^2+8*q12*q13^2*q23+8*q12^2*q13*q33+8*q12*q13*q23*q33+2*q12^2*q33^2+2*q12*q23*q33^2,-8*q12^2*q13^3+8*n1*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n1*q12*q13^2*q23+8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n1*q12^2*q13*q33-12*q12^2*q13^2*q33+12*n1*q12^2*q13^2*q33-8*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n1*q12*q13*q23*q33+4*M`j'^2*q12^2*q33^2-4*M`j'^2*n1*q12^2*q33^2-6*q12^2*q13*q33^2+6*n1*q12^2*q13*q33^2-q12^2*q33^3+n1*q12^2*q33^3)+prf(-4*M`j'^2*q12^2*q13+4*M`j'^2*n1*q12^2*q13+4*M`j'^2*n2*q12^2*q13-4*M`j'^2*n3*q12^2*q13-4*M`j'^2*n4*q12^2*q13+16*M`j'^2*n2*q12*q13^2-16*M`j'^2*n3*q12*q13^2-20*q12^2*q13^2+4*n1*q12^2*q13^2+8*n3*q12^2*q13^2+8*n4*q12^2*q13^2-8*n2*q12*q13^3+8*n3*q12*q13^3+8*M`j'^2*n2*q12*q13*q23-4*M`j'^2*n3*q12*q13*q23-4*M`j'^2*n4*q12*q13*q23-20*q12*q13^2*q23+4*n1*q12*q13^2*q23+8*n3*q12*q13^2*q23+8*n4*q12*q13^2*q23+4*M`j'^2*q13*q23^2-4*M`j'^2*n1*q13*q23^2+4*M`j'^2*n2*q13*q23^2-4*M`j'^2*q12^2*q33+4*M`j'^2*n1*q12^2*q33-2*M`j'^2*n3*q12^2*q33-2*M`j'^2*n4*q12^2*q33+16*M`j'^2*n2*q12*q13*q33-16*M`j'^2*n3*q12*q13*q33-20*q12^2*q13*q33+4*n1*q12^2*q13*q33+8*n3*q12^2*q13*q33+8*n4*q12^2*q13*q33-12*n2*q12*q13^2*q33+12*n3*q12*q13^2*q33-4*M`j'^2*q12*q23*q33+4*M`j'^2*n1*q12*q23*q33-2*M`j'^2*n3*q12*q23*q33-2*M`j'^2*n4*q12*q23*q33-20*q12*q13*q23*q33+4*n1*q12*q13*q23*q33+8*n3*q12*q13*q23*q33+8*n4*q12*q13*q23*q33+4*M`j'^2*n2*q12*q33^2-4*M`j'^2*n3*q12*q33^2-5*q12^2*q33^2+n1*q12^2*q33^2+2*n3*q12^2*q33^2+2*n4*q12^2*q33^2-6*n2*q12*q13*q33^2+6*n3*q12*q13*q33^2-5*q12*q23*q33^2+n1*q12*q23*q33^2+2*n3*q12*q23*q33^2+2*n4*q12*q23*q33^2-n2*q12*q33^3+n3*q12*q33^3,-8*q12^2*q13^3+8*n1*q12^2*q13^3-16*M`j'^2*q12*q13^2*q23+16*M`j'^2*n1*q12*q13^2*q23+8*M`j'^2*q12^2*q13*q33-8*M`j'^2*n1*q12^2*q13*q33-12*q12^2*q13^2*q33+12*n1*q12^2*q13^2*q33-8*M`j'^2*q12*q13*q23*q33+8*M`j'^2*n1*q12*q13*q23*q33+4*M`j'^2*q12^2*q33^2-4*M`j'^2*n1*q12^2*q33^2-6*q12^2*q13*q33^2+6*n1*q12^2*q13*q33^2-q12^2*q33^3+n1*q12^2*q33^3)); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?pos_,n4?{,>1}) = mbox1l(1+n1,-1+n2,1+n3,-1+n4)*prf(-(n3*q13),-q12+n4*q12-q23+n4*q23)+mbox1l(2+n1,n2,n3,-2+n4)*prf(2*q12*q13+2*n1*q12*q13,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,n2,-1+n3,n4)*prf(q33,2*q13+q33)+mbox1l(2+n1,-1+n2,n3,-1+n4)*prf(-(q13*q33)-n1*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(2+n1,n2,-1+n3,-1+n4)*prf(q12*q33+n1*q12*q33+q13*q33+n1*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n2*q13^2+2*n2*q13*q23-n2*q12*q33+n2*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33)+mbox1l(1+n1,n2,n3,-1+n4)*prf(-4*q12*q13-2*n1*q12*q13+2*n4*q12*q13-2*n2*q13^2+2*n3*q13^2-2*q13*q23-2*n2*q13*q23+2*n4*q13*q23-q12*q33-n1*q12*q33+n2*q12*q33-n2*q13*q33+n3*q13*q33,-2*q12*q13+2*n4*q12*q13-2*q13*q23+2*n4*q13*q23-q12*q33+n4*q12*q33-q23*q33+n4*q23*q33); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?{,>1},n4?pos_) = mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n2*q12,-2*q13+2*n3*q13-q33+n3*q33)+mbox1l(1+n1,-1+n2,n3,n4)*prf(-q13,q12+q23)+mbox1l(2+n1,n2,-1+n3,-1+n4)*prf(2*q12*q13+2*n1*q12*q13,-2*q12*q13+2*n3*q12*q13-2*q13*q23+2*n3*q13*q23-q12*q33+n3*q12*q33-q23*q33+n3*q23*q33)+mbox1l(n1,1+n2,-1+n3,n4)*prf(-2*n2*q12-2*n2*q13-2*n2*q23-n2*q33,-2*q13+2*n3*q13-q33+n3*q33)+mbox1l(2+n1,-1+n2,-1+n3,n4)*prf(-(q13*q33)-n1*q13*q33,-2*q12*q13+2*n3*q12*q13-2*q13*q23+2*n3*q13*q23-q12*q33+n3*q12*q33-q23*q33+n3*q23*q33)+mbox1l(2+n1,n2,-2+n3,n4)*prf(2*q12*q33+2*n1*q12*q33+q13*q33+n1*q13*q33+q23*q33+n1*q23*q33,-2*q12*q13+2*n3*q12*q13-2*q13*q23+2*n3*q13*q23-q12*q33+n3*q12*q33-q23*q33+n3*q23*q33)+mbox1l(1+n1,1+n2,-2+n3,n4)*prf(2*n2*q12*q13+2*n2*q13^2+2*n2*q12*q23+4*n2*q13*q23+2*n2*q23^2+n2*q13*q33+n2*q23*q33,-2*q12*q13+2*n3*q12*q13-2*q13*q23+2*n3*q13*q23-q12*q33+n3*q12*q33-q23*q33+n3*q23*q33)+mbox1l(1+n1,n2,-1+n3,n4)*prf(-4*q12*q13-2*n1*q12*q13+2*n3*q12*q13-2*q13^2-2*n2*q13^2+2*n3*q13^2-2*q13*q23-2*n2*q13*q23+2*n3*q13*q23-3*q12*q33-2*n1*q12*q33+n2*q12*q33+n3*q12*q33-q13*q33-n2*q13*q33+n3*q13*q33-2*q23*q33-n1*q23*q33+n3*q23*q33,-2*q12*q13+2*n3*q12*q13-2*q13*q23+2*n3*q13*q23-q12*q33+n3*q12*q33-q23*q33+n3*q23*q33); Identify,ifmatch->jump mbox1l(n1?pos_,n2?pos_,n3?pos_,n4?{,>1}) = mbox1l(n1,n2,1+n3,-1+n4)*prf(n3,-1+n4)+mbox1l(1+n1,1+n2,n3,-2+n4)*prf(-2*n1*q12,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(1+n1,n2,n3,-1+n4)*prf(n1*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(n1,1+n2,-1+n3,n4)*prf(2*q12+2*q13+2*q23+q33,2*q13+q33)+mbox1l(1+n1,1+n2,-1+n3,-1+n4)*prf(2*n1*q12-n1*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(n1,2+n2,-1+n3,-1+n4)*prf(-2*q12-2*n2*q12-2*q13-2*n2*q13-2*q23-2*n2*q23-q33-n2*q33,-2*q13+2*n4*q13-q33+n4*q33)+mbox1l(n1,1+n2,n3,-1+n4)*prf(4*q12+2*n2*q12-2*n4*q12+2*q13+2*n2*q13-2*n3*q13+4*q23+2*n2*q23-2*n4*q23+q33+n2*q33-n3*q33,-2*q13+2*n4*q13-q33+n4*q33); Label jump; #call lrttMergeIndices(mbox1l) * Mapped Sectors: Identify mbox1l(n1?neg0_,n2?neg0_,n3?pos_,n4?neg0_) = mbox1l(0,0,n4,n3)*(-mbox1l(-1,0,0,0)+mbox1l(0,0,-1,0)+mbox1l(0,0,0,-1)+2*q13*mbox1l(0,0,0,0))^(-n1)*(-mbox1l(0,-1,0,0)+mbox1l(0,0,-1,0)+mbox1l(0,0,0,-1)-2*prf(q12+q23,1)*mbox1l(0,0,0,0))^(-n2); #call lrttMergeIndices(mbox1l) Identify mbox1l(n1?neg0_,n2?pos_,n3?neg0_,n4?neg0_) = mbox1l(0,n4,0,n2)*(mbox1l(0,-1,0,0)-mbox1l(0,0,-1,0)+mbox1l(0,0,0,-1)+2*prf(q12+q23,1)*mbox1l(0,0,0,0))^(-n3)*(-mbox1l(-1,0,0,0)+mbox1l(0,-1,0,0)+mbox1l(0,0,0,-1)+2*prf(q13+q23,1)*mbox1l(0,0,0,0))^(-n1); #call lrttMergeIndices(mbox1l) Identify mbox1l(n1?pos_,n2?neg0_,n3?neg0_,n4?neg0_) = mbox1l(n4,0,0,n1)*(mbox1l(-1,0,0,0)-mbox1l(0,0,-1,0)+mbox1l(0,0,0,-1)-2*q13*mbox1l(0,0,0,0))^(-n3)*(mbox1l(-1,0,0,0)-mbox1l(0,-1,0,0)+mbox1l(0,0,0,-1)-2*prf(2*q12+q13+q23,1)*mbox1l(0,0,0,0))^(-n2); #call lrttMergeIndices(mbox1l) #call lrttKin2Prf Identify M`j'^n1? = prf(M`j'^n1,1); #ifdef `MBOX1Lq33EQq44' Multiply replace_(q23,-q12-q13); #endif * Hide MIs: Identify mbox1l(0,0,0,1) = mbox1lm`j'm(0,0,0,1); Identify mbox1l(0,0,1,1) = mbox1lm`j'm(0,0,1,1); Identify mbox1l(0,1,0,1) = mbox1lm`j'm(0,1,0,1); Identify mbox1l(1,0,0,1) = mbox1lm`j'm(1,0,0,1); Identify mbox1l(1,1,0,0) = mbox1lm`j'm(1,1,0,0); Identify mbox1l(0,1,1,1) = mbox1lm`j'm(0,1,1,1); Identify mbox1l(1,0,1,1) = mbox1lm`j'm(1,0,1,1); Identify mbox1l(1,1,0,1) = mbox1lm`j'm(1,1,0,1); Identify mbox1l(1,1,1,0) = mbox1lm`j'm(1,1,1,0); Identify mbox1l(1,1,1,1) = mbox1lm`j'm(1,1,1,1); * Zero Sectors: Identify mbox1l(n1?neg0_,n2?neg0_,n3?neg0_,n4?neg0_) = 0; If (Count(mbox1l,1) > 0) Redefine red "0"; .sort #enddo * Merge the extra ep-dependent rational polys into the rest, now that * the reduction is done. #message Merge tmpprf into prf... Identify tmpprf(n1?,n2?) = prf(n1,n2); .sort * Check: Drop; Local check = test - ( + mbox1lm1m(0,0,0,1) * ( + prf(4*q33^3*M1^2 - q33^4 + 20*q13*q33^2*M1^2 - 4*q13*q33^3 - 16* q12*q33^2*M1^2 + 3*q12*q33^3 - 40*q12*q13*q33*M1^2 + 6*q12*q13*q33^2 + 8*q12^2*q33*M1^2 + 16*q12^2*q13*M1^2 - 4*ep*q33^3*M1^2 + ep*q33^4 - 20*ep*q13*q33^2*M1^2 + 4*ep*q13*q33^3 + 16*ep*q12*q33^2*M1^2 - 3* ep*q12*q33^3 + 40*ep*q12*q13*q33*M1^2 - 6*ep*q12*q13*q33^2 - 8*ep* q12^2*q33*M1^2 - 16*ep*q12^2*q13*M1^2,512*q13^2*q33*M1^10 - 256*q13^2 *q33^2*M1^8 + 32*q13^2*q33^3*M1^6 + 256*q12*q33^2*M1^10 - 192*q12* q33^3*M1^8 + 48*q12*q33^4*M1^6 - 4*q12*q33^5*M1^4 + 512*q12*q13*q33* M1^10 - 512*q12*q13*q33^2*M1^8 + 160*q12*q13*q33^3*M1^6 - 16*q12*q13* q33^4*M1^4 - 256*q12*q13^2*M1^10 - 448*q12*q13^2*q33*M1^8 + 256*q12* q13^2*q33^2*M1^6 - 32*q12*q13^2*q33^3*M1^4 - 128*q12^2*q33*M1^10 - 64 *q12^2*q33^2*M1^8 + 88*q12^2*q33^3*M1^6 - 24*q12^2*q33^4*M1^4 + 2* q12^2*q33^5*M1^2 - 256*q12^2*q13*M1^10 - 64*q12^2*q13*q33*M1^8 + 224* q12^2*q13*q33^2*M1^6 - 80*q12^2*q13*q33^3*M1^4 + 8*q12^2*q13*q33^4* M1^2 + 256*q12^2*q13^2*M1^8 + 64*q12^2*q13^2*q33*M1^6 - 64*q12^2* q13^2*q33^2*M1^4 + 8*q12^2*q13^2*q33^3*M1^2 + 64*q12^3*q33*M1^8 - 32* q12^3*q33^2*M1^6 + 4*q12^3*q33^3*M1^4 + 128*q12^3*q13*M1^8 - 96*q12^3 *q13*q33*M1^6 + 16*q12^3*q13*q33^2*M1^4 - 64*q12^3*q13^2*M1^6 + 16* q12^3*q13^2*q33*M1^4) ) + mbox1lm1m(0,0,1,1) * ( + prf(q33^2 + 4*q13*q33 + 4*q13^2 - 2*ep*q33^2 - 8*ep*q13*q33 - 8*ep *q13^2,32*q13^3*M1^4 + 16*q12*q13*q33*M1^4 - 4*q12*q13*q33^2*M1^2 + 32*q12*q13^2*M1^4 - 16*q12*q13^2*q33*M1^2 - 16*q12*q13^3*M1^2) ) + mbox1lm1m(0,1,0,1) * ( + prf(2*q13*q33^2 - q12*q33^2 - 2*q12*q13*q33 - 4*ep*q13*q33^2 + 2* ep*q12*q33^2 + 4*ep*q12*q13*q33,64*q12*q13^2*q33*M1^4 - 16*q12*q13^2* q33^2*M1^2 + 32*q12^2*q33^2*M1^4 - 16*q12^2*q33^3*M1^2 + 2*q12^2* q33^4 + 64*q12^2*q13*q33*M1^4 - 48*q12^2*q13*q33^2*M1^2 + 8*q12^2*q13 *q33^3 - 32*q12^2*q13^2*M1^4 - 32*q12^2*q13^2*q33*M1^2 + 8*q12^2* q13^2*q33^2 - 16*q12^3*q33*M1^4 + 4*q12^3*q33^2*M1^2 - 32*q12^3*q13* M1^4 + 16*q12^3*q13*q33*M1^2 + 16*q12^3*q13^2*M1^2) ) + mbox1lm1m(0,1,1,1) * ( + prf( - 2*ep*q13^2,4*q12^2*q13^2 + 4*q12^2*q13*q33 - 8*q12^2*q13* M1^2 + q12^2*q33^2 - 4*q12^2*q33*M1^2 - 8*q12*q13^2*M1^2) ) + mbox1lm1m(1,0,0,1) * ( + prf( - 16*q13^2*q33^2*M1^4 + 4*q13^2*q33^3*M1^2 - 16*q12*q33^3* M1^4 + 8*q12*q33^4*M1^2 - q12*q33^5 - 40*q12*q13*q33^2*M1^4 + 26*q12* q13*q33^3*M1^2 - 4*q12*q13*q33^4 + 20*q12*q13^2*q33^2*M1^2 - 4*q12* q13^2*q33^3 + 8*q12^2*q33^2*M1^4 - 2*q12^2*q33^3*M1^2 + 16*q12^2*q13* q33*M1^4 - 8*q12^2*q13*q33^2*M1^2 - 8*q12^2*q13^2*q33*M1^2 + 32*ep* q13^2*q33^2*M1^4 - 8*ep*q13^2*q33^3*M1^2 + 32*ep*q12*q33^3*M1^4 - 16* ep*q12*q33^4*M1^2 + 2*ep*q12*q33^5 + 80*ep*q12*q13*q33^2*M1^4 - 52*ep *q12*q13*q33^3*M1^2 + 8*ep*q12*q13*q33^4 - 40*ep*q12*q13^2*q33^2*M1^2 + 8*ep*q12*q13^2*q33^3 - 16*ep*q12^2*q33^2*M1^4 + 4*ep*q12^2*q33^3* M1^2 - 32*ep*q12^2*q13*q33*M1^4 + 16*ep*q12^2*q13*q33^2*M1^2 + 16*ep* q12^2*q13^2*q33*M1^2,512*q12*q13^3*q33*M1^8 - 256*q12*q13^3*q33^2* M1^6 + 32*q12*q13^3*q33^3*M1^4 + 256*q12^2*q13*q33^2*M1^8 - 192*q12^2 *q13*q33^3*M1^6 + 48*q12^2*q13*q33^4*M1^4 - 4*q12^2*q13*q33^5*M1^2 + 512*q12^2*q13^2*q33*M1^8 - 512*q12^2*q13^2*q33^2*M1^6 + 160*q12^2* q13^2*q33^3*M1^4 - 16*q12^2*q13^2*q33^4*M1^2 - 256*q12^2*q13^3*M1^8 - 192*q12^2*q13^3*q33*M1^6 + 128*q12^2*q13^3*q33^2*M1^4 - 16*q12^2* q13^3*q33^3*M1^2 - 128*q12^3*q13*q33*M1^8 + 64*q12^3*q13*q33^2*M1^6 - 8*q12^3*q13*q33^3*M1^4 - 256*q12^3*q13^2*M1^8 + 192*q12^3*q13^2* q33*M1^6 - 32*q12^3*q13^2*q33^2*M1^4 + 128*q12^3*q13^3*M1^6 - 32* q12^3*q13^3*q33*M1^4) ) + mbox1lm1m(1,0,1,1) * ( + prf(4*ep*q12*q13^2 + 4*ep*q12*q13*q33 - 8*ep*q12*q13*M1^2 + ep*q12 *q33^2 - 4*ep*q12*q33*M1^2 - 4*ep*q13^2*M1^2, - 8*q12^2*q13^2*M1^2 - 8*q12^2*q13*q33*M1^2 + 16*q12^2*q13*M1^4 - 2*q12^2*q33^2*M1^2 + 8* q12^2*q33*M1^4 + 16*q12*q13^2*M1^4) ) + mbox1lm1m(1,1,0,0) * ( + prf( - 4*q33^2*M1^2 + q33^3 - 12*q13*q33*M1^2 + 4*q13*q33^2 + 4* q12*q33*M1^2 - q12*q33^2 + 8*q12*q13*M1^2 - 2*q12*q13*q33 + 8*ep* q33^2*M1^2 - 2*ep*q33^3 + 24*ep*q13*q33*M1^2 - 8*ep*q13*q33^2 - 8*ep* q12*q33*M1^2 + 2*ep*q12*q33^2 - 16*ep*q12*q13*M1^2 + 4*ep*q12*q13*q33 ,128*q13^2*q33*M1^6 - 32*q13^2*q33^2*M1^4 + 64*q12*q33^2*M1^6 - 32* q12*q33^3*M1^4 + 4*q12*q33^4*M1^2 + 128*q12*q13*q33*M1^6 - 96*q12*q13 *q33^2*M1^4 + 16*q12*q13*q33^3*M1^2 - 64*q12*q13^2*M1^6 - 128*q12* q13^2*q33*M1^4 + 32*q12*q13^2*q33^2*M1^2 - 32*q12^2*q33*M1^6 - 24* q12^2*q33^2*M1^4 + 16*q12^2*q33^3*M1^2 - 2*q12^2*q33^4 - 64*q12^2*q13 *M1^6 - 32*q12^2*q13*q33*M1^4 + 48*q12^2*q13*q33^2*M1^2 - 8*q12^2*q13 *q33^3 + 64*q12^2*q13^2*M1^4 + 32*q12^2*q13^2*q33*M1^2 - 8*q12^2* q13^2*q33^2 + 16*q12^3*q33*M1^4 - 4*q12^3*q33^2*M1^2 + 32*q12^3*q13* M1^4 - 16*q12^3*q13*q33*M1^2 - 16*q12^3*q13^2*M1^2) ) + mbox1lm1m(1,1,0,1) * ( + prf(2*ep*q12*q13*q33 - 4*ep*q12*q13*M1^2 + ep*q12*q33^2 - 4*ep*q12 *q33*M1^2 - 4*ep*q13*q33^2 + 8*ep*q13*q33*M1^2 - 2*ep*q33^3 + 8*ep* q33^2*M1^2,8*q12^2*q13^2*M1^2 + 8*q12^2*q13*q33*M1^2 - 16*q12^2*q13* M1^4 + 2*q12^2*q33^2*M1^2 - 8*q12^2*q33*M1^4 + 4*q12*q13^2*q33^2 - 16 *q12*q13^2*q33*M1^2 - 16*q12*q13^2*M1^4 + 4*q12*q13*q33^3 - 24*q12* q13*q33^2*M1^2 + 32*q12*q13*q33*M1^4 + q12*q33^4 - 8*q12*q33^3*M1^2 + 16*q12*q33^2*M1^4 - 8*q13^2*q33^2*M1^2 + 32*q13^2*q33*M1^4) ) + mbox1lm1m(1,1,1,0) * ( + prf(2*ep*q13, - 4*q12*q13^2 - 4*q12*q13*q33 + 8*q12*q13*M1^2 - q12 *q33^2 + 4*q12*q33*M1^2 + 8*q13^2*M1^2) ) + mbox1lm1m(1,1,1,1) * ( + prf(q13*q33 + 2*q13^2 + 2*ep*q13*q33 + 4*ep*q13^2,8*q13^2*M1^2 + 4 *q12*q33*M1^2 - q12*q33^2 + 8*q12*q13*M1^2 - 4*q12*q13*q33 - 4*q12* q13^2) ) ); Print check; .end assert result("check") =~ expr("0") *--#] jodavies_prf_1 : *--#[ jodavies_dollar_locks : #- #: TermsInSmall 2M * A larger version of this test can be used to easily demonstrate the * performance improvement due to max/min dollar locking changes in TFORM, * see PR 807. Symbol x,i; CFunction sum; #define N "{32*8}" *#define BLOCK "200000" #define BLOCK "20" Local test = #do i = 0,{`N'-1} + sum(i,`i'*`BLOCK',{`i'+1}*`BLOCK'-1,x^i) #enddo ; .sort Identify sum(?a) = sum_(?a); .sort #$min = `N'*`BLOCK'; #$max = -1; If (Count(x,1) > $max) $max = count_(x,1); If (Count(x,1) < $min) $min = count_(x,1); ModuleOption maximum $max; ModuleOption minimum $min; .sort #message max: `$max' #message min: `$min' .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~max: 5119 EOF assert stdout =~ exact_pattern(<<'EOF') ~~~min: 0 EOF *--#] jodavies_dollar_locks : *--#[ tueda_prf_1 : #- Off Statistics; S ep,n1,...,n5; CF Z,rat; PolyRatFun rat; #define N "10" L F = Z(`N',`N',`N',`N',`N'); term; #do i=1,{`N'*3-2} id ifmatch->`i',Z(n1?pos_,n2?pos_,n3?pos_,n4?pos_,n5?pos_) = +Z(n1-1,n2,n3,n4,n5)*rat(-7+2*n5+n4+n3+n2+n1+3*ep,-3+n5+n2+n1+ep) +Z(n1,n2,n3,n4-1,n5)*rat(-7+2*n5+n4+n3+n2+n1+3*ep,-3+n5+n4+n3+ep) +Z(n1,n2,n3,n4,n5-1)*rat(3-n5-n3-n2-ep,-3+n5+n2+n1+ep)*rat(-4+n5+n3+n2+2*ep,-3+n5+n4+n3+ep); id Z(n1?pos_,n2?pos_,n3?pos_,n4?pos_,n5?pos_) = +Z(n1,n2-1,n3,n4,n5)*rat(-7+2*n5+n4+n3+n2+n1+3*ep,-3+n5+n2+n1+ep) +Z(n1,n2,n3-1,n4,n5)*rat(-7+2*n5+n4+n3+n2+n1+3*ep,-3+n5+n4+n3+ep) +Z(n1,n2,n3,n4,n5-1)*rat(3-n5-n4-n1-ep,-3+n5+n2+n1+ep)*rat(-4+n5+n4+n1+2*ep,-3+n5+n4+n3+ep); label `i'; sort; #enddo endterm; #ifndef `EXACT' .sort PolyRatFun; id Z(?a,0,?b) = replace_(ep,1/2); id rat(n1?,n2?) = n1/n2; #endif P +s; .end assert result("F") =~ expr("+ 14680089444100552191986912125917036600599334564/4011728794505561362873666565") *--#] tueda_prf_1 : form-5.0.1/check/fixes.frm0000644000175100017510000031370015217035721011053 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ SparseTable1 : #ifndef `TableSize' #define TableSize "10" #endif * Bugs reported 2004-04-06 by Misha Tentukov * PrintTable and FillExpression did not work with non-sparse tables * Fixed 2005-09-27 cf f; s x; ctable Tab(1:`TableSize'); ctable TabNew(1:`TableSize'); #do i=1,`TableSize',1 Fill Tab(`i')=f(`i'); .sort #enddo * BUG1 (not all elements are printed): PrintTable Tab; bracket x; .sort L expr1=table_(Tab,x); print; .sort bracket x; .sort * BUG 2 ( seems only TabNew(1) is ok - further everything is broken): Fillexpression TabNew=expr1(x); .sort #do i=1,`TableSize' L e`i'=TabNew(`i'); #enddo print; .sort .end assert succeeded? assert result("expr1") =~ expr("f(1)*x + f(2)*x^2 + f(3)*x^3 + f(4)*x^4 + f(5)*x^5 + f(6)*x^6 + f(7)*x^7 + f(8)*x^8 + f(9)*x^9 + f(10)*x^10") assert result("e10") =~ expr("f(10)") *--#] SparseTable1 : *--#[ SymNonZero : * Bug reported 2005-09-27 by Aneesh Manohar * Symmetrize did not make expression y equal to zero * Fixed 2005-10-09 cfunctions f,g; symbols a,b; local x=f(a,b)-f(b,a); local y=f(g(a),b)-f(b,g(a)); symmetrize f; .sort print; .end assert succeeded? assert result("x") =~ expr("0") assert result("y") =~ expr("0") *--#] SymNonZero : *--#[ NegDimension : * Parser accepted negative numbers as arguments to Dimension, Tracen, ... * Fixed 2009-09-08 Dimension -1; I i; L f = d_(i,i); print; .end assert compile_error? *--#] NegDimension : *--#[ Transform-mulargs_1 : CF f; Auto S x; L F = f(,...,); * Consume ebuf. (Assume the default setup parameters on 64-bit systems.) #do i=1,10 id f(?a,x1?,x2?,?c) = f(?a,x1,x2,?c); #enddo * This extends ebuf. transform f,mulargs(1,last); * Crashed here. id f(?a) = f(?a); * Check a "hash", just in case. multiply replace_(,...,); id f(x?) = x; P; .end # Only for 64-bit systems. Otherwise "Sorted function argument too long". #require wordsize == 4 assert succeeded? assert result("F") =~ expr("2187") *--#] Transform-mulargs_1 : *--#[ Forum3t187 : * bug in argument environment? [function specified by a set] CF f1,f2,f3; Set ff1: f1; Set ff2: f2; Set ff3: f3; L F = f1(1) + f2(2) + f3(3); argument ff2; discard; endargument; P; .end assert succeeded? assert result("F") =~ expr("f1(1)+f2(0)+f3(3)") *--#] Forum3t187 : *--#[ Discussion639 : #- Off stats; CFunction eps(antisymmetric); Vector p1,p2,p3; Local zero = eps(p1,p2,p3,p1+p2); ChainOut eps; SplitArg eps; Repeat Identify eps(p1?,p2?) = eps(p1)+eps(p2); ChainIn eps; * the result should be zero without a sort here Print; .end assert succeeded? assert result("zero") =~ expr("0") *--#] Discussion639 : *--#[ Issue7_1 : * SegFault when #optimizing trivial bracket Symbol x; Local expr = x; Bracket x; Print; .sort Format O3; #optimize expr Print; .end assert succeeded? assert result("expr", 0) =~ expr("+ x * ( 1 )") assert result("expr", 1) =~ expr("x") *--#] Issue7_1 : *--#[ Issue7_2 : * nontrivial bracket case was OK Symbol x,y; Local expr = x*(12+y); Bracket x; Print; .sort Format O3; #optimize expr Print; .end assert succeeded? assert result("expr", 0) =~ expr("+ x * ( 12 + y )") # See #364 assert result("expr", 1) =~ expr("Z1_*x") || result("expr", 1) =~ expr("x*Z1_") *--#] Issue7_2 : *--#[ Issue7_3 : Symbols x,y,z; L expr = 1; AB x,y,z; Format O3; .sort #optimize expr Print; .end assert succeeded? assert result("expr") =~ expr("1") *--#] Issue7_3 : *--#[ Issue8 : * Bug with function replacement Symbols a, b; Functions fun, nDUMMY1, nDUMMY2; Local expr= fun(a)*fun(b) ; Id nDUMMY1?(?args1) * nDUMMY2?(?args2) = 1; .sort Print; .end assert succeeded? assert result("expr") =~ expr("1") *--#] Issue8 : *--#[ Issue10 : #- Local test1 = 1; Local test2 = 1; .sort IntoHide; NIntoHide test2; * test1 should be multiplied here Multiply 2; .sort * test1 should not be multiplied here Multiply 2; .sort UnHide; Print; .end assert succeeded? assert result("test1") =~ expr("2"); assert result("test2") =~ expr("4"); *--#] Issue10 : *--#[ Issue21 : * Occurs() with two or more terms in function arguments may get freeze S x; CF f; L F = f(1+x); if (occurs(x)); id f(?a) = 1; endif; P; .end assert succeeded? assert result("F") =~ expr("1") *--#] Issue21 : *--#[ Issue23 : #- CFunction f,g; Symbol x; Local F = (x+1)^2*(f(x)+g(x))^2; Local G = (x+1)^2*(f(x)+g(x))^2; Format Mathematica; Bracket x; Print +s F; .sort Print +s G; .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') F = ( + x * ( + 2*f[x]^2 + 4*f[x]*g[x] + 2*g[x]^2 ) + x^2 * ( + f[x]^2 + 2*f[x]*g[x] + g[x]^2 ) + f[x]^2 + 2*f[x]*g[x] + g[x]^2 ); EOF assert stdout =~ exact_pattern(<<'EOF') G = ( + f[x]^2 + 2*f[x]^2*x + f[x]^2*x^2 + 2*f[x]*g[x] + 4*f[x]*g[x]*x + 2*f[x]*g[x]*x^2 + g[x]^2 + 2*g[x]^2*x + g[x]^2*x^2 ); EOF *--#] Issue23 : *--#[ Issue25 : * [tform] ZERO_ is always 1 when InParallel mode L F1 = 1; ModuleOption inparallel; .sort #message ZERO_F1 = `ZERO_F1' #message ZERO_ = `ZERO_' .end assert succeeded? assert stdout =~ /~~~ZERO_F1 = 0/ assert stdout =~ /~~~ZERO_ = 0/ *--#] Issue25 : *--#[ Issue30_1 : * Substitutions just after putinside/antiputinside may fail S x; CF f; L F1 = 1+x+x^2; L F2 =-1-x-x^2; putinside f, x; *argument; endargument; * <-- (1) id f( 1) = 0; id f(-1) = 0; id f( x) = 0; id f(-x) = 0; id f( x^2) = 0; id f(-x^2) = 0; P; .end assert succeeded? assert result("F1") =~ expr("0") assert result("F2") =~ expr("0") *--#] Issue30_1 : *--#[ Issue30_2 : S x; CF f; L F1 = 1+x+x^2; L F2 =-1-x-x^2; antiputinside f, x; *argument; endargument; * <-- (1) id f( 1) = 0; id f(-1) = 0; P; .end assert succeeded? assert result("F1") =~ expr("0") assert result("F2") =~ expr("0") *--#] Issue30_2 : *--#[ Issue30_3: CF f; S x; L F = 1; $a = f; inside $a; putinside f,x; endinside; *inside $a; endinside; * <-- (1) workaround P " a=%$;", $a; $a = f($a); P " a=%$;", $a; ModuleOption local $a; .end assert succeeded? assert result("a", 0) =~ expr("f*f(1)") assert result("a", 1) =~ expr("f(f*f(1))") *--#] Issue30_3 : *--#[ Issue37_1 : * Polyratfun infinite loop in Print statement S ep; CF rat; PolyRatFun rat(expand,ep,6); L F = rat(ep,ep); Print; .end assert succeeded? assert result("F") =~ expr("rat(1)") *--#] Issue37_1 : *--#[ Issue37_2 : S ep; CF rat; PolyRatFun rat(expand,ep,6); L F = rat(1,1)*rat(ep,ep); Print; .end assert succeeded? assert result("F") =~ expr("rat(1)") *--#] Issue37_2 : *--#[ Issue38 : * Wrong normalization of PolyRatFun CF num,rat; PolyRatFun rat; S n1,x,ep; L F1 = num(n1)*num(1/2); L F2 = num(n1)*num(-1/2); L F3 = rat(1,1) - rat(1,1); L F4 = rat(x,1)*rat(1+ep,1); id num(x?) = rat(x,1); P; .end assert succeeded? assert result("F1") =~ expr("rat(n1,2)") assert result("F2") =~ expr("rat( - n1,2)") assert result("F3") =~ expr("0") assert result("F4") =~ expr("rat(x*ep + x,1)") *--#] Issue38 : *--#[ Issue39 : * Freeze when PolyRatFun contains dot products V a; CF rat; PolyRatFun rat; L F = rat(a.a,1); P; .end assert runtime_error? *--#] Issue39 : *--#[ Issue41 : * replace_ in #assign S n; #$x = n * replace_(n,n+1); L F = `$x'; P; .end assert succeeded? assert result("F") =~ expr("1+n") *--#] Issue41 : *--#[ Issue42_1 : * Factorize/FactDollar are much slower than FactArg CF num; S ep,n1,...,n14; L F = +(n1)^5*(n2)^2*(n5)^4*(n6)^4*(n7)^7*(n8)^10*(n9)^21*(-8589934592) *(-1+n5)^2*(1+n9)*(30-19*n9+2*n9^2-18*n8+2*n8*n9-64*n7+14*n7*n9+ 16*n7*n8+12*n7^2-22*n6+4*n6*n9+4*n6*n8+8*n6*n7+4*n6^2+12*n5-2*n5* n9+4*n5*n8-4*n5*n6-4*n5^2+20*n4-6*n4*n9+4*n4*n8-4*n4*n7-8*n4*n6+4 *n4^2-2*n3*n9+4*n3*n7+4*n3*n5-4*n3*n4-32*n2+8*n2*n9+2*n2*n8+22*n2 *n7+8*n2*n6-2*n2*n5-4*n2*n4+6*n2^2+6*n1+7*n1*n9+6*n1*n7+10*n1*n6- 6*n1*n5-12*n1*n4+4*n1*n2-2*n1^2-16*ep+8*ep*n9+8*ep*n8+32*ep*n7+8* ep*n6-16*ep*n5-16*ep*n4+16*ep*n2) ; .sort * FactArg L F1 = num(F); factarg num; chainout num; .sort * #FactDollar * FIXME: ParFORM hangs. (#46) #$F2 = F; #factdollar $F2 L F2 = num(`$F2[1]') #do i=2,`$F2[0]' * num(`$F2[`i']') #enddo ; .sort * FactDollar L F3 = 1; inexpression F3; $F3 = F; factdollar $F3; do $i=1,$F3[0]; multiply num($F3[$i]); enddo; endinexpression; ModuleOption local $i,$F3; .sort * FIXME: Factorize still have the performance issue. (#44) #if 0 L F4 = F; Factorize F4; .sort #endif P; .end # ParFORM hangs for #FactDollar (#46) #pend_if mpi? assert succeeded? f = expr(""" num(n1)^5*num(n2)^2*num(n5)^4*num(n6)^4*num(n7)^7*num(n8)^10*num(n9)^21* num( - 8589934592)*num( - 1 + n5)^2*num(1 + n9)*num(30 - 19*n9 + 2*n9^2 - 18*n8 + 2*n8*n9 - 64*n7 + 14*n7*n9 + 16*n7*n8 + 12*n7^2 - 22*n6 + 4* n6*n9 + 4*n6*n8 + 8*n6*n7 + 4*n6^2 + 12*n5 - 2*n5*n9 + 4*n5*n8 - 4*n5*n6 - 4*n5^2 + 20*n4 - 6*n4*n9 + 4*n4*n8 - 4*n4*n7 - 8*n4*n6 + 4*n4^2 - 2* n3*n9 + 4*n3*n7 + 4*n3*n5 - 4*n3*n4 - 32*n2 + 8*n2*n9 + 2*n2*n8 + 22*n2* n7 + 8*n2*n6 - 2*n2*n5 - 4*n2*n4 + 6*n2^2 + 6*n1 + 7*n1*n9 + 6*n1*n7 + 10*n1*n6 - 6*n1*n5 - 12*n1*n4 + 4*n1*n2 - 2*n1^2 - 16*ep + 8*ep*n9 + 8* ep*n8 + 32*ep*n7 + 8*ep*n6 - 16*ep*n5 - 16*ep*n4 + 16*ep*n2) """) assert result("F1") =~ f assert result("F2") =~ f assert result("F3") =~ f *--#] Issue42_1 : *--#[ Issue42_2 : S x; L F = gcd_( (1+x), 2*(1+x), 3*(1+x) ); P; .end assert succeeded? assert result("F") =~ expr("1+x") *--#] Issue42_2 : *--#[ Issue42_3 : S n1,...,n4; L F1 = (1+n1)*(1+n2)*n1*n2*n3; L F2 = (1+n2)*n1*n2*n3*n4; L F3 = (1+n4)*n1*n2*n3*n4^2; L F = gcd_(F1,F2,F3); P F; .end assert succeeded? assert result("F") =~ expr("n1*n2*n3") *--#] Issue42_3 : *--#[ Issue42_4 : #procedure PrintFactorizedDollar(name,dollar) #write " `name' = (%$)%", `dollar'[1] #do i=2,``dollar'[0]' #write "*(%$)%", `dollar'[`i'] #enddo #write ";" #endprocedure S x,y; #$a = (1-x)*(1+y); #$b = (1-x)*(1-y); #factdollar $a #factdollar $b #call PrintFactorizedDollar(F1,$a) #call PrintFactorizedDollar(F2,$b) .end assert succeeded? assert result("F1") =~ expr("(-1)*(-1+x)*(1+y)") assert result("F2") =~ expr("(-1+y)*(-1+x)") *--#] Issue42_4 : *--#[ Issue45 : * FactDollar still broken #procedure PrintFactorizedDollar(name,dollar) #write " `name' = (%$)%", `dollar'[1] #do i=2,``dollar'[0]' #write "*(%$)%", `dollar'[`i'] #enddo #write ";" #endprocedure S x,y; #$a = 1+x-y; * <-- The bug was found for this. #$b = 2*(1+x-y); #$c = (1+x+y)*(1+x-y); #factdollar $a #factdollar $b #factdollar $c #call PrintFactorizedDollar(F1,$a) #call PrintFactorizedDollar(F2,$b) #call PrintFactorizedDollar(F3,$c) .end assert succeeded? assert result("F1") =~ expr("(-1)*(-1+y-x)") assert result("F2") =~ expr("(-1+y-x)*(-2)") assert result("F3") =~ expr("(-1)*(-1+y-x)*(1+y+x)") *--#] Issue45 : *--#[ Issue48 : * Memory error on dollar matching CFunction TOPO,topo; CFunction color; Symbol M1,M2,x,cOlNA,cOlNR,ca,cf,nf,[dabc^2/n],[d4RR/n],[d4RA/n],[d4AA/n]; L Diagrams= +topo(M1)*color(24*[d4RR/n]*cOlNA*cOlNR^-1+12*ca*[dabc^2/n]+ ca^2*cf*nf) +topo(M2)*color(24*[d4RA/n]*cOlNA*cOlNR^-1+24*cf^4-72*ca*cf^3 +66*ca^2*cf^2-19*ca^3*cf) ; .sort id topo(x?$topo) = 1; id color(x?$color) = 1; $color = $color * topo($topo); ModuleOption noparallel; .sort L Color = `$color'; P; .end assert succeeded? assert result("Diagrams") =~ expr("2") assert result("Color") =~ expr(" 24*topo(M2)*cf^4 - 72*topo(M2)*ca*cf^3 + 66*topo(M2)*ca^2*cf^2 - 19* topo(M2)*ca^3*cf + 24*topo(M2)*cOlNA*cOlNR^-1*[d4RA/n]") *--#] Issue48 : *--#[ Issue52 : * CopySpectator crashes when empty CreateSpectator TMP, "xTMP"; S x; L F = (1+x)^2; .sort CopySpectator G = TMP; P; .end assert succeeded? assert result("F") =~ expr("1 + 2*x + x^2") assert result("G") =~ expr("0") *--#] Issue52 : *--#[ Issue54_1 : * Transform,replace xarg_ acts only on symbols CF f; S a; L xx = f(a,1); Transform,f,replace(1,last)=(xarg_,2*xarg_); P; .end assert succeeded? assert result("xx") =~ expr("f(2*a,2)") *--#] Issue54_1 : *--#[ Issue54_2 : CF f; S a; L xx = f(a,a^2,1,2); Transform,f,replace(1,last)=(xarg_,2*xarg_,1,3); Print; .end assert succeeded? assert result("xx") =~ expr("f(2*a,2*a^2,3,4)") *--#] Issue54_2 : *--#[ Issue55_1 : * Pattern matching with sets, and (ex-)PolyRatFun CFunction CFunction coeff,coeff2; Symbol x,y,z; Symbol ca,cf,zeta2; Local test1 = + dum_( - 7117/81 - 64/9*zeta2)*ca^2*cf; Local test2 = + dum_(1 + 576/7117*zeta2)*coeff(- 7117,81)*ca^2*cf; .sort Identify coeff(x?neg_,y?) = -coeff(-x,y); Identify dum_(z?)*coeff(x?,y?) = dum_(z * x/y); Print +s; .sort PolyRatFun coeff; Normalize dum_; Print +s; .sort PolyRatFun; .sort Identify coeff(x?neg_,y?) = -coeff(-x,y); *Identify coeff(x?,y?) = coeff2(x,y); *Identify coeff2(x?neg_,y?) = -coeff2(-x,y); Print +s; .end assert succeeded? assert result("test1") =~ expr("- (1 + 576/7117*zeta2)*coeff(7117,81)*ca^2*cf") assert result("test2") =~ expr("- (1 + 576/7117*zeta2)*coeff(7117,81)*ca^2*cf") *--#] Issue55_1 : *--#[ Issue55_2 : * Pattern matching with sets, and (ex-)PolyRatFun CFunction CF frac; S x,y; L F = - 2/3*x; P; .sort(PolyRatFun=frac); *.sort; * putting .sort is useless for this bug *argument frac,1;endargument; * workaround id frac(x?neg_,y?) = - frac(-x,y); * doesn't match P; .end assert succeeded? assert result("F") =~ expr("- frac(2,3)*x") *--#] Issue55_2 : *--#[ Issue56 : * PolyRatFun(expand) does not expand substituted expressions CF rat; S x; PolyRatFun rat; L F = rat(1,1+x); L G = rat(1-x,1); .sort PolyRatFun rat(expand,x,2); Drop; L H = F - G; *.sort; * <-- (1) P; .end assert succeeded? assert result("H") =~ expr("rat(x^2)") *--#] Issue56 : *--#[ Issue59_1 : * Crash when PolyRatFun(expand) CF num,rat; S x; PolyRatFun rat(expand,x,2); L F = *...* * *...* ; id num(x?) = rat(x,1); .sort P +s; .end assert succeeded? assert result("F") =~ expr(' + rat( - 3319889381431113865517677688157339126513795072000000000000 - 103946485016901161789833595241629175725192946647040000000000*x - 1536456092437457859275118833518144965878613654110208000000000*x^2) ') *--#] Issue59_1 : *--#[ Issue59_2 : CF rat; S x; PolyRatFun rat(expand,x,2); L F1 = rat(1+x,1)^270; L F2 = rat(10+10*x,1)^47; P; .end assert succeeded? assert result("F1") =~ expr(' rat(1 + 270*x + 36315*x^2) ') assert result("F2") =~ expr(' rat(100000000000000000000000000000000000000000000000 + 47000000000000000\ 00000000000000000000000000000000*x + 10810000000000000000000000000000000\ 0000000000000000*x^2) ') *--#] Issue59_2 : *--#[ Issue60 : * No error for skipped semicolon in Save statement Symbol x; Global test = x; .store Save test.sav .end assert compile_error? *--#] Issue60 : *--#[ Issue61 : * IntoHide + Bracket for expressions with bracket index S x,y; L F = 1+x; B+ y; .sort IntoHide F; B x; .sort L G = F[x]; P; .end assert succeeded? assert result("G") =~ expr("1") *--#] Issue61 : *--#[ Issue69 : * No warnings/errors for the same labels On allwarning; L F = 1; goto 1; label 1; multiply 2; label 1; multiply 3; label 1; multiply 5; P; .end assert compile_error? *--#] Issue69 : *--#[ Issue73 : * "PolyRatFun cannot have zero arguments" when used in function S ep; CF rat,K; PolyRatfun rat; L F = K(rat(ep+1,1)) + K(rat(1,1)); P; .end assert succeeded? assert result("F") =~ expr("K(rat(ep + 1,1))*rat(1,1) + K(rat(1,1))*rat(1,1)") *--#] Issue73 : *--#[ Issue74 : * occurs() freezes with tensors #74 CF a,acc; S x,y; I i,j; V p,q; CT t; CF f,g; L F1 = 1; L F2 = x; L F3 = 1/x; L F4 = i; L F5 = p; L F6 = p(i); L F7 = p(N1_?); L F8 = p.p; L F9 = p.q; L F10 = t; L F11 = t(i); L F12 = t(p); L F13 = f; L F14 = f(1); L F15 = f(x); L F16 = f(-x); L F17 = f(1/x); L F18 = f(x+y); L F19 = f(i); L F20 = f(-i); L F21 = f(i+j); L F22 = f(p); L F23 = f(-p); L F24 = f(p+q); L F25 = f(p(i)); L F26 = f(p(N1_?)); L F27 = f(p.p); L F28 = f(p.q); L F29 = f(t); L F30 = f(t(i)); L F31 = f(t(p)); L F32 = g(f(x)); L F33 = g(f(i)); L F34 = g(f(p)); L F35 = g(f(t)); L F36 = g(g(f)); L F37 = g_(i,p); L F38 = g_(1,i,p); L F39 = g(1,g(2,3-f(x))+g(t(p),t(i))); L F40 = d_(p,i); if (occurs(x)) multiply a(1); if (occurs(i)) multiply a(2); if (occurs(p)) multiply a(3); if (occurs(t)) multiply a(4); if (occurs(f)) multiply a(5); chainin a; antiputinside acc,a; id acc(?a) = 1; P; .end assert succeeded? assert result("F1") =~ expr("1") assert result("F2") =~ expr("a(1)") assert result("F3") =~ expr("a(1)") assert result("F4") =~ expr("a(2)") assert result("F5") =~ expr("a(3)") assert result("F6") =~ expr("a(2,3)") assert result("F7") =~ expr("a(3)") assert result("F8") =~ expr("a(3)") assert result("F9") =~ expr("a(3)") assert result("F10") =~ expr("a(4)") assert result("F11") =~ expr("a(2,4)") assert result("F12") =~ expr("a(3,4)") assert result("F13") =~ expr("a(5)") assert result("F14") =~ expr("a(5)") assert result("F15") =~ expr("a(1,5)") assert result("F16") =~ expr("a(1,5)") assert result("F17") =~ expr("a(1,5)") assert result("F18") =~ expr("a(1,5)") assert result("F19") =~ expr("a(2,5)") assert result("F20") =~ expr("a(2,5)") assert result("F21") =~ expr("a(2,5)") assert result("F22") =~ expr("a(3,5)") assert result("F23") =~ expr("a(3,5)") assert result("F24") =~ expr("a(3,5)") assert result("F25") =~ expr("a(2,3,5)") assert result("F26") =~ expr("a(3,5)") assert result("F27") =~ expr("a(3,5)") assert result("F28") =~ expr("a(3,5)") assert result("F29") =~ expr("a(4,5)") assert result("F30") =~ expr("a(2,4,5)") assert result("F31") =~ expr("a(3,4,5)") assert result("F32") =~ expr("a(1,5)") assert result("F33") =~ expr("a(2,5)") assert result("F34") =~ expr("a(3,5)") assert result("F35") =~ expr("a(4,5)") assert result("F36") =~ expr("a(5)") assert result("F37") =~ expr("a(2,3)") assert result("F38") =~ expr("a(2,3)") assert result("F39") =~ expr("a(1,2,3,4,5)") assert result("F40") =~ expr("a(2,3)") *--#] Issue74 : *--#[ Issue77_1 : * Freeze when pattern matchings with powers of dollar variables ($x^n?) S x,n; L F = 1; #$x = x; id $x^n? = 1; P; ModuleOption local $x; .end assert succeeded? assert result("F") =~ expr("1") *--#] Issue77_1 : *--#[ Issue77_2 : S x,y,z,n; V p,q; L F = x^3 * y^5 * p.q^6; #$x = x*y*p.q; id $x^n? = z^n; P; ModuleOption local $x; .end assert succeeded? assert result("F") =~ expr("p.q^3*y^2*z^3") *--#] Issue77_2 : *--#[ Issue78_1 : * Minus sign is ignored in set restriction V p,p1; CF vx; L F1 = vx(-p1); L F2 = F1; inexpression F1; id vx(p?!{p1,-p1}) = 1; endinexpression; inexpression F2; id vx(p?!{-p1,p1}) = 1; endinexpression; Print; .end assert succeeded? assert result("F1") =~ expr("vx(-p1)") assert result("F2") =~ expr("vx(-p1)") *--#] Issue78_1 : *--#[ Issue78_2 : V Q; CF vx; L F1 = vx(-Q); L F2 = F1; inexpression F1; id vx(Q?{Q,-Q}) = 1; endinexpression; inexpression F2; id vx(Q?{-Q,Q}) = 1; endinexpression; Print; .end assert succeeded? assert result("F1") =~ expr("1") assert result("F2") =~ expr("1") *--#] Issue78_2 : *--#[ Issue82 : * Minus sign matching bug in latest version V p1,p2; CF vx; L F = vx(-p2); id vx(p2?!{p1}) = 1; Print; .end assert succeeded? assert result("F") =~ expr("1") *--#] Issue82 : *--#[ Issue88 : * Strange error in 'also once' in combination with 'replace_' cf ABB; i mu; L test = 1; once ABB(mu?) * ABB(mu?) = 1; also once ABB(mu?, ?b, mu?) = replace_(mu, N100_?); P; .end assert succeeded? assert result("test") =~ expr("1") *--#] Issue88 : *--#[ Issue90_1 : * Errors in symbol powers CFunction SP; Symbol nn, shat; Vector k1,k2,k3; Local testExpr0 = shat^(-1+nn); Local testExpr1 = shat^(-3+nn); Local testExpr4 = SP(k2,k3)*(shat)^(-3+nn); Argument; Identify nn = 2; EndArgument; Print +s; .end assert succeeded? assert result("testExpr0") =~ expr("+shat") assert result("testExpr1") =~ expr("+shat^-1") assert result("testExpr4") =~ expr("+SP(k2,k3)*shat^-1") *--#] Issue90_1 : *--#[ Issue90_2: Symbol i,x,y,n; Local test1 = 5^(n) * sum_(i,1,n, x^i); Multiply replace_(n,3); Print +s test1; .sort Local test2 = 5^(-n); Multiply replace_(n,3); Print +s test2; .sort Local test3 = 5^(-n) * sum_(i,1,n, x^i); Multiply replace_(n,3); Print +s test3; .end assert succeeded? assert result("test1") =~ expr("+ 125*x + 125*x^2 + 125*x^3") assert result("test2") =~ expr("+ 1/125") assert result("test3") =~ expr("+ 1/125*x + 1/125*x^2 + 1/125*x^3") *--#] Issue90_2 : *--#[ Issue94 : * No check for Dirac gamma matrices without any arguments CF f; L F1 = 123*g5_; L F2 = 123*g6_; L F3 = 123*g7_; L F4 = 123*g_; L F5 = 123*gi_; L F6 = f(1000*g5_); L F7 = f(10000*g5_); .end # Runtime errors may freeze ParFORM. assert runtime_error? *--#] Issue94 : *--#[ Issue95 : #- #: filepatches 32 #: largepatches 32 #: largesize 6250000 #: maxtermsize 1250 #: smallsize 1250000 #: smallextension 2500032 #: termsinsmall 12500 Off Statistics; Symbol x,n; * One fewer term than reported in the Issue, since now the * non-x term is in the initial definition of test. #define NTERMS "266905" Local test = sum_(n,1,`NTERMS',x^n) - `NTERMS'*(`NTERMS'+1)/2; .sort * Check all terms present Identify x^n?pos_ = n; Print; .end # This takes a long time for tform under valgrind. # tform -w4 also doesn't crash here anyway (but -w2 does). #pend_if valgrind? && threaded? # Also doesn't run properly for 32bit form. #require wordsize >= 4 assert succeeded? assert result("test") =~ expr("0") *--#] Issue95 : *--#[ Issue95b : #- #:filepatches 16 #:largepatches 20 #:maxtermsize 200 #:termsinsmall 16 Off stats; #define N "323" S x,k; L F = sum_(k,1,`N',x^k); .sort L CheckZero = F - {`N'*(`N'+1)/2}; id x^k?pos_ = k; Print CheckZero; .end assert succeeded? assert result("CheckZero") =~ expr("0") *--#] Issue95b : *--#[ Issue97_1 : * "Program terminating" with oldFactArg and dot products V e1, e2, k1, k2; S a, b; CF dotM; L testbad = dotM(e1.k1*e2.k1); L testok = dotM(a*b); .sort On oldFactArg; factarg dotM; P; .end assert succeeded? assert result("testbad") =~ expr("dotM(e1.k1,e2.k1,1)") assert result("testok") =~ expr("dotM(a,b,1)") *--#] Issue97_1 : *--#[ Issue97_2 : On OldFactArg; V p1,p2,p3,p4; S x; CF f; T t; L OK1 = f(t(p1)*x); L OK2 = f(t(p1,p2)*x); L OK3 = f(t(p1,p2,p3)*x); L BAD = f(t(p1,p2,p3,p4)*x); factarg f; P; .end assert succeeded? assert result("OK1") =~ expr("f(t(p1),x,1)") assert result("OK2") =~ expr("f(t(p1,p2),x,1)") assert result("OK3") =~ expr("f(t(p1,p2,p3),x,1)") assert result("BAD") =~ expr("f(t(p1,p2,p3,p4),x,1)") *--#] Issue97_2 : *--#[ Issue104 : * Leading zeroes in rational numbers not handled consistently Local test1 = 0001; Local test2 = 00001; Local test3 = 00010; Local test4 = 00011; Print +s; .end assert succeeded? assert result("test1") =~ expr("+ 1") assert result("test2") =~ expr("+ 1") assert result("test3") =~ expr("+ 10") assert result("test4") =~ expr("+ 11") *--#] Issue104 : *--#[ Issue105 : * Crash by replace_(x,0) S x; V p; CF f; L F = f(p.p+x); L G = f(p.p*x); multiply replace_(x,0); P; .end assert succeeded? assert result("F") =~ expr("f(p.p)") assert result("G") =~ expr("f(0)") *--#] Issue105 : *--#[ Issue106 : * Crash with replace_ and nested functions cfunction prop, mom; vector q1, q2, k1, k2, p; l test = prop(mom(-q1-q2+p)); multiply replace_(q1,k1-k2); print+s; .sort multiply replace_(q2,k2); print+s; .end CF f,g; V p1,p2; L F1 = f(f(p1-p2)); L F2 = f(f(f(p1-p2))); L F3 = f(f(f(f(p1-p2)+g(p1-p2))+g(p1-p2))); multiply replace_(p1,p2); P; .end assert succeeded? assert result("test") =~ expr("+ prop(mom(- k1 + p))") assert result("F1") =~ expr("f(f(0))") assert result("F2") =~ expr("f(f(f(0)))") assert result("F3") =~ expr("f(f(f(f(0)+g(0))+g(0)))") *--#] Issue106 : *--#[ Issue111 : * PolyRatFun(expand) doesn't expand numeric coefficients in one go S x; CF rat; PolyRatFun rat(expand,x,3); L F = rat(1+x); .sort multiply 2; *.sort; * <-- workaround P; .sort Drop; L F1 = 3/5; L F2 = 6/5; L F3 = 2/5; L F4 = 12345678901234567890123456789012345678901234567890; L F5 = 2/5 * rat(1+x); L F6 = 2/5 * rat(1,1-x); L F7 = 2/5 * rat(1+x) * rat(1-2*x); L F8 = 2/5 * rat(1+x) * rat(1,1-x); L F9 = 2/5 * rat(1,1+x) * rat(1,1-2*x); multiply 5/3; P; .end assert succeeded? assert result("F") =~ expr("rat(2 + 2*x)") assert result("F1") =~ expr("rat(1)") assert result("F2") =~ expr("rat(2)") assert result("F3") =~ expr("rat(2/3)") assert result("F4") =~ expr("rat(20576131502057613150205761315020576131502057613150)") assert result("F5") =~ expr("rat(2/3 + 2/3*x)") assert result("F6") =~ expr("rat(2/3 + 2/3*x + 2/3*x^2 + 2/3*x^3)") assert result("F7") =~ expr("rat(2/3 - 2/3*x - 4/3*x^2)") assert result("F8") =~ expr("rat(2/3 + 4/3*x + 4/3*x^2 + 4/3*x^3)") assert result("F9") =~ expr("rat(2/3 + 2/3*x + 2*x^2 + 10/3*x^3)") *--#] Issue111 : *--#[ Issue113 : * ?a crashes the program if used only on the rhs CF f; L F = f; id f(?a) = f(?a); id f = f(?a); Print; .end assert compile_error? *--#] Issue113 : *--#[ Issue114 : * Crash on PolyRatFun(expand) when the result is zero CF rat; S x; L F = rat(x^10,1-x); P; .sort PolyRatFun rat(expand,x,5); P; .end assert succeeded? assert result("F") =~ expr("rat(x^10 + x^11 + x^12 + x^13 + x^14 + x^15)") *--#] Issue114 : *--#[ Issue117_1 : * Id not matching when using ?a and symmetric function S n1,n2; CF f,g(s); L F = f(n1,n2)*g(n1,n2); id f(n1?,n2?,?a)*g(n1?,n2?) = 1; * works if g not symmetric or ?a is removed Print; .end assert succeeded? assert result("F") =~ expr("1") *--#] Issue117_1 : *--#[ Issue117_2 : S n1,n2; CF f(s),g(s); id f(n1?,n2?,?a)*g(n1?,n2?) = 1; .end assert compile_error? *--#] Issue117_2 : *--#[ Issue117_3 : S n1,n2; S x1,x2,x3; CF f,g(s); L F1 = f(x1,x2)*g(x1,x2); L F2 = f(x2,x1)*g(x1,x2); L F3 = f(x1,x2,x3)*g(x1,x2); L F4 = f(x2,x1,x3)*g(x1,x2); L F5 = f(x1,x2)*f(x2,x1,x3)*g(x2,x1)^2; id f(n1?,n2?,?a) * g(n1?,n2?) = 1; P; .end assert succeeded? assert result("F1") =~ expr("1") assert result("F2") =~ expr("1") assert result("F3") =~ expr("1") assert result("F4") =~ expr("1") assert result("F5") =~ expr("1") *--#] Issue117_3 : *--#[ Issue121 : * repeat ignored in some output terms of dd_ V p1,p2,p3,p4; CF f; L F = f(p1,p2,p3,p4)*f(p3,p4); repeat id once f(?a) = dd_(?a); P +s; .end assert succeeded? assert result("F") =~ expr(" + p1.p2*p3.p4^2 + p1.p3*p2.p4*p3.p4 + p1.p4*p2.p3*p3.p4 ") *--#] Issue121 : *--#[ Issue125_1 : * Form compiler allows lone ? on rhs CF f; L F = f; id f = f(?); .end assert compile_error? *--#] Issue125_1 : *--#[ Issue125_2 : V p; I mu; CF f; L F = p(mu); id p = f(?); P; .end assert succeeded? assert result("F") =~ expr("f(mu)") *--#] Issue125_2 : *--#[ Issue126 : * Print rejects local-to be unhidden expressions L F = 1; .sort Hide; .sort Unhide; P F; .end assert succeeded? assert result("F") =~ expr("1") *--#] Issue126 : *--#[ Issue128 : * The result check here requires the old prf sign convention: On oldprfsign; * Rational arithmetic giving pi_ CF rat; PolyRatFun rat; S cw,sw,e; *S MZ,sp12; * <-- This fixes the problem. S sp12,MZ; L F = cw * sw * e * rat(- MZ, 2 * sp12 - 1 * MZ); L G = 2 * cw * sw * e * rat(- MZ, 4 * sp12 - 2 * MZ); .sort PolyRatFun rat; * <-- workaround: renormalize rat .sort L FF = F^2; L GG = G^2; P +s; .end assert succeeded? assert result("F") =~ expr(" + cw*sw*e*rat(MZ, - 2*sp12 + MZ) ") assert result("G") =~ expr(" + cw*sw*e*rat(MZ, - 2*sp12 + MZ) ") assert result("FF") =~ expr(" + cw^2*sw^2*e^2*rat(MZ^2,4*sp12^2 - 4*sp12*MZ + MZ^2) ") assert result("GG") =~ expr(" + cw^2*sw^2*e^2*rat(MZ^2,4*sp12^2 - 4*sp12*MZ + MZ^2) ") *--#] Issue128 : *--#[ Issue129_1 : * Redefining a hidden expression #129 L F = 1; .sort #procedure redefine() Hide F; .sort L F = F + 1; .sort #endprocedure #do i=1,5 #call redefine() #enddo On names; P; .end assert succeeded? assert result("F") =~ expr("6") assert stdout =~ exact_pattern(<<'EOF') Expressions F(local) Expressions to be printed F EOF *--#] Issue129_1 : *--#[ Issue129_2: L F = 1; .sort #procedure redefine() Hide F; .sort L tmp = 1; .sort Drop tmp; L F = F + 1; .sort #endprocedure #do i=1,5 #call redefine() #enddo On names; P; .end assert succeeded? assert result("F") =~ expr("6") assert stdout =~ exact_pattern(<<'EOF') Expressions F(local) Expressions to be printed F EOF *--#] Issue129_2 : *--#[ Issue139 : * Corrupted characters in printing f(-2147483648) CF f; * Check numbers near danguous ones up to 64 bits. * 2^15 = 32768 L F15p6 = f(+32766); L F15p7 = f(+32767); L F15p8 = f(+32768); L F15p9 = f(+32769); L F15p0 = f(+32770); L F15m6 = f(-32766); L F15m7 = f(-32767); L F15m8 = f(-32768); L F15m9 = f(-32769); L F15m0 = f(-32770); * 2^16 = 65536 L F16p4 = f(+65534); L F16p5 = f(+65535); L F16p6 = f(+65536); L F16p7 = f(+65537); L F16p8 = f(+65538); L F16m4 = f(-65534); L F16m5 = f(-65535); L F16m6 = f(-65536); L F16m7 = f(-65537); L F16m8 = f(-65538); * 2^31 = 2147483648 L F31p6 = f(+2147483646); L F31p7 = f(+2147483647); L F31p8 = f(+2147483648); L F31p9 = f(+2147483649); L F31p0 = f(+2147483650); L F31m6 = f(-2147483646); L F31m7 = f(-2147483647); L F31m8 = f(-2147483648); L F31m9 = f(-2147483649); L F31m0 = f(-2147483650); * 2^32 = 4294967296 L F32p4 = f(+4294967294); L F32p5 = f(+4294967295); L F32p6 = f(+4294967296); L F32p7 = f(+4294967297); L F32p8 = f(+4294967298); L F32m4 = f(-4294967294); L F32m5 = f(-4294967295); L F32m6 = f(-4294967296); L F32m7 = f(-4294967297); L F32m8 = f(-4294967298); * 2^63 = 9223372036854775808 L F63p6 = f(+9223372036854775806); L F63p7 = f(+9223372036854775807); L F63p8 = f(+9223372036854775808); L F63p9 = f(+9223372036854775809); L F63p0 = f(+9223372036854775810); L F63m6 = f(-9223372036854775806); L F63m7 = f(-9223372036854775807); L F63m8 = f(-9223372036854775808); L F63m9 = f(-9223372036854775809); L F63m0 = f(-9223372036854775810); * 2^64 = 18446744073709551616 L F64p4 = f(+18446744073709551614); L F64p5 = f(+18446744073709551615); L F64p6 = f(+18446744073709551616); L F64p7 = f(+18446744073709551617); L F64p8 = f(+18446744073709551618); L F64m4 = f(-18446744073709551614); L F64m5 = f(-18446744073709551615); L F64m6 = f(-18446744073709551616); L F64m7 = f(-18446744073709551617); L F64m8 = f(-18446744073709551618); P; .end assert succeeded? assert result("F15p6") =~ expr("f(32766)") assert result("F15p7") =~ expr("f(32767)") assert result("F15p8") =~ expr("f(32768)") assert result("F15p9") =~ expr("f(32769)") assert result("F15p0") =~ expr("f(32770)") assert result("F15m6") =~ expr("f(-32766)") assert result("F15m7") =~ expr("f(-32767)") assert result("F15m8") =~ expr("f(-32768)") assert result("F15m9") =~ expr("f(-32769)") assert result("F15m0") =~ expr("f(-32770)") assert result("F16p4") =~ expr("f(65534)") assert result("F16p5") =~ expr("f(65535)") assert result("F16p6") =~ expr("f(65536)") assert result("F16p7") =~ expr("f(65537)") assert result("F16p8") =~ expr("f(65538)") assert result("F16m4") =~ expr("f(-65534)") assert result("F16m5") =~ expr("f(-65535)") assert result("F16m6") =~ expr("f(-65536)") assert result("F16m7") =~ expr("f(-65537)") assert result("F16m8") =~ expr("f(-65538)") assert result("F31p6") =~ expr("f(2147483646)") assert result("F31p7") =~ expr("f(2147483647)") assert result("F31p8") =~ expr("f(2147483648)") assert result("F31p9") =~ expr("f(2147483649)") assert result("F31p0") =~ expr("f(2147483650)") assert result("F31m6") =~ expr("f(-2147483646)") assert result("F31m7") =~ expr("f(-2147483647)") assert result("F31m8") =~ expr("f(-2147483648)") assert result("F31m9") =~ expr("f(-2147483649)") assert result("F31m0") =~ expr("f(-2147483650)") assert result("F32p4") =~ expr("f(4294967294)") assert result("F32p5") =~ expr("f(4294967295)") assert result("F32p6") =~ expr("f(4294967296)") assert result("F32p7") =~ expr("f(4294967297)") assert result("F32p8") =~ expr("f(4294967298)") assert result("F32m4") =~ expr("f(-4294967294)") assert result("F32m5") =~ expr("f(-4294967295)") assert result("F32m6") =~ expr("f(-4294967296)") assert result("F32m7") =~ expr("f(-4294967297)") assert result("F32m8") =~ expr("f(-4294967298)") assert result("F63p6") =~ expr("f(9223372036854775806)") assert result("F63p7") =~ expr("f(9223372036854775807)") assert result("F63p8") =~ expr("f(9223372036854775808)") assert result("F63p9") =~ expr("f(9223372036854775809)") assert result("F63p0") =~ expr("f(9223372036854775810)") assert result("F63m6") =~ expr("f(-9223372036854775806)") assert result("F63m7") =~ expr("f(-9223372036854775807)") assert result("F63m8") =~ expr("f(-9223372036854775808)") assert result("F63m9") =~ expr("f(-9223372036854775809)") assert result("F63m0") =~ expr("f(-9223372036854775810)") assert result("F64p4") =~ expr("f(18446744073709551614)") assert result("F64p5") =~ expr("f(18446744073709551615)") assert result("F64p6") =~ expr("f(18446744073709551616)") assert result("F64p7") =~ expr("f(18446744073709551617)") assert result("F64p8") =~ expr("f(18446744073709551618)") assert result("F64m4") =~ expr("f(-18446744073709551614)") assert result("F64m5") =~ expr("f(-18446744073709551615)") assert result("F64m6") =~ expr("f(-18446744073709551616)") assert result("F64m7") =~ expr("f(-18446744073709551617)") assert result("F64m8") =~ expr("f(-18446744073709551618)") *--#] Issue139 : *--#[ Issue146 : * Memory bug via expanding the triple dot operator Auto S x; L F = x1+...+x123; #$n = 1; .sort L G = x1+...+x1000; #$m = F; .end assert succeeded? *--#] Issue146 : *--#[ Issue149_1 : * Index matches to -1 but crashes in output Index mu; CF f; L F1 = f(-1); L F2 = +...+; id f(mu?) = mu; P; .end assert succeeded? assert result("F1") =~ expr("f(-1)") assert result("F2") =~ expr("8256 + f(-2) + f(-1) + f(129) + f(130)") *--#] Issue149_1 : *--#[ Issue149_2 : Index mu; CF f1(s),f2(a),f3(c),f4(r); L F1 = +...+; L F2 = +...+; L F3 = +...+; L F4 = +...+; id f1?(mu?) = mu; P; .end assert succeeded? assert result("F1") =~ expr("8256 + f1(-2) + f1(-1) + f1(129) + f1(130)") assert result("F2") =~ expr("8256 + f2(-2) + f2(-1) + f2(129) + f2(130)") assert result("F3") =~ expr("8256 + f3(-2) + f3(-1) + f3(129) + f3(130)") assert result("F4") =~ expr("8256 + f4(-2) + f4(-1) + f4(129) + f4(130)") *--#] Issue149_2 : *--#[ Issue151 : * Compiler crashes with Print #do i=1,200 P "123456789012345678901234567890"; P "%t"; #enddo .end assert succeeded? *--#] Issue151 : *--#[ Issue153_1 : * Pattern with index and set restriction matches to number I mu1,...,mu9; CF f; Set indices: mu1,...,mu9; Set indices2: mu1,...,mu9, 127, 128; L F1 = f(132); L F2 = +...+; id f(mu1?indices) = 1; id f(mu1?indices2) = 0; P; .end assert succeeded? assert result("F1") =~ expr("f(132)") assert result("F2") =~ expr("f(126) + f(129) + f(130) + f(131) + f(132)") *--#] Issue153_1 : *--#[ Issue153_2 : I mu1,...,mu9; CF f1(s),f2(a),f3(c),f4(r); Set indices: mu1,...,mu9; Set indices2: mu1,...,mu9, 127, 128; L F1 = +...+; L F2 = +...+; L F3 = +...+; L F4 = +...+; id f1?(mu1?indices) = 1; id f1?(mu1?indices2) = 0; P; .end assert succeeded? assert result("F1") =~ expr("f1(126) + f1(129) + f1(130) + f1(131) + f1(132)") assert result("F2") =~ expr("f2(126) + f2(129) + f2(130) + f2(131) + f2(132)") assert result("F3") =~ expr("f3(126) + f3(129) + f3(130) + f3(131) + f3(132)") assert result("F4") =~ expr("f4(126) + f4(129) + f4(130) + f4(131) + f4(132)") *--#] Issue153_2 : *--#[ Issue154 : * CompressSize insufficient while the compression is off, when Keep Brackets Off compress; I mu1,...,mu16; L F = g_(1,mu1,...,mu16); B g_; .sort; Keep Brackets; tracen,1; .sort Drop; L F1 = termsin_(F); P; .end # Too slow on Travis CI. ParFORM didn't have this bug. #pend_if travis? && (!linux? || valgrind? || mpi?) #time_dilation 2.0 assert succeeded? assert result("F1") =~ expr("2027025") *--#] Issue154 : *--#[ Issue162 : * Missing Expr[x] with B+ for functions #define N "5" #define M "2" #define P "3" S x; CF x1,...,x`M'; S x{`M'+1},...,x`N'; * Test input. L F = (x1+...+x`N')^`P'; .sort:input; * Bracket for some functions. B+ x1,...,x`M'; Print[]; .sort:bracket; Hide; * Check if all entries exist. L FF = F; B x1,...,x`M'; .sort:test input; Keep Brackets; #define failed "0" $x = term_; $y = F[$x]; $n = termsin_($y); if ($n == 0); P "Error: F[%$] == %$", $x, $y; redefine failed "1"; endif; ModuleOption local $n,$x,$y; .sort:test; #if `failed' #terminate #endif .end assert succeeded? *--#] Issue162 : *--#[ Issue163 : * Normalize statement doesn't work for "MINVECTOR" CF f1,f2; V p; L F1 = f1(-p); L F2 = f2(-p); normalize f1; normalize (0) f2; P; .end assert succeeded? assert result("F1") =~ expr("-f1(p)") assert result("F2") =~ expr("f2(p)") *--#] Issue163 : *--#[ Issue165 : * [tform] reading a bracket may crash with B+ when the expression doesn't fit in the scratch buffer #:MaxTermSize 200 #:ScratchSize 12800 CF f,g; S n; #define N "100" #define M "100" L F = +...+; multiply +...+; B+ f; *B- f; * <-- (1) *ModuleOption noparallel; .sort id g(n?) = F[f(n)]; *ModuleOption noparallel; * <-- (2) .sort * Checksum id f(n?) = n; id g(n?) = n; P; .end # Known to fail with ParFORM (#166) #pend_if mpi? assert succeeded? assert result("F") =~ expr("2550250000") *--#] Issue165 : *--#[ Issue167 : * Mystery of count_ in functions S x; CF f; L F = 1 + x + x^2; multiply f(count_(x,1)); P; .sort Drop; L G = 1 + x + x^2; $x = f(count_(x,1)); multiply $x; P; ModuleOption local $x; .end assert succeeded? assert result("F") =~ expr("f(0) + f(0)*x + f(0)*x^2") assert result("G") =~ expr("f(0) + f(1)*x + f(2)*x^2") *--#] Issue167 : *--#[ Issue169 : * Crash from multiply replace_ in large expression S x; CF den; L F = + 16608736983689726473/192*den(2+x) + 18358130244940416000*den(2+x) ; multiply replace_(x,1); P +s; .end assert succeeded? assert result("F") =~ expr("+ 3541369744012249598473/192*den(3)") *--#] Issue169 : *--#[ Issue178 : * PolyRatFun performance regression * Josh's example: Symbol a,b,c,ep; CFunction redprf,epprf; Local test1 = + epprf(-1, - 1 + ep)*redprf(1,1) + epprf(-1,1 - 3*ep + 2*ep^2)*redprf(-1,1) ; .sort PolyRatFun redprf; Identify redprf(a?,b?) = redprf(a*c,b*c); Identify epprf(a?,b?) = redprf(a,b); .sort Print; .end assert succeeded? assert result("test1") =~ expr("redprf(-2,2*ep - 1)") *--#] Issue178 : *--#[ Issue180 : * Broken RAT S ep; CF rat,RAT; PolyRatFun rat,RAT; L F = 1; P "A1:%t"; multiply RAT(1+ep,1); P "A2:%t"; P; .sort P "B1:%t"; multiply RAT(1+ep,1); P "B2:%t"; P; .sort P; .end assert succeeded? assert result("F") =~ expr("rat(1,ep^2 + 2*ep + 1)") *--#] Issue180 : *--#[ Issue183 : #: MaxTermSize 16K #: SubTermsInSmall 800 CF f; Auto S x; L F = f(,...,); *repeat id f(x1?,x2?,?a) = f(x1*x2,?a); * error: Sorted function argument... transform f,mulargs(1,last); * silent crash P; .end assert runtime_error?("Term too complex during normalization") *--#] Issue183 : *--#[ Issue185 : * Wrong result of content_ * This is OK. S x,y; #$p = (x/3+2/y)^2; #$c = content_($p); #$q = $p/$c; L C1 = $c; L Q1 = $q; .sort * This was BAD. S x; #$p = 1+1/x; #$c = content_($p); #$q = $p/$c; L C2 = $c; L Q2 = $q; .sort * Workaround. S x,xxx; #$p = 1+1/x; #$tmp = $p*xxx; #$c = content_($tmp)/xxx; #$q = $p/$c; L C3 = $c; L Q3 = $q; P; .end assert succeeded? assert result("C1") =~ expr("1/9*y^-2") assert result("Q1") =~ expr("36+12*x*y+x^2*y^2") assert result("C2") =~ expr("x^-1") assert result("Q2") =~ expr("1+x") assert result("C3") =~ expr("x^-1") assert result("Q3") =~ expr("1+x") *--#] Issue185 : *--#[ Issue186 : * $args not expanded for distrib_ S x1,...,x4; CF f; L F = f(x1,...,x4); id f(?a$a) = 1; multiply distrib_(1,1,f,dummy_,$a); P; ModuleOption local $a; .end assert succeeded? assert result("F") =~ expr("f(x1) + f(x2) + f(x3) + f(x4)") *--#] Issue186 : *--#[ Issue190 : * Polyratfun coming from function argument does not add properly Auto S x1,x2,ep; CF f,rat; Polyratfun rat; * x1 and x2 should have coefficient -1 L F = +f((rat(1-ep,1)*x1-2*x2)*rat(1,1+ep)) +f((rat(1-ep,1)*x2-2*x1)*rat(1,1+ep)) ; id f(x1?) = x1; Print +s; .end assert succeeded? assert result("F") =~ expr(" + x2*rat(-1,1) + x1*rat(-1,1) ") *--#] Issue190 : *--#[ Issue191 : * gcd_ crashes for zero $-variables S x; * immediate values #define a1 "10" #define a2 "-20" #define a3 "100000000000000000000" #define a4 "-200000000000000000000" #define a5 "x" #define a6 "-x" #define a7 "1+x" L F0 = gcd_(0,0); #do i=1,7 L Fa`i' = gcd_(0,`a`i''); L Fb`i' = gcd_(`a`i'',0); #enddo L Fc1 = gcd_(0,1+x,0,0,0); L Fc2 = gcd_(0,1+x,0,-x,0,0); L Fc3 = gcd_(0,1+x,0,1-x^2,0,0); P; .sort Drop; * subexpressions L a0 = 0; L a00 = 0; L a1 = 10; L a2 = -20; L a3 = 100000000000000000000; L a4 = -200000000000000000000; L a5 = x; L a6 = -x; L a7 = 1+x; L G0 = gcd_(a0,a00); #do i=1,7 L Ga`i' = gcd_(a0,a`i'); L Gb`i' = gcd_(a`i',a0); #enddo L Gc1 = gcd_(0,a7,0,0,a0); L Gc2 = gcd_(0,a7,0,a3,0,a0); L Gc3 = gcd_(0,a7,0,1-x^2,0,a0); P; .sort Drop; * $-variables #$a0 = 0; #$a00 = 0; #$a1 = 10; #$a2 = -20; #$a3 = 100000000000000000000; #$a4 = -200000000000000000000; #$a5 = x; #$a6 = -x; #$a7 = 1+x; L H0 = gcd_($a0,$a00); #do i=1,7 L Ha`i' = gcd_($a0,$a`i'); L Hb`i' = gcd_($a`i',$a0); #enddo L Hc1 = gcd_(0,$a7,0,0,$a0); L Hc2 = gcd_(0,$a7,0,$a3,0,$a0); L Hc3 = gcd_(0,$a7,0,1-x^2,0,$a0); P; .end assert succeeded? assert result("F0") =~ expr("0") assert result("Fa1") =~ expr("10") assert result("Fa2") =~ expr("-20") assert result("Fa3") =~ expr("100000000000000000000") assert result("Fa4") =~ expr("-200000000000000000000") assert result("Fa5") =~ expr("x") assert result("Fa6") =~ expr("-x") assert result("Fa7") =~ expr("1+x") for i in 1..7 assert result("Fb#{i}") == result("Fa#{i}") end assert result("Fc1") =~ expr("1+x") assert result("Fc2") =~ expr("1") assert result("Fc3") =~ expr("1+x") assert result("G0") =~ expr("0") for i in 1..7 assert result("Ga#{i}") == result("Fa#{i}") assert result("Gb#{i}") == result("Fa#{i}") end for i in 1..3 assert result("Gc#{i}") == result("Fc#{i}") end assert result("H0") =~ expr("0") for i in 1..7 assert result("Ha#{i}") == result("Fa#{i}") assert result("Hb#{i}") == result("Fa#{i}") end for i in 1..3 assert result("Hc#{i}") == result("Fc#{i}") end *--#] Issue191 : *--#[ Issue192_1 : * Also related: Issue 334. Global abcdefghijklmnop = 16; Global abcdefghijklmnopq = 17; .store Save test.res; .end assert warning?("saved expr name over 16 char: abcdefghijklmnopq") *--#] Issue192_1 : *--#[ Issue192_2 : * Also related: Issue 334. Global abcdefghijklmnop = 16; Global abcdefghijklmnopq = 17; .store Save test.res abcdefghijklmnopq; .end assert warning?("saved expr name over 16 char: abcdefghijklmnopq") *--#] Issue192_2 : *--#[ Issue192_3 : * Also related: Issue 334. Global abcdefghijklmnop = 16; Global abcdefghijklmnopq = 17; .store Save test.res abcdefghijklmnop; .end assert succeeded? *--#] Issue192_3 : *--#[ Issue192_4 : * Also related: Issue 334. Global abcdefghijklmnop1 = 17; Global abcdefghijklmnop2 = 17; .store #do i = 1,2 Save test.res abcdefghijklmnop`i'; #enddo .end assert warning?("saved expr name over 16 char: abcdefghijklmnop1") assert warning?("saved expr name over 16 char: abcdefghijklmnop2") *--#] Issue192_4 : *--#[ Issue197 : * mul_ ignores denominator factors #if "{2^32}" == "0" * LONG has 4 bytes, which indicates WORD has 2 bytes. * Avoid the "polynomials too large" error. #define n "3" #else #define n "5" #endif S x,y,z; L F1 = mul_(2/3,5/7); L F2 = mul_(1/2+x/3,1/5+x/7); P; .sort Drop; L A1 = (5000000029/7+3/2*x-5/11*x/y+7/8*y*z+z-x*z)^`n'; L A2 = (3/4-1/9*x+9/5000000039*x*y+5/12*y*z+2/z*z^3)^`n'; .sort Drop; L G1 = A1 * A2; L G2 = mul_(A1,A2); .sort Drop; L Nterms = termsin_(G1); L Zero = G1 - G2; P; .end assert succeeded? assert result("F1") =~ expr("10/21") assert result("F2") =~ expr("1/10 + 29/210*x + 1/21*x^2") if wordsize == 2 assert result("Nterms") =~ expr("333") else assert result("Nterms") =~ expr("1351") end assert result("Zero") =~ expr("0") *--#] Issue197 : *--#[ Issue214 : #- #: MaxTermSize 500 #: ScratchSize 1K #: SortIOSize 1K Off compress; Symbol x,y,z,i; CFunction f; Local test = sum_(i,1,100,f(i*(x+y))*(x+y)^20) - 52824783675150; Bracket f; .sort Keep Brackets; Identify f(x?) = x; .sort Identify x = 1; Identify y = 2; Print +s; .end # This is not valgrind clean under parform #pend_if valgrind? && mpi? assert succeeded? assert result("test") =~ expr("0") *--#] Issue214 : *--#[ Issue219 : * Corrupted characters in {-9223372036854775808} #$n32 = -2^31; #$n64 = -2^63; #$n128 = -2^127; L F32 = {`$n32'}; L F64 = {`$n64'}; L F128 = {`$n128'}; * In previous versions, "(" was returned from the preprocessor calculator * on systems using two's complement for signed numbers, leading to an * "Unmatched ()" error. Note that overflow/underflow doesn't give any errors in * the preprocessor calculator (e.g., for F128), just gives a strange number * (though in a strict sense it is an undefined behaviour and can cause a crash; * let's hope compilers will take a little more time to become so insidious). P; .end assert succeeded? *--#] Issue219 : *--#[ Issue211 : * Unexpected code in ReNumber #: TermsInSmall 128 #: LargePatches 16 #: FilePatches 4 #: SubTermsInSmall 64 #: SubLargePatches 8 #: SubFilePatches 2 CFunction f,g; Symbol x,y; * 128*16=2048 terms cause a sort of the large buffer to disk. * multiples of 2048*4=8192 terms cause a stage 4 sort #define NTERMS "40001" #define ARGNTERMS "2001" Local test1 = +...+; Local test2 = g(+...+); .sort * Cancel all terms, but keep distance so that most terms only cancel in the final sort Identify f(x?) = f(x) - f(`NTERMS'-x+1); Argument g; Identify f(x?) = f(x) - f(`ARGNTERMS'-x+1); EndArgument; Print; .end # Only for 64-bit systems. Otherwise "Output term too large". #require wordsize == 4 # For now it fails because # "Currently Stage 4 sorts are not allowed for function arguments or $ variables." assert runtime_error? #assert succeeded? #assert result("test1") =~ expr("0") #assert result("test2") =~ expr("g(0)") *--#] Issue211 : *--#[ Issue222 : * accessing #factdollar factors causes program termination Symbol x; #$a = 1; * Error *#$a = x; * Fine #factdollar $a; #write "Number of factors in `$a' is `$a[0]'" #write "Factor 1 is `$a[1]'" .end assert succeeded? *--#] Issue222 : *--#[ Issue230 : #- #: MaxTermSize 16K #: SubTermsInSmall 800 Off Statistics; Symbol x1,...,x11; CFunction f; Local test = f(x1+...+x11) - (x1+...+x11)^4; Identify f(x1?) = f(x1,x1,x1,x1); .sort Transform f mulargs(1,last); Identify f(x1?) = x1; Print +s; .end assert succeeded? assert result("test") =~ expr("0") *--#] Issue230 : *--#[ Issue231 : Symbol x,y,z; Local F = x + y + x*z; .sort #do i=1,9 CreateSpectator S`i',"S`i'.spec"; #enddo If (Count(y,1) > 0) ToSpectator S1; .sort * Remove some spectators, making holes #do i=1,9,2 RemoveSpectator S`i'; #enddo * Add to a spectator after making "holes" If (Count(z,1) > 0) ToSpectator S4; .sort * Retrieve: CopySpectator G = S4; .sort * Empty RemoveSpectator S4; Print; .sort On Codes; * New spectator, should fill in the first "hole" CreateSpectator S1 "S1.spec"; .end assert succeeded? assert result("F") =~ expr("x") assert result("G") =~ expr("x*z") assert stdout =~ exact_pattern(<<'EOF') Expressions F(local)(0) S2(spectator)(1) S6(spectator)(2) S8(spectator)(3) G(local)(4) S1(spectator)(5) EOF *--#] Issue231 : *--#[ Issue251_1 #- Symbol x,a0,...,a3; Local F = +...+; Bracket x; .sort Local G = + 1 / F[1] + x * (-F[x]) / F[1]^2 + x^2 * (F[x]^2 - F[1]*F[x^2]) / F[1]^3 + x^3 * (-F[x]^3 + 2*F[1]*F[x]*F[x^2] - F[1]^2*F[x^3]) / F[1]^4 ; Print +s G; .end assert succeeded? assert result("G") =~ expr(" + a0^-1 - x*a0^-2*a1 + x^2*a0^-3*a1^2 - x^2*a0^-2*a2 - x^3*a0^-4*a1^3 + 2*x^3*a0^-3*a1*a2 - x^3*a0^-2*a3 ") *--#] Issue251_1 *--#[ Issue251_2 #- Symbol x,a0,...,a3; Local F = +...+; Bracket x; .sort Local G = + 1 / F[1] + x * (-F[x]) / F[1]^2 + x^2 * (F[x]^2 - F[1]*F[x^2]) / F[1]^3 + x^3 * (-F[x]^3 + 2*F[1]*F[x]*F[x^2] - F[1]^2*F[x^3] #do i = 1,100 + F[1]^1 #enddo ) / F[1]^4 ; Print +s G; .end assert succeeded? assert result("G") =~ expr(" + a0^-1 - x*a0^-2*a1 + x^2*a0^-3*a1^2 - x^2*a0^-2*a2 - x^3*a0^-4*a1^3 + 100*x^3*a0^-3 + 2*x^3*a0^-3*a1*a2 - x^3*a0^-2*a3 ") *--#] Issue251_2 *--#[ Issue253 : * Memory error for local $-variable in TFORM #$x = 0; ModuleOption local $x; .end assert succeeded? *--#] Issue253 : *--#[ Issue258 : * gcd_ gives wrong results S s,t,m; L test1 = 1/5*s + 1/5*(s+t)*m; L test2 = (s+t)*m; L result1 = gcd_(test1*replace_(s,t,t,m,m,s),test2*replace_(s,t,t,m,m,s)); L result2 = gcd_(test1,test2); * Previous versions gave * result1 = 1 (correct), but had Valgrind errors * result2 = m (wrong) P; .end assert succeeded? assert result("result1") =~ expr("1") assert result("result2") =~ expr("1") *--#] Issue258 : *--#[ Issue260 : * gcd_ doesn't give the correct result S x1,...,x5; #$a = 34*x2^2*x5 + x1^2*x2*x4*x5 + x1^5; #$b = x4^5 + x3^5 + x2*x3*x5^3; #$g = x3*x4^4 + x2^3*x4 + x1*x3; #$p = $a * $g; #$q = $b * $g; L F1 = gcd_($p,$q); .sort #$a = 79*x2 + x2^4 + x1*x3*x4; #$b = x4^5 + x1*x3^4 + x1^5; #$g = x2^4*x3 + 84*x1^5; #$p = $a * $g; #$q = $b * $g; L F2 = gcd_($p,$q); P; .end assert succeeded? assert result("F1") =~ expr("x3*x4^4 + x2^3*x4 + x1*x3") assert result("F2") =~ expr("x2^4*x3 + 84*x1^5") *--#] Issue260 : *--#[ Issue261_1 : * Division by zero error by mul_(1,0) S x; #$x = 1 + x + x^2; #$z = 0; L F1 = mul_(1,0); L F2 = mul_(0,1); L F3 = mul_(0,0); L F4 = mul_($x,$z); L F5 = mul_($z,$x); L F6 = mul_($z,$z); L F7 = mul_($x,0); L F8 = mul_(0,$x); L F9 = mul_(1,$z); L F10 = mul_($z,1); L F12 = div_(0,1); L F15 = div_($z,$x); L F18 = div_(0,$x); L F20 = div_($z,1); L F22 = rem_(0,1); L F25 = rem_($z,$x); L F28 = rem_(0,$x); L F30 = rem_($z,1); L F32 = inverse_(0,1); L F35 = inverse_($z,$x); L F38 = inverse_(0,$x); L F40 = inverse_($z,1); P; .end assert succeeded? assert result("F1") =~ expr("0") assert result("F2") =~ expr("0") assert result("F3") =~ expr("0") assert result("F4") =~ expr("0") assert result("F5") =~ expr("0") assert result("F6") =~ expr("0") assert result("F7") =~ expr("0") assert result("F8") =~ expr("0") assert result("F9") =~ expr("0") assert result("F10") =~ expr("0") assert result("F12") =~ expr("0") assert result("F15") =~ expr("0") assert result("F18") =~ expr("0") assert result("F20") =~ expr("0") assert result("F22") =~ expr("0") assert result("F25") =~ expr("0") assert result("F28") =~ expr("0") assert result("F30") =~ expr("0") assert result("F32") =~ expr("0") assert result("F35") =~ expr("0") assert result("F38") =~ expr("0") assert result("F40") =~ expr("0") *--#] Issue261_1 : *--#[ Issue261_2 : L F11 = div_(1,0); P; .end assert runtime_error? *--#] Issue261_2 : *--#[ Issue261_3 : L F23 = rem_(0,0); P; .end assert runtime_error? *--#] Issue261_3 : *--#[ Issue261_4 : S x; #$x = 1 + x + x^2; #$z = 0; L F34 = inverse_($x,$z); P; .end assert runtime_error? *--#] Issue261_4 : *--#[ Issue261_5 : #$z = 0; L F16 = div_($z,$z); P; .end assert runtime_error? *--#] Issue261_5 : *--#[ Issue261_6 : S x; #$x = 1 + x + x^2; L F27 = rem_($x,0); P; .end assert runtime_error? *--#] Issue261_6 : *--#[ Issue261_7 : #$z = 0; L F39 = inverse_(1,$z); P; .end assert runtime_error? *--#] Issue261_7 : *--#[ Issue267 : #- CFunction f,g,h,i; Local test = f + g + h(1,2) + i(1,2) + h(1,2,3) + i(1,2,3); Transform f addargs(1,last); Transform g mulargs(1,last); Transform h addargs(1,3); Transform i mulargs(1,3); Print; .end assert succeeded? assert result("test") =~ expr("f + g + h(1,2) + h(6) + i(2) + i(6)"); *--#] Issue267 : *--#[ Issue268_1 : * Invalid read in Normalize #define N "9999" CF f; S x1,x2; L F = f(1,...,`N'); id f(x1?,?a,x2?) = f(?a); id f(?a,x2?) = x2+1; P; .end # On 32-bit systems, "Term too complex during substitution" error occurs. #require wordsize >= 4 assert succeeded? assert result("F") =~ expr("9999") *--#] Issue268_1 : *--#[ Issue268_2 : #define N "9999" CF f; L F = f(1,...,`N'); id f(?a) = nargs_(?a); P; .end # On 32-bit systems, "Term too complex during substitution" error occurs. #require wordsize >= 4 assert succeeded? assert result("F") =~ expr("9999") *--#] Issue268_2 : *--#[ Issue271 : #- #define N "16" Symbol x,n; Local test = -{`N'*(`N'+1)/2} + +...+; .sort #$split = 0; Identify x^n?pos_ = n; $split = $split + term_; ModuleOption sum $split; .sort #message split = `$split' Print; .end assert succeeded? assert stdout =~ exact_pattern(<+...+; .sort #$split = 0; $split = $split + term_; ModuleOption sum $split; .sort #message split = `$split' Print; .end # This symbolic sum doesn't work in TFORM, but does work in ParFORM: #pend_if threaded? assert succeeded? assert stdout =~ exact_pattern(<= 4 assert succeeded? assert result("test") =~ expr("prf(2,1)") *--#] Issue468 : *--#[ Issue486 : On codes; Symbol x,y; Set empty; Set nonempty: x,y; .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') empty(13): nonempty(14): x y EOF *--#] Issue486 : *--#[ Issue490_1 : T t; I i1,...,i4; L F = t(i1,i3)*t(i2,i4); id t(i1?,?a)*t(i2?,?b) = t(i1,i2,?a,?b); P; .end assert succeeded? assert result("F") =~ expr("t(i1,i2,i3,i4)") *--#] Issue490_1 : *--#[ Issue490_2 : T t(cyclic); I i1,...,i4; L F = t(i1,i3)*t(i2,i4); id t(i1?,?a)*t(i2?,?b) = t(i1,i2,?a,?b); P; .end assert succeeded? assert result("F") =~ expr("t(i1,i2,i3,i4)") *--#] Issue490_2 : *--#[ Issue490_3 : T t(cyclic); I i1,...,i6; L F = t(i1,i3,i2,i5)*t(i1,i4,i2,i6); id t(i1?,?a,i2?,?c)*t(i1?,?b,i2?,?d) = t(i1,i2)*t(?a,?b)*t(?c,?d); P; .end assert succeeded? assert result("F") =~ expr("t(i1,i2)*t(i3,i4)*t(i5,i6)") *--#] Issue490_3 : *--#[ Issue490_4 : T t; CF f; I i1,i2; L F = t(i1,i2)*t(i1,i2); id t(?a)*t(?a) = f(?a); P; .end assert succeeded? assert result("F") =~ expr("f(i1,i2)") *--#] Issue490_4 : *--#[ Issue499_1 : * Freeze in parsing complex conjugate S x#c; L F = x#; .end assert compile_error?("Complex conjugate operator (#) is not implemented") *--#] Issue499_1 : *--#[ Issue499_2 : S x#c; L F = #x; .end assert compile_error?("Illegal position for #") *--#] Issue499_2 : *--#[ Issue508 : Off statistics; cf f g; s N; on highfirst; l F = #do i=1,5000 + f(`i')*(g(1+N/`i')*g(N/`i'-1))^25 #enddo ; .sort makeinteger g; id f(N?) = N^50; id g(N?) = 1; print; .end #require linux? #ulimit -v 8_200_000 # We assume more memory than a 32bit system can provide #require wordsize >= 4 assert succeeded? assert result("F") =~ expr("5000") *--#] Issue508 : *--#[ Issue512_1 : #- * Sort which fills SmallExtension: * These are the smallest buffer sizes that are OK for -w4 tform workers #: SmallSize 10240064 #: SmallExtension 15360096 #: TermsInSmall 100K Symbol x,n; CFunction g,f,prf; Local test = (+...+)*(+...+); .sort PolyRatFun prf; Identify f(x?) = prf(n-x,n+x); .end # Fails due to polynomial size on 32bit builds #require wordsize >= 4 # This set of buffer sizes does not cause the error in ParFORM. #pend_if mpi? assert runtime_error?("Please increase SmallExtension setup parameter.") *--#] Issue512_1 : *--#[ Issue512_2 : #- * Sort which fills SubSmallExtension: * These are the default sizes at the time of writing: #: SubSmallSize 2560016 #: SubSmallExtension 3840032 * These are not default: #: SubTermsInSmall 100K Symbol x,n; CFunction f,g,prf; Local test = 1; .sort PolyRatFun prf; Term; Multiply (+...+)*(+...+); Identify f(x?) = prf(n-x,n+x); EndTerm; .end # Fails due to polynomial size on 32bit builds #require wordsize >= 4 assert runtime_error?("Please increase SubSmallExtension setup parameter.") *--#] Issue512_2 : *--#[ Issue512_3 : #- * Sort which fits in SmallExtension, but needs GarbHand #: SmallSize 10240064 #: SmallExtension 20360K #: TermsInSmall 100K Symbol x,n; CFunction g,f,prf; Local test = (+...+)*(+...+); .sort PolyRatFun prf; Identify f(x?) = prf(n-x,n+x); .end # Fails due to polynomial size on 32bit builds #require wordsize >= 4 assert succeeded? *--#] Issue512_3 : *--#[ Issue512_4 : #- * Sort which fits in SubSmallExtension, but needs GarbHand * These are the default sizes at the time of writing: #: SubSmallSize 2560016 * These are not default: #: SubSmallExtension 5090K #: SubTermsInSmall 100K Symbol x,n; CFunction f,g,prf; Local test = 1; .sort PolyRatFun prf; Term; Multiply (+...+)*(+...+); Identify f(x?) = prf(n-x,n+x); EndTerm; .end # Fails due to polynomial size on 32bit builds #require wordsize >= 4 assert succeeded? *--#] Issue512_4 : *--#[ Issue546 : #- Off statistics; Symbol x,y; Local test = + 1 + 3*x + 3/4*x^2 + (2^y-1)*x^3 + (2^y)*x^4 + 1/(2^y-1)*x^5 + 1/(2^y)*x^6 + 3/(2^y-1)*x^7 + 3/(2^y)*x^8 + (2^y)/(2^y-1)*x^9 + (2^y-1)/(2^y)*x^10 + (2^y)/(2^y+1)*x^11 ; .sort Drop; Local test31 = replace_(y,31)*test; Local test32 = replace_(y,32)*test; #message C Format C; Print +s; .sort #message Fortran Format Fortran; Print +s; .sort #message Doublefortran Format Doublefortran; Print +s; .sort #message Quadfortran Format Quadfortran; Print +s; .sort #message Fortran90 Format Fortran90; Print +s; .sort #message Fortran90_ki Format Fortran90,_ki; Print +s; .sort #message Pfortran; Format Pfortran; Print +s; .sort #message Float Format Float; Print +s; .sort #message Normal Format Normal; Print +s; .sort .end # 32bit FORM prints these differently: there a WORD is 16 bits so 2^31-1 etc # all require multiple WORD to store, and so trigger a floating suffix. #require wordsize >= 4 assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~C test31 = + 1 + 3*x + 3./4.*pow(x,2) + 2147483647*pow(x,3) + 2147483648*pow(x,4) + 1./2147483647.*pow(x,5) + 1./2147483648.*pow(x,6) + 3./2147483647.*pow(x,7) + 3./2147483648.*pow(x,8) + 2147483648./2147483647.*pow(x,9) + 2147483647./2147483648.*pow(x,10) + 2147483648./2147483649.*pow(x,11) ; test32 = + 1 + 3*x + 3./4.*pow(x,2) + 4294967295*pow(x,3) + 4294967296.*pow(x,4) + 1./4294967295.*pow(x,5) + 1./4294967296.*pow(x,6) + 1./1431655765.*pow(x,7) + 3./4294967296.*pow(x,8) + 4294967296./4294967295.*pow(x,9) + 4294967295./4294967296.*pow(x,10) + 4294967296./4294967297.*pow(x,11) ; ~~~Fortran test31 = + 1 & + 3*x & + 3./4.*x**2 & + 2147483647*x**3 & + 2147483648.*x**4 & + 1./2147483647.*x**5 & + 1./2147483648.*x**6 & + 3./2147483647.*x**7 & + 3./2147483648.*x**8 & + 2147483648./2147483647.*x**9 & + 2147483647./2147483648.*x**10 & + 2147483648./2147483649.*x**11 & test32 = + 1 & + 3*x & + 3./4.*x**2 & + 4294967295.*x**3 & + 4294967296.*x**4 & + 1./4294967295.*x**5 & + 1./4294967296.*x**6 & + 1./1431655765.*x**7 & + 3./4294967296.*x**8 & + 4294967296./4294967295.*x**9 & + 4294967295./4294967296.*x**10 & + 4294967296./4294967297.*x**11 & ~~~Doublefortran test31 = + 1 & + 3*x & + 3.D0/4.D0*x**2 & + 2147483647*x**3 & + 2147483648.D0*x**4 & + 1.D0/2147483647.D0*x**5 & + 1.D0/2147483648.D0*x**6 & + 3.D0/2147483647.D0*x**7 & + 3.D0/2147483648.D0*x**8 & + 2147483648.D0/2147483647.D0*x**9 & + 2147483647.D0/2147483648.D0*x**10 & + 2147483648.D0/2147483649.D0*x**11 & test32 = + 1 & + 3*x & + 3.D0/4.D0*x**2 & + 4294967295.D0*x**3 & + 4294967296.D0*x**4 & + 1.D0/4294967295.D0*x**5 & + 1.D0/4294967296.D0*x**6 & + 1.D0/1431655765.D0*x**7 & + 3.D0/4294967296.D0*x**8 & + 4294967296.D0/4294967295.D0*x**9 & + 4294967295.D0/4294967296.D0*x**10 & + 4294967296.D0/4294967297.D0*x**11 & ~~~Quadfortran test31 = + 1 & + 3*x & + 3.Q0/4.Q0*x**2 & + 2147483647*x**3 & + 2147483648.Q0*x**4 & + 1.Q0/2147483647.Q0*x**5 & + 1.Q0/2147483648.Q0*x**6 & + 3.Q0/2147483647.Q0*x**7 & + 3.Q0/2147483648.Q0*x**8 & + 2147483648.Q0/2147483647.Q0*x**9 & + 2147483647.Q0/2147483648.Q0*x**10 & + 2147483648.Q0/2147483649.Q0*x**11 & test32 = + 1 & + 3*x & + 3.Q0/4.Q0*x**2 & + 4294967295.Q0*x**3 & + 4294967296.Q0*x**4 & + 1.Q0/4294967295.Q0*x**5 & + 1.Q0/4294967296.Q0*x**6 & + 1.Q0/1431655765.Q0*x**7 & + 3.Q0/4294967296.Q0*x**8 & + 4294967296.Q0/4294967295.Q0*x**9 & + 4294967295.Q0/4294967296.Q0*x**10 & + 4294967296.Q0/4294967297.Q0*x**11 & ~~~Fortran90 test31 = + 1 & + 3*x & + 3./4.*x**2 & + 2147483647*x**3 & + 2147483648.*x**4 & + 1./2147483647.*x**5 & + 1./2147483648.*x**6 & + 3./2147483647.*x**7 & + 3./2147483648.*x**8 & + 2147483648./2147483647.*x**9 & + 2147483647./2147483648.*x**10 & + 2147483648./2147483649.*x**11 & test32 = + 1 & + 3*x & + 3./4.*x**2 & + 4294967295.*x**3 & + 4294967296.*x**4 & + 1./4294967295.*x**5 & + 1./4294967296.*x**6 & + 1./1431655765.*x**7 & + 3./4294967296.*x**8 & + 4294967296./4294967295.*x**9 & + 4294967295./4294967296.*x**10 & + 4294967296./4294967297.*x**11 & ~~~Fortran90_ki test31 = + 1_ki & + 3_ki*x & + 3_ki/4_ki*x**2 & + 2147483647_ki*x**3 & + 2147483648_ki*x**4 & + 1_ki/2147483647_ki*x**5 & + 1_ki/2147483648_ki*x**6 & + 3_ki/2147483647_ki*x**7 & + 3_ki/2147483648_ki*x**8 & + 2147483648_ki/2147483647_ki*x**9 & + 2147483647_ki/2147483648_ki*x**10 & + 2147483648_ki/2147483649_ki*x**11 & test32 = + 1_ki & + 3_ki*x & + 3_ki/4_ki*x**2 & + 4294967295_ki*x**3 & + 4294967296_ki*x**4 & + 1_ki/4294967295_ki*x**5 & + 1_ki/4294967296_ki*x**6 & + 1_ki/1431655765_ki*x**7 & + 3_ki/4294967296_ki*x**8 & + 4294967296_ki/4294967295_ki*x**9 & + 4294967295_ki/4294967296_ki*x**10 & + 4294967296_ki/4294967297_ki*x**11 & ~~~Pfortran test31 = + one & + 3*x & + ((one*3)/4)*x**2 & + 2147483647*x**3 & + 2147483648.D0*x**4 & + (one/2147483647)*x**5 & + (one/2147483648.D0)*x**6 & + ((one*3)/2147483647)*x**7 & + ((one*3)/2147483648.D0)*x**8 & + ((one*2147483648.D0)/2147483647)*x**9 & + ((one*2147483647)/2147483648.D0)*x**10 & + ((one*2147483648.D0)/2147483649.D0)*x**11 & test32 = + one & + 3*x & + ((one*3)/4)*x**2 & + 4294967295.D0*x**3 & + 4294967296.D0*x**4 & + (one/4294967295.D0)*x**5 & + (one/4294967296.D0)*x**6 & + (one/1431655765)*x**7 & + ((one*3)/4294967296.D0)*x**8 & + ((one*4294967296.D0)/4294967295.D0)*x**9 & + ((one*4294967295.D0)/4294967296.D0)*x**10 & + ((one*4294967296.D0)/4294967297.D0)*x**11 & ~~~Float test31 = + 1.E+0 & + 3.E+0*x & + 7.5E-1*x**2 & + 2.147483647E+9*x**3 & + 2.147483648E+9*x**4 & + 4.656612875E-10*x**5 & + 4.656612873E-10*x**6 & + 1.396983862E-9*x**7 & + 1.396983861E-9*x**8 & + 1.000000000E+0*x**9 & + 9.999999995E-1*x**10 & + 9.999999995E-1*x**11 & test32 = + 1.E+0 & + 3.E+0*x & + 7.5E-1*x**2 & + 4.294967295E+9*x**3 & + 4.294967296E+9*x**4 & + 2.328306437E-10*x**5 & + 2.328306436E-10*x**6 & + 6.984919311E-10*x**7 & + 6.984919309E-10*x**8 & + 1.000000000E+0*x**9 & + 9.999999997E-1*x**10 & + 9.999999997E-1*x**11 & ~~~Normal test31 = + 1 + 3*x + 3/4*x^2 + 2147483647*x^3 + 2147483648*x^4 + 1/2147483647*x^5 + 1/2147483648*x^6 + 3/2147483647*x^7 + 3/2147483648*x^8 + 2147483648/2147483647*x^9 + 2147483647/2147483648*x^10 + 2147483648/2147483649*x^11 ; test32 = + 1 + 3*x + 3/4*x^2 + 4294967295*x^3 + 4294967296*x^4 + 1/4294967295*x^5 + 1/4294967296*x^6 + 1/1431655765*x^7 + 3/4294967296*x^8 + 4294967296/4294967295*x^9 + 4294967295/4294967296*x^10 + 4294967296/4294967297*x^11 ; EOF *--#] Issue546 : *--#[ Issue525 : #:threadbucketsize 5 #:processbucketsize 5 S x; L F = (1-x)^100; L F1 = 1; L F2 = 1; .sort #define x "0" if (expression(F1)) redefine x "1"; .sort id x = `x'; P F; .end assert succeeded? assert result("F") =~ expr("0") *--#] Issue525 : *--#[ Issue544 : #- Off Statistics; Symbol x; Vector D,p,q; CFunction tag; CFunction f,g,h,i,j,k,l,m; CFunction F,G,H,I,J,K,L,M; #define N "3" Local test = #do i = -`N',`N' + f(p,`i') + f(-q,`i') + f(p,q,`i') + f(-p,q,`i') + f(p,-q,`i') + f(-p,-q,`i') #enddo ; * Use tags to make sure the cancellation is unique Identify f(?a) = + (f(?a) - F(?a)) * tag(f,?a) + (g(?a) - G(?a)) * tag(g,?a) + (h(?a) - H(?a)) * tag(h,?a) + (i(?a) - I(?a)) * tag(i,?a) + (j(?a) - J(?a)) * tag(j,?a) + (k(?a) - K(?a)) * tag(k,?a) + (l(?a) - L(?a)) * tag(l,?a) + (m(?a) - M(?a)) * tag(m,?a) ; .sort Identify f(p?,x?) = D.p^x; Identify f(p?,q?,x?) = p.q^x; Identify g(p?,x?) = D.p^-x; Identify g(p?,q?,x?) = p.q^-x; Identify h(p?,x?) = (D.p)^x; Identify h(p?,q?,x?) = (p.q)^x; Identify i(p?,x?) = D.p^(x); Identify i(p?,q?,x?) = p.q^(x); * And with - signs on the pattern vector: Identify j(-p?,x?) = D.p^x; Identify j(-p?,-q?,x?) = p.q^x; Identify k(-p?,x?) = D.p^-x; Identify k(-p?,-q?,x?) = p.q^-x; Identify l(-p?,x?) = (D.p)^x; Identify l(-p?,-q?,x?) = (p.q)^x; Identify m(-p?,x?) = D.p^(x); Identify m(-p?,-q?,x?) = p.q^(x); * Cancel all terms, with no pattern for the power #do i = -`N',`N' Identify F(p?,`i') = D.p^`i'; Identify F(p?,q?,`i') = p.q^`i'; Identify G(p?,`i') = D.p^-`i'; Identify G(p?,q?,`i') = p.q^-`i'; Identify H(p?,`i') = (D.p)^`i'; Identify H(p?,q?,`i') = (p.q)^`i'; Identify I(p?,`i') = D.p^(`i'); Identify I(p?,q?,`i') = p.q^(`i'); Identify J(-p?,`i') = D.p^`i'; Identify J(-p?,-q?,`i') = p.q^`i'; Identify K(-p?,`i') = D.p^-`i'; Identify K(-p?,-q?,`i') = p.q^-`i'; Identify L(-p?,`i') = (D.p)^`i'; Identify L(-p?,-q?,`i') = (p.q)^`i'; Identify M(-p?,`i') = D.p^(`i'); Identify M(-p?,-q?,`i') = p.q^(`i'); #enddo Print +s; .end assert succeeded? assert result("test") =~ expr("0") *--#] Issue544 : *--#[ Issue554_1 : CF f; S x; L F = f(x); id f(x?{}) = x; print; .end assert succeeded? assert result("F") =~ expr("f(x)") *--#] Issue554_1 : *--#[ Issue554_2 : CF f; S x; L F = f(x); id f(x?!{}) = x; print; .end assert succeeded? assert result("F") =~ expr("x") *--#] Issue554_2 : *--#[ Issue554_3 : CF f; S x; Set empty: ; L F = f(x); id f(x?empty) = x; print; .end assert succeeded? assert result("F") =~ expr("f(x)") *--#] Issue554_3 : *--#[ Issue554_4 : CF f; S x; Set empty: ; L F = f(x); id f(x?!empty) = x; print; .end assert succeeded? assert result("F") =~ expr("x") *--#] Issue554_4 : *--#[ Issue554_5 : CF f; S x,y; L F = f(1)+f(2)+f(3); id f(x?{}) = x; id f(y?{1,2}) = x^y; print; .end assert succeeded? assert result("F") =~ expr("x + x^2 + f(3)") *--#] Issue554_5 : *--#[ Issue554_6 : #- CF f,g,h,i; S x; #$x1 = f(1,3,5); #$x2 = f(); #inside $x1 if (match(f(?a$a))); endif; #endinside #inside $x2 if (match(f(?a$b))); endif; #endinside L F = f(1,2,3,4,5,6); L G = g(1,2,3,4,5,6); L H = h(1,2,3,4,5,6); L I = i(1,2,3,4,5,6); repeat id f(?a,x? {`$a',},?b) = x * f(?a,?b); repeat id g(?a,x?!{`$a',},?b) = x * g(?a,?b); repeat id h(?a,x? {`$b',},?b) = x * h(?a,?b); repeat id i(?a,x?!{`$b',},?b) = x * i(?a,?b); P; .end assert succeeded? assert result("F") =~ expr("15*f(2,4,6)") assert result("G") =~ expr("48*g(1,3,5)") assert result("H") =~ expr("h(1,2,3,4,5,6)") assert result("I") =~ expr("720*i") *--#] Issue554_6 : *--#[ Issue563 : #: SubTermsInSmall 64 CFunction f,g; Symbol a; * Generate a function arg with more than SubTermsInSmall terms: * Make sure one of the factors has more than SubTermsInSmall itself. * Use functions to trigger LocalConvertToPoly and the EndSort there. Local F = f((g(1)+g(2)) * (+...+)) - g(1+2, 1+...+65); FactArg f; Argument f; Identify g(a?) = a; EndArgument; Identify g(?a) = f(?a); Print F; .end assert succeeded? assert result("F") =~ expr("0") *--#] Issue563 : *--#[ Issue567_1 : CF rat; Vector v; PolyRatFun rat; Local F = rat(v,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_1 : *--#[ Issue567_2 : CF rat; Index i; PolyRatFun rat; Local F = rat(i,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_2 : *--#[ Issue567_3a : CF rat; Function f; PolyRatFun rat; Local F = rat(f,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_3a : *--#[ Issue567_3b : CF rat; CFunction f; PolyRatFun rat; Local F = rat(f,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_3b : *--#[ Issue567_3c : CF rat; Table f(1); PolyRatFun rat; Local F = rat(f,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_3c : *--#[ Issue567_3d : CF rat; CTable f(1); PolyRatFun rat; Local F = rat(f,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_3d : *--#[ Issue567_3e : CF rat; Tensor f; PolyRatFun rat; Local F = rat(f,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_3e : *--#[ Issue567_3f : CF rat; CTensor f; PolyRatFun rat; Local F = rat(f,1); .end assert runtime_error?("ERROR: polynomials and polyratfuns must contain symbols only") *--#] Issue567_3f : *--#[ Issue577_1 : #- Off stats; Symbol x,y,z; Local test1 = 1; .sort Hide test1; Local test2 = 2; .sort Local test3 = 3; #if ( isnumerical(test1) ) #message test1 #endif #if ( isnumerical(test2) ) #message test2 #endif * This causes and error and terminate: test3 is not defined when preprocessing. *#if ( isnumerical(test3) ) * #message test3 *#endif #message module1 .sort #if ( isnumerical(test1) ) #message test1 #endif #if ( isnumerical(test2) ) #message test2 #endif #if ( isnumerical(test3) ) #message test3 #endif #message module2 .sort Local test4 = x*firstterm_(test1) + y*firstterm_(test2) + z*firstterm_(test3); Local test5 = x*firstterm_(test4); Multiply 2; print; .end # ParFORM has valgrind errors with this. See discussion in PR 586. #pend_if valgrind? && mpi? assert succeeded? assert result("test2") =~ expr("4") assert result("test3") =~ expr("6") assert result("test4") =~ expr("6*z + 4*y + 2*x") # This one does not work in TFORM. Consider it to be "illegal". # assert result("test5") =~ expr("12*x*z") assert stdout =~ exact_pattern(<<'EOF') ~~~test1 ~~~test2 ~~~module1 ~~~test1 ~~~test2 ~~~test3 ~~~module2 EOF *--#] Issue577_1 : *--#[ Issue577_2 : #- Off stats; Local test3 = 3; * This causes and error and terminate: test3 is not defined when preprocessing. #if ( isnumerical(test3) ) #message test3 #endif .end # ParFORM has valgrind errors with this. See discussion in PR 586. #pend_if valgrind? && mpi? assert runtime_error?("isnumerical: expression is not yet defined!") *--#] Issue577_2 : *--#[ Issue599 : #- On names; Off statistics; CFunction A1,...,A6; Symbol j,x,z,y; Local ff = + A1(1) + A2(2) + A3(3) + A4(1) + A5(2) + A6(3) ; Identify A1(j?{1,2,3}[x]) = A1({ 10, 20, 30}[x]); Identify A2(j?{1,2,3}[x]) = A2({+10,+20,+30}[x]); Identify A3(j?{1,2,3}[x]) = A3({-10,-20,-30}[x]); Identify A4(j?{1,2,3}[x]) = A4({+-10,--20,-+30}[x]); Identify A5(j?{1,2,3}[x]) = A5({--10,-+20,+-30}[x]); Identify A6(j?{1,2,3}[x]) = A6({-+10,+-20,--30}[x]); Print; .end assert succeeded? assert result("ff") =~ expr("A1(10) + A2(20) + A3(-30) + A4(-10) + A5(-20) + A6(30)") assert stdout =~ exact_pattern(<<'EOF') Sets {}: 1 2 3 {}: 10 20 30 {}: -10 -20 -30 {}: -10 20 -30 {}: 10 -20 -30 {}: -10 -20 30 EOF *--#] Issue599 : *--#[ Issue615 : #- Off stats; Index i1,i2,i3,i4; CFunction f; Set sumind: i2,i3; Local test1 = f(i1,i2,i3,i4)^2; Local test2 = f(i1,i2,i3,i4)^2; Repeat; If (Match(f(?a,i1?sumind$sum,?b))) Sum $sum; EndRepeat; InExpression test2; Repeat; If (Match(f(?a,i1?!dummyindices_$sum,?b))) Sum $sum; EndRepeat; EndInExpression; ModuleOption,local $sum; Print; .end assert succeeded? assert result("test1") =~ expr("f(i1,N1_?,N2_?,i4)^2") assert result("test2") =~ expr("f(N1_?,N2_?,N3_?,N4_?)^2") *--#] Issue615 : *--#[ Issue617_1 : #- Model TMP; Particle s; Particle i; Particle v; Particle cf; Particle f; Particle ct; Particle t; Particle ctab; Particle tab; EndModel; Symbol s; Index i; Vector v; CFunction cf; Function f; CTensor ct; Tensor t; CTable ctab(1:2,3:4); NTable tab(1:2,3:4); .end assert runtime_error?("s has been declared as a function already") assert runtime_error?("v has been declared as a function already") assert runtime_error?("i has been declared as a function already") assert runtime_error?("Function or Tensor cf already declared as a Particle") assert runtime_error?("Function or Tensor f already declared as a Particle") assert runtime_error?("Function or Tensor ct already declared as a Particle") assert runtime_error?("Function or Tensor t already declared as a Particle") assert runtime_error?("(N)(C)Tables should not be declared previously") *--#] Issue617_1 : *--#[ Issue617_2 : #- Symbol s; Index i; Vector v; CFunction cf; Function f; CTensor ct; Tensor t; CTable ctab(1:2,3:4); NTable tab(1:2,3:4); Model TMP; Particle s; Particle i; Particle v; Particle cf; Particle f; Particle ct; Particle t; Particle ctab; Particle tab; EndModel; .end assert runtime_error?("s has been declared as a symbol already") assert runtime_error?("Name of particle previously declared as another variable: s") assert runtime_error?("i has been declared as an index already") assert runtime_error?("Name of particle previously declared as another variable: i") assert runtime_error?("v has been declared as a vector already") assert runtime_error?("Name of particle previously declared as another variable: v") assert runtime_error?("Name of particle previously declared as another variable: cf") assert runtime_error?("Name of particle previously declared as another variable: f") assert runtime_error?("Name of particle previously declared as another variable: ct") assert runtime_error?("Name of particle previously declared as another variable: t") assert runtime_error?("Name of particle previously declared as another variable: ctab") assert runtime_error?("Name of particle previously declared as another variable: tab") *--#] Issue617_2 : *--#[ Issue631_1 : #procedure foo(?a) #message `toupper_(abc)' #message `toupper_(a,b,c)' #message `toupper_(`?a')' #message `tolower_(ABC)' #message `tolower_(A,B,C)' #message `tolower_(`?a')' #message `?a' #endprocedure #call foo(1,2,3,abc,a,b,c,ABC,A,B,C) .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~ABC ~~~A,B,C ~~~1,2,3,ABC,A,B,C,ABC,A,B,C ~~~abc ~~~a,b,c ~~~1,2,3,abc,a,b,c,abc,a,b,c ~~~1,2,3,abc,a,b,c,ABC,A,B,C EOF *--#] Issue631_1 : *--#[ Issue631_2 : #- #define MYTOUPPER(x,y) "toupper_(`~x',`~y')" #procedure foo(x,y) #message ``MYTOUPPER(`x',`y')'' #message `toupper_(`x',`y')' #endprocedure #call foo(a,b) #message ``MYTOUPPER(c,d)'' .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~A,B ~~~A,B ~~~C,D EOF *--#] Issue631_2 : *--#[ Issue631_3 : #- #define str "abcde" #do i = 0,6 #message takeleft_(`str',`i') = `takeleft_(`str',`i')' #message takeright_(`str',`i') = `takeright_(`str',`i')' #message keepleft_(`str',`i') = `keepleft_(`str',`i')' #message keepright_(`str',`i') = `keepright_(`str',`i')' #enddo .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~takeleft_(abcde,0) = abcde ~~~takeright_(abcde,0) = abcde ~~~keepleft_(abcde,0) = ~~~keepright_(abcde,0) = ~~~takeleft_(abcde,1) = bcde ~~~takeright_(abcde,1) = abcd ~~~keepleft_(abcde,1) = a ~~~keepright_(abcde,1) = e ~~~takeleft_(abcde,2) = cde ~~~takeright_(abcde,2) = abc ~~~keepleft_(abcde,2) = ab ~~~keepright_(abcde,2) = de ~~~takeleft_(abcde,3) = de ~~~takeright_(abcde,3) = ab ~~~keepleft_(abcde,3) = abc ~~~keepright_(abcde,3) = cde ~~~takeleft_(abcde,4) = e ~~~takeright_(abcde,4) = a ~~~keepleft_(abcde,4) = abcd ~~~keepright_(abcde,4) = bcde ~~~takeleft_(abcde,5) = ~~~takeright_(abcde,5) = ~~~keepleft_(abcde,5) = abcde ~~~keepright_(abcde,5) = abcde ~~~takeleft_(abcde,6) = ~~~takeright_(abcde,6) = ~~~keepleft_(abcde,6) = abcde ~~~keepright_(abcde,6) = abcde EOF *--#] Issue631_3 : *--#[ Issue633 : s x,y,z; c f; v p; g ff1 = f(5*x) + f(-5*x) + f(-x) + f(x); g ff2 = f(5*p) + f(-5*p) + f(-p) + f(p); factarg f; print; .end assert succeeded? assert result("ff1") =~ expr("f(x) + f(-5,x) + f(-1,x) + f(5,x)") assert result("ff2") =~ expr("f(p) + f(-5,p) + f(-1,p) + f(5,p)") *--#] Issue633 : *--#[ Issue633_2 : on oldfactarg; s x,y,z; c f; v p; g ff1 = f(5*x) + f(-5*x) + f(-x) + f(x); g ff2 = f(5*p) + f(-5*p) + f(-p) + f(p); factarg f; print; .end assert succeeded? assert result("ff1") =~ expr("f(x) + f(x,-1,1) + f(x,-1,5) + f(x,5)") assert result("ff2") =~ expr("f(p) + f(p,-1,1) + f(p,-1,5) + f(p,5)") *--#] Issue633_2 : *--#[ Issue642 : #- Off statistics; CFunction d; CFunction f,g; Symbol a,b,c; CFunction h; Local F = * Example terms with args that are in fast notation and full expressions + f(1,a,2) + f(1,-a,2) + f(1,a+b,2) + f(1,h,2) + f(1,h(1,2),2) + f(1,h(a),2) + f(1,h(a)+a,2) ; Identify f(?a) = f(?a) - g(?a); * Produce test terms where f appears at the beginning, end, * and in the middle of the term data. Multiply 1+d(1,2,3); Multiply 1+h(1,2,3); .sort Identify f(?a) = putfirst_(f,2,?a); Identify g(a?,b?,c?) = f(b,a,c); Print; .end assert succeeded? assert result("F") =~ expr("0") *--#] Issue642 : *--#[ Issue646 : #StartFloat 9d Local F = mzv_+euler_+mzvhalf_; Evaluate; Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F") =~ expr("mzv_ + euler_ + mzvhalf_") *--#] Issue646 : *--#[ Issue647 : #- #define NEXPR "4" Symbol x; #do i = 1,`NEXPR' Local F`i' = x^`i'; Local G`i' = x^`i'; #enddo .sort Hide; .sort UnHide; #do i = 1,`NEXPR' Local diff`i' = F`i' - G`i'; #enddo ModuleOption inparallel; .sort Print; .end assert succeeded? assert result("diff1") =~ expr("0") assert result("diff2") =~ expr("0") assert result("diff3") =~ expr("0") assert result("diff4") =~ expr("0") *--#] Issue647 : *--#[ Issue664 : #- #StartFloat 64b Evaluate 1; .end #pend_if wordsize == 2 assert compile_error?("should be a built in function that can be evaluated numerically.") *--#] Issue664 : *--#[ Issue666 : #- #$repcount = 1; Local test = 1; Multiply 2; .sort:iter `$repcount++'; Multiply 2; .sort:iter `$repcount++'; Print; .end assert succeeded? assert result("test") =~ expr("4") *--#] Issue666 : *--#[ Issue668_1 : * Check error message for invalid setup parameter: #:x #message test .end assert runtime_error?("Setups in .frm file: Keyword not recognized: x") *--#] Issue668_1 : *--#[ Issue668_2 : * Check error message for invalid setup parameter: * In this case, an unexpected end-of-file as in the original report. #system printf "#:x">temp.frm #system `FORM' temp.frm .end #pend_if mpi? #require linux? assert runtime_error?("Setups in .frm file: Keyword not recognized: x") *--#] Issue668_2 : *--#[ Issue695_1 : #StartFloat 20b CFunction f; Local F1 = f(1.0)+f(1.0); Local F2 = f(1.0)/3+f(1.0)*2.0; Local F3 = 1.0*f(1.0)/3+f(1.0)*2.0; Local F4 = f(1.0)+f(1.1); Local F5 = f(0.5)+f(1/2); Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F1") =~ expr("2*f(1.0e+00)") assert result("F2") =~ expr("2.33333e+00*f(1.0e+00)") assert result("F3") =~ expr("2.33333e+00*f(1.0e+00)") assert result("F4") =~ expr("f(1.0e+00) + f(1.1e+00)") assert result("F5") =~ expr("f(1/2) + f(5.0e-01)") *--#] Issue695_1 : *--#[ Issue695_2 : #StartFloat 9d Symbol a,b; CFunction f; Local F = 1.0*f(a); .sort #endfloat Local F = F + f(a); Print; .end #pend_if wordsize == 2 assert succeeded? assert result("F") =~ expr("f(a) + f(a)*float_(2,3,1,340282366920938463463374607431768211456)") *--#] Issue695_2 : *--#[ Issue710_1 : #- Off statistics; Index uu1; CFunction fun; Local expr = fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?); Bracket fun,e_; .sort Keep Brackets; Sum uu1; Print; .end assert succeeded? assert result("expr") =~ expr("fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?)") *--#] Issue710_1 : *--#[ Issue710_2 : #- Off statistics; CFunction fun; Local expr = fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?); Bracket fun,e_; .sort Keep Brackets; ReNumber; Print; .end assert succeeded? assert result("expr") =~ expr("fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?)") *--#] Issue710_2 : *--#[ Issue710_3 : #- Off statistics; CFunction fun; Local expr = fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?); Bracket fun,e_; .sort Keep Brackets; ReNumber,1; Print; .end assert succeeded? assert result("expr") =~ expr("fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?)") *--#] Issue710_3 : *--#[ Issue710_4 : #- Off statistics; Index i1,i2,i3,i4; CFunction fun; Local expr1 = fun(i1,i2)*fun(i3,i4)*e_(i1,i2,i3,i4); Local expr2 = fun(i2,i1)*fun(i4,i3)*e_(i1,i2,i3,i4); Local expr3 = fun(i2,i1)*fun(i3,i4)*e_(i1,i2,i3,i4); Bracket fun,e_; .sort Keep Brackets; Sum i1,...,i4; Print; .end assert succeeded? assert result("expr1") =~ expr("fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?)") assert result("expr2") =~ expr("fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?)") assert result("expr3") =~ expr("- fun(N1_?,N2_?)*fun(N3_?,N4_?)*e_(N1_?,N2_?,N3_?,N4_?)") *--#] Issue710_4 : *--#[ Issue710_4 : #- Off statistics; CFunction indhide; Index i1,i2,i3,i4; Vector v1,v2,v3,v4; Local expr = v1(i1)*v2(i2)*v3(i3)*v4(i4)*indhide(e_(i1,i2,i3,i4)); Sum i1,i2,i3,i4; Print; .end assert succeeded? assert result("expr") =~ expr("indhide(e_(N1_?,N2_?,N3_?,N4_?))*v1(N1_?)*v2(N2_?)*v3(N3_?)*v4(N4_?)") *--#] Issue710_4 : *--#[ Issue710_5 : #- Off statistics; CFunction indhide; Index i1,i2,i3,i4; Vector v1,v2,v3,v4; Local expr = v1(i1)*v2(i2)*v3(i3)*v4(i4)*indhide(e_(i1,i2,i3,i4)); Bracket v1,v2,v3,v4,indhide; .sort Keep Brackets; Sum i1,i2,i3,i4; Print; .end assert succeeded? assert result("expr") =~ expr("indhide(e_(N1_?,N2_?,N3_?,N4_?))*v1(N1_?)*v2(N2_?)*v3(N3_?)*v4(N4_?)") *--#] Issue710_5 : *--#[ Issue747_1 : #- Off Statistics; Symbol a; CFunction f,g; Local test = f(a)^2; #do i = 1,2 Identify,once f(a?$dol) = g(a); FactDollar $dol; Do $i = 1,$dol[0]; Print "In %t factor %$ is %$",$i,$dol[$i]; Enddo; ModuleOption local $dol,$i; .sort #enddo Print; .end assert succeeded? assert result("test") =~ expr("g(a)^2") assert stdout =~ exact_pattern(<<'EOF') In + f(a)*g(a) factor 1 is a In + g(a)^2 factor 1 is a EOF *--#] Issue747_1 : *--#[ Issue747_2 : #- Off Statistics; Symbol a; #$dol = a; #FactDollar $dol #FactDollar $dol #do i = 1,`$dol[0]' #message Factor `i' is `$dol[`i']' #enddo .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') ~~~Factor 1 is a EOF *--#] Issue747_2 : *--#[ Issue750 : #- Off Statistics; NTensor A,B,C; CTensor D,E,F; NFunction a,b,c; CFunction d,e,f; AutoDeclare Vector p; AutoDeclare Index mu; Local testNT1 = A(mu1) *B(mu1) *C(mu1); Local testNT2 = A(mu1,mu2) *B(mu1,mu2) *C(mu1,mu2); Local testNT3 = A(mu1,mu2,mu3)*B(mu1,mu2,mu3)*C(mu1,mu2,mu3); Local testCT1 = D(mu1) *E(mu1) *F(mu1); Local testCT2 = D(mu1,mu2) *E(mu1,mu2) *F(mu1,mu2); Local testCT3 = D(mu1,mu2,mu3)*E(mu1,mu2,mu3)*F(mu1,mu2,mu3); Local testNF1 = a(mu1) *b(mu1) *c(mu1); Local testNF2 = a(mu1,mu2) *b(mu1,mu2) *c(mu1,mu2); Local testNF3 = a(mu1,mu2,mu3)*b(mu1,mu2,mu3)*c(mu1,mu2,mu3); Local testCF1 = d(mu1) *e(mu1) *f(mu1); Local testCF2 = d(mu1,mu2) *e(mu1,mu2) *f(mu1,mu2); Local testCF3 = d(mu1,mu2,mu3)*e(mu1,mu2,mu3)*f(mu1,mu2,mu3); * Replace the last first, to make sure the non-commuting * versions stay in-order in the single-index case. Identify C(?a) = putfirst_(C,2,?a); Identify F(?a) = putfirst_(F,2,?a); Identify c(?a) = putfirst_(c,2,?a); Identify f(?a) = putfirst_(f,2,?a); Identify B(?a) = putfirst_(B,2,?a); Identify E(?a) = putfirst_(E,2,?a); Identify b(?a) = putfirst_(b,2,?a); Identify e(?a) = putfirst_(e,2,?a); Identify A(?a) = putfirst_(A,2,?a); Identify D(?a) = putfirst_(D,2,?a); Identify a(?a) = putfirst_(a,2,?a); Identify d(?a) = putfirst_(d,2,?a); Print; .end assert succeeded? assert result("testNT1") =~ expr("putfirst_(A,2,mu1)*putfirst_(B,2,mu1)*putfirst_(C,2,mu1)") assert result("testNT2") =~ expr("A(mu2,mu1)*B(mu2,mu1)*C(mu2,mu1)") assert result("testNT3") =~ expr("A(mu2,mu1,mu3)*B(mu2,mu1,mu3)*C(mu2,mu1,mu3)") assert result("testCT1") =~ expr("putfirst_(F,2,mu1)*putfirst_(E,2,mu1)*putfirst_(D,2,mu1)") assert result("testCT2") =~ expr("D(mu2,mu1)*E(mu2,mu1)*F(mu2,mu1)") assert result("testCT3") =~ expr("D(mu2,mu1,mu3)*E(mu2,mu1,mu3)*F(mu2,mu1,mu3)") assert result("testNF1") =~ expr("putfirst_(a,2,mu1)*putfirst_(b,2,mu1)*putfirst_(c,2,mu1)") assert result("testNF2") =~ expr("a(mu2,mu1)*b(mu2,mu1)*c(mu2,mu1)") assert result("testNF3") =~ expr("a(mu2,mu1,mu3)*b(mu2,mu1,mu3)*c(mu2,mu1,mu3)") assert result("testCF1") =~ expr("putfirst_(f,2,mu1)*putfirst_(e,2,mu1)*putfirst_(d,2,mu1)") assert result("testCF2") =~ expr("d(mu2,mu1)*e(mu2,mu1)*f(mu2,mu1)") assert result("testCF3") =~ expr("d(mu2,mu1,mu3)*e(mu2,mu1,mu3)*f(mu2,mu1,mu3)") *--#] Issue750 : *--#[ Issue760 : ModuleOption foo1; ModuleOption parallel,foo2; ModuleOption foo3,parallel; .end assert preprocess_error?("Unrecognized module option: foo1") assert preprocess_error?("Unrecognized module option: foo2") assert preprocess_error?("Unrecognized module option: foo3") *--#] Issue760 : *--#[ Issue766 : * Unintended "&" in some warning messages CF f(s,s); CF f>=x<=x; ModuleOption local,$a; .end assert return_value == 0 assert warning?("Excess information in symmetric properties") assert warning?("Illegal information in number of arguments properties") assert warning?("Undefined $-variable") *--#] Issue766 : *--#[ Issue782 : S $s; V $v; I $i; F $f; Set $ss; Local $test = 1; .end assert compile_error?("Illegally formed name in symbol statement") assert compile_error?("Illegally formed name in vector statement") assert compile_error?("Illegally formed name in index statement") assert compile_error?("Illegally formed function/tensor name") assert compile_error?("Illegal name for set") assert compile_error?("Illegal name for expression") *--#] Issue782 : *--#[ Issue796 : * Regression: the fix for 796 deadlocks here: Symbol x; Local test = +...+; #$maxpow = 0; $maxpow = max_($maxpow,count_(x,1)); ModuleOption maximum $maxpow; .sort #message maxpow: `$maxpow' .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') maxpow: 128 EOF *--#] Issue796 : *--#[ Issue796b : * Regression: the fix for 796 deadlocks here: Symbol x; Local test = +...+; #$minpow = 129; $minpow = min_($minpow,count_(x,1)); ModuleOption minimum $minpow; .sort #message minpow: `$minpow' .end assert succeeded? assert stdout =~ exact_pattern(<<'EOF') minpow: 1 EOF *--#] Issue796b : *--#[ Issue796c : * This case has always deadlocked: Symbol x; Local test = +...+; #$sumpow = 129; $sumpow = max_($sumpow,count_(x,1)); ModuleOption sum $sumpow; .sort #message sumpow: `$sumpow' .end # ParFORM does not pass this test #pend_if mpi? assert succeeded? assert stdout =~ exact_pattern(<<'EOF') sumpow: 129 EOF *--#] Issue796c : *--#[ PullReq535 : * This test requires more than the specified 50K workspace. #:maxtermsize 200 #:workspace 50000 S x1,...,x19; L F = (x1+...+x19)^4; Format O1; .sort #optimize F L G = `optimvalue_'; P G; .end assert succeeded? assert result("G") =~ expr("389") *--#] PullReq535 : *--#[ PullReq649_1 : * Test warning message when modifying a dollar variable forces * a module into sequential mode * need an expression with a non-zero value Local expr = 1; * and a new module, since parallel execution does not work * in the module defining an expression .sort $a = 1; .end #require threaded? || mpi? assert warning?("This module is forced to run in sequential mode due to $-variable: $a") *--#] PullReq649_1 : *--#[ PullReq649_2 : * same as `PullReq649_1` with a longer variable name Local expr = 1; .sort $n1MdWu6rNU1d29yW3ukhzV7YuY = 1; .end #require threaded? || mpi? assert warning?("This module is forced to run in sequential mode due to $-variable: $n1MdWu6rNU1d29yW3ukhzV7YuY") *--#] PullReq649_2 : *--#[ PullReq649_3 : * assigning in the preprocessor should not veto parallel execution Local expr = 1; .sort #$a = 1; .end assert succeeded? *--#] PullReq649_3 : *--#[ PullReq649_4 : * assigning through pattern matching Local expr = 1; .sort Symbol x; id x?$a = x; .end #require threaded? || mpi? assert warning?("This module is forced to run in sequential mode due to $-variable: $a") *--#] PullReq649_4 : *--#[ PullReq649_5 : * don't veto parallel execution if there is a matching moduleoption statement Local expr = 1; .sort $a = 1; moduleoption local $a; .end assert succeeded? *--#] PullReq649_5 : *--#[ PullReq649_6 : Local expr = 1; .sort $a = 1; moduleoption sum $a; .end assert succeeded? *--#] PullReq649_6 : *--#[ PullReq649_7 : Local expr = 1; .sort $a = 1; moduleoption minimum $a; .end assert succeeded? *--#] PullReq649_7 : *--#[ PullReq649_8 : Local expr = 1; .sort $a = 1; moduleoption maximum $a; .end assert succeeded? *--#] PullReq649_8 : *--#[ PullReq649_9 : * *do veto* if the moduleoption statement is for the wrong variable Local expr = 1; .sort #$b = 1; $a = 1; moduleoption local $b; .end #require threaded? || mpi? assert warning?("This module is forced to run in sequential mode due to $-variable: $a") *--#] PullReq649_9 : *--#[ PullReq652 : #- Off statistics; #$a = 0; Local test = 1; $b = 0; * Test no leaks when working inside a 0 dollar variable #inside $a Multiply 2; #endinside Inside $a; Multiply 2; EndInside; Inside $b; Multiply 2; EndInside; ModuleOption local $a,$b; Print; .end assert succeeded? assert result("test") =~ expr("1") *--#] PullReq652 : *--#[ PullReq691 : #- #: SubTermsInSmall 112 #: SubLargePatches 10 * A par=2 EndSort, which ends in the PObuffer. * This tests a repaired memory leak. Symbol x; #$dol = +...+; .end assert succeeded? *--#] PullReq691 : *--#[ PullReq807_1 : CF f; S x; L F = (+...+)^4; dropcoefficient; .sort #do i=1,10 if (match(f(`i'))); $x = `i'; endif; #enddo id f(x?) = x; ModuleOption maximum $x; .sort P; .sort #message $x: `$x' .end assert succeeded? assert result("F") =~ expr("752752") assert stdout =~ exact_pattern(<<'EOF') ~~~$x: 10 EOF *--#] PullReq807_1 : *--#[ PullReq807_2 : L F = 1; if (1) $x = 0; ModuleOption minimum $x; .sort P; * AM.exitflag is corrupted .end assert succeeded? assert result("F") =~ expr("1") *--#] PullReq807_2 : *--#[ PullReq843_1 : #- #: TermsInSmall 16 #: LargePatches 10 #: FilePatches 16 #: SubTermsInSmall 16 #: SubLargePatches 10 #: SubFilePatches 10 Off statistics; Off threadstats; CFunction f,sum; Symbol i,j,x; #define N "{2*1776+1}" #define BLOWUP "{160+1}" * Generate enough terms to cause a stage sort: Local test = {`N'*(`N'+1)/2} #do i = 1,`N' - f(x^`i') #enddo ; .sort * Generate enough terms in a sub-buffer sort to create a sort file: Argument f; Identify x^i?pos_ = sum_(j,1,`BLOWUP',x^i*i/`BLOWUP'); EndArgument; * Cancel everything: Identify f(x?) = x; Identify x^i? = 1; Print; .end assert succeeded? assert result("test") =~ expr("0") *--#] PullReq843_1 : *--#[ PullReq843_2 : #- #: TermsInSmall 16 #: LargePatches 10 #: FilePatches 16 #: SubTermsInSmall 16 #: SubLargePatches 10 #: SubFilePatches 10 Off statistics; Off threadstats; CFunction f,sum; Symbol i,j,x; #define N "{2*1776+1}" #define BLOWUP "{160+1}" * Generate enough terms to cause a stage sort: Local test = {`N'*(`N'+1)/2} #do i = 1,`N' - x^`i' #enddo ; .sort * Generate enough terms in a sub-buffer sort to create a sort file: Term; Identify x^i?pos_ = sum_(j,1,`BLOWUP',x^i*i/`BLOWUP'); EndTerm; * Cancel everything: Identify x^i? = 1; Print; .end assert succeeded? assert result("test") =~ expr("0") *--#] PullReq843_2 : *--#[ PullReq843_3 : #- #: TermsInSmall 16 #: LargePatches 10 #: FilePatches 16 #: SubTermsInSmall 16 #: SubLargePatches 10 #: SubFilePatches 10 Off statistics; Off threadstats; CFunction f,sum; Symbol i,j,x; #define N "{2*1776+1}" #define BLOWUP "{160+1}" * Generate enough terms to cause a stage sort: Local test = {`N'*(`N'+1)/2} #do i = 1,`N' - f(x^`i') #enddo ; .sort #$dol = 1; * Generate enough terms in a sub-buffer sort to create a sort file: Identify f(x?$dol) = 1; Inside $dol; Identify x^i?pos_ = sum_(j,1,`BLOWUP',x^i*i/`BLOWUP'); EndInside; Multiply $dol; * Cancel everything: Identify x^i? = 1; Print; ModuleOption local $dol; .end assert succeeded? assert result("test") =~ expr("0") *--#] PullReq843_3 : *--#[ Issue808 : #do i=0,9 Global E`i' = `i'; #enddo .store #do i=1,80 Global F1 = E{`i' % 10}*E2*E3*E4; #enddo .sort .end assert succeeded? *--#] Issue808 : form-5.0.1/check/benchmark-fu.sh0000644000175100017510000000055215217035721012123 #!/bin/sh # This is intended to be run from "make check". trap 'exit 1' 1 2 13 15 status=0 for form in $TEST_BINS; do case $form in *tform*|*parform*|*tvorm*|*parvorm*) ;; *) # For now, only the sequential version. "$form" -v | head -1 "$form" -q -D QUIET "$srcdir/formunit/fu.frm" || status=1 ;; esac done exit $status form-5.0.1/check/Makefile.am0000644000175100017510000000243115217035721011257 TEST_BINS = if BUILD_FORM TEST_BINS += $(top_builddir)/sources/form$(EXEEXT) endif if BUILD_TFORM TEST_BINS += $(top_builddir)/sources/tform$(EXEEXT) endif if BUILD_PARFORM TEST_BINS += $(top_builddir)/sources/parform$(EXEEXT) endif TEST_OPTS = TESTS = if CONFIG_RUBY TESTS_ENVIRONMENT = \ RUBY="$(RUBY)" \ TEST_BINS="$(TEST_BINS)" \ TEST_OPTS="$(TEST_OPTS)" \ "$(SHELL)" TESTS += check-help.sh else TESTS_ENVIRONMENT = \ TEST_BINS="$(TEST_BINS)" \ "$(SHELL)" endif TESTS += benchmark-fu.sh EXTRA_DIST = \ .diagrams_cache/feyngraph_qcd_3_none.dat \ .diagrams_cache/feyngraph_qcd_3_onepi_opicomponents1.dat \ .diagrams_cache/qgraf_qcd_glu_glu_3_none.dat \ .diagrams_cache/qgraf_qcd_glu_glu_3_onepifloop.dat \ .diagrams_cache/qgraf_qcd_quaQUA_gluglu_2_onepifloop.dat \ .diagrams_cache/qgraf_qcd_qua_qua_3_none.dat \ .diagrams_cache/qgraf_qcd_qua_qua_3_onepifloop.dat \ .diagrams_cache/qgraf_qcd_qua_quaglu_3_onepifloop.dat \ benchmark-fu.sh \ check-help.sh \ check.rb \ coverage.frm \ diagrams.frm \ diagrams/diagrams.h \ examples.frm \ extra/checkpoint.frm \ extra/color.frm \ extra/forcer.frm \ extra/mincer.frm \ extra/multithreaded.frm \ extra/mzv-dm.frm \ extra/series.frm \ extra/z-fmft.frm \ features.frm \ fixes.frm \ formunit/fu.frm \ polynomial.frm \ user.frm form-5.0.1/check/check-help.sh0000644000175100017510000000030415217035721011557 #!/bin/sh # This is intended to be run from "make check". trap 'exit 1' 1 2 13 15 status=0 for form in $TEST_BINS; do "$RUBY" "$srcdir/check.rb" "$form" $TEST_OPTS || status=1 done exit $status form-5.0.1/check/diagrams.frm0000644000175100017510000000650315217035721011524 * Compares the diagram generator with others. * * When run outside the testsuite, this file must be on the include path. * For example, run: * form -D TEST=XXX -I check check/diagrams.frm * #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ feyngraph_qcd_3_none : #include- diagrams/diagrams.h #call DoComparison(feyngraph,qcd,in=,out=,loops=3,form_options=,feyngraph_options=,options=forcecacheread) .end assert succeeded? assert nterms("F1", 0) == 74; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] feyngraph_qcd_3_none : *--#[ feyngraph_qcd_3_onepi_opicomponents1 : #include- diagrams/diagrams.h #call DoComparison(feyngraph,qcd,in=,out=,loops=3,form_options=ONEPI_,feyngraph_options=opi_components=1,options=forcecacheread) .end assert succeeded? assert nterms("F1", 0) == 19; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] feyngraph_qcd_3_onepi_opicomponents1 : *--#[ qgraf_qcd_qua_qua_3_none : #include- diagrams/diagrams.h #call DoComparison(qgraf,qcd,in=qua,out=qua,loops=3,form_options=,qgraf_options=,options=forcecacheread) .end # Too many subexpressions for the 32-bit version. #require wordsize >= 4 assert succeeded? assert nterms("F1", 0) == 1001; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] qgraf_qcd_qua_qua_3_none : *--#[ qgraf_qcd_glu_glu_3_none : #include- diagrams/diagrams.h #call DoComparison(qgraf,qcd,in=glu,out=glu,loops=3,form_options=,qgraf_options=,options=forcecacheread) .end # Too many subexpressions for the 32-bit version. #require wordsize >= 4 assert succeeded? assert nterms("F1", 0) == 2829; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] qgraf_qcd_glu_glu_3_none : *--#[ qgraf_qcd_qua_qua_3_onepifloop : #include- diagrams/diagrams.h #call DoComparison(qgraf,qcd,in=qua,out=qua,loops=3,form_options=ONEPI_,FLOOP_,qgraf_options=onepi,floop,options=forcecacheread) .end # The option does not fit into a 16-bit WORD. #require wordsize >= 4 assert succeeded? assert nterms("F1", 0) == 89; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] qgraf_qcd_qua_qua_3_onepifloop : *--#[ qgraf_qcd_glu_glu_3_onepifloop : #include- diagrams/diagrams.h #call DoComparison(qgraf,qcd,in=glu,out=glu,loops=3,form_options=ONEPI_,FLOOP_,qgraf_options=onepi,floop,options=forcecacheread) .end # The option does not fit into a 16-bit WORD. #require wordsize >= 4 assert succeeded? assert nterms("F1", 0) == 222; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] qgraf_qcd_glu_glu_3_onepifloop : *--#[ qgraf_qcd_qua_quaglu_3_onepifloop : #include- diagrams/diagrams.h #call DoComparison(qgraf,qcd,in=qua,out=qua,glu,loops=3,form_options=ONEPI_,FLOOP_,qgraf_options=onepi,floop,options=forcecacheread) .end # The option does not fit into a 16-bit WORD. #require wordsize >= 4 assert succeeded? assert nterms("F1", 0) == 664; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] qgraf_qcd_qua_quaglu_3_onepifloop : *--#[ qgraf_qcd_quaQUA_gluglu_2_onepifloop : #include- diagrams/diagrams.h #call DoComparison(qgraf,qcd,in=qua,QUA,out=glu,glu,loops=2,form_options=ONEPI_,FLOOP_,qgraf_options=onepi,floop,options=forcecacheread) .end # The option does not fit into a 16-bit WORD. #require wordsize >= 4 assert succeeded? assert nterms("F1", 0) == 211; assert nterms("F1") == 0; assert nterms("F2") == 0; *--#] qgraf_qcd_quaQUA_gluglu_2_onepifloop : form-5.0.1/check/.diagrams_cache/0000755000175100017510000000000015217035744012300 5form-5.0.1/check/.diagrams_cache/qgraf_qcd_glu_glu_3_none.dat0000644000175100017510000263067015217035721017631 * Compared with qgraf-3.6.10 * Number of diagrams: FORM: 2829, QGRAF: 2829 -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+1/2*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/4*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/4*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -1/4*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/16*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,QUA(-k6),qua(-k5),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,GHO(-k6),gho(-k5),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/4*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,QUA(-k6),qua(-k5),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,GHO(-k6),gho(-k5),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/4*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,QUA(-k6),qua(-k5),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,GHO(-k6),gho(-k5),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -1/4*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -1/4*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/8*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/2*topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/4*topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/4*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/4*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) 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+topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(k4))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(-k7),gho(k5),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -1/2*topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -1/2*topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/4*topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k4),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k4),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k4),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(k6),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(k6),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(k6),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(k4),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(k4),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(k4),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(k6),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(k6),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(k6),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,QUA(k5),qua(k4),glu(k6))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,QUA(k5),qua(k4),glu(k6))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,QUA(k5),qua(k4),glu(k6))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,GHO(k5),gho(k4),glu(k6))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,GHO(k5),gho(k4),glu(k6))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,GHO(k5),gho(k4),glu(k6))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(k6))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(k6))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/4*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(k6))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k6),glu(k7)) -topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k6),glu(k7)) +1/2*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,QUA(k5),qua(k4),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,GHO(k5),gho(k4),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +1/2*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(-k7),glu(k3))*node_(7,g,GHO(k5),gho(k4),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -1/2*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,glu(k4),glu(k5),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -1/2*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(-k7),glu(k3))*node_(7,g,glu(k4),glu(k5),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +1/8*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(12)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(q1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(-k8),qua(k6),glu(k4))*node_(8,g,QUA(k5),qua(k8),glu(k7)) 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+1/2*topo_(14)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/4*topo_(14)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/4*topo_(14)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) 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+1/2*topo_(15)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +1/2*topo_(15)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/4*topo_(15)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) 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-1/4*topo_(15)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/8*topo_(15)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(q1),glu(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(16)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k3))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(q1),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+1/2*topo_(16)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,glu(q1),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(16)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,glu(q1),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(16)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k3))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(q1),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+1/2*topo_(16)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,glu(q1),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(16)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,glu(q1),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(16)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k3))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(q1),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k3))*node_(6,g,QUA(-k6),qua(k4),glu(q1))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k3))*node_(6,g,QUA(-k6),qua(k4),glu(q1))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k3))*node_(6,g,QUA(-k6),qua(k4),glu(q1))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(q1))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(q1))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(q1))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k3))*node_(6,g,GHO(-k6),gho(k4),glu(q1))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k3))*node_(6,g,GHO(-k6),gho(k4),glu(q1))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k3))*node_(6,g,GHO(-k6),gho(k4),glu(q1))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k3))*node_(6,g,GHO(k4),gho(-k6),glu(q1))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k3))*node_(6,g,GHO(k4),gho(-k6),glu(q1))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k3))*node_(6,g,GHO(k4),gho(-k6),glu(q1))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -1/2*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/4*topo_(20)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k3))*node_(6,g,QUA(k4),qua(-k7),glu(-k6))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(k7),qua(k8),glu(q1)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k3))*node_(6,g,GHO(k4),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k3))*node_(6,g,GHO(k4),gho(-k7),glu(-k6))*node_(7,g,GHO(-k8),gho(k5),glu(k6))*node_(8,g,GHO(k7),gho(k8),glu(q1)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(q1)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,GHO(-k7),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(q1)) -1/2*topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(k2),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,glu(k5),glu(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) 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+topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k3))*node_(6,g,GHO(k4),gho(-k7),glu(-k6))*node_(7,g,GHO(-k8),gho(k5),glu(k6))*node_(8,g,GHO(k7),gho(k8),glu(q1)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(q1)) +topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,GHO(-k7),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(q1)) -1/2*topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(k2),gho(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,glu(k5),glu(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -1/2*topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -1/2*topo_(21)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k3))*node_(6,g,QUA(k4),qua(-k7),glu(-k6))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(k7),qua(k8),glu(q1)) 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+topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(-k6),qua(-k7),glu(k4))*node_(7,g,QUA(-k8),qua(k6),glu(k5))*node_(8,g,QUA(k7),qua(k8),glu(q1)) +topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(q1)) +topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,GHO(-k6),gho(-k7),glu(k4))*node_(7,g,GHO(-k8),gho(k6),glu(k5))*node_(8,g,GHO(k7),gho(k8),glu(q1)) +topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,GHO(-k7),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(q1)) -topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,glu(k5),glu(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k4),glu(-k3))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) 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+topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(k3),gho(k2),glu(-k5))*node_(6,g,GHO(-k6),gho(-k7),glu(k4))*node_(7,g,GHO(-k8),gho(k6),glu(k5))*node_(8,g,GHO(k7),gho(k8),glu(q1)) +topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(k3),gho(k2),glu(-k5))*node_(6,g,GHO(-k7),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(q1)) -topo_(41)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(k3),gho(k2),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,glu(k5),glu(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) 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-1/2*topo_(42)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(42)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k4),glu(-k3))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(q1))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) +topo_(42)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(-k4))*node_(5,g,GHO(k2),gho(k3),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(42)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(-k4))*node_(5,g,GHO(k2),gho(k3),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(42)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(-k4))*node_(5,g,GHO(k2),gho(k3),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(42)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k4),gho(k1),glu(-k3))*node_(5,g,GHO(k2),gho(-k5),glu(k3))*node_(6,g,GHO(-k6),gho(k4),glu(q1))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) 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+1/2*topo_(65)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(k2),qua(-k5),glu(-k6))*node_(6,g,QUA(k5),qua(k3),glu(q1))*node_(7,g,glu(k4),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(65)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(k2),qua(-k5),glu(-k6))*node_(6,g,QUA(k5),qua(k3),glu(q1))*node_(7,g,glu(k4),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -topo_(65)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k3),qua(k5),glu(q1))*node_(7,g,QUA(-k7),qua(k7),glu(k4))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) 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+1/8*topo_(342)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(k1),glu(-k2))*node_(4,g^2,glu(k2),glu(-k3),glu(k3),glu(-k4))*node_(5,g^2,glu(q1),glu(k4),glu(-k5),glu(k5)) +1/8*topo_(343)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(k1),glu(-k2))*node_(4,g^2,glu(q1),glu(k2),glu(-k3),glu(-k4))*node_(5,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) +1/12*topo_(344)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(k1),glu(-k2))*node_(4,g^2,glu(k2),glu(-k3),glu(-k4),glu(-k5))*node_(5,g^2,glu(q1),glu(k3),glu(k4),glu(k5)) +1/8*topo_(345)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(q1),glu(-k1),glu(-k2))*node_(4,g^2,glu(k1),glu(k2),glu(-k3),glu(-k4))*node_(5,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) +1/8*topo_(346)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(q1),glu(-k1),glu(-k2))*node_(4,g^2,glu(k1),glu(-k3),glu(k3),glu(-k4))*node_(5,g^2,glu(k2),glu(k4),glu(-k5),glu(k5)) +1/12*topo_(347)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(q1),glu(-k1),glu(-k2))*node_(4,g^2,glu(k1),glu(-k3),glu(-k4),glu(-k5))*node_(5,g^2,glu(k2),glu(k3),glu(k4),glu(k5)) +1/12*topo_(348)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(-k2),glu(-k3))*node_(4,g^2,glu(k1),glu(k2),glu(k3),glu(-k4))*node_(5,g^2,glu(q1),glu(k4),glu(-k5),glu(k5)) +1/8*topo_(349)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(-k2),glu(-k3))*node_(4,g^2,glu(k1),glu(k2),glu(-k4),glu(k4))*node_(5,g^2,glu(q1),glu(k3),glu(-k5),glu(k5)) +1/4*topo_(350)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(-k2),glu(-k3))*node_(4,g^2,glu(k1),glu(k2),glu(-k4),glu(-k5))*node_(5,g^2,glu(q1),glu(k3),glu(k4),glu(k5)) +1/4*topo_(351)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(-k2),glu(-k3))*node_(4,g^2,glu(q1),glu(k1),glu(k2),glu(-k4))*node_(5,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) form-5.0.1/check/.diagrams_cache/qgraf_qcd_quaQUA_gluglu_2_onepifloop.dat0000644000175100017510000017445415217035721022122 * Compared with qgraf-3.6.10 * Number of diagrams: FORM: 211, QGRAF: 211 topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k5),qua(k3),glu(k2))*node_(8,g,QUA(p2),qua(-k6),glu(k4))*node_(9,g,QUA(-k7),qua(k5),glu(q1))*node_(10,g,QUA(k6),qua(k7),glu(q2)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(k3),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g,glu(q1),glu(k5),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(-k4),qua(-k3),glu(k1))*node_(7,g,QUA(k3),qua(k2),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g,glu(q1),glu(k5),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(k1),glu(-k3),glu(-k4))*node_(7,g,QUA(-k5),qua(k2),glu(k3))*node_(8,g,QUA(p2),qua(-k6),glu(k4))*node_(9,g,QUA(-k7),qua(k5),glu(q1))*node_(10,g,QUA(k6),qua(k7),glu(q2)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k5),qua(k3),glu(k2))*node_(8,g,QUA(p2),qua(-k6),glu(k4))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(k6),qua(k7),glu(q1)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(k3),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(-k4),qua(-k3),glu(k1))*node_(7,g,QUA(k3),qua(k2),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(k1),glu(-k3),glu(-k4))*node_(7,g,QUA(-k5),qua(k2),glu(k3))*node_(8,g,QUA(p2),qua(-k6),glu(k4))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(k6),qua(k7),glu(q1)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k5),qua(k3),glu(k2))*node_(8,g,glu(q1),glu(k4),glu(-k6))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(p2),qua(k7),glu(k6)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(k3),glu(-k5))*node_(8,g,QUA(-k6),qua(k4),glu(q1))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,QUA(p2),qua(k6),glu(k7)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(-k4),qua(-k3),glu(k1))*node_(7,g,QUA(k3),qua(k2),glu(-k5))*node_(8,g,QUA(-k6),qua(k4),glu(q1))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,QUA(p2),qua(k6),glu(k7)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(k1),glu(-k3),glu(-k4))*node_(7,g,QUA(-k5),qua(k2),glu(k3))*node_(8,g,glu(q1),glu(k4),glu(-k6))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(p2),qua(k7),glu(k6)) +topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g,glu(k4),glu(k5),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q1))*node_(8,g,QUA(k3),qua(-k5),glu(-k6))*node_(9,g,QUA(k5),qua(k4),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q1))*node_(8,g,QUA(k3),qua(-k6),glu(-k5))*node_(9,g,QUA(-k7),qua(k4),glu(k5))*node_(10,g,QUA(k6),qua(k7),glu(q2)) -topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(q2),glu(k3),glu(-k5))*node_(9,g,QUA(-k6),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k6),glu(k5)) -topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(q2),glu(k3),glu(-k5))*node_(9,g,GHO(-k6),gho(-k7),glu(k4))*node_(10,g,GHO(k7),gho(k6),glu(k5)) +1/2*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(q2),glu(k3),glu(-k5))*node_(9,g,glu(k4),glu(-k6),glu(-k7))*node_(10,g,glu(k5),glu(k6),glu(k7)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q1))*node_(8,g,QUA(k3),qua(-k5),glu(q2))*node_(9,g,QUA(-k6),qua(k4),glu(-k7))*node_(10,g,QUA(k5),qua(k6),glu(k7)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,QUA(-k5),qua(-k6),glu(k3))*node_(9,g,glu(q2),glu(k4),glu(-k7))*node_(10,g,QUA(k6),qua(k5),glu(k7)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,GHO(-k5),gho(-k6),glu(k3))*node_(9,g,glu(q2),glu(k4),glu(-k7))*node_(10,g,GHO(k6),gho(k5),glu(k7)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g,glu(q2),glu(k4),glu(-k7))*node_(10,g,glu(k5),glu(k6),glu(k7)) +topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q1))*node_(8,g,QUA(k3),qua(-k5),glu(-k6))*node_(9,g,QUA(-k7),qua(k4),glu(q2))*node_(10,g,QUA(k5),qua(k7),glu(k6)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g,glu(k4),glu(k5),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(k3),qua(-k5),glu(-k6))*node_(9,g,QUA(k5),qua(k4),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(k3),qua(-k6),glu(-k5))*node_(9,g,QUA(-k7),qua(k4),glu(k5))*node_(10,g,QUA(k6),qua(k7),glu(q1)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(q1),glu(k3),glu(-k5))*node_(9,g,QUA(-k6),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k6),glu(k5)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(q1),glu(k3),glu(-k5))*node_(9,g,GHO(-k6),gho(-k7),glu(k4))*node_(10,g,GHO(k7),gho(k6),glu(k5)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(q1),glu(k3),glu(-k5))*node_(9,g,glu(k4),glu(-k6),glu(-k7))*node_(10,g,glu(k5),glu(k6),glu(k7)) +topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(k3),qua(-k5),glu(q1))*node_(9,g,QUA(-k6),qua(k4),glu(-k7))*node_(10,g,QUA(k5),qua(k6),glu(k7)) -topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(-k5),qua(-k6),glu(k3))*node_(9,g,glu(q1),glu(k4),glu(-k7))*node_(10,g,QUA(k6),qua(k5),glu(k7)) -topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,GHO(-k5),gho(-k6),glu(k3))*node_(9,g,glu(q1),glu(k4),glu(-k7))*node_(10,g,GHO(k6),gho(k5),glu(k7)) +1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g,glu(q1),glu(k4),glu(-k7))*node_(10,g,glu(k5),glu(k6),glu(k7)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(k3),qua(-k5),glu(-k6))*node_(9,g,QUA(-k7),qua(k4),glu(q1))*node_(10,g,QUA(k5),qua(k7),glu(k6)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(-k5),glu(k2))*node_(8,g,QUA(-k6),qua(k4),glu(k3))*node_(9,g,QUA(k5),qua(-k7),glu(q1))*node_(10,g,QUA(k7),qua(k6),glu(q2)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k5),qua(-k4),glu(k2))*node_(8,g,QUA(k4),qua(-k6),glu(k3))*node_(9,g,QUA(-k7),qua(k5),glu(q1))*node_(10,g,QUA(k6),qua(k7),glu(q2)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k4),gho(-k5),glu(k2))*node_(8,g,GHO(-k6),gho(k4),glu(k3))*node_(9,g,GHO(k5),gho(-k7),glu(q1))*node_(10,g,GHO(k7),gho(k6),glu(q2)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k5),gho(-k4),glu(k2))*node_(8,g,GHO(k4),gho(-k6),glu(k3))*node_(9,g,GHO(-k7),gho(k5),glu(q1))*node_(10,g,GHO(k6),gho(k7),glu(q2)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(k3),glu(k4),glu(-k6))*node_(9,g,glu(q1),glu(k5),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(k3),qua(k4),glu(-k6))*node_(9,g,glu(q1),glu(k5),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,QUA(k3),qua(-k6),glu(k4))*node_(9,g,QUA(-k7),qua(k5),glu(q1))*node_(10,g,QUA(k6),qua(k7),glu(q2)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(-k5),glu(k2))*node_(8,g,QUA(-k6),qua(k4),glu(k3))*node_(9,g,QUA(k5),qua(-k7),glu(q2))*node_(10,g,QUA(k7),qua(k6),glu(q1)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k5),qua(-k4),glu(k2))*node_(8,g,QUA(k4),qua(-k6),glu(k3))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(k6),qua(k7),glu(q1)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k4),gho(-k5),glu(k2))*node_(8,g,GHO(-k6),gho(k4),glu(k3))*node_(9,g,GHO(k5),gho(-k7),glu(q2))*node_(10,g,GHO(k7),gho(k6),glu(q1)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k5),gho(-k4),glu(k2))*node_(8,g,GHO(k4),gho(-k6),glu(k3))*node_(9,g,GHO(-k7),gho(k5),glu(q2))*node_(10,g,GHO(k6),gho(k7),glu(q1)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(k3),glu(k4),glu(-k6))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(k3),qua(k4),glu(-k6))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,QUA(k3),qua(-k6),glu(k4))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(k6),qua(k7),glu(q1)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(-k5),glu(k2))*node_(8,g,QUA(-k7),qua(-k6),glu(k3))*node_(9,g,QUA(k6),qua(k4),glu(q1))*node_(10,g,QUA(k5),qua(k7),glu(q2)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k5),qua(-k4),glu(k2))*node_(8,g,QUA(-k6),qua(-k7),glu(k3))*node_(9,g,QUA(k4),qua(k6),glu(q1))*node_(10,g,QUA(k7),qua(k5),glu(q2)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k4),gho(-k5),glu(k2))*node_(8,g,GHO(-k7),gho(-k6),glu(k3))*node_(9,g,GHO(k6),gho(k4),glu(q1))*node_(10,g,GHO(k5),gho(k7),glu(q2)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k5),gho(-k4),glu(k2))*node_(8,g,GHO(-k6),gho(-k7),glu(k3))*node_(9,g,GHO(k4),gho(k6),glu(q1))*node_(10,g,GHO(k7),gho(k5),glu(q2)) +topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(k3),glu(-k6),glu(-k7))*node_(9,g,glu(q1),glu(k4),glu(k6))*node_(10,g,glu(q2),glu(k5),glu(k7)) +topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(k3),qua(-k6),glu(-k7))*node_(9,g,QUA(k6),qua(k4),glu(q1))*node_(10,g,glu(q2),glu(k5),glu(k7)) +topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,QUA(k3),qua(-k7),glu(-k6))*node_(9,g,glu(q1),glu(k4),glu(k6))*node_(10,g,QUA(k7),qua(k5),glu(q2)) +topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(q1),glu(k3),glu(-k6))*node_(9,g,glu(k4),glu(k6),glu(-k7))*node_(10,g,glu(q2),glu(k5),glu(k7)) +topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(k3),qua(-k6),glu(q1))*node_(9,g,QUA(k6),qua(k4),glu(-k7))*node_(10,g,glu(q2),glu(k5),glu(k7)) +topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,QUA(k3),qua(-k6),glu(q1))*node_(9,g,QUA(k6),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k5),glu(q2)) +topo_(14)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(q2),glu(k3),glu(-k6))*node_(9,g,glu(k4),glu(k6),glu(-k7))*node_(10,g,glu(q1),glu(k5),glu(k7)) +topo_(14)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(k3),qua(-k6),glu(q2))*node_(9,g,QUA(k6),qua(k4),glu(-k7))*node_(10,g,glu(q1),glu(k5),glu(k7)) +topo_(14)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,QUA(k3),qua(-k6),glu(q2))*node_(9,g,QUA(k6),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k5),glu(q1)) -topo_(15)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(-k5),glu(k2))*node_(8,g,QUA(k5),qua(k4),glu(-k6))*node_(9,g,glu(q1),glu(k3),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) -topo_(15)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k4),gho(-k5),glu(k2))*node_(8,g,GHO(k5),gho(k4),glu(-k6))*node_(9,g,glu(q1),glu(k3),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +1/2*topo_(15)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(k4),glu(k5),glu(-k6))*node_(9,g,glu(q1),glu(k3),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(15)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(-k6),qua(k4),glu(k5))*node_(9,g,QUA(k3),qua(-k7),glu(q1))*node_(10,g,QUA(k7),qua(k6),glu(q2)) -topo_(16)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(-k5),glu(k2))*node_(8,g,QUA(k5),qua(k4),glu(-k6))*node_(9,g,glu(q2),glu(k3),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) -topo_(16)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k4),gho(-k5),glu(k2))*node_(8,g,GHO(k5),gho(k4),glu(-k6))*node_(9,g,glu(q2),glu(k3),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +1/2*topo_(16)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(k4),glu(k5),glu(-k6))*node_(9,g,glu(q2),glu(k3),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(16)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(-k6),qua(k4),glu(k5))*node_(9,g,QUA(k3),qua(-k7),glu(q2))*node_(10,g,QUA(k7),qua(k6),glu(q1)) +topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(-k5),qua(k3),glu(-k6))*node_(9,g,QUA(-k7),qua(k5),glu(k4))*node_(10,g,QUA(p2),qua(k7),glu(k6)) +topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(-k6),qua(k3),glu(-k5))*node_(9,g,glu(k4),glu(k5),glu(-k7))*node_(10,g,QUA(p2),qua(k6),glu(k7)) +topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(-k6),qua(-k5),glu(k3))*node_(9,g,QUA(k5),qua(k4),glu(-k7))*node_(10,g,QUA(p2),qua(k6),glu(k7)) +topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g,QUA(-k7),qua(k4),glu(k5))*node_(10,g,QUA(p2),qua(k7),glu(k6)) -topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(p2),qua(k3),glu(-k5))*node_(9,g,QUA(-k6),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k6),glu(k5)) -topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(p2),qua(k3),glu(-k5))*node_(9,g,GHO(-k6),gho(-k7),glu(k4))*node_(10,g,GHO(k7),gho(k6),glu(k5)) +1/2*topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(p2),qua(k3),glu(-k5))*node_(9,g,glu(k4),glu(-k6),glu(-k7))*node_(10,g,glu(k5),glu(k6),glu(k7)) +topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(p2),qua(-k5),glu(k3))*node_(9,g,QUA(-k6),qua(k4),glu(-k7))*node_(10,g,QUA(k5),qua(k6),glu(k7)) +topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(-k5),qua(k3),glu(-k6))*node_(9,g,QUA(p2),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k5),glu(k6)) -topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(-k5),qua(-k6),glu(k3))*node_(9,g,QUA(p2),qua(k4),glu(-k7))*node_(10,g,QUA(k6),qua(k5),glu(k7)) -topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,GHO(-k5),gho(-k6),glu(k3))*node_(9,g,QUA(p2),qua(k4),glu(-k7))*node_(10,g,GHO(k6),gho(k5),glu(k7)) +1/2*topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g,QUA(p2),qua(k4),glu(-k7))*node_(10,g,glu(k5),glu(k6),glu(k7)) +topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(-k5),qua(-k4),glu(k2))*node_(8,g,QUA(k4),qua(k3),glu(-k6))*node_(9,g,QUA(p2),qua(k5),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,QUA(-k6),qua(k3),glu(k4))*node_(9,g,QUA(p2),qua(-k7),glu(k5))*node_(10,g,QUA(k7),qua(k6),glu(q2)) +topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(-k6),qua(k4),glu(k3))*node_(9,g,QUA(p2),qua(-k7),glu(k5))*node_(10,g,QUA(k7),qua(k6),glu(q2)) +topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,glu(k3),glu(k4),glu(-k6))*node_(9,g,QUA(p2),qua(k5),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(-k5),qua(-k4),glu(k2))*node_(8,g,QUA(k4),qua(k3),glu(-k6))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(p2),qua(k7),glu(k6)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,QUA(-k6),qua(k3),glu(k4))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,QUA(p2),qua(k6),glu(k7)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(-k6),qua(k4),glu(k3))*node_(9,g,glu(q2),glu(k5),glu(-k7))*node_(10,g,QUA(p2),qua(k6),glu(k7)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,glu(k3),glu(k4),glu(-k6))*node_(9,g,QUA(-k7),qua(k5),glu(q2))*node_(10,g,QUA(p2),qua(k7),glu(k6)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(-k4),qua(-k5),glu(k2))*node_(8,g,QUA(-k7),qua(k3),glu(-k6))*node_(9,g,QUA(p2),qua(k4),glu(k6))*node_(10,g,QUA(k5),qua(k7),glu(q2)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,QUA(-k6),qua(k3),glu(-k7))*node_(9,g,QUA(p2),qua(k6),glu(k4))*node_(10,g,glu(q2),glu(k5),glu(k7)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,glu(k3),glu(-k6),glu(-k7))*node_(9,g,QUA(p2),qua(k4),glu(k6))*node_(10,g,glu(q2),glu(k5),glu(k7)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k5),qua(k2),glu(-k4))*node_(8,g,QUA(-k6),qua(-k7),glu(k3))*node_(9,g,QUA(p2),qua(k6),glu(k4))*node_(10,g,QUA(k7),qua(k5),glu(q2)) +topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,QUA(p2),qua(k3),glu(-k6))*node_(9,g,glu(k4),glu(k6),glu(-k7))*node_(10,g,glu(q2),glu(k5),glu(k7)) +topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(p2),qua(-k6),glu(k3))*node_(9,g,QUA(k6),qua(k4),glu(-k7))*node_(10,g,glu(q2),glu(k5),glu(k7)) 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+topo_(33)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q2),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(-k6),qua(k4),glu(k5))*node_(9,g,glu(q1),glu(k3),glu(-k7))*node_(10,g,QUA(p2),qua(k6),glu(k7)) +topo_(34)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,glu(k2),glu(-k5),glu(-k6))*node_(8,g,QUA(p2),qua(k3),glu(k5))*node_(9,g,glu(q1),glu(k4),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(34)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,QUA(-k5),qua(-k6),glu(k2))*node_(8,g,QUA(p2),qua(k5),glu(k3))*node_(9,g,QUA(-k7),qua(k4),glu(q1))*node_(10,g,QUA(k6),qua(k7),glu(q2)) +topo_(34)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(-k3),qua(-k4),glu(k1))*node_(7,g,QUA(-k6),qua(k2),glu(-k5))*node_(8,g,QUA(p2),qua(k3),glu(k5))*node_(9,g,QUA(k4),qua(-k7),glu(q1))*node_(10,g,QUA(k7),qua(k6),glu(q2)) +topo_(34)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(k1),glu(-k3),glu(-k4))*node_(7,g,QUA(-k5),qua(k2),glu(-k6))*node_(8,g,QUA(p2),qua(k5),glu(k3))*node_(9,g,glu(q1),glu(k4),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k6),qua(-k5),glu(k2))*node_(8,g,QUA(k5),qua(k3),glu(q1))*node_(9,g,QUA(p2),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k6),glu(q2)) +topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k5),glu(-k6))*node_(8,g,glu(q1),glu(k3),glu(k5))*node_(9,g,QUA(p2),qua(k4),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(-k4),qua(-k3),glu(k1))*node_(7,g,QUA(-k5),qua(k2),glu(-k6))*node_(8,g,QUA(k3),qua(k5),glu(q1))*node_(9,g,QUA(p2),qua(k4),glu(-k7))*node_(10,g,glu(q2),glu(k6),glu(k7)) +topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(k1),glu(-k3),glu(-k4))*node_(7,g,QUA(-k6),qua(k2),glu(-k5))*node_(8,g,glu(q1),glu(k3),glu(k5))*node_(9,g,QUA(p2),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k6),glu(q2)) +topo_(36)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k6),qua(-k5),glu(k2))*node_(8,g,QUA(k5),qua(k3),glu(q2))*node_(9,g,QUA(p2),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k6),glu(q1)) +topo_(36)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k5),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(k5))*node_(9,g,QUA(p2),qua(k4),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(36)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(-k4),qua(-k3),glu(k1))*node_(7,g,QUA(-k5),qua(k2),glu(-k6))*node_(8,g,QUA(k3),qua(k5),glu(q2))*node_(9,g,QUA(p2),qua(k4),glu(-k7))*node_(10,g,glu(q1),glu(k6),glu(k7)) +topo_(36)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(k1),glu(-k3),glu(-k4))*node_(7,g,QUA(-k6),qua(k2),glu(-k5))*node_(8,g,glu(q2),glu(k3),glu(k5))*node_(9,g,QUA(p2),qua(-k7),glu(k4))*node_(10,g,QUA(k7),qua(k6),glu(q1)) +topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(-k4),glu(-k5))*node_(8,g,glu(q2),glu(k4),glu(-k6))*node_(9,g^2,glu(k2),glu(k3),glu(k5),glu(k6)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(p2),qua(k3),glu(-k5))*node_(8,g,glu(q1),glu(k5),glu(-k6))*node_(9,g^2,glu(q2),glu(k2),glu(k4),glu(k6)) +topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(p2),qua(k3),glu(-k5))*node_(8,g,glu(q2),glu(k5),glu(-k6))*node_(9,g^2,glu(q1),glu(k2),glu(k4),glu(k6)) +topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k5),qua(k3),glu(q1))*node_(8,g,QUA(p2),qua(k5),glu(-k6))*node_(9,g^2,glu(q2),glu(k2),glu(k4),glu(k6)) +topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k5),qua(k3),glu(q2))*node_(8,g,QUA(p2),qua(k5),glu(-k6))*node_(9,g^2,glu(q1),glu(k2),glu(k4),glu(k6)) +1/2*topo_(47)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k3),glu(-k4))*node_(8,g,glu(q2),glu(-k5),glu(-k6))*node_(9,g^2,glu(k2),glu(k4),glu(k5),glu(k6)) +1/2*topo_(48)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k3),glu(-k4))*node_(8,g,glu(q1),glu(-k5),glu(-k6))*node_(9,g^2,glu(k2),glu(k4),glu(k5),glu(k6)) +topo_(49)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k3),glu(-k4),glu(-k5))*node_(8,g,glu(q1),glu(k4),glu(-k6))*node_(9,g^2,glu(q2),glu(k2),glu(k5),glu(k6)) +topo_(50)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k3),glu(-k4),glu(-k5))*node_(8,g,glu(q2),glu(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(k2),glu(k5),glu(k6)) +1/2*topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k3),glu(-k4))*node_(8,g,glu(k4),glu(-k5),glu(-k6))*node_(9,g^2,glu(q2),glu(k2),glu(k5),glu(k6)) +1/2*topo_(52)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k3),glu(-k4))*node_(8,g,glu(q2),glu(k4),glu(-k5))*node_(9,g^2,glu(k2),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(53)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k3),glu(-k4))*node_(8,g,glu(k4),glu(-k5),glu(-k6))*node_(9,g^2,glu(q1),glu(k2),glu(k5),glu(k6)) +1/2*topo_(54)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k3),glu(-k4))*node_(8,g,glu(q1),glu(k4),glu(-k5))*node_(9,g^2,glu(k2),glu(k5),glu(-k6),glu(k6)) -topo_(55)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(-k5),glu(k3))*node_(8,g,QUA(k5),qua(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k2),glu(k6)) -topo_(55)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k4),gho(-k5),glu(k3))*node_(8,g,GHO(k5),gho(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k2),glu(k6)) +1/2*topo_(55)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k3),glu(-k4),glu(-k5))*node_(8,g,glu(k4),glu(k5),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k2),glu(k6)) +1/2*topo_(56)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(p2),qua(k3),glu(-k4))*node_(8,g,glu(q2),glu(-k5),glu(-k6))*node_(9,g^2,glu(k2),glu(k4),glu(k5),glu(k6)) +topo_(58)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(-k4),qua(k3),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g^2,glu(q2),glu(k2),glu(k5),glu(k6)) +1/2*topo_(59)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(p2),qua(k3),glu(-k4))*node_(8,g,glu(k4),glu(-k5),glu(-k6))*node_(9,g^2,glu(q2),glu(k2),glu(k5),glu(k6)) +1/2*topo_(60)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(p2),qua(k3),glu(-k4))*node_(8,g,glu(q2),glu(k4),glu(-k5))*node_(9,g^2,glu(k2),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(61)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,QUA(-k4),qua(k3),glu(q2))*node_(8,g,QUA(p2),qua(k4),glu(-k5))*node_(9,g^2,glu(k2),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(62)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q2))*node_(7,g,QUA(p2),qua(k3),glu(-k4))*node_(8,g,glu(q1),glu(-k5),glu(-k6))*node_(9,g^2,glu(k2),glu(k4),glu(k5),glu(k6)) +topo_(64)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q2))*node_(7,g,QUA(-k4),qua(k3),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(k2),glu(k5),glu(k6)) +1/2*topo_(65)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q2))*node_(7,g,QUA(p2),qua(k3),glu(-k4))*node_(8,g,glu(k4),glu(-k5),glu(-k6))*node_(9,g^2,glu(q1),glu(k2),glu(k5),glu(k6)) +1/2*topo_(66)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q2))*node_(7,g,QUA(p2),qua(k3),glu(-k4))*node_(8,g,glu(q1),glu(k4),glu(-k5))*node_(9,g^2,glu(k2),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(67)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q2))*node_(7,g,QUA(-k4),qua(k3),glu(q1))*node_(8,g,QUA(p2),qua(k4),glu(-k5))*node_(9,g^2,glu(k2),glu(k5),glu(-k6),glu(k6)) +topo_(68)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k5),qua(k3),glu(k4))*node_(8,g,QUA(p2),qua(k5),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k2),glu(k6)) +topo_(69)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(p2),qua(k3),glu(-k5))*node_(8,g,glu(q2),glu(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(k2),glu(k5),glu(k6)) +topo_(70)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(p2),qua(k3),glu(-k5))*node_(8,g,glu(q1),glu(k4),glu(-k6))*node_(9,g^2,glu(q2),glu(k2),glu(k5),glu(k6)) +topo_(71)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(-k4))*node_(7,g,QUA(-k5),qua(k3),glu(-k6))*node_(8,g,QUA(p2),qua(k5),glu(k4))*node_(9,g^2,glu(q1),glu(q2),glu(k2),glu(k6)) +topo_(71)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,QUA(p2),qua(k4),glu(k5))*node_(9,g^2,glu(q1),glu(q2),glu(k2),glu(k6)) +topo_(72)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k4),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(k3),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k5),glu(k6)) +topo_(72)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(-k4),qua(-k3),glu(k1))*node_(7,g,QUA(k3),qua(k2),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k5),glu(k6)) +1/2*topo_(73)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g^2,glu(q2),glu(k4),glu(k5),glu(k6)) +1/2*topo_(74)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(q2),glu(k3),glu(-k5))*node_(9,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(75)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(k3),glu(-k5),glu(-k6))*node_(9,g^2,glu(q1),glu(k4),glu(k5),glu(k6)) +1/2*topo_(76)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(q1),glu(k3),glu(-k5))*node_(9,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +topo_(77)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(k3),glu(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k5),glu(k6)) +topo_(77)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,QUA(p2),qua(-k3),glu(k1))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(k3),qua(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k5),glu(k6)) +1/2*topo_(78)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(q1),glu(k3),glu(-k6))*node_(9,g^2,glu(q2),glu(k4),glu(k5),glu(k6)) +1/2*topo_(79)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(q2),glu(k3),glu(-k6))*node_(9,g^2,glu(q1),glu(k4),glu(k5),glu(k6)) +1/2*topo_(80)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(k4),glu(-k5),glu(-k6))*node_(9,g^2,glu(q2),glu(k3),glu(k5),glu(k6)) +1/2*topo_(81)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(q2),glu(k4),glu(-k5))*node_(9,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(82)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q1),glu(k2),glu(-k4))*node_(8,g,glu(q2),glu(-k5),glu(-k6))*node_(9,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) +1/2*topo_(83)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(k4),glu(-k5),glu(-k6))*node_(9,g^2,glu(q1),glu(k3),glu(k5),glu(k6)) +1/2*topo_(84)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(q1),glu(k4),glu(-k5))*node_(9,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(85)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,glu(q1),glu(-k5),glu(-k6))*node_(9,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) -topo_(86)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(-k5),glu(k2))*node_(8,g,QUA(k5),qua(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k3),glu(k6)) -topo_(86)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,GHO(-k4),gho(-k5),glu(k2))*node_(8,g,GHO(k5),gho(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k3),glu(k6)) +1/2*topo_(86)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(k4),glu(k5),glu(-k6))*node_(9,g^2,glu(q1),glu(q2),glu(k3),glu(k6)) +topo_(87)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(q1),glu(k4),glu(-k6))*node_(9,g^2,glu(q2),glu(k3),glu(k5),glu(k6)) +topo_(88)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,glu(q2),glu(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(k3),glu(k5),glu(k6)) +1/2*topo_(89)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(q2),glu(k2),glu(-k4))*node_(8,g,QUA(p2),qua(k3),glu(-k5))*node_(9,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(90)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q1))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,QUA(p2),qua(k3),glu(-k6))*node_(9,g^2,glu(q2),glu(k4),glu(k5),glu(k6)) +1/2*topo_(91)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(q2))*node_(8,g,QUA(p2),qua(k4),glu(-k5))*node_(9,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +topo_(93)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q1),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g^2,glu(q2),glu(k3),glu(k5),glu(k6)) +1/2*topo_(94)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(-k3),qua(k1),glu(q2))*node_(7,g,glu(k2),glu(-k4),glu(-k5))*node_(8,g,QUA(p2),qua(k3),glu(-k6))*node_(9,g^2,glu(q1),glu(k4),glu(k5),glu(k6)) +topo_(95)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(q2),glu(k1),glu(-k3))*node_(7,g,QUA(-k4),qua(k2),glu(-k5))*node_(8,g,QUA(p2),qua(k4),glu(-k6))*node_(9,g^2,glu(q1),glu(k3),glu(k5),glu(k6)) +topo_(96)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k2),qua(p1),glu(-k1))*node_(6,g,glu(k1),glu(-k3),glu(-k4))*node_(7,g,QUA(-k5),qua(k2),glu(-k6))*node_(8,g,QUA(p2),qua(k5),glu(k3))*node_(9,g^2,glu(q1),glu(q2),glu(k4),glu(k6)) +1/2*topo_(97)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g^2,glu(k2),glu(k3),glu(-k4),glu(-k5))*node_(8,g^2,glu(q1),glu(q2),glu(k4),glu(k5)) +1/2*topo_(98)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g^2,glu(k2),glu(-k4),glu(k4),glu(-k5))*node_(8,g^2,glu(q1),glu(q2),glu(k3),glu(k5)) +1/2*topo_(99)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g^2,glu(q1),glu(k2),glu(-k4),glu(-k5))*node_(8,g^2,glu(q2),glu(k3),glu(k4),glu(k5)) +1/2*topo_(100)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g^2,glu(q2),glu(k2),glu(-k4),glu(-k5))*node_(8,g^2,glu(q1),glu(k3),glu(k4),glu(k5)) +1/2*topo_(101)*node_(1,1,QUA(-p1))*node_(2,1,qua(-p2))*node_(3,1,glu(-q1))*node_(4,1,glu(-q2))*node_(5,g,QUA(-k1),qua(p1),glu(-k2))*node_(6,g,QUA(p2),qua(k1),glu(-k3))*node_(7,g^2,glu(q1),glu(q2),glu(k2),glu(-k4))*node_(8,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) form-5.0.1/check/.diagrams_cache/qgraf_qcd_qua_quaglu_3_onepifloop.dat0000644000175100017510000063413715217035721021552 * Compared with qgraf-3.6.10 * Number of diagrams: FORM: 664, QGRAF: 664 topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,QUA(-k7),qua(-k6),glu(k4))*node_(8,g,QUA(k6),qua(k5),glu(-k8))*node_(9,g,QUA(q1),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,glu(k4),glu(-k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(k6))*node_(9,g,QUA(q1),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(-k7))*node_(8,g,QUA(-k8),qua(k6),glu(k5))*node_(9,g,QUA(q1),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(-k7),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(k6),glu(-k8))*node_(9,g,QUA(q1),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(-k7))*node_(8,g,QUA(-k8),qua(k6),glu(k5))*node_(9,g,QUA(q1),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k7),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(k6),glu(-k8))*node_(9,g,QUA(q1),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,QUA(-k7),qua(-k6),glu(k4))*node_(8,g,QUA(k6),qua(k5),glu(-k8))*node_(9,g,QUA(q1),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,glu(k4),glu(-k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(k6))*node_(9,g,QUA(q1),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(q2))*node_(9,g,QUA(k6),qua(-k8),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(q2))*node_(9,g,QUA(k6),qua(-k8),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(k6),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k8),qua(k5),glu(-k7))*node_(9,g,QUA(k6),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(k6),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k8),qua(k5),glu(-k7))*node_(9,g,QUA(k6),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(-k9),qua(k7),glu(k8))*node_(10,g,QUA(k6),qua(k9),glu(q2)) -topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k5))*node_(9,g,QUA(k8),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k6),glu(k9)) -topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k5))*node_(9,g,GHO(k8),gho(k7),glu(-k9))*node_(10,g,glu(q2),glu(k6),glu(k9)) +1/2*topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k7),glu(k8),glu(-k9))*node_(10,g,glu(q2),glu(k6),glu(k9)) -topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k5))*node_(9,g,QUA(k8),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k6),glu(k9)) -topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k5))*node_(9,g,GHO(k8),gho(k7),glu(-k9))*node_(10,g,glu(q2),glu(k6),glu(k9)) +1/2*topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k7),glu(k8),glu(-k9))*node_(10,g,glu(q2),glu(k6),glu(k9)) +topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,QUA(q1),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(-k9),qua(k7),glu(k8))*node_(10,g,QUA(k6),qua(k9),glu(q2)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,glu(q2),glu(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(-k9),qua(k7),glu(k6))*node_(10,g,QUA(q1),qua(k9),glu(k8)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,glu(q2),glu(k4),glu(-k6))*node_(8,g,QUA(-k8),qua(k5),glu(-k7))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,QUA(-k8),qua(-k7),glu(k5))*node_(9,g,QUA(k7),qua(k6),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,QUA(-k9),qua(k6),glu(k7))*node_(10,g,QUA(q1),qua(k9),glu(k8)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,QUA(-k8),qua(-k7),glu(k5))*node_(9,g,QUA(k7),qua(k6),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,QUA(-k9),qua(k6),glu(k7))*node_(10,g,QUA(q1),qua(k9),glu(k8)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,glu(q2),glu(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(-k9),qua(k7),glu(k6))*node_(10,g,QUA(q1),qua(k9),glu(k8)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,glu(q2),glu(k4),glu(-k6))*node_(8,g,QUA(-k8),qua(k5),glu(-k7))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) +topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,glu(q2),glu(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(-k9),qua(k7),glu(k8))*node_(10,g,QUA(q1),qua(k9),glu(k6)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,QUA(-k7),qua(-k8),glu(k5))*node_(9,g,QUA(k8),qua(k7),glu(-k9))*node_(10,g,QUA(q1),qua(k6),glu(k9)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,GHO(-k7),gho(-k8),glu(k5))*node_(9,g,GHO(k8),gho(k7),glu(-k9))*node_(10,g,QUA(q1),qua(k6),glu(k9)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(k3),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k7),glu(k8),glu(-k9))*node_(10,g,QUA(q1),qua(k6),glu(k9)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,QUA(-k7),qua(-k8),glu(k5))*node_(9,g,QUA(k8),qua(k7),glu(-k9))*node_(10,g,QUA(q1),qua(k6),glu(k9)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,GHO(-k7),gho(-k8),glu(k5))*node_(9,g,GHO(k8),gho(k7),glu(-k9))*node_(10,g,QUA(q1),qua(k6),glu(k9)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(q2))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k7),glu(k8),glu(-k9))*node_(10,g,QUA(q1),qua(k6),glu(k9)) +topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,glu(q2),glu(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(-k9),qua(k7),glu(k8))*node_(10,g,QUA(q1),qua(k9),glu(k6)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(k3),glu(k2))*node_(7,g,glu(k4),glu(-k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(-k9))*node_(9,g,QUA(q1),qua(k8),glu(k6))*node_(10,g,glu(q2),glu(k7),glu(k9)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(k3),qua(k2),glu(-k5))*node_(7,g,QUA(-k7),qua(k4),glu(-k6))*node_(8,g,QUA(-k8),qua(-k9),glu(k5))*node_(9,g,QUA(q1),qua(k8),glu(k6))*node_(10,g,QUA(k9),qua(k7),glu(q2)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,QUA(-k6),qua(-k7),glu(k4))*node_(8,g,QUA(-k9),qua(k5),glu(-k8))*node_(9,g,QUA(q1),qua(k6),glu(k8))*node_(10,g,QUA(k7),qua(k9),glu(q2)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(k3))*node_(7,g,glu(k4),glu(-k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(-k9))*node_(9,g,QUA(q1),qua(k8),glu(k6))*node_(10,g,glu(q2),glu(k7),glu(k9)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,QUA(-k5),qua(-k6),glu(k3))*node_(8,g,QUA(-k7),qua(k5),glu(k4))*node_(9,g,QUA(k6),qua(-k8),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,QUA(-k6),qua(-k5),glu(k3))*node_(8,g,QUA(k5),qua(-k7),glu(k4))*node_(9,g,QUA(-k8),qua(k6),glu(-k9))*node_(10,g,QUA(k7),qua(k8),glu(k9)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,GHO(-k5),gho(-k6),glu(k3))*node_(8,g,GHO(-k7),gho(k5),glu(k4))*node_(9,g,GHO(k6),gho(-k8),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,GHO(-k6),gho(-k5),glu(k3))*node_(8,g,GHO(k5),gho(-k7),glu(k4))*node_(9,g,GHO(-k8),gho(k6),glu(-k9))*node_(10,g,GHO(k7),gho(k8),glu(k9)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,glu(k4),glu(k5),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,glu(k4),glu(k5),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,glu(k4),glu(k5),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(q2))*node_(7,g,QUA(k3),qua(-k5),glu(-k6))*node_(8,g,QUA(k5),qua(k4),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(q2))*node_(7,g,QUA(k3),qua(-k5),glu(-k6))*node_(8,g,QUA(k5),qua(k4),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(q2))*node_(7,g,QUA(k3),qua(-k5),glu(-k6))*node_(8,g,QUA(k5),qua(k4),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(q2))*node_(7,g,QUA(k3),qua(-k6),glu(-k5))*node_(8,g,QUA(-k7),qua(k4),glu(k5))*node_(9,g,QUA(k6),qua(-k8),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,QUA(-k5),qua(-k6),glu(k3))*node_(8,g,QUA(-k7),qua(-k8),glu(k4))*node_(9,g,QUA(k6),qua(k5),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,QUA(-k5),qua(-k6),glu(k3))*node_(8,g,GHO(-k7),gho(-k8),glu(k4))*node_(9,g,QUA(k6),qua(k5),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,QUA(-k5),qua(-k6),glu(k3))*node_(8,g,glu(k4),glu(-k7),glu(-k8))*node_(9,g,QUA(k6),qua(k5),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,GHO(-k5),gho(-k6),glu(k3))*node_(8,g,QUA(-k7),qua(-k8),glu(k4))*node_(9,g,GHO(k6),gho(k5),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,GHO(-k5),gho(-k6),glu(k3))*node_(8,g,GHO(-k7),gho(-k8),glu(k4))*node_(9,g,GHO(k6),gho(k5),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,GHO(-k5),gho(-k6),glu(k3))*node_(8,g,glu(k4),glu(-k7),glu(-k8))*node_(9,g,GHO(k6),gho(k5),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k4))*node_(9,g,glu(k5),glu(k6),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k4))*node_(9,g,glu(k5),glu(k6),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) +1/4*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,glu(k4),glu(-k7),glu(-k8))*node_(9,g,glu(k5),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(q2))*node_(7,g,QUA(k3),qua(-k5),glu(-k6))*node_(8,g,QUA(-k7),qua(k4),glu(-k8))*node_(9,g,QUA(k5),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k7),glu(k8)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,QUA(-k6),qua(-k5),glu(k3))*node_(8,g,QUA(-k7),qua(-k8),glu(k4))*node_(9,g,QUA(k5),qua(k7),glu(-k9))*node_(10,g,QUA(k8),qua(k6),glu(k9)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,GHO(-k6),gho(-k5),glu(k3))*node_(8,g,GHO(-k7),gho(-k8),glu(k4))*node_(9,g,GHO(k5),gho(k7),glu(-k9))*node_(10,g,GHO(k8),gho(k6),glu(k9)) +1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k2),glu(-k4))*node_(7,g,glu(k3),glu(-k5),glu(-k6))*node_(8,g,glu(k4),glu(-k7),glu(-k8))*node_(9,g,glu(k5),glu(k7),glu(-k9))*node_(10,g,glu(k6),glu(k8),glu(k9)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(q2))*node_(7,g,QUA(k3),qua(-k6),glu(-k5))*node_(8,g,QUA(-k7),qua(k4),glu(-k8))*node_(9,g,QUA(-k9),qua(k7),glu(k5))*node_(10,g,QUA(k6),qua(k9),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(q2))*node_(7,g,QUA(k3),qua(-k6),glu(-k5))*node_(8,g,QUA(-k8),qua(k4),glu(-k7))*node_(9,g,glu(k5),glu(k7),glu(-k9))*node_(10,g,QUA(k6),qua(k8),glu(k9)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(-k6),qua(k4),glu(k3))*node_(8,g,QUA(k5),qua(-k7),glu(-k8))*node_(9,g,QUA(k7),qua(k6),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k5),qua(-k4),glu(k2))*node_(7,g,QUA(k4),qua(-k6),glu(k3))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(k6),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(-k6),gho(k4),glu(k3))*node_(8,g,GHO(k5),gho(-k7),glu(-k8))*node_(9,g,GHO(k7),gho(k6),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k5),gho(-k4),glu(k2))*node_(7,g,GHO(k4),gho(-k6),glu(k3))*node_(8,g,GHO(-k7),gho(k5),glu(-k8))*node_(9,g,GHO(k6),gho(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(k6),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(k4))*node_(8,g,QUA(-k8),qua(k5),glu(-k7))*node_(9,g,QUA(k6),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k5),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(q2))*node_(9,g,QUA(k6),qua(-k8),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k5))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k5))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) +1/2*topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k5))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(k4),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k5))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) +1/2*topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(k4),glu(-k6))*node_(8,g,glu(k5),glu(-k7),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(k4))*node_(8,g,QUA(-k7),qua(k5),glu(-k8))*node_(9,g,QUA(k6),qua(-k9),glu(q2))*node_(10,g,QUA(k9),qua(k7),glu(k8)) -topo_(14)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k5),qua(-k4),glu(k2))*node_(7,g,QUA(-k6),qua(-k7),glu(k3))*node_(8,g,QUA(k4),qua(k6),glu(-k8))*node_(9,g,QUA(k7),qua(k5),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) 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+topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(-k6),glu(-k7))*node_(8,g,QUA(k6),qua(k4),glu(-k8))*node_(9,g,glu(q2),glu(k5),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(-k7),glu(-k6))*node_(8,g,QUA(-k8),qua(k4),glu(k6))*node_(9,g,glu(q2),glu(k5),glu(-k9))*node_(10,g,QUA(k7),qua(k8),glu(k9)) +topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(-k7))*node_(8,g,QUA(k6),qua(-k8),glu(k4))*node_(9,g,QUA(-k9),qua(k5),glu(q2))*node_(10,g,QUA(k8),qua(k9),glu(k7)) +topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k7),glu(-k6))*node_(8,g,glu(k4),glu(k6),glu(-k8))*node_(9,g,QUA(-k9),qua(k5),glu(q2))*node_(10,g,QUA(k7),qua(k9),glu(k8)) -topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(-k6),glu(-k7))*node_(8,g,glu(q2),glu(k4),glu(k6))*node_(9,g,QUA(-k8),qua(-k9),glu(k5))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(-k6),glu(-k7))*node_(8,g,glu(q2),glu(k4),glu(k6))*node_(9,g,GHO(-k8),gho(-k9),glu(k5))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(-k6),glu(-k7))*node_(8,g,glu(q2),glu(k4),glu(k6))*node_(9,g,glu(k5),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(-k6),glu(-k7))*node_(8,g,QUA(k6),qua(k4),glu(q2))*node_(9,g,QUA(-k8),qua(-k9),glu(k5))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(-k6),glu(-k7))*node_(8,g,QUA(k6),qua(k4),glu(q2))*node_(9,g,GHO(-k8),gho(-k9),glu(k5))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(-k6),glu(-k7))*node_(8,g,QUA(k6),qua(k4),glu(q2))*node_(9,g,glu(k5),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(18)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k7),glu(-k6))*node_(8,g,glu(q2),glu(k4),glu(k6))*node_(9,g,QUA(-k8),qua(k5),glu(-k9))*node_(10,g,QUA(k7),qua(k8),glu(k9)) -topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k5),qua(-k4),glu(k2))*node_(7,g,glu(q2),glu(k3),glu(-k6))*node_(8,g,QUA(k4),qua(-k8),glu(-k7))*node_(9,g,QUA(-k9),qua(k5),glu(k7))*node_(10,g,QUA(k8),qua(k9),glu(k6)) -topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k5),gho(-k4),glu(k2))*node_(7,g,glu(q2),glu(k3),glu(-k6))*node_(8,g,GHO(k4),gho(-k8),glu(-k7))*node_(9,g,GHO(-k9),gho(k5),glu(k7))*node_(10,g,GHO(k8),gho(k9),glu(k6)) +1/2*topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(q2),glu(k3),glu(-k6))*node_(8,g,glu(k4),glu(-k7),glu(-k8))*node_(9,g,glu(k5),glu(k7),glu(-k9))*node_(10,g,glu(k6),glu(k8),glu(k9)) +topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(q2))*node_(8,g,QUA(-k8),qua(-k7),glu(k4))*node_(9,g,QUA(k7),qua(k5),glu(-k9))*node_(10,g,QUA(k6),qua(k8),glu(k9)) +topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(q2))*node_(8,g,glu(k4),glu(-k7),glu(-k8))*node_(9,g,QUA(-k9),qua(k5),glu(k7))*node_(10,g,QUA(k6),qua(k9),glu(k8)) -topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,QUA(-k6),qua(-k7),glu(k3))*node_(8,g,glu(k4),glu(-k8),glu(-k9))*node_(9,g,glu(q2),glu(k5),glu(k8))*node_(10,g,QUA(k7),qua(k6),glu(k9)) -topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,GHO(-k6),gho(-k7),glu(k3))*node_(8,g,glu(k4),glu(-k8),glu(-k9))*node_(9,g,glu(q2),glu(k5),glu(k8))*node_(10,g,GHO(k7),gho(k6),glu(k9)) +1/2*topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k3),glu(-k6),glu(-k7))*node_(8,g,glu(k4),glu(-k8),glu(-k9))*node_(9,g,glu(q2),glu(k5),glu(k8))*node_(10,g,glu(k6),glu(k7),glu(k9)) +topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(k3),qua(-k6),glu(-k7))*node_(8,g,QUA(-k9),qua(k4),glu(-k8))*node_(9,g,glu(q2),glu(k5),glu(k8))*node_(10,g,QUA(k6),qua(k9),glu(k7)) +topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(k3),qua(-k6),glu(-k7))*node_(8,g,QUA(-k9),qua(-k8),glu(k4))*node_(9,g,QUA(k8),qua(k5),glu(q2))*node_(10,g,QUA(k6),qua(k9),glu(k7)) -topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,glu(k3),glu(-k7),glu(-k8))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) -topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,glu(k3),glu(-k7),glu(-k8))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +1/2*topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,glu(k3),glu(-k7),glu(-k8))*node_(9,g,glu(k6),glu(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(k5))*node_(8,g,QUA(k3),qua(-k7),glu(-k8))*node_(9,g,QUA(k7),qua(k6),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(k5))*node_(8,g,QUA(k3),qua(-k8),glu(-k7))*node_(9,g,QUA(-k9),qua(k6),glu(k7))*node_(10,g,QUA(k8),qua(k9),glu(q2)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) -1/2*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) -1/2*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -1/2*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -1/2*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/4*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,glu(q2),glu(k3),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(q1),qua(-k3),glu(k1))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(k5))*node_(8,g,QUA(k3),qua(-k7),glu(q2))*node_(9,g,QUA(-k8),qua(k6),glu(-k9))*node_(10,g,QUA(k7),qua(k8),glu(k9)) +topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k3))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) +topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k3))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) -1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,glu(k3),glu(-k7),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k3))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) +topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k3))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) -1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,glu(k3),glu(-k7),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,QUA(-k7),qua(-k8),glu(k3))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,GHO(-k7),gho(-k8),glu(k3))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,GHO(k8),gho(k7),glu(k9)) +1/4*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,glu(k3),glu(-k7),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) 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+topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(-k7),qua(k3),glu(-k6))*node_(8,g,QUA(q1),qua(k4),glu(k6))*node_(9,g,QUA(k5),qua(-k8),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,QUA(-k6),qua(k3),glu(-k7))*node_(8,g,QUA(q1),qua(k6),glu(k4))*node_(9,g,QUA(-k8),qua(-k9),glu(k5))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,QUA(-k6),qua(k3),glu(-k7))*node_(8,g,QUA(q1),qua(k6),glu(k4))*node_(9,g,GHO(-k8),gho(-k9),glu(k5))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,QUA(-k6),qua(k3),glu(-k7))*node_(8,g,QUA(q1),qua(k6),glu(k4))*node_(9,g,glu(k5),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(q2),glu(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(-k6),glu(-k7))*node_(8,g,QUA(q1),qua(k4),glu(k6))*node_(9,g,QUA(-k8),qua(-k9),glu(k5))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(q2),glu(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(-k6),glu(-k7))*node_(8,g,QUA(q1),qua(k4),glu(k6))*node_(9,g,GHO(-k8),gho(-k9),glu(k5))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/2*topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(q2),glu(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(-k6),glu(-k7))*node_(8,g,QUA(q1),qua(k4),glu(k6))*node_(9,g,glu(k5),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(q2),glu(k1),glu(-k3))*node_(6,g,QUA(-k5),qua(k2),glu(-k4))*node_(7,g,QUA(-k6),qua(-k7),glu(k3))*node_(8,g,QUA(q1),qua(k6),glu(k4))*node_(9,g,QUA(-k8),qua(k5),glu(-k9))*node_(10,g,QUA(k7),qua(k8),glu(k9)) -topo_(32)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(-k5),qua(-k4),glu(k2))*node_(7,g,QUA(q1),qua(k3),glu(-k6))*node_(8,g,QUA(k4),qua(-k8),glu(-k7))*node_(9,g,QUA(-k9),qua(k5),glu(k7))*node_(10,g,QUA(k8),qua(k9),glu(k6)) 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+topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) -1/2*topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) +topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) -1/2*topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -1/2*topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) -1/2*topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,GHO(-k8),gho(-k9),glu(k6))*node_(10,g,GHO(k9),gho(k8),glu(k7)) +1/4*topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,QUA(q1),qua(k3),glu(-k7))*node_(9,g,glu(k6),glu(-k8),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +topo_(35)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(q2),glu(k1),glu(-k3))*node_(6,g,QUA(-k4),qua(k2),glu(-k5))*node_(7,g,QUA(-k6),qua(k4),glu(k5))*node_(8,g,QUA(q1),qua(-k7),glu(k3))*node_(9,g,QUA(-k8),qua(k6),glu(-k9))*node_(10,g,QUA(k7),qua(k8),glu(k9)) -topo_(36)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(-k4),qua(-k5),glu(k2))*node_(7,g,QUA(k5),qua(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(k3),glu(-k8))*node_(9,g,QUA(q1),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k7),glu(k8)) -topo_(36)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,GHO(-k4),gho(-k5),glu(k2))*node_(7,g,GHO(k5),gho(k4),glu(-k6))*node_(8,g,QUA(-k7),qua(k3),glu(-k8))*node_(9,g,QUA(q1),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k7),glu(k8)) +1/2*topo_(36)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,glu(k2),glu(-k4),glu(-k5))*node_(7,g,glu(k4),glu(k5),glu(-k6))*node_(8,g,QUA(-k7),qua(k3),glu(-k8))*node_(9,g,QUA(q1),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k7),glu(k8)) 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+1/2*topo_(38)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(k7))*node_(9,g,QUA(q1),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +1/2*topo_(38)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,glu(k5),glu(k7),glu(-k8))*node_(9,g,QUA(q1),qua(k6),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k6),qua(-k5),glu(k2))*node_(7,g,QUA(-k7),qua(k3),glu(k4))*node_(8,g,QUA(k5),qua(k7),glu(-k8))*node_(9,g,QUA(-k9),qua(k6),glu(q2))*node_(10,g,QUA(q1),qua(k9),glu(k8)) +topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,glu(k2),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(k3),glu(k4))*node_(8,g,QUA(-k8),qua(k7),glu(k5))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) -topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,QUA(k4),qua(k3),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(k7))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) -topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,QUA(k4),qua(k3),glu(-k7))*node_(8,g,glu(k5),glu(k7),glu(-k8))*node_(9,g,QUA(-k9),qua(k6),glu(q2))*node_(10,g,QUA(q1),qua(k9),glu(k8)) -topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,GHO(-k3),gho(-k4),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,GHO(k4),gho(k3),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(k7))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) -topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,GHO(-k3),gho(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,GHO(k4),gho(k3),glu(-k7))*node_(8,g,glu(k5),glu(k7),glu(-k8))*node_(9,g,QUA(-k9),qua(k6),glu(q2))*node_(10,g,QUA(q1),qua(k9),glu(k8)) +1/2*topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(k7))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(q1),qua(k8),glu(k9)) +1/2*topo_(39)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,glu(k5),glu(k7),glu(-k8))*node_(9,g,QUA(-k9),qua(k6),glu(q2))*node_(10,g,QUA(q1),qua(k9),glu(k8)) +topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k2))*node_(7,g,QUA(-k7),qua(k3),glu(k4))*node_(8,g,QUA(q1),qua(k5),glu(-k8))*node_(9,g,QUA(k6),qua(-k9),glu(q2))*node_(10,g,QUA(k9),qua(k7),glu(k8)) +topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,glu(k2),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(k3),glu(k4))*node_(8,g,QUA(q1),qua(-k8),glu(k5))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) -topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,QUA(k4),qua(k3),glu(-k7))*node_(8,g,QUA(q1),qua(k5),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,QUA(k4),qua(k3),glu(-k7))*node_(8,g,QUA(q1),qua(-k8),glu(k5))*node_(9,g,QUA(-k9),qua(k6),glu(q2))*node_(10,g,QUA(k8),qua(k9),glu(k7)) -topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,GHO(-k3),gho(-k4),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,GHO(k4),gho(k3),glu(-k7))*node_(8,g,QUA(q1),qua(k5),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) -topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,GHO(-k3),gho(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,GHO(k4),gho(k3),glu(-k7))*node_(8,g,QUA(q1),qua(-k8),glu(k5))*node_(9,g,QUA(-k9),qua(k6),glu(q2))*node_(10,g,QUA(k8),qua(k9),glu(k7)) +1/2*topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,QUA(q1),qua(k5),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(-k9))*node_(10,g,glu(k7),glu(k8),glu(k9)) +1/2*topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,QUA(q1),qua(-k8),glu(k5))*node_(9,g,QUA(-k9),qua(k6),glu(q2))*node_(10,g,QUA(k8),qua(k9),glu(k7)) +topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,glu(k2),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(k3),glu(k4))*node_(8,g,glu(k5),glu(-k8),glu(-k9))*node_(9,g,glu(q2),glu(k6),glu(k8))*node_(10,g,QUA(q1),qua(k7),glu(k9)) -topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,QUA(k4),qua(k3),glu(-k7))*node_(8,g,QUA(-k9),qua(k5),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(k8))*node_(10,g,QUA(q1),qua(k9),glu(k7)) -topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,QUA(k4),qua(k3),glu(-k7))*node_(8,g,QUA(-k9),qua(-k8),glu(k5))*node_(9,g,QUA(k8),qua(k6),glu(q2))*node_(10,g,QUA(q1),qua(k9),glu(k7)) -topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,GHO(-k3),gho(-k4),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,GHO(k4),gho(k3),glu(-k7))*node_(8,g,QUA(-k9),qua(k5),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(k8))*node_(10,g,QUA(q1),qua(k9),glu(k7)) -topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,GHO(-k3),gho(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,GHO(k4),gho(k3),glu(-k7))*node_(8,g,QUA(-k9),qua(-k8),glu(k5))*node_(9,g,QUA(k8),qua(k6),glu(q2))*node_(10,g,QUA(q1),qua(k9),glu(k7)) +1/2*topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,QUA(-k9),qua(k5),glu(-k8))*node_(9,g,glu(q2),glu(k6),glu(k8))*node_(10,g,QUA(q1),qua(k9),glu(k7)) +1/2*topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,QUA(-k9),qua(-k8),glu(k5))*node_(9,g,QUA(k8),qua(k6),glu(q2))*node_(10,g,QUA(q1),qua(k9),glu(k7)) +topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(-k6),qua(-k5),glu(k2))*node_(7,g,QUA(-k7),qua(k3),glu(k4))*node_(8,g,QUA(k5),qua(-k9),glu(-k8))*node_(9,g,QUA(q1),qua(k6),glu(k8))*node_(10,g,QUA(k9),qua(k7),glu(q2)) +topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,glu(k2),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(k3),glu(k4))*node_(8,g,QUA(-k8),qua(-k9),glu(k5))*node_(9,g,QUA(q1),qua(k8),glu(k6))*node_(10,g,QUA(k9),qua(k7),glu(q2)) 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-topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,GHO(-k3),gho(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,GHO(k4),gho(k3),glu(-k7))*node_(8,g,glu(k5),glu(-k8),glu(-k9))*node_(9,g,QUA(q1),qua(k6),glu(k8))*node_(10,g,glu(q2),glu(k7),glu(k9)) +1/2*topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,QUA(-k8),qua(k5),glu(-k9))*node_(9,g,QUA(q1),qua(k8),glu(k6))*node_(10,g,glu(q2),glu(k7),glu(k9)) +1/2*topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,glu(k3),glu(k4),glu(-k7))*node_(8,g,glu(k5),glu(-k8),glu(-k9))*node_(9,g,QUA(q1),qua(k6),glu(k8))*node_(10,g,glu(q2),glu(k7),glu(k9)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,QUA(-k7),qua(k3),glu(k5))*node_(8,g,QUA(k4),qua(k6),glu(-k8))*node_(9,g,QUA(q1),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k4),qua(-k3),glu(k1))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,QUA(k3),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k4),glu(k6))*node_(9,g,QUA(q1),qua(-k9),glu(k7))*node_(10,g,QUA(k9),qua(k8),glu(q2)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,QUA(-k7),qua(k5),glu(k3))*node_(8,g,glu(k4),glu(k6),glu(-k8))*node_(9,g,QUA(q1),qua(k7),glu(-k9))*node_(10,g,glu(q2),glu(k8),glu(k9)) 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+topo_(47)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k4),qua(k1),glu(-k3))*node_(6,g,QUA(-k5),qua(-k6),glu(k2))*node_(7,g,QUA(q1),qua(k5),glu(k3))*node_(8,g,QUA(-k7),qua(k4),glu(q2))*node_(9,g,QUA(k6),qua(-k8),glu(-k9))*node_(10,g,QUA(k8),qua(k7),glu(k9)) +topo_(47)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,QUA(-k3),qua(-k4),glu(k1))*node_(6,g,QUA(-k6),qua(k2),glu(-k5))*node_(7,g,QUA(q1),qua(k3),glu(k5))*node_(8,g,QUA(k4),qua(-k7),glu(q2))*node_(9,g,QUA(-k8),qua(k6),glu(-k9))*node_(10,g,QUA(k7),qua(k8),glu(k9)) -topo_(47)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k2),qua(p1),glu(-k1))*node_(5,g,glu(k1),glu(-k3),glu(-k4))*node_(6,g,QUA(-k5),qua(k2),glu(-k6))*node_(7,g,QUA(q1),qua(k5),glu(k3))*node_(8,g,glu(q2),glu(k4),glu(-k7))*node_(9,g,QUA(-k8),qua(-k9),glu(k6))*node_(10,g,QUA(k9),qua(k8),glu(k7)) 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+1/4*topo_(205)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(-k4),glu(-k5))*node_(7,g^2,glu(k2),glu(k3),glu(-k6),glu(-k7))*node_(8,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) +1/2*topo_(208)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(q1),qua(k3),glu(-k5))*node_(7,g^2,glu(k2),glu(k4),glu(-k6),glu(-k7))*node_(8,g^2,glu(q2),glu(k5),glu(k6),glu(k7)) +1/2*topo_(209)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(q1),qua(k3),glu(-k5))*node_(7,g^2,glu(q2),glu(k2),glu(k4),glu(-k6))*node_(8,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(213)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k3),glu(-k4))*node_(7,g^2,glu(k2),glu(k4),glu(-k5),glu(-k6))*node_(8,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(214)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k3),glu(-k4),glu(-k5))*node_(7,g^2,glu(k2),glu(k4),glu(-k6),glu(-k7))*node_(8,g^2,glu(q2),glu(k5),glu(k6),glu(k7)) +1/2*topo_(215)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k3),glu(-k4),glu(-k5))*node_(7,g^2,glu(q2),glu(k2),glu(k4),glu(-k6))*node_(8,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(216)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k3),glu(-k4))*node_(7,g^2,glu(k2),glu(-k5),glu(k5),glu(-k6))*node_(8,g^2,glu(k4),glu(k6),glu(-k7),glu(k7)) +1/6*topo_(217)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(k3),glu(-k4))*node_(7,g^2,glu(k2),glu(-k5),glu(-k6),glu(-k7))*node_(8,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) +1/4*topo_(218)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k3),glu(-k4),glu(-k5))*node_(7,g^2,glu(k2),glu(-k6),glu(k6),glu(-k7))*node_(8,g^2,glu(q2),glu(k4),glu(k5),glu(k7)) +1/4*topo_(219)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(k3),glu(-k4),glu(-k5))*node_(7,g^2,glu(q2),glu(k2),glu(-k6),glu(-k7))*node_(8,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) +1/4*topo_(220)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(-k4),glu(-k5))*node_(7,g^2,glu(k2),glu(-k6),glu(k6),glu(-k7))*node_(8,g^2,glu(k3),glu(k4),glu(k5),glu(k7)) +1/4*topo_(221)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(-k4),glu(-k5),glu(-k6))*node_(7,g^2,glu(k2),glu(k4),glu(-k7),glu(k7))*node_(8,g^2,glu(q2),glu(k3),glu(k5),glu(k6)) +1/4*topo_(222)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(-k4),glu(-k5))*node_(7,g^2,glu(k2),glu(k4),glu(-k6),glu(k6))*node_(8,g^2,glu(k3),glu(k5),glu(-k7),glu(k7)) +1/2*topo_(223)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(-k4),glu(-k5))*node_(7,g^2,glu(k2),glu(k4),glu(-k6),glu(-k7))*node_(8,g^2,glu(k3),glu(k5),glu(k6),glu(k7)) +1/2*topo_(224)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(-k4),glu(-k5),glu(-k6))*node_(7,g^2,glu(q2),glu(k2),glu(k4),glu(-k7))*node_(8,g^2,glu(k3),glu(k5),glu(k6),glu(k7)) +1/2*topo_(225)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(-k4),glu(-k5),glu(-k6))*node_(7,g^2,glu(k2),glu(k4),glu(k5),glu(-k7))*node_(8,g^2,glu(q2),glu(k3),glu(k6),glu(k7)) +1/4*topo_(226)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(q2),glu(-k4),glu(-k5))*node_(7,g^2,glu(k2),glu(k4),glu(k5),glu(-k6))*node_(8,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(227)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(q1),qua(k1),glu(-k3))*node_(6,g,glu(-k4),glu(-k5),glu(-k6))*node_(7,g^2,glu(q2),glu(k2),glu(k4),glu(k5))*node_(8,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(228)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(q1),qua(k3),glu(-k4))*node_(7,g^2,glu(k2),glu(k4),glu(-k5),glu(-k6))*node_(8,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(229)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(q1),qua(k3),glu(-k4))*node_(7,g^2,glu(k2),glu(-k5),glu(k5),glu(-k6))*node_(8,g^2,glu(k4),glu(k6),glu(-k7),glu(k7)) +1/6*topo_(230)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(q2))*node_(6,g,QUA(q1),qua(k3),glu(-k4))*node_(7,g^2,glu(k2),glu(-k5),glu(-k6),glu(-k7))*node_(8,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) +1/2*topo_(235)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(q1),qua(k3),glu(-k5))*node_(7,g^2,glu(k2),glu(k5),glu(-k6),glu(-k7))*node_(8,g^2,glu(q2),glu(k4),glu(k6),glu(k7)) +1/2*topo_(236)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(q1),qua(k3),glu(-k5))*node_(7,g^2,glu(q2),glu(k2),glu(k5),glu(-k6))*node_(8,g^2,glu(k4),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(237)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(q1),qua(k3),glu(-k5))*node_(7,g^2,glu(k2),glu(-k6),glu(k6),glu(-k7))*node_(8,g^2,glu(q2),glu(k4),glu(k5),glu(k7)) +1/2*topo_(238)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,1,glu(-q2))*node_(4,g,QUA(-k1),qua(p1),glu(-k2))*node_(5,g,QUA(-k3),qua(k1),glu(-k4))*node_(6,g,QUA(q1),qua(k3),glu(-k5))*node_(7,g^2,glu(q2),glu(k2),glu(-k6),glu(-k7))*node_(8,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) form-5.0.1/check/.diagrams_cache/feyngraph_qcd_3_onepi_opicomponents1.dat0000644000175100017510000000557715217035721022207 * Compared with feyngraph 0.1.0b4+gf7ae8f4 * Number of diagrams: FORM: 19, FeynGraph: 19 1/4*topo_(1)*node_(1,g,QUA(-k1),qua(-k2),glu(-k3))*node_(2,g,QUA(k2),qua(k1),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k3))*node_(4,g,QUA(k6),qua(k5),glu(k4)) -1/2*topo_(1)*node_(1,g,QUA(-k3),qua(-k1),glu(-k2))*node_(2,g,QUA(k1),qua(-k4),glu(k2))*node_(3,g,QUA(-k5),qua(k3),glu(-k6))*node_(4,g,QUA(k4),qua(k5),glu(k6)) +1/2*topo_(1)*node_(1,g,GHO(-k1),gho(-k2),glu(-k3))*node_(2,g,GHO(k2),gho(k1),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k3))*node_(4,g,QUA(k6),qua(k5),glu(k4)) +1/4*topo_(1)*node_(1,g,GHO(-k1),gho(-k2),glu(-k3))*node_(2,g,GHO(k2),gho(k1),glu(-k4))*node_(3,g,GHO(-k5),gho(-k6),glu(k3))*node_(4,g,GHO(k6),gho(k5),glu(k4)) -1/2*topo_(1)*node_(1,g,GHO(-k3),gho(-k1),glu(-k2))*node_(2,g,GHO(k1),gho(-k4),glu(k2))*node_(3,g,GHO(-k5),gho(k3),glu(-k6))*node_(4,g,GHO(k4),gho(k5),glu(k6)) -1/4*topo_(1)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,glu(k1),glu(k2),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k3))*node_(4,g,QUA(k6),qua(k5),glu(k4)) -1/4*topo_(1)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,glu(k1),glu(k2),glu(-k4))*node_(3,g,GHO(-k5),gho(-k6),glu(k3))*node_(4,g,GHO(k6),gho(k5),glu(k4)) +1/16*topo_(1)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,glu(k1),glu(k2),glu(-k4))*node_(3,g,glu(k3),glu(-k5),glu(-k6))*node_(4,g,glu(k4),glu(k5),glu(k6)) -1/4*topo_(2)*node_(1,g,QUA(-k3),qua(-k2),glu(-k1))*node_(2,g,QUA(-k4),qua(-k5),glu(k1))*node_(3,g,QUA(k2),qua(k4),glu(-k6))*node_(4,g,QUA(k5),qua(k3),glu(k6)) -1/4*topo_(2)*node_(1,g,GHO(-k3),gho(-k2),glu(-k1))*node_(2,g,GHO(-k4),gho(-k5),glu(k1))*node_(3,g,GHO(k2),gho(k4),glu(-k6))*node_(4,g,GHO(k5),gho(k3),glu(k6)) -1/3*topo_(2)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,QUA(-k5),qua(-k4),glu(k1))*node_(3,g,QUA(k4),qua(-k6),glu(k2))*node_(4,g,QUA(k6),qua(k5),glu(k3)) -1/3*topo_(2)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,GHO(-k5),gho(-k4),glu(k1))*node_(3,g,GHO(k4),gho(-k6),glu(k2))*node_(4,g,GHO(k6),gho(k5),glu(k3)) +1/24*topo_(2)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,glu(k1),glu(-k4),glu(-k5))*node_(3,g,glu(k2),glu(k4),glu(-k6))*node_(4,g,glu(k3),glu(k5),glu(k6)) -1/4*topo_(3)*node_(1,g,QUA(-k1),qua(-k2),glu(-k3))*node_(2,g,QUA(k2),qua(k1),glu(-k4))*node_(3,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) -1/4*topo_(3)*node_(1,g,GHO(-k1),gho(-k2),glu(-k3))*node_(2,g,GHO(k2),gho(k1),glu(-k4))*node_(3,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) +1/8*topo_(3)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,glu(k1),glu(k2),glu(-k4))*node_(3,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) +1/8*topo_(4)*node_(1,g,glu(-k1),glu(-k2),glu(-k3))*node_(2,g,glu(k1),glu(-k4),glu(-k5))*node_(3,g^2,glu(k2),glu(k3),glu(k4),glu(k5)) +1/16*topo_(5)*node_(1,g^2,glu(-k1),glu(k1),glu(-k2),glu(-k3))*node_(2,g^2,glu(k2),glu(k3),glu(-k4),glu(k4)) +1/48*topo_(6)*node_(1,g^2,glu(-k1),glu(-k2),glu(-k3),glu(-k4))*node_(2,g^2,glu(k1),glu(k2),glu(k3),glu(k4)) form-5.0.1/check/.diagrams_cache/qgraf_qcd_glu_glu_3_onepifloop.dat0000644000175100017510000015544215217035721021041 * Compared with qgraf-3.6.10 * Number of diagrams: FORM: 222, QGRAF: 222 -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k4),glu(-k3))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(k4),qua(-k7),glu(-k6))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(k7),qua(k8),glu(q1)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k4),glu(-k3))*node_(5,g,GHO(-k5),gho(k2),glu(k3))*node_(6,g,GHO(k4),gho(-k7),glu(-k6))*node_(7,g,GHO(-k8),gho(k5),glu(k6))*node_(8,g,GHO(k7),gho(k8),glu(q1)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(k4),glu(-k7))*node_(7,g,QUA(k5),qua(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,GHO(-k4),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(k4),glu(-k7))*node_(7,g,GHO(k5),gho(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) +1/2*topo_(1)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,glu(k5),glu(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -topo_(2)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,QUA(k2),qua(-k5),glu(k3))*node_(6,g,QUA(-k6),qua(k4),glu(q1))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -topo_(2)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k4),glu(-k3))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(k4),qua(-k6),glu(q1))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(2)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k4),gho(k1),glu(-k3))*node_(5,g,GHO(k2),gho(-k5),glu(k3))*node_(6,g,GHO(-k6),gho(k4),glu(q1))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -topo_(2)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k4),glu(-k3))*node_(5,g,GHO(-k5),gho(k2),glu(k3))*node_(6,g,GHO(k4),gho(-k6),glu(q1))*node_(7,g,GHO(-k7),gho(k5),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -topo_(2)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(2)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(2)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,glu(q1),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(q1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(q1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(q1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(q1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(k4))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(q1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(q1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(q1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(q1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(q1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(q1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(q1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(q1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(q1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(q1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(q1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(q1))*node_(5,g,GHO(-k5),gho(k2),glu(-k4))*node_(6,g,GHO(k3),gho(-k6),glu(k4))*node_(7,g,GHO(-k7),gho(k5),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(k4),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(k4),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(-k7),gho(k5),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(3)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(4)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(q1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(-k8),qua(k6),glu(k4))*node_(8,g,QUA(k5),qua(k8),glu(k7)) -topo_(4)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(q1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k5),glu(k7)) -topo_(4)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(q1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(-k8),gho(k6),glu(k4))*node_(8,g,GHO(k5),gho(k8),glu(k7)) -topo_(4)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(q1))*node_(5,g,GHO(-k5),gho(k2),glu(-k4))*node_(6,g,GHO(k3),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(-k8),glu(k4))*node_(8,g,GHO(k8),gho(k5),glu(k7)) -topo_(4)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,QUA(k4),qua(k6),glu(-k8))*node_(8,g,QUA(k7),qua(k5),glu(k8)) -topo_(4)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(-k6),gho(-k7),glu(k3))*node_(7,g,GHO(k4),gho(k6),glu(-k8))*node_(8,g,GHO(k7),gho(k5),glu(k8)) +1/2*topo_(4)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k6),glu(-k8))*node_(8,g,glu(k5),glu(k7),glu(k8)) -topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(q1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(-k6),glu(k5))*node_(7,g,QUA(-k7),qua(k3),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(q1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(-k6),qua(k4),glu(k5))*node_(7,g,QUA(k3),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(q1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(-k6),glu(k5))*node_(7,g,GHO(-k7),gho(k3),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(q1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(-k6),gho(k4),glu(k5))*node_(7,g,GHO(k3),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k3))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k3))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k3))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k3))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -1/2*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k3))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -1/2*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k3))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/4*topo_(5)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(q1),glu(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) 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+topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,GHO(-k3),gho(-k4),glu(k1))*node_(5,g,QUA(-k5),qua(-k6),glu(k2))*node_(6,g,GHO(k4),gho(k3),glu(-k7))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) +1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,GHO(-k3),gho(-k4),glu(k1))*node_(5,g,GHO(-k5),gho(-k6),glu(k2))*node_(6,g,GHO(k4),gho(k3),glu(-k7))*node_(7,g,GHO(k6),gho(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(-k6),glu(k2))*node_(6,g,glu(k3),glu(k4),glu(-k7))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -1/2*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,GHO(-k5),gho(-k6),glu(k2))*node_(6,g,glu(k3),glu(k4),glu(-k7))*node_(7,g,GHO(k6),gho(k5),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) +1/8*topo_(6)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,glu(k3),glu(k4),glu(-k7))*node_(7,g,glu(k5),glu(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -topo_(7)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(p1))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(k2),qua(-k6),glu(-k5))*node_(6,g,QUA(-k7),qua(k3),glu(k4))*node_(7,g,QUA(-k8),qua(k7),glu(k5))*node_(8,g,QUA(k6),qua(k8),glu(q1)) 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-topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k4),glu(-k3))*node_(5,g,GHO(-k6),gho(k2),glu(-k5))*node_(6,g,glu(k3),glu(k5),glu(-k7))*node_(7,g,GHO(k4),gho(k6),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(-k6),glu(k2))*node_(6,g,QUA(k3),qua(k5),glu(-k7))*node_(7,g,QUA(k6),qua(k4),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) -1/2*topo_(8)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,GHO(-k4),gho(-k3),glu(k1))*node_(5,g,GHO(-k5),gho(-k6),glu(k2))*node_(6,g,GHO(k3),gho(k5),glu(-k7))*node_(7,g,GHO(k6),gho(k4),glu(-k8))*node_(8,g,glu(q1),glu(k7),glu(k8)) 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-topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(-k6),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(-k7),glu(k5))*node_(7,g,QUA(k7),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k6),glu(q1)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(-k4))*node_(5,g,GHO(k2),gho(-k5),glu(-k6))*node_(6,g,GHO(k5),gho(k3),glu(-k7))*node_(7,g,glu(k4),glu(k7),glu(-k8))*node_(8,g,glu(q1),glu(k6),glu(k8)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(p1))*node_(4,g,GHO(-k3),gho(k1),glu(-k4))*node_(5,g,GHO(k2),gho(-k6),glu(-k5))*node_(6,g,GHO(-k7),gho(k3),glu(k5))*node_(7,g,GHO(-k8),gho(k7),glu(k4))*node_(8,g,GHO(k6),gho(k8),glu(q1)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(-k5),gho(k2),glu(-k6))*node_(6,g,GHO(k3),gho(k5),glu(-k7))*node_(7,g,glu(k4),glu(k7),glu(-k8))*node_(8,g,glu(q1),glu(k6),glu(k8)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(-k6),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(-k7),glu(k5))*node_(7,g,GHO(k7),gho(-k8),glu(k4))*node_(8,g,GHO(k8),gho(k6),glu(q1)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(-k6),glu(k2))*node_(6,g,QUA(-k7),qua(k5),glu(k3))*node_(7,g,QUA(-k8),qua(k7),glu(k4))*node_(8,g,QUA(k6),qua(k8),glu(q1)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k6),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(-k7),glu(k3))*node_(7,g,QUA(k7),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k6),glu(q1)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,GHO(-k5),gho(-k6),glu(k2))*node_(6,g,GHO(-k7),gho(k5),glu(k3))*node_(7,g,GHO(-k8),gho(k7),glu(k4))*node_(8,g,GHO(k6),gho(k8),glu(q1)) -topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,GHO(-k6),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(-k7),glu(k3))*node_(7,g,GHO(k7),gho(-k8),glu(k4))*node_(8,g,GHO(k8),gho(k6),glu(q1)) +topo_(9)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,glu(k3),glu(k5),glu(-k7))*node_(7,g,glu(k4),glu(k7),glu(-k8))*node_(8,g,glu(q1),glu(k6),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k3),qua(k5),glu(q1))*node_(7,g,QUA(-k7),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k3),qua(k5),glu(q1))*node_(7,g,GHO(-k7),gho(-k8),glu(k4))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(p1))*node_(4,g,QUA(k1),qua(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k3),qua(k5),glu(q1))*node_(7,g,glu(k4),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(-k5),gho(k2),glu(-k6))*node_(6,g,GHO(k3),gho(k5),glu(q1))*node_(7,g,QUA(-k7),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(-k5),gho(k2),glu(-k6))*node_(6,g,GHO(k3),gho(k5),glu(q1))*node_(7,g,GHO(-k7),gho(-k8),glu(k4))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(p1))*node_(4,g,GHO(k1),gho(-k3),glu(-k4))*node_(5,g,GHO(-k5),gho(k2),glu(-k6))*node_(6,g,GHO(k3),gho(k5),glu(q1))*node_(7,g,glu(k4),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,glu(q1),glu(k3),glu(k5))*node_(7,g,QUA(-k7),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -1/2*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,glu(q1),glu(k3),glu(k5))*node_(7,g,GHO(-k7),gho(-k8),glu(k4))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/4*topo_(10)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(p1),glu(-k1),glu(-k2))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,glu(q1),glu(k3),glu(k5))*node_(7,g,glu(k4),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(-k3))*node_(4,g,QUA(k1),qua(-k4),glu(-k5))*node_(5,g,QUA(-k6),qua(k2),glu(-k7))*node_(6,g,QUA(k4),qua(k6),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k5)) -topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(-k3))*node_(4,g,GHO(k1),gho(-k4),glu(-k5))*node_(5,g,GHO(-k6),gho(k2),glu(-k7))*node_(6,g,GHO(k4),gho(k6),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k5)) -1/2*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(k1),glu(-k4),glu(-k5))*node_(5,g,QUA(-k6),qua(-k7),glu(k2))*node_(6,g,QUA(k7),qua(k6),glu(k4))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k5)) -1/2*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(k1),glu(-k4),glu(-k5))*node_(5,g,GHO(-k6),gho(-k7),glu(k2))*node_(6,g,GHO(k7),gho(k6),glu(k4))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k5)) +1/4*topo_(11)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(k1),glu(-k4),glu(-k5))*node_(5,g,glu(k2),glu(-k6),glu(-k7))*node_(6,g,glu(k4),glu(k6),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k5)) +1/2*topo_(12)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k1),qua(-k2),glu(-k3))*node_(4,g,QUA(-k4),qua(-k5),glu(-k6))*node_(5,g,QUA(k2),qua(k1),glu(-k7))*node_(6,g,QUA(k5),qua(k4),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) +topo_(12)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(-k3))*node_(4,g,QUA(-k4),qua(-k5),glu(-k6))*node_(5,g,GHO(k2),gho(k1),glu(-k7))*node_(6,g,QUA(k5),qua(k4),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) +1/2*topo_(12)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k1),gho(-k2),glu(-k3))*node_(4,g,GHO(-k4),gho(-k5),glu(-k6))*node_(5,g,GHO(k2),gho(k1),glu(-k7))*node_(6,g,GHO(k5),gho(k4),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) -1/2*topo_(12)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,QUA(-k4),qua(-k5),glu(-k6))*node_(5,g,glu(k1),glu(k2),glu(-k7))*node_(6,g,QUA(k5),qua(k4),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) -1/2*topo_(12)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,GHO(-k4),gho(-k5),glu(-k6))*node_(5,g,glu(k1),glu(k2),glu(-k7))*node_(6,g,GHO(k5),gho(k4),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) +1/8*topo_(12)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(-k4),glu(-k5),glu(-k6))*node_(5,g,glu(k1),glu(k2),glu(-k7))*node_(6,g,glu(k4),glu(k5),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) -1/2*topo_(13)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,QUA(-k2),qua(-k1),glu(-k3))*node_(4,g,QUA(-k4),qua(-k5),glu(-k6))*node_(5,g,QUA(k1),qua(k4),glu(-k7))*node_(6,g,QUA(k5),qua(k2),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) -1/2*topo_(13)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,GHO(-k2),gho(-k1),glu(-k3))*node_(4,g,GHO(-k4),gho(-k5),glu(-k6))*node_(5,g,GHO(k1),gho(k4),glu(-k7))*node_(6,g,GHO(k5),gho(k2),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) +1/4*topo_(13)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(-k4),glu(-k5),glu(-k6))*node_(5,g,glu(k1),glu(k4),glu(-k7))*node_(6,g,glu(k2),glu(k5),glu(k7))*node_(7,g^2,glu(p1),glu(q1),glu(k3),glu(k6)) 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+1/4*topo_(70)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(q1),glu(k1),glu(-k4))*node_(5,g^2,glu(p1),glu(k2),glu(k3),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(71)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(q1),glu(k1),glu(-k4))*node_(5,g^2,glu(p1),glu(k2),glu(k4),glu(-k5))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/2*topo_(72)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(q1),glu(-k4),glu(-k5))*node_(5,g^2,glu(p1),glu(k1),glu(k4),glu(-k6))*node_(6,g^2,glu(k2),glu(k3),glu(k5),glu(k6)) +1/2*topo_(73)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(k1),glu(-k4),glu(-k5))*node_(5,g^2,glu(p1),glu(k2),glu(k4),glu(-k6))*node_(6,g^2,glu(q1),glu(k3),glu(k5),glu(k6)) +1/4*topo_(74)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(-k4),glu(-k5),glu(-k6))*node_(5,g^2,glu(p1),glu(k1),glu(k2),glu(k4))*node_(6,g^2,glu(q1),glu(k3),glu(k5),glu(k6)) +1/4*topo_(75)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g,glu(-k1),glu(-k2),glu(-k3))*node_(4,g,glu(q1),glu(-k4),glu(-k5))*node_(5,g^2,glu(p1),glu(k1),glu(k2),glu(k4))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/8*topo_(76)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(q1),glu(-k1),glu(-k2))*node_(4,g^2,glu(k1),glu(k2),glu(-k3),glu(-k4))*node_(5,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) +1/8*topo_(77)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(q1),glu(-k1),glu(-k2))*node_(4,g^2,glu(k1),glu(-k3),glu(k3),glu(-k4))*node_(5,g^2,glu(k2),glu(k4),glu(-k5),glu(k5)) +1/12*topo_(78)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(q1),glu(-k1),glu(-k2))*node_(4,g^2,glu(k1),glu(-k3),glu(-k4),glu(-k5))*node_(5,g^2,glu(k2),glu(k3),glu(k4),glu(k5)) +1/4*topo_(79)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(-k2),glu(-k3))*node_(4,g^2,glu(k1),glu(k2),glu(-k4),glu(-k5))*node_(5,g^2,glu(q1),glu(k3),glu(k4),glu(k5)) +1/4*topo_(80)*node_(1,1,glu(-p1))*node_(2,1,glu(-q1))*node_(3,g^2,glu(p1),glu(-k1),glu(-k2),glu(-k3))*node_(4,g^2,glu(q1),glu(k1),glu(k2),glu(-k4))*node_(5,g^2,glu(k3),glu(k4),glu(-k5),glu(k5)) form-5.0.1/check/.diagrams_cache/qgraf_qcd_qua_qua_3_onepifloop.dat0000644000175100017510000005557615217035721021046 * Compared with qgraf-3.6.10 * Number of diagrams: FORM: 89, QGRAF: 89 topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k5),qua(k3),glu(k2))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(-k6),qua(k4),glu(-k7))*node_(7,g,QUA(-k8),qua(k6),glu(k5))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,QUA(q1),qua(k7),glu(k8)) +topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k5),qua(k3),glu(k2))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(2)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(k4),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(k4),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(-k7),gho(k5),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(3)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,QUA(k4),qua(k6),glu(-k8))*node_(8,g,QUA(k7),qua(k5),glu(k8)) -topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(-k6),gho(-k7),glu(k3))*node_(7,g,GHO(k4),gho(k6),glu(-k8))*node_(8,g,GHO(k7),gho(k5),glu(k8)) +1/2*topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k6),glu(-k8))*node_(8,g,glu(k5),glu(k7),glu(k8)) +topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k5),glu(k7)) +topo_(4)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k7),glu(-k6))*node_(7,g,glu(k4),glu(k6),glu(-k8))*node_(8,g,QUA(k7),qua(k5),glu(k8)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k3))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k3))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k3))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k3))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -1/2*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k3))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -1/2*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k3))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/4*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(-k6),qua(k4),glu(k5))*node_(7,g,QUA(k3),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k4),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k4),qua(k3),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) -topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k4),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,GHO(k4),gho(k3),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,glu(k3),glu(k4),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k6),qua(-k5),glu(k2))*node_(6,g,QUA(-k7),qua(k3),glu(k4))*node_(7,g,QUA(k5),qua(k7),glu(-k8))*node_(8,g,QUA(q1),qua(k6),glu(k8)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,QUA(-k7),qua(k3),glu(k4))*node_(7,g,QUA(-k8),qua(k7),glu(k5))*node_(8,g,QUA(q1),qua(k8),glu(k6)) -topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k4),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k4),qua(k3),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k7))*node_(8,g,QUA(q1),qua(k8),glu(k6)) -topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k4),glu(k1))*node_(5,g,QUA(-k6),qua(k2),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k7))*node_(7,g,glu(k5),glu(k7),glu(-k8))*node_(8,g,QUA(q1),qua(k6),glu(k8)) -topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k4),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,GHO(k4),gho(k3),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k7))*node_(8,g,QUA(q1),qua(k8),glu(k6)) -topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k4),glu(k1))*node_(5,g,QUA(-k6),qua(k2),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k7))*node_(7,g,glu(k5),glu(k7),glu(-k8))*node_(8,g,QUA(q1),qua(k6),glu(k8)) +1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,glu(k3),glu(k4),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k7))*node_(8,g,QUA(q1),qua(k8),glu(k6)) +1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k6),qua(k2),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k7))*node_(7,g,glu(k5),glu(k7),glu(-k8))*node_(8,g,QUA(q1),qua(k6),glu(k8)) +topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k3),qua(k5),glu(-k7))*node_(7,g,QUA(-k8),qua(k4),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k6),qua(k2),glu(-k5))*node_(6,g,glu(k3),glu(k5),glu(-k7))*node_(7,g,QUA(-k8),qua(k6),glu(k4))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k6),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k3),glu(-k7))*node_(7,g,glu(k4),glu(k7),glu(-k8))*node_(8,g,QUA(q1),qua(k6),glu(k8)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,QUA(-k7),qua(k3),glu(k5))*node_(7,g,QUA(-k8),qua(k7),glu(k4))*node_(8,g,QUA(q1),qua(k8),glu(k6)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,QUA(-k6),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(-k7),glu(k3))*node_(7,g,QUA(k7),qua(k4),glu(-k8))*node_(8,g,QUA(q1),qua(k6),glu(k8)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,glu(k3),glu(k5),glu(-k7))*node_(7,g,QUA(-k8),qua(k4),glu(k7))*node_(8,g,QUA(q1),qua(k8),glu(k6)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(k3),qua(k5),glu(-k7))*node_(7,g,QUA(-k8),qua(k4),glu(k7))*node_(8,g,QUA(q1),qua(k8),glu(k6)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(-k7),qua(k5),glu(k3))*node_(7,g,QUA(-k8),qua(k7),glu(k4))*node_(8,g,QUA(q1),qua(k8),glu(k6)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k6),qua(k2),glu(-k5))*node_(6,g,glu(k3),glu(k5),glu(-k7))*node_(7,g,glu(k4),glu(k7),glu(-k8))*node_(8,g,QUA(q1),qua(k6),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k4),glu(k1))*node_(5,g,QUA(-k6),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k3),glu(k5))*node_(7,g,QUA(k4),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(q1),qua(k5),glu(k3))*node_(7,g,QUA(-k7),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(q1),qua(k5),glu(k3))*node_(7,g,GHO(-k7),gho(-k8),glu(k4))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(q1),qua(k5),glu(k3))*node_(7,g,glu(k4),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -1/2*topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(-k6))*node_(6,g,QUA(k5),qua(k4),glu(-k7))*node_(7,g^2,glu(k2),glu(k3),glu(k6),glu(k7)) -1/2*topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(-k6))*node_(6,g,GHO(k5),gho(k4),glu(-k7))*node_(7,g^2,glu(k2),glu(k3),glu(k6),glu(k7)) +1/4*topo_(13)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(-k4),glu(-k5),glu(-k6))*node_(6,g,glu(k4),glu(k5),glu(-k7))*node_(7,g^2,glu(k2),glu(k3),glu(k6),glu(k7)) +topo_(14)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k5),qua(k3),glu(-k6))*node_(6,g,QUA(q1),qua(k5),glu(-k7))*node_(7,g^2,glu(k2),glu(k4),glu(k6),glu(k7)) +1/2*topo_(15)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(q1),qua(k3),glu(-k5))*node_(6,g,glu(k5),glu(-k6),glu(-k7))*node_(7,g^2,glu(k2),glu(k4),glu(k6),glu(k7)) +1/2*topo_(16)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g^2,glu(k2),glu(k5),glu(k6),glu(k7)) -1/2*topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k3))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g^2,glu(k2),glu(k6),glu(-k7),glu(k7)) -1/2*topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k3))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g^2,glu(k2),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(17)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g^2,glu(k2),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(19)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k5),qua(k3),glu(k4))*node_(6,g,QUA(q1),qua(k5),glu(-k6))*node_(7,g^2,glu(k2),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k5),qua(k3),glu(-k6))*node_(6,g,QUA(q1),qua(k5),glu(k4))*node_(7,g^2,glu(k2),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k5),glu(-k6))*node_(6,g,QUA(q1),qua(k4),glu(k5))*node_(7,g^2,glu(k2),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k3),glu(-k5),glu(-k6))*node_(6,g,QUA(q1),qua(k4),glu(-k7))*node_(7,g^2,glu(k2),glu(k5),glu(k6),glu(k7)) +1/2*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(24)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(24)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(25)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) -1/2*topo_(26)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) -1/2*topo_(26)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(26)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(27)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g^2,glu(k3),glu(k5),glu(k6),glu(k7)) +1/2*topo_(28)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(q1),qua(k5),glu(k3))*node_(7,g^2,glu(k4),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(29)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,QUA(q1),qua(k3),glu(-k7))*node_(7,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) +1/4*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g^2,glu(k2),glu(k3),glu(-k4),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/4*topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g^2,glu(k2),glu(-k4),glu(k4),glu(-k5))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/6*topo_(32)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g^2,glu(k2),glu(-k4),glu(-k5),glu(-k6))*node_(6,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) form-5.0.1/check/.diagrams_cache/qgraf_qcd_qua_qua_3_none.dat0000644000175100017510000100772515217035721017625 * Compared with qgraf-3.6.10 * Number of diagrams: FORM: 1001, QGRAF: 1001 -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(k3),gho(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(1)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+1/2*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/4*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/4*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -1/4*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/16*topo_(5)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,QUA(-k6),qua(-k5),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,GHO(-k6),gho(-k5),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/4*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,QUA(-k6),qua(-k5),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,GHO(-k6),gho(-k5),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/4*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(k4),glu(k2))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,QUA(-k6),qua(-k5),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -1/2*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,GHO(-k6),gho(-k5),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -1/4*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -1/4*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/8*topo_(6)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(k4))*node_(6,g,glu(k3),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(k4))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(k4))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(k4))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -1/2*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/4*topo_(7)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/4*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/4*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -1/2*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/8*topo_(8)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(k4),qua(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(k4))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(k4),gho(k3),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(k4))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(-k7),gho(k5),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -1/2*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/4*topo_(9)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k4),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k4),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(-k6),glu(-k7))*node_(7,g,QUA(k6),qua(k4),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(k6),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(k6),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(k6),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(k4),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(k4),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(-k3),glu(k1))*node_(5,g,GHO(-k4),gho(k2),glu(-k5))*node_(6,g,GHO(k3),gho(-k6),glu(-k7))*node_(7,g,GHO(k6),gho(k4),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(k6),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(k6),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(k6),glu(k5))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,QUA(k5),qua(k4),glu(k6))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,QUA(k5),qua(k4),glu(k6))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,QUA(k5),qua(k4),glu(k6))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,GHO(k5),gho(k4),glu(k6))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,GHO(k5),gho(k4),glu(k6))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,GHO(k5),gho(k4),glu(k6))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(k6))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -1/2*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(k6))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/4*topo_(10)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(k6))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(k4),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k6),glu(k7)) -topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(k4),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k6),glu(k7)) +1/2*topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,QUA(k5),qua(k4),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,GHO(k5),gho(k4),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) +1/2*topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(-k7),glu(k3))*node_(7,g,GHO(k5),gho(k4),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -1/2*topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,glu(k4),glu(k5),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -1/2*topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(-k7),glu(k3))*node_(7,g,glu(k4),glu(k5),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) +1/8*topo_(11)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g,glu(k4),glu(k5),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k6),qua(k3),glu(-k7))*node_(7,g,QUA(-k8),qua(k6),glu(k4))*node_(8,g,QUA(k5),qua(k8),glu(k7)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(-k2),glu(k1))*node_(5,g,QUA(k2),qua(-k5),glu(-k4))*node_(6,g,QUA(-k7),qua(k3),glu(-k6))*node_(7,g,glu(k4),glu(k6),glu(-k8))*node_(8,g,QUA(k5),qua(k7),glu(k8)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k6),gho(k3),glu(-k7))*node_(7,g,GHO(-k8),gho(k6),glu(k4))*node_(8,g,GHO(k5),gho(k8),glu(k7)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(-k2),glu(k1))*node_(5,g,GHO(k2),gho(-k5),glu(-k4))*node_(6,g,GHO(-k7),gho(k3),glu(-k6))*node_(7,g,glu(k4),glu(k6),glu(-k8))*node_(8,g,GHO(k5),gho(k7),glu(k8)) -1/2*topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(-k6),qua(-k7),glu(k3))*node_(7,g,QUA(k4),qua(k6),glu(-k8))*node_(8,g,QUA(k7),qua(k5),glu(k8)) -1/2*topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(-k6),gho(-k7),glu(k3))*node_(7,g,GHO(k4),gho(k6),glu(-k8))*node_(8,g,GHO(k7),gho(k5),glu(k8)) -topo_(12)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k7),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(-k8),glu(k4))*node_(8,g,QUA(k8),qua(k7),glu(k5)) 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-topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k5),qua(k3),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(20)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k5),qua(k3),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k5),qua(k3),glu(-k4))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,QUA(q1),qua(k7),glu(k8)) +topo_(21)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k5),qua(k3),glu(-k4))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) -topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k4),qua(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k4),qua(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k4),qua(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(22)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(k2))*node_(5,g,QUA(-k5),qua(k3),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,QUA(-k5),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +1/2*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/4*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,GHO(-k5),gho(-k6),glu(k4))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/4*topo_(23)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(q1),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k5),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/4*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -1/2*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/4*topo_(30)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,QUA(q1),qua(k7),glu(k8)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,QUA(q1),qua(k7),glu(k8)) -topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,GHO(-k3),gho(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +1/2*topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,QUA(q1),qua(k7),glu(k8)) +1/2*topo_(31)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(k3))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(32)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) +topo_(32)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) -1/2*topo_(32)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(32)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k3),qua(k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) 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-topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(40)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k5),qua(k3),glu(k2))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(-k6),qua(k4),glu(-k7))*node_(7,g,QUA(-k8),qua(k6),glu(k5))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(-k7),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k8))*node_(8,g,QUA(q1),qua(k7),glu(k8)) +topo_(41)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g,QUA(-k8),qua(k5),glu(k6))*node_(8,g,QUA(q1),qua(k8),glu(k7)) +topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,QUA(-k5),qua(k3),glu(k2))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k4),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(k3),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(-k4),qua(-k3),glu(k1))*node_(5,g,QUA(k3),qua(k2),glu(-k5))*node_(6,g,QUA(q1),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(42)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(k3))*node_(6,g,QUA(q1),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(k4),glu(k3))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(k4),glu(k3))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(k4),glu(k3))*node_(7,g,QUA(k5),qua(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(k4),glu(k3))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(k4),glu(k3))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(k4),glu(k3))*node_(7,g,GHO(k5),gho(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) -1/2*topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(k6),gho(k5),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) -topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) +1/2*topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(43)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k6),glu(k4))*node_(7,g,QUA(k6),qua(k5),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) 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+topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,glu(k6),glu(-k8),glu(k8)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/4*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k5))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k5))*node_(8,g,glu(k6),glu(-k8),glu(k8)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -1/2*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/4*topo_(44)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(k7))*node_(8,g,glu(k6),glu(-k8),glu(k8)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(-k6),qua(k4),glu(k3))*node_(7,g,QUA(k5),qua(-k7),glu(-k8))*node_(8,g,QUA(k7),qua(k6),glu(k8)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k5),qua(-k4),glu(k2))*node_(6,g,QUA(k4),qua(-k6),glu(k3))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(-k6),gho(k4),glu(k3))*node_(7,g,GHO(k5),gho(-k7),glu(-k8))*node_(8,g,GHO(k7),gho(k6),glu(k8)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k5),gho(-k4),glu(k2))*node_(6,g,GHO(k4),gho(-k6),glu(k3))*node_(7,g,GHO(-k7),gho(k5),glu(-k8))*node_(8,g,GHO(k6),gho(k7),glu(k8)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(-k8),glu(k5))*node_(8,g,QUA(k8),qua(k7),glu(k6)) -topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(-k8),glu(k5))*node_(8,g,GHO(k8),gho(k7),glu(k6)) +1/2*topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(k3),qua(k4),glu(-k6))*node_(7,g,glu(k5),glu(-k7),glu(-k8))*node_(8,g,glu(k6),glu(k7),glu(k8)) +topo_(45)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k6),glu(k4))*node_(7,g,QUA(-k7),qua(k5),glu(-k8))*node_(8,g,QUA(k6),qua(k7),glu(k8)) -1/2*topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(k3))*node_(7,g,QUA(-k7),qua(k7),glu(k4))*node_(8,g,QUA(-k8),qua(k8),glu(k5)) -topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(k3))*node_(7,g,GHO(-k7),gho(k7),glu(k4))*node_(8,g,QUA(-k8),qua(k8),glu(k5)) -1/2*topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(k3))*node_(7,g,GHO(-k7),gho(k7),glu(k4))*node_(8,g,GHO(-k8),gho(k8),glu(k5)) +1/2*topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(k3))*node_(7,g,glu(k4),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k5)) +1/2*topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(k3))*node_(7,g,glu(k4),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k5)) -1/8*topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(k3))*node_(7,g,glu(k4),glu(-k7),glu(k7))*node_(8,g,glu(k5),glu(-k8),glu(k8)) -1/2*topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k6),glu(k3))*node_(7,g,QUA(-k7),qua(k7),glu(k4))*node_(8,g,QUA(-k8),qua(k8),glu(k5)) -topo_(46)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k6),glu(k3))*node_(7,g,GHO(-k7),gho(k7),glu(k4))*node_(8,g,QUA(-k8),qua(k8),glu(k5)) 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+topo_(49)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k5),qua(k2),glu(-k4))*node_(6,g,QUA(k3),qua(-k7),glu(-k6))*node_(7,g,glu(k4),glu(k6),glu(-k8))*node_(8,g,QUA(k7),qua(k5),glu(k8)) +topo_(50)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(k3),glu(k6),glu(-k7))*node_(8,g,QUA(-k8),qua(k8),glu(k7)) +topo_(50)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(k3),glu(k6),glu(-k7))*node_(8,g,GHO(-k8),gho(k8),glu(k7)) 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+1/2*topo_(50)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,QUA(q1),qua(-k3),glu(k1))*node_(5,g,QUA(-k4),qua(k2),glu(-k5))*node_(6,g,QUA(-k6),qua(k4),glu(k5))*node_(7,g,QUA(k3),qua(k6),glu(-k7))*node_(8,g,glu(k7),glu(-k8),glu(k8)) -topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k3))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k3))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/2*topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k3))*node_(8,g,glu(k6),glu(-k8),glu(k8)) -topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k3))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k3))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) +1/2*topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k3))*node_(8,g,glu(k6),glu(-k8),glu(k8)) +1/2*topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(k7))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) +1/2*topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g,glu(k3),glu(-k7),glu(k7))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) 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+1/2*topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,QUA(-k7),qua(k7),glu(k3))*node_(8,g,glu(k6),glu(-k8),glu(k8)) -topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k3))*node_(8,g,QUA(-k8),qua(k8),glu(k6)) -topo_(51)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g,GHO(-k7),gho(k7),glu(k3))*node_(8,g,GHO(-k8),gho(k8),glu(k6)) 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+1/4*topo_(147)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k3),glu(-k6),glu(-k7))*node_(7,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) -1/2*topo_(148)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,QUA(-k4),qua(-k5),glu(k2))*node_(6,g,QUA(k5),qua(k4),glu(-k6))*node_(7,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) -1/2*topo_(148)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,GHO(-k4),gho(-k5),glu(k2))*node_(6,g,GHO(k5),gho(k4),glu(-k6))*node_(7,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) +1/4*topo_(148)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(k5),glu(-k6))*node_(7,g^2,glu(k3),glu(k6),glu(-k7),glu(k7)) -1/2*topo_(149)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(k4))*node_(7,g^2,glu(k3),glu(k5),glu(-k7),glu(k7)) -1/2*topo_(149)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k6),glu(k4))*node_(7,g^2,glu(k3),glu(k5),glu(-k7),glu(k7)) +1/4*topo_(149)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(k6))*node_(7,g^2,glu(k3),glu(k5),glu(-k7),glu(k7)) +1/2*topo_(150)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(k4),glu(-k6),glu(-k7))*node_(7,g^2,glu(k3),glu(k5),glu(k6),glu(k7)) -1/2*topo_(151)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,QUA(-k6),qua(k6),glu(-k7))*node_(7,g^2,glu(k3),glu(k4),glu(k5),glu(k7)) -1/2*topo_(151)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,GHO(-k6),gho(k6),glu(-k7))*node_(7,g^2,glu(k3),glu(k4),glu(k5),glu(k7)) +1/4*topo_(151)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g,glu(k2),glu(-k4),glu(-k5))*node_(6,g,glu(-k6),glu(k6),glu(-k7))*node_(7,g^2,glu(k3),glu(k4),glu(k5),glu(k7)) +1/4*topo_(152)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,QUA(q1),qua(k3),glu(k4))*node_(7,g^2,glu(k5),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(153)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k2),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k3),glu(-k4))*node_(5,g,QUA(-k5),qua(k2),glu(-k6))*node_(6,g,QUA(q1),qua(k5),glu(k3))*node_(7,g^2,glu(k4),glu(k6),glu(-k7),glu(k7)) +1/2*topo_(154)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(-k3),qua(k1),glu(-k4))*node_(5,g,glu(k2),glu(-k5),glu(-k6))*node_(6,g,QUA(q1),qua(k3),glu(-k7))*node_(7,g^2,glu(k4),glu(k5),glu(k6),glu(k7)) +1/8*topo_(155)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g^2,glu(k2),glu(k3),glu(-k4),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/8*topo_(156)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g^2,glu(k2),glu(-k4),glu(k4),glu(-k5))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/12*topo_(157)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(k1),glu(-k2),glu(-k3))*node_(5,g^2,glu(k2),glu(-k4),glu(-k5),glu(-k6))*node_(6,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) +1/8*topo_(158)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(-k2),glu(-k3),glu(-k4))*node_(5,g^2,glu(k1),glu(k2),glu(-k5),glu(k5))*node_(6,g^2,glu(k3),glu(k4),glu(-k6),glu(k6)) -1/4*topo_(159)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(-k4),glu(k4),glu(-k5))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) -1/4*topo_(159)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(-k4),glu(k4),glu(-k5))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/8*topo_(159)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(-k2),glu(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(-k4),glu(k4),glu(-k5))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/12*topo_(160)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(-k2),glu(-k3),glu(-k4))*node_(5,g^2,glu(k1),glu(-k5),glu(k5),glu(-k6))*node_(6,g^2,glu(k2),glu(k3),glu(k4),glu(k6)) +1/4*topo_(161)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(-k2),glu(-k3),glu(-k4))*node_(5,g^2,glu(k1),glu(k2),glu(k3),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) -1/4*topo_(162)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(k3),glu(-k4),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) -1/4*topo_(162)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(k3),glu(-k4),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/8*topo_(162)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(-k2),glu(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(k3),glu(-k4),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/4*topo_(163)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(-k2),glu(-k3),glu(-k4))*node_(5,g^2,glu(k1),glu(k2),glu(-k5),glu(-k6))*node_(6,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) -1/6*topo_(164)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,QUA(-k2),qua(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(-k4),glu(-k5),glu(-k6))*node_(6,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) -1/6*topo_(164)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,GHO(-k2),gho(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(-k4),glu(-k5),glu(-k6))*node_(6,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) +1/12*topo_(164)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(q1),qua(p1),glu(-k1))*node_(4,g,glu(-k2),glu(k2),glu(-k3))*node_(5,g^2,glu(k1),glu(-k4),glu(-k5),glu(-k6))*node_(6,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) +1/4*topo_(165)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g^2,glu(k2),glu(k3),glu(-k4),glu(-k5))*node_(6,g^2,glu(k4),glu(k5),glu(-k6),glu(k6)) +1/4*topo_(166)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g^2,glu(k2),glu(-k4),glu(k4),glu(-k5))*node_(6,g^2,glu(k3),glu(k5),glu(-k6),glu(k6)) +1/6*topo_(167)*node_(1,1,QUA(-p1))*node_(2,1,qua(-q1))*node_(3,g,QUA(-k1),qua(p1),glu(-k2))*node_(4,g,QUA(q1),qua(k1),glu(-k3))*node_(5,g^2,glu(k2),glu(-k4),glu(-k5),glu(-k6))*node_(6,g^2,glu(k3),glu(k4),glu(k5),glu(k6)) form-5.0.1/check/.diagrams_cache/feyngraph_qcd_3_none.dat0000644000175100017510000002631615217035721016770 * Compared with feyngraph 0.1.0b4+gf7ae8f4 * Number of diagrams: FORM: 74, FeynGraph: 74 -1/2*topo_(1)*node_(1,g,QUA(-k1),qua(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k2))*node_(4,g,QUA(k6),qua(k5),glu(k4)) -1/2*topo_(1)*node_(1,g,QUA(-k1),qua(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,GHO(-k5),gho(-k6),glu(k2))*node_(4,g,GHO(k6),gho(k5),glu(k4)) +1/4*topo_(1)*node_(1,g,QUA(-k1),qua(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,glu(k2),glu(-k5),glu(-k6))*node_(4,g,glu(k4),glu(k5),glu(k6)) -topo_(1)*node_(1,g,GHO(-k1),gho(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k2))*node_(4,g,QUA(k6),qua(k5),glu(k4)) -topo_(1)*node_(1,g,GHO(-k1),gho(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,GHO(-k5),gho(-k6),glu(k2))*node_(4,g,GHO(k6),gho(k5),glu(k4)) +1/2*topo_(1)*node_(1,g,GHO(-k1),gho(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,glu(k2),glu(-k5),glu(-k6))*node_(4,g,glu(k4),glu(k5),glu(k6)) -1/2*topo_(1)*node_(1,g,GHO(-k1),gho(k1),glu(-k2))*node_(2,g,GHO(-k3),gho(k3),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k2))*node_(4,g,QUA(k6),qua(k5),glu(k4)) -1/2*topo_(1)*node_(1,g,GHO(-k1),gho(k1),glu(-k2))*node_(2,g,GHO(-k3),gho(k3),glu(-k4))*node_(3,g,GHO(-k5),gho(-k6),glu(k2))*node_(4,g,GHO(k6),gho(k5),glu(k4)) +1/4*topo_(1)*node_(1,g,GHO(-k1),gho(k1),glu(-k2))*node_(2,g,GHO(-k3),gho(k3),glu(-k4))*node_(3,g,glu(k2),glu(-k5),glu(-k6))*node_(4,g,glu(k4),glu(k5),glu(k6)) +1/2*topo_(1)*node_(1,g,glu(-k1),glu(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k2))*node_(4,g,QUA(k6),qua(k5),glu(k4)) +1/2*topo_(1)*node_(1,g,glu(-k1),glu(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,GHO(-k5),gho(-k6),glu(k2))*node_(4,g,GHO(k6),gho(k5),glu(k4)) -1/4*topo_(1)*node_(1,g,glu(-k1),glu(k1),glu(-k2))*node_(2,g,QUA(-k3),qua(k3),glu(-k4))*node_(3,g,glu(k2),glu(-k5),glu(-k6))*node_(4,g,glu(k4),glu(k5),glu(k6)) +1/2*topo_(1)*node_(1,g,glu(-k1),glu(k1),glu(-k2))*node_(2,g,GHO(-k3),gho(k3),glu(-k4))*node_(3,g,QUA(-k5),qua(-k6),glu(k2))*node_(4,g,QUA(k6),qua(k5),glu(k4)) +1/2*topo_(1)*node_(1,g,glu(-k1),glu(k1),glu(-k2))*node_(2,g,GHO(-k3),gho(k3),glu(-k4))*node_(3,g,GHO(-k5),gho(-k6),glu(k2))*node_(4,g,GHO(k6),gho(k5),glu(k4)) -1/4*topo_(1)*node_(1,g,glu(-k1),glu(k1),glu(-k2))*node_(2,g,GHO(-k3),gho(k3),glu(-k4))*node_(3,g,glu(k2),glu(-k5),glu(-k6))*node_(4,g,glu(k4),glu(k5),glu(k6)) 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-R checkpoint.frm # fail * form -D TEST=checkpoint_1 -R checkpoint.frm # ok * We check the result at the end of the program, by which we expect * possible deficits in snapshot/recovery would be detected. * Unix is required. ParFORM is not supported. #ifndef `N' #define N "8" #endif #ifdef `QUIET' Off stats; #endif #define StopThenContinueLockFilePrefix ".stc-" #define StopThenContinueCounter "0" #procedure StopThenContinue(?exitcode) #ifdef `?exitcode' #define exitcode "`?exitcode'" #else #define exitcode "-1" #endif #define counter "`StopThenContinueCounter++'" #define lockfilename "`StopThenContinueLockFilePrefix'`counter'.tmp" * NOTE: for timestamps, the checkpoint feature uses TimeWallClock(), * which has only a centisecond precision. We may need some sleep * to guarantee that a snapshot file will be created (for low N, * in particular; though the wall clock value is supposed to increase * monotonically, I experienced cases where * TimeWallClock(1) - AC.CheckpointStamp == -1). * 0.05 seconds should be enough, but the POSIX sleep command assumes * an integral number as its argument; we fall back to 1 second when * it does not work. #system sleep 0.05 2>/dev/null || sleep 1 .sort:StopThenContinue-`counter'; #system -e test -f `lockfilename' #define error "`SYSTEMERROR_'" #write <`lockfilename'> "" #close <`lockfilename'> #if `error' #message Program intentionally stopped at `counter' (exitcode=`exitcode') #terminate `?exitcode' #endif #remove <`lockfilename'> #endprocedure #procedure AssertEqual(expr1,expr2) #$AssertEqualExpr1 = `expr1'; #$AssertEqualExpr2 = `expr2'; #$AssertEqualExpr3 = $AssertEqualExpr1 - $AssertEqualExpr2; #$AssertEqualExpr1 = nterms_($AssertEqualExpr3); #if `$AssertEqualExpr1' == 0 #message Assertion OK: `expr1' == `expr2' #else #message Assertion Failed: `expr1' == `expr2' #terminate #endif #endprocedure #call StopThenContinue(0) On checkpoint; Auto S x; L F = (x1+...+x15); L G = (x1+...+x15)^`N'; #$n1 = 6; #$e1 = 1+x1+...+x15; #define a1 "20" .sort #call StopThenContinue() id x1 = x1 + x2 + x3 + x4 + x5; #$n2 = 7; #$e2 = x1+...+x15; #define a2 "21" .sort #call StopThenContinue() id x6 = -x1; id x7 = -x2; id x8 = -x3; id x9 = -x4; id x10 = -x5; id x11 = -x2; id x12 = -x3; id x13 = -x4; id x14 = -x5; #$e3 = $e1 - $e2; #message x15 -> {`$n1'*`$n2'-`a1'-`a2'+`$e3'} id x15 = {`$n1'*`$n2'-`a1'-`a2'+`$e3'}; #ifndef `QUIET' Print; #endif .sort #call AssertEqual(F,2) #call AssertEqual(G,{2^`N'}) .end #system -e `FORM' 1.frm #system -e `FORM' -R 1.frm #system `FORM' -R 1.frm .end #require unix? #pend_if mpi? || valgrind? assert stdout =~ exact_pattern("Assertion OK: F") assert stdout =~ exact_pattern("Assertion OK: G") *--#] checkpoint_1 : form-5.0.1/check/extra/color.frm0000644000175100017510000001160215217035721012172 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ color_tloop : #- * This is a modified version of tloop.frm from the color.h example files. Off Statistics; * Larger than 5 becomes extremely slow under valgrind. #define SIZE "5" *#define ALTERNATEMETHOD "1" * * Test program for the color traces in the paper and a few more. * The paper: "Color traces for arbitrary groups" * by T. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren. * * The object is to express color traces in terms of group invariants * in such a way that the group has not been specified yet. The few * remaining invariants can be substituted afterwards. The expressions * in terms of invariants are better for publications. One sees more * about the structure of the problem this way. * * All declarations are made in the file cfactors.h * One needs version 3 or later of FORM to run these programs. * The programs will handle all color structures with up to 14 vertices. * One vertex is one generator in any representation. * Currently the program handles only one type of non-adjoint representaion. * If there are two different representations of such type one has to * try to run the problem in stages. * * Examples are: * One quark-loop with SIZE gluons in a maximally non-planar configuration * (TYPE = qloop) * Same but qluon loop (everything in the adjoint representation) * (TYPE = gloop) * Two quark loops with SIZE connecting gluons like a circular ladder. * (TYPE = qqloop) * Same with one quark loop and one gluon loop. * (TYPE = qgloop) * Same with two gluon loops. * (TYPE = ggloop) * The Coxeter graph (diagram with 14 vertices in the adjoint representation * in which there are no loops with fewer than 6 lines) (TYPE = g14) * * One should not choose SIZE larger than 7 or most likely the simplification * routine cannot simplify the final result completely (in some rare cases * it can though for SIZE = 8). * For execution times, see the paper. * It does get very slow for quarks and SIZE > 7. * * Program by J.Vermaseren, 24-may-1997 * #include color.h AutoDeclare Index i,j,k; CFunction acc; Symbol x; .global G Q{2*`SIZE'} = *...* **...* *replace_(i{`SIZE'*2+1},i1); G G{2*`SIZE'} = *...* **...* *replace_(i{`SIZE'*2+1},i1); G QQ`SIZE' = *...* **...* *replace_(i{`SIZE'+1},i1,k{`SIZE'+1},k1); G QG`SIZE' = *...* **...* *replace_(i{`SIZE'+1},i1,k{`SIZE'+1},k1); G GG`SIZE' = *...* **...* *replace_(i{`SIZE'+1},i1,k{`SIZE'+1},k1); * These take too long under valgrind. *G girth14 = * f(i1,i2,i3)*f(i1,i4,i5)*f(i2,i6,i7)*f(i3,i8,i9) * *f(i4,i10,i11)*f(i5,i12,i13)*f(i6,i14,i15)*f(i7,i16,i17) * *f(i8,i18,i19)*f(i9,i20,i21) * *f(i10,i21,i15)*f(i13,i19,i14)*f(i17,i11,i18)*f(i12,i16,i20); * *G girth24 = * f(i36,i1,i2)*f(i36,i3,i4)*f(i1,i5,i6)*f(i2,i7,i8) * *f(i3,i9,i10)*f(i4,i11,i12)*f(i5,i13,i14)*f(i6,i15,i16) * *f(i7,i17,i18)*f(i8,i19,i20)*f(i9,i21,i22)*f(i10,i23,i24) * *f(i11,i25,i26)*f(i12,i27,i28)*f(i13,i23,i29)*f(i14,i27,i30) * *f(i15,i25,i31)*f(i16,i21,i32)*f(i17,i26,i29)*f(i18,i32,i33) * *f(i19,i31,i34)*f(i20,i22,i30)*f(i24,i34,i35)*f(i28,i33,i35); * *G fiveq = T(i1,i2,j1)*T(i2,i3,j2)*T(i3,i1,j3)* * T(i4,i5,j2)*T(i5,i6,j4)*T(i6,i4,j5)* * T(i7,i8,j4)*T(i8,i9,j6)*T(i9,i7,j7)* * T(i10,i11,j6)*T(i11,i12,j1)*T(i12,i10,j8)* * T(i13,i14,j3)*T(i14,i15,j5)*T(i15,i16,j7)*T(i16,i13,j8); Sum i1,...,i{`SIZE'*2},j1,...,j`SIZE',k1,...,k`SIZE'; .sort #call color #call SORT(tloop-1) #call adjoint #call SORT(tloop-2) .sort #call simpli id acc(x?) = x; *Print +s; .sort * Check results Local Q10 = - Q10 + NA*I2R*cR^4 - 5*NA*I2R*cA*cR^3 + 35/4*NA*I2R*cA^2*cR^2 - 155/24*NA*I2R*cA^3*cR + 125/72*NA*I2R*cA^4 + 5*d44(cOlpR1,cOlpA1)*cR - 6*d44(cOlpR1,cOlpA1)*cA + 1/3*d44(cOlpA1,cOlpA2)*I2R ; Local G10 = - G10 - 1/36*NA*cA^5 + 2/3*d44(cOlpA1,cOlpA2)*cA ; Local QQ5 = - QQ5 - 5/144*NA*I2R^2*cA^3 + 11/48*d33(cOlpR1,cOlpR2)*cA^2 - 5/6*d44(cOlpR1,cOlpR2)*cA + 1/6*d44(cOlpR1,cOlpA1)*I2R + d55(cOlpR1,cOlpR2) ; Local QG5 = - QG5 - 5/144*i_*NA*I2R*cA^4 - 3/4*d44(cOlpR1,cOlpA1)*i_*cA + 1/12*d44(cOlpA1,cOlpA2)*i_*I2R ; Local GG5 = - GG5 + 5/144*NA*cA^5 + 2/3*d44(cOlpA1,cOlpA2)*cA ; .sort #do ex = {`activeexprnames_'} #if `ZERO_`ex'' == 0 #message Error in `ex' #terminate #endif #enddo .end assert succeeded? *--#] color_tloop : form-5.0.1/check/extra/mzv-dm.frm0000644000175100017510000013603615217035721012277 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ mzv-dm-hexall : #- * This is a minor modification of "hexall.frm" from the MZV datamine, * https://www.nikhef.nl/~form/datamine/alternating/rational/alldepth/alldepth.html * WEIGHT 6 is fast, and the "alt" tables are inside hexall.h * Modifications at the end of the program to verify the results. * We use the default FORM buffer settings. #define WEIGHT "6" * Program to compute the complete alternating MZV's * of a given weight (indicated by the parameter WEIGHT). * * Settings via form.set because they are rather detailed. * And we carry this program between computers of different types. * Don't forget to disable the Modulus in form.set!!!!!! * * We need the alt tables in separate files. * We assume that these tables only contain finite elements. * * Program is an adaptation of hex.frm. * Made by J.Vermaseren, 8-aug-2008 * *--#[ Settings : * *#define ONLYBASIS "1" * #ifndef `WEIGHT' #define WEIGHT "12" #endif #define MAXDEPTH "16" #if ( `MAXDEPTH' > `WEIGHT' ) #redefine MAXDEPTH "`WEIGHT'" #endif * * Below is the optimum as determined in a number of trial runs. * It isn't 100% clear though whether this optimum has survived * later changes in orderings. * *#define GROUPING "1024" #ifndef `GROUPING' #switch `WEIGHT' #case 12 #define GROUPING "2048" #break #default #$ngrouping = {2^{((4*3^{`WEIGHT'-2})^%)/2+2}}; #define GROUPING "`$ngrouping'" #break #endswitch #endif #ifdef `ONLYBASIS' *#define MODULUS "2147479273" #endif #include hexall.h #ifdef `MODULUS' #message Run with Weight = `WEIGHT', GROUPING = `GROUPING', Calculus modulus `MODULUS' #else #message Run with Weight = `WEIGHT', GROUPING = `GROUPING', Rational calculus #endif #ifndef `ONLYBASIS' #call readalts({`WEIGHT'-1}) #endif .global *--#] Settings : *--#[ Master Equation : * * Construct the expression FF that will contain the final result. * We only do the finite elements. * At first it will contain 2^{`WEIGHT'-2} objects but duality will * remove either half or almost half the elements. * S xmaxpow(:`MAXDEPTH'); Off Parallel; L FF = E(`WEIGHT'-2,1)*xmaxpow+E(`WEIGHT'-2,-1)*xmaxpow; repeat id E(n?pos_,?a) = E(n-1,0,?a)+E(n-1,1,?a)*xmaxpow+E(n-1,-1,?a)*xmaxpow; id E(0,?a) = E(0,?a)+E(-1,?a)*xmaxpow; id xmaxpow^n? = 1; .sort On Parallel; id E(?a)=E(?a)*H(?a); #call frombasis(`WEIGHT') * * The following enforces a better ordering inside the equations. * #call convert(E,`WEIGHT',0) #call convert(H,`WEIGHT',0) * * The bracket is essential! * B+ E; .sort Off Statistics; Hide FF; .sort * * $count will tell what is the number of the identity we are constructing * $dcount tell how many H-function have not been eliminated yet. * $jj counts the elements in the group that we treat simultaneously. * #$count = 0; #$dcount = termsin_(FF) - 1; #$jj = 0; * *--#] Master Equation : *--#[ The relations : * #do DEPTH = 1,`MAXDEPTH' #message entering DEPTH = `DEPTH' * *--#[ Stuffles : * #if ( `DEPTH' > 1 ) #message doing stuffles * Off Parallel; L Gen = E(`DEPTH')*EE({`WEIGHT'-`DEPTH'-1}); id EE(-1) = 1; repeat id E(x?{>1},?a) = E(x-1,1,?a); repeat id EE(x?pos_,?a) = EE(x-1,0,?a); id EE(?a) = E(?a); shuffle,E; id E(?a,0) = 0; .sort On Parallel; ArgImplode,E; id E(?a) = E(?a)*fff(?a); Multiply replace_(fff,ffs); #do i = 1,`DEPTH' id ffs(x?,?a) = ffs(?a)*fun`i'(-x); #enddo id ffs(?a) = 1; id E(x?,?b) = EE(x)*E(?b)+EE(-x)*E(?b); repeat id EE(?a)*E(x?,?b) = EE(?a,x)*E(?b)+EE(?a,-x)*E(?b); id EE(?a)*E = E(?a); *---------------------------------------------------------------- *id E(x1?,...,x`DEPTH'?) = *#do i = 1,`DEPTH'/2 * +E(x1,...,x`i')*E(,...,)*funa0(`i') *#enddo * ; *---------------------------------------------------------------- Multiply,( #do i = 1,`DEPTH'/2 +EE(`i')*funa0(`i') #enddo ); repeat id EE(x?pos_,?a)*E(x1?,?b) = EE(x-1,?a,x1)*E(?b); id EE(0,?a) = E(?a); *---------------------------------------------------------------- id E(1,?a) = 0; .sort DropCoefficient; id E(x1?,?a)*E(x2?,?b) = E(x1,?a)*E(x2,?b)*funa2(-min_(abs_(x1),abs_(x2))); ArgExplode,E; .sort Off Parallel; InParallel; Drop Gen; #do relation = Gen #$jj = $jj+1; L F`$jj' = `relation'; #if ( `$jj' >= `GROUPING' ) #call solvestuffle #$jj = 0; #endif #enddo #call solvestuffle #$jj = 0; .sort #endif * *--#] Stuffles : *--#[ Shuffles : * #if ( `DEPTH' > 1 ) * #do SHUFFLE = 1,1 #message doing shuffles (`SHUFFLE')({`DEPTH'-`SHUFFLE'}) * Off Parallel; L Gen = E(`DEPTH')*EE({`WEIGHT'-`DEPTH'-1}); id EE(-1) = 1; repeat id E(x?{>1},?a) = E(x-1,1,?a); repeat id EE(x?pos_,?a) = EE(x-1,0,?a); id EE(?a) = E(?a); shuffle,E; id E(?a,0) = 0; ArgImplode,E; Multiply EE; #do i = 1,`SHUFFLE' id EE(?a)*E(x?,?b) = EE(?a,x)*E(?b); #enddo id EE(?a) = E(?a); .sort On Parallel; DropCoefficient; * * The next sets the lower weight in the single depth object first. * id E(x1?) = E(x1)*fun(x1); *id E(x1?) = E(x1)*fun(abs_(x1)); * * Look for the number of ones. The fewer the better. * #do i = 1,1 id E(?a) = E(R,R(?a)); repeat; id E(R(?a),R(`i',?b)) = E(R(?a,`i'),R(?b))*x; id E(R(?a),R(x1?!{`i',`i'},?b)) = E(R(?a,x1),R(?b)); endrepeat; id E(R(?a),R) = E(?a); id x^n? = fun`i'(n); #enddo * * Empirical restrictions * *id E(1,x?,?a) = 0; *if ( count(fun0,1) == 2 ); *elseif ( match(fun0(1)) ); *elseif ( match(fun1(0)) ); *elseif ( match(fun1(1)*fun0(2)) ); *else; * Discard; *endif; * * Look for sum of squares of indices * id E(x1?,?a) = E(x1^2,R(x1),R(?a)); repeat id E(x?,R(?a),R(x1?,?b)) = E(x+x1^2,R(?a,x1),R(?b)); id E(x?,R(?a),R) = E(x,?a); id E(x1?,?a)*E(x2?,?b) = E(?a)*E(?b)*funa1(-max_(x1,x2)); * * Look for the leading index. * id E(x1?,?a)*E(x2?,?b) = E(x1,?a)*E(x2,?b)*funa2(-min_(x1,x2))*funa3(-x1-x2); * * Number of negative indices * repeat; id,once,E(?a) = EE(?a)*Eb; repeat id EE(x?,?a)*Eb(?b) = EE(?a)*Eb(?b,x)+EE(?a)*Eb(?b,-x)*xs; id EE = 1; id Eb(?a) = Ec(?a); endrepeat; id Ec(?a) = E(?a); id E(1,1,?a) = 0; id E(1,x?,?a) = 0; id E(1)^2 = 0; id xs^n? = fun(-n); *id xs^n? = 1; * if ( match(E(x?)) ); id E(x?)*E(?a) = E(x)*E(?a)*EE(x,?a)*ffs; else; id E(?b)*E(?a) = E(?b)*E(?a)*EE(?b,?a)*ffs; endif; repeat id ffs(?a)*EE(x?,?b) = ffs(?a,sig_(x))*EE(?b); id EE = 1; id ffs(?a) = funa0(?a); ArgExplode,E; .sort DropCoefficient; .sort #$jj = 0; InParallel; Drop Gen; #do relation = Gen #$jj = $jj+1; L F`$jj' = `relation'; #if ( `$jj' >= `GROUPING' ) #call solveshuffle #$jj = 0; #endif #enddo #call solveshuffle #$jj = 0; .sort #enddo #endif * *--#] Shuffles : *--#[ Double : * #message doing doubling Off Parallel; L Gen = E(`DEPTH')*EE(`WEIGHT'-`DEPTH'-1); id EE(-1) = 0; repeat id E(x?{>1},?a) = E(x-1,1,?a); repeat id EE(x?pos_,?a) = EE(x-1,0,?a); id EE(?a) = E(?a); Shuffle,E; id E(1,?a) = 0; id E(?a,0) = 0; .sort DropCoefficient; .sort #$jj = 0; InParallel; Drop Gen; #do relation = Gen #$jj = $jj+1; L F`$jj' = `relation'; #if ( `$jj' >= `GROUPING' ) #call solvedouble #$jj = 0; #endif #enddo #call solvedouble #$jj = 0; .sort * *--#] Double : *--#[ GenDouble : * #if ( ( `DEPTH' > 1 ) && ( `DEPTH' <= {`WEIGHT'-4} ) ) #message doing generalized doubling Off Parallel; L Gen = E(`DEPTH')*EE(`WEIGHT'-`DEPTH'-1); id EE(-1) = 0; repeat id E(x?{>1},?a) = E(x-1,1,?a); repeat id EE(x?pos_,?a) = EE(x-1,0,?a); id EE(?a) = E(?a); Shuffle,E; id E(1,?a) = 0; id E(?a,0) = 0; .sort DropCoefficient; ArgImplode,E; id E(?a,x?) = E(?a)*EE(x); repeat id E(?a,x1?,x2?)*EE(?b) = E(?a,x1)*(EE(x2,?b)+EE(-x2,?b)); id E(?a)*EE(?b) = E(?a,?b); .sort #$jj = 0; InParallel; Drop Gen; #do relation = Gen #$jj = $jj+1; L F`$jj' = `relation'; #if ( `$jj' >= `GROUPING' ) #call solvegendouble #$jj = 0; #endif #enddo #call solvegendouble #$jj = 0; .sort #endif * *--#] GenDouble : * #enddo * *--#] The relations : *--#[ Output : .sort Drop; ndrop FF; .sort On Statistics; On Parallel; Format nospaces; Format 80; UnHide FF; * * In the output the bracket indicates the H-function and the contents of * the bracket what it is equal to. * The remaining H functions are renamed as HH. This way they can be * found easily in an editor. * #call convert(E,`WEIGHT',1) #call convert(H,`WEIGHT',1) id H(?a) = HH(?a); id E(?a) = H(?a); B H; Print +f; *--#] Output : .sort *Off Parallel; *ArgImplode,H; *if ( count(HH,1) == 0 ) Discard; *B HH; *Print +f; *.sort *B HH; *Print[] +f; *.end *--#[ Verify result Off parallel; Local diff = FF - ( +H(-1,-1,-1,-1,-1,-1)*(1/720*ln2^6) +H(-1,-1,-1,-1,-1,1)*(-1/720*ln2^6+11/280*z2^3-2/9*e3^2+1/4*h51-1/2*h3111) +H(-1,-1,-1,-1,0,-1)*(1/48*ln2^4*z2-1/18*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+4/3*ln2*z2*e3-31/15*ln2*e5+2*ln2*h311+11/56*z2^3-10/9*e3^2+5/4*h51-5/2*h3111) +H(-1,-1,-1,-1,0,1)*(1/24*ln2^4*z2-5/36*ln2^3*e3+3/80*ln2^2*z2^2+1/4*ln2*z2*e3-5/12*ln2*e5-1/2*ln2*h311-81/560*z2^3-1/4*z2*h31+7/8*e3^2-h51+h3111) +H(-1,-1,-1,-1,1,-1)*(-1/720*ln2^6-1/3*ln2*z2*e3+31/60*ln2*e5-1/2*ln2*h311-11/56*z2^3+10/9*e3^2-5/4*h51+5/2*h3111) +H(-1,-1,-1,-1,1,1)*(1/720*ln2^6+1/3*ln2*z2*e3-31/60*ln2*e5+1/2*ln2*h311+11/70*z2^3-8/9*e3^2+h51-h3111) +H(-1,-1,-1,0,-1,-1)*(1/36*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-2*ln2*z2*e3+31/10*ln2*e5-3*ln2*h311-11/28*z2^3+20/9*e3^2-5/2*h51+5*h3111) +H(-1,-1,-1,0,-1,1)*(-1/4*ln2^4*z2+17/18*ln2^3*e3-11/40*ln2^2*z2^2+1/2*ln2^2*h31-10/3*ln2*z2*e3+323/60*ln2*e5-3/2*ln2*h311-2/7*z2^3+z2*h31+17/12*e3^2-5/2*h51-1/2*h3111) +H(-1,-1,-1,0,0,-1)*(1/6*ln2^3*e3-1/16*ln2^2*z2^2-7/12*ln2*z2*e3+59/60*ln2*e5-ln2*h311-263/1680*z2^3+1/4*z2*h31+5/6*e3^2-5/4*h51+2*h3111) +H(-1,-1,-1,0,0,1)*(2/9*ln2^3*e3-3/40*ln2^2*z2^2-1/2*ln2^2*h31+1/3*ln2*z2*e3-2/5*ln2*e5+2*ln2*h311+61/120*z2^3+z2*h31-37/12*e3^2+3*h51-3*h3111) +H(-1,-1,-1,0,1,-1)*(1/4*ln2^4*z2-29/36*ln2^3*e3+1/5*ln2^2*z2^2-1/2*ln2^2*h31+31/12*ln2*z2*e3-62/15*ln2*e5+3*ln2*h311+121/140*z2^3-59/12*e3^2+13/2*h51-7/2*h3111) +H(-1,-1,-1,0,1,1)*(2/9*ln2^3*e3-1/8*ln2^2*z2^2-1/4*ln2^2*h31+1/3*ln2*z2*e3-17/60*ln2*e5+1/2*ln2*h311-71/560*z2^3-1/4*z2*h31+49/72*e3^2) +H(-1,-1,-1,1,-1,-1)*(-1/720*ln2^6+1/80*ln2^2*z2^2-1/4*ln2^2*h31+4/3*ln2*z2*e3-31/15*ln2*e5+2*ln2*h311+11/28*z2^3-20/9*e3^2+5/2*h51-5*h3111) +H(-1,-1,-1,1,-1,1)*(1/720*ln2^6-1/80*ln2^2*z2^2+1/4*ln2^2*h31-4/3*ln2*z2*e3+31/15*ln2*e5-2*ln2*h311-121/210*z2^3+59/18*e3^2-4*h51+7/2*h3111) +H(-1,-1,-1,1,0,-1)*(-1/48*ln2^4*z2+1/18*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-4/3*ln2*z2*e3+31/15*ln2*e5-2*ln2*h311-367/560*z2^3-1/4*z2*h31+137/36*e3^2-21/4*h51+h3111) +H(-1,-1,-1,1,0,1)*(-1/24*ln2^4*z2+5/36*ln2^3*e3-3/80*ln2^2*z2^2-1/4*ln2*z2*e3+5/12*ln2*e5+1/2*ln2*h311+169/280*z2^3-1/4*z2*h31-31/9*e3^2+23/4*h51-7/2*h3111) +H(-1,-1,-1,1,1,-1)*(1/720*ln2^6-1/80*ln2^2*z2^2+1/4*ln2^2*h31-ln2*z2*e3+31/20*ln2*e5-1/2*ln2*h311-11/210*z2^3+5/18*e3^2+1/2*h3111) +H(-1,-1,-1,1,1,1)*(-1/720*ln2^6+1/80*ln2^2*z2^2-1/4*ln2^2*h31+ln2*z2*e3-31/20*ln2*e5+1/2*ln2*h311+23/140*z2^3-8/9*e3^2) +H(-1,-1,0,-1,-1,-1)*(1/80*ln2^2*z2^2-1/4*ln2^2*h31+4/3*ln2*z2*e3-31/15*ln2*e5+2*ln2*h311+11/28*z2^3-20/9*e3^2+5/2*h51-5*h3111) +H(-1,-1,0,-1,-1,1)*(3/8*ln2^4*z2-7/4*ln2^3*e3+11/20*ln2^2*z2^2+1/4*ln2^2*h31+25/6*ln2*z2*e3-211/30*ln2*e5+ln2*h311+71/140*z2^3-3/2*z2*h31-5/2*e3^2+15/4*h51) +H(-1,-1,0,-1,0,-1)*(1/16*ln2^2*z2^2-ln2^2*h31+5/2*ln2*z2*e3-59/15*ln2*e5+4*ln2*h311+263/560*z2^3-3/4*z2*h31-91/36*e3^2+15/4*h51-6*h3111) +H(-1,-1,0,-1,0,1)*(3/80*ln2^2*z2^2+2/3*ln2*z2*e3-11/10*ln2*e5-2*ln2*h311-411/560*z2^3-5/2*z2*h31+331/72*e3^2-13/4*h51+4*h3111) +H(-1,-1,0,-1,1,-1)*(-3/4*ln2^4*z2+35/12*ln2^3*e3-27/40*ln2^2*z2^2-5/2*ln2^2*h31-1/12*ln2*z2*e3+49/60*ln2*e5+5/2*ln2*h311-11/70*z2^3+3/4*e3^2+3/2*h3111) +H(-1,-1,0,-1,1,1)*(3/8*ln2^4*z2-7/3*ln2^3*e3+69/80*ln2^2*z2^2+5/2*ln2^2*h31-7/3*ln2*z2*e3+133/60*ln2*e5-7/2*ln2*h311+23/280*z2^3+3/4*z2*h31-1/6*e3^2-3*h51+3/2*h3111) +H(-1,-1,0,0,-1,-1)*(1/2*ln2^2*h31-2/3*ln2*z2*e3+59/60*ln2*e5-ln2*h311+1/72*e3^2) +H(-1,-1,0,0,-1,1)*(-7/6*ln2^3*e3+11/20*ln2^2*z2^2+3/2*ln2^2*h31-13/12*ln2*z2*e3+49/60*ln2*e5-3*ln2*h311-437/560*z2^3-1/2*z2*h31+343/72*e3^2-13/2*h51+4*h3111) +H(-1,-1,0,0,0,-1)*(7/40*ln2^2*z2^2+1/2*ln2*z2*e3-17/15*ln2*e5-13/42*z2^3-1/2*z2*h31+71/36*e3^2-5/2*h51) +H(-1,-1,0,0,0,1)*(1/5*ln2^2*z2^2+ln2*z2*e3-59/30*ln2*e5-11/168*z2^3-z2*h31+2/3*e3^2) +H(-1,-1,0,0,1,-1)*(7/6*ln2^3*e3-41/80*ln2^2*z2^2-ln2^2*h31-1/4*ln2*z2*e3+13/12*ln2*e5+ln2*h311-3/280*z2^3-1/9*e3^2+3/4*h51+h3111) +H(-1,-1,0,0,1,1)*(1/20*ln2^2*z2^2-1/2*ln2*z2*e3+3/5*ln2*e5+ln2*h311+13/20*z2^3+z2*h31-34/9*e3^2+3*h51-3*h3111) +H(-1,-1,0,1,-1,-1)*(3/8*ln2^4*z2-7/6*ln2^3*e3+13/80*ln2^2*z2^2+9/4*ln2^2*h31-10/3*ln2*z2*e3+149/30*ln2*e5-5*ln2*h311-341/280*z2^3+7*e3^2-39/4*h51+9/2*h3111) +H(-1,-1,0,1,-1,1)*(-3/4*ln2^4*z2+35/12*ln2^3*e3-5/8*ln2^2*z2^2-13/4*ln2^2*h31+8/3*ln2*z2*e3-209/60*ln2*e5+4*ln2*h311+223/560*z2^3-19/8*e3^2+15/4*h51-3/2*h3111) +H(-1,-1,0,1,0,-1)*(11/80*ln2^2*z2^2-ln2^2*h31+9/4*ln2*z2*e3-19/5*ln2*e5+4*ln2*h311+79/80*z2^3-199/36*e3^2+15/2*h51-6*h3111) +H(-1,-1,0,1,0,1)*(3/20*ln2^2*z2^2+1/6*ln2*z2*e3-43/60*ln2*e5-2*ln2*h311-37/70*z2^3-z2*h31+241/72*e3^2-13/4*h51+4*h3111) +H(-1,-1,0,1,1,-1)*(3/8*ln2^4*z2-7/12*ln2^3*e3-9/80*ln2^2*z2^2+ln2^2*h31-ln2*z2*e3+11/6*ln2*e5-3/2*ln2*h311-1/10*z2^3+1/2*e3^2-3/4*h51) +H(-1,-1,0,1,1,1)*(1/5*ln2^2*z2^2-1/4*ln2*z2*e3-7/20*ln2*e5+1/2*ln2*h311+111/560*z2^3+1/4*z2*h31-7/8*e3^2+h51-h3111) +H(-1,-1,1,-1,-1,-1)*(-1/720*ln2^6+1/36*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-2*ln2*z2*e3+31/10*ln2*e5-3*ln2*h311-11/28*z2^3+20/9*e3^2-5/2*h51+5*h3111) +H(-1,-1,1,-1,-1,1)*(1/720*ln2^6-1/36*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+2*ln2*z2*e3-31/10*ln2*e5+3*ln2*h311+11/14*z2^3-323/72*e3^2+6*h51-9/2*h3111) +H(-1,-1,1,-1,0,-1)*(-1/48*ln2^4*z2+1/18*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-9/4*ln2*z2*e3+211/60*ln2*e5-7/2*ln2*h311-263/560*z2^3+3/4*z2*h31+91/36*e3^2-15/4*h51+6*h3111) +H(-1,-1,1,-1,0,1)*(-1/24*ln2^4*z2+5/36*ln2^3*e3-3/80*ln2^2*z2^2+7/12*ln2*z2*e3-47/60*ln2*e5-2*ln2*h311-8/7*z2^3+3/4*z2*h31+58/9*e3^2-45/4*h51+15/2*h3111) +H(-1,-1,1,-1,1,-1)*(1/720*ln2^6-1/36*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+3*ln2*z2*e3-23/5*ln2*e5+3/2*ln2*h311+11/70*z2^3-31/36*e3^2-3/2*h3111) +H(-1,-1,1,-1,1,1)*(-1/720*ln2^6+1/36*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-3*ln2*z2*e3+23/5*ln2*e5-3/2*ln2*h311-29/60*z2^3+191/72*e3^2) +H(-1,-1,1,0,-1,-1)*(-1/36*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+2*ln2*z2*e3-31/10*ln2*e5+3*ln2*h311+341/280*z2^3-251/36*e3^2+39/4*h51-9/2*h3111) +H(-1,-1,1,0,-1,1)*(1/4*ln2^4*z2-17/18*ln2^3*e3+11/40*ln2^2*z2^2-1/2*ln2^2*h31+41/12*ln2*z2*e3-169/30*ln2*e5+11/2*ln2*h311+673/280*z2^3-491/36*e3^2+19*h51-12*h3111) +H(-1,-1,1,0,0,-1)*(-1/6*ln2^3*e3+1/16*ln2^2*z2^2+7/12*ln2*z2*e3-59/60*ln2*e5+ln2*h311+391/336*z2^3+1/2*z2*h31-241/36*e3^2+37/4*h51-3*h3111) +H(-1,-1,1,0,0,1)*(-2/9*ln2^3*e3+3/40*ln2^2*z2^2+1/2*ln2^2*h31-1/3*ln2*z2*e3+2/5*ln2*e5-2*ln2*h311-169/336*z2^3+1/2*z2*h31+209/72*e3^2-5*h51+4*h3111) +H(-1,-1,1,0,1,-1)*(-1/4*ln2^4*z2+29/36*ln2^3*e3-1/5*ln2^2*z2^2+1/2*ln2^2*h31-8/3*ln2*z2*e3+263/60*ln2*e5-7*ln2*h311-43/14*z2^3+631/36*e3^2-25*h51+15*h3111) +H(-1,-1,1,0,1,1)*(-2/9*ln2^3*e3+1/8*ln2^2*z2^2+1/4*ln2^2*h31-1/3*ln2*z2*e3+17/60*ln2*e5-1/2*ln2*h311-47/140*z2^3-3/4*z2*h31+145/72*e3^2+3/4*h51+1/2*h3111) +H(-1,-1,1,1,-1,-1)*(1/720*ln2^6-1/36*ln2^3*e3+1/40*ln2^2*z2^2-1/20*ln2*e5+1/72*e3^2) +H(-1,-1,1,1,-1,1)*(-1/720*ln2^6+1/36*ln2^3*e3-1/40*ln2^2*z2^2+1/20*ln2*e5-23/56*z2^3+85/36*e3^2-15/4*h51+3/2*h3111) +H(-1,-1,1,1,0,-1)*(1/48*ln2^4*z2-1/18*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+9/4*ln2*z2*e3-211/60*ln2*e5+7/2*ln2*h311+263/280*z2^3-383/72*e3^2+7*h51-11/2*h3111) +H(-1,-1,1,1,0,1)*(1/24*ln2^4*z2-5/36*ln2^3*e3+3/80*ln2^2*z2^2-7/12*ln2*z2*e3+47/60*ln2*e5+2*ln2*h311+55/112*z2^3+3/4*z2*h31-103/36*e3^2+13/4*h51-4*h3111) +H(-1,-1,1,1,1,-1)*(-1/720*ln2^6+1/36*ln2^3*e3-1/40*ln2^2*z2^2-1/3*ln2*z2*e3+7/12*ln2*e5+1/2*ln2*h311+337/840*z2^3-169/72*e3^2+15/4*h51-3/2*h3111) +H(-1,-1,1,1,1,1)*(1/720*ln2^6-1/36*ln2^3*e3+1/40*ln2^2*z2^2+1/3*ln2*z2*e3-7/12*ln2*e5-1/2*ln2*h311+1/70*z2^3-h51+h3111) +H(-1,0,-1,-1,-1,-1)*(-1/3*ln2*z2*e3+31/60*ln2*e5-1/2*ln2*h311-11/56*z2^3+10/9*e3^2-5/4*h51+5/2*h3111) +H(-1,0,-1,-1,-1,1)*(-1/4*ln2^4*z2+49/36*ln2^3*e3-39/80*ln2^2*z2^2-3/4*ln2^2*h31-31/12*ln2*z2*e3+93/20*ln2*e5+1/2*ln2*h311-69/280*z2^3+z2*h31+19/18*e3^2-5/4*h51-3/2*h3111) +H(-1,0,-1,-1,0,-1)*(-23/12*ln2*z2*e3+59/20*ln2*e5-3/80*z2^3+3/4*z2*h31+1/18*e3^2) +H(-1,0,-1,-1,0,1)*(-5/12*ln2*z2*e3+2/3*ln2*e5+57/560*z2^3+3/2*z2*h31-59/72*e3^2-3/4*h51) +H(-1,0,-1,-1,1,-1)*(3/4*ln2^4*z2-7/2*ln2^3*e3+79/80*ln2^2*z2^2+13/4*ln2^2*h31-1/6*ln2*z2*e3-11/12*ln2*e5-11/2*ln2*h311-11/40*z2^3+11/6*e3^2-15/4*h51+9/2*h3111) +H(-1,0,-1,-1,1,1)*(-1/2*ln2^4*z2+119/36*ln2^3*e3-103/80*ln2^2*z2^2-4*ln2^2*h31+19/4*ln2*z2*e3-103/20*ln2*e5+15/2*ln2*h311+37/80*z2^3-3/4*z2*h31-113/36*e3^2+7*h51-11/2*h3111) +H(-1,0,-1,0,-1,-1)*(2/3*ln2*z2*e3-59/60*ln2*e5-2*ln2*h311-121/280*z2^3+89/36*e3^2-15/4*h51+6*h3111) +H(-1,0,-1,0,-1,1)*(-1/5*ln2^2*z2^2+2*ln2^2*h31-43/6*ln2*z2*e3+343/30*ln2*e5-4*ln2*h311-71/140*z2^3+2*z2*h31+43/18*e3^2-4*h51) +H(-1,0,-1,0,0,-1)*(-ln2*z2*e3+17/10*ln2*e5+215/336*z2^3+z2*h31-71/18*e3^2+5*h51) +H(-1,0,-1,0,0,1)*(-7/2*ln2*z2*e3+83/15*ln2*e5-5/21*z2^3+2*z2*h31+11/12*e3^2-5/2*h51) +H(-1,0,-1,0,1,-1)*(1/5*ln2^2*z2^2-2*ln2^2*h31+22/3*ln2*z2*e3-35/3*ln2*e5+6*ln2*h311+62/35*z2^3-179/18*e3^2+12*h51-8*h3111) +H(-1,0,-1,0,1,1)*(11/12*ln2*z2*e3-41/30*ln2*e5-177/280*z2^3-z2*h31+265/72*e3^2-2*h51+2*h3111) +H(-1,0,-1,1,-1,-1)*(-3/4*ln2^4*z2+35/12*ln2^3*e3-53/80*ln2^2*z2^2-11/4*ln2^2*h31+19/12*ln2*z2*e3-53/30*ln2*e5+5*ln2*h311+121/280*z2^3-31/12*e3^2+15/4*h51-6*h3111) +H(-1,0,-1,1,-1,1)*(ln2^4*z2-77/18*ln2^3*e3+19/20*ln2^2*z2^2+11/2*ln2^2*h31-41/6*ln2*z2*e3+289/30*ln2*e5-11*ln2*h311-79/40*z2^3+409/36*e3^2-31/2*h51+11*h3111) +H(-1,0,-1,1,0,-1)*(-2/5*ln2^2*z2^2+4*ln2^2*h31-21/2*ln2*z2*e3+103/6*ln2*e5-16*ln2*h311-221/40*z2^3-z2*h31+565/18*e3^2-42*h51+24*h3111) +H(-1,0,-1,1,0,1)*(-3/8*ln2^2*z2^2+5/2*ln2*z2*e3-37/15*ln2*e5+4*ln2*h311+303/140*z2^3-233/18*e3^2+35/2*h51-12*h3111) +H(-1,0,-1,1,1,-1)*(-7/4*ln2^3*e3+39/40*ln2^2*z2^2+3/2*ln2^2*h31-7/4*ln2*z2*e3+16/15*ln2*e5+31/35*z2^3-19/4*e3^2+15/2*h51-3*h3111) +H(-1,0,-1,1,1,1)*(-1/4*ln2^4*z2+35/18*ln2^3*e3-49/40*ln2^2*z2^2-11/4*ln2^2*h31+23/6*ln2*z2*e3-43/15*ln2*e5+4*ln2*h311+107/280*z2^3-1/4*z2*h31-28/9*e3^2+2*h51-2*h3111) +H(-1,0,0,-1,-1,-1)*(ln2*h311+121/840*z2^3-5/6*e3^2+5/4*h51-2*h3111) +H(-1,0,0,-1,-1,1)*(7/6*ln2^3*e3-11/16*ln2^2*z2^2-5/2*ln2^2*h31+13/3*ln2*z2*e3-317/60*ln2*e5+5*ln2*h311+1147/1680*z2^3-1/2*z2*h31-301/72*e3^2+6*h51-4*h3111) +H(-1,0,0,-1,0,-1)*(-5/6*ln2*z2*e3+41/30*ln2*e5-215/336*z2^3+65/18*e3^2-5*h51) +H(-1,0,0,-1,0,1)*(3*ln2*z2*e3-67/15*ln2*e5+85/168*z2^3-35/12*e3^2+5/2*h51) +H(-1,0,0,-1,1,-1)*(-7/3*ln2^3*e3+13/10*ln2^2*z2^2+2*ln2^2*h31-2/3*ln2*z2*e3-11/10*ln2*e5-2*ln2*h311+59/84*z2^3-32/9*e3^2+5*h51) +H(-1,0,0,-1,1,1)*(7/6*ln2^3*e3-63/80*ln2^2*z2^2-3/2*ln2^2*h31+1/3*ln2*z2*e3+11/10*ln2*e5+2*ln2*h311-871/1680*z2^3-1/2*z2*h31+185/72*e3^2-5/2*h51) +H(-1,0,0,0,-1,-1)*(2/3*ln2*z2*e3-29/30*ln2*e5+13/42*z2^3-65/36*e3^2+5/2*h51) +H(-1,0,0,0,-1,1)*(-3/4*ln2^2*z2^2-5/2*ln2*z2*e3+92/15*ln2*e5-13/15*z2^3+25/6*e3^2-4*h51) +H(-1,0,0,0,0,-1)*(ln2*e5-7/40*z2^3+1/2*e3^2) +H(-1,0,0,0,0,1)*(16/15*ln2*e5-23/70*z2^3+4/3*e3^2-h51) +H(-1,0,0,0,1,-1)*(3/4*ln2^2*z2^2+2*ln2*z2*e3-157/30*ln2*e5+613/840*z2^3-7/2*e3^2+4*h51) +H(-1,0,0,0,1,1)*(-4/3*ln2*z2*e3+32/15*ln2*e5-49/120*z2^3+20/9*e3^2-3/2*h51) +H(-1,0,0,1,-1,-1)*(7/6*ln2^3*e3-49/80*ln2^2*z2^2+1/2*ln2^2*h31-37/12*ln2*z2*e3+111/20*ln2*e5-3*ln2*h311-103/84*z2^3+247/36*e3^2-37/4*h51+3*h3111) +H(-1,0,0,1,-1,1)*(-7/3*ln2^3*e3+13/10*ln2^2*z2^2+2*ln2^2*h31+1/2*ln2*z2*e3-57/20*ln2*e5-3*ln2*h311+83/1680*z2^3-1/2*z2*h31+5/18*e3^2-3/4*h51+3*h3111) +H(-1,0,0,1,0,-1)*(-1/3*ln2*z2*e3+7/10*ln2*e5-71/105*z2^3-1/2*z2*h31+23/6*e3^2-5*h51) +H(-1,0,0,1,0,1)*(4*ln2*z2*e3-88/15*ln2*e5+451/840*z2^3-z2*h31-109/36*e3^2+7/2*h51) +H(-1,0,0,1,1,-1)*(7/6*ln2^3*e3-41/80*ln2^2*z2^2-1/2*ln2^2*h31-5/4*ln2*z2*e3+151/60*ln2*e5-167/840*z2^3+37/36*e3^2-3/4*h51+h3111) +H(-1,0,0,1,1,1)*(-4/3*ln2*z2*e3+32/15*ln2*e5+29/210*z2^3+1/2*z2*h31-11/12*e3^2-h3111) +H(-1,0,1,-1,-1,-1)*(1/4*ln2^4*z2-7/9*ln2^3*e3+13/80*ln2^2*z2^2+1/4*ln2^2*h31+11/12*ln2*z2*e3-31/20*ln2*e5+1/2*ln2*h311+187/280*z2^3-137/36*e3^2+21/4*h51-h3111) +H(-1,0,1,-1,-1,1)*(-7/12*ln2^3*e3+13/40*ln2^2*z2^2+1/2*ln2^2*h31-1/3*ln2*z2*e3-1/2*ln2*h311+1/56*z2^3) +H(-1,0,1,-1,0,-1)*(2/5*ln2^2*z2^2-4*ln2^2*h31+39/4*ln2*z2*e3-95/6*ln2*e5+16*ln2*h311+109/20*z2^3+z2*h31-280/9*e3^2+42*h51-24*h3111) +H(-1,0,1,-1,0,1)*(3/8*ln2^2*z2^2-7/2*ln2*z2*e3+127/30*ln2*e5-4*ln2*h311-171/70*z2^3+1033/72*e3^2-19*h51+12*h3111) +H(-1,0,1,-1,1,-1)*(-ln2^4*z2+77/18*ln2^3*e3-19/20*ln2^2*z2^2-11/2*ln2^2*h31+91/12*ln2*z2*e3-107/10*ln2*e5+19/2*ln2*h311+8/7*z2^3-119/18*e3^2+8*h51-8*h3111) +H(-1,0,1,-1,1,1)*(3/4*ln2^4*z2-49/12*ln2^3*e3+5/4*ln2^2*z2^2+25/4*ln2^2*h31-23/3*ln2*z2*e3+201/20*ln2*e5-23/2*ln2*h311-223/140*z2^3+3/4*z2*h31+37/4*e3^2-23/2*h51+9*h3111) +H(-1,0,1,0,-1,-1)*(-3/4*ln2*z2*e3+37/30*ln2*e5-2*ln2*h311-19/20*z2^3+97/18*e3^2-15/2*h51+6*h3111) +H(-1,0,1,0,-1,1)*(-23/40*ln2^2*z2^2+2*ln2^2*h31-37/12*ln2*z2*e3+199/30*ln2*e5-4*ln2*h311+27/140*z2^3+2*z2*h31-155/72*e3^2) +H(-1,0,1,0,0,-1)*(1/6*ln2*z2*e3+11/30*ln2*e5+1199/1680*z2^3+z2*h31-14/3*e3^2+5*h51) +H(-1,0,1,0,0,1)*(-8/3*ln2*z2*e3+24/5*ln2*e5-8/105*z2^3+2*z2*h31-7/18*e3^2-3/2*h51) +H(-1,0,1,0,1,-1)*(23/40*ln2^2*z2^2-2*ln2^2*h31+47/12*ln2*z2*e3-461/60*ln2*e5+6*ln2*h311+8/7*z2^3-107/18*e3^2+8*h51-8*h3111) +H(-1,0,1,0,1,1)*(4*ln2*z2*e3-88/15*ln2*e5+1/80*z2^3-z2*h31-1/9*e3^2+5/4*h51+2*h3111) +H(-1,0,1,1,-1,-1)*(1/2*ln2^4*z2-35/36*ln2^3*e3-1/80*ln2^2*z2^2+2*ln2^2*h31-37/12*ln2*z2*e3+73/15*ln2*e5-5*ln2*h311-32/35*z2^3+373/72*e3^2-7*h51+11/2*h3111) +H(-1,0,1,1,-1,1)*(-3/4*ln2^4*z2+7/3*ln2^3*e3-11/40*ln2^2*z2^2-19/4*ln2^2*h31+37/6*ln2*z2*e3-547/60*ln2*e5+11*ln2*h311+85/56*z2^3-z2*h31-209/24*e3^2+27/2*h51-21/2*h3111) +H(-1,0,1,1,0,-1)*(-1/4*ln2*z2*e3+53/60*ln2*e5-1/8*z2^3-1/4*z2*h31+25/72*e3^2) +H(-1,0,1,1,0,1)*(-8/3*ln2*z2*e3+24/5*ln2*e5-13/16*z2^3-1/2*z2*h31+295/72*e3^2-15/4*h51) +H(-1,0,1,1,1,-1)*(1/4*ln2^4*z2-7/36*ln2^3*e3+1/4*ln2^2*z2^2+5/4*ln2^2*h31-25/12*ln2*z2*e3+137/60*ln2*e5-4*ln2*h311-197/280*z2^3+311/72*e3^2-6*h51+11/2*h3111) +H(-1,0,1,1,1,1)*(16/15*ln2*e5-1/560*z2^3+1/4*z2*h31-65/72*e3^2+1/4*h51-1/2*h3111) +H(-1,1,-1,-1,-1,-1)*(-1/720*ln2^6+1/48*ln2^4*z2-1/18*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+4/3*ln2*z2*e3-31/15*ln2*e5+2*ln2*h311+11/56*z2^3-10/9*e3^2+5/4*h51-5/2*h3111) +H(-1,1,-1,-1,-1,1)*(1/720*ln2^6-1/48*ln2^4*z2+1/18*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-4/3*ln2*z2*e3+31/15*ln2*e5-2*ln2*h311-859/1680*z2^3-1/4*z2*h31+107/36*e3^2-4*h51+3*h3111) +H(-1,1,-1,-1,0,-1)*(-1/48*ln2^4*z2+1/18*ln2^3*e3+3/40*ln2^2*z2^2-ln2^2*h31+7/3*ln2*z2*e3-56/15*ln2*e5+4*ln2*h311+7/20*z2^3-3/2*z2*h31-31/18*e3^2+15/4*h51-9/2*h3111) +H(-1,1,-1,-1,0,1)*(-1/24*ln2^4*z2+5/36*ln2^3*e3+1/20*ln2^2*z2^2-1/4*ln2^2*h31-5/6*ln2*z2*e3+16/15*ln2*e5+5/2*ln2*h311+199/280*z2^3-3/4*z2*h31-283/72*e3^2+15/2*h51-6*h3111) +H(-1,1,-1,-1,1,-1)*(1/720*ln2^6-1/48*ln2^4*z2+1/18*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-35/12*ln2*z2*e3+9/2*ln2*e5-3/2*ln2*h311-3/80*z2^3+3/4*z2*h31+1/18*e3^2) +H(-1,1,-1,-1,1,1)*(-1/720*ln2^6+1/48*ln2^4*z2-1/18*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+35/12*ln2*z2*e3-9/2*ln2*e5+3/2*ln2*h311+187/210*z2^3-179/36*e3^2+15/4*h51-3/2*h3111) +H(-1,1,-1,0,-1,-1)*(-1/36*ln2^3*e3+3/80*ln2^2*z2^2-3/4*ln2^2*h31+13/12*ln2*z2*e3-33/20*ln2*e5+3/2*ln2*h311+67/560*z2^3+3/4*z2*h31-29/36*e3^2-3/2*h3111) +H(-1,1,-1,0,-1,1)*(1/4*ln2^4*z2-17/18*ln2^3*e3-1/8*ln2^2*z2^2+7/2*ln2^2*h31-13/2*ln2*z2*e3+107/10*ln2*e5-13*ln2*h311-277/70*z2^3-z2*h31+811/36*e3^2-61/2*h51+21*h3111) +H(-1,1,-1,0,0,-1)*(-1/6*ln2^3*e3+1/16*ln2^2*z2^2-1/6*ln2*z2*e3+1/2*ln2*e5-991/1680*z2^3+29/9*e3^2-5*h51) +H(-1,1,-1,0,0,1)*(-2/9*ln2^3*e3+3/40*ln2^2*z2^2+1/2*ln2^2*h31-5/2*ln2*z2*e3+49/12*ln2*e5-ln2*h311-881/1680*z2^3+25/9*e3^2-13/4*h51+h3111) +H(-1,1,-1,0,1,-1)*(-1/4*ln2^4*z2+29/36*ln2^3*e3+1/5*ln2^2*z2^2-7/2*ln2^2*h31+37/6*ln2*z2*e3-51/5*ln2*e5+29/2*ln2*h311+135/28*z2^3+z2*h31-248/9*e3^2+38*h51-24*h3111) +H(-1,1,-1,0,1,1)*(-2/9*ln2^3*e3+1/8*ln2^2*z2^2+1/4*ln2^2*h31+1/2*ln2*z2*e3-17/20*ln2*e5-2*ln2*h311-17/140*z2^3+55/72*e3^2-4*h51+7/2*h3111) +H(-1,1,-1,1,-1,-1)*(1/720*ln2^6-1/48*ln2^4*z2+1/18*ln2^3*e3+1/80*ln2^2*z2^2-1/6*ln2*z2*e3+1/5*ln2*e5-67/560*z2^3-3/4*z2*h31+29/36*e3^2+3/2*h3111) +H(-1,1,-1,1,-1,1)*(-1/720*ln2^6+1/48*ln2^4*z2-1/18*ln2^3*e3-1/80*ln2^2*z2^2+1/6*ln2*z2*e3-1/5*ln2*e5+1/112*z2^3-1/18*e3^2) +H(-1,1,-1,1,0,-1)*(1/48*ln2^4*z2-1/18*ln2^3*e3-3/40*ln2^2*z2^2+ln2^2*h31-7/3*ln2*z2*e3+56/15*ln2*e5-4*ln2*h311-661/560*z2^3-z2*h31+62/9*e3^2-8*h51+8*h3111) +H(-1,1,-1,1,0,1)*(1/24*ln2^4*z2-5/36*ln2^3*e3-1/20*ln2^2*z2^2+1/4*ln2^2*h31+5/6*ln2*z2*e3-16/15*ln2*e5-5/2*ln2*h311-71/70*z2^3-z2*h31+215/36*e3^2-8*h51+13/2*h3111) +H(-1,1,-1,1,1,-1)*(-1/720*ln2^6+1/48*ln2^4*z2-1/18*ln2^3*e3-1/80*ln2^2*z2^2+11/12*ln2*z2*e3-19/15*ln2*e5-3/2*ln2*h311-461/560*z2^3+169/36*e3^2-15/2*h51+3*h3111) +H(-1,1,-1,1,1,1)*(1/720*ln2^6-1/48*ln2^4*z2+1/18*ln2^3*e3+1/80*ln2^2*z2^2-11/12*ln2*z2*e3+19/15*ln2*e5+3/2*ln2*h311+29/112*z2^3+1/4*z2*h31-3/2*e3^2+4*h51-7/2*h3111) +H(-1,1,0,-1,-1,-1)*(-1/80*ln2^2*z2^2+1/4*ln2^2*h31-4/3*ln2*z2*e3+31/15*ln2*e5-2*ln2*h311-477/560*z2^3-1/4*z2*h31+59/12*e3^2-13/2*h51+7/2*h3111) +H(-1,1,0,-1,-1,1)*(-3/8*ln2^4*z2+7/4*ln2^3*e3-7/20*ln2^2*z2^2-9/4*ln2^2*h31+7/2*ln2*z2*e3-107/20*ln2*e5+7*ln2*h311+1147/560*z2^3+1/2*z2*h31-93/8*e3^2+61/4*h51-21/2*h3111) +H(-1,1,0,-1,0,-1)*(-1/16*ln2^2*z2^2+ln2^2*h31-5/2*ln2*z2*e3+59/15*ln2*e5-4*ln2*h311-197/112*z2^3-2*z2*h31+187/18*e3^2-12*h51+8*h3111) +H(-1,1,0,-1,0,1)*(-3/80*ln2^2*z2^2-2/3*ln2*z2*e3+11/10*ln2*e5+2*ln2*h311+391/560*z2^3-z2*h31-139/36*e3^2+15/2*h51-6*h3111) +H(-1,1,0,-1,1,-1)*(3/4*ln2^4*z2-35/12*ln2^3*e3+11/40*ln2^2*z2^2+13/2*ln2^2*h31-37/3*ln2*z2*e3+193/10*ln2*e5-37/2*ln2*h311-277/56*z2^3+28*e3^2-38*h51+24*h3111) +H(-1,1,0,-1,1,1)*(-3/8*ln2^4*z2+7/3*ln2^3*e3-53/80*ln2^2*z2^2-9/2*ln2^2*h31+33/4*ln2*z2*e3-721/60*ln2*e5+23/2*ln2*h311+267/80*z2^3+1/2*z2*h31-457/24*e3^2+23*h51-15*h3111) +H(-1,1,0,0,-1,-1)*(-1/2*ln2^2*h31+2/3*ln2*z2*e3-59/60*ln2*e5+ln2*h311+3/280*z2^3+1/2*z2*h31-1/9*e3^2-3/4*h51-h3111) +H(-1,1,0,0,-1,1)*(7/6*ln2^3*e3-11/20*ln2^2*z2^2-3/2*ln2^2*h31+4*ln2*z2*e3-359/60*ln2*e5+3*ln2*h311+599/560*z2^3-101/18*e3^2+23/4*h51-3*h3111) +H(-1,1,0,0,0,-1)*(-7/40*ln2^2*z2^2-1/2*ln2*z2*e3+17/15*ln2*e5-533/1680*z2^3+13/6*e3^2-4*h51) +H(-1,1,0,0,0,1)*(-1/5*ln2^2*z2^2-ln2*z2*e3+59/30*ln2*e5-13/420*z2^3+19/36*e3^2-3/2*h51) +H(-1,1,0,0,1,-1)*(-7/6*ln2^3*e3+41/80*ln2^2*z2^2+ln2^2*h31-8/3*ln2*z2*e3+49/12*ln2*e5-ln2*h311-19/80*z2^3+8/9*e3^2) +H(-1,1,0,0,1,1)*(-1/20*ln2^2*z2^2+1/2*ln2*z2*e3-3/5*ln2*e5-ln2*h311+61/560*z2^3-19/36*e3^2-9/4*h51+2*h3111) +H(-1,1,0,1,-1,-1)*(-3/8*ln2^4*z2+7/6*ln2^3*e3+3/80*ln2^2*z2^2-17/4*ln2^2*h31+97/12*ln2*z2*e3-127/10*ln2*e5+13*ln2*h311+351/112*z2^3-1/2*z2*h31-71/4*e3^2+25*h51-15*h3111) +H(-1,1,0,1,-1,1)*(3/4*ln2^4*z2-35/12*ln2^3*e3+9/40*ln2^2*z2^2+29/4*ln2^2*h31-181/12*ln2*z2*e3+118/5*ln2*e5-20*ln2*h311-199/40*z2^3+3/4*z2*h31+28*e3^2-38*h51+24*h3111) +H(-1,1,0,1,0,-1)*(-11/80*ln2^2*z2^2+ln2^2*h31-9/4*ln2*z2*e3+19/5*ln2*e5-4*ln2*h311-135/112*z2^3-5/4*z2*h31+127/18*e3^2-8*h51+8*h3111) +H(-1,1,0,1,0,1)*(-3/20*ln2^2*z2^2-1/6*ln2*z2*e3+43/60*ln2*e5+2*ln2*h311+543/560*z2^3+1/2*z2*h31-205/36*e3^2+31/4*h51-6*h3111) +H(-1,1,0,1,1,-1)*(-3/8*ln2^4*z2+7/12*ln2^3*e3+5/16*ln2^2*z2^2-3*ln2^2*h31+15/2*ln2*z2*e3-243/20*ln2*e5+19/2*ln2*h311+1361/560*z2^3+1/4*z2*h31-55/4*e3^2+35/2*h51-27/2*h3111) +H(-1,1,0,1,1,1)*(-1/5*ln2^2*z2^2+1/4*ln2*z2*e3+7/20*ln2*e5-1/2*ln2*h311-421/560*z2^3-3/4*z2*h31+149/36*e3^2-15/4*h51+5/2*h3111) +H(-1,1,1,-1,-1,-1)*(1/720*ln2^6-1/48*ln2^4*z2+7/36*ln2^3*e3-1/16*ln2^2*z2^2+1/12*ln2*z2*e3-1/20*ln2*e5+67/1680*z2^3+1/4*z2*h31-5/18*e3^2-1/2*h3111) +H(-1,1,1,-1,-1,1)*(-1/720*ln2^6+1/48*ln2^4*z2-7/36*ln2^3*e3+1/16*ln2^2*z2^2-1/12*ln2*z2*e3+1/20*ln2*e5-17/560*z2^3+5/24*e3^2) +H(-1,1,1,-1,0,-1)*(1/48*ln2^4*z2-1/18*ln2^3*e3-3/40*ln2^2*z2^2+ln2^2*h31-13/6*ln2*z2*e3+113/30*ln2*e5-7/2*ln2*h311-461/560*z2^3+z2*h31+157/36*e3^2-15/2*h51+3*h3111) +H(-1,1,1,-1,0,1)*(1/24*ln2^4*z2-5/36*ln2^3*e3-1/20*ln2^2*z2^2+1/4*ln2^2*h31-1/12*ln2*z2*e3+43/60*ln2*e5+ln2*h311+7/8*z2^3+z2*h31-197/36*e3^2+6*h51-9/2*h3111) +H(-1,1,1,-1,1,-1)*(-1/720*ln2^6+1/48*ln2^4*z2-7/36*ln2^3*e3+1/16*ln2^2*z2^2-1/6*ln2*z2*e3+3/10*ln2*e5+3/2*ln2*h311+489/560*z2^3-61/12*e3^2+15/2*h51-3*h3111) +H(-1,1,1,-1,1,1)*(1/720*ln2^6-1/48*ln2^4*z2+7/36*ln2^3*e3-1/16*ln2^2*z2^2+1/6*ln2*z2*e3-3/10*ln2*e5-3/2*ln2*h311-69/80*z2^3-3/4*z2*h31+373/72*e3^2-6*h51+9/2*h3111) +H(-1,1,1,0,-1,-1)*(1/36*ln2^3*e3-3/80*ln2^2*z2^2+3/4*ln2^2*h31-13/12*ln2*z2*e3+33/20*ln2*e5-3/2*ln2*h311+1/16*z2^3-11/36*e3^2+3/4*h51) +H(-1,1,1,0,-1,1)*(-1/4*ln2^4*z2+17/18*ln2^3*e3+1/8*ln2^2*z2^2-7/2*ln2^2*h31+29/4*ln2*z2*e3-751/60*ln2*e5+9*ln2*h311+57/40*z2^3-7/4*z2*h31-251/36*e3^2+13*h51-15/2*h3111) +H(-1,1,1,0,0,-1)*(1/6*ln2^3*e3-1/16*ln2^2*z2^2+1/6*ln2*z2*e3-1/2*ln2*e5+103/1680*z2^3+1/4*z2*h31+5/36*e3^2+3/4*h51-h3111) +H(-1,1,1,0,0,1)*(2/9*ln2^3*e3-3/40*ln2^2*z2^2-1/2*ln2^2*h31+5/2*ln2*z2*e3-49/12*ln2*e5+ln2*h311+43/840*z2^3-z2*h31+35/72*e3^2+3/2*h51) +H(-1,1,1,0,1,-1)*(1/4*ln2^4*z2-29/36*ln2^3*e3-1/5*ln2^2*z2^2+7/2*ln2^2*h31-83/12*ln2*z2*e3+721/60*ln2*e5-21/2*ln2*h311-127/56*z2^3+1/4*z2*h31+439/36*e3^2-35/2*h51+27/2*h3111) +H(-1,1,1,0,1,1)*(2/9*ln2^3*e3-1/8*ln2^2*z2^2-1/4*ln2^2*h31-1/2*ln2*z2*e3+17/20*ln2*e5+2*ln2*h311+377/560*z2^3+3/4*z2*h31-277/72*e3^2+25/4*h51-5*h3111) +H(-1,1,1,1,-1,-1)*(-1/720*ln2^6+1/48*ln2^4*z2-7/36*ln2^3*e3+3/16*ln2^2*z2^2+1/4*ln2^2*h31-1/12*ln2*z2*e3-1/5*ln2*e5-ln2*h311-179/420*z2^3+61/24*e3^2-15/4*h51+3/2*h3111) +H(-1,1,1,1,-1,1)*(1/720*ln2^6-1/48*ln2^4*z2+7/36*ln2^3*e3-3/16*ln2^2*z2^2-1/4*ln2^2*h31+1/12*ln2*z2*e3+1/5*ln2*e5+ln2*h311+61/80*z2^3+3/4*z2*h31-157/36*e3^2+4*h51-3*h3111) +H(-1,1,1,1,0,-1)*(-1/48*ln2^4*z2+1/18*ln2^3*e3+3/40*ln2^2*z2^2-ln2^2*h31+13/6*ln2*z2*e3-113/30*ln2*e5+7/2*ln2*h311+569/560*z2^3+1/2*z2*h31-127/24*e3^2+6*h51-11/2*h3111) +H(-1,1,1,1,0,1)*(-1/24*ln2^4*z2+5/36*ln2^3*e3+1/20*ln2^2*z2^2-1/4*ln2^2*h31+1/12*ln2*z2*e3-43/60*ln2*e5-ln2*h311-41/560*z2^3+1/4*z2*h31+23/18*e3^2-15/4*h51+3*h3111) +H(-1,1,1,1,1,-1)*(1/720*ln2^6-1/48*ln2^4*z2+7/36*ln2^3*e3-3/16*ln2^2*z2^2-1/4*ln2^2*h31+1/3*ln2*z2*e3+11/20*ln2*e5+1/2*ln2*h311-3/16*z2^3-1/4*z2*h31+49/72*e3^2) +H(-1,1,1,1,1,1)*(-1/720*ln2^6+1/48*ln2^4*z2-7/36*ln2^3*e3+3/16*ln2^2*z2^2+1/4*ln2^2*h31-1/3*ln2*z2*e3-11/20*ln2*e5-1/2*ln2*h311+53/280*z2^3+2/9*e3^2-1/4*h51+1/2*h3111) +H(0,-1,-1,-1,-1,-1)*(11/280*z2^3-2/9*e3^2+1/4*h51-1/2*h3111) +H(0,-1,-1,-1,-1,1)*(1/16*ln2^4*z2-7/18*ln2^3*e3+13/80*ln2^2*z2^2+1/4*ln2^2*h31+7/6*ln2*z2*e3-31/15*ln2*e5+51/280*z2^3-1/2*z2*h31-31/36*e3^2+h51) +H(0,-1,-1,-1,0,-1)*(-463/1680*z2^3-1/4*z2*h31+59/36*e3^2-5/2*h51) +H(0,-1,-1,-1,0,1)*(-223/840*z2^3-5/4*z2*h31+121/72*e3^2) +H(0,-1,-1,-1,1,-1)*(-1/4*ln2^4*z2+49/36*ln2^3*e3-39/80*ln2^2*z2^2-3/4*ln2^2*h31-35/12*ln2*z2*e3+31/6*ln2*e5-27/56*z2^3+z2*h31+43/18*e3^2-11/4*h51+3/2*h3111) +H(0,-1,-1,-1,1,1)*(3/16*ln2^4*z2-49/36*ln2^3*e3+3/5*ln2^2*z2^2+3/2*ln2^2*h31-7/12*ln2*z2*e3-1/5*ln2*e5-3*ln2*h311+3/140*z2^3+1/2*z2*h31+7/36*e3^2-3*h51+3*h3111) +H(0,-1,-1,0,-1,-1)*(121/280*z2^3-179/72*e3^2+15/4*h51) +H(0,-1,-1,0,-1,1)*(7/3*ln2*z2*e3-217/60*ln2*e5+99/112*z2^3+5/4*z2*h31-365/72*e3^2+7/4*h51) +H(0,-1,-1,0,0,-1)*(71/560*z2^3-25/36*e3^2+h51) +H(0,-1,-1,0,0,1)*(29/70*z2^3+3/2*z2*h31-5/2*e3^2) +H(0,-1,-1,0,1,-1)*(-7/3*ln2*z2*e3+217/60*ln2*e5-53/280*z2^3+z2*h31+61/72*e3^2-h51) +H(0,-1,-1,0,1,1)*(-1/560*z2^3+1/72*e3^2) +H(0,-1,-1,1,-1,-1)*(3/8*ln2^4*z2-7/4*ln2^3*e3+9/16*ln2^2*z2^2+11/2*ln2*z2*e3-91/10*ln2*e5+3*ln2*h311+241/280*z2^3-3/2*z2*h31-9/2*e3^2+6*h51-9/2*h3111) +H(0,-1,-1,1,-1,1)*(-7/16*ln2^4*z2+77/36*ln2^3*e3-5/8*ln2^2*z2^2-5/4*ln2^2*h31-10/3*ln2*z2*e3+23/4*ln2*e5+ln2*h311-131/140*z2^3-3/4*z2*h31+377/72*e3^2-7/4*h51-h3111) +H(0,-1,-1,1,0,-1)*(1/5*ln2^2*z2^2-2*ln2^2*h31+23/3*ln2*z2*e3-743/60*ln2*e5+8*ln2*h311+797/336*z2^3-z2*h31-941/72*e3^2+35/2*h51-12*h3111) +H(0,-1,-1,1,0,1)*(3/16*ln2^2*z2^2-35/12*ln2*z2*e3+217/60*ln2*e5-659/840*z2^3-z2*h31+355/72*e3^2-7/4*h51) +H(0,-1,-1,1,1,-1)*(-1/8*ln2^4*z2+14/9*ln2^3*e3-61/80*ln2^2*z2^2-7/4*ln2^2*h31+7/4*ln2*z2*e3-27/20*ln2*e5+3*ln2*h311+229/560*z2^3-193/72*e3^2+15/4*h51-5/2*h3111) +H(0,-1,-1,1,1,1)*(3/16*ln2^4*z2-14/9*ln2^3*e3+37/40*ln2^2*z2^2+2*ln2^2*h31-5/4*ln2*z2*e3-4/15*ln2*e5-4*ln2*h311-15/112*z2^3+1/4*z2*h31+14/9*e3^2-4*h51+4*h3111) +H(0,-1,0,-1,-1,-1)*(-121/840*z2^3+5/6*e3^2-5/4*h51-2*h3111) +H(0,-1,0,-1,-1,1)*(1/10*ln2^2*z2^2-ln2^2*h31+10/3*ln2*z2*e3-65/12*ln2*e5+4*ln2*h311+61/210*z2^3-11/4*z2*h31-85/72*e3^2+27/4*h51-4*h3111) +H(0,-1,0,-1,0,-1)*(-319/560*z2^3-z2*h31+31/9*e3^2-4*h51) +H(0,-1,0,-1,0,1)*(-89/80*z2^3-5*z2*h31+7*e3^2) +H(0,-1,0,-1,1,-1)*(-1/5*ln2^2*z2^2+2*ln2^2*h31-49/6*ln2*z2*e3+391/30*ln2*e5-6*ln2*h311-221/120*z2^3+z2*h31+91/9*e3^2-13*h51+8*h3111) +H(0,-1,0,-1,1,1)*(1/10*ln2^2*z2^2-ln2^2*h31+37/12*ln2*z2*e3-151/30*ln2*e5+2*ln2*h311+557/336*z2^3+5/2*z2*h31-685/72*e3^2+9/2*h51-2*h3111) +H(0,-1,0,0,-1,-1)*(-17/105*z2^3+17/18*e3^2-3/2*h51) +H(0,-1,0,0,-1,1)*(9/2*ln2*z2*e3-217/30*ln2*e5+355/336*z2^3-67/12*e3^2+7/2*h51) +H(0,-1,0,0,0,-1)*(-29/120*z2^3+5/3*e3^2-4*h51) +H(0,-1,0,0,0,1)*(239/840*z2^3-4/3*e3^2) +H(0,-1,0,0,1,-1)*(-9/2*ln2*z2*e3+217/30*ln2*e5-449/840*z2^3+8/3*e3^2-h51) +H(0,-1,0,0,1,1)*(82/105*z2^3+3/2*z2*h31-163/36*e3^2) +H(0,-1,0,1,-1,-1)*(1/10*ln2^2*z2^2-ln2^2*h31+29/6*ln2*z2*e3-457/60*ln2*e5+2*ln2*h311+377/1680*z2^3-3/2*z2*h31-67/72*e3^2+3/2*h51) +H(0,-1,0,1,-1,1)*(-1/5*ln2^2*z2^2+2*ln2^2*h31-49/6*ln2*z2*e3+391/30*ln2*e5-6*ln2*h311-73/30*z2^3-z2*h31+493/36*e3^2-25/2*h51+6*h3111) +H(0,-1,0,1,0,-1)*(3/560*z2^3) +H(0,-1,0,1,0,1)*(-459/560*z2^3-3*z2*h31+91/18*e3^2) +H(0,-1,0,1,1,-1)*(1/10*ln2^2*z2^2-ln2^2*h31+61/12*ln2*z2*e3-8*ln2*e5+4*ln2*h311+2371/1680*z2^3-1/2*z2*h31-71/9*e3^2+10*h51-6*h3111) +H(0,-1,0,1,1,1)*(179/1680*z2^3+3/4*z2*h31-17/24*e3^2) +H(0,-1,1,-1,-1,-1)*(-1/4*ln2^4*z2+35/36*ln2^3*e3-5/16*ln2^2*z2^2+5/4*ln2^2*h31-16/3*ln2*z2*e3+509/60*ln2*e5-9/2*ln2*h311-201/280*z2^3+z2*h31+139/36*e3^2-21/4*h51+5*h3111) +H(0,-1,1,-1,-1,1)*(3/16*ln2^4*z2-7/12*ln2^3*e3+3/20*ln2^2*z2^2-3/2*ln2^2*h31+13/2*ln2*z2*e3-301/30*ln2*e5+9/2*ln2*h311+29/16*z2^3+3/4*z2*h31-31/3*e3^2+19/2*h51-9/2*h3111) +H(0,-1,1,-1,0,-1)*(-2/5*ln2^2*z2^2+4*ln2^2*h31-43/4*ln2*z2*e3+263/15*ln2*e5-16*ln2*h311-1781/420*z2^3+z2*h31+427/18*e3^2-33*h51+24*h3111) +H(0,-1,1,-1,0,1)*(-3/8*ln2^2*z2^2+23/3*ln2*z2*e3-31/3*ln2*e5+331/210*z2^3+z2*h31-683/72*e3^2+5*h51) +H(0,-1,1,-1,1,-1)*(1/2*ln2^4*z2-7/3*ln2^3*e3+3/5*ln2^2*z2^2+3/2*ln2^2*h31+7/4*ln2*z2*e3-16/5*ln2*e5-3/2*ln2*h311+31/140*z2^3-7/6*e3^2) +H(0,-1,1,-1,1,1)*(-7/16*ln2^4*z2+7/3*ln2^3*e3-57/80*ln2^2*z2^2-9/4*ln2^2*h31-11/4*ln2*z2*e3+99/20*ln2*e5+9/2*ln2*h311-451/560*z2^3-3/4*z2*h31+53/12*e3^2+9/4*h51-9/2*h3111) +H(0,-1,1,0,-1,-1)*(1/12*ln2*z2*e3-1/4*ln2*e5+4*ln2*h311+703/280*z2^3+z2*h31-1043/72*e3^2+20*h51-12*h3111) +H(0,-1,1,0,-1,1)*(31/40*ln2^2*z2^2-4*ln2^2*h31+85/12*ln2*z2*e3-41/3*ln2*e5+12*ln2*h311+319/140*z2^3-z2*h31-839/72*e3^2+19*h51-12*h3111) +H(0,-1,1,0,0,-1)*(5/6*ln2*z2*e3-31/15*ln2*e5+261/560*z2^3-z2*h31-11/6*e3^2+6*h51) +H(0,-1,1,0,0,1)*(37/6*ln2*z2*e3-31/3*ln2*e5+411/560*z2^3-2*z2*h31-107/36*e3^2+5*h51) +H(0,-1,1,0,1,-1)*(-31/40*ln2^2*z2^2+4*ln2^2*h31-97/12*ln2*z2*e3+299/20*ln2*e5-16*ln2*h311-89/20*z2^3+2*z2*h31+218/9*e3^2-38*h51+24*h3111) +H(0,-1,1,0,1,1)*(-59/12*ln2*z2*e3+217/30*ln2*e5-843/560*z2^3-1/4*z2*h31+311/36*e3^2-7/2*h51) +H(0,-1,1,1,-1,-1)*(-1/8*ln2^4*z2-7/18*ln2^3*e3+3/10*ln2^2*z2^2+3/4*ln2^2*h31-23/12*ln2*z2*e3+29/12*ln2*e5-5/2*ln2*h311-77/80*z2^3+203/36*e3^2-15/2*h51+4*h3111) +H(0,-1,1,1,-1,1)*(3/16*ln2^4*z2-19/80*ln2^2*z2^2+1/2*ln2^2*h31+23/12*ln2*z2*e3-161/60*ln2*e5-3/2*ln2*h311+69/112*z2^3+z2*h31-83/24*e3^2-1/4*h51+3/2*h3111) +H(0,-1,1,1,0,-1)*(1/5*ln2^2*z2^2-2*ln2^2*h31+6*ln2*z2*e3-619/60*ln2*e5+8*ln2*h311+2053/840*z2^3+1/4*z2*h31-953/72*e3^2+33/2*h51-12*h3111) +H(0,-1,1,1,0,1)*(3/16*ln2^2*z2^2-2/3*ln2*z2*e3-31/60*ln2*e5+1483/1680*z2^3+11/4*z2*h31-311/72*e3^2+1/4*h51) +H(0,-1,1,1,1,-1)*(-1/8*ln2^4*z2+7/12*ln2^3*e3-13/20*ln2^2*z2^2-ln2^2*h31-2/3*ln2*z2*e3+11/4*ln2*e5+5/2*ln2*h311+3/40*z2^3-1/2*z2*h31-23/24*e3^2+4*h51-3*h3111) +H(0,-1,1,1,1,1)*(1/16*ln2^4*z2-7/12*ln2^3*e3+39/80*ln2^2*z2^2+3/4*ln2^2*h31+1/6*ln2*z2*e3-161/60*ln2*e5-3/2*ln2*h311+5/14*z2^3-1/2*z2*h31-4/9*e3^2-1/4*h51+3/2*h3111) +H(0,0,-1,-1,-1,-1)*(h3111) +H(0,0,-1,-1,-1,1)*(-7/18*ln2^3*e3+11/40*ln2^2*z2^2+ln2^2*h31-7/3*ln2*z2*e3+29/10*ln2*e5-3*ln2*h311-67/280*z2^3+z2*h31+3/2*e3^2-9/2*h51+3*h3111) +H(0,0,-1,-1,0,-1)*(113/210*z2^3+1/2*z2*h31-55/18*e3^2+h51) +H(0,0,-1,-1,0,1)*(41/168*z2^3+z2*h31-3/2*e3^2) +H(0,0,-1,-1,1,-1)*(7/6*ln2^3*e3-63/80*ln2^2*z2^2-3/2*ln2^2*h31+5/3*ln2*z2*e3-9/10*ln2*e5+2*ln2*h311-143/560*z2^3+1/4*z2*h31+31/36*e3^2+3/4*h51-h3111) +H(0,0,-1,-1,1,1)*(-7/9*ln2^3*e3+3/5*ln2^2*z2^2+3/2*ln2^2*h31-5/6*ln2*z2*e3-1/5*ln2*e5-3*ln2*h311-67/140*z2^3-z2*h31+61/18*e3^2-3*h51+3*h3111) +H(0,0,-1,0,-1,-1)*(1/15*z2^3-17/36*e3^2+7/2*h51) +H(0,0,-1,0,-1,1)*(-13/6*ln2*z2*e3+31/10*ln2*e5+43/210*z2^3+2*z2*h31-5/4*e3^2-3/2*h51) +H(0,0,-1,0,0,-1)*(5/8*z2^3-7/2*e3^2+6*h51) +H(0,0,-1,0,0,1)*(4/35*z2^3-1/2*e3^2) +H(0,0,-1,0,1,-1)*(13/6*ln2*z2*e3-31/10*ln2*e5-29/336*z2^3+z2*h31+1/6*e3^2-h51) +H(0,0,-1,0,1,1)*(-403/840*z2^3+95/36*e3^2) +H(0,0,-1,1,-1,-1)*(-7/6*ln2^3*e3+3/4*ln2^2*z2^2+37/12*ln2*z2*e3-91/15*ln2*e5+2*ln2*h311+33/40*z2^3-3/4*z2*h31-149/36*e3^2+13/4*h51-3*h3111) +H(0,0,-1,1,-1,1)*(14/9*ln2^3*e3-41/40*ln2^2*z2^2-ln2^2*h31-5/2*ln2*z2*e3+23/4*ln2*e5+ln2*h311-349/560*z2^3+1/2*z2*h31+26/9*e3^2-7/4*h51-h3111) +H(0,0,-1,1,0,-1)*(7/6*ln2*z2*e3-31/15*ln2*e5-211/1680*z2^3-1/2*z2*h31+7/6*e3^2-4*h51) +H(0,0,-1,1,0,1)*(-7*ln2*z2*e3+31/3*ln2*e5-631/840*z2^3+3*z2*h31+73/18*e3^2-5*h51) +H(0,0,-1,1,1,-1)*(-11/80*ln2^2*z2^2-1/2*ln2^2*h31-3/4*ln2*z2*e3+101/60*ln2*e5+2*ln2*h311+247/560*z2^3-1/2*z2*h31-49/18*e3^2+23/4*h51-3*h3111) +H(0,0,-1,1,1,1)*(-7/18*ln2^3*e3+13/40*ln2^2*z2^2+1/2*ln2^2*h31+17/6*ln2*z2*e3-157/30*ln2*e5-ln2*h311+27/40*z2^3-3/2*z2*h31-28/9*e3^2+3/2*h51+h3111) +H(0,0,0,-1,-1,-1)*(-1/14*z2^3+4/9*e3^2-3/2*h51) +H(0,0,0,-1,-1,1)*(3/8*ln2^2*z2^2+1/3*ln2*z2*e3-31/15*ln2*e5+9/280*z2^3-z2*h31+2/3*e3^2+h51) +H(0,0,0,-1,0,-1)*(-5/24*z2^3+4/3*e3^2-4*h51) +H(0,0,0,-1,0,1)*(-97/420*z2^3+4/3*e3^2) +H(0,0,0,-1,1,-1)*(-3/4*ln2^2*z2^2-3/2*ln2*z2*e3+31/6*ln2*e5-257/560*z2^3+4/3*e3^2) +H(0,0,0,-1,1,1)*(3/8*ln2^2*z2^2+7/3*ln2*z2*e3-31/6*ln2*e5+59/70*z2^3-z2*h31-34/9*e3^2+5/2*h51) +H(0,0,0,0,-1,-1)*(h51) +H(0,0,0,0,-1,1)*(-31/15*ln2*e5+39/70*z2^3-4/3*e3^2+h51) +H(0,0,0,0,0,-1)*(31/140*z2^3) +H(0,0,0,0,0,1)*(8/35*z2^3) +H(0,0,0,0,1,-1)*(31/15*ln2*e5-111/280*z2^3+1/2*e3^2) +H(0,0,0,0,1,1)*(6/35*z2^3-8/9*e3^2) +H(0,0,0,1,-1,-1)*(3/8*ln2^2*z2^2+7/6*ln2*z2*e3-31/10*ln2*e5+7/40*z2^3-1/2*z2*h31-1/3*e3^2-h51) +H(0,0,0,1,-1,1)*(-3/4*ln2^2*z2^2-3/2*ln2*z2*e3+31/6*ln2*e5-121/140*z2^3+131/36*e3^2-5/2*h51) +H(0,0,0,1,0,-1)*(-221/840*z2^3+5/3*e3^2-4*h51) +H(0,0,0,1,0,1)*(-32/105*z2^3+16/9*e3^2) +H(0,0,0,1,1,-1)*(3/8*ln2^2*z2^2-5/6*ln2*z2*e3+9/70*z2^3-1/2*z2*h31-7/36*e3^2+3/2*h51) +H(0,0,0,1,1,1)*(23/70*z2^3-16/9*e3^2) +H(0,0,1,-1,-1,-1)*(7/18*ln2^3*e3-19/80*ln2^2*z2^2+1/2*ln2^2*h31-29/12*ln2*z2*e3+61/15*ln2*e5-ln2*h311+33/560*z2^3+3/4*z2*h31-43/72*e3^2+3/2*h51) +H(0,0,1,-1,-1,1)*(-3/80*ln2^2*z2^2-3/2*ln2^2*h31+19/4*ln2*z2*e3-209/30*ln2*e5+4*ln2*h311+731/560*z2^3+1/2*z2*h31-547/72*e3^2+15/2*h51-4*h3111) +H(0,0,1,-1,0,-1)*(-7/6*ln2*z2*e3+31/15*ln2*e5+23/60*z2^3+z2*h31-47/18*e3^2+4*h51) +H(0,0,1,-1,0,1)*(7*ln2*z2*e3-31/3*ln2*e5+137/120*z2^3-2*z2*h31-227/36*e3^2+5*h51) +H(0,0,1,-1,1,-1)*(-14/9*ln2^3*e3+41/40*ln2^2*z2^2+ln2^2*h31+5/2*ln2*z2*e3-23/4*ln2*e5-ln2*h311+111/280*z2^3-5/3*e3^2) +H(0,0,1,-1,1,1)*(7/6*ln2^3*e3-67/80*ln2^2*z2^2-ln2^2*h31-10/3*ln2*z2*e3+137/20*ln2*e5+2*ln2*h311-303/280*z2^3+3/2*z2*h31+187/36*e3^2-5/4*h51-2*h3111) +H(0,0,1,0,-1,-1)*(347/1680*z2^3-43/36*e3^2+5/2*h51) +H(0,0,1,0,-1,1)*(-11/3*ln2*z2*e3+31/6*ln2*e5-109/210*z2^3+2*z2*h31+53/18*e3^2-5/2*h51) +H(0,0,1,0,0,-1)*(113/280*z2^3-13/6*e3^2+6*h51) +H(0,0,1,0,0,1)*(-4/35*z2^3+8/9*e3^2) +H(0,0,1,0,1,-1)*(11/3*ln2*z2*e3-31/6*ln2*e5+691/1680*z2^3+z2*h31-49/18*e3^2-h51) +H(0,0,1,0,1,1)*(-29/30*z2^3+16/3*e3^2) +H(0,0,1,1,-1,-1)*(7/9*ln2^3*e3-17/40*ln2^2*z2^2+1/2*ln2^2*h31-19/6*ln2*z2*e3+329/60*ln2*e5-3*ln2*h311-41/40*z2^3+1/2*z2*h31+45/8*e3^2-15/2*h51+4*h3111) +H(0,0,1,1,-1,1)*(-7/6*ln2^3*e3+7/10*ln2^2*z2^2+1/2*ln2^2*h31+31/12*ln2*z2*e3-31/6*ln2*e5+47/56*z2^3-z2*h31-301/72*e3^2+5/2*h51) +H(0,0,1,1,0,-1)*(5/336*z2^3+1/36*e3^2-h51) +H(0,0,1,1,0,1)*(53/105*z2^3-8/3*e3^2) +H(0,0,1,1,1,-1)*(7/18*ln2^3*e3-3/16*ln2^2*z2^2-25/12*ln2*z2*e3+71/20*ln2*e5-ln2*h311-379/560*z2^3-1/4*z2*h31+67/18*e3^2-11/4*h51+2*h3111) +H(0,0,1,1,1,1)*(6/35*z2^3-8/9*e3^2) +H(0,1,-1,-1,-1,-1)*(1/16*ln2^4*z2-7/36*ln2^3*e3+3/40*ln2^2*z2^2-3/4*ln2^2*h31+19/12*ln2*z2*e3-149/60*ln2*e5+3/2*ln2*h311+1/80*z2^3-1/4*z2*h31-1/72*e3^2-h3111) +H(0,1,-1,-1,-1,1)*(-1/8*ln2^4*z2+7/12*ln2^3*e3-19/80*ln2^2*z2^2+1/2*ln2^2*h31-11/4*ln2*z2*e3+91/20*ln2*e5-3/2*ln2*h311-31/40*z2^3-3/4*z2*h31+53/12*e3^2-15/4*h51+3/2*h3111) +H(0,1,-1,-1,0,-1)*(1/5*ln2^2*z2^2-2*ln2^2*h31+37/12*ln2*z2*e3-103/20*ln2*e5+8*ln2*h311+583/420*z2^3-9/4*z2*h31-271/36*e3^2+14*h51-12*h3111) +H(0,1,-1,-1,0,1)*(3/16*ln2^2*z2^2-19/4*ln2*z2*e3+403/60*ln2*e5-599/840*z2^3+301/72*e3^2-13/4*h51) +H(0,1,-1,-1,1,-1)*(3/16*ln2^4*z2-7/6*ln2^3*e3+33/80*ln2^2*z2^2+3/2*ln2^2*h31-ln2*z2*e3+14/15*ln2*e5-3/2*ln2*h311+277/560*z2^3+3/2*z2*h31-35/12*e3^2+7/4*h51) +H(0,1,-1,-1,1,1)*(-1/8*ln2^4*z2+7/6*ln2^3*e3-21/40*ln2^2*z2^2-9/4*ln2^2*h31+9/2*ln2*z2*e3-59/10*ln2*e5+9/2*ln2*h311+361/280*z2^3-181/24*e3^2+15/2*h51-9/2*h3111) +H(0,1,-1,0,-1,-1)*(-1/12*ln2*z2*e3+1/4*ln2*e5-4*ln2*h311-279/140*z2^3+5/4*z2*h31+101/9*e3^2-37/2*h51+12*h3111) +H(0,1,-1,0,-1,1)*(-31/40*ln2^2*z2^2+4*ln2^2*h31-16/3*ln2*z2*e3+317/30*ln2*e5-12*ln2*h311-177/70*z2^3-2*z2*h31+125/9*e3^2-35/2*h51+12*h3111) +H(0,1,-1,0,0,-1)*(-5/6*ln2*z2*e3+31/15*ln2*e5-23/40*z2^3+z2*h31+8/3*e3^2-6*h51) +H(0,1,-1,0,0,1)*(-37/6*ln2*z2*e3+31/3*ln2*e5-199/280*z2^3+2*z2*h31+28/9*e3^2-5*h51) +H(0,1,-1,0,1,-1)*(31/40*ln2^2*z2^2-4*ln2^2*h31+19/3*ln2*z2*e3-237/20*ln2*e5+16*ln2*h311+135/28*z2^3+z2*h31-244/9*e3^2+38*h51-24*h3111) +H(0,1,-1,0,1,1)*(59/12*ln2*z2*e3-217/30*ln2*e5+247/280*z2^3-2*z2*h31-43/9*e3^2+7/2*h51) +H(0,1,-1,1,-1,-1)*(-7/16*ln2^4*z2+35/18*ln2^3*e3-43/80*ln2^2*z2^2-1/4*ln2^2*h31-47/12*ln2*z2*e3+131/20*ln2*e5-5/2*ln2*h311-659/560*z2^3-3/2*z2*h31+245/36*e3^2-23/4*h51+4*h3111) +H(0,1,-1,1,-1,1)*(1/2*ln2^4*z2-7/3*ln2^3*e3+3/5*ln2^2*z2^2+3/2*ln2^2*h31+7/4*ln2*z2*e3-16/5*ln2*e5-3/2*ln2*h311+31/280*z2^3-3/4*z2*h31-5/12*e3^2+3/2*h3111) +H(0,1,-1,1,0,-1)*(-2/5*ln2^2*z2^2+4*ln2^2*h31-43/4*ln2*z2*e3+263/15*ln2*e5-16*ln2*h311-101/21*z2^3-11/4*z2*h31+248/9*e3^2-33*h51+24*h3111) +H(0,1,-1,1,0,1)*(-3/8*ln2^2*z2^2+23/3*ln2*z2*e3-31/3*ln2*e5+479/840*z2^3-7/2*z2*h31-28/9*e3^2+5*h51) +H(0,1,-1,1,1,-1)*(3/16*ln2^4*z2-7/4*ln2^3*e3+59/80*ln2^2*z2^2+2*ln2^2*h31+7/6*ln2*z2*e3-169/60*ln2*e5-7/2*ln2*h311-163/560*z2^3+3/4*z2*h31+11/6*e3^2-23/4*h51+3*h3111) +H(0,1,-1,1,1,1)*(-1/4*ln2^4*z2+7/4*ln2^3*e3-9/10*ln2^2*z2^2-9/4*ln2^2*h31-5/3*ln2*z2*e3+133/30*ln2*e5+9/2*ln2*h311-9/140*z2^3+2*z2*h31-11/18*e3^2+5/2*h51-9/2*h3111) +H(0,1,0,-1,-1,-1)*(121/840*z2^3-3/4*z2*h31-17/24*e3^2+2*h51-2*h3111) +H(0,1,0,-1,-1,1)*(23/80*ln2^2*z2^2-ln2^2*h31+17/12*ln2*z2*e3-67/20*ln2*e5+4*ln2*h311+127/168*z2^3-271/72*e3^2+23/4*h51-4*h3111) +H(0,1,0,-1,0,-1)*(-79/140*z2^3-4*z2*h31+35/9*e3^2) +H(0,1,0,-1,0,1)*(-19/70*z2^3-2*z2*h31+35/18*e3^2) +H(0,1,0,-1,1,-1)*(-23/40*ln2^2*z2^2+2*ln2^2*h31-13/6*ln2*z2*e3+317/60*ln2*e5-6*ln2*h311-611/420*z2^3+z2*h31+67/9*e3^2-13*h51+8*h3111) +H(0,1,0,-1,1,1)*(23/80*ln2^2*z2^2-ln2^2*h31-10/3*ln2*z2*e3+15/4*ln2*e5+2*ln2*h311+209/420*z2^3+3*z2*h31-23/9*e3^2+1/4*h51-2*h3111) +H(0,1,0,0,-1,-1)*(-17/840*z2^3+3/2*z2*h31-1/36*e3^2-5/2*h51) +H(0,1,0,0,-1,1)*(5/2*ln2*z2*e3-31/6*ln2*e5+701/840*z2^3-125/36*e3^2+5/2*h51) +H(0,1,0,0,0,-1)*(-67/840*z2^3+4/3*e3^2-4*h51) +H(0,1,0,0,0,1)*(10/21*z2^3-16/9*e3^2) +H(0,1,0,0,1,-1)*(-5/2*ln2*z2*e3+31/6*ln2*e5-857/1680*z2^3+16/9*e3^2-h51) +H(0,1,0,0,1,1)*(53/105*z2^3-8/3*e3^2) +H(0,1,0,1,-1,-1)*(23/80*ln2^2*z2^2-ln2^2*h31+3/4*ln2*z2*e3-29/15*ln2*e5+2*ln2*h311-5/168*z2^3-2*z2*h31+25/36*e3^2+5/2*h51) +H(0,1,0,1,-1,1)*(-23/40*ln2^2*z2^2+2*ln2^2*h31-13/6*ln2*z2*e3+317/60*ln2*e5-6*ln2*h311-313/240*z2^3-z2*h31+247/36*e3^2-35/4*h51+6*h3111) +H(0,1,0,1,0,-1)*(3/112*z2^3-3*z2*h31+4/9*e3^2+4*h51) +H(0,1,0,1,0,1)*(3/70*z2^3) +H(0,1,0,1,1,-1)*(23/80*ln2^2*z2^2-ln2^2*h31+11/2*ln2*z2*e3-271/30*ln2*e5+4*ln2*h311+2381/1680*z2^3+5/4*z2*h31-145/18*e3^2+29/4*h51-6*h3111) +H(0,1,0,1,1,1)*(-32/105*z2^3+16/9*e3^2) +H(0,1,1,-1,-1,-1)*(3/16*ln2^4*z2-7/18*ln2^3*e3+1/10*ln2^2*z2^2-ln2^2*h31+7/2*ln2*z2*e3-65/12*ln2*e5+4*ln2*h311+57/56*z2^3+1/2*z2*h31-47/8*e3^2+27/4*h51-9/2*h3111) +H(0,1,1,-1,-1,1)*(-1/8*ln2^4*z2+1/16*ln2^2*z2^2+5/4*ln2^2*h31-14/3*ln2*z2*e3+209/30*ln2*e5-4*ln2*h311-577/560*z2^3+3/4*z2*h31+35/6*e3^2-15/2*h51+4*h3111) +H(0,1,1,-1,0,-1)*(1/5*ln2^2*z2^2-2*ln2^2*h31+19/4*ln2*z2*e3-433/60*ln2*e5+8*ln2*h311+1987/840*z2^3+11/4*z2*h31-169/12*e3^2+15*h51-12*h3111) +H(0,1,1,-1,0,1)*(3/16*ln2^2*z2^2-7*ln2*z2*e3+217/20*ln2*e5-487/840*z2^3+7/2*z2*h31+59/24*e3^2-21/4*h51) +H(0,1,1,-1,1,-1)*(-7/16*ln2^4*z2+7/4*ln2^3*e3-31/80*ln2^2*z2^2-7/4*ln2^2*h31-25/12*ln2*z2*e3+15/4*ln2*e5+2*ln2*h311-103/560*z2^3-3/4*z2*h31+11/12*e3^2+7/4*h51-1/2*h3111) +H(0,1,1,-1,1,1)*(3/8*ln2^4*z2-7/4*ln2^3*e3+1/2*ln2^2*z2^2+5/2*ln2^2*h31+37/12*ln2*z2*e3-11/2*ln2*e5-5*ln2*h311-5/14*z2^3-3*z2*h31+209/72*e3^2-5/2*h51+5*h3111) +H(0,1,1,0,-1,-1)*(1/16*z2^3-7/24*e3^2+3/4*h51) +H(0,1,1,0,-1,1)*(35/12*ln2*z2*e3-341/60*ln2*e5+53/560*z2^3-2*z2*h31+7/8*e3^2+11/4*h51) +H(0,1,1,0,0,-1)*(-1/140*z2^3+3/2*z2*h31+4/9*e3^2-h51) +H(0,1,1,0,0,1)*(-13/70*z2^3+16/9*e3^2) +H(0,1,1,0,1,-1)*(-35/12*ln2*z2*e3+341/60*ln2*e5-87/560*z2^3-1/4*z2*h31+h51) +H(0,1,1,0,1,1)*(-4/35*z2^3+8/9*e3^2) +H(0,1,1,1,-1,-1)*(3/16*ln2^4*z2-7/36*ln2^3*e3+3/16*ln2^2*z2^2+25/12*ln2*z2*e3-71/20*ln2*e5+ln2*h311+309/560*z2^3+1/4*z2*h31-55/18*e3^2+3*h51-5/2*h3111) +H(0,1,1,1,-1,1)*(-1/4*ln2^4*z2+7/12*ln2^3*e3-1/4*ln2^2*z2^2-5/4*ln2^2*h31-25/12*ln2*z2*e3+229/60*ln2*e5+3*ln2*h311+7/16*z2^3+7/4*z2*h31-49/18*e3^2+5/4*h51-3*h3111) +H(0,1,1,1,0,-1)*(11/336*z2^3+3/4*z2*h31+1/3*e3^2-5/2*h51) +H(0,1,1,1,0,1)*(10/21*z2^3-16/9*e3^2) +H(0,1,1,1,1,-1)*(1/16*ln2^4*z2+13/80*ln2^2*z2^2+1/4*ln2^2*h31+1/2*ln2*z2*e3-1/15*ln2*e5-ln2*h311-13/35*z2^3-1/2*z2*h31+16/9*e3^2-5/4*h51+3/2*h3111) +H(0,1,1,1,1,1)*(8/35*z2^3) ); .sort #if `ZERO_diff' == 0 #message Error in WEIGHT `WEIGHT' result #terminate #endif Print diff; *--#] .end assert succeeded? assert result("diff") =~ expr("0") *--#] mzv-dm-hexall : form-5.0.1/check/extra/z-fmft.frm0000644000175100017510000001121215217035721012254 * Requires the FMFT library: https://github.com/apik/fmft * These tests are adapted from "tests.frm" there. * The filename starts with "z-" such that it doesn't run in * the same "group" as the Forcer tests, in the CI. #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ FMFT10 : #- Off statistics; #include- fmft.hh CF fmftint; Local test = fmftint(-2,2,1,1,1,1,1,1,2,0); id fmftint(n1?,n2?,n3?,n4?,n5?,n6?,n7?,n8?,n9?,n10?) = 1/d1^n1/d2^n2/d3^n3/d4^n4/d5^n5/d6^n6/d7^n7/d8^n8/d9^n9/d10^n10; .sort #call fmft .sort Drop; Local diff = test - ( PR11d*rat(6*d^2 - 56*d + 128,3*d - 15) + PR11*rat( - 5*d^3 + 73*d^2 - 344*d + 528,12*d - 60) + PR10*rat( - 10*d^3 + 120*d^2 - 486*d + 648,27*d - 135) + PR9d*rat(165*d^2 - 1282*d + 2454,6*d - 30) + PR9*rat( - 36*d^3 + 438*d^2 - 1763*d + 2348,6*d - 30) + PR8*rat( - d^3 + 8*d^2 + 51*d - 198, 54*d - 270) + PR7*rat( - 29019*d^4 + 413105*d^3 - 2187116*d^2 + 5099196* d - 4411296,1728*d^2 - 15552*d + 34560) + PR6*rat(143*d^3 - 1360*d^2 + 4119*d - 3942,54*d - 270) + PR5*rat(690*d^4 - 9927*d^3 + 53236*d^2 - 126157*d + 111486,54*d^2 - 468*d + 990) + PR4d*rat(49549*d^4 - 841308* d^3 + 5320223*d^2 - 14841540*d + 15399900,1728*d^4 - 29376*d^3 + 184896* d^2 - 509760*d + 518400) + PR4*rat( - 52292*d^6 + 1172896*d^5 - 10870123 *d^4 + 53277372*d^3 - 145616437*d^2 + 210346260*d - 125381700,8640*d^4 - 146880*d^3 + 924480*d^2 - 2548800*d + 2592000) + PR3*rat(10769*d^6 - 220232*d^5 + 1837263*d^4 - 7989592*d^3 + 19065208*d^2 - 23627232*d + 11872368,3456*d^4 - 58752*d^3 + 369792*d^2 - 1019520*d + 1036800) + PR2* rat(9441*d^5 - 152160*d^4 + 968003*d^3 - 3032544*d^2 + 4666900*d - 2815200,5184*d^3 - 65664*d^2 + 274752*d - 380160) + PR1*rat( - 111*d^6 + 1886*d^5 - 12895*d^4 + 45480*d^3 - 87640*d^2 + 87872*d - 35952,864* d^4 - 15264*d^3 + 100512*d^2 - 292320*d + 316800) ); Print diff; .end assert succeeded? assert result("diff") =~ expr("0") *--#] FMFT10 : *--#[ FMFT13 : #- Off statistics; #include- fmft.hh CF fmftint; Local test = fmftint(-2,3,0,1,1,1,1,1,2,0); id fmftint(n1?,n2?,n3?,n4?,n5?,n6?,n7?,n8?,n9?,n10?) = 1/d1^n1/d2^n2/d3^n3/d4^n4/d5^n5/d6^n6/d7^n7/d8^n8/d9^n9/d10^n10; .sort #call fmft .sort Drop; Local diff = test - ( PR10*rat(d^3 + 7*d^2 - 78*d + 144,216) + PR8*rat(d^3 - 17*d^2 + 66*d - 72,72) + PR7*rat(27*d^4 + 160*d^3 - 2229*d^2 + 6230*d - 5712,3456*d - 13824) + PR6*rat(13*d^3 - 70*d^2 + 112*d - 48,432) + PR4d*rat( - 5873*d^3 + 96660*d^2 - 469369*d + 711138,17280*d^2 - 120960*d + 207360) + PR4*rat( 2164*d^5 - 53456*d^4 + 491087*d^3 - 2128092*d^2 + 4392611*d - 3477390, 86400*d^2 - 604800*d + 1036800) + PR3*rat(703*d^5 - 12112*d^4 + 79731* d^3 - 253394*d^2 + 391604*d - 236184,6912*d^2 - 48384*d + 82944) + PR2* rat( - 63*d^4 + 221*d^3 + 356*d^2 - 1460*d + 736,6912*d - 27648) + PR1* rat(77*d^4 - 712*d^3 + 2424*d^2 - 3616*d + 2000,1152*d - 4608) ); Print diff; .end assert succeeded? assert result("diff") =~ expr("0") *--#] FMFT13 : *--#[ FMFT31 : #- Off statistics; #include- fmft.hh CF fmftint; Local test = fmftint(-1,1,1,1,1,1,1,1,3,0); id fmftint(n1?,n2?,n3?,n4?,n5?,n6?,n7?,n8?,n9?,n10?) = 1/d1^n1/d2^n2/d3^n3/d4^n4/d5^n5/d6^n6/d7^n7/d8^n8/d9^n9/d10^n10; .sort #call fmft .sort Drop; Local diff = test - ( PR11d*rat(3*d - 14,12) + PR11*rat( - d^2 + 10*d - 24,24) + PR10*rat( - 2*d + 6,9) + PR9d*rat( - 135*d^2 + 1102*d - 2196,24*d - 120) + PR9*rat(33*d^3 - 412*d^2 + 1698*d - 2312,24*d - 120) + PR8*rat( - d^3 + 8*d^2 - 21*d + 18,36*d - 180) + PR7*rat(4026*d^4 - 59105*d^3 + 321419*d^2 - 766846*d + 676496,1152*d^2 - 10368*d + 23040) + PR6*rat( - 35*d^3 + 355*d^2 - 1132*d + 1124,72*d - 360) + PR5*rat( - 285*d^4 + 4227*d^3 - 23287*d^2 + 56525*d - 51036,108*d^2 - 936*d + 1980) + PR4d*rat( - 6246*d^4 + 107677* d^3 - 691972*d^2 + 1963115*d - 2072950,1152*d^4 - 19584*d^3 + 123264*d^2 - 339840*d + 345600) + PR4*rat(19656*d^6 - 449052*d^5 + 4232454*d^4 - 21066049*d^3 + 58388404*d^2 - 85419675*d + 51502350,17280*d^4 - 293760* d^3 + 1848960*d^2 - 5097600*d + 5184000) + PR3*rat( - 1310*d^6 + 27305* d^5 - 231976*d^4 + 1026155*d^3 - 2487202*d^2 + 3125300*d - 1589336,2304* d^4 - 39168*d^3 + 246528*d^2 - 679680*d + 691200) + PR2*rat( - 81*d^5 + 1341*d^4 - 8748*d^3 + 28039*d^2 - 44030*d + 27024,216*d^3 - 2736*d^2 + 11448*d - 15840) + PR1*rat(9*d^6 - 150*d^5 + 1009*d^4 - 3512*d^3 + 6696* d^2 - 6656*d + 2704,216*d^4 - 3816*d^3 + 25128*d^2 - 73080*d + 79200) ); Print diff; .end assert succeeded? assert result("diff") =~ expr("0") *--#] FMFT31 : form-5.0.1/check/extra/mincer.frm0000644000175100017510000002305715217035721012340 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ minceex2 : #- * This is a modified version of the example which comes with minceex.tgz. #include- minceex.h #include- treatqaqa.prc Off Statistics; #define GAUGE "0" #define POW "2" #define PROJ "0" #define CURRENT "F2" #define MSBAR "1" #message GAUGE = `GAUGE', POW = `POW', PROJ = `PROJ'; * * Now some variables that are calcdia specific * AutoDeclare Symbol z,x,k,y; AutoDeclare index ii,mu,nu,ro,si,ka,la; I K1,K2; *Format nospaces; .global #ifdef `CHILD' #include diagram`CHILD'.h #else *#include diagram.h L d9c=+vqg(1,mu1)*fp(1,p2)*vqg(1,mu2)*fp(1,p3)*vqg(1,MU)*fp(1,p4)*vqg(1,mu3)*\ fp(1,p5)*vqg(1,mu4)*fp(1,p6)*vqg(1,NU)*fp(1,p1)*vqg(1,mu5)*v3g(mu6,-[P+p1],\ mu7,-p7,mu8,[P+p2])*Dg(mu1,mu8,[P+p2])*Dg(mu2,mu4,p8)*Dg(mu3,mu7,p7)*Dg(mu5\ ,mu6,[P+p1]) #define NAME "d9c" #define TOPO "no" #define SUBTOPO "12" #endif ; #call rename(`TOPO') #call special(`TOPO') #call treatqaqa .sort * * Now we look for special cases that can be made faster * #call redoTOPO #call integral(`TOPO',0) #call propagators #ifdef `GAUGE' #if ( `GAUGE' >= 0 ) if ( count(xi,1) > `GAUGE' ) Discard; #endif #endif #ifdef `WITHEXPANSION' Bracket xi; Print +f +s; .sort Multiply ep; #call expansion(6) .sort Multiply ep^-1/2; #endif .sort Drop; Local diff = d9c - ( BasicNOIntegral*rat( - 384*ep^8 - 1696*ep^7 + 4992*ep^6 - 2136*ep^5 - 448*ep^4 + 968*ep^3 - 832*ep^2 + 384*ep - 64,8*ep^2 - 14*ep + 3) + GschemeConstants(0,0)*BasicT1Integral*rat(27648*ep^15 - 195840*ep^14 - 343680*ep^13 + 803520*ep^12 + 1246176*ep^11 - 1272672*ep^10 - 1151520* ep^9 + 957872*ep^8 + 714192*ep^7 - 697088*ep^6 - 51728*ep^5 + 238016* ep^4 - 104032*ep^3 + 18352*ep^2 - 1056*ep,96*ep^7 + 184*ep^6 - 156*ep^5 - 458*ep^4 - 147*ep^3 + 103*ep^2 + 27*ep - 9) + GschemeConstants(0,0)^2 *GschemeConstants(1,0)*rat(23040*ep^17 + 532608*ep^16 + 1136064*ep^15 - 1916768*ep^14 - 4050640*ep^13 + 1126944*ep^12 + 4923760*ep^11 - 1652076* ep^10 - 1430780*ep^9 + 1240236*ep^8 - 6616*ep^7 - 1392932*ep^6 + 940332* ep^5 + 364204*ep^4 - 578232*ep^3 + 204504*ep^2 - 29568*ep + 1440,96* ep^11 + 440*ep^10 + 420*ep^9 - 810*ep^8 - 1731*ep^7 - 609*ep^6 + 675* ep^5 + 475*ep^4 - 36*ep^2) + GschemeConstants(0,0)^2*GschemeConstants(2, 0)*rat( - 35328*ep^15 - 416640*ep^14 - 1206976*ep^13 + 202336*ep^12 + 3340112*ep^11 + 2979040*ep^10 - 1120000*ep^9 - 1748944*ep^8 - 54512*ep^7 + 331648*ep^6 - 148976*ep^5 + 154048*ep^4 + 101968*ep^3 - 131184*ep^2 + 10752*ep + 576,24*ep^9 + 132*ep^8 + 222*ep^7 - 21*ep^6 - 489*ep^5 - 597*ep^4 - 297*ep^3 - 54*ep^2) + GschemeConstants(0,0)*GschemeConstants( 1,0)*GschemeConstants(2,0)*rat(912384*ep^19 + 10126080*ep^18 + 32486400* ep^17 - 32112384*ep^16 - 129704832*ep^15 + 6938672*ep^14 + 142865984* ep^13 + 29654488*ep^12 - 86908036*ep^11 - 32951720*ep^10 + 46159128*ep^9 + 10332596*ep^8 - 19502292*ep^7 + 2353272*ep^6 + 4274592*ep^5 - 2006868 *ep^4 - 78592*ep^3 + 299112*ep^2 - 77856*ep + 5472,864*ep^13 + 3888* ep^12 + 3216*ep^11 - 8664*ep^10 - 15930*ep^9 - 2133*ep^8 + 10656*ep^7 + 4986*ep^6 - 2154*ep^5 - 1425*ep^4 + 108*ep^3 + 108*ep^2)); Print +s; .end assert succeeded? assert result("diff") =~ expr("0") *--#] minceex2 : *--#[ minceex4 : #- * This is a modified version of the example which comes with minceex.tgz. #include- minceex.h #include- treatqaqa.prc Off Statistics; #define GAUGE "0" #define POW "4" #define PROJ "0" #define CURRENT "F2" #define MSBAR "1" #message GAUGE = `GAUGE', POW = `POW', PROJ = `PROJ'; * * Now some variables that are calcdia specific * AutoDeclare Symbol z,x,k,y; AutoDeclare index ii,mu,nu,ro,si,ka,la; I K1,K2; *Format nospaces; .global #ifdef `CHILD' #include diagram`CHILD'.h #else *#include diagram.h L d9c=+vqg(1,mu1)*fp(1,p2)*vqg(1,mu2)*fp(1,p3)*vqg(1,MU)*fp(1,p4)*vqg(1,mu3)*\ fp(1,p5)*vqg(1,mu4)*fp(1,p6)*vqg(1,NU)*fp(1,p1)*vqg(1,mu5)*v3g(mu6,-[P+p1],\ mu7,-p7,mu8,[P+p2])*Dg(mu1,mu8,[P+p2])*Dg(mu2,mu4,p8)*Dg(mu3,mu7,p7)*Dg(mu5\ ,mu6,[P+p1]) #define NAME "d9c" #define TOPO "no" #define SUBTOPO "12" #endif ; #call rename(`TOPO') #call special(`TOPO') #call treatqaqa .sort * * Now we look for special cases that can be made faster * #call redoTOPO #call integral(`TOPO',0) #call propagators #ifdef `GAUGE' #if ( `GAUGE' >= 0 ) if ( count(xi,1) > `GAUGE' ) Discard; #endif #endif #ifdef `WITHEXPANSION' Bracket xi; Print +f +s; .sort Multiply ep; #call expansion(6) .sort Multiply ep^-1/2; #endif .sort Drop; Local diff = d9c - ( BasicNOIntegral*rat( - 2304*ep^11 - 7232*ep^10 + 52000*ep^9 + 18160*ep^8 - 114872*ep^7 - 91176*ep^6 + 39656*ep^5 + 2032*ep^4 + 416*ep^3 + 24168* ep^2 - 23376*ep + 4608,48*ep^3 - 204*ep^2 + 228*ep - 45) + GschemeConstants(0,0)*BasicT1Integral*rat(27648*ep^21 - 516864*ep^20 - 3994112*ep^19 - 4253952*ep^18 + 33084608*ep^17 + 126363536*ep^16 + 119266688*ep^15 - 373133320*ep^14 - 1152987376*ep^13 - 491716608*ep^12 + 1502474704*ep^11 + 977746688*ep^10 - 1553743792*ep^9 - 190578368*ep^8 + 928197648*ep^7 - 530750040*ep^6 + 127311552*ep^5 - 1788976*ep^4 - 5651008*ep^3 + 1262784*ep^2 - 138240*ep,384*ep^11 + 2272*ep^10 + 1456* ep^9 - 15584*ep^8 - 34512*ep^7 - 618*ep^6 + 64479*ep^5 + 59969*ep^4 + 4013*ep^3 - 12919*ep^2 - 1800*ep + 900) + GschemeConstants(0,0)^2* GschemeConstants(1,0)*rat( - 681984*ep^25 - 4028928*ep^24 + 30485760* ep^23 + 308835072*ep^22 + 547931904*ep^21 - 2811462304*ep^20 - 14396648176*ep^19 - 19187749024*ep^18 + 23314444608*ep^17 + 104940053952 *ep^16 + 115883017456*ep^15 + 2432489392*ep^14 - 92180742080*ep^13 - 38313734648*ep^12 + 21762074288*ep^11 - 31000077880*ep^10 - 42553905504* ep^9 + 79077155256*ep^8 + 21490049040*ep^7 - 67631487480*ep^6 + 31397120800*ep^5 - 5285019968*ep^4 + 882770432*ep^3 + 231957120*ep^2 - 104799744*ep + 4976640,1152*ep^17 + 17952*ep^16 + 106608*ep^15 + 253392* ep^14 - 160656*ep^13 - 2311950*ep^12 - 4924581*ep^11 - 2103234*ep^10 + 8135736*ep^9 + 14715084*ep^8 + 7900773*ep^7 - 2965308*ep^6 - 5140632* ep^5 - 1611936*ep^4 + 205200*ep^3 + 129600*ep^2) + GschemeConstants(0,0) ^2*GschemeConstants(2,0)*rat( - 216576*ep^23 - 5999744*ep^22 - 67223936* ep^21 - 339143552*ep^20 - 535105088*ep^19 + 2379379240*ep^18 + 14115407424*ep^17 + 27832941760*ep^16 + 5470276600*ep^15 - 84856605328* ep^14 - 184233479784*ep^13 - 176330297192*ep^12 - 55476773000*ep^11 + 40106128128*ep^10 + 37842213784*ep^9 + 9905154984*ep^8 + 19017680048* ep^7 + 4642553608*ep^6 - 20224103440*ep^5 + 2239915360*ep^4 + 1885640256 *ep^3 + 1080892416*ep^2 + 208714752*ep + 9953280,288*ep^15 + 4752*ep^14 + 30960*ep^13 + 90936*ep^12 + 38034*ep^11 - 558279*ep^10 - 1749240*ep^9 - 2036232*ep^8 + 458928*ep^7 + 4438827*ep^6 + 5967630*ep^5 + 3989196* ep^4 + 1377000*ep^3 + 194400*ep^2) + GschemeConstants(0,0)* GschemeConstants(1,0)*GschemeConstants(2,0)*rat(12441600*ep^27 + 241436160*ep^26 + 2367744768*ep^25 + 10821396480*ep^24 + 11958792064* ep^23 - 91453237152*ep^22 - 422826539856*ep^21 - 612335646096*ep^20 + 555540699096*ep^19 + 3284346867128*ep^18 + 4250586842880*ep^17 + 351374300560*ep^16 - 4438997900512*ep^15 - 3318133410424*ep^14 + 1904859439392*ep^13 + 2636129161552*ep^12 - 1099209124824*ep^11 - 1167398292216*ep^10 + 947152336592*ep^9 + 180023292400*ep^8 - 443242365600*ep^7 + 71547538392*ep^6 + 77098297952*ep^5 - 23731782976* ep^4 - 2606689024*ep^3 + 851670912*ep^2 - 21385728*ep + 34836480,10368* ep^19 + 160704*ep^18 + 943200*ep^17 + 2156976*ep^16 - 1893240*ep^15 - 21289068*ep^14 - 42156126*ep^13 - 9612999*ep^12 + 86474421*ep^11 + 130685994*ep^10 + 39750372*ep^9 - 67459635*ep^8 - 60975099*ep^7 - 1731780*ep^6 + 15592104*ep^5 + 4220208*ep^4 - 1004400*ep^3 - 388800*ep^2 )); Print +s; .end # Too slow #pend_if valgrind? assert succeeded? assert result("diff") =~ expr("0") *--#] minceex4 : *--#[ testmincer1 : #- #include mincer2.h .global * * We try here a diagram with a ladder topology * Local F = Q.p1^2*Q.p3^2/p1.p1^3/p2.p2/p3.p3^3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 *Q.Q^2; * * The diagrams should be multiplied by ep^3 first. * Probably this should have been done inside mincer but for historical * reasons it isn't and if I change it now many programs will have a problem. * Multiply ep^3; #call integral(la) Print; .end assert succeeded? assert result("F") =~ expr(" - 6695/5184 - 1/48*ep^-3 + 41/288*ep^-2 - 1541/6912*ep^-1 + 5/4*z5 - 1/ 6*z3 + 2342947/248832*ep + 25/8*ep*z6 + 15/2*ep*z5 - 1/4*ep*z4 + 3017/ 576*ep*z3 - 35/2*ep*z3^2 - 1608359/46656*ep^2 + 317/16*ep^2*z7 + 75/4* ep^2*z6 + 18*ep^2*z5 + 3017/384*ep^2*z4 + 27467/1728*ep^2*z3 - 1083/16* ep^2*z3*z4 - 105*ep^2*z3^2 ") *--#] testmincer1 : *--#[ testmincer2 : #- #include mincer2.h .global * * We try here a diagram with a ladder topology * Local F = Q.p1^2*Q.p3^2/p1.p1^3/p2.p2/p3.p3^3/p4.p4/p5.p5*Q.Q; * * The diagrams should be multiplied by ep^3 first. * This gives results to order ep. * Probably this should have been done inside mincer but for historical * reasons it isn't and if I change it now many programs will have a problem. * Multiply ep^3; #call integral(t1) Print; .end assert succeeded? assert result("F") =~ expr(" - 25/64 + 5/16*ep^-2 - 1/2*ep^-1 + 3/8*z3 - 49/16*ep + 9/16*ep*z4 + 33/ 4*ep*z3 + 2201/256*ep^2 + 21/8*ep^2*z5 + 99/8*ep^2*z4 - 87/16*ep^2*z3 - 1485/256*ep^3 + 45/8*ep^3*z6 + 231/4*ep^3*z5 - 261/32*ep^3*z4 - 33/2* ep^3*z3 - 9/8*ep^3*z3^2 ") *--#] testmincer2 : form-5.0.1/check/extra/multithreaded.frm0000644000175100017510000000226015217035721013707 #:FilePatches 16 #:LargePatches 2 #:TermsInSmall 4 #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ multithreaded_1 : #:FilePatches 16 #:LargePatches 2 #:TermsInSmall 4 * NOTE: tform -w4 -F -D TEST=multithreaded_1 multithreaded.frm * should write the whole output to the log file (if not broken). * Nothing should be printed in the standard output. * This test checks the correct behaviour of threadstats discussed in: * https://github.com/vermaseren/form/issues/470 #ifndef `N1' #define N1 "1" #endif #ifndef `N2' #define N2 "2" #endif #ifndef `N3' #define N3 "2" #endif #ifdef `TEST' S x1,...,x9; L F = (x1+...+x9)^`N1'; .sort multiply (x1+...+x9)^`N2'; .sort multiply (x1+...+x9)^`N3'; .sort repeat id x1? = 1; P +f; #endif .end L F = 1; P; .sort #system `FORM' -F -D TEST 1.frm .end assert succeeded? # If the -F option in the above execution of (T)FORM works correctly, # then F = 59049 is not printed in the standard output. So, the last # printed expression of F must be 1. assert result("F") =~ expr("1") # The result should be written in the log file. assert file("1.log") =~ pattern("59049") *--#] multithreaded_1 : form-5.0.1/check/extra/forcer.frm0000644000175100017510000002630015217035721012335 * Requires the Forcer library: https://github.com/benruijl/forcer. #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ Forcer_example : #include- forcer.h L F = + 1//.../* Q.p3*Q.p4*vx(Q,p1,p5,p6)*vx(-p1,p2,p3)*vx(-p5,-p6,p4)*vx(-Q,-p2,-p3,-p4) + 1//.../* vx(-Q,p2,p3)*vx(p1,-p2,p5)*vx(-p1,p4,Q)*vx(-p3,-p4,-p5)*ex(p1,p4) ; #call Forcer(msbarexpand=4) B ep; P; .end assert succeeded? assert result("F") =~ expr(" + ep^-3 * ( 1/24 ) + ep^-2 * ( 25/72 ) + ep^-1 * ( 433/216 ) + ep * ( 89089/1944 - 57/32*z4 - 725/72*z3 ) + 6457/648 + 115/24*z3 ") *--#] Forcer_example : *--#[ Forcer_1 : * timeout = 60 seconds. #include- forcer.h CF f,f1,f2,f3; V p2,p3; S x3; * Give 1 or -1. n1 is not used. Table randomsign(n1?); Fill randomsign() = random_(2)*2-3; * Zip two functions as: * zip(f1,f2(p1,...,pN),f3(q1,...,qN)) -> f1(p1,q1,...,pN,qN), * for N >= 1. Table zip(f1?(?a1),f2?(p2?,?a2),f3?(p3?,?a3)); Fill zip() = + thetap_(nargs_(?a2,?a3)) * zip(f1(?a1,p2,p3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2,p3) ; * Element-wise multiplication as: * emul(f1,f2(p1,...,pN),f3(a1,...,aN)) -> f1(p1*a1,...,pN*aN) * for N >= 1. Table emul(f1?(?a1),f2?(p2?,?a2),f3?(x3?,?a3)); Fill emul() = + thetap_(nargs_(?a2,?a3)) * emul(f1(?a1,p2*x3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2*x3) ; L F1 = #do i=1,3 + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,0) #enddo ; L F2 = #do i=1,3 + Zno`i'(2,1,1,1,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,2,1,1,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,2,1,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,2,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,2,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,2,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,2,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,2,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,2,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,2,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,2,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,-1,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,-1,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,-1) #enddo ; id Zno1(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p10) *vx(p2,-p3,p9) *vx(p1,-p2,p11) *vx(-p5,p6,-p11) *vx(-p6,p7,-p10) *vx(-p7,p8,-p9) *vx(-p1,-p8,Q) //.../ /p2.p4^n12/Q.p2^n13/Q.p3^n14 ; id Zno2(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p11) *vx(p6,p7,p10) *vx(p2,-p3,-p10) *vx(p1,-p2,p9) *vx(-p5,-p6,-p9) *vx(-p7,p8,-p11) *vx(-p1,-p8,Q) //.../ /Q.p2^n12/p1.p4^n13/Q.p3^n14 ; id Zno3(n1?,...,n14?) = +vx(-Q,p3,p4) *vx(p6,p8,p10) *vx(p5,-p10,p11) *vx(p1,-p3,-p5) *vx(-p4,-p8,p9) *vx(p7,-p9,-p11) *vx(p2,-p6,-p7) *vx(-p1,-p2,Q) //.../ /Q.p6^n12/Q.p8^n13/p3.p6^n14 ; * Make a random permutation of the loop momenta. The result should be the same. multiply f1(p1,...,p11); multiply ranperm_(f2,p1,...,p11); multiply f3(,...,); id f2(?a)*f3(?b) = emul(f2,f2(?a),f3(?b)); id f1(?a)*f2(?b) = zip(f1,f1(?a),f2(?b)); id f1(?a) = replace_(?a); ModuleOption noparallel; .sort:input; #call Forcer(msbarexpand=4) B ep; P; .end # Too slow, but is supposed to pass. #pend_if valgrind? assert succeeded? assert result("F1") =~ expr(" + ep^-1 * ( - 35/2*z5 ) + 21/2*z7 - 175/4*z6 + 105/4*z5 - 95/2*z3^2 ") assert result("F2") =~ expr(" + ep^-4 * ( 15/2 ) + ep^-3 * ( 383/12 ) + ep^-2 * ( - 2089/18 ) + ep^-1 * ( 1466/9 - 1245/8*z5 - 728*z3 ) - 2183/12 + 441/2*z7 - 6225/16*z6 - 57155/48*z5 - 2169/2*z4 - 17198/9* z3 - 3705/8*z3^2 ") *--#] Forcer_1 : *--#[ Forcer_1-expand : * timeout = 60 seconds. #include- forcer.h CF f,f1,f2,f3; V p2,p3; S x3; * Give 1 or -1. n1 is not used. Table randomsign(n1?); Fill randomsign() = random_(2)*2-3; * Zip two functions as: * zip(f1,f2(p1,...,pN),f3(q1,...,qN)) -> f1(p1,q1,...,pN,qN), * for N >= 1. Table zip(f1?(?a1),f2?(p2?,?a2),f3?(p3?,?a3)); Fill zip() = + thetap_(nargs_(?a2,?a3)) * zip(f1(?a1,p2,p3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2,p3) ; * Element-wise multiplication as: * emul(f1,f2(p1,...,pN),f3(a1,...,aN)) -> f1(p1*a1,...,pN*aN) * for N >= 1. Table emul(f1?(?a1),f2?(p2?,?a2),f3?(x3?,?a3)); Fill emul() = + thetap_(nargs_(?a2,?a3)) * emul(f1(?a1,p2*x3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2*x3) ; L F1 = #do i=1,3 + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,0) #enddo ; L F2 = #do i=1,3 + Zno`i'(2,1,1,1,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,2,1,1,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,2,1,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,2,1,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,2,1,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,2,1,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,2,1,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,2,1,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,2,1,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,2,1,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,2,0,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,-1,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,-1,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,-1) #enddo ; id Zno1(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p10) *vx(p2,-p3,p9) *vx(p1,-p2,p11) *vx(-p5,p6,-p11) *vx(-p6,p7,-p10) *vx(-p7,p8,-p9) *vx(-p1,-p8,Q) //.../ /p2.p4^n12/Q.p2^n13/Q.p3^n14 ; id Zno2(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p11) *vx(p6,p7,p10) *vx(p2,-p3,-p10) *vx(p1,-p2,p9) *vx(-p5,-p6,-p9) *vx(-p7,p8,-p11) *vx(-p1,-p8,Q) //.../ /Q.p2^n12/p1.p4^n13/Q.p3^n14 ; id Zno3(n1?,...,n14?) = +vx(-Q,p3,p4) *vx(p6,p8,p10) *vx(p5,-p10,p11) *vx(p1,-p3,-p5) *vx(-p4,-p8,p9) *vx(p7,-p9,-p11) *vx(p2,-p6,-p7) *vx(-p1,-p2,Q) //.../ /Q.p6^n12/Q.p8^n13/p3.p6^n14 ; * Make a random permutation of the loop momenta. The result should be the same. multiply f1(p1,...,p11); multiply ranperm_(f2,p1,...,p11); multiply f3(,...,); id f2(?a)*f3(?b) = emul(f2,f2(?a),f3(?b)); id f1(?a)*f2(?b) = zip(f1,f1(?a),f2(?b)); id f1(?a) = replace_(?a); ModuleOption noparallel; .sort:input; #call Forcer(msbarexpand=4,polyratfunexpand=15) B ep; P; .end # Too slow, but is supposed to pass. #pend_if valgrind? assert succeeded? assert result("F1") =~ expr(" + ep^-1 * ( - 35/2*z5 ) + 21/2*z7 - 175/4*z6 + 105/4*z5 - 95/2*z3^2 ") assert result("F2") =~ expr(" + ep^-4 * ( 15/2 ) + ep^-3 * ( 383/12 ) + ep^-2 * ( - 2089/18 ) + ep^-1 * ( 1466/9 - 1245/8*z5 - 728*z3 ) - 2183/12 + 441/2*z7 - 6225/16*z6 - 57155/48*z5 - 2169/2*z4 - 17198/9* z3 - 3705/8*z3^2 ") *--#] Forcer_1-expand : *--#[ Forcer_2 : * An easier version of the above, for checking with valgrind * timeout = 60 seconds. #include- forcer.h CF f,f1,f2,f3; V p2,p3; S x3; * Give 1 or -1. n1 is not used. Table randomsign(n1?); Fill randomsign() = random_(2)*2-3; * Zip two functions as: * zip(f1,f2(p1,...,pN),f3(q1,...,qN)) -> f1(p1,q1,...,pN,qN), * for N >= 1. Table zip(f1?(?a1),f2?(p2?,?a2),f3?(p3?,?a3)); Fill zip() = + thetap_(nargs_(?a2,?a3)) * zip(f1(?a1,p2,p3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2,p3) ; * Element-wise multiplication as: * emul(f1,f2(p1,...,pN),f3(a1,...,aN)) -> f1(p1*a1,...,pN*aN) * for N >= 1. Table emul(f1?(?a1),f2?(p2?,?a2),f3?(x3?,?a3)); Fill emul() = + thetap_(nargs_(?a2,?a3)) * emul(f1(?a1,p2*x3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2*x3) ; L F1 = #do i=1,2 + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,0) #enddo ; L F2 = #do i=1,2 + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,-1,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,-1,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,-1) #enddo ; id Zno1(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p10) *vx(p2,-p3,p9) *vx(p1,-p2,p11) *vx(-p5,p6,-p11) *vx(-p6,p7,-p10) *vx(-p7,p8,-p9) *vx(-p1,-p8,Q) //.../ /p2.p4^n12/Q.p2^n13/Q.p3^n14 ; id Zno2(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p11) *vx(p6,p7,p10) *vx(p2,-p3,-p10) *vx(p1,-p2,p9) *vx(-p5,-p6,-p9) *vx(-p7,p8,-p11) *vx(-p1,-p8,Q) //.../ /Q.p2^n12/p1.p4^n13/Q.p3^n14 ; id Zno3(n1?,...,n14?) = +vx(-Q,p3,p4) *vx(p6,p8,p10) *vx(p5,-p10,p11) *vx(p1,-p3,-p5) *vx(-p4,-p8,p9) *vx(p7,-p9,-p11) *vx(p2,-p6,-p7) *vx(-p1,-p2,Q) //.../ /Q.p6^n12/Q.p8^n13/p3.p6^n14 ; * Make a random permutation of the loop momenta. The result should be the same. multiply f1(p1,...,p11); multiply ranperm_(f2,p1,...,p11); multiply f3(,...,); id f2(?a)*f3(?b) = emul(f2,f2(?a),f3(?b)); id f1(?a)*f2(?b) = zip(f1,f1(?a),f2(?b)); id f1(?a) = replace_(?a); ModuleOption noparallel; .sort:input; #call Forcer(msbarexpand=4) B ep; P; .end assert succeeded? assert result("F1") =~ expr(" + ep^-1 * ( - 15*z5 ) + 21/2*z7 - 75/2*z6 + 55*z5 - 51*z3^2 ") assert result("F2") =~ expr(" + 161/2*z7 + 20*z5 + 18*z3^2 ") *--#] Forcer_2 : *--#[ Forcer_2-expand : * An easier version of the above, for checking with valgrind * timeout = 60 seconds. #include- forcer.h CF f,f1,f2,f3; V p2,p3; S x3; * Give 1 or -1. n1 is not used. Table randomsign(n1?); Fill randomsign() = random_(2)*2-3; * Zip two functions as: * zip(f1,f2(p1,...,pN),f3(q1,...,qN)) -> f1(p1,q1,...,pN,qN), * for N >= 1. Table zip(f1?(?a1),f2?(p2?,?a2),f3?(p3?,?a3)); Fill zip() = + thetap_(nargs_(?a2,?a3)) * zip(f1(?a1,p2,p3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2,p3) ; * Element-wise multiplication as: * emul(f1,f2(p1,...,pN),f3(a1,...,aN)) -> f1(p1*a1,...,pN*aN) * for N >= 1. Table emul(f1?(?a1),f2?(p2?,?a2),f3?(x3?,?a3)); Fill emul() = + thetap_(nargs_(?a2,?a3)) * emul(f1(?a1,p2*x3),f2(?a2),f3(?a3)) + delta_(nargs_(?a2,?a3)) * f1(?a1,p2*x3) ; L F1 = #do i=1,2 + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,0) #enddo ; L F2 = #do i=1,2 + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,-1,0,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,-1,0) + Zno`i'(1,1,1,1,1,1,1,1,1,1,1,0,0,-1) #enddo ; id Zno1(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p10) *vx(p2,-p3,p9) *vx(p1,-p2,p11) *vx(-p5,p6,-p11) *vx(-p6,p7,-p10) *vx(-p7,p8,-p9) *vx(-p1,-p8,Q) //.../ /p2.p4^n12/Q.p2^n13/Q.p3^n14 ; id Zno2(n1?,...,n14?) = +vx(-Q,p4,p5) *vx(p3,-p4,p11) *vx(p6,p7,p10) *vx(p2,-p3,-p10) *vx(p1,-p2,p9) *vx(-p5,-p6,-p9) *vx(-p7,p8,-p11) *vx(-p1,-p8,Q) //.../ /Q.p2^n12/p1.p4^n13/Q.p3^n14 ; id Zno3(n1?,...,n14?) = +vx(-Q,p3,p4) *vx(p6,p8,p10) *vx(p5,-p10,p11) *vx(p1,-p3,-p5) *vx(-p4,-p8,p9) *vx(p7,-p9,-p11) *vx(p2,-p6,-p7) *vx(-p1,-p2,Q) //.../ /Q.p6^n12/Q.p8^n13/p3.p6^n14 ; * Make a random permutation of the loop momenta. The result should be the same. multiply f1(p1,...,p11); multiply ranperm_(f2,p1,...,p11); multiply f3(,...,); id f2(?a)*f3(?b) = emul(f2,f2(?a),f3(?b)); id f1(?a)*f2(?b) = zip(f1,f1(?a),f2(?b)); id f1(?a) = replace_(?a); ModuleOption noparallel; .sort:input; #call Forcer(msbarexpand=4,polyratfunexpand=15) B ep; P; .end assert succeeded? assert result("F1") =~ expr(" + ep^-1 * ( - 15*z5 ) + 21/2*z7 - 75/2*z6 + 55*z5 - 51*z3^2 ") assert result("F2") =~ expr(" + 161/2*z7 + 20*z5 + 18*z3^2 ") *--#] Forcer_2-expand : form-5.0.1/check/extra/series.frm0000644000175100017510000001175615217035721012360 * test the functionality of the series package * https://github.com/a-maier/series #ifndef `TEST' #message Use -D TEST=XXX #terminate #else #include `NAME_' # `TEST' #endif .end *--#[ series : #- #define CUT "5" #define TESTS "15" #define FAIL "0" off stats; off warnings; #include- series.h S ep,c,d0,...,d`CUT'; CF pow; L foo=c*ep^-2++...+; #message Test1: Inversion #call series(ep,{`CUT'+2}) #call invert(foo,bar) L [0]=foo*bar-1; if(count(ep,1)>`CUT')discard; .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test2: Exponentiation & Logarithm #call series(ep,`CUT') #call exp(foo,bar) #call log(bar,bar) L [0]=bar-foo ; id 1/exp(c?)=exp(-c); repeat id exp(d0?)*exp(d1?)=exp(d0+d1); id exp(0)=1; id log(exp(c?))=c; .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test3: Power L [-2]=-2; L [-1/2]=-1/2; #call series(ep,{`CUT'+2}) #call power(foo,[-2],bar) #call power(bar,[-1/2],bar2) drop bar; skip; nskip bar2; id 1/exp(c?)=exp(-c); repeat id exp(d0?)*exp(d1?)=exp(d0+d1); id exp(0)=1; argument exp; id log(exp(c?))=c; endargument; id exp(log(c?))=c; if(count(ep,1)>`CUT')discard; .sort drop bar2,[-2],[-1/2]; L [0]=foo-bar2; .sort #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #call init({2*{`CUT'+2}}) #message Test4: inverse function .sort cf den; skip foo; L [0]=foo*den(foo)-1; #call expand(den) .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test5: exponential & logarithm function .sort cf exp,log; skip foo; L [0]=exp(log(foo))-foo; argument exp; #call expand(log) endargument; #call expand(exp) id exp(log(c?))=c; .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test6: power function .sort cf power; skip foo; L [0]=power(power(foo,-2),-1/2)-foo; argument power; #call expand(power) endargument; argument power; id exp( - 2*log(ep^-2*c))=(ep^-2*c)^-2; endargument; #call expand(power) id exp( - 1/2*log(ep^4*c^-2))=ep^-2*c; .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test7: local expansion variable .sort s x; cf den; skip foo; l [0x] = 1-(1-x)*den(1-x); l [0ep] = 1-(1-ep)*den(1-ep); #call expand(den,x,{`CUT'-1}) #call expand(den) .sort drop [0x],[0ep]; #if (termsin([0x])>0) || (termsin([0ep])>0) #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test8: products of denominators .sort cf den; skip foo; L [0]=den(foo)*den(foo)-den(foo*foo); #call expand(den) .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test9: products of exponentials .sort cf exp; skip foo; L [0]= exp(foo)*exp(-foo) - 1; #call expand(exp) .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test10: products of logarithms .sort cf log; skip foo; L [0]= log(1+c*x)*log(1+d0*x) - c*d0*x^2; #call expand(log,x,2) #call expand(log,x,2) id log(1) = 0; .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test11: products of powers .sort cf pow; skip foo; L [0]= 1 - pow(foo,foo)*pow(foo,-foo); #call expand(pow) .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test12: products of Gamma functions .sort cf Gamma; skip foo; L [0]= 1 - Gamma(1+c*x)*Gamma(1-c*x); #call expand(Gamma,x,1) #call expand(Gamma,x,1) id Gamma(1) = 1; .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test13: multiple denominators with poles .sort skip foo; L [0]= x*den(x)^2 - 1/x; #call expand(den,x,-1) .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test14: nontrivial normalisation .sort s A,a,c; skip foo; L [0] = ( + den(A - a + c*x^2)* den(A + a + c*x^2) + den( - a + A)^2*den(a + A)*c*x^2 - den( - a + A)*den(a + A) + den( - a + A)*den(a + A)^2*c*x^2 ); #call expand(den,x,2) .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #message Test15: nontrivial normalisation .sort skip foo; L [0] = ( + den(1 + c*x^2*den(A - a))* den(1 + c*x^2*den(A + a)) - 1 + c*x^2*(den(A - a) + den(A + a)) ); #call expand(den,x,2) print+s; .sort drop [0]; #if termsin([0])>0 #message FAILED #redefine FAIL "{`FAIL'+1}" #else #message passed #endif #if `FAIL'==0 #message All tests passed #else #message Failed `FAIL'/`TESTS' tests #terminate 1 #endif .end assert succeeded? *--#] series : form-5.0.1/doc/0000755000175100017510000000000015217035744007000 5form-5.0.1/doc/form.10000644000175100017510000000762715217035721007754 .TH FORM 1 "2026-01-27" .SH NAME FORM \- Symbolic manipulation system .SH SYNOPSIS .B form .RB [ .IR options ] .IR inputfile .SH DESCRIPTION .PP FORM is a symbolic manipulation system. The \fBform\fR command reads a text file (which should have a name that ends with the extension \fB.frm\fR, or \fB-\fR to read the standard input) containing definitions of mathematical expressions as well as statements that tell it how to manipulate these expressions. It is widely used in the theoretical particle physics community, but it is not restricted to applications in this specific field. .PP \fBtform\fR is the threaded version using POSIX Threads. .PP \fBparform\fR is the multiprocessing version using MPI. .SH OPTIONS .TP .BR "-" Read the input from stdin instead of from a file. .TP .BR "-c" Error checking only. Notice that this will not work properly if there are conditionals in the preprocessor phase that depend on results obtained at earlier stages of the program. .TP .BR "-C" Next argument is the filename of the log file. The default is the filename of the FORM script with the .log extension. .TP .BR "-d, -D" Next argument/option is the name of a preprocessor variable that will be defined before the run starts. A specific value can be assigned with the syntax \fB-d\fR\ \fIVARIABLENAME\fR=\fIVALUE\fR. The default value is 1. .TP .BR "-f" Output goes only to log file. .TP .BR "-F" Output only to log file. Further like \fB-L\fR or \fB-ll\fR. .TP .BR "-h" Wait for some key to be touched before finishing the run. Basically only for some old window based systems. .TP .BR "-I" Next argument/option is the path of a directory for include, procedure and subroutine files. .TP .BR "-l" Make a regular log file. .TP .BR "-ll, -L" Make a log file without intermediate statistics. .TP .BR "-M" This option is ignored. The PID (process identifier) of the process is now always included in the name of the temporary files. .TP .BR "-p" Next argument/option is the path of a directory for input, include, procedure and subroutine files. .TP .BR "-pipe" Indicates that FORM is started up as the receiving end of a pipe. Action will be taken to set up the proper communication channels. .TP .BR "-q, -si" Quiet option. Only output expressions are printed. .TP .BR "-R" Recover from a crash. .TP .BR "-s" Next argument/option is the path of a directory for a setup file. .TP .BR "-S" Next argument/option is the name of a setup file. .TP .BR "-t" Next argument/option is the path of a directory for temporary files. .TP .BR "-ts" Next argument/option is the path of a directory for temporary sort files. .TP .BR "-T" Puts FORM in a mode in which the maximum totalsize is measured and printed at the end of the program. .TP .BR "-v" Only the version will be printed. The program terminates immediately after it. .TP .BR "-vv" Same as \fB-v\fR, but prints verbose version information. .TP .BR "-w" This should be followed immediately by a number without any space. The number indicates the number of worker threads for \fBtform\fR. All other versions of FORM ignore this parameter. .TP .BR "-W" Turn on the wall-clock time mode in the statistics. .TP .BR "-z" The number following is a timelimit for the program in second. .TP .BR "-Z" Removes the \fB.str\fR file on crash, whatever its contents. Under ordinary circumstances at a crash a \fB.str\fR file will not be removed if it has a nonzero content. .TP .BR "-y" Run only the preprocessor and dump its output. .SH ENVIRONMENT .TP \fBFORMPATH\fR The directory in which FORM will look for procedures and header files, assuming it cannot find them in the current directory. .TP \fBFORMTMP\fR The directory in which FORM will make its temporary files. .TP \fBFORMTMPSORT\fR The directory in which FORM will make its temporary sort files. .TP \fBFORMSETUP\fR The full path and name of a setup file. .SH SEE ALSO .TP \fBhttps://www.nikhef.nl/~form/\fR The FORM home site. .TP \fBhttps://github.com/form-dev/form/\fR The repository on GitHub. form-5.0.1/doc/devref/0000755000175100017510000000000015217035744010253 5form-5.0.1/doc/devref/cvs.tex0000644000175100017510000000453115217035721011506 \section{CVS} The CVS repository resides in \C{/user/form/cvs\_repository}. It is advisable to set the environment variable \C{CVSROOT} accordingly, like (using bash shell syntax) {\scriptsize \begin{verbatim} export CVSROOT=:ext:myusername@mytrustedmachine.nikhef.nl:/user/form/cvs_repository \end{verbatim}} A mailing list exists for CVS commits. The administration interface for this mailing list can be found under the web address \LINK{https://mailman.nikhef.nl/cgi-bin/admin/form-cvs} A password is required. Click {\it Membership Management} and then {\it Mass Subscription} to add new people. The personal details of the subscribers like the email address or the name can be changed under {\it Membership Management} as well. The triggering of the CVS commits mails is done in the following way. In the file \C{loginfo} in the directory \C{CVSROOT} (inside the repository) the default action for logging is set such that the script \C{/user/form/cvs-log.sh} will be called with the committer's user name and the CVS mailing list user name. The shell script does some simple message transformation and then uses the command \C{mail} to send the commit mail to the mailing list. \subsection{Some useful CVS idioms} To just show what would be updated/changed without actually modifying anything, use \begin{verbatim} cvs -n update \end{verbatim} If \C{cvs -n update} has shown you that something new in the repository will be merged into your directory and you want to know in advance what the details are, you can do for each of the files involved a \begin{verbatim} cvs status \end{verbatim} and note the version number of your local file, and then do a \begin{verbatim} cvs diff -r \end{verbatim} to see the differences. In case you want to compile an older version of \FORM\ (maybe to find out whether a certain bug is already present or not), do \begin{verbatim} cvs update -D "" \end{verbatim} to checkout the sources as they were on a certain date, e.g. \\ \C{cvs update -D "2006-05-12"}. The files will get the so-called sticky flag, which do prevent simple \C{cvs update} commands in the future to update to the latest version from the repository. To remove the sticky flag on a file use \begin{verbatim} cvs update -A \end{verbatim} Without the filename all files will have the sticky flag removed. form-5.0.1/doc/devref/devref.tex.in0000644000175100017510000000461315217035721012574 \input{version.tex} \def\formversiondesc{\repoversiondesc} \def\formdate{\repodate} %begin{latexonly} % To avoid latex2html/latex2html#37 \providecommand{\repoversiondesc}{@VERSION@???} \providecommand{\repodate}{\today} %end{latexonly} \documentclass[11pt,titlepage]{article} \usepackage{makeidx} %begin{latexonly} \makeatletter \renewcommand*\l@section{\@dottedtocline{1}{1.5em}{3.0em}} \renewcommand*\l@subsection{\@dottedtocline{2}{1.5em}{3.0em}} \makeatother % Use hyperref package (hyperlinks) with correct option for pdflatex/latex: \usepackage{ifpdf} \ifpdf \RequirePackage[pdftex]{hyperref} \else \RequirePackage[hypertex]{hyperref} \fi % and link indices back to text: \hypersetup{hyperindex,pagebackref,pdfpagemode={None},draft=false} %end{latexonly} \providecommand{\texorpdfstring}[2]{#1}% htmlonly \newcommand{\emptypage}{\newpage \thispagestyle{empty} \tiny{\ } \normalsize} \newcommand{\clearemptydoublepage}{\newpage{\pagestyle{empty}\cleardoublepage}} \newcommand{\C}[1]{{\tt #1}} \newcommand{\LINK}[1]{{\tt #1}} \newcommand{\FORM}{{\sc FORM}} \newcommand{\TFORM}{{\sc TFORM}} \newcommand{\PARFORM}{{\sc ParFORM}} \makeindex \begin{document} \thispagestyle{empty} \title{\Huge FORM \\ \Large version \formversiondesc \\ \huge Developer's reference manual} \date{\formdate} \author{J.A.M.Vermaseren et al.} \maketitle \clearemptydoublepage \emptypage \clearemptydoublepage \pagenumbering{roman} \setcounter{page}{1} \clearemptydoublepage \tableofcontents \clearemptydoublepage \emptypage \clearemptydoublepage \pagenumbering{arabic} \setcounter{page}{1} \section{Initial remarks} This document is intended for people who are interested in understanding how \FORM\ works internally, how to find and correct bugs in the source code, and how to extend \FORM\ by implementing new features. It is assumed, that the source code is available, either as a package or directly via CVS access to the \FORM\ repository. The \FORM\ package contains many files and several subdirectories. The actual sources of \FORM, \TFORM, and \PARFORM\ are all in the directory \C{sources} (see section \ref{sec:source} for an overview). Documentation can be found in the directory \C{doc}. The testing suite is contained in the directory \C{check}. \input{@srcdir@/source} \input{@srcdir@/formrun} \section{Specific topics} \input{@srcdir@/indepth} \input{@srcdir@/testsuite} \input{@srcdir@/cvs} \printindex \end{document} form-5.0.1/doc/devref/version.tex.in0000644000175100017510000000031715217035744013010 \def\repoversion{5.0.1} \def\repoversiondesc{5.0.1} \def\reporevision{v5.0.1} \def\repodate{ 9 April 2024} \def\repomajorversion{5} \def\repominorversion{0} \def\repopatchversion{1} \def\repoversionsuffix{} form-5.0.1/doc/devref/Makefile.am0000644000175100017510000000707615217035721012234 TEXSRC = \ cvs.tex \ devref.tex \ formrun.tex \ indepth.tex \ source.tex \ testsuite.tex MAIN = devref TEXFILES = $(TEXSRC) $(MAIN).tex version.tex EXTRA_DIST = $(TEXSRC) .PHONY: dvi latex2html html ps pdf clean-local update_version_tex # NOTE: htlatex invalidate .aux, .idx, .dvi files. HTMLCLEANFILES = idxmake.dvi idxmake.log $(MAIN).4ct $(MAIN).4dx $(MAIN).4ix \ $(MAIN).4tc $(MAIN).aux $(MAIN).css $(MAIN).dvi $(MAIN).html $(MAIN)2.html \ $(MAIN).idv $(MAIN).idx $(MAIN).ilg $(MAIN).ind $(MAIN).lg $(MAIN).log \ $(MAIN).tmp $(MAIN).xref CLEANFILES = $(MAIN).pdf $(MAIN).ps $(MAIN).toc $(DATEFILE) texput.log \ version.tex $(HTMLCLEANFILES) clean-local: rm -rf html $(MAIN) # Automatic versioning. version.tex: update_version_tex $(UPDATE_VERSION_TEX) dist-hook: $(DISTHOOK_VERSION_TEX) if FIXED_VERSION UPDATE_VERSION_TEX = \ [ -f version.tex ] || $(LN_S) "$(srcdir)/version.tex.in" version.tex DISTHOOK_VERSION_TEX = \ cp "$(srcdir)/version.tex.in" "$(distdir)/version.tex.in" else UPDATE_VERSION_TEX = \ $(SHELL) "$(top_srcdir)/scripts/git-version-gen.sh" -C "$(srcdir)" -t -o version.tex --date-format '%e %B %Y' DISTHOOK_VERSION_TEX = \ $(SHELL) "$(top_srcdir)/scripts/git-version-gen.sh" -C "$(srcdir)" -t -o "$(distdir)/version.tex.in" --date-format '%e %B %Y' endif #################### CONFIG_TEX if CONFIG_TEX dvi: $(MAIN).dvi if CONFIG_MAKEINDEX $(MAIN).dvi: $(TEXFILES) $(LATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(LATEX) $(MAIN).tex; done $(MAKEINDEX) $(MAIN) $(LATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(LATEX) $(MAIN).tex; done else $(MAIN).dvi: $(TEXFILES) $(LATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(LATEX) $(MAIN).tex; done endif ########## CONFIG_LATEX2HTML if CONFIG_LATEX2HTML latex2html: $(MAIN)/$(MAIN).html $(MAIN)/$(MAIN).html: $(MAIN).dvi LATEX2HTML="$(LATEX2HTML)" $(top_srcdir)/scripts/run-latex2html.sh $(MAIN).tex endif ########## CONFIG_LATEX2HTML ########## CONFIG_HTLATEX if CONFIG_HTLATEX html: html/$(MAIN).html if CONFIG_MAKEINDEX html/$(MAIN).html: $(TEXFILES) mkdir -p html $(HTLATEX) $(MAIN) "html,mathml-" "" "-dhtml/" $(TEX) '\def\filename{{$(MAIN)}{idx}{4dx}{ind}} \input idxmake.4ht' $(MAKEINDEX) -o $(MAIN).ind $(MAIN).4dx $(HTLATEX) $(MAIN) "html,mathml-" "" "-dhtml/" sed 's/table.tabular {margin-left: auto; margin-right: auto;}/table.tabular {margin-left: inherit;}/' html/$(MAIN).css >html/$(MAIN).css.tmp mv html/$(MAIN).css.tmp html/$(MAIN).css rm -f $(HTMLCLEANFILES) else html/$(MAIN).html: $(DATEFILE) mkdir -p html $(HTLATEX) $(MAIN) "html,mathml-" "" "-dhtml/" rm -f $(HTMLCLEANFILES) endif endif ########## CONFIG_HTLATEX ########## CONFIG_PS if CONFIG_PS ps: $(DATEFILE) $(MAIN).ps $(MAIN).ps: $(DATEFILE) $(MAIN).dvi $(DVIPS) -o $(MAIN).ps $(MAIN).dvi endif ########## CONFIG_PS ########## CONFIG_PDF if CONFIG_PDF pdf: $(MAIN).pdf if CONFIG_MAKEINDEX $(MAIN).pdf: $(TEXFILES) $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done $(MAKEINDEX) $(MAIN) $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done else $(MAIN).pdf: $(TEXFILES) $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done endif endif ########## CONFIG_PDF endif #################### CONFIG_TEX form-5.0.1/doc/devref/formrun.tex0000644000175100017510000007542315217035721012413 \section{Discussion of a typical \FORM\ run} We discuss in the following what is happening inside \FORM\ when it executes a given program. The discussion focuses more on the interplay between the various parts of \FORM\ and on key concepts of the internal data representation than on in-depth details of the code. For the latter, the reader is referred to section \ref{sec:indepth}. This section should for better comprehension be read with the referenced \FORM\ source files opened aside. We consider the following exemplary \FORM\ program \C{test.frm} (which we run with the command "\C{form test}"): \begin{verbatim} 1 #define N "3" 2 3 Symbol x, y, z; 4 5 L f = (x+y)^2 - (x+z)^`N'; 6 L g = f - x; 7 8 Brackets x; 9 Print; 10 .sort 11 12 #do i=2,3 13 Id x?^`i' = x; 14 #enddo 15 16 Print +s; 17 .end \end{verbatim} The entry function \C{main()} is in \C{startup.c}. It does various initializations before it calls the preprocessor \C{PreProcessor()}, which actually deals with the \FORM\ program. The code shows some typical features: Preprocessor macros are frequently used to select code specific to certain configurations. The two most common macros can be seen here: \C{WITHPTHREADS} for a \TFORM\ executable and \C{PARALLEL} for a \PARFORM\ executable. Macros are used to access the global data contained in the variable \C{A}, like \C{AX.timeout} for example. The code uses (usually) own functions instead of standard functions provided by the C library for common tasks. Examples in \C{main()} are \C{strDup1} or \C{MesPrint} (replacing \C{printf()}). Another very often used function is \C{Malloc1()} replacing \C{malloc()}. The reasons are better portability and the inclusion of special features. \C{Malloc1()} for example makes a custom memory debugger available while \C{MesPrint()} knows among other things how to print encoded expressions from the internal buffers. % needs to be rewritten -> The initializations in \C{main()} are done in several steps. Some like the initialization of \C{A} with zeros is done directly, most others are done by calls to dedicated functions. The initializations are split up according to the type of objects involved and the available information at this point. The command line parameters passed to \FORM\ (none in our example run) are treated in the function \C{DoTail()}. After that, files are opened and also parsed for additional settings. Then, as all settings are known, the large part of the internal data is allocated and initialized. Finally, recovery settings are checked, threads are started if necessary, timers are started, and variable initializations that might need to be repeated later (e.g. clear modules) are done in \C{IniVars()}. The call to \C{OpenInput()} reads the actual \FORM\ program into memory. The input is handled in an abstract fashion as character streams. The stream implementation (\C{tools.c}) offers several functions to open, close, and read from a stream. Streams can be of different types including files, in-memory data like parts of other streams or dollar variables, as well as external channels. The access to the characters in all streams though is nicely uniform. In \C{OpenInput()} a stream is representing our input file. Most of the logic there deals with the jump to the requested module (skipping clear instructions). It uses the function \C{GetInput()} to get the next character in the stream. Which stream it reads from is determined by the variable \C{AC.CurrentStream}. This global variable in the sub-struct \C{C\_const} of the \C{ALLGLOBALS} variable \C{A} is an example of how the different parts of \FORM\ typically communicate with each other by means of global variables. Next is the preprocessor. The preprocessor is implemented in the function \C{PreProcessor()} in \C{pre.c}. This function consists basically of two nested for-loops without conditions (\C{for (;;) \{ \ldots \}}). The outer loop deals with one \FORM\ module for each iteration, the inner loop deals with one input line. We have certain initializations done before in our example the code runs into the inner loop, where \C{GetInput()} reads our input file. The variables are all set such that the reading starts from the beginning of out input file. The input in variable \C{c} is tested for special cases. Whitespaces are skipped. Comments starting with a star \C{*} (unless \C{AP.ComChar} is set to a different character) are also skipped including whole folds. The crucial check on \C{c} is the if-clause that checks it for being a preprocessor command (\C{\#}), a module statement (\C{.}), or something else which is usually an ordinary statement. \begin{verbatim} 1 #define N "3" \end{verbatim} In our case, we have a preprocessor command in the input. The function \C{PreProInstruction()} is called to read and interpret the rest of the line. The first part deals with the loading of the command in a dedicated buffer. For the moment, we ignore the details for the special treatment of cases when we are already inside a if or switch clause in a \FORM\ program. In our run, the function \C{LoadInstruction(0)} is simply called. \C{LoadInstruction()} copies input into the preprocessor instruction buffer. Three variables govern this buffer: \C{AP.preStart} points to the start of the buffer, \C{AP.preFill} to the point where new input can be copied to, and \C{AP.preStop} to (roughly) the end of the buffer. This setup is quite typical for buffers in \FORM. The memory is allocated at the start of \FORM. Later, like at the end of \C{LoadInstruction()}, if the buffer gets to small, it can be replaced by a larger memory patch with the help of utility functions like \C{DoubleLList()}. The contents is copied from the old to the new buffer. Since this dynamical resizing of buffers needs to be done with most buffers occasionally, most buffers in \FORM\ store data such that it easily allows for copying, i.e. usually C pointers are avoided and instead numbers representing offsets are used. Since the preprocessor instruction buffer just contains characters there is no problem here. In \C{LoadInstruction()} with our input and the mode set to 5 the input is just copied directly without any special actions taking except for a zero that is added at the end of the data. \C{PreProInstruction()} examines the data in the preprocessor instruction buffer for special cases, and then does a look-up in the \C{precommands} variable. This is a vector of type \C{KEYWORD} which enables the translation of a string (the command) to a function pointer (the C function that performs the operations requested by preprocessor command). \C{FindKeyword()} does these translations and the found function pointer is then dereferenced with the rest of the input in the instruction buffer as an argument. The function pointer will point to \C{DoDefine()} in our case. \C{DoDefine()} just calls \C{TheDefine()} that does the work. The if-clauses for \\ \C{AP.PreSwitchModes} and \C{AP.PreIfStack} are present in most of the functions dealing with preprocessor commands. They check whether we are in a preprocessor if or switch block that is not to be considered, because the condition didn't hold. Then, the standard action is to just exit the current function leaving it with no effect. Since there are preprocessor commands like \C{\#else} or \C{\#endif} this decision can only be taken at this level of the execution and requires the repeated use of this idiom. The function scans through possible arguments and the value. In the value, special characters are interpreted. Ultimately, the preprocessor variable is created and assigned in the called function \C{PutPreVar()}. The variable \C{chartype} deserves an explanation. One will find it used very often in the C code that does input parsing. \C{chartype} is actually a macro standing in for \C{FG.cTable}. This global, statically initialized (in \C{inivar.h}) vector contains a value of every possible ASCII character describing its parsing type. The parsing type groups different ASCII characters such that the syntax checking is facilitated, see \C{inivar.h} for details. In \C{PutPreVar()} we get into the details of the name administration. We will just comment on some of the more general features. \C{NumPre} and \C{PreVar} are macros to access elements in \C{AP.PreVarList}. The type of \C{AP.PreVarList} is \C{LIST}. This is a generic type for all kinds of lists and it is used for many other variables in \FORM. A \C{LIST} stores list entries in a piece of dynamically allocated memory that has no defined type (\C{void *}). The utility functions for managing \C{LIST}s like \C{FromList()} are ignorant about the actual contents and perform list-specific operations like adding, removing or resizing a list. An actual entry can be accessed by some pointer arithmetic and type casting. The \C{PreVar} macro contains such a cast to the type \C{PREVAR} which represents a preprocessor variable. \C{PutPreVar()} creates a new list entry for us and basically copies the contents of the parameter \C{value} to the memory allocated to \C{PREVAR}'s \C{name}. So, by writing \C{PreVar[0]->name} or \C{PreVar[0]->value} we could access the strings \C{N} or \C{3}. In \C{TheDefine()} the function \C{Terminate()} is used several times. This function ultimately exits the program, but first tries to clean up things and print information about the problems causing this program termination. \begin{verbatim} 2 3 Symbol x, y, z; \end{verbatim} In our run, we return to the function \C{PreProcessor()} and start a new inner loop iteration that reads a new line. After skipping the empty line we end up in the else-branch of the big if-clause testing \C{c} this time. Here the major steps are: we check again whether we are in a preprocessor if or switch, call \C{LoadStatement()} to read and prepare the input, and call \C{CompileStatement()} to perform the actions requested by the statement. Th programs enters the compiler stage. We also see a call to \C{UngetChar()}, which puts back the character that has been read into the input stream. This is necessary, because \\ \C{LoadStatement()} and \C{CompileStatement()} need the complete line for parsing. The variable \C{AP.PreContinuation} is used several times. This variable deals with statements that span several input lines. \C{LoadStatement()} can recognize unfinished statements and sets this variable accordingly. \C{LoadStatement()} basically copies the input to the compiler's input buffer at \C{AC.iBuffer} (which has \C{AC.iPointer} and \C{AC.iStop} associated to it). It modifies the copy if necessary. The modification are to replace spaces by commas or insert commas at the right spots to separate tokens. The interpretation steps that are following rely on these synactic conventions. The call to \C{CompileStatement()} is done only if no errors occurred and all lines of a statement have been gathered into the compiler's input buffer. \C{CompileStatement()} is called with the address of this input buffer and tries to identify the statement. Like in the preprocessor, the input string is search in a vector of \C{KEYWORD}s (in \C{compiler.c} and if found, a function pointer is dereferenced to the function that actually deals with the command and its options and arguments. Here, we have actually two vectors of \C{KEYWORD}s, because some statements might be stated in abbreviated form. The function \C{findcommand()} deals with the search. \C{CompileStatement()} does some small extra work, like for example checking the correct order of statements. In our case, it calls the function \C{CoSymbol()}. This functions is in file \C{name.c}, because as a declaration it basically adds something to the name administration. Functions for other statements can be found in \C{compcomm.c} and \C{compexpr.c}. \C{CoSymbol()} loops over the arguments and adds proper variable names together with their options to the symbols list \C{AC.Symbols} and the name administration (in the call to \C{AddSymbol()}. In our case, we have \C{x}, \C{y}, and \C{z} added. We have already encountered the basic mechanism of how a specific struct is added to a \C{LIST}. The name administration was not explained before, though. Symbols can appear in expressions that need to be encoded. The coding for symbols can simply be its entry index in the list \C{AC.Symbols}, but symbols also need to be recognized when an expression is parsed. Therefore a efficient look-up mechanism is required. This is achieved by a second data structure that holds the name strings in a tree for fast searching. The data in the symbol list does not contain the name string itself, but contains a reference (a index) into this name string tree. The tree is managed by generalized functions and types that are also used for other, similar objects like vectors, indices, etc. The functions for name trees are located in the first part of the file \C{name.c}. The types \C{NAMENODE} and \C{NAMETREE} are defined in \C{structs.h}. \C{NAMENODE}s are the node of a balanced binary tree. It does not hold the name string just an index into \C{NAMETREE}. The actual data is contained in \C{NAMETREE} that constitute one tree. This type has buffers for the nodes and for the name strings. This has the benefit of avoiding small malloc calls for individual nodes. Also, since all referencing is done via offsets into these buffers, a relocation or serialization of such a tree is very easy. In the struct \C{C\_const} (aka the global \C{AC}) several name trees are defined, for dollar variables, expressions, etc. The symbols added in our example program go into the nametree referenced by \C{AC.activenames}, which is at this point equal to \C{AC.varnames}. Our program returns to the \C{PreProcessor()} and starts parsing the next lines: \begin{verbatim} 5 L f = (x+y)^2 - (x+z)^`N'; 6 L g = f - x; \end{verbatim} This time the function \C{DoExpr()} will get called (via \C{CoLocal()}) for each line to do the parsing. The function \C{DoExpr()} first tries to figure out what type of \C{Local} statement we have. In our cases we have an actual assignment. With the call to \C{GetVar()} we check whether a variable of the same name already exists. The search is done in the nametrees \C{AC.varnames} and \C{AC.exprnames}. Since our names are new we don't find a previous variable and simply call \C{EntVar()}. \C{EntVar()} creates an entry in \C{AC.ExpressionList} and puts the name into the \C{AC.exprnames} nametree. The entry in \C{AC.ExpressionList} is of type \C{struct ExPrEsSiOn}. There are more struct elements than in the case of symbols, but the principle is the same. Up to now, the right-hand-side (RHS) has not been looked at and therefore no information about it is saved in the expression's entry yet. The connection between the expression's entry in the \C{AC.ExpressionList} and the data containing the RHS will be made via the elements \C{prototype} and \C{onfile} as we will describe soon. The access to elements in \C{AC.ExpressionList} is facilitated by the macro \C{Expressions}. The following code in \C{DoExpr()} builds up a so-called prototype and puts the RHS in encoded form into the buffer system via the call to \C{CompileAlgebra()}. \FORM\ uses the allocated memory in \C{AT.WorkSpace} for operations like the generation of terms. This memory stores \C{WORD}s and is used in a stack-like fashion with the help of the pointer \C{AT.WorkPointer}. A function can write to this memory and set \C{AT.WorkPointer} beyond the written data to insure that other functions that are called and might use the workspace as well do not overwrite this data. It is the responsibility of the function to reset \C{AT.WorkPointer} to its original value again (see variable \C{OldWork} in our case). Every thread in \TFORM\ will have its own private work space. \FORM\ now uses \C{AT.WorkSpace} to build up a data structure that contains everything that needs to be known at a later stage about the expression that is parsed. The creation and the layout of the data is quite typical. First comes a header that signifies what is coming. Here, it is \C{TYPEEXPRESSION}. Then comes the length of the whole data, i.e. the total number of occupied \C{WORD}s. The actual contents is following, which is a so-called subexpression that we will discuss soon. The contents is followed by a coefficient and a zero, which signifies the end of the data. {\bf Coefficients} are coded in \FORM\ always in the following manner: Since coefficients can in general be fractional numbers, we encode an integer numerator and an integer denominator. The integers can have arbitrary length (limited only by the buffer sizes, see the setup variables \C{MaxNumberSize} and \C{MaxTermSize}) and are encoded in \C{WORD}-pieces in little-endian convention. The number of allocated \C{WORD}s is always the same for the numerator and the denominator. The last word of the coefficient contains the size of the whole coefficient in words. The formal structure of a coefficients is therefore like this: \begin{center} {\it NUMERATOR WORDS, DENOMINATOR WORDS, LENGTH}. \end{center} The integers are always unsigned, i.e. positive. Negative fractions are encoded by a negative length. Examples (with 16bit words): $2^{16}+2 = 65538$ gives words 2,1,1,0,5 and $-5/2$ gives $5,2,-3$. The data structure in \C{AT.WorkSpace} is basically an instruction for the generator, a central function that does the main work during the execution of the \FORM\ program, to generate an expression. The content of the expression is a subexpression. This is a pointer to the real content of the expression and will be substituted later after the execution. The main reason for this delayed expression insertion is that it can often save a lot of intermediate operations and data space and thereby speed up \FORM. A case where such a thing can happen is, when an expression is used at different places and the different parts are brought together by some operations. Then, cancellations may occur or terms can be factored out and when the expressions finally is inserted the workload is less. In our example run, the data that will later instruct the generator to create an expression looks in total like this: \begin{center} {\it TYPEEXPRESSION, SUBEXPSIZE+3, 9, SUBEXPRESSION, \\ SUBEXPSIZE, 0, 1, AC.cbufnum, 1, 1, 3, 0} \end{center} We used the macro names as in the actual code. \C{AC.cbufnum} is a variable that is the index of the compile buffer used for this parsed statement. At the end of the data preparation phase the pointer \C{AT.WorkPointer} is set beyond the data on the trailing zero, the pointer \C{AT.ProtoType}, which is used soon in following functions is set to the word \C{SUBEXPRESSION}. The expression will be put into the scratch buffer system. This system comprises the small and large buffers and the scratch files. Where new data to the scratch buffers will be stored is of no concern to a function like \C{DoExpr()}, it simply uses several utility functions for that purpose. Still, we need to initialize the variable \C{pos} here that will indicate the position of the data, i.e. the expression, in the scratch file. Next, the function \C{CompileAlgebra()} is called to parse the right hand side and put the codified expression into the \FORM\ buffers. It basically calls two functions: \C{tokenize} and \C{CompileSubExpressions}. \C{tokenize} is the tokenizer that translates the input character string in a sanitized and partly interpreted string of codes. It will look up the variables named in the input string and put the index they have in the name administration into the tokenized output. Our input string is transformed into the code string like this \begin{verbatim} ( -13 LPARENTHESIS x -1 TSYMBOL 5 + -26 TPLUS y -1 TSYMBOL 6 ) -14 RPARENTHESIS ^ -25 TPOWER 2 -8 TNUMBER 2 - -27 TMINUS ( -13 LPARENTHESIS x -1 TSYMBOL 5 + -26 TPLUS z -1 TSYMBOL 7 ) -14 RPARENTHESIS ^ -25 TPOWER `N' -8 TNUMBER 3 -29 TENDOFIT \end{verbatim} This code string then lies in the \C{AC.tokens} buffer where it is used by subsequent functions. The function \C{CompileSubExpression()} finds terms in an expression that might be reused at another place and extracts them. As one can see in the code, the function looks for terms in parentheses and works recursively. The end of such a term is each time marked with \C{TENDOFIT}. Then, the function \C{CodeGenerator()} called at the end of \C{CompileSubExpression()} does the real work. In our example \C{CodeGenerator()} first gets the data \begin{center} {\it LPARENTHESIS, TSYMBOL, 5, TPLUS, TSYMBOL, 6, TENDOFIT} \end{center} as a parameter, which is the term $x+y$. It builds up the actual term encoding in the workspace and first reserves for that enough space there. One can see the pointer arithmetic using constants like \C{AM.MaxTal}, which is the maximum number of words a number can occupy. It reserves space for the coefficient, an integer, and the actual term. Once a token is recognized, the equivalent term data is written to the workspace and the function \C{CompleteTerm} is called. This function completes the data to \begin{center} {\it 8, 1, 4, 5, 1, 1, 1, 3, 0}. \end{center} The first word is the total length, i.e. 8 words. This is the length of the whole expression. The second word is the type of the term, which is a symbol. It is the value \C{SYMBOL} as defined in \C{ftypes.h}. This macro definition \C{SYMBOL} has the value 1 (in the \FORM\ version at this time this reference is written). Following the type signifying word is the length of the term, which is 4. Several such terms could follow each other, but we only have one term at the moment. Finally, we have the trailing words for the coefficient being 1 and a terminating zero. The meaning and interpretation of the words in the data of a single term after the type word and the length word are dependent on the type. For symbols, we have pairs of word, where the first word is the index of the symbol in the name administration and the second word is the exponent. Here we have symbol 5 ($ = x$) with an exponent 1. After \C{CompleteTerm()} has constructed the whole expression it copies the data to the compile buffers with the help of the function \C{AddNtoC()}. The compile buffers contain the instruction for the execution engine, the \C{Processor()}, that will start when the \C{.sort} command is parsed. Our terms are put into the right-hand-side buffers in the compile buffer. When the \C{Processor()} will read these buffers one after the other, it will take the terms and put them into the scratch buffer system. Then, they become the expressions upon which further statements do act. The compile buffers are stored in the list \C{AC.cbufList} and we get access to the elements via the cast \C{((CBUF *)(AC.cbufList.lijst))}. This cast is defined as a preprocessor macro called \C{cbuf}. The element \C{cbuf[0]->numrhs} (0 is the current compile buffer we are using) gives the number of entries in \C{cbuf[0]->rhs}, which is an array of pointer into \C{cbuf[0]->Buffer}. We have 3 elements: \begin{verbatim} cbuf[0]->rhs[1] --> 8, 1, 4, 5, 1, 1, 1, 3, 8, 1, 4, 6, 1, 1, 1, 3, 0 cbuf[0]->rhs[2] --> 8, 1, 4, 5, 1, 1, 1, 3, 8, 1, 4, 7, 1, 1, 1, 3, 0 cbuf[0]->rhs[3] --> 9, 6, 5, 1, 2, 0, 1, 1, 3, 9, 6, 5, 2, 3, 0, 1, 1, -3, 0 \end{verbatim} \C{cbuf[0]->rhs[0]} is not used and the data lies consecutively in \\ \C{cbuf[0]->Buffer}. The meaning of the first two entries has already been explained. These are expressions containing $x+y$ and $x+z$, respectively. The last expression uses subexpressions that have the type \C{SUBEXPRESSION} $ = 6$. The length of a subexpression is 5 and the contents $1,2,0$ means that expression 1 needs to be inserted with an exponent of 2. The zero is a dirty flag that signals to the processor the state of the subexpression. Here in the compile buffers it is simply cleared to zero. The contents $2,3,0$ of the second subexpression should be obvious. Finally, we have an negative coefficient for the second subexpression which accounts for the minus sign between the parentheses in our original expression. We return to the function \C{DoExpr()} where the prototype of the expression is put into the scratch system via the call \C{PutOut()} and we are finished with this line in the input file. The next line defining a second local expression works the same. We come to the parsing of the following statements: \begin{verbatim} 7 8 Brackets x; 9 Print; \end{verbatim} The bracket statement is dealt with in function \C{DoBrackets()}. It sets the flag \C{AR.BracketOn} to 1 and constructs the term that will stand outside the bracket. This term is copied into the \C{AT.BrackBuf} buffer, where it can be used by the execution engine when it needs to insert this heading term into an expression. The print statement is parsed in function \C{DoPrint()}. Since we don't have any arguments to \C{Print} all active expressions shall be printed. \C{DoPrint()} just loops through the \C{Expressions} list and sets the \C{printflag} to 1 for each expression. With the next statement in our input file \begin{verbatim} 10 .sort \end{verbatim} we will get to know the other central parts of \FORM: the processor and the sorting routines. The code in the \C{PreProcessor()} will call \C{ExecModule()} which calls \C{DoExecute()}. We can ignore a lot of code there that is only for parallelized versions of \FORM. There are three important functions calls happening. First, \C{RevertScratch()} is called. \FORM\ uses three scratch buffers: input buffer, output buffer, and the hide buffer. The usual mode of operation is to apply statements on expressions in the input buffer, sort and normalize the result, and write it into the output buffer. This repeats for every executing module and therefore an important optimization is made: the input buffer and the output buffer simply change their roles. \C{RevertScratch()} does this job. The second and third important calls are to \C{Processor()} and \C{WriteAll()}. \C{Processor()} is, as the name suggests, the main processor that executes statements and deals with the results. A lot of initialization work is done before we go into the large loop over the expressions that spans almost the whole function. Our expressions have as regular expressions from the scratch buffers the \C{inmem} flag set to zero, so we go into the else branch of the checking if-clause. There we go to the case of a \C{LOCALEXPRESSION}. The main logic here is to do a single call to \C{GetTerm()} to get the first term from the input file and copy that to the output with the call to \C{PutOut()}. This first term, which is a subexpression, serves as a header for the expression. It follows a (while-)loop that calls \C{GetTerm()}, and if there are still terms, the loop executes its body and calls \C{Generator()}. After this loop, some clean-up and a final \C{EndSort()} is done, before the outer loop over the expressions repeats. \C{Generator()} is the function where the read input, which is {\it 9, 6, 5, 3, 1, 0, 1, 1, 3}, will be substituted and expanded. \C{Generator()} gets the term in the workspace and first tries to do all substitutions (\C{SUBEXPRESSION}), then applies the statements in the compile buffers to the normalized terms, substitutes again if necessary, do brackets, and finally sorts the result. The call to \C{TestSub()} does the search for subexpressions. \C{TestSub()} will find a subexpression in our case and return the number (3) of this subexpression and set other global variables ready for the following steps. In \C{Generator()} we enter therefore the if-clause checking \C{replac}$> 0$. Depending on the power of the subexpression different operations are taken. We have our subexpression to the power one only, which is an easy case. The actual substitution is performed by the function \C{InsertTerm()}. Since the new term might again contain subexpressions we do a recursive call to \C{Generator()}. Our expression contains several layers of subexpressions which are all dealt with as described above. Only the powers of the other subexpressions are different from one, so we get slightly more work to be done which involves the expansion of the terms using binomials. Finally, the call to \C{TestSub()} at the beginning of \C{Generator()} will return zero. The function \C{Normalize()} is called, which puts the terms in a canonical form, i.e. terms are ordered and collected with the correct coefficient. In our example, as the first fully substituted term we have {\it 12, 1, 4, 6, 1, 1, 4, 6, 1, 1, 1, 3} before the call to \C{Normalize()}, which means we have a term $x*x$. \C{Normalize()} makes this into {\it 8, 1, 4, 6, 2, 1, 1, 3}, which is $x^2$. Then, we loop over the statements in the compile buffer. \C{level} is the instruction counter. We have a long switch-clause that interprets the statement type identifiers like \C{TYPECOUNT}. Statements with \C{TYPEEXPRESSION} are not treated here. So we loop over all the compile buffer statements here and only call \C{TestMatch()} at the loop's end. This function has no effect in our example, because we have no pattern matching going on. Then, the function \C{PutBracket()} is called to deal with brackets. Brackets are implemented by putting the special code \C{HAAKJE} inside the expression. The terms before the \C{HAAKJE} are outside the bracket, everything following it will be inside the bracket. At the end of the loop over the terms in the expressions, the function \C{StoreTerm()} is called. This function puts the result of the processing in the output scratch buffers. Finally, we return to \C{Processor()}. There the final sorting is started. Also, the printing of the expressions is done here. The parsing in \C{PreProcessor()} continues with \begin{verbatim} 11 12 #do i=2,3 13 Id x?^`i' = x; 14 #enddo \end{verbatim} Here we have a somewhat more complicated example of preprocessor instructions. The do-loop is treated in \C{DoDo()} which sets up data structures (\C{DOLOOP}) to guide the preprocessor when it is parsing the loop body. The statement line will then be presented to the compiler two times and with the correct values of the preprocessor variable \C{i}. The compiler deals with this statement in \C{CoId()} which is just calling \C{CoIdExpression()}. \C{CoIdExpression()} puts a \C{TYPEIDNEW} code into the lhs compile buffer. This tells the processor later how to do the pattern matching. The rhs is the term \C{x} that will be inserted. The parsing continues and ends with \begin{verbatim} 15 16 Print +s; 17 .end \end{verbatim} The way these statements are treated and how the program is executed has already been described. The pattern matching is something that has not occurred before, though. We will not describe it here, since there is a dedicated section in this manual for that. After the final sorting, \FORM\ will clean up temporary files and other resources that are not automatically freed by the operating system before \FORM\ ends itself. form-5.0.1/doc/devref/indepth.tex0000644000175100017510000001714415217035721012352 \label{sec:indepth} \subsection{Pattern matching} to be written \subsection{The problem of dummy indices} \FORM\ has a indices that can be automatically renumbered. With this we mean that when we have an expression like \begin{verbatim} f(i)*g(i)*h(j)*k(j)-f(j)*g(j)*h(i)*k(i) \end{verbatim} we can say \begin{verbatim} Sum i,j; \end{verbatim} and \FORM\ will change the expression into \begin{verbatim} f(N1_?)*g(N1_?)*h(N2_?)*k(N2_?)-f(N2_?)*g(N2_?)*h(N1_?)*k(N1_?) \end{verbatim} in which \C{Ni\_?} are internal indices. These internal indices follow a number of rules: \begin{enumerate} \item their numbers (\C{AC.CurDum}) start at \C{AM.IndDum}, which again starts at \C{AM.DumInd+WILDOFFSET} and \C{AM.DumInd} starts at \C{AM.OffsetIndex + 2*WILDOFFSET}. Hence \C{AC.CurDum} starts at \C{AM.OffsetIndex +\\ 3*WILDOFFSET}. Because we need this extra space \C{WILDOFFSET} cannot be too large and this limits the number of indices that is allowed. \item The dimension of the dummy indices is equal to the default dimension. \item The internal (dummy) indices can be renamed at any time in order to create uniquely minimal terms. In the above expression that would mean that the second term would be 'rearranged' into \begin{verbatim} f(N2_?)*g(N2_?)*h(N1_?)*k(N1_?) --> f(N1_?)*g(N1_?)*h(N2_?)*k(N2_?) \end{verbatim} and the expression becomes zero. \end{enumerate} There are problems with this concept. \begin{enumerate} \item Multiplying expressions with dummy indices could give a repetition of the same indices as in \C{(f(N1\_?)*g(N1\_?))\^{}3}. This has been solved partially as can be seen with the following program: \begin{verbatim} CF f,g; L F = (f(N1_?)*g(N1_?))^3; L G = f(N1_?)*g(N1_?); .sort L G3 = G^3; Print; .end \end{verbatim} The routine that takes care of the proper shifts in dummy numbers is \C{MoveDummies()}. As one can see from the example, the \C{SUBEXPRESSION} to a power isn't treated this way. It would have a serious impact on the speed. With the \C{G\^{}3} it is different because that is slower to begin with. \item Keep Brackets is extremely dangerous. The problem here is \begin{verbatim} f(N1_?)*(g(N1_?)*h(N2_?)*k(N2_?)+g(N2_?)*h(N1_?)*k(N2_?)) \end{verbatim} What is inside the brackets is invisible during the module. Hence a renumbering that involves \C{f(N1\_?)} only can change \C{N1\_?} into \C{N2?\_} (\FORM\ doesn't know there is already a \C{N2\_?}) and anyway, the corresponding \C{N1\_?} remains as it is. It means that there are complicatetions with \C{Sum}, \C{Trace4} and things like \C{id p = f(?);} which can generate dummy indices. \end{enumerate} The second problem requires some action. \begin{enumerate} \item[A] When Keep Brackets is active, renumbering should not be allowed, until the contents are multiplied with the outside of the brackets. \item[B] The multiplying with the contents of the bracket should follow the same procedure as the multiplication with a complete expression \\ (\C{MoveDummies()}). \item[C] Introduction of new dummy indices should be above \C{AM.IndDum + WILDOFFSET/2}. These should vanish when the term is renumbered after multiplying the outside of the bracket with the inside. \end{enumerate} \C{Trace4} involves the creation of dummy indices, but these vanish again without renumbering. Hence they don't cause problems. In order to implement \C{A-C} we have to have a good look at all routines that use \C{AR.CurDum} and call \C{ReNumber()} or \C{DetCurDum()}. \subsection{Values of indices (and vectors)} The indices and vectors share common use. That means that vectors can occur in the places that are reserved for indices. In addition we have various types of indices. Hence it is important to know what range of values in an index location refers to what. \begin{enumerate} \item Special values: \begin{tabular}{p{6em}rp{20em}} \C{GAMMA1} & 0 & Dirac unit matrix \\ \C{GAMMA5} & -1 & Dirac gamma 5 (only defined in 4 dimensions) \\ \C{GAMMA6} & -2 & Dirac (1+gamma5) (only defined in 4 dimensions) \\ \C{GAMMA7} & -3 & Dirac (1-gamma5) (only defined in 4 dimensions) \end{tabular} The above 4 indices are to be used only inside the function \C{g\_}. \begin{tabular}{p{6em}rp{20em}} \C{FUNNYVEC} & -4 & Used in \C{replace\_} to indicate a vector with an unspecified index. Hence \C{VECTOR,4,numvec,FUNNYVEC} instead of \C{INDEX,3,numvec}. \\ \C{FUNNYWILD} & -5 & Used to indicate an argument field wildcard like \C{?a} inside a tensor. \\ \C{SUMMEDIND} & -6 & Used in \C{DELTA} to indicate \C{d\_(mu,mu)-4} as generated in traces. \\ \C{NOINDEX} & -7 & Used by \C{ExecArg()} in splitting a multi-delta or multi-index. Taking out one to make a new argument we leave the old one with two or one empty spots. \\ \C{FUNNYDOLLAR} & -8 & Used to indicate a dollar variable inside a tensor. \\ \C{EMPTYINDEX} & -9 & Used in the bracket statement to indicate a \C{d\_}. Because \C{d\_} isn't a regular function we cannot use the function notation and it needs two arguments. \\ \C{MINSPEC} & -10 & \end{tabular} \C{MINSPEC} must be smaller than all the other special values. \item Fixed indices. They are in the range of 1 to \C{AM.OffsetIndex-1}. \item Vectors are in the range from \\ \C{AM.OffsetVector = -2*WILDOFFSET+MINSPEC;} \\ to \\ \C{AM.OffsetVector + WILDOFFSET} \item Wildcard vectors are in the range \\ \C{AM.OffsetVector + WILDOFFSET} \\ to \\ \C{AM.OffsetVector + 2*WILDOFFSET} \item Regular indices are in the range from \\ \C{AM.OffsetIndex} to \C{AM.OffsetIndex + WILDOFFSET} \item Wildcard indices are in the range \\ \C{AM.OffsetIndex + WILDOFFSET (=AM.WilInd)} \\ to \\ \C{AM.OffsetIndex + 2*WILDOFFSET (=AM.DumInd)} \item Unused in the range of \\ \C{AM.OffsetIndex + 2*WILDOFFSET (=AM.DumInd)} \\ to \\ \C{AM.OffsetIndex + 3*WILDOFFSET (=AM.IndDum)} \item Summed indices (\C{Ni\_?}) are in the range of \\ \C{AM.OffsetIndex + 3*WILDOFFSET (=AM.IndDum)} to \\ \C{AM.OffsetIndex + 4*WILDOFFSET} \item Unused in the range of \\ \C{AM.OffsetIndex + 4*WILDOFFSET} \\ to \\ \C{AM.OffsetIndex + 5*WILDOFFSET (=AM.mTraceDum)} \item Summed indices as generated by the trace routines are above \\ \C{AM.OffsetIndex + 5*WILDOFFSET (=AM.mTraceDum)} \end{enumerate} {\it Note (JV)}: I am not sure why there are unused regions. I must have had a reason for them, but I have forgotten about it (it was more than 20 years ago). And then, maybe it is used somewhere in a totally untransparent way. {\it Note 2 (JV)}: It was good to make this list. It turned out that in several places the code that checks for wildcard indices was only limited from below, not from above. It would of course be very rare to run into trouble with this, but it is better to have the code formally correct. One never knows. This was particularly the case in \C{FindRest()} (in \C{findpat.c}). There may be more. It is best to repair this, whenever encountered. From the above it should be clear that on a 32-bits computer \\ \C{5*WILDOFFSET+AM.OffsetIndex+nTraceDummies < 2\^{}{15}} \\ in which \C{nTraceDummies} is the number of dummies that can be introduced when taking a 4-dimensional trace. If we assume that we will not take traces of more than 200 gamma matrices (each with a different index, because otherwise there are contractions) \C{nTraceDummies} will be at most 100. \C{AM.OffsetIndex} is by default 128. The value that we selected for \C{WILDOFFSET} is 6100 which allows a maximum value of 2167 for \C{AM.OffsetIndex}. form-5.0.1/doc/devref/source.tex0000644000175100017510000003253615217035721012221 \section{Overview of the source code} \label{sec:source} Here we will discuss general aspects of the source code, i.e. the files contained in the directory \C{sources}. \FORM\ is written in ANSI C. The code is split up in header files \C{*.h} and source files \C{*.c}. Files usually don't come in pairs of a header file with the declarations and a source file with the definitions, but instead most declarations are collected in a few headers. The declaration of function headers is done in \C{declare.h} for example. The most prominent exceptions are \C{parallel.h} and \C{minos.h}. Each file usually contains many hundred lines of code. To make the files more accessible, the code is structure by so--called folds. If you use the editor STedi, the code will be visualized correctly. If you use a vi--compatible editor, it is advisable to activate folds and set the foldmarkers to \C{set foldmarker=\#[,\#]} % Folds in Emacs anybody?? \subsection{The header files} % INDENTATION HACK to be improved! $\quad\;\:$\begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{declare.h} & Contains the declarations of all publicly relevant functions as well as of commonly used macros like \C{NCOPY} or \C{LOCK}. \\ \C{form3.h} & Global settings and macro definitions like word size or version number. It includes several different system header files depending on the computer's architecture.\\ \C{fsizes.h} & Defines macros that determine the size and layout of \FORM's internal data like the sizes of the work buffers etc. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{ftypes.h} & Contains preprocessor definitions of the codes used in the internal representation of parsed input and expressions. \\ \C{fwin.h} & Special settings for the Windows operating system. \\ \C{inivar.h} & Contains the initialization of various global data like the \FORM\ function names or the character table for parsing. It also defines the global struct \C{A}, and for \TFORM\ the struct pointer \C{AB}. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{minos.h} & Dedicated header to the minos.c source file. \\ \C{parallel.h} & Dedicated header to the parallel.c source file. \\ \C{portsignals.h} & Preprocessor definition of the OS signals \FORM\ can deal with. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{structs.h} & Defines the structs that contain almost all of \FORM's internal data. \\ \C{unix.h} & Special definitions for Unix--like operating systems. \\ \C{variable.h} & Some convenience preprocessor definitions to ease the access to global variables, like \C{cbuf} or \C{AC}. \\ \end{tabular} \subsection{The source files} % INDENTATION HACK to be improved! $\quad\;\:$\begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{argument.c} & Code for the \C{argument} and \C{term} \FORM\ statements. \\ \C{bugtool.c} & Low-level debugging code. \\ \C{checkpoint.c} & Code to test for checkpoint conditions, to create snapshots, and to recover from snapshot data. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{comexpr.c} & Functions the compiler calls to translate a statement that involves an algebraic expression, e.g. \C{Local} or \C{Id}. \\ \C{compcomm.c} & Functions the compiler calls to translate a statement that neither involves an algebraic expression nor is a variable declaration. \\ \C{compiler.c} & Main compiler code. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{compress.c} & Code for GZIP (de-)compression in sort files. \\ \C{comtool.c} & Utility functions for the compiler, like \C{AddRHS}. \\ \C{dollar.c} & Code dealing with dollar variables. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{execute.c} & Code for the execution phase of a module. Also, code dealing with brackets in \FORM\ expressions. \\ \C{extcmd.c} & External command code. \\ \C{factor.c} & Simple factorizing code for dollar variables and expressions. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{findpat.c} & Pattern matching for symbols and dot products. \\ \C{function.c} & Pattern matching for functions. \\ \C{if.c} & Code for the \C{if} statement. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{index.c} & Code for bracket indexing. \\ \C{lus.c} & Code to find loops in index contractions. \\ \C{message.c} & Text output functions, like \C{MesPrint} or \C{PrintTerm}. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{minos.c} & The minos database. \\ \C{module.c} & Code for module execution and the \C{moduleoption}, \C{exec} and \C{pipe} statements. \\ \C{mpi2.c} & MPI2 code for \PARFORM. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{mpi.c} & MPI1 code for \PARFORM. \\ \C{names.c} & Name administration code to deal with the declaration of \FORM\ variables. \\ \C{normal.c} & Code to normalize terms, i.e. bring them to standard form. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{opera.c} & Code for doing traces, contractions, and tensor conversions. \\ \C{optim.c} & Code to optimize FORTRAN or C output. \\ \C{parallel.c} & \PARFORM\ (MPI-independant code). \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{pattern.c} & General pattern matching and substitution. \\ \C{poly.c} & Code for polynomial arithmetic (experimental). \\ \C{polynito.c} & Code for polynomial arithmetic and manipulation. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{pre.c} & The preprocessor. \\ \C{proces.c} & The central processor. \\ \C{ratio.c} & Partial fractioning and summing functions. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{reken.c} & Code for numerics. \\ \C{reshuf.c} & Utility functions for the renumbering of dummy indices, and for statements like \C{shuffle}, \C{stuffle}, \C{multiply}. \\ \C{sch.c} & Code for the textual output of terms and expressions. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{setfile.c} & Code to deal with setup parameters and setup files. \\ \C{smart.c} & Code doing optimized pattern matching. \\ \C{sort.c} & Code for the sorting of expressions. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{startup.c} & Start of program (\C{main()}). Code for the startup and shutdown phase of \FORM. \\ \C{store.c} & Code to read from disk or write to disk terms and expressions. Also, store file and save file management. \\ \C{symmetr.c} & Pattern matching for functions with symmetric properties. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{tables.c} & Code for the tablebases. \\ \C{threads.c} & \TFORM. Almost all of the \TFORM\ specific code. \\ \C{token.c} & The tokenizer. \\ \end{tabular} \begin{tabular}{p{0.2\textwidth}p{0.65\textwidth}} \C{tools.c} & Utility functions to deal with streams, files, strings, memory management, and timers. \\ \C{unixfile.c} & Wrapper functions for UNIX file I/O functions. \\ \C{wildcard.c} & Code for wildcards. \end{tabular} \subsection{The global structs} \FORM\ keeps its data organized in several global structs. These structs are defined in \C{structs.h} (in the fold \C{A}) and come by the names \C{M\_const}, \C{P\_const}, \ldots. The various global variables are grouped in these structs according to their r\^ole in the program. The fold commentaries give details on this. \C{M\_const} is for global settings at startup and \C{.clear}, for example. The various structs are collected in the struct \C{AllGlobals}. In the case of sequential \FORM, this struct is made into the type \C{ALLGLOBALS}, and in \C{inivar.h}, the global variable \C{A} is defined having this type. This global variable \C{A} holds all the data defined in the various structs. In \C{variable.h} several macros are defined to simplify (and more importantly unify) the access to the struct elements. For example, one can access the variable \C{S0} in \C{T\_const} as \C{AT.S0}. With the multi-threaded version \TFORM\ things are a little bit more complicated, because some data needs to be replicated and made private for each thread. This kind of data is situated in the structs \C{N\_const}, \C{R\_const}, and \C{T\_const}. For \TFORM, these structs are collected in the struct \C{AllPrivates} (which makes up the type \C{ALLPRIVATES}), all other structs go into the \C{AllGlobals} struct. The global variable \C{A} now contains only the non-thread specific data. For each thread a \C{AllPrivates} struct is dynamically allocated and the global pointer variable (in \C{inivar.h}) \C{AB} holds their references. \C{AB} is an array of pointers where the index corresponds to the thread number. The macros defined in \C{variable.h} to access the global struct data are made such that they transparently work with the \C{AB} array. The user doesn't need to care about these details and can still write as in the previous example \C{AT.S0}. This keeps the code of sequential \FORM\ and multi-threaded \TFORM\ uniform. The only small price one has to pay to make this uniform access by macros possible is to make sure every function in \FORM\ knows in which thread it is executed. The \C{AN}, \C{AR}, and \C{AT} macros use a variable \C{B}, which is set to the correct entry in \C{AB} by one of two ways. First, a function can use the macro \C{GETIDENTITY} (defined in \C{declare.h}). In \TFORM\, it calls \C{WhoAmI()} to get the thread number, declares the pointer \C{B}, and sets \C{B} to point to the correct entry in \C{AB}. In sequential \FORM\ this macro is empty. The second way is to get the variable \C{B} as a parameter from the caller. For this method the macros \C{PHEAD}, \C{PHEAD0}, \C{BHEAD}, and \C{BHEAD0} exist (defined in \C{ftypes.h}), which can be used in the parameter list of the function declarations. The variants with a zero differ only by not including a trailing comma, which is not allowed if no other parameters are following in the declaration. Usually, \C{PHEAD} is used in the declaration (it includes type information), while \C{BHEAD} appears in the calling of functions. Which way to set \C{B} is chosen, depends on the use of the function. The \C{PHEAD} method is faster than \C{GETIDENTITY} and should be preferred in functions that are called very often. On the other hand, \C{GETIDENTITY} is more general as it does not rely on every caller to supply \C{B}. The elements of the structs are of various types. Some types are just simple macros mapping directly to built-in types (see \C{form3.h}) like \C{WORD}, others are names for structs that are defined (mostly) in \C{structs.h}. Often, variables of the same type are grouped together to help the compiler with alignment. Also, a lot of structs use macros like \C{PADLONG} (\C{unix.h} or \C{fwin.h}) to pad a struct such that its size is a multiple of a built-in type size. This again is to help with the data alignment. Most struct elements have comments that explain their use. These commentaries often include the information where this element was once located in the old version 2 of \FORM\ (it is the pair of parentheses with or without a capital letter inside). Pointers come in two flavors: Some pointers reference a dynamically allocated piece of memory, basically owning this memory. Others just reference another variable or point into allocated memory. The first kind is usually marked with \C{[D]} for easy identification. These pointers often need to be treated particularly, e.g. during the snapshot creation, when recovering, or when shutting down. During start up (\C{main()}), all the memory of these global structs, i.e. their element variables, is initialized to zero. \subsection{Configuration} The source code evaluates several preprocessor definitions that can be defined by the user. According to these definitions the executable can be configured in different ways. As a default, the sequential version of \FORM\ is generated. But if, for example, the preprocessor variable \C{WITHPTHREADS} is defined, the multi-threaded version \TFORM\ will be compiled. These preprocessor variables can be set when calling the compiler, like \C{gcc -c -DWITHPTHREADS -o pre.o pre.c} The most commonly considered preprocessor variables are: \\ \C{WITHPTHREADS}, \C{PARALLEL}, \C{WITHZLIB}, \C{WITHGMP}, \C{WITHSORTBOTS}, \C{LINUX}, \\ \C{OPTERON}, \C{DEBUGGING}. The first two change the flavor of the executable: \TFORM\ or \PARFORM. The next two configure whether \FORM\ uses the zlib library for compression during sorts or the GMP library for arbitrary precision arithmetics. The next decides whether \FORM\ uses dedicated sorting threads in \TFORM. \C{LINUX} specifies that the executable is to be compiled for a Linux or UNIX compliant operating system. An alternative here would be to set the variable \C{ALPHA} or \C{MYWIN64} instead, but these builds are less common. \C{OPTERON} has to be set if one compiles a 64bit executable. \C{DEBUGGING} enables some features for a non-release debugging version of the executable (commonly named \C{vorm} or \C{tvorm}). When using the autoconf setup, the settings concerning the operating system, architecture (32/64bit), and flavor of the executable are automatically done right. Additional settings like \C{WITHZLIB} can be changed by manually editing the file \C{config.h}, which is included in \C{form3.h}. Version numbers and production date can also be set, but then one either needs to edit the appropriate lines in \C{form3.h} when in a manual compiling setup, or by editing \C{configure.ac} in an autoconf setup. form-5.0.1/doc/devref/testsuite.tex0000644000175100017510000003574615217035721012760 \section{The test suite} The subdirectory \C{check} contains a test suite for \FORM. Using the autoconf facilities the checks can be started with the command \C{make check}. Otherwise, one can issue the command \C{ruby form.rb} in the \C{check} directory. The test suite is written in the language Ruby\footnote{\LINK{http://www.ruby-lang.org}}. Ruby itself already offers a unit testing framework and this is used with as minimal as possible extensions to make the creation of test cases for \FORM\ programs easy. All the extensions to the built-in Ruby testing framework (\C{Test::Unit}) are contained in the file \C{form.rb}. This file also contains code to load test cases from other \C{*.rb} files in the \C{check} directory. Therefore all test cases are contained in appropriately named \C{*.rb} files. The makefile's purpose is to integrate the call \C{ruby form.rb} into the autoconf system. {\it Side note:} The choice to use Ruby and its built-in test framework was taken for several reasons: It makes sense to use or adapt already existing testing frameworks in order to keep the extra cost of maintenance as low as possible for the \FORM\ programmers. There are numerous systems available on the market, some are part of a language runtime environment (libraries), and some are dedicated programs with a custom configuration language. Since the tests for \FORM\ programs center mainly about text processing, i.e. comparing the textual \FORM\ output to a correct answer, we need powerful text processing facilities like pattern matching. But we also need file operations and information from the operating system to check the run of a \FORM\ program, eventually. All this is readily available in the testing frameworks of scripting languages, like Ruby, Python, or Tcl. Ruby was ultimately chosen, because the mixing of \FORM\ code with the steering scripting language code looked nicest, and the small amount of extra (Ruby) syntax necessary makes it convenient to add new test cases. A new test case can be implemented in the following way. First of all, we need a \FORM\ program that is to be run. It might be a program that exhibits an actual bug in (a previous version of) \FORM\ or that contains generic code that should be guaranteed to work, also in coming releases of \FORM. It might also be code that deliberately crashes \FORM\ or causes other errors, like syntax errors, if this behavior of \FORM\ is to be assumed. Usually, the \FORM\ program is rather short or can be made such. In this case, we are going to mix the Ruby and the \FORM\ code in one file. Alternatively, the \FORM\ program can also be kept in a separate file. This option will be discussed later. Now, either one choses an existing \C{*.rb} file (not \C{form.rb}) or starts a new one. The name of the file should fit the test case scenario. In this file we need to define a Ruby class that will contain our \FORM\ code as well as the checks (assertions) we want to impose on the run. The generic frame of this test case definition looks like this: \begin{verbatim} class [Test name] < FormTest def setup [Setup code, usually this includes the FORM program code] end def test1 [Execution code, and the assertion and testing code] end end \end{verbatim} The text in the brackets [ ] needs to be filled with our specific code. The details of the Ruby code itself will be explained later. For a start, it is usually advisable just to copy an existing test case and modify it. Every class defined in this way will be used for the testing. First, Ruby will run the code in the class method \C{setup}, and then it runs \C{test1}. A complete test might look like this: \begin{verbatim} class SymbolIdTest < FormTest def setup input <<-EOF S x, y; L f = (x+y)^100; id x = y; print; .end EOF end def test1 execute FORM assert no_problem assert result("f") =~ pattern("1267650600228229401496703205376*y^100;") end end \end{verbatim} We have chose the name \C{SymbolIdTest} for our class. We defined the \FORM\ program in-line with a so called here document (\C{<<-EOF ... EOF}). We do run the \FORM\ executable. Alternatives would be \TFORM, for example. The assertions we have are that no problem occurred, i.e. no syntax error, no runtime error, or similar things. We also check the output of our \FORM\ program. We compare via pattern matching the result of the expression \C{f} with the correct answer. The function \C{result()} extracts the appropriate line from the output, \C{=\~{}} is the pattern matching operator in Ruby, and the function \C{pattern()} prepares special characters like the caret (\^{}) for the pattern matcher. Next time we run the test suite, our test will be run as well. If no assertions are violated, we will only see the number of successful tests and assertions increased in the summary output. Even though the extra Ruby syntax is kept to a minimum and is rather straightforward, some remarks about the Ruby language are useful here. Classes are defined by the keyword \C{class}, and methods (or functions) are declared with the keyword \C{def}. These definitions are always ended with the keyword \C{end}. \C{FormTest} is a class defined in \C{form.rb} that contains all the special code for \FORM\ test and that is derived from the built-in Ruby test case class \C{TestCase}. For every test case we derive again from this class (\C{class B < A} says that \C{B} is derived from \C{A}). We don't need semicolons to end a line and indentation is arbitrary. Class names should be capitalized. In Ruby, parentheses around the arguments of functions can often be omitted. We use this possibility when we call the functions \C{input}, \C{execute}, and \C{assert}. We could have written \C{execute(FORM)} as well, for example. The here document (\C{<<-EOF ... EOF}) can also use other markers instead of \C{EOF}, of course. The minus sign before \C{EOF} allows the end marker to be indented. Comments are started with a \#. One class can actually contain more than one test. The testing framework will call the method \C{setup} and then a method whose name starts with \C{test} (Note: in newer versions of Ruby the name could be just \C{test}, but older versions ($\ge$1.8.x) require at least one following extra character). If there are more methods starting with \C{test}, each will be called and for each \C{setup} will be called first. In \C{setup} we need to prepare everything for the execution of \FORM. We can either use \C{input} to in-line the source directly, or we can use \C{input\_file} with a string as an argument to reference an external file, e.g. \begin{verbatim} input_file "parsebug.frm" \end{verbatim} The function \C{input} will create a temporary \FORM\ file for the contents. The name of the file is defined in \C{form.rb}. The executable will later be run with the given name or the name of the temporary file as an argument. If additional arguments need to be given to the executable, the function \C{extra\_parameter} can be used, like e.g. \begin{verbatim} extra_parameter "-w4 -l" \end{verbatim} Sometimes one might need to prepare more things for a \FORM\ run, like setting up certain files or starting an external program. This needs to be done by ordinary Ruby code. For this, some more of the Ruby language needs to be known by the user. In the class methods with a name starting with \C{test} we put the code to run the \FORM\ executable and to test the outcome. Usually, the first line will be the call to the executable itself, either \begin{verbatim} execute FORM \end{verbatim} or \begin{verbatim} execute TFORM \end{verbatim} (\PARFORM\ is not supported yet). The function \C{execute} will run the executable with the necessary or requested arguments, but it will run it under the supervision of the \C{strace} system utility. Therefore \C{strace} needs to be present on the system (options to enable or disable the use of \C{strace} will probably be added in the future). \C{strace} is used to get detailed information about the return value or possible failure states of the executable. The output of \C{strace} will be saved in a temporary file and made available to the test case programmer in a Ruby variable. The regular output and the error channel output will be available in Ruby variables as well. The Ruby variables containing the output are \C{\@@strace\_out}, \C{\@@stdout}, and \C{\@@stderr} (the leading \@@-sign is Ruby syntax for specifying instance variables, i.e. variables belonging to a certain object). These variables are the primary source for doing tests. In principle, these variables can be investigated directly, for example via pattern matching like \begin{verbatim} if @strace_out =~ /Segmentation fault/ ... end \end{verbatim} which checks whether a segmentation fault has occurred (the slashes in Ruby define a pattern). But for the most common cases some test functions exist that encapsulate necessary pattern matching details. These functions return true or false values which can be used as arguments to the \C{assert} function. The \C{assert} function raises an error if the argument is false. Available tests functions are: \begin{tabular}{lp{20em}} \C{crash} & true if a crash (segmentation fault) occurred \\ \C{warning} & true if \FORM\ has issued a warning \\ \C{compile\_error} & true if \FORM\ has found a syntax error \\ \C{runtime\_error} & true if \FORM\ has terminated prematurely \\ \C{error} & true if \C{compile\_error} or \C{runtime\_error} is true or the standard error channel contains data \\ \C{problem} & true if \C{warning} or \C{error} or \C{crash} is true \end{tabular} Additionally, the logical opposite of each function exists with a name starting with \C{no\_}, like \C{no\_problem} or \C{no\_crash}. There is also the function \C{return\_value} which gives the return value of the \FORM\ program as an integer, so one could do a check like \begin{verbatim} assert return_value == 66 \end{verbatim} If pattern matching is coded directly, like in our example, some details have to be considered. The operator \C{=\~{}} will try to match a string with a pattern. The variables like \C{\@@stdout} are actually strings (they do contain the carriage return and/or line feed for multi-line output). Patterns in Ruby are written between slashes and various characters are interpreted in a special way (following the widely used regex-syntax). There are four functions to facilitate things: \C{result()}, \C{pattern()}, \C{exact\_result()}, and \C{exact\_pattern()}. \C{result()} takes a string being the name of an expression and returns a string that only contains the lines belonging to the last output of this expression. If it is not the last output of an expression that is wished for, a second numeric parameter can be given that specifies the index of the output (counting starts at 0). While \C{result()} removes all line breaks and whitespaces, \C{exact\_result()} leaves them in place. \C{pattern()} transforms special characters in the given string, removes whitespaces and line breaks, and returns the string as a pattern. Since \FORM\ expressions usually contain a lot of special characters like +, *, ., etc. they cannot not be simply used in a pattern. \C{pattern()} transforms these characters automatically into the correct regex equivalent, e.g. + becomes \textbackslash +. With it, a \FORM\ expression can be directly given as an argument and used in a pattern matching (see example). \C{exact\_pattern()} does not treat whitespaces and line breaks in a special way as \C{pattern()} does and can therefore be used when a exact comparison is required (if for example a bug in the output functions of \FORM\ had caused some whitespace or line breaks to be missing and a test case were required to check for this behavior). If one doesn't want or cannot use the \C{assert} function, one can signal a test failure to the testing framework by raising an \C{AssertionFailedError} directly, like for example \begin{verbatim} if return_value != 2 raise AssertionFailedError.new("return value is wrong!") end \end{verbatim} Suppose a \FORM\ program should have deleted some file (\C{\#remove}), one could implement the following test \begin{verbatim} if File.exist?("thenameofthefile") raise AssertionFailedError.new("File still exists!") end \end{verbatim} The testing framework actually not only calls \C{setup} and each \C{test} method but also a method called \C{teardown}. This method is responsible for cleaning up things at the end of each test run. The class \C{FormTest} provides such a \C{teardown} method that will be inherited by the users test case class unless it is overwritten. It calls the method \C{remove\_files} to delete all temporary files that have been created so far. \C{remove\_files} can be called by the user directly. If \C{teardown} is to be replaced by a specific implementation, it is advisable to still call \C{FormTest}'s \C{teardown} (using Ruby's command \C{super}), like for example \begin{verbatim} ... def teardown super File.delete("extra.log") end ... \end{verbatim} At last, a complete example as it is actually contained in the repository. {\scriptsize \begin{verbatim} #[ SparseTable1 : =begin Bugs reported 2004-04-06 by Misha Tentukov PrintTable and FillExpression did not work with non-sparse tables Fixed 2005-09-27 =end class SparseTable1 < FormTest def setup input <<-EOF cf f; s x; ctable Tab(1:`TableSize'); ctable TabNew(1:`TableSize'); #do i=1,`TableSize',1 Fill Tab(`i')=f(`i'); .sort #enddo * BUG1 (not all elements are printed): PrintTable Tab; bracket x; .sort L expr1=table_(Tab,x); print; .sort bracket x; .sort * BUG 2 ( seems only TabNew(1) is ok - further everything is broken): Fillexpression TabNew=expr1(x); .sort #do i=1,`TableSize' L e`i'=TabNew(`i'); #enddo print; .sort .end EOF extra_parameter "-D TableSize=10" end def test1 execute FORM assert no_problem assert result("expr1") =~ pattern(<<-EOF f(1)*x + f(2)*x^2 + f(3)*x^3 + f(4)*x^4 + f(5)*x^5 + f(6)*x^6 + f(7)*x^7 + f(8)*x^8 + f(9)*x^9 + f(10)*x^10; EOF ) assert result("e10") =~ /\s+f\(10\);/ end end #] SparseTable1 : \end{verbatim}} Some remarks. Folds are used (to structure a long file). \C{=begin} and \C{=end} define a commentary block. Here useful information are given about the bug that triggered the test case. The input is not modified compared to the original \FORM\ program, it is just directly pasted into this Ruby file. We use \C{extra\_parameter} to define a preprocessor variable for the run. We check \C{expr1} to a multi-line reference. Since we use \C{pattern()} (instead of \C{exact\_pattern()}), we can be sloppy about the indentation and the whitespaces. The expression \C{e10} is matched to a pattern done "by hand" instead (just to show the principle). For such a test case, where we are mostly interested about the correctness of the calculation, the first assertion (\C{assert no\_problem}) is a standard. form-5.0.1/doc/devref/Makefile.in0000644000175100017510000004301315217035732012236 # Makefile.in generated by automake 1.16.5 from Makefile.am. # @configure_input@ # Copyright (C) 1994-2021 Free Software Foundation, Inc. # This Makefile.in is free software; the Free Software Foundation # gives unlimited permission to copy and/or distribute it, # with or without modifications, as long as this notice is preserved. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY, to the extent permitted by law; without # even the implied warranty of MERCHANTABILITY or FITNESS FOR A # PARTICULAR PURPOSE. @SET_MAKE@ VPATH = @srcdir@ am__is_gnu_make = { \ if test -z '$(MAKELEVEL)'; then \ false; \ elif test -n '$(MAKE_HOST)'; then \ true; \ elif test -n '$(MAKE_VERSION)' && test -n '$(CURDIR)'; then \ true; \ else \ false; 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It is assumed, that the source code is available, either as a package or directly via CVS access to the \FORM\ repository. The \FORM\ package contains many files and several subdirectories. The actual sources of \FORM, \TFORM, and \PARFORM\ are all in the directory \C{sources} (see section \ref{sec:source} for an overview). Documentation can be found in the directory \C{doc}. The testing suite is contained in the directory \C{check}. \input{./source} \input{./formrun} \section{Specific topics} \input{./indepth} \input{./testsuite} \input{./cvs} \printindex \end{document} form-5.0.1/doc/Makefile.am0000644000175100017510000000007015217035721010744 SUBDIRS = doxygen manual devref dist_man1_MANS = form.1 form-5.0.1/doc/manual/0000755000175100017510000000000015217035744010255 5form-5.0.1/doc/manual/pattern.tex0000644000175100017510000002662615217035721012403 \chapter{Pattern matching} \label{pattern} Substitutions\index{substitutions}\index{pattern matching} are made in \FORM\ by specifying a generic object that should be replaced by an expression. This generic object is called a pattern\index{pattern}. Patterns that the user may already be familiar with are the regular expressions in many UNIX\index{UNIX} based systems or just a statement like \verb:ls *.frm: to list only files of which the name ends in \verb:.frm:. In this case the \verb:*: is called a wildcard\index{wildcard} that can take any string value. In symbolic manipulation there will be wildcards also, but their nature will be different. They are also indicated in a different way. In \FORM\ wildcard variables are indicated by attaching a question\index{question mark} mark (?) to the name of a variable. The type of the variable indicates what type of object we are looking for. Assume the following id\index{id} statements: \begin{verbatim} Functions f,g; Symbol x; id f(g?,x) = g(x,x); \end{verbatim} In this statement g will match any function and hence all occurrences of f, in which the first argument is a function and the second argument is the symbol x, will match. In the right hand side the function g will be substituted by whatever identity g had to assume in the left hand side to make the match. Hence \verb:f(f,x): will be replaced by \verb:f(x,x):. In general function wildcards\index{wildcard!function} can only match functions. Even though tensors are special functions, regular function wildcards cannot match tensors, and tensor wildcards cannot match functions. However commuting\index{commuting} function wildcards can match noncommuting\index{noncommuting} functions {\sl et vice versa}. Index\index{wildcard!index} wildcards can only match indices. The dimension of the indices is not relevant. Hence: \begin{verbatim} id f(mu?,mu?) = 4; \end{verbatim} would match both \verb:f(ka,ka): and \verb:f(2,2):. We will see later how to be more selective about such matches. When the same wildcard occurs more than once in a pattern, it should be matched by the same object in all its occurrences. Hence the above pattern would not match \verb:f(mu,nu):. There is one complication concerning the above rule of index wildcards only matching indices. \FORM\ writes contractions with vectors in a special shorthand notation called Schoonschip\index{Schoonschip} notation. Hence \verb:f(mu)*p(mu): becomes \verb:f(p):. This means that the substitution \begin{verbatim} id f(mu?)*g(nu?) = fg(mu,nu); \end{verbatim} should also replace the term \verb:f(p)*g(q): by \verb:fg(p,q):. In this case it looks like the wildcard indices matched the vectors. This is however not the case, because if we take the previous pattern (with the \verb:f(mu?,mu?):), it is not going to match the term \verb:f(p,p):, because this term should be read as something of the type \verb:f(mu,nu)*p(mu)*p(nu): and that term does not fit the pattern \verb:f(mu?,mu?):. Vector\index{wildcard!vector} wildcards can match vectors, but they can also match vector-like expressions in function arguments. A vector-like expression is an expression in which all terms contain one single vector without indices, possibly multiplied by other objects like coefficients, functions or symbols. Hence \begin{verbatim} id f(p?) = p.p; \end{verbatim} would match \verb:f(q):, \verb:f(2*q-r): and \verb:f(a*q+f(x)*r):, if p, q and r are vectors, and a and x are symbols, and f is a function. It would not match \verb:f(x): and neither would it match \verb:f(q*r):, nor \verb:f(a*q+x):. Wildcard\index{wildcard!symbol} symbols are the most flexible objects. They can match symbols, numbers and expressions that do not contain loose indices or vectors without indices. These last objects are called scalar\index{scalar objects} objects. Hence wildcard symbols can match all scalar objects. In \begin{verbatim} id x^n? = x^(n+1)/(n+1); \end{verbatim} the wildcard symbol n would normally match a numerical integer power. In \begin{verbatim} id f(x?) = x^2; \end{verbatim} there would be a match with \verb:f(y):, with \verb:f(1+2*y): and with \verb:f(p.p):, but there would not be a match with \verb:f(p): if p is a vector. There is one extra type of wildcards. This type is rather special. It refers to groups of function arguments\index{wildcard!argument field}\index{argument field wildcard}. The number of arguments is not specified. These variables are indicated by a question mark followed by a name (just the opposite of the other wildcard variables), and in the right hand side they are also written with the leading question mark: \begin{verbatim} id f(?name) = g(1,?name); \end{verbatim} In this statement\index{?name} all occurrences of f with any number of arguments (including no arguments) will match. Hence \verb:f(mu,nu): will be replaced by \verb:g(1,mu,nu):. In the case that f is a regular function and g is a tensor, it is conceivable that the arguments in \verb:?name: will not fit inside a tensor. For instance \verb:f(x):, with x a symbol, would match and \FORM\ would try to put the symbol inside the tensor g. This would result in a runtime error. In general \FORM\ will only accept arguments that are indices or single vectors for a substitution into a tensor. The object \verb:?name: is called an {\bf argument field wildcard}. One should realize that the use of multiple argument field wildcards can make the pattern matching slow. \begin{verbatim} id f(?a,p1?,?b,p2?,?c,p3?,?d)*g(?e,p3?,?f,p1?,?g,p2?,?h) = .... \end{verbatim} may involve considerable numbers of tries, especially when there are many occurrences of f and g in a term. One should be very careful with this. A complication is the pattern matching in functions with symmetry properties. In principle \FORM\ has to try all possible permutations before it can conclude that a match does not occur. This can become rather time consuming when many wildcards are involved. \FORM\ has a number of tricks built in, in an attempt to speed this up, but it is clear that for many cases these tricks are not enough. This type of pattern matching is one of the weakest aspects of `artificial intelligence' in general. It is hoped that in future versions it can be improved. For the moment the practical consequence is that argument field wildcards cannot be used in symmetric and antisymmetric functions. If one needs to make a generic replacement in a symmetric function one cannot use \begin{verbatim} CFunction f(symmetric),g(symmetric); id f(?a) = ....; \end{verbatim} but one could try something like \begin{verbatim} CFunction f(symmetric),ff,g(symmetric); id f(x1?,...,x5?) = ff(x1,...,x5); id ff(?a) = ...; id ff(?a) = f(?a); \end{verbatim} if f has for instance 5 arguments. If different numbers of arguments are involved, one may need more than one statement here or a statement with the replace\_\index{replace\_} function: \begin{verbatim} Multiply replace_(f,ff); \end{verbatim} It just shows that one should at times be a bit careful with overuse of (anti)symmetric functions. Cyclic functions do not have this restriction. When there are various possibilities for a match, \FORM\ will just take the first one it encounters. Because it is not fixed how \FORM\ searches for matches (in future versions the order of trying may be changed without notice) one should try to avoid ambiguities\index{ambiguity} as in \begin{verbatim} id f(?a,?b) = g(?a)*h(?b); \end{verbatim} Of course the current search method is fully consistent (and starts with all arguments in \verb:?a: and none in \verb:?b: etc, but a future pattern matcher may do it in a different order. When two argument field wildcards in the left hand side have the same name, a match will only occur, when they match the same objects. Hence \begin{verbatim} id f(?a,?a) = g(?a); \end{verbatim} will match \verb:f(a,b,a,b): or just \verb:f: (in which case \verb:?a: will have zero arguments), but it will not match \verb:f(b,b,b):. Sometimes it is useful when a search can be restricted to a limited set of objects. For this \FORM\ knows the concept of sets\index{set}. If the name of a set is attached after the question mark, this is an indication for \FORM\ to look only for matches in which the wildcard becomes one of the members of the set: \begin{verbatim} Symbols a,a1,a2,a3,b,c; Set aa:a1,a2,a3; id f(a?aa) = ... \end{verbatim} would match \verb:f(a1): but not \verb:f(b):. Sets can also be defined dynamically\index{set!dynamical} by enclosing the elements between curly brackets\index{bracket!curly} as in: \begin{verbatim} Symbols a,a1,a2,a3,b,c; id f(a?{a1,a2,a3}) = ... \end{verbatim} Sets\index{Set of symbols} of symbols can contain (small integer) numbers as well. Similarly sets\index{set of indices} of indices can contain fixed indices (positive numbers less than the value of fixindex\index{fixindex} (see the chapter on the setup \ref{setup}). This means that some sets can be ambiguous\index{set!ambiguous} in their nature. Sometimes sets\index{sets!array} can be used as some type of array\index{array}. In the case of \begin{verbatim} Symbols a,a1,a2,a3,b,c,n; Set aa:a1,a2,a3; id f(a?aa[n]) = ... \end{verbatim} not only does `a' have to be an element of the set aa, but if it is an element of that set, n will become the number of the element that has been matched. Hence for \verb:f(a2): the wildcard a would become \verb:a2: and the wildcard n would become 2. These objects can be used in the right-hand side. One can also use sets in the right-hand side with an index like the n of the previous example: \begin{verbatim} Symbols a,a1,a2,a3,b1,b2,b3,c,n; Functions f,g1,g2,g3; Set aa:a1,a2,a3; Set bb:b1,b2,b3; Set gg:g1,g2,g3; id f(a?aa[n]) = gg[n](bb[n]); \end{verbatim} which would replace \verb:f(a2): by \verb:g2(b2):. One cannot do arithmetic\index{arithmetic} with the number of the array element. Constructions like \verb:bb[n+1]: are not allowed. There is one more mechanism by which the array nature of sets can be used. In the statement (declarations as before) \begin{verbatim} id f(a?aa?bb) = a*f(a); \end{verbatim} a will have to be an element of the set aa, but after the matching it takes the identity of the corresponding\index{set!corresponding element} element of the set bb. Hence \verb:f(a2): becomes after this statement \verb:b2*f(b2):. Wildcards can also give their value directly to \$-variables\index{wildcard!\$-variable}\index{\$-variable} (see chapter \ref{dollars} about the \$-variables). If a \$-variable is attached to a wildcard (if there is a set restriction, it should be after the set) the \$-variable will obtain the same contents as the wildcard, provided a match occurs. If there is more than one match, the last match will be in the \$-variable. \begin{verbatim} id f(a?$w) = f(a); \end{verbatim} will put the match of a in \verb:$w:. Hence in the case of \verb:f(a2): the \$-variable will have the value \verb:a2:. In the case of \verb:f(a2)*f(a3): the eventual value of \verb:$w: depends on the order in which \FORM\ does the matching. This is not specified and it would not be a good strategy to make programs that will depend on it. A future pattern matcher might do it differently! But one could do things like \begin{verbatim} while ( match(f(a?$w)) ); id f($w) = .... id g($w) = .... endwhile; \end{verbatim} just to make sure with which match one is working. form-5.0.1/doc/manual/parallel.tex0000644000175100017510000005215615217035721012517 \chapter{The parallel version} \label{parallel} %--#[ Introduction : \FORM\ has two versions that can make use of several processors simultaneously. Which version can be used profitably depends very much on the architecture of the computer one is using. Each version has its own control commands which are ignored by the other version and the sequential version of \FORM\@. The parallel versions are: \begin{itemize} \item \ParFORM\index{ParFORM}: This version runs on processors that have their own memory and preferably their own disk. Each processor gets a copy of the complete program and MPI\index{MPI} is used for the communication\index{communication}. When the network connections are very fast one can also use \ParFORM\ on computer clusters. \ParFORM\ was developed at the university of Karlsruhe\index{Karlsruhe}. \item \TFORM\index{TFORM}: This version uses POSIX threads and runs on computers which have several processors with a shared memory. Data is kept as common data as much as possible and only when a worker thread gets a task a minimal amount of data is copied to its private buffers. Currently it seems to perform best on computers with two or four processors. \end{itemize} Both \ParFORM\ and \TFORM\ suffer from the same bottlenecks\index{bottleneck}. At the beginning of a module there is a single expression, managed by a master process which then has to distribute the terms over the workers. At the end of the module the sorted results of the workers have to be gathered in by the master\index{master} and merged into a single expression again. Efficiency depends critically on how fast the terms can be given to the workers\index{workers}, how well the load for the workers is balanced and how much time the master has to spend in the final stages of the sorting. Another factor is the complexity of the operations inside the module. If the module has very few and simple statements, the gain in performance will be much less than when the module has much work to do for each term. The \ParFORM\ and \TFORM\ specific code is internally completely separated. This offers the possibility that sooner or later the two can be combined to allow efficient running on clusters of dual or quad processor machines. Whether this would give significant extra benefits needs to be investigated. When this project will be undertaken depends very much on the availability of such computers. Because \ParFORM{} uses MPI\index{MPI} and because different MPI environments are normally not binary compatible, the port to a new machine requires a recompilation of the source code and a relinking to the MPI library. Hence we do not have executables in the distribution site. One needs to build \ParFORM{} on one's computer. For \TFORM\ the situation is much more favorable. Its treatment of the parallelization follows the standard for POSIX\index{POSIX} threads (or PThreads) for which the libraries are implemented on almost any UNIX\index{UNIX} system and many other systems. The ideal of a parallel version of \FORM\ is that it should execute nearly any regular \FORM\ program, whether it was written for parallelization or not. And it should execute much faster on several processors than the sequential version on a single processor. The performance is given by the improvement factor which is the execution time of the sequential version divided by the execution time of the parallel version as measured in real time (not CPU time) on a computer that has no other major tasks. The ideal would of course be that a computer with N processors would give an improvement factor of N. It should be easy to see that this ideal cannot be reached, due to the bottlenecks described above. Also the compilation takes place on a single processor and the instructions of the preprocessor are typically also tasks for a single thread/processor. Yet for small numbers of processors one can do rather well. Many old calculations, when repeated with \TFORM\ would give improvement\index{improvement factor} factors above 1.7 on a dual pentium\index{pentium} machine and around 3 or a bit higher on a quad opteron\index{opteron} machine. This was without modifying even a single statement in the programs. Of course these numbers depend very much on the type of the problem and the programming style used. As of yet there is very little experience with parallel versions of \FORM\@. Hence people will have to discover what are good ways of getting the most out of their computer. It is expected that there will be much progress in the coming years. First we will now discuss the running of the two versions. After that we will describe some common syntactic problems. %--#] Introduction : %--#[ TFORM : \section{TFORM} \label{tform} Let us assume that the executable of \TFORM\index{TFORM} is called tform. It is used exactly the same way as the sequential version of \FORM\ (named form) is used with the exception of the possibility to specify the number of worker\index{worker} threads with the -w option. The command \begin{verbatim} tform -w4 calcdia \end{verbatim} would execute the program in the file calcdia.frm, using 4 worker threads, in addition to the one master thread. When the -w option is not given or when only one worker thread is asked for, tform will run the whole program inside the master\index{master} thread. Because tform always has some overhead this is usually a little bit slower than using form. Strange enough there are exceptions although this may have to do with the fact that measuring the time of a program doesn't always give the same numbers. It is also possible to specify the number of worker threads in the setup file, using the line \begin{verbatim} Threads 4 \end{verbatim} for 4 threads. And as with all setup parameters one can pass this information also via the environment variable FORM\_threads or with the line \begin{verbatim} #: Threads 4 \end{verbatim} at the beginning of the program file. When the master passes terms to the workers, it has to signal\index{signal} the workers that there is some data. In their turn, each worker has to send the master a signal when it has completed its task and it is ready for more. Such signals cost time. Hence it is usually best to send terms in groups, called buckets\index{bucket}. The optimal number of terms in a bucket depends very much on the problem and the size of the expression. Bigger buckets mean less overhead in signals. If the buckets are too big the workers may have to wait too much. Values between 100 and 1000 are usually rather good. There is a default bucket size which is typically around 500. The user can change this value in two ways: The first is with the ThreadBucketSize\index{threadbucketsize} setup parameter in the form.set file (or at the startup of the program file, or with the FORM\_threadbucketsize environment variable) and the second is with the ThreadBucketSize statement (see \ref{substathreadbucketsize}) which is a declaration like Symbol or Dimension. The first terms in an expression will be sent in smaller buckets to get the workers something to do as soon as possible. Usually the bigger buckets give a better performance, but they suffer from a nasty side-effect. Complicated terms that need much execution time have a tendency to stick together. Hence there can be one bucket with most of the difficult terms and at the end of the module all workers and the master have to wait for one worker to finish. This can be improved with a load\index{load balancing} balancing mechanism. The current version will take terms from the buckets of workers that take more time than the others. By default this mechanism is on, but it can be switched on or off with the `on ThreadLoadBalancing\index{threadloadbalancing};' and `off ThreadLoadBalancing;' statements. It can also be set as one of the setup parameters in the form.set file with \begin{verbatim} ThreadLoadBalancing OFF \end{verbatim} or \begin{verbatim} ThreadLoadBalancing ON \end{verbatim} or at the start of the program or in the environment. The LINUX\index{LINUX} operating system tries to cache\index{cache} files that are to be written to disk. Somehow, when several big files have to be written it gets all confused (it is not known in what way). This means that if tform produces 4 large sort files\index{file!sort} eventually the system becomes intolerably slow. At one time a test program was 4.5 times slower with 4 worker processors than with just the master running, even though the master had a single even bigger sort file. This has been improved by having the file-to-file sort of the threads changed into a file-to-masterbuffers-to-combined-output. Yet the writing and subsequent merging of the 4 files at the same time can be disastrous. Work is done to improve this, but it may not be easy to circumvent facilities of the operating system. Apparently the quality of the drivers is crucial here. One can switch the parallel processing on or off (for the complete module) at any moment in the program with the statements\index{on!threads}\index{off!threads} \begin{verbatim} On Threads; Off Threads; \end{verbatim} or using the moduleoption statement (\ref{substamoduleoption}) that affects \TFORM{}'s behaviour for just the current module: \begin{verbatim} ModuleOption Parallel; ModuleOption NoParallel; \end{verbatim} Additionally one can switch the statistics per thread on or off with \begin{verbatim} On ThreadStats; Off ThreadStats; \end{verbatim} When the thread\index{on!threadstats}\index{on!threadstats} statistics are switched off only the statistics of the master thread are printed which is usually only the final statistics for each of the expressions. The timing information in the statistics is the CPU\index{CPU time} time spent by the thread that prints the statistics. Hence the total CPU time spent is the sum of the time of all workers and the time of the master. In good running the time of the master should be the smallest number. When the statistics per thread are switched off, only the statistics of the master process will be printed with this `small' number. Hence it may look like the program isn't progressing very much. For debugging purposes the term by term print\index{print} statement (see \ref{substaprint}) is equipped with the \verb:%W: and \verb:%w: format strings. The first will cause the printing of the number of the current thread and the CPU-time used thus far in that thread. The second will only print the number of the current thread. The thread with the number zero is the master thread. Putting a statement like \begin{verbatim} Print +f "<%W> %t"; \end{verbatim} would show which thread is processing which term and when. These are all the commands that specifically concern \TFORM\@. When more experience is gained using \TFORM, more parameters and commands may become available. The fact that the threads need private\index{private} data makes that \TFORM\ will use more memory than \FORM\@. Most of the buffers are not very large, but of course there are some buffers which need to be large, like the sort buffers and the scratch input\index{input}/hide\index{hide} buffers. The sizes that the user specifies for these buffers are for the corresponding buffers of the master. The workers get each 1/N times the size for these buffers, when there are N workers. In the case that makes these buffers too small because of for instance MaxTermSize, the buffers may become larger. %--#] TFORM : %--#[ ParFORM : \section{ParFORM} \label{parform} Let us call the executable of \ParFORM\index{ParFORM} parform. The user must execute parform as an MPI\index{MPI} application. In many MPI implementations, this is done by using the mpirun\index{mpirun} command: \begin{verbatim} mpirun -np 4 parform calcdia \end{verbatim} This example executes the program in the file calcdia.frm, using 4 processes,in which one process is the master process and the other 3 processes are the worker processes. One has to keep in mind that in some MPI implementations environment variables will not be passed to an MPI application. Alternatively extra options are needed for passing them. If one wants to run \ParFORM{} under a job scheduler on a computer cluster environment, one may need to write a job script, which depends to a great extent on the environment. \ParFORM{} uses MPI for communications between the master and workers. Actually terms are distributed by using point-to-point send/receive operations of MPI\@. Since there is some latency for establishing a connection between processes, especially between those running on different computers, it is best to send terms in groups, like buckets in \TFORM{}. The default number of terms in a bucket is currently 1000 in \ParFORM{}. It can be changed with the ProcessBucketSize statement (\ref{substaprocessbucketsize}\index{processbucketsize}) if this is deemed necessary. It can also be changed for the current module with the statement (\ref{substamoduleoption}\index{moduleoption!processbucketsize}). \begin{verbatim} ModuleOption ProcessBucketSize number; \end{verbatim} And finally it can also be changed in the setup, using the ProcessBucketSize (\ref{setupprocessbucketsize}) setup parameter. The first terms in an expression will be sent in smaller buckets to get the workers something to do as soon as possible. One can switch the parallel processing on or off (for the complete module) at any moment in the program with the statements\index{on!parallel}% \index{off!parallel} \begin{verbatim} On Parallel; Off Parallel; \end{verbatim} or using the moduleoption statement (\ref{substamoduleoption}) that affects \ParFORM{}'s behaviour for just the current module: \begin{verbatim} ModuleOption Parallel; ModuleOption NoParallel; \end{verbatim} Additionally one can switch the statistics per process on or off with \begin{verbatim} On ProcessStats; Off ProcessStats; \end{verbatim} When the process\index{on!processstats}\index{on!processstats} statistics are switched off only the statistics of the master process are printed which are usually only the final statistics for each of the expressions. As in \TFORM{}, \verb:%W: and \verb:%w: in the term by term print\index{print} statement (see \ref{substaprint}) are available in \ParFORM{}. They print the number of the current process and the CPU-time used thus far in that process. In principle one can run all \FORM{} or \TFORM{} programs with \ParFORM{}. In practice \ParFORM{} is not so efficient for some problems, in which more data have to be synchronized between the master and the workers. The cases for which \ParFORM{} needs to send data via MPI include: \begin{itemize} \item The redefine statements, which modify preprocessor variables on the workers. \item Modifying \$-variables in regular statements with a moduleoption statement (see \ref{pardollars}, \ref{substamoduleoption} and~\ref{dollars-in-parallel}). \item Expression names appearing in right hand sides of definition or substitution statements. \end{itemize} The last case may need more explanation. Consider the following code: \begin{verbatim} Local G = F; id a = F; \end{verbatim} where the expression F is supposed to be already defined. The point is that these substitutions of the expression F are performed on the workers. The workers, however, do not know the contents of the expression F because it is stored on the master. Therefore, before executing this module \ParFORM{} needs to make the master broadcast the expression F to the workers. This may be quite time-consuming because the expression could be very large. %--#] ParFORM : %--#[ Some problems : \section{Some problems} \label{dollars-in-parallel} Both parallel versions share a number of problems which are inherent to running in an environment in which the order\index{order of terms} in which terms are processed isn't deterministic\index{deterministic}. Most of these problems concern \verb:$:-variables. They present a mix between private and common information. Consider the code \begin{verbatim} id f(x?$xvar) = g(x); id ...... id a^n? = b^n*h($var); \end{verbatim} Of course one could do this simple example differently, but we are discussing the principle. What we have here is that each term that passes the first statement will acquire its own value of \verb:$var:, to be used a bit later. It is clear that if we have a common administration of \verb:$:-variables we would have to `lock'\index{lock} the value for a considerable amount of time, thereby spoiling much of the gains of parallel processing. Hence in this case it would be best that each worker maintains its own local value of \verb:$var:. But in the following example we have the opposite: \begin{verbatim} #$xmax = -1; if ( count(x,1) > $xmax ) $xmax = count_(x,1); \end{verbatim} Here we collect a maximum power in the variable \verb:$xmax:. If each worker would have a local value of \verb:$xmax:, the question is what to do with all these local values at the end of the module. A human will see that here we are collecting a maximum, but the computer cannot and should not see this. Hence the general rule in parallel processing is that when there are \verb:$:-variables\index{\$-variable} obtaining a value during the algebraic phase of a module the entire module is run sequentially, unless \FORM\ has been helped with a moduleoption statement for each of the variables involved. Hence in the last example \begin{verbatim} ModuleOption Maximum $xmax; \end{verbatim} would tell \FORM\ how to combine the local values in \ParFORM\ (\ParFORM\ maintains local values of all \verb:$:-variables). In \TFORM\ it would put the value directly into the central administration, provided it is bigger than the previous value. Only during the update the variable would have to be locked. There are several options in the moduleoption statement: \begin{itemize} \item Maximum\index{moduleoption!maximum}: The variable must have a numerical value and the maximum is collected. \item Minimum\index{moduleoption!minimum}: The variable must have a numerical value and the minimum is collected. \item Sum\index{moduleoption!sum}: The variable must have a numerical value and the sum is collected. \item Local\index{moduleoption!local}: The value will be kept privately and no attempt is made to put it in the central administration, neither during the execution of the module, nor at the end. If there was already a variable by this name in the central administration it will keep the value it had before the module started execution. At the end of the module, all private values will be forgotten. \end{itemize} The redefine statement is a major inefficiency in a parallel environment. It redefines a preprocessor variable and there is only a single bookkeeping for such variables. This means that the variable has to be sent to the master process (\ParFORM) or that a lock has to be placed to prevent other workers to write to the same storage simultaneously (\TFORM). In addition the final value in the preprocessor variable will be determined by the last term processed in any of the workers. This may not be the same term in different runs. It is up to the user to write programs that still give correct results under such conditions. The best way around the inefficiency is using \verb:$:-variables and preprocessor instructions. We show this in an example in which we construct the equivalent of a conditional repeat that includes a .sort instruction. \begin{verbatim} #do i = 1,1 statements if ( count(x,1) > 0 ) redefine i "0"; .sort #enddo \end{verbatim} To run this in parallel, it is better to use the following code. \begin{verbatim} #do i = 1,1 #$i = 1; statements if ( count(x,1) > 0 ) $i = 0; ModuleOption minimum $i; .sort #redefine i "`$i'" #enddo \end{verbatim} In this program the centrally stored value of \verb:$i: is updated at most once. Admittedly it is not as simple as the redefine statement, but it works in all versions of \FORM\ starting with version 3.0. It should be noted that when a new expression is defined in its defining module it starts out as a single term. Hence it cannot benefit from parallelization in that module. Therefore the code \begin{verbatim} #define MAX "200" Symbols x0,...,x10; Local F = (x0+...+x`MAX')^3; id x1 = -x2-...-x`MAX'; .end \end{verbatim} will execute inside a single worker while \begin{verbatim} #define MAX "200" Symbols x0,...,x10; Local F = (x0+...+x`MAX')^3; .sort id x1 = -x2-...-x`MAX'; .end \end{verbatim} will make the first expansion inside a single worker and the more costly substitution can be made in parallel. A better load\index{load balancing} balancing algorithm in which at any node in the expansion tree tasks can be given to idle workers would solve this problem, but due to some complications this has not yet been implemented. The structure of \FORM\ will however allow such an implementation. %\footnote{In the year 1991 version 1 of FORM was parallelized on a %computer at FNAL along these lines. It was however rather primitive and %lack of access to suitable computers stopped further development at that %moment.} %--#] Some problems : form-5.0.1/doc/manual/polynomials.tex0000644000175100017510000005061615217035721013270 \chapter{Polynomials and Factorization} \label{polynomials} \noindent Starting with version 4, \FORM{} is equipped with powerful handling of rational polynomials and with factorization capabilities. Because this creates many new possibilities, it brings a whole new category of commands with it. We will list most of these here. \noindent First there are the rational polynomials. These work a bit like the PolyFun~\ref{substapolyfun}, but now with two arguments: a numerator and a denominator. Instead of PolyFun the function is designated as PolyRatFun~\ref{substapolyratfun} as in the example below: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_1) \begin{verbatim} Symbol x,y; CFunction rat; PolyRatFun rat; L F = rat(x+y,x-y)+rat(x-y,x+y); Print; .end F = rat(2*x^2 + 2*y^2,x^2 - y^2); \end{verbatim} Dealing with a PolyRatFun can be very handy, but one should realize that there is a limit to the size of the arguments, because the PolyRatFun with its arguments is part of a term and hence is limited by the maximum size of a term~\ref{setupmaxtermsize}. One should also take into account that the manipulation of multivariate polynomials, and in particular the GCD operation, can be rather time consuming. \noindent The PolyRatFun has one limitation as compared to the regular PolyFun: in its arguments one may use only symbols. Of course \FORM{} is equipped with a mechanism to replace other objects by extra internally generated symbols~\ref{substaextrasymbols}. One could imagine \FORM{} to automatically convert these objects to symbols, do the polynomial arithmetic and then convert back. This is done with factorization and the gcd\_~\ref{fungcd}\index{gcd\_}\index{function!gcd\_}, div\_~\ref{fundiv}\index{div\_}\index{function!div\_} and rem\_~\ref{funrem}\index{rem\_}\index{function!rem\_} functions. But because the addition of PolyRatFun's is such a frequent event, this would be very costly in time. Hence it is better that the user does this once in a controlled way. \noindent The PolyFun and PolyRatFun declarations are mutually exclusive. The PolyRatFun is considered a special type of PolyFun and there can be only one PolyFun at any moment. If one wants to switch back to a mode in which there is neither a PolyFun nor a PolyRatFun one can use \begin{verbatim} PolyRatFun; \end{verbatim} to indicate that after this there is no function with that status. \noindent When a PolyRatFun has only a single argument, this argument is interpreted as the numerator of a fraction. \FORM{} will add automatically a second argument which has the value 1. \noindent The second important polynomial facility is factorization. This is not necessarily something trivial. First of all, with very lengthy multivariate input, this can be unpractically slow. Second of all, there are various types of objects that we may factorize and each has its special needs. One of those needs is access to the factors, which is different for the factors of function arguments, of \$-expressions or even complete expressions. In addition \$-expressions should be factorizable either from the preprocessor or on a term by term basis. Let us start with function arguments. \noindent One can factorize function arguments with the FactArg statement~\ref{substafactarg}. The factors are each represented by a separate argument as in % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_2) % TODO: the term order has been changed. \begin{verbatim} Symbol x,y; CFunction f1,f2; Local F = f1(x^4-y^4)+f2(3*y^4-3*x^4); FactArg,f1,f2; Print; .end F= f1(y-x,y+x,y^2+x^2,-1)+f2(y-x,y+x,y^2+x^2,3); \end{verbatim} Overall constants and overall signs are taken separately as one can see. If one wants the factors in separate functions one can use the ChainOut~\ref{substachainout} command as in % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_3) % TODO: the term order has been changed. \begin{verbatim} Symbol x,y; CFunction f1,f2; Local F = f2(3*y^4-3*x^4); FactArg,f2; Print; .sort F= f2(y-x,y+x,y^2+x^2,3); ChainOut,f2; id f2(x?number_) = x; Print; .end F= 3*f2(y-x)*f2(y+x)*f2(y^2+x^2); \end{verbatim} \noindent Factorization of expressions is a bit more complicated. Clearly this cannot be a command at the term level. Hence we had two options on how to implement this. One would have been as a preprocessor instruction, which we did not select, and the other is as some type of format statement, which is what we did opt for. In the case we factorize an expression, the original unfactorized expression is replaced by the factorized version. After that we keep the factorized version only and that may bring some restrictions with it. Of course, in the same way one can factorize an expression, one can unfactorize it. The corresponding statements are Factorize~\ref{substafactorize}, NFactorize~\ref{substanfactorize}, UnFactorize~\ref{substaunfactorize} and NUnFactorize~\ref{substanunfactorize}. These statements are used at the end of the module in the same place as one might use the bracket statement~\ref{substabracket}. It should be noticed however that a factorized expression will never apply the bracket mechanism. They are mutually exclusive, because internally we use the bracket mechanism with a built in symbol factor\_ to indicate the factors. Here is an example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_4) \begin{verbatim} Symbol x,y; Local F = x^4-y^4; Print; .sort Time = 0.00 sec Generated terms = 2 F Terms in output = 2 Bytes used = 64 F= -y^4+x^4; Print; Factorize F; .end Time = 0.00 sec Generated terms = 2 F Terms in output = 2 Bytes used = 64 Time = 0.00 sec Generated terms = 7 F Terms in output = 7 factorize Bytes used = 288 F= (-1) *(y-x) *(y+x) *(y^2+x^2); \end{verbatim} We have printed the statistics in this example to show that the factorization prints its own statistics. This factorization is executed after the expression has been completed and before manipulations on the next expression start. This way it is possible to overwrite the first output by the factorized output and we do not loose diskspace unnecessarily. \noindent The next question is of course how to find out how many factors an expression has and how to access individual factors. There is a function numfactors\_ which gives the number of factors in an expression: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_5) % TODO: the term order has been changed. \begin{verbatim} Symbol x,y; Local F1 = x^4-y^4; Local F2 = 0; Local F3 = 1; Local F4 = x^4-y^4; Print; Factorize F1,F2,F3; .sort F1= (-1) *(y-x) *(y+x) *(y^2+x^2); F2=0; F3= (1); F4= -y^4+x^4; #do i = 1,4 #$n`i' = numfactors_(F`i'); #message expression F`i' has `$n`i'' factors ~~~expression F1 has 4 factors #enddo ~~~expression F2 has 1 factors ~~~expression F3 has 1 factors ~~~expression F4 has 0 factors .end \end{verbatim} As we see, an expression that is zero still gives one factor when it is factorized. When the expression is not factorized it will return 0 in all cases. The factors can be accessed easily once one knows that the factors are stored by means of the bracket mechanism and the n-th factor is the bracket with the n-th power of the symbol factor\_ outside the bracket: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_6) \begin{verbatim} Symbol x,y; Local F = x^4-y^4; Factorize F; .sort #$n = numfactors_(F); #do i = 1,`$n' Local F`i' = F[factor_^`i']; #enddo Print; .end F= (-1) *(y-x) *(y+x) *(y^2+x^2); F1= -1; F2= y-x; F3= y+x; F4= y^2+x^2; \end{verbatim} \noindent It is also possible to put an expression in the input in a factorized format. For this we have the LocalFactorized~\ref{substalfactorized} and GlobalFactorized~\ref{substagfactorized} commands. These commands can be abbreviated to LFactorized, GFactorized or even LF and GF\@. One should notice that these commands do not execute a factorization. They accept the factors as the user provides them: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_7) \begin{verbatim} Symbol x,y; LocalFactorize E = -(x+1)*(x+2)*((x+3)*(x+4)); Print; .end E = ( - 1 ) * ( 1 + x ) * ( 2 + x ) * ( 12 + 7*x + x^2 ); \end{verbatim} \noindent This can go to some extremes when we feed in expressions containing powers and expressions that are potentially already factorized: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_8) \begin{verbatim} Symbol x,y; LocalFactorize E = -(x+1)*(x+2)*((x+3)*(x+4)); Local F = -(x+1)*(x+2)*((x+3)*(x+4)); Print; .sort E= (-1) *(1+x) *(2+x) *(12+7*x+x^2); F= -24-50*x-35*x^2-10*x^3-x^4; LF G = (x-1)*(x+2)^2*E^2*F^2; Print G; .end G= (-1+x) *(2+x) *(2+x) *(-1) *(1+x) *(2+x) *(12+7*x+x^2) *(-1) *(1+x) *(2+x) *(12+7*x+x^2) *(-24-50*x-35*x^2-10*x^3-x^4) *(-24-50*x-35*x^2-10*x^3-x^4); \end{verbatim} \noindent To put some order in this one may factorize the new expression again: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_9) \begin{verbatim} Symbol x,y; LocalFactorize E = -(x+1)*(x+2)*((x+3)*(x+4)); Local F = -(x+1)*(x+2)*((x+3)*(x+4)); .sort LF G = (x-1)*(x+2)^2*E^2*F^2; Print G; Factorize G; .end G= (-1+x) *(1+x) *(1+x) *(1+x) *(1+x) *(2+x) *(2+x) *(2+x) *(2+x) *(2+x) *(2+x) *(3+x) *(3+x) *(3+x) *(3+x) *(4+x) *(4+x) *(4+x) *(4+x); \end{verbatim} \noindent In this case all constants are multiplied, all factors are factorized, and all factors in the new format are sorted. \noindent The case that one or more factors are zero is special. In principle the zero factors are kept as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_10) \begin{verbatim} Symbol x,y; LocalFactorize E = -0*(x+1)*(x+2)*0*((x+3)*(x+4)); Print; .end E= (-1) *(0) *(1+x) *(2+x) *(0) *(12+7*x+x^2); \end{verbatim} \noindent This way one can see what has happened when a substitution makes a factor zero. When we factorize this expression again however the whole expression becomes zero. If this is not intended and one would like to continue with the factors that are nonzero we have the keepzero option in the factorize statement as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_11) \begin{verbatim} Symbol x,y; Format Nospaces; LocalFactorize E = -0*3*(x+1)*(x+2)/2*0*((x+3)*(x+4)); Print; .sort E= (-1) *(0) *(3) *(1+x) *(2+x) *(1/2) *(0) *(12+7*x+x^2); Print; Factorize(keepzero) E; .end E= (0) *(-3/2) *(1+x) *(2+x) *(3+x) *(4+x); \end{verbatim} \noindent We see here that first all constants are separate factors and the new factorization combines them. The keepzero option does the same with the factors that are zero. The zero factor will always be the first. Hence it is rather easy to test for whether the total expression should actually be zero. We just have to look whether \verb:E[factor_]: is zero. \noindent The unfactorize~\ref{substaunfactorize} statement is the opposite of the factorize statement. It takes the factorized expression and multiplies out the factors. It also uses the current brackets for formatting the output. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_12) \begin{verbatim} Symbol x,y; LFactorized F = (x+1)*(x+y)*(y+1); Print; .sort F= (1+x) *(y+x) *(1+y); Print; Bracket x; UnFactorize F; .end F= +x*(1+2*y+y^2) +x^2*(1+y) +y+y^2; \end{verbatim} \noindent In principle there are various models by which the unfactorization can be done in an efficient way. In addition it would be less efficient when the master would do all the work as is the case with the factorize statement. Currently this statement is still being developed internally. It is possible to make ones own emulation of it. Here we give the `brute force' way: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_13) \begin{verbatim} Symbol x,y; LFactorized F = (x+1)*(x+y)*(y+1); Print; .sort F= (1+x) *(y+x) *(1+y); #$num = numfactors_(F); Local G = *...*; Bracket x; Print; .end F= (1+x) *(y+x) *(1+y); G= +x*(1+2*y+y^2) +x^2*(1+y) +y+y^2; \end{verbatim} \noindent Factorization of \$-expressions is yet a different thing. The \$-expressions do not have a bracket mechanism. Hence we need different ways of storing the factors. In the case of expressions we have to work in a way that is potentially disk based. With \$-expressions we work in allocated memory. Hence we also store the factors in allocated memory. In that case we can keep both the original and the factors. The factors are accessed by referring to their number between braces. The number zero refers to the number of factors: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_14) \begin{verbatim} Symbol x,y; CFunction f; Off Statistics; #$a = x^4-y^4; Local F = f(x^4-y^4)+f(x^6-y^6); Print; .sort F= f(-y^4+x^4)+f(-y^6+x^6); #factdollar $a; #do i = 1,`$a[0]' #write <> "Factor `i' of `$a' is `$a[`i']'" Factor 1 of -y^4+x^4 is -1 #enddo Factor 2 of -y^4+x^4 is y-x Factor 3 of -y^4+x^4 is y+x Factor 4 of -y^4+x^4 is y^2+x^2 id f(x?$b) = f(x); FactDollar $b; do $i = 1,$b[0]; Print "Factor %$ of %$ is %$",$i,$b,$b[$i]; enddo; Print; ModuleOption noparallel; * suppresses noparallel warning with TFORM .end Factor 1 of -y^4+x^4 is -1 Factor 2 of -y^4+x^4 is y-x Factor 3 of -y^4+x^4 is y+x Factor 4 of -y^4+x^4 is y^2+x^2 Factor 1 of -y^6+x^6 is -1 Factor 2 of -y^6+x^6 is y-x Factor 3 of -y^6+x^6 is y+x Factor 4 of -y^6+x^6 is y^2-x*y+x^2 Factor 5 of -y^6+x^6 is y^2+x*y+x^2 F= f(-y^4+x^4)+f(-y^6+x^6); \end{verbatim} \noindent We see here a variety of new features. The preprocessor can factorize \$a with the \#FactDollar instruction. We do indeed pick up the number of factors in the preprocessor as `\$a[0]' and the factors themselves as `\$a[1]' etc. For the \$-variable that needs to be manipulated during running time things as a bit more complicated. We define \$b as part of a wildcard pattern matching. This is still rather normal. Then we use the FactDollar statement. Notice that for each term we will have a different \$b. To access the factors we cannot use the preprocessor methods because those are only available at compile time. Hence we cannot use the preprocessor \#do instruction and therefore we need an execution time do statement. The loop parameter will have to be a \$-variable as well. The do statement and the print statement show now how one can use the factors. In the output one can see that indeed we had two different contents for \$b. And the arguments of the function f remain unaffected. \noindent One may also ask for the number of factors in a \$-expression with the numfactors\_ function as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_15) \begin{verbatim} Symbol x,y; CFunction f; Format Nospaces; #$a = x^4-y^4; #factdollar $a; Local F = f(numfactors_($a)) +f(<$a[1]>,...,<$a[`$a[0]']>); Print; .end F= f(-1,y-x,y+x,y^2+x^2)+f(4); \end{verbatim} \noindent Note that in the second case we need to use the construction `\$a[0]' because the preprocessor needs to substitute the number immediately in order to expand the triple dot operator. This cannot wait till execution time. \noindent Some remarks. \noindent The time needed for a factorization depends strongly on the number of variables used. For example factorization of $x^{60}-1$ is much faster than factorization of $x^{60}-y^{60}$. One could argue that the second formula can be converted into the first, but there is a limit to what \FORM{} should do and what the user should do. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_16) \begin{verbatim} Symbol x,y; Format NoSpaces; On ShortStats; Local F1 = x^60-1; Local F2 = y^60-x^60; Factorize F1,F2; Print; .end 0.00s 1> 2--> 2: 52 F1 0.07s 1> 51--> 51: 1524 F1 factorize 0.07s 1> 2--> 2: 64 F2 1.17s 1> 51--> 51: 1944 F2 factorize F1= (-1+x) *(1-x+x^2) *(1-x+x^2-x^3+x^4) *(1-x+x^3-x^4+x^5-x^7+x^8) *(1+x) *(1+x+x^2) *(1+x+x^2+x^3+x^4) *(1+x-x^3-x^4-x^5+x^7+x^8) *(1-x^2+x^4) *(1-x^2+x^4-x^6+x^8) *(1+x^2) *(1+x^2-x^6-x^8-x^10+x^14+x^16); F2= (y-x) *(y+x) *(y^2-x*y+x^2) *(y^4-x*y^3+x^2*y^2-x^3*y+x^4) *(y^4+x*y^3+x^2*y^2+x^3*y+x^4) *(y^2+x*y+x^2) *(y^2+x^2) *(y^8-x*y^7+x^3*y^5-x^4*y^4+x^5*y^3-x^7*y+x^8) *(y^8+x*y^7-x^3*y^5-x^4*y^4-x^5*y^3+x^7*y+x^8) *(y^8-x^2*y^6+x^4*y^4-x^6*y^2+x^8) *(y^4-x^2*y^2+x^4) *(y^16+x^2*y^14-x^6*y^10-x^8*y^8-x^10*y^6+x^14*y^2+x^16); \end{verbatim} \noindent When one has a factorized expression and one uses the multiply statement, all terms in the factorized expression are multiplied the specified amount. This may lead to a counterintuitive result: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_17) \begin{verbatim} Symbols a,b; LF F = (a+b)^2; multiply 2; Print; .end F = ( 2*b + 2*a ) * ( 2*b + 2*a ); \end{verbatim} This is a consequence of the way we store the factors. This way each factor will be multiplied by two. If one would like to add a factor one can do this by the following simple mechanism: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (PolyandFact_18) \begin{verbatim} Symbols a,b; LF F = (a+b)^2; .sort LF F = 2*F; Print; .end F = ( 2 ) * ( b + a ) * ( b + a ); \end{verbatim} \noindent In version 3 there were some experimental polynomial functions like polygcd\_\index{polygcd\_}\index{function!polygcd\_}. These have been removed as their functionality has been completely taken over by the new functions gcd\_~\ref{fungcd}, div\_~\ref{fundiv} and rem\_~\ref{funrem} and some statements like normalize~\ref{substanormalize}, makeinteger~\ref{substamakeinteger} and factarg~\ref{substafactarg}. Unlike regular functions, the functions gcd\_, div\_ and rem\_ have the peculiarity that if one of the arguments is just an expression or a \$-expression, this expression is not evaluated until the function is evaluated. This means that the evaluated expression does not have to fit inside the maximum size reserved for a single term. In some cases, when the gcd\_ function is invoked with many arguments, the expression may not have to be evaluated at all! The GCD of the other arguments may be one already. %\begin{verbatim} %\end{verbatim} %\begin{verbatim} %\end{verbatim} %\begin{verbatim} %\end{verbatim} form-5.0.1/doc/manual/metric.tex0000644000175100017510000002621615217035721012204 \chapter{A few notes on the use of a metric} \label{metric} \noindent When \FORM\ was designed, it was decided to make its syntax more or less independent of a choice of the metric\index{metric}. Hence statements and facilities that programs like Schoonschip\index{Schoonschip} or REDUCE\index{REDUCE} provide but which depend on the choice of a metric have been left out. Instead there are facilities to implement any choice of the metric, when the need really arises. When one makes a proper study of it, it turns out that one usually has to do very little or nothing. \hfill \vspace{2mm} \noindent First one should realize that \FORM\ does not know any specific metric by itself. Dotproducts are just objects of manipulation. It is assumed that when a common index of two vectors is contracted, this works out properly into a scalar object. This means that if one has a metric with upper and lower indices\index{indices!upper}\index{indices!lower}, one index is supposed to be an upper index and the other is supposed to be a lower index. If the user does not like this, it is his/her responsibility to force the system into a different action. This is reflected in the fact that \FORM\ does not have an internal metric tensor\index{tensor!metric} $\eta_{\mu\nu}$. It has only a Kronecker\index{Kronecker} delta\index{delta!Kronecker} $\delta_{\mu\nu} =$ \verb:d_(mu,nu): with \verb:p(mu)*d_(mu,nu)*q(nu): $\rightarrow$ \verb:p.q: when mu and nu are summable indices\index{indices!summable}. \hfill \vspace{2mm} \noindent The dependency of a metric usually enters with statements like $p^2 = \pm m^2$, which the user should provide anyway, because \FORM\ does not have such knowledge. Connected to this is the choice of a propagator\index{propagator} as either $\gamma_\mu p_\mu + m$ or $\gamma_\mu p_\mu + i\ m$. This is also something the user should provide. The only objects that \FORM\ recognizes and that could be considered as metric-dependent are the gamma matrices\index{matrices!gamma} and the Levi-Civita\index{Levi-Civita} tensor\index{tensor!Levi-Civita} \verb:e_:. Because the trace of a $\gamma_5$ involves a Levi-Civita tensor, the two are intimately connected. The anticommutator of two gamma matrices is defined with the Kronecker delta. Amazingly enough that works out well, provided that, if such Kronecker delta's survive in the output, they are interpreted as a metric tensor. This should be done with great care, because at such a point one does something that depends of the metric; one may have to select whether the indices are upper or lower indices. One should check carefully that the way the output is interpreted leads indeed to the results that are expected. This is anyway coupled to how one should interpret the input, because in such a case one would also have an input with `open' indices and give them a proper interpretation. The rule is that generally one does not have to do anything. The upper indices in the input will be upper indices in the output and the same for lower indices. \hfill \vspace{2mm} \noindent The contraction\index{contraction} of two Levi-Civita tensors will give products of Kronecker delta's. This means that formally there could be an error of the sign of the determinant of the metric tensor, if one would like the Kronecker delta to play the role of a metric tensor. Hence it is best to try to avoid such a situation. \hfill \vspace{2mm} \noindent In \FORM\ the $\gamma_5$ is an object that anticommutes with the $\gamma_\mu$ and has $\gamma_5\gamma_5 = 1$. Its properties in the trace are \begin{eqnarray} Tr[\gamma_5\gamma_{m_1}\gamma_{m_2}\gamma_{m_3}\gamma_{m_4}] & = & 4 \epsilon_{\mu_1\mu_2\mu_3\mu_4} \nonumber \end{eqnarray} This has a number of interesting consequences. The V-A and V+A currents are represented by $\gamma_7\gamma_\mu = (1-\gamma_5)\gamma_\mu$ and $\gamma_6\gamma_\mu = (1+\gamma_5)\gamma_\mu$ respectively. Under conjugation we have to replace $\gamma_5$ by $-\gamma_5$ as is not uncommon. \hfill \vspace{2mm} \noindent There was a time that a conjugation\index{conjugation} operation was planned in \FORM\@. As time progressed, it was realized that this would introduce problems with some of the internal objects. Hence some objects have the property that they are considered imaginary\index{imaginary}. In practise \FORM\ does not do anything with this. Neither does it do anything with the declarations real\index{real}, complex\index{complex} and imaginary\index{imaginary}. If ever a way is found to implement a conjugation operator that will make everybody happy, it may still be built in. \hfill \vspace{2mm} \noindent The above should give the user enough information to convert any specific metric to what is needed to make \FORM\ do what is expected from it. Afterwards one can convert back, provided no metric\index{metric} specific operations are done. Such metric specific things are for instance needed in some types of approximations in which one substitutes objects by (vector)components halfway the calculation. In that case one cannot rely on that the conversions at the beginning and the end will be compensating each other. For this case \FORM\ allows the user to define a private metric. All the tools exist to make this a success with the exception of a loss in speed of course. Let us have a look at the contraction of two Levi-Civita tensors in an arbitrary metric: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (NotesMetric_1) \begin{verbatim} Indices m1,m2,m3,n1,n2,n3,i1,i2,i3; Cfunction eta(symmetric),e(antisymmetric); Off Statistics; * * We have our own Levi-Civita tensor e * Local F = e(m1,m2,m3)*e(m1,m2,m3); * * We write the contraction as * id e(m1?,m2?,m3?)*e(n1?,n2?,n3?) = e_(m1,m2,m3)*e_(i1,i2,i3)* eta(n1,i1)*eta(n2,i2)*eta(n3,i3); * * Now we can use the internal workings of the contract: * Contract; Print +s; .sort F = + eta(i1,i1)*eta(i2,i2)*eta(i3,i3) - eta(i1,i1)*eta(i2,i3)^2 - eta(i1,i2)^2*eta(i3,i3) + 2*eta(i1,i2)*eta(i1,i3)*eta(i2,i3) - eta(i1,i3)^2*eta(i2,i2) ; * * For specifying a metric we need individual components: * Sum i1,1,2,3; Sum i2,1,2,3; Sum i3,1,2,3; Print +s; .sort F = + 6*eta(1,1)*eta(2,2)*eta(3,3) - 6*eta(1,1)*eta(2,3)^2 - 6*eta(1,2)^2*eta(3,3) + 12*eta(1,2)*eta(1,3)*eta(2,3) - 6*eta(1,3)^2*eta(2,2) ; * * And now we can provide the metric tensor * id eta(1,1) = 1; id eta(2,2) = 1; id eta(3,3) = -1; id eta(1,2) = 0; id eta(1,3) = 0; id eta(2,3) = 0; Print +s; .end F = - 6 ; \end{verbatim} This is the ultimate in flexibility\index{flexibility} of course. It can also be worked out in a different way. In this case we try to change the behaviour of the Kronecker\index{Kronecker} delta\index{delta!Kronecker} a bit. This is dangerous\index{dangerous} and needs, in addition to a good understanding of what is happening, good testing to make sure that what the user wants is indeed what does happen. Here we use the FixIndex\index{fixindex} (\ref{substafixindex}) statement. This one assigns specific values to selected diagonal elements of the Kronecker delta. Of course it is the responsibility of the user to make sure that the calculation will indeed run into those elements. This is by no means automatic, because when \FORM\ uses formal indices it never writes them out in components. Moreover, it would not be defined what would be the components connected to an index. The index could run over $0,1,2,3$ or over $1,2,3,4$, or maybe even over $5,7,9,11$. And what does an n-dimensional index run over? In the above example it is the sum (\ref{substasum}) statement that determines this. Hence this is fully under the control of the user. Therefore a proper way to deal with the above example would be % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (NotesMetric_2) \begin{verbatim} Indices i1,i2,i3; FixIndex 1:1,2:1,3:-1; Off Statistics; * Local F = e_(i1,i2,i3)*e_(i1,i2,i3); Sum i1,1,2,3; Sum i2,1,2,3; Sum i3,1,2,3; Print +s; .sort F = + 6*e_(1,2,3)*e_(1,2,3) ; Contract; Print +s; .end F = - 6 ; \end{verbatim} In the case that one would like to exchange the order of the summation and the contraction, while using the FixIndex mechanism, one needs to be more careful. In that case we have to prevent the indices from being summed over while they are indices of a Kronecker delta, because as long as the indices are symbolic, \FORM\ will replace \verb:d_(i1,i1): by the dimension of \verb:i1:, and that is not what we want. Hence we have to declare the indices to be non-summable by giving them dimension zero: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (NotesMetric_3) \begin{verbatim} Indices i1=0,i2=0,i3=0; FixIndex 1:1,2:1,3:-1; Off Statistics; * Local F = e_(i1,i2,i3)*e_(i1,i2,i3); Contract; Print +s; .sort F = + d_(i1,i1)*d_(i2,i2)*d_(i3,i3) - d_(i1,i1)*d_(i2,i3)*d_(i2,i3) - d_(i1,i2)*d_(i1,i2)*d_(i3,i3) + 2*d_(i1,i2)*d_(i1,i3)*d_(i2,i3) - d_(i1,i3)*d_(i1,i3)*d_(i2,i2) ; Sum i1,1,2,3; Sum i2,1,2,3; Sum i3,1,2,3; Print +s; .end F = - 6 ; \end{verbatim} As we can see, the automatic summation over the indices is not performed now and this gives us a chance to do the summation manually. After that the fixindex statement can have its effect. \hfill \vspace{2mm} \noindent It should be clear from the above examples that it is usually much easier to manipulate the input in such a way that the terms with two Levi-Civita tensors have the negative sign from the beginning. This would give programs that are less complicated and much faster. \hfill \vspace{2mm} \noindent Hence we are faced with the situation that in normal cases one does not do anything. If one wants to go beyond this and wants to interfere with the inner workings themselves by for instance inserting a factor $i$ in front of the $\gamma_5$ and emulating the upper and lower indices of a favorite metric, this leads from one problem to the next. Extreme care is needed. This is usually done by people who have first worked with other programs in which things don't work as naturally as in \FORM\@. By the time one has really figured out how to deal with the metric and how to make use of the internal algorithms of \FORM, one usually does not have to do very much again. \hfill \vspace{2mm} \noindent As in the Zen\index{Zen} saying: \hfill \vspace{2mm} \noindent To the beginning student mountains\index{mountains} are mountains and water\index{water} is water. To the advanced student\index{student} mountains stop being mountains and water stops being water. To the master\index{master} mountains are mountains again and water is water again. \hfill \vspace{2mm} \noindent Of course the modern master also checks that what he expects the system to do, is indeed what the system does. form-5.0.1/doc/manual/functions.tex0000644000175100017510000015165715217035721012741 \chapter{Functions} \label{functions} %--#[ General : \noindent Functions\index{function} are objects that can have arguments. There exist several types of functions in \FORM\@. First there is the distinction between commuting\index{commuting} and noncommuting\index{noncommuting} functions. Commuting functions commute with all other objects. This property is used by the normalization routines that bring terms into standard form. Noncommuting functions do not commute necessarily with other noncommuting functions. They do however commute with objects that are considered to be commuting, like symbols, vectors and commuting functions. Various instances of the same noncommuting function but with different arguments do not commute either. \noindent The next subdivision of the category of functions is in regular functions\index{function!regular}, tensors\index{tensor} and tables\index{table}. Tensors are special functions that can have only indices or vectors for their arguments. If an argument is a vector, it is assumed that this vector is there as the result of an index contraction. Tables are functions with automatic substitution rules. A table must have at least one table\index{table index} index\index{index!table}. Each time during normalization \FORM\ will check whether an instance of a table can be substituted. This means that undefined table elements will slow the program down somewhat. \noindent All the various types of functions are declared with their own declaration statements. These are described in the chapter for the statements (see chapter~\ref{statements}). %--#] General : %--#[ Wildcards : One of the useful properties of functions is the wildcarding\index{wildcard} of their arguments during pattern matching. The following argument wildcards are possible: \leftvitem{2cm}{x?} \rightvitem{14cm}{Here x is a symbol. This symbol can match either a symbol, any numerical argument, or a complete subexpression argument that is not vectorlike or indexlike.} \leftvitem{2cm}{i?} \rightvitem{14cm}{Here i is an index. This index can match either an index, a vector (actually the dummy\index{dummy} index\index{index!dummy} of the vector that was contracted), or a complete subexpression that is vector like (again actually the contracted dummy index).} \leftvitem{2cm}{v?} \rightvitem{14cm}{Here v is a vector. This vector can match either a vector or a complete subexpression that is vector like.} \leftvitem{2cm}{f?} \rightvitem{14cm}{Here f is any functiontype. This function can match any function. It is the responsibility of the user to avoid problems in the right-hand side if f happens to match a tensor.} \leftvitem{2cm}{?a} \rightvitem{14cm}{This is an argument\index{argument field} field wildcard\index{wildcard!argument field}. This can match a complete set of arguments. The set can be empty. Argument field wildcards have a name that starts with a question mark followed by a name. They do not have to be declared as there cannot be confusion.} %--#] Wildcards : \noindent In addition to the above syntax \FORM\ knows a number of special functions with well defined properties. All these functions have a name that ends in an underscore. In addition the names of these built in objects are case insensitive. This means for instance that the factorial function can be referred to as \verb:fac_:, \verb:Fac_: or \verb:FAC_: or whatever the user considers more readable. The built in functions are: %--#[ abs_ : \section{abs\_}\index{abs\_}\index{function!abs\_} \label{funabs} \noindent With one argument that is numerical it evaluates into the absolute value of the argument. %--#] abs_ : %--#[ bernoulli_ : \section{bernoulli\_}\index{bernoulli\_}\index{function!bernoulli\_} \label{funbernoulli} \noindent If it has one nonzero integer argument n, it evaluates into the n-th coefficient in the power series expansion of $x/(1-e^{-x})$. %--#] bernoulli_ : %--#[ binom_ : \section{binom\_}\index{binom\_}\index{function!binom\_} \label{funbinom} \noindent binom\_(n,i) $= n!/(i!(n-i)!)$. If the arguments are non integer or negative, no substitution is made. %--#] binom_ : %--#[ conjg_ : \section{conjg\_}\index{conjg\_}\index{function!conjg\_} \label{funconjg} \noindent Currently not doing anything. %--#] conjg_ : %--#[ content_ : \section{content\_}\index{content\_}\index{function!content\_} \label{funcontent} \noindent This function expects the name of a single expression or a dollar variable for its argument. If it finds this the content of this expression or dollar variable is returned. The content is defined as a term that has \begin{itemize} \item for its numerator the GCD of the numerators of all terms in the expression. \item for its denominator the LCM of the denominators of all terms in the expression. \item all the common subexpressions in all terms of the expression. \item the most negative powers of all symbols and dotproducts with negative powers in the terms of the expression. \end{itemize} When there are no negative powers and no denominators in the coefficients, this definition of the content co\"{\i}ncides with the classical definition of the content of a polynomial over the integers. Our content has the property that if we divide the expression by it, we are left with an expression of which the coefficients are all integer, there are no negative powers and the GCD of all terms combined is one. \noindent This function has one limitation. It will not consider noncommuting objects. Neither will it consider denominator functions. \noindent Caveat: this function is evaluated each time it is encountered. Therefore the best thing is to evaluate it once in the definition of a dollar variable or an expression as in \begin{verbatim} #$x = content_(F); Local G = (a+b)^10*$x; \end{verbatim} Here the content is computed only once. In \begin{verbatim} Local G = (a+b)^10*content_(F); \end{verbatim} 11 terms are generated and the content is only worked out when the terms are normalized. This means that it will be evaluated 11 times. If one does not like dollar variables and still wants to evaluate the content only once the code would be \begin{verbatim} Local G = ab^10*content_(F); id ab = a+b; \end{verbatim} because now the term will be normalized before the substitution makes it into eleven terms. This assumes of course that the content does not contain the variable ab. %--#] content_ : %--#[ count_ : \section{count\_}\index{count\_}\index{function!count\_} \label{funcount} \noindent Similar to the count object in the if statement (see \ref{substaif}). This function expects the same arguments as the count object and returns the corresponding count value for the current term. %--#] count_ : %--#[ d_ : \section{d\_}\index{d\_}\index{function!d\_} \label{fund} \noindent The kronecker\index{kronecker} delta\index{delta!kronecker}. Should have two indices for arguments. Often indicated as $\delta^{\mu\nu}$. In automatic summation over the indices the d\_ often vanishes again as in \verb:d_(mu,nu)*p(mu)*q(nu): $\rightarrow$ \verb:p.q: and similar replacements. Internally this object is treated in a rather special way. Hence it will not match a function wildcard. %--#] d_ : %--#[ dd_ : \section{dd\_}\index{dd\_}\index{function!dd\_} \label{fundd} \noindent This is a combinatorics\index{combinatorics} function. The tensor dd\_ with an even number of indices is equal to the totally symmetric tensor built up from products of kronecker delta's. Each term in this symmetric combination is normalized to one. In principle there are $n!/(2^{n/2}(n/2)!$ terms in this combination. The profit comes when some or all the indices are contracted with vectors and some of these vectors are identical. In that case \FORM\ will use combinatorics to generate only different terms, each with the proper prefactor. This can result in great time and space savings. %--#] dd_ : %--#[ delta_ : \section{delta\_}\index{delta\_}\index{function!delta\_} \label{fundelta} \noindent With one numerical argument the result is one if the argument is zero and zero otherwise. With two arguments the result is one if the arguments are numerical and identical. If they are numerical and they differ the result is zero. In all other cases nothing is done. %--#] delta_ : %--#[ deltap_ : \section{deltap\_}\index{deltap\_}\index{function!deltap\_} \label{fundeltap} \noindent If one argument and it is numerical the result is zero if the argument is zero and one otherwise. If two arguments, the result is zero if the arguments are numerical and identical. If they are numerical and they differ the result is one. In all other cases nothing is done. %--#] deltap_ : %--#[ denom_ : \section{denom\_}\index{denom\_}\index{function!denom\_} \label{fundenom} \noindent Internal function to describe denominators. Has a single argument. \verb:den(a+b): is printed as \verb:1/(a+b):. %--#] denom_ : %--#[ diagrams_ : % %\section{diagrams\_}\index{diagrams\_}\index{function!diagrams\_} %\label{fundiagrams} %\noindent For a description of this function, please see the section on %diagrams~\ref{diagrams}. % %--#] diagrams_ : %--#[ distrib_ : \section{distrib\_}\index{distrib\_}\index{function!distrib\_} \label{fundistrib} \noindent This is a combinatorics\index{combinatorics} function. It should have at least five arguments. If we have \begin{verbatim} distrib_(type,n,f1,f2,x1,...,xm) \end{verbatim} with type and n integers, f1 and f2 functions and then a number of arguments there can be action if $-2 \le$ type $\le 2$. The typical action is that the arguments \verb:x1,...,xm: will be divided over the two functions in all possible ways. For each possibility a new term is generated. The relative order of the arguments is kept. If type is negative it is assumed that the collection of x-arguments is antisymmetric\index{antisymmetric} and hence the number of permutations needed to make the split will determine whether there will be a minus sign on the resulting term. When type is zero all possible divisions are generated. Hence there will be $2^m$ divisions. The second argument is then not relevant. If type is 1 or -1 the second parameter says that the first function should obtain n arguments. The remaining arguments go to the second function. If type is 2 or -2 the second function should obtain n arguments. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_distrib_1) \begin{verbatim} Symbols x1,...,x4; CFunctions f,f1,f2; Local F = f(x1,...,x4); id f(?a) = distrib_(-1,2,f1,f2,?a); Print +s; .end F = + f1(x1,x2)*f2(x3,x4) - f1(x1,x3)*f2(x2,x4) + f1(x1,x4)*f2(x2,x3) + f1(x2,x3)*f2(x1,x4) - f1(x2,x4)*f2(x1,x3) + f1(x3,x4)*f2(x1,x2) ; \end{verbatim} When adjacent x-arguments are identical \FORM\ uses combinatorics to avoid generating more terms than necessary. %--#] distrib_ : %--#[ div_ : \section{div\_}\index{div\_}\index{function!div\_} \label{fundiv} \noindent \verb:div_(x1,x2): is replaced by the quotient of the arguments. The arguments can be any valid subexpressions, provided the whole function fits inside a term. When an argument is only an active expression or a \$-expression it is only expanded during the division. This way the contents of such expressions can exceed the maximum term size. One should however realize that in that case the operation takes place in allocated memory. This function replaces the experimental function polydiv\_\index{polydiv\_}\index{function!polydiv\_} that existed in version 3. %--#] div_ : %--#[ dum_ : \section{dum\_}\index{dum\_}\index{function!dum\_} \label{fundum} \noindent Special function for printing virtual\index{virtual bracket} brackets\index{bracket}. \verb:dum_(a+b): is printed as \verb:(a+b):: the name of this function is not printed! %--#] dum_ : %--#[ dummy_ : \section{dummy\_}\index{dummy\_}\index{function!dummy\_} \label{fundummy} \noindent For internal use only. %--#] dummy_ : %--#[ dummyten_ : \section{dummyten\_}\index{dummyten\_}\index{function!dummyten\_} \label{fundummyten} \noindent For internal use only. %--#] dummyten_ : %--#[ e_ : \section{e\_}\index{e\_}\index{function!e\_} \label{fune} \noindent The Levi-Civita\index{Levi-Civita tensor} tensor\index{tensor!Levi-Civita}. It is a totally antisymmetric\index{antisymmetric} tensor with well defined contraction rules (see \ref{substacontract}). %--#] e_ : %--#[ edge_ : % %\section{edge\_}\index{edge\_}\index{function!edge\_} %\label{funedge} %\noindent For a description of this function, please see the section on %diagrams~\ref{diagrams}. % %--#] edge_ : %--#[ exp_ : \section{exp\_}\index{exp\_}\index{function!exp\_} \label{funexp} \noindent Internal function with two arguments. Represents argument1 to the power argument2. Of course it is printed in the standard power notation. %--#] exp_ : %--#[ exteuclidean_ : \section{exteuclidean\_}\index{exteuclidean\_}\index{function!exteuclidean\_} \label{funexteuclidean} \noindent This is a number function. It expects two positive integer arguments. It then computes the Greatest Common Divider of these arguments with the use of the extended Euclidean algorithm. The answer will be in the same function but now there will be four arguments as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_exteuclidean_1) \begin{verbatim} Symbols x1,x2,x3,x4; Local F = exteuclidean_(54,84); Print; .sort F = exteuclidean_(54,84,-3,2); id exteuclidean_(x1?,x2?,x3?,x4?) = x1*x3+x2*x4; Print; .end F = 6; \end{verbatim} \noindent We can see that we obtain the GCD with the relation that is characteristic for the extended Euclidean algorithm. When the two arguments are relative prime, one obtains the so-called modinverses of these numbers: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_exteuclidean_2) \begin{verbatim} Symbols x1,x2,x3,x4,a,b; Local F = exteuclidean_(97,101); Print; .sort F = exteuclidean_(97,101,25,-24); id exteuclidean_(x1?,x2?,x3?,x4?) = x1*x3+x2*x4 +a*mod2_(1/97,101)+b*mod2_(1/101,97); Print; .end F = 1 - 24*b + 25*a; \end{verbatim} \noindent Here 25 is the inverse of 97 when we calculate modulus 101 and -24 is the inverse of 101 when we calculate modulus 97. \noindent This function can be very handy when a calculation has been done modulus various prime numbers and one would like to know the result modulus the product of these numbers. This combination is done with the aid of the Chinese remainder theorem\index{Chinese remainder theorem}: \begin{verbatim} #procedure ChineseRemainder(NAME,NAME1,NAME2,M1,M2,PAR) * * Assumes that NAME1 is an expression mod $M1 * Assumes that NAME2 is an expression mod $M2 * Creates $ch1r and $ch2r with the property that * the expression NAME = NAME1*$ch1r+NAME2*$ch2rn * is the corresponding equation mod $M1*$M2 * Modulus 0; * we need to switch off previous settings. #$ch1r = exteuclidean_($`M1',$`M2'); #inside $ch1r; id exteuclidean_(xxx1?,xxx2?,xxx3?,xxx4?) = xxx2*xxx4; #endinside; #$ch2r = exteuclidean_($`M1',$`M2'); #inside $ch2r; id exteuclidean_(xxx1?,xxx2?,xxx3?,xxx4?) = xxx1*xxx3; #endinside; #$MM12 = $`M1'*$`M2'; Modulus,plusmin,`$MM12'; Local `NAME' = `NAME1i'*$ch1r+`NAME2i'*$ch2r; .sort * #endprocedure \end{verbatim} %--#] exteuclidean_ : %--#[ extrasymbol_ : \section{extrasymbol\_}\index{extrasymbol\_}\index{function!extrasymbol\_} \label{funextrasymbol} \noindent This function expects a single argument. This argument can be a number or an extra symbol(see \ref{extrasymbols}). In either case the function is replaced by the expression that the corresponding extra symbol stands for. \noindent If there are more arguments or the argument does not represent a legal extra symbol, no substitution is made. %--#] extrasymbol_ : %--#[ fac_ : \section{fac\_}\index{fac\_}\index{function!fac\_} \label{funfac} \noindent The factorial\index{factorial} function. If it has a single nonzero integer argument n it is replaced by n! but if the result is bigger than the maximum allowable number an error will result. %--#] fac_ : %--#[ factorin_ : \section{factorin\_}\index{factorin\_}\index{function!factorin\_} \label{funfactorin} \noindent When the argument is a single \$-variable\index{\$-variable} or an expression\index{expression} the function is replaced by the common factor in the terms of that \verb:$:-variable or expression. This common factor consists in the first place of all symbolic objects that occur in all terms. In addition the numerical factor consists of the GCD\index{GCD} of all numerators and the LCM\index{LCM} of all denominators. Hence if the \verb:$:-variable or expression is divided by the result of factorin\_ all coefficients become integer. %--#] factorin_ : %--#[ farg_ : \section{farg\_}\index{farg\_}\index{function!farg\_} \label{funfarg} \noindent For internal use only. %--#] farg_ : %--#[ firstbracket_ : \section{firstbracket\_}\index{firstbracket\_}\index{function!firstbracket\_} \label{funfirstbracket} \noindent In the case that there is a single argument and this single argument is the name of an expression, this function is replaced by the part that is outside brackets in the first term of the expression. If there are no brackets the function is replaced by one. %--#] firstbracket_ : %--#[ firstterm_ : \section{firstterm\_}\index{firstterm\_}\index{function!firstterm\_} \label{funfirstterm} \noindent This function expects the name of an expression or a dollar variable for its (single) argument. It will return the first term in this expression or dollar variable. When it has to obtain the first term of an expression, \FORM{} uses the expression in the representation in which it was stored at the end of the previous module. If the expression did not exist in the previous module, it will attempt to use the expression as defined and processed in the current expression. If the expression has only been defined in the current module and has not yet been processed (as is the case when referring to the first term in the current expression) the answer will be unspecified. This use is considered illegal, even though it does not generate an error message. %--#] firstterm_ : %--#[ float_ : \section{float\_}\index{float\_}\index{function!float\_} \label{funfloat} \noindent Internal function to describe floating point numbers. For a description, of this function, see chapter~\ref{floatingpoint} on the floating point system. %--#] float_ : %--#[ g5_ : \section{g5\_}\index{g5\_}\index{function!g5\_} \label{fungfive} \noindent The $\gamma_5$ Dirac gamma matrix. We assume here that it anticommutes with the other Dirac\index{Dirac} gamma\index{gamma matrices} matrices. Anybody who does not like that should program private libraries (this should not be too difficult with the cycle symmetric functions (see~\ref{substafunctions}). There should be a single index to indicate the spinline. %--#] g5_ : %--#[ g6_ : \section{g6\_}\index{g6\_}\index{function!g6\_} \label{fungsix} \noindent There should be a single index to indicate the spinline. As in Schoonschip\index{Schoonschip} we use $\gamma_6 = 1+\gamma_5$. %--#] g6_ : %--#[ g7_ : \section{g7\_}\index{g7\_}\index{function!g7\_} \label{fungseven} \noindent There should be a single index to indicate the spinline. As in Schoonschip\index{Schoonschip} we use $\gamma_7 = 1-\gamma_5$. %--#] g7_ : %--#[ g_ : \section{g\_}\index{g\_}\index{function!g\_} \label{fung} \noindent The Dirac\index{Dirac} gamma\index{gamma matrices} matrix. Its first argument should be an index (either symbolic or numeric). Then follow zero, one or more indices to indicate a string of gamma matrices that belong together. Gamma matrices with the same first index are considered to belong together, but as long as the indices are symbolic no assumptions are made about whether they go together or not. Hence no commutation or anticommutation properties are applied for different spin lines unless the spinline indices are both numeric. %--#] g_ : %--#[ gcd_ : \section{gcd\_}\index{gcd\_}\index{function!gcd\_} \label{fungcd} \noindent \verb:gcd_(x1,...,xn): is replaced by the greatest common divisor of the arguments. The arguments can be any valid subexpressions, provided the whole function fits inside a term. When an argument is only an active expression or a \$-expression it is only expanded during evaluation of the GCD\@. This way the contents of such expressions can exceed the maximum term size. One should however realize that in that case the operation takes place in allocated memory. This function replaces the experimental function polygcd\_\index{polygcd\_}\index{function!polygcd\_} that existed in version 3. %--#] gcd_ : %--#[ gi_ : \section{gi\_}\index{gi\_}\index{function!gi\_} \label{fungi} \noindent The unit Dirac gamma matrix. Should have a single index to indicate its spin line. Its is identical to a regular gamma matrix with no Lorenz indices: \verb:gi_(n) = g_(n): %--#] gi_ : %--#[ id_ : \section{id\_}\index{id\_}\index{function!id\_} \label{funid} \noindent This function is a crossbreed between the replace\_\index{replace\_}~\ref{funreplace} function and the id statement\index{substaidentify}~\ref{substaidentify}. To become active it needs an even number of arguments. The odd numbered arguments can be anything of the types: \begin{description} \item[] a single symbol, possibly to an integer power. \item[] a single dotproducts, possibly to an integer power. \item[] a single function, possibly with any number and type of arguments. \end{description} When \FORM{} encounters an id\_ function the last step of normalizing a term is to replace the id function by a number substitutions in which the odd arguments are replaced by the following even arguments. These are not wildcard substitutions as in the replace\_ function, but substitutions as in regular id statements. The matching of the odd arguments is done in a single step as in an id-al construction~\ref{substaalso}. Hence \begin{verbatim} id_(x^2,y+z,y,u+v,x,z+u) \end{verbatim} effectively becomes \begin{verbatim} id x^2 = y+z; al y = u+v; al x = z+u; \end{verbatim} \FORM{} treats multiple occurrences of the id\_ function one at a time. It takes the leftmost occurrence first, takes the patterns from the term, expands the right hand sides, tries to normalize the resulting terms and only then continues with the next id\_ function. For this reason the id\_ function is noncommuting. %--#] id_ : %--#[ integer_ : \section{integer\_}\index{integer\_}\index{function!integer\_} \label{funinteger} \noindent This is a rounding\index{rounding} function. It should have either one or two arguments. If there is a single argument and it is numeric, it will be rounded down to become an integer. If there are two arguments of which the first is numeric and the second is either 1, 0 or -1, the result will be the rounded value of the first argument. If the second argument is 1, the rounding will be down, when it is -1, the rounding will be up and when it is zero the rounding will be towards zero. In all other cases nothing is done. %--#] integer_ : %--#[ inverse_ : \section{inverse\_}\index{inverse\_}\index{function!inverse\_} \label{funinverse} \noindent \verb:inverse_(x1,x2): expects two arguments which are polynomials in the same single variable. The return expression $x_3$ has the property that $x_1 x_3$ divided by $x_2$ has remainder 1. Or in other words: $x_3$ is the inverse of $x_1$ modulus $x_2$. The arguments can be any valid subexpressions, provided the whole function fits inside a term. When an argument is an active expression or a \$-expression it is only expanded during the division. This way the contents of such expressions can exceed the maximum term size. One should however realize that in that case the operation takes place in allocated memory. %--#] inverse_ : %--#[ invfac_ : \section{invfac\_}\index{invfac\_}\index{function!invfac\_} \label{funinvfac} \noindent One divided by the factorial\index{factorial} function. If it has a single nonzero integer argument n, it is replaced by 1/n!, but if this results in a number bigger than the maximum allowable number an error will result. %--#] invfac_ : %--#[ makerational_ : \section{makerational\_}\index{makerational\_}\index{function!makerational\_} \label{funmakerational} \noindent This function takes two arguments. Both are integers. We assume calculus modulus the second argument. The function is then replaced by a fraction of which both elements are less than the square root of the second argument and that, in calculus modulus this second number would give the same result as the first number modulus the second number. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_makerational_1) \begin{verbatim} #$m = prime_(1); #write <> "The prime number is %$",$m The prime number is 2147483587 L F = MakeRational_(12345678,$m); Print; .sort F = 9719/38790; Modulus `$m'; Print; .end F = 12345678; \end{verbatim} \noindent This function can be used to reconstruct fractions when calculus has been done modulus one or more prime numbers. %--#] makerational_ : %--#[ match_ : \section{match\_}\index{match\_}\index{function!match\_} \label{funmatch} \noindent Currently not active. Replaced automatically by 1. %--#] match_ : %--#[ max_ : \section{max\_}\index{max\_}\index{function!max\_} \label{funmax} \noindent If all its arguments are numeric, this function returns the maximum value of these arguments. %--#] max_ : %--#[ maxpowerof_ : \section{maxpowerof\_}\index{maxpowerof\_}\index{function!maxpowerof\_} \label{funmaxpowerof} \noindent If this function has a single argument that is a symbol, it returns the maximum power restriction of this symbol. If none was given it will be the installation dependent value MAXPOWER which is 10000 on 32\index{32 bits} bit machines and 500000000 on 64\index{64 bits} bit machines. %--#] maxpowerof_ : %--#[ min_ : \section{min\_}\index{min\_}\index{function!min\_} \label{funmin} \noindent If all its arguments are numeric, this function returns the minimum value of these arguments. %--#] min_ : %--#[ minpowerof_ : \section{minpowerof\_}\index{minpowerof\_}\index{function!minpowerof\_} \label{funminpowerof} \noindent If this function has a single argument that is a symbol, it returns the minimum power restriction of this symbol. If none was given it will be the installation dependent value -MAXPOWER which is -10000 on 32 bit machines. %--#] minpowerof_ : %--#[ mod_ : \section{mod\_}\index{mod\_}\index{function!mod\_} \label{funmod} \noindent If there are two integer arguments and the second argument is a positive short integer (less than $2^{15}$ on 32 bit computers and less than $2^{31}$ on 64 bit computers) the return value is the first argument modulus the second. Note that if the second argument is not a prime number and the first argument contains a denominator, division by zero could occur. It is up to the user to avoid such cases. See also the mod2\_ function~\ref{funmod2} and the rem\_ function~\ref{funrem}. The function has one peculiarity: when the second argument is one, the function is left untouched. %--#] mod_ : %--#[ mod2_ : \section{mod2\_}\index{mod2\_}\index{function!mod2\_} \label{funmod2} \noindent This gives basically the same action as the mod\_ function (see \ref{funmod}), but the answer will be in the range $-[(p-1)/2]$ to $+[(p+1)/2]$. %--#] mod2_ : %--#[ moebius_ : \section{moebius\_}\index{moebius\_}\index{function!moebius\_} \label{funmoebius} \noindent The Moebius function. It has the property: \begin{itemize} \item moebius\_(1) = 1 \item moebius\_(n) = 0 if n can be divided by the square of a prime number \item moebius\_(n) = 1 if n contains an even number of different prime factors \item moebius\_(n) = -1 if n contains an odd number of different prime factors \end{itemize} The number n must be a positive integer for the evaluation to take place. The argument should be no bigger than can be allowed by the biggest primes in Form. This means for a 64-bit computer arguments above $2^{31}$ may not give a correct result with the current algorithms that try for prime factors. There is a second algorithm that does not suffer from this problem: \begin{verbatim} id moebius_(n) = 1-sum_(j,1,n-1,integer_(n/j)*moebius_(j)); \end{verbatim} but this algorithm needs all lower values and hence is inherently quadratic. Therefore we did not use it. %--#] moebius_ : %--#[ mul_ : \section{mul\_}\index{mul\_}\index{function!mul\_} \label{funmul} \noindent \verb|mul_(x,y)| is replaced by \verb|x*y|, but internally the multiplication is performed via polynomial routines introduced in \FORM{} version 4. This can be faster than the normal way of multiplications for big polynomials: e.g., \verb|mul_($x,$y)| where the \$-variables \verb|$x| and \verb|$y| store big polynomials. A drawback is, because the polynomial routines accept only symbols, all non-symbolic objects in the operands are temporarily translated to (commuting) extra symbols. This process breaks the ordering of non-commutative objects in the result. %--#] mul_ : %--#[ nargs_ : \section{nargs\_}\index{nargs\_}\index{function!nargs\_} \label{funnargs} \noindent Is replaced by an integer indicating the number of arguments that the function has. %--#] nargs_ : %--#[ node_ : \section{node\_}\index{topologies\_}\index{function!node\_} \label{funtonode} \noindent For a description of this function, please see the section on diagrams~\ref{diagrams}. %--#] node_ : %--#[ nterms_ : \section{nterms\_}\index{nterms\_}\index{function!nterms\_} \label{funnterms} \noindent If this function has only one argument it is replaced by the number of terms inside this argument. %--#] nterms_ : %--#[ numfactors_ : \section{numfactors\_}\index{numfactors\_}\index{function!numfactors\_} \label{funnumfactors} \noindent This function returns the number of factors in a factorized expression (see the chapter on polynomials~\ref{polynomials}) or dollar variable~\ref{dollars}. It expects a single argument which should be the name of an expression or a dollar variable. If the expression or dollar variable has not been factorized, the function returns zero. %--#] numfactors_ : %--#[ partitions_ : \section{partitions\_}\index{partitions\_}\index{function!partitions\_} \label{funpartitions} \noindent This function generates all partitions of a list of arguments into $n$ parts. Each part consists of a function name and a size. This function exploits symmetries of the arguments to make sure that no argument is generated twice. Instead, a combinatorial prefactor is computed. The syntax distinguishes three cases: \begin{verbatim} 1] partitions_(n,[function,n1,]_1,...,[function,nn,]_n,arguments) 2] partitions_(n,[function,n1,]_1,...,[function,0],arguments) 3] partitions_(0,function,n1,arguments) \end{verbatim} In the first case, the first entry specifies the number of partitions $n$. It should be followed by $n$ parts, defined by a function name and the number of arguments for that function. The final entries are the arguments that will be distributed over the functions. The number of arguments should be the same as the sum of all the function argument sizes. There are no restrictions on the type of arguments. The second case is the same as the first, except that the last partition has a 0 for the size. This means that any leftover arguments are collected in this term. Thus \path{partitions_(2,f1,3,f2,0,arguments)} yields the same as \texttt{distrib\_(1,3,f1,f2,arguments)}. The third case, determined by a 0 for the number of partitions followed by one part, spreads the arguments over a repeated instance of that part. Thus \path{partitions_(0,f1,2,arguments)} is similar to \texttt{dd\_(arguments)}. In case of a deviation from the above rules, no action will be taken. Some examples are given below: \begin{verbatim} partitions_(2,f1,2,f2,1,x1,x1,x3) = + f1(x1,x1)*f2(x3) + 2*f1(x1,x3)*f2(x1) ; partitions_(3,f1,2,f2,1,f3,0,x1,x1,x1,x2,x2,x2) = + 3*f1(x1,x1)*f2(x1)*f3(x2,x2,x2) + 9*f1(x1,x1)*f2(x2)*f3(x1,x2,x2) + 18*f1(x1,x2)*f2(x1)*f3(x1,x2,x2) + 18*f1(x1,x2)*f2(x2)*f3(x1,x1,x2) + 9*f1(x2,x2)*f2(x1)*f3(x1,x1,x2) + 3*f1(x2,x2)*f2(x2)*f3(x1,x1,x1) ; partitions_(0,f1,3,x1,x1,x1,x4,x5,x6) = + f1(x1,x1,x1)*f1(x4,x5,x6) + 3*f1(x1,x1,x4)*f1(x1,x5,x6) + 3*f1(x1,x1,x5)*f1(x1,x4,x6) + 3*f1(x1,x1,x6)*f1(x1,x4,x5) ; \end{verbatim} %--#] partitions_ : %--#[ pattern_ : \section{pattern\_}\index{pattern\_}\index{function!pattern\_} \label{funpattern} \noindent Currently not active. Replaced automatically by 1. %--#] pattern_ : %--#[ perm_ : \section{perm\_}\index{perm\_}\index{function!perm\_} \label{funperm} \noindent Generates all permutations of the arguments, with exception of the first argument which should be the name of a function. This function will then have the permuted arguments as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_perm_1) \begin{verbatim} CFunction f; Symbols x1,...,x3; Local F = perm_(f,x1,x2,x3); Print +s; .end F = + f(x1,x2,x3) + f(x1,x3,x2) + f(x2,x1,x3) + f(x2,x3,x1) + f(x3,x1,x2) + f(x3,x2,x1) ; \end{verbatim} The permutations are generated with an algorithm that takes subsequent cyclic permutations. If one puts a nonzero integer before the function argument the output terms will be multiplied by -1 when the permutation is odd. When the function name is the only argument the answer will be just this function without arguments. One could argue that technically the answer should be zero, but this way the attention of the user may be attracted to the occurrence which might not be the case when the term 'just vanishes'. It is however rather simple to add a statement that makes such a function zero. %--#] perm_ : %--#[ poly_ : \section{poly\_}\index{poly\_}\index{function!poly\_} \label{funpoly} \noindent This was an experimental function in version 3. It was for internal use with a whole category of other experimental functions of which the functionality has been replaced by better working functions that are more general. This category included the functions polyadd\_\index{polyadd\_}\index{function!polyadd\_}, polydiv\_\index{polydiv\_}\index{function!polydiv\_}, polygcd\_\index{polygcd\_}\index{function!polygcd\_}, polyintfac\_\index{polyintfac\_}\index{function!polyintfac\_}, polymul\_\index{polymul\_}\index{function!polymul\_}, polynorm\_\index{polynorm\_}\index{function!polynorm\_}, polyrem\_\index{polyrem\_}\index{function!polyrem\_} and polysub\_\index{polysub\_}\index{function!polysub\_}. See also the chapter on polynomials~\ref{polynomials} and the functions gcd\_~\ref{fungcd}, div\_~\ref{fundiv} and rem\_~\ref{funrem}. %--#] poly_ : %--#[ prime_ : \section{prime\_}\index{prime\_}\index{function!prime\_} \label{funprime} \noindent For a number of internal operations \FORM{} needs prime numbers that are neither very large nor very small. Hence it generates, when needed prime numbers that still fit inside a single \FORM{} word, but are maximal within that limitation. Hence for a 64-bits computer in which the largest positive `small' integer in \FORM{} is $2^{31}-1$, it works its way down from there. Once it has determined that a number is prime it stores it in a list. The function prime\_ gives access to this list. The single argument n (n a positive integer) makes that \verb:prime_(n): will be replaced by the n-th member of the list. There is a limitation to the size of the list which is implementation dependent. The number will anyway never be smaller than the maximum power that is allowed for symbols. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_prime_1) \begin{verbatim} Symbols x1,x2,x3,x4; ON highfirst; Local F = x1*prime_(1)+x2*prime_(2) +x3*prime_(3)+x4*prime_(4); Print; .end F = 2147483587*x1 + 2147483579*x2 + 2147483563*x3 + 2147483549*x4; \end{verbatim} This function is useful when calculations generate very large intermediate coefficients, but in the end the answer is relatively simple again. In that case one can do the calculation modulus one or more prime numbers. If more prime numbers are used the Chinese remainder theorem\index{Chinese remainder theorem} can be used (see the exteuclidean\_ function~\ref{funexteuclidean} to combine the results and the makerational\_ function~\ref{funmakerational} can be used if fractions have to be reconstructed). An example of this kind of use is given in the simple Groebner basis procedure that is in the packages library in the \FORM{} site. %--#] prime_ : %--#[ putfirst_ : \section{putfirst\_}\index{putfirst\_}\index{function!putfirst\_} \label{funputfirst} \noindent This function allows one to select a given argument by its number. The syntax is: \begin{verbatim} putfirst_(name,argument_number,arguments...); \end{verbatim} It will select the argument indicated by ``argument\_number'' in the argument field ``arguments'' and output this as the first argument in the function or tensor specified by ``name''. This argument will then be followed by the remaining arguments. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_putfirst_1) \begin{verbatim} S a,a1,...,a10; CF f,g; L F = g(a,a1,...,a10); id g(?a) = putfirst_(f,4,?a); Print; .end F = f(a3,a,a1,a2,a4,a5,a6,a7,a8,a9,a10); \end{verbatim} %--#] putfirst_ : %--#[ random_ : \section{random\_}\index{random\_}\index{function!random\_} \label{funrandom} \noindent A random number generator. When the function has a single positive integer argument, the function will return a pseudo random number in the range of one to that number inclusive. Hence one can imitate a die roll with the call random\_(6). The program uses a random number generator as described in vol 2 of the "Art of computer programming, vol2" by D. Knuth with the parameters set at 89,38 to give as long a cycle as possible. For very large numbers the program pastes several random numbers together. The generator can be initialized with the preprocessor \#setrandom~\ref{presetrandom}\index{\#setrandom} instruction. When running with \TFORM{} or \ParFORM{} each worker runs an independent generator with its own seed. The seeds of the workers are derived from the seed of the master and the number of the worker in a non-trivial way. It should be noted however that with workers it may be impossible to reproduce previous runs as it is non-deterministic which term ends up in which worker. %--#] random_ : %--#[ ranperm_ : \section{ranperm\_}\index{ranperm\_}\index{function!ranperm\_} \label{funranperm} \noindent Generates a random permutation of the arguments, with exception of the first argument which should be the name of a function. This function will then have the permuted arguments as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_ranperm_1) \begin{verbatim} CFunction f; Symbols x1,...,x5; Local F = ranperm_(f,1,2,3,4,5,6) +ranperm_(f,x1,x2,x3+x1,x4,x5); Print +s; .end F = + f(x5,x1,x3 + x1,x4,x2) + f(3,1,6,2,4,5) ; \end{verbatim} The permutation is generated with the same random number generator that is used by the function random\_~\ref{funrandom}\index{random}\index{function!random\_} and hence is susceptible to the same initialization procedure that can be executed with the \#setrandom~\ref{presetrandom}\index{setrandom} instruction. %--#] ranperm_ : %--#[ rem_ : \section{rem\_}\index{rem\_}\index{function!rem\_} \label{funrem} \noindent \verb:rem_(x1,x2): is replaced by the remainder of the division of $x_1$ by $x_2$. The arguments can be any valid subexpressions, provided the whole function fits inside a term. When an argument is only an active expression or a \$-expression it is only expanded during the division. This way the contents of such expressions can exceed the maximum term size. One should however realize that in that case the operation takes place in allocated memory. This function replaces the experimental function polyrem\_\index{polyrem\_}\index{function!polyrem\_} that existed in version 3. %--#] rem_ : %--#[ replace_ : \section{replace\_}\index{replace\_}\index{function!replace\_} \label{funreplace} \noindent This function defines a rather general purpose replacement\index{replacement} mechanism. It should have pairs of arguments. Each pair consists of a single symbol, index, vector or function, followed by what this object should be replaced by in the entire term. Functions can only be replaced by functions, indices only by indices. A vector can be replaced by a single vector or by a vector like expression. A symbol can be replaced by a single symbol, a numerical expression or a complete subexpression that is not index like or vector like. This mechanism is sometimes needed to make replacements in ways that are very hard with the id\index{id} statements because those do not make replacements automatically inside function arguments (see \ref{substaidnew}). It also allows to exchange two variables as the replacements are executed simultaneously by the wildcard substitution mechanism. \begin{verbatim} Multiply replace_(x,y,y,x); \end{verbatim} will exchange x and y. Because there is no definite order in which multiple replace\_ functions are treated, one should not use more than a single one at the same time inside a term. At times multiple replace\_ functions may lead to confusion inside \FORM\@. %--#] replace_ : %--#[ reverse_ : \section{reverse\_}\index{reverse\_}\index{function!reverse\_} \label{funreverse} \noindent Can only occur as an argument of a function. Is replaced by the reversed string of its own arguments. %--#] reverse_ : %--#[ root_ : \section{root\_}\index{root\_}\index{function!root\_} \label{funroot} \noindent If we have \verb:root_(n,x): and \verb:n: is a positive integer and \verb:x: is a rational number and \verb:y: is a rational number with $y^n = x$ (no imaginary numbers are considered and negative numbers are avoided if possible. Only one root is given) then \verb:root_(n,x): is replaced by \verb:y:. This function was originally intended for internal use. Do not hold it against the author that \verb:root_(2,1): is replaced by \verb:1:. In the case that it is needed the user should manipulate the sign or the complexity properties externally. %--#] root_ : %--#[ setfun_ : \section{setfun\_}\index{setfun\_}\index{function!setfun\_} \label{funsetfun} \noindent Currently not active. %--#] setfun_ : %--#[ sig_ : \section{sig\_}\index{sig\_}\index{function!sig\_} \label{funsig} \noindent Is replaced by the sign of the (numerical) argument, i.e.\ by -1 if there is a single negative argument and by +1 if there is a single numerical argument that is greater or equal to zero. %--#] sig_ : %--#[ sign_ : \section{sign\_}\index{sign\_}\index{function!sign\_} \label{funsign} \noindent \verb:sign_(n): is replaced by \verb:(-1)^n: if n is an integer. %--#] sign_ : %--#[ sizeof_ : \section{sizeof\_}\index{sizeof\_}\index{function!sizeof\_} \label{funsizeof} \noindent If there is a single argument and this argument is the name of an active (or previously active during the current job) expression, the function is replaced by the number\index{number of \FORM{} words} of \FORM{} words in this expression. Stored expressions that were entered via a load statement (see \ref{substaload}) are excluded from this because for them this information is not readily available. %--#] sizeof_ : %--#[ sum_ : \section{sum\_}\index{sum\_}\index{function!sum\_} \label{funsum} \noindent General purpose sum\index{sum} function. The first argument should be the summation parameter (a symbol). The second argument is the starting point of summation, the third argument the `upper' limit and a potential fourth argument the increment. These numbers should all be integers. Summation stops when the summation parameter obtains a value that has passed the upper limit. The last argument is the summand, the object to be summed over. It can be any subexpression. If it contains the summation parameter, it will be replaced by its value for each generated term. Examples: \begin{verbatim} sum_(j,1,4,sign_(j)*x^j/j) sum_(i,1,9,2,sign_((i-1)/2)*x^i*invfac_(i)) \end{verbatim} %--#] sum_ : %--#[ sump_ : \section{sump\_}\index{sump\_}\index{function!sump\_} \label{funsump} \noindent Special sum function. Its arguments are like for the sum\_ function, but each new term is the product of the previously generated term with the last argument in which the current value of the summation parameter has been substituted. The first term is always one. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Fun_sump_1) \begin{verbatim} Symbol i,x; Local F = sump_(i,0,5,x/i); Print; .end F = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5; \end{verbatim} This function is a leftover from the Schoonschip\index{Schoonschip} days. The ordinary sum\_ function is much more readable. %--#] sump_ : %--#[ table_ : \section{table\_}\index{table\_}\index{function!table\_} \label{funtable} \noindent For action the arguments should be the name of a table and then either the name of a function or one symbol for each dimension of the table. In the case of the list of symbols the return value will be a monomial in the given symbols in which the powers of the symbols correspond to the table indices of the defined table elements with the coefficients the table contents corresponding to those indices. In the case of a function name the return value will be a sum over terms in which the table elements are indicated by arguments in the given function while these functions are then multiplied by the corresponding table elements. This is one way to put a complete table inside an expression and store it (with the save statement of \ref{substasave}) in a binary way for a future run in which the table can be filled again with the fillexpression\index{fillexpression} (see \ref{substafillexpression}) statement. Note that for obvious reasons one should avoid using symbols or functions that also occur inside the table definitions. %--#] table_ : %--#[ tbl_ : \section{tbl\_}\index{tbl\_}\index{function!tbl\_} \label{funtbl} \noindent This function is the `table stub function' as used by the tablebase\index{tablebase} construction. This is explained in chapter \ref{tablebase}. It is mainly for internal use, but it could occur in the output. %--#] tbl_ : %--#[ term_ : \section{term\_}\index{term\_}\index{function!term\_} \label{funterm} \noindent This function has no arguments. It is replaced by the current term. It can be used to load the current term into a dollar variable as in \begin{verbatim} $x = term_; \end{verbatim} %--#] term_ : %--#[ termsin_ : \section{termsin\_}\index{termsin\_}\index{function!termsin\_} \label{funtermsin} \noindent If there is a single argument and this argument is the name of an active (or previously active during the current job) expression, the function is replaced by the number\index{number of terms} of terms in this expression. Stored expressions that were entered via a load statement (see \ref{substaload}) are excluded from this because for them \FORM\ would have to actually count the terms. %--#] termsin_ : %--#[ termsinbracket_ : \section{termsinbracket\_}\index{termsinbracket\_}\index{function!termsinbracket\_} \label{funtermsinbracket} \noindent If there is no argument, or the single argument is zero, the function is replaced by the number of terms in the current bracket\index{bracket}, provided the expression has been bracketed at its last sort and a keep brackets statement (see \ref{substakeep}) has been used. Note that the terms have to be counted. Hence this is a relatively expensive command. More options will be implemented in the future. %--#] termsinbracket_ : %--#[ theta_ : \section{theta\_}\index{theta\_}\index{function!theta\_} \label{funtheta} \noindent If there is a single numerical argument x the function is replaced by one if $x \ge 0$ and by zero if $x < 0$. If there are two numerical arguments $x_1$ and $x_2$ the function is replaced by one if $x_1 = x_2$ or if the arguments are in natural order (if theta\_ would be a symmetric function there would be no reason to exchange the arguments) and by zero if the arguments are not in natural order (they would be exchanged in a symmetric function). In all other cases nothing is done. %--#] theta_ : %--#[ thetap_ : \section{thetap\_}\index{thetap\_}\index{function!thetap\_} \label{funthetap} \noindent If there is a single numerical argument x the function is replaced by one if $x > 0$ and by zero if $x \le 0$. If there are two numerical arguments $x_1$ and $x_2$ the function is replaced by zero if $x_1 = x_2$ or if the arguments are not in natural order. If the arguments are in natural order the function is replaced by one. In all other cases nothing is done. %--#] thetap_ : %--#[ tofloat_ : \section{tofloat\_}\index{tofloat\_}\index{function!tofloat\_} \label{funtofloat} \noindent Currently not active. %--#] tofloat_ : %--#[ topologies_ : \section{topologies\_}\index{topologies\_}\index{function!topologies\_} \label{funtopologies} \noindent For a description of this function, please see the section on diagrams~\ref{diagrams}. %--#] topologies_ : %--#[ torat_ : \section{torat\_}\index{torat\_}\index{function!torat\_} \label{funtorat} \noindent Currently not active. %--#] torat_ : %--#[ Reserved names : \section{Extra reserved names} \noindent In addition there are reserved function names for the common mathematical functions. Since \FORM{} 5.0, these functions can be evaluated numerically. See also chapter~\ref{floatingpoint} on the floating point system. These functions are: \leftvitem{3cm}{sqrt\_}\index{sqrt\_}\index{function!sqrt\_} \rightvitem{13cm}{The regular square root.} \leftvitem{3cm}{ln\_}\index{ln\_}\index{function!ln\_} \rightvitem{13cm}{The natural logarithm.} \leftvitem{3cm}{eexp\_}\index{eexp\_}\index{function!exp\_} \rightvitem{13cm}{The exponential function.} \leftvitem{3cm}{gamma\_}\index{gamma\_}\index{function!gamma\_} \rightvitem{13cm}{The gamma function.} \leftvitem{3cm}{agm\_}\index{agm\_}\index{function!agm\_} \rightvitem{13cm}{The arithmetic-geometric mean function.} \leftvitem{3cm}{sin\_}\index{sin\_}\index{function!sin\_} \rightvitem{13cm}{The sine function.} \leftvitem{3cm}{cos\_}\index{cos\_}\index{function!cos\_} \rightvitem{13cm}{The cosine function.} \leftvitem{3cm}{tan\_}\index{tan\_}\index{function!tan\_} \rightvitem{13cm}{The tangent function.} \leftvitem{3cm}{asin\_}\index{asin\_}\index{function!asin\_} \rightvitem{13cm}{The inverse of the sine function.} \leftvitem{3cm}{acos\_}\index{acos\_}\index{function!acos\_} \rightvitem{13cm}{The inverse of the cosine function.} \leftvitem{3cm}{atan\_}\index{atan\_}\index{function!atan\_} \rightvitem{13cm}{The inverse of the tangent function.} \leftvitem{3cm}{atan2\_}\index{atan2\_}\index{function!atan2\_} \rightvitem{13cm}{Another inverse of the tangent function.} \leftvitem{3cm}{sinh\_}\index{sinh\_}\index{function!sinh\_} \rightvitem{13cm}{The hyperbolic sine function.} \leftvitem{3cm}{cosh\_}\index{cosh\_}\index{function!cosh\_} \rightvitem{13cm}{The hyperbolic cosine function.} \leftvitem{3cm}{tanh\_}\index{tanh\_}\index{function!tanh\_} \rightvitem{13cm}{The hyperbolic tangent function.} \leftvitem{3cm}{asinh\_}\index{asinh\_}\index{function!asinh\_} \rightvitem{13cm}{The inverse of the hyperbolic sine function.} \leftvitem{3cm}{acosh\_}\index{acosh\_}\index{function!acosh\_} \rightvitem{13cm}{The inverse of the hyperbolic cosine function.} \leftvitem{3cm}{atanh\_}\index{atanh\_}\index{function!atanh\_} \rightvitem{13cm}{The inverse of the hyperbolic tangent function.} \leftvitem{3cm}{li2\_}\index{li2\_}\index{function!li2\_} \rightvitem{13cm}{The dilogarithm function.} \leftvitem{3cm}{mzv\_}\index{mzv\_}\index{function!mzv\_} \rightvitem{13cm}{The multiple zeta values.} \leftvitem{3cm}{euler\_}\index{euler\_}\index{function!euler\_} \rightvitem{13cm}{The Euler sums.} \leftvitem{3cm}{mzvhalf\_}\index{mzvhalf\_}\index{function!mzvhalf\_} \rightvitem{13cm}{The harmonic polylogarithms of argument 1/2.} \noindent In addition there are some names that have been reserved for future use. \leftvitem{3cm}{lin\_}\index{lin\_}\index{function!lin\_} \rightvitem{13cm}{The polylogarithm function.} \leftvitem{3cm}{hpl\_}\index{hpl\_}\index{function!hpl\_} \rightvitem{13cm}{The harmonic polylogarithm function.} \leftvitem{3cm}{mpl\_}\index{mpl\_}\index{function!mpl\_} \rightvitem{13cm}{The multiple polylogarithm function.} \noindent The user is allowed to use these functions, but it could be that in the future they will develop a nontrivial behaviour. Hence caution is required. %--#] Reserved names : form-5.0.1/doc/manual/variable.tex0000644000175100017510000013170615217035721012507 \chapter{Variables} \label{ch-variables} The objects of symbolic manipulations are expressions\index{expression}. Expressions are built up from terms\index{terms} and terms are composed of variables. {\FORM} knows several types of variables, each of which has special rules assigned to it. The types of variables are symbols, vectors, indices, functions, sets, and expressions. In addition there are tensors and tables which are special functions, preprocessor variables\index{variables!preprocessor} (see chapter~\ref{preprocessor}), and there are dollar variables\index{variables!dollar} (see chapter~\ref{dollars}). The expressions are used either in the definition of an expression or in the right hand side of an expression or a substitution. When an expression is used in the right hand side of another expression or a substitution, it will be replaced by its contents at the first opportunity. Therefore an expression will never occur as a variable in the output of other expressions and we will ignore their potential presence in the remainder of this chapter. Similarly preprocessor variables and dollar variables will be replaced immediately when they are encountered. The right hand side of an expression can consist of symbols, vectors, indices, functions and elements of a set. All these objects have to be declared before they can be used. The rules connected to each of these types of variables are described in the sections below. \section{Names} There are two types of names\index{names}. Regular names\index{names!definition} consist of alphabetic and numeric characters with the condition that the first character must be alphabetic. {\FORM} is case sensitive with respect to names. In addition there are {\bf formal names}. These names start with the character \verb:[: and end with a matching character \verb:]:. In between there can be any characters that are not intercepted by the preprocessor. This allows the use of variables like \verb:[x+a]:. Using formal names can improve the readability of programs very much, while at the same time giving the user the benefits of the greater speed. The use of denominators\index{denominators} that are composite (like \verb:1/(x+a):) is usually rather costly in time. Often \verb:1/[x+a]: is equally readable, while leading to the same results. Note however that the variable \verb:[x+a]: will have to be declared properly. On the other hand: {\FORM} may not have to know about x and a. These formal names can also be used for the names of expressions, but they are not valid for the names of dollar variables and the names of preprocessor variables\index{variables!preprocessor}. Some names may contain special characters. All built in objects have for their last character an underscore\index{underscore} (\_). Dotproducts\index{dotproducts} (the scalar product of two vectors) consist of two vectors separated either by a period or by a dollar sign. The dollar sign is used by {\FORM}, when the output of the program has to be Fortran\index{fortran} compatible. The user can replace the dollar sign in the output by an arbitrary character by defining the variable "DotChar"\index{dotchar} in the setup\index{setup file} file. How this is done is explained in chapter~\ref{setup}. In the input the user may apply either the notation with the period or the notation with the dollar. It is however recommended to use the period\index{period} because in future versions the notation with the dollar may be dropped. The above conventions avoid the possibility of conflicts with reserved names, allowing the user full freedom when choosing names. The dollar sign is also used as the first character in the name of dollar variables\index{variables!dollar}. The rest of the name should consist of alphanumeric characters of which the first should be alphabetic. The names of preprocessor variables\index{variables!preprocessor} should also consist of alphanumeric characters of which the first should be alphabetic. Also here the ones that are defined by the system have a trailing underscore\index{underscore} (\_) character. With respect to the user defined names {\FORM} is case sensitive. This means that the variables a and A are different objects. With respect to system defined objects {\FORM} is case insensitive. Hence both d\_ and D\_ indicate the same Kronecker delta. In many languages the use of the underscore\index{underscore} (\_) character is also permitted in the definition of user defined names. In {\FORM} this is NOT the case. Even though the earlier manuals `forbade' this specifically there was a bug in earlier versions that permitted it to some degree. And because people don't read manuals, there were those who used this character and even made it into a vital part of their naming conventions. This then broke when version 3 was introduced. It should be clear though that the underscore character is reserved for a completely different type of future use and hence nothing can be done about this. Just remember: it is never a good idea to use undocumented features without consulting with the development team first. The complex conjugate\index{conjugate!complex} of a complex quantity is indicated by the character \verb:#: appended to the name of the variable. In the current version of {\FORM} not much is done with it. The latest approach is that it is seen as obsolete. If possible, please avoid using it. The length of names\index{names!length} is not restricted in {\FORM}. There is one exception to this rule: names of expressions cannot be longer than 16 characters. Of course in practise there are physical limits on the size of names, posed by the size of the memory of the computer being used. \section{Symbols} \label{sect-symbols} Symbols\index{symbols} are plain objects that behave most like normal variables in hand manipulations. Many hand manipulations concern polynomial formulae of simple algebraic variables. {\FORM} assumes that symbols commute with all other objects and have a power connected to them. This power is limited to an installation dependent maximum and minimum. A power outside this range will lead to an error message. The user may override this built in restriction by one of private design that is more restrictive. Any power that falls outside the user defined range leads to the removal of the term that contains the variable with this power. Such a power restriction can be defined for each symbol separately. Symbols can also have complex conjugation\index{conjugation!complex} properties. A symbol can be declared to be real, imaginary or complex. This property is only relevant, when the complex conjugation operator is used. This operator has not been implemented and currently there are no plans to do so. The syntax of the statement that defines symbols is given by (see also \ref{substasymbols}): \begin{verbatim} S[ymbols] name[#{R|I|C}][(min:max)]; \end{verbatim} Each variable is declared by the presence of its name in a symbol-statement. If the \# symbol is appended, it should be followed by either the character C, I or R to indicate whether the variable is complex\index{complex}, imaginary\index{imaginary} or real\index{real}. The \#R is not really necessary, as the type `real' is the default. It is not relevant whether the C, I, R are in upper or in lower case. A power restriction\index{restriction!power} is indicated with a range between regular parentheses. If one of the two numbers is not present, the default value is taken. This default value is installation dependent, but it is at least -10000 and 10000 respectively. Each symbol-statement can define more than one variable. In that case the variables have to be separated either by comma's or by blanks. Example: \begin{verbatim} S x,y,z,a#c,b#c,c#c,r(-5:5),s(:20),t#i(6:9); \end{verbatim} In this statement x, y and z are normal real algebraic variables. The variables a, b and c are complex. This means that for each of these variables two entries are reserved in the property lists: one for the variable and one for its complex conjugate. The variable r has a power restriction: Any power outside the specified range will cause the term containing this power to be eliminated. This is particularly useful in power series expansions. The restrictions on s are such that there is no limitation on the minimum power of s --with the exception of the built in restrictions-- but a term with a power of s that is larger than 20 is eliminated. The variable t is imaginary. This means that under complex conjugation it changes sign. Its power restrictions are somewhat uncommon. Any power outside the range 6 to 9 is eliminated. There is however one exception: a term that does not contain t to any power ($t^0$) is not affected. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Symbols_1) \begin{verbatim} s x(:10),y; L F=y^7; id y=x+x^2; print; .end Time = 0.01 sec Generated terms = 4 F Terms in output = 4 Bytes used = 54 F = x^7 + 7*x^8 + 21*x^9 + 35*x^10; \end{verbatim} Note that all terms with a power greater than 10 do not even count as generated terms. They are intercepted immediately after the replacement, before any possible additional statements can be carried out. There are several built in symbols\index{symbols!built in}. They are: \noindent i\_\index{i\_}: it is defined by \verb:i_^2 = -1: and this property is used by {\FORM} to simplify terms. It is the only symbol that cannot be used as a dimension or a wildcard. \noindent pi\_\index{pi\_}: a reserved variable which indicates the constant $\pi$. \noindent ee\_\index{ee\_}: a reserved variable which indicates the basis of the natural logarithm $e$. \noindent em\_\index{em\_}: a reserved variable which indicates the Euler-Mascheroni constant $\gamma_{\mathrm{E}}$. \noindent coeff\_\index{coeff\_}: this variable is automatically replaced by the coefficient of the current term. \noindent num\_\index{num\_}: this variable is automatically replaced by the numerator of the coefficient of the current term. \noindent den\_\index{den\_}: this variable is automatically replaced by the denominator of the coefficient of the current term. \noindent extrasymbols\_\index{extrasymbols\_}: this symbol represents the number of extra symbols (see \ref{sect-extrasymbols}). \section{Vectors} \label{sect-vectors} A vector\index{vectors} is an object with a single index\index{index}. This index represents a number that indicates which component of the vector is meant. Vectors have a dimension\index{dimension} connected to them which is the dimension of the vector space in which they are defined. In {\FORM} this dimension is by default set to 4. If the user likes to change this default, this can be done with the `Dimension'-statement. The use of this command affects the dimension of all vectors and the default dimension of indices. Its syntax is (see also \ref{substadimension}): \begin{verbatim} Dimension number; \end{verbatim} or \begin{verbatim} Dimension symbol; \end{verbatim} The number must be a number that fits inside a {\FORM} word which is an installation dependent size, but it will be at least 32767. The number must be positive or zero. Negative values are illegal. If a symbol is specified, it must have been declared before. Any symbol may be used with the exception of i\_\index{i\_}. The declaration of vectors (see \ref{substavectors}) is rather straightforward: \begin{verbatim} V[ector] name [,MoreNames]; \end{verbatim} The names of the vectors may be separated either by comma's or by blanks. Example: \begin{verbatim} V p,q; I mu,nu; L F=p(mu)*q(nu); \end{verbatim} \section{Indices} \label{sect-indices} Indices\index{indices}\index{index} are objects that represent a number that is used as an integer argument for counting purposes. They are used mostly as the arguments of vectors or multidimensional arrays (or tensors). Their main property is that they have a dimension\index{dimension}. This dimension indicates what values the index can take. A four-dimensional index can usually take the values 1 to 4. A very important property of an index is found in the convention that it is assumed that an index that is used twice in the same term is summed over. This is called the Einstein\index{Einstein} summation\index{summation!Einstein} convention. Hence the term p(mu)$*$q(mu) is equivalent to the scalar product of the vectors p and q (which can also be written as p.q). There are of course also indices that should not be summed over. Such indices we call zero-dimensional. This is just a convention. To declare indices we use the statement (see also \ref{substaindex}): \begin{verbatim} Index name[={number|symbol}] [,othername[={number|symbol}]]; \end{verbatim} When the equals sign is used, this indicates the specification of a dimension. Indices that are not followed by an equals sign get the dimension that is currently the default dimension (see also \ref{substadimension})). The dimension can be either a number that is zero or positive (zero indicates that the summation convention does not apply for this index) or it can be any symbol with the exception of the symbol i\_. The symbol must have been declared before. The most important use of the dimension of an index is the built in rule that a Kronecker\index{Kronecker} delta\index{delta!Kronecker} with twice the same index is replaced by the dimension of this index, provided this index has a non-zero dimension. Therefore when mu is 4-dimensional, d\_(mu, mu) will be replaced by 4 and when nu is n-dimensional, d\_(nu,nu) will be replaced by n. If rho is zero dimensional, the expression d\_(rho,rho) is left untouched. In addition to the symbolic indices there is a number of fixed indices\index{indices!fixed} with a numeric\index{indices!numeric} value. The values of these indices runs from zero to an installation dependent number (usually 127). Users who like a different maximum value should consult chapter~\ref{setup} about the setup parameters. The numeric indices are all assumed to have dimension zero, hence no summation is applied to them. This means that they can be used for vector components. It is therefore perfectly legal to use: \begin{verbatim} V p,q,r; L F=p(1)*q(1)*r(1)+p(2)*q(2)*r(2); \end{verbatim} When two numeric indices occur inside the same Kronecker delta, a value is substituted for this delta. Normally this value is one, when the two indices are identical and zero, when they are different. The value for the diagonal elements can be changed with the `FixIndex'-statement (see also \ref{substafixindex}): \begin{verbatim} Fi[xIndex] number:value [,number:value]; \end{verbatim} This command assigns to d\_(number,number) the given value. This value must fit inside a single {\FORM} word. This means that this value can at least be in the range -32768 to +32767. For more details on the size of a {\FORM} word one should consult the installation manual. In the case of summable indices\index{indices!summable} the use of three times the same index in the same term would cause problems. {\FORM} will execute the contraction for the first pair it encounters, after which the third index is left. In the case of four or more indices the pairing for the contractions depends on the order in which the parts of the term are processed. Hence to the user the result may seem to be quasi random. Nothing can be done about this and the user should guard against such ambiguous notation\index{notation!ambiguous}. There is a special version of the index declarations that is used for traces\index{traces} of gamma\index{gamma matrices} matrices\index{matrices!gamma} in n dimensions. If an index is declared with \begin{verbatim} Symbols n,epsilon; Index m=n:epsilon; \end{verbatim} its dimension will be n and it is assumed that epsilon can be used for $(n-4)$ during the taking of the trace of a string of gamma matrices. It is also possible to use this notation in the dimension-statement. See also chapter~\ref{gammaalgebra} on the gamma matrices. \section{Functions} \label{sect-functions} There are two classes of functions\index{functions}: {\bf commuting functions} which commute automatically with all other objects, and {\bf non-commuting functions} which do not necessarily commute with other non-commuting functions. An object is declared to be a commuting\index{commuting} function\index{function!commuting} with the `cfunction' command. Of this command the first two characters are mandatory, the others optional. An object is declared to be a non-commuting\index{non-commuting} function\index{function!non-commuting} with the `function' command. Here only the f is mandatory. The declaration of a function knows one option. This option concerns the complexity properties of the function. It is indicated by a \# following the name, after which one of the characters R, I, C specifies whether the function is real\index{real}, imaginary\index{imaginary} or complex\index{complex}. The declaration that a function is real is unnecessary as `real' is the default property. Example: \begin{verbatim} CF fa,fb,fc; F ga,gb,gc#c; \end{verbatim} In this example the functions fa, fb, fc are commuting and the functions ga, gb and gc are not necessarily commuting. In addition the function gc is complex. More about functions and their conventions is explained in chapter~\ref{functions}. Within the commutation classes there are several types of special functions. Currently these are tensors\index{tensors} and tables\index{tables}. The tables are described in section~\ref{substatable} and in chapter~\ref{tablebase}. Tensors\index{tensors} are special functions. Their arguments can be indices and vectors only. When an argument is a vector, it is assumed that this vector has been put in this position as the result of an Einstein\index{Einstein} summation\index{summation!Einstein}, i.e., there used to be an index in this position, but the index was contracted with the index of the vector. Hence {\FORM} assumes that there is a linearity property with respect to such vectors. Tensors are declared with one of the following statements (see also pages~\ref{substatensors}, \ref{substantensors}, \ref{substactensors}): \begin{verbatim} T[ensors] t1; CT[ensors] t2; NT[ensors] t3; \end{verbatim} The type `ntensor' indicates a non-commuting tensor, while the other two types indicate commuting tensors. Note that the 'T' is a commuting tensor, while the 'F' indicates a non-commuting function. In addition to the above declarations one may add the same complexity properties that can be added for functions. This is currently not very useful though as there exists no complex conjugation operator yet. Internally a tensor is a function with special properties. Hence when function properties are discussed, usually these properties refer also to tensors, unless the type of the arguments would not allow the operations or arguments specified. \section{Sets} \label{sect-sets} A set\index{sets} is a (non-empty) collection of variables that should all be of the same type. This type can be symbols, vectors, indices or functions. A set has a name which can be used to refer to it, and this name may not coincide with any of the other names in the program. A set is declared by giving its name, followed by a colon\index{colon}, after which the elements of the set are listed. The first element determines the type of all the elements of the set. All elements must have been declared as variables before the set-statement. There can be only one set per statement. Example (see also \ref{substaset}): \begin{verbatim} s xa, xb, xc, xd, ya, x, y; i mu, nu, rho; set exxes: xa, xb, xc, xd; set yyy: xc, xd, xb, ya; set indi: mu, nu, rho, 1, 2, 3; set xandy: xa, ya; \end{verbatim} We see here that a single symbol (xa) can belong to more than one set. Also the fixed indices (1, 2 and 3) can be elements of a set of indices and the numbers that can be powers can also be members of a set of symbols (usually -9999 to + 9999). If this can cause confusion, {\FORM} will give a warning and interpret the set as a set of symbols. In addition to the user defined sets there are some built in sets with a special meaning. These are: \begin{description} \item[int\_]\index{int\_} This is a set of symbols. It refers to all integer numbers that fit inside a {\FORM} word. \item[pos\_]\index{pos\_} This is a set of symbols. They are the positive integers that fit inside a {\FORM} word. \item[pos0\_]\index{pos0\_} A set of symbols. They are all non-negative integers that fit inside a {\FORM} word. \item[neg\_]\index{neg\_} A set of symbols. They are all negative integers that fit inside a {\FORM} word. \item[neg0\_]\index{neg0\_} A set of symbols. They are all non-positive integers that fit inside a {\FORM} word. \item[symbol\_]\index{symbol\_} The set of all formal symbols. It excludes integers, numbers and whole function arguments. \item[fixed\_]\index{fixed\_} The set of all fixed indices. \item[index\_]\index{index\_} The set of all indices. \item[vector\_]\index{index\_} The set of all (auto)declared vectors. \item[number\_]\index{number\_} The set of all rational numbers. \item[even\_]\index{even\_} This is a set of symbols. It refers to all even integer numbers that fit inside a {\FORM} word. \item[odd\_]\index{odd\_} This is a set of symbols. It refers to all odd integer numbers that fit inside a {\FORM} word. \item[dummyindices\_]\index{dummyindices\_} This is a set of indices. It refers to all indices of the type Nm\_? (m a positive integer) that were obtained by summing over indices with a sum statement\index{sum} \ref{substasum}. \end{description} Sets can be used during wildcarding\index{wildcarding}. When x is a symbol, the notation x? indicates `any symbol'. This is sometimes more than we want. In the case that we would like `any symbol that belongs to the set exxes' we would write x?exxes which is an unique notation as usually the question mark cannot be followed by a name. There should be no blank between the question mark and the name of the set. The object x?indi would result in a type mismatch error, if x is a symbol and indi a set of indices. This use of wildcards belonging to sets can be extended even more: The notation x?exxes?yyy means that x should belong to the set exxes, and its replacement should be the corresponding element of set yyy. At first this notation looks unnecessarily complicated. The statement \begin{verbatim} id x?exxes?yyy = x; \end{verbatim} should have the much simpler syntax \begin{verbatim} id exxes = yyy; \end{verbatim} This last notation cannot be maintained, when the patterns are more complicated, hence it has been omitted altogether. When things become really complicated\index{complicated}, the sets can be used as kind of an array. They can be used with a fixed array index (running from 1 for the first element). When they have a symbolic argument (must be a symbol), they are either in the right hand side of an id-statement and the symbol must be replaced by a number by means of a wildcard substitution or in the left hand side and the symbol is automatically seen as a wildcard. The set must still follow the question mark of a wildcard. An example will clarify the above: \begin{verbatim} s a1,a2,a3,b1,b2,b3,x,n; f g1,g2,g3,g; set aa:a1,a2,a3; set bb:b1,b2,b3; set gg:g1,g2,g3; id g(x?aa[n]) = gg[n](bb[n]) + bb[2]*n; \end{verbatim} The n in the left hand side is automatically a symbol wildcard. x must match an element in aa and n takes its number. In the right hand side \verb:gg[n]: becomes an array element, when the n is substituted. The same holds for \verb:bb[n]:. The element \verb:bb[2]: is immediately replaced by b2, so there is rarely profit by using this, unless the preprocessor had something to do with the construction of this quantity. As should be clear from the above: the array elements are indicated with straight braces\index{braces}. Another use of sets is in the select option\index{option!select} of the id-statement. This is discussed in chapter~\ref{pattern} on pattern\index{pattern matching} matching. Neither the array properties of the sets nor the select option of the id-statement can be used in conjunction with the built in sets. These sets are not supposed to have a finite number of indices. Apart from the above sets that were formally declared and used by name there is a second way to use sets. These sets are called {\bf implicitly declared sets\index{sets!implicitly declared}}. They are declared at the position that they are used and their use defines their contents. The elements of the set should be enclosed by a pair of curly brackets\index{brackets!curly} and the set is placed at the position where otherwise the name of the set would be used: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Sets_1) \begin{verbatim} Symbols a1,a2,a3,b1,b2,b3,x,n; CFunctions g1,g2,g3,g; Local expr = g(a1)+g(a2)+g(a3)+g(x); id,g(x?{a1,a2,a3}[n]) = {g1,g2,g3}[n]({b1,b2,b3}[n]); print; .end expr = g1(b1) + g2(b2) + g3(b3) + g(x); \end{verbatim} Such a set exists internally only till the end of the module in which it is used. It can be used at all positions where named sets can be used. Hence they can also be used, when the array properties of sets are considered. The preprocessor has to be able to distinguish these sets from strings for its calculator\index{calculator!preprocessor} (see chapter~\ref{preprocessor}). Usually this is no problem, because any regular name contains at least one character that is not accepted by this calculator. If the only elements in the set are numeric the comma\index{comma} will tell the preprocessor that it is a set and the calculator should not be used. This leaves the case of a set with a single numeric element. By placing a comma either before or after it the use of the calculator is vetoed. For the interpretation of the set this makes no difference. When it is possible to demand an object to be inside a set\index{set!inside}, it should also be possible to demand that an object be outside a set\index{set!outside}. This is done with the `?!' operator instead of the `?' operator. The extra exclamation\index{exclamation} mark is like a `not' operator. It can be used only, when its use makes sense. Hence it cannot be used in conjunction with the array properties of sets and together with the select option of the id-statement. So its only use is in patterns of the type \begin{verbatim} x?!setname x?!{a,b,c} \end{verbatim} as is done in \begin{verbatim} id x^n?!{,-1} = x^(n+1)/(n+1); \end{verbatim} There is a variation of the second type that is not possible with named sets\index{sets!named}: \begin{verbatim} Symbols a,b,x,y,z; CFunction f; id f(x?!{a,y?,z?})*f(y?!{b,x?,z?})*f(z?!{x?,y?}) = ......... \end{verbatim} In this complicated pattern the z is easiest: It is not allowed to be equal to the objects that will be substituted for the wildcards x and y. The symbol x cannot be equal to the wildcards y and z, but in addition it should not be equal to a. A similar condition holds for y. One could argue that at least one of these conditions is superfluous from the strictly logical viewpoint. It depends however on the order of the declarations in how {\FORM} runs through the pattern, so it would require some trying to see which `not' specifications are superfluous. If for instance the first function is matched first, there is still no assignment for z. This means that the z? in the set cannot be used yet and hence it places no restrictions on x. Therefore it is the x? in the last function that causes x and z to be different. If on the other hand the last function would be matched first, we need the z? in the set of the first function. From the strict logical viewpoint, {\FORM} could go back over the pattern and still make the appropriate rejections, but this would cost too much extra time. As one can see, it is safer to specify both. \section{The autodeclare conventions} As we have seen above, all variables that are introduced by the user have to be declared. As such {\FORM} is a strong\index{strong typing} typing language. This isn't always handy. Hence it is possible to introduce some rules about the automatic declaration of classes of variables. This is done with the AutoDeclare\index{autodeclare} statement (see also \ref{substaautodeclare}). If we use the statements \begin{verbatim} AutoDeclare Symbol x,tt; AutoDeclare CFunction f,t; \end{verbatim} any object encountered by the compiler of which the name starts with the character x will automatically be declared as a symbol. Also objects of which the name starts with the characters tt will be declared as symbols. Objects of which the name starts with the characters f or t, but not with the string tt, and that have not yet been declared will be declared automatically as commuting functions. As one can see, in the case of potential conflicts\index{conflicts} (like with t and tt) the more restrictive one takes precedence. This is independent of the order of the AutoDeclare statements. One disadvantage of the use of the AutoDeclare statement is that one looses a certain amount of control over the order of declaration of the variables, as now they will be declared in the order in which they occur in the statements. The order of the declaration determines the ordering of the objects in the output. \section{Name lists} \label{sect-namelists} Sometimes it is necessary to see how {\FORM} has interpreted a set of declarations. It can also be that declarations were made in an unlisted include file and that the user wants to know what variables have been defined. The lists\index{lists} of active variables\index{variables!lists} can be printed with the statement \begin{verbatim} On names; \end{verbatim} This statement sets a flag that causes the listing of all name tables and default properties that are active at the moment that the compiler has finished compiling the current module and all modules after. The printing is just before the algebra processor takes over for the execution of the module -- assuming that no error condition exists. If the `On names' is specified in a module that ends with a .global-instruction, the name lists will be printed at the end of each module, as printing the name lists will then be the default option. If one likes to switch this flag off, this can be done with the statement \begin{verbatim} Off names; \end{verbatim} which prohibits the printing of the name lists in the current module and all modules following. \section{Dummy indices} \label{sect-dummies} Sometimes indices\index{indices!dummy} are to be summed over but due to the evaluation procedures some terms contain the index mu and other terms contain the index nu. There is a command to sum over indices in such a way that {\FORM} recognizes that the exact name of the index is irrelevant. This is the `sum'-statement (see also \ref{substasum}):% % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Dummy_indices_1) \begin{verbatim} i mu,nu; f f1,f2; L F=f1(mu)*f2(mu)+f1(nu)*f2(nu); sum mu; sum nu; print; .end \end{verbatim} At first the expression contains two terms. After the summations {\FORM} recognizes the terms as identical. In the output we see the term: \begin{verbatim} 2*f1(N1_?)*f2(N1_?) \end{verbatim} The \verb:N1_?: are dummy indices. The dimension of these dummy indices is the current default dimension\index{dimension!default} as set with the last dimension-statement. This may look like it is a restriction, but in practice it is possible to declare the default dimension to have one value in one module, take some sums, and do some more operations, and then give the default dimension another value in the next module. It should be realized however that then the dimension of the already existing dummy indices may change with it. The scheme that is used to renumber\index{renumber} the indices\index{indices!renumber} in a term is quite involved. It will catch nearly all possibilities, but in order to avoid to try all $n!$ permutations, when there are n pairs of dummy indices, {\FORM} does not try everything. It is possible to come up with examples in which the scheme is not perfect. It is left as a challenge for the reader to find such an example. In the case that the scheme isn't sufficient one can use the Renumber statement (see \ref{substarenumber}) to force a complete renumbering. As this involves n! attempts in which n is the number of different dummy indices, this can become time consuming. These dummy indices can be used to solve a well known problem in the automatic summation of indices. This problem occurs, when summed indices are found inside a subexpression that is raised to a power: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Dummy_indices_2) \begin{verbatim} Index mu,nu; CFunctions f,g; Vectors p,q; Local F = (f(mu)*g(mu))^2; sum mu; id f(nu?) = p(nu); id g(nu?) = q(nu); print; .end F = p.p*q.q; \end{verbatim} Clearly the answer is not what we had in mind, when we made the program. There is an easy way out: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Dummy_indices_3) \begin{verbatim} Index mu,nu; Symbol x; CFunctions f,g; Vectors p,q; Local F = x^2; repeat; id,once,x = f(mu)*g(mu); sum mu; endrepeat; id f(nu?) = p(nu); id g(nu?) = q(nu); print; .end F = p.q^2; \end{verbatim} This time things went better, because each sum-statement moves an index mu to a new dummy index. There are some extra problems connected to dummy indices. Assume that we have the expression F which contains % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Dummy_indices_4) \begin{verbatim} F = f(N1_?,N2_?)*f(N2_?,N1_?); \end{verbatim} and next we have the module % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Dummy_indices_4) \begin{verbatim} Indices mu,nu,rho,si; Vectors p1,p2,p3,v; Tensor g; Local G = e_(mu,nu,rho,si)*g(mu,nu,p1,v)*g(rho,si,p2,v); sum mu,nu,rho,si; Multiply F^3; id v = e_(p1,p2,p3,?); print; .end G = f(N1_?,N2_?)*f(N2_?,N1_?)*f(N3_?,N4_?)*f(N4_?,N3_?)* f(N5_?,N6_?)*f(N6_?,N5_?)*g(N7_?,N8_?,p1,N9_?)* g(N10_?,N11_?,p2,N12_?)*e_(p1,p2,p3,N9_?)* e_(p1,p2,p3,N12_?)*e_(N7_?,N8_?,N10_?,N11_?); \end{verbatim} Here the situation with the dummy indices becomes rather messy, and all earlier versions of {\FORM} were not prepared for this. Their answer could be: \begin{verbatim} G = f(N1_?,N2_?)*f(N1_?,N2_?)*f(N1_?,N2_?)*f(N2_?,N1_?)* f(N2_?,N1_?)*f(N2_?,N1_?)*g(N1_?,N2_?,p2,N3_?)* g(N4_?,N5_?,p1,N6_?)*e_(p1,p2,p3,N3_?)* e_(p1,p2,p3,N6_?)*e_(N1_?,N2_?,N4_?,N5_?); \end{verbatim} which is clearly not what the program is supposed to give. In the current version we have made the tracing of the dummy indices and the renumbering of them at the proper moment a lot better. It is however not complete as a complete implementation might severely influence the speed of execution at some points. The scheme is complete for the inclusion of local and global expressions. On the other hand it doesn't work for the contents of dollar variables\index{variables!dollar}. Neither does it work for dummy indices introduced in user defined code as in \begin{verbatim} id x^n? = (f(N1_?)*g(N1_?))^n; \end{verbatim} For the latter case we showed a workaround above. Anyway there is a certain ambiguity here. Just imagine we write \begin{verbatim} id x^n? = f(N1_?)^n*g(N1_?)^n; \end{verbatim} Formally it is exactly the same, but what we mean is far from clear. For the dollar variables we considered the contracted dummy indices rare enough that it doesn't merit sacrificing speed. And then there is one more little caveat\index{caveat}. Global expressions that were stored with older versions of {\FORM} than version 3.2, but are read with version 3.2 or later would have a problem if the expression were to contain dummy indices. The newer version of the .sav files\index{files!.sav} will contain information about the dummy indices. {\FORM} can still read the old versions but will have to `invent' information by assuming that there are no dummy indices. If there are expressions with such dummy indices the best is to copy the expressions to a new expression and let the copying be followed by a .sort. That should set things straight. A final remark: if an elegant solution is found with which the above cases could be made to work without the penalty in execution time, it will be built in in the future. One must also take care when working with extra symbols when processing expressions which contain dummy indices. Dummy indices which are inside the extra symbol definitions are not visible to {\FORM}'s renumbering routines, which can lead to ambiguous results. For example: \begin{verbatim} CFunction f,g; Index mu; Local test = f(mu,mu)*g(N1_?,N1_?); ArgToExtraSymbol g; Sum mu; Argument g; FromPolynomial; EndArgument; Print; .end test = f(N1_?,N1_?)*g(N1_?,N1_?); \end{verbatim} \section{Kronecker delta's} \label{sect-kroneckerdelta} The built in object d\_ represents the Kronecker\index{Kronecker} delta\index{delta!Kronecker}. Even though this object looks a little bit like a tensor, internally it isn't treated as such. Actually it has its own data type. It must have exactly two arguments and these arguments should be either indices or vectors. A d\_ with at least one vector is immediately replaced, either by a vector with an index (if there is one vector and one index) or by a dotproduct (when there are two vectors). If a Kronecker delta contains an index that occurs also at another position in the same term, and if that index is summable, and if the index occurs as the index of a vector, inside a tensor, inside another d\_ or as the argument of a function, and the object inside which it occurs is not inside the argument of a function itself (unless the d\_ is inside the same argument) then the Einstein\index{Einstein} summation\index{summation!Einstein} convention is used and the d\_ is eliminated, while the second occurrence of the index is replaced by the other index in the d\_ (Are you still with us?). When a Kronecker delta has two identical indices and these indices are summable, the d\_ is replaced by the dimension of the index. If they are fixed indices, the d\_ is replaced by one, unless this value has been altered with the fixindex-statement. Some examples of Kronecker delta's are given in section~\ref{fund}. \section{Extra Symbols} \label{sect-extrasymbols} \label{extrasymbols} Starting with version 4.0 \FORM{} is equipped with a mechanism to replace non-symbol objects by internally generated symbols. These are called the extra symbols. Their numbering starts at maximum number allowed for internal objects and then counts down. Hence their ordering will be opposite to what might otherwise be expected. It is possible to control their representation when they are to be printed in the output. For this there is the ExtraSymbols (\ref{substaextrasymbols}) statement. The definitions of the extra symbols can be made visible with the \%X option in the \#write preprocessor instruction. Extra symbols can be introduced by the user with the ToPolynomial statement (\ref{substatopolynomial}). This statement replaces all objects that are not numbers or symbols to positive powers by extra symbols. This may be needed for some new manipulations and can also be very handy for output that is to be treated by for instance a FORTRAN or C compiler. The FromPolynomial statement replaces the extra symbols again by their original meaning. Care should be taken if extra symbol definitions include dummy indices, see \ref{sect-dummies}. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Var_Extra_Symbols_1) \begin{verbatim} Vector p,q,p1,p2; CFunction f; CFunction Dot,InvDot; Symbol x,x1,x2; Set pdot:p,q; Off Statistics; Local F = x+x^2+1/x+1/x^2+f(x1)+f(x2)*p.q*x+f(x2)/p.q^2; id p1?pdot.p2?pdot = Dot(p1,p2); id 1/p1?pdot.p2?pdot = InvDot(p1,p2); Print; .sort F = x^-2 + x^-1 + x + x^2 + f(x1) + f(x2)*Dot(p,q)*x + f(x2)*InvDot(p,q)^2; ExtraSymbols,array,Y; Format DOUBLEFORTRAN; ToPolynomial; Print; .sort F = & Y(1) + Y(1)**2 + Y(2) + Y(5)**2*Y(3) + x + x*Y(4)*Y(3) + x**2 #write " SUBROUTINE sub(Y)" #write "*" #write "* Compute the extra symbols. Generated on `DATE_'" #write "*" #write " REAL*8 Y(`EXTRASYMBOLS_')" #write " REAL*8 Dot,InvDot" #write " Dot(p1,p2)=p1(1)*p2(1)-p1(2)*p2(2)-p1(3)*p2(3)\ -p1(4)*p2(4)" #write " InvDot(p1,p2)=1.D0/(Dot(p1,p2))" #write "*" #write "* We still have to add definitions here." #write "* And we have to import all the variables." #write "*" #write "%X" #write "*" #write " RETURN" #write " END" ExtraSymbols,underscore,Z; Format Normal; Format 80; Print; .end F = Z1_ + Z1_^2 + Z2_ + Z5_^2*Z3_ + x + x*Z4_*Z3_ + x^2; FromPolynomial; Print; .end F = x^-2 + x^-1 + x + x^2 + f(x1) + f(x2)*Dot(p,q)*x + f(x2)*InvDot(p,q)^2; \end{verbatim} In the ExtraSymbols statement we say that we want the extra symbols to be presented as an array with the name Y. The alternative is a set of symbols with names ending in an underscore, but that would not make the FORTRAN compiler very happy. Then we convert the expression to symbols. As one can see, everything got converted to elements of an array Y which are treated as symbols. After we have written the file sub.f (notice that EXTRASYMBOLS\_ is a built in symbol indicating the number of extra symbols) we change the representation to the (default) notation with an underscore and the character Z. The contents of the file sub.f are: \begin{verbatim} SUBROUTINE sub(Y) * * Compute the extra symbols. Generated on Sat Apr 2 20:40:33 2011 * REAL*8 Y(5) REAL*8 Dot,InvDot Dot(p1,p2)=p1(1)*p2(1)-p1(2)*p2(2)-p1(3)*p2(3)-p1(4)*p2(4) InvDot(p1,p2)=1.D0/(Dot(p1,p2)) * * We still have to add definitions here. * And we have to import all the variables. * Y(1)=x**(-1) Y(2)=f(x1) Y(3)=f(x2) Y(4)=Dot(p,q) Y(5)=InvDot(p,q) * RETURN END \end{verbatim} As one can see, with very little effort this routine can be made into a proper subroutine that computes all elements of the array Y which can then be used for computing the expression F. \section{Restrictions} There is a restriction\index{restrictions} on the total number of variables\index{variables!total number of} that {\FORM} can handle. For the number of symbols, vectors, indices, functions and sets together the exact number depends on the type of computer. For a computer with a 32-bits processor this number is 32768. This includes the built in objects. Individual types of variables (like symbols) are usually restricted to about 8000. For a computer with a 64-bits processor the maximum has been set arbitrarily at 2000000000. In addition there are restrictions on the total amount of memory\index{memory!total amount of} needed by {\FORM} to maintain an administration of all these variables. These restrictions are set by the memory allocator of the computer on which {\FORM} is running. \section{Some common bugs} There is a type of error\index{error}\index{bug} by the user (including at times the author) that is so common that it deserves mentioning here. Consider the code: \begin{verbatim} Symbol x1,x2 Index m1,m2; \end{verbatim} As a statement it is perfectly legal\index{legal}, but it may produce rather funny errors at a later stage when we try to use m1 or m2. Inspection with the `On names;' statement shows that we have the symbols x1,x2,Index,m1,m2. This is most likely not what the user wanted. Closer inspection shows that we forgot the semicolon at the end of the symbol statement. We should have had: \begin{verbatim} Symbol x1,x2; Index m1,m2; \end{verbatim} This is the most common error for which {\FORM} cannot give a direct error message (it is after all a legal statement). Hence when faced with mysterious errors or error messages, one could have a good look by using the `On names' statement. Maybe it shows something, and if not, one has to look for other causes. form-5.0.1/doc/manual/sorting.tex0000644000175100017510000003545715217035721012415 \chapter{Sorting and statistics} \label{sorting} The sorting system is a vital part of \FORM\ and one of the main reasons why the speed of \FORM\ compares so favorably with other systems. A good understanding of what happens during the sorting\index{sorting} of expressions is essential if one wants to write efficient\index{efficient} programs. In essence the sorting is done by a tree\index{tree sort} sort. However due to the nature of mathematical expressions there is a complication. When two terms are identical with the possible exception of their coefficient, we will add their coefficients, put this new coefficient in the place of the coefficient of the first term, and drop the second term. If the new coefficient happens to be zero, both terms are dropped. Hence the number of terms during the sort is not fixed. For a tree sort this is not a major complication\index{complication}. What is more annoying though is that the new coefficient may take more space inside the storage than either of the old coefficients. Let us have a look now at what happens in a \FORM\ program. Much can be seen from the statistics. \begin{verbatim} S x1,...,x4; L F = (x1+...+x4)^4; .end Time = 0.01 sec Generated terms = 35 F Terms in output = 35 Bytes used = 628 \end{verbatim} In this case the program generated 35 terms. Whenever a term is generated and \FORM\ is done with it (no more statements will act on it), \FORM\ will write it into a buffer which is called the small buffer. Additionally it stores a pointer to the location of this term inside the small buffer. Next it will continue generating terms. This process will be stopped by either of three conditions: \begin{enumerate} \item \FORM\ is finished generating terms. \item The last generated term does not fit inside the space remaining in the small buffer. \item There is no space for a pointer to the last generated term inside the array of pointers. \end{enumerate} In either of these three cases \FORM\ will sort the contents of the small\index{small buffer} buffer\index{buffer!small}. This sorting is done `by pointers' and hence it is important that the whole small buffer fits inside the physical memory of the computer. If this would not be the case, some very inefficient swapping of memory might be the result. During this sorting \FORM\ may run into the problem that the coefficient of two combined terms does not fit in the place of one of the two old coefficients. This means that the combined term will need more space, but because the old terms might be enclosed by other terms, this space may not be available locally. To this end \FORM\ has some spare space in the small buffer which is called the small\index{small extension} extension\index{extension!small}. Actually the term SmallExtension\index{smallextension} is used for the combination of the small buffer and its extra space. The extra space is at least $1/6$ times the size of the small buffer, but typically it will be about $1/3$ the size of the small buffer. In some exceptional cases (with heavy use of a polynomial coefficient via the PolyFun\index{polyfun} command) bigger sizes might be useful. In the case that the new combined term needs more space than each of the old terms, the new term is placed in the extension space. If, during the sort, the extension space becomes exhausted, \FORM\ will make a garbage\index{garbage collection} collection of the entire extended small buffer. This will always result in the extension space becoming empty again, because the notation of the terms in \FORM\ is such the new combined term will at most occupy an amount of space equal to the sum of the spaces of the original two terms. In older versions of \FORM\ this garbage collection was executed by means of a temporary disk file. In the new version it is done inside the memory by temporarily allocating a new buffer. Anyway such garbage collections are relatively rare. In the above example, the sorting occurred because the generation of terms was finished. Hence the sorted output is written away in such a way that it can be used as input for a potential next module (or to be printed). Hence let us change the size of the small buffer: \begin{verbatim} #: SmallSize 300 S x1,...,x4; L F = (x1+...+x4)^4; .end Time = 0.00 sec Generated terms = 13 F 1 Terms left = 13 Bytes used = 236 Time = 0.00 sec Generated terms = 26 F 1 Terms left = 26 Bytes used = 476 Time = 0.00 sec Generated terms = 35 F 1 Terms left = 35 Bytes used = 632 Time = 0.00 sec Generated terms = 35 F Terms in output = 35 Bytes used = 628 \end{verbatim} Now the size of the small buffer will be only 300 bytes. As a result the 13-th term does not fit. We can see this in the statistics: the 13-th term has been generated and \FORM\ sorts the small buffer. The output of the 12 sorted terms is written to another buffer, called the large\index{large buffer} buffer\index{buffer!large}. Inside the large buffer the terms are lightly compressed. This compression is related to the fact that in each `patch'\index{patch} the terms are already sorted and hence we may not have to repeat the identical beginnings of each term. Hence the amount of space used after this sort is less than the 300 bytes of the small buffer, even though the 13-th term gave an overflow for these 300 bytes. The small buffer fills up again at the 26-th term and again it is sorted and the results written to the large buffer. Finally, after 35 terms, the generation is finished. Hence the remains in the small buffer are also sorted and written as a third `patch' into the large buffer. Then the large buffer is sorted. For this a different sort technique is used. It is assumed that the large buffer is not always residing inside the physical memory. Hence parts of it may be swapped out temporarily. With the size of current days memories this may not happen very often, unless one sets the size of the buffer to something comparable to the memory size of the computer and several programs are running at the same time. Anyway, swapping will not affect the large buffer very much. \FORM\ will merge the `patches' by going sequentially through them with a method called `tree\index{tree of losers} of losers' in the book by Knuth\index{Knuth} (the art of computer programming, vol. 3). Because it goes sequentially through the patches, uses all the information it reads and never needs it again, this method is indeed rather well resistant to swapping. The next complication is of course when the large buffer is full. This can be either because its byte space is full, or because the maximum number of patches is exceeded. Because the sorting method uses quite a few variables for each patch, there is a space allocated for them and hence there is a maximum number of patches. If we set this to 2 (just for demonstration purposes) we obtain: \begin{verbatim} #: SmallSize 200 #: LargePatches 2 S x1,...,x4; L F = (x1+...+x4)^4; .end Time = 0.00 sec Generated terms = 9 F 1 Terms left = 9 Bytes used = 164 Time = 0.00 sec Generated terms = 17 F 1 Terms left = 17 Bytes used = 312 Time = 0.00 sec Generated terms = 26 F 1 Terms left = 26 Bytes used = 478 Time = 0.00 sec F Terms active = 26 Bytes used = 474 Time = 0.00 sec Generated terms = 35 F 1 Terms left = 35 Bytes used = 630 Time = 0.00 sec F Terms active = 35 Bytes used = 786 Time = 0.00 sec Generated terms = 35 F Terms in output = 35 Bytes used = 628 \end{verbatim} We see that after the third small buffer has been sorted, the third patch cannot be written to the large buffer. Hence the large buffer is sorted (indicated by the special statistics involving the phrase `Terms active'). The result of this is written as a sorted patch to the sort\index{sort file} file. This file is one of the temporary\index{temporary files} files that \FORM\ can create. It has the extension .sor\index{.sor extension}. Now the third patch can be written into the --by now empty-- large buffer. At the end of term generation, the last small buffer is sorted, its results written into the large buffer, then that is sorted and its results written as the final patch into the sort file. Then, finally the patches in the sort file are merged in a method similar to the way the large buffer is sorted. This final sort is a disk\index{disk to disk sort} to disk sort. Hence it can use the disk rather intensely and the use of the CPU may drop temporarily, although it is nothing so dramatic as when the computer is involved in heavy inefficient swapping as can be the case with many other algebra programs. Also, this is usually only a small fraction of the running time of the program. The exception may be when \FORM\ is running several processes and they are all using disk sorts simultaneously. In that case some file systems may not be very good at handling the ensuing traffic\index{traffic jam} jams. Also the disk to disk sort will have a maximum number of patches that can be sorted simultaneously. If this number is exceeded there will be one or more extra stages\index{stages in the sorting} in the sorting, all of which will be disk to disk sorts. It is advisable to tune the setup parameters in such a way that one can prevent this, because it involves usually needless use of resources. One can try to increase the parameter FilePatches\index{filepatches}, but the problem is that \FORM\ uses a caching\index{caching} system to buffer the inputs from the sort file. The cache buffers have to have a size that is at least twice the maximum size of a term. For each patch it needs a buffer and all buffers together should fit inside the combination of the large buffer and the small extended buffer. This puts an upper limit on the number of file patches. Additionally this buffer (SortIOsize\index{sortiosize}) should not be very small, because otherwise the disk IO operations are very inefficient. Hence it helps often to increase the size of the small buffer and the large buffer first. That gives fewer patches. Additionally it in turn can allow for more file patches that are not too small. One thing that one can see now is that if terms are to cancel or to add, it is advantageous if this happens already in an early stage of the sorting. This means that it is most efficient if these terms will end up in the small buffer at the same time. This should explain the example given in the section on brackets\index{brackets}. This way fewer terms are written to the large buffer and/or the sort file, which means that less disk space will be used. The sizes of buffers involved can all be tuned to a given hardware. How this is done is explained in the chapter on the setup\index{setup} \ref{setup}. By specifying \texttt{On SortVerbose;}\index{on!sortverbose} (see \ref{substaon}), more information is printed in the final sorting statistics of each expression, which take the form: \begin{verbatim} Time = 0.00 sec Generated terms = 64 test1 Terms in output = 64 Bytes used = 4888 Unsorted bytes = 6144 Small Buffer = 0, 0 Large Buffer = 0, 0 Comparisons = 63 \end{verbatim} The additional information includes the total size of the generated terms before cancellations, merging or compression, the number of times the small buffer was sorted due to reaching TermsInSmall, or SmallSize, the number of times the large buffer was sorted due to reaching LargePatches, or LargeSize, and the total number of term comparisons made during the sort. In particular, the information on why the small and large buffers were sorted helps when configuring their sizes, as described in \ref{setup}. When \FORM\ is dealing with the arguments\index{arguments of functions} of functions and if an argument is a multiterm subexpression, also such subexpressions need to be sorted. In older versions of \FORM\ this was done inside the at that moment remaining space of the small buffer and its extension. The reason was that such subexpressions would be rather short (they would have to fit inside a function argument and were hence limited by the maximum size of a term) and buffer space was hard to come by in computers with small memories. In the new version of \FORM\ other subexpression sorts were added: the sorting in the term environment (see \ref{substaterm}) and the sorting of \$-expressions. Both sorts do not have the restriction of the maximum size of a term. They can result in expressions that are arbitrarily long (although that might not give efficient programs). Hence the sorting of subexpressions have now their own buffers. And more than one such set may be needed if for instance the term environment is used in a nested fashion. Of course the settings for the buffers of this `subsort' are not quite as large as for the main buffers. And the user can of course also influence their settings as explained in the chapter on the setup \ref{setup}. This chapter gives also all default values. There is one restriction on the sorting of function arguments and \$-expressions: They are not allowed to go into the stage4 sorting. Any such attempt will result in an error message and the suggestion to raise the size of the buffers for this type of sorting. When \FORM\ is running in parallel mode (either \TFORM\ or \ParFORM) each worker will need its own buffers. In \ParFORM\ in which the processors each control their own memory, the size of each of these buffers are the same as for the master process. In \TFORM\ with its shared memory the sizes that the user selects for the sort buffers and the scratch file caches refer to the buffers of the master thread. The workers each get basically buffers with 1/N times the size of the buffer of the master. They may be made a bit bigger when potential conflicts with MaxTermSize occur. form-5.0.1/doc/manual/dollar.tex0000644000175100017510000003416215217035721012175 \chapter{The dollar variables} \label{dollars} In the older versions of \FORM\ there were two types of variables: the preprocessor variables\index{variables!preprocessor} and the algebraic variables\index{variables!algebraic}. The preprocessor variables are string variables that are used by the edit features of the preprocessor to prepare the input for the compiler part of \FORM\@. The algebraic objects are the expressions and the various algebraic variables like the symbols, functions, vectors etc. There existed however very few possibilities to communicate from the algebraic level to the decision taking at the preprocessor level. This has changed dramatically with version 3 and the introduction of the dollar variables\index{variables!dollar}. Dollar variables are basically (little) expressions that can be used to store various types of information. They can be used both as preprocessor objects as well as algebraic objects. They can also be defined and given contents both by the preprocessor and during execution on a term by term basis. Dollar variables are kept in memory. Hence it is important not to make them too big, because in that case performance might suffer. What is a legal name for a dollar variable? Dollar variables have a name that consists of a dollar sign (\verb:$:) followed by an alphabetic character and then potentially more alphanumeric characters. Hence \verb:$a: and \verb:$var: and \verb:$r4t78y0: are legal names and \verb:$1a: is not a legal name. The variables do not have to be declared. However \FORM\ will complain if a dollar variable is being used, before it has encountered a statement or an instruction in which the variable has been given a value. Hence giving a variable a value counts at the same time as a declaration. What can be stored in a dollar variable? \begin{itemize} \item Algebraic expressions as in \verb:$var = (a+b)^2;: \item Individual objects like indices, numbers, symbols. \item Zero. \item Parts of a term. \item Argument\index{argument field} fields that consist of zero, one or more arguments. \end{itemize} Actually, the parts of a term are treated as a complete term and hence as a special case of an algebraic expression. Internally they are stored slightly differently for speed, but at the user level this should not be noticeable. Actually, with the exception of the argument fields, \FORM\ can convert one type into the other and will try so, depending on the use that is made of the specific dollar variable. In the case that a variable is used in a way that should not be possible (like the content of a variable is a symbol, but it is used in a position where an index is expected) there will be a runtime\index{runtime error} error\index{error!runtime}. How is a variable used? \begin{itemize} \item As a preprocessor variable\index{variable!preprocessor}. This is done by putting the variable between a pair of `' as in \verb:`$var':. In this case the regular print routines of \FORM\ make a textual representation\index{representation!textual} of the variable as it exists at the moment that the preprocessor encounters this object, and this string is then substituted by the preprocessor as if it were the contents of a preprocessor variable. \item Like an expression during execution time. This would be the case in the statement \begin{verbatim} id x = y + $var; \end{verbatim} in which \verb:$var: is substituted in a way that is similar to the substitution of a local expression \verb:F: in the statement \begin{verbatim} id x = y + F; \end{verbatim} except for that the dollar variable is always stored in the CPU memory. \item As an algebraic object during execution time. This could be the case with any value of the variable that is not an expression. An example would be \begin{verbatim} id f(?a) = f(?a,$var); \end{verbatim} in which the dollar variable contains an argument field. \item As an algebraic object in a delayed substitution of a pattern or a special statement. This may need some clarification. If we have the statement \begin{verbatim} id f($var) = anything; \end{verbatim} the compiler does not substitute the current value of \verb:$var:. The reason is that \verb:$var: could have a different value for each term that runs into this statement, while the compiler compiles the statement only once. Hence \FORM\ will substitute the value of \verb:$var: only at the moment that it will attempt the pattern matching. This is called delayed\index{delayed substitution} substitution\index{substitution!delayed}. If one likes the compiler to substitute a value, one can basically let the preprocessor take care of this by typing \begin{verbatim} id f(`$var') = anything; \end{verbatim} A similar delayed substitution takes place in statements of the type \verb:Trace,$var;:. \end{itemize} How does one give a value to a dollar variable? \begin{itemize} \item In the preprocessor. This is done with an instruction of the type \verb:#$var = 0;:. This is an instruction that can run over more than one line. The r.h.s.\ can be any algebraic expression. Specifically it can contain dollar variables or local/global expressions. Such expressions are worked out during the preprocessing. Hence this variable acquires a value immediately. \item During execution when control reaches a statement of the form \verb:$var = expression;:. Again the r.h.s.\ can contain any normal algebraic expression including dollar variables and local/global expressions. The r.h.s.\ will be evaluated and the value will be assigned to \verb:$var:. In the case that \verb:$var: had already a value, the old value will be deleted and the new value will be `installed'. \item During execution when the dollar variable is assigned the value of a wildcard as in \begin{verbatim} id f(x?$var) = whatever; \end{verbatim} If the function \verb:f: occurs more than once in a term, \verb:$var: will have the value of the last match. In the case that the value of the first match is needed one can use the option `once' in the id-statement as in \begin{verbatim} id,once,f(x?$var) = whatever; \end{verbatim} In general one can paste the dollar variable to the end of any wildcard description. Hence one can use \verb:id f(x?{1,2,3}$var) = ...;: and \begin{verbatim} id f(x?set[n?$var1]$var2) = ...; \end{verbatim} \end{itemize} Note the difference between \verb:#$a = 0;: and \verb:$a = 0;:. One CANNOT make a wildcard\index{wildcard} construction for dollar variables themselves as in \verb:id f($var?) = ...;: Dollar variables CANNOT have arguments as in \verb:$var(2): or something equivalent. There is however a solution at the preprocessor level for this by defining individual variables \verb:$var1: to \verb:$varn: and then using \verb:$var`i': or \verb:`$var`i'': for some preprocessor variable \verb:i:. The exception is the indication of factors when a dollar variable has been factorized (see the \#factdollar instruction~\ref{prefactdollar} and the factdollar statement~\ref{substafactdollar}). This is explained later in this chapter and in the chapter about polynomials~\ref{polynomials}. Printing dollar\index{dollar!printing} variables: \begin{itemize} \item In the preprocessor one can use the \verb:#write: instruction (see \ref{prewrite}). \item During execution one can use the Print statement (see \ref{substaprint}). \end{itemize} In both cases one should use the format\index{format} string. The syntax is described in the chapters on these statements. The format descriptor of a dollar variable is \verb:%$: and this looks after the format string for the next dollar variable. Of course one can also use the dollar variable as a preprocessor variable when printing/writing in the preprocessor. Examples. Counting terms: \begin{verbatim} S a,b; Off statistics; L F = (a+b)^6; #$a = 0; $a = $a+1; Print " >> After %t we have %$ term(s)",$a; #write " ># $a = `$a'" ># $a = 0 .sort >> After + a^6 we have 1 term(s) >> After + 6*a^5*b we have 2 term(s) >> After + 15*a^4*b^2 we have 3 term(s) >> After + 20*a^3*b^3 we have 4 term(s) >> After + 15*a^2*b^4 we have 5 term(s) >> After + 6*a*b^5 we have 6 term(s) >> After + b^6 we have 7 term(s) #write " ># $a = `$a'" ># $a = 7 .end \end{verbatim} \noindent Maximum power of x in an expression: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (DolVars_1) \begin{verbatim} S x,a,b; Off statistics; L F = (a+b)^4+a*(a+x)^3; .sort #$a = 0; if ( count(x,1) > $a ) $a = count_(x,1); Print " >> After %t the maximum power of x is %$",$a; #write " ># $a = `$a'" ># $a = 0 .sort >> After + 3*x*a^3 the maximum power of x is 1 >> After + 3*x^2*a^2 the maximum power of x is 2 >> After + x^3*a the maximum power of x is 3 >> After + 4*a*b^3 the maximum power of x is 3 >> After + 6*a^2*b^2 the maximum power of x is 3 >> After + 4*a^3*b the maximum power of x is 3 >> After + 2*a^4 the maximum power of x is 3 >> After + b^4 the maximum power of x is 3 #write " ># $a = `$a'" ># $a = 3 .end \end{verbatim} Starting with version 4, \FORM\ has the capability to factorize polynomials (see the chapter on polynomials~\ref{polynomials}). One type of objects that can be factorized is the dollar variables. The immediate question here is how to access the factors. As we mentioned before in this chapter, normally there is no direct way to use arguments for dollar variables. For the factors however we have a way of indexing the dollar variables as in \verb:$var[1]:,...,\verb:$var[n]: when there are n factors. The number of factors can be obtained as \verb:$var[0]:. In the index field can only be (nonnegative integer) numbers, dollar variables or factors of dollar variables that evaluate into (nonnegative integer) numbers. \begin{verbatim} Symbol x,y; CFunction f1,f2; Local F = f1(x^2+2*x*y+y^2)+f1(x^4-y^4); id f1(x?$x) = f2(x); FactDollar,$x; Do $i = 1,$x[0]; Print "In %t factor %$ is %$",$i,$x[$i]; Enddo; .end In + f2(y^2 + 2*x*y + x^2) factor 1 is y + x In + f2(y^2 + 2*x*y + x^2) factor 2 is y + x In + f2( - y^4 + x^4) factor 1 is - 1 In + f2( - y^4 + x^4) factor 2 is y - x In + f2( - y^4 + x^4) factor 3 is y + x In + f2( - y^4 + x^4) factor 4 is y^2 + x^2 \end{verbatim} One thing to note is that the use of \begin{verbatim} f(<$x[1]>,...,<$x[$x[0]]>) \end{verbatim} is illegal. \verb:$x[0]: will be inserted during execution time, while the expansion of the triple dot operator is done by the preprocessor. Hence we should use \verb:`$x[0]': but then \verb:$x: must be known and factorized already at compile time. \section{Dollar variables in a parallel environment} \label{pardollars} When \FORM\ is used for parallel\index{parallel processing} processing, either by means of \ParFORM\index{ParFORM} or by means of \TFORM\index{TFORM}, there can be a problem with the dollar variables as in principle there is a central administration and dollar variables that are defined during running will in general have the last assigned value. In a parallel environment this can be nondeterministic\index{nondeterministic}. Look for instance at the following example: \begin{verbatim} S x,a,b; CF f; L F = f(a+b) + f(a+2*b); .sort id f(x?$x) = f(x); Multiply,$x; Print; .end \end{verbatim} Usually this program will give the 'correct' answer, but in principle one thread could define \verb:$x: and then the next thread could overwrite this value before the first thread has used it. This is serious. Hence \FORM\ will veto\index{veto} the use of multiple threads/processors for modules in which dollar variables obtain values during the execution of the program, unless the user can give \FORM\ more information about the use of the dollar variables. In the above case the value of \verb:$x: will be local to each term and hence to each thread\index{thread}. The value in previous terms is unimportant. We can tell this to \FORM\ with a variety of the moduleoption\index{moduleoption} statement (see \ref{substamoduleoption}). This would be: \begin{verbatim} S x,a,b; CF f; L F = f(a+b) + f(a+2*b); .sort id f(x?$x) = f(x); Multiply,$x; Print; ModuleOption,local,$x; .end \end{verbatim} In this case \FORM\ makes at the start of the execution of the module a copy of whatever value \verb:$x: has at that moment for each thread/processor (in this case no value yet and hence it gets set to zero) and then each thread/processor uses its own copy during execution. After the module has been completed the local copies are removed and the original global value is accessible again. This way execution will be safe in a parallel environment. There are more cases that \FORM\ can handle in a parallel environment. These are also options in the moduleoption statement: \begin{verbatim} ModuleOption,maximum,$a; ModuleOption,minimum,$b; ModuleOption,sum,$c; \end{verbatim} Here we say that \verb:$a: is accumulating a maximum numerical value, \verb:$b: collects a minimum numerical value and \verb:$c: is a numerical sum. In all three cases there is a central administration and the use of the variables has to be blocked for other threads/processors during the updating of the values. Sometimes that can be efficient, but in other programs that may actually make them slower. One should experiment. A sample program is given below: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (DolVarsParallel_1) \begin{verbatim} S a1,...,a10; L F = (a1+...+a10)^3; .sort #$c = 0; Print +f "<%w> %t"; Multiply,(a1+...+a10); $c = $c+1; ModuleOption,sum,$c; .sort #message $c = `$c' #$max = 0; #$min = 10; if ( count(a1,1) > $max ) $max = count_(a1,1); if ( count(a4,1) < $min ) $min = count_(a4,1); ModuleOption,maximum,$max; ModuleOption,minimum,$min; .sort #message $max = `$max' #message $min = `$min' .end \end{verbatim} The print statement is showing which thread is dealing with which term. form-5.0.1/doc/manual/calculus.tex0000644000175100017510000001016715217035721012532 The routines inside FORM that deal with the coefficients are all written in C (and hence not in assembler language!). This enhances the portability greatly. It are these routines that determine the word size in \FORM\@. The requirement that the multiplication of two words must be a rather natural operation makes that on a 32-bits architecture the word size becomes 16 bits and on a 64-bits architecture it becomes 32 bits. In some 32-bits processors one could use a 32 bits multiplication and recover the full 64 bits result by looking at two registers. Similarly divisions can be done that way. But this requires assembly language programming, because in C the only way one can do this is by first casting one of the numbers to (long long int) and then the compiler usually creates several multiplications all except one being superfluous. The fact that the use of low level GMP routines can give a slightly faster code is entirely due to the fact that indeed they work with these longer words and use assembly level routines. Originally the low level calculus routines (addition, multiplication, division and the calculation of GCD's) were fully optimized for relatively short numbers. The idea being that for most calculations that is what occurs most of the time. Over the years computers became bigger and people were taking expansions further and further and hence the speed of these routines became a noticeable factor. This was mostly the GCD routine. In the past the GCD algorithm had been studied and compares had been made between the Euclidean and the binary algorithms. The performance of the binary algorithm depends rather crucially on how one can shift through an array of integers and in the C language this isn't very efficient. Hence this algorithm was abandoned in the late 80's. Of course, due to the fact that it uses only shifts and subtractions asymptotically it is faster than the Euclidean algorithm, but in the past the region in which it was more efficient wasn't reached. When the calculation of GCD's became a real problem a new algorithm for longer numbers was invented which turned out to be a little bit like an improved version of the Lehmer-Euclid algorithm. This made the behaviour for big integers much better. At yet a later stage the GMP library was introduced and applied for numbers that are longer than just a few words. Here we need some conversion from FORM words to the words that the GMP routines need. For a GCD calculation this is however a negligible factor. The improvement in speed was far less dramatic than hoped for, even though GMP works with longer words and has its central code in assembler language. But faster is faster and hence FORM can use now three of the low level GMP routines (GCD, multiplication and division) for its big numbers. The improvement coming from the multiplication and the division routines has thus far been only a few percent. This was for calculations with numbers that occupy tenths of words. If FORM could use the double words from the C code, probably the conversion to the GMP notation would more than offset the benefit of the use of low level assembly routines. When very long numbers will be used with thousands of words the situation is different. In that case GMP has special algorithms that were never built for FORM. But for the moment most FORM programs have not reached such cases yet. Whenever this is the case for a program it is best to run this program on a computer that provides the GMP library with its operating system. When the GMP library is not available on a system, FORM will use its own routines, which, as mentioned, are not bad, but were not meant for such extreme cases. The higher level routines for calculus of rational numbers can be done in any language. The algorithms are standard and can be found in any decent text book. It are the low level routines that determine the eventual speed. For these objects the GMP library would probably slow FORM down to a significant degree as on the object level they are much messed up with memory allocation problems, and at the memory management level FORM doesn't have any of these problems. form-5.0.1/doc/manual/manual.tex.in0000644000175100017510000000657515217035721012611 \input{version.tex} \def\formmajorversion{\repomajorversion} \def\formminorversion{\repominorversion} \def\formversiondesc{\repoversiondesc} \def\formdate{\repodate} %begin{latexonly} % To avoid latex2html/latex2html#37 \providecommand{\repoversiondesc}{@VERSION@???} \providecommand{\repodate}{\today} %end{latexonly} \documentclass[11pt]{report} \usepackage{makeidx} %begin{latexonly} \makeatletter \renewcommand*\l@section{\@dottedtocline{1}{1.5em}{3.0em}} \makeatother % Use hyperref package (hyperlinks) with correct option for pdflatex/latex: \usepackage{ifpdf} \ifpdf \RequirePackage[pdftex]{hyperref} \else \RequirePackage[hypertex]{hyperref} \fi % and link indices back to text: \hypersetup{hyperindex,pagebackref,pdfpagemode={None},draft=false} %end{latexonly} \providecommand{\texorpdfstring}[2]{#1}% htmlonly \newcommand{\pfill}{\hfill} \newcommand{\emptypage}{\newpage \thispagestyle{empty} \tiny{\ } \normalsize} \newcommand{\lefttabitem}[1]{\noindent{\begin{minipage}[t]{4cm}{#1} \end{minipage}}\vspace{1mm}} \newcommand{\leftvitem}[2]{\noindent{\begin{minipage}[t]{#1}{#2} \end{minipage}}\vspace{1mm}} \newcommand{\tabitem}[1]{{\begin{minipage}[t]{12cm}{#1}\end{minipage}} \vspace{1mm}} \newcommand{\rightvitem}[2]{{\begin{minipage}[t]{#1}{#2}\end{minipage}} \vspace{1mm}} \newcommand{\clearemptydoublepage}{\newpage{\pagestyle{empty}\cleardoublepage}} \textheight 655pt % Height of text (including footnotes and figures, % excluding running head and foot). % Note 1cm = 28.453pt \textwidth 16.5cm % Width of text line. % % Need to move the origin on the page to centre the block of text: % \hoffset -2.15cm \voffset -1.7cm % settings good for IBM 3812 printer \def\FORM{{\sc FORM}} \def\TFORM{{\sc TFORM}} \def\ParFORM{{\sc ParFORM}} \def\Andre#1{{\sl #1}} \def\Remark#1{{\sl #1}} \def\Tr{{\rm Tr}} \def\hash{\symbol{"23}} \def\sign#1{(\!-\!1)^{#1}} \def\binom#1#2{ \left(\!\! \begin{array}{c} #1 \\ #2 \end{array}\!\! \right) } \def\plus{\!+\!} \def\minus{\!-\!} \def\mydot{\!\!\cdot\!} \def\nn{\nonumber \\ &&} \def\nne{\nonumber \\ & = &} \makeindex \begin{document} \begin{titlepage} \title{\Huge FORM \\ \Large version \formversiondesc \\ \huge Reference manual} \date{\formdate} \author{J.A.M.~Vermaseren, J.~Davies, T.~Kaneko, J.~Kuipers, C.~Marinissen, B.~Ruijl, \\M.~Tentyukov, T.~Ueda and J.~Vollinga} \end{titlepage} \maketitle %\clearemptydoublepage %\pagenumbering{roman} %\setcounter{page}{1} %\clearemptydoublepage %\tableofcontents %%\emptypage %\clearemptydoublepage %\pagenumbering{arabic} \setcounter{page}{2} \clearemptydoublepage \emptypage \clearemptydoublepage \pagenumbering{roman} \setcounter{page}{1} \clearemptydoublepage \tableofcontents \clearemptydoublepage \emptypage \clearemptydoublepage \pagenumbering{arabic} \setcounter{page}{1} \input{@srcdir@/startup} \input{@srcdir@/variable} \input{@srcdir@/prepro} \input{@srcdir@/module} \input{@srcdir@/pattern} \input{@srcdir@/dollar} \input{@srcdir@/statements} \input{@srcdir@/functions} \input{@srcdir@/bracket} \input{@srcdir@/optim} \input{@srcdir@/polynomials} \input{@srcdir@/tablebas} \input{@srcdir@/dict} \input{@srcdir@/gamma} \input{@srcdir@/metric} \input{@srcdir@/sorting} \input{@srcdir@/setup} \input{@srcdir@/parallel} \input{@srcdir@/external} \input{@srcdir@/spectators} \input{@srcdir@/diagrams} \input{@srcdir@/float.tex} \printindex \end{document} form-5.0.1/doc/manual/version.tex.in0000644000175100017510000000031615217035744013011 \def\repoversion{5.0.1} \def\repoversiondesc{5.0.1} \def\reporevision{v5.0.1} \def\repodate{22 June 2026} \def\repomajorversion{5} \def\repominorversion{0} \def\repopatchversion{1} \def\repoversionsuffix{} form-5.0.1/doc/manual/prepro.tex0000644000175100017510000025640015217035721012230 \chapter{The preprocessor} \label{preprocessor} %--#[ General : The preprocessor\index{preprocessor} is a program segment that reads and edits\index{edit} the input, after which the processed input is offered to the compiler\index{compiler} part of \FORM\@. When a module\index{module} instruction is encountered by the preprocessor, the compilation is halted and the module is executed. The compiler buffers are cleared and \FORM\ will continue with the next module. The preprocessor acts almost purely on character strings. As such it does not know about the algebraic properties of the objects it processes. Additionally the preprocessor also filters out the commentary\index{commentary}. The commands for the preprocessor are called instructions. Preprocessor instructions start with the character \# as the first non-blank character in a line. After this there are several possibilities. \begin{description} \item[\#:]\index{\#:} Special syntax for setup parameters at the beginning of the program. See the chapter on the setup parameters. \item[\#$-$, \#$+$]\index{\#$-$}\index{\#$+$} Turns the listing of the input off or on. \item[\#name]\index{\#name} Preprocessor command. The syntax of the various commands will be discussed below. \item[\#\$name]\index{\#\$name} Giving a value to a dollar variable in the preprocessor. See chapter \ref{dollars} on dollar variables. \end{description} %--#] General : %--#[ The preprocessor variables : \section{The preprocessor variables} \label{preprovariables} In order to help in the edit\index{edit} function the preprocessor is equipped with variables\index{preprocessor variables} that can be defined or redefined by the user or by other preprocessor actions. Preprocessor variables have regular names that are composed of strings of alphanumeric characters of which the first one must be alphabetic. When they are defined one just uses this name. When they are used the name should be enclosed between a backquote\index{backquote} and a quote\index{quote} as if these were some type of brackets. Hence `a2r' is the reference to a regular preprocessor variable. Preprocessor variables contain strings of characters. No interpretation is given to these strings. The backquote/quote pairs can be nested. Hence `a`i'r' will result in the preprocessor variable `i' to be substituted first. If this happens to be the string "2", the result after the first substitution would be `a2r' and then \FORM\ would look for its string value. The use of the backquotes is different from the earlier versions of \FORM\@. There the preprocessor variables would be enclosed in a pair of quotes and no nesting\index{nesting} was possible. \FORM\ still understands this old notation because it does not lead to ambiguities. The user is however strongly advised to use the new notation with the backquotes, because in future versions the old\index{old notation} notation may not be recognized any longer. \noindent \FORM\ has a number of built in preprocessor variables. They are: \begin{description} \item[VERSION\_] The current version\index{VERSION\_} (or ``major version''), as the ``1'' in 1.2.3. \item[SUBVERSION\_] The current sub-version\index{SUBVERSION\_} (or ``minor version''), as the ``2'' in 1.2.3. \item[SUBSUBVERSION\_] The current sub-sub-version\index{SUBSUBVERSION\_} (or ``patch version''), as the ``3'' in 1.2.3. \item[NAME\_] The name\index{NAME\_} of the program file. \item[DATE\_] The date\index{DATE\_} of the current run. \item[CMODULE\_] The number\index{CMODULE\_} of the current module. \item[SHOWINPUT\_] If input listing\index{SHOWINPUT\_} is on: 1, if off: 0. \item[EXTRASYMBOLS\_] The current number of extra symbols\index{EXTRASYMBOLS\_} (see \ref{substaextrasymbols}). \item[OLDNUMEXTRASYMBOLS\_] The number of extra symbols\index{OLDNUMEXTRASYMBOLS\_} before the current optimization started (see chapter \ref{optimization}). \item[OPTIMMINVAR\_] The number of the first extra symbol\index{OPTIMMINVAR\_} needed for the current optimization (see chapter \ref{optimization}). \item[OPTIMMAXVAR\_] The number of the last extra symbol\index{OPTIMMAXVAR\_} needed for the current optimization (see chapter \ref{optimization}). \item[OPTIMSCHEME\_] The best Horner scheme\index{OPTIMSCHEME\_} found for the current optimization (see chapter~\ref{optimization}). \item[OPTIMVALUE\_] The number of arithmetic operations\index{OPTIMVALUE\_} in the resulting expression for the current optimization (see chapter~\ref{optimization}). \item[PID\_] The process identifier (PID) \index{PID} \index{PID\_} of the running process. In \ParFORM{} (\ref{parform}), it represents the PID of the master process in order to ensure that all the processes in a job use the same number. A recovered session from a checkpoint (\ref{checkpoints}) keeps using the PID of the crushed session. \item[STOPWATCH\_] Same as `TIMER\_'. \item[SYSTEMERROR\_] The return value of the last \#system\ref{presystem} command when invoked with the -e\index{SYSTEMERROR\_} option. \item[TIME\_] The running time\index{time\_} till the moment of call in the string format with a decimal point and two digits after the decimal point. This is the same format as in the statistics. \item[TIMER\_] The running time\index{timer\_} since the last reset in milliseconds. Hence, unlike `time\_' this value can be used in the preprocessor calculator and in numerical compares in \#if instructions. See also the \#reset (see \ref{prereset}) instruction. \item[NUMACTIVEEXPRS\_] The number of the currently active expressions. \item[ACTIVEEXPRNAMES\_] The list of the currently active expression names separated by commas. This can be passed to \#do lvar=\{...\} instruction~(\ref{predo}) like: \begin{verbatim} #do e = {`activeexprnames_'} #ifdef `e' Local `e' = `e' + something; #endif #enddo \end{verbatim} \item[UNCHANGED\_] Takes the value 1 if all active expressions were unchanged in the previous module, and 0 otherwise. `UNCHANGED\_exprname' is 1 if the expression ``exprname'' was unchanged in the previous module, and 0 otherwise. \item[ZERO\_] Takes the value 1 if all active expressions were zero in the previous module, and 0 otherwise. `ZERO\_exprname' is 1 if the expression ``exprname'' was zero in the previous module, and 0 otherwise. \end{description} \noindent If \FORM\ cannot find a preprocessor variable, because it has neither been defined by the user, nor is it one of the built in variables, it will look in the systems environment\index{environment} to see whether there is an environment variable by that name. If this is the case its string value will be substituted. \noindent Preprocessor variables can have arguments and thereby become macros. One should consult the description of the \#define~\ref{predefine} instruction about the delayed substitution feature to avoid the value of the preprocessor variables in the macro would be substituted immediately during the definition. Hence proper use is \begin{verbatim} #define EXCHANGE(x,y) "Multiply replace_(`~x',`~y',`~y',`~x');" \end{verbatim} \noindent \FORM{} has the following built in macros: \begin{description} \item[TOLOWER\_(string)] in which the character string in the argument is converted to lower case. After this it will become input. \item[TOUPPER\_(string)] in which the character string in the argument is converted to upper case. After this it will become input. \end{description} as well as macros which allow one to edit the names of variables, \begin{description} \item[KEEPLEFT\_(string,n)] keep only the first n characters of string. After this it will become input. \item[KEEPRIGHT\_(string,n)] keep only the last n characters of string. After this it will become input. \item[TAKELEFT\_(string,n)] remove the first n characters of string. After this it will become input. \item[TAKERIGHT\_(string,n)] remove the last n characters of string. After this it will become input. \end{description} Note that these macro names are not case sensitive. %--#] The preprocessor variables : %--#[ Calculator : \section{The preprocessor calculator} \label{calculator} Sometimes a preprocessor\index{preprocessor variable!numeric} variable should be interpreted as a number and some arithmetic\index{arithmetic} should be done with it. For this \FORM\ is equipped with what is called the preprocessor calculator\index{calculator}. When the input reading device encounters a left curly\index{curly bracket} bracket\index{bracket!curly} \verb:{:, it will read till the matching right curly bracket \verb:}: and then test whether the characters (after substitution of preprocessor variables) can be interpreted as a numerical expression. If it is not a valid numerical expression the whole string, including the curly brackets, will be passed on to the later stages of the program. If it is a numerical expression, it will be evaluated, and the whole string, including the curly brackets, will be replaced by a textual representation of the result. Example: \begin{verbatim} Local F`i' = F{`i'-1}+F{`i'-2}; \end{verbatim} If the preprocessor variable i has the value 11, the calculator makes this into \begin{verbatim} Local F11 = F10+F9; \end{verbatim} Valid numerical expressions can contain the characters \begin{verbatim} 0 1 2 3 4 5 6 7 8 9 + - * / % ( ) { } & | ^ ! \end{verbatim} The use of parentheses is as in regular arithmetic. The curly brackets fulfil the same role, as one can nest these brackets of course. Operators are: \begin{description} \item[$+$] Regular addition\index{addition}. \item[$-$] Regular subtraction\index{subtraction}. \item[$\ast$] Regular multiplication\index{multiplication}. \item[$/$] Regular (integer) division\index{division}. \item[$\%$] The remainder\index{remainder} after (integer) division as in the language C\index{C}. \item[$\&$] And\index{and} operator. This is a bitwise operator. \item[$|$] Or\index{or} operator. This is a bitwise or. \item[$\wedge$] Exponent\index{exponent} operator. \item[$!$] Factorial\index{factorial}. This is a postfix operator. \item[$\wedge\%$] A postfix ${}^2\!\log$. This means that it takes\index{twolog} the ${}^2\!\log$ of the object to the left of it. \item[$\wedge/$] A postfix square\index{square root} root. This means that it takes the square root of the object to the left of it. \end{description} Note that all arithmetic\index{arithmetic} is done over the integers and that there is a finite range. On 32\index{32 bits} bit systems this range will be $2^{31}-1$ to $-2^{31}$, while on 64\index{64 bits} bit systems this will be $2^{63}-1$ to $-2^{63}$. In particular this means that \verb:{13^/}: becomes \verb:3:. The preprocessor calculator is only meant for some simple counting and organization of the program flow. Hence there is no large degree of sophistication. Very important is that the comma\index{comma} character is not a legal character for the preprocessor calculator. This can be used to avoid some problems. Suppose one needs to make a substitution of the type: \begin{verbatim} id f(x?!{0}) = 1/x; \end{verbatim} in which the value zero should be excluded from the pattern matching (see dynamical\index{set!dynamical} sets in chapter \ref{pattern} on pattern matching). This would not work, because the preprocessor would make this into \begin{verbatim} id f(x?!0) = 1/x; \end{verbatim} which is illegal syntax. Hence the proper trick is to write \begin{verbatim} id f(x?!{,0}) = 1/x; \end{verbatim} With the comma the preprocessor will leave this untouched, and hence now the set is passed properly. Good use of the preprocessor calculator can make life much easier for \FORM\@. For example the following statements \begin{verbatim} id f(`i') = 1/(`i'+1); id f(`i') = 1/{`i'+1}; \end{verbatim} are quite different in nature. In the first statement the compiler gets an expression with a composite denominator. The compiler never tries to simplify expressions by doing algebra on them. Sometimes this may not be optimal, but there are cases in which it would cause wrong results (in particular when noncommuting and commuting functions are mixed and wildcards are used). Hence the composite denominator has to be worked out during run time for each term separately. The second statement has the preprocessor work out the sum and hence the compiler gets a simple fraction and less time will be needed during running. Note that \begin{verbatim} id f(`i') = {1/(`i'+1)}; \end{verbatim} would most likely not produce the desired result, because the preprocessor calculator works only over the integers. Hence, unless i is equal to zero or -2, the result would be zero (excluding of course the fatal error when i is equal to -1). %--#] Calculator : %--#[ ... : \section{The triple dot operator} \label{tripledot} The last\index{...} stage of the actions of the preprocessor involves the triple dot operator. It indicates a repeated pattern as in \verb:a1+...+a4: which would expand into \verb:a1+a2+a3+a4:. This operator is used in two different ways. First the most general way: \begin{verbatim} operator1...operator2 \end{verbatim} in which the less\index{less than} than and greater\index{greater than} than signs serve as boundaries for the patterns. The operators can be any pair of the following: \begin{description} \item[+\ +]\index{+...+} Repetitions will be separated by plus signs. \item[--\ --]\index{-...-} Repetitions will be separated by minus signs. \item[+\ --]\index{+...-} Repetitions will be separated by alternating signs. First will be plus. \item[--\ +]\index{-...+} Repetitions will be separated by alternating signs. First will be minus. \item[$\ast\ \ast$]\index{*...*} Repetitions will be separated by $\ast$. \item[/\ /]\index{/.../} Repetitions will be separated by /. \item[,\ ,]\index{,...,} Repetitions will be separated by comma's. \item[:\ :]\index{:...:} Repetitions will be separated by {\it single} dots. %\item[+\ +]\index{.@$+\cdots+$} Repetitions will be separated by plus signs. %\item[--\ --]\index{.@$-\cdots-$} Repetitions will be separated by minus signs. %\item[+\ --]\index{.@$+\cdots-$} Repetitions will be separated by alternating signs. %First will be plus. %\item[--\ +]\index{.@$-\cdots+$} Repetitions will be separated by alternating signs. %First will be minus. %\item[$\ast\ \ast$]\index{.@$\ast\cdots\ast$} Repetitions will be separated by $\ast$. %\item[/\ /]\index{.@$/\cdots/$} Repetitions will be separated by /. %\item[,\ ,]\index{.@$,\cdots,$} Repetitions will be separated by comma's. %\item[:\ :]\index{.@$:\cdots:$} Repetitions will be separated by {\it single} dots. \end{description} For such a pair of operators \FORM\ will inspect the patterns\index{pattern} and see whether the differences between the two patterns are just numbers. If the differences are numbers and the absolute value of the difference of each matching pair is always the same (a difference of zero is allowed too; it leads to no action for the pair), then \FORM\ will expand the pattern, running from the first to the last in increments of one. For each pair the counter can either run up or run down, depending on whether the number in the first pattern is greater or less than the number in the second pattern. Example: \begin{verbatim} Local F = -...+; \end{verbatim} leads to \begin{verbatim} Local F = a1b6(c3)-a2b5(c4)+a3b4(c5)-a4b3(c6); \end{verbatim} The second form is a bit simpler. It recognizes that there are special cases that can be written in a more intuitive way. If there is only a single number to be varied, and it is the end of the pattern, and the rest of the patterns consists only of alphanumeric characters of which the first is an alphabetic character, we do not need the less than/greater than combination. This is shown in \begin{verbatim} Symbol a1,...,a12; \end{verbatim} There is one extra exception. The variables used this way may have a question mark after them to indicate that they are wildcards: \begin{verbatim} id f(a1?,...,a4?) = g(a1,...,a4,a1+...+a4); \end{verbatim} This construction did not exist in earlier versions of \FORM\ (version 1 and version 2). There one needed the \#do\index{\#do} instruction for many of the above constructions, creating code that was very hard to read. The \verb:...: operator should improve the readability of the programs very much. %--#] ... : %--#[ add : \section{\#add} \label{preadd} \noindent Syntax: \#add object: "string" \noindent See chapter \ref{dictionaries} on dictionaries. \noindent Adds words to an open dictionary. %--#] add : %--#[ addseparator : \section{\#addseparator} \label{preaddseparator} \noindent Syntax: \#addseparator character \noindent See also \#rmseparator (\ref{prermseparator}), \#call (\ref{precall}), \#do (\ref{predo}) \noindent Adds a character\index{\#addseparator} to the list of permissible separator characters for arguments of \#call or \#do instructions. By default the two characters that are permitted are the comma and the character \verb:|:. Blanks, tabs and double quotes are ignored. Note that the comma must be specified between double quotes as in \begin{verbatim} #addseparator "," \end{verbatim} %--#] addseparator : %--#[ append : \section{\#append} \label{preappend} \noindent Syntax: \#append $<$filename$>$ \noindent See also write (\ref{prewrite}), close (\ref{preclose}), create (\ref{precreate}), remove (\ref{preremove}) \noindent Opens\index{\#append} the named file for writing. The file will be positioned at the end. The next \#write\index{\#write} instruction will add to it. %--#] append : %--#[ appendpath : \section{\#appendpath} \label{preappendpath} \noindent Syntax: \#appendpath pathname \noindent See also prependpath~(\ref{preprependpath}) \noindent Appends the given path relative to the current file to the end of the \FORM{} path\index{path}. %--#] appendpath : %--#[ break : \section{\#break} \label{prebreak} \noindent Syntax: \#break \noindent See also switch (\ref{preswitch}), endswitch (\ref{preendswitch}), case (\ref{precase}), default (\ref{predefault}) \noindent If the\index{\#break} lines before were not part of the control flow ({\it i.e.} these lines are used for the later stages of the program), this instruction is ignored. If they are part of the control flow, the flow will continue after the matching \#endswitch\index{\#endswitch} instruction. The \#break instruction must of course be inside the range of a \#switch\index{\#switch}/\#endswitch construction. %--#] break : %--#[ breakdo : \section{\#breakdo} \label{prebreakdo} \noindent Syntax: \#breakdo [{\tt<}number{\tt>}] \noindent See also \#do (\ref{predo}) and \#enddo (\ref{preenddo}) \noindent The \#breakdo\index{\#breakdo} instruction allows one to jump out of a \#do loop. If a (nonzero integer) number is specified it indicates the number of loops the program should terminate. Control will continue after the \#enddo instruction of the number of loops indicated by `number'. The default value is one. If the value is zero the statement has no effect. %--#] breakdo : %--#[ call : \section{\#call} \label{precall} \noindent Syntax: \#call procname(var1,...,varn) \noindent See also procedure (\ref{preprocedure}), endprocedure (\ref{preendprocedure}) \noindent This instruction\index{\#call} calls the procedure\index{procedure} with the name procname. The result is that \FORM\ looks for this procedure, first in its procedure buffers\index{buffer!procedure} (for procedures that were defined in the regular text stream as explained under the \#procedure\index{\#procedure} instruction), then it looks for a file by the name procname.prc in the current directory, and if it still has not found the procedure, it looks in the directories indicated by the path\index{path} variable in either the setup file or at the start of the program (see chapter \ref{setup} on the setup file). Next it looks for the -p option in the command that started \FORM\ (see the chapter on running \FORM). If this -p option has not been used \FORM\ will see whether there is an environment variable by the name FORMPATH\index{FORMPATH}. The directories indicated there will be searched for the file procname.prc. If \FORM\ cannot find the file, there will be an error message and execution will be stopped immediately. Once the procedure has been located, \FORM\ reads the whole file and then determines whether the number of parameters is identical in the \#call\index{\#call} instruction and the \#procedure\index{\#procedure} instruction. A difference is a fatal error. The parameter field consists of strings, separated by commas. If a string contains a comma, this comma should be preceded by a backslash\index{backslash} character (\verb:\:). If a string should contain a linefeed\index{linefeed}, one should `escape' this linefeed by putting a backslash and continue on the next line. Before version 3 of \FORM\ the syntax was different. The parentheses were curly brackets and the separators the symbol \verb:|:. This was made to facilitate the use of strings that might contain commas. In practise however, this turned out to be far from handy. In addition the new preprocessor calculator is a bit more active and hence an instruction of the type \begin{verbatim} #call test{1} \end{verbatim} will now be intercepted by the preprocessor calculator\index{calculator} and changed into \begin{verbatim} #call test1 \end{verbatim} Because there are many advantages to the preprocessor calculator treating the parameters of the procedures before they are called (in the older versions it did not do this), the notation has been changed. \FORM\ still understands the old notation, provided that there is no conflict with the preprocessor calculator. Hence \begin{verbatim} #call test{1|a} #call test{1,a} #call test(1|a) #call test(1,a) \end{verbatim} are all legal and give the same result, but only the last notation will work in future versions of \FORM\@. Nowadays also the use of the argument field wildcard (see chapter \ref{pattern} on pattern matching) is allowed as in the regular functions: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Pre_call_1) \begin{verbatim} #define a "1" #define bc2 "x" #define bc3 "y" #define b "c`~a'" #procedure hop(c,?d); #redefine a "3" #message This is the call: `c',`?d' #endprocedure #redefine a "2" #message This is b: `b' ~~~This is b: c2 #call hop(`b`!b''`!b'`b'`!b'`b',`~a',`b',`a') ~~~This is the call: xc2c3c2c3,3,c3,2 .end \end{verbatim} We also see here that the rules about delayed substitution (see also the \#define\index{\#define} instruction in section \ref{predefine}) apply. The use of `!b' cancels the delayed substitution that is asked for in the definition of b. The default extension for procedure files is .prc\index{.prc}, but it is possible to change this. There are two different ways: One is with the \#procedureExtension\index{\#procedureExtension} instruction in section \ref{preprocedureextension}. The other is via the setup (see the chapter on the setup file, chapter \ref{setup}). %--#] call : %--#[ case : \section{\#case} \label{precase} \noindent Syntax: \#case string \noindent See also switch (\ref{preswitch}), endswitch (\ref{preendswitch}), break (\ref{prebreak}), default (\ref{predefault}) \noindent The lines after the \#case\index{\#case} instruction will be used if either this is the first \#case\index{\#case} instruction of which the string matches the string in the \#switch\index{\#switch} instruction, or the control flow was already using the lines before this \#case instruction and there was no \#break\index{\#break} instruction (this is called fall-through). The control flow will include lines either until the next matching \#break instruction, or until the matching \#endswitch\index{\#endswitch} instruction. %--#] case : %--#[ clearoptimize : \section{\#clearoptimize} \label{preclearoptimize} \noindent Syntax: \#clearoptimize See the chapter about optimization \ref{optimization} %--#] clearoptimize : %--#[ close : \section{\#close} \label{preclose} \noindent Syntax: \#close $<$filename$>$ \noindent See also write (\ref{prewrite}), append (\ref{preappend}), create (\ref{precreate}), remove (\ref{preremove}) \noindent This instruction closes\index{\#close} the file\index{file!close} by the given name, if such a file had been opened by the previous \#write\index{\#write} instruction. Normally \FORM\ closes all such files at the end of execution. Hence the user would not have to worry about this. The use of a subsequent \#write instruction with the same file name will remove the old contents and hence start basically a new file. There are times that this is useful. %--#] close : %--#[ closedictionary : \section{\#closedictionary} \label{preclosedictionary} \noindent Syntax: \#closedictionary \noindent See chapter \ref{dictionaries} on dictionaries. \noindent Either closes an open dictionary (\ref{preopendictionary}) or stops using the dictionary (\ref{preusedictionary}) that is currently used for output translation. %--#] closedictionary : %--#[ commentchar : \section{\#commentchar} \label{precommentchar} \noindent Syntax: \#commentchar character \noindent The specified\index{\#commentchar} character should be a single non-whitespace character. There may be white space (blanks and/or tabs) before or after it. The character will take over the role of the comment character. {\it i.e.} any line that starts with this character in column 1 will be considered commentary\index{commentary}. This feature was provided because output of some other algebra programs could put the multiplication sign in column 1 in longer expressions. The default commentary character is $\ast$. %--#] commentchar : %--#[ continuedo : \section{\#continuedo} \label{precontinuedo} \noindent Syntax: \#continuedo [{\tt<}number{\tt>}] \noindent See also \#do (\ref{predo}) and \#enddo (\ref{preenddo}) \noindent The \#continuedo\index{\#continuedo} instruction allows one to jump to the next iteration of a \#do loop. If a (nonzero integer) number is specified it indicates the number of enclosing loops that the program should continue to the next iteration of. Control will continue at the beginning of the next iteration of the enclosing loop indicated by `number'. The default value is one. If the value is zero the instruction has no effect. %--#] continuedo : %--#[ create : \section{\#create} \label{precreate} \noindent Syntax: \#append $<$filename$>$ \noindent See also write (\ref{prewrite}), close (\ref{preclose}), append (\ref{preappend}), remove (\ref{preremove}) \noindent Opens the named\index{\#create} file for writing. If the file existed already, its previous contents will be lost. The next \#write\index{\#write} instruction will add to it. In principle this instruction is not needed, because the \#write instruction would create the file if it had not been opened yet at the moment of writing. %--#] create : %--#[ default : \section{\#default} \label{predefault} \noindent Syntax: \#default \noindent See also switch (\ref{preswitch}), endswitch (\ref{preendswitch}), case (\ref{precase}), break (\ref{prebreak}) \noindent Control\index{\#default} flow continues after this instruction if there is no \#case\index{\#case} instruction of which the string matches the string in the \#switch\index{\#switch} instruction. Control flow also continues after this instruction, if the lines before were included and there was no \#break\index{\#break} instruction to stop the control flow (fall-through). Control flow will stop either when a matching \#break instruction is reached, or when a matching \#endswitch\index{\#endswitch} is encountered. In the last case of course control flow will continue after the \#endswitch instruction. %--#] default : %--#[ define : \section{\#define} \label{predefine} \noindent Syntax: \#define name "string" \noindent See also redefine (\ref{preredefine}), undefine (\ref{preundefine}) \noindent in which name\index{\#define} refers to the name of the preprocessor\index{preprocessor variable} variable\index{variable!preprocessor} to be defined and the contents of the string will form the value of the variable. The double quotes are mandatory delimiters of the string. The use of the \#define\index{\#define} instruction creates a new instance of the preprocessor variable with the given name. This means that the old instance\index{instance} remains. If for some reason the later instance becomes undefined (see for instance \#undefine), the older instance will be the one that is active. If the old definition is to be overwritten, one should use the \#redefine\index{\#redefine} instruction. As of version 3.2 preprocessor variables can also have arguments as in the C\index{C} language. Hence \#define var(a,b) "(`\verb:~:a'+`\verb:~:b'+`c')" is allowed. The parameters should be referred to inside a pair of `' as with all preprocessor variables. A special feature is the socalled delayed\index{delayed substitution} substitution\index{substitution!delayed}. With macros like the above the question is always {\sl when} a preprocessor variable will be substituted. Take for instance % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Pre_define_1) \begin{verbatim} #define c "3" #define var1(a,b) "(`~a'+`~b'+`c')" #define var2(a,b) "(`~a'+`~b'+`~c')" #redefine c "4" Local F1 = `var1(1,2)'; Local F2 = `var2(1,2)'; Print; .end F1 = 6; F2 = 7; \end{verbatim} The parameter c will be substituted immediately when var1 is defined. In var2 it will be only substituted when var2 is used. It should be clear that a and b should also be used in the delayed fashion because they do not exist yet at the moment of the definition of var1 and var2. Notice also that the whole macro\index{macro}, with its arguments should be placed between the backquote and the quote. Another example can be found with the \#call\index{\#call} instruction. See section \ref{precall} %--#] define : %--#[ do : \section{\#do} \label{predo} \noindent Syntax: \#do lvar = i1,i2 \#do lvar = i1,i2,i3 \#do lvar = $\{$string1$|$...$|$stringn$\}$ \#do lvar = $\{$string1,...,stringn$\}$ \#do lvar = nameofexpression \noindent See also enddo (\ref{preenddo}) \noindent The \#do\index{\#do} instruction\index{do loop} needs a matching \#enddo\index{\#enddo} instruction. All code in-between these two instructions will be read as many times as indicated in the parameter field of the \#do instruction. The parameter lvar is a preprocessor variable of which the value is determined by the other parameters. Inside the loop it should be referred to by enclosing its name between a backquote/quote pair as is usual for preprocessor variables. The various possible parameter fields have the following meaning: \begin{description} \item[\#do lvar = i1,i2] The parameters i1 and i2 should be integers or names of dollar expressions that evaluate into integers. The first time in the loop lvar will get the value of i1 (as a string) and each next time its value will be one greater (translated into a string again). The last time in the loop the value of lvar will be the greatest integer that is less or equal to i2. If i2 is less than i1, the loop is skipped completely. If i2 is the name of a dollar variable, each time the control reaches the end of the loop the dollar variable is evaluated and the current value is used. \item[\#do lvar = i1,i2,i3] The parameters i1,i2 and i3 should be integers or names of dollar expressions that evaluate into integers. The first time in the loop lvar will get the value of i1 (as a string) and each next time its value will be incremented by adding i3 (translated into a string again). If i3 is positive, the last value of lvar will be the one for which lvar+i3 is greater than i2. If i2 is less than i1, the loop is skipped completely. If i3 is negative the last value of lvar will be the one for which lvar+i3 is less than i2. If i3 is zero there will be an error. If i2 or i3 are the names of a dollar variable, each time the control reaches the end of the loop the dollar variable(s) is/are evaluated and the current value is used. \item[\#do lvar = $\{$string1$|$...$|$stringn$\}$] The first time in the loop the value of lvar is the string indicated by string1, the next time will be string2 etc till the last time when it will be stringn. This is called a listed\index{listed loop} loop\index{loop!listed}. The notation with the $|$ is an old notation which is still accepted. The new notation uses a comma instead. \item[\#do lvar = $\{$string1,...,stringn$\}$] The first time in the loop the value of lvar is the string indicated by string1, the next time will be string2 etc till the last time when it will be stringn. This is called a listed\index{listed loop} loop\index{loop!listed}. \item[\#do lvar = expression] The loop variable will take one by one for its value all the terms of the given expression. This is protected against changing the expression inside the loop by making a copy of the expression inside the memory. Hence one should be careful with very big expressions. An expression that is zero gives a loop over zero terms, hence the loop is never executed. \end{description} The first two types of \#do instructions are called numerical\index{numerical loop} loops\index{loop!numerical}. In the parameters of numerical loops the preprocessor calculator\index{calculator} is invoked automatically. One should make sure not to use a leading $\{$ for the first numerical parameter in such a loop. This would be interpreted as belonging to a listed loop. After a loop has been finished, the corresponding preprocessor variable will be undefined. This means that if there is a previous preprocessor variable by the same name, the value of the \#do instruction will be used inside the loop, and afterwards the old value will be active again. It is allowed to overwrite the value of a preprocessor \#do instruction variable. This can be very useful to create the equivalent of a repeat loop that contains .sort instructions as in \begin{verbatim} #do i = 1,1 id,once,x = y+2; if ( count(x,1) > 0 ) redefine i "0"; .sort #enddo \end{verbatim} A few remarks are necessary here. The redefine\index{redefine} statement (see section \ref{substaredefine}) should be before the last .sort\index{.sort} inside the loop, because the \#do instruction is part of the preprocessor. Hence the value of i is considered before the module is executed. This means that if the redefine would be after the .sort, two things would go wrong: First the loop would be terminated before the redefine would ever make a chance of being executed. Second the statement would be compiled in the expectation that there is a variable i, but then the loop would be terminated. Afterwards, when the statement is being executed it would refer to a variable that does not exist any longer. If one wants to make a loop over the externals of the brackets of an expression only, one needs to do some work. Assume we have the expression F and we want to loop over the brackets in x and y: \begin{verbatim} L FF = F; Bracket x,y; .sort CF acc,acc2; Skip F; Collect acc,acc2; id acc(x?) = 1; id acc2(x?)= 1; B x,y; .sort Skip F; Collect acc; id acc(x?) = 1; .sort #do i = FF L G = F[`i']; . . #enddo \end{verbatim} Notice that we have to do the collect\index{collect} trick twice because the first time the bracket could be too long for one term. The second time that restriction doesn't exist because besides the x and the y there are only integer coefficients. %--#] do : %--#[ else : \section{\#else} \label{preelse} \noindent Syntax: \#else \noindent See also if (\ref{preif}), endif (\ref{preendif}), elseif (\ref{preelseif}), ifdef (\ref{preifdef}), ifndef (\ref{preifndef}) \noindent This instruction\index{\#else} is used inside a \#if\index{\#if}/\#endif\index{\#endif} construction. The code that follows it until the \#endif instruction will be read if the condition of the \#if instruction (and of none of the corresponding \#elseif\index{\#elseif} instructions) is not true. If any of these conditions is true, this code is skipped. The reading is stopped after the matching \#endif is encountered and continued after this matching \#endif instruction. %--#] else : %--#[ elseif : \section{\#elseif} \label{preelseif} \noindent Syntax: \#elseif ( condition ) \noindent See also if (\ref{preif}), endif (\ref{preendif}), else (\ref{preelse}) \noindent The syntax\index{\#elseif} of the condition is identical to the syntax for the condition in the \#if\index{\#if} instruction. The \#elseif instruction can occur between an \#if and an \#endif\index{\#endif} instruction, before a possible matching \#else\index{\#else} instruction. The code after this condition till the next \#elseif instruction, or till a \#else instruction or till a \#endif instruction, whatever comes first, will be read if the condition in the \#elseif instruction is true and none of the conditions in matching previous \#if or \#elseif instructions were true. The reading is stopped after the matching \#elseif/\#else/\#endif is encountered and continued after the matching \#endif instruction. Example \begin{verbatim} #if ( `i' == 2 ) some code #elseif ( `i' == 3 ) more code #elseif ( `j' >= "x2y" ) more code #else more code #endif \end{verbatim} %--#] elseif : %--#[ enddo : \section{\#enddo} \label{preenddo} \noindent Syntax: \#enddo \noindent See also do (\ref{predo}) \noindent Used to\index{\#enddo} terminate\index{terminate} a preprocessor do\index{do loop} loop. See the \#do\index{\#do} instruction. %--#] enddo : %--#[ endfloat : \section{\#endfloat} \label{preendfloat} \noindent Syntax: \#endfloat \noindent See also startfloat (\ref{prestartfloat}) and chapter~\ref{floatingpoint} on the floating point capability. %--#] endfloat : %--#[ endif : \section{\#endif} \label{preendif} \noindent Syntax: \#endif \noindent See also if (\ref{preif}), else (\ref{preelse}), elseif (\ref{preelseif}), ifdef (\ref{preifdef}), ifndef (\ref{preifndef}) \noindent Used to terminate\index{\#endif} a \#if\index{\#if}, \#ifdef\index{\#ifdef} or \#ifndef\index{\#ifndef} construction. Reading will continue after it. %--#] endif : %--#[ endinside : \section{\#endinside} \label{preendinside} \noindent Syntax: \#endinside \noindent See also \#inside (\ref{preinside}) \noindent Used to\index{\#endinside} terminate a \#inside construction in the preprocessor. For more details, see the \#inside\index{\#inside} instruction. %--#] endinside : %--#[ endprocedure : \section{\#endprocedure} \label{preendprocedure} \noindent Syntax: \#endprocedure \noindent See also procedure (\ref{preprocedure}), call (\ref{precall}) \noindent Each procedure\index{procedure} must be terminated by an \#endprocedure\index{\#endprocedure} instruction. If the procedure resides in its own file, the \#endprocedure will cause the closing of the file. Hence any text that is in the file after the \#endprocedure instruction will be ignored. When control reaches the \#endprocedure instruction, all (local) preprocessor variables\index{variables!preprocessor} that were defined inside the procedure and all parameters of the call of the procedure will become undefined. %--#] endprocedure : %--#[ endswitch : \section{\#endswitch} \label{preendswitch} \noindent Syntax: \#endswitch \noindent See also switch (\ref{preswitch}), case (\ref{precase}), break (\ref{prebreak}), default (\ref{predefault}) \noindent This instruction marks the end\index{\#endswitch} of a \#switch\index{\#switch} construction. After none or one of the cases of the \#switch construction has been included in the control flow, reading will continue after the matching \#endswitch instruction. Each \#switch needs a \#endswitch, unless a .end instruction is encountered first. %--#] endswitch : %--#[ exchange : \section{\#exchange} \label{preexchange} \noindent Syntax: \#exchange expr1,expr2 \#exchange \$var1,\$var2 \noindent Exchanges\index{\#exchange} the names of two expressions\index{expression}. This means that the contents of the expressions remain where they are. Hence the order in which the expressions are processed remains the same, but the name under which one has to refer to them has been changed. In the variety with the dollar variables\index{\$-variable} the contents of the variables are exchanged. This is not much work, because dollar variables reside in memory and hence only two pointers to the contents have to be exchanged (and some extra information about the contents). This instruction can be very useful when sorting expressions or dollar variables by their contents. %--#] exchange : %--#[ external : \section{\#external} \label{preexternal} \noindent Syntax: \#external ["prevar"] systemcommand \noindent Starts the command\index{\#external} in the background, connecting to its standard\index{standard output}\index{standard input} input\index{input!standard} and output\index{output!standard}. By default, the \#external command has no controlling terminal, the standard error stream is redirected to \verb|/dev/null| and the command is run in a subshell in a new session and in a new process group (see the preprocessor instruction \verb|#setexternalattr|). The optional parameter ``prevar'' is the name of a preprocessor variable placed between double quotes. If it is present, the ``descriptor'' (small positive integer number) of the external command is stored into this variable and can be used for references to this external command (if there is more than one external command running simultaneously). The external command that is started last becomes the ``current'' (active) external command. All further instructions \#fromexternal\index{\#fromexternal} and \#toexternal\index{\#toexternal} deal with the current external command. %--#] external : %--#[ factdollar : \section{\#factdollar} \label{prefactdollar} \noindent Syntax: \#factdollar \$-variable \noindent See also the chapters on polynomials \ref{polynomials} and \$-variables \ref{dollars} \noindent The \#factdollar\index{\#factdollar} instruction causes the factorization of the indicated \$-variable. After this instruction and until the \$-variable is redefined there will be two versions of the variable: one is the original unfactorized version and the other is a list of factors. If the name of the variable is \$a the factors can be accessed as $\$a[1],\cdots,\$a[n]$. The total number of factors is given by $\$a[0]$. These factors can also be treated as preprocessor variables by putting them between quotes as in `$\$a[2]$'. %--#] factdollar : %--#[ fromexternal : \section{\#fromexternal} \label{prefromexternal} \noindent Syntax: \#fromexternal[$+-$] ["[\$]varname" [maxlength]] \noindent Appends\index{\#fromexternal} the output of the current external command to the \FORM\ program. The semantics differ depending on the optional arguments. After the external command sends the prompt\index{prompt}, \FORM\ will continue with a next line after the line containing the \#fromexternal instruction. The prompt string is not appended. The optional $+$ or $-$ sign after the name has influence on the listing of the content. The varieties are: \#fromexternal[$+-$] \noindent The semantics is similar to the \#include\index{\#include} instruction but folders are not supported. \#fromexternal[$+-$] "[\$]varname" \noindent is used to read the text from the running external command into the preprocessor variable varname, or into the dollar variable \$varname if the name of the variable starts with the dollar sign ``\$''. \#fromexternal[$+-$] "[\$]varname" maxlength \noindent is used to read the text from the running external command into the preprocessor (or dollar) variable varname. Only the first maxlength characters are stored. %--#] fromexternal : %--#[ if : \section{\#if} \label{preif} \noindent Syntax: \#if ( condition ) \noindent See also endif (\ref{preendif}), else (\ref{preelse}), elseif (\ref{preelseif}), ifdef (\ref{preifdef}), ifndef (\ref{preifndef}) \noindent The \#if\index{\#if} instruction should be accompanied by a matching \#endif\index{\#endif} instruction. In addition there can be between the \#if and the \#endif some \#elseif\index{\#elseif} instructions and/or a single \#else\index{\#else} instruction. The condition is a logical variable that is true if its value is not equal to zero, and false if its value is zero. Hence it is allowed to use \begin{verbatim} #if `i' statements #endif \end{verbatim} provided that i has a value which can be interpreted as a number. If there is just a string that cannot be seen as a logical\index{logical} condition or a number it will be interpreted as false. The regular syntax of the simple condition is \begin{verbatim} #if `i' == st2x statements #endif \end{verbatim} or \begin{verbatim} #if ( `i' == st2x ) statements #endif \end{verbatim} in which the compare is a numerical compare if both strings can be seen as numbers, while it will be a string compare if at least one of the two cannot be seen as a numerical object. One can also use more complicated conditions as in \begin{verbatim} #if ( ( `i' > 5 ) && ( `j' > `i' ) ) \end{verbatim} These are referred to as composite conditions. The possible operators are \begin{description} \item[$>$] Greater than, either in numerical or in lexicographical sense. \item[$<$] Less than, either in numerical or in lexicographical sense. \item[$>=$] Greater than or equal to, either in numerical or in lexicographical sense. \item[$<=$] Less than or equal to, either in numerical or in lexicographical sense. \item[$==$ or $=$] Equal to. \item[$!=$] Not equal to. \item[$\&\&$] Logical and operator to combine conditions. \item[$||$] Logical or operator to combine conditions. \end{description} If the condition evaluates to true, the lines after the \#if instruction will be read until the first matching \#elseif instruction, or a \#else instruction or a \#endif instruction, whatever comes first. After such an instruction is encountered input reading stops and continues after the matching \#endif instruction. Like with the regular if-statement (see \ref{substaif}), there are some special functions that allow the asking of questions about objects. These are \leftvitem{3cm}{exists()} \rightvitem{13cm}{The argument of exists\index{exists} is the name of an expression or a \$-variable. This function then returns one if this object exists, cq.\ has been defined. Otherwise it returns zero. } \leftvitem{3cm}{isdefined()} \rightvitem{13cm}{The argument of isdefined\index{isdefined} is the name of a preprocessor variable. This function then returns one if this object has been defined. Otherwise it returns zero. Technically \texttt{\#ifdef `VAR'} and \texttt{\#if ( isdefined(VAR) )} are the same. The isdefined function allows for greater flexibility in composite conditions.} \leftvitem{3cm}{isfactorized()} \rightvitem{13cm}{The argument of isfactorized\index{isfactorized} is the name of an expression or a \$-variable. This function then returns one if the object has been factorized. Otherwise it returns zero. } \leftvitem{3cm}{isnumerical()} \rightvitem{13cm}{The argument of isnumerical\index{isnumerical} is the name of an expression or a \$-variable. This function then returns one if the object contains a single term that is purely numerical in nature. Otherwise it returns zero. } \leftvitem{3cm}{maxpowerof()} \rightvitem{13cm}{The argument of maxpowerof\index{maxpowerof} is the name of a symbol. This function then evaluates into the maximum power of that symbol as it has been declared. If no maximum power has been set in the declaration of the symbol, the general maximum power for symbols is returned (see \ref{substasymbols}).} \leftvitem{3cm}{minpowerof()} \rightvitem{13cm}{The argument of minpowerof\index{minpowerof} is the name of a symbol. This function then evaluates into the minimum power of that symbol as it has been declared. If no minimum power has been set in the declaration of the symbol, the general minimum power for symbols is returned (see \ref{substasymbols}).} \leftvitem{3cm}{sizeof()} \rightvitem{13cm}{The argument of termsin\index{termsin} is the name of an expression or a \$-variable. This function then evaluates into the number of \FORM{} words in that expression or variable.} \leftvitem{3cm}{termsin()} \rightvitem{13cm}{The argument of termsin\index{termsin} is the name of an expression or a \$-variable. This function then evaluates into the number of terms in that expression.} %--#] if : %--#[ ifdef : \section{\#ifdef} \label{preifdef} \noindent Syntax: \#ifdef `prevar' \noindent See also if (\ref{preif}), endif (\ref{preendif}), else (\ref{preelse}), ifndef (\ref{preifndef}) \noindent If the named\index{\#ifdef} preprocessor variable has been defined the condition is true, else it is false. For the rest the instruction behaves like the \#if\index{\#if} instruction. An alternative is to use the isdefined object inside the \#if instruction. %--#] ifdef : %--#[ ifndef : \section{\#ifndef} \label{preifndef} \noindent Syntax: \#ifndef `prevar' \noindent See also if (\ref{preif}), endif (\ref{preendif}), else (\ref{preelse}), ifdef (\ref{preifdef}) \noindent If the named\index{\#ifndef} preprocessor variable has been defined the condition is false, else it is true. For the rest the instruction behaves like the \#if\index{\#if} instruction. %--#] ifndef : %--#[ include : \section{\#include} \label{preinclude} \noindent Syntax: \#include[$-+$] filename \#include[$-+$] filename \# foldname \noindent The named\index{\#include} file is searched for and opened. Reading\index{reading} continues from this file until its end. Then the file will be closed and reading continues after the \#include instruction. If a foldname\index{foldname} is specified, \FORM\ will only read the contents of the first fold\index{fold} it encounters in the given file that has the specified name. The file is searched for in the current directory, then in the path specified in the path\index{path} variable in the setup file or at the beginning of the program (see chapter \ref{setup} on the setup file). Next it will look in the path specified in the -p option when \FORM\ is started (see the chapter on running \FORM). If this option has not been used, \FORM\ will look for the environment variable FORMPATH\index{FORMPATH}. If this variable exists it will be interpreted as a path and \FORM\ will search the indicated directories for the given file. If none is found there will be an error message and execution will be halted. The optional $+$ or $-$ sign after the name has influence on the listing of the contents of the file. A $-$ sign will have the effect of a \#$-$ instruction during the reading of the file. A plus sign will have the effect of a \#$+$ instruction during the reading of the file. A fold is defined by a starting line of the format: \begin{verbatim} *--#[ name : \end{verbatim} and a closing line of the format \begin{verbatim} *--#] name : \end{verbatim} in which the first character is actually the current commentary\index{commentary} character (see the \#commentchar instruction). All lines between two such lines are considered to be the contents of the fold. If \FORM\ decides that it needs this fold, it will read these contents and put them in its input stream. More about folds is explained in the manual of the STedi editor which is also provided in the \FORM\ distribution. %--#] include : %--#[ inside : \section{\#inside} \label{preinside} \noindent Syntax: \#inside \$var1 [more \$variables] \noindent See also \#endinside (\ref{preendinside}) \noindent Used to\index{\#inside} execute a few statements on the contents of one or more dollar variables (see \ref{dollars}) during compilation time. Although this is a preprocessor instruction one can use the triple dot operator provided one uses the generic version with the $<>$. \noindent The statements in the scope of the \#inside / \#endinside construction must be regular executable statements. They may not contain end-of-module instructions like the .sort instruction. It is allowed to use dollar variables, procedures and preprocessor do loops and if's, but it is not allowed to nest the \#inside / \#endinside constructions. %--#] inside : %--#[ message : \section{\#message} \label{premessage} \noindent Syntax: \#message themessagestring \noindent This instruction places a message\index{\#message} in the output that is clearly marked as such. It is printed with an initial three characters in front as in \begin{verbatim} Symbols a,b,c; #message Simple example; ~~~Simple example; Local F = (a+b+c)^10; .end Time = 0.00 sec Generated terms = 66 F Terms in output = 66 Bytes used = 1138 \end{verbatim} Note that the semicolon\index{semicolon} is not needed and if present is printed as well. If one needs messages without this clear marking, one should use the \#write\index{\#write} instruction. %--#] message : %--#[ opendictionary : \section{\#opendictionary} \label{preopendictionary} \noindent Syntax: \#opendictionary name \noindent See chapter \ref{dictionaries} on dictionaries. \noindent Opens a dictionary and makes it ready for adding words to it. If the dictionary does not exist yet, it will be created. %--#] opendictionary : %--#[ optimize : \section{\#optimize} \label{preoptimize} \noindent Syntax: \#optimize nameofoneexpression See the chapter about optimization \ref{optimization} %--#] optimize : %--#[ pipe : \section{\#pipe} \label{prepipe} \noindent Syntax: \#pipe systemcommand \noindent See also system (\ref{presystem}) \noindent This\index{\#pipe} forces a system command to be executed by the operating system. The complete string (excluding initial blanks or tabs) is passed to the operating system. Next \FORM\ will intercept the output of whatever is produced and read that as input. Hence, whenever output is produced \FORM\ will take action, and it will wait when no output is ready. After the command has been finished, \FORM\ will continue with the next line. This instruction has only been implemented on systems that support pipes\index{pipe}. This is mainly UNIX\index{UNIX} and derived systems. Note that this instruction also introduces operating system dependent code. Hence it should be used with great care. %--#] pipe : %--#[ preout : \section{\#preout} \label{prepreout} \noindent Syntax: \#preout ON \#preout OFF \noindent Turns\index{\#preout} listing of the output of the preprocessor to the compiler on or off. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Pre_preout_1) \begin{verbatim} #PreOut ON S a1,...,a4; S,a1,a2,a3,a4 L F = (a1+...+a4)^2; L,F=(a1+a2+a3+a4)^2 id a4 = -a1; id,a4=-a1 .end Time = 0.00 sec Generated terms = 10 F Terms in output = 3 Bytes used = 52 \end{verbatim} %--#] preout : %--#[ prependpath : \section{\#prependpath} \label{preprependpath} \noindent Syntax: \#prependpath pathname \noindent See also appendpath~(\ref{preappendpath}) \noindent Prepends the given path relative to the current file to the beginning of the \FORM{} path\index{path}. %--#] prependpath : %--#[ printtimes : \section{\#printtimes} \label{preprinttimes} \noindent Syntax: \#printtimes \noindent Prints\index{\#printtimes} the current execution time and real time in the same way as done at the end of the program. Helps in monitoring the real time passed in \TFORM{} jobs. Example: \begin{verbatim} #Printtimes 423.59 sec + 5815.88 sec: 6239.47 sec out of 1215.29 sec \end{verbatim} %--#] printtimes : %--#[ procedure : \section{\#procedure} \label{preprocedure} \noindent Syntax: \#procedure name(var1,...,varn) \noindent See also endprocedure (\ref{preendprocedure}), call (\ref{precall}) \noindent Name\index{\#procedure} is the name of the procedure\index{procedure}. It will be referred to by this name. If the procedure resides in a separate file the name of the file should be name.prc and the \#procedure instruction should form the first line of the file. The \# should be the first character of the file. The parameter field is optional. If there are no parameters, the procedure should also be called without parameters (see the \#call instruction). The parameters (here called var1 to varn) are preprocessor variables and hence they should be referred to between a backquote\index{backquote}/quote\index{quote} pair as in `var1' to `varn'. If there exist already variables with such names when the procedure is called, the new definition comes on top of the old one. Hence in the procedure (and procedures called from it, unless the same problems occurs there too, as would be the case with recursions) the new definition is used, and it is released again when control returns from the procedure. After that the old definition will be in effect again. If the procedure is included in the regular input stream, \FORM\ will read the text of the procedure until the \#endprocedure\index{\#endprocedure} instruction and store it in a special buffer. When the procedure is called, \FORM\ will read the procedure from this buffer, rather than from a file. In systems where file transfer is slow (very busy server with a slow network) this may be faster, especially when many small procedures are called. One way to make libraries\index{library!making a}\index{library} that contain many procedures and maybe more code is to put all procedures into one header (.h) file and include this file at the beginning of the program with a \#include\index{\#include} instruction. This way one has all procedures load and one knows for sure that it are the proper procedures as it guards against the inadvertently picking up of procedures from other directories. It also makes for fewer files and hence makes for better housekeeping. %--#] procedure : %--#[ procedureextension : % NEW@@@ \section{\#procedureextension} \label{preprocedureextension} \noindent Syntax: \#procedureextension string \noindent See also \#call (\ref{precall}) \noindent The default\index{\#procedureextension} extension of procedures is .prc\index{.prc} in \FORM\@. It is however possible that this clashes with the extensions used by other programs like the Grace\index{Grace} system (Yuasa et al, Prog. Theor. Phys. Suppl. 138(2000)18 ). In that case it is possible to change the extension of the procedures in the current program. This is either done via the setup (page \ref{setup}) or by the \#procedureextension instruction of the preprocessor. The new string replaces the string prc, used by default. For the new string the following restrictions hold: \begin{enumerate} \item The first character must be alphabetic \item No whitespace characters (blanks and/or tabs) are allowed \end{enumerate} For the rest any characters can be used. \noindent The new extension will remain valid either till the next \#procedureextension instruction or to the next .clear\index{.clear} instruction (page \ref{instrclear}), whatever comes first. %--#] procedureextension : %--#[ prompt : \section{\#prompt} \label{preprompt} \noindent Syntax: \#prompt [newprompt] \noindent Sets a new prompt\index{\#prompt} for the current external command (if present) and all further (newly started) external commands. If newprompt is an empty string, the default prompt (an empty line) will be used. The prompt\index{prompt} is a line consisting of a single prompt string. By default, this is an empty string. %--#] prompt : %--#[ redefine : \section{\#redefine} \label{preredefine} \noindent Syntax: \#redefine name "string" \noindent See also define (\ref{predefine}), undefine (\ref{preundefine}) \noindent in which\index{\#redefine} name refers to the name of the preprocessor\index{preprocessor variable} variable\index{variable!preprocessor} to be redefined. The contents of the string will be its new value. If no variable of the given name exists yet, the instruction will be equivalent to the \#define\index{\#define} instruction. %--#] redefine : %--#[ remove : \section{\#remove} \label{preremove} \noindent Syntax: \#remove $<$filename$>$ \noindent See also write (\ref{prewrite}), append (\ref{preappend}), create (\ref{precreate}), close (\ref{preclose}) \noindent Deletes\index{\#remove} the named file from the system. Under UNIX\index{UNIX} this would be equivalent to the instruction \begin{verbatim} #system rm filename \end{verbatim} and under MS-DOS\index{MS-DOS} oriented systems like Windows\index{Windows} it would be equivalent to \begin{verbatim} #system del filename \end{verbatim} The difference with the \#system\index{\#system} instruction is that the \#remove\index{\#remove} instruction does not depend on the particular syntax of the operating system. Hence the \#remove instruction can always be used. %--#] remove : %--#[ reset : \section{\#reset} \label{prereset} \noindent Syntax: \#reset [{\tt<}keyword{\tt>}] \noindent See also `TIMER\_' preprocessor variable. \noindent Currently the only keywords that are allowed are timer and stopwatch. They have the same effect, which is to reset the timer for the `timer\_' (or `stopwatch\_) preprocessor variable (see \ref{preprovariables}). %--#] reset : %--#[ reverseinclude : \section{\#reverseinclude} \label{prereverseinclude} \noindent Syntax: \#reverseinclude[$-+$] filename \#reverseinclude[$-+$] filename \# foldname \noindent This instruction is identical to the \#include \ref{preinclude} instruction, with the exception that the statements and instructions in the file are read in reverse order. This can be useful at times when code is generated in a particular order in a file and one would like to 'undo' this code. It is somewhat related to the effects of the debugflag option (\ref{optimdebugflag}) in the optimization options of the format statement \ref{optimization}. There are a few limitations. If, for instance, linefeeds or semicolons occur inside preprocessor variables, the reading routines cannot see this. Additionally unfinished strings (unmatched double quotes) will result in a fatal error. On the other hand the fold structure remains preserved. %--#] reverseinclude : %--#[ rmexternal : \section{\#rmexternal} \label{prermexternal} \noindent Syntax: \#rmexternal [n] \noindent Terminates\index{\#rmexternal} an external command. The integer number n must be either the descriptor of a running external command, or 0. If n is 0, then all external programs will be terminated. If n is not specified, the current external command will be terminated. The action of this instruction depends on the attributes of the external channel (see the \#setexternalattr\index{\#setexternalattr} (section \ref{setexternalcommunication}) instruction). By default, the instruction closes the commands' IO channels, sends a KILL\index{KILL signal} signal to every process in its process group and waits for the external command to be finished. %--#] rmexternal : %--#[ rmseparator : \section{\#rmseparator} \label{prermseparator} \noindent Syntax: \#rmseparator character \noindent See also \#addseparator (\ref{preaddseparator}), \#call (\ref{precall}), \#do (\ref{predo}) \noindent Removes a character\index{\#rmseparator} from the list of permissible separator characters for arguments of \#call or \#do instructions. By default the two characters that are permitted are the comma and the character \verb:|:. Blanks, tabs and double quotes are ignored. Note that the comma must be specified between double quotes as in \begin{verbatim} #rmseparator "," \end{verbatim} %--#] rmseparator : %--#[ setexternal : \section{\#setexternal} \label{presetexternal} \noindent Syntax: \#setexternal n \noindent Sets\index{\#setexternal} the ``current'' external command. The instructions \#toexternal\index{\#toexternal} and \#fromexternal\index{\#fromexternal} deal with the current external command. The integer number n must be the descriptor of a running external command. %--#] setexternal : %--#[ setexternalattr : \section{\#setexternalattr} \label{presetexternalattr} \noindent Syntax: \#setexternalattr list\_of\_attributes \noindent sets\index{\#setexternalattr} attributes for {\em newly started} external commands. Already running external commands are not affected. The list of attributes is a comma separated list of pairs attribute=value, e.g.: \begin{verbatim} #setexternalattr shell=noshell,kill=9,killall=false \end{verbatim} Possible attributes are: \begin{description} \item[kill\index{kill}] specifies the signal to be sent to the external command either before the termination of the \FORM\ program or by the preprocessor instruction \verb|#rmexternal|. By default this is 9 ( SIGKILL\index{SIGKILL signal}). Number 0 means that no signal will be sent. \item[killall\index{killall}] Indicates whether the kill signal will be sent to the whole group or only to the initial process. Possible values are ``\verb|true|'' and ``\verb|false|''. By default, the kill signal will be sent to the whole group. \item[daemon\index{daemon}] Indicates whether the command should be ``daemonized'', i.e. the initial process will be passed to the init process and will belong to the new process group in the new session. Possible values are ``\verb|true|'' and ``\verb|false|''. By default, ``\verb|true|''. \item[shell\index{shell}] specifies which shell\index{shell} is used to run a command. (Starting an external command in a subshell permits to start not only executable files but also scripts\index{script} and pipelined\index{pipelined job} jobs. The disadvantage is that there is no way to detect failure upon startup since usually the shell is started successfully.) By default this is ``\verb|/bin/sh -c|''. If set \verb|shell=noshell|, the command will be stared by the instruction \#external\index{\#external} directly but not in a subshell, so the command should be a name of the executable file rather than a system command. The instruction \#external will duplicate the actions of the shell in searching for an executable file if the specified file name does not contain a slash (/) character. The search path is the path specified in the environment by the PATH\index{PATH} variable. If this variable isn't specified, the default path ``\verb|:/bin:/usr/bin|'' is used. \item[stderr\index{stderr}] specifies a file to redirect the standard\index{standard error} error stream to. By default it is ``\verb|/dev/null|''. If set \verb|stderr=terminal|, no redirection occurs. \end{description} Only attributes that are explicitly mentioned are changed, all others remain unchanged. Note, changing attributes should be done with care. For example, \begin{verbatim} #setexternalattr daemon=false \end{verbatim} starts a command in the subshell within the current process group with default attributes kill=9 and killall=true. The instruction \#rmexternal\index{\#rmexternal} sends the KILL\index{KILL signal} signal to the wholegroup, which means that also \FORM\ itself will be killed. %--#] setexternalattr : %--#[ setrandom : \section{\#setrandom} \label{presetrandom} \noindent Syntax: \#setrandom number \noindent See also random\_ (\ref{funrandom}) and ranperm\_ (\ref{funranperm}) \noindent The \#setrandom\index{\#setrandom} instruction initializes the random number generator random\_~\ref{funrandom}\index{random\_}\index{function!random\_}. The number that is used as a seed can have the length of two words in \FORM\@. This means that on a 32-bits computer it can be an (unsigned) 32-bits integer and on a 64-bits computer it can be an (unsigned) 64 bits integer. If there is no \#setrandom instruction the random number generator is initialized in a built in standard way. The \#setrandom instruction also initializes the random number generators of the workers when one uses \TFORM{} or \ParFORM\@. They are initialized with different seeds that are derived in a non-trivial way from the seed given by the user and the number of the worker. %--#] setrandom : %--#[ show : \section{\#show} \label{preshow} \noindent Syntax: \#show [preprocessorvariablename[s]] \noindent If no names\index{\#show} are present, the contents of all preprocessor variables\index{variable!preprocessor} will be printed to the regular output. If one or more preprocessor variables are specified (separated by comma's), only their contents will be printed. The preprocessor variables should be represented by their name only. No enclosing backquote/quote should be used, because that would force a substitution of the preprocessor variable before the instruction gets to see the name. Example: \begin{verbatim} #define MAX "3" Symbols a1,...,a`MAX'; L F = (a1+...+a`MAX')^2; #show #The preprocessor variables: 0: VERSION_ = "3" 1: SUBVERSION_ = "2" 2: NAMEVERSION_ = "" 3: DATE_ = "Wed Feb 28 08:43:20 2007" 4: NAME_ = "testpre.frm" 5: CMODULE_ = "1" 6: MAX = "3" .end Time = 0.00 sec Generated terms = 6 F Terms in output = 6 Bytes used = 102 \end{verbatim} We see that the variable MAX has indeed the value 3. There are six additional variables which have been defined by \FORM\ itself. Hence the trailing underscore which cannot be used in user defined names. The current version of \FORM\ is shown in the variable VERSION\_\index{VERSION\_} and the name of the current program is given in the variable NAME\_\index{NAME\_}. For more about the system defined preprocessor variables see \ref{preprovariables}. There is another preprocessor variable that does not show in the listings. Its name is SHOWINPUT\_\index{SHOWINPUT\_}. This variable has the value one if the listing of the input is on and the value zero if the listing of the input is off. %--#] show : %--#[ skipextrasymbols : \section{\#skipextrasymbols} \label{preskipextrasymbols} \noindent Syntax: \#skipextrasymbols positivenumber \noindent See also ExtraSymbols~(\ref{substaextrasymbols}) and the chapter on optimization~(\ref{optimization}). \noindent This instructions adds a number of dummy extra symbols\index{extra symbols} to the list of extra symbols~(\ref{substaextrasymbols}). This can be used when several optimizations are done on an expression in such a way that the extra symbols of previous optimizations are still present. Normally the number space for them is erased in a \#clearoptimize instruction. This can be avoided with a sequence like \begin{verbatim} #skipextrasymbols,{`optimmaxvar_'-`optimminvar_'+1} \end{verbatim} In this case the numbering of the next optimization will start after the last extra symbol of the previous optimization. One should realize however that the definitions of the extra symbols are not kept once the new optimization is started or once a \#clearoptimize instruction is issued. Example: \begin{verbatim} #- S a,b,c,d,e; L F = (a+b+c+d+3*e)^3; B b; .sort ExtraSymbols,array,w; Format O3,stats=ON; #optimize F #write <> " %4O" .sort #SkipExtraSymbols,{`optimmaxvar_'-`optimminvar_'+1} id b = b+1; Print +f; B b; .end \end{verbatim} Because the O3 format is still active, the final printing uses the optimization as well. If the \#SkipExtraSymbols instruction would have been omitted, the numbering would start again from one, while the rhs.\ of their definitions would contain the old extra symbols. The result would be incorrect. %--#] skipextrasymbols : %--#[ sortreallocate : \section{\#sortreallocate} \label{presortreallocate} \noindent Syntax: \#sortreallocate\index{\#sortreallocate} \noindent See also ``On sortreallocate;'' (\ref{substaon}). \noindent Reallocates the small and large buffer (also on the worker threads) at the end of the current module. In some cases this can significantly reduce \FORM's memory usage as measured by ``resident set size''. %--#] sortreallocate : %--#[ startfloat : \section{\#startfloat} \label{prestartfloat} \noindent Syntax: \#startfloat $<$precision$>$ [,MZV=$<$weight$>$] \noindent See also endfloat (\ref{preendfloat}) and chapter~\ref{floatingpoint} on the floating point capability. %--#] startfloat : %--#[ switch : \section{\#switch} \label{preswitch} \noindent Syntax: \#switch string \noindent See also endswitch (\ref{preendswitch}), case (\ref{precase}), break (\ref{prebreak}), default (\ref{predefault}) \noindent the\index{\#switch} string could for instance be a preprocessor variable as in \begin{verbatim} #switch `i' \end{verbatim} The \#switch\index{\#switch} instruction, together with \#case\index{\#case}, \#break\index{\#break}, \#default\index{\#default} and \#endswitch\index{\#endswitch}, allows the user to conveniently make code for a number of cases that are distinguished by the value of a preprocessor variable. In the past this was only possible with the use of folds\index{folds} in the \#include\index{\#include} instruction and the corresponding include file\index{file!include} (see \ref{preinclude}). Because few people have an editor like STedi (see the \FORM\ distribution site) that can handle the folds in a proper way, it was judged that the more common switch mechanism might be friendlier. The proper syntax of a complete construction would be \begin{verbatim} #switch `par' #case 1 some statements #break #case ax2 other statements #break #default more statements #break #endswitch \end{verbatim} The number of cases is not limited. The compare between the strings in the \#switch instruction and in the \#case instructions is as a text string. Hence numerical strings have no special meaning. If a \#break instruction is omitted, control may go into another case. This is called fall-through\index{fall-through}. This is a way in which one can have the same statements for several cases. The \#default instruction is not mandatory. \FORM\ will look for the first case of which the string matches the string in the \#switch instruction. Input reading (control flow) starts after this \#case instruction, and continues till either a \#break instruction is encountered, or the \#endswitch is met. After that input reading continues after the \#endswitch instruction. If no case has a matching string, input reading starts after the \#default instruction. If no \#default instruction is found, input reading continues after the matching \#endswitch instruction. \#switch constructions can be nested\index{nested}. They can be combined with \#if\index{\#if} constructions, \#do\index{\#do} instructions, etc. but they should obey normal nesting rules (as with nesting of brackets\index{bracket} of different types). %--#] switch : %--#[ system : \section{\#system} \label{presystem} \noindent Syntax: \#system [-e] systemcommand \noindent See also pipe (\ref{prepipe}) \noindent This forces a system\index{\#system} command to be executed by the operating system. The complete string (excluding initial blanks or tabs) is passed to the operating system. \FORM\ will then wait until control is returned. Note that this instruction introduces operating system dependent code. Hence it should be used with great care. \noindent Without the -e option execution of the Form program will halt if the system command returns an error. With the -e option the Form program will continue execution. The value of the return code of the system command can be found in the SYSTEMERROR\_\index{SYSTEMERROR\_} preprocessor variable. %--#] system : %--#[ terminate : \section{\#terminate} \label{preterminate} \noindent Syntax: \#terminate [exitcode] \noindent This forces \FORM\ to terminate\index{\#terminate} execution immediately. If an exit code is given (an integer number), this will be the return value that \FORM\ gives to the shell program from which it was run. If no return value is specified, the value -1 will be returned. %--#] terminate : %--#[ timeoutafter : \section{\#timeoutafter} \label{pretimeoutafter} \noindent Syntax: \#timeoutafter $<$Number of seconds$>$ \noindent This instruction starts a timer. When the given time expires the current program will be terminated, unless the timer is reset before this time. Resetting the timer is dome with the "\#timeoutafter 0" instruction. The purpose of this instruction is to prevent runaway programs, because a given subpart takes much more time than it should. Example: \begin{verbatim} .sort #timeoutafter 1000 #call problematicprocedure .sort #timeoutafter 0 \end{verbatim} If one runs many diagrams with a make-like facility like minos, diagrams that behave in an unexpected way can be killed this way and minos can continue with the next diagram. Later one can see which diagrams caused problems and one may study what the problem was. %--#] timeoutafter : %--#[ toexternal : \section{\#toexternal} \label{pretoexternal} \noindent Syntax: \#toexternal "formatstring" $<$,variables$>$ \noindent Sends\index{\#toexternal} the output to the current external command. The semantics of the \verb|"formatstring"| and the \verb|[,variables]| is the same as for the \#write\index{\#write} instruction, except for the trailing end-of-line symbol. In contrast to the \#write instruction, the \#toexternal instruction does not append any new line symbol to the end of its output. %--#] toexternal : %--#[ undefine : \section{\#undefine} \label{preundefine} \noindent Syntax: \#undefine name \noindent See also define (\ref{predefine}), redefine (\ref{preredefine}) \noindent \index{\#undefine} Name refers to the name of the preprocessor variable\index{variable!preprocessor} to be undefined. This statement causes the given preprocessor variable to be removed from the stack of preprocessor variables. If an earlier instance of this variable existed (other variable with the same name), it will become active again. There are various other ways by which preprocessor variables can become undefined. All variables belonging to a procedure are undefined at the end of a procedure, and so are all other preprocessor variables that were defined inside this procedure. The same holds for the preprocessor variable that is used as a loop parameter in the \#do\index{\#do} instruction. %--#] undefine : %--#[ usedictionary : \section{\#usedictionary} \label{preusedictionary} \noindent Syntax: \#usedictionary name \#usedictionary name (options) \noindent See chapter \ref{dictionaries} on dictionaries. \noindent Starts using a dictionary for output translation. %--#] usedictionary : %--#[ write : \section{\#write} \label{prewrite} \noindent Syntax: \#write [$<$filename$>$] "formatstring" [,variables] \noindent See also append (\ref{preappend}), create (\ref{precreate}), remove (\ref{preremove}), close (\ref{preclose}) \noindent If there\index{\#write} is no file specified, the output will be to the regular output\index{output channel} channel. If a file is specified, \FORM\ will look whether this file is open already. If it is open already, the specified output will be added to the file. If it is not open yet it will be opened. Any previous contents will be lost. This would be equivalent to using the \#create\index{\#create} instruction first. If output has to be added to an existing file, the \#append\index{\#append} instruction should be used first. The format\index{format string} string is like a format string in the language C\index{C}. This means that it is placed between double quotes. It will contain text that will be printed, and it will contain special character sequences for special actions. These sequences and the corresponding actions are: \begin{description} \item[$\backslash$n] A newline\index{newline} character. \item[$\backslash$t] A tab\index{tab} character. \item[$\backslash$"] A double\index{double quote} quote character. \item[$\backslash$b] A backslash\index{backslash} character. \item[\%\%] The character \%\index{\%}. \item[\%] If the last character in the string, it causes the omission of a linefeed\index{linefeed} at the end of the printing. Note that if this happens in the regular output (as opposed to a file) there may be interference with the listing of the input. \item[\%\$] A dollar variable\index{\$-variable}. The variable should be indicated in the list of variables. Each occurrence of \%\$ will look for the next variable. \item[\%e] An active expression\index{expression}. The expression should be indicated in the list of variables. Each occurrence of \%e will look for the next variable. Unlike the output caused by the print statement the expression will be printed without its name and there will also be no \verb:=: sign unless there is one in the format string of course. If the current output format is fortran\index{fortran} output there is an extra option. After the name of the expression one should put between parentheses the name to be used when there are too many continuation cards. \item[\%+e] Like \%e, but like the +s option in the Print statement\ref{substaprint} where each term starts on a new line. \item[\%E] Like \%e, but whereas the \%e terminates the expression with a ;, the \%E does not give this trailing semicolon\index{semicolon}. \item[\%+E] Like \%E, but like the +s option in the Print statement\ref{substaprint} where each term starts on a new line. \item[\%s] A string\index{string}. The string should be given in the list of variables and be enclosed between double quotes. Each occurrence of \%s will look for the next variable in the list. \item[\%f] A file\index{file}. The name of the file will be expected in the list of variables. The file is searched for in the current directory, then in path indicated by the path variable in the setup file or at the beginning of the file (see chapter \ref{setup} on the setup file), then in the path specified in the -p option when \FORM\ is started (see the chapter on running \FORM). If this option has not been used, \FORM\ will look for the environment variable FORMPATH\index{FORMPATH}. If this variable exists it will be interpreted as a path and \FORM\ will search the indicated directories for the given file. If none is found there will be an error message and execution will be halted. \item[\%X] Forces the printing of the list of extra symbols (\ref{sect-extrasymbols}) and their definitions\index{extrasymbols}. \item[\%O] Forces the printing of the definitions of the extra symbols in the buffer with the temporary variables from the previous optimization (see the chapter on optimizations \ref{optimization}). \end{description} If no special variables are asked for (by means of \%\$, \%e, \%E or \%s) the list of variables will be ignored (if present). Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Pre_write_1) \begin{verbatim} Symbols a,b; L F = a+b; #$a1 = a+b; #$a2 = (a+b)^2; #$a3 = $a1^3; #write " One power: %$\n Two powers: %$\n Three powers: %$\n%s"\ ,$a1,$a2,$a3," The end" One power: b+a Two powers: b^2+2*a*b+a^2 Three powers: b^3+3*a*b^2+3*a^2*b+a^3 The end .end Time = 0.00 sec Generated terms = 2 F Terms in output = 2 Bytes used = 32 \end{verbatim} We see that the writing occurs immediately after the \#write\index{\#write} instruction, because it is done by the preprocessor. Hence the output comes before the execution of the expression F. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Pre_write_2) \begin{verbatim} S x1,...,x10; L MyExpression = (x1+...+x10)^4; .sort Format Fortran; #write " FUNCTION fun(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)" #write " REAL x1,x2,x3,x4,x5,x6,x7,x8,x9,x10" #write " fun = %e",MyExpression(fun) #write " RETURN" #write " END" .end \end{verbatim} Some remarks are necessary here. Because the \#write is a preprocessor instruction, the .sort\index{.sort} is essential. Without it, the expression has not been worked out at the moment we want to write. The name of the expression is too long for fortran\index{fortran}, and hence the output file will use a different name (in this case the name `fun' was selected). The output file looks like % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Pre_write_2) % TODO: the term order has been changed. \begin{verbatim} FUNCTION fun(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10) REAL x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 fun = 24*x1*x2*x3*x4 + 24*x1*x2*x3*x5 + 24*x1*x2*x3*x6 + 24*x1*x2 & *x3*x7 + 24*x1*x2*x3*x8 + 24*x1*x2*x3*x9 + 24*x1*x2*x3*x10 + 12* ..... & x8 + 4*x6**3*x9 + 4*x6**3*x10 + x6**4 + 24*x7*x8*x9*x10 + 12*x7* & x8*x9**2 fun = fun + 12*x7*x8*x10**2 + 12*x7*x8**2*x9 + 12*x7*x8**2*x10 + & 4*x7*x8**3 + 12*x7*x9*x10**2 + 12*x7*x9**2*x10 + 4*x7*x9**3 + 4* & x7*x10**3 + 12*x7**2*x8*x9 + 12*x7**2*x8*x10 + 6*x7**2*x8**2 + & 12*x7**2*x9*x10 + 6*x7**2*x9**2 + 6*x7**2*x10**2 + 4*x7**3*x8 + & 4*x7**3*x9 + 4*x7**3*x10 + x7**4 + 12*x8*x9*x10**2 + 12*x8*x9**2 & *x10 + 4*x8*x9**3 + 4*x8*x10**3 + 12*x8**2*x9*x10 + 6*x8**2* & x9**2 + 6*x8**2*x10**2 + 4*x8**3*x9 + 4*x8**3*x10 + x8**4 + 4*x9 & *x10**3 + 6*x9**2*x10**2 + 4*x9**3*x10 + x9**4 + x10**4 RETURN END \end{verbatim} and each time after 19 continuation lines we have to break the expression and use the \verb:fun = fun +: trick to continue. %--#] write : %--#[ Some remarks : \section{Some remarks} It should be noted that the various constructions like \#do\index{\#do}/\#enddo\index{\#enddo}, \#procedure\index{\#procedure}/\#endprocedure\index{\#endprocedure}, \#switch\index{\#switch}/\#endswitch\index{\#endswitch} and \#if\index{\#if}/\#endif\index{\#endif} all create a certain environment. These environments cannot be interweaved. This means that one cannot make code of the type \begin{verbatim} #do i = 1,5 #if ( `MAX' > `i' ) id f(`i') = g`i'(x); #enddo some statements #do i = 1,5 #endif #enddo \end{verbatim} whether this could be considered useful or not. Similarly one cannot make a construction that might be very useful: \begin{verbatim} #do i = 1,5 #do j`i' = 1,3 #enddo some statements #do i = 1,5 #enddo #enddo \end{verbatim} Currently the syntax does not allow this. This may change in the future. %--#] Some remarks : form-5.0.1/doc/manual/optim.tex0000644000175100017510000004575515217035721012062 \chapter{Output optimization} \label{optimization} One of the uses of symbolic programs is to prepare formulas for further numerical processing\index{numerical processing}. Technically speaking such processing is not part of computer algebra, although some packages may provide facilities for this. In \FORM\ such facilities, such as Monte Carlo integration, do not exist at the moment, but, starting with version 4.1, \FORM\ does provide statements to construct outputs in C or Fortran that are highly optimized with respect to the number of arithmetic operations\index{arithmetic operations} that are needed for their evaluation. The algorithms used for this are described in the papers \begin{itemize} \item Code Optimization in FORM - \url{https://arxiv.org/abs/1310.7007} \item Improving multivariate Horner schemes with Monte Carlo tree search - \url{https://arxiv.org/abs/1207.7079} \item Combining Simulated Annealing and Monte Carlo Tree Search for Expression Simplification - \url{https://arxiv.org/abs/1312.0841} \item Why Local Search Excels in Expression Simplification - \url{https://arxiv.org/abs/1409.5223} \end{itemize} In short, an optimal Horner scheme is constructed after which common subexpressions are eliminated. The methods for finding the optimal scheme can use a simple heuristic, Monte Carlo Tree Search, or a Stochastic Local Search approach such as Simulated Annealing In this section the precise format of the commands that concern the optimizations will be described. In optimized output \FORM\ needs temporary variables\index{temporary variables}. In order to avoid conflicts with user defined objects \FORM\ uses the extra symbols \ref{substaextrasymbols}\index{extra symbols} for these variables. This means that the user can control their output representation in the standard way. In addition there are preprocessor variables that tell how many of these extra symbols were needed: \begin{description} \item[optimminvar\_] The number of extra symbols before the optimization process started\index{optimminvar\_}. \item[optimmaxvar\_] The number of extra symbols after the optimization process finished\index{optimmaxvar\_}. \end{description} Each new optimization will remove the old optimization results and start the extra symbols from the number there were before the optimization started. Because this may cause interference with the functioning of the extrasymbol statement, regular printing with output optimization and the extrasymbol statement cannot occur inside the same module. Such occurrence would result in an error message. Because the output optimization is done for expressions that contain only symbols\index{symbols}, \FORM\ has to convert all non-symbols and negative powers of symbols to extra symbols\index{extra symbols} before it starts the optimization. This is another reason why interference between the extrasymbol \ref{substaextrasymbols}\index{extra symbols} statement and output optimizations is forbidden. When the results are printed, the definition of the extra symbols that are introduced this way are printed as well. \FORM\ has two ways to perform optimizations. The first and easiest is in the regular output. If one asks for optimization (by specifying the proper format for this) and follows this by a print statement, the output printed will be in optimized form. This is however just a representation of the expression and the next module will obtain the original expression for its input. The more useful way to obtain an optimized output is with the \#optimize instruction. To use this instruction properly one should understand what \FORM\ does when it optimizes an expression. The whole process of optimization takes place inside the memory. Hence, \FORM\ cannot optimize expressions that do not fit inside the CPU memory. The notation is however fairly compact and \FORM\ needs far less space than for instance the compiler (and gives better results). The result of the optimization is stored inside a buffer. There is only a single optimization buffer\index{optimization buffer} and the preprocessor variables optimminvar\_\index{optimminvar\_} and optimmaxvar\_\index{optimmaxvar\_} refer to the contents of this buffer. When the \#optimize instruction is used it loads this buffer and the contents stay around until either a \#clearoptimize instruction is used or a new \#optimize instruction is issued. The \#optimize instruction changes the original expression to its optimized shape in which it is usually a very short expression that refers to one or more extra symbols. The optimization information is automatically erased, and with it the expression that was optimized, when a second \#optimize instruction is issued. Clearing the optimization buffer means that the information of the first expression is irretrievably lost and the contents of the first expression become meaningless, because its extra symbols have been erased. Hence if the user still needs this expression it is necessary to make a copy of it before optimization. The optimization buffers, and the optimized expression, can be removed by the user with the \#clearoptimize instruction. This is mandatory before the use of a ToPolynomial \ref{substatopolynomial}\index{ToPolynomial} statement, because that may introduce new extra symbols. The contents of the optimization buffer\index{optimization buffer} can be written with the \%O combination in the format string in the \#write instruction. This means that it is easy to write this output to file. Consider for instance the following program: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (OutputOptimization_1) \begin{verbatim} CF f; S a,b,c; L H = f(a)+f(b)+(a+b+c)^2; L G = f(c)+(a+b+c)^3; Format O2; Print +f; .sort ExtraSymbols,array,w; Format Fortran; #optimize G #write " REAL*8 w(`optimmaxvar_')" #write "%O" #write " G = %e",G #clearoptimize .sort #optimize H #write " REAL*8 w(`optimmaxvar_')" #write "%O" #write " H = %e",H .end \end{verbatim} This program shows the two different methods and shows what is left of the expressions G and H. It also shows that we have to deal with the expressions one by one when we use the \#optimize instruction, while in the regular printing of the output this is not needed because the expression itself remains in its unoptimized version. \section{Optimization options of the Format statement} The \verb|Format| statement has a number of options to control the code optimization. The easiest to use are the following: \begin{description} \item[O0] Switches off all optimizations and prints the output the normal \FORM\ way. This is the default. \item[O1] Activates the lowest level of optimization. It is very fast, i.e., linear in the size of the expression, and gives reasonably efficient code. \item[O2] Activates the medium level of optimization. This is slower than the previous setting, but usually gives better results. \item[O3] Activates the highest level of optimization using MCTS\@. It can be rather slow, but usually gives even better results. \item[O4] Activates the highest level of optimization using Local Stochastic Search. It is usually much faster than MCTS and may give better results. \end{description} Below we show how to use O4 and how it compares to O2: \begin{verbatim} #- S a,b,c,d,e,f,g,h,i,j,k,l,m,n; L G = (4*a^4+b+c+d + i^4 + g*n^3)^10 + (a*h + e + f*i*j + g + h)^8 + (i + j + k + l + m + n)^12; L H = G; Format O2; .sort #optimize G #write "Optimized with O2:" #write "Optimized with Horner scheme: `optimscheme_'" #write "Number of operations in output: `optimvalue_'" #clearoptimize .sort Format O4,saIter=1000; * use 1000 iterations for optimization #optimize H #write "Optimized with O4:" #write "Optimized with Horner scheme: `optimscheme_'" #write "Number of operations in output: `optimvalue_'" .end \end{verbatim} which gives the output: \begin{verbatim} Optimized with O2: Optimized with Horner scheme: i,n,j,m,l,k,g,a,d,c,b,h,f,e Number of operations in output: 2578 Optimized with O4: Optimized with Horner scheme: m,h,k,a,l,e,n,g,j,c,f,b,i,d Number of operations in output: 1937 \end{verbatim} The preprocessor variable optimscheme\_ \index{optimscheme\_} gives the best Horner scheme that the program found and the preprocessor optimvalue\_ \index{optimvalue\_} gives the number of arithmetic operations in the resulting expression. These levels of optimization refer to some default settings of all controlling parameters. These default values are in Tab.~\ref{tbl:defaults}. It is also possible to set each parameter individually to fine-tune the optimization process. The parameters that can be set are divided in several categories. First, it is possible to set which Horner schemes\index{Horner scheme} are tried: \begin{description} \item[Horner=(Occurrence $|$ MCTS $|$ SA)] Determines whether an occurrence order\index{occurrence order} Horner scheme is used, or whether MCTS\index{MCTS}\index{Monte Carlo tree search}, or Stochastic Local Search is employed to find Horner schemes. \item[HornerDirection=(Forward $|$ Backward $|$ ForwardOrBackward $|$] \hfill {\bf ForwardAndBackward)} Forward makes that the MCTS search in the O3 option will determine the outermost variables in the multivariate Horner scheme first and then work its way inward. In the case of backward, the tree search determines the innermost variable first. In some cases this can give much better results when there are many common subexpressions involving a limited number of variables. ForwardOrBackward tries both of these schemes. ForwardAndBackward fills the order from both sides simultaneously, resulting in more options, but also a much larger search tree. If there are many variables, it could make the search tree too large to obtain good results. \hfill \\ When the option Horner=Occurrence is used the option backward will switch to something called `anti-occurrence' which means that the most frequent variable corresponds to the innermost brackets. \end{description} In the case of MCTS\index{MCTS}\index{Monte Carlo tree search} there are various parameters that can control the search process: \begin{description} \item[MCTSConstant=$<$\emph{value}$>$] This sets the constant $C_P$ in the UCT formula that governs the Monte Carlo tree search. It is supposed to be given as a real number with a decimal point (no floating point notation that includes powers). \item[MCTSNumExpand=$<$\emph{value}$>$] The number of times the tree is traversed and hence the number of times that a Horner scheme is constructed. \item[MCTSNumKeep=$<$\emph{value}$>$] During the MCTS procedure \FORM\ only tries to construct a proper ordering for the Horner scheme, followed by a common subexpression elimination in the style of the O1 option. The best `value' schemes are remembered and for those a common subexpression elimination in the style of the O2 option is done afterward. This second style elimination is far more costly. In nearly all cases the best O2-style scheme is in the very few top O1-style schemes. \item[MCTSNumRepeat=$<$\emph{value}$>$] Sometimes it is more advantageous to run a new tree search several times, each with a smaller number of expansions. This parameter tells how many times we will run with a new tree. The total number of tree traversals is the product of MCTSNumRepeat and MCTSNumExpand. \item[MCTSNumExpand=$<$\emph{value1*value2}$>$] Makes \FORM\ to run `value1' trees, each with `value2' Horner scheme constructions. Hence this option is equivalent to the combination \hfill \\ MCTSNumRepeat=$<$\emph{value1}$>$, MCTSNumExpand=$<$\emph{value2}$>$. \item[MCTSTimeLimit=$<$\emph{value}$>$] The maximum time in seconds that is used when searching through the tree. \item[MCTSDecayMode=$<$\emph{value}$>$] Determines how the $C_P$ parameter in the UCT formula decreases: \begin{center} \begin{tabular}{|c|l|} \hline value & effect\\ \hline 0 & no decay\\ 1 & linear decay with iteration number\\ 2 & faster decay for the final iterations\\ 3 & decrease with iteration number and with node depth\\ \hline \end{tabular} \end{center} % 0 means there %is no decay, 1 means a linear decay with iteration number, 2 a more %aggressive decay for the final iterations, and MCTSDecayMode=3 . %The default value is 1. \end{description} For Stochastic Local Search the following parameters can be set: \begin{description} \item[saIter=$<$\emph{value}$>$] Number of optimization steps that will be performed. This has the most influence on the quality of the simplification. The default value is 1000. \item[saMaxT=$<$\emph{value}$>$] Maximum temperature used in Simulated Annealing. The higher the temperature, the more exploration occurs. The default value is 2000. \item[saMinT=$<$\emph{value}$>$] Minimum temperature used in Simulated Annealing. The lower the temperature, the more exploitation occurs. The default value is 1. \end{description} The cooling rate from saMaxT to saMinT is exponential in saIter. More information can be found in the research papers. The Horner methods generate a number of Horner schemes: one or two in the case of occurrence order schemes, depending of the direction parameter, and a number equal to MCTSNumKeep in the case of MCTS\@. Next, for each stored Horner scheme other optimizations are performed as determined by the following parameter: \begin{description} \item[Method=(None $|$ CSE $|$ Greedy $|$ CSEGreedy)] Determines what method is used for optimizing the generated Horner schemes. CSE\index{CSE}\index{Common subexpression elimination} performs a simple common subexpression elimination and Greedy performs greedy optimizations\index{greedy optimizations} (see the paper for more explanations) which are more sophisticated versions of CSE's. CSEGreedy performs CSE followed by greedy optimizations; usually this is somewhat faster than just greedy optimizations, but it gives slightly worse results. The option None does nothing after applying the Horner scheme and is only useful for debugging purposes. \end{description} When the method of greedy optimizations is used, repeatedly all potential optimizations are determined and a few of them are performed. The following parameters are used to tune the greedy method: \begin{description} \item[GreedyMaxPerc] The percentage of the possible optimizations that is performed. \item[GreedyMinNum] The minimum number of possible optimizations that is performed. \item[GreedyTimeLimit] The maximum time in seconds that is spent in the process of greedy optimization. \end{description} There are also two more general settings: \begin{description} \item[Stats=(On $|$ Off)] This parameter determines whether statistics of the optimization are shown. Statistics are printed in the format {\tt *** STATS: original 1P 16M 5A : 23} {\tt *** STATS: optimized 0P 10M 5A : 15} in which P indicates power operations (at least a third power), M the number of multiplications and A the number of additions/subtractions. The last number is the total number of operations in which an $n$-th power counts as $n-1$ operations. \item[TimeLimit=$<$\emph{value}$>$] This set both the MCTSTimeLimit and the GreedyTimeLimit to half of the given value. \end{description} Finally there are some parameters that are of a rather specialized nature. They can be used for debugging\index{debugging} purposes or in the case that one knows already what is the best Horner scheme. Their default values are Off. \begin{description} \item[DebugFlag=(On $|$ Off)] \label{optimdebugflag} In the case that the value is On, the list of temporary variables is printed in reverse order with the string "id " in front. This makes them into a set of \FORM\ substitutions that undo the optimizations. One can use this for instance to make sure that the optimized code is identical to the original. \item[PrintScheme=(On $|$ Off)] This option (when On) will print the Horner scheme. That is the order in which the variables were taken outside parentheses. \item[Scheme=(list of symbols)] The list should be enclosed by parentheses and the symbols should be separated by either blanks or comma's. This option will fix the Horner scheme\index{Horner scheme} to be used. One could for instance use the output of the PrintScheme option for this to avoid a lengthy search when a good order of the variables is already known. Things become a bit tricky when extra symbols are involved. One should make sure that their labelling is identical to when the scheme was created! When extra symbols are used in their array/vector notation, one needs to separate them by comma's, because blank spaces next to parentheses are eliminated by the preprocessor. If one specifies the wrong number of variables, the results can be quite unpredictable. At the moment of compilation \FORM\ does not know the variables that are actually used. The safe thing is to verify the actual variables with a testrun using the PrintScheme option in the O1 mode. \end{description} { \small \begin{table}[!ht] \centering \begin{tabular}{|l|c|c|c|c|} \hline & O1 & O2 & O3 (default) & O4 (default) \\ \hline Horner & occurrence & occurrence & MCTS & SA \\ HornerDirection & OR & OR & OR & OR \\ MCTSConstant & --- & --- & 1.0 & --- \\ MCTSNumExpand & --- & --- & 1000 & --- \\ MCTSNumKeep & --- & --- & 10 & --- \\ MCTSNumRepeat & --- & --- & 1 & --- \\ MCTSTimeLimit & --- & --- & 0 & --- \\ MCTSDecayMode & --- & --- & 1 & --- \\ saIter & --- & --- & --- & 1000 \\ saMinT & --- & --- & --- & 1 \\ saMaxT & --- & --- & --- & 2000 \\ Method & cse & greedy & greedy & greedy \\ GreedyMinNum & --- & 10 & 10 & 10 \\ GreedyMaxPerc & --- & 5 & 5 & 5 \\ GreedyTimeLimit & --- & 0 & 0 & 0 \\ Stats & off & off & off & off \\ TimeLimit & 0 & 0 & 0 & 0 \\ \hline \end{tabular} \caption{Values for the various parameters in the predefined optimization levels. OR stands for ForwardOrBackward.} \label{tbl:defaults} \end{table} } All options should be specified in a single format statement and be separated either by commas or blank spaces. When \verb|Format Optimize| is used, first the default settings are taken and then the options that are specified overwrite them. It is allowed to have the O1, O2, O3, O4 optimization specifications followed by options. In that case the program first sets the values of those specifications and then modifies according to what it encounters in the rest of the statement. form-5.0.1/doc/manual/tablebas.tex0000644000175100017510000003622215217035721012474 \chapter{The TableBase} \label{tablebase} The tablebase\index{tablebase} statement controls a database\index{database}-like structure that allows \FORM\ to control massive amounts of data in the form of tables and table\index{table elements}\index{table} elements. The contents of a tablebase are formed by one or more table declarations and a number of fill\index{fill} statements. These fill statements however are not immediately compiled. For each fill statement a special fill statement is generated and compiled that is of the form \begin{verbatim} Fill tablename(indices) = tbl_(tablename,indices,arguments); \end{verbatim} The function tbl\_\index{tbl\_} is a special function to make a temporary table substitution. It indicates that the corresponding element can be found in a tablebase that has been opened. At a later stage one can tell \FORM\ to see which table elements are actually needed and then only those will be loaded from the tablebase and compiled. Tablebases have a special internal structure and the right hand sides of the fill statements are actually stored in a compressed\index{compressed} state. These tablebases can be created with special statements and uploaded with any previously compiled table. Hence one can prepare a tablebase in a previous job, to be used at a later stage, without the time penalty of loading the whole table at that later stage. Assume we have a file named no11fill.h that loooks like \begin{verbatim} Symbols ...; Table,sparse,no11fill(11,N?); Fill no11fill(-3,1,1,1,1,1,1,1,0,0,0) = .... Fill no11fill(-2,1,1,1,1,1,1,1,0,0,0) = .... etc. \end{verbatim} It should be noted that only sparse\index{sparse} tables can be stored inside a tablebase. The right hand sides could be typically a few kilobytes of formulas and there could be a few thousand of these fill statements. To make this into a tablebase one would use the program \begin{verbatim} #- #include no11fill.h #+ TableBase "no11.tbl" create; TableBase "no11.tbl" addto no11fill; .end \end{verbatim} The include\index{\#include} instruction makes that \FORM\ reads and compiles the table. Then the first tablebase statement creates a new tablebase file by the name no11.tbl. If such a file existed already, the old version will be lost. If one would like to add to an existing tablebase, one should use the `open'\index{open} keyword. The second tablebase statement adds the table no11fill to the tablebase file no11.tbl. This takes care of declaring the table, making an index of all elements that have been filled and putting their right hand sides, in compressed form, into the tablebase. The compression is based on the zlib\index{zlib} library, provided by Jean-loup Gailly\index{Gailly!Jean-loup} and Mark Adler\index{Adler!Mark} (version 1.2.3, July 18, 2005) and it strikes a nice balance between speed and compression ratio. The tablebase can be loaded in a different program as in \begin{verbatim} TableBase "no11.tbl" open; \end{verbatim} This loads the main index\index{index!main} of the file into memory. To protect against accidentally adding additional table to an existing tablebase or in case tablebases are stored in shared directories where not all users have write access, they can be opened using \begin{verbatim} TableBase "no11.tbl" open, readonly; \end{verbatim} Trying to add tables to a tablebase opened in read-only mode results in an error. If one would like to compile the short version of the fill statements (the normal action at this point) one needs to use the load\index{load} option. Without any names of tables it will read the index of all tables. If tables are specified, only the index of those tables is taken and the proper tbl\_ fill statements are generated: \begin{verbatim} TableBase "no11.tbl" open; TableBase "no11.tbl" load no11fill; \end{verbatim} If one would like to compile\index{compile} the complete tables, rather than just the shortened versions, one can use the enter option as in: \begin{verbatim} TableBase "no11.tbl" open; TableBase "no11.tbl" enter no11fill; \end{verbatim} Let us assume we used the load option. Hence now an occurrence of a table element will be replaced by the stub\index{stub function}-function tbl\_\index{tbl\_}. In order to have this replaced by the actual right hand side of the original fill statement we have to do some more work. At a given moment we have to make \FORM\ look which elements are actually needed. This is done with the TestUse\index{testuse} statement as in \begin{verbatim} TestUse no11fill; \end{verbatim} This does nothing visible. It just marks internally which elements will be needed and have not been entered yet. The actual entering of the needed elements is done with the use\index{use} option:\begin{verbatim} TableBase "no11.tbl" use; \end{verbatim} If many elements are needed, this statement may need some compilation time. Note however that this is time at a moment that it is clear that the elements are needed, which is entirely different from a fixed time at the startup of a program when the whole table is loaded as would have to be done before the tablebase statement existed. Usually however only a part of the table is needed, and in the extreme case only one or two elements. In that case the profit is obvious. At this point the proper elements are available inside the system, but because we have two versions of the table (one the short version with tbl\_, the other the complete elements) we have to tell \FORM\ to apply the proper definitions with the `apply'\index{apply} statement. \begin{verbatim} Apply; \end{verbatim} Now the actual rhs will be inserted. One may wonder why this has to be done in such a `slow' way with this much control over the process. The point is that at the moment the table elements are recognized, one may not want the rhs yet, because it may be many lines. Yet one may want to take the elements away from the main stream of action. Similarly, having a table element recognized at a certain stage, may not mean automatically that it will be needed. The coefficient may still become zero during additional manipulations. Hence the user is left with full control over the process, even though that may lead to slightly more programming. It will allow for the fastest program. For the name of a tablebase we advise the use of the extension .tbl\index{.tbl} to avoid confusion. Note that the above scheme may need several applications, if table elements refer in their definition to other table elements. This can be done with a construction like: \begin{verbatim} #do i = 1,1 TestUse; .sort TableBase "basename.tbl" use; Apply; if ( count(tbl_,1) ) Redefine i "0"; .sort #enddo \end{verbatim} It will stay in the loop until there are no more tbl\_ functions to be resolved. \medskip\noindent The complete syntax (more is planned): %--#[ addto : \section{addto} \label{tbladdto} \noindent Syntax: TableBase "file.tbl" addto tablename; TableBase "file.tbl" addto tablename(tableelement); \noindent See also open (\ref{tblopen}) and create (\ref{tblcreate}). \noindent Adds\index{addto} the contents of a (sparse\index{sparse}) table to a tablebase. The base must be either an existing tablebase (made accessible with an open statement) or a new tablebase (made available with a create statement). In the first version what is added is the collection of all fill statements that have been used to define elements of the indicated table, in addition to a definition of the table (if that had not been done yet). In the second version only individual elements of the indicated table are added. These elements are indicated as it should be in the left hand side of a fill\index{fill} statement. \noindent One is allowed to specify more than one table, or more than one element. If one likes to specify anything after an element, it should be realized that one needs to use a comma for a separator, because blank spaces after a parenthesis are seen as irrelevant. \noindent Examples: \begin{verbatim} TableBase "no11.tbl" open; TableBase "no11.tbl" load; TableBase "no11.tbl" addto no11filb; TableBase "no11.tbl" addto no11fill(-3,1,1,1,1,2,1,1,0,0,0), no11fill(-2,1,1,2,1,1,1,1,0,0,0); \end{verbatim} %--#] addto : %--#[ apply : \section{apply} \label{tblapply} \noindent Syntax: Apply [number] [tablename(s)]; \noindent See also testuse (\ref{tbltestuse}) and use (\ref{tbluse}). \noindent The actual application\index{apply} of fill\index{fill} statements that were taken from the tablebases. If no tables are specified, this is done for all tables, otherwise only for the tables whose names are mentioned. The elements must have been registered as used before with the application of a testuse\index{testuse} statement, and they must have been compiled from the tablebase with the use\index{use} option of the tablebase statement. The number refers to the maximum number of table elements that can be substituted in each term. This way one can choose to replace only one element at a time. If no number is present all occurrences will be replaced. This refers also to occurrences inside function arguments. If only a limited number is specified in the apply statement, the occurrences inside function arguments have priority. %--#] apply : %--#[ audit : \section{audit} \label{tblaudit} \noindent Syntax: TableBase "file.tbl" audit; \noindent See also open (\ref{tblopen}) \noindent Prints\index{audit} a list of all tables and table elements that are defined in the specified tablebase. This tablebase needs to be opened first. As of the moment there are no options for the audit. Future options might include formatting of the output. %--#] audit : %--#[ create : \section{create} \label{tblcreate} \noindent Syntax: TableBase "file.tbl" create; \noindent See also open (\ref{tblopen}) \noindent This creates\index{create} a new file\index{file!new} with the indicated name. This file will be initialized as a tablebase. If there was already a file with the given name, its old contents will be lost. If one would like to add to an existing tablebase, one should use the `open'\index{open} option. %--#] create : %--#[ enter : \section{enter} \label{tblenter} \noindent Syntax: TableBase "file.tbl" enter; TableBase "file.tbl" enter tablename(s); \noindent See also open (\ref{tblenter}) and load (\ref{tblload}). \noindent Scans\index{enter} the specified tablebase and (in the first variety) creates for all elements of all tables in the tablebase a fill\index{fill} statement with its full contents. This is at times faster than reading the fill statements from a regular input file\index{file!input}, because the tablebase has its contents compressed\index{compress}. Hence this costs less file access time. When table names are specified, only the tables that are mentioned have their elements treated this way. \noindent The tablebase must of course be open for its contents to be available. \noindent If one would like \FORM\ to only see what elements are available and load that information one should use the load\index{load} option. %--#] enter : %--#[ load : \section{load} \label{tblload} \noindent Syntax: TableBase "file.tbl" load; TableBase "file.tbl" load tablename(s); \noindent See also open (\ref{tblopen}) and enter (\ref{tblenter}). \noindent Scans\index{load} the index of the specified tablebase and (in the first variety) creates for all elements of all tables in the tablebase a fill\index{fill} statement of the type \begin{verbatim} Fill tablename(indices) = tbl_(tablename,indices,arguments); \end{verbatim} This is the fill statement that will be used when elements of one of these tables are encountered. The function tbl\_ is called the (table)stub function. When table names are specified, only the tables that are mentioned have their elements treated this way. \noindent The tablebase must of course be open for its contents to be available. \noindent If one would like to actually load the complete fill statements, one should use the enter option. %--#] load : %--#[ off : \section{off} \label{tbloff} \noindent Syntax: TableBase "file.tbl" off subkey; \noindent See also addto (\ref{tbladdto}) and off (\ref{tblon}). \noindent Currently\index{off} only the subkey `compress'\index{compress} is recognized. It makes sure that no compression is used when elements are being stored in a tablebase with the addto\index{addto} option. This could be interesting when the right hand sides of the fill statements are relatively short. %--#] off : %--#[ on : \section{on} \label{tblon} \noindent Syntax: TableBase "file.tbl" on subkey; \noindent See also addto (\ref{tbladdto}) and off (\ref{tbloff}). \noindent Currently\index{on} only the subkey `compress'\index{compress} is recognized. It makes sure that compression with the gzip\index{gzip} algorithms is used when elements are being stored in a tablebase with the addto\index{addto} option. This is the default. %--#] on : %--#[ open : \section{open} \label{tblopen} \noindent Syntax: TableBase "file.tbl" open; TableBase "file.tbl" open, readonly; \noindent See also create (\ref{tblcreate}) \noindent This opens\index{open} an existing file with the indicated name. It is assumed that the file has been created\index{create} with the `create' option in a previous \FORM\ program. It gives the user access to the contents of the tablebase. In addition it allows the user to add to its contents. If the read-only option is set, no contents can be added. \noindent Just like with other files, \FORM\ will look for the file in in current directory and in all other directories mentioned in the environment variable `FORMPATH'\index{FORMPATH} (see for instance the \#call\index{\#call} (\ref{precall}) and the \#include\index{\#include} (\ref{preinclude}) instructions). %--#] open : %--#[ testuse : \section{testuse} \label{tbltestuse} \noindent Syntax: TestUse; TestUse tablename(s); \noindent See also use (\ref{tbluse}). \noindent Tests\index{testuse} for all elements of the specified tables (if no tables are mentioned, this is done for all tables) whether they are used in a stub\index{stub} function tbl\_\index{tbl\_}. If so, this indicates that these elements must be compiled from a tablebase, provided this has not been done already. The compilation will have to be done at a time, specified by the user. This can be done with the use\index{use} option. All this statement does is set some flags in the internals of \FORM\ for the table elements that are encountered in the currently active expressions. %--#] testuse : %--#[ use : \section{use} \label{tbluse} \noindent Syntax: TableBase "file.tbl" use; TableBase "file.tbl" use tablename(s); \noindent See also testuse (\ref{tbltestuse}) and apply (\ref{tblapply}). \noindent Causes\index{use} those elements of the specified tables to be compiled, that a previous testuse\index{testuse} statement has encountered and that have not yet been compiled before. If no tables are mentioned this is done for all tables. The right hand sides of the definition of the table elements will not yet be substituted. That is done with an apply\index{apply} statement. %--#] use : form-5.0.1/doc/manual/spectators.tex0000644000175100017510000001450215217035721013103 \chapter{Spectators} \label{spectators} At times expressions contain many terms that will not be treated for many modules to come. For the actions in those modules they are considered spectator terms and they may consume much computer time due to their presence during the sorting. For this we have the spectator system in which we can send those terms to a special file, named a spectator file, in such a way that they can be picked up at a convenient time in the future. In short: \noindent Spectators are expressions together with a \index{filename}filename. The file is for storage when the spectator becomes too big. Create a spectator with the statement\index{createspectator} \begin{verbatim} CreateSpectator Exprname,"filename"; \end{verbatim} The file will be made in the same directory where the temporary files are made. Example: \begin{verbatim} CreateSpectator Yintegrals,"Yfile.spec"; \end{verbatim} One may send terms to a spectator with the executable statement\index{tospectator} \begin{verbatim} ToSpectator Exprname; \end{verbatim} An example would be \begin{verbatim} if ( count(Z,1) == 0 ) ToSpectator Yintegrals; \end{verbatim} The terms are dumped into the file as they are at the moment the ToSpectator statement is executed. No brackets etc. In the future they may be compressed. At the moment they are not. Recovery of the contents of the spectator is done with the CopySpectator statement as in\index{copyspectator} \begin{verbatim} CopySpectator NewExp = Yintegrals; \end{verbatim} Currently you can only read the spectators this way. You cannot make more complicated constructions. You can only do things with the terms of the spectator expression after the contents have been put in your new expression. The spectator file remains in existence. In later modules you can still add to it. You cannot read from and add to the same spectator in the same module. The CopySpectator command can be followed by executable statements in the same module. This may not be economical because the contents of the spectator have not been sorted. There could be identical terms that occur many times or even cancel. Better sort them first. A spectator can be removed from the system with the statement\index{removespectator} \begin{verbatim} RemoveSpectator Yintegrals; \end{verbatim} It is also possible to truncate a spectator down to zero length with\index{emptyspectator} \begin{verbatim} EmptySpectator Yintegrals; \end{verbatim} You can have as many spectators as you like, but they all have some cache buffers. There may also be limitations in the file system on the maximum number of open files. The filename for the spectator is purely for the sake of the users administration and recognition. You cannot carry the file over to other programs. There is no variable administration in it as in the saved files. The .global instruction makes a spectator file survive a .store. It is up to the user to make sure that all the variables in it also survive the .store. There is no checking! One use of the spectator system would be when integrating many different terms by means of a very prolonged recursion system in which integrals of a given complexity are reduced to integrals of lower complexity, but each such reduction may take quite a few steps. One could have: \begin{verbatim} #do i = `MAXCOMPLEXITY'-1,0,-1 CreateSpectator complex`i',"complex`i'.spec"; #enddo Local F`MAXCOMPLEXITY' = ....; #do i = `MAXCOMPLEXITY'-1,1,-1 #do ii = 1,1; * routine for doing a part of the recursion level `i' .... #do j = `i'-1,0,-1 if ( complexityofterm == `i' ) ToSpectator complex`i'; #enddo if ( notyetfinished ) redefine ii "0"; .sort #enddo Drop F{`i'+1}; CopySpectator F`i' = complex`i'; .sort RemoveSpectator complex`i'; #enddo * * and finally, assuming that complexity zero means finished: * Drop F1; CopySpectator F0 = complex0; .sort RemoveSpectator complex0; \end{verbatim} Some remarks are called for here. If one works with the polyratfun\index{polyratfun} concept and the rational polynomials\index{rational polynomials} become rather complicated, the sorting after the CopySpectator statement can have serious bottleneck problems in \index{TFORM}\TFORM{} and \index{ParFORM}\ParFORM{} because the addition of those polynomials can be rather expensive and much of it ends up in the master processor. This can be made better with the following construction (assuming the function rat was declared as polyratfun at the moment of all the ToSpectator statements that wrote to the spectator): \begin{verbatim} PolyRatFun; Drop F1; CopySpactator F0 = complex0; ABracket+ rat; .sort PolyRatFun rat; RemoveSpectator complex0; .sort \end{verbatim} First we remove the declaration of rat as polyratfun. Then we read the spectator and sort it such that all terms that should be added eventually are grouped together. This sorting is very cheap as only identical terms are combined. Then we declare the polyratfun again and because of the way the terms are sorted nearly all additions take place inside the workers, hence at maximum parallelization efficiency. The above method still contains one inefficiency: because the polyratfun is declared again, the contents of the rat function need to be 'normalized' again, while they were already normalized. This involves calculating a gcd of the numerator and the denominator, which is an expensive operation and is useless in this case. For this we have a special option in the polyratfun declaration: \begin{verbatim} PolyRatFun rat-; \end{verbatim} This will skip the normalization on the input of the module. One should note however that if one uses this option under different conditions in which the input rat function might not be normalized, the program might crash or even give wrong answers. Hence this option should only be used with the highest degree of caution! This is an option for very experienced users only. No support is given concerning programs that run correctly without the use of this option and fail when using it. It should be noted that in the sequential version of \FORM{} this construction is not needed at all, because there is only one processor anyway. form-5.0.1/doc/manual/Makefile.am0000644000175100017510000000750415217035721012232 TEXSRC = \ bracket.tex \ calculus.tex \ diagrams.tex \ dict.tex \ dollar.tex \ external.tex \ float.tex \ functions.tex \ gamma.tex \ metric.tex \ module.tex \ optim.tex \ parallel.tex \ pattern.tex \ polynomials.tex \ prepro.tex \ setup.tex \ sorting.tex \ spectators.tex \ startup.tex \ statements.tex \ tablebas.tex \ variable.tex MAIN = manual TEXFILES = $(TEXSRC) $(MAIN).tex version.tex EXTRA_DIST = $(TEXSRC) .PHONY: dvi latex2html html ps pdf clean-local update_version_tex # NOTE: htlatex invalidate .aux, .idx, .dvi files. HTMLCLEANFILES = idxmake.dvi idxmake.log $(MAIN).4ct $(MAIN).4dx $(MAIN).4ix \ $(MAIN).4tc $(MAIN).aux $(MAIN).css $(MAIN).dvi $(MAIN).html $(MAIN)2.html \ $(MAIN).idv $(MAIN).idx $(MAIN).ilg $(MAIN).ind $(MAIN).lg $(MAIN).log \ $(MAIN).tmp $(MAIN).xref CLEANFILES = $(MAIN).pdf $(MAIN).ps $(MAIN).toc $(DATEFILE) texput.log \ version.tex $(HTMLCLEANFILES) clean-local: rm -rf html $(MAIN) # Automatic versioning. version.tex: update_version_tex $(UPDATE_VERSION_TEX) dist-hook: $(DISTHOOK_VERSION_TEX) if FIXED_VERSION UPDATE_VERSION_TEX = \ [ -f version.tex ] || $(LN_S) "$(srcdir)/version.tex.in" version.tex DISTHOOK_VERSION_TEX = \ cp "$(srcdir)/version.tex.in" "$(distdir)/version.tex.in" else UPDATE_VERSION_TEX = \ $(SHELL) "$(top_srcdir)/scripts/git-version-gen.sh" -C "$(srcdir)" -t -o version.tex --date-format '%e %B %Y' DISTHOOK_VERSION_TEX = \ $(SHELL) "$(top_srcdir)/scripts/git-version-gen.sh" -C "$(srcdir)" -t -o "$(distdir)/version.tex.in" --date-format '%e %B %Y' endif #################### CONFIG_TEX if CONFIG_TEX dvi: $(MAIN).dvi if CONFIG_MAKEINDEX $(MAIN).dvi: $(TEXFILES) $(LATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(LATEX) $(MAIN).tex; done $(MAKEINDEX) $(MAIN) $(LATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(LATEX) $(MAIN).tex; done else $(MAIN).dvi: $(TEXFILES) $(LATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(LATEX) $(MAIN).tex; done endif ########## CONFIG_LATEX2HTML if CONFIG_LATEX2HTML latex2html: $(MAIN)/$(MAIN).html $(MAIN)/$(MAIN).html: $(MAIN).dvi LATEX2HTML="$(LATEX2HTML)" $(top_srcdir)/scripts/run-latex2html.sh $(MAIN).tex endif ########## CONFIG_LATEX2HTML ########## CONFIG_HTLATEX if CONFIG_HTLATEX html: html/$(MAIN).html if CONFIG_MAKEINDEX html/$(MAIN).html: $(TEXFILES) mkdir -p html $(HTLATEX) $(MAIN) "html,mathml-" "" "-dhtml/" $(TEX) '\def\filename{{$(MAIN)}{idx}{4dx}{ind}} \input idxmake.4ht' $(MAKEINDEX) -o $(MAIN).ind $(MAIN).4dx $(HTLATEX) $(MAIN) "html,mathml-" "" "-dhtml/" sed 's/table.tabular {margin-left: auto; margin-right: auto;}/table.tabular {margin-left: inherit;}/' html/$(MAIN).css >html/$(MAIN).css.tmp mv html/$(MAIN).css.tmp html/$(MAIN).css rm -f $(HTMLCLEANFILES) else html/$(MAIN).html: $(DATEFILE) mkdir -p html $(HTLATEX) $(MAIN) "html,mathml-" "" "-dhtml/" rm -f $(HTMLCLEANFILES) endif endif ########## CONFIG_HTLATEX ########## CONFIG_PS if CONFIG_PS ps: $(DATEFILE) $(MAIN).ps $(MAIN).ps: $(DATEFILE) $(MAIN).dvi $(DVIPS) -o $(MAIN).ps $(MAIN).dvi endif ########## CONFIG_PS ########## CONFIG_PDF if CONFIG_PDF pdf: $(MAIN).pdf if CONFIG_MAKEINDEX $(MAIN).pdf: $(TEXFILES) $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done $(MAKEINDEX) $(MAIN) $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done else $(MAIN).pdf: $(TEXFILES) $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done endif endif ########## CONFIG_PDF endif #################### CONFIG_TEX form-5.0.1/doc/manual/external.tex0000644000175100017510000003760015217035721012542 \chapter{External communication} \label{externalcommunication} To communicate\index{communication!external} with other programs \FORM\ is equipped with special commands. One set of commands is rather simple in nature: the \#pipe\index{\#pipe} (see section \ref{prepipe}) and \#system\index{\#system} (see section \ref{presystem}) instructions allow \FORM\ to run programs in the regular command\index{command shell} shell\index{shell}. Sometimes however much more sophistication is needed because these instructions have a rather large overhead and need to start new processes each time they are executed. Hence a second more extensive set of instructions was developed that allows the start of an external process\index{process!external}, keep it open and maintain a two way communication\index{communication!two way} with it. Similarly it is possible to start \FORM\ in such a way from other programs. Many details of the method of implementation and a number of examples are given in a separate paper which can also found in the \FORM\ site (http://www.nikhef.nl/$\sim$form) under publications (look for the file extform.ps\index{extform.ps} or extform.pdf\index{extform.pdf}). Here we will just show the essentials and the syntax. The basic idea is to open (by means of the preprocessor) a number of external channels\index{channel!external} (there is no reason to be restricted to just one) by starting the corresponding program in a command shell. This program is kept running and a number is assigned to each channel. Next we can select a channel and communicate with it. To not run into syntactic problems, because the external program may have different ideas of what a formula should look like, one may have to install filters\index{filter}. These are additional programs that should be prepared before the \FORM\ program is started that process the communication to convert from one notation to the other. %--#[ #external : \section{\#external} \label{external} \noindent Syntax: \#external ["prevar"] systemcommand \noindent See also \noindent Starts\index{\#external} the command in the background, connecting to its standard input and output. By default, the external command has no controlling terminal, the standard error stream is redirected to \verb|/dev/null| and the command is run in a subshell in a new session and in a new process group (see the preprocessor instruction \verb|#setexternalattr|). The optional parameter ``prevar'' is the name of a preprocessor variable placed between double quotes. If it is present, the ``descriptor'' (small positive integer number) of the external command is stored into this variable and can be used for references to this external command (if there is more than one external command running simultaneously). The external command that is started last becomes the ``current'' (active) external command. All further instructions \#fromexternal\index{\#fromexternal} and \#toexternal\index{\#toexternal} deal with the current external command. %--#] #external : %--#[ #toexternal : \section{\#toexternal} \label{toexternalcommunication} \noindent Syntax: \#toexternal "formatstring" [,variables] \noindent See also \noindent Sends\index{\#toexternal} the output to the current external\index{\#external} command. The semantics of the \verb|"formatstring"| and the \verb|[,variables]| is the same as for the \#write\index{\#write} instruction, except for the trailing end-of-line symbol. In contrast to the \#write instruction, the \#toexternal instruction does not append any newline\index{newline} symbol to the end of its output. %--#] #toexternal : %--#[ #fromexternal : \section{\#fromexternal} \label{fromexternalcommunication} \noindent Syntax: \#fromexternal[$+-$] ["[\$]varname" [maxlength]] \noindent Appends\index{\#fromexternal} the output of the current external\index{\#external} command to the \FORM\ program. The semantics differ depending on the optional arguments. After the external command sends the prompt, \FORM\ will continue with a next line after the line containing the \#fromexternal instruction. The prompt string is not appended. The optional + or - sign after the name has influence on the listing of the content. The varieties are: \#fromexternal[$+-$] \noindent The semantics is similar to the \#include\index{\#include} instruction but folders\index{folders} are not supported. \#fromexternal[$+-$] "[\$]varname" \noindent is used to read the text from the running external command into the preprocessor variable varname, or into the dollar variable \$varname if the name of the variable starts with the dollar sign ``\$''. \#fromexternal[$+-$] "[\$]varname" maxlength \noindent is used to read the text from the running external command into the preprocessor (or dollar) variable varname. Only the first maxlength characters are stored. %--#] #fromexternal : %--#[ #prompt : \section{\#prompt} \label{promptcommunication} \noindent Syntax: \#prompt [newprompt] \noindent Sets\index{\#prompt} a new prompt for the current external command (if present) and all further (newly started) external commands. If newprompt is an empty string, the default prompt (an empty line) will be used. The prompt is a line consisting of a single prompt string. By default, this is an empty string. %--#] #prompt : %--#[ #setexternal : \section{\#setexternal} \label{setexternalcommunication} \noindent Syntax: \#setexternal n \noindent Sets the ``current'' external\index{\#setexternal} command. The instructions \#toexternal\index{\#toexternal} and \#fromexternal\index{\#fromexternal} deal with the current external command. The integer number n must be the descriptor of a running external command. %--#] #setexternal : %--#[ #rmexternal : \section{\#rmexternal} \label{rmexternalcommunication} \noindent Syntax: \#rmexternal [n] \noindent Terminates an external\index{\#rmexternal} command. The integer number n must be either the descriptor of a running external command, or 0. If n is 0, then all external programs will be terminated. If n is not specified, the current external command will be terminated. The action of this instruction depends on the attributes of the external channel (see the \#setexternalattr\index{\#setexternalattr} (section \ref{setexternalcommunication}) instruction). By default, the instruction closes the commands' IO channels, sends a KILL\index{KILL signal} signal to every process in its process group and waits for the external command to be finished. %--#] #rmexternal : %--#[ #setexternalattr : \section{\#setexternalattr} \label{setexternalattrcommunication} \noindent Syntax: \#setexternalattr list\_of\_attributes \noindent sets\index{\#setexternalattr} attributes for {\em newly started} external commands. Already running external commands are not affected. The list of attributes is a comma separated list of pairs attribute=value, e.g.: \begin{verbatim} #setexternalattr shell=noshell,kill=9,killall=false \end{verbatim} Possible attributes are: \begin{description} \item[kill\index{kill}] Specifies which signal is to be sent to the external command either before the termination of the \FORM\ program or by the preprocessor instruction \#rmexternal\index{\#rmexternal}. By default this is 9 (SIGKILL\index{SIGKILL signal}). Number 0 means that no signal will be sent. \item[killall\index{killall}] Indicates whether the KILL\index{KILL signal} signal will be sent to the whole group or only to the initial process. Possible values are ``\verb|true|'' and ``\verb|false|''. By default, the kill signal will be sent to the whole group. \item[daemon\index{daemon}] Indicates whether the command should be ``daemonized'', i.e. the initial process will be passed to the init process and will belong to the new process group in the new session. Possible values are ``\verb|true|'' and ``\verb|false|''. By default, ``\verb|true|''. \item[shell\index{shell}] specifies which shell\index{shell} is used to run a command. (Starting an external command in a subshell permits to start not only executable files but also scripts and pipelined jobs. The disadvantage is that there is no way to detect failure upon startup since usually the shell is started successfully.) By default this is ``\verb|/bin/sh -c|''. If set \verb|shell=noshell|, the command will be started by the instruction \#external\index{\#external} directly but not in a subshell, so the command should be a name of the executable file rather than a system command. The instruction \#external will duplicate the actions of the shell in searching for an executable file if the specified file name does not contain a slash (/) character. The search path\index{path!search} is the path specified in the environment by the PATH\index{PATH} variable. If this variable isn't specified, the default path ``\verb|:/bin:/usr/bin|'' is used. \item[stderr\index{stderr}] specifies a file to redirect the standard error\index{error stream} stream to. By default it is ``\verb|/dev/null|''. If set \verb|stderr=terminal|, no redirection occurs. \end{description} Only attributes that are explicitly mentioned are changed, all others remain unchanged. Note, changing attributes should be done with care. For example, \begin{verbatim} #setexternalattr daemon=false \end{verbatim} starts a command in the subshell within the current process group with default attributes kill=9 and killall=true. The instruction \#rmexternal\index{\#rmexternal} sends the KILL\index{KILL signal} signal to the whole group, which means that also \FORM\ itself will be killed. %--#] #setexternalattr : %--#[ An example : \section{An example} An example of the above instructions could be: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (ExtComm_1) \begin{verbatim} 1 symbol a,b; 2 3 #external "n1" cat -u 4 5 #external "n2" cat -u 6 7 * cat simply repeats its input. The default prompt is an 8 * empty line. So we use "\n\n" here -- one "\n" is to finish 9 * the line, and the next "\n" is the prompt: 10 #toexternal "(a+b)^2\n\n" 11 12 #setexternal `n1' 13 * For this channel the prompt will be "READY\n": 14 #toexternal "(a+b)^3\nREADY\n" 15 16 #setexternal `n2' 17 * Set the default prompt: 18 #prompt 19 Local aPLUSbTO2= 20 #fromexternal 21 ; 22 23 #setexternal `n1' 24 #prompt READY 25 Local aPLUSbTO3= 26 #fromexternal 27 ; 28 29 #rmexternal `n1' 30 #rmexternal `n2' 31 32 Print; 33 .end \end{verbatim} Two external channels are opened in lines 3 and 5. The UNIX\index{UNIX} utility ``\verb|cat|'' simply repeats its input. The option ``\verb|-u|'' is used to prevent the output buffering. The option is ignored by the GNU\index{GNU} \verb|cat| utility but is mandatory for non-GNU versions of \verb|cat|. After line 5 the current external channel is `\verb|n2|'. The default prompt is an empty line so in line 10 ``\verb|\n\n|'' is used -- one``\verb|\n|'' is to finish the line, and the next ``\verb|\n|'' is the prompt. Line 12 switches the current channel to `\verb|n1|'. For this channel the prompt will be ``\verb|READY|'', see line 24, hence the expression is finished by ``\verb|\nREADY\n|''. Line 16 switches to the `\verb|n2|' external channel and line 18 sets the default prompt (which is extra in this example since the default prompt was not changed up to now). Results (just a literal repetition of the sent expressions) are read in lines 20 and 26. Lines 29 and 30 close the external channels. %--#] An example : %--#[ Embedding : \section{Embedding FORM in other applications} \label{embeddingcommunication} The external channel instructions permit \FORM\ to swallow an external program. The same mechanism can be used in order to {\em embed\index{embed}} \FORM\ in other applications. There is a possibility to start \FORM\ from another program providing one (or more) communication channels (see below). These channels will be visible from a \FORM\ program as ``pre-opened''\index{pre-opened external channels} external channels existing after \FORM\ starts. There is no need to open them with the \#external\index{\#external} instruction. In this case, the preprocessor variable ``PIPES\_''\index{PIPES\_} is defined and is equal to the total number of the pre-opened external channels. Pre-opened external channel descriptors are contained in the preprocessor variables ``PIPE1\_''\index{PIPE1\_}, ``PIPE2\_''\index{PIPE2\_}, etc. For example, if `PIPES\_'\index{PIPES\_} is 3 then there are 3 pre-opened external channels with the descriptors `PIPE1\_', `PIPE2\_' and `PIPE3\_' so e.g.\ the following instruction could be used: \begin{verbatim} #setexternal `PIPE2_' \end{verbatim} without \begin{verbatim} #external "PIPE2_" \end{verbatim} The external channel attributes make no sense for the pre-opened channel (see the \#setexternalattr\index{\#setexternalattr} instruction (section \ref{setexternalattrcommunication})). Formally, they are as follows: \begin{verbatim} kill=0, killall=false, daemon=false, stderr=/dev/tty, shell=noshell \end{verbatim} In order to activate the pre-opened external channels, the parent application must follow some standards. Here we describe a low-level protocol\index{protocol!lowlevel}, the corresponding C-interface\index{C-interface} is available from the \FORM\ distribution site under packages and then externalchannels. Before starting \FORM, the parent application must create one or more pairs of pipes. A pipe\index{pipe} is a pair of file descriptors, one is for reading and another is for writing. In LINUX\index{LINUX}, see ``man 2 pipe''. The read-only descriptor of the first pipe in the pair and the write-only descriptor of the second pipe must be passed to \FORM\ as an argument of a command line option ``\verb|-pipe|'' in ASCII decimal format. The argument of the option is a comma-separated list of pairs ``\verb|r#,w#|'' where ``\verb|r#|'' is a read-only descriptor and ``\verb|w#|'' is a write-only descriptor; alternatively, an environment variable FORM\_PIPES\index{FORM\_PIPES} containing this list can be used (the command line option overrides the environment variable). For example, to start \FORM\ with two pre-opened external channels the parent application has to create first four pipes. Lets us suppose the first pipe was created with the descriptors 5 and 6, the second pipe has the descriptors 7 and 8, the third pipe has the descriptors 9 and 10 and the fourth pipe has the descriptors 11 and 12. The descriptors 5 and 8 will be used by \FORM\ as the input and the output for the first pre-opened external channel while the descriptors 9 and 12 will be used by \FORM\ as the input and the output for the second pre-opened external channel. Then the parent application must start \FORM\ with the following command line option: \begin{verbatim} -pipe 5,8,9,12 \end{verbatim} Upon startup, \FORM\ sends its PID\index{PID} (the Process Identifier) in ASCIIdecimal format with an appended newline character to the descriptor 8 and then \FORM\ will wait for the answer from the descriptor 5. The answer must be two comma-separated integers in ASCII decimal format followed by a newline character. The first integer corresponds to the \FORM\ PID while the second one is the parent process PID\@. If the answer is not obtained after some timeout, or if it is not correct (i.e.\ it is not a list of two integers or the first integer is not the \FORM\ PID) then \FORM\ fails. If everything is correct, \FORM\ creates the pre-opened channel and puts its descriptor in the preprocessor variable ``PIPE1\_''. Then \FORM\ processes the second pair of arguments, ``\verb|9,12|''. After all pairs have been processed \FORM\ creates the preprocessor variable ``PIPES\_'' and puts into this variable the total number of created pre-opened external channels. The order of processing the pairs of numbers in the argument is fixed exactly as it was described above i.e.\ from the left to the right. %--#] Embedding : form-5.0.1/doc/manual/dict.tex0000644000175100017510000003727315217035721011651 \chapter{Dictionaries} \label{dictionaries} At times one would like to manipulate the output to facilitate further processing. A standard example is that the output formula should be included in a \LaTeX{} file. Also the use of terms in the output as patterns with wildcards in the LHS of an id-statements needs textual translation. Another example is the representation of fractions in a numerical program that works with floating point numbers. Complete solutions for such problems are not included in \FORM{}, but with the partial solution of `dictionaries'\index{dictionaries} one can do quite a lot already. In \FORM{} a dictionary is a collection of `words'\index{word} together with their translation\index{translation}. The word can be a number, a variable, a function with its arguments or a special output token like a multiplication sign or a power indicator. The translation can be any string. Generic patterns have not been implemented. That would be more like grammar and involves special complications. As shown later, currently there is one exception to this rule. A dictionary is defined with the preprocessor\index{\#opendictionary} instruction \begin{verbatim} #opendictionary name \end{verbatim} in which `name' is the name of the dictionary. There can be more dictionaries, provided they have different names. It is allowed to open already existing dictionaries. Only one dictionary can be open at a given time. Dictionaries are closed with the instruction\index{\#closedictionary} \begin{verbatim} #closedictionary \end{verbatim} and because there can be only one open dictionary, it is clear which dictionary should be closed. A dictionary is opened to add words to it. This is done with the \#add instruction\index{\#add} as in \begin{verbatim} #add x1: "x_1" #add *: "\ " #add mu: "\mu" \end{verbatim} which would tell the system that when the dictionary is in use, the variable \verb:x1: should be printed as the string \verb:x_1: and a multiplication sign should become a backslash character followed by a blank space. The (index) mu would be printed as the string \verb:\mu:. A dictionary can be used\index{\#usedictionary} with the \begin{verbatim} #usedictionary name <(options)> \end{verbatim} instruction. At the moment a dictionary is being used there cannot be any open dictionaries. Hence we can stop using a dictionary with the \begin{verbatim} #closedictionary \end{verbatim} instruction\index{\#closedictionary} without running into inconsistencies. The options control partial use of a dictionary, as for instance only for individual variables, or only for numbers. They can also control whether translations should be made inside function arguments or inside dollar variables (when used as preprocessor variables). What words are allowed? \begin{description} \item[variable] This can be the name of a symbol, a vector, an index or a function (this includes commuting functions, non-commuting functions, tensors and tables). \item[number] This must be a positive integer number. \item[fraction] This must be a positive rational number. \item[special character] Currently this can be the multiplication sign (\verb:*:), or the power sign (\verb:^: or \verb:**:). \item[a range] Indicated between parentheses, this is a range\index{range} of extra symbols. There can be more than one range. \item[a function with arguments] This would be a complete function subterm. \end{description} The options in the \#usedictionary should be enclosed between parentheses and separated by comma's. They can be: \begin{description} \item[allnumbers] All numbers will be looked up in the dictionary. \item[integersonly] Only integer numbers will be looked up. \item[nonumbers] Numbers will not be looked up. \item[numbersonly] Only numbers will be looked up. \item[novariables] Loose variables will not be looked up. \item[variablesonly] Only loose variables will be looked up. \item[nospecials] Specials (multiplication signs and power signs) will not be looked up. \item[specialsonly] Only specials (multiplication signs and power signs) will be looked up. \item[nofunwithargs] Functions with arguments will not be looked up. \item[funwithargsonly] Only functions with arguments will be looked up. \item[warnings] Warnings\index{warnings} concern the look up of numbers. If a fortran or C format is being used and the dictionary cannot be used in such a way that floating point notation and/or decimal points can be avoided, a warning will be given. \item[nowarnings] No floating point warnings are given. \item[infunctions] Substitutions are also made inside function arguments. \item[notinfunctions] No substitutions are made inside function arguments. \item[\$] Substitutions are made also when dollar variables are expanded. The default is that this is not done. \end{description} The defaults are that all potential objects are looked up (also inside function arguments) and no warnings are given. The use is best illustrated with a few examples. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Dictionaries_1) \begin{verbatim} Symbols x1,y2,z3,N; Indices mu,nu,ro,si; Tensor tens; CFunction S,R,f; ExtraSymbols array w; #OpenDictionary test #add x1: "x_1" #add y2: "y^{(2)}" #add z3: "{\cal Z}" #add *: " " #add S(R(1),N): "S_1(N)" #add S(R(2),N): "S_2(N)" #add S(R(1,1),N): "S_{1,1}(N)" #add f: "\ln" #add mu: "\mu" #add nu: "\nu" #add ro: "\rho" #add si: "\sigma" #add tens: "T" #CloseDictionary Local F = x1*y2*z3 + S(R(1),N) + S(R(1,1),N) + S(R(2),N) + tens(mu,nu,ro,si) + f(x1+1); #usedictionary test Print +s; .end \end{verbatim} This program gives for its output \begin{verbatim} F = + x_1 y^2 {\cal Z} + T(\mu,\nu,\rho,\sigma) + S_1(N) + S_{1,1}(N) + S_2(N) + \ln(1 + x_1) ; \end{verbatim} Of course, there is nothing here that could not have been done with a good text editor, but having this inside the \FORM{} program makes that if there are changes in the \FORM{} program, it will be less work to implement them in the eventual \LaTeX{} files. Things become different when numerical\index{numerical output} output is involved. Take for instance the fraction $1/3$ inside a FORTRAN\index{fortran} program. Using the option \begin{verbatim} Format Fortran; \end{verbatim} one would obtain \begin{verbatim} 1./3. \end{verbatim} and with\index{doublefortran} \begin{verbatim} Format DoubleFortran; \end{verbatim} one would obtain \begin{verbatim} 1.D0/3.D0 \end{verbatim} while using\index{quadfortran} \begin{verbatim} Format QuadFortran; \end{verbatim} one would obtain \begin{verbatim} 1.Q0/3.Q0 \end{verbatim} which means that one might have three varieties of the same program, depending on the precision in which one would like run it. It would be far better to have a single version and only determine in the make file what the precision should be. The FORTRAN code for such a program could look like \begin{verbatim} REAL one,three,third PARAMETER (one=1,three=3,third=one/three) \end{verbatim} after which one should either use the name 'third' or a construction like 'one/three'. Let us take a simple program like \begin{verbatim} Symbol x,n; Format DoubleFortran; Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); Print; .end F = & 1.D0/7.D0*x + 1.D0/2.D0*x**2 + x**3 + 5.D0/4.D0*x**4 + x**5 + 1.D & 0/2.D0*x**6 + 1.D0/7.D0*x**7 + 1.D0/56.D0*x**8 \end{verbatim} If we define a dictionary we can make this into % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Dictionaries_2) \begin{verbatim} Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "TWO" #add 5: "FIVE" #add 7: "SEVEN" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers Print; .end F = & 1/SEVEN*x + 1/TWO*x**2 + x**3 + FIVE/4*x**4 + x**5 + 1/TWO*x**6 & + 1/SEVEN*x**7 + 1.D0/56.D0*x**8 \end{verbatim} one can see that some of the numbers have been replaced by text strings. In particular these are the numbers 2, 5 and 7. The output is now presented in such a way that the compiler can do the rest, provided we do this with all numbers that occur, and we feed the proper information to the compiler. One can also replace complete fractions as in % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Dictionaries_3) \begin{verbatim} Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "TWO" #add 5: "FIVE" #add 7: "SEVEN" #add 1/2: "HALF" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers Print; .end F = & 1/SEVEN*x + HALF*x**2 + x**3 + FIVE/4*x**4 + x**5 + HALF*x**6 + & 1/SEVEN*x**7 + 1.D0/56.D0*x**8 \end{verbatim} because the fractions take precedence. The next question is how one makes sure to have all numbers that need replacement? For that one can use the warnings option: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Dictionaries_4) \begin{verbatim} Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "TWO" #add 5: "FIVE" #add 7: "SEVEN" #add 1/2: "HALF" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers (warnings) Print; .end Time = 0.00 sec Generated terms = 8 F Terms in output = 8 Bytes used = 204 F = & 1/SEVEN*x + HALF*x**2 + x**3 + FIVE/4*x**4 + x**5 + HALF*x**6 + >>>>>>>>Could not translate coefficient with dictionary numbers<<<<<<<<< <<< & 1/SEVEN*x**7 + 1.D0/56.D0*x**8 \end{verbatim} In this case the line after the warning contains a fraction that was not substituted. This allows one to add either $56$ or $1/56$ to the dictionary. This gives the program % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Dictionaries_5) \begin{verbatim} Symbol x,n; Format DoubleFortran; #OpenDictionary numbers #add 2: "cd2" #add 5: "cd5" #add 7: "cd7" #add 56: "cd56" #add 1/2: "c1d2" #add 5/4: "c5d4" #CloseDictionary Local F = (1+x)^7/7; id x^n? = x*x^n/(n+1); #UseDictionary numbers (warnings) Print; .end F = & 1/cd7*x + c1d2*x**2 + x**3 + c5d4*x**4 + x**5 + c1d2*x**6 + 1/ & cd7*x**7 + 1/cd56*x**8 \end{verbatim} Here we have selected a different notation that allows extension easily. A good way to do this now is to put the dictionary in a file numbers.hh and the corresponding FORTRAN definitions in a file numbers.h and then include these files in the proper places. The numbers.hh file would be \begin{verbatim} #OpenDictionary numbers #add 2: "cd2" #add 5: "cd5" #add 7: "cd7" #add 56: "cd56" #add 1/2: "c1d2" #add 5/4: "c5d4" #CloseDictionary \end{verbatim} and the numbers.h file would be \begin{verbatim} REAL cd2,cd5,cd7,cd56,c1d2,c5d4 PARAMETER (cd2=2,cd5=5,cd7=7,cd56=56,c1d2=1/cd2,c5d4=cd5/4) \end{verbatim} and when the dictionary file is updated one may update the FORTRAN file simultaneously. Setting the precision of the declaration REAL\index{real} can be done by compiler options. These may depend on the compiler. One should consult the manpages. Printing the extra symbols\index{extra symbols} (\ref{substaextrasymbols}) may be a bit trickier. A range\index{range} is indicated with a pair of parentheses enclosing one or two (positive) numbers. If there are two numbers, they should be separated by a comma. There can be more than one range. In the substitution one can use the wildcards \verb:%#: and \verb:%@: to indicate the number of the extra symbol. The first wildcard indicates the number of the symbol and the second starts it counting with 1 from the beginning of the range. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Dictionaries_6) \begin{verbatim} Symbol x; CFunction f; #OpenDictionary ranges #add (1,2): "w(%#)" #add (3): "ww(%#)" #add (4,6): "www(%@)" #CloseDictionary Local F = +...+; ToPolynomial; Print; .sort F = x*Z1_ + x^2*Z2_ + x^3*Z3_ + x^4*Z4_ + x^5*Z5_ + x^6*Z6_; #UseDictionary ranges Print; .end F = x*w(1) + x^2*w(2) + x^3*ww(3) + x^4*www(1) + x^5*www(2) + x^6*www(3); \end{verbatim} The use of the dictionaries in dollar variables can best be shown with an example that has much in common with graph theory. Assume we have an expression that contains all topologies we are interested in, with a notation for the momenta. The function vx represents a vertex and we use it as a symmetric function. Here we show two topologies from massless two-loop propagators: \begin{verbatim} +vx(p0,p1,-p4)*vx(-p1,p2,p5)*vx(q0,-p2,-p3)*vx(p4,p3,-p5)*topo(1) +vx(p0,p1,p2)*vx(-p1,p3,p4)*vx(q0,-p2,-p3,-p4)*topo(2) \end{verbatim} where the q0 momentum is taken to be -p0. The problem is what happens when in a diagram of topology one, one of the lines is removed. If for instance the p1 line is removed, we will end up with the second topology, but the question is: how should we relabel the momenta to obtain the notation of topology 2. Taking out p1 gives us: \begin{verbatim} +vx(p0,-p4,p2,p5)*vx(q0,-p2,-p3)*vx(p4,p3,-p5)*topo(1) \end{verbatim} and to see what renaming we need is usually a major source of errors. We can do this automatically if we can substitute the second topology into the remainder of the first using proper wildcards and storing the matches in dollar variables. This can be done with a dictionary: \begin{verbatim} #OpenDictionary match #add p0: "p0?{p0,q0}$p0" #add q0: "q0?{p0,q0}$q0" #do i = 1,5 #add p`i': "p`i'?$p`i'" #enddo #CloseDictionary \end{verbatim} We put the various candidate topologies that could match, one by one, into the variable \$child as in (after using brackets on the expression with the topologies): \begin{verbatim} #$child = Topologies[topo(2)]; \end{verbatim} but generating an id-statement from it would be very laborious without the dictionaries: \begin{verbatim} id `$Orig' = 1; \end{verbatim} would result in: \begin{verbatim} id vx(-p2,-p3,q0)*vx(-p4,p0,p2,p5)*vx(-p5,p3,p4) = 1; \end{verbatim} but with the dictionary activated as in \begin{verbatim} #inside $child #UseDictionary match($) id `$Orig' = 1; #CloseDictionary #endinside \end{verbatim} the generated code is \begin{verbatim} id vx(-p2?$p2,-p3?$p3,q0?{p0,q0}$q0)*vx(-p4?$p4,p0?{p0,q0}$p0, p2?$p2,p5?$p5)*vx(-p5?$p5,p3?$p3,p4?$p4) = 1; \end{verbatim} and from the dollar variables we can generate a statement with the the renumbering \begin{verbatim} id topo(1) = topo(2)*replace_(p0,-p0,p1,q1,p2,-p2,p3,-p1,p4,p3,p5,-p4); \end{verbatim} We used $p_1\rightarrow q_1$ as initialization before the pattern matching and $p_0 = q_0$ we can replace by $p_0 = p_0$. The $q_1$ should be replaced by means of momentum conservation, but that goes beyond the scope of this example. It should be clear from the above that the dictionaries are the beginning of a new development. One should expect more capabilities in the future and suggestions are highly appreciated, provided they lead to something that can be implemented in a reasonable amount of time. Hence, for instance, there will not be a complete \LaTeX{} output format that can take line length into account. form-5.0.1/doc/manual/setup.tex0000644000175100017510000007667015217035721012072 \chapter{The setup} \label{setup} When \FORM\ is started, it has a number of settings\index{setup} built in that were determined during its installation\index{installation}. If the user would like to alter these settings, it is possible to either specify their desired values in a setup file\index{file!setup} or to do so at the beginning of the program file\index{file!program}. There are two ways in which \FORM\ can find a setup file. The first way is by having a file named `form.set'\index{form.set} in the current directory. If such a file is present, \FORM\ will open it and interpret its contents as setup parameters. If this file is not present, one may specify a setup file with the -s option in the command tail. This option must precede the name of the input file. After the -s follow one or more blanks or tabs and then the full name of the setup file. \FORM\ will try to read startup parameters from this file. If a file `form.set' is present, \FORM\ will ignore the -s option and its corresponding file name. This order of interpretation allows the user to define an alias with a standard setup file which can be overruled by a local setup file. If, in the beginning of the program file, before any other statements with the exception of the \#- instruction and commentary statements, there are lines that start with \#: the remaining contents of these lines are interpreted exactly like the lines in the setup file. The specifications in the program file take precedence\index{precedence} over all other specifications. If neither of the above methods is used, \FORM\ will use a built in set of parameters. Their values may depend on the installation and are given below. The following is a list of parameters that can be set. The syntax is rather simple: The full word must be specified (case insensitive), followed by one or more blanks or tabs and the desired number, string or character. Anything after this is considered to be commentary. In the setup file lines that do not start with an alphabetic character are seen as commentary. The sizes of the buffers are given in bytes, unless mentioned otherwise. A word is 2 bytes for 32\index{32 bits} bit machines and 4 bytes for 64\index{64 bits} bit machines. In \FORM\ version 3.3 and later, it is also allowed to define preprocessor variables\index{preprocessor variables} (see also \ref{preprovariables}) in the setup file. In addition one can use preprocessor variables in the setup, provided it is not in the name of the parameter/keyword. \leftvitem{4.0cm}{bracketindexsize\index{setup!bracketindexsize}\index{bracketindexsize}} \rightvitem{12.6cm}{Maximum size in bytes of any individual index of a bracketted expression. Each expression will have its own index. The index starts with a relatively small size and will grow if needed. But it will never grow beyond the specified size. If more space is needed, \FORM\ will start skipping brackets and find those back later by linear search. See also chapter~\ref{brackets} and section~\ref{substabracket}.} \leftvitem{4.0cm}{CommentChar\index{setup!commentchar}\index{commentchar}} \rightvitem{12.6cm}{This should be followed by one or more blanks and a single non-blank character. This character will be used to indicate commentary, instead of the regular $*$ in column 1.} \leftvitem{4.0cm}{CompressSize\index{setup!compresssize}\index{compresssize}} \rightvitem{12.6cm}{When compressing output terms, \FORM\ needs a compression buffer. This buffer deals recursively with compression and decompression of terms that are either written or read. Its size will be at least MaxTermSize but when there is heavy use of expressions in the right hand side of definitions or substitution it would have to be considerably longer. It is hoped that in the future this parameter can be eliminated. CompressSize should be given in bytes.} \leftvitem{4.0cm}{ConstIndex\index{setup!constindex}\index{constindex}} \rightvitem{12.6cm}{This is the number of indices that are considered to be constant indices like in fixed vector components (the so-called fixed indices). The size of this parameter is not coupled to any array space, but it should not go much beyond 1000 on a 32\index{32 bits} bit machine. On a 64\index{64 bits} bit machine it can go considerably further.} \leftvitem{4.0cm}{ContinuationLines\index{setup!continuationlines}\index{continuationlines}} \rightvitem{12.6cm}{The maximum number of continuation lines, after which expressions will be broken apart when printed. The value of 0 means that no limit is imposed. The precise format of continuation lines depend on the current format (see \ref{substaformat}) settings; \#write instruction also allows for additional control (see \ref{prewrite}).} \leftvitem{4.0cm}{Define\index{setup!define}\index{define}} \rightvitem{12.6cm}{The syntax is as in the \#define instruction in the preprocessor (see \ref{preprovariables}), with the remark that in the setup file there should be no leading \# character as that would make the line into commentary. Example: \hfill \\ {\tt\ \ \ \ define MODULUS "31991"} \hfill \\ which could be used at a later point in the program to activate a modulus statement (see \ref{substamodulus}).} \leftvitem{4.0cm}{DotChar\index{setup!dotchar}\index{dotchar}} \rightvitem{12.6cm}{There should be a single character following this name (and the blank(s) after it). This character will be used instead of the \_, when dotproducts\index{dotproducts} are printed in Fortran\index{Fortran} output. This option is needed because some Fortran compilers do not recognize the underscore as a valid character. In the olden days one could use here the dollar character but nowadays many Fortran compilers do not recognize this character as belonging to a variable name.} \leftvitem{4.0cm}{FunctionLevels\index{setup!functionlevels}\index{functionlevels}} \rightvitem{12.6cm}{The maximum number of levels that may occur, when functions have functions in their arguments.} \leftvitem{4.0cm}{HideSize\index{setup!hidesize}\index{hidesize}} \rightvitem{12.6cm}{The size of the hide buffer. The size of this buffer is normally set equal to scratchsize (see below). If one uses the setting of HideSize after the setting of ScratchSize, one can give the hide buffer its own size. There are cases that this can make the program faster.} \leftvitem{4.0cm}{IncDir\index{setup!incdir}\index{incdir}} \rightvitem{12.6cm}{Directory (or path of directories) in which \FORM\ will look for files if they are not to be found in the current directory. This involves files for the \#include\index{\#include} and \#call\index{\#call} instructions. This variable takes precedence over the Path\index{setup!path}\index{path} variable.} %\leftvitem{4.0cm}{IndentSpace\index{setup!indentspace}\index{indentspace}} %\rightvitem{12.6cm}{} \leftvitem{4.0cm}{InsideFirst\index{setup!insidefirst}\index{insidefirst}} \rightvitem{12.6cm}{Not having any effect at the moment.} \leftvitem{4.0cm}{JumpRatio\index{setup!jumpratio}\index{jumpratio}} \rightvitem{12.6cm}{See the endswitch (\ref{substaendswitch}) statement.} \leftvitem{4.0cm}{MaxNumberSize\index{setup!maxnumbersize}\index{maxnumbersize}} \rightvitem{12.6cm}{Allows the setting of the maximum size of the numbers in \FORM\@. The number should be given in words. For 32\index{32 bits} bit systems a word is two bytes and for 64\index{64 bits} bit systems a word is 4 bytes. The number size is always limited by the maximum size of the terms (see MaxTermSize). Actually it has to be less than half of MaxTermSize because a coefficient contains both a numerator and a denominator. It is not always a good idea to have the number size at its maximum value, especially when MaxTermSize is large. In that case it could be very long before a runaway algorithm runs into limitations of size (arithmetic for very long fractions is not very fast due to the continuous need for computing GCD's)} \leftvitem{4.0cm}{MaxTermSize\index{setup!maxtermsize}\index{maxtermsize}} \rightvitem{12.6cm}{This\label{setupmaxtermsize} is the maximum size that an individual term may occupy in words. This size does not affect any allocations. One should realize however that the larger this size is the heavier the demand can be on the workspace, because the workspace acts as a heap during the execution and sometimes allocations have to be made in advance, before \FORM\ knows what the actual size of the term will be. Consequently the evaluation tree cannot be very deep, when WorkSpace / MaxTermSize is not very big. MaxTermSize controls mainly how soon \FORM\ starts complaining about terms that are too complicated. Its absolute maximum is 32568 on 32\index{32 bits} bit systems and about $10^9$ on 64\index{64 bits} bit systems (of course the workspace would have to be considerably larger than that....).} \leftvitem{4.0cm}{MaxWildCards\index{setup!maxwildcards}\index{maxwildcards}} \rightvitem{12.6cm}{The maximum number of wildcards that can be active in a single matching of a pattern. Under normal circumstance the default value of 100 should be more than enough.} \leftvitem{4.0cm}{NoSpacesInNumbers\index{setup!nospacesinnumbers}\index{nospacesinnumbers}} \rightvitem{12.6cm}{Long\label{nospacesinnumbers} numbers are usually spread over several lines by placing a backspace character at the end of each line and then continuing at the next line. For cosmetic purposes \FORM\ puts usually a few blank spaces at the beginning of the new line. \FORM\ itself can read this but some programs cannot. Hence one can put \FORM\ in a mode in which these blanks are omitted. The values of the variable are ON or OFF\@. There is also a command to change this behaviour at runtime. See the on and off commands in sections \ref{staonnospacesinnumbers} and \ref{staoffnospacesinnumbers}.} \leftvitem{4.0cm}{NumStoreCaches\index{setup!numstorecaches}\index{numstorecaches}} \rightvitem{12.6cm}{This number determines how many store caches (see the description of the SizeStoreCache setup parameter below) there will be. In the case of parallel processing this will be the number of caches per processor.} \leftvitem{4.0cm}{NwriteStatistics\index{setup!nwritestatistics}\index{nwritestatistics}} \rightvitem{12.6cm}{When this word is mentioned, the default setting for the statistics is that no run time statistics will be shown. Ordinarily they will be shown.} \leftvitem{4.0cm}{NwriteThreadStatistics\index{setup!nwritethreadstatistics} \index{nwritethreadstatistics}} \rightvitem{12.6cm}{\vspace{1ex}This variable has the values ON or OFF\@. It controls for \TFORM{} whether the statistics of the individual threads will be printed. The default value is ON.} \leftvitem{4.0cm}{OldOrder\index{setup!oldorder}\index{oldorder}} \rightvitem{12.6cm}{A special flag (values ON/OFF) by which one can still select the old option of not checking for the order of statements inside a module. This should be used only in the case that it is nearly impossible to change a program to the new mode in which the order of the statements (declarations etc) is relevant. In the future this old mode may not exist.} \leftvitem{4.0cm}{Parentheses\index{setup!parentheses}\index{parentheses}} \rightvitem{12.6cm}{The maximum number of nestings of parentheses or functions inside functions. The variable may be eliminated in a later version.} \leftvitem{4.0cm}{Path\index{setup!path}\index{path}} \rightvitem{12.6cm}{Directory (or path of directories) in which \FORM\ will look for files if they are not to be found in the current directory. This involves files for the \#include\index{\#include} and \#call\index{\#call} instructions. \FORM\ will test this path after a potential path specified as IncDir\index{setup!incdir}\index{incdir}.} %\leftvitem{4.0cm}{PolyGCDchoice\index{setup!polygcdchoice}\index{polygcdchoice}} %\rightvitem{12.6cm}{} \leftvitem{4.0cm}{ProcedureExtension\index{setup!procedureEetension}\index{procedureextension}} \rightvitem{12.6cm}{The extension that will be used by \FORM\ for finding the procedures that are in separate files. Restrictions on the strings used are as explained in the preprocessor \#procedureextension\index{\#procedureextension} instruction in section \ref{preprocedureextension}.} \leftvitem{4.0cm}{ProcessBucketSize\index{setup!processbucketsize}\index{processbucketsize}} \rightvitem{12.6cm}{\label{setupprocessbucketsize} For the parallel version \ParFORM\@. It is ignored in other versions. Tells \ParFORM\ how many terms there should be in the buckets that are being distributed over the secondary processors. See also \ref{substaprocessbucketsize}.} \leftvitem{4.0cm}{ResetTimeOnClear\index{setup!resettimeonclear}\index{resettimeonclear}} \rightvitem{12.6cm}{The value is ON or OFF\@. The default value is ON\@. This means that by default the clock is reset after each .clear\index{.clear} (see chapter \ref{modules} on modules) instruction at the end of a module.} \leftvitem{4.0cm}{ScratchSize\index{setup!scratchsize}\index{scratchsize}} \rightvitem{12.6cm}{The size of the input and the output buffers for the regular algebra processing. Terms are read in in chunks this size and are written to the output file using buffers of this size. There are either two or three of these buffers, depending on whether the hide\index{hide} facility is being used (see \ref{substahide}). These buffers must have a size that is at least as large as the MaxTermSize\index{maxtermsize}. These buffers act as caches for the files with the extension .sc1\index{.sc1}, .sc2\index{.sc2} and .sc3\index{.sc3}. See also the HideSize parameter above for the independent setting of the size of the hide buffer.} \leftvitem{4.0cm}{SizeStoreCache\index{setup!sizestorecache}\index{sizestorecache}} \rightvitem{12.6cm}{The size of the caches\index{caches} that are used for reading terms when stored expressions are used in the r.h.s.\ of a statement. Typically there are several such caches and they make the reading much faster. In the case of parallel processing these caches become very important because without them the different processes may all want to read from the .str\index{.str} file\index{file!store} at the same time and execution speed will suffer badly. The number of store caches is determined by the NumStoreCaches\index{numstorecaches} setup parameter which is described above. The size of these caches doesn't have to be very large as compared to some of the other buffers. It is recommended though to have them at least as large as MaxTermSize\index{maxtermsize} (see above).} \leftvitem{4.0cm}{SortType\index{setup!sorttype}\index{sorttype}} \rightvitem{12.6cm}{Possible values are "lowfirst"\index{lowfirst}, "highfirst"\index{highfirst} and "powerfirst"\index{powerfirst}. "lowfirst" is the default. Determines the order in which the terms are placed during sorting. In the case of lowfirst, lower powers of symbols and dotproducts come before higher powers. In the case of highfirst it is the opposite. In the case of powerfirst the combined powers of all symbols together are considered and the highest combined powers come first. See also the on\index{on} statement in \ref{substaon}.} \leftvitem{4.0cm}{TempDir\index{setup!tempdir}\index{tempdir}} \rightvitem{12.6cm}{This variable should contain the name of a directory that is the directory in which \FORM\ should make its temporary files. If the -t option is used when \FORM\ is started, the TempDir variable in the setup file is ignored. \FORM\ can create a number of different temporary files.} \leftvitem{4.0cm}{TempSortDir\index{setup!tempsortdir}\index{tempsortdir}} \rightvitem{12.6cm}{This variable should contain the name of a directory that is the directory in which \FORM{} should make its temporary sort files. If the -ts option is used when \FORM{} is started, the TempSortDir variable in the setup file is ignored. If TempSortDir is not specified, then the value of TempDir is used also for sort files.} \leftvitem{4.0cm}{ThreadBucketSize\index{setup!threadbucketsize}\index{threadbucketsize}} \rightvitem{12.6cm}{Only relevant for \TFORM\@. The size of the number of terms sent to the workers simultaneously. For details see the chapter on the parallel version (\ref{parallel}).} \leftvitem{4.0cm}{ThreadLoadBalancing\index{setup!threadloadbalancing}\index{threadloadbalancing}} \rightvitem{12.6cm}{\indent Only relevant for \TFORM\@. Possible values are ON or OFF\@. For details see the chapter on the parallel version (\ref{parallel}).} \leftvitem{4.0cm}{Threads\index{setup!threads}\index{threads}} \rightvitem{12.6cm}{Only relevant for \TFORM\ (see chapter on the parallel version). Specifies the default number of worker threads to be used. The values 0 and 1 will indicate that running will only be done by the master thread (\ref{parallel}).} \leftvitem{4.0cm}{ThreadScratchOutSize\index{setup!threadscratchoutsize}\index{threadscratchoutsize}} \rightvitem{12.6cm}{The size of the output scratch buffers for each of the worker threads. These buffers will be used by \TFORM{} when the InParallel statement~\ref{substainparallel} is active. They are used to catch the output of the expressions as processed by the individual workers before they are copied to the output scratch buffer/file of the master. The output scratch buffer/file of each worker will never contain more than one expression at a time.} \leftvitem{4.0cm}{ThreadScratchSize\index{setup!threadscratchsize}\index{threadscratchsize}} \rightvitem{12.6cm}{The size of the input scratch buffers for each of the worker threads. These buffers are only used when the main scratch buffers of the master process aren't sufficient and scratch files have been made. When the buffers of the master are big enough, the workers only use pointers to the buffer of the master. Once there are scratch files the buffer is used for caching the input from those files. In that case each worker has its own cache. For reading purposes it can actually be counter productive if these buffers are very large. This parameter sets the value for the input and the hide\index{hide} scratch files. The output scratch size for the workers is set with the ThreadScratchOutSize parameter.} %\leftvitem{4.0cm}{ThreadSortFileSynch\index{setup!threadsortfilesynch}\index{threadsortfilesynch}} %\rightvitem{12.6cm}{\indent Only relevant for \TFORM. Possible values are ON %or OFF. For details see the chapter on the parallel version (\ref{parallel}).} \leftvitem{4.0cm}{TotalSize\index{setup!totalsize}\index{totalsize}} \rightvitem{12.6cm}{Puts \FORM\ in a mode in which it tries to determine the maximum space occupied by all expressions at any given moment during the execution of the program. This space is the sum of the input/output/hide scratch files, the sort file(s) and the .str file. This maximum is printed at the end of the program. The same can be obtained with the "On TotalSize" statement (see \ref{ontotalsize}) or the -T option in the command tail when \FORM\ is started (see \ref{running}).} \leftvitem{4.0cm}{WorkSpace\index{setup!workspace}\index{workspace}} \rightvitem{12.6cm}{The size of the heap that is used by the algebra processor when it is evaluating the substitution tree. It will contain terms, half finished terms and other information. The size of the workspace may be a limitation on the depth of a substitution tree.} \leftvitem{4.0cm}{WTimeStats\index{setup!wtimestats}\index{wtimestats}} \rightvitem{12.6cm}{Turns on the wall-clock time mode in the statistics. See the `\texttt{On wtimestats}' statement~\ref{substaon}.} Variables that take a path\index{path} for their value expect a sequence of directories, separated by colon characters as in the UNIX\index{UNIX} way to define such objects. The above parameters are conceptually relatively easy. The parameters that are still left are more complicated and are often restricted in their size by some relationships. Hence it is necessary to understand the sorting inside \FORM\ a little bit before using them. On the other hand these parameters can influence the performance noticeably. See also chapter \ref{sorting} for more details. When terms are send to `output' by the main algebra engine, they are put inside a buffer. This buffer is called the `small\index{small buffer} buffer\index{buffer!small}'. Its size is given by the variable {\sl SmallSize\index{smallsize}}. When this buffer is full, or when the number of terms in this buffer exceeds a given maximum, indicated by the variable {\sl TermsInSmall\index{termsinsmall}}, the contents of the buffer are sorted. The sorting is done by pointers, hence it is important that the small buffer resides inside the physical memory. During the sorting it may happen that coefficients are added. The sum of two rational numbers can take more space than any of the individual numbers, so there will be a space problem. This has been solved by the construction of an extension to the small buffer. The variable {\sl SmallExtension\index{smallextension}} is the size of the small buffer together with this extension. The value for SmallExtension will always be at least 7/6 times the value of SmallSize. The result of the sorting of the small buffer is written to the `large\index{large buffer} buffer\index{buffer!large}' (with the size {\sl LargeSize\index{largesize}}) as a single object and the filling of the small buffer can resume. Whenever there is not enough room in the large buffer for the result of sorting the small buffer, or whenever there are already a given number of these sorted `patches' in it (controlled by the variable {\sl LargePatches\index{largepatches}}) the buffer will be sorted by merging the patches\index{patch} to make room for the new results. The output is written to the sort file as a single patch. Then the results from the small buffer can be written to the large buffer. This game can continue till no more terms are generated. In the end it will be necessary to sort the results in the intermediate sort file\index{file!sort}. This can be done with up to {\sl FilePatches\index{filepatches}} at a time. Because file operations are notoriously slow the combination of the small buffer, the small extension and the large buffer is used for caching\index{cache} purposes. Hence this space can be split in `FilePatches' caches. The limitation is that each cache should be capable to contain at least two terms of maximal size. This means that the sum of SmallExtension and LargeSize must be at least FilePatches times 2*MaxTermSize*(bytes in short integer). It is possible to set the size of these caches directly with the variable {\sl SortIOsize\index{sortiosize}}. If the variable is too large, the variable FilePatches may be adjusted by \FORM\@. If there are more than FilePatches patches in the sort file, a second sort file is needed for the output of each `superpatch'\index{superpatch}. When the first sort file has been treated, the second sort file can be treated in exactly the same way as its predecessor. This process will finish eventually. When there are at most FilePatches patches in a sort file, the output of their merging can be written directly to the regular output. For completeness we give a list of all these variables: \leftvitem{3cm}{FilePatches\index{setup!filepatches}\index{filepatches}} \rightvitem{13cm}{The maximum number of patches that can be merged simultaneously, when the intermediate sort file is involved.} \leftvitem{3cm}{LargePatches\index{setup!largepatches}\index{largepatches}} \rightvitem{13cm}{The maximum number of patches that is allowed in the large buffer. The large buffer may reside in virtual memory, due to the nature of the sort that is applied to it.} \leftvitem{3cm}{TermsInSmall\index{setup!termsinsmall}\index{termsinsmall}} \rightvitem{13cm}{The maximum number of terms that is allowed in the small buffer before it is sorted. The sorted result is either copied to the large buffer or written to the intermediate sort file (when LargeSize is too small).} \leftvitem{3cm}{SmallSize\index{setup!smallsize}\index{smallsize}} \rightvitem{13cm}{The size of the small buffer in bytes.} \leftvitem{3cm}{SmallExtension\index{setup!smallextension}\index{smallextension}} \rightvitem{13cm}{The size of the small buffer plus its extension.} \leftvitem{3cm}{LargeSize\index{setup!largesize}\index{largesize}} \rightvitem{13cm}{The size of the large buffer.} \leftvitem{3cm}{SortIOsize\index{setup!sortiosize}\index{sortiosize}} \rightvitem{13cm}{The size of the buffer that is used to write to the intermediate sorting file and to read from it. It should be noted that if this buffer is not very large, the sorting of large files may become rather slow, depending on the operating system. Hence we recommend a potential fourth stage in the sorting over having this number too small to fit more filepatches in the combined small and large buffer. Setting the small and large buffers to a decent size may avoid all problems by a: making more space for the caching, b: creating fewer file patches to start with.} There is a second set of the above setup parameters for sorts of subexpressions\index{subexpressions} as in function arguments or in the term environment (see \ref{substaterm}). Because these things can happen with more than one level, whatever allocations have to be made (during runtime when needed) may have to be made several times. Hence one should be far more conservative here than with the global allocations. Anyway, those sorts should rarely involve anything very big. With the function arguments the condition is that the final result will fit inside a single term, but with the term environment no such restriction exists. The relevant variables here are subfilepatches, sublargepatches, sublargesize, subsmallextension, subsmallsize, subsortiosize and subtermsinsmall. Their meanings are the same as for the variables without the sub in front. When \FORM\ is running in parallel mode (either \TFORM\ or \ParFORM) each worker will need its own buffers. In \ParFORM\ in which the processors each control their own memory, the size of each of these buffers are the same as for the master process. In \TFORM\ with its shared memory the above sizes refer to the buffers of the master thread. The workers each get basically buffers with 1/N times the size of the buffer of the master. This may get made a bit bigger when potential conflicts with MaxTermSize occur. The (typically) largest buffers (the small and large buffers) may be reallocated at the end of a single module (see \#sortreallocate (\ref{presortreallocate})) or at the end of each module (see ``On sortreallocate;'' (\ref{substaon})). In some cases this can significantly reduce \FORM's memory usage as measured by ``resident set size''. For programs which consist of a large number of very quickly-running modules, this can incur a noticable performance penalty if performed every module. The default settings are \begin{center} \begin{tabular}{lrrr} Variable & 32-bits & 64-bits & tform 64-bits \\ \hline bracketindexsize & 200000 & 200000 & 200000 \\ commentchar & $*$ & $*$ & $*$ \\ compresssize & 90000 & 90000 & 90000 \\ constindex & 128 & 128 & 128 \\ continuationlines & 15 & 15 & 15 \\ dotchar & . & . & . \\ filepatches & 256 & 256 & 256 \\ functionlevels & 30 & 30 & 30 \\ hidesize & 50000000 & 50000000 & 50000000 \\ incdir & . & . & . \\ %indentspace & & & \\ insidefirst & ON & ON & ON \\ largepatches & 256 & 256 & 256 \\ largesize & 50000000 & 800000000 & 1500000000 \\ maxnumbersize & 200 & 200 & 200 \\ maxtermsize & 10000 & 40000 & 40000 \\ maxwildcards & 100 & 100 & 100 \\ nospacesinnumbers & OFF & OFF & OFF \\ numstorecaches & 4 & 4 & 4 \\ nwritefinalstatistics & OFF & OFF & OFF \\ nwritestatistics & OFF & OFF & OFF \\ nwritethreadstatistics &OFF & OFF & OFF \\ oldorder & OFF & OFF & OFF \\ parentheses & 100 & 100 & 100 \\ path & . & . & . \\ %polygcdchoice & 0 & 0 & 0 \\ processbucketsize & 1000 & 1000 & 1000 \\ scratchsize & 50000000 & 500000000 & 500000000 \\ sizestorecache & 32768 & 32768 & 32768 \\ smallextension & 20000000 & 300000000 & 600000000 \\ smallsize & 10000000 & 150000000 & 300000000 \\ sortiosize & 100000 & 100000 & 100000 \\ sorttype & lowfirst & lowfirst & lowfirst \\ subfilepatches & 64 & 64 & 64 \\ sublargepatches & 64 & 64 & 64 \\ sublargesize & 26880512 & 26880512 & 26880512 \\ subsmallextension & 3840032 & 3840032 & 3840032 \\ subsmallsize & 2560016 & 2560016 & 2560016 \\ subsortiosize & 32768 & 32768 & 32768 \\ subtermsinsmall & 10000 & 10000 & 10000 \\ tempdir & . & . & . \\ tempsortdir & . & . & . \\ termsinsmall & 100000 & 2000000 & 3000000 \\ threadbucketsize & 500 & 500 & 500 \\ threadloadbalancing & ON & ON & ON \\ threads & 0 & 0 & 0 \\ threadsortfilesynch & OFF & OFF & OFF \\ threadscratchoutsize & 2500000 & 2500000 & 2500000 \\ threadscratchsize & 100000 & 100000 & 100000 \\ workspace & 10000000 & 40000000 & 40000000 %zipsize & 32768 & 32768 & 32768 \end{tabular} \end{center} If one compares these numbers with the corresponding numbers for older versions one will notice that here we assume that the standard computer will have much more memory available than in the `old time'. Basically we expect that a serious \FORM\ user has at least 64 Mbytes available. If it is considerably less one should define a setup file with smaller settings. More recently a new notation for large numbers has been allowed. One can use the characters K, M, G and T to indicate kilo (three zeroes), mega (6 zeroes), giga (9 zeroes) and tera (12 zeros) as in 10M for 10000000. To find out what the setup values are, one can use the `ON,setup;' statement (\ref{substaon}). In version 3.3 and later one may use environment\index{environment} variables for the values of the setup parameters, either in the setup file or at the beginning of the .frm file. The environment variable is used as a preprocessor variable in the sense that its name is enclosed in a backquote-quote pair as in \verb:`VARNAME':. The variable will be looked for and if found it will be substituted. This can however not be done in a recursive way, because the regular routines that take care of the preprocessor variables are not active yet when the setups are read. form-5.0.1/doc/manual/startup.tex0000644000175100017510000001565315217035721012426 \chapter{Running FORM} \label{running} The proper way to invoke the running\index{running \FORM} of \FORM\ depends on the operating system that is being used. Here we will consider the UNIX\index{UNIX} operating system and its derivatives. The version for computers with the Windows operating system use Cygwin\index{Cygwin}, which is a UNIX derivative as well and hence it functions similarly. In all cases a proper call of \FORM\ is \begin{verbatim} form [options] inputfile \end{verbatim} The input file\index{file!input} should have a name that ends in the extension \verb:.frm:. It is however not needed to specify this extension. If this extension is absent, \FORM\ will add it. Example: \begin{verbatim} form myformprogram \end{verbatim} and \FORM{} will look for the file \verb:myformprogram.frm:. It is also possible to use the standard input as the input, rather than a file, by giving \verb:-: for the \verb:inputfile: (which is currently not supported by \ParFORM{}, though). The options are separated by blanks and start with a minus sign, followed by one or more alphabetic characters. They are: \begin{description} \item[-c] Error checking only. Notice that this will not work properly if there are conditionals in the preprocessor phase that depend on results obtained at earlier stages of the program. \item[-C] Next argument/option is a custom filename for the log file. \item[-d] Next argument/option is the name of a preprocessor variable that will be defined before the run starts. A specific value can be assigned with the syntax {\tt -d VARIABLENAME=VALUE}. The default value is 1. \item[-D] Same as -d. \item[-f] Output goes only to log file. \item[-F] Output only to log file. Further like -L or -ll. \item[-h] Wait for some key to be touched before finishing the run. Basically only for some old window based systems. \item[-I] Next argument/option is the path of a directory for include, procedure and subroutine files. \item[-l] Make a regular log file. \item[-ll] Make a log file without intermediate statistics. \item[-L] Same as -ll. \item[-M] This option is ignored. The PID (process identifier) of the process is now always included in the name of the temporary files. \item[-p] Next argument/option is the path of a directory for input, include, procedure and subroutine files. \item[-{pipe}] Indicates that \FORM\ is started up as the receiving end of a pipe. Action will be taken to set up the proper communication channels. \item[-q] Quiet option. Only output expressions are printed. \item[-R] Recover from a crash. See the checkpoint mechanism in \ref{checkpoints}. \item[-s] Next argument/option is the path of a directory for a setup file. \item[-si] Same as -q. \item[-S] Next argument/option is the name of a setup file. \item[-t] Next argument/option is the path of a directory for temporary files. \item[-ts] Next argument/option is the path of a directory for temporary sort files. \item[-T] Puts\index{totalsize} \FORM\ in a mode in which the maximum totalsize is measured and printed at the end of the program. For more information see the "On TotalSize;" statement~\ref{ontotalsize}. \item[-v] Only the version will be printed. The program terminates immediately after it. \item[-vv] Same as -v, but prints verbose version information. \item[-w] This should be followed immediately by a number. The number indicates the number of worker threads for \TFORM\@. All other versions of \FORM\ ignore this parameter. It should be noted that \TFORM\ is a different program. For more information, please consult chapter~\ref{parallel}. \item[-W] Turn on the wall-clock time mode in the statistics. See the `\texttt{On wtimestats}' statement~\ref{substaon}. \item[-y] Run only the preprocessor and dump its output. \item[-z] The number following is a timelimit for the program in second. \item[-Z] Removes the .str file on crash, whatever its contents. Under ordinary circumstances at a crash a .str file will not be removed if it has a nonzero content. \end{description} \noindent The log\index{log} file\index{file!log} is a file in which all output is collected, even when the output appears on the screen already. This makes it possible to follow the progress of the program and have a record of everything at the same time. The default name of the log file is identical to the name of the program without the extension \verb:.frm: but with the extra extension \verb:.log:. Example: \begin{center} \begin{verbatim} form -t /LocalDisk/mydir -l myformprogram \end{verbatim} \end{center} \FORM\ will run the program in the file \verb:myformprogram.frm:. Its output will both be written to the screen and into the file \verb:myformprogram.log:. The temporary files (if any) will be made in the directory \verb:/LocalDisk/mydir:. This last feature is very useful, because writing temporary files across a network can sometimes slow things down considerably. The second way to pass parameters to \FORM\ during startup is by means of environment\index{environment variables} variables, assuming of course that the system supports them. The following variables are supported: \begin{description} \item[FORMPATH]\index{FORMPATH} The directory in which \FORM\ will look for procedures and header files, assuming it cannot find them in the current directory. \item[FORMTMP]\index{FORMTMP} The directory in which \FORM\ will make its temporary files\index{file!temporary}. \item[FORMTMPSORT]\index{FORMTMPSORT} The directory in which \FORM{} will make its temporary sort files. \item[FORMSETUP]\index{FORMSETUP} The full path and name of a setup file\index{file!setup}. \end{description} It should be noted that when a parameter is specified both in the command tail and in the environment the value of the command tail will be used. The third way to pass parameters at startup is by means of a setup file\index{file!setup}. One of the first things \FORM\ does is to locate such a startup file. The procedure that is being followed for this is: \begin{itemize} \item If the command tail specifies a setup file, \FORM\ will use this file, ignoring all other indications with respect to the setup file. This assumes of course that this file exists. If it does not exist \FORM\ passes on to the next option. \item If the command tail specifies a path for the setup file, \FORM\ will try to open the file "form.set" in this directory. If this cannot be done (by lack of rights or because the file does not exist) \FORM\ passes on to the next option. \item Next \FORM\ tries to open the file "form.set"\index{form.set} in the current directory.\item If all else fails, \FORM\ will look for the environment parameter FORMSETUP and use its value as the name of a setup file. \end{itemize} If all the above attempts fail, \FORM\ will not use a setup file. For more information about the setup file one should consult the corresponding chapter on page \ref{setup}. form-5.0.1/doc/manual/float.tex0000644000175100017510000003075715217035721012033 \chapter{Floating point arithmetic} \label{floatingpoint} Starting with version 5.0, \FORM{} is equiped with arbitrary precision floating point arithmetic. The low level routines are handled by the GMP and MPFR libraries, which are available on most systems and if missing can be easily picked up from the internet. This chapter describes the commands, functions, and behaviour of \FORM's floating point sytem. \section{Initializing and closing the floating point system} Before any floating-point operations can be performed, \FORM{} must activate the floating point system and set the working precision. This initialization allocates the internal data structures used by the GMP and MPFR libraries. The system remains active until the end of the program, or until it is explicitly closed. The two statements that control these operations are: \begin{description} \item[\#StartFloat] This instruction initializes the floating point system and allocates the necessary internal arrays. It takes either one or two arguments: \begin{verbatim} #StartFloat [,MZV=] \end{verbatim} The first argument is mandatory and specifies the desired precision. It must be a positive integer followed by either a \texttt{b} (for precision in bits) or \texttt{d} (for precision in decimal digits). \FORM{} will round to at least this precision. The second argument is optional and only needed when working with multiple zeta values (MZVs) or Euler sums. It specifies the maximum weight that will be used. The evaluation of the sums requires a number of auxiliary arrays that depend on this weight. The default weight is zero. \item[\#EndFloat] This instruction releases all arrays allocated for the floating point system. Note that if one would like to change the precision during a run, this is now possible with a new \texttt{\#StartFloat} instruction. \end{description} Example programs that illustrate the use of these statements and the functionality of \FORM's floating point system are given below. \section{Conversion between rational and floating point coefficients} A term in an expression can have a rational or floating point coefficient. The following statements convert between the two. \begin{description} \item[ToFloat] Converts rational coefficients to floating point numbers in the precision specified by \texttt{\#StartFloat}. From this point on, the coefficient will be floating point. \item[ToRational] Attempts to convert floating point coefficients to rational numbers. To this end it uses continued fractions as in \begin{eqnarray} x & \;\rightarrow\; & n_0 + \frac{1}{\,n_1 + \frac{1}{\,n_2 + \frac{1}{\,n_3 + \cdots}}}\;, \nonumber \end{eqnarray} with $x$ a floating point number. The algorithm keeps track of the remaining precision and if $1/n_i$ is close to this precision it truncates the sequence at $n_{i-1}$. After that it works out the corresponding fraction. It could be that $x$ cannot be expressed as a fraction within the given precision. This can usually be seen by that the fractions are `rather wild', or that the result changes when the precision is increased. This statement can also be abbreviated as \texttt{ToRat}. \end{description} The above statements operate on ground level coefficient only. To convert numbers inside a function argument, one must use the \texttt{Argument} environment. For example: \begin{verbatim} CFunction f; #StartFloat 10d Local F = 0.1666666666*f(0.1428571429); ToRat; Print "<1> %t"; Argument f; ToRat; EndArgument; Print "<2> %t"; .end <1> + 1/6*f(1.428571429e-01) <2> + 1/6*f(1/7) \end{verbatim} The argument environment may be nested. Similarly, the statements \texttt{Evaluate}, \texttt{StrictRounding} and \texttt{Chop} act at the ground level. To have them act on function argument, one uses the \texttt{Argument} environment. These statements are explained further below. \section{Evaluation of functions and symbols} Before version 5.0, \FORM{} already reserved function names for many common mathematical functions. These functions can now be evaluated numerically using: \begin{description} \item[Evaluate] This statement evaluates the mathematical functions and or symbols numerically: \begin{verbatim} Evaluate [function(s)],[symbol(s)]; \end{verbatim} where the argument specifies the function(s) and/or symbol(s) to evaluate. More than one function and/or symbol may be listed. If this statement is used without arguments, all floating point functions and symbols that \FORM{} knows will be evaluated. Currently, the full list of functions that can be evaluated numerically reads \begin{verbatim} sqrt_, ln_, eexp_, li2_, gamma_, agm_, sin_, cos_, tan_, asin_, acos_, atan_, atan2_, sinh_, cosh_, tanh_, asinh_, acosh_, atanh_, mzv_, euler_, mzvhalf_, \end{verbatim} where the functions on the last line denote the multiple zeta values, Euler sums and harmonic polylogarithms of argument $1/2$ respectively. The list of symbols/constants that can be evaluated is \begin{verbatim} pi_, ee_, em_, \end{verbatim} where \texttt{ee\_}\index{ee\_} denotes the basis of the natural logarithm and \texttt{em\_}\index{em\_} the Euler-Mascheroni constant. In addition, the functions \texttt{lin\_}, \texttt{hpl\_} and \texttt{mpl\_} are reserved function names, but currently have no numerical evaluation. \end{description} \section{Rounding behaviour} \begin{description} \item[StrictRounding] This statement rounds floating point numbers to a given precision: \begin{verbatim} StrictRounding []; \end{verbatim} where \texttt{} is an optional argument that specifies the rounding precision in either digits or bits, using the same syntax as \texttt{\#startfloat}. If omitted, the default precision is used. Internally, the GMP and MPFR libraries may use extra precision beyond that set by \texttt{\#startfloat}. As a result, terms that print the same may still differ slightly due to this extra precision and therefore fail to merge. For example: \begin{verbatim} #startfloat 6d CFunction f; Local F = f(1.0)+f(1.0000001); Print; .sort \end{verbatim} results in \texttt{F = f(1.0e+00)+f(1.0e+00);}. Although it may appear that the terms should merge, the extra precision maintained by GMP prevents this, even though it is not displayed at 6 digits of precision. Using the strictrounding statement, one can force rounding to exactly 6 digits. Indeed: \begin{verbatim} Argument f; strictrounding; Argument; Print; .end \end{verbatim} results in \texttt{F = 2*f(1.0e+00);}. Notice that rounding in bits may produce unexpected results when viewed in decimal digits. For example, the decimal number 1.1e-4 cannot be represented exactly in binary. Its binary representation, up to 20 bits of precision, is $1.1100110101011111101*2^{-14}$. When rounded to 5 bits, this becomes $1.1101*2^{-14}$, which in decimal digits appears as 1.10626220703125e-04. \item[Chop] This statement removes floating point numbers that are {\em smaller} in absolute magnitude than a specified threshold. It takes one argument: \begin{verbatim} Chop ; \end{verbatim} All floating point numbers with absolute value {\em less} than \texttt{} are replaced by 0. Terms with no floating point coefficient are left untouched. The threshold \texttt{} can be a floating point number, integer, rational number, or power. Because statements in \FORM{} act term by term, it is often important to sort before invoking the chop statement. Otherwise, terms might be removed individually, while after sorting and combining, their combined floating point coefficient could exceed the specified chop threshold. \item[Format floatprecision] This instruction controls how many digits are displayed when printing floating point numbers. It only affects output formatting and does not influence the internal precision or accuracy of computations. It can be used in three ways: in case of \begin{verbatim} Format floatprecision; \end{verbatim} \FORM{} prints floats with the number of digits specified by the current \texttt{\#startfloat} instruction. With \begin{verbatim} Format floatprecision ; \end{verbatim} \FORM{} prints the number of digits specified by \texttt{}. The syntax is the same as for the precision in \texttt{\#startfloat}. If the requested precision exceeds the precision specified by \texttt{\#startfloat}, only the available digits are printed. Finally, with \begin{verbatim} Format floatprecision off; \end{verbatim} the floating point numbers are printed in raw internal format, see also section \ref{sec:float_raw}. \end{description} \section{Examples} The following example shows some work with Multiple Zeta Values (MZV's): \begin{verbatim} #StartFloat 500b, MZV=15 L F1 = -mzv_(8,1,1,5) +29056868/39414375*mzv_(2)^6*mzv_(3) -47576/40425*mzv_(2)^5*mzv_(5) -163291/18375*mzv_(2)^4*mzv_(7) -4/105*mzv_(2)^3*mzv_(3)^3 -450797/11025*mzv_(2)^3*mzv_(9) +7/5*mzv_(2)^2*mzv_(3)^2*mzv_(5) +16/25*mzv_(2)^2*mzv_(3)*mzv_(5,3) +454049/1400*mzv_(2)^2*mzv_(11) -16/25*mzv_(2)^2*mzv_(5,3,3) +3*mzv_(2)*mzv_(3)^2*mzv_(7) +61/14*mzv_(2)*mzv_(3)*mzv_(5)^2 +2/7*mzv_(2)*mzv_(3)*mzv_(7,3) +2172853/420*mzv_(2)*mzv_(13) -2/7*mzv_(2)*mzv_(7,3,3) +1/7*mzv_(2)*mzv_(5,5,3) -33/4*mzv_(3)^2*mzv_(9) -133/6*mzv_(3)*mzv_(5)*mzv_(7) -25/9*mzv_(3)*mzv_(9,3) -244/105*mzv_(5)^3 -359/105*mzv_(5)*mzv_(7,3) +3/10*mzv_(7)*mzv_(5,3) +89/18*mzv_(9,3,3) +569/105*mzv_(7,3,5); L F2 = mzv_(15); Evaluate mzv_; Print +f; .sort F1 = 9.1234206877960755900164875575406726239325002222490534540605137258846994\ 916348297032751308227224952419629422497720599224543719959652966613231560\ 6913926e+03; F2 = 1.0000305882363070204935517285106450625876279487068581775065699328933322\ 671563422795730723343470175484943669684442492832530297757588781904321794\ 40477e+00; Skip F1,F2; L X = F1/F2; Torational; Print +f; .end X = 229903169/25200; 0.08 sec out of 0.09 sec \end{verbatim} In the first module, \texttt{\#startfloat} initializes the floating point system with 500 bits of precision and a maximum weight for the MZVs and Euler sums of 15. The \texttt{mzv\_} functions are then evaluated with the \texttt{Evaluate} statement. In the second module we divide the numbers and convert the result to a rational. It is a good idea to try this with various precisions to see whether this is stable. With 60 bits the final answer would be \begin{verbatim} 145537942402475031/15952490572234; \end{verbatim} while at 150 bits we have already the same answer as with 500 bits. The fraction that is obtained by this program can be proven to be correct. \section{Raw form} \label{sec:float_raw} Internally, floating point numbers are represented by the function \texttt{float\_}, i.e. \texttt{float\_(prec, size, exp, limbs)}. The integer arguments encode the internal representation of the floating point number as in the GMP library: \begin{description} \item[prec] The precision of the mantissa in limbs. \item[size] The number of limbs currently in use. \item[exp] The exponent, determining the location of the implied radix point. \item[limbs] The limbs packed as the numerator of a \FORM{} rational. \end{description} In a normalized term containing \texttt{float\_}, the rational coefficient must be either $1/1$ or $-1/1$, where the sign of the term is absorbed into the rational coefficient. Furthermore, the \texttt{float\_} is protected from the pattern matcher and from statements that act on functions -- such as \texttt{Transform}, \texttt{Argument}, \texttt{Normalize} etc. The following program illustrates this: % \begin{verbatim} CFunction f; #StartFloat 10d Local F = 1.23456789 + f(1,2); Identify f?(?a) = f(10); Print "<1> %t"; .sort <1> + 1.23456789e+00 <1> + f(10) #EndFloat Normalize; Print "<2> %t"; .sort <2> + float_(2,3,1,420101683733788795657820481376616399786) <2> + 10*f(1) #StartFloat 5d Print "<3> %t"; .end <3> + 1.2346e+00 <3> + 10*f(1) \end{verbatim} % As shown, the \texttt{id}-statement does not effect the \texttt{float\_} function. Here we also see the use of the preprocessor statement \texttt{\#EndFloat} which closes the floating point system. After this statement, the \texttt{float\_} function becomes a regular function. Its protected status, however, persists so that \texttt{id}-statements or statements like \texttt{Normalize} still do not modify it. form-5.0.1/doc/manual/bracket.tex0000644000175100017510000002537215217035721012336 \chapter{Brackets} \label{brackets} At times one would like to order the output in a specific way. In an expression which is for instance a polynomial in terms of the symbol $x$, one might want to make this behaviour in terms of $x$ more apparent by printing the output in such a way, that all powers of $x$ are outside parentheses\index{parentheses}, and the whole rest is inside parentheses. This is done with the bracket\index{bracket} statement: \begin{verbatim} Bracket x; \end{verbatim} or in short notation \begin{verbatim} B x; \end{verbatim} One can specify more than one object in the bracket statement, but only a single bracket statement (the last one) is considered. Bracket statements belong to the module in which they occur. Hence they are forgotten after the next end-of-module. If a vector is mentioned in a bracket statement, all occurrences of this vector as a loose vector, a vector with any index, inside a dotproduct, or inside a tensor are taken outside brackets. If the vector occurs inside a non-commuting tensor, all other non commuting objects that are to the left of this tensor will also be taken outside the parentheses. When a function or tensor is mentioned in a bracket statement, it is not allowed to have any arguments in the bracket statement. All occurrences of this function will be pulled outside brackets. If the function is non-commuting, all other functions and/or tensors that are non-commuting and are to the left of the specific function(s) or tensor(s) will also be outside parentheses. The opposite of the bracket statement is the antibracket\index{antibracket} statement: \begin{verbatim} AntiBracket x; \end{verbatim} or \begin{verbatim} ABracket x; \end{verbatim} or \begin{verbatim} AB x; \end{verbatim} This statement causes also brackets in the output, but now everything is put outside brackets, except for powers of x and coefficients. This way one can make the $x$-dependence apparent differently. Because the bracket statement causes a different ordering of the terms when storing the expression, one can use this ordering in the next module. There are various ways to do this. One can use the contents of a given bracket in a r.h.s.\ expression as in % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Brackets_1) \begin{verbatim} Symbols a,b,c,x; L F = a*x^2+b*x+c; B x; .sort L Discriminant = F[x]^2-4*F[x^2]*F[1]; Print; .end \end{verbatim} The outside of the bracket is placed between braces\index{braces} after the name of the expression. The bracket that has nothing outside is referred to with the number 1. If a bracket is empty, its contents will be represented by the value zero. The regular algorithm by which \FORM{} finds brackets in an expression, is to start from the beginning and inspect each term until it finds the appropriate bracket. This is fully in the spirit of the sequential treatment of expressions in \FORM{}. This can however be rather slow\index{slow} in big expressions that reside on a disk. Hence there is the bracket\index{bracket index} index\index{index!bracket} feature. It is invoked by putting a $+$-sign after the bracket (or B) statement as in \begin{verbatim} Bracket+ x; \end{verbatim} or \begin{verbatim} B+ x; \end{verbatim} This option causes \FORM{} to build a tree of (disk) positions for the different brackets, with the condition that the whole storage of this tree of brackets does not exceed a given maximum space, named `bracketindexsize'\index{bracketindexsize} (see chapter~\ref{setup} on the setup parameters). If the index would need more space \FORM{} will start skipping brackets in the index. This means that it will have to look for the bracket in a sequential fashion, but starting from the position indicated by the previous bracket in the index. This will still be very fast, provided the index is not very small. When the bracket index option is used, \FORM\ will not compress the expressions that use such an index with the zlib compression, even if the user asked for this in an earlier statement. The use of the index indicates that the brackets are going to be used intensively, and hence the continuous decompression that would result would destroy most of the profit that comes from the index. If the brackets are only for cosmetics in the output, it is better not to use the index option. It does use resources to construct the index\index{index tree} tree\index{tree!index}. Also when brackets are only used sequentially as in the features discussed below, the presence of the index is not beneficial. It should only be applied when contents of brackets are used in the above way (like with the discriminant). There are several statements that make use of the bracket ordering: \begin{itemize} \item Keep\index{keep brackets} Brackets; This statement takes from the input one term at a time as usual, but then it takes the part outside the brackets, executes the statements of the module only on that part of the term, and then, when all statements of the module have had their effect, the resulting term(s) is/are multiplied by the full content of the bracket. The next term taken from the input will be the first term of the next bracket. This way one can hide part of the terms for the pattern matcher. Also one can avoid that the same matching will occur many times, as in an expression of the type \begin{verbatim} + f(y)*(x+x^2+x^3+x^4+1) \end{verbatim} If we would want to make a replacement of the type \begin{verbatim} Keep Brackets; id f?{f1,f2,f3}(u?) = f(u+1)/u; \end{verbatim} the pattern matching and the substitution would have to be done only once, rather than 5 times, as would be the case if the Keep bracket statement would not be used. \item Collect\index{collect} FunctionName; The contents of the various brackets will be placed inside a function with the given name. Hence \begin{verbatim} + f(y)*(x+x^2+x^3+x^4+1) + f(y^2)*(x+2*x^2+3*x^3+4*x^4+1) \end{verbatim} with \begin{verbatim} Collect h; \end{verbatim} would result in: \begin{verbatim} + f(y)*h(x+x^2+x^3+x^4+1) + f(y^2)*h(x+2*x^2+3*x^3+4*x^4+1) \end{verbatim} This can be very useful to locate $x$-dependence even further, because bracketing the new expression in terms of $h$ could make very clear whether a given polynomial in $x$ would factor the whole expression, or which factors are occurring. To bring \verb:h(x+1): and \verb:h(2*x+2): to multiples of the same objects one should consult the pages on the normalize\index{normalize} (\ref{substanormalize}) and makeinteger\index{makeinteger} (\ref{substamakeinteger}) statements. The Collect statement, together with the PolyFun\index{polyfun} statement, can also be very useful, if the variable $x$ (or other variables) is temporarily not playing much of a role in the pattern matching. It can make the program much faster. For more information on the collect statement one should consult section~\ref{substacollect}. \end{itemize} \noindent Restrictions: The bracket index can only be used with active expressions. Hence the access of specific brackets in stored expressions will always be of the slow variety. To make it faster, one can copy the expression into a local expression with indexed brackets, use it, and drop the expression when it is not needed any longer. The brackets can also be used to save space on the disk in problems in which the expressions become rather large. Let us assume the following simple problem: \begin{verbatim} Symbols x1,...,x12; Local F = (x1+...+x12)^10; .sort id x1 = x4+x7; .end \end{verbatim} If the program is run like this the expression F contains 352716 terms after the sort and after the id the sorting in the .end results in a final stage sort\index{sort!final stage} of which the statistics are: \begin{verbatim} Time = 46.87 sec F Terms active = 504240 Bytes used = 13462248 Time = 52.09 sec Generated terms = 646646 F Terms in output = 184756 Bytes used = 4883306 \end{verbatim} We see, that the intermediate sort file still contains more than 500000 terms and more than 13 Mbytes, while the final result contains less than 5 Mbytes. Why is this? When the terms in \FORM\ are sorted first come the powers of \verb:x1:, because this is the variable that was declared first. Hence the terms that do not have powers of \verb:x1: come much later in the input and will not be compared with the terms generated by the substitution of for instance a single power of \verb:x1: until very late in the sorting. What can we do about this? We can try to group the terms in the first sort such that after the substitution like terms will be `very close' to each other and hence will add quickly. This is done in the program \begin{verbatim} Symbols x1,...,x12; Local F = (x1+...+x12)^10; AntiBracket x1,x4,x7; .sort id x1 = x4+x7; .end \end{verbatim} Now all powers of the mentioned variables will be inside the brackets and all other variables will be outside. Because the terms inside the brackets are all following each other in the input of the second module, terms that will add will be generated closely together. The result is visible in the final statistics: \begin{verbatim} Time = 47.23 sec F Terms active = 184761 Bytes used = 4928008 Time = 48.40 sec Generated terms = 646646 F Terms in output = 184756 Bytes used = 4883306 \end{verbatim} Now the final step of the sorting has already almost the proper number of terms. The difference is due to brackets that are half in one `patch' on the disk and half in the next `patch' (for the meaning of the patches, one should read the part about sorting\index{sorting} in chapter~\ref{setup} on the setup file. It should be rather clear now that this saves disk space and the corresponding amount of time. These early cancellations can also be seen in the first statistics message of the second module. In the first case it is \begin{verbatim} Time = 19.76 sec Generated terms = 10431 F 5216 Terms left = 8065 Bytes used = 239406 \end{verbatim} and in the second case it is \begin{verbatim} Time = 22.82 sec Generated terms = 10124 F 5835 Terms left = 3186 Bytes used = 96678 \end{verbatim} This also causes a more efficient use of the large buffer and again a better use of the disk. There have been cases in which this `trick' was essential to keep the sort file inside the available disk space. form-5.0.1/doc/manual/diagrams.tex0000644000175100017510000003270115217035721012504 \chapter{Diagram generation} \label{diagrams} Starting with version 5.0, \FORM{} is equipped with the diagram generator of Toshiaki Kaneko: ``A Feynman graph generator for any order of coupling constants'', Toshiaki Kaneko (Meiji Gakuin U.), Comput.Phys.Commun. 92 (1995) 127-152, e-Print: hep-th/9408107. Recently, he has reprogrammed it as a C++ library, accompanied with a manual. \FORM{} makes use of this library and has built its own syntax around it, based on many years of experience working with the QGRAF generator (``Automatic Feynman graph generation'', Paulo Nogueira: J.Comput.Phys. 105 (1993) 279-289) and the problems encountered with the large number of diagrams used with the Mincer and Forcer programs. The library has been programmed in such a way that more features should not be too hard to implement if required. In version 4.3 the diagram generator was not yet complete. Effectively it only accepted one type of scalar particle, but one could define vertices with any number of particles. Hence it could be used as a fast topology generator. The old ``topologies\_'' function has been removed in version 5.0. For the \FORM{} implementation in version 5.0 and later, the concept of ``models'' has been introduced, as well as two new types of variable, a number of new functions and a number of new preprocessor variables. To begin, one must define a ``Model''\index{model}\index{diagrams!model} which contains the fields and vertices to be used for the generation of Feynman graphs. A Model definition is finished with ``EndModel''\index{endmodel}\index{diagrams!endmodel}. A ``Particle''\index{particle}\index{diagrams!particle} is defined with the syntax: \begin{verbatim} Particle particlename[,antiparticlename] [,] [,external]; \end{verbatim} A Particle may optionally have an antiparticle\index{antiparticle}\index{diagrams!antiparticle} name assigned to it; if no antiparticle is specified the particle is its own antiparticle. The \texttt{} denotes bosonic (\texttt{+}) or fermionic (\texttt{-}) statistics and the \texttt{} denotes the dimension of the particle's spin representation; for example, a scalar is defined with \texttt{+1}, an electron with \texttt{-2} and a gluon with \texttt{+3}. The spin information is used by the generator to forbid invalid vertices, but does not ultimately affect the generation of the graphs. Neglecting the sign and spin information is equivalent to specifying \texttt{+1}. The \texttt{external} option specifies that the Particle should appear only as an external leg. Note that attempting to define an external scalar particle as \texttt{Particle MyScalar,external;} will produce a Particle called ``MyScalar'' with antiparticle ``external''. This case must be defined using \texttt{Particle MyScalar,1,external;}. Following the Particle definitions inside the Model scope, one defines interaction vertices. An N-point Vertex\index{vertex}\index{diagrams!vertex} is defined as follows, where $N\geq2$: \begin{verbatim} Vertex particle1,...,particleN: coupling; \end{verbatim} The coupling should be a (product of) symbol(s) to integer powers. Symbols used here will be declared automatically if not already declared. Multiple models, with different names, may be defined within a single \FORM{} script. Some concrete examples follow: \begin{verbatim} Model PHI3; Particle phi, +1; Vertex phi,phi,phi: g; EndModel; \end{verbatim} \begin{verbatim} Model PHI4; Particle phi, +1; Vertex phi,phi,phi,phi: g^2; EndModel; \end{verbatim} \begin{verbatim} Model QCD; Particle qua,QUA, -2; Particle gho,GHO, -1; Particle glu, +3; Vertex QUA,qua,glu: g; Vertex GHO,gho,glu: g; Vertex glu,glu,glu: g; Vertex glu,glu,glu,glu: g^2; EndModel; \end{verbatim} % TODO: reinstate this example once we have it working in the new grcc setup. %In some cases one might want to generate diagrams in which the internal %(multi)loop propagators are represented as special edges. This requires the %definition of more complicated models as in %\begin{verbatim} % #do i = 0,`LOOPS' % Model QCD`i'; % Particle qua,QUA,-2; % Particle gho,GHO,-1; % Particle glu,+3; % Vertex qua,QUA,glu:g; % Vertex gho,GHO,glu:g; % Vertex glu,glu,glu:g; % Vertex glu,glu,glu,glu:g^2; % #do j = 1,`i'-1 % Vertex qua,QUA:g^{2*`j'}; % Vertex gho,GHO:g^{2*`j'}; % Vertex glu,glu:g^{2*`j'}; % #enddo % EndModel; % #enddo %\end{verbatim} %in which the two-point vertices are the propagators with j loops. As one %can see in this example, one can have vertices with identical particle %contents but different powers of the coupling constants. Once a Model has been defined, Feynman graphs may be generated with the new ``diagrams\_''\index{diagrams\_}\index{function!diagrams\_}\index{diagrams!diagrams\_} function, which has the following syntax: \begin{verbatim} diagrams_(model_name, incoming_particle_set, outgoing_particle_set, external_momenta_set, internal_momenta_set, number_of_loops_or_couplings, options); \end{verbatim} Here, \texttt{model\_name} is the name of the user-defined Model, and \texttt{incoming\_particle\_set} and \texttt{outgoing\_particle\_set} are \FORM{} sets of Particle names, for example ``\texttt{\{phi\}}'' or ``\texttt{\{glu,glu\}}'', representing the desired scattering amplitude. At two or more loops, it is also possible to generate vacuum graphs by specifying empty sets for both the incoming and outgoing particles. \texttt{external\_momenta\_set} and \texttt{internal\_momenta\_set} are \FORM{} sets of vectors to be used to represent internal and external particle momenta, respectively. These can be defined sets, such as \begin{verbatim} Vector q1,...,q10, k1,...,k10; Set ext : q1,...,q10; Set int : k1,...,k10; \end{verbatim} or defined dynamically in the call of diagrams\_ by providing, for example, \{q1,q2\}. The vectors in the external and internal sets must not come with a minus sign, and the sets must not contain any repeated entries. The \texttt{number\_of\_loops\_or\_couplings} can be set either to a number denoting the number of loops required, or to specific powers of the coupling constants used in the Model vertices, for example ``\texttt{g\^{}2}'' or ``\texttt{gs\^{}2 * gw\^{}2}''. Finally, the \texttt{options} argument can be used to control the generation and output formatting of the graphs. The options are \FORM{} pre-processor variables, and should be added together. If no filtering options are specified (by passing ``\texttt{0}'' or omitting the argument entirely), all connected graphs are generated. The graph-filtering keywords are defined to be compatible with their counterparts in QGRAF and are given below. Options which are inverse to each other may not be specified simultaneously. The user must be careful not to accidentally specify a keyword twice; this will not have the intended effect, but rather generate a different keyword entirely. This subtlety may be improved in the future. \begin{description} \item[\textbf{\texttt{`OnePI\_'}, \texttt{`OnePR\_'}}:] \index{diagrams!onepi}\index{diagrams!onepr} generate only one-particle irreducible (reducible) graphs. \item[\textbf{\texttt{`OnShell\_'}, \texttt{`OffShell\_'}:}] \index{diagrams!onshell}\index{diagrams!offshell} generate only graphs without (with) self-energy corrections on external lines. \item[\textbf{\texttt{`NoSigma\_'}, \texttt{`Sigma\_'}:}] \index{diagrams!nosigma}\index{diagrams!sigma} generate only graphs without (with) any self-energy corrections on any line. \item[\textbf{\texttt{`NoSnail\_'}, \texttt{`Snail\_'}:}] \index{diagrams!nosnail}\index{diagrams!snail} generate only graphs without (with) snails. \item[\textbf{\texttt{`NoTadpole\_'}, \texttt{`Tadpole\_'}:}] \index{diagrams!notadpole}\index{diagrams!tadpole} generate only graphs without (with) tadpoles. \item[\textbf{\texttt{`Simple\_'}, \texttt{`NotSimple\_'}:}] \index{diagrams!simple}\index{diagrams!notsimple} generate only graphs without (with) any vertices connected by two or more edges. \item[\textbf{\texttt{`Bipart\_'}, \texttt{`NonBipart\_'}:}] \index{diagrams!bipart}\index{diagrams!nonbipart} generate only bipartite (non-bipartite) graphs. \item[\textbf{\texttt{`CyclI\_'}, \texttt{`CyclR\_'}:}] \index{diagrams!cycli}\index{diagrams!cyclr} generate only cycle irreducible (reducible) graphs. \item[\textbf{\texttt{`Floop\_'}, \texttt{`NotFloop\_'}:}] \index{diagrams!floop}\index{diagrams!notfloop} generate only graphs which do not (do) contain closed fermion loops with an odd number of vertices. \end{description} Graph generation is further controlled with the options: \begin{description} \item[\textbf{\texttt{`WithSymmetrizeI\_'}, \texttt{`WithSymmetrizeF\_'}:}] \index{diagrams!withsymmetrizei}\index{diagrams!withsymmetrizef} symmetrize between the initial (final) state particles. For example, when generating a boson propagator one could define both external particles as incoming and provide the \texttt{`WithSymmetrizeI\_'} option. \item[\textbf{\texttt{`TopologiesOnly\_'}:}] \index{diagrams!topologiesonly} generate only the distinct topologies which appear in the requested amplitude. In this mode, Particle information is not given in the output, but only the momenta flowing into each vertex. The topology numbering in the \texttt{topo\_}\index{topo\_}\index{function!topo\_}\index{diagrams!topo\_} tags is consistent with and without this option, such that graphs in the full output are produced with their topologies already identified. Preparatory work can be performed efficiently at the level of the topologies before processing the full graph output. \end{description} In addition to the filtering keywords, the following options control the formatting of the output: \begin{description} \item[\textbf{\texttt{`WithEdges\_'}:}] \index{diagrams!withedges} produce also \texttt{edge\_} functions which contain propagator momenta and the numbers of the vertices to which they connect. \item[\textbf{\texttt{`WithoutNodes\_'}:}] \index{diagrams!withoutnodes} omit the \texttt{node\_} functions, which describe the fields and momenta which flow into each vertex. \item[\textbf{\texttt{`WithBlocks\_'}:}] \index{diagrams!withblocks} \index{block\_}\index{function!block\_}\index{diagrams!block\_}tag each graph's ``blocks'', sub-graphs which are connected to the rest of the graph by a single vertex, in the \texttt{block\_} function. \item[\textbf{\texttt{`WithOnePISets\_'}:}] \index{diagrams!withonepisets} \index{onepi\_}\index{function!onepi\_}\index{diagrams!onepi\_}tag each graph's one-particle irreducible subsets of vertices in the \texttt{onepi\_} function. \end{description} With the above options and example models in mind, we now display some example output from the generator. The options: \begin{verbatim} Local gluglu1 = diagrams_(QCD, {glu}, {glu}, int, ext, 1, `WithEdges_'+`OnShell_'+`NoTadpole_'+`NoSnail_'); \end{verbatim} produce: \begin{verbatim} gluglu1 = - topo_(1) *node_(1,1,glu(-k1)) *node_(2,1,glu(-k2)) *node_(3,g,QUA(-q1),qua(-q2),glu(k1)) *node_(4,g,QUA(q2),qua(q1),glu(k2)) *edge_(1,glu(k1),1,3) *edge_(2,glu(k2),2,4) *edge_(3,qua(q1),3,4) *edge_(4,QUA(q2),3,4) - topo_(1) *node_(1,1,glu(-k1)) *node_(2,1,glu(-k2)) *node_(3,g,GHO(-q1),gho(-q2),glu(k1)) *node_(4,g,GHO(q2),gho(q1),glu(k2)) *edge_(1,glu(k1),1,3) *edge_(2,glu(k2),2,4) *edge_(3,gho(q1),3,4) *edge_(4,GHO(q2),3,4) + 1/2 *topo_(1) *node_(1,1,glu(-k1)) *node_(2,1,glu(-k2)) *node_(3,g,glu(k1),glu(-q1),glu(-q2)) *node_(4,g,glu(k2),glu(q1),glu(q2)) *edge_(1,glu(k1),1,3) *edge_(2,glu(k2),2,4) *edge_(3,glu(q1),3,4) *edge_(4,glu(q2),3,4) ; \end{verbatim} The \texttt{node\_}\index{node\_}\index{function!node\_}\index{diagrams!node\_} function arguments give their id number, the coupling associated with the vertex they represent, and the Particle fields which connect to them (which are functions of the incoming momenta). The \texttt{edge\_}\index{edge\_}\index{function!edge\_}\index{diagrams!edge\_} function arguments give their id number, the Particle and momentum of the associated propagator, and the id numbers of the \texttt{node\_} functions which they connect. External particles have a special \texttt{node\_} function containing a single field and a coupling of 1. Specifying additionally \texttt{`TopologiesOnly\_'} produces just the single contributing topology: \begin{verbatim} gluglu1 = + topo_(1) *node_(1,1,-k1) *node_(2,1,-k2) *node_(3,g,k1,-q1,-q2) *node_(4,g,k2,q1,q2) *edge_(1,k1,1,3) *edge_(2,k2,2,4) *edge_(3,q1,3,4) *edge_(4,q2,3,4) ; \end{verbatim} In this case, Particle information is omitted from the \texttt{node\_} and \texttt{edge\_} functions. The \texttt{topo\_} tags are consistent with the tags present in the full graph output, produced when \texttt{`TopologiesOnly\_'} is not specified. To assist with debugging configuration problems or to see more information on the internals of the diagram generator, one may specify ``On GrccVerbose;''. form-5.0.1/doc/manual/module.tex0000644000175100017510000003446015217035721012206 \chapter{Modules} \label{modules} Modules\index{module} are the basic execution\index{execution} blocks. Statements\index{statements} are always part of a module, and they will be executed only when the module is executed. This is directly opposite to preprocessor instructions which are executed when they are encountered in the input stream. Modules are terminated by a line that starts with a period\index{period}. Such a line is called the module\index{module instruction} instruction. Once the module instruction has been recognized, the compilation of the module is terminated and the module will be executed. All active expressions will be processed one by one, term by term. When each term of an expression has been through all statements of the module, the combined results of all operations on all the terms of the expression will be sorted and the resulting expression will be sent to the output. This can be an intermediate file\index{file!intermediate}, or it can be some memory\index{memory}, depending on the size of the output. If the combined output of all active expressions is less than the parameter ``ScratchSize''\index{ScratchSize}, the results stay in memory. ScratchSize is one of the setup parameters (see chapter \ref{setup}). A module consists in general of several types of statements: \begin{description} \item [Declarations\index{declarations}] These are the declarations of variables. \item [Specifications\index{specifications}] These tell what to do with existing expressions as a whole. \item [Definitions\index{definitions}] These define new expressions. \item [Executable\index{executable statements} statements] The operations on all active expressions. \item [Output specifications\index{output specifications}] These specify the output representation. \item [End-of-module specifications\index{end of module specifications}] Extra settings that are for this module only. \item [Mixed statements\index{mixed statements}] They can occur in various classes. Most notably the print statement. \end{description} Statements must occur in such an order that no statement follows a statement of a later category, except as described bellow. This is different from earlier versions of \FORM\ in which the order of the statements was not fixed. This did cause a certain amount of confusion about the workings of \FORM\@. The exceptions are: \begin{itemize} \item Mixed statements are permitted in the executable statements, output specifications, and end-of-module specifications parts of a module. \item \texttt{Format}\index{format} statements are permitted anywhere. \item \texttt{ModuleOption}\index{moduleoption} statements that control how \$-variables are handled during parallel execution are permitted anywhere. \end{itemize} The last exception allows such \texttt{ModuleOption} statements to appear inside procedures that use \$-variables and do not contain a \texttt{.sort}. For example, the following structure is valid: \begin{verbatim} #procedure SortlessProc $procLocalDollar = ... ModuleOption local $procLocalDollar; * more executable statements here #endprocedure #call SortlessProc * more executable statements here .sort \end{verbatim} There are several types of modules. \begin{description} \item[.sort\index{.sort}] \label{instrsort} The general end-of-module. Causes execution of all active expressions, and prepares them for the next module. \item[.end\index{.end}] \label{instrend} Executes all active expressions and terminates the program. \item[.store\index{.store}] \label{instrstore} Executes all active expressions. Then it writes all active global expressions to an intermediate storage file\index{file!storage} and removes all other non-global expressions. Removes all memory of declarations except for those that were made before a .global instruction. \item[.global\index{.global}] \label{instrglobal} No execution of expressions. It just saves declarations made thus far from being erased by a .store instruction. \item[.clear\index{.clear}] \label{instrclear} Executes all active expressions. Then it clears all buffers with the exception of the main input stream. Continues execution in the main input stream as if the program had started at this point. The only parameters that cannot be changed at this point are the setup parameters. They remain. By default also the clock\index{clock} is reset. If this is not desired this can be changed by means of the ResetTimeOnClear\index{resettimeonclear} setup variable (see chapter \ref{setup}). \end{description} Each program must be terminated by a .end instruction. If such an instruction is absent and \FORM\ encounters an end-of-input it will issue a warning and generate a .end instruction. Module instructions can contain a special commentary that will be printed in all statistics that are generated during the execution of the module. This special commentary is restricted to 24 characters (the statistics have a fixed format and hence there is only a limited amount of space available). This commentary is initiated by a colon and terminated by a semicolon. The characters between this colon and the semicolon are the special message, also called advertisement. Example \begin{verbatim} .sort:Eliminate x; \end{verbatim} would give in the statistics something like \begin{verbatim} Time = 0.46 sec Generated terms = 360 F Terms in output = 360 Eliminate x Bytes used = 4506 \end{verbatim} If the statistics are switched off, there will be no printing of this advertisement either. For backwards compatibility there is still an obsolete\index{obsolete} mechanism to pass module options via the module instructions. This is a feature which will probably disappear in future versions of \FORM\@. We do give the syntax to allow the user to identify the option properly and enable proper translation into the moduleoption\index{moduleoption} statement (see \ref{substamoduleoption}). \begin{verbatim} .sort(PolyFun=functionname); .sort(PolyFun=functionname):advertisement; \end{verbatim} causes the given function to be treated as a polynomial\index{polyfun} function. This means that its (single) argument would be treated as the coefficient of the terms. The action of \FORM\ on individual terms is \begin{enumerate} \item Ignore polynomial functions with more than one argument. \item If there is no polynomial function with a single argument, generate one with the argument 1.\item If there is more than one polynomial function with a single argument, multiply the arguments and replace these functions with a single polynomial function with the product of the arguments for a single argument. \item Multiply the argument of the polynomial function with the coefficient of the term. Replace the coefficient itself by one. \end{enumerate} If, after this, two terms differ only in the argument of their polynomial function \FORM\ will add the arguments and replace the two terms by a single term which is identical to the two previous terms except for that the argument of its polynomial function is the sum of their two arguments. It should be noted that the proper placement of .sort\index{.sort} instructions in a \FORM\ program is an art by itself. Too many .sort instructions cause too much sorting, which can slow execution down considerably. It can also cause the writing of intermediate expressions which are much larger than necessary, if the next statements would cause great simplifications. Not enough .sort instructions can make that cancellations are postponed unnecessarily and hence much work will be done double. This can slow down execution by a big factor. First an example of a superfluous .sort: \begin{verbatim} S a1,...,a7; L F = (a1+...+a7)^16; .sort Time = 31.98 sec Generated terms = 74613 F Terms in output = 74613 Bytes used = 1904316 id a7 = a1+a2+a3; .end Time = 290.34 sec F Terms active = 87027 Bytes used = 2253572 Time = 295.20 sec Generated terms = 735471 F Terms in output = 20349 Bytes used = 538884 \end{verbatim} Without the sort the same program gives: \begin{verbatim} S a1,...,a7; L F = (a1+...+a7)^16; id a7 = a1+a2+a3; .end Time = 262.79 sec F Terms active = 94372 Bytes used = 2643640 Time = 267.81 sec Generated terms = 735471 F Terms in output = 20349 Bytes used = 538884 \end{verbatim} and we see that the sorting in the beginning is nearly completely wasted. Now a clear example of not enough .sort instructions. A common problem is the substitution of one power\index{power series} series into another. If one does this in one step one could have: \begin{verbatim} #define MAX "36" S j,x(:`MAX'),y(:`MAX'); * * Power series expansion of ln_(1+x) * L F = -sum_(j,1,`MAX',sign_(j)*x^j/j); * * Substitute the expansion of x = exp_(y)-1 * id x = x*y; #do j = 2,`MAX'+1 id x = 1+x*y/`j'; #enddo Print; .end Time = 76.84 sec Generated terms = 99132 F Terms in output = 1 Bytes used = 18 F = y; \end{verbatim} With an extra .sort inside the loop one obtains for the same program (after suppressing some of the statistics: \begin{verbatim} #define MAX "36" S j,x(:`MAX'),y(:`MAX'); * * Power series expansion of ln_(1+x) * L F = -sum_(j,1,`MAX',sign_(j)*x^j/j); * * Substitute the expansion of x = exp_(y)-1 * id x = x*y; #do j = 2,`MAX'+1 id x = 1+x*y/`j'; .sort: step `j'; Time = 0.46 sec Generated terms = 360 F Terms in output = 360 step 2 Bytes used = 4506 #enddo . . . Time = 3.07 sec Generated terms = 3 F Terms in output = 1 step 37 Bytes used = 18 Print; .end Time = 3.07 sec Generated terms = 1 F Terms in output = 1 Bytes used = 18 F = y; \end{verbatim} It is very hard to give general rules that are more specific than what has been said above. The user should experiment with the placements of the .sort before making a very large run. \section{Checkpoints} \label{checkpoints} If\index{checkpoints} \FORM\ programs have to run for a long time, the reliability of the hardware(computer system or network) or of the software infrastructure becomes a critical issue. Program termination\index{termination} due to unforeseen failures may waste days or weeks of invested execution time. The checkpoint mechanism was introduced to protect long running \FORM\ programs as good as possible from such accidental interruptions. With activated checkpoints \FORM\ will save its internal state and data from time to time on the hard disk. This data then allows a recovery from a crash\index{crash}. The checkpoint mechanism can be activated or deactivated by {\tt On}\index{on} and {\tt Off}\index{off} statements. If the user has activated checkpoints, recovery\index{recovery} data will be written to disk at the end of a module execution. Options allow to influence the details of the saving mechanism. If a program is terminated during execution, \FORM\ can be restarted with the {\tt -R} option and it will continue its execution at the last saved recovery point. The syntax of the checkpoint activation and deactivation is \begin{verbatim} On checkpoint []; Off checkpoint; \end{verbatim} If no options are given, the recovery data will be saved at the end of every module\index{module}. If one gives a time\index{time} \begin{verbatim} On checkpoint []; \end{verbatim} the saving will only be done if the given time has passed after the last saving. Possible unit specifiers are {\tt s, m, h, d} and the number will then be interpreted as seconds, minutes, hours, or days, respectively. The default unit is seconds. If one needs to run a script\index{run a script} before or after the saving, one can specify a script filename. \begin{verbatim} On checkpoint runbefore=""; On checkpoint runafter=""; On checkpoint run=""; \end{verbatim} The option {\tt run}\index{run} sets both the scripts to be run before and after saving.The scripts must have the executable flag set and they must reside in the execution path of the shell\index{shell} (unless the filename already contains the proper path). The scripts receive the module number\index{module number} as an argument (accessible as \$1 inside the script). The return value of the script running before the saving will be interpreted. If the script returns an error (non-zero return value), a message will be issued and the saving will be skipped. The recovery data will be written to files named {\tt FORMrecv.*} with various name extensions. If a file {\tt FORMrecv.tmp} exists, \FORM\ will not run unless one gives it the recovery option\index{recovery option} {\tt -R}. This is to prevent the unintentional loss of recovery data. If \FORM\ terminates successfully, all the additional data files will be removed. The additional recovery files will be created in the directory containing the scratch files. The extra files will occupy roughly as much space as the scratch files\index{scratch files} and the save\index{save files} and hide files\index{hide files} combined. This extra space must be made available, of course. If recovery data exists and \FORM\ is started with the {\tt -R} option, \FORM\ will continue execution after the last module that successfully wrote the recovery data. All the command line parameters that have been given to the crashed \FORM\ program\index{crashed \FORM\ program} must also be given to the recovering \FORM\ program. The input files are not part of the recovery data and will be read in anew when recovering. 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while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done @CONFIG_MAKEINDEX_TRUE@@CONFIG_PDF_TRUE@@CONFIG_TEX_TRUE@ $(MAKEINDEX) $(MAIN) @CONFIG_MAKEINDEX_TRUE@@CONFIG_PDF_TRUE@@CONFIG_TEX_TRUE@ $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done @CONFIG_MAKEINDEX_FALSE@@CONFIG_PDF_TRUE@@CONFIG_TEX_TRUE@$(MAIN).pdf: $(TEXFILES) @CONFIG_MAKEINDEX_FALSE@@CONFIG_PDF_TRUE@@CONFIG_TEX_TRUE@ $(PDFLATEX) $(MAIN).tex; while [ `grep -v 'Package: rerunfilecheck' $(MAIN).log | grep -c Rerun` -gt 0 ]; do $(PDFLATEX) $(MAIN).tex; done ########## CONFIG_PDF #################### CONFIG_TEX # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: form-5.0.1/doc/manual/gamma.tex0000644000175100017510000003154115217035721012000 \chapter{Dirac algebra} \label{gammaalgebra} For its use in high\index{high energy physics} energy physics \FORM\ is equipped with a built-in class of functions. These are the gamma\index{gamma matrices} matrices of the Dirac\index{Dirac algebra} algebra which are generically denoted by g\_\index{g\_}. The gamma matrices fulfill the relations: \begin{verbatim} {g_(j1,mu),g_(j1,nu)} = 2 * d_(mu,nu) [g_(j1,mu),g_(j2,nu)] = 0 j1 not equal to j2. \end{verbatim} The first argument is a so-called spin\index{spin line} line index. When gamma matrices have the same spin line, they belong to the same Dirac algebra and commute with the matrices of other Dirac algebra's. The indices mu and nu are over space-time and are therefore usually running from 1 to 4 (or from 0 to 3 in Bjorken \& Drell metric\index{Bjorken \& Drell metric}). The totally antisymmetric product e\_(m1,m2,...,mn)\*g\_(j,m1)\*...\*g\_(j, mn)/n! is defined to be gamma5 or g5\_(j). The notation 5\index{g5\_} finds its roots in 4 dimensional space-time. The unit matrix is denoted by gi\_(j). In four dimensions a basis of the Dirac algebra can be given by: \begin{verbatim} gi_(j) g_(j,mu) [g_(j,mu),g_(j,nu)]/2 g5_(j)*g_(j,mu) g5_(j) \end{verbatim} In a different number of dimensions this basis is correspondingly different. We introduce the following notation for convenience: \begin{verbatim} g6_(j) = gi(j) + g5_(j) (from Schoonschip) g7_(j) = gi(j) - g5_(j) g_(j,mu,nu) = g_(j,mu)*g_(j,nu) (from Reduce) g_(j,mu,nu,.....,ro,si) = g_(j,mu,nu,.....,ro)*g_(j,si) g_(j,5_) = g5_(j) g_(j,6_) = g6_(j) g_(j,7_) = g7_(j) \end{verbatim} The common operation on gamma matrices is to obtain the trace\index{trace} of a string of gamma matrices. This is done with the statement: \leftvitem{4cm}{trace4\index{trace4}, j} \rightvitem{12cm}{Take the trace in 4 dimensions of the combination of all gamma matrices with spin line j in the current term. Any non-commuting objects that may be between some of these matrices are ignored. It is the users responsibility to issue this statement only after all functions of the relevant matrices are resolved. The four refers to special tricks\index{tricks} that can be applied in four dimensions. This allows for relatively compact expressions. For the complete syntax, consult \ref{substatrace}.} \leftvitem{4cm}{tracen\index{tracen}, j} \rightvitem{12cm}{Take the trace in an unspecified number of dimensions. This number of dimensions is considered to be even. The traces are evaluated by only using the anticommutation properties of the matrices. As the number of dimensions is not specified the occurrence of a g5\_(j) is a fatal error. In general the expressions that are generated this way are longer than the four dimensional expressions. For the complete syntax, consult \ref{substatracen}.} It is possible to alter the value of the trace of the unit\index{unit matrix} matrix gi\_(j).\index{gi\_} Its default value is 4, but by using the statement (see \ref{substaunittrace}) \begin{verbatim} unittrace value; \end{verbatim} it can be altered. Value may be any positive short number ($< 2^{15}$ on 32\index{32 bits} bit machines and $< 2^{31}$ on 64\index{64 bits} bit machines) or a single symbol with the exception of the symbol i\_.\index{i\_} There are several options for the 4-dimensional traces. These options find their origin in the Chisholm\index{Chisholm} relation that is valid in 4 dimensions but not in a general number of dimensions. This relation can be found in the literature. It is given by: \begin{eqnarray} \gamma_\mu Tr[\gamma_\mu S] & = & 2(S + S^R) \nonumber \end{eqnarray} \noindent in which S is a string of gamma matrices with an odd number of matrices ($\gamma_5$ counts for an even number of matrices). $S^R$ is the reversed string. This relation can be used to combine traces with common indices. The use of this relation is the default for trace4\index{trace4}. If it needs to be switched off, one should add the extra option `nocontract': \begin{verbatim} trace4,nocontract,j; \end{verbatim} The option `contract'\index{contract} is the default but it can be used to enhance the readability of the program. The second option that refers to this relation is the option `symmetrize'\index{symmetrize}. Often it happens that there are two or more common indices in two spin lines. Without the symmetrize option (or with the `nosymmetrize'\index{nosymmetrize} option) the first of these indices is taken and the relation is applied to it. With the `symmetrize' option the average over all possibilities is taken. This means of course that if there are two common indices the amount of work is doubled. There is however a potentially large advantage. In some traces that involve the use of $\gamma_5$ the use of automatic algorithms results often in an avalanche of terms with a single Levi-Civita tensor, while symmetry arguments can show that these terms should add up to zero. By working out the traces in a more symmetric fashion \FORM\ is often capable of eliminating all or nearly all of these Levi-Civita tensors. Normally such an elimination is rather complicated. It involves relations that have so far defied proper implementation, even though people have been looking for such algorithms already for a long time. Hence the use of the symmetry from the beginning seems at the moment the best bet. It is possible to only apply the Chisholm\index{Chisholm} identity without taking the trace. This is done with the chisholm statement (see \ref{substachisholm}). The n dimensional traces can use a special feature, when the declaration of the indices involved will allow it. When an index has been declared as n-dimensional and the dimension is followed by a second symbol as in \begin{verbatim} symbols n,nn; index mu=n:nn; \end{verbatim} and if the index \verb:mu: is a contracted index in a single n-dimensional trace, then the formula for this trace can be shortened by using \verb:nn: (one term) instead of the quantity $(n-4)$ (two terms). This can make the taking of the n-dimensional traces significantly faster. \vspace{3mm} \noindent Algorithms\index{algorithms}: \FORM\ has been equipped with several built in rules to keep the number of generated terms to a minimum during the evaluation of a trace. These rules are: \begin{description} \item [rule 0] Strings with an odd number of matrices (gamma5 counts for an even number of matrices) have a trace that is zero, when using trace4 or tracen. \item [rule 1] A string of gamma matrices is first scanned for adjacent matrices that have the same contractable index, or that are contracted with the same vector. If such a pair is found, the relations %\begin{eqnarray} % \gamma^\mu\gamma^\nu & = & 1\times \delta^{\mu\nu} \nonumber \\ % \gamma^p\gamma^p & = & 1\times p\mydot p \nonumber %\end{eqnarray} \begin{verbatim} g_(1,mu,mu) = gi_(1)*d_(mu,mu) g_(1,p1,p1) = gi_(1)*p1.p1 \end{verbatim} \noindent are applied. \item [rule 2] Next there is a scan for a pair of the same contractable indices that has an odd number of other matrices in between. This is done only for 4 dimensions (trace4) and the dimension of the indices must be 4. If found, the Chisholm\index{Chisholm} identity is applied: %\begin{eqnarray} % \gamma^\mu\gamma^{m_1}\gamma^{m_2}\cdots\gamma^{m_n}\gamma^\mu & = & % -2\gamma^{m_n}\cdots\gamma^{m_2}\gamma^{m_1} \nonumber \\ %\end{eqnarray} \begin{verbatim} g_(1,mu,m1,m2,...mn,mu) = -2*g_(1,mn,...,m2,m1) \end{verbatim} \item [rule 3] Then (again only for trace4) there is a search for a pair of matrices with the same 4 dimensional index and an even number of matrices in between. If found, one of the following variations of the Chisholm\index{Chisholm} identity is applied: \begin{verbatim} g_(1,mu,m1,m2,mu) = 4*gi_(1)*d_(m1,m2) g_(1,mu,m1,m2,...,mj,mn,mu) = 2*g_(1,mn,m1,m2,...,mj) +2*g_(1,mj,...,m2,m1,mn) \end{verbatim} \item [rule 4] Then there is a scan for pairs of matrices that have the same index or that are contracted with the same vector. If found, the identity: \begin{verbatim} g_(1,mu,m1,m2,...,mj,mn,mu) = 2*d_(mu,mn)*g_(1,mu,m1,m2,...,mj) -2*d_(mu,mj)*g_(1,mu,m1,m2,...,mn) .... -/+2*d_(mu,m2)*g_(1,mu,m1,...,mj,mn) +/-2*d_(mu,m1)*g_(1,mu,m2,...,mj,mn) -/+ d_(mu,mu)*g_(1,m1,m2,...,mj,mn) \end{verbatim} \noindent is used to 'anticommute'\index{anticommute} these identical objects till they become adjacent and can be eliminated with the application of rule 1. In the case of an n-dimensional trace and when \verb:mu: is an index (it might also be a vector in the above formula) for which the definition of the dimension involved two symbols, there is a shorter formula. In that case the last three terms can be combined into two terms: \begin{verbatim} -/+(n-4)*g_(1,m1,m2,...,mj,mn) -/+4*d_(m1,m2)*g_(1,m3,m4,...,mj,mn) \end{verbatim} \noindent It should be clear now that this formula is only superior, when there is a single symbol to represent $(n-4)$. After this all gamma matrices that are left have a different index or are contracted with different vectors. These are treated using: \item [rule5] Traces in 4 dimensions for which all gamma matrices have a different index, or are contracted with a different four-vector are evaluated using the reduction formula \begin{verbatim} g_(1,mu,nu,ro) = g_(1,5_,si)*e_(mu,nu,ro,si) +d_(mu,nu)*g_(1,ro) -d_(mu,ro)*g_(1,nu) +d_(nu,ro)*g_(1,mu) \end{verbatim} For tracen the generating algorithm is based on the generation of all possible pairs of indices/vectors that occur in the gamma matrices in combination with their proper sign. When the dimension is not specified, there is no shorter expression. \end{description} \noindent Remarks: When an index is declared to have dimension n and the command trace4 is used, the special 4 dimensional rules 2 and 3 are not applied to this index. The application of rule 1 or 4 will then give the correct results. The result will nevertheless be wrong due to rule 5, when there are at least 10 gamma matrices left after the application of the first 4 rules, as the two algorithms in rule 5 give a difference only, when there are at least 10 gamma matrices. For counting gamma matrices the $\gamma_5$ counts for 4 matrices with respect to this rule. The result is unpredictable, when both indices in four dimensions and indices in n dimensions occur in the same string of gamma matrices. Therefore one should be very careful, when using the four dimensional trace under the condition that the results need to be correct in n dimensions. This is sometimes needed, when a $\gamma_5$ is involved. The tracen-statement will not allow the presence of a $\gamma_5$. In general it is best to emulate n-dimensional traces with a $\gamma_5$ separately. The eventual trace, with all matrices with a different index, can be generated with the use of the 'distrib\_' function: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (DiracAlgebra_1) \begin{verbatim} * * Symmetric trace of a gamma5 and 12 regular matrices * I m1,...,m12; F G5,g1,g2; L F = G5(m1,...,m12); id G5(?a) = distrib_(-1,4,g1,g2,?a); id g1(?a) = e_(?a); id g2(?a) = g_(1,?a); tracen,1; .end Time = 1.07 sec Generated terms = 51975 F Terms in output = 51975 Bytes used = 919164 \end{verbatim} This rather symmetric result is in contrast to the 4-dimensional result which is much shorter, but it is very unsymmetric: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (DiracAlgebra_2) \begin{verbatim} * * Regular trace of a gamma5 and 12 regular matrices * I m1,...,m12; L F = g_(1,5_,m1,...,m12); trace4,1; .end Time = 0.02 sec Generated terms = 1053 F Terms in output = 1029 Bytes used = 20284 \end{verbatim} The precise workings of the distrib\_\index{distrib\_} function is given in \ref{fundistrib}. One should be careful when using projection operators of spinors. The sloppy way is to write \begin{verbatim} (g_(1,p)+m) \end{verbatim} but technically this is not correct. The correct way is \begin{verbatim} (g_(1,p)+m*gi_(1)) \end{verbatim} to avoid the possibility that in the end a trace will be taken over a term that does not have any gamma matrix. If the projection operator is however multiplied by other gamma matrices, it makes no difference whether the unit matrix is present. That is why the sloppy notation will almost always give the correct result. Almost always.... form-5.0.1/doc/manual/statements.tex0000644000175100017510000102465015217035721013111 \chapter{Statements} \label{statements} %--#[ abrackets : \section{abrackets, antibrackets} \label{substaabrackets} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & ab[rackets][+][-] {\tt<}list of names{\tt>}; \\ & antib[rackets][+][-] {\tt<}list of names{\tt>}; \\ See also & bracket (\ref{substabracket}) and the chapter on brackets (\ref{brackets}) \end{tabular} \vspace{4mm} \noindent This statement\index{abrackets}\index{antibrackets} does the opposite of the bracket statement (see \ref{substabracket}). In the bracket statement the variables that are mentioned are placed outside brackets and inside the brackets are all other objects. In the antibracket statement the variables in the list are the only objects that are not placed outside the brackets. For the rest of the syntax, see the bracket statement (section \ref{substabracket}). % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Antibracket_1) \noindent For example \begin{verbatim} Symbols x, y; Local F = (1+x+x^2)*(1+y+y^2); AntiBracket y; Print; .end F = + x * ( 1 + y + y^2 ) + x^2 * ( 1 + y + y^2 ) + 1 + y + y^2; \end{verbatim} \vspace{10mm} %--#] abrackets : %--#[ also : \section{also} \label{substaalso} \noindent \begin{tabular}{ll} Type & Executable Statement \\ Syntax & a[lso] [options] {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}), idold (\ref{substaidold}) \end{tabular} \vspace{4mm} \noindent The also\index{also} statement should follow either an id\index{id} statement or another also statement. The action is that the pattern matching in the also statement takes place immediately after the pattern matching of the previous id statement (or also statement) and after possible matching patterns have been removed, but before the r.h.s. expressions are inserted. It is identical to the idold statement (see \ref{substaidold}). Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Also_1) \begin{verbatim} Symbols x,y,cosphi,sinphi; Local F = x+y; id x = cosphi*x-sinphi*y; also y = sinphi*x+cosphi*y; Print; .end F = - y*sinphi + y*cosphi + x*sinphi + x*cosphi; \end{verbatim} \noindent The options are explained in the section on the id statement (see \ref{substaidentify}). \vspace{10mm} %--#] also : %--#[ antiputinside : \section{antiputinside} \label{substaantiputinside} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & antiputinside {\tt<}name of function{\tt>} [,$<$antibracket information$>$]; \\ See also & PutInside (\ref{substaputinside}) \end{tabular}\vspace{4mm} \noindent This statement\index{antiputinside} puts all parts of the term with the exception of the variables in the antibracket information inside a function argument. The function must be a regular function (hence no tensor or table which are special types of functions). The antibracket\index{antibracket} information should adhere to the syntax of the bracket statement (\ref{substabracket}, \ref{substaabrackets}) and all occurrences of all variables with the exception of the antibracket variables will be put inside the function. The coefficient will also be put inside the function. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Antiputinside_1) \begin{verbatim} Symbols x, y, z; Cfunction f; Local F = 10 + x + y^2 + y*z; Antiputinside f,x; Print; .end F = f(y*z) + f(y^2) + f(1)*x + f(10); \end{verbatim} \vspace{10mm} %--#] antiputinside : %--#[ antisymmetrize : \section{antisymmetrize} \label{substaantisymmetrize} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & an[tisymmetrize] \verb:{:{\tt<}name of function/tensor{\tt>} [{\tt<}argument specifications{\tt>}];\verb:}: \\ See also & symmetrize (\ref{substasymmetrize}), cyclesymmetrize (\ref{substacyclesymmetrize}), rcyclesymmetrize (\ref{substarcyclesymmetrize}) \end{tabular} \vspace{4mm} \noindent The argument specifications are explained in the section on the symmetrize statements (see \ref{substasymmetrize}).\medskip \noindent The action of this statement\index{antisymmetrize} is to anti-symmetrize the (specified) arguments of the functions that are mentioned. This means that the arguments are brought to `natural order' in the notation of \FORM\ and each exchange of arguments or groups of arguments results in a minus sign in the coefficient of the term. The `natural order' may depend on the order of declaration of the variables. If two arguments or groups of arguments that are part in the anti-symmetrization are identical, the function is replaced by zero. \vspace{10mm} %--#] antisymmetrize : %--#[ apply : \section{apply} \label{substaapply} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & apply ["{\tt<}tablename(s){\tt>}"]; \\ See also & tablebases (\ref{tablebase}), apply (\ref{tblapply}) \end{tabular} \vspace{4mm} \noindent This statement\index{apply} is explained in the chapter on tablebases.\vspace{10mm} %--#] apply : %--#[ argexplode : \section{argexplode} \label{substaargexplode} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & argexplode [{\tt<}list of functions{\tt>}] \\ See also & argimplode (\ref{substaargimplode}) \end{tabular} \vspace{4mm} \noindent See the description of the ArgImplode~\ref{substaargimplode} statement. \vspace{10mm} %--#] argexplode : %--#[ argimplode : \section{argimplode} \label{substaargimplode} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & argimplode [{\tt<}list of functions{\tt>}] \\ See also & argexplode (\ref{substaargexplode}) \end{tabular} \vspace{4mm} \noindent This is a rather specialized statement. It converts one notation of indices, used for harmonic sums\index{sums!harmonic}\index{harmonic sums}, harmonic polylogarithms\index{polylogarithms!harmonic}\index{harmonic polylogarithms} and multiple zeta values\index{multiple zeta values} into its alternative notation. The two notations are: \begin{verbatim} Z(0,0,0,1,0,0,-1) Z(4,-3) \end{verbatim} In the first notation the indices can only be 0, 1 and -1. In the second notation there can be no zeroes. The `ArgImplode,Z;' statement\index{argimplode} would be equivalent to the statement % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_ArgImplode_1) \begin{verbatim} repeat id Z(?a,0,x?!{0,0},?b) = Z(?a,x+sig_(x),?b); \end{verbatim} and takes one from the first notation to the second. Example: \begin{verbatim} CFunction Z; Local F = Z(0,0,0,1,0,0,-1); ArgImplode Z; Print; .end F = Z(4,-3); \end{verbatim} \vspace{4mm} \noindent The `ArgExplode,Z;' statement\index{argexplode} is equivalent to the statement % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_ArgImplode_1) \begin{verbatim} repeat id Z(?a,x?!{1,0,-1},?b) = Z(?a,0,x-sig_(x),?b); \end{verbatim} and takes one from the second notation to the first. The reason that these statements have been built in lies in the fact that for many indices the repeat statements started to become very time-consuming. Example: \begin{verbatim} CFunction Z; Local F = Z(4,-3); ArgExplode Z; Print; .end F = Z(0,0,0,1,0,0,-1); \end{verbatim} \noindent For the harmonic sums, the harmonic polylogarithms and the multiple zeta values one can use the summer6 and the harmpol packages in the \FORM\ distribution. They are described in the papers J.~A.~M. Vermaseren, {\it Harmonic sums, Mellin transforms and integrals}, {\em Int. J. Mod. Phys.} {\bf A14} (1999) 2037, http://arxiv.org/abs/hep-ph/9806280. E.~Remiddi and J.~A.~M. Vermaseren, {\it Harmonic polylogarithms}, {\em Int. J. Mod. Phys.} {\bf A15} (2000) 725, http://arxiv.org/abs/hep-ph/9905237. \vspace{10mm} %--#] argimplode : %--#[ argtoextrasymbol : \section{argtoextrasymbol} \label{substaargtoextrasymbol} \noindent \begin{tabular}{ll} Type & Executable statement \\ Syntax & argtoextrasymbol [tonumber] [{\tt<}argument specifications{\tt>}]; \\ See also & topolynomial (\ref{substatopolynomial}) and extrasymbols (\ref{substaextrasymbols}, \ref{sect-extrasymbols}). \end{tabular} \vspace{4mm} \noindent Converts function arguments into extra symbols. An argument will be replaced with an extra symbol. The arguments that have been encountered before are replaced with the same extra symbols. Unlike the \texttt{topolynomial} statement (\ref{substatopolynomial}), the replacement occurs even for arguments consisting only of numbers and symbols (including extra symbols). Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Argtoextrasymbol_1) \begin{verbatim} Symbols x, y; Cfunction f; Local F = f(x + 1); Local F1 = f(y,x + 1); Argtoextrasymbol; Print; .end F = f(Z1_); F1 = f(Z2_,Z1_); \end{verbatim} \vspace{4mm} \noindent The \texttt{tonumber} option requests that function arguments are converted to positive integers corresponding to extra symbols. This provides an efficient mapping from any expression (stored as a function argument) to a number. \vspace{4mm} \noindent The function arguments to be converted can be specified in the same way as the \texttt{argument} statement (see \ref{substaargument}). \vspace{10mm} %--#] argtoextrasymbol : %--#[ argument : \section{argument} \label{substaargument} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & argument [{\tt<}argument specifications{\tt>}] \\ & \ \ \ \ \ \ \ \ \ \ \ \ \verb:{:{\tt<}name of function/set{\tt>} [{\tt<}argument specifications{\tt>}]\verb:}:; \\ See also & endargument (\ref{substaendargument}) \end{tabular} \vspace{4mm} \noindent This statement starts an argument\index{argument} environment\index{environment!argument}. Such an environment is terminated by an endargument statement (see \ref{substaendargument}). Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Argument_1) \begin{verbatim} Symbols x, y, z; CFunction f; Local F = f(x + 2*y + z^2); Argument; Identify y = x; Endargument; Print; .end F = f(z^2 + 3*x); \end{verbatim} \vspace{4mm} The statements between the argument and the endargument\index{endargument} statements will be applied only to the function arguments as specified by the remaining information in the argument statement. This information is given by: \begin{itemize} \item No further information: the statements are applied to all arguments of all functions. \item A series of numbers: the statements are applied to the given arguments of all functions. \item A function name (or a set of functions), possibly followed by a series of numbers: the statements are applied to the numbered arguments of the function specified. If a set of functions was specified, all the functions in the set will be taken. If no numbers are specified, all arguments of the function (or elements of the set) are taken. \end{itemize} The combination of a function (or set) possibly followed by numbers of arguments, can occur as many times as needed. The generic numbers of arguments that refer to all functions work in addition to the numbers specified for individual functions. Example\vspace{1mm} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Argument_2) \begin{verbatim} Symbols x,y; CFunction f, f1, f2, f3; Local F = f(x,x,x,x) + f1(x,x,x,x) + f2(x,x) + f3(x); Argument 2,f,1,{f,f1},3,4; Identify x = y; Endargument; Print; .end F = f(y,y,y,y) + f1(x,y,y,y) + f2(x,y) + f3(x); \end{verbatim} This specifies the second argument of all functions. In addition the first argument of \verb:f: will be taken and then also the third and fourth arguments of \verb:f: and \verb:f1: will be taken. \vspace{4mm} \noindent Argument/endargument constructions can be nested. \vspace{10mm} %--#] argument : %--#[ autodeclare : \section{auto, autodeclare} \label{substaautodeclare} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & autodeclare {\tt<}variable type{\tt>} {\tt<}list of variables to be declared{\tt>}; \\ & auto {\tt<}variable type{\tt>} {\tt<}list of variables to be declared{\tt>}; \end{tabular} \vspace{4mm} \noindent The variable\index{auto}\index{autodeclare} types are \vspace{1mm} \lefttabitem{s[ymbol]} \tabitem{Declaration of symbols\index{symbols}. For options see \ref{substasymbols}.} \lefttabitem{v[ector]} \tabitem{Declaration of vectors\index{vectors}. For options see \ref{substavectors}.} \lefttabitem{i[ndex]} \tabitem{Declaration of indices\index{index}. For options see \ref{substaindex}.} \lefttabitem{i[ndices]} \tabitem{Declaration of indices\index{indices}. For options see \ref{substaindex}.} \lefttabitem{f[unctions]} \tabitem{Declaration of noncommuting\index{noncommuting} functions\index{functions!noncommuting}. For options see \ref{substanfunctions}.} \lefttabitem{nf[unctions]} \tabitem{Declaration of noncommuting functions. For options see \ref{substanfunctions}.} \lefttabitem{cf[unctions]} \tabitem{Declaration of commuting\index{commuting} functions\index{functions!commuting}. For options see \ref{substacfunctions}.} \lefttabitem{co[mmuting]} \tabitem{Declaration of commuting functions. For options see \ref{substacfunctions}.} \lefttabitem{t[ensors]} \tabitem{Declaration of commuting tensors\index{tensors!commuting}. For options see \ref{substatensors}.} \lefttabitem{nt[ensors]} \tabitem{Declaration of noncommuting tensors\index{tensors!noncommuting}. For options see \ref{substantensors}.} \lefttabitem{ct[ensors]} \tabitem{Declaration of commuting tensors\index{tensors!commuting}. For options see \ref{substactensors}.} \noindent The action of the autodeclare statement is to set a default for variable types. In a statement of the type \begin{verbatim} AutoDeclare Symbol a,bc,def; \end{verbatim} all undeclared variables of which the name starts with the character a, the string bc or the string def will be interpreted as symbols and entered in the name tables as such. In the case there are two statements as in \begin{verbatim} AutoDeclare CFunction b,d; AutoDeclare Symbol a,bc,def; \end{verbatim} all previously undeclared variables of which the name starts with a, bc or def will be declared as symbols. All other previously undeclared variables of which the name starts with a b or a d will be declared as commuting functions. This is independent of the order of the autodeclare statements. {\FORM} starts looking for the most detailed matches first. Hence the variable defi will match with the string def first. \vspace{4mm} \noindent It is also allowed to use the properties of the various variables in the autodeclare statement: \begin{verbatim} AutoDeclare Index i=4,i3=3,i5=5; \end{verbatim} This declares all previously undeclared variables of which the name starts with an i to be four dimensional indices, unless their names start with i3 in which case they will be three dimensional indices, or their names start with i5 in which case they will be five dimensional indices. \vspace{10mm} %--#] autodeclare : %--#[ bracket : \section{bracket} \label{substabracket} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & b[rackets][+][-] {\tt<}list of names{\tt>}; \\ See also & antibracket (\ref{substaabrackets}), keep (\ref{substakeep}), collect(\ref{substacollect}) and the chapter on brackets (\ref{brackets}) \end{tabular} \vspace{4mm} \noindent This statement causes the output to be reorganized in such a way that all objects in the `list of names' are placed outside brackets\index{bracket} and all remaining objects inside brackets\index{brackets}. This grouping will remain till the next time that the expression is active and is being manipulated. Hence the brackets can survive skip (see \ref{substaskip}), hide (see \ref{substahide}) and even save (see \ref{substasave}) and load (see \ref{substaload}) statements. The bracket information can be used by the collect (see \ref{substacollect}) and keep (see \ref{substakeep}) statements, as well in r.h.s.\ expressions when the contents of individual brackets of an expression can be picked up (see \ref{brackets}). The usage of brackets may also impact sorting performance due to the reordering of terms in the expression (see chapter \ref{brackets}). \vspace{4mm} \noindent The list of names can contain names of symbols, vectors, functions, tensors and sets. In addition it can contain dotproducts. There should be only one bracket or antibracket (see \ref{substaabrackets}) statement in each module. If there is more than one, only the last one has an effect. The presence of a set has the same effect as having all the symbolic elements of the set declared in the (anti)bracket statement.\vspace{4mm} \noindent The presence of a $+$ or $-$ after the bracket (or anti bracket) refers to potential indexing of the brackets\index{brackets!indexing}. Usually {\FORM} has the information inside the terms in an expression. If it needs to search for a particular bracket it does so by starting at the beginning of that expression. This can be slow. If one likes to access individual brackets, it may be faster to tell {\FORM} to make an index by putting the $+$ after the bracket or antibracket keyword. For more information, see the chapter on brackets (see \ref{brackets}). A $-$ indicates that no index should be made. Currently this is the default and hence there is no need to use this option. It is present just in case the default might be changed in a future version of {\FORM} (in which {\FORM} might for instance try to determine by itself what seems best. This option exists for case that the user would like to overrule such a mechanism). \vspace{4mm} \noindent For example \begin{verbatim} Symbols x, y; Local F = (1+x+x^2)*(1+y+y^2); Bracket y; Print; .end F = + y * ( 1 + x + x^2 ) + y^2 * ( 1 + x + x^2 ) + 1 + x + x^2; \end{verbatim} \noindent See also the antibracket statement in \ref{substaabrackets}. \vspace{10mm} %--#] bracket : %--#[ break : % \section{break} \label{substabreak} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & break; \\ \\ See also & case (\ref{substacase}), switch (\ref{substaswitch}), default(\ref{substadefault}), endswitch (\ref{substaendswitch}). \end{tabular} \vspace{4mm} \noindent When a break statement is reached in a switch construction the next statement to be executed is the first statement after the corresponding endswitch statement. \vspace{10mm} % %--#] break : %--#[ case : % \section{case} \label{substacase} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & case,number; \\ \\ See also & switch (\ref{substaswitch}), break (\ref{substabreak}), default(\ref{substadefault}), endswitch (\ref{substaendswitch}). \end{tabular} \vspace{4mm} \noindent The cases in a switch construction are marked by a number. This number must be an integer that can be represented inside a {\FORM} word. On a 64-bit processor this would be an integer in the range $-2^{31}$ to $2^{31}-1$. If the dollar variable in the switch statement has the same value as the integer in the case statement, the next statement to be executed is the first statement after the case statement. Usually cases are terminated by break statements, but if there is no break statement 'fall through' may occur in which execution continues with the first statement after the next case statement or default statement. \vspace{10mm} % %--#] case : %--#[ cfunctions : \section{cfunctions} \label{substacfunctions} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & c[functions] {\tt<}list of functions to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}, \ref{sect-functions}), nfunctions (\ref{substanfunctions}) \end{tabular} \vspace{4mm} \noindent This statement declares commuting\index{commuting} functions\index{functions!commuting}. The name of a function can be followed by some information that specifies additional properties of the preceding function, which are the same as those for functions (see \ref{substafunctions}). Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Commute_1) \begin{verbatim} CFunction f,g; Symbol x; Local F = f(x)*g(x) + g(x)*f(x); Print; .end F = 2*f(x)*g(x); \end{verbatim} \vspace{10mm} %--#] cfunctions : %--#[ chainin : \section{chainin} \label{substachainin} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & Chainin,name of function; \\ See also & chainout (\ref{substachainout}) \end{tabular} \vspace{4mm} \noindent Has\index{chainin} the same effect as the statement \begin{verbatim} repeat id f(?a)*f(?b) = f(?a,?b); \end{verbatim} if f is the name of the function specified. The chainin statement is just a faster shortcut. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Chainin_1) \begin{verbatim} Function f; Symbol x,y,z; Local F = f(x)*f(y)*f(z); ChainIn f; Print; .end F = f(x,y,z); \end{verbatim} \vspace{10mm} %--#] chainin : %--#[ chainout : \section{chainout} \label{substachainout} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & Chainout,name of function; \\ See also & chainin (\ref{substachainin}) \end{tabular} \vspace{4mm} \noindent Has\index{chainout} the same effect as the statement \begin{verbatim} repeat id f(x1?,x2?,?a) = f(x1)*f(x2,?a); \end{verbatim} if f is the name of the function specified. The chainout statement is just a much faster shortcut. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Chainout_1) \begin{verbatim} Function f; Symbol x,y,z; Local F = f(x,y,z); ChainOut f; Print; .end F = f(x)*f(y)*f(z) \end{verbatim} \vspace{10mm} %--#] chainout : %--#[ chisholm : \section{chisholm} \label{substachisholm} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & chisholm [options] {\tt<}spinline indices{\tt>}; \\ See also & trace4 (\ref{substatrace}) and the chapter on gamma algebra (\ref{gammaalgebra}) \end{tabular} \vspace{4mm} \noindent This statement\index{chisholm} applies the identity \begin{eqnarray} \gamma_a\gamma_\mu\gamma_b \Tr[\gamma_\mu S] & = & 2\gamma_a( S + S^R ) \gamma_b \nonumber \end{eqnarray} in order to contract traces. $S$ is here a string of gamma\index{gamma matrices} matrices and $S^R$ is the reverse string. This identity is particularly useful when the matrices $\gamma_6 = 1+\gamma_5$ and/or $\gamma_7 = 1-\gamma_5$ are involved. The spinline\index{spinline} index refers to which trace should be eliminated this way. The options are \vspace{1mm} \lefttabitem{symmetrize} \tabitem{If there is more than one contraction with other gamma matrices, the answer will be the sum of the various contractions, divided by the number of different contractions. This will often result in a minimization of the number of $\gamma_5$ matrices left in the final results.} \lefttabitem{nosymmetrize} \tabitem{The first contraction encountered will be taken. No attempt is made to optimize with respect to the number of $\gamma_5$ matrices left.} \noindent IMPORTANT: the above identity is only valid in 4 dimensions. For more details, see chapter \ref{gammaalgebra} on gamma\index{gamma algebra} algebra. \vspace{10mm} %--#] chisholm : %--#[ chop : \section{chop} \label{substachop} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & chop $<$threshold$>$; \\ \end{tabular} \vspace{4mm} \noindent See chapter~\ref{floatingpoint} on the floating point capability. %--#] chop : %--#[ cleartable : \section{cleartable} \label{substacleartable} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & ClearTable [{\tt<}list of tables{\tt>}] \end{tabular} \vspace{4mm} \noindent This statement clears the tables that are mentioned. Sometimes (sparse) tables can take so much space that there is no room for new elements, while old elements are not needed any longer. In that case one can clear the table and start all over again with filling it. It is also useful when one wants to reuse a table, but now with a different content. \vspace{10mm} %--#] cleartable : %--#[ collect : \section{collect} \label{substacollect} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & collect {\tt<}name of function{\tt>}; \\ & collect {\tt<}name of function{\tt>} {\tt<}name of other function{\tt>}; \\ & collect {\tt<}name of function{\tt>} {\tt<}name of other function{\tt>} {\tt<}percentage{\tt>}; \\ See also & bracket (\ref{substabracket}), antibracket (\ref{substaabrackets}) and the chapter on brackets (\ref{brackets}) \end{tabular} \vspace{4mm} \noindent Upon processing\index{collect} the expressions (hence expressions in hide as well as skipped expressions do not take part in this) the contents of the brackets\index{brackets} (if there was a bracket or antibracket\index{antibracket} statement in the preceding module) are collected and put inside the argument of the named function. Hence if the expression \verb:F: is given by % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Collect_1) \begin{verbatim} S a,b,c; CF cfun; L F = a*(b^2+c) + a^2*(b+6) + b^3 + c*b + 12; B a; .sort Collect cfun; Print; .end F = cfun(6 + b)*a^2 + cfun(12 + b*c + b^3) + cfun(c + b^2)*a; \end{verbatim} The major complication\index{complication} occurs if the content of a bracket is so long that it will not fit inside a single term. The maximum size of a term is limited by the setup parameter maxtermsize\index{maxtermsize} (see \ref{setupmaxtermsize}). If this size is exceeded, {\FORM} will split the bracket contents over more than one term, in each of which it will be inside the named function. It will issue a warning that it has done so. \vspace{4mm} \noindent If a second function is specified (the alternative\index{alternative} collect function) and if a bracket takes more space than can be put inside a single term, the bracket contents will be split over more than one term, in each of which it will be inside the alternative collect function. In this case there is no need for a warning\index{warning} as the user can easily check whether this has occurred by checking whether the alternative function is present in the expression. \vspace{4mm} \noindent If additionally a percentage\index{percentage} is specified (an integer in the range of 1 to 99) this determines how big the argument must be as compared to MaxTermSize (see chapter \ref{setup} on the setup) before use is made of the alternate collect function. \vspace{10mm} %--#] collect : %--#[ commuteinset : \section{commuteinset} \label{substacommuteinset} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & commuteinset {\tt<}$\{$list of noncommuting functions/tensors$\}${\tt>}; \\ See also & functions (\ref{substafunctions}) \end{tabular} \vspace{4mm} \noindent This statement\index{commuteinset} allows one or more sets of noncommuting functions and or tensors for its argument(s). The functions inside each set will commute with each other. It is allowed to have the same function inside more than one set. For a function to commute with itself (with for instance different arguments) it needs to be specified twice inside the same set. In that case it is more efficient to have a separate set with only two arguments. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_CommuteInSet_1) \begin{verbatim} I i1,...,i10; F A1,...,A10; CommuteInSet{A1,A3,A5},{A1,g_},{A1,A1}; L F = A5*A1*A5*A1*A5*A2*A3*A5*A1*A5*A3*A1; L G = g_(2,i1)*g_(2,i2,i3)*A1(i2)*g_(1,i4)*g_(1,5_,i5,i6) *A1(i1)*A1(i3)*g5_(1)*A3(i5)*A3(i4)*g5_(1); Print +f +s; .end F = + A1*A1*A5*A5*A5*A2*A1*A1*A3*A3*A5*A5; G = + g_(1,i4,i5,i6)*g_(2,i1,i2,i3)*A1(i1)*A1(i2)*A1(i3)* A3(i5)*A3(i4)*g_(1,5_); \end{verbatim} \vspace{10mm} %--#] commuteinset : %--#[ commuting : \section{commuting} \label{substacommuting} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & co[mmuting] {\tt<}list of functions to be declared{\tt>}; \\ See also & cfunctions (\ref{substacfunctions}), functions (\ref{substafunctions}) \end{tabular} \vspace{4mm} \noindent This statement\index{commuting} is completely identical to the cfunction statement (see \ref{substacfunctions}). \vspace{10mm} %--#] commuting : %--#[ compress : \section{compress} \label{substacompress} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & comp[ress] {\tt<}on/off{\tt>}; \\ See also & on (\ref{substaon}), off (\ref{substaoff}) \end{tabular} \vspace{4mm} \noindent This statement\index{compress} is obsolete. The user should try to use the compress option of the on (see \ref{substaon}) or the off (see \ref{substaoff}) statements. \vspace{10mm} %--#] compress : %--#[ contract : \section{contract} \label{substacontract} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & contract [{\tt<}argument specifications{\tt>}]; \end{tabular} \vspace{4mm} %TODO: add link to the example in form for pedestrians: Some FORM Examples/Levi-Civita \noindent Statement\index{contract} causes the contraction of pairs of Levi-Civita\index{Levi-Civita} tensors\index{tensor!Levi-Civita} \verb:e_: (see also \ref{functions}) into combinations of Kronecker\index{Kronecker} delta's\index{delta!Kronecker}. If there are contracted indices, and if their dimension is identical to the number of indices of the Levi-Civita tensors, the regular shortcuts are taken. If there are contracted indices with a different dimension, the contraction treats these indices temporarily as different and lets the contraction be ruled by the contraction mechanism of the Kronecker delta's. In practise this means that the dimension will enter via $\delta^{\mu}_{\mu} \rightarrow {\rm dim}(\mu)$. \vspace{4mm} \noindent In {\FORM} there are no upper\index{upper} and lower\index{lower} indices\index{indices!lower}\index{indices!upper}. Of course the user can emulate those. The contract statement always assumes that there is a proper distribution of upper and lower indices if the user decided to work in a metric in which this makes a difference. Note however that due to the fact that the Levi-Civita tensor is considered to be imaginary, there is usually no need to do anything special. This is explained in the chapter on functions (see \ref{functions}). \vspace{4mm} \noindent There are several options to control which contractions will be taken. They are \vspace{1mm} \lefttabitem{Contract;} \tabitem{Here only a single pair of Levi-Civita tensors will be contracted. The pair that is selected by {\FORM} is the pair that will give the smallest number of terms in their contraction.} \leftvitem{4cm}{Contract {\tt <}number{\tt>};} \rightvitem{12cm}{This tells {\FORM} to keep contracting pairs of Levi-Civita tensors until there are {\tt <}number{\tt>} or {\tt <}number{\tt>}$+1$ Levi-Civita tensors left. A common example is Contract 0; which will contract as many pairs as possible.} \leftvitem{4cm}{Contract:{\tt<}number{\tt>};} \rightvitem{12cm}{Here the number indicates the number of indices in the Levi-Civita tensors to be contracted. Only a single pair will be contracted and it will be the pair that gives the smallest number of terms.} \leftvitem{4cm}{Contract:{\tt<}number{\tt>} \hfill {\tt<}number{\tt>};} \rightvitem{12cm}{The First number refers to the number of indices in the Levi-Civita tensors to be contracted. The second number refers to the number of Levi-Civita tensors that should be left (if possible) after contraction.} \noindent Note that the order in which {\FORM} selects the contractions is by looking at which pair will give the smallest number of terms. This means that usually the largest buildup of terms is at the end. This is not always the case, because there can be a complicated network of contracted indices. \vspace{10mm} %--#] contract : %--#[ copyspectator : \section{copyspectator} \label{substacopyspectator} \noindent \begin{tabular}{ll} Type & Definition statement\\ Syntax & copyspectator {\tt<}exprname{\tt>} = {\tt<}spectator{\tt>}; \end{tabular} \vspace{4mm} \noindent See chapter~\ref{spectators} on spectators. \vspace{10mm} %--#] copyspectator : %--#[ createspectator : \section{createspectator} \label{substacreatespectator} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & createspectator {\tt<}spectatorname{\tt>}, "{\tt<}filename{\tt>}"; \end{tabular} \vspace{4mm} \noindent See chapter~\ref{spectators} on spectators. \vspace{10mm} %--#] createspectator : %--#[ ctable : \section{ctable} \label{substactable} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & ctable {\tt<}options{\tt>} {\tt<}table to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}), table (\ref{substatable}), ntable (\ref{substantable}) \end{tabular} \vspace{4mm} \noindent This statement declares a commuting\index{commuting} table\index{table!commuting} and is identical to the table command (see \ref{substatable}) which has the commuting property as its default. \vspace{10mm} %--#] ctable : %--#[ ctensors : \section{ctensors} \label{substactensors} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & ct[ensors] {\tt<}list of tensors to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}), tensors (\ref{substatensors}), ntensors (\ref{substantensors}) \end{tabular} \vspace{4mm} \noindent This statement declares commuting\index{commuting} tensors\index{tensor!commuting}. It is equivalent to the tensor statement (see \ref{substatensors}) which has the commuting property as its default. \noindent The options that exist for properties of tensors are the same as those for functions (see \ref{substafunctions}). \vspace{10mm} %--#] ctensors : %--#[ cyclesymmetrize : \section{cyclesymmetrize} \label{substacyclesymmetrize} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & cy[clesymmetrize] \verb:{:{\tt<}name of function/tensor{\tt>} [{\tt<}argument specifications{\tt>}];\verb:}: \\ See also & symmetrize (\ref{substasymmetrize}), antisymmetrize (\ref{substaantisymmetrize}), rcyclesymmetrize (\ref{substarcyclesymmetrize}) \end{tabular} \vspace{4mm} \noindent The argument\index{cyclesymmetrize} specifications are explained in the section on the symmetrize statements (see \ref{substasymmetrize}). \medskip \noindent The action of this statement is to cycle-symmetrize the (specified) arguments of the functions that are mentioned. This means that the arguments are brought to `natural order' in the notation of \FORM\ by trying cyclic permutations of the arguments or groups of arguments. The `natural order' may depend on the order of declaration of the variables. \vspace{10mm} %--#] cyclesymmetrize : %--#[ deallocatetable : \section{deallocatetable} \label{substadeallocatetable} \noindent \begin{tabular}{ll} Type & Declaration\\ Syntax & DeallocateTable,name(s) of sparse table(s); \\ See also & table (\ref{substatable}), fill (\ref{substafill}), table bases (\ref{tablebase}) \end{tabular} \vspace{4mm} \noindent Works\index{deallocatetable} only for sparse\index{sparse} tables\index{table!sparse}. Deallocates all definitions of elements as obtained with `Fill'\index{fill} statements as if there never were any `Fill' statements for the given tables. This statement exists because sometimes cleaning up big tables is needed when they take too much memory. This can be the case when a big tablebase has been used. \vspace{10mm} %--#] deallocatetable : %--#[ default : % \section{default} \label{substadefault} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & default; \\ \\ See also & case (\ref{substacase}), break (\ref{substabreak}), switch(\ref{substaswitch}), endswitch (\ref{substaendswitch}). \end{tabular} \vspace{4mm} \noindent This is the default case in a switch construction. \vspace{10mm} % %--#] default : %--#[ delete : \section{delete} \label{substadelete} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & delete storage; \\ See also & save (\ref{substasave}), load (\ref{substaload}) \\ Syntax & delete extrasymbols; \\ Syntax & delete extrasymbols\textgreater{}number; \\ See also & extrasymbols (\ref{substaextrasymbols}) \\ \end{tabular} \vspace{4mm} \noindent This statement has currently two varieties. The delete storage\index{delete} clears the complete storage\index{storage file} file\index{file!storage} and reduces it to zero size. The effect is that all stored expressions are removed from the system. Because it is impossible to remove individual expressions from the store file (there is no mechanism to fill the resulting holes) it is the only way to clean up the storage file. If some expressions should be excluded from this elimination process, one should copy them first into active global expressions, then delete the storage file, after which the expressions can be written to storage again with a .store\index{.store} instruction. \noindent The delete extrasymbols\index{delete}\index{} variety removes extra symbols\index{extra symbols} from the list. The default is that all extra symbols are removed, but one can also remove the symbols above a given number as in \begin{verbatim} #$es = `extrasymbols_'; ToPolynomial; ....some code.... .sort * now the new extra symbols are not needed anylonger Delete extrasymbols>`$es'; \end{verbatim} \vspace{10mm} %--#] delete : %--#[ denominators : \section{denominators} \label{substadenominators} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & denominators functionname; \end{tabular} \vspace{4mm} \noindent This statement\index{denominators} allows the user to rename all occurrences of the built-in denominator function. This built-in function is kind of an oddity inside \FORM\@. Denominators are presented by a very special function which doesn't really have a name and hence is rather hard to address. In addition there are special rules connected to denominators. Hence it is usually better to collect denominators inside functions that have been defined by the user and hence allow the user to manipulate them at will. Yet, objects can end up inside denominator functions, especially when output from other programs is read in. Hence this statement allows all occurrences of the denominator function to be renamed into the function that is given in the statement. This function will work well together with the PolyRatFun statement in which we define a PolyFun with two arguments of which the second acts as a denominator and the first as a numerator: \begin{verbatim} Symbols x, y; Cfunction rat, den; PolyRatFun rat; Local F = 1/(x+y); Denominators den; Identify den(x?) = rat(1,x); Print; .end F = rat(1,x + y); \end{verbatim} For more about this one should consult the part on the PolyRatFun\index{polyratfun} statement (\ref{substapolyratfun}) and the chapter on polynomials (still to be included because the current version can handle only polynomials in a single variable and is also not optimized for many occurrences that have identical denominators). \vspace{10mm} %--#] denominators : %--#[ dimension : \section{dimension} \label{substadimension} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & d[imension] {\tt<}number or symbol{\tt>}; \\ See also & index (\ref{substaindex}) \end{tabular} \vspace{4mm} \noindent Sets the default dimension\index{dimension!default}. This default dimension determines the dimension of the indices\index{indices} that are being declared without dimension specification as well as the dimension of all dummy indices\index{indices!dummy}. At the moment an index is declared and there is no dimension specification, {\FORM} looks for the default dimension and uses that. This index will then have this dimension, even when the default dimension is changed at a later moment. The dummy indices always have the dimension of the current default dimension. If the default dimension is changed the dimension of all dummy indices changes with it. Varieties: \vspace{1mm} \leftvitem{4cm}{Dimension {\tt<}number{\tt>};} \rightvitem{12cm}{Declares the number to be the default dimension. The number must be smaller than 32768 on 32bit architectures or 2147483648 on 64bit architectures. Negative numbers are not allowed. If one wants to work with negative dimensions, the practical workaround is to use a symbolic dimension and later replace that symbol appropriately.} \leftvitem{4cm}{Dimension {\tt<}symbol{\tt>};} \rightvitem{12cm}{Symbol must be the name of a symbol, either previously declared or declarable because of an auto-declaration (see \ref{substaautodeclare}). Declares the symbol to be the default dimension.} \leftvitem{4cm}{Dimension \hfill {\tt<}symbol{\tt>}:{\tt<}symbol{\tt>};} \rightvitem{12cm}{The symbols\index{symbols} must be the names of symbols, either previously declared or declarable because of an auto-declaration (see \ref{substaautodeclare}). The first symbol will be the default dimension. The second symbol will be the first symbol minus 4. It will be used as such in the trace\index{trace contractions} contractions\index{contractions!trace}. See also \ref{substatracen} and \ref{substaindex}.} \noindent Examples: \begin{verbatim} Dimension 3; Dimension n; Dimension n:[n-4]; \end{verbatim} The default dimension in {\FORM} is 4. \vspace{10mm} %--#] dimension : %--#[ discard : \section{discard} \label{substadiscard} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & dis[card]; \end{tabular} \vspace{4mm} \noindent This statement discards\index{discard} the current term. It can be very useful in statements of the type % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Discard_1) \begin{verbatim} Symbols x; Local F = x^3 + x^4 + x^5 + x^6; if ( count(x,1) > 5 ) Discard; Print; .end F = x^3 + x^4 + x^5; \end{verbatim} which eliminates all terms that have more than five powers of x. \vspace{10mm} %--#] discard : %--#[ disorder : \section{disorder} \label{substadisorder} \noindent \begin{tabular}{ll} Type & Executable statement \\ Syntax & disorder {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement is identical to the disorder\index{disorder} option\index{option!disorder} of the id\index{id statement}\index{id} statement (see \ref{substaidentify}). It is just a shorthand notation for `id disorder'. \vspace{10mm} %--#] disorder : %--#[ do : \section{do} \label{substado} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & do \$loopvar = lowvalue,highvalue\verb:{:,increment\verb:}:; \\ See also & enddo (\ref{substaenddo}) \end{tabular} \vspace{4mm} \noindent The syntax is the typical syntax for do-loops. The loop variable has to be a dollar variable. For parallel performance this variable can be declared local in a moduleoption (see \ref{substamoduleoption}) statement, unless it is also used in other ways in the current module. The loop parameters should either be (short) integers or dollar variables or factors of dollar variables provided they evaluate at run time to (short) integers. The enddo statement should be in the same module as the do statement. In addition it should be properly nested with if, repeat, while and argument constructions. \noindent The do-loop facility is in principle superfluous, because the repeat~(\ref{substarepeat}), if~(\ref{substaif}) and the pattern matcher can basically do everything the do-loop can do. Sometimes however the do-loop is easier to program and gives more readable code as shown here: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Do_1) %TODO: this needs to be improved (also change in test file) \begin{verbatim} Symbol x,y; CFunction f; LocalFactorized F = (1+y)*(2+y)*(3+y)*(4+y)*(5+y); .sort #$nf = numfactors_(F); Local G = +...+; Do $i = 1,$nf; Identify,only x^$i = f(F[factor_^$i]); Enddo; Print; ModuleOption local $i; .end F = ( 1 + y ) * ( 2 + y ) * ( 3 + y ) * ( 4 + y ) * ( 5 + y ); G = f(1 + y) + f(2 + y) + f(3 + y) + f(4 + y) + f(5 + y); \end{verbatim} \noindent versus \begin{verbatim} id,only,x^n?{1,2,3,4,5} = ff(n); repeat id ff(n?pos_) = ff(n-1)*f(F[factor_^n]); id ff(n?neg0_) = 1; \end{verbatim} \noindent One should note that the do-loop is evaluated at run time. Hence the dollar variables need to be evaluated at run time as well. Therefore, if it is possible, the preprocessor variety (see \ref{predo}) is almost always faster in execution as in \begin{verbatim} #do i = 1,5 id,only,x^`i' = f(F[factor_^`i']); #enddo \end{verbatim} \noindent This can of course not be done in constructions like \begin{verbatim} id f1(x?$x) = f2(x); FactDollar,$x; Do $i = 1,$x[0]; Multiply f($i,$x[$i]); Enddo; \end{verbatim} \noindent because here \verb:$x: and its factors are only known at run time and may be different for each term. \vspace{10mm} %--#] do : %--#[ drop : \section{drop} \label{substadrop} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & drop; \\ & drop {\tt<}list of expressions{\tt>}; \\ See also & ndrop (\ref{substandrop}) \end{tabular} \vspace{4mm} \noindent In the first variety this statement\index{drop} eliminates all expressions\index{expression} from the system. In the second variety it eliminates only the expressions that are mentioned from the system. All expressions that are to be dropped can still be used in the r.h.s.\ of other expressions inside the current module. Basically the expressions to be dropped are not treated for execution and after the module has finished completely they are removed. See also the ndrop statement~\ref{substandrop}. Example: \begin{verbatim} Local F1 = 1; Local F2 = 2; Local F3 = 3; .sort Drop; Ndrop F1; Print; .end F1 = 1; \end{verbatim} \vspace{10mm} %--#] drop : %--#[ dropcoefficient : \section{dropcoefficient} \label{substadropcoefficient} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & DropCoefficient; \end{tabular} \vspace{4mm} \noindent This statement replaces the coefficient of the current term by one. In principle it has the same effect as \begin{verbatim} Multiply 1/coeff_; \end{verbatim} Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_DropCoefficient_1) \begin{verbatim} Symbols x; Local F = 1 + 10*x + 20*x^2; DropCoefficient; Print; .end F = 1 + x + x^2; \end{verbatim} Inside an Argument/EndArgument\index{argument}\index{endargument} environment this statement would drop the coefficient of the terms inside the argument. Example: \begin{verbatim} Symbols x; Cfunction f; Local F = f(1 + 5*x + 10*x^2); Argument; DropCoefficient; Endargument; Print; .end F = f(1 + x + x^2); \end{verbatim} \vspace{10mm} %--#] dropcoefficient : %--#[ dropsymbols : \section{dropsymbols} \label{substadropsymbols} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & DropSymbols; \end{tabular} \vspace{4mm} \noindent This statement removes all symbols from a term. Example: \begin{verbatim} Symbols x, y, z; Local F = 1 + x + x^2 + z^3 + 2^2*y^4; Dropsymbols; Print; .end F = 8; \end{verbatim} \vspace{4mm} It has the same effect as \begin{verbatim} id,many,x?^n? = 1; \end{verbatim} (x and n are symbols) except for that it is much faster. \vspace{10mm} %--#] dropsymbols : %--#[ else : \section{else} \label{substaelse} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & else; \\ See also & if (\ref{substaif}), elseif (\ref{substaelseif}), endif (\ref{substaendif}) \end{tabular} \vspace{4mm} \noindent To be used in combination with an if statement (see \ref{substaif}). The statements following the else\index{else statement}\index{else} statement until the matching endif\index{endif statement}\index{endif} statement (see \ref{substaendif}) will be executed for the current term if the conditions of the matching proceeding if\index{if statement}\index{if} statement and/or all corresponding elseif\index{elseif} statements (see \ref{substaelseif}) are false. If any of the conditions of the matching proceeding if or elseif statements are true the statements following the else statement will be skipped. \vspace{10mm} %--#] else : %--#[ elseif : \section{elseif} \label{substaelseif} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & elseif ( {\tt<}condition{\tt>} ); \\ See also & if (\ref{substaif}), else (\ref{substaelse}), endif (\ref{substaendif}) \end{tabular} \vspace{4mm} \noindent Should be proceeded by an if\index{if statement}\index{if} statement (see \ref{substaif}) and followed at least by a matching endif\index{endif statement}\index{endif} statement (see \ref{substaendif}). If the conditions of the proceeding matching if statement and all proceeding matching elseif\index{elseif statement}\index{elseif} statements are false the condition of this elseif statement will be evaluated. If it is true, the statements following it until the next matching elseif, else\index{else statement}\index{else} or endif statement will be executed. If not, control is passed to this next elseif, else or endif statement. The syntax for the condition is exactly the same as for the condition in the if statement. \vspace{10mm} %--#] elseif : %--#[ emptyspectator : \section{emptyspectator} \label{substaemptyspectator} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & emptyspectator {\tt<}spectator{\tt>}; \end{tabular} \vspace{4mm} \noindent See chapter~\ref{spectators} on spectators. \vspace{10mm} %--#] emptyspectator : %--#[ endargument : \section{endargument} \label{substaendargument} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endargument; \\ See also & argument (\ref{substaargument}) \end{tabular} \vspace{4mm} \noindent Terminates an argument environment\index{environment!argument} (see \ref{substaargument}). The argument\index{argument} statement and its corresponding endargument\index{endargument} statement must belong to the same module. Argument environments can be nested with all other environments. \vspace{10mm} %--#] endargument : %--#[ enddo : \section{enddo} \label{substaenddo} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & enddo; \\ See also & do (\ref{substado}) \end{tabular} \vspace{4mm} See the do statement (\ref{substado}). \vspace{10mm} %--#] enddo : %--#[ endif : \section{endif} \label{substaendif} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endif; \\ See also & if (\ref{substaif}), elseif (\ref{substaelseif}), else (\ref{substaelse}) \end{tabular} \vspace{4mm} \noindent Terminates an if\index{if statement}\index{if} construction (see \ref{substaif}, \ref{substaelseif} and \ref{substaelse}). If should be noted that if\index{endif statement}\index{endif} constructions can be nested. \vspace{10mm} %--#] endif : %--#[ endinexpression : \section{endinexpression} \label{substaendinexpression} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endinexpression; \\ See also & inexpression(\ref{substainexpression}) \end{tabular} \vspace{4mm} \noindent Only to be used in combination with the inexpression\index{endinexpression}\index{inexpression} statement. The combination \begin{verbatim} InExpression,expr; Statements; EndInExpression; \end{verbatim} is a more readable version of the construction \begin{verbatim} if ( expression(expr) ); Statements; endif; \end{verbatim} \vspace{10mm} %--#] endinexpression : %--#[ endinside : \section{endinside} \label{substaendinside} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endinside; \\ See also & inside (\ref{substainside}) and the chapter on \$-variables (\ref{dollars}) \end{tabular}\vspace{4mm} \noindent Terminates an `inside'\index{inside} environment\index{environment!inside} (see \ref{substainside}) which is used to operate on the contents of \$-variables\index{\$-variable} (see \ref{dollars}).\vspace{10mm} %--#] endinside : %--#[ endrepeat : \section{endrepeat} \label{substaendrepeat} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endrepeat; \\ See also & repeat (\ref{substarepeat}), while (\ref{substawhile}) \end{tabular} \vspace{4mm} \noindent Ends the repeat\index{repeat} environment\index{environment!repeat}. The repeat environment is started with a repeat statement (see \ref{substarepeat}). The repeat and its matching endrepeat\index{endrepeat} should be inside the same module. Repeat environments can be nested with all other environments (and other repeat environments). \vspace{10mm} %--#] endrepeat : %--#[ endswitch : % \section{endswitch} \label{substaendswitch} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endswitch; \\ \\ See also & case (\ref{substacase}), break (\ref{substabreak}), default(\ref{substadefault}), switch (\ref{substaswitch}). \end{tabular} \vspace{4mm} \noindent Ends a switch construction. It collects the various cases, puts them in order and decides whether the lookup of cases should be done by means of a jumptable, or by binary searching. The ratio (spread in cases)/(number of cases) determines whether a jumptable is constructed. The default value below which a jumptable is constructed is 4. This value can be changed in the setups (see the section on the setups \ref{setup}) with the variable jumpratio. \vspace{10mm} % %--#] endswitch : %--#[ endterm : \section{endterm} \label{substaendterm} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endterm; \\ See also & term (\ref{substaterm}), sort (\ref{substasort}) \end{tabular} \vspace{4mm} \noindent Terminates a term\index{term} environment\index{environment!term} (see \ref{substaterm}). Term environments\index{endterm} can be nested with other term environments and with other environments in general. The whole environment should be part of one single module. See also \ref{substasort}. \vspace{10mm} %--#] endterm : %--#[ endwhile : \section{endwhile} \label{substaendwhile} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & endwhile; \\ See also & while (\ref{substawhile}), repeat (\ref{substarepeat}) \end{tabular} \vspace{4mm} \noindent Terminates a while\index{while} environment\index{environment!while} (see \ref{substawhile}). The while statement and its corresponding endwhile\index{endwhile} statement must be part of the same module. \vspace{10mm} %--#] endwhile : %--#[ evaluate : \section{evaluate} \label{substaevaluate} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & evaluate [$<$function(s)$>$][,$<$symbol(s)$>$]; \\ \end{tabular} \vspace{4mm} \noindent See chapter~\ref{floatingpoint} on the floating point capability. %--#] evaluate : %--#[ exit : \section{exit} \label{substaexit} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & exit ["{\tt<}string{\tt>}"]; \\ See also & setexitflag (\ref{substasetexitflag}) \end{tabular} \vspace{4mm} \noindent Causes execution to be aborted\index{exit}\index{aborted} immediately. The string will be printed in the output. This can be used to indicate where \FORM\ ran into the exit statement. \vspace{10mm} %--#] exit : %--#[ extrasymbols : \section{extrasymbols} \label{substaextrasymbols} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & extrasymbols,array\textbar{}vector\textbar{}underscore,name; \\ See also & ToPolynomial (\ref{substatopolynomial}), FromPolynomial (\ref{substafrompolynomial}), ArgToExtraSymbol (\ref{substaargtoextrasymbol}) \\& and extra symbols (\ref{sect-extrasymbols}). \end{tabular} \vspace{4mm} \noindent Starting with version 4.0 of \FORM{} some built in operations or statements can only deal with symbols and numbers. Examples of this are factorization~(\ref{substafactarg}) (which uses the topolynomial facilities automatically) and output simplification (see the Format statement \ref{substaformat}). The ToPolynomial statement\index{topolynomial} takes each term, looks for objects that are not symbols to positive powers and replaces them by symbols. If the object has been encountered before the same symbol will be used, otherwise a new symbol will be defined. The object represented by the `extra symbol'\index{extra symbols} is stored internally and can be printed if needed with the \%X option in the \#write instruction (\ref{prewrite}). The representation of the extra symbols is by default the name Z followed by a number and an underscore character. If another name is desired this should be specified in an `ExtraSymbols' statement. The name given may contain only alphabetic characters! Because some compilers do not like the underscore character, there is an alternative notation for the extra symbols. This is just for cosmetic reasons and one cannot feed these symbols into the compiler this way. This is with an array notation. The statement \begin{verbatim} ExtraSymbols,array,Ab; \end{verbatim} would cause the second extra symbol to be printed as {\tt Ab(2)}. The total number of defined extra symbols is given by the built in symbol extrasymbols\_. The option vector in the ExtraSymbols statement is identical to the option array and the option underscore reverts the notation back to the default notation with the trailing underscore. \vspace{10mm} %--#] extrasymbols : %--#[ factarg : \section{factarg} \label{substafactarg} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & factarg options \verb:{:{\tt<}name of function/set{\tt>} [{\tt<}argument specifications{\tt>}]\verb:}:; \\ See also & splitarg (\ref{substasplitarg}) \end{tabular} \vspace{4mm} \noindent Splits\index{factarg} the indicated function\index{function arguments} arguments into individual factors. The argument specifications are as in the splitarg\index{splitarg} statement (see \ref{substasplitarg}). There are a few extra options: \leftvitem{2cm}{(0)} \rightvitem{14cm}{Eliminates the coefficient\index{coefficient} of the term in the argument. Similar to Normalize,(0),....} \leftvitem{2cm}{(1)} \rightvitem{14cm}{The coefficient of the term and its sign are pulled out separately.} \leftvitem{2cm}{(-1)} \rightvitem{14cm}{The coefficient is pulled out with its sign.} \noindent In the case of the above options only the coefficient is treated. When these options are not used the whole term is treated as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_FactArg_1) % TODO: On OldFactArg \begin{verbatim} Symbols a,b,c; CFunctions f,f1,f2,f3; Local F = f(-3*a*b)+f(3*a*b) +f1(-3*a*b)+f1(3*a*b) +f2(-3*a*b)+f2(3*a*b) +f3(-3*a*b)+f3(3*a*b); FactArg,f; Factarg,(0),f1; Factarg,(1),f2; Factarg,(-1),f3; Print; .end F = f(a,b,-1,3) + f(a,b,3) + 2*f1(a*b) + f2(a*b,-1,3) + f2(a*b,3) + f3(a*b,-3) + f3(a*b,3); \end{verbatim} When no extra options are used, starting with version 4.0, the whole argument is factorized over the rationals. This means that \begin{verbatim} f(x^2+2*x*y+y^2) --> f(y + x,y + x,1) \end{verbatim} It should be noticed that \FORM{} can although the internal algorithms can only factorize expressions with numbers and symbols, \FORM{} redefines all non-symbol objects temporarily into symbols and at the end substitutes them back. This is done with a mechanism that is similar to that of the ToPolynomial statement. See also the On OldfactArg; and Off OldFactArg statements for a compatibility mode with versions before version 4.0. \vspace{10mm} %--#] factarg : %--#[ factdollar : \section{factdollar} \label{substafactdollar} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & factdollar {\tt<}name of dollar variable{\tt>}; \\ See also & the chapter on polynomials~\ref{polynomials}. \end{tabular} \vspace{4mm} \noindent The FactDollar statement will factorize a dollar expression. If the dollar expression was already factorized the old factors will be removed first. Unlike expressions (see \ref{substafactorize}) where only either the expanded or the factorized version exists, with dollar expressions we have both versions simultaneously. This means that one can refer to the complete dollar in its unfactorized form and its factors. The factors are indicated between braces as in \verb:$x[1]: which would be the first factor. The number of factors of \verb:$x: is given by \verb:$x[0]:. One can also obtain the number of factors of a dollar variable with the numfactors\_ function (see \ref{funnumfactors}). \noindent The index indicating the number of the factor can be a nonzero integer, no greater than the number of factors, or (a factor of) a dollar variable that evaluates into such a number. Composite expressions are not allowed. They should be worked out first in a separate dollar variable, after which this dollar variable can then be used as a factor indicator. \vspace{10mm} %--#] factdollar : %--#[ factorize : \section{factorize} \label{substafactorize} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & factorize \verb:{:{\tt<}name of expression(s){\tt>}\verb:}:; \\ See also & the chapter on polynomials~\ref{polynomials}. \end{tabular} \vspace{4mm} \noindent Example % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Factorize_1) \begin{verbatim} Symbols x; Local F = x^3 + 3*x^2 + 3*x + 1; Factorize; Print; .end F = ( 1 + x ) * ( 1 + x ) * ( 1 + x ); \end{verbatim} \noindent If no expressions are mentioned all expressions will be affected by the action of this statement. One may exclude certain expressions with the nfactorize statement (see \ref{substanfactorize}). If one or more expressions are mentoned they will be added to the list of expressions that will be affected. \noindent The statement causes the output expression(s) that is/are marked as such to be factorized after they have been processed and already written to the output. This means that each expression, after having been written, is read again and factorized. Then the factorized result is written over the original output. After that \FORM{} will start executing the statements of the current module on the next expression, sort it, write it to output, and if necessary read it again and factorize it. \noindent Expressions never exists in two varieties as the dollar variable that have been factorized. It is either unfactorized (default) or factorized. An expression remains factorized until an UnFactorize statement is encountered that mentions that this expression should be brought to unfactorized representation (see also UnFactorize~\ref{substaunfactorize} and NunFactorize~\ref{substanunfactorize}). \noindent One should realize that factorization of complicated expressions can be a rather costly operation. \vspace{10mm} %--#] factorize : %--#[ fill : \section{fill} \label{substafill} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & fill {\tt<}tableelement{\tt>} = {\tt<}expression{\tt>} [,{\tt<}moreexpressions{\tt>}]; \\ See also & table (\ref{substatable}), fillexpression (\ref{substafillexpression}), printtable (\ref{substaprinttable}) \end{tabular} \vspace{4mm} \noindent The standard\index{fill} way to define elements of a table\index{table}. In the left hand side one specifies the table element without the extra function arguments that could potentially occur (see \ref{substatable}). In the right hand side one specifies what the table element should be substituted by. Example: \begin{verbatim} Table tab(1:2,1:2,x?); Fill tab(1,1) = x+y; Fill tab(2,1) = (x+y)^2; Fill tab(1,2) = tab(1,1)+y; Fill tab(2,2) = tab(2,1)+y^2; \end{verbatim} The first fill statement is a bit like a continuous attempt to try the substitution \begin{verbatim} id tab(1,1,x?) = x+y; \end{verbatim} The last two fill statements show that one could use the table recursively\index{recursively}. If a real loop occurs the program may terminate due to stack\index{stack overflow} overflow. \noindent It is possible to define several table elements in one statement. In that case the various elements are separated by commas. The last index is the first one to be raised. This means that in the above example one could have written: \begin{verbatim} Table tab(1:2,1:2,x?); Fill tab(1,1) = x+y,tab(1,1)+y,(x+y)^2,tab(2,1)+y^2; \end{verbatim}\vspace{10mm} \noindent One warning\index{warning} is called for. One should avoid using expressions in the right hand side of fill statements: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Fill_1) \begin{verbatim} Table B(1:1); Local dummy = 1; .sort Fill B(1) = dummy; Drop dummy; .sort Local F = B(1); Print; .end \end{verbatim} In the example a crash will result, because when we use the table element the expression dummy doesn't exist anymore. In a fill statement the r.h.s. is not expanded. Hence it keeps the reference to the expression dummy. When the table element is used the reference to the expression dummy is inserted and expanded. Hence one obtains the contents of dummy that exist at the moment of use. This is illustrated in the following example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Fill_2) \begin{verbatim} Table B(1:1); Local dummy = 1; .sort Fill B(1) = dummy; .sort Local F = B(1); Print; .sort Drop; .sort Local dummy = 2; .sort Local F = B(1); Print; .end \end{verbatim} The final value of F will be 2, not 1. \noindent A way to get around this problem is to force the evaluation of the table definition by using dollar\index{dollar} variables\index{variable!dollar}: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Fill_3) \begin{verbatim} Table B(1:1); Local dummy = 1; .sort #$value = dummy; Fill B(1) = `$value'; Drop dummy; .sort Local F = B(1); Print; .end \end{verbatim} Here we use the character representation of the contents of the dollar variable to obtain an expression that doesn't need any further evaluation. If we would put \begin{verbatim} fill B(1) = $value; \end{verbatim} a reference to the dollar variable would be inserted and it would only be evaluated at use again. In principle this could cause similar problems. \noindent Not dropping the expression dummy can sometimes give the correct result, but is potentially still unsafe. % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Fill_4) \begin{verbatim} Table B(1:1); Local u = 2; Local dummy = 1; .sort Fill B(1) = dummy; Drop dummy; .sort Local v = 5; Local F = B(1); Print; .end \end{verbatim} Here the answer will be 5, because after u has been dropped the expressions will be renumbered. Hence now dummy becomes the first expression, and eventually v becomes the second expression. The references in the table elements are not renumbered. Hence the r.h.s.\ of B(1) keeps pointing at the second expression, which at the moment of application has the value 5. One can see now also why the original example crashes. First dummy was the first expression and at the moment of application F is the first (existing) expression. Hence the substitution of B(1) causes a self reference and hence an infinite loop. Eventually some buffer will overflow\index{overflow}. \vspace{10mm} %--#] fill : %--#[ fillexpression : \section{fillexpression} \label{substafillexpression} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & fillexpression {\tt<}table{\tt>} = {\tt<}expression{\tt>}({\tt<}x1{\tt>},...,{\tt<}xn{\tt>}); \\ & fillexpression {\tt<}table{\tt>} = {\tt<}expression{\tt>}({\tt<}funname{\tt>}); \\ See also & table (\ref{substatable}), fill (\ref{substafill}) and the table\_ function (\ref{funtable}) \end{tabular}\vspace{4mm} \noindent Used\index{fillexpression} to dynamically\index{dynamical loading} load\index{loading dynamically} a table\index{table} during runtime. When there are n symbols (here called x1 to xn) it is assumed that the table is n-dimensional. The expression must previously have been bracketed in these symbols and each of the brackets\index{brackets} has the effect of a fill\index{fill} statement in which the powers of the x1 to xn refer to the table elements. Brackets that do not have a corresponding table element are skipped. \noindent In the case that only a function name is specified the arguments of the function refer to the table elements. \vspace{10mm} %--#] fillexpression : %--#[ fixindex : \section{fixindex} \label{substafixindex} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & fi[xindex] \verb:{:{\tt<}number{\tt>}:{\tt<}value{\tt>}\verb:}:; \\ See also & index (\ref{substaindex}) and chapter \ref{metric}. \end{tabular} \vspace{4mm} \noindent Defines \verb:d_(number,number) = value: in which number is the number\index{fixindex} of a fixed\index{fixed index} index\index{index} (hence a positive short integer with a value less than ConstIndex\index{constindex} (see \ref{setup}). The value should be a short\index{short integer} integer, i.e.\ its absolute value should be less than $2^{15}$ on 32\index{32 bits} bit computers and less than $2^{31}$ on 64\index{64 bits} bit computers. One can define more than one fixed index in one statement. Before one would like to solve problems involving the choice of a metric with this statement, one should consult the chapter on the use of a metric\index{metric} (chapter \ref{metric}). \vspace{10mm} %--#] fixindex : %--#[ format : \section{format} \label{substaformat} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & fo[rmat] {\tt<}option{\tt>}; \\ See also & print (\ref{substaprint}) \end{tabular} \vspace{4mm} \noindent Controls the format\index{format} for the printing\index{printing} of expressions. There is a variety of options. \leftvitem{3.5cm}{$<$number$>$} \rightvitem{13cm}{Output will be printed using the indicated number of characters per line. The default is 72. Numbers outside the range 1-255 are corrected to 72. Positive numbers less than 39 are corrected to 39.} \leftvitem{3.5cm}{float\index{float}\index{format!float} \hfill \\ \null\quad{\tt[}$<$number$>${\tt]}} \rightvitem{13cm}{Numbers are printed in floating\index{floating point} point notation, even though internally they remain fractions. This is purely cosmetic. If no number is specified the precision of the output will be 10 digits. If a number is specified it indicates the number of digits to be used for the precision.} \leftvitem{3.5cm}{rational\index{rational}\index{format!rational}} \rightvitem{13cm}{Output format is switched back to rational numbers (in contrast to floating point output). This is the default.} \leftvitem{3.5cm}{floatprecision\index{floatprecision}\index{format!floatprecision} \hfill \\ \null{\tt[}$<$off$>\!|\!<$number$>${\tt]}} \rightvitem{13cm}{See chapter~\ref{floatingpoint} on the floating point capability.} \leftvitem{3.5cm}{nospaces\index{nospaces}\index{format!nospaces}} \rightvitem{13cm}{The output is printed without the spaces that make the output slightly more readable. This gives a more compact output.} \leftvitem{3.5cm}{spaces\index{spaces}\index{format!spaces}} \rightvitem{13cm}{The output is printed with extra spaces between the terms and around certain operators to make it slightly more readable. This is the default.} \leftvitem{3.5cm}{O0\index{optimize}\index{format!optimize}} \rightvitem{13cm}{\FORM\ will turn off output optimization. See the section on output optimization \ref{optimization}} \leftvitem{3.5cm}{O1[options]\index{optimize}\index{format!optimize}} \rightvitem{13cm}{\FORM\ will use level 1 output optimization. See the section on output optimization \ref{optimization}} \leftvitem{3.5cm}{O2[options]\index{optimize}\index{format!optimize}} \rightvitem{13cm}{\FORM\ will use level 2 output optimization. See the section on output optimization \ref{optimization}} \leftvitem{3.5cm}{O3[options]\index{optimize}\index{format!optimize}} \rightvitem{13cm}{\FORM\ will use level 3 output optimization. See the section on output optimization \ref{optimization}.} \leftvitem{3.5cm}{fortran\index{fortran}\index{format!fortran}} \rightvitem{13cm}{The output is printed in a way that is readable by a fortran compiler. This includes continuation characters and the splitting of the output into blocks of no more than 15 continuation lines. This number can be changed with the setup parameter ContinuationLines (see \ref{setup}). In addition dotproducts are printed with the `dotchar' in the place of the period between the vectors. This dotchar can be set in the setup file (see \ref{setup}). Its default is the underscore character.} \leftvitem{3.5cm}{doublefortran\index{doublefortran}\index{format!doublefortran}} \rightvitem{13cm}{Same as the fortran mode, but fractions are printed with double floating point numbers, because some compilers convert numbers like 1.\ into 1.E0. With this format \FORM\ will force double precision by using 1.D0.} \leftvitem{3.5cm}{quadruplefortran\index{quadruplefortran}\index{format!quadruplefortran}} \rightvitem{13cm}{Same as the fortran mode, but fractions are printed with quadruple floating point numbers, because some compilers convert numbers like 1.\ into 1.E0. With this format \FORM\ will force quadruple precision by using 1.Q0.} \leftvitem{3.5cm}{quadfortran\index{quadfortran}\index{format!quadfortran}} \rightvitem{13cm}{Same as quadruplefortran.} \leftvitem{3.5cm}{fortran90\index{fortran90}\index{format!fortran90}} \rightvitem{13cm}{Similar to the fortran option, but prints the continuation lines according to the syntax of Fortran 90. If the fortran90 option is followed by a comma and a string that does not contain white space or other comma's, this string is attached to all numbers in coefficients of terms. Example: \hfill \\ {\tt\ \ \ \ \ \ Format Fortran90,.0\_ki;} \hfill \\ %\begin{verbatim} % Format Fortran90,.0_ki; %\end{verbatim} which would give in the printout: \hfill \\ {\tt\ \ \ \ \ \ +23.0\_ki/32.0\_ki*a**2\& } \hfill \\ {\tt\ \ \ \ \&\ +34.0\_ki/1325.0\_ki*a**3} \hfill \\ %\begin{verbatim} % +23.0_ki/32.0_ki*a**2& % & +34.0_ki/1325.0_ki*a**3 %\end{verbatim} When there is no string attached it defaults to a period as in the regular Fortran option. } \leftvitem{3.5cm}{C\index{C}\index{format!C}} \rightvitem{13cm}{Output will be C compatible. The exponent\index{exponent operator} operator ($\wedge$) is represented by the function pow\index{pow}. It is the responsibility of the user that this function will be properly defined. Dotproducts are printed with the `dotchar'\index{dotchar} in the place of the period between the vectors. This dotchar can be set in the setup file (see \ref{setup}). Its default is the underscore\index{underscore character} character.} \leftvitem{3.5cm}{maple\index{maple}\index{format!maple}} \rightvitem{13cm}{Output will be as much as possible compatible with Maple format. It is not guaranteed that this is perfect.} \leftvitem{3.5cm}{mathematica\index{mathematica}\index{format!mathematica}} \rightvitem{13cm}{Output will be as much as possible compatible with Mathematica format. It is not guaranteed that this is perfect.} \leftvitem{3.5cm}{reduce\index{reduce}\index{format!reduce}} \rightvitem{13cm}{Output will be as much as possible compatible with Reduce format. It is not guaranteed that this is perfect.} \noindent The last few formats have not been tried out extensively. The author is open for suggestions. \leftvitem{3.5cm}{normal\index{normal}\index{format!normal}} \rightvitem{13cm}{Will return to the regular \FORM\ formatting mode.} \noindent If the statement has no arguments the formatting will be reset to the mode it was in when the program started.\vspace{4mm} %\leftvitem{3.5cm}{} %\rightvitem{13cm}{} %\leftvitem{3.5cm}{} %\rightvitem{13cm}{} \vspace{10mm} %--#] format : %--#[ frompolynomial : \section{frompolynomial} \label{substafrompolynomial} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & frompolynomial \\ See also & factarg (\ref{substafactarg}), ToPolynomial (\ref{substatopolynomial}) and ExtraSymbols (\ref{substaextrasymbols}, \ref{sect-extrasymbols}). \end{tabular} \vspace{4mm} \noindent Starting with version 4.0 of \FORM{} some built in operations or statements can only deal with symbols and numbers. Examples of this are factorization~(\ref{substafactarg}) and output simplification (still to be implemented). Whereas the ToPolynomial statement takes each term, looks for objects that are not symbols to positive powers and replaces them by symbols the FromPolynomial does the opposite: it replaces the newly defined extra symbols and replaces them back by their original meaning. \vspace{10mm} %--#] frompolynomial : %--#[ functions : \section{functions} \label{substafunctions} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & f[unctions] {\tt<}list of functions to be declared{\tt>}; \\ See also & cfunctions (\ref{substacfunctions}), nfunctions (\ref{substanfunctions}), tensors (\ref{substatensors}), ctensors (\ref{substactensors}), ntensors (\ref{substantensors}), \\ & table (\ref{substatable}), ctable (\ref{substactable}), ntable (\ref{substantable}) \end{tabular} \vspace{4mm} \noindent Used to declare one or more functions\index{functions}. The functions declared with this statement will be noncommuting\index{noncommuting}. For commuting\index{commuting} functions one should use the cf[unctions] statement (see \ref{substacfunctions}). Functions can have a number of properties that can be set in the declaration. This is done by appending the options to the name of the function. These options are: \leftvitem{4.1cm}{name{\hash}r} \rightvitem{12cm}{The function is considered to be a real\index{real} function (default).} \leftvitem{4.1cm}{name{\hash}c} \rightvitem{12cm}{The function is considered to be a complex\index{complex} function. This means that internally two spaces are reserved. One for the variable name and one for its complex conjugate name{\hash}.} \leftvitem{4.1cm}{name{\hash}i} \rightvitem{12cm}{The function is considered to be imaginary\index{imaginary}.} \leftvitem{4.1cm}{name(s[ymmetric])} \rightvitem{12cm}{The function is totally symmetric\index{symmetric}. This means that during normalization {\FORM} will order the arguments according to its internal notion of order by trying permutations. The result will depend on the order of declaration of variables.} \leftvitem{4.1cm}{name(a[ntisymmetric])} \rightvitem{12cm}{The function is totally antisymmetric\index{antisymmetric}. This means that during normalization {\FORM} will order the arguments according to its internal notion of order and if the resulting permutation of arguments is odd the coefficient of the term will change sign. The order will depend on the order of declaration of variables.} \leftvitem{4.1cm}{name(c[yclesymmetric])} \rightvitem{12cm}{The function is cycle\index{cycle symmetric} symmetric\index{symmetric!cycle} in all its arguments. This means that during normalization {\FORM} will order the arguments according to its internal notion of order by trying cyclic permutations. The result will depend on the order of declaration of variables.} \leftvitem{4.1cm}{name(r[cyclesymmetric) name(r[cyclic]) name(r[eversecyclic])} \rightvitem{12cm}{The function is reverse\index{reverse cycle symmetric} cycle symmetric\index{symmetric!reverse cycle} in all its arguments. This means that during normalization {\FORM} will order the arguments according to its internal notion of order by trying cyclic permutations and/or a complete reverse order of all arguments. The result will depend on the order of declaration of variables.} \leftvitem{4.1cm}{name$<$number name$<=$number name$>$number name$>=$number} \rightvitem{12cm}{The function has a restriction on the number of arguments. If the number of arguments of an occurrence of the function is not fulfilling the condition during normalization {\FORM} will set the term equal to zero.}\vspace{2mm} \noindent The complexity properties, the symmetric properties and the number of arguments restrictions can be combined. In that case the complexity properties should come first and the argument restrictions should come last as in \begin{verbatim} Function f1#i(symmetric)>=4<8; Function f1#i<=8; \end{verbatim} \vspace{10mm} %--#] functions : %--#[ funpowers : \section{funpowers} \label{substafunpowers} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & funpowers {\tt<}on/off{\tt>}; \\ See also & on (\ref{substaon}), off (\ref{substaoff}) \end{tabular} \vspace{4mm} \noindent This statement\index{funpowers} is obsolete\index{obsolete}. The user should try to use the funpowers option of the on\index{on} (see \ref{substaon}) or the off\index{off} (see \ref{substaoff}) statements. \vspace{10mm} %--#] funpowers : %--#[ gfactorized : \section{gfactorized} \label{substagfactorized} \noindent \begin{tabular}{ll} Type & Definition statement\\ Syntax & g[lobal]factorized {\tt<}option{\tt>}; \\ See also & the chapter on polynomials~\ref{polynomials}, the factorize statement~\ref{substafactorize} and the LocalFactorized \\ & statement~\ref{substalfactorized}.\hfill \end{tabular} \smallskip \noindent The syntax is like the syntax of the LocalFactorized (or LFactorized) statement~\ref{substalfactorized}. The only difference is that now the expression defined by the statement will become a global expression (see the Global statement~\ref{substaglobal}). \vspace{10mm} %--#] gfactorized : %--#[ global : \section{global} \label{substaglobal} \noindent \begin{tabular}{ll} Type & Definition statement\\ Syntax & g[lobal] {\tt<}name{\tt>} = {\tt<}expression{\tt>}; \\ & g[lobal] {\tt<}names of expressions{\tt>}; \\ See also & local (\ref{substalocal}) \end{tabular} \vspace{4mm} \noindent Used to define a global\index{global} expression\index{expression}. A global expression is an expression that remains active until the first .store\index{.store} instruction. At that moment it is stored into the `storage file'\index{storage file}\index{file!storage} and stops being manipulated. After this it can still be used in the right hand side of expressions and id\index{id} statements (see \ref{substaidnew}). Global expressions that have been put in the storage file can be saved to a disk file\index{file!disk} with the save statement (see \ref{substasave}) for use in later programs. \noindent There are two versions of the global statement. In the first the expression is defined and filled with a right hand side expression. The left hand side and the right hand side are separated by an = sign. In this case the expression can have arguments which will serve as dummy\index{dummy arguments} arguments after the global expression has been stored with a .store instruction. Note that this use of arguments can often be circumvented with the replace\_ function (see \ref{funreplace}) as in \begin{verbatim} Global F(a,b) = (a+b)^2; .store Local FF = F(x,y); Local GG = F*replace_(a,x,b,y); \end{verbatim} because both definitions give the same result. \noindent The second version of the global statement has no = sign and no right hand side. It can be used to change a local\index{local} expression into a global expression. \vspace{10mm} %--#] global : %--#[ goto : \section{goto} \label{substagoto} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & go[to] {\tt<}label{\tt>}; \\ See also & label (\ref{substalabel}) \end{tabular} \vspace{4mm} \noindent Causes\index{goto} processing to proceed at the indicated label\index{label} statement (see \ref{substalabel}). This label statement must be in the same module. \vspace{10mm} %--#] goto : %--#[ hide : \section{hide} \label{substahide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & hide; \\ & hide {\tt<}list of expressions{\tt>}; \\ See also & nhide (\ref{substanhide}), unhide (\ref{substaunhide}), nunhide (\ref{substanunhide}), pushhide (\ref{substapushhide}), pophide (\ref{substapophide}) \end{tabular} \vspace{4mm} \noindent In the first variety this statement marks all currently active expressions for being put in hidden\index{hide} storage. In the second variety it marks only the specified active\index{active expressions} expressions as such. \vspace{4mm} \noindent If an expression is marked for being hidden, it will be copied to the `hide\index{hide file} file'\index{file!hide}, a storage which is either in memory or on file depending on the combined size of all expressions being hidden. If this size exceeds the size of the setup parameter scratchsize\index{scratchsize} (see \ref{setup}) the storage will be on file. If it is less, the storage will be in memory. An expression that has been hidden is not affected by the statements in the modules as long as it remains hidden, but it can be used inside other expressions in the same way skipped\index{skipped expressions} expressions (see \ref{substaskip}) or active expressions can be used. In particular all its bracket\index{bracket} information (see \ref{substabracket}) is retained and can be accessed, including possible bracket\index{bracket index} indexing. \vspace{4mm} \noindent The hide mechanism is particularly useful if an expression is not needed for a large number of modules. It has also advantages over the storing of global expressions after a .store\index{.store} instruction (see \ref{instrstore}), because the substitution of global expressions is slower (name definitions may have changed and have to be checked) and also a possible bracket index is not maintained by the .store instruction. \vspace{4mm} \noindent Expressions can be returned from a hidden status into active expressions with the unhide\index{unhide} statement (see \ref{substaunhide}). One might want to consult the nhide\index{nhide} statement (\ref{substahide}) as well. \vspace{4mm} \noindent When an expression is marked to be hidden it will remain just marked until execution starts in the current module. When it is the turn of the expression to be executed, it is copied to the hide file instead. \vspace{4mm} \noindent Note that a .store instruction will simultaneously remove all expressions from the hide system. \vspace{10mm} %--#] hide : %--#[ identify : \section{identify} \label{substaidentify} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & id[entify] [{\tt<}options{\tt>}] {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & also (\ref{substaalso}), idnew (\ref{substaidnew}), idold (\ref{substaidold}) \end{tabular}\vspace{4mm} \noindent The statement\index{id}\index{identify} tries to match the pattern\index{pattern}. If the pattern matches one or more times, it will be replaced by the expression in the r.h.s.\ taking the possible wildcard\index{wildcard} substitutions into account. For the description of the patterns, see chapter \ref{pattern}. \noindent The options are \vspace{1mm} \lefttabitem{multi\index{multi}} \tabitem{This option is for combinations of symbols and dotproducts only and it does not use wildcard powers. \FORM\ determines how many times the pattern fits in one pattern matching action. Then the r.h.s.\ is substituted to that power. It is the default for these kinds of patterns.} \lefttabitem{many\index{many}} \tabitem{This is the default for patterns that contain other objects than symbols and dotproducts. The pattern is matched and taken out. Then \FORM\ tries again to match the pattern in the remainder of the term. This is repeated until there is no further match. Then for each match the r.h.s. is substituted (with its own wildcard substitutions).} \lefttabitem{select\index{select}} \tabitem{This option should be followed by one or more sets\index{set}. After the sets the pattern can be specified. The pattern will only be substituted if none of the objects mentioned in the sets will be left after the pattern has been taken out. This holds only for objects 'at ground level'; i.e.\ the pattern matcher will not look inside function arguments for this. Note that this is a special case of the option 'only'.} \lefttabitem{once\index{once}} \tabitem{The pattern is matched only once, even if it occurs more than once in the term. The first match that \FORM\ encounters is taken. When wildcards are involved, this may depend on the order of declaration of variables. It could also be installation dependent. Also the setting of properorder\index{properorder} (see \ref{substaon} and \ref{substaoff}) could be relevant. Try to write programs in such a way that the outcome does not depend on which match is taken.} \lefttabitem{only\index{only}} \tabitem{The pattern will match only if there is an exact match in the powers of the symbols and dotproducts present.} \lefttabitem{ifmatch$-\!\!>$\index{ifmatch}} \tabitem{This option should be followed by the name (or number) of a label\index{label}. If the pattern matches, the replacement will be made after which the execution continues at the label.} \lefttabitem{ifnomatch$-\!\!>$\index{ifmatch}} \tabitem{This option should be followed by the name (or number) of a label\index{label}. If the pattern does not match, execution continues at the label.} \lefttabitem{disorder\index{disorder}} \tabitem{This option is used for products of noncommuting\index{noncommuting} functions\index{functions!noncommuting} or tensors\index{tensors!noncommuting}. The match will only take place if the order of the functions in the match is different from what \FORM\ would have made of it if the functions would be commuting\index{commuting}. Hence if the functions in the term are in the order that \FORM\ would give them if they would be commuting (which depends on the order of declaration) there will be no match. This can be rather handy when using wildcards as in {\tt F(a?)*F(b?)}.} \lefttabitem{all\index{all}} \tabitem{This option is rather special in that it generates all possible matches one by one. Normally, when there are many possible matches, \FORM\ takes the first one it encounters. In the case of the all option it will run through all possible matches and produce all of them. There are however severe restrictions. First of all, other options are not allowed simultaneously, although ifmatch$-\!\!>$ and ifnomatch$-\!\!>$ are allowed because technically they are no options that concern the pattern matching. In addition it is not allowed to be in an idold/also statement, and it cannot be followed by such a statement. Most severely: it can have only functions in the left hand side. These functions can have all kinds of arguments, but outside the functions symbols, vectors, dotproducts etc.\ are not allowed. This is due to the fact that the backtracking when a wildcard combination fails, does not include such objects and it is this backtracking mechanism that is used to generate all matches. For the purpose of the all option tensors and unsubstituted tables count as functions. It should also be known that the all option cannot be used in the if(match()) construction. It would not make sense there anyway.} \noindent Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Identify_1) \begin{verbatim} Vector Q,p1,...,p5,q1,...,q5; Cfunction V(s),replace; Format 60; * This is a t1 topology: L F = V(Q,p1,p4)*V(p1,p2,p5)* V(p2,p3,Q)*V(p3,p4,p5); $t = term_; id,all,$t*replace_(,...,) = $t*replace(,...,); Print +s; ModuleOption noparallel; * suppresses noparallel warning with TFORM .end F = + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p1,q1,p2,q2,p3,q3,p4,q4,p5,q5) + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p2,q1,p1,q2,p4,q3,p3,q4,p5,q5) + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p3,q1,p4,q2,p1,q3,p2,q4,p5,q5) + V(Q,p1,p4)*V(Q,p2,p3)*V(p1,p2,p5)*V(p3,p4,p5)* replace(p4,q1,p3,q2,p2,q3,p1,q4,p5,q5) ; \end{verbatim} This program produces all renumberings of the momenta in the t1 topology that produce the same topology. The interesting thing here is that one does not have to know the topology to produce all topologically equivalent terms. There are two options in the id,all statement: \hfill \\ \lefttabitem{all(n[ormalize])} \tabitem{Here the final answer is divided by the number of matches. In the example above that would be 4.} \lefttabitem{all($<$number$>$)} \tabitem{The number between the parentheses will be the maximum number of matches allowed. This means that once this number is reached, no further matches are produced.} \vspace{10mm} %--#] identify : %--#[ idnew : \section{idnew} \label{substaidnew} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & idn[ew] [{\tt<}options{\tt>}] {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}), also (\ref{substaalso}), idold (\ref{substaidold}) \end{tabular} \vspace{4mm} \noindent This statement\index{idnew} and its options are completely identical to the regular id\index{id} or identify\index{identify} statement (see \ref{substaidentify}). \vspace{10mm} %--#] idnew : %--#[ idold : \section{idold} \label{substaidold} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & ido[ld] [{\tt<}options{\tt>}] {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}), also (\ref{substaalso}), idnew (\ref{substaidnew}) \end{tabular}\vspace{4mm} \noindent This statement\index{idold} and its options are completely identical to the regular also\index{also} statement (see \ref{substaalso}). The options are described with the id\index{id} or identify\index{identify} statement (see \ref{substaidentify}). \vspace{10mm} %--#] idold : %--#[ if : \section{if} \label{substaif} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & if ( {\tt<}condition{\tt>} ); \\ & if ( {\tt<}condition{\tt>} ) {\tt<}executable statement{\tt>} \\ See also & elseif (\ref{substaelseif}), else (\ref{substaelse}), endif (\ref{substaendif}) \end{tabular} \vspace{4mm} \noindent Used\index{if} for executing parts of code only when certain conditions\index{condition} are met. Works together with the else\index{else} statement (see \ref{substaelse}), the elseif\index{elseif} statement (see \ref{substaelseif}) and the endif\index{endif} statement (see \ref{substaendif}). There are two versions. In the first the if statement must be accompanied by at least an endif statement. In that case the statements between the if statement and the endif statement will be executed if the condition is met. It is also possible to use elseif and else statements to be more flexible. This is done in the same way as in almost all computer languages. \noindent In the second form the if statement does not terminate with a semicolon\index{semicolon}. It is followed by a single regular statement. No endif statement should be used. The single statement will be executed if the condition is met. \noindent The condition in the if statement should be enclosed by parentheses. Its primary components are: \leftvitem{3.5cm}{count()\index{count}} \rightvitem{13cm}{Returns an integer power counting value for the current term. Should have arguments that come in pairs. The first element of the pair is a variable. The second is its integer weight\index{weight}. The types of variables that are allowed are symbols, dotproducts, functions, tensors, tables and vectors. The weights can be positive as well as negative. They have to be short integers (Absolute value $< 2^{15}$ on 32\index{32 bits} bit computers and $< 2^{31}$ on 64\index{64 bits} bit computers). The vectors can have several options appended to their name. This is done by putting a + after the name of the vector and have this followed by one or more of the following letters: \noindent \begin{tabular}{ll} v & Loose vectors with an index are taken into account. \\ d & Vectors inside dotproducts are taken into account. \\ f & Vectors inside tensors are taken into account. \\ ?set & \begin{minipage}[t]{11cm}{The set should be a set of functions. Vectors inside the functions that are members of the set are taken into account. It is assumed that those functions are linear in the given vector}\end{minipage} \end{tabular} \vspace{1mm} When no options are specified the result is identical to +vfd.} \leftvitem{3.5cm}{match()\index{match}} \rightvitem{13cm}{The argument of the match condition can be any left hand side of an id statement, including options as once\index{once}, only\index{only}, multi\index{multi}, many\index{many} and select\index{select} (see \ref{substaidnew}). The id of the id statement should not be included. \FORM\ will invoke the pattern\index{pattern matcher} matcher and see how many times the pattern matches. This number is returned. In the case of once or only this is of course at most one.} \leftvitem{3.5cm}{expression()\index{expression}} \rightvitem{13cm}{The argument(s) of this condition is/are a list of expressions. In the case that the current term belongs to any of the given expressions the return value is 1. If it does not belong to any of the given expressions the return value is 0.} \leftvitem{3.5cm}{occurs()\index{expression}} \rightvitem{13cm}{The argument(s) of this condition is/are a list of variables. In the case that any of the variables occurs inside the current term (including inside function arguments) the return value is 1. Otherwise the return value is zero.} \leftvitem{3.5cm}{findloop()\index{findloop}} \rightvitem{13cm}{The arguments are as in the replaceloop\index{replaceloop} statement (see \ref{substareplaceloop}) with the exception of the outfun which should be omitted. If \FORM\ detects an index\index{index loop} loop in the current term that fulfils the specified conditions the return value is 1. It is 0 otherwise.} \leftvitem{3.5cm}{multipleof()\index{multipleof}} \rightvitem{13cm}{The argument should be a positive integer. This object is to be compared with a number (could be obtained from a condition) and if this number is an integer multiple of the argument there will be a match. If should be obvious that such a compare only makes sense for the == and != operators.} \leftvitem{3.5cm}{$<$integer$>$} \rightvitem{13cm}{To be compared either with another number, the result of a condition or a multipleof object.} \leftvitem{3.5cm}{coefficient\index{coefficient}} \rightvitem{13cm}{Represents the coefficient of the current term.} \leftvitem{3.5cm}{\$-variable} \rightvitem{13cm}{Will be evaluated at runtime when the if statement is encountered. Should evaluate into a numerical value. If it does not, an error will result.} \noindent All the above primary components result in numerical objects. Such objects can be compared to each other in structures of the type $<$obj1$>$ $<$operator$>$ $<$obj2$>$. The result of such a compare is either true (or 1) or false (or 0). The operators are: \leftvitem{2cm}{$>$} \rightvitem{14cm}{Results in true if object 1 is greater than object 2.} \leftvitem{2cm}{$<$} \rightvitem{14cm}{Results in true if object 1 is less than object 2.} \leftvitem{2cm}{$=$} \rightvitem{14cm}{Same as ==.} \leftvitem{2cm}{$==$} \rightvitem{14cm}{Results in true if both objects have the same value.} \leftvitem{2cm}{$>=$} \rightvitem{14cm}{Results in true if object 1 is greater than or equal to object 2.} \leftvitem{2cm}{$<=$} \rightvitem{14cm}{Results in true if object 1 is less than or equal to object 2.} \leftvitem{2cm}{$!=$} \rightvitem{14cm}{Results in true if object 1 does not have the same value as object 2.} If the condition for true is not met, false is returned. Several of the above compares can be combined with logical operators. For this it is necessary to enclose the above compares within parentheses. This forces \FORM\ to interpret the hierarchy\index{hierarchy} of the operators properly. The extra logical operators are \leftvitem{2cm}{$||$} \rightvitem{14cm}{The or operation. True if at least one of the objects 1 and 2 is true (or nonzero). False or zero if both are false or zero.} \leftvitem{2cm}{$\&\&$} \rightvitem{14cm}{The and operation. True if both the objects 1 and 2 are true (or nonzero). False or zero if at least one is false or zero.} \noindent Example: \begin{verbatim} if ( ( match(f(1,x)*g(?a)) && ( count(x,1,v+d,1) == 3 ) ) || ( expression(F1,F2) == 0 ) ); some statements endif; if ( ( ( match(f(1,x)*g(?a)) == 0 ) && ( count(x,1,v+d,1) == 3 ) ) || expression(F1,F2) ); some statements endif; \end{verbatim} We see that \verb:match(): is equivalent to \verb:( match() != 0 ): and something similar for \verb:expression():. This shorthand\index{shorthand} notation can make a program slightly more readable. {\bf Warning! } The if-statement knows only logical values as the result of operations. Hence the answer to anything that contains parenthesis (which counts as the evaluation of an expression) is either true (1) or false (0). Hence the object (5) evaluates to true. \vspace{10mm} %--#] if : %--#[ ifmatch : \section{ifmatch} \label{substaifmatch} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & ifmatch$-\!\!>$ {\tt<}label{\tt>} {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement\index{ifmatch} is identical to the ifmatch option of the id statement (see \ref{substaidentify}). Hence \begin{verbatim} ifmatch-> .... \end{verbatim} is just a shorthand notation for \begin{verbatim} id ifmatch-> .... \end{verbatim} \vspace{10mm} %--#] ifmatch : %--#[ ifnomatch : \section{ifnomatch} \label{substaifnomatch} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & ifnomatch$-\!\!>$ {\tt<}label{\tt>} {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement\index{ifnomatch} is identical to the ifnomatch option of the id statement (see \ref{substaidentify}). Hence \begin{verbatim} ifnomatch-> .... \end{verbatim} is just a shorthand notation for \begin{verbatim} id ifnomatch-> .... \end{verbatim} \vspace{10mm} %--#] ifnomatch : %--#[ index : \section{index, indices} \label{substaindex} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & i[ndex] {\tt<}list of indices to be declared{\tt>}; \\ & i[ndices] {\tt<}list of indices to be declared{\tt>}; \\ See also & dimension (\ref{substadimension}), fixindex (\ref{substafixindex}) \end{tabular} \vspace{4mm} \noindent Declares one or more indices\index{index}\index{indices}. In the declaration of an index one can specify its dimension\index{dimension}. This is done by appending one or two options to the name of the index to be declared:\vspace{4mm} \leftvitem{3.5cm}{name=dim} \rightvitem{13cm}{The dimension is either a nonnegative integer or a previously declared symbol. If the dimension is zero\index{zero!dimension} this means that no dimension is attached to the index. The consequence is that the index cannot be summed over and index contractions are not performed for this index. If no dimension is specified the default dimension will be assumed (see the dimension statement \ref{substadimension}).} \leftvitem{3.5cm}{name=dim:ext} \rightvitem{13cm}{The dimension is a symbol as above. Ext is an extra symbol which indicates the value of dim-4. This option is useful when traces over gamma matrices are considered (see \ref{substatrace} and \ref{substatracen}).} \vspace{10mm} %--#] index : %--#[ inexpression : \section{inexpression} \label{substainexpression} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & inexpression,name(s) of expression(s); \\ See also & endinexpression~(\ref{substaendinexpression}) \end{tabular} \vspace{4mm} \noindent The combination\index{inexpression} \begin{verbatim} InExpression,expr; Statements; EndInExpression; \end{verbatim} is a more readable version of the construction \begin{verbatim} if ( expression(expr) ); Statements; endif; \end{verbatim} \vspace{10mm} %--#] inexpression : %--#[ inparallel : \section{inparallel} \label{substainparallel} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & inparallel; \\ & inparallel {\tt<}list of expressions{\tt>}; \\ See also & NotInParallel (\ref{substanotinparallel}), ModuleOption (\ref{substamoduleoption}) \end{tabular} \vspace{4mm} \noindent This statement is only active in the context of \TFORM\index{TFORM} and \ParFORM\index{ParFORM}. It causes (small) expressions to be executed side by side. Normally the terms of expressions are distributed over the processors and the expressions are executed one by one. This isn't very efficient for small expressions because there is a certain amount of overhead. When there are many small expressions, this statement can cause each expression to be executed by its own processor. A consequence is that the expressions now can finish in a semi-random order and hence may end up in the output in a order that is different from when this statement isn't used. The proper order is restored in the first module that comes after and that doesn't use this option. One should be careful using this statement for big expressions, because in that case the sorting may need sort files and the output may temporarily need scratch files and the simultaneous use of many files can slow execution down significantly. \noindent In the case that no expressions are mentioned, all active expressions will be affected. When there is a list of expressions, only those mentioned will be affected, provided they are active. Several of these statements will work cumulatively. This statement doesn't affect expressions that are still to be defined inside the current module. If it is needed to affect such expressions inside the current module, one should use the InParallel option of the ModuleOption~\ref{substamoduleoption}\index{ModuleOption} statement. This statement works independently of the `On Parallel;'~\ref{substaon} and `Off Parallel;'~\ref{substaoff} statements. \vspace{10mm} %--#] inparallel : %--#[ inside : \section{inside} \label{substainside} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & inside {\tt<}list of \$-variables{\tt>}; \\ See also & endinside (\ref{substaendinside}) and the chapter on \$-variables (\ref{dollars}) \end{tabular} \vspace{4mm} \noindent works\index{inside} a bit like the argument\index{argument} statement (see \ref{substaargument}) but with \$-variables\index{\$-variable} instead of with functions. An inside statement should be paired with an endinside\index{endinside} statement (see \ref{substaendinside}) inside the same module. The statements in-between will then be executed on the contents of the \$-variables that are mentioned. One should pay some attention to the order of the action. The \$-variables are treated sequentially. Hence, after the first one has been treated its contents are substituted by the new value. Then the second one is treated. If it uses the contents of the first variable, it will use the new value. If the first variable uses the contents of the second variable it will use its old value. Redefining any of the listed \$-variables in the range of the `inside-environment' is very dangerous. It is not specified what \FORM\ will do. Most likely it will be unpleasant\index{unpleasant}. \vspace{10mm} %--#] inside : %--#[ insidefirst : \section{insidefirst} \label{substainsidefirst} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & insidefirst {\tt<}on/off{\tt>}; \\ See also & on (\ref{substaon}), off (\ref{substaoff}) \end{tabular} \vspace{4mm} \noindent This statement\index{insidefirst} is obsolete\index{obsolete}. The user should try to use the insidefirst option of the on (see \ref{substaon}) or the off (see \ref{substaoff}) statements. \vspace{10mm} %--#] insidefirst : %--#[ intohide : \section{intohide} \label{substaintohide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & intohide; \\ & intohide {\tt<}list of expressions{\tt>}; \\ See also & hide (\ref{substahide}) \end{tabular} \vspace{4mm} \noindent In the first variety this statement marks all currently active expressions for being put in hidden\index{hide} storage at the end of the module, after it has been processed. In the second variety it marks only the specified active\index{active expressions} expressions as such. \vspace{4mm} \noindent The difference with the hide (\ref{substahide}) statement is that in the hide statement the expression is copied immediately into the hide system and it will not be processed in the current module, while in the intohide statement the expression is first processed and its final output in this module is sent to the hide system rather than to the regular scratch system. The effect is the same as not putting the intohide statement in the current module and putting a hide statement in the next, but it saves one copy operation and it is possibly a bit more economical with the disk space. \vspace{4mm} \noindent Note that a .store instruction will simultaneously remove all expressions from the hide system. \vspace{10mm} %--#] intohide : %--#[ keep : \section{keep} \label{substakeep} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & keep brackets; \\ See also & bracket (\ref{substabracket}), antibracket (\ref{substaabrackets}) and the chapter on brackets (\ref{brackets}) \end{tabular} \vspace{4mm} \noindent The effect\index{keep brackets}\index{keep}\index{brackets!keep} of this statement is that during execution of the current module the contents of the brackets are not considered. The statements only act on the `outside' of the brackets. Only when the terms are considered finished and are ready for the sorting are they multiplied by the contents of the brackets. At times this can save much computer time as complicated pattern matching and multiplications of function arguments with large fractions have to be done only once, rather than for each complete term separately (assuming that each bracket contains a large number of terms). \noindent There can be some nasty side effects. Assume an expression like: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Keep_1) \begin{verbatim} F = f(i1,x)*(g(i1,y)+g(i1,z)); B f; .sort Keep Brackets; sum i1; \end{verbatim} the result will be \begin{verbatim} F = f(N1_?,x)*g(i1,y)+f(N1_?,x)*g(i1,z); \end{verbatim} because at the moment of summing over i1 \FORM\ is not looking inside the brackets and hence it never sees the second occurrence of i1. There are some beneficial applications of the keep statement in the `mincer'\index{mincer} package that comes with the \FORM\ distribution. In this package the most costly step was made faster by a significant factor (depending on the problem) due to the keep brackets statement. \vspace{10mm} %--#] keep : %--#[ label : \section{label} \label{substalabel} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & la[bel] {\tt<}name of label{\tt>}; \\ See also & goto (\ref{substagoto}) \end{tabular} \vspace{4mm} \noindent Places a label\index{label} at the current location. The name of the label can be any name or positive number. Control can be transferred to the position of the label by a goto\index{goto} statement (see \ref{substagoto}) or the ifmatch\index{ifmatch} option of an id statement (see \ref{substaidentify}). The only condition is that the goto statement and the label must be inside the same module. Once the module is terminated all existing labels are forgotten. This means that in a later module a label with the same name can be used again (this may not improve readability though but it is a good thing when third party libraries are used). \vspace{10mm} %--#] label : %--#[ lfactorized : \section{lfactorized} \label{substalfactorized} \noindent \begin{tabular}{ll} Type & Definition statement\\ Syntax & l[ocal]factorized {\tt<}name{\tt>} = {\tt<}expression{\tt>}; \\ See also & the chapter on polynomials~\ref{polynomials} and the factorize statement~\ref{substafactorize}. \end{tabular} \vspace{4mm} \noindent Used to define a local\index{local} expression in factorized notation and keep it that way. The factors are recognized by multiplication and division signs at lowest bracket level. For the rest the expression is treated as a regular local expression. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_LFactorized_1) \begin{verbatim} Symbols x,y,z; LocalFactorized F1 = 3*(x+y)*(y+z)*((x+z)*(2*x+1)); LocalFactorized F2 = 3*(x+y)*(y+z)+((x+z)*(2*x+1)); Print; .end F1 = ( 3 ) * ( y + x ) * ( z + y ) * ( z + x + 2*x*z + 2*x^2 ); F2 = ( z + 3*y*z + 3*y^2 + x + 5*x*z + 3*x*y + 2*x^2 ); \end{verbatim} \noindent As one can see in the second expression, the plus at ground level makes that there is only one factor. In the first expression the last factor is seen as a single factor and not two factor2 because of the extra parentheses. Only parentheses at ground level are used to recognize factors. If one needs those factors anyway, one should either leave away those parentheses or use an extra Factorize statement to have \FORM{} refactorize the expression. \vspace{10mm} %--#] lfactorized : %--#[ load : \section{load} \label{substaload} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & loa[d] {\tt<}filename{\tt>} [{\tt<}list of expressions{\tt>}]; \\ See also & save (\ref{substasave}), delete (\ref{substadelete}) \end{tabular} \vspace{4mm} \noindent Loads\index{load} a previously saved\index{saved file} file\index{file!saved} (see \ref{substasave}). If no expressions are specified all expressions in the file are put in the storage file\index{file!storage} and obtain the status of stored global expressions. If a list of expressions is specified all those expressions are loaded and possible other expressions are ignored. If a specified expression is not present, an error will result. If one does not know exactly what expressions are present in a file one could load the file without a list of expressions, because \FORM\ will list all expressions that it encountered. \vspace{10mm} %--#] load : %--#[ local : \section{local} \label{substalocal} \noindent \begin{tabular}{ll} Type & Definition statement\\ Syntax & l[ocal] {\tt<}name{\tt>} = {\tt<}expression{\tt>}; \\ & l[ocal] {\tt<}names of expressions{\tt>}; \\ See also & global (\ref{substaglobal}) \end{tabular} \vspace{4mm} \noindent Used to define a local\index{local} expression. A local expression is an expression that will be dropped\index{drop} when a .store\index{.store} instruction is encountered. If this is not what is intended one should use global\index{global} expressions (see \ref{substaglobal}). The statement can also be used to change the status of a global expression into that of a local expression. In that case there is no = sign and no right hand side. \vspace{10mm} %--#] local : %--#[ makeinteger : \section{makeinteger} \label{substamakeinteger} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & makeinteger [{\tt<}argument specifications{\tt>}] \\ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \verb:{:{\tt<}name of function/set{\tt>} [{\tt<}argument specifications{\tt>}]\verb:}:; \\ See also & normalize (\ref{substanormalize}) \end{tabular} \vspace{4mm} \noindent Normalizes\index{makeinteger} the indicated argument\index{argument} of the indicated functions(s) in such a way that all terms in this argument have integer coefficients\index{coefficients!integer} with a their greatest common divider being one. This still leaves the possibility that the first term of this argument may be negative. If this is not desired one can first normalize\index{normalize} the argument and then make its coefficients integer. The overall factor that is needed to make the coefficients like described is taken from the overall factor of the complete term. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_MakeInteger_1) \begin{verbatim} S a,b,c; CF f; L F = f(22/3*a+14/5*b+18/7*c); MakeInteger,f; Print +f; .end F = 2/105*f(135*c + 147*b + 385*a); \end{verbatim} \noindent Note that this feature can be used to make outputs look much more friendly. It can be used in combination with the AntiBracket\index{antibracket} statement (\ref{substaabrackets}) and the function dum\_\index{dum\_} (\ref{fundum}) to imitate a smart extra level of brackets and make outputs shorter. It is possible to introduce a scale factor when extracting the coefficient and multiplying it into the complete term. \leftvitem{4cm}{MakeInteger,$\wedge$,f;} \rightvitem{12cm}{The number n must be an integer (may be negative) and if the coefficient that is extracted is c the whole term is multiplied by the factor $c^n$.} \vspace{10mm} %--#] makeinteger : %--#[ many : \section{many} \label{substamany} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & many {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement\index{many} is identical to the many option of the id\index{id} statement (see \ref{substaidentify}). Hence \begin{verbatim} many .... \end{verbatim} is just a shorthand notation for \begin{verbatim} id many .... \end{verbatim} \vspace{10mm} %--#] many : %--#[ merge : % \section{merge} \label{substamerge} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & merge,functionname; \\ & merge,once,functionname; \\ See also & shuffle (\ref{substashuffle}) \end{tabular} \vspace{4mm} \noindent This statement is exactly the same as the shuffle\index{shuffle} statement (see \ref{substashuffle}). \vspace{10mm} % %--#] merge : %--#[ metric : \section{metric} \label{substametric} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & metric {\tt<}option{\tt>}; \end{tabular} \smallskip \noindent Remark: statement\index{metric} is inactive\index{inactive}. Should have no effect. \vspace{10mm} %--#] metric : %--#[ moduleoption : \section{moduleoption} \label{substamoduleoption} \noindent \begin{tabular}{ll} Type & Module control statement\\ Syntax & moduleoption {\tt<}option{\tt>}[,{\tt<}value{\tt>}]; \\ See also & polyfun (\ref{substapolyfun}), processbucketsize (\ref{substaprocessbucketsize}), dollar variables (\ref{pardollars}) \end{tabular} \vspace{4mm} \noindent Used\index{moduleoption} to set a mode for just the current module. It overrides the normal setting and will revert to this normal setting after this module. The settings are: \leftvitem{3.5cm}{parallel\index{moduleoption!parallel}} \rightvitem{13cm}{Allows parallel\index{parallel} execution of the current module if all other conditions are right. This is the default.} \leftvitem{3.5cm}{noparallel\index{moduleoption!noparallel}} \rightvitem{13cm}{Vetoes parallel\index{parallel} execution of the current module.} \leftvitem{3.5cm}{inparallel\index{moduleoption!inparallel}} \rightvitem{13cm}{This option is more or less equivalent to the InParallel~\ref{substainparallel} statement. The difference is that because this statement comes at the end of the module, its effects include also the expressions that have been defined inside the current module. This is not the case for the InParallel statement. The InParallel option can be followed by the names of expressions. If no such names are present, all active expressions are affected. Otherwise only the expressions that are mentioned are affected. Once this option is mentioned no more options can be used inside the same ModuleOption statement. This is to avoid potential confusion that could arise when expressions are used with a name identical to the name of one of the options.} \leftvitem{3.5cm}{notinparallel\index{moduleoption!notinparallel}} \rightvitem{13cm}{This option is more or less equivalent to the NotInParallel~\ref{substanotinparallel} statement. The difference is that because this statement comes at the end of the module, its effects include also the expressions that have been defined inside the current module. This is not the case for the NotInParallel statement. The NotInParallel option can be followed by the names of expressions. If no such names are present, all active expressions are affected. Otherwise only the expressions that are mentioned are affected. Once this option is mentioned no more options can be used inside the same ModuleOption statement. This is to avoid potential confusion that could arise when expressions are used with a name identical to the name of one of the options.} \leftvitem{3.5cm}{polyfun\index{moduleoption!polyfun}} \rightvitem{13cm}{Possibly followed by the name of a `polyfun'\index{polyfun}. Is similar to the polyfun statement (see \ref{substapolyfun}) but only valid for the current module.} \leftvitem{3.5cm}{polyratfun\index{moduleoption!polyfun}} \rightvitem{13cm}{Possibly followed by the name of a `polyratfun'\index{polyratfun}. Is similar to the polyfun statement (see \ref{substapolyratfun}) but only valid for the current module. If there is second name, it refers to the inverse polyratfun. More complicated options of the polyratfun statement cannot be used here.} \leftvitem{3.5cm}{processbucketsize\index{moduleoption!processbucketsize}} \rightvitem{13cm}{Followed by a number. Similar to the processbucketsize\index{processbucketsize} statement (see \ref{substaprocessbucketsize}) but only valid for the current module.} \leftvitem{3.5cm}{local\index{moduleoption!local}} \rightvitem{13cm}{Should be followed by a list of \$-variables. Indicates that the contents of the indicated \$-variables\index{\$-variable} are not relevant once the module has been finished, and neither is the term by term order in which the \$-variables obtain their value. In practice each processor\index{processor}/thread\index{thread} will work with its own copy of this variable.} \leftvitem{3.5cm}{maximum\index{moduleoption!maximum}} \rightvitem{13cm}{Should be followed by a list of \$-variables\index{\$-variable}. Indicates that only the maximum value of the \$-variables is relevant once the module has finished. The term-by-term order in which the \$-variables obtain their value is not relevant. In practice each processor\index{processor}/thread \index{thread} will work with its own copy of the variable, and the maximal value is kept at the end of term processing. The variables should contain numbers only.} \leftvitem{3.5cm}{minimum\index{moduleoption!minimum}} \rightvitem{13cm}{Should be followed by a list of \$-variables\index{\$-variable}. Indicates that only the minimum value of the \$-variables is relevant once the module has finished. The term-by-term order in which the \$-variables obtain their value is not relevant. In practice each processor\index{processor}/thread \index{thread} will work with its own copy of the variable, and the minimal value is kept at the end of term processing. The variables should contain numbers only.} \leftvitem{3.5cm}{sum\index{moduleoption!sum}} \rightvitem{13cm}{Should be followed by a list of \$-variables\index{\$-variable}. Indicates that the specified \$-variables represent a sum. The term-by-term order in which the \$-variables obtain their value is not relevant. In practice, this is a global dollar variable for which all parallel read and write accesses are protected by locks. The variables should contain numbers only.} \noindent The options `local', `maximum', `minimum' and `sum' are for parallel versions of \FORM\@. The presence of \$-variables can be a problem when the order of processing of the terms is not well defined. These options tell \FORM\ what these \$-variables are used for. In the above cases \FORM\ can take the appropriate action when gathering information from the various processors. This will allow parallel\index{parallel execution} execution of the current module. If \$-variables are used in a module and they are defined on a term by term basis, the normal action of \FORM\ will be to veto parallel execution unless it is clear that no confusion can occur. See also chapter \ref{parallel} on the parallel version and section \ref{pardollars} on the dollar variables.\vspace{10mm} %--#] moduleoption : %--#[ modulus : \section{modulus} \label{substamodulus} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & m[odulus] [option(s)] {\tt<}value{\tt>}; \end{tabular} \vspace{4mm} \noindent Defines all calculus to be modulus\index{modulus} the given integer value, provided this number is positive. % If this number is less than the %(installation dependent but at least 10000) maximum power for symbols and %dotproducts the powers of symbols and dotproducts are reduced with the %relation $x^{value} = x$. \noindent The modulus calculus extends itself to fractions\index{fractions}. This means that if the value is not a prime number division by zero could result. It is the responsibility of the user to avoid such problems. \noindent When the value in the modulus statement is either 0 or 1 the statement would be meaningless. It is used as a signal to \FORM\ that modulus calculus should be switched off again. The options are \begin{description} \item[NoFunctions] Modulus calculus is not performed inside function arguments. \item[AlsoFunctions] Modulus calculus is also performed inside function arguments. \item[CoefficientsOnly] Modulus calculus is neither performed inside function arguments nor on powers of symbols. \item[PlusMin] The values of numbers are reduced to the range $(-value+1)/2$ to $(value-1)/2$. \item[Positive] The values of numbers are reduced to the range $0$ to $value-1$. \item[NoDollars] The modulus calculus is not performed inside dollar variables. \item[AlsoDollars] The modulus calculus is performed also inside dollar expressions. \item[InverseTable] To speed up calculations all inverses are computed by means of a table. If the modulus value is very big, this table may be too big for the memory. That would result in an error message. \item[NoInverseTable] No Table of Inverses is constructed. They are calculated whenever needed. \item[AlsoPowers] Reduction is also used on powers of symbols with the relation $x^mod = x$ if mod is the given value \item[NoPowers] No reduction on powers is done. \item[PrintPowersOf] The proper syntax is here printpowersof(generator) in which generator is supposed to be a generator for calculus modulus the given value, which means that all numbers will be written as a power of the generator. If the number turns out not to be a proper generator an error will be given. Note that finding the powers is done by means of the construction of a table. Hence, if the modulus value is very big the table might not fit inside memory. This will result in an error message. \end{description} The default mode is NoFunctions, Positive, NoInverseTable, NoDollars, NoPowers. The current syntax (version 4.0 and later) differs slightly from the previous syntax. As however there were many bugs in the old implementation we suspect that a slight change of the options does not inconvenience any many users. %--#] modulus : %--#[ multi : \section{multi} \label{substamulti} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & multi {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement is identical to the multi\index{multi} option of the id\index{id} statement (see \ref{substaidentify}). Hence \begin{verbatim} multi .... \end{verbatim} is just a shorthand notation for \begin{verbatim} id multi .... \end{verbatim} \vspace{10mm} %--#] multi : %--#[ multibracket : ???????????? % %\section{multibracket} %\label{substamultibracket} % %\noindent \begin{tabular}{ll} %Type & Output control statement\\ %Syntax & multibracket ?????????????? %\\ See also & bracket (\ref{substabracket}) %\end{tabular} \vspace{4mm} % %\vspace{10mm} % %--#] multibracket : %--#[ multiply : \section{multiply} \label{substamultiply} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & mu[ltiply] [{\tt<}option{\tt>}] {\tt<}expression{\tt>}; \end{tabular} \vspace{4mm} \noindent Statement multiplies\index{multiply} all terms by the given expression. It is advisable to use the options when noncommuting variables are involved. They are:\vspace{1mm} \lefttabitem{left\index{multiply!left}} \tabitem{Multiplication is from the left.} \lefttabitem{right\index{multiply!right}} \tabitem{Multiplication is from the right.} \noindent There is no guarantee\index{guarantee} as to what the default is with respect to multiplication from the left or from the right. It is up to {\FORM} to decide what it considers to be most efficient when neither option is present. \vspace{4mm} \noindent Note that one should not abbreviate this command to `multi', because there is a separate multi\index{multi} command (see \ref{substamulti}). \vspace{10mm} %--#] multiply : %--#[ ndrop : \section{ndrop} \label{substandrop} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & ndrop; \\ & ndrop {\tt<}list of expressions{\tt>}; \\ See also & drop (\ref{substadrop}) \end{tabular} \vspace{4mm} In the first variety\index{ndrop} this statement cancels all drop\index{drop} plans. This means that all expressions scheduled for being dropped will be restored to their previous status of local or global expressions. In the second variety this happens only to the expressions that are specified. Example: \begin{verbatim} Drop; Ndrop F1,F2; \end{verbatim} This drops all expressions, except for the expressions \verb:F1: and \verb:F2:. \vspace{10mm} %--#] ndrop : %--#[ nfactorize : \section{nfactorize} \label{substanfactorize} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & nfactorize \verb:{:{\tt<}name of expression(s){\tt>}\verb:}:; \\ See also & the chapter on polynomials~\ref{polynomials} and \ref{substafactorize}. \end{tabular} \vspace{4mm} \noindent When one uses a factorize (see \ref{substafactorize}) statement without arguments all expressions will be marked for factorization. If one would like to exclude a few expressions this can be done with the NFactorize statement. There should be at least one expression mentioned as in: \begin{verbatim} Factorize; NFactorize expr12,expr29; \end{verbatim} One can also use the Factorize statement with a number of expressions after which the NFactorize statement can remove some from the list again as in: \begin{verbatim} Factorize expr1,...,expr100; NFactorize expr12,expr29; \end{verbatim} \vspace{10mm} %--#] nfactorize : %--#[ nfunctions : \section{nfunctions} \label{substanfunctions} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & n[functions] {\tt<}list of functions to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}), cfunctions (\ref{substacfunctions}) \end{tabular} \vspace{4mm} \noindent This statement\index{nfunction} declares noncommuting\index{noncommuting} functions. It is equal to the function\index{function} statement (see \ref{substafunctions}) which has the noncommuting property as its default. \vspace{10mm} %--#] nfunctions : %--#[ nhide : \section{nhide} \label{substanhide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & nhide; \\ & nhide {\tt<}list of expressions{\tt>}; \\ See also & hide (\ref{substahide}), unhide (\ref{substaunhide}), nunhide (\ref{substanunhide}), pushhide (\ref{substapushhide}), pophide (\ref{substapophide}) \end{tabular} \vspace{4mm} \noindent In its first variety\index{nhide} this statement undoes all hide\index{hide} plans that exist thus far in the current module. In the second variety it does this only for the specified active\index{active} expressions. See the hide statement in \ref{substahide}. Example: \begin{verbatim} Hide; Nhide F1,F2; \end{verbatim} Here all active expressions will be transferred to the hide file except for the expressions \verb:F1: and \verb:F2:. \vspace{10mm} %--#] nhide : %--#[ nintohide : \section{nintohide} \label{substanintohide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & nintohide; \\ & nintohide {\tt<}list of expressions{\tt>}; \\ See also & hide (\ref{substahide}), unhide (\ref{substaunhide}), nunhide (\ref{substanunhide}), pushhide (\ref{substapushhide}), pophide (\ref{substapophide}), intohide (\ref{substaintohide}) \end{tabular} \vspace{4mm} \noindent In its first variety\index{nintohide} this statement undoes all intohide\index{intohide} plans that exist thus far in the current module. In the second variety it does this only for the specified active\index{active} expressions. See the intohide statement in \ref{substaintohide}. Example: \begin{verbatim} Intohide; Nintohide F1,F2; \end{verbatim} Here all active expressions will be transferred to the hide file at the end of the current module, except for the expressions \verb:F1: and \verb:F2:. \vspace{10mm} %--#] nhide : %--#[ normalize : \section{normalize} \label{substanormalize} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & normalize options \verb:{:{\tt<}name of function/set{\tt>} [{\tt<}argument specifications{\tt>}]\verb:}:; \\ See also & argument (\ref{substaargument}), splitarg (\ref{substasplitarg}), makeinteger (\ref{substamakeinteger}) \end{tabular} \vspace{4mm} \noindent Normalizes\index{normalize} the indicated arguments\index{argument} of the indicated functions. Normalization means that the argument will be multiplied by the inverse of its coefficient\index{coefficient} (provided it is not zero). This holds for single term arguments. For multiple term arguments the inverse of the coefficient of the first term of the argument is used. The options and the argument specifications are as in the SplitArg\index{splitarg} statement (see \ref{substasplitarg}). Under normal circumstances the coefficient that is removed from the argument(s) is multiplied into the coefficient of the term. This can be avoid with the extra option \verb:(0):. Hence \leftvitem{4cm}{Normalize,f;} \rightvitem{12cm}{changes {\tt f(2*x+3*y)} into {\tt 2*f(x+3/2*y)} but} \leftvitem{4cm}{Normalize,(0),f;} \rightvitem{12cm}{changes {\tt f(2*x+3*y)} into {\tt f(x+3/2*y)}.} A more flexible way to extract the coefficient of the (first) term is by providing a scale factor as in \leftvitem{4cm}{Normalize,$\wedge$,f;} \rightvitem{12cm}{The number n must be an integer (may be negative) and if the coefficient of the first term was c the whole term is multiplied by the factor $c^n$.} \vspace{10mm} %--#] normalize : %--#[ notinparallel : \section{notinparallel} \label{substanotinparallel} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & notinparallel; \\ & notinparallel {\tt<}list of expressions{\tt>}; \\ See also & InParallel (\ref{substainparallel}), ModuleOption (\ref{substamoduleoption}) \end{tabular} \vspace{4mm} \noindent This statement is only active in the context of \TFORM\index{TFORM} and \ParFORM\index{ParFORM}. It vetoes (small) expressions to be executed side by side. For a complete explanation of this type of running one should look at the InParallel~\ref{substainparallel} statement. Because the default is that expressions are executed one by one, the major use of this statement is in constructions like: \begin{verbatim} InParallel; NotInParallel F1,F25; \end{verbatim} which would first mark all expressions to be executed in simultaneous mode and then make an exception for {\tt F1} and {\tt F25}. \vspace{10mm} %--#] notinparallel : %--#[ nprint : \section{nprint} \label{substanprint} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & np[rint] {\tt<}list of names of expressions{\tt>}; \\ See also & print (\ref{substaprint}) \end{tabular} \vspace{4mm} \noindent Statement\index{nprint} is used to take expressions from the list of expressions to be printed. When a print\index{print} statement is used (see \ref{substaprint}) without specification of expressions, all active expressions are marked for printing. With this statement one can remove a number of them from the list. \vspace{10mm} %--#] nprint : %--#[ nskip : \section{nskip} \label{substanskip} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & nskip; \\ & nskip {\tt<}list of expressions{\tt>}; \\ See also & skip (\ref{substaskip}) \end{tabular} \vspace{4mm} \noindent In the first variety\index{nskip} it causes the cancellation of all skip\index{skip} plans (see \ref{substaskip}) for expressions. The status of these expressions is restored to their previous status (active local or global expressions). In the second variety this is done for the specified expressions only. Example: \begin{verbatim} Skip; Nskip F1,F2; \end{verbatim} This causes all active expressions to be skipped except for the expressions \verb:F1: and \verb:F2:. \vspace{10mm} %--#] nskip : %--#[ ntable : \section{ntable} \label{substantable} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & ntable {\tt<}options{\tt>} {\tt<}table to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}), table (\ref{substatable}), ctable (\ref{substactable}) \end{tabular} \vspace{4mm} \noindent This statement\index{ntable} declares a noncommuting\index{noncommuting} table\index{table!noncommuting}. For the rest it is identical to the table\index{table} command (see \ref{substatable}) which has the commuting property as its default. \vspace{10mm} %--#] ntable : %--#[ ntensors : \section{ntensors} \label{substantensors} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & nt[ensors] {\tt<}list of tensors to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}), tensors (\ref{substatensors}), ctensors (\ref{substactensors}) \end{tabular} \vspace{4mm} \noindent This statement\index{ntensor} declares noncommuting\index{noncommuting} tensors\index{tensor!noncommuting}. Note that it is not equivalent to the tensors statement (see \ref{substatensors}) which has the commuting property as its default. \noindent The options that exist for properties of tensors are the same as those for functions (see \ref{substafunctions}). \vspace{10mm} %--#] ntensors : %--#[ nunfactorize : \section{nunfactorize} \label{substanunfactorize} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & nunfactorize \verb:{:{\tt<}name of expression(s){\tt>}\verb:}:; \\ See also & the chapter on polynomials~\ref{polynomials} and \ref{substaunfactorize}. \end{tabular} \vspace{4mm} \noindent When one uses an UnFactorize (see \ref{substaunfactorize}) statement without arguments all expressions will be marked for unfactorization. If one would like to exclude a few expressions this can be done with the NUnFactorize statement. There should be at least one expression specified, as in: \begin{verbatim} UnFactorize; NUnFactorize expr12,expr29; \end{verbatim} One can also use the UnFactorize statement with a number of expressions after which the NUnFactorize statement can remove some from the list again, as in: \begin{verbatim} UnFactorize expr1,...,expr100; NUnFactorize expr12,expr29; \end{verbatim} \vspace{10mm} %--#] nunfactorize : %--#[ nunhide : \section{nunhide} \label{substanunhide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & nunhide; \\ & nunhide {\tt<}list of expressions{\tt>}; \\ See also & hide (\ref{substahide}), nhide (\ref{substanhide}), unhide (\ref{substaunhide}), pushhide (\ref{substapushhide}), pophide (\ref{substapophide}) \end{tabular} \vspace{4mm} \noindent In its first variety\index{nunhide} this statement undoes all unhide\index{unhide} (see \ref{substaunhide} and \ref{substahide}) plans that the system has in the current module. In its second variety this happens only with the specified expressions. Example: \begin{verbatim} Unhide; Nunhide F1,F2; \end{verbatim} All expressions are taken from the hide\index{hide} system, except for the expressions \verb:F1: and \verb:F2:. \vspace{10mm} %--#] nunhide : %--#[ nwrite : \section{nwrite} \label{substanwrite} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & nw[rite] {\tt<}keyword{\tt>}; \\ See also & on (\ref{substaon}), off (\ref{substaoff}) \end{tabular} \vspace{4mm} \noindent This statement\index{nwrite} is considered obsolete\index{obsolete}. All its varieties have been taken over by the off\index{off} statement (see \ref{substaoff}) and the on\index{on} statement (see \ref{substaon}). The current version of {\FORM} will still recognize it, but the user is advised to avoid its usage. In future versions of {\FORM} it is scheduled to be used for a different kind of writing and hence its syntax may change considerably. The conversion program conv2to3\index{conv2to3} should help in the conversion of programs that have been written for version 2. For completeness we still give the syntax and how it should be converted. The keywords are: \vspace{4mm} \leftvitem{3.5cm}{stats\index{nwrite!stats}} \rightvitem{13cm}{Same as: Off stats;} \leftvitem{3.5cm}{statistics\index{nwrite!statistics}} \rightvitem{13cm}{Same as: Off statistics;} \leftvitem{3.5cm}{shortstats\index{nwrite!shortstats}} \rightvitem{13cm}{Same as: Off shortstats;} \leftvitem{3.5cm}{shortstatistics\index{nwrite!shortstatistics}} \rightvitem{13cm}{Same as: Off shortstatistics;} \leftvitem{3.5cm}{warnings\index{nwrite!warnings}} \rightvitem{13cm}{Same as: Off warnings;} \leftvitem{3.5cm}{allwarnings\index{nwrite!allwarnings}} \rightvitem{13cm}{Same as: Off allwarnings;} \leftvitem{3.5cm}{setup\index{nwrite!setup}} \rightvitem{13cm}{Same as: Off setup;} \leftvitem{3.5cm}{names\index{nwrite!names}} \rightvitem{13cm}{Same as: Off names;} \leftvitem{3.5cm}{allnames\index{nwrite!allnames}} \rightvitem{13cm}{Same as: Off allnames;} \leftvitem{3.5cm}{shortstats\index{nwrite!shortstats}} \rightvitem{13cm}{Same as: Off shortstats;} \leftvitem{3.5cm}{highfirst\index{nwrite!highfirst}} \rightvitem{13cm}{Same as: Off highfirst;} \leftvitem{3.5cm}{lowfirst\index{nwrite!lowfirst}} \rightvitem{13cm}{Same as: Off lowfirst;} \leftvitem{3.5cm}{powerfirst\index{nwrite!powerfirst}} \rightvitem{13cm}{Same as: Off powerfirst;} \vspace{10mm} %--#] nwrite : %--#[ off : \section{off} \label{substaoff} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & off {\tt<}keyword{\tt>}; \\ & off {\tt<}keyword{\tt>} {\tt<}option{\tt>}; \\ See also & on (\ref{substaon}) \end{tabular} \vspace{4mm} \noindent Statement\index{off} to control settings\index{settings} during execution. Many of these settings replace older statements. The settings and their keywords are: \leftvitem{3.5cm}{allnames\index{off!allnames}} \rightvitem{13cm}{Turns the allnames mode off. The default.} \leftvitem{3.5cm}{allwarnings\index{off!allwarnings}} \rightvitem{13cm}{Turns off the printing of all warnings.} \leftvitem{3.5cm}{backtrace\index{off!backtrace}} \rightvitem{13cm}{Disables the printing of a stack trace on termination. This is the default for normal form builds.} \leftvitem{3.5cm}{checkpoint\index{off!checkpoint}} \rightvitem{13cm}{Deactivates the checkpoint mechanism. See \ref{checkpoints}.} \leftvitem{3.5cm}{compress\index{off!compress}} \rightvitem{13cm}{Turns compression mode off.} \leftvitem{3.5cm}{finalstats\index{off!finalstats}} \rightvitem{13cm}{Turns off the last line of statistics that is normally printed at the end of the run (introduced in version 3.2).} \leftvitem{3.5cm}{flint\index{off!flint}} \rightvitem{13cm}{Disables the interface to FLINT; use FORM's built-in polynomial routines.} \leftvitem{3.5cm}{grccverbose\index{off!grccverbose}} \rightvitem{13cm}{Disables extra print statements from the diagram generator. This is the default.} \leftvitem{3.5cm}{highfirst\index{off!highfirst}} \rightvitem{13cm}{Puts the sorting in a low first mode.} \leftvitem{3.5cm}{humanstatistics\index{off!humanstats}} \rightvitem{13cm}{Disables the printing of human-readable numbers and units in the statistics. This is the default.} \leftvitem{3.5cm}{humanstats\index{off!humanstats}} \rightvitem{13cm}{Same as `Off humanstatistics;'} \leftvitem{3.5cm}{insidefirst\index{off!insidefirst}} \rightvitem{13cm}{Not active at the moment.} \leftvitem{3.5cm}{lowfirst\index{off!lowfirst}} \rightvitem{13cm}{Leaves the default low first mode and puts the sorting in a high first mode.} \leftvitem{3.5cm}{names\index{off!names}} \rightvitem{13cm}{Turns the names mode off. This is the default.} \leftvitem{3.5cm}{nospacesinnumbers\index{off!nospacesinnumbers}} \rightvitem{13cm}{\label{staoffnospacesinnumbers}\vspace{1ex}Allows very long numbers to be printed with leading blank spaces at the beginning of a new line. The numbers are usually broken up by placing a backslash character at the end of the line and then continuing at the next line. For cosmetic purposes \FORM\ puts usually a few blank spaces at the beginning of the line. \FORM\ itself can read this but some programs cannot. This option can be turned off by the `on nospacesinnumbers;' statement. The printing of the blank characters can be restored by turning this variable off. See also page \ref{nospacesinnumbers} for a corresponding variable in the setup file.} \leftvitem{3.5cm}{oldfactarg\index{off!oldfactarg}} \rightvitem{13cm}{\label{staoffoldfactarg}Switches the use of the FactArg statement~\ref{substafactarg}\index{factarg} to the new mode of version 4 or later in which expressions in the argument of the mentioned function are completely factored over the rationals. The default is off.} \leftvitem{3.5cm}{oldprfsign\index{off!oldprfsign}} \rightvitem{13cm}{\label{staoffoldprfsign} See \ref{staonoldprfsign}.} \leftvitem{3.5cm}{parallel\index{off!parallel}} \rightvitem{13cm}{Disallows the running of the program in parallel mode (only relevant for parallel versions of \FORM).} \leftvitem{3.5cm}{powerfirst\index{off!powerfirst}} \rightvitem{13cm}{Puts the sorting back into `highfirst' mode.} \leftvitem{3.5cm}{processstats\index{off!processstats}} \rightvitem{13cm}{Turns the process by process printing of the statistics in \ParFORM{} off. Only the master process will be printing statistics. Other versions of \FORM{} will ignore this option.} \leftvitem{3.5cm}{propercount\index{off!propercount}} \rightvitem{13cm}{Turns the propercounting mode off. This means that for the generated terms in the statistics not only the `ground level' terms are counted but also terms that were generated inside function arguments.} \leftvitem{3.5cm}{properorder\index{off!properorder}} \rightvitem{13cm}{Turns the properorder mode off. This is the default.} \leftvitem{3.5cm}{setup\index{off!setup}} \rightvitem{13cm}{Switches off the mode in which the setup parameters are printed. This is the default.} \leftvitem{3.5cm}{stats\index{off!stats}} \rightvitem{13cm}{Same as `Off statistics'.} \leftvitem{3.5cm}{statistics\index{off!statistics}} \rightvitem{13cm}{Turns off the printing of statistics.} \leftvitem{3.5cm}{shortstats\index{off!shortstats}} \rightvitem{13cm}{Same as `Off shortstatistics'.} \leftvitem{3.5cm}{shortstatistics\index{off!shortstatistics}} \rightvitem{13cm}{Takes the writing of the statistics back from shorthand mode to the regular statistics mode in which each statistics messages takes three lines of text and one blank line.} \leftvitem{3.5cm}{sortreallocate\index{off!sortreallocate}} \rightvitem{13cm}{Turns off the reallocation of the small and large buffer at the end of each module.} \leftvitem{3.5cm}{sortverbose\index{off!sortverbose}} \rightvitem{13cm}{Turns off the printing of additional information in the sorting statistics.} \leftvitem{3.5cm}{threadloadbalancing\index{off!threadloadbalancing}} \rightvitem{13cm}{\vspace{1.5ex}Disables the loadbalancing mechanism of \TFORM\ in parallel mode. In other versions of \FORM\ this option is ignored.} \leftvitem{3.5cm}{threads\index{off!threads}} \rightvitem{13cm}{Disallows multithreaded running in \TFORM\@. In other versions of \FORM\ this option is ignored.} \leftvitem{3.5cm}{threadstats\index{off!threadstats}} \rightvitem{13cm}{Turns off the thread by thread printing of the statistics in \TFORM\@. Only the master thread will be printing statistics. Other versions of \FORM\ will ignore this option.} \leftvitem{3.5cm}{totalsize\index{off!totalsize}} \rightvitem{13cm}{Switches the totalsize mode off. For a more detailed description of the totalsize mode, see the "On TotalSize;" command~\ref{ontotalsize}.} \leftvitem{3.5cm}{warnings\index{off!warnings}} \rightvitem{13cm}{Turns off the printing of warnings.} \leftvitem{3.5cm}{wtimestats\index{off!wtimestats}} \rightvitem{13cm}{Disables the wall-clock time in the timing information in the statistics on the master.} \noindent If a description is too short, one should also consult the description in the on statement (see \ref{substaon}). \vspace{10mm} %--#] off : %--#[ on : \section{on} \label{substaon} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & on {\tt<}keyword{\tt>}; \\ & on {\tt<}keyword{\tt>} {\tt<}option{\tt>}; \\ See also & off (\ref{substaoff}) \end{tabular} \vspace{4mm} \noindent New statement to control settings during execution. Many of these settings replace older statements. The settings and their keywords are: \leftvitem{3.5cm}{allnames\index{on!allnames}} \rightvitem{13cm}{Same as `On names' but additionally all system variables are printed as well. Default is off. } \leftvitem{3.5cm}{allwarnings\index{on!allwarnings}} \rightvitem{13cm}{Puts the printing of warnings in a mode in which all warnings, even the very unimportant warnings are printed.} \leftvitem{3.5cm}{backtrace\index{on!backtrace}} \rightvitem{13cm}{Attempt to print a stack trace on termination, to assist with debugging. This is off by default for normal form builds and on by default for the debug binaries (vorm, tvorm, parvorm). For best results eu-addr2line or addr2line should be installed on the system.} \leftvitem{3.5cm}{checkpoint\index{on!checkpoint}} \rightvitem{13cm}{Activates the checkpoint mechanism that allows for the recovery of a crashed \FORM\ session. See \ref{checkpoints} for detailed information.} \leftvitem{3.5cm}{compress\index{on!compress}} \rightvitem{13cm}{Turns compression mode on. This compression is a relatively simple compression that hardly costs extra computer time but saves roughly a factor two in disk storage. The old statement was `compress on' but this should be avoided in the future. This setting is the default if \FORM\ has not been compiled with gzip or zstd support.} \leftvitem{3.5cm}{compress,gzip\index{gzip}} \rightvitem{13cm}{This setting is the default, if \FORM\ has been compiled with gzip support but not with zstd support. This option may be followed by a comma or a space and a single digit. It activates the gzip compression for the sort file. This compression can make the intermediate sort file considerably shorter at the cost of some CPU time. The digit indicates the compression level. Zero means no compression and 9 is the highest level. The default level is 6. Above that the compression becomes very slow and doesn't gain very much extra.} \leftvitem{3.5cm}{compress,zstd\index{zstd}} \rightvitem{13cm}{This setting is the default, if \FORM\ has been compiled with zstd support. This option may be followed by a comma or a space and a single digit. It activates the zstd compression for the sort file. This compression performs better than gzip, both in terms of compression/ decompression rates and compression ratio. The digit indicates the compression level. Zero means no compression and 9 is the highest level. The default level is 6. Above that the compression becomes very slow and doesn't gain very much extra.} \leftvitem{3.5cm}{fewerstatistics\index{on!fewerstatistics}} \rightvitem{13cm}{Determines how many of the statistics \FORM\ prints when a small buffer is full. The keyword can be followed by a positive integer in which case one out of that many of these statistics will be printed. If no number is given the default value of 10 is used. When the number that follows is zero, statistics are never printed when sorting the small buffer.} \leftvitem{3.5cm}{fewerstats\index{on!fewerstats}} \rightvitem{13cm}{Same as the above fewerstatistics.} \leftvitem{3.5cm}{finalstats\index{on!finalstats}} \rightvitem{13cm}{Determines whether \FORM\ prints a final line of run time statistics at the end of the run. Default is on.} \leftvitem{3.5cm}{flint\index{on!flint}} \rightvitem{13cm}{Enables the interface to FLINT for polynomial operations. This is the default if \FORM\ has been compiled with FLINT support. Currently this supports PolyRatFun\index{polyratfun} (\ref{substapolyratfun}), FactArg\index{factarg} (\ref{substafactarg}), FactDollar\index{factdollar}\index{prefactdollar} (\ref{prefactdollar}, \ref{substafactdollar}), div\_\index{div\_}\index{function!div\_} (\ref{fundiv}), rem\_\index{rem\_}\index{function!rem\_} (\ref{funrem}), mul\_\index{mul\_}\index{function!mul\_} (\ref{funmul}), gcd\_\index{gcd\_}\index{function!gcd\_} (\ref{fungcd}), and inverse\_\index{inverse\_}\index{function!inverse\_} (\ref{funinverse}). \FORM\ still uses its built-in routines for Factorize\index{factorize} (\ref{substafactorize}) and when using Modulus\index{modulus} (\ref{substamodulus}) mode. Note that occasionally the overall sign of gcd\_ may differ from that of the built-in routine.} \leftvitem{3.5cm}{grccverbose\index{on!grccverbose}} \rightvitem{13cm}{Enable extra print statements from the diagram generator. Useful for debugging error messages. Default is off.} \leftvitem{3.5cm}{highfirst\index{on!highfirst}} \rightvitem{13cm}{In this mode polynomials are sorted in a way that high powers come before low powers.} \leftvitem{3.5cm}{humanstatistics\index{on!humanstats}} \rightvitem{13cm}{If enabled, human-readable numbers and units are included in the statistics printing. Disabled by default.} \leftvitem{3.5cm}{humanstats\index{on!humanstats}} \rightvitem{13cm}{Same as the above humanstatistics.} %\leftvitem{3.5cm}{indentspace\index{on!indentspace}} %\rightvitem{13cm}{Not active at the moment.} \leftvitem{3.5cm}{insidefirst\index{on!insidefirst}} \rightvitem{13cm}{Not active at the moment.} \leftvitem{3.5cm}{lowfirst\index{on!lowfirst}} \rightvitem{13cm}{In this mode polynomials are sorted in a way that low powers come before high powers. This is the default.} \leftvitem{3.5cm}{names\index{on!names}} \rightvitem{13cm}{Turns on the mode in which at the end of each module the names of all variables that have been defined by the user are printed. This is an inspection mode for debugging by the user. Default is off.} \leftvitem{3.5cm}{nospacesinnumbers\index{on!nospacesinnumbers}} \rightvitem{13cm}{\label{staonnospacesinnumbers}\vspace{1ex}Makes that very long numbers are printed with no leading blank spaces at the beginning of a new line. The numbers are usually broken up by placing a backspace character at the end of the line and then continuing at the next line. For cosmetic purposes \FORM\ puts usually a few blank spaces at the beginning of the line. \FORM\ itself can read this but some programs cannot. Hence this printing of the blank characters can be omitted by turning this variable on. See also page \ref{nospacesinnumbers} for a corresponding variable in the setup file.} \leftvitem{3.5cm}{oldfactarg\index{on!oldfactarg}} \rightvitem{13cm}{\label{staonoldfactarg}Switches the use of the FactArg statement~\ref{substafactarg}\index{factarg} to the old mode from before version 4. This is a compatibility mode to allow oldprograms that rely on a specific working of the FactArg statement to still run. The default is off.} \leftvitem{3.5cm}{oldprfsign\index{on!oldprfsign}} \rightvitem{13cm}{\label{staonoldprfsign} Forces the numerator/denominator sign convention of PolyRatFun~\ref{substapolyratfun} of \FORM\ versions prior to 5.1, when using FLINT for polynomial arithmetic. Enabling this leads to a loss of performance in multivariate cases.} \leftvitem{3.5cm}{parallel\index{on!parallel}} \rightvitem{13cm}{Allows the running of the program in parallel mode unless other problems prevent this. This is of course only relevant for parallel versions of \FORM\@. The default is on.} \leftvitem{3.5cm}{powerfirst\index{on!powerfirst}} \rightvitem{13cm}{In this mode polynomials are sorted in a way that high powers come before low powers. The most relevant is however the combined power of all symbols.} \leftvitem{3.5cm}{processstats\index{on!processstats}} \rightvitem{13cm}{Only active for \ParFORM{}. It determines whether all processes print their run time statistics or only the master process does so. Default is on.} \leftvitem{3.5cm}{propercount\index{on!propercount}} \rightvitem{13cm}{Sets the counting of the terms during generation into `propercount' mode. This means that only terms at the `ground level' are counted and terms inside functions arguments are not counted in the statistics. This setting is the default.} \leftvitem{3.5cm}{properorder\index{on!properorder}} \rightvitem{13cm}{Turns the properorder mode on. The default is off. In the properorder mode \FORM\ pays particular attention to function arguments when bringing terms and expressions to normal form. This may cost a considerable amount of extra time. In normal mode \FORM\ is a bit sloppy (and much faster) about this, resulting sometimes in an ordering that appears without logic. This concerns only function arguments! This mode is mainly intended for the few moments in which the proper ordering is important.} \leftvitem{3.5cm}{setup\index{on!setup}} \rightvitem{13cm}{Causes the printing of the current setup parameters for inspection. Default is off.} \leftvitem{3.5cm}{shortstatistics\index{on!shortstatistics}} \rightvitem{13cm}{Puts the writing of the statistics in a shorthand mode in which the complete statistics are written on a single line only.} \leftvitem{3.5cm}{shortstats\index{on!shortstats}} \rightvitem{13cm}{Same as `On shortstatistics'.} \leftvitem{3.5cm}{sortreallocate\index{on!sortreallocate}} \rightvitem{13cm}{Reallocate the small and large buffer (also on the worker threads) at the end of every module. In some cases this can significantly reduce \FORM's memory usage as measured by ``resident set size''. For programs which consist of a large number of very quickly-running modules, this can incur a noticable performance penalty. See also \#sortreallocate (\ref{presortreallocate}) for a single-module version of this feature.} \leftvitem{3.5cm}{sortverbose\index{on!sortverbose}} \rightvitem{13cm}{Turns on the printing of additional information in the sorting statistics. See \ref{sorting} for more information.} \leftvitem{3.5cm}{statistics\index{on!statistics}} \rightvitem{13cm}{Turns the writing of runtime statistics on. This is the default. It is possible to change this default with one of the setup parameters in the setup file (see \ref{setup}).} \leftvitem{3.5cm}{stats\index{on!stats}} \rightvitem{13cm}{Same as `On statistics'.} \leftvitem{3.5cm}{threadloadbalancing\index{on!threadloadbalancing}} \rightvitem{13cm}{\vspace{1.5ex}Causes the load balancing mechanism in \TFORM{} to be turned on or off. Default is on. Ignored by other versions of \FORM.} \leftvitem{3.5cm}{threads\index{on!threads}} \rightvitem{13cm}{Allows the running of the program in multithreaded mode unless other problems prevent this. This is of course only relevant for \TFORM\@. Other versions of \FORM\ ignore this. The default is on.} \leftvitem{3.5cm}{threadstats\index{on!threadstats}} \rightvitem{13cm}{Only active for \TFORM\@. It determines whether all threads print their run time statistics or only the master thread does so. Default is on.} \leftvitem{3.5cm}{totalsize\index{on!totalsize}} \rightvitem{13cm}{\label{ontotalsize} Puts \FORM\ in a mode\index{totalsize} in which it tries to determine the maximum space occupied by all expressions at any given moment during the execution of the program. This space is the sum of the input/output/hide scratch files, the sort file(s) and the .str file. This maximum is printed at the end of the program. The same can be obtained with the "TotalSize ON" command in the setup (see \ref{setup}) or the -T option in the command tail when \FORM\ is started (see \ref{running}).} \leftvitem{3.5cm}{warnings\index{on!warnings}} \rightvitem{13cm}{Turns on the printing of warnings in regular mode. This is the default.} \leftvitem{3.5cm}{wtimestats\index{on!wtimestats}} \rightvitem{13cm}{Prints the wall-clock time in the timing information in the statistics. The wall-clock time is indicated by `\texttt{WTime}' instead of `\texttt{Time}' in the normal statistics with `\texttt{shortstatistics}' turned off. For parallel versions, it affects the statistics only on the master, and does not change those on the workers. The same can be obtained with the \texttt{-W} option in the command line options of \FORM{} (see \ref{running}) or `\texttt{WTimeStats ON}' in the setup (see \ref{setup}). Default is off.} \vspace{10mm} %--#] on : %--#[ once : \section{once} \label{substaonce} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & once {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement\index{once} is identical to the once option of the id\index{id} statement (see \ref{substaidentify}). Hence \begin{verbatim} once .... \end{verbatim} is just a shorthand notation for \begin{verbatim} id once .... \end{verbatim} \vspace{10mm} %--#] once : %--#[ only : \section{only} \label{substaonly} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & only {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement\index{only} is identical to the only option of the id\index{id} statement (see \ref{substaidentify}). Hence \begin{verbatim} only .... \end{verbatim} is just a shorthand notation for \begin{verbatim} id only .... \end{verbatim} \vspace{10mm} %--#] only : %--#[ polyfun : \section{polyfun} \label{substapolyfun} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & polyfun {\tt<}name of function{\tt>}; \\ & polyfun; \\ See also & moduleoption (\ref{substamoduleoption}) \end{tabular}\vspace{4mm} \noindent Declares the specified\index{polyfun} function to be the `polyfun'. The polyfun is a function of which the single argument\index{argument} is considered to be the coefficient\index{coefficient} of the term. If two terms are otherwise identical the arguments of their polyfun will be added during the sorting, even if these arguments are little expressions. Hence % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_PolyFun_1) \begin{verbatim} PolyFun acc; Local F = 3*x^2*acc(1+y+y^2)+2*x^2*acc(1-y+y^2); \end{verbatim} will result in \begin{verbatim} F = x^2*acc(5+y+5*y^2); \end{verbatim} Note that the external numerical coefficient\index{coefficient} is also pulled inside the polyfun. \noindent If the polyfun statement has no argument, \FORM\ reverts to its default mode in which no polyfun exists. This does not change any terms. If one would like to remove the polyfun from the terms one has to do that `manually' as in \begin{verbatim} PolyFun; id acc(x?) = x; \end{verbatim} in which we assume that previously the function acc had been declared to be the `polyfun'. \vspace{10mm} %--#] polyfun : %--#[ polyratfun : \section{polyratfun} \label{substapolyratfun} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & polyratfun {\tt<}name of function{\tt>}; \\ & polyratfun {\tt<}name of function{\tt>},{\tt<}name of function{\tt>}; \\ & polyratfun; \\ See also & polyfun (\ref{substapolyfun}), moduleoption (\ref{substamoduleoption}) \end{tabular}\vspace{4mm} \noindent Declares the specified\index{polyratfun} function to be the `polyratfun'. The polyratfun is a function with two arguments\index{argument} which together form a rational polynomial that acts as the coefficient\index{coefficient} of the term. If two terms are otherwise identical the arguments of their polyratfun will be added during the sorting, even if these arguments are little nontrivial. Hence % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_PolyRatFun_1) \begin{verbatim} PolyRatFun acc; Local F = 3*x^2*acc(1+y+y^2,1-y)+2*x^2*acc(1-y+y^2,1+y); \end{verbatim} will result in \begin{verbatim} F = x^2*acc(-y^3-10*y^2-2*y-5,y^2-1); \end{verbatim} Note that the external numerical coefficient\index{coefficient} is also pulled inside the polyratfun. \noindent If the polyratfun statement has no argument, \FORM\ reverts to its default mode in which no polyratfun exists. This does not change any terms. \noindent The polyratfun has many similarities with the polyfun (see \ref{substapolyfun}). At any moment there can only be at most either one polyfun or one polyratfun. Occurrences of the polyfun or the polyratfun with the wrong number or the wrong type of arguments are treated as regular functions. \noindent There is a fundamental difference between the polyfun and the polyratfun. The last one is far more restrictive. It can have only numbers and symbols for its arguments. Also the ordering of the terms in the arguments can be different. In the polyratfun the terms are always sorted with the highest power first. In the polyfun the ordering is as with the regular terms. By default the lowest powers come first as one usually likes for power series expansions. \noindent When two functions are specified, the first will be the PolyRatFun, and the second will be its inverse as in \begin{verbatim} PolyRatFun rat,RAT; \end{verbatim} in which case \begin{verbatim} RAT(x1,x2) = rat(x2,x1) \end{verbatim} This can be handy when one needs to solve systems of equations by manual interference. In that case exchanging numerators and denominators can be rather messy, while just changing a name is far less error-prone. \noindent In many cases it may be very wasteful to keep full track of the complete rational polynomial. An example is the reduction of a complicated 4-loop massless propagator diagram for which the rational polynomials can easily have hundreds of powers of the dimension parameter $D=4-2\epsilon$. In the end one has to expand in terms of $\epsilon$ although it is not known in advance to how many powers. For this there are two extra options in the polyratfun statement. The first is \begin{verbatim} PolyRatFun rat(divergence,x); \end{verbatim} in which x is the name of the symbol of interest. In this case the polyratfun keeps only its most divergent term in this variable x and gives it the coefficient one. The result is that terms will never cancel and at the end of the calculation one can see how many poles in x were maximally present, and hence how far one has to expand in x. Because the contents of the polyratfun are extremely simple, the expensive rational arithmetic is completely absent and things should go rather fast. \noindent In the second option one can specify how far one should expand: \begin{verbatim} PolyRatFun rat(expand,x,power); \end{verbatim} In this case the denominator can only be a polynomial in the variable x. It will be expanded and multiplied by the numerator and eventually all terms with powers of x that are greater than 'power' will be discarded. The remaining incidence of the function rat will then have only one argument, like the polyfun (see \ref{substapolyfun}). The advantage is that now the addition of two coefficients is a simple and straightforward operation that does not need the expensive polynomial GCD computations. \noindent Of course one can program such expansions externally and maybe better suited for the problem at hand, but using this option of the polyratfun is much faster and gives fewer chances of mistakes. \vspace{10mm} %--#] polyratfun : %--#[ pophide : \section{pophide} \label{substapophide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & pophide; \\ See also & hide (\ref{substahide}), nhide (\ref{substanhide}), unhide (\ref{substaunhide}), nunhide (\ref{substanunhide}), pushhide (\ref{substapushhide}) \end{tabular} \vspace{4mm} \noindent Undoes\index{pophide} the action of the most recent pushhide\index{pushhide} statement (see \ref{substapushhide}). If there is no matching pushhide statement an error will result: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_PushPopHide_2) \begin{verbatim} Local F1 = 1; .sort PushHide; Multiply 2; .sort PopHide; .sort PopHide; .end pushpophide-2.frm Line 9 --> PopHide statement without corresponding PushHide s tatement \end{verbatim} \vspace{10mm} %--#] pophide : %--#[ print : \section{print} \label{substaprint} \noindent \begin{tabular}{ll} Type & Print statement\\ Syntax & Print [{\tt<}options{\tt>}]; \\ & Print \verb:{:[{\tt<}options{\tt>}] {\tt<}expression{\tt>}\verb:}:; \\ & Print [{\tt<}options{\tt>}] "{\tt<}format string{\tt>}" [{\tt<}objects{\tt>}]; \\ See also & print[\,] (\ref{substaprintc}), nprint (\ref{substanprint}), printtable (\ref{substaprinttable}) \end{tabular}\vspace{4mm} \noindent General purpose print\index{print} statement. It has three modes. In the first two modes flags are set for the printing of expressions after the current module has been finished. The third mode concerns printing during execution. This allows the printing of individual terms or \$-variables\index{\$-variable} on a term by term basis. It should be considered as a useful debugging\index{debugging} device. \noindent In the first mode all active\index{active} expressions are scheduled for printing. The options are\vspace{2mm} \leftvitem{2cm}{{\tt<}filename{\tt>}} \rightvitem{14cm}{The results will be printed to the file. The {\tt<} and {\tt>} are mandatory for this option.} This option can only be used in the version that prints out individual terms, i.e.\ the version with the format string. \leftvitem{1cm}{+f} \rightvitem{15cm}{Printing will be only to the log\index{log} file\index{file!log}.} \leftvitem{1cm}{-f} \rightvitem{15cm}{Printing will be both to the screen\index{screen} and to the log\index{log} file\index{file!log}. This is the default.} \leftvitem{1cm}{+s} \rightvitem{15cm}{Each term will start a new line. This is called the single\index{single term mode} term mode\index{mode!single term}.} \leftvitem{1cm}{+ss} \rightvitem{15cm}{Each term will start a new line. In addition each internal group will start a new line. A group is either a single function or all symbols together, or all dotproducts together, or all vectors together, or all Kronecker delta's together.} \leftvitem{1cm}{+sss} \rightvitem{15cm}{Like the +ss option but now each symbol and its power will start a new line. The same for individual dotproducts (and their power), vectors and Kronecker delta's.} \leftvitem{1cm}{-s} \rightvitem{15cm}{Regular term mode. There can be more terms in a line. Linebreaks\index{linebreaks} are placed when the line is full. The line size is set in the format\index{format} statement (see \ref{substaformat}). This is the default.} \leftvitem{1cm}{-ss} \rightvitem{15cm}{Lowers the single term mode to -s. If one would like to switch off the single term mode altogether, -s suffices.} \leftvitem{1cm}{-sss} \rightvitem{15cm}{Lowers the single term mode to -ss. If one would like to switch off the single term mode altogether, -s suffices.} \noindent In the second mode one can specify individual\index{individual expressions} expressions to be printed. The options hold for all the expressions that follow them until new options are specified. The options are the same as for the first mode. \noindent In the third mode there is a format\index{format string} string as for the printf\index{printf} command in the C\index{C} programming language. Of course the control characters are not exactly the same as for the C language because the objects are different. The special characters are: \leftvitem{1cm}{\%t\index{print!\%t}} \rightvitem{15cm}{The current term will be printed at this position including its sign, even if this is a plus sign.} \leftvitem{1cm}{\%T\index{print!\%T}} \rightvitem{15cm}{The current term will be printed at this position. If its coefficient is positive no leading plus sign is printed.} \leftvitem{1cm}{\%w\index{print!\%w}} \rightvitem{15cm}{The number of the current thread will be printed. This is for \TFORM\ only. In the sequential version this combination is skipped. The number zero refers to the master thread.} \leftvitem{1cm}{\%W\index{print!\%W}} \rightvitem{15cm}{The number of the current thread and its CPU-time at the moment of printing. This is for \TFORM\ only. In the sequential version this combination is skipped. The number zero refers to the master thread.} \leftvitem{1cm}{\%\$\index{print!\%\$}} \rightvitem{15cm}{A dollar expression will be printed at this position. The name(s) of the dollar expression(s) should follow the format string in the order in which they are used in the format string.} \leftvitem{1cm}{\%\%\index{print!\%\%}} \rightvitem{15cm}{The character \%.} \leftvitem{1cm}{\%} \rightvitem{15cm}{If this is the last character of the string no linefeed will be printed at the end of the print command.} \leftvitem{1cm}{$\backslash$n} \rightvitem{15cm}{A linefeed\index{linefeed}.} \noindent Each call is terminated with a linefeed\index{linefeed}. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Print_1) \begin{verbatim} Symbols a,b,c; Local F = 3*a+2*b; Print "> %T"; id a = b+c; Print ">> %t"; Print; .end > 3*a >> + 3*b >> + 3*c > 2*b >> + 2*b F = 5*b + 3*c; \end{verbatim} \noindent In the third mode one can also use the +/--\,f options of the first mode. This should be placed before the format string as in \begin{verbatim} Print +f "(%$) %t",$var; \end{verbatim} \noindent Because of the mixed nature of this statement it can occur in more than one location in the module. \vspace{10mm} %--#] print : %--#[ print[] : \section{\texorpdfstring{print[\,]}{print[ ]}} \label{substaprintc} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & print[\,] \verb:{:[{\tt<}options{\tt>}] {\tt<}name{\tt>}\verb:}:; \\ See also & print (\ref{substaprint}) \end{tabular}\vspace{4mm} \noindent Print\index{print} statement\index{print[]} to cause the printing of expressions at the end of the current module. Is like the first two modes of the regular print statement (see \ref{substaprint}), but when printing \FORM\ does not print the contents of each bracket\index{bracket}, only the number of terms inside the bracket. Is to be used in combination with a bracket or an antibracket\index{antibracket} statement (see \ref{substabracket} and \ref{substaabrackets}). Apart from this the options are identical to those of the first two modes of the print statement. \vspace{10mm} %--#] print[] : %--#[ printtable : \section{printtable} \label{substaprinttable} \noindent \begin{tabular}{ll} Type & Print statement\\ Syntax & printtable [{\tt<}options{\tt>}] {\tt<}tablename{\tt>}; \\ & printtable [{\tt<}options{\tt>}] {\tt<}tablename{\tt>} $>$ {\tt<}filename{\tt>}; \\ & printtable [{\tt<}options{\tt>}] {\tt<}tablename{\tt>} $>\!\!>$ {\tt<}filename{\tt>}; \\ See also & print (\ref{substaprint}), table (\ref{substatable}), fill (\ref{substafill}), fillexpression (\ref{substafillexpression}), \\ & and the table\_ function (\ref{funtable}) \end{tabular}\vspace{4mm} \noindent Almost\index{printtable} the opposite of a FillExpression\index{fillexpression} statement (see \ref{substafillexpression}). Prints\index{print} the contents of a table\index{table} according to the current format (see \ref{substaformat}). The output can go to standard output, the log\index{log} file\index{file!log} or a specified file. The elements of the table that have been defined and filled are written in the form of fill\index{fill} statements (see \ref{substafill}) in such a way that they can be read in a future program to fill the table with the current contents. This is especially useful when the fillexpression statement has been used to dynamically extend tables based on what \FORM\ has encountered during running. This way those elements will not have to be computed again in future programs. \noindent The options are \leftvitem{1.3cm}{+f} \rightvitem{14.7cm}{Output is to the logfile and not to the screen.} \leftvitem{1.3cm}{-f} \rightvitem{14.7cm}{Output is both to the logfile and to the screen. This is the default.} \leftvitem{1.3cm}{+s} \rightvitem{14.7cm}{Output will be in a mode in which each new term starts a new line.} \leftvitem{1.3cm}{-s} \rightvitem{14.7cm}{Output will be in the regular mode in which new terms continue to be written on the same line within the limits of the number of characters per line as set in the format statement. Default is 72 characters per line. This can be changed with the format\index{format} statement (see \ref{substaformat}).} \noindent If redirection to a file is specified output will be only to this file. The +f option will be ignored. There are two possibilities: \leftvitem{2.8cm}{$>$ filename} \rightvitem{13.2cm}{The old contents of the file with name `filename' will be overwritten\index{overwrite}.} \leftvitem{2.8cm}{$>\!\!>$ filename} \rightvitem{13.2cm}{The table will be appended\index{append} to the file with the name `filename'. This allows the writing of more than one table to a file.} \vspace{10mm} %--#] printtable : %--#[ processbucketsize : \section{processbucketsize} \label{substaprocessbucketsize} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & processbucketsize {\tt<}value{\tt>}; \\ See also & moduleoption (\ref{substamoduleoption}), setup (\ref{setupprocessbucketsize}) \end{tabular}\vspace{4mm} \noindent Sets the number of terms\index{processbucketsize} in the buckets that are sent to the secondary processors in \ParFORM\index{ParFORM}, one of the parallel\index{parallel} versions of \FORM\ (see chapter \ref{parallel}). In all other versions this statement is ignored. See also the moduleoption (\ref{substamoduleoption}) statement and the corresponding parameter for the setup (\ref{setupprocessbucketsize}). \vspace{10mm} %--#] processbucketsize : %--#[ propercount : \section{propercount} \label{substapropercount} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & propercount {\tt<}on/off{\tt>}; \\ See also & on (\ref{substaon}), off (\ref{substaoff}) \end{tabular} \vspace{4mm} \noindent This statement\index{propercount} is obsolete\index{obsolete}. The user should try to use the propercount option of the on\index{on} (see \ref{substaon}) or the off\index{off} (see \ref{substaoff}) statements. \vspace{10mm} %--#] propercount : %--#[ pushhide : \section{pushhide} \label{substapushhide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & pushhide; \\ See also & hide (\ref{substahide}), nhide (\ref{substanhide}), unhide (\ref{substaunhide}), nunhide (\ref{substanunhide}), pophide (\ref{substapophide}) \end{tabular} \vspace{4mm} \noindent Hides\index{hide} all currently\index{pushhide}-active expressions (see \ref{substahide}). The pophide\index{pophide} statement (see \ref{substapophide}) can be used to to un-hide the expressions hidden by the most recent pushhide statement. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_PushPopHide_1) \begin{verbatim} Local F1 = 1; .sort PushHide; Local F2 = 1; * This statement does not affect F1: Multiply 2; .sort PushHide; Local F3 = 1; * This statement does not affect F1,F2: Multiply 2; .sort PopHide; * This statement does not affect F1: Multiply 2; .sort PopHide; * This statement affects all expressions: Multiply 2; Print; .end F1 = 2; F2 = 8; F3 = 8; \end{verbatim} \vspace{10mm} %--#] pushhide : %--#[ putinside : \section{putinside} \label{substaputinside} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & putinside {\tt<}name of function{\tt>} [,$<$bracket information$>$]; \\ See also & AntiPutInside (\ref{substaantiputinside}) \end{tabular}\vspace{4mm} \noindent This statement\index{putinside} puts the complete term inside a function argument. The function must be a regular function (hence no tensor or table which are special types of functions). If there is bracket\index{bracket} information, this information should adhere to the syntax of the bracket statement (\ref{substaantiputinside}) and only occurrences of the bracket variables will be put inside the function. The coefficient will also be put inside the function. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Putinside_1) \begin{verbatim} Symbols x, y, z; Cfunction f; Local F = 1 + x + 2*x + y^2+ z^3; Putinside f,x; Print; .end F = f(2*x) + f(x) + f(1) + f(1)*z^3 + f(1)*y^2; \end{verbatim} \vspace{10mm} %--#] putinside : %--#[ ratio : \section{ratio} \label{substaratio} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & ratio {\tt<}symbol1{\tt>} {\tt<}symbol2{\tt>} {\tt<}symbol3{\tt>}; \end{tabular} \vspace{4mm} \noindent This statement\index{ratio} can be used for limited but fast partial\index{partial fractioning} fractioning. In the statement \begin{verbatim} ratio a,b,c; \end{verbatim} in which \verb:a:, \verb:b: and \verb:c: should be three symbols {\FORM} will assume that $c = b-a$ and then make the substitutions \begin{eqnarray} \frac{1}{a^m}\frac{1}{b^n} & = & \sum_{i=0}^{m-1}\sign{i} \binom{n-1+i}{n-1}\frac{1}{a^{m-i}}\frac{1}{c^{n+i}} +\sum_{i=0}^{n-1}\sign{m} \binom{m-1+i}{m-1}\frac{1}{b^{n-i}}\frac{1}{c^{m+i}} \nonumber \\ \frac{b^n}{a^m} & = & \sum_{i=0}^n\binom{n}{i}\frac{c^i}{a^{m-n+i}} \ \ \ \ \ \ \ \hfill m\ge n \nonumber \\ \frac{b^n}{a^m} & = & \sum_{i=0}^{m-1}\binom{n}{i}\frac{c^{n-i}}{a^{m-i}} + \sum_{i=0}^{n-m}\binom{m-1+i}{m-1} c^ib^{n-m-i} \ \ \ \ \ \ \ \hfill m} [{\tt<}argument specifications{\tt>}];\verb:}: \\ See also & symmetrize (\ref{substasymmetrize}), cyclesymmetrize (\ref{substacyclesymmetrize}), antisymmetrize (\ref{substaantisymmetrize}) \end{tabular} \vspace{4mm} \noindent The argument\index{rcyclesymmetrize} specifications are explained in the section on the symmetrize\index{symmetrize} statement (see \ref{substasymmetrize}). \medskip \noindent The action of this statement is to reverse\index{reverse cycle symmetrize}-cycle-symmetrize \index{symmetrize!reverse cycle} the (specified) arguments of the functions that are mentioned. This means that the arguments are brought to `natural order' in the notation of \FORM\ by trying cyclic and reverse cyclic permutations\index{permutations} of the arguments or groups of arguments. The `natural order' may depend on the order of declaration of the variables. \vspace{10mm} %--#] rcyclesymmetrize : %--#[ redefine : \section{redefine} \label{substaredefine} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & r[edefine] {\tt<}preprocessor variable{\tt>} "{\tt<}string{\tt>}"; \\ See also & preprocessor variables in the chapter on the preprocessor (\ref{preprocessor}) \end{tabular} \vspace{4mm} \noindent This statement\index{redefine} can be used to change the contents of preprocessor\index{preprocessor variables} variables\index{variables!preprocessor}. The new contents can be used after the current module has finished execution and the preprocessor becomes active again for further translation and compilation\index{compilation}. This termwise adaptation of the value of a preprocessor variable can be very useful in setting up multi module loops until a certain condition is not met any longer. Example: \begin{verbatim} #do i = 1,1 statements; if ( condition ) redefine i "0"; .sort #enddo \end{verbatim} As long as there is a term that fulfils the condition the loop\index{loop} will continue. This defines effectively a while loop\index{loop!while} (see \ref{substawhile}) over various modules. Note that the .sort\index{.sort} instruction is essential. Note also that a construction like \begin{verbatim} if ( count(x,1) > 3 ) redefine i "`i'+1"; \end{verbatim} is probably not going to do what the user intends. It is not going to count terms with more than three powers of x. The preprocessor will insert the compile time value of the preprocessor variable i. If this is 0, then each time a term has more than three powers of x, i will get the string value \verb:0+1:. If one would like to do such counting, one should use a dollar variable\index{\$-variable} (see \ref{dollars}). \vspace{10mm} %--#] redefine : %--#[ removespectator : \section{removespectator} \label{substaremovespectator} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & removespectator {\tt<}spectator{\tt>}; \end{tabular} \vspace{4mm} \noindent See chapter~\ref{spectators} on spectators. \vspace{10mm} %--#] removespectator : %--#[ renumber : \section{renumber} \label{substarenumber} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & renumber {\tt<}number{\tt>}; \\ See also & sum (\ref{substasum}) \end{tabular}\vspace{4mm} \noindent Renumbers\index{renumber} the dummy\index{dummy} indices\index{indices!dummy}. Dummy indices are indices of the type \verb:N1_?:. Normally \FORM\ tries to renumber these indices to make the internal representation of a term `minimal'. It does not try exhaustively though. Especially interference with symmetric or antisymmetric functions is far from perfect. This is due to considerations of economy. With the renumber statement the user can force \FORM\ to do better. The allowable options are: \leftvitem{1cm}{0} \rightvitem{15cm}{All exchanges of one pair of dummy indices are tried until all pair exchanges yield no improvements. This is the default if no option is specified.} \leftvitem{1cm}{1} \rightvitem{15cm}{If there are N sets of dummy indices all N! permutations\index{permutations} are tried. This can be very costly when a large number of indices is involved. Use with care!}\vspace{10mm} %--#] renumber : %--#[ repeat : \section{repeat} \label{substarepeat} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & repeat; \\ & repeat {\tt<}executable statement{\tt>} \\ See also & endrepeat (\ref{substaendrepeat}), while (\ref{substawhile}) \end{tabular} \vspace{4mm} \noindent The repeat\index{repeat} statement starts a repeat\index{repeat environment} environment. It is terminated with an endrepeat\index{endrepeat} statement (see \ref{substaendrepeat}). The repeat statement and its matching endrepeat statement should be inside the same module. \vspace{4mm} \noindent The statements inside the repeat environment should all be executable statements (or print statements) and if any of the executable statements inside the environment has changed the current term, the action of the endrepeat statement will be to bring control back to the beginning of the environment. In that sense the repeat/endrepeat combination acts as \begin{verbatim} do executable statements while any action due to any of the statements \end{verbatim} The second form of the statement is a shorthand\index{shorthand} notation: \begin{verbatim} repeat; single statement; endrepeat; \end{verbatim} is equivalent to \begin{verbatim} repeat single statement; \end{verbatim} \noindent Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Repeat_1) \begin{verbatim} Symbols x, y, z; CFunction f, g; Local F = f(x)*g(y)*g(z); Repeat; Identify f(?a)*g(?b) = f(?a,?b); Endrepeat; Print; .end F = f(x,y,z); \end{verbatim} \vspace{4mm} Particular attention should be given to avoid infinite\index{infinite loop} loops\index{loop!infinite} as in \begin{verbatim} repeat id a = a+1; \end{verbatim} A more complicated infinite loop is \begin{verbatim} repeat; id S(x1?)*R(x2?) = T(x1,x2,x2-x1); id T(x1?,x2?,x3?pos_) = T(x1,x2-2,x3-1)*X(x2); id T(x1?,x2?,x3?) = S(x1)*R(x2); endrepeat; \end{verbatim} If the current term is S(2)*R(2), the statements in the loop do not change it in the end. Yet the program goes into an infinite loop, because the first id statement will change the term (action) and the third statement will change it back. {\FORM} does not check that the term is the same again. Hence there is action inside the repeat environment and hence the statements will be executed again. This kind of hidden action is a major source of premature\index{premature} terminations\index{termination!premature} of {\FORM} programs. \vspace{4mm} \noindent Repeat environments can be nested\index{nested} with all other environments (and of course also with other repeat/endrepeat combinations). \vspace{10mm} %--#] repeat : %--#[ replaceloop : \section{replaceloop} \label{substareplaceloop} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & replaceloop {\tt<}parameters{\tt>}; \\ See also & the findloop option of the if statement (\ref{substaif}) \end{tabular}\vspace{4mm} \noindent This statement\index{replaceloop} causes the substitution of index\index{index loop} loops\index{loop!index}. An index loop is a sequence of contracted indices in which the indices are arguments of various instances of the same function and each contracted\index{contracted indices} index\index{index!contracted} occurs once in one instance of the function and once in another instance of the function. Such a contraction defines a connection and if a number of such connections between occurrences of the function form a loop this structure is a candidate for replacement. Examples of such loops are: \begin{verbatim} f(i1,i2,j1)*f(i2,i1,j2) f(i1,i2,j1)*f(i2,i3,j2)*f(i1,i3,j3) f(i1,k1,i2,j1)*f(k2,i2,i3,j2)*f(i1,k3,i3,j3) \end{verbatim} The first term has a loop of two functions or vertices\index{vertices} and the other two terms each define a loop of three vertices. The parameters are: \leftvitem{4cm}{$<$name$>$} \rightvitem{12cm}{The name of the function that defines the `vertices'. This must always be the first parameter.} \leftvitem{4cm}{arguments=number} \rightvitem{12cm}{Only occurrences of the vertex function with the specified number of arguments will be considered. The specification of this parameter is mandatory.} \leftvitem{4cm}{loopsize=number} \rightvitem{12cm}{Only a loop with this number of vertices will be considered.} \leftvitem{4cm}{loopsize=all} \rightvitem{12cm}{All loop\index{loopsize} sizes will be considered and the smallest loop is substituted.} \leftvitem{4cm}{loopsize$<$number} \rightvitem{12cm}{Only loops with fewer vertices than `number' will be considered and the smallest loop will be substituted.} \leftvitem{4cm}{outfun=$<$name$>$} \rightvitem{12cm}{Name of an output function in which the remaining arguments of all the vertex functions will be given. This parameter is mandatory.} \leftvitem{4cm}{include-$<$name$>$} \rightvitem{12cm}{Name of a summable index that must be one of the links in the loop. This parameter is optional.} \noindent The loopsize\index{loopsize} parameter is mandatory. Hence one of its options must be specified. The order of the parameters is not important. The only important thing is that the name of the vertex function must be first. The names of the keywords may be abbreviated as in \begin{verbatim} ReplaceLoop f,a=3,l=all,o=ff,i=i2; \end{verbatim} although this does not improve the readability of the program. Hence a more readable abbreviated version might be \begin{verbatim} ReplaceLoop f,arg=3,loop=all,out=ff,inc=i2; \end{verbatim} \noindent The action of the statement is to remove the vertex functions that constitute the loop and replace them by the output function. This outfun will have the arguments of all the vertex functions minus the contracted indices that define the loop. The order of the arguments is the order in which they are encountered when following the loop. The order of the arguments in the outfun depends however on the order in which \FORM\ encounters the vertices. Hence the outfun will often be cyclesymmetric\index{symmetric!cycle}\index{cyclesymmetric} (see \ref{substafunctions} and \ref{substacyclesymmetrize}). If \FORM\ has to exchange indices to make a `proper loop' (i.e.\ giving relevance to the first index as if it is something incoming and the second index as if it is something outgoing) and if the vertex function is antisymmetric\index{antisymmetric}\index{symmetric!anti}, each exchange will result in a minus sign. Examples: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_ReplaceLoop_1) % TODO: the term order has been changed. \begin{verbatim} Functions f(antisymmetric),ff(cyclesymmetric); Indices i1,...,i8; Local F = f(i1,i4,i2)*f(i5,i2,i3)*f(i3,i1,i6)*f(i4,i7,i8); ReplaceLoop f,arg=3,loop=3,out=ff; \end{verbatim} would result in \begin{verbatim} -f(i4,i7,i8)*ff(i4,i5,i6) \end{verbatim} and % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_ReplaceLoop_2) % TODO: the term order has been changed. \begin{verbatim} Functions f(antisymmetric),ff(cyclesymmetric); Indices i1,...,i9; Local F = f(i1,i4,i2)*f(i5,i2,i3)*f(i3,i1,i6)*f(i4,i7,i8) *f(i6,i7,i8); ReplaceLoop f,arg=3,loop=all,out=ff; \end{verbatim} would give \begin{verbatim} -f(i1,i4,i2)*f(i5,i2,i3)*f(i3,i1,i6)*ff(i4,i6) \end{verbatim} because the smallest loop will be taken. A number of examples can be found in the package\index{package!color} `color'\index{color package} for group theory\index{group theory} invariants that is part of the \FORM\ distribution. \noindent A related object is the findloop\index{findloop} option of the if\index{if} statement (see \ref{substaif}). This option just probes whether a loop is present but makes no replacements.\vspace{10mm} %--#] replaceloop : %--#[ save : \section{save} \label{substasave} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & sa[ve] {\tt<}filename{\tt>} [{\tt<}names of global expressions{\tt>}]; \\ See also & load (\ref{substaload}) \end{tabular}\vspace{4mm} \noindent Saves\index{save} the contents of the store\index{store file} file\index{file!store} (all global expressions that were stored in .store\index{.store} instructions) to a file with the indicated name. If a list of expressions is provided only those expressions are saved and the others are ignored. \noindent Together with the load\index{load} statement (see \ref{substaload}) the save statement provides a mechanism to transfer data in internal notation from one program to another. It is the preferred method to keep results of a lengthy job for further analysis without the need for the long initial running time. \noindent In order to avoid confusion .sav\label{ex:sav}\index{.sav} is the preferred extension\index{extension!.sav} of saved files.\vspace{10mm} %--#] save : %--#[ select : \section{select} \label{substaselect} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & select {\tt<}list of sets{\tt>} {\tt<}pattern{\tt>} = {\tt<}expression{\tt>}; \\ See also & identify (\ref{substaidentify}) \end{tabular} \vspace{4mm} \noindent This statement\index{select} is identical to the select option of the id\index{id} statement (see \ref{substaidentify}). Hence \begin{verbatim} select .... \end{verbatim} is just a shorthand notation for \begin{verbatim} id select .... \end{verbatim} \vspace{10mm} %--#] select : %--#[ set : \section{set} \label{substaset} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & set {\tt<}set to be declared{\tt>}[(option)]:{\tt<}element{\tt>} [{\tt<}more elements{\tt>}];\\ See also & Sets (\ref{sect-sets}) \end{tabular} \vspace{4mm} \noindent Declares a single set\index{set} and specifies its elements\index{elements}. Sets have a type of variables connected to them. There can be sets of symbols, sets of functions, sets of vectors, sets of indices and sets of numbers. For the purpose of sets tensors\index{tensor} and tables\index{table} count as functions. \noindent There can also be mixed sets\index{set!mixed} of indices and numbers. When a number could be either a fixed index or just a number \FORM\ will keep the type of the set unfixed. This can change either when the next element is a symbolic index or a number that cannot be a fixed index (like a negative number). If the status does not get resolved the set can be used in the wildcarding of both symbols and indices. Normally sets of numbers can be used only in the wildcarding of symbols. Currently the only option is the ordered set\index{set!ordered}\index{ordered set}, indicated by \begin{verbatim} Set name(ordered):x4,x3,x1,x6,x2; \end{verbatim} which would be stored as x1,x2,x3,x4,x6 if that would be the order of declaration. \vspace{10mm} %--#] set : %--#[ setexitflag : \section{setexitflag} \label{substasetexitflag} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & setexitflag; \\ See also & exit (\ref{substaexit}) \end{tabular} \vspace{4mm} \noindent Causes\index{setexitflag} termination\index{termination} of the program after execution\index{execution} of the current module has finished. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Setexitflag_1) \begin{verbatim} CFunction f; Symbol x; Local test = +...+; Identify f(x?even_) = x; If (Match(f(x?))); Print "Error: unreplaced f: %t"; SetExitFlag; EndIf; .sort Error: unreplaced f: + f(1) Error: unreplaced f: + f(3) Error: unreplaced f: + f(5) Print; .end \end{verbatim} Here, suppose we would like to replace all cfunctions f with some pre-computed results. It might be useful to terminate the program if any f remains unreplaced, and print a list of all of them. If the exit statement (see \ref{substaexit}) were used instead, only the first remaining f is printed and the program would terminate immediately. The setexitflag statement is more useful in such a scenario. \vspace{10mm} %--#] setexitflag : %--#[ shuffle : % \section{shuffle} \label{substashuffle} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & shuffle,functionname; \\ & shuffle,once,functionname; \\ See also & stuffle (\ref{substastuffle}) \\ & merge (\ref{substamerge}) \end{tabular} \vspace{4mm} \noindent This statement is exactly the same as the merge\index{merge} statement. It takes two occurrences of the mentioned function and outputs terms, each with one function in which the two argument lists have been merged in all different ways, keeping the relative ordering of the two lists preserved. It is the opposite of the distrib\_\index{distrib\_}\index{function!distrib\_} function (see \ref{fundistrib}). Hence % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Shuffle_1) \begin{verbatim} Local F = f(a,b)*f(c,d); shuffle,f; \end{verbatim} will result in \begin{verbatim} +f(a,b,c,d)+f(a,c,b,d)+f(a,c,d,b)+f(c,a,b,d)+f(c,a,d,b)+f(c,d,a,b) \end{verbatim} One can also obtain the same result with the statements \begin{verbatim} Multiply,ff; repeat id f(x1?,?a)*f(x2?,?b)*ff(?c) = +f(?a)*f(x2,?b)*ff(?c,x1) +f(x1,?a)*f(?b)*ff(?c,x2); id f(?a)*f(?b)*ff(?c) = f(?c,?a,?b); \end{verbatim} but the advantage of the shuffle statement is that is also does a certain amount of combinatorics when there are identical arguments. Unfortunately the combinatorics doesn't extend over groups of arguments that are identical as in \begin{verbatim} CF f; L F = f(0,1,0,1,0,1)*f(0,1,0,1,0,1); Shuffle,f; .end Time = 0.00 sec Generated terms = 141 F Terms in output = 32 Bytes used = 892 \end{verbatim} It does get the combinatorics between two zeroes or two ones, but it cannot handle the groups. The explicit method above however doesn't do any combinatorics and generates 924 terms. One of the applications of this statement is in the field of harmonic sums\index{harmonic sum}, harmonic polylogarithms\index{harmonic polylogarithm} and multiple zeta values\index{multiple zeta value}\index{MZV}. Its twin brother is the stuffle statement\index{stuffle} (see \ref{substastuffle}). When the option once is mentioned, only one pair will be contracted this way. Without this option all occurrences of the function inside a term will be treated till there are only terms with a single occurrence of the function. \vspace{10mm} % %--#] shuffle : %--#[ skip : \section{skip} \label{substaskip} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & skip; \\ & skip {\tt<}list of expressions{\tt>}; \\ See also & nskip (\ref{substanskip}) \end{tabular} \vspace{4mm} \noindent In the first\index{skip} variety this statement marks all active\index{active} expressions that are in existence at the moment this statement is compiled, to be skipped. In the second variety this is done only to the active expressions that are specified. If an expression is skipped in a given module, the statements in the module have no effect on it. Also it will not be sorted\index{sort} again at the end of the module. This means that any bracket\index{bracket} information (see \ref{substabracket}) in the expression remains the way it was. Consult also the nskip\index{nskip} statement in \ref{substanskip}. \vspace{4mm} \noindent Skipped expressions can be used in the expressions in the r.h.s.\ of id\index{id} statements (see \ref{substaidentify}) or multiply\index{multiply} statements (see \ref{substamultiply}), etc. \vspace{10mm} %--#] skip : %--#[ sort : \section{sort} \label{substasort} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & sort; \\ See also & term (\ref{substaterm}), endterm (\ref{substaendterm}) \end{tabular} \vspace{4mm} \noindent Statement\index{sort} to be used inside the term\index{term} environment\index{environment!term} (see \ref{substaterm} and \ref{substaendterm}). It forces a sort in the same way as a .sort\index{.sort} instruction forces a sort for entire expressions. \vspace{10mm} %--#] sort : %--#[ splitarg : \section{splitarg} \label{substasplitarg} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & splitarg options \verb:{:{\tt<}name of function/set{\tt>} [{\tt<}argument specifications{\tt>}]\verb:}:; \\ See also & splitfirstarg (\ref{substasplitfirstarg}), splitlastarg (\ref{substasplitlastarg}), factarg (\ref{substafactarg}) \end{tabular}\vspace{4mm} \noindent Takes\index{splitarg} the indicated arguments\index{argument} of a function and if such an argument is a subexpression that consists on more than one term, each term becomes a separate argument of the function. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Splitarg_1) \begin{verbatim} CFunction f; Symbol a,b,c,d; Local test = f(a + b - 5*c*d); SplitArg f; Print; .end test = f( - 5*c*d,b,a); \end{verbatim} The format for the argument specifications is similar to the argument statement \index{argument} (see \ref{substaargument}), except here only one function or set of functions may be given. The splitarg action is only applied to the specified arguments of the given functions. If no (sets of) functions or no arguments are specified, the action is applied to all functions (including built-in functions) or all arguments. \noindent In addition, the following options modify the behaviour of splitarg: \vspace{3mm} \leftvitem{5cm}{(term)} \rightvitem{11cm}{Only terms that are a numerical multiple of the given term are split off. The terms that are split off will trail the remainder. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Splitarg_2) \begin{verbatim} CFunction f,g; Symbol x; Local test = f(2 + 3*x + 4*x^2) + g(2 + 3*x + 4*x^2) + h(x + x*y + x^2*y); SplitArg (x) f; SplitArg (x^2) g; SplitArg (x*y) h; Print; .end test = f(2 + 4*x^2,3*x) + g(2 + 3*x,4*x^2) + h(x + x^2*y,x*y); \end{verbatim} \vspace{3mm} \leftvitem{5cm}{((term))} \rightvitem{11cm}{Only terms that contain the given term will be split off. The terms that are split off will trail the remainder. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Splitarg_3) \begin{verbatim} CFunction f; Symbol x,y; Local test = f(2 + 3*x + 4*x^2 + 5*x*y + 6*y); SplitArg ((x)) f; Print; .end test = f(2 + 6*y,3*x,5*x*y,4*x^2); \end{verbatim} \vspace{10mm} %--#] splitarg : %--#[ splitfirstarg : \section{splitfirstarg} \label{substasplitfirstarg} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & splitfirstarg \verb:{:{\tt<}name of function/set{\tt>} [{\tt<}argument specifications{\tt>}]\verb:}:; \\ See also & splitarg (\ref{substasplitarg}), splitlastarg (\ref{substasplitlastarg}) \end{tabular}\vspace{4mm} \noindent Similar to \index{splitfirstarg} the SplitArg\index{splitarg} statement (see \ref{substasplitarg}). Splits the given argument(s) into their first term and a remainder. The arguments are replaced by the remainder\index{remainder}, followed by the first term. The argument specifications are as for SplitArg. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Splitfirstarg_1) \begin{verbatim} CFunction f; Symbol x; Local test = f(1 + x + x^2 + x^3); SplitFirstArg f; Print; .end test = f(x + x^2 + x^3,1); \end{verbatim} \vspace{10mm} %--#] splitfirstarg : %--#[ splitlastarg : \section{splitlastarg} \label{substasplitlastarg} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & splitlastarg \verb:{:{\tt<}name of function/set{\tt>} [{\tt<}argument specifications{\tt>}]\verb:}:; \\ See also & splitarg (\ref{substasplitarg}), splitfirstarg (\ref{substasplitfirstarg}) \end{tabular}\vspace{4mm} \noindent Similar to \index{splitlastarg} the SplitArg\index{splitarg} statement (see \ref{substasplitarg}). Splits the given argument(s) into their last term and a remainder. The arguments are replaced by the remainder\index{remainder}, followed by the last term. The argument specifications are as for SplitArg. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Splitlastarg_1) \begin{verbatim} CFunction f; Symbol x; Local test = f(1 + x + x^2 + x^3); SplitLastArg f; Print; .end test = f(1 + x + x^2,x^3); \end{verbatim} \vspace{10mm} %--#] splitlastarg : %--#[ strictrounding : \section{strictrounding} \label{substastrictrounding} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & strictrounding [$<$precision$>$]; \\ \end{tabular} \vspace{4mm} \noindent See chapter~\ref{floatingpoint} on the floating point capability. %--#] strictrounding : %--#[ stuffle : % \section{stuffle} \label{substastuffle} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & stuffle,functionname+; \\ & stuffle,functionname-; \\ & stuffle,once,functionname+; \\ & stuffle,once,functionname-; \\ \\ See also & shuffle (\ref{substashuffle}) \end{tabular} \vspace{4mm} \noindent This statement takes two occurrences of the mentioned function and outputs terms, each with one function in which the two argument lists have been merged according to the rules for nested sums. The plus and minus signs refer to ones favorite definition for nested sums. In the case of the plus sign, the definition is \begin{eqnarray} \sum_{i=1}^N \sum_{i=1}^N & = & \sum_{i=1}^N \sum_{j=1}^{i-1} + \sum_{j=1}^N \sum_{i=1}^{j-1} + \sum_{i=j=1}^N \nonumber \end{eqnarray} while in the case of the minus the definition is \begin{eqnarray} \sum_{i=1}^N \sum_{i=1}^N & = & \sum_{i=1}^N \sum_{j=1}^{i} + \sum_{j=1}^N \sum_{i=1}^{j} - \sum_{i=j=1}^N \nonumber \end{eqnarray} It is assumed that we have harmonic sums\index{harmonic sum} (see the summer library in the \FORM\ distribution). For such sums we expect functions with lists of nonzero integer arguments. Example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Stuffle_1) \begin{verbatim} CF S,R; Symbols N,n; L F = S(R(1,-3),N)*S(R(-5,1),N); id S(R(?a),n?)*S(R(?b),n?) = S(?a)*S(?b)*R(n); Stuffle,S-; id S(?a)*R(n?) = S(R(?a),n); Print +s; .end Time = 0.00 sec Generated terms = 12 F Terms in output = 12 Bytes used = 462 F = + S(R(-6,-4),N) - S(R(-6,-3,1),N) - S(R(-6,1,-3),N) - S(R(-5,1,-4),N) + S(R(-5,1,-3,1),N) + 2*S(R(-5,1,1,-3),N) - S(R(-5,2,-3),N) - S(R(1,-5,-4),N) + S(R(1,-5,-3,1),N) + S(R(1,-5,1,-3),N) + S(R(1,-3,-5,1),N) - S(R(1,8,1),N) ; \end{verbatim} The above program is equivalent to the basis procedure in the summer library. As with the shuffle\index{shuffle} statement (see \ref{substashuffle}) a certain amount of combinatorics has been built in. When the option once is mentioned, only one pair will be contracted this way. Without this option all occurrences of the function inside a term will be treated till there are only terms with a single occurrence of the function. The stuffle command takes also the effect of roots of unity~\ref{rootofunity}\index{root of unity} into account in the same way that the signs of alternating sums are taken into account. This means that the sum indices don't have to be integers, but could be multiples of a single symbol that has been declared to be a root of unity~\ref{substasymbols}. \vspace{10mm} % %--#] stuffle : %--#[ sum : \section{sum} \label{substasum} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & sum {\tt<}list of indices{\tt>}; \\ See also & renumber (\ref{substarenumber}) \end{tabular}\vspace{4mm} \noindent The specified list of indices will be summed\index{sum} over. There are two varieties: in the first, an index should be followed by a sequence of non-negative short integers. In this case, the summation means that for each of the integers, a new instance of the term is created in which the index is replaced by that integer. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Sum_1) \begin{verbatim} CFunction f; Index mu,nu; Local test1 = f(mu,mu); Local test2 = f(mu,nu); Local test3 = f(mu,nu)*f(mu,nu); Sum mu,0,1,2, nu,0,1,2; Print; .end test1 = f(0,0) + f(1,1) + f(2,2); test2 = f(0,0) + f(0,1) + f(0,2) + f(1,0) + f(1,1) + f(1,2) + f(2,0) + f(2,1) + f(2,2); test3 = f(0,0)^2 + f(0,1)^2 + f(0,2)^2 + f(1,0)^2 + f(1,1)^2 + f(1,2)^2 + f(2,0)^2 + f(2,1)^2 + f(2,2)^2; \end{verbatim} In the second variety the index should be either the last object in the statement or followed by another index. In this case the index is replaced by an internal dummy\index{dummy} index\index{index!dummy} of the type \verb:N1_?: (or with another number instead of `1'). Such indices have the current default\index{default dimension} dimension\index{dimension!default} and can be renamed at will by \FORM\ in order to bring terms into standard notation. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Sum_2) \begin{verbatim} CFunction f,g; Index mu,nu; Local test1 = f(mu,nu)*g(mu,nu); Local test2 = f(N2_?,N1_?)*g(N2_?,N1_?); Sum mu,nu; Print; .end test1 = f(N1_?,N2_?)*g(N1_?,N2_?); test2 = f(N1_?,N2_?)*g(N1_?,N2_?); \end{verbatim} Note that in the `test2' expression here, \FORM\ has re-arranged the dummy indices into the canonical form. The two types of sum statement may be mixed, as in: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Sum_3) \begin{verbatim} CFunction f,g; Index mu,nu; Local test = f(mu,nu)*g(mu,nu); Sum mu, nu,0,1,2; Print; .end test = f(N1_?,0)*g(N1_?,0) + f(N1_?,1)*g(N1_?,1) + f(N1_?,2)*g(N1_?,2); \end{verbatim} The user can use these dummy indices in the left hand side of identify\index{id}\index{identify} statements, but should recognise that they do not represent wildcards for the pattern matcher. Attempting to use them as wildcards as in `{\tt N1\_??}' is also not valid. \vspace{10mm} %--#] sum : %--#[ switch : % \section{switch} \label{substaswitch} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & switch,\$-variable; \\ \\ See also & case (\ref{substacase}), break (\ref{substabreak}), default(\ref{substadefault}), endswitch (\ref{substaendswitch}). \end{tabular} \vspace{4mm} \noindent The argument of the switch statement should be a dollar variable which evaluates into an integer that first inside a {\FORM} word. On a 64-bit processor this would be an integer in the range $-2^{31}$ to $2^{31}-1$. The switch statement should be paired with an endswitch statement. Between the two there will be a number of cases, each marked by an integer. If the value of the dollar variable corresponds to the value of one of these cases, execution will continue with the first statement after the corresponding case statement. Example: \begin{verbatim} id f(x?$x) = f(x); switch $x; case -1; some statements break; case 3; more statements break; case 4; case 5; and a few more break; default; and the default action break; endswitch; \end{verbatim} In principle the action is the same as in any computer language that has a switch construction, including the fall-through between case 4 and case 5. Whether the selection of the cases goes by binary search in a sorted list or by jumptable is determined by the endswitch statement. \vspace{10mm} % %--#] switch : %--#[ symbols : \section{symbols} \label{substasymbols} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & s[ymbols] {\tt<}list of symbols to be declared{\tt>}; \end{tabular}\vspace{4mm} \noindent Declares one or more symbols\index{symbol}. Each symbol can be followed by a number of options. These are (assuming that x is the symbol to be declared): \leftvitem{2.4cm}{x\hash{}r} \rightvitem{13.8cm}{The symbol is real\index{real}. This is the default.} \leftvitem{2.4cm}{x\hash{}c} \rightvitem{13.8cm}{The symbol is complex\index{complex}. This means that two spaces are reserved for this symbol, one for x and one for x\hash{} (the complex conjugate).} \leftvitem{2.4cm}{x\hash{}i} \rightvitem{13.8cm}{The symbol is imaginary\index{imaginary}.} \leftvitem{2.4cm}{x\hash{}=number} \rightvitem{13.8cm}{The symbol is a number-th root of unity\index{root of unity}\label{rootofunity} This means that the number-th power of the symbol will be replaced by one and half this power (if even) by -1. Negative powers will be replaced by corresponding positive powers.} \leftvitem{2.4cm}{x(:5)} \rightvitem{13.8cm}{The symbol has the maximum power 5. This means that $x^6$ and higher powers are automatically eliminated during the normalization\index{normalization} of a term. Of course any other number, positive or negative, is allowed.} \leftvitem{2.4cm}{x(-3:)} \rightvitem{13.8cm}{The symbol has the minimum power -3. This means that $x^{-4}$ and lower powers are automatically eliminated during the normalization of a term. Of course any other number, positive or negative, is allowed. Note that when the minimum power is positive, terms that have no power of x should technically be eliminated, but \FORM\ will not do so. Such an action can be achieved at any moment with a combination of the count\index{if!count}\index{count} option of an if\index{if} statement (see \ref{substaif}) and a discard\index{discard} statement (see \ref{substadiscard}).} \leftvitem{2.4cm}{x(-3:5)} \rightvitem{13.8cm}{The combination of a maximum and a minimum power restriction (see above).}\vspace{4mm} \noindent Complexity properties and power restrictions can be combined. In that case the complexity properties come first and then the power restrictions.\vspace{10mm} %--#] symbols : %--#[ symmetrize : \section{symmetrize} \label{substasymmetrize} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & symm[etrize] \verb:{:{\tt<}name of function/tensor{\tt>} [{\tt<}argument specifications{\tt>}];\verb:}: \\ See also & antisymmetrize (\ref{substaantisymmetrize}), cyclesymmetrize (\ref{substacyclesymmetrize}), rcyclesymmetrize (\ref{substarcyclesymmetrize}) \end{tabular} \vspace{4mm} \noindent The arguments\index{symmetrize} consist of the name of a function (or a tensor), possibly followed by some specifications. Hence we have the following varieties: \vspace{1mm} \leftvitem{5cm}{{\tt<}name{\tt>}} \rightvitem{11cm}{The function is symmetrized in all its arguments.} \leftvitem{5cm}{{\tt<}name{\tt><}numbers{\tt>}} \rightvitem{11cm}{The function is symmetrized in the arguments that are mentioned. If there are fewer arguments than the highest number mentioned in the list or arguments, no symmetrization will take place.} \leftvitem{5cm}{{\tt<}name{\tt>:<}number{\tt>}} \rightvitem{11cm}{Only functions with the specified number of arguments will be considered. Note: the number should follow the colon directly without intermediate space or comma.} \leftvitem{5cm}{{\tt<}name{\tt>:<}number{\tt><}numbers{\tt>}} \rightvitem{11cm}{If there is a number immediately following the colon, only functions with exactly that number of arguments will be considered. If the list of arguments contains numbers greater than this number, they will be ignored. If no number follows the colon directly, this indicates that symmetrization will take place, no matter the number of arguments of the function. If the list of arguments has numbers greater than the number of arguments of the function, these numbers will be ignored.} \leftvitem{5cm}{{\tt<}name{\tt>} {\tt<}(groups of numbers){\tt>}} \rightvitem{11cm}{The groups are specified as lists of numbers of arguments between parenthesis. All groups must have the same number of arguments or there will be a compile error. The groups are symmetrized as groups. The arguments do not have to be adjacent. Neither do they have to be ordered. The symmetrization\index{symmetrization} takes place in a way that the first elements of the groups are most significant, etc. If any argument number is greater than the number of arguments of the function, no symmetrization will take place.} \leftvitem{5cm}{{\tt<}name{\tt>:<}number{\tt>} {\tt<}(groups of numbers){\tt>}} \rightvitem{11cm}{The groups are specified as lists of numbers of arguments between parenthesis. All groups must have the same number of arguments or there will be a compile error. The groups are symmetrized as groups. The arguments do not have to be adjacent. Neither do they have to be ordered. The symmetrization takes place in a way that the first elements of the groups are most significant, etc. If no number follows the colon directly symmetrization takes place no matter the number of arguments of the function. Groups that contain a number that is greater than the number of arguments of the function will be ignored. If a number follows the colon directly, only functions with that number of arguments will be symmetrized. Again, groups that contain a number that is greater than the number of arguments of the function will be ignored.} \vspace{3mm} \noindent The action of this statement is to symmetrize the (specified) arguments of the functions that are mentioned. This means that the arguments are brought to `natural order' in the notation of \FORM\ by trying permutations\index{permutation} of the arguments or groups of arguments. The `natural order' may depend on the order of declaration of the variables. \vspace{4mm} \noindent Examples: \begin{verbatim} Symmetrize Fun; Symmetrize Fun 1,2,4; Symmetrize Fun:5; Symmetrize Fun: 1,2,4; Symmetrize Fun:5 1,2,4; Symmetrize Fun (1,6),(7,3),(5,2); Symmetrize Fun:8 (1,6),(7,3),(5,2); Symmetrize Fun: (1,6),(7,3),(5,2); \end{verbatim} \vspace{10mm} %--#] symmetrize : %--#[ table : \section{table} \label{substatable} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & table {\tt<}options{\tt>} {\tt<}table to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}), ctable (\ref{substactable}), ntable (\ref{substantable}), fill (\ref{substafill}) \end{tabular}\vspace{4mm} \noindent The statement declares a single table\index{table}. A table is a very special instance of a function. Hence it can be either commuting\index{commuting} or noncommuting\index{noncommuting}. The table statement declares its function to be commuting. A noncommuting table is declared with the ntable\index{ntable} statement (see \ref{substantable}). A table has a number of table\index{table indices} indices (in the case of zero indices the table has to be sparse) and after that it can have a number of regular function arguments with or without wildcarding. The table indices can come in two varieties: matrix\index{matrix like} like or sparse\index{sparse}. In the case of a matrix like table\index{table!matrix like}, for each of the indices a range has to be specified. \FORM\ then reserves a location for each of the potential elements. For a sparse table\index{table!sparse} one only specifies the number of indices. Sparse tables take less space, but they require more time searching whether an element has been defined. For a matrix like table \FORM\ can look directly whether an element has been defined. Hence one has a tradeoff between space and speed. A zero-dimensional (sparse) table has of course only a single element.\vspace{4mm} \noindent Table elements are defined with the fill\index{fill} statement (see \ref{substafill}). Fill statements for table elements cannot be used before the table has been declared with a table or ntable statement.\vspace{4mm} \noindent When \FORM\ encounters an unsubstituted table it will look for its indices. Then it can check whether the table element has been defined. If not, it can either complain (when the `strict'\index{strict} option is used) or continue without substitution. Note that an unsubstituted table element is a rather expensive object as \FORM\ will frequently check whether it can be substituted (new elements can be defined in a variety of ways....). If the indices match a defined table element, \FORM\ will check whether the remaining arguments of the table will match the function-type arguments given in the table declaration in the same way regular function arguments are matched. Hence these arguments can contain wildcards\index{wildcards} and even argument\index{argument field} field wildcards. If a match occurs, the table is replaced immediately. \noindent The options are \lefttabitem{check\index{table!check}} \tabitem{A check is executed on table boundaries. An element that is outside the table boundaries (regular matrix type tables only) will cause an error message and execution will be halted.} \lefttabitem{relax\index{table!relax}} \tabitem{Normally all elements of a table should be defined during execution and an undefined element will give an error message. The relax option switches this off and undefined elements will remain as if they are regular functions.} \lefttabitem{sparse\index{table!sparse}} \tabitem{The table is considered to be sparse. In the case of a sparse table only the number of indices should be specified. Ranges are not relevant. Each table element is stored separately. Searching for table elements is done via a balanced tree\index{tree!balanced}. This takes of course more time than the matrix type search with is just by indexing. A matrix like table\index{table!matrix like} is the default.} \lefttabitem{strict\index{table!strict}} \tabitem{If this option is specified all table elements that are encountered during execution should be defined. An undefined table element will result in an error and execution is halted. Additionally all table elements should be properly defined at the end of the module in which the table has been defined.} \lefttabitem{zerofill\index{table!zerofill}} \tabitem{Any undefined table element is considered to be zero.} \lefttabitem{onefill\index{table!onefill}} \tabitem{Any undefined table element is considered to be one.}\vspace{10mm} \noindent The defaults are that the table is matrix like and table elements that cannot be substituted will result in an error.\vspace{4mm} \noindent Ranges for indices in matrix like tables are indicated with a colon as in \begin{verbatim} Symbol x; Table t1(1:3,-2:4); Table t2(0:3,0:3,x?); Table sparse,t3(4); \end{verbatim} The table \verb:t1: is two dimensional and has 21 elements. The table \verb:t2: is also two dimensional and has 16 elements. In addition there is an extra argument which can be anything that a wildcard symbol will match. The table \verb:t3: is a sparse table with 4 indices.\vspace{4mm} \noindent If the computer on which \FORM\ runs is a 32\index{32 bits} bit computer no table can have more than $2^{15} = 32768$ elements. On a 64\index{64 bits} bit computer the limit is $2^{31}$, but one should take into account that each element declared causes some overhead. \vspace{4mm} \noindent If the wildcarding in the declaration of a table involves the definition of a dollar variable\index{\$-variable} (this is allowed! See \ref{dollars}) parallel execution of the entire remainder of the \FORM\ program is switched off. This is of course only relevant for parallel versions of \FORM\@. But if at all possible one should try to find better solutions than this use of dollar variables, allowing future parallel processing of the program. \noindent In some cases tables are built up slowly during the execution of a program and used incrementally. This means that more and more CPU memory is needed. Eventually this can cause a crash by lack of memory. In the case that the earlier elements of the table aren't needed anymore, one could use the ClearTable~\ref{substacleartable} statement. \vspace{10mm} %--#] table : %--#[ tablebase : \section{tablebase} \label{substatablebase} \noindent This statement is explained in the chapter on tablebases\index{tablebase} (\ref{tablebase}). \vspace{10mm} %--#] tablebase : %--#[ tensors : \section{tensors} \label{substatensors} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & t[ensors] {\tt<}list of tensors to be declared{\tt>}; \\ See also & functions (\ref{substafunctions}), ctensors (\ref{substactensors}), ntensors (\ref{substantensors}) \end{tabular}\vspace{4mm} \noindent A tensor\index{tensor} is a special function that can have only indices for its arguments. If an index a contracted with the index of a vector Schoonschip\index{Schoonschip} notation is used. This means that the vector is written as a pseudo argument of the tensor. It should always be realized that in that case in principle the actual argument is a dummy index. Tensors come in two varieties: commuting\index{commuting} and noncommuting\index{noncommuting}. The tensor statement declares a tensor to be commuting. In order to declare a tensor to be noncommuting one should use the ntensor\index{ntensor} statement (see \ref{substantensors}). Thus `tensor' is equivalent to `ctensor'; note that this differs from the convention of functions, where `function' is equivalent to `nfunction' and not to `cfunction'. \noindent The options that exist for properties of tensors are the same as those for functions (see \ref{substafunctions}). \vspace{10mm} %--#] tensors : %--#[ term : \section{term} \label{substaterm} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & term; \\ See also & endterm (\ref{substaendterm}), sort (\ref{substasort}) \end{tabular} \vspace{4mm} \noindent This statement begins a term\index{term} environment \index{environment!term}, which is terminated with the endterm\index{endterm} statement (see \ref{substaendterm}). It causes the current term to be processed as if it were a small expression; the statements inside the environment are applied to it and one can sort the results with the sort\index{sort} statement (see \ref{substasort}) (not to be confused with the .sort \index{.sort} instruction, which terminates a module). Inside the term environment, one may only use executable statements or term-wise print statements (see \ref{substaprint}). When the end of the term environment is reached, the resulting terms are sorted and then the module execution proceeds with the resulting terms. This environment can be nested\index{nested}. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Term_1) \begin{verbatim} CFunction f; Symbol x; Local test = f(10); Term; Repeat Identify f(x?{>1}) = f(x-1) + f(x-2); EndTerm; Print; .end Time = 0.00 sec Generated terms = 2 test Terms in output = 2 Bytes used = 64 test = 34*f(0) + 55*f(1); \end{verbatim} Here, one can see in the sorting statistics that only 2 terms are generated at the lowest level, rather than the full $34+55=89$. \vspace{10mm} %--#] term : %--#[ testuse : \section{testuse} \label{substatestuse} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & testuse ["{\tt<}tablename(s){\tt>}"]; \\ See also & tablebases (\ref{tablebase}), testuse (\ref{tbltestuse}) \end{tabular} \vspace{4mm} \noindent This statement\index{testuse} is explained in the chapter on tablebases\index{tablebase}.\vspace{10mm} %--#] testuse : %--#[ threadbucketsize : \section{threadbucketsize} \label{substathreadbucketsize} \noindent \begin{tabular}{ll} Type & Declaration\\ Syntax & ThreadBucketSize,number; \\ See also & the section on \TFORM~(\ref{tform}) \end{tabular} \vspace{4mm} \noindent This statement\index{threadbucketsize} is only active in \TFORM\index{TFORM}. In all other versions of \FORM\ it is ignored. It sets the size of the buckets\index{bucket} that the master\index{master} thread prepares for treatment by the workers. Bigger buckets means less overhead in signals, but when the buckets are too big the workers may have to wait too long before getting tasks. The best bucket size is usually between 100 and 1000, although this depends very much on the problem. The default value is currently 500. For more ways to set this variable one should consult the section on \TFORM\ (\ref{tform}). To find out what its value is, use the `ON,setup;' statement (\ref{substaon} and \ref{setup}). \vspace{10mm} %--#] threadbucketsize : %--#[ tofloat : \section{tofloat} \label{substatofloat} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & tofloat; \end{tabular} \vspace{4mm} \noindent See chapter~\ref{floatingpoint} on the floating point capability. %--#] tofloat : %--#[ topolynomial : \section{topolynomial} \label{substatopolynomial} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & topolynomial[,OnlyFunctions[,{\tt<}list of functions{\tt>}]]; \\ See also & factarg (\ref{substafactarg}), FromPolynomial (\ref{substafrompolynomial}), ArgToExtraSymbol (\ref{substaargtoextrasymbol}) \\& and ExtraSymbols (\ref{substaextrasymbols}, \ref{sect-extrasymbols}). \end{tabular} \vspace{4mm} \noindent Starting with version 4.0 of \FORM{} some built in operations or statements can only deal with symbols and numbers. Examples of this are factorization~(\ref{substafactarg}) and output simplification (still to be implemented). The ToPolynomial statement takes each term, looks for objects that are not symbols to positive powers and replaces them by symbols. If the object has been encountered before, the same symbol will be used, otherwise a new symbol will be defined. The object represented by the `extra symbol' is stored internally and can be printed if needed with the \%X option in the \#write instruction (\ref{prewrite}). Note that negative powers of symbols will also be replaced. In some cases one would like to do this only for a subset of objects. It is possible to do this only for functions, using the OnlyFunctions option. If no functions are specified, all functions will be replaced by extra symbols. If a list of functions is specified, only those functions will be replaced. \vspace{10mm} %--#] topolynomial : %--#[ torational : \section{torational} \label{substatorational} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & torational; \end{tabular} \vspace{4mm} \noindent See chapter~\ref{floatingpoint} on the floating point capability. %--#] torational : %--#[ tospectator : \section{tospectator} \label{substatospectator} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & tospectator {\tt<}spectator{\tt>}; \end{tabular} \vspace{4mm} \noindent See chapter~\ref{spectators} on spectators. \vspace{10mm} %--#] tospectator : %--#[ totensor : \section{totensor} \label{substatotensor} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & totensor [nosquare] [functions] [!{\tt<}vector or set{\tt>}] {\tt<}vector{\tt>} {\tt<}tensor{\tt>}; \\ & totensor [nosquare] [functions] [!{\tt<}vector or set{\tt>}] {\tt<}tensor{\tt>} {\tt<}vector{\tt>}; \\ See also & tovector (\ref{substatovector}) \end{tabular} \vspace{4mm} \noindent Looks for multiple\index{totensor} occurrences of the given vector, either inside dotproducts, contracted with a tensor, as an argument of a function or as a loose vector with an index. In each occurrence in which the vector has been contracted, a dummy index is introduced to make the contraction apparent. Then all of these vectors and their indices are replaced by the specified tensor with all the indices, as in: \begin{eqnarray} p^{\mu_1}p^{\mu_2}p^{\mu_3} & \rightarrow & t^{\mu_1\mu_2\mu_3} \nonumber \end{eqnarray} For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_ToTensor_1) \begin{verbatim} Vector p,p1,p2; Function f; Index mu; Tensor tt,t; Local F = p.p1^2 * f(p,p1) * p(mu) * tt(p1,p,p2,p); ToTensor functions, p,t; Print; .end F = f(N1_?,p1)*tt(p1,N2_?,p2,N3_?)*t(p1,p1,mu,N1_?,N2_?,N3_?); \end{verbatim} \vspace{4mm} \noindent The options are \leftvitem{3.5cm}{nosquare\index{totensor!nosquare}} \rightvitem{13cm}{Dotproducts with twice the specified vector (the square of the vector) are not considered.} \leftvitem{3.5cm}{functions\index{totensor!functions}} \rightvitem{13cm}{Vectors that are arguments of regular functions will also be considered. By default, these are not considered.} \leftvitem{3.5cm}{!vector\index{totensor!"!vector}} \rightvitem{13cm}{Dotproducts involving the specified vector are not considered.} \leftvitem{3.5cm}{!set\index{totensor!"!set}} \rightvitem{13cm}{The set should be a set of vectors. All dotproducts involving a vector in the set are not considered.}\vspace{10mm} %--#] totensor : %--#[ tovector : \section{tovector} \label{substatovector} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & tovector {\tt<}tensor{\tt>} {\tt<}vector{\tt>}; \\ & tovector {\tt<}vector{\tt>} {\tt<}tensor{\tt>}; \\ See also & totensor (\ref{substatotensor}) \end{tabular} \vspace{4mm} \noindent The opposite\index{tovector} of the totensor\index{totensor} statement. The tensor is replaced by a product of the given vectors, each with one of the indices of the tensor as in: \begin{eqnarray} t^{\mu_1\mu_2\mu_3} & \rightarrow & p^{\mu_1}p^{\mu_2}p^{\mu_3} \nonumber \end{eqnarray} For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_ToVector_1) \begin{verbatim} Tensor t1,t2; Vector v1,v2; Index mu1,mu2,mu3; Local test = t1(mu1,mu2,mu3) + t2(mu1,mu2,mu3); ToVector t1,v1; ToVector v2,t2; Print; .end test = v1(mu1)*v1(mu2)*v1(mu3) + v2(mu1)*v2(mu2)*v2(mu3); \end{verbatim} \vspace{10mm} %--#] tovector : %--#[ trace4 : \section{trace4} \label{substatrace} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & trace4 [{\tt<}options{\tt>}] {\tt<}index{\tt>}; \\ See also & tracen (\ref{substatracen}), chisholm (\ref{substachisholm}), unittrace (\ref{substaunittrace}) \\ & and the chapter on gamma algebra (\ref{gammaalgebra}) \end{tabular} \vspace{4mm} \noindent Takes the trace\index{trace4} of the gamma\index{gamma matrices} matrices with the given trace\index{trace line} line index\index{index!trace line}. It assumes that the matrices are defined in four dimensions, hence it uses some relations that are only valid in four dimensions. For details about these relations and other methods used, consult chapter~\ref{gammaalgebra} on gamma matrices. The options are: \vspace{4mm} \lefttabitem{contract\index{trace4!contract}} \tabitem{Try to use the Chisholm\index{Chisholm} identity to eliminate this trace and contract it with other gamma matrices. See also \ref{substachisholm}. This is the default.} \lefttabitem{nocontract\index{trace4!nocontract}} \tabitem{Do not use the Chisholm\index{Chisholm} identity to eliminate this trace and contract it with other gamma matrices. See also \ref{substachisholm}.} \lefttabitem{nosymmetrize\index{trace4!nosymmetrize}} \tabitem{When using the Chisholm\index{Chisholm} identity to eliminate this trace and contract it with other gamma matrices, do not do it in the symmetric fashion, but use the first contraction encountered. See also \ref{substachisholm}.} \lefttabitem{notrick\index{trace4!notrick}} \tabitem{The final stage of trace taking, when all indices are different and there are no contractions with identical vectors, as well as no $\gamma_5$ matrices present, is done with n-dimensional methods, rather than with 4-dimensional tricks.} \lefttabitem{symmetrize} \tabitem{When using the Chisholm identity to eliminate this trace and contract it with other gamma matrices, try to do it in the symmetric fashion. See also \ref{substachisholm}.} \lefttabitem{trick} \tabitem{The final stage of trace taking, when all indices are different and there are no contractions with identical vectors is done using the 4-dimensional relation $\gamma^a\gamma^b\gamma^c = \epsilon^{abcd}\gamma_5\gamma^d +\gamma^a\delta^{bc}-\gamma^b\delta^{ac}+\gamma^c\delta^{ab}$ This gives a shorter result for long traces. It is the default. } \vspace{10mm} %--#] trace4 : %--#[ tracen : \section{tracen} \label{substatracen} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & tracen {\tt<}index{\tt>}; \\ See also & trace4 (\ref{substatrace}), chisholm (\ref{substachisholm}), unittrace (\ref{substaunittrace}) \\ & and the chapter on gamma algebra (\ref{gammaalgebra}) \end{tabular} \vspace{4mm} \noindent Takes\index{tracen} the trace of the gamma\index{gamma matrices} matrices with the spin\index{spin line} line indicated by the index. It is assumed that the trace is over a symbolic number of dimensions. Hence no special 4-dimensional tricks are used. The presence of $\gamma_5$, $\gamma_6$ or $\gamma_7$ is not tolerated. When indices are contracted {\FORM} will try to use the special symbol for the dimension$-4$ if it has been defined in the declaration of the index (see \ref{substaindex}. This results in relatively compact expressions. For more details on the algorithm used, see chapter~\ref{gammaalgebra} on gamma matrices. \vspace{10mm} %--#] tracen : %--#[ transform : \section{transform} \label{substatransform} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & transform,function(s),{\tt<}one or more transformations{\tt>}; \end{tabular} \vspace{4mm} \noindent The transform statement\index{Transform} manipulates function arguments and fields of arguments. It allows speedy transformations without the need for multiple statements or repeat loops. The function(s) on which the statement will act are indicated as individual, comma or blank-space separated functions or sets of functions. If there is more than one transformation, the transformations are separated by commas (or blanks, unless the blank space would not induce a comma). Each transformation consists of its keyword, indicating its type, followed by a range of arguments that is enclosed by parentheses. After that, transformation-specific information may follow. The range\index{range} is specified as two comma-separated indicators, as in: \begin{verbatim} (1,4) (3,last) (last-6,last-2) \end{verbatim} The special keyword \verb:last:\index{last} refers to the last argument of the function, and \verb:last-1: refers to the next-to-last argument, etc. If the first number is bigger than the second, the arguments will be processed in reverse order whenever this is relevant. In the descriptions below we will indicate the range by (r1,r2). The numbers in the above examples may be also dollar variables, provided they evaluate into numbers at the time of execution. Hence \begin{verbatim} ($x,$y) ($x,last) (last-$x,last-2) \end{verbatim} are potentially legal ranges. One may not use \verb:$x+2: or other expression which still needs evaluation. The transformations that are allowed currently are: \leftvitem{3.2cm}{\bf replace\index{transform!replace}\index{replace}} \rightvitem{13cm}{replace(r1,r2)=(from1,to1,from2,to2,...,fromn,ton), in which the ``from,to'' pairs are as for the replace\_ function (see \ref{funreplace}). Here, however, there is more flexibility than in the replace\_ function: one may replace (small) numbers, as in {\tt replace(1,last)=(0,1,1,0)}, which would replace arguments that are zero by one, and arguments that are one by zero. Some ``generic argument'' objects have been introduced, given by xarg\_, iarg\_, parg\_ and farg\_, which match symbols, indices, vectors and functions respectively. These allow one to use the replaced argument in a non-trivial expression. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_3) \begin{verbatim} Symbol a; Vector p; CFunction f1,f2; Local test = f1(0,1) + f2(2,a) + f2(2,p); Transform f1 replace(1,last)=(0,1,1,0); * This will not affect f2(2,p) because xarg_ does not match vectors: Transform f2 replace(1,last)=(xarg_,2*xarg_+1); Print; .end test = f1(1,0) + f2(5,1 + 2*a) + f2(5,p); \end{verbatim} \leftvitem{3.2cm}{\bf encode\index{transform!encode}\index{encode}} \rightvitem{13cm}{encode(r1,r2):base=n will interpret the arguments as the digits in a base-n number system, and replace the digits with a single argument containing the number in base 10. The base and resulting number must fit within a single \FORM{} word, and the input digits must be less than the specified base. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_4) \begin{verbatim} CFunction f2,f3; Local test = f2(1,1,0,1) + f3(1,1,0,1); Transform f2 encode(1,last):base=2; Transform f3 encode(1,last):base=3; Print; .end test = f2(13) + f3(37); \end{verbatim} \leftvitem{3.2cm}{\bf decode\index{transform!decode}\index{decode}} \rightvitem{13cm}{decode(r1,r2):base=n will do the opposite of encode. It will take a single argument, the smallest of r1 and r2, and expand it into digits in a base-n number system. It outputs a number of digits corresponding to the largest of r1 and r2, which replace the original argument. If this number is not sufficiently large to convert the argument, no change is made. If r2 is less than r1, the digits are produced in reverse order. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_5) \begin{verbatim} CFunction f2,f3,F2,F3; Local test = f2(13) + f2(100) + f3(37) + F2(13) + F3(37); Transform f2 decode(1,5):base=2; Transform f3 decode(1,5):base=3; Transform F2 decode(5,1):base=2; Transform F3 decode(5,1):base=3; Print; .end test = f2(0,1,1,0,1) + f2(100) + f3(0,1,1,0,1) + F2(1,0,1,1,0) + F3(1,0,1,1,0); \end{verbatim} \leftvitem{3.2cm}{\bf tosumnotation\index{transform!tosumnotation}\index{tosumnotation} \index{transform!implode}\index{implode}} \rightvitem{13cm}{tosumnotation(r1,r2) or implode(r1,r2) realizes an encoding in which zeroes are absorbed as extra values in the first nonzero argument that follows. This is used when dealing with harmonic sums and harmonic polylogarithms. This is similar to the {\tt ArgImplode} statement (see \ref{substaargimplode}), with the difference that here a single symbol is allowed as an argument which generically represents +/-1. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_6) \begin{verbatim} CFunction f; Symbol a; Local test = f(0,0,1,0,a,0,0,0,-1); Transform f implode(1,last); Print; .end test = f(3,2*a,-4); \end{verbatim} \leftvitem{3.2cm}{\bf tointegralnotation\index{transform!tointegralnotation} \index{tointegralnotation}\index{transform!explode}\index{explode}} \rightvitem{13cm}{tointegralnotation(r1,r2) or explode(r1,r2) undoes what tosumnotation/implode might have done, similar to the {\tt ArgExplode} statement (see \ref{substaargexplode}). Hence each integer with an absolute value $n$ generates $n-1$ zeroes followed by the sign of the original integer. As for tosumnotation, a single symbol (which generically represents +/-1) is allowed, possibly multipled by a (small) integral coefficient. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_7) \begin{verbatim} CFunction f; Symbol a; Local test = f(3,2*a,-4); Transform f explode(1,last); Print; .end test = f(0,0,1,0,a,0,0,0,-1); \end{verbatim} \leftvitem{3.2cm}{\bf permute\index{transform!permute}\index{permute}} \rightvitem{13cm}{permute(n1,...,ni),(m1,...,mj),...~will permute the function arguments according to the specified cycles. The cycles are executed in the order in which they are given, and may overlap. There is no restriction on how many cycles may be provided. Dollar variables may be used to provide the cycles, including dollar variables containing argument fields obtained from argument field wildcards. Unlike the other transformations, the keyword {\tt last} can not be used here. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_8) \begin{verbatim} CFunction f,cyc; Symbol a1,...,a7; Local test = f(a1,a2,a3,a4,a5,a6,a7)*cyc(2,6); Identify cyc(?a$cyc) = 1; Transform f permute(1,3,5)($cyc); ModuleOption local $cyc; Print; .end test = f(a3,a6,a5,a4,a1,a2,a7); \end{verbatim} \leftvitem{3.2cm}{\bf reverse\index{transform!reverse}\index{reverse}} \rightvitem{13cm}{reverse(r1,r2) reverses the order of the arguments in specified range. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_9) \begin{verbatim} CFunction f; Local test = f(1,...,10); Transform f reverse(3,7); Print; .end test = f(1,2,7,6,5,4,3,8,9,10); \end{verbatim} \leftvitem{3.2cm}{\bf dedup\index{transform!dedup}\index{dedup}} \rightvitem{13cm}{dedup(r1,r2) removes duplicates from the arguments in the range, keeping the first. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_10) \begin{verbatim} CFunction f,g; Function h,i; Symbol x; Vector p; Index mu; Local test = f(100,g(1),g(2)^2,x,x^2,mu,p,p.p,1/p.p,h*i,i*h); Identify f(?a) = f(?a,?a); Transform f dedup(1,last); Print; .end test = f(100,g(1),g(2)^2,x,x^2,mu,p,p.p,p.p^-1,h*i,i*h); \end{verbatim} \leftvitem{3.2cm}{\bf cycle\index{transform!cycle}\index{cycle}} \rightvitem{13cm}{cycle(r1,r2)=+/-number will perform a cyclic permutation of the indicated range of arguments. If the number is preceded by a - the cycling is to the left. If there is a plus sign the cycling is to the right. Note that either the plus or the minus sign is mandatory. The number following the +/- sign is also allowed to be a dollar variable, provided it evaluates to a legal number during execution. The case cycle(r1,rn)=-1 is equivalent to permute(r1,...,rn) where r1,...,rn are consecutive integers. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_11) \begin{verbatim} CFunction f,g,h; Local test = f(1,...,9) + g(1,...,9) + h(1,...,9); Transform f cycle(3,7)=-1; Transform g permute(3,...,7); Transform h cycle(3,7)=+2; Print; .end test = f(1,2,4,5,6,7,3,8,9) + g(1,2,4,5,6,7,3,8,9) + h(1,2,6,7,3,4,5,8,9); \end{verbatim} \leftvitem{3.2cm}{\bf islyndon\index{transform!islyndon}\index{islyndon}} \rightvitem{13cm}{islyndon(r1,r2)=(yes,no) will test whether the indicated range of arguments forms a Lyndon word\index{Lyndon word} according to the ordering of arguments in \FORM\@. The yes and no arguments are what the main term will be multiplied by when the range forms a Lyndon word or does not, respectively. Because the definition of a Lyndon word is the unique minimal cyclic permutation of the arguments, and because often we may need the unique maximal cyclic permutation, there are varieties: for the minimum one may also explicitly specify islyndon$<$(r1,r2)=(yes,no) or islyndon-(r1,r2)=(yes,no), while for the maximum one may use islyndon$>$(r1,r2)=(yes,no) or islyndon+(r1,r2)=(yes,no). For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_12) \begin{verbatim} CFunction f; Symbol y,n; Local test = f(0) + f(1) + f(0,1) + f(0,0,1) + f(0,1,1) + f(0,0) + f(1,0) + f(1,1) + f(1,0,0) + f(0,1,0) + f(1,0,1); Transform f islyndon(1,last)=(y,n); Print; .end test = f(0)*y + f(0,0)*n + f(0,0,1)*y + f(0,1)*y + f(0,1,0)*n + f(0,1,1)*y + f(1)*y + f(1,0)*n + f(1,0,0)*n + f(1,0,1)*n + f(1,1)*n; \end{verbatim} \leftvitem{3.2cm}{\bf tolyndon\index{transform!tolyndon}\index{tolyndon}} \rightvitem{13cm}{tolyndon(r1,r2)=(yes,no) will permute the given range in a cyclic manner until it is (if possible) a Lyndon word\index{Lyndon word} according to the ordering of arguments in \FORM\@. The yes and no arguments are what the main term will be multiplied by when afterwards the range forms a Lyndon word or does not, respectively. As for islyndon, one may specifically work with minimal or maximal cyclic permutations by specifying $<$/- or $>$/+ markers, respectively. If the result is not a Lyndon word, it will be a minimal or maximal cyclic permutation that is not unique. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_13) \begin{verbatim} CFunction f; Symbol y,n; Local test = f(0) + f(1) + f(0,1) + f(0,0,1) + f(0,1,1) + f(0,0) + f(1,0) + f(1,1) + f(1,0,0) + f(0,1,0) + f(1,0,1); Transform f tolyndon(1,last)=(y,n); Print; .end test = f(0)*y + f(0,0)*n + 3*f(0,0,1)*y + 2*f(0,1)*y + 2*f(0,1,1)*y + f(1)*y + f(1,1)*n; \end{verbatim} \leftvitem{3.2cm}{\bf addargs\index{transform!addargs}\index{addargs}} \rightvitem{13cm}{addargs(r1,r2) replaces the indicated range of arguments by their sum. This is effectively the inverse of the SplitArg statement (see \ref{substasplitarg}). For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_14) \begin{verbatim} CFunction f; Symbol x; Local test = f(,...,); Transform f addargs(1,last); Print; .end test = f(x + x^2 + x^3 + x^4 + x^5); \end{verbatim} \leftvitem{3.2cm}{\bf mulargs\index{transform!mulargs}\index{mulargs}} \rightvitem{13cm}{mulargs(r1,r2) replaces the indicated range of arguments by their product. This is effectively the inverse of the FactArg statement (see \ref{substafactarg}). For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_15) \begin{verbatim} CFunction f; Symbol x; Local test = f(,...,); Transform f mulargs(1,last); Print; .end test = f(x^15); \end{verbatim} \leftvitem{3.2cm}{\bf dropargs\index{transform!dropargs}\index{dropargs}} \rightvitem{13cm}{dropargs(r1,r2) removes the indicated range of arguments. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_16) \begin{verbatim} CFunction f,g Local test = f(1,...,5) + g(1,...,5); Transform f dropargs(2,4); Transform g dropargs(1,last); Print; .end test = f(1,5) + g; \end{verbatim} \leftvitem{3.2cm}{\bf selectargs\index{transform!selectargs}\index{selectargs}} \rightvitem{13cm}{selectargs(r1,r2) removes all arguments with the exception of the indicated range of arguments. For example:} % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_17) \begin{verbatim} CFunction f,g Local test = f(1,...,5) + g(1,...,5); Transform f selectargs(2,4); Transform g selectargs(1,last); Print; .end test = f(2,3,4) + g(1,2,3,4); \end{verbatim} As a final example, assume that we have some Multiple Zeta Values\index{Multiple Zeta Value}\index{MZV} (see the papers on harmonic sums\index{harmonic sums}, harmonic polylogarithms\index{harmonic polylogarithm} and the MZV data mine\index{MZV data mine}) in the sum notation, but for calculational reasons we would like to use a binary encoding (as used in the MZV programs). We could have % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_2) \begin{verbatim} Symbol x,x1,x2; CF H,H1; Off Statistics; L F = H(3,4,2,6,1,1,1,2); repeat id H(?a,x?!{0,1},?b) = H(?a,0,x-1,?b); Print; .sort F = H(0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,1,1,1,0,1); Multiply H1; repeat id H(x?,?a)*H1(?b) = H(?a)*H1(?b,1-x); id H1(?a)*H = H(?a); Print; .sort F = H(1,1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0); repeat id H(x1?,x2?,?a) = H(2*x1+x2,?a); Print; .end F = H(907202); \end{verbatim} The same program written using the transform statement is greatly simplified and runs faster: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_Transform_1) \begin{verbatim} Symbol x,x1,x2; CF H,H1; Off Statistics; L F = H(3,4,2,6,1,1,1,2); Transform,H,explode(1,last), replace(1,last)=(0,1,1,0), encode(1,last):base=2; Print; .end F = H(907202); \end{verbatim} \vspace{10mm} %--#] transform : %--#[ tryreplace : \section{tryreplace} \label{substatryreplace} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & tryreplace \verb:{:{\tt<}name{\tt>} {\tt<}replacement{\tt>}\verb:}:; \\ See also & the replace\_ function (\ref{funreplace}) \end{tabular} \vspace{4mm} The tryreplace\index{tryreplace} statement takes a list of potential replacements with a syntax similar to the arguments of the replace\_\index{replace\_} function\index{function!replace\_} (see \ref{funreplace}). {\FORM} will make a copy of the current term and make the listed replacements. If the resulting term comes before the current term in the sort-ordering of {\FORM} (which depends, for example, on the declaration order of the objects in the term), the current term is replaced by the new term. Otherwise, the current term is unchanged. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_TryReplace_1) \begin{verbatim} Symbol x,y,z; Local test = x+z; * These will replace x by y but not z by y, because z * comes before y in the default sort ordering: TryReplace x,y; TryReplace z,y; Print; .end test = z + y; \end{verbatim} \vspace{10mm} %--#] tryreplace : %--#[ unfactorize : \section{unfactorize} \label{substaunfactorize} \noindent \begin{tabular}{ll} Type & Output control statement\\ Syntax & unfactorize \verb:{:{\tt<}name of expression(s){\tt>}\verb:}:; \\ See also & the chapter on polynomials~\ref{polynomials} and the factorize statement~\ref{substafactorize}. \end{tabular} \vspace{4mm} \noindent Without arguments the statement causes all expressions that were factorized to be 'unfactorized'. This means that all factors are multiplied and the expression is replaced by this new version. Like the factorize statement this statement is an output control statement, which means that it takes effect after an expression has been processed in the current module (see also the factorize~\ref{substafactorize} statement). \noindent Because an immediate multiplication of all factors is sometimes far from optimal, \FORM{} uses a binary scheme to combine factors. After each step there will be a sort operation. This means that when statistics are printed, there may be several statistics for this step. \noindent When the statement has arguments, these arguments should be names of expressions; in this case the unfactorization is applied only to the expressions that are specified. \noindent If one wants to unfactorize all expressions except for a few, one can use the unfactorize statement without arguments and then exclude specific expressions which should not be treated with the nunfactorize statement (see \ref{substanunfactorize}). \vspace{10mm} %--#] unfactorize : %--#[ unhide : \section{unhide} \label{substaunhide} \noindent \begin{tabular}{ll} Type & Specification statement\\ Syntax & unhide; \\ & unhide {\tt<}list of expressions{\tt>}; \\ See also & hide (\ref{substahide}), nhide (\ref{substanhide}), nunhide (\ref{substanunhide}), pushhide (\ref{substapushhide}), pophide (\ref{substapophide}) \end{tabular} \vspace{4mm} \noindent In its\index{unhide} first variety this statement causes all expressions in the hide\index{hide} file\index{file!hide} to become active\index{active} expressions again. In its second variety only the specified expressions are taken from the hide system and become active again. An expression that is made active again can be manipulated again in the module in which the unhide statement occurs. For more information one should look at the hide statement in \ref{substahide}. \vspace{4mm} \noindent Note that if only a number of expressions are taken from the hide system, the hide file may be left with `holes', i.e.\ space between the remaining expressions that no longer contain relevant information. {\FORM} has no mechanism to use the space in these holes. Hence if space is at a premium and many holes develop, one should unhide all expressions (which causes the hide system to be started from zero size again) and then send the relevant expressions back to the hide system. \vspace{10mm} %--#] unhide : %--#[ unittrace : \section{unittrace} \label{substaunittrace} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & u[nittrace] {\tt<}value{\tt>}; \\ See also & trace4 (\ref{substatrace}), tracen (\ref{substatracen}), chisholm (\ref{substachisholm}) \\ & and the chapter on gamma algebra (\ref{gammaalgebra}). \end{tabular} \vspace{4mm} \noindent Sets\index{unittrace} the value of the trace of the unit\index{unit matrix} matrix\index{matrix!unit} in the Dirac\index{Dirac} algebra\index{algebra!Dirac} (i.e.\ the object \verb:g1_(n): for trace line \verb:n:)). The parameter \verb:value: can be either a short positive number or any symbol with the exception of \verb:i_:. See also chapter~\ref{gammaalgebra}. \vspace{10mm} %--#] unittrace : %--#[ vectors : \section{vectors} \label{substavectors} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & v[ectors] {\tt<}list of vectors to be declared{\tt>}; \end{tabular} \vspace{4mm} \noindent Used for the declaration of vectors\index{vector}. Example: \begin{verbatim} Vectors p,q,q1,q2,q3; \end{verbatim} \vspace{10mm} %--#] vectors : %--#[ while : \section{while} \label{substawhile} \noindent \begin{tabular}{ll} Type & Executable statement\\ Syntax & while ( condition ); \\ See also & endwhile (\ref{substaendwhile}), repeat (\ref{substarepeat}), if (\ref{substaif}) \end{tabular} \vspace{4mm} \noindent This statement\index{while} starts a while environment\index{environment!while}. It should be paired with an endwhile\index{endwhile} statement (see \ref{substaendwhile}) which terminates the while environment. The statements between the while and the endwhile statements will be executed as long as the condition is met. For a description of the condition syntax one should consult the if\index{if} statement (see \ref{substaif}). The while/endwhile combination is equivalent to a nested repeat and if environment. If only a single statement is inside the environment, one can also use {\tt while ( condition ) statement;}. For example: % THIS EXAMPLE IS PART OF THE TESTSUITE. CHANGES HERE SHOULD BE APPLIED THERE AS % WELL! (Sta_While_1) \begin{verbatim} Symbol x,y,z; Local Fx = (1+x)^6; Local Fy = (1+y)^6; Local Fz = (1+z)^6; While (Count(x,1) > 3); Multiply 1/x; EndWhile; Repeat; If (Count(y,1) > 3); Multiply 1/y; EndIf; EndRepeat; While (Count(z,1) > 3) Multiply 1/z; Print; .end Fx = 1 + 6*x + 15*x^2 + 42*x^3; Fy = 1 + 6*y + 15*y^2 + 42*y^3; Fz = 1 + 6*z + 15*z^2 + 42*z^3; \end{verbatim} Of course one should try to avoid infinite\index{infinite loop} loops\index{loops!infinite}. In order to maximize the speed of {\FORM} not all internal stacks are protected and hence the result may be that {\FORM} crashes. It is also possible that {\FORM} may detect a shortage of buffer space and quit with an error message. \vspace{4mm} \noindent For each term for which execution reaches the endwhile statement, control jumps back to the while statement. The condition is checked, and if it is met the statements within the while environment are executed again on the term. Otherwise, execution continues after the endwhile statement. \vspace{10mm} %--#] while : %--#[ write : \section{write} \label{substawrite} \noindent \begin{tabular}{ll} Type & Declaration statement\\ Syntax & w[rite] {\tt<}keyword{\tt>}; \\ See also & on (\ref{substaon}), off (\ref{substaoff}) \end{tabular} \vspace{4mm} \noindent This statement\index{write} is considered obsolete\index{obsolete}. All its varieties have been taken over by the on\index{on} statement (see \ref{substaon}) and the off\index{off} statement (see \ref{substaoff}). The current version of {\FORM} will still recognize it, but the user is advised to avoid its usage. In future versions of {\FORM} it is scheduled to be used for a different kind of writing and hence its syntax may change considerably. The conversion program conv2to3 should help in the conversion of programs written for version 2. For completeness we still give the syntax and how it should be converted. The keywords are: \vspace{4mm} \leftvitem{3.5cm}{allnames\index{write!allnames}} \rightvitem{13cm}{Same as: On allnames;} \leftvitem{3.5cm}{allwarnings\index{write!allwarnings}} \rightvitem{13cm}{Same as: On allwarnings;} \leftvitem{3.5cm}{highfirst\index{write!highfirst}} \rightvitem{13cm}{Same as: On highfirst;} \leftvitem{3.5cm}{lowfirst\index{write!lowfirst}} \rightvitem{13cm}{Same as: On lowfirst;} \leftvitem{3.5cm}{names\index{write!names}} \rightvitem{13cm}{Same as: On names;} \leftvitem{3.5cm}{powerfirst\index{write!powerfirst}} \rightvitem{13cm}{Same as: On powerfirst;} \leftvitem{3.5cm}{setup\index{write!setup}} \rightvitem{13cm}{Same as: On setup;} \leftvitem{3.5cm}{shortstatistics\index{write!shortstatistics}} \rightvitem{13cm}{Same as: On shortstatistics;} \leftvitem{3.5cm}{shortstats\index{write!shortstats}} \rightvitem{13cm}{Same as: On shortstats;} \leftvitem{3.5cm}{statistics\index{write!statistics}} \rightvitem{13cm}{Same as: On statistics;} \leftvitem{3.5cm}{stats\index{write!stats}} \rightvitem{13cm}{Same as: On stats;} \leftvitem{3.5cm}{warnings\index{write!warnings}} \rightvitem{13cm}{Same as: On warnings;} \vspace{10mm} %--#] write : form-5.0.1/doc/Makefile.in0000644000175100017510000005217415217035732010773 # Makefile.in generated by automake 1.16.5 from Makefile.am. # @configure_input@ # Copyright (C) 1994-2021 Free Software Foundation, Inc. # This Makefile.in is free software; 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PROJECT_NAME = FORM # The PROJECT_NUMBER tag can be used to enter a project or revision number. # This could be handy for archiving the generated documentation or # if some version control system is used. PROJECT_NUMBER = $(PROJECT_NUMBER) # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) # base path where the generated documentation will be put. # If a relative path is entered, it will be relative to the location # where doxygen was started. If left blank the current directory will be used. OUTPUT_DIRECTORY = # The OUTPUT_LANGUAGE tag is used to specify the language in which all # documentation generated by doxygen is written. Doxygen will use this # information to generate all constant output in the proper language. # The default language is English, other supported languages are: # Brazilian, Catalan, Chinese, Chinese-Traditional, Croatian, Czech, Danish, Dutch, # Finnish, French, German, Greek, Hungarian, Italian, Japanese, Japanese-en # (Japanese with English messages), Korean, Norwegian, Polish, Portuguese, # Romanian, Russian, Serbian, Slovak, Slovene, Spanish, Swedish, and Ukrainian. OUTPUT_LANGUAGE = English # This tag can be used to specify the encoding used in the generated output. # The encoding is not always determined by the language that is chosen, # but also whether or not the output is meant for Windows or non-Windows users. # In case there is a difference, setting the USE_WINDOWS_ENCODING tag to YES # forces the Windows encoding (this is the default for the Windows binary), # whereas setting the tag to NO uses a Unix-style encoding (the default for # all platforms other than Windows). USE_WINDOWS_ENCODING = NO # If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will # include brief member descriptions after the members that are listed in # the file and class documentation (similar to JavaDoc). # Set to NO to disable this. BRIEF_MEMBER_DESC = YES # If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend # the brief description of a member or function before the detailed description. # Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the # brief descriptions will be completely suppressed. REPEAT_BRIEF = YES # This tag implements a quasi-intelligent brief description abbreviator # that is used to form the text in various listings. Each string # in this list, if found as the leading text of the brief description, will be # stripped from the text and the result after processing the whole list, is used # as the annotated text. Otherwise, the brief description is used as-is. If left # blank, the following values are used ("$name" is automatically replaced with the # name of the entity): "The $name class" "The $name widget" "The $name file" # "is" "provides" "specifies" "contains" "represents" "a" "an" "the" ABBREVIATE_BRIEF = # If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then # Doxygen will generate a detailed section even if there is only a brief # description. ALWAYS_DETAILED_SEC = NO # If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all inherited # members of a class in the documentation of that class as if those members were # ordinary class members. Constructors, destructors and assignment operators of # the base classes will not be shown. INLINE_INHERITED_MEMB = NO # If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full # path before files name in the file list and in the header files. If set # to NO the shortest path that makes the file name unique will be used. FULL_PATH_NAMES = NO # If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag # can be used to strip a user-defined part of the path. Stripping is # only done if one of the specified strings matches the left-hand part of # the path. It is allowed to use relative paths in the argument list. STRIP_FROM_PATH = # If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter # (but less readable) file names. This can be useful is your file systems # doesn't support long names like on DOS, Mac, or CD-ROM. SHORT_NAMES = NO # If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen # will interpret the first line (until the first dot) of a JavaDoc-style # comment as the brief description. If set to NO, the JavaDoc # comments will behave just like the Qt-style comments (thus requiring an # explicit @brief command for a brief description. JAVADOC_AUTOBRIEF = NO # The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen # treat a multi-line C++ special comment block (i.e. a block of //! or /// # comments) as a brief description. This used to be the default behaviour. # The new default is to treat a multi-line C++ comment block as a detailed # description. Set this tag to YES if you prefer the old behaviour instead. MULTILINE_CPP_IS_BRIEF = NO # If the DETAILS_AT_TOP tag is set to YES then Doxygen # will output the detailed description near the top, like JavaDoc. # If set to NO, the detailed description appears after the member # documentation. DETAILS_AT_TOP = NO # If the INHERIT_DOCS tag is set to YES (the default) then an undocumented # member inherits the documentation from any documented member that it # re-implements. INHERIT_DOCS = YES # If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC # tag is set to YES, then doxygen will reuse the documentation of the first # member in the group (if any) for the other members of the group. By default # all members of a group must be documented explicitly. DISTRIBUTE_GROUP_DOC = YES # The TAB_SIZE tag can be used to set the number of spaces in a tab. # Doxygen uses this value to replace tabs by spaces in code fragments. TAB_SIZE = 4 # This tag can be used to specify a number of aliases that acts # as commands in the documentation. An alias has the form "name=value". # For example adding "sideeffect=\par Side Effects:\n" will allow you to # put the command \sideeffect (or @sideeffect) in the documentation, which # will result in a user-defined paragraph with heading "Side Effects:". # You can put \n's in the value part of an alias to insert newlines. ALIASES = # Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C sources # only. Doxygen will then generate output that is more tailored for C. # For instance, some of the names that are used will be different. The list # of all members will be omitted, etc. OPTIMIZE_OUTPUT_FOR_C = YES # Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java sources # only. Doxygen will then generate output that is more tailored for Java. # For instance, namespaces will be presented as packages, qualified scopes # will look different, etc. OPTIMIZE_OUTPUT_JAVA = NO # Set the SUBGROUPING tag to YES (the default) to allow class member groups of # the same type (for instance a group of public functions) to be put as a # subgroup of that type (e.g. under the Public Functions section). Set it to # NO to prevent subgrouping. Alternatively, this can be done per class using # the \nosubgrouping command. SUBGROUPING = YES #--------------------------------------------------------------------------- # Build related configuration options #--------------------------------------------------------------------------- # If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in # documentation are documented, even if no documentation was available. # Private class members and static file members will be hidden unless # the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES EXTRACT_ALL = NO # If the EXTRACT_PRIVATE tag is set to YES all private members of a class # will be included in the documentation. EXTRACT_PRIVATE = NO # If the EXTRACT_STATIC tag is set to YES all static members of a file # will be included in the documentation. EXTRACT_STATIC = NO # If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs) # defined locally in source files will be included in the documentation. # If set to NO only classes defined in header files are included. EXTRACT_LOCAL_CLASSES = YES # If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all # undocumented members of documented classes, files or namespaces. # If set to NO (the default) these members will be included in the # various overviews, but no documentation section is generated. # This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_MEMBERS = NO # If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all # undocumented classes that are normally visible in the class hierarchy. # If set to NO (the default) these classes will be included in the various # overviews. This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_CLASSES = NO # If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all # friend (class|struct|union) declarations. # If set to NO (the default) these declarations will be included in the # documentation. HIDE_FRIEND_COMPOUNDS = NO # If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any # documentation blocks found inside the body of a function. # If set to NO (the default) these blocks will be appended to the # function's detailed documentation block. HIDE_IN_BODY_DOCS = NO # The INTERNAL_DOCS tag determines if documentation # that is typed after a \internal command is included. If the tag is set # to NO (the default) then the documentation will be excluded. # Set it to YES to include the internal documentation. INTERNAL_DOCS = NO # If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate # file names in lower-case letters. If set to YES upper-case letters are also # allowed. This is useful if you have classes or files whose names only differ # in case and if your file system supports case sensitive file names. Windows # users are advised to set this option to NO. CASE_SENSE_NAMES = YES # If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen # will show members with their full class and namespace scopes in the # documentation. If set to YES the scope will be hidden. HIDE_SCOPE_NAMES = YES # If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen # will put a list of the files that are included by a file in the documentation # of that file. SHOW_INCLUDE_FILES = YES # If the INLINE_INFO tag is set to YES (the default) then a tag [inline] # is inserted in the documentation for inline members. INLINE_INFO = YES # If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen # will sort the (detailed) documentation of file and class members # alphabetically by member name. If set to NO the members will appear in # declaration order. SORT_MEMBER_DOCS = NO # The GENERATE_TODOLIST tag can be used to enable (YES) or # disable (NO) the todo list. This list is created by putting \todo # commands in the documentation. GENERATE_TODOLIST = YES # The GENERATE_TESTLIST tag can be used to enable (YES) or # disable (NO) the test list. This list is created by putting \test # commands in the documentation. GENERATE_TESTLIST = YES # The GENERATE_BUGLIST tag can be used to enable (YES) or # disable (NO) the bug list. This list is created by putting \bug # commands in the documentation. GENERATE_BUGLIST = YES # The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or # disable (NO) the deprecated list. This list is created by putting # \deprecated commands in the documentation. GENERATE_DEPRECATEDLIST= YES # The ENABLED_SECTIONS tag can be used to enable conditional # documentation sections, marked by \if sectionname ... \endif. ENABLED_SECTIONS = # The MAX_INITIALIZER_LINES tag determines the maximum number of lines # the initial value of a variable or define consists of for it to appear in # the documentation. If the initializer consists of more lines than specified # here it will be hidden. Use a value of 0 to hide initializers completely. # The appearance of the initializer of individual variables and defines in the # documentation can be controlled using \showinitializer or \hideinitializer # command in the documentation regardless of this setting. MAX_INITIALIZER_LINES = 30 # Set the SHOW_USED_FILES tag to NO to disable the list of files generated # at the bottom of the documentation of classes and structs. If set to YES the # list will mention the files that were used to generate the documentation. SHOW_USED_FILES = YES #--------------------------------------------------------------------------- # configuration options related to warning and progress messages #--------------------------------------------------------------------------- # The QUIET tag can be used to turn on/off the messages that are generated # by doxygen. Possible values are YES and NO. If left blank NO is used. QUIET = NO # The WARNINGS tag can be used to turn on/off the warning messages that are # generated by doxygen. Possible values are YES and NO. If left blank # NO is used. WARNINGS = YES # If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings # for undocumented members. If EXTRACT_ALL is set to YES then this flag will # automatically be disabled. WARN_IF_UNDOCUMENTED = YES # If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for # potential errors in the documentation, such as not documenting some # parameters in a documented function, or documenting parameters that # don't exist or using markup commands wrongly. WARN_IF_DOC_ERROR = YES # The WARN_FORMAT tag determines the format of the warning messages that # doxygen can produce. The string should contain the $file, $line, and $text # tags, which will be replaced by the file and line number from which the # warning originated and the warning text. WARN_FORMAT = "$file:$line: $text" # The WARN_LOGFILE tag can be used to specify a file to which warning # and error messages should be written. If left blank the output is written # to stderr. WARN_LOGFILE = #--------------------------------------------------------------------------- # configuration options related to the input files #--------------------------------------------------------------------------- # The INPUT tag can be used to specify the files and/or directories that contain # documented source files. You may enter file names like "myfile.cpp" or # directories like "/usr/src/myproject". Separate the files or directories # with spaces. INPUT = @top_srcdir@/sources # If the value of the INPUT tag contains directories, you can use the # FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank the following patterns are tested: # *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh *.hxx *.hpp # *.h++ *.idl *.odl *.cs *.php *.php3 *.inc FILE_PATTERNS = *.c *.cc *.h # The RECURSIVE tag can be used to turn specify whether or not subdirectories # should be searched for input files as well. Possible values are YES and NO. # If left blank NO is used. RECURSIVE = NO # The EXCLUDE tag can be used to specify files and/or directories that should # excluded from the INPUT source files. This way you can easily exclude a # subdirectory from a directory tree whose root is specified with the INPUT tag. EXCLUDE = # The EXCLUDE_SYMLINKS tag can be used select whether or not files or directories # that are symbolic links (a Unix filesystem feature) are excluded from the input. EXCLUDE_SYMLINKS = NO # If the value of the INPUT tag contains directories, you can use the # EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude # certain files from those directories. EXCLUDE_PATTERNS = # The EXAMPLE_PATH tag can be used to specify one or more files or # directories that contain example code fragments that are included (see # the \include command). EXAMPLE_PATH = # If the value of the EXAMPLE_PATH tag contains directories, you can use the # EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank all files are included. EXAMPLE_PATTERNS = # If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be # searched for input files to be used with the \include or \dontinclude # commands irrespective of the value of the RECURSIVE tag. # Possible values are YES and NO. If left blank NO is used. EXAMPLE_RECURSIVE = NO # The IMAGE_PATH tag can be used to specify one or more files or # directories that contain image that are included in the documentation (see # the \image command). IMAGE_PATH = # The INPUT_FILTER tag can be used to specify a program that doxygen should # invoke to filter for each input file. Doxygen will invoke the filter program # by executing (via popen()) the command , where # is the value of the INPUT_FILTER tag, and is the name of an # input file. Doxygen will then use the output that the filter program writes # to standard output. INPUT_FILTER = # If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using # INPUT_FILTER) will be used to filter the input files when producing source # files to browse (i.e. when SOURCE_BROWSER is set to YES). FILTER_SOURCE_FILES = NO #--------------------------------------------------------------------------- # configuration options related to source browsing #--------------------------------------------------------------------------- # If the SOURCE_BROWSER tag is set to YES then a list of source files will # be generated. Documented entities will be cross-referenced with these sources. # Note: To get rid of all source code in the generated output, make sure also # VERBATIM_HEADERS is set to NO. SOURCE_BROWSER = YES # Setting the INLINE_SOURCES tag to YES will include the body # of functions and classes directly in the documentation. INLINE_SOURCES = NO # Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct # doxygen to hide any special comment blocks from generated source code # fragments. Normal C and C++ comments will always remain visible. STRIP_CODE_COMMENTS = YES # If the REFERENCED_BY_RELATION tag is set to YES (the default) # then for each documented function all documented # functions referencing it will be listed. REFERENCED_BY_RELATION = YES # If the REFERENCES_RELATION tag is set to YES (the default) # then for each documented function all documented entities # called/used by that function will be listed. REFERENCES_RELATION = YES # If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen # will generate a verbatim copy of the header file for each class for # which an include is specified. Set to NO to disable this. VERBATIM_HEADERS = YES #--------------------------------------------------------------------------- # configuration options related to the alphabetical class index #--------------------------------------------------------------------------- # If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index # of all compounds will be generated. Enable this if the project # contains a lot of classes, structs, unions or interfaces. ALPHABETICAL_INDEX = YES # If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then # the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns # in which this list will be split (can be a number in the range [1..20]) COLS_IN_ALPHA_INDEX = 5 # In case all classes in a project start with a common prefix, all # classes will be put under the same header in the alphabetical index. # The IGNORE_PREFIX tag can be used to specify one or more prefixes that # should be ignored while generating the index headers. IGNORE_PREFIX = #--------------------------------------------------------------------------- # configuration options related to the HTML output #--------------------------------------------------------------------------- # If the GENERATE_HTML tag is set to YES (the default) Doxygen will # generate HTML output. GENERATE_HTML = YES # The HTML_OUTPUT tag is used to specify where the HTML docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `html' will be used as the default path. HTML_OUTPUT = html # The HTML_FILE_EXTENSION tag can be used to specify the file extension for # each generated HTML page (for example: .htm,.php,.asp). If it is left blank # doxygen will generate files with .html extension. HTML_FILE_EXTENSION = .html # The HTML_HEADER tag can be used to specify a personal HTML header for # each generated HTML page. If it is left blank doxygen will generate a # standard header. HTML_HEADER = # The HTML_FOOTER tag can be used to specify a personal HTML footer for # each generated HTML page. If it is left blank doxygen will generate a # standard footer. HTML_FOOTER = # The HTML_STYLESHEET tag can be used to specify a user-defined cascading # style sheet that is used by each HTML page. It can be used to # fine-tune the look of the HTML output. If the tag is left blank doxygen # will generate a default style sheet. Note that doxygen will try to copy # the style sheet file to the HTML output directory, so don't put your own # stylesheet in the HTML output directory as well, or it will be erased! HTML_STYLESHEET = # If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes, # files or namespaces will be aligned in HTML using tables. If set to # NO a bullet list will be used. HTML_ALIGN_MEMBERS = YES # If the GENERATE_HTMLHELP tag is set to YES, additional index files # will be generated that can be used as input for tools like the # Microsoft HTML help workshop to generate a compressed HTML help file (.chm) # of the generated HTML documentation. GENERATE_HTMLHELP = NO # If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can # be used to specify the file name of the resulting .chm file. You # can add a path in front of the file if the result should not be # written to the html output directory. CHM_FILE = # If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can # be used to specify the location (absolute path including file name) of # the HTML help compiler (hhc.exe). If non-empty doxygen will try to run # the HTML help compiler on the generated index.hhp. HHC_LOCATION = # If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag # controls if a separate .chi index file is generated (YES) or that # it should be included in the master .chm file (NO). GENERATE_CHI = NO # If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag # controls whether a binary table of contents is generated (YES) or a # normal table of contents (NO) in the .chm file. BINARY_TOC = NO # The TOC_EXPAND flag can be set to YES to add extra items for group members # to the contents of the HTML help documentation and to the tree view. TOC_EXPAND = NO # The DISABLE_INDEX tag can be used to turn on/off the condensed index at # top of each HTML page. The value NO (the default) enables the index and # the value YES disables it. DISABLE_INDEX = NO # This tag can be used to set the number of enum values (range [1..20]) # that doxygen will group on one line in the generated HTML documentation. ENUM_VALUES_PER_LINE = 4 # If the GENERATE_TREEVIEW tag is set to YES, a side panel will be # generated containing a tree-like index structure (just like the one that # is generated for HTML Help). For this to work a browser that supports # JavaScript, DHTML, CSS and frames is required (for instance Mozilla 1.0+, # Netscape 6.0+, Internet explorer 5.0+, or Konqueror). Windows users are # probably better off using the HTML help feature. GENERATE_TREEVIEW = NO # If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be # used to set the initial width (in pixels) of the frame in which the tree # is shown. TREEVIEW_WIDTH = 250 #--------------------------------------------------------------------------- # configuration options related to the LaTeX output #--------------------------------------------------------------------------- # If the GENERATE_LATEX tag is set to YES (the default) Doxygen will # generate Latex output. GENERATE_LATEX = NO # The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `latex' will be used as the default path. LATEX_OUTPUT = latex # The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be # invoked. If left blank `latex' will be used as the default command name. LATEX_CMD_NAME = latex # The MAKEINDEX_CMD_NAME tag can be used to specify the command name to # generate index for LaTeX. If left blank `makeindex' will be used as the # default command name. MAKEINDEX_CMD_NAME = makeindex # If the COMPACT_LATEX tag is set to YES Doxygen generates more compact # LaTeX documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_LATEX = NO # The PAPER_TYPE tag can be used to set the paper type that is used # by the printer. Possible values are: a4, a4wide, letter, legal and # executive. If left blank a4wide will be used. PAPER_TYPE = a4wide # The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX # packages that should be included in the LaTeX output. EXTRA_PACKAGES = # The LATEX_HEADER tag can be used to specify a personal LaTeX header for # the generated latex document. The header should contain everything until # the first chapter. If it is left blank doxygen will generate a # standard header. Notice: only use this tag if you know what you are doing! LATEX_HEADER = # If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated # is prepared for conversion to pdf (using ps2pdf). The pdf file will # contain links (just like the HTML output) instead of page references # This makes the output suitable for online browsing using a pdf viewer. PDF_HYPERLINKS = NO # If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of # plain latex in the generated Makefile. Set this option to YES to get a # higher quality PDF documentation. USE_PDFLATEX = NO # If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode. # command to the generated LaTeX files. This will instruct LaTeX to keep # running if errors occur, instead of asking the user for help. # This option is also used when generating formulas in HTML. LATEX_BATCHMODE = NO # If LATEX_HIDE_INDICES is set to YES then doxygen will not # include the index chapters (such as File Index, Compound Index, etc.) # in the output. LATEX_HIDE_INDICES = NO #--------------------------------------------------------------------------- # configuration options related to the RTF output #--------------------------------------------------------------------------- # If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output # The RTF output is optimized for Word 97 and may not look very pretty with # other RTF readers or editors. GENERATE_RTF = NO # The RTF_OUTPUT tag is used to specify where the RTF docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `rtf' will be used as the default path. RTF_OUTPUT = rtf # If the COMPACT_RTF tag is set to YES Doxygen generates more compact # RTF documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_RTF = NO # If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated # will contain hyperlink fields. The RTF file will # contain links (just like the HTML output) instead of page references. # This makes the output suitable for online browsing using WORD or other # programs which support those fields. # Note: wordpad (write) and others do not support links. RTF_HYPERLINKS = NO # Load stylesheet definitions from file. Syntax is similar to doxygen's # config file, i.e. a series of assignments. You only have to provide # replacements, missing definitions are set to their default value. RTF_STYLESHEET_FILE = # Set optional variables used in the generation of an rtf document. # Syntax is similar to doxygen's config file. RTF_EXTENSIONS_FILE = #--------------------------------------------------------------------------- # configuration options related to the man page output #--------------------------------------------------------------------------- # If the GENERATE_MAN tag is set to YES (the default) Doxygen will # generate man pages GENERATE_MAN = NO # The MAN_OUTPUT tag is used to specify where the man pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `man' will be used as the default path. MAN_OUTPUT = man # The MAN_EXTENSION tag determines the extension that is added to # the generated man pages (default is the subroutine's section .3) MAN_EXTENSION = .3 # If the MAN_LINKS tag is set to YES and Doxygen generates man output, # then it will generate one additional man file for each entity # documented in the real man page(s). These additional files # only source the real man page, but without them the man command # would be unable to find the correct page. The default is NO. MAN_LINKS = NO #--------------------------------------------------------------------------- # configuration options related to the XML output #--------------------------------------------------------------------------- # If the GENERATE_XML tag is set to YES Doxygen will # generate an XML file that captures the structure of # the code including all documentation. GENERATE_XML = NO # The XML_OUTPUT tag is used to specify where the XML pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `xml' will be used as the default path. XML_OUTPUT = xml # The XML_SCHEMA tag can be used to specify an XML schema, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_SCHEMA = # The XML_DTD tag can be used to specify an XML DTD, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_DTD = # If the XML_PROGRAMLISTING tag is set to YES Doxygen will # dump the program listings (including syntax highlighting # and cross-referencing information) to the XML output. Note that # enabling this will significantly increase the size of the XML output. XML_PROGRAMLISTING = YES #--------------------------------------------------------------------------- # configuration options for the AutoGen Definitions output #--------------------------------------------------------------------------- # If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will # generate an AutoGen Definitions (see autogen.sf.net) file # that captures the structure of the code including all # documentation. Note that this feature is still experimental # and incomplete at the moment. GENERATE_AUTOGEN_DEF = NO #--------------------------------------------------------------------------- # configuration options related to the Perl module output #--------------------------------------------------------------------------- # If the GENERATE_PERLMOD tag is set to YES Doxygen will # generate a Perl module file that captures the structure of # the code including all documentation. Note that this # feature is still experimental and incomplete at the # moment. GENERATE_PERLMOD = NO # If the PERLMOD_LATEX tag is set to YES Doxygen will generate # the necessary Makefile rules, Perl scripts and LaTeX code to be able # to generate PDF and DVI output from the Perl module output. PERLMOD_LATEX = NO # If the PERLMOD_PRETTY tag is set to YES the Perl module output will be # nicely formatted so it can be parsed by a human reader. This is useful # if you want to understand what is going on. On the other hand, if this # tag is set to NO the size of the Perl module output will be much smaller # and Perl will parse it just the same. PERLMOD_PRETTY = YES # The names of the make variables in the generated doxyrules.make file # are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX. # This is useful so different doxyrules.make files included by the same # Makefile don't overwrite each other's variables. PERLMOD_MAKEVAR_PREFIX = #--------------------------------------------------------------------------- # Configuration options related to the preprocessor #--------------------------------------------------------------------------- # If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will # evaluate all C-preprocessor directives found in the sources and include # files. ENABLE_PREPROCESSING = YES # If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro # names in the source code. If set to NO (the default) only conditional # compilation will be performed. Macro expansion can be done in a controlled # way by setting EXPAND_ONLY_PREDEF to YES. MACRO_EXPANSION = YES # If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES # then the macro expansion is limited to the macros specified with the # PREDEFINED and EXPAND_AS_PREDEFINED tags. EXPAND_ONLY_PREDEF = YES # If the SEARCH_INCLUDES tag is set to YES (the default) the includes files # in the INCLUDE_PATH (see below) will be search if a #include is found. SEARCH_INCLUDES = YES # The INCLUDE_PATH tag can be used to specify one or more directories that # contain include files that are not input files but should be processed by # the preprocessor. INCLUDE_PATH = # You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard # patterns (like *.h and *.hpp) to filter out the header-files in the # directories. If left blank, the patterns specified with FILE_PATTERNS will # be used. INCLUDE_FILE_PATTERNS = *.h # The PREDEFINED tag can be used to specify one or more macro names that # are defined before the preprocessor is started (similar to the -D option of # gcc). The argument of the tag is a list of macros of the form: name # or name=definition (no spaces). If the definition and the = are # omitted =1 is assumed. PREDEFINED = \ "PADPOINTER(a1,a2,a3,a4)=" \ "PADLONG(a1,a2,a3)=" \ "PADINT(a1,a2)=" \ "PADWORD(a1)=" # If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then # this tag can be used to specify a list of macro names that should be expanded. # The macro definition that is found in the sources will be used. # Use the PREDEFINED tag if you want to use a different macro definition. EXPAND_AS_DEFINED = # If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then # doxygen's preprocessor will remove all function-like macros that are alone # on a line, have an all uppercase name, and do not end with a semicolon. Such # function macros are typically used for boiler-plate code, and will confuse the # parser if not removed. SKIP_FUNCTION_MACROS = YES #--------------------------------------------------------------------------- # Configuration::addtions related to external references #--------------------------------------------------------------------------- # The TAGFILES option can be used to specify one or more tagfiles. # Optionally an initial location of the external documentation # can be added for each tagfile. The format of a tag file without # this location is as follows: # TAGFILES = file1 file2 ... # Adding location for the tag files is done as follows: # TAGFILES = file1=loc1 "file2 = loc2" ... # where "loc1" and "loc2" can be relative or absolute paths or # URLs. If a location is present for each tag, the installdox tool # does not have to be run to correct the links. # Note that each tag file must have a unique name # (where the name does NOT include the path) # If a tag file is not located in the directory in which doxygen # is run, you must also specify the path to the tagfile here. TAGFILES = # When a file name is specified after GENERATE_TAGFILE, doxygen will create # a tag file that is based on the input files it reads. GENERATE_TAGFILE = # If the ALLEXTERNALS tag is set to YES all external classes will be listed # in the class index. If set to NO only the inherited external classes # will be listed. ALLEXTERNALS = NO # If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed # in the modules index. If set to NO, only the current project's groups will # be listed. EXTERNAL_GROUPS = YES # The PERL_PATH should be the absolute path and name of the perl script # interpreter (i.e. the result of `which perl'). PERL_PATH = /usr/bin/perl #--------------------------------------------------------------------------- # Configuration options related to the dot tool #--------------------------------------------------------------------------- # If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will # generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with base or # super classes. Setting the tag to NO turns the diagrams off. Note that this # option is superseded by the HAVE_DOT option below. This is only a fallback. It is # recommended to install and use dot, since it yields more powerful graphs. CLASS_DIAGRAMS = YES # If set to YES, the inheritance and collaboration graphs will hide # inheritance and usage relations if the target is undocumented # or is not a class. HIDE_UNDOC_RELATIONS = YES # If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is # available from the path. This tool is part of Graphviz, a graph visualization # toolkit from AT&T and Lucent Bell Labs. The other options in this section # have no effect if this option is set to NO (the default) HAVE_DOT = NO # If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen # will generate a graph for each documented class showing the direct and # indirect inheritance relations. Setting this tag to YES will force the # the CLASS_DIAGRAMS tag to NO. CLASS_GRAPH = YES # If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen # will generate a graph for each documented class showing the direct and # indirect implementation dependencies (inheritance, containment, and # class references variables) of the class with other documented classes. COLLABORATION_GRAPH = YES # If the UML_LOOK tag is set to YES doxygen will generate inheritance and # collaboration diagrams in a style similar to the OMG's Unified Modeling # Language. UML_LOOK = NO # If set to YES, the inheritance and collaboration graphs will show the # relations between templates and their instances. TEMPLATE_RELATIONS = NO # If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT # tags are set to YES then doxygen will generate a graph for each documented # file showing the direct and indirect include dependencies of the file with # other documented files. INCLUDE_GRAPH = YES # If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and # HAVE_DOT tags are set to YES then doxygen will generate a graph for each # documented header file showing the documented files that directly or # indirectly include this file. INCLUDED_BY_GRAPH = YES # If the CALL_GRAPH and HAVE_DOT tags are set to YES then doxygen will # generate a call dependency graph for every global function or class method. # Note that enabling this option will significantly increase the time of a run. # So in most cases it will be better to enable call graphs for selected # functions only using the \callgraph command. CALL_GRAPH = NO # If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen # will graphical hierarchy of all classes instead of a textual one. GRAPHICAL_HIERARCHY = YES # The DOT_IMAGE_FORMAT tag can be used to set the image format of the images # generated by dot. Possible values are png, jpg, or gif # If left blank png will be used. DOT_IMAGE_FORMAT = png # The tag DOT_PATH can be used to specify the path where the dot tool can be # found. If left blank, it is assumed the dot tool can be found on the path. DOT_PATH = # The DOTFILE_DIRS tag can be used to specify one or more directories that # contain dot files that are included in the documentation (see the # \dotfile command). DOTFILE_DIRS = # The MAX_DOT_GRAPH_WIDTH tag can be used to set the maximum allowed width # (in pixels) of the graphs generated by dot. If a graph becomes larger than # this value, doxygen will try to truncate the graph, so that it fits within # the specified constraint. Beware that most browsers cannot cope with very # large images. MAX_DOT_GRAPH_WIDTH = 1024 # The MAX_DOT_GRAPH_HEIGHT tag can be used to set the maximum allows height # (in pixels) of the graphs generated by dot. If a graph becomes larger than # this value, doxygen will try to truncate the graph, so that it fits within # the specified constraint. Beware that most browsers cannot cope with very # large images. MAX_DOT_GRAPH_HEIGHT = 1024 # The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the # graphs generated by dot. A depth value of 3 means that only nodes reachable # from the root by following a path via at most 3 edges will be shown. Nodes that # lay further from the root node will be omitted. Note that setting this option to # 1 or 2 may greatly reduce the computation time needed for large code bases. Also # note that a graph may be further truncated if the graph's image dimensions are # not sufficient to fit the graph (see MAX_DOT_GRAPH_WIDTH and MAX_DOT_GRAPH_HEIGHT). # If 0 is used for the depth value (the default), the graph is not depth-constrained. MAX_DOT_GRAPH_DEPTH = 0 # If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will # generate a legend page explaining the meaning of the various boxes and # arrows in the dot generated graphs. GENERATE_LEGEND = YES # If the DOT_CLEANUP tag is set to YES (the default) Doxygen will # remove the intermediate dot files that are used to generate # the various graphs. DOT_CLEANUP = YES #--------------------------------------------------------------------------- # Configuration::addtions related to the search engine #--------------------------------------------------------------------------- # The SEARCHENGINE tag specifies whether or not a search engine should be # used. If set to NO the values of all tags below this one will be ignored. SEARCHENGINE = NO form-5.0.1/doc/doxygen/DoxyfileLATEX.in0000644000175100017510000012751315217035721013312 # Doxyfile 1.3.5 # This file describes the settings to be used by the documentation system # doxygen (www.doxygen.org) for a project # # All text after a hash (#) is considered a comment and will be ignored # The format is: # TAG = value [value, ...] # For lists items can also be appended using: # TAG += value [value, ...] # Values that contain spaces should be placed between quotes (" ") #--------------------------------------------------------------------------- # Project related configuration options #--------------------------------------------------------------------------- # The PROJECT_NAME tag is a single word (or a sequence of words surrounded # by quotes) that should identify the project. PROJECT_NAME = FORM # The PROJECT_NUMBER tag can be used to enter a project or revision number. # This could be handy for archiving the generated documentation or # if some version control system is used. PROJECT_NUMBER = $(PROJECT_NUMBER) # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) # base path where the generated documentation will be put. # If a relative path is entered, it will be relative to the location # where doxygen was started. If left blank the current directory will be used. OUTPUT_DIRECTORY = # The OUTPUT_LANGUAGE tag is used to specify the language in which all # documentation generated by doxygen is written. Doxygen will use this # information to generate all constant output in the proper language. # The default language is English, other supported languages are: # Brazilian, Catalan, Chinese, Chinese-Traditional, Croatian, Czech, Danish, Dutch, # Finnish, French, German, Greek, Hungarian, Italian, Japanese, Japanese-en # (Japanese with English messages), Korean, Norwegian, Polish, Portuguese, # Romanian, Russian, Serbian, Slovak, Slovene, Spanish, Swedish, and Ukrainian. OUTPUT_LANGUAGE = English # This tag can be used to specify the encoding used in the generated output. # The encoding is not always determined by the language that is chosen, # but also whether or not the output is meant for Windows or non-Windows users. # In case there is a difference, setting the USE_WINDOWS_ENCODING tag to YES # forces the Windows encoding (this is the default for the Windows binary), # whereas setting the tag to NO uses a Unix-style encoding (the default for # all platforms other than Windows). USE_WINDOWS_ENCODING = NO # If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will # include brief member descriptions after the members that are listed in # the file and class documentation (similar to JavaDoc). # Set to NO to disable this. BRIEF_MEMBER_DESC = YES # If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend # the brief description of a member or function before the detailed description. # Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the # brief descriptions will be completely suppressed. REPEAT_BRIEF = YES # This tag implements a quasi-intelligent brief description abbreviator # that is used to form the text in various listings. Each string # in this list, if found as the leading text of the brief description, will be # stripped from the text and the result after processing the whole list, is used # as the annotated text. Otherwise, the brief description is used as-is. If left # blank, the following values are used ("$name" is automatically replaced with the # name of the entity): "The $name class" "The $name widget" "The $name file" # "is" "provides" "specifies" "contains" "represents" "a" "an" "the" ABBREVIATE_BRIEF = # If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then # Doxygen will generate a detailed section even if there is only a brief # description. ALWAYS_DETAILED_SEC = NO # If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all inherited # members of a class in the documentation of that class as if those members were # ordinary class members. Constructors, destructors and assignment operators of # the base classes will not be shown. INLINE_INHERITED_MEMB = NO # If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full # path before files name in the file list and in the header files. If set # to NO the shortest path that makes the file name unique will be used. FULL_PATH_NAMES = NO # If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag # can be used to strip a user-defined part of the path. Stripping is # only done if one of the specified strings matches the left-hand part of # the path. It is allowed to use relative paths in the argument list. STRIP_FROM_PATH = # If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter # (but less readable) file names. This can be useful is your file systems # doesn't support long names like on DOS, Mac, or CD-ROM. SHORT_NAMES = NO # If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen # will interpret the first line (until the first dot) of a JavaDoc-style # comment as the brief description. If set to NO, the JavaDoc # comments will behave just like the Qt-style comments (thus requiring an # explicit @brief command for a brief description. JAVADOC_AUTOBRIEF = NO # The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen # treat a multi-line C++ special comment block (i.e. a block of //! or /// # comments) as a brief description. This used to be the default behaviour. # The new default is to treat a multi-line C++ comment block as a detailed # description. Set this tag to YES if you prefer the old behaviour instead. MULTILINE_CPP_IS_BRIEF = NO # If the DETAILS_AT_TOP tag is set to YES then Doxygen # will output the detailed description near the top, like JavaDoc. # If set to NO, the detailed description appears after the member # documentation. DETAILS_AT_TOP = NO # If the INHERIT_DOCS tag is set to YES (the default) then an undocumented # member inherits the documentation from any documented member that it # re-implements. INHERIT_DOCS = YES # If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC # tag is set to YES, then doxygen will reuse the documentation of the first # member in the group (if any) for the other members of the group. By default # all members of a group must be documented explicitly. DISTRIBUTE_GROUP_DOC = YES # The TAB_SIZE tag can be used to set the number of spaces in a tab. # Doxygen uses this value to replace tabs by spaces in code fragments. TAB_SIZE = 4 # This tag can be used to specify a number of aliases that acts # as commands in the documentation. An alias has the form "name=value". # For example adding "sideeffect=\par Side Effects:\n" will allow you to # put the command \sideeffect (or @sideeffect) in the documentation, which # will result in a user-defined paragraph with heading "Side Effects:". # You can put \n's in the value part of an alias to insert newlines. ALIASES = # Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C sources # only. Doxygen will then generate output that is more tailored for C. # For instance, some of the names that are used will be different. The list # of all members will be omitted, etc. OPTIMIZE_OUTPUT_FOR_C = YES # Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java sources # only. Doxygen will then generate output that is more tailored for Java. # For instance, namespaces will be presented as packages, qualified scopes # will look different, etc. OPTIMIZE_OUTPUT_JAVA = NO # Set the SUBGROUPING tag to YES (the default) to allow class member groups of # the same type (for instance a group of public functions) to be put as a # subgroup of that type (e.g. under the Public Functions section). Set it to # NO to prevent subgrouping. Alternatively, this can be done per class using # the \nosubgrouping command. SUBGROUPING = YES #--------------------------------------------------------------------------- # Build related configuration options #--------------------------------------------------------------------------- # If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in # documentation are documented, even if no documentation was available. # Private class members and static file members will be hidden unless # the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES EXTRACT_ALL = NO # If the EXTRACT_PRIVATE tag is set to YES all private members of a class # will be included in the documentation. EXTRACT_PRIVATE = NO # If the EXTRACT_STATIC tag is set to YES all static members of a file # will be included in the documentation. EXTRACT_STATIC = NO # If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs) # defined locally in source files will be included in the documentation. # If set to NO only classes defined in header files are included. EXTRACT_LOCAL_CLASSES = YES # If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all # undocumented members of documented classes, files or namespaces. # If set to NO (the default) these members will be included in the # various overviews, but no documentation section is generated. # This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_MEMBERS = NO # If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all # undocumented classes that are normally visible in the class hierarchy. # If set to NO (the default) these classes will be included in the various # overviews. This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_CLASSES = NO # If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all # friend (class|struct|union) declarations. # If set to NO (the default) these declarations will be included in the # documentation. HIDE_FRIEND_COMPOUNDS = NO # If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any # documentation blocks found inside the body of a function. # If set to NO (the default) these blocks will be appended to the # function's detailed documentation block. HIDE_IN_BODY_DOCS = NO # The INTERNAL_DOCS tag determines if documentation # that is typed after a \internal command is included. If the tag is set # to NO (the default) then the documentation will be excluded. # Set it to YES to include the internal documentation. INTERNAL_DOCS = NO # If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate # file names in lower-case letters. If set to YES upper-case letters are also # allowed. This is useful if you have classes or files whose names only differ # in case and if your file system supports case sensitive file names. Windows # users are advised to set this option to NO. CASE_SENSE_NAMES = YES # If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen # will show members with their full class and namespace scopes in the # documentation. If set to YES the scope will be hidden. HIDE_SCOPE_NAMES = NO # If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen # will put a list of the files that are included by a file in the documentation # of that file. SHOW_INCLUDE_FILES = YES # If the INLINE_INFO tag is set to YES (the default) then a tag [inline] # is inserted in the documentation for inline members. INLINE_INFO = YES # If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen # will sort the (detailed) documentation of file and class members # alphabetically by member name. If set to NO the members will appear in # declaration order. SORT_MEMBER_DOCS = NO # The GENERATE_TODOLIST tag can be used to enable (YES) or # disable (NO) the todo list. This list is created by putting \todo # commands in the documentation. GENERATE_TODOLIST = YES # The GENERATE_TESTLIST tag can be used to enable (YES) or # disable (NO) the test list. This list is created by putting \test # commands in the documentation. GENERATE_TESTLIST = YES # The GENERATE_BUGLIST tag can be used to enable (YES) or # disable (NO) the bug list. This list is created by putting \bug # commands in the documentation. GENERATE_BUGLIST = YES # The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or # disable (NO) the deprecated list. This list is created by putting # \deprecated commands in the documentation. GENERATE_DEPRECATEDLIST= YES # The ENABLED_SECTIONS tag can be used to enable conditional # documentation sections, marked by \if sectionname ... \endif. ENABLED_SECTIONS = # The MAX_INITIALIZER_LINES tag determines the maximum number of lines # the initial value of a variable or define consists of for it to appear in # the documentation. If the initializer consists of more lines than specified # here it will be hidden. Use a value of 0 to hide initializers completely. # The appearance of the initializer of individual variables and defines in the # documentation can be controlled using \showinitializer or \hideinitializer # command in the documentation regardless of this setting. MAX_INITIALIZER_LINES = 30 # Set the SHOW_USED_FILES tag to NO to disable the list of files generated # at the bottom of the documentation of classes and structs. If set to YES the # list will mention the files that were used to generate the documentation. SHOW_USED_FILES = YES #--------------------------------------------------------------------------- # configuration options related to warning and progress messages #--------------------------------------------------------------------------- # The QUIET tag can be used to turn on/off the messages that are generated # by doxygen. Possible values are YES and NO. If left blank NO is used. QUIET = NO # The WARNINGS tag can be used to turn on/off the warning messages that are # generated by doxygen. Possible values are YES and NO. If left blank # NO is used. WARNINGS = YES # If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings # for undocumented members. If EXTRACT_ALL is set to YES then this flag will # automatically be disabled. WARN_IF_UNDOCUMENTED = YES # If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for # potential errors in the documentation, such as not documenting some # parameters in a documented function, or documenting parameters that # don't exist or using markup commands wrongly. WARN_IF_DOC_ERROR = YES # The WARN_FORMAT tag determines the format of the warning messages that # doxygen can produce. The string should contain the $file, $line, and $text # tags, which will be replaced by the file and line number from which the # warning originated and the warning text. WARN_FORMAT = "$file:$line: $text" # The WARN_LOGFILE tag can be used to specify a file to which warning # and error messages should be written. If left blank the output is written # to stderr. WARN_LOGFILE = #--------------------------------------------------------------------------- # configuration options related to the input files #--------------------------------------------------------------------------- # The INPUT tag can be used to specify the files and/or directories that contain # documented source files. You may enter file names like "myfile.cpp" or # directories like "/usr/src/myproject". Separate the files or directories # with spaces. INPUT = @top_srcdir@/sources # If the value of the INPUT tag contains directories, you can use the # FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank the following patterns are tested: # *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh *.hxx *.hpp # *.h++ *.idl *.odl *.cs *.php *.php3 *.inc FILE_PATTERNS = *.c *.cc *.h # The RECURSIVE tag can be used to turn specify whether or not subdirectories # should be searched for input files as well. Possible values are YES and NO. # If left blank NO is used. RECURSIVE = NO # The EXCLUDE tag can be used to specify files and/or directories that should # excluded from the INPUT source files. This way you can easily exclude a # subdirectory from a directory tree whose root is specified with the INPUT tag. EXCLUDE = # The EXCLUDE_SYMLINKS tag can be used select whether or not files or directories # that are symbolic links (a Unix filesystem feature) are excluded from the input. EXCLUDE_SYMLINKS = NO # If the value of the INPUT tag contains directories, you can use the # EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude # certain files from those directories. EXCLUDE_PATTERNS = # The EXAMPLE_PATH tag can be used to specify one or more files or # directories that contain example code fragments that are included (see # the \include command). EXAMPLE_PATH = # If the value of the EXAMPLE_PATH tag contains directories, you can use the # EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank all files are included. EXAMPLE_PATTERNS = # If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be # searched for input files to be used with the \include or \dontinclude # commands irrespective of the value of the RECURSIVE tag. # Possible values are YES and NO. If left blank NO is used. EXAMPLE_RECURSIVE = NO # The IMAGE_PATH tag can be used to specify one or more files or # directories that contain image that are included in the documentation (see # the \image command). IMAGE_PATH = # The INPUT_FILTER tag can be used to specify a program that doxygen should # invoke to filter for each input file. Doxygen will invoke the filter program # by executing (via popen()) the command , where # is the value of the INPUT_FILTER tag, and is the name of an # input file. Doxygen will then use the output that the filter program writes # to standard output. INPUT_FILTER = # If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using # INPUT_FILTER) will be used to filter the input files when producing source # files to browse (i.e. when SOURCE_BROWSER is set to YES). FILTER_SOURCE_FILES = NO #--------------------------------------------------------------------------- # configuration options related to source browsing #--------------------------------------------------------------------------- # If the SOURCE_BROWSER tag is set to YES then a list of source files will # be generated. Documented entities will be cross-referenced with these sources. # Note: To get rid of all source code in the generated output, make sure also # VERBATIM_HEADERS is set to NO. SOURCE_BROWSER = YES # Setting the INLINE_SOURCES tag to YES will include the body # of functions and classes directly in the documentation. INLINE_SOURCES = NO # Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct # doxygen to hide any special comment blocks from generated source code # fragments. Normal C and C++ comments will always remain visible. STRIP_CODE_COMMENTS = YES # If the REFERENCED_BY_RELATION tag is set to YES (the default) # then for each documented function all documented # functions referencing it will be listed. REFERENCED_BY_RELATION = YES # If the REFERENCES_RELATION tag is set to YES (the default) # then for each documented function all documented entities # called/used by that function will be listed. REFERENCES_RELATION = YES # If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen # will generate a verbatim copy of the header file for each class for # which an include is specified. Set to NO to disable this. VERBATIM_HEADERS = YES #--------------------------------------------------------------------------- # configuration options related to the alphabetical class index #--------------------------------------------------------------------------- # If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index # of all compounds will be generated. Enable this if the project # contains a lot of classes, structs, unions or interfaces. ALPHABETICAL_INDEX = YES # If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then # the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns # in which this list will be split (can be a number in the range [1..20]) COLS_IN_ALPHA_INDEX = 5 # In case all classes in a project start with a common prefix, all # classes will be put under the same header in the alphabetical index. # The IGNORE_PREFIX tag can be used to specify one or more prefixes that # should be ignored while generating the index headers. IGNORE_PREFIX = #--------------------------------------------------------------------------- # configuration options related to the HTML output #--------------------------------------------------------------------------- # If the GENERATE_HTML tag is set to YES (the default) Doxygen will # generate HTML output. GENERATE_HTML = NO # The HTML_OUTPUT tag is used to specify where the HTML docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `html' will be used as the default path. HTML_OUTPUT = html # The HTML_FILE_EXTENSION tag can be used to specify the file extension for # each generated HTML page (for example: .htm,.php,.asp). If it is left blank # doxygen will generate files with .html extension. HTML_FILE_EXTENSION = .html # The HTML_HEADER tag can be used to specify a personal HTML header for # each generated HTML page. If it is left blank doxygen will generate a # standard header. HTML_HEADER = # The HTML_FOOTER tag can be used to specify a personal HTML footer for # each generated HTML page. If it is left blank doxygen will generate a # standard footer. HTML_FOOTER = # The HTML_STYLESHEET tag can be used to specify a user-defined cascading # style sheet that is used by each HTML page. It can be used to # fine-tune the look of the HTML output. If the tag is left blank doxygen # will generate a default style sheet. Note that doxygen will try to copy # the style sheet file to the HTML output directory, so don't put your own # stylesheet in the HTML output directory as well, or it will be erased! HTML_STYLESHEET = # If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes, # files or namespaces will be aligned in HTML using tables. If set to # NO a bullet list will be used. HTML_ALIGN_MEMBERS = YES # If the GENERATE_HTMLHELP tag is set to YES, additional index files # will be generated that can be used as input for tools like the # Microsoft HTML help workshop to generate a compressed HTML help file (.chm) # of the generated HTML documentation. GENERATE_HTMLHELP = NO # If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can # be used to specify the file name of the resulting .chm file. You # can add a path in front of the file if the result should not be # written to the html output directory. CHM_FILE = # If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can # be used to specify the location (absolute path including file name) of # the HTML help compiler (hhc.exe). If non-empty doxygen will try to run # the HTML help compiler on the generated index.hhp. HHC_LOCATION = # If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag # controls if a separate .chi index file is generated (YES) or that # it should be included in the master .chm file (NO). GENERATE_CHI = NO # If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag # controls whether a binary table of contents is generated (YES) or a # normal table of contents (NO) in the .chm file. BINARY_TOC = NO # The TOC_EXPAND flag can be set to YES to add extra items for group members # to the contents of the HTML help documentation and to the tree view. TOC_EXPAND = NO # The DISABLE_INDEX tag can be used to turn on/off the condensed index at # top of each HTML page. The value NO (the default) enables the index and # the value YES disables it. DISABLE_INDEX = NO # This tag can be used to set the number of enum values (range [1..20]) # that doxygen will group on one line in the generated HTML documentation. ENUM_VALUES_PER_LINE = 4 # If the GENERATE_TREEVIEW tag is set to YES, a side panel will be # generated containing a tree-like index structure (just like the one that # is generated for HTML Help). For this to work a browser that supports # JavaScript, DHTML, CSS and frames is required (for instance Mozilla 1.0+, # Netscape 6.0+, Internet explorer 5.0+, or Konqueror). Windows users are # probably better off using the HTML help feature. GENERATE_TREEVIEW = NO # If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be # used to set the initial width (in pixels) of the frame in which the tree # is shown. TREEVIEW_WIDTH = 250 #--------------------------------------------------------------------------- # configuration options related to the LaTeX output #--------------------------------------------------------------------------- # If the GENERATE_LATEX tag is set to YES (the default) Doxygen will # generate Latex output. GENERATE_LATEX = YES # The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `latex' will be used as the default path. LATEX_OUTPUT = latex # The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be # invoked. If left blank `latex' will be used as the default command name. LATEX_CMD_NAME = latex # The MAKEINDEX_CMD_NAME tag can be used to specify the command name to # generate index for LaTeX. If left blank `makeindex' will be used as the # default command name. MAKEINDEX_CMD_NAME = makeindex # If the COMPACT_LATEX tag is set to YES Doxygen generates more compact # LaTeX documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_LATEX = NO # The PAPER_TYPE tag can be used to set the paper type that is used # by the printer. Possible values are: a4, a4wide, letter, legal and # executive. If left blank a4wide will be used. PAPER_TYPE = a4wide # The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX # packages that should be included in the LaTeX output. EXTRA_PACKAGES = # The LATEX_HEADER tag can be used to specify a personal LaTeX header for # the generated latex document. The header should contain everything until # the first chapter. If it is left blank doxygen will generate a # standard header. Notice: only use this tag if you know what you are doing! LATEX_HEADER = # If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated # is prepared for conversion to pdf (using ps2pdf). The pdf file will # contain links (just like the HTML output) instead of page references # This makes the output suitable for online browsing using a pdf viewer. PDF_HYPERLINKS = NO # If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of # plain latex in the generated Makefile. Set this option to YES to get a # higher quality PDF documentation. USE_PDFLATEX = NO # If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode. # command to the generated LaTeX files. This will instruct LaTeX to keep # running if errors occur, instead of asking the user for help. # This option is also used when generating formulas in HTML. LATEX_BATCHMODE = NO # If LATEX_HIDE_INDICES is set to YES then doxygen will not # include the index chapters (such as File Index, Compound Index, etc.) # in the output. LATEX_HIDE_INDICES = NO #--------------------------------------------------------------------------- # configuration options related to the RTF output #--------------------------------------------------------------------------- # If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output # The RTF output is optimized for Word 97 and may not look very pretty with # other RTF readers or editors. GENERATE_RTF = NO # The RTF_OUTPUT tag is used to specify where the RTF docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `rtf' will be used as the default path. RTF_OUTPUT = rtf # If the COMPACT_RTF tag is set to YES Doxygen generates more compact # RTF documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_RTF = NO # If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated # will contain hyperlink fields. The RTF file will # contain links (just like the HTML output) instead of page references. # This makes the output suitable for online browsing using WORD or other # programs which support those fields. # Note: wordpad (write) and others do not support links. RTF_HYPERLINKS = NO # Load stylesheet definitions from file. Syntax is similar to doxygen's # config file, i.e. a series of assignments. You only have to provide # replacements, missing definitions are set to their default value. RTF_STYLESHEET_FILE = # Set optional variables used in the generation of an rtf document. # Syntax is similar to doxygen's config file. RTF_EXTENSIONS_FILE = #--------------------------------------------------------------------------- # configuration options related to the man page output #--------------------------------------------------------------------------- # If the GENERATE_MAN tag is set to YES (the default) Doxygen will # generate man pages GENERATE_MAN = NO # The MAN_OUTPUT tag is used to specify where the man pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `man' will be used as the default path. MAN_OUTPUT = man # The MAN_EXTENSION tag determines the extension that is added to # the generated man pages (default is the subroutine's section .3) MAN_EXTENSION = .3 # If the MAN_LINKS tag is set to YES and Doxygen generates man output, # then it will generate one additional man file for each entity # documented in the real man page(s). These additional files # only source the real man page, but without them the man command # would be unable to find the correct page. The default is NO. MAN_LINKS = NO #--------------------------------------------------------------------------- # configuration options related to the XML output #--------------------------------------------------------------------------- # If the GENERATE_XML tag is set to YES Doxygen will # generate an XML file that captures the structure of # the code including all documentation. GENERATE_XML = NO # The XML_OUTPUT tag is used to specify where the XML pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `xml' will be used as the default path. XML_OUTPUT = xml # The XML_SCHEMA tag can be used to specify an XML schema, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_SCHEMA = # The XML_DTD tag can be used to specify an XML DTD, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_DTD = # If the XML_PROGRAMLISTING tag is set to YES Doxygen will # dump the program listings (including syntax highlighting # and cross-referencing information) to the XML output. Note that # enabling this will significantly increase the size of the XML output. XML_PROGRAMLISTING = YES #--------------------------------------------------------------------------- # configuration options for the AutoGen Definitions output #--------------------------------------------------------------------------- # If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will # generate an AutoGen Definitions (see autogen.sf.net) file # that captures the structure of the code including all # documentation. Note that this feature is still experimental # and incomplete at the moment. GENERATE_AUTOGEN_DEF = NO #--------------------------------------------------------------------------- # configuration options related to the Perl module output #--------------------------------------------------------------------------- # If the GENERATE_PERLMOD tag is set to YES Doxygen will # generate a Perl module file that captures the structure of # the code including all documentation. Note that this # feature is still experimental and incomplete at the # moment. GENERATE_PERLMOD = NO # If the PERLMOD_LATEX tag is set to YES Doxygen will generate # the necessary Makefile rules, Perl scripts and LaTeX code to be able # to generate PDF and DVI output from the Perl module output. PERLMOD_LATEX = NO # If the PERLMOD_PRETTY tag is set to YES the Perl module output will be # nicely formatted so it can be parsed by a human reader. This is useful # if you want to understand what is going on. On the other hand, if this # tag is set to NO the size of the Perl module output will be much smaller # and Perl will parse it just the same. PERLMOD_PRETTY = YES # The names of the make variables in the generated doxyrules.make file # are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX. # This is useful so different doxyrules.make files included by the same # Makefile don't overwrite each other's variables. PERLMOD_MAKEVAR_PREFIX = #--------------------------------------------------------------------------- # Configuration options related to the preprocessor #--------------------------------------------------------------------------- # If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will # evaluate all C-preprocessor directives found in the sources and include # files. ENABLE_PREPROCESSING = YES # If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro # names in the source code. If set to NO (the default) only conditional # compilation will be performed. Macro expansion can be done in a controlled # way by setting EXPAND_ONLY_PREDEF to YES. MACRO_EXPANSION = YES # If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES # then the macro expansion is limited to the macros specified with the # PREDEFINED and EXPAND_AS_PREDEFINED tags. EXPAND_ONLY_PREDEF = YES # If the SEARCH_INCLUDES tag is set to YES (the default) the includes files # in the INCLUDE_PATH (see below) will be search if a #include is found. SEARCH_INCLUDES = YES # The INCLUDE_PATH tag can be used to specify one or more directories that # contain include files that are not input files but should be processed by # the preprocessor. INCLUDE_PATH = # You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard # patterns (like *.h and *.hpp) to filter out the header-files in the # directories. If left blank, the patterns specified with FILE_PATTERNS will # be used. INCLUDE_FILE_PATTERNS = *.h # The PREDEFINED tag can be used to specify one or more macro names that # are defined before the preprocessor is started (similar to the -D option of # gcc). The argument of the tag is a list of macros of the form: name # or name=definition (no spaces). If the definition and the = are # omitted =1 is assumed. PREDEFINED = \ "PADPOINTER(a1,a2,a3,a4)=" \ "PADLONG(a1,a2,a3)=" \ "PADINT(a1,a2)=" \ "PADWORD(a1)=" # If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then # this tag can be used to specify a list of macro names that should be expanded. # The macro definition that is found in the sources will be used. # Use the PREDEFINED tag if you want to use a different macro definition. EXPAND_AS_DEFINED = # If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then # doxygen's preprocessor will remove all function-like macros that are alone # on a line, have an all uppercase name, and do not end with a semicolon. Such # function macros are typically used for boiler-plate code, and will confuse the # parser if not removed. SKIP_FUNCTION_MACROS = YES #--------------------------------------------------------------------------- # Configuration::addtions related to external references #--------------------------------------------------------------------------- # The TAGFILES option can be used to specify one or more tagfiles. # Optionally an initial location of the external documentation # can be added for each tagfile. The format of a tag file without # this location is as follows: # TAGFILES = file1 file2 ... # Adding location for the tag files is done as follows: # TAGFILES = file1=loc1 "file2 = loc2" ... # where "loc1" and "loc2" can be relative or absolute paths or # URLs. If a location is present for each tag, the installdox tool # does not have to be run to correct the links. # Note that each tag file must have a unique name # (where the name does NOT include the path) # If a tag file is not located in the directory in which doxygen # is run, you must also specify the path to the tagfile here. TAGFILES = # When a file name is specified after GENERATE_TAGFILE, doxygen will create # a tag file that is based on the input files it reads. GENERATE_TAGFILE = # If the ALLEXTERNALS tag is set to YES all external classes will be listed # in the class index. If set to NO only the inherited external classes # will be listed. ALLEXTERNALS = NO # If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed # in the modules index. If set to NO, only the current project's groups will # be listed. EXTERNAL_GROUPS = YES # The PERL_PATH should be the absolute path and name of the perl script # interpreter (i.e. the result of `which perl'). PERL_PATH = /usr/bin/perl #--------------------------------------------------------------------------- # Configuration options related to the dot tool #--------------------------------------------------------------------------- # If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will # generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with base or # super classes. Setting the tag to NO turns the diagrams off. Note that this # option is superseded by the HAVE_DOT option below. This is only a fallback. It is # recommended to install and use dot, since it yields more powerful graphs. CLASS_DIAGRAMS = YES # If set to YES, the inheritance and collaboration graphs will hide # inheritance and usage relations if the target is undocumented # or is not a class. HIDE_UNDOC_RELATIONS = YES # If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is # available from the path. This tool is part of Graphviz, a graph visualization # toolkit from AT&T and Lucent Bell Labs. The other options in this section # have no effect if this option is set to NO (the default) HAVE_DOT = NO # If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen # will generate a graph for each documented class showing the direct and # indirect inheritance relations. Setting this tag to YES will force the # the CLASS_DIAGRAMS tag to NO. CLASS_GRAPH = YES # If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen # will generate a graph for each documented class showing the direct and # indirect implementation dependencies (inheritance, containment, and # class references variables) of the class with other documented classes. COLLABORATION_GRAPH = YES # If the UML_LOOK tag is set to YES doxygen will generate inheritance and # collaboration diagrams in a style similar to the OMG's Unified Modeling # Language. UML_LOOK = NO # If set to YES, the inheritance and collaboration graphs will show the # relations between templates and their instances. TEMPLATE_RELATIONS = NO # If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT # tags are set to YES then doxygen will generate a graph for each documented # file showing the direct and indirect include dependencies of the file with # other documented files. INCLUDE_GRAPH = YES # If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and # HAVE_DOT tags are set to YES then doxygen will generate a graph for each # documented header file showing the documented files that directly or # indirectly include this file. INCLUDED_BY_GRAPH = YES # If the CALL_GRAPH and HAVE_DOT tags are set to YES then doxygen will # generate a call dependency graph for every global function or class method. # Note that enabling this option will significantly increase the time of a run. # So in most cases it will be better to enable call graphs for selected # functions only using the \callgraph command. CALL_GRAPH = NO # If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen # will graphical hierarchy of all classes instead of a textual one. GRAPHICAL_HIERARCHY = YES # The DOT_IMAGE_FORMAT tag can be used to set the image format of the images # generated by dot. Possible values are png, jpg, or gif # If left blank png will be used. DOT_IMAGE_FORMAT = png # The tag DOT_PATH can be used to specify the path where the dot tool can be # found. If left blank, it is assumed the dot tool can be found on the path. DOT_PATH = # The DOTFILE_DIRS tag can be used to specify one or more directories that # contain dot files that are included in the documentation (see the # \dotfile command). DOTFILE_DIRS = # The MAX_DOT_GRAPH_WIDTH tag can be used to set the maximum allowed width # (in pixels) of the graphs generated by dot. If a graph becomes larger than # this value, doxygen will try to truncate the graph, so that it fits within # the specified constraint. Beware that most browsers cannot cope with very # large images. MAX_DOT_GRAPH_WIDTH = 1024 # The MAX_DOT_GRAPH_HEIGHT tag can be used to set the maximum allows height # (in pixels) of the graphs generated by dot. If a graph becomes larger than # this value, doxygen will try to truncate the graph, so that it fits within # the specified constraint. Beware that most browsers cannot cope with very # large images. MAX_DOT_GRAPH_HEIGHT = 1024 # The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the # graphs generated by dot. A depth value of 3 means that only nodes reachable # from the root by following a path via at most 3 edges will be shown. Nodes that # lay further from the root node will be omitted. Note that setting this option to # 1 or 2 may greatly reduce the computation time needed for large code bases. Also # note that a graph may be further truncated if the graph's image dimensions are # not sufficient to fit the graph (see MAX_DOT_GRAPH_WIDTH and MAX_DOT_GRAPH_HEIGHT). # If 0 is used for the depth value (the default), the graph is not depth-constrained. MAX_DOT_GRAPH_DEPTH = 0 # If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will # generate a legend page explaining the meaning of the various boxes and # arrows in the dot generated graphs. GENERATE_LEGEND = YES # If the DOT_CLEANUP tag is set to YES (the default) Doxygen will # remove the intermediate dot files that are used to generate # the various graphs. DOT_CLEANUP = YES #--------------------------------------------------------------------------- # Configuration::addtions related to the search engine #--------------------------------------------------------------------------- # The SEARCHENGINE tag specifies whether or not a search engine should be # used. If set to NO the values of all tags below this one will be ignored. SEARCHENGINE = NO form-5.0.1/doc/doxygen/DoxyfilePDFLATEX.in0000644000175100017510000012752315217035721013645 # Doxyfile 1.3.5 # This file describes the settings to be used by the documentation system # doxygen (www.doxygen.org) for a project # # All text after a hash (#) is considered a comment and will be ignored # The format is: # TAG = value [value, ...] # For lists items can also be appended using: # TAG += value [value, ...] # Values that contain spaces should be placed between quotes (" ") #--------------------------------------------------------------------------- # Project related configuration options #--------------------------------------------------------------------------- # The PROJECT_NAME tag is a single word (or a sequence of words surrounded # by quotes) that should identify the project. PROJECT_NAME = FORM # The PROJECT_NUMBER tag can be used to enter a project or revision number. # This could be handy for archiving the generated documentation or # if some version control system is used. PROJECT_NUMBER = $(PROJECT_NUMBER) # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) # base path where the generated documentation will be put. # If a relative path is entered, it will be relative to the location # where doxygen was started. If left blank the current directory will be used. OUTPUT_DIRECTORY = # The OUTPUT_LANGUAGE tag is used to specify the language in which all # documentation generated by doxygen is written. Doxygen will use this # information to generate all constant output in the proper language. # The default language is English, other supported languages are: # Brazilian, Catalan, Chinese, Chinese-Traditional, Croatian, Czech, Danish, Dutch, # Finnish, French, German, Greek, Hungarian, Italian, Japanese, Japanese-en # (Japanese with English messages), Korean, Norwegian, Polish, Portuguese, # Romanian, Russian, Serbian, Slovak, Slovene, Spanish, Swedish, and Ukrainian. OUTPUT_LANGUAGE = English # This tag can be used to specify the encoding used in the generated output. # The encoding is not always determined by the language that is chosen, # but also whether or not the output is meant for Windows or non-Windows users. # In case there is a difference, setting the USE_WINDOWS_ENCODING tag to YES # forces the Windows encoding (this is the default for the Windows binary), # whereas setting the tag to NO uses a Unix-style encoding (the default for # all platforms other than Windows). USE_WINDOWS_ENCODING = NO # If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will # include brief member descriptions after the members that are listed in # the file and class documentation (similar to JavaDoc). # Set to NO to disable this. BRIEF_MEMBER_DESC = YES # If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend # the brief description of a member or function before the detailed description. # Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the # brief descriptions will be completely suppressed. REPEAT_BRIEF = YES # This tag implements a quasi-intelligent brief description abbreviator # that is used to form the text in various listings. Each string # in this list, if found as the leading text of the brief description, will be # stripped from the text and the result after processing the whole list, is used # as the annotated text. Otherwise, the brief description is used as-is. If left # blank, the following values are used ("$name" is automatically replaced with the # name of the entity): "The $name class" "The $name widget" "The $name file" # "is" "provides" "specifies" "contains" "represents" "a" "an" "the" ABBREVIATE_BRIEF = # If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then # Doxygen will generate a detailed section even if there is only a brief # description. ALWAYS_DETAILED_SEC = NO # If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all inherited # members of a class in the documentation of that class as if those members were # ordinary class members. Constructors, destructors and assignment operators of # the base classes will not be shown. INLINE_INHERITED_MEMB = NO # If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full # path before files name in the file list and in the header files. If set # to NO the shortest path that makes the file name unique will be used. FULL_PATH_NAMES = NO # If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag # can be used to strip a user-defined part of the path. Stripping is # only done if one of the specified strings matches the left-hand part of # the path. It is allowed to use relative paths in the argument list. STRIP_FROM_PATH = # If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter # (but less readable) file names. This can be useful is your file systems # doesn't support long names like on DOS, Mac, or CD-ROM. SHORT_NAMES = NO # If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen # will interpret the first line (until the first dot) of a JavaDoc-style # comment as the brief description. If set to NO, the JavaDoc # comments will behave just like the Qt-style comments (thus requiring an # explicit @brief command for a brief description. JAVADOC_AUTOBRIEF = NO # The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen # treat a multi-line C++ special comment block (i.e. a block of //! or /// # comments) as a brief description. This used to be the default behaviour. # The new default is to treat a multi-line C++ comment block as a detailed # description. Set this tag to YES if you prefer the old behaviour instead. MULTILINE_CPP_IS_BRIEF = NO # If the DETAILS_AT_TOP tag is set to YES then Doxygen # will output the detailed description near the top, like JavaDoc. # If set to NO, the detailed description appears after the member # documentation. DETAILS_AT_TOP = NO # If the INHERIT_DOCS tag is set to YES (the default) then an undocumented # member inherits the documentation from any documented member that it # re-implements. INHERIT_DOCS = YES # If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC # tag is set to YES, then doxygen will reuse the documentation of the first # member in the group (if any) for the other members of the group. By default # all members of a group must be documented explicitly. DISTRIBUTE_GROUP_DOC = YES # The TAB_SIZE tag can be used to set the number of spaces in a tab. # Doxygen uses this value to replace tabs by spaces in code fragments. TAB_SIZE = 4 # This tag can be used to specify a number of aliases that acts # as commands in the documentation. An alias has the form "name=value". # For example adding "sideeffect=\par Side Effects:\n" will allow you to # put the command \sideeffect (or @sideeffect) in the documentation, which # will result in a user-defined paragraph with heading "Side Effects:". # You can put \n's in the value part of an alias to insert newlines. ALIASES = # Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C sources # only. Doxygen will then generate output that is more tailored for C. # For instance, some of the names that are used will be different. The list # of all members will be omitted, etc. OPTIMIZE_OUTPUT_FOR_C = YES # Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java sources # only. Doxygen will then generate output that is more tailored for Java. # For instance, namespaces will be presented as packages, qualified scopes # will look different, etc. OPTIMIZE_OUTPUT_JAVA = NO # Set the SUBGROUPING tag to YES (the default) to allow class member groups of # the same type (for instance a group of public functions) to be put as a # subgroup of that type (e.g. under the Public Functions section). Set it to # NO to prevent subgrouping. Alternatively, this can be done per class using # the \nosubgrouping command. SUBGROUPING = YES #--------------------------------------------------------------------------- # Build related configuration options #--------------------------------------------------------------------------- # If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in # documentation are documented, even if no documentation was available. # Private class members and static file members will be hidden unless # the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES EXTRACT_ALL = NO # If the EXTRACT_PRIVATE tag is set to YES all private members of a class # will be included in the documentation. EXTRACT_PRIVATE = NO # If the EXTRACT_STATIC tag is set to YES all static members of a file # will be included in the documentation. EXTRACT_STATIC = NO # If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs) # defined locally in source files will be included in the documentation. # If set to NO only classes defined in header files are included. EXTRACT_LOCAL_CLASSES = YES # If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all # undocumented members of documented classes, files or namespaces. # If set to NO (the default) these members will be included in the # various overviews, but no documentation section is generated. # This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_MEMBERS = NO # If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all # undocumented classes that are normally visible in the class hierarchy. # If set to NO (the default) these classes will be included in the various # overviews. This option has no effect if EXTRACT_ALL is enabled. HIDE_UNDOC_CLASSES = NO # If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all # friend (class|struct|union) declarations. # If set to NO (the default) these declarations will be included in the # documentation. HIDE_FRIEND_COMPOUNDS = NO # If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any # documentation blocks found inside the body of a function. # If set to NO (the default) these blocks will be appended to the # function's detailed documentation block. HIDE_IN_BODY_DOCS = NO # The INTERNAL_DOCS tag determines if documentation # that is typed after a \internal command is included. If the tag is set # to NO (the default) then the documentation will be excluded. # Set it to YES to include the internal documentation. INTERNAL_DOCS = NO # If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate # file names in lower-case letters. If set to YES upper-case letters are also # allowed. This is useful if you have classes or files whose names only differ # in case and if your file system supports case sensitive file names. Windows # users are advised to set this option to NO. CASE_SENSE_NAMES = YES # If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen # will show members with their full class and namespace scopes in the # documentation. If set to YES the scope will be hidden. HIDE_SCOPE_NAMES = NO # If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen # will put a list of the files that are included by a file in the documentation # of that file. SHOW_INCLUDE_FILES = YES # If the INLINE_INFO tag is set to YES (the default) then a tag [inline] # is inserted in the documentation for inline members. INLINE_INFO = YES # If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen # will sort the (detailed) documentation of file and class members # alphabetically by member name. If set to NO the members will appear in # declaration order. SORT_MEMBER_DOCS = NO # The GENERATE_TODOLIST tag can be used to enable (YES) or # disable (NO) the todo list. This list is created by putting \todo # commands in the documentation. GENERATE_TODOLIST = YES # The GENERATE_TESTLIST tag can be used to enable (YES) or # disable (NO) the test list. This list is created by putting \test # commands in the documentation. GENERATE_TESTLIST = YES # The GENERATE_BUGLIST tag can be used to enable (YES) or # disable (NO) the bug list. This list is created by putting \bug # commands in the documentation. GENERATE_BUGLIST = YES # The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or # disable (NO) the deprecated list. This list is created by putting # \deprecated commands in the documentation. GENERATE_DEPRECATEDLIST= YES # The ENABLED_SECTIONS tag can be used to enable conditional # documentation sections, marked by \if sectionname ... \endif. ENABLED_SECTIONS = # The MAX_INITIALIZER_LINES tag determines the maximum number of lines # the initial value of a variable or define consists of for it to appear in # the documentation. If the initializer consists of more lines than specified # here it will be hidden. Use a value of 0 to hide initializers completely. # The appearance of the initializer of individual variables and defines in the # documentation can be controlled using \showinitializer or \hideinitializer # command in the documentation regardless of this setting. MAX_INITIALIZER_LINES = 30 # Set the SHOW_USED_FILES tag to NO to disable the list of files generated # at the bottom of the documentation of classes and structs. If set to YES the # list will mention the files that were used to generate the documentation. SHOW_USED_FILES = YES #--------------------------------------------------------------------------- # configuration options related to warning and progress messages #--------------------------------------------------------------------------- # The QUIET tag can be used to turn on/off the messages that are generated # by doxygen. Possible values are YES and NO. If left blank NO is used. QUIET = NO # The WARNINGS tag can be used to turn on/off the warning messages that are # generated by doxygen. Possible values are YES and NO. If left blank # NO is used. WARNINGS = YES # If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings # for undocumented members. If EXTRACT_ALL is set to YES then this flag will # automatically be disabled. WARN_IF_UNDOCUMENTED = YES # If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for # potential errors in the documentation, such as not documenting some # parameters in a documented function, or documenting parameters that # don't exist or using markup commands wrongly. WARN_IF_DOC_ERROR = YES # The WARN_FORMAT tag determines the format of the warning messages that # doxygen can produce. The string should contain the $file, $line, and $text # tags, which will be replaced by the file and line number from which the # warning originated and the warning text. WARN_FORMAT = "$file:$line: $text" # The WARN_LOGFILE tag can be used to specify a file to which warning # and error messages should be written. If left blank the output is written # to stderr. WARN_LOGFILE = #--------------------------------------------------------------------------- # configuration options related to the input files #--------------------------------------------------------------------------- # The INPUT tag can be used to specify the files and/or directories that contain # documented source files. You may enter file names like "myfile.cpp" or # directories like "/usr/src/myproject". Separate the files or directories # with spaces. INPUT = @top_srcdir@/sources # If the value of the INPUT tag contains directories, you can use the # FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank the following patterns are tested: # *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh *.hxx *.hpp # *.h++ *.idl *.odl *.cs *.php *.php3 *.inc FILE_PATTERNS = *.c *.cc *.h # The RECURSIVE tag can be used to turn specify whether or not subdirectories # should be searched for input files as well. Possible values are YES and NO. # If left blank NO is used. RECURSIVE = NO # The EXCLUDE tag can be used to specify files and/or directories that should # excluded from the INPUT source files. This way you can easily exclude a # subdirectory from a directory tree whose root is specified with the INPUT tag. EXCLUDE = # The EXCLUDE_SYMLINKS tag can be used select whether or not files or directories # that are symbolic links (a Unix filesystem feature) are excluded from the input. EXCLUDE_SYMLINKS = NO # If the value of the INPUT tag contains directories, you can use the # EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude # certain files from those directories. EXCLUDE_PATTERNS = # The EXAMPLE_PATH tag can be used to specify one or more files or # directories that contain example code fragments that are included (see # the \include command). EXAMPLE_PATH = # If the value of the EXAMPLE_PATH tag contains directories, you can use the # EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp # and *.h) to filter out the source-files in the directories. If left # blank all files are included. EXAMPLE_PATTERNS = # If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be # searched for input files to be used with the \include or \dontinclude # commands irrespective of the value of the RECURSIVE tag. # Possible values are YES and NO. If left blank NO is used. EXAMPLE_RECURSIVE = NO # The IMAGE_PATH tag can be used to specify one or more files or # directories that contain image that are included in the documentation (see # the \image command). IMAGE_PATH = # The INPUT_FILTER tag can be used to specify a program that doxygen should # invoke to filter for each input file. Doxygen will invoke the filter program # by executing (via popen()) the command , where # is the value of the INPUT_FILTER tag, and is the name of an # input file. Doxygen will then use the output that the filter program writes # to standard output. INPUT_FILTER = # If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using # INPUT_FILTER) will be used to filter the input files when producing source # files to browse (i.e. when SOURCE_BROWSER is set to YES). FILTER_SOURCE_FILES = NO #--------------------------------------------------------------------------- # configuration options related to source browsing #--------------------------------------------------------------------------- # If the SOURCE_BROWSER tag is set to YES then a list of source files will # be generated. Documented entities will be cross-referenced with these sources. # Note: To get rid of all source code in the generated output, make sure also # VERBATIM_HEADERS is set to NO. SOURCE_BROWSER = YES # Setting the INLINE_SOURCES tag to YES will include the body # of functions and classes directly in the documentation. INLINE_SOURCES = NO # Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct # doxygen to hide any special comment blocks from generated source code # fragments. Normal C and C++ comments will always remain visible. STRIP_CODE_COMMENTS = YES # If the REFERENCED_BY_RELATION tag is set to YES (the default) # then for each documented function all documented # functions referencing it will be listed. REFERENCED_BY_RELATION = YES # If the REFERENCES_RELATION tag is set to YES (the default) # then for each documented function all documented entities # called/used by that function will be listed. REFERENCES_RELATION = YES # If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen # will generate a verbatim copy of the header file for each class for # which an include is specified. Set to NO to disable this. VERBATIM_HEADERS = YES #--------------------------------------------------------------------------- # configuration options related to the alphabetical class index #--------------------------------------------------------------------------- # If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index # of all compounds will be generated. Enable this if the project # contains a lot of classes, structs, unions or interfaces. ALPHABETICAL_INDEX = YES # If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then # the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns # in which this list will be split (can be a number in the range [1..20]) COLS_IN_ALPHA_INDEX = 5 # In case all classes in a project start with a common prefix, all # classes will be put under the same header in the alphabetical index. # The IGNORE_PREFIX tag can be used to specify one or more prefixes that # should be ignored while generating the index headers. IGNORE_PREFIX = #--------------------------------------------------------------------------- # configuration options related to the HTML output #--------------------------------------------------------------------------- # If the GENERATE_HTML tag is set to YES (the default) Doxygen will # generate HTML output. GENERATE_HTML = NO # The HTML_OUTPUT tag is used to specify where the HTML docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `html' will be used as the default path. HTML_OUTPUT = html # The HTML_FILE_EXTENSION tag can be used to specify the file extension for # each generated HTML page (for example: .htm,.php,.asp). If it is left blank # doxygen will generate files with .html extension. HTML_FILE_EXTENSION = .html # The HTML_HEADER tag can be used to specify a personal HTML header for # each generated HTML page. If it is left blank doxygen will generate a # standard header. HTML_HEADER = # The HTML_FOOTER tag can be used to specify a personal HTML footer for # each generated HTML page. If it is left blank doxygen will generate a # standard footer. HTML_FOOTER = # The HTML_STYLESHEET tag can be used to specify a user-defined cascading # style sheet that is used by each HTML page. It can be used to # fine-tune the look of the HTML output. If the tag is left blank doxygen # will generate a default style sheet. Note that doxygen will try to copy # the style sheet file to the HTML output directory, so don't put your own # stylesheet in the HTML output directory as well, or it will be erased! HTML_STYLESHEET = # If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes, # files or namespaces will be aligned in HTML using tables. If set to # NO a bullet list will be used. HTML_ALIGN_MEMBERS = YES # If the GENERATE_HTMLHELP tag is set to YES, additional index files # will be generated that can be used as input for tools like the # Microsoft HTML help workshop to generate a compressed HTML help file (.chm) # of the generated HTML documentation. GENERATE_HTMLHELP = NO # If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can # be used to specify the file name of the resulting .chm file. You # can add a path in front of the file if the result should not be # written to the html output directory. CHM_FILE = # If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can # be used to specify the location (absolute path including file name) of # the HTML help compiler (hhc.exe). If non-empty doxygen will try to run # the HTML help compiler on the generated index.hhp. HHC_LOCATION = # If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag # controls if a separate .chi index file is generated (YES) or that # it should be included in the master .chm file (NO). GENERATE_CHI = NO # If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag # controls whether a binary table of contents is generated (YES) or a # normal table of contents (NO) in the .chm file. BINARY_TOC = NO # The TOC_EXPAND flag can be set to YES to add extra items for group members # to the contents of the HTML help documentation and to the tree view. TOC_EXPAND = NO # The DISABLE_INDEX tag can be used to turn on/off the condensed index at # top of each HTML page. The value NO (the default) enables the index and # the value YES disables it. DISABLE_INDEX = NO # This tag can be used to set the number of enum values (range [1..20]) # that doxygen will group on one line in the generated HTML documentation. ENUM_VALUES_PER_LINE = 4 # If the GENERATE_TREEVIEW tag is set to YES, a side panel will be # generated containing a tree-like index structure (just like the one that # is generated for HTML Help). For this to work a browser that supports # JavaScript, DHTML, CSS and frames is required (for instance Mozilla 1.0+, # Netscape 6.0+, Internet explorer 5.0+, or Konqueror). Windows users are # probably better off using the HTML help feature. GENERATE_TREEVIEW = NO # If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be # used to set the initial width (in pixels) of the frame in which the tree # is shown. TREEVIEW_WIDTH = 250 #--------------------------------------------------------------------------- # configuration options related to the LaTeX output #--------------------------------------------------------------------------- # If the GENERATE_LATEX tag is set to YES (the default) Doxygen will # generate Latex output. GENERATE_LATEX = YES # The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `latex' will be used as the default path. LATEX_OUTPUT = pdflatex # The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be # invoked. If left blank `latex' will be used as the default command name. LATEX_CMD_NAME = pdflatex # The MAKEINDEX_CMD_NAME tag can be used to specify the command name to # generate index for LaTeX. If left blank `makeindex' will be used as the # default command name. MAKEINDEX_CMD_NAME = makeindex # If the COMPACT_LATEX tag is set to YES Doxygen generates more compact # LaTeX documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_LATEX = NO # The PAPER_TYPE tag can be used to set the paper type that is used # by the printer. Possible values are: a4, a4wide, letter, legal and # executive. If left blank a4wide will be used. PAPER_TYPE = a4wide # The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX # packages that should be included in the LaTeX output. EXTRA_PACKAGES = # The LATEX_HEADER tag can be used to specify a personal LaTeX header for # the generated latex document. The header should contain everything until # the first chapter. If it is left blank doxygen will generate a # standard header. Notice: only use this tag if you know what you are doing! LATEX_HEADER = # If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated # is prepared for conversion to pdf (using ps2pdf). The pdf file will # contain links (just like the HTML output) instead of page references # This makes the output suitable for online browsing using a pdf viewer. PDF_HYPERLINKS = YES # If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of # plain latex in the generated Makefile. Set this option to YES to get a # higher quality PDF documentation. USE_PDFLATEX = YES # If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode. # command to the generated LaTeX files. This will instruct LaTeX to keep # running if errors occur, instead of asking the user for help. # This option is also used when generating formulas in HTML. LATEX_BATCHMODE = NO # If LATEX_HIDE_INDICES is set to YES then doxygen will not # include the index chapters (such as File Index, Compound Index, etc.) # in the output. LATEX_HIDE_INDICES = NO #--------------------------------------------------------------------------- # configuration options related to the RTF output #--------------------------------------------------------------------------- # If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output # The RTF output is optimized for Word 97 and may not look very pretty with # other RTF readers or editors. GENERATE_RTF = NO # The RTF_OUTPUT tag is used to specify where the RTF docs will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `rtf' will be used as the default path. RTF_OUTPUT = rtf # If the COMPACT_RTF tag is set to YES Doxygen generates more compact # RTF documents. This may be useful for small projects and may help to # save some trees in general. COMPACT_RTF = NO # If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated # will contain hyperlink fields. The RTF file will # contain links (just like the HTML output) instead of page references. # This makes the output suitable for online browsing using WORD or other # programs which support those fields. # Note: wordpad (write) and others do not support links. RTF_HYPERLINKS = NO # Load stylesheet definitions from file. Syntax is similar to doxygen's # config file, i.e. a series of assignments. You only have to provide # replacements, missing definitions are set to their default value. RTF_STYLESHEET_FILE = # Set optional variables used in the generation of an rtf document. # Syntax is similar to doxygen's config file. RTF_EXTENSIONS_FILE = #--------------------------------------------------------------------------- # configuration options related to the man page output #--------------------------------------------------------------------------- # If the GENERATE_MAN tag is set to YES (the default) Doxygen will # generate man pages GENERATE_MAN = NO # The MAN_OUTPUT tag is used to specify where the man pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `man' will be used as the default path. MAN_OUTPUT = man # The MAN_EXTENSION tag determines the extension that is added to # the generated man pages (default is the subroutine's section .3) MAN_EXTENSION = .3 # If the MAN_LINKS tag is set to YES and Doxygen generates man output, # then it will generate one additional man file for each entity # documented in the real man page(s). These additional files # only source the real man page, but without them the man command # would be unable to find the correct page. The default is NO. MAN_LINKS = NO #--------------------------------------------------------------------------- # configuration options related to the XML output #--------------------------------------------------------------------------- # If the GENERATE_XML tag is set to YES Doxygen will # generate an XML file that captures the structure of # the code including all documentation. GENERATE_XML = NO # The XML_OUTPUT tag is used to specify where the XML pages will be put. # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `xml' will be used as the default path. XML_OUTPUT = xml # The XML_SCHEMA tag can be used to specify an XML schema, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_SCHEMA = # The XML_DTD tag can be used to specify an XML DTD, # which can be used by a validating XML parser to check the # syntax of the XML files. XML_DTD = # If the XML_PROGRAMLISTING tag is set to YES Doxygen will # dump the program listings (including syntax highlighting # and cross-referencing information) to the XML output. Note that # enabling this will significantly increase the size of the XML output. XML_PROGRAMLISTING = YES #--------------------------------------------------------------------------- # configuration options for the AutoGen Definitions output #--------------------------------------------------------------------------- # If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will # generate an AutoGen Definitions (see autogen.sf.net) file # that captures the structure of the code including all # documentation. Note that this feature is still experimental # and incomplete at the moment. GENERATE_AUTOGEN_DEF = NO #--------------------------------------------------------------------------- # configuration options related to the Perl module output #--------------------------------------------------------------------------- # If the GENERATE_PERLMOD tag is set to YES Doxygen will # generate a Perl module file that captures the structure of # the code including all documentation. Note that this # feature is still experimental and incomplete at the # moment. GENERATE_PERLMOD = NO # If the PERLMOD_LATEX tag is set to YES Doxygen will generate # the necessary Makefile rules, Perl scripts and LaTeX code to be able # to generate PDF and DVI output from the Perl module output. PERLMOD_LATEX = NO # If the PERLMOD_PRETTY tag is set to YES the Perl module output will be # nicely formatted so it can be parsed by a human reader. This is useful # if you want to understand what is going on. On the other hand, if this # tag is set to NO the size of the Perl module output will be much smaller # and Perl will parse it just the same. PERLMOD_PRETTY = YES # The names of the make variables in the generated doxyrules.make file # are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX. # This is useful so different doxyrules.make files included by the same # Makefile don't overwrite each other's variables. PERLMOD_MAKEVAR_PREFIX = #--------------------------------------------------------------------------- # Configuration options related to the preprocessor #--------------------------------------------------------------------------- # If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will # evaluate all C-preprocessor directives found in the sources and include # files. ENABLE_PREPROCESSING = YES # If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro # names in the source code. If set to NO (the default) only conditional # compilation will be performed. Macro expansion can be done in a controlled # way by setting EXPAND_ONLY_PREDEF to YES. MACRO_EXPANSION = YES # If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES # then the macro expansion is limited to the macros specified with the # PREDEFINED and EXPAND_AS_PREDEFINED tags. EXPAND_ONLY_PREDEF = YES # If the SEARCH_INCLUDES tag is set to YES (the default) the includes files # in the INCLUDE_PATH (see below) will be search if a #include is found. SEARCH_INCLUDES = YES # The INCLUDE_PATH tag can be used to specify one or more directories that # contain include files that are not input files but should be processed by # the preprocessor. INCLUDE_PATH = # You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard # patterns (like *.h and *.hpp) to filter out the header-files in the # directories. If left blank, the patterns specified with FILE_PATTERNS will # be used. INCLUDE_FILE_PATTERNS = *.h # The PREDEFINED tag can be used to specify one or more macro names that # are defined before the preprocessor is started (similar to the -D option of # gcc). The argument of the tag is a list of macros of the form: name # or name=definition (no spaces). If the definition and the = are # omitted =1 is assumed. PREDEFINED = \ "PADPOINTER(a1,a2,a3,a4)=" \ "PADLONG(a1,a2,a3)=" \ "PADINT(a1,a2)=" \ "PADWORD(a1)=" # If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then # this tag can be used to specify a list of macro names that should be expanded. # The macro definition that is found in the sources will be used. # Use the PREDEFINED tag if you want to use a different macro definition. EXPAND_AS_DEFINED = # If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then # doxygen's preprocessor will remove all function-like macros that are alone # on a line, have an all uppercase name, and do not end with a semicolon. Such # function macros are typically used for boiler-plate code, and will confuse the # parser if not removed. SKIP_FUNCTION_MACROS = YES #--------------------------------------------------------------------------- # Configuration::addtions related to external references #--------------------------------------------------------------------------- # The TAGFILES option can be used to specify one or more tagfiles. # Optionally an initial location of the external documentation # can be added for each tagfile. The format of a tag file without # this location is as follows: # TAGFILES = file1 file2 ... # Adding location for the tag files is done as follows: # TAGFILES = file1=loc1 "file2 = loc2" ... # where "loc1" and "loc2" can be relative or absolute paths or # URLs. If a location is present for each tag, the installdox tool # does not have to be run to correct the links. # Note that each tag file must have a unique name # (where the name does NOT include the path) # If a tag file is not located in the directory in which doxygen # is run, you must also specify the path to the tagfile here. TAGFILES = # When a file name is specified after GENERATE_TAGFILE, doxygen will create # a tag file that is based on the input files it reads. GENERATE_TAGFILE = # If the ALLEXTERNALS tag is set to YES all external classes will be listed # in the class index. If set to NO only the inherited external classes # will be listed. ALLEXTERNALS = NO # If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed # in the modules index. If set to NO, only the current project's groups will # be listed. EXTERNAL_GROUPS = YES # The PERL_PATH should be the absolute path and name of the perl script # interpreter (i.e. the result of `which perl'). PERL_PATH = /usr/bin/perl #--------------------------------------------------------------------------- # Configuration options related to the dot tool #--------------------------------------------------------------------------- # If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will # generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with base or # super classes. Setting the tag to NO turns the diagrams off. Note that this # option is superseded by the HAVE_DOT option below. This is only a fallback. It is # recommended to install and use dot, since it yields more powerful graphs. CLASS_DIAGRAMS = YES # If set to YES, the inheritance and collaboration graphs will hide # inheritance and usage relations if the target is undocumented # or is not a class. HIDE_UNDOC_RELATIONS = YES # If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is # available from the path. This tool is part of Graphviz, a graph visualization # toolkit from AT&T and Lucent Bell Labs. The other options in this section # have no effect if this option is set to NO (the default) HAVE_DOT = NO # If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen # will generate a graph for each documented class showing the direct and # indirect inheritance relations. Setting this tag to YES will force the # the CLASS_DIAGRAMS tag to NO. CLASS_GRAPH = YES # If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen # will generate a graph for each documented class showing the direct and # indirect implementation dependencies (inheritance, containment, and # class references variables) of the class with other documented classes. COLLABORATION_GRAPH = YES # If the UML_LOOK tag is set to YES doxygen will generate inheritance and # collaboration diagrams in a style similar to the OMG's Unified Modeling # Language. UML_LOOK = NO # If set to YES, the inheritance and collaboration graphs will show the # relations between templates and their instances. TEMPLATE_RELATIONS = NO # If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT # tags are set to YES then doxygen will generate a graph for each documented # file showing the direct and indirect include dependencies of the file with # other documented files. INCLUDE_GRAPH = YES # If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and # HAVE_DOT tags are set to YES then doxygen will generate a graph for each # documented header file showing the documented files that directly or # indirectly include this file. INCLUDED_BY_GRAPH = YES # If the CALL_GRAPH and HAVE_DOT tags are set to YES then doxygen will # generate a call dependency graph for every global function or class method. # Note that enabling this option will significantly increase the time of a run. # So in most cases it will be better to enable call graphs for selected # functions only using the \callgraph command. CALL_GRAPH = NO # If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen # will graphical hierarchy of all classes instead of a textual one. GRAPHICAL_HIERARCHY = YES # The DOT_IMAGE_FORMAT tag can be used to set the image format of the images # generated by dot. Possible values are png, jpg, or gif # If left blank png will be used. DOT_IMAGE_FORMAT = png # The tag DOT_PATH can be used to specify the path where the dot tool can be # found. If left blank, it is assumed the dot tool can be found on the path. DOT_PATH = # The DOTFILE_DIRS tag can be used to specify one or more directories that # contain dot files that are included in the documentation (see the # \dotfile command). DOTFILE_DIRS = # The MAX_DOT_GRAPH_WIDTH tag can be used to set the maximum allowed width # (in pixels) of the graphs generated by dot. If a graph becomes larger than # this value, doxygen will try to truncate the graph, so that it fits within # the specified constraint. Beware that most browsers cannot cope with very # large images. MAX_DOT_GRAPH_WIDTH = 1024 # The MAX_DOT_GRAPH_HEIGHT tag can be used to set the maximum allows height # (in pixels) of the graphs generated by dot. If a graph becomes larger than # this value, doxygen will try to truncate the graph, so that it fits within # the specified constraint. Beware that most browsers cannot cope with very # large images. MAX_DOT_GRAPH_HEIGHT = 1024 # The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the # graphs generated by dot. A depth value of 3 means that only nodes reachable # from the root by following a path via at most 3 edges will be shown. Nodes that # lay further from the root node will be omitted. Note that setting this option to # 1 or 2 may greatly reduce the computation time needed for large code bases. Also # note that a graph may be further truncated if the graph's image dimensions are # not sufficient to fit the graph (see MAX_DOT_GRAPH_WIDTH and MAX_DOT_GRAPH_HEIGHT). # If 0 is used for the depth value (the default), the graph is not depth-constrained. MAX_DOT_GRAPH_DEPTH = 0 # If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will # generate a legend page explaining the meaning of the various boxes and # arrows in the dot generated graphs. GENERATE_LEGEND = YES # If the DOT_CLEANUP tag is set to YES (the default) Doxygen will # remove the intermediate dot files that are used to generate # the various graphs. 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AC_DEFUN([AM_SUBST_NOTMAKE], [_AM_SUBST_NOTMAKE($@)]) # Check how to create a tarball. -*- Autoconf -*- # Copyright (C) 2004-2021 Free Software Foundation, Inc. # # This file is free software; the Free Software Foundation # gives unlimited permission to copy and/or distribute it, # with or without modifications, as long as this notice is preserved. # _AM_PROG_TAR(FORMAT) # -------------------- # Check how to create a tarball in format FORMAT. # FORMAT should be one of 'v7', 'ustar', or 'pax'. # # Substitute a variable $(am__tar) that is a command # writing to stdout a FORMAT-tarball containing the directory # $tardir. # tardir=directory && $(am__tar) > result.tar # # Substitute a variable $(am__untar) that extract such # a tarball read from stdin. # $(am__untar) < result.tar # AC_DEFUN([_AM_PROG_TAR], [# Always define AMTAR for backward compatibility. Yes, it's still used # in the wild :-( We should find a proper way to deprecate it ... 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The last is the most sensitive to ports. * In the past nearly every port to another OS or computer gave trouble. * Nowadays it is slightly better but the poor POSIX compliance of LINUX * again gave problems for the multithreaded version. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : Note: TERMMALLOCDEBUG tests part of the TermMalloc and NumberMalloc system. To work properly it needs MEMORYMACROS in declare.h not to be defined to make sure that all calls will be diverted to the routines here. #define TERMMALLOCDEBUG #define FILLVALUE 126 #define MALLOCDEBUGOUTPUT #define MALLOCDEBUG 1 */ #ifndef FILLVALUE #define FILLVALUE 0 #endif /* The enhanced malloc debugger, see comments in the beginning of the file mallocprotect.h MALLOCPROTECT == -1 -- protect left side, used block is left-aligned. MALLOCPROTECT == 0 -- protect both sides, used block is left-aligned; MALLOCPROTECT == 1 -- protect both sides, used block is right-aligned; ATTENTION! The macro MALLOCPROTECT must be defined BEFORE #include mallocprotect.h #define MALLOCPROTECT 1 */ #include "form3.h" FILES **filelist; int numinfilelist = 0; int filelistsize = 0; #ifdef MALLOCDEBUG #define BANNER (4*sizeof(LONG)) void *malloclist[60000]; LONG mallocsizes[60000]; char *mallocstrings[60000]; int nummalloclist = 0; #endif #ifdef GPP extern "C" getdtablesize(); #endif #ifdef WITHSTATS LONG numwrites = 0; LONG numreads = 0; LONG numseeks = 0; LONG nummallocs = 0; LONG numfrees = 0; #endif #ifdef MALLOCPROTECT #ifdef TRAPSIGNALS #error "MALLOCPROTECT": undefine "TRAPSIGNALS" in unix.h first! #endif #include "mallocprotect.h" #ifdef M_alloc #undef M_alloc #endif #define M_alloc mprotectMalloc #endif #ifdef TERMMALLOCDEBUG WORD **DebugHeap1, **DebugHeap2; #endif /* #] Includes : #[ Streams : #[ LoadInputFile : */ UBYTE *LoadInputFile(UBYTE *filename, int type) { int handle; LONG filesize; UBYTE *buffer, *name = filename; POSITION scrpos; handle = LocateFile(&name,type); if ( handle < 0 ) return(0); PUTZERO(scrpos); SeekFile(handle,&scrpos,SEEK_END); TELLFILE(handle,&scrpos); filesize = BASEPOSITION(scrpos); PUTZERO(scrpos); SeekFile(handle,&scrpos,SEEK_SET); buffer = (UBYTE *)Malloc1(filesize+2,"LoadInputFile"); if ( ReadFile(handle,buffer,filesize) != filesize ) { Error1("Read error for file ",name); M_free(buffer,"LoadInputFile"); if ( name != filename ) M_free(name,"FromLoadInputFile"); CloseFile(handle); return(0); } CloseFile(handle); if ( type == PROCEDUREFILE || type == SETUPFILE ) { buffer[filesize] = '\n'; buffer[filesize+1] = 0; } else { buffer[filesize] = 0; } if ( name != filename ) M_free(name,"FromLoadInputFile"); return(buffer); } /* #] LoadInputFile : #[ ReadFromStream : */ UBYTE ReadFromStream(STREAM *stream) { UBYTE c; POSITION scrpos; #ifdef WITHPIPE if ( stream->type == PIPESTREAM ) { #ifndef WITHMPI FILE *f; int cc; RWLOCKR(AM.handlelock); f = (FILE *)(filelist[stream->handle]); UNRWLOCK(AM.handlelock); cc = getc(f); if ( cc == EOF ) return(ENDOFSTREAM); c = (UBYTE)cc; #else if ( stream->pointer >= stream->top ) { /* The master reads the pipe and broadcasts it to the slaves. */ LONG len; if ( PF.me == MASTER ) { FILE *f; UBYTE *p, *end; RWLOCKR(AM.handlelock); f = (FILE *)filelist[stream->handle]; UNRWLOCK(AM.handlelock); p = stream->buffer; end = stream->buffer + stream->buffersize; while ( p < end ) { int cc = getc(f); if ( cc == EOF ) { break; } *p++ = (UBYTE)cc; } len = p - stream->buffer; PF_BroadcastNumber(len); } else { len = PF_BroadcastNumber(0); } if ( len > 0 ) { PF_Bcast(stream->buffer, len); } stream->pointer = stream->buffer; stream->inbuffer = len; stream->top = stream->buffer + stream->inbuffer; if ( stream->pointer == stream->top ) return ENDOFSTREAM; } c = (UBYTE)*stream->pointer++; #endif if ( stream->eqnum == 1 ) { stream->eqnum = 0; stream->linenumber++; } if ( c == LINEFEED ) stream->eqnum = 1; return(c); } #endif /*[14apr2004 mt]:*/ #ifdef WITHEXTERNALCHANNEL if ( stream->type == EXTERNALCHANNELSTREAM ) { int cc; cc = getcFromExtChannel(); /*[18may20006 mt]:*/ /*if ( cc == EOF ) return(ENDOFSTREAM);*/ if ( cc < 0 ){ if( cc == EOF ) return(ENDOFSTREAM); else{ Error0("No current external channel"); Terminate(-1); } }/*if ( cc < 0 )*/ /*:[18may20006 mt]*/ c = (UBYTE)cc; if ( stream->eqnum == 1 ) { stream->eqnum = 0; stream->linenumber++; } if ( c == LINEFEED ) stream->eqnum = 1; return(c); } #endif /*ifdef WITHEXTERNALCHANNEL*/ /*:[14apr2004 mt]*/ if ( stream->type == INPUTSTREAM ) { if ( stream->pointer < stream->top ) { c = *stream->pointer++; } else { if ( ReadFile(stream->handle,&c,1) != 1 ) { return(ENDOFSTREAM); } if ( stream->fileposition == 0 ) { if ( !stream->buffer ) { stream->buffersize = 32; stream->buffer = (UBYTE *)Malloc1(stream->buffersize,"input stream buffer"); stream->pointer = stream->top = stream->buffer; } else { if ( stream->top - stream->buffer >= stream->buffersize ) { LONG oldsize = stream->buffersize; DoubleBuffer((void**)&stream->buffer,(void**)&stream->top,sizeof(UBYTE),"double input stream buffer"); stream->buffersize = stream->top - stream->buffer; stream->pointer = stream->top = stream->buffer + oldsize; } } *stream->pointer = c; stream->pointer = ++stream->top; stream->inbuffer++; } } if ( stream->eqnum == 1 ) { stream->eqnum = 0; stream->linenumber++; } if ( c == LINEFEED ) stream->eqnum = 1; return(c); } if ( stream->pointer >= stream->top ) { if ( stream->type != FILESTREAM ) return(ENDOFSTREAM); if ( stream->fileposition != stream->bufferposition+stream->inbuffer ) { stream->fileposition = stream->bufferposition+stream->inbuffer; SETBASEPOSITION(scrpos,stream->fileposition); SeekFile(stream->handle,&scrpos,SEEK_SET); } stream->bufferposition = stream->fileposition; stream->inbuffer = ReadFile(stream->handle, stream->buffer,stream->buffersize); if ( stream->inbuffer <= 0 ) return(ENDOFSTREAM); stream->top = stream->buffer + stream->inbuffer; stream->pointer = stream->buffer; stream->fileposition = stream->bufferposition + stream->inbuffer; } if ( stream->eqnum == 1 ) { stream->eqnum = 0; stream->linenumber++; } c = *(stream->pointer)++; if ( c == LINEFEED ) stream->eqnum = 1; return(c); } /* #] ReadFromStream : #[ GetFromStream : */ UBYTE GetFromStream(STREAM *stream) { UBYTE c1, c2; if ( stream->isnextchar > 0 ) { return(stream->nextchar[--stream->isnextchar]); } c1 = ReadFromStream(stream); if ( c1 == LINEFEED || c1 == CARRIAGERETURN ) { c2 = ReadFromStream(stream); if ( c2 == c1 || ( c2 != LINEFEED && c2 != CARRIAGERETURN ) ) { stream->isnextchar = 1; stream->nextchar[0] = c2; } return(LINEFEED); } else return(c1); } /* #] GetFromStream : #[ LookInStream : */ UBYTE LookInStream(STREAM *stream) { UBYTE c = GetFromStream(stream); UngetFromStream(stream,c); return(c); } /* #] LookInStream : #[ OpenStream : */ STREAM *OpenStream(UBYTE *name, int type, int prevarmode, int raiselow) { STREAM *stream; UBYTE *rhsofvariable, *s, *newname, c; POSITION scrpos; int handle, num; LONG filesize; switch ( type ) { case REVERSEFILESTREAM: case FILESTREAM: /* Notice that FILESTREAM is only used for text files: The #include files and the main input file (.frm) Hence we do not worry about files longer than 2 Gbytes. */ newname = name; handle = LocateFile(&newname,-1); if ( handle < 0 ) return(0); PUTZERO(scrpos); SeekFile(handle,&scrpos,SEEK_END); TELLFILE(handle,&scrpos); filesize = BASEPOSITION(scrpos); PUTZERO(scrpos); SeekFile(handle,&scrpos,SEEK_SET); if ( filesize > AM.MaxStreamSize && type == FILESTREAM ) filesize = AM.MaxStreamSize; stream = CreateStream((UBYTE *)"filestream"); /* The extra +1 in the Malloc1 is potentially needed in ReverseStatements! */ stream->buffer = (UBYTE *)Malloc1(filesize+1,"name of input stream"); stream->inbuffer = ReadFile(handle,stream->buffer,filesize); if ( type == REVERSEFILESTREAM ) { if ( ReverseStatements(stream) ) { M_free(stream->buffer,"name of input stream"); return(0); } } stream->top = stream->buffer + stream->inbuffer; stream->pointer = stream->buffer; stream->handle = handle; stream->buffersize = filesize; stream->fileposition = stream->inbuffer; if ( newname != name ) stream->name = newname; else if ( name ) stream->name = strDup1(name,"name of input stream"); else stream->name = 0; stream->prevline = stream->linenumber = 1; stream->eqnum = 0; break; case PREVARSTREAM: if ( ( rhsofvariable = GetPreVar(name,WITHERROR) ) == 0 ) return(0); stream = CreateStream((UBYTE *)"var-stream"); stream->buffer = stream->pointer = s = rhsofvariable; while ( *s ) s++; stream->top = s; stream->inbuffer = s - stream->buffer; stream->name = AC.CurrentStream->name; stream->linenumber = AC.CurrentStream->linenumber; stream->prevline = AC.CurrentStream->prevline; stream->eqnum = AC.CurrentStream->eqnum; stream->pname = strDup1(name,"stream->pname"); stream->olddelay = AP.AllowDelay; s = stream->pname; while ( *s ) s++; while ( s[-1] == '+' || s[-1] == '-' ) s--; *s = 0; UnsetAllowDelay(); break; case DOLLARSTREAM: if ( ( num = GetDollar(name) ) < 0 ) { WORD numfac = 0; /* Here we have to test first whether we have $x[1], $x[0] or just an undefined $x. */ s = name; while ( *s && *s != '[' ) s++; if ( *s == 0 ) return(0); c = *s; *s = 0; if ( ( num = GetDollar(name) ) < 0 ) return(0); *s = c; s++; if ( *s == 0 || FG.cTable[*s] != 1 || *s == ']' ) { MesPrint("@Illegal factor number for dollar variable"); return(0); } while ( *s && FG.cTable[*s] == 1 ) { numfac = 10*numfac+*s++-'0'; } if ( *s != ']' || s[1] != 0 ) { MesPrint("@Illegal factor number for $ variable"); return(0); } stream = CreateStream((UBYTE *)"dollar-stream"); stream->buffer = stream->pointer = s = WriteDollarFactorToBuffer(num,numfac,1); } else { stream = CreateStream((UBYTE *)"dollar-stream"); stream->buffer = stream->pointer = s = WriteDollarToBuffer(num,1); } while ( *s ) s++; stream->top = s; stream->inbuffer = s - stream->buffer; stream->name = AC.CurrentStream->name; stream->linenumber = AC.CurrentStream->linenumber; stream->prevline= AC.CurrentStream->prevline; stream->eqnum = AC.CurrentStream->eqnum; stream->pname = strDup1(name,"stream->pname"); s = stream->pname; while ( *s ) s++; while ( s[-1] == '+' || s[-1] == '-' ) s--; *s = 0; /* We 'stole' the buffer. Later we can free it. */ AO.DollarOutSizeBuffer = 0; AO.DollarOutBuffer = 0; AO.DollarInOutBuffer = 0; break; case PREREADSTREAM: case PREREADSTREAM2: case PREREADSTREAM3: case PRECALCSTREAM: stream = CreateStream((UBYTE *)"calculator"); stream->buffer = stream->pointer = s = name; while ( *s ) s++; stream->top = s; stream->inbuffer = s - stream->buffer; stream->name = AC.CurrentStream->name; stream->linenumber = AC.CurrentStream->linenumber; stream->prevline = AC.CurrentStream->prevline; stream->eqnum = 0; break; #ifdef WITHPIPE case PIPESTREAM: stream = CreateStream((UBYTE *)"pipe"); #ifndef WITHMPI { FILE *f; if ( ( f = popen((char *)name,"r") ) == 0 ) { Error0("@Cannot create pipe"); } stream->handle = CreateHandle(); RWLOCKW(AM.handlelock); filelist[stream->handle] = (FILES *)f; UNRWLOCK(AM.handlelock); } stream->buffer = stream->top = 0; stream->inbuffer = 0; #else { /* Only the master opens the pipe. */ FILE *f; if ( PF.me == MASTER ) { f = popen((char *)name, "r"); PF_BroadcastNumber(f == 0); if ( f == 0 ) Error0("@Cannot create pipe"); } else { if ( PF_BroadcastNumber(0) ) Error0("@Cannot create pipe"); f = (FILE *)123; /* dummy */ } stream->handle = CreateHandle(); RWLOCKW(AM.handlelock); filelist[stream->handle] = (FILES *)f; UNRWLOCK(AM.handlelock); } /* stream->buffer as a send/receive buffer. */ stream->buffersize = AM.MaxStreamSize; stream->buffer = (UBYTE *)Malloc1(stream->buffersize, "pipe buffer"); stream->inbuffer = 0; stream->top = stream->buffer; stream->pointer = stream->buffer; #endif stream->name = strDup1((UBYTE *)"pipe","pipe"); stream->prevline = stream->linenumber = 1; stream->eqnum = 0; break; #endif /*[14apr2004 mt]:*/ #ifdef WITHEXTERNALCHANNEL case EXTERNALCHANNELSTREAM: {/*Block*/ int n, *tmpn; if( (n=getCurrentExternalChannel()) == 0 ) Error0("@No current external channel"); stream = CreateStream((UBYTE *)"externalchannel"); stream->handle = CreateHandle(); tmpn = (int *)Malloc1(sizeof(int),"external channel handle"); *tmpn = n; RWLOCKW(AM.handlelock); filelist[stream->handle] = (FILES *)tmpn; UNRWLOCK(AM.handlelock); }/*Block*/ stream->buffer = stream->top = 0; stream->inbuffer = 0; stream->name = strDup1((UBYTE *)"externalchannel","externalchannel"); stream->prevline = stream->linenumber = 1; stream->eqnum = 0; break; #endif /*ifdef WITHEXTERNALCHANNEL*/ /*:[14apr2004 mt]*/ case INPUTSTREAM: /* * Assume that "name" stores a file descriptor (UNIX) or a FILE * pointer (Windows). We don't close it automatically on closing * the INPUTSTREAM stream (e.g., for stdin). */ stream = CreateStream((UBYTE *)"input stream"); stream->handle = CreateHandle(); { FILES *f = (FILES *)Malloc1(sizeof(int),"input stream handle"); /* NOTE: in both cases name=0 indicates stdin. */ #ifdef UNIX f->descriptor = (int)(ssize_t)name; #else f = name ? (FILES *)name : stdin; #endif RWLOCKW(AM.handlelock); filelist[stream->handle] = f; UNRWLOCK(AM.handlelock); } stream->buffer = stream->pointer = stream->top = 0; stream->inbuffer = 0; stream->name = strDup1((UBYTE *)(name ? "INPUT" : "STDIN"),"input stream name"); stream->prevline = stream->linenumber = 1; stream->eqnum = 0; /* * fileposition == -1: default * fileposition == 0: cache the input * See also: ReadFromStream, TryFileSetups */ stream->fileposition = -1; break; default: return(0); } stream->bufferposition = 0; stream->isnextchar = 0; stream->type = type; stream->previousNoShowInput = AC.NoShowInput; stream->afterwards = raiselow; if ( AC.CurrentStream ) stream->previous = AC.CurrentStream - AC.Streams; else stream->previous = -1; stream->FoldName = 0; if ( prevarmode == 0 ) stream->prevars = -1; else if ( prevarmode > 0 ) stream->prevars = NumPre; else if ( prevarmode < 0 ) stream->prevars = -prevarmode-1; AC.CurrentStream = stream; if ( type == PREREADSTREAM || type == PREREADSTREAM3 || type == PRECALCSTREAM || type == DOLLARSTREAM ) AC.NoShowInput = 1; return(stream); } /* #] OpenStream : #[ LocateFile : */ int LocateFile(UBYTE **name, int type) { int handle, namesize, i; UBYTE *s, *to, *u1, *u2, *newname, *indir; handle = OpenFile((char *)(*name)); if ( handle >= 0 ) return(handle); if ( type == SETUPFILE && AM.SetupFile ) { handle = OpenFile((char *)(AM.SetupFile)); if ( handle >= 0 ) return(handle); MesPrint("Could not open setup file %s",(char *)(AM.SetupFile)); } namesize = 4; s = *name; while ( *s ) { s++; namesize++; } if ( type == SETUPFILE ) indir = AM.SetupDir; else indir = AM.IncDir; if ( indir ) { s = indir; i = 0; while ( *s ) { s++; i++; } newname = (UBYTE *)Malloc1(namesize+i,"LocateFile"); s = indir; to = newname; while ( *s ) *to++ = *s++; if ( to > newname && to[-1] != SEPARATOR ) *to++ = SEPARATOR; s = *name; while ( *s ) *to++ = *s++; *to = 0; handle = OpenFile((char *)newname); if ( handle >= 0 ) { *name = newname; return(handle); } M_free(newname,"LocateFile, incdir/file"); } if ( type == SETUPFILE ) { handle = OpenFile(setupfilename); if ( handle >= 0 ) return(handle); s = (UBYTE *)getenv("FORMSETUP"); if ( s ) { handle = OpenFile((char *)s); if ( handle >= 0 ) return(handle); MesPrint("Could not open setup file %s",s); } } if ( type != SETUPFILE && AM.Path ) { u1 = AM.Path; while ( *u1 ) { u2 = u1; i = 0; #ifdef WINDOWS while ( *u1 && *u1 != ';' ) { u1++; i++; } #else while ( *u1 && *u1 != ':' ) { if ( *u1 == '\\' ) u1++; u1++; i++; } #endif newname = (UBYTE *)Malloc1(namesize+i,"LocateFile"); s = u2; to = newname; while ( s < u1 ) { #ifndef WINDOWS if ( *s == '\\' ) s++; #endif *to++ = *s++; } if ( to > newname && to[-1] != SEPARATOR ) *to++ = SEPARATOR; s = *name; while ( *s ) *to++ = *s++; *to = 0; handle = OpenFile((char *)newname); if ( handle >= 0 ) { *name = newname; return(handle); } M_free(newname,"LocateFile Path/file"); if ( *u1 ) u1++; } } if ( type != SETUPFILE && type >= -1 ) Error1("LocateFile: Cannot find file",*name); return(-1); } /* #] LocateFile : #[ CloseStream : */ STREAM *CloseStream(STREAM *stream) { int newstr = stream->previous, sgn; UBYTE *t, numbuf[24]; LONG x; if ( stream->FoldName ) { M_free(stream->FoldName,"stream->FoldName"); stream->FoldName = 0; } if ( stream->type == FILESTREAM || stream->type == REVERSEFILESTREAM ) { CloseFile(stream->handle); if ( stream->buffer != 0 ) M_free(stream->buffer,"name of input stream"); stream->buffer = 0; } #ifdef WITHPIPE else if ( stream->type == PIPESTREAM ) { RWLOCKW(AM.handlelock); #ifdef WITHMPI if ( PF.me == MASTER ) #endif pclose((FILE *)(filelist[stream->handle])); filelist[stream->handle] = 0; numinfilelist--; UNRWLOCK(AM.handlelock); #ifdef WITHMPI if ( stream->buffer != 0 ) { M_free(stream->buffer, "pipe buffer"); stream->buffer = 0; } #endif } #endif /*[14apr2004 mt]:*/ #ifdef WITHEXTERNALCHANNEL else if ( stream->type == EXTERNALCHANNELSTREAM ) { int *tmpn; RWLOCKW(AM.handlelock); tmpn = (int *)(filelist[stream->handle]); filelist[stream->handle] = 0; numinfilelist--; UNRWLOCK(AM.handlelock); M_free(tmpn,"external channel handle"); } #endif /*ifdef WITHEXTERNALCHANNEL*/ /*:[14apr2004 mt]*/ else if ( stream->type == INPUTSTREAM ) { FILES *f; RWLOCKW(AM.handlelock); f = filelist[stream->handle]; filelist[stream->handle] = 0; numinfilelist--; UNRWLOCK(AM.handlelock); M_free(f,"input stream handle"); } else if ( stream->type == PREVARSTREAM && ( stream->afterwards == PRERAISEAFTER || stream->afterwards == PRELOWERAFTER ) ) { t = stream->buffer; x = 0; sgn = 1; while ( *t == '-' || *t == '+' ) { if ( *t == '-' ) sgn = -sgn; t++; } if ( FG.cTable[*t] == 1 ) { while ( *t && FG.cTable[*t] == 1 ) x = 10*x + *t++ - '0'; if ( *t == 0 ) { if ( stream->afterwards == PRERAISEAFTER ) x = sgn*x + 1; else x = sgn*x - 1; NumToStr(numbuf,x); PutPreVar(stream->pname,numbuf,0,1); } } } else if ( stream->type == DOLLARSTREAM && ( stream->afterwards == PRERAISEAFTER || stream->afterwards == PRELOWERAFTER ) ) { if ( stream->afterwards == PRERAISEAFTER ) x = 1; else x = -1; DollarRaiseLow(stream->pname,x); if ( stream->buffer ) M_free(stream->buffer,"stream->buffer"); stream->buffer = 0; } else if ( stream->type == PRECALCSTREAM || stream->type == DOLLARSTREAM ) { if ( stream->buffer ) M_free(stream->buffer,"stream->buffer"); stream->buffer = 0; } if ( stream->name && stream->type != PREVARSTREAM && stream->type != PREREADSTREAM && stream->type != PREREADSTREAM2 && stream->type != PREREADSTREAM3 && stream->type != PRECALCSTREAM && stream->type != DOLLARSTREAM ) { M_free(stream->name,"stream->name"); } stream->name = 0; /* if ( stream->type != FILESTREAM ) */ AC.NoShowInput = stream->previousNoShowInput; stream->buffer = 0; /* To make sure we will not reuse it */ stream->pointer = 0; /* Look whether we have to pop preprocessor variables. */ if ( stream->prevars >= 0 ) { while ( NumPre > stream->prevars ) { NumPre--; M_free(PreVar[NumPre].name,"PreVar[NumPre].name"); PreVar[NumPre].name = PreVar[NumPre].value = 0; } } if ( stream->type == PREVARSTREAM ) { AP.AllowDelay = stream->olddelay; ClearMacro(stream->pname); M_free(stream->pname,"stream->pname"); } else if ( stream->type == DOLLARSTREAM ) { M_free(stream->pname,"stream->pname"); } AC.NumStreams--; if ( newstr >= 0 ) return(AC.Streams + newstr); else return(0); } /* #] CloseStream : #[ CreateStream : */ STREAM *CreateStream(UBYTE *where) { STREAM *newstreams; int numnewstreams,i; int offset; if ( AC.NumStreams >= AC.MaxNumStreams ) { if ( AC.MaxNumStreams == 0 ) numnewstreams = 10; else numnewstreams = 2*AC.MaxNumStreams; newstreams = (STREAM *)Malloc1(sizeof(STREAM)*(numnewstreams+1),"CreateStream"); if ( AC.MaxNumStreams > 0 ) { offset = AC.CurrentStream - AC.Streams; for ( i = 0; i < AC.MaxNumStreams; i++ ) { newstreams[i] = AC.Streams[i]; } AC.CurrentStream = newstreams + offset; } else newstreams[0].previous = -1; AC.MaxNumStreams = numnewstreams; if ( AC.Streams ) M_free(AC.Streams,(char *)where); AC.Streams = newstreams; } newstreams = AC.Streams+AC.NumStreams++; newstreams->name = 0; return(newstreams); } /* #] CreateStream : #[ GetStreamPosition : */ LONG GetStreamPosition(STREAM *stream) { return(stream->bufferposition + ((LONG)stream->pointer-(LONG)stream->buffer)); } /* #] GetStreamPosition : #[ PositionStream : */ void PositionStream(STREAM *stream, LONG position) { POSITION scrpos; if ( position >= stream->bufferposition && position < stream->bufferposition + stream->inbuffer ) { stream->pointer = stream->buffer + (position-stream->bufferposition); } else if ( stream->type == FILESTREAM ) { SETBASEPOSITION(scrpos,position); SeekFile(stream->handle,&scrpos,SEEK_SET); stream->inbuffer = ReadFile(stream->handle,stream->buffer,stream->buffersize); stream->pointer = stream->buffer; stream->top = stream->buffer + stream->inbuffer; stream->bufferposition = position; stream->fileposition = position + stream->inbuffer; stream->isnextchar = 0; } else { Error0("Illegal position for stream"); Terminate(-1); } } /* #] PositionStream : #[ ReverseStatements : Reverses the order of the statements in the buffer. We allocate an extra buffer and copy a bit to and from. Note that there are some nasties that cannot be resolved. */ int ReverseStatements(STREAM *stream) { UBYTE *spare = (UBYTE *)Malloc1((stream->inbuffer+1)*sizeof(UBYTE),"Reverse copy"); UBYTE *top = stream->buffer + stream->inbuffer, *in, *s, *ss, *out; out = spare+stream->inbuffer+1; in = stream->buffer; while ( in < top ) { s = in; if ( *s == AP.ComChar ) { toeol:; for(;;) { if ( s == top ) { *--out = '\n'; break; } if ( *s == '\\' ) { s++; if ( s >= top ) { /* This is an error! */ irrend: MesPrint("@Irregular end of reverse include file."); return(1); } } else if ( *s == '\n' ) { s++; ss = s; while ( ss > in ) *--out = *--ss; in = s; if ( out[0] == AP.ComChar && ss+6 < s && out[3] == '#' ) { /* For folds we have to exchange begin and end */ if ( out[4] == '[' ) out[4] = ']'; else if ( out[4] == ']' ) out[4] = '['; } break; } s++; } continue; } while ( s < top && ( *s == ' ' || *s == '\t' ) ) s++; if ( *s == '#' ) { /* preprocessor instruction */ goto toeol; /* read to end of line */ } if ( *s == '.' ) { /* end-of-module instruction */ goto toeol; /* read to end of line */ } /* Here we have a regular statement. In principle we scan to ; and its \n but there are special cases. 1: ; inside a string (in print "......;";) 2: multiple statements on one line. 3: ; + commentary after some blanks. 4: `var' can cause problems..... */ while ( s < top ) { if ( *s == ';' ) { s++; while ( s < top && ( *s == ' ' || *s == '\t' ) ) s++; while ( s < top && *s == '\n' ) s++; if ( s >= top && s[-1] != '\n' ) *s++ = '\n'; ss = s; while ( ss > in ) *--out = *--ss; in = s; break; } else if ( *s == '"' ) { s++; while ( s < top ) { if ( *s == '"' ) break; if ( *s == '\\' ) { s++; } s++; } if ( s >= top ) goto irrend; } else if ( *s == '\\' ) { s++; if ( s >= top ) goto irrend; } s++; } if ( in < top ) { /* Like blank lines at the end */ if ( s >= top && s[-1] != '\n' ) *s++ = '\n'; ss = s; while ( ss > in ) *--out = *--ss; in = s; } } if ( out == spare ) stream->inbuffer++; if ( out > spare+1 ) { MesPrint("@Internal error in #reverseinclude instruction."); return(1); } memcpy((void *)(stream->buffer),(void *)out,(size_t)(stream->inbuffer*sizeof(UBYTE))); M_free(spare,"Reverse copy"); return(0); } /* #] ReverseStatements : #] Streams : #[ Files : #[ StartFiles : */ void StartFiles(void) { int i = CreateHandle(); filelist[i] = Ustdout; AM.StdOut = i; AC.StoreHandle = -1; AC.LogHandle = -1; #ifndef WITHPTHREADS AR.Fscr[0].handle = -1; AR.Fscr[1].handle = -1; AR.Fscr[2].handle = -1; AR.FoStage4[0].handle = -1; AR.FoStage4[1].handle = -1; AR.infile = &(AR.Fscr[0]); AR.outfile = &(AR.Fscr[1]); AR.hidefile = &(AR.Fscr[2]); AR.StoreData.Handle = -1; #endif AC.Streams = 0; AC.MaxNumStreams = 0; } /* #] StartFiles : #[ OpenFile : */ int OpenFile(char *name) { FILES *f; int i; if ( ( f = Uopen(name,"rb") ) == 0 ) return(-1); /* Usetbuf(f,0); */ i = CreateHandle(); RWLOCKW(AM.handlelock); filelist[i] = f; UNRWLOCK(AM.handlelock); return(i); } /* #] OpenFile : #[ OpenAddFile : */ int OpenAddFile(char *name) { FILES *f; int i; POSITION scrpos; if ( ( f = Uopen(name,"a+b") ) == 0 ) return(-1); /* Usetbuf(f,0); */ i = CreateHandle(); RWLOCKW(AM.handlelock); filelist[i] = f; UNRWLOCK(AM.handlelock); TELLFILE(i,&scrpos); SeekFile(i,&scrpos,SEEK_SET); return(i); } /* #] OpenAddFile : #[ ReOpenFile : */ int ReOpenFile(char *name) { FILES *f; int i; POSITION scrpos; if ( ( f = Uopen(name,"r+b") ) == 0 ) return(-1); i = CreateHandle(); RWLOCKW(AM.handlelock); filelist[i] = f; UNRWLOCK(AM.handlelock); TELLFILE(i,&scrpos); SeekFile(i,&scrpos,SEEK_SET); return(i); } /* #] ReOpenFile : #[ CreateFile : */ int CreateFile(char *name) { FILES *f; int i; if ( ( f = Uopen(name,"w+b") ) == 0 ) return(-1); i = CreateHandle(); RWLOCKW(AM.handlelock); filelist[i] = f; UNRWLOCK(AM.handlelock); return(i); } /* #] CreateFile : #[ CreateLogFile : */ int CreateLogFile(char *name) { FILES *f; int i; if ( ( f = Uopen(name,"w+b") ) == 0 ) return(-1); Usetbuf(f,0); i = CreateHandle(); RWLOCKW(AM.handlelock); filelist[i] = f; UNRWLOCK(AM.handlelock); return(i); } /* #] CreateLogFile : #[ CloseFile : */ void CloseFile(int handle) { if ( handle >= 0 ) { FILES *f; /* we need this variable to be thread-safe */ RWLOCKW(AM.handlelock); f = filelist[handle]; filelist[handle] = 0; numinfilelist--; UNRWLOCK(AM.handlelock); Uclose(f); } } /* #] CloseFile : #[ CopyFile : */ /** Copies a file with name *source to a file named *dest. * The involved files must not be open. * Returns non-zero if an error occurred. * Uses if possible the combined large and small sorting buffers as cache. */ int CopyFile(char *source, char *dest) { #define COPYFILEBUFSIZE 40960L FILE *in, *out; size_t countin, countout, sumcount; char *buffer = NULL; sumcount = (AM.S0->LargeSize+AM.S0->SmallEsize)*sizeof(WORD); if ( sumcount <= COPYFILEBUFSIZE ) { sumcount = COPYFILEBUFSIZE; buffer = (char*)Malloc1(sumcount, "file copy buffer"); } else { buffer = (char *)(AM.S0->lBuffer); } in = fopen(source, "rb"); if ( in == NULL ) { perror("CopyFile: "); return(1); } out = fopen(dest, "wb"); if ( out == NULL ) { perror("CopyFile: "); return(2); } while ( !feof(in) ) { countin = fread(buffer, 1, sumcount, in); if ( countin != sumcount ) { if ( ferror(in) ) { perror("CopyFile: "); return(3); } } countout = fwrite(buffer, 1, countin, out); if ( countin != countout ) { perror("CopyFile: "); return(4); } } fclose(in); fclose(out); if ( sumcount <= COPYFILEBUFSIZE ) { M_free(buffer, "file copy buffer"); } return(0); } /* #] CopyFile : #[ CreateHandle : We need a lock here. Problem: the same lock is needed inside Malloc1 and M_free which is used in DoubleList when we use MALLOCDEBUG Conclusion: MALLOCDEBUG will have to be a bit unsafe */ int CreateHandle(void) { int i, j; #ifndef MALLOCDEBUG RWLOCKW(AM.handlelock); #endif if ( filelistsize == 0 ) { filelistsize = 10; filelist = (FILES **)Malloc1(sizeof(FILES *)*filelistsize,"file handle"); for ( j = 0; j < filelistsize; j++ ) filelist[j] = 0; numinfilelist = 1; i = 0; } else if ( numinfilelist >= filelistsize ) { void **fl = (void **)filelist; i = filelistsize; if ( DoubleList((void ***)(&fl),&filelistsize,(int)sizeof(FILES *), "list of open files") != 0 ) Terminate(-1); filelist = (FILES **)fl; for ( j = i; j < filelistsize; j++ ) filelist[j] = 0; numinfilelist = i + 1; } else { i = filelistsize; for ( j = 0; j < filelistsize; j++ ) { if ( filelist[j] == 0 ) { i = j; break; } } numinfilelist++; } filelist[i] = (FILES *)(filelist); /* Just for now to not get into problems */ /* The next code is not needed when we use open. It may be needed when we use fopen. fopen is used in minos.c without this central administration. */ if ( numinfilelist > MAX_OPEN_FILES ) { #ifndef MALLOCDEBUG UNRWLOCK(AM.handlelock); #endif MesPrint("More than %d open files",MAX_OPEN_FILES); Error0("System limit. This limit is not due to FORM!"); } else { #ifndef MALLOCDEBUG UNRWLOCK(AM.handlelock); #endif } return(i); } /* #] CreateHandle : #[ ReadFile : */ LONG ReadFile(int handle, UBYTE *buffer, LONG size) { LONG inbuf = 0, r; FILES *f; char *b; b = (char *)buffer; for(;;) { /* Gotta do difficult because of VMS! */ RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); #ifdef WITHSTATS numreads++; #endif r = Uread(b,1,size,f); if ( r < 0 ) return(r); if ( r == 0 ) return(inbuf); inbuf += r; if ( r == size ) return(inbuf); if ( r > size ) return(-1); size -= r; b += r; } } /* #] ReadFile : #[ ReadPosFile : Gets words from a file(handle). First tries to get the information from the buffers. Reads a file at a position. Updates the position. Places a lock in the case of multithreading. Exists for multiple reading from the same file. size is the number of WORDs to read!!!! We may need some strategy in the caching. This routine is used from GetOneTerm only. The problem is when it reads brackets and the brackets are read backwards. This is very uneconomical because each time it may read a large buffer. On the other hand, reading piece by piece in GetOneTerm takes much overhead as well. Two strategies come to mind: 1: keep things as they are but limit the size of the buffers. 2: have the position of 'pos' at about 1/3 of the buffer. this is of course guess work. Currently we have implemented the first method by creating the setup parameter threadscratchsize with the default value 100K. In the test program much bigger values gave a slower program. */ LONG ReadPosFile(PHEAD FILEHANDLE *fi, UBYTE *buffer, LONG size, POSITION *pos) { GETBIDENTITY LONG i, retval = 0; WORD *b = (WORD *)buffer, *t; if ( fi->handle < 0 ) { fi->POfill = (WORD *)((UBYTE *)(fi->PObuffer) + BASEPOSITION(*pos)); t = fi->POfill; while ( size > 0 && fi->POfill < fi->POfull ) { *b++ = *t++; size--; } } else { if ( ISLESSPOS(*pos,fi->POposition) || ISGEPOSINC(*pos,fi->POposition, ((UBYTE *)(fi->POfull)-(UBYTE *)(fi->PObuffer))) ) { /* The start is not inside the buffer. Fill the buffer. */ fi->POposition = *pos; LOCK(AS.inputslock); SeekFile(fi->handle,pos,SEEK_SET); retval = ReadFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize); UNLOCK(AS.inputslock); fi->POfull = fi->PObuffer+retval/sizeof(WORD); fi->POfill = fi->PObuffer; if ( fi != AR.hidefile ) AR.InInBuf = retval/sizeof(WORD); else AR.InHiBuf = retval/sizeof(WORD); } else { fi->POfill = (WORD *)((UBYTE *)(fi->PObuffer) + DIFBASE(*pos,fi->POposition)); } if ( fi->POfill + size <= fi->POfull ) { t = fi->POfill; while ( size > 0 ) { *b++ = *t++; size--; } } else { for (;;) { i = fi->POfull - fi->POfill; t = fi->POfill; if ( i > size ) i = size; size -= i; while ( --i >= 0 ) *b++ = *t++; if ( size == 0 ) break; ADDPOS(fi->POposition,(UBYTE *)(fi->POfull)-(UBYTE *)(fi->PObuffer)); LOCK(AS.inputslock); SeekFile(fi->handle,&(fi->POposition),SEEK_SET); retval = ReadFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize); UNLOCK(AS.inputslock); fi->POfull = fi->PObuffer+retval/sizeof(WORD); fi->POfill = fi->PObuffer; if ( fi != AR.hidefile ) AR.InInBuf = retval/sizeof(WORD); else AR.InHiBuf = retval/sizeof(WORD); if ( retval == 0 ) { t = fi->POfill; break; } } } } retval = (UBYTE *)b - buffer; fi->POfill = t; ADDPOS(*pos,retval); return(retval); } /* #] ReadPosFile : #[ WriteFile : */ LONG WriteFileToFile(int handle, UBYTE *buffer, LONG size) { FILES *f; LONG retval, totalwritten = 0, stilltowrite; RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); while ( totalwritten < size ) { stilltowrite = size - totalwritten; #ifdef WITHSTATS numwrites++; #endif retval = Uwrite((char *)buffer+totalwritten,1,stilltowrite,f); if ( retval < 0 ) return(retval); if ( retval == 0 ) return(totalwritten); totalwritten += retval; } /* if ( handle == AC.LogHandle || handle == ERROROUT ) FlushFile(handle); */ return(totalwritten); } #ifndef WITHMPI /*[17nov2005]:*/ WRITEFILE WriteFile = &WriteFileToFile; /* LONG (*WriteFile)(int handle, UBYTE *buffer, LONG size) = &WriteFileToFile; */ /*:[17nov2005]*/ #else WRITEFILE WriteFile = &PF_WriteFileToFile; #endif /* #] WriteFile : #[ SeekFile : */ void SeekFile(int handle, POSITION *offset, int origin) { FILES *f; RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); #ifdef WITHSTATS numseeks++; #endif if ( origin == SEEK_SET ) { Useek(f,BASEPOSITION(*offset),origin); SETBASEPOSITION(*offset,(Utell(f))); return; } else if ( origin == SEEK_END ) { Useek(f,0,origin); } SETBASEPOSITION(*offset,(Utell(f))); } /* #] SeekFile : #[ TellFile : */ LONG TellFile(int handle) { POSITION pos; TELLFILE(handle,&pos); #ifdef WITHSTATS numseeks++; #endif return(BASEPOSITION(pos)); } void TELLFILE(int handle, POSITION *position) { FILES *f; RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); SETBASEPOSITION(*position,(Utell(f))); } /* #] TellFile : #[ FlushFile : */ void FlushFile(int handle) { FILES *f; RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); Uflush(f); } /* #] FlushFile : #[ GetPosFile : */ int GetPosFile(int handle, fpos_t *pospointer) { FILES *f; RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); return(Ugetpos(f,pospointer)); } /* #] GetPosFile : #[ SetPosFile : */ int SetPosFile(int handle, fpos_t *pospointer) { FILES *f; RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); return(Usetpos(f,(fpos_t *)pospointer)); } /* #] SetPosFile : #[ SynchFile : It may be that when we use many sort files at the same time there is a big traffic jam in the cache. This routine is experimental, just to see whether this improves the situation. It could also be that the internal disk of the Quad opteron norma is very slow. */ void SynchFile(int handle) { FILES *f; if ( handle >= 0 ) { RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); Usync(f); } } /* #] SynchFile : #[ TruncateFile : It may be that when we use many sort files at the same time there is a big traffic jam in the cache. This routine is experimental, just to see whether this improves the situation. It could also be that the internal disk of the Quad opteron norma is very slow. */ void TruncateFile(int handle) { FILES *f; if ( handle >= 0 ) { RWLOCKR(AM.handlelock); f = filelist[handle]; UNRWLOCK(AM.handlelock); Utruncate(f); } } /* #] TruncateFile : #[ GetChannel : Checks whether we have this file already. If so, we return its handle. If not and mode == 0, we open the file first and add it to the buffers. */ int GetChannel(char *name,int mode) { CHANNEL *ch; int i; FILES *f; for ( i = 0; i < NumOutputChannels; i++ ) { if ( channels[i].name == 0 ) continue; if ( StrCmp((UBYTE *)name,(UBYTE *)(channels[i].name)) == 0 ) return(channels[i].handle); } if ( mode == 1 ) { MesPrint("&File %s in print statement is not open",name); MesPrint(" You should open it first with a #write or #append instruction"); return(-1); } for ( i = 0; i < NumOutputChannels; i++ ) { if ( channels[i].name == 0 ) break; } if ( i < NumOutputChannels ) { ch = &(channels[i]); } else { ch = (CHANNEL *)FromList(&AC.ChannelList); } ch->name = (char *)strDup1((UBYTE *)name,"name of channel"); ch->handle = CreateFile(name); RWLOCKR(AM.handlelock); f = filelist[ch->handle]; UNRWLOCK(AM.handlelock); Usetbuf(f,0); /* We turn the buffer off!!!!!!*/ return(ch->handle); } /* #] GetChannel : #[ GetAppendChannel : Checks whether we have this file already. If so, we return its handle. If not, we open the file first and add it to the buffers. */ int GetAppendChannel(char *name) { CHANNEL *ch; int i; FILES *f; for ( i = 0; i < NumOutputChannels; i++ ) { if ( channels[i].name == 0 ) continue; if ( StrCmp((UBYTE *)name,(UBYTE *)(channels[i].name)) == 0 ) return(channels[i].handle); } for ( i = 0; i < NumOutputChannels; i++ ) { if ( channels[i].name == 0 ) break; } if ( i < NumOutputChannels ) { ch = &(channels[i]); } else { ch = (CHANNEL *)FromList(&AC.ChannelList); } ch->name = (char *)strDup1((UBYTE *)name,"name of channel"); ch->handle = OpenAddFile(name); RWLOCKR(AM.handlelock); f = filelist[ch->handle]; UNRWLOCK(AM.handlelock); Usetbuf(f,0); /* We turn the buffer off!!!!!!*/ return(ch->handle); } /* #] GetAppendChannel : #[ CloseChannel : Checks whether we have this file already. If so, we close it. */ int CloseChannel(char *name) { int i; for ( i = 0; i < NumOutputChannels; i++ ) { if ( channels[i].name == 0 ) continue; if ( channels[i].name[0] == 0 ) continue; if ( StrCmp((UBYTE *)name,(UBYTE *)(channels[i].name)) == 0 ) { CloseFile(channels[i].handle); M_free(channels[i].name,"CloseChannel"); channels[i].name = 0; return(0); } } return(0); } /* #] CloseChannel : #[ UpdateMaxSize : Updates the maximum size of the combined input/output/hide scratch files, the sort files and the .str file. The result becomes only visible with either ON totalsize; #: totalsize ON; or the -T in the command tail. To be called, whenever a file is closed/removed or truncated to zero. We have no provisions yet for expressions that remain inside the small or large buffer during the sort. The space they use there is currently ignored. */ void UpdateMaxSize(void) { POSITION position, sumsize; int i; FILEHANDLE *scr; #ifdef WITHMPI /* Currently, it works only on the master. The sort files on the slaves * are ignored. (TU 11 Oct 2011) */ if ( PF.me != MASTER ) return; #endif PUTZERO(sumsize); if ( AM.PrintTotalSize ) { /* First the three scratch files */ #ifdef WITHPTHREADS scr = AB[0]->R.Fscr; #else scr = AR.Fscr; #endif for ( i = 0; i <=2; i++ ) { if ( scr[i].handle < 0 ) { SETBASEPOSITION(position,(scr[i].POfull-scr[i].PObuffer)*sizeof(WORD)); } else { position = scr[i].filesize; } ADD2POS(sumsize,position); } /* Now the sort file(s) */ #ifdef WITHPTHREADS { int j; ALLPRIVATES *B; for ( j = 0; j < AM.totalnumberofthreads; j++ ) { B = AB[j]; if ( AT.SS && AT.SS->file.handle >= 0 ) { position = AT.SS->file.filesize; /* MLOCK(ErrorMessageLock); MesPrint("%d: %10p",j,&(AT.SS->file.filesize)); MUNLOCK(ErrorMessageLock); */ ADD2POS(sumsize,position); } if ( AR.FoStage4[0].handle >= 0 ) { position = AR.FoStage4[0].filesize; ADD2POS(sumsize,position); } } } #else if ( AT.SS && AT.SS->file.handle >= 0 ) { position = AT.SS->file.filesize; ADD2POS(sumsize,position); } if ( AR.FoStage4[0].handle >= 0 ) { position = AR.FoStage4[0].filesize; ADD2POS(sumsize,position); } #endif /* And of course the str file. */ ADD2POS(sumsize,AC.StoreFileSize); /* Finally the test whether it is bigger */ if ( ISLESSPOS(AS.MaxExprSize,sumsize) ) { #ifdef WITHPTHREADS LOCK(AS.MaxExprSizeLock); if ( ISLESSPOS(AS.MaxExprSize,sumsize) ) AS.MaxExprSize = sumsize; UNLOCK(AS.MaxExprSizeLock); #else AS.MaxExprSize = sumsize; #endif } } return; } /* #] UpdateMaxSize : #] Files : #[ Strings : #[ StrCmp : */ int StrCmp(UBYTE *s1, UBYTE *s2) { while ( *s1 && *s1 == *s2 ) { s1++; s2++; } return((int)*s1-(int)*s2); } /* #] StrCmp : #[ StrICmp : */ int StrICmp(UBYTE *s1, UBYTE *s2) { while ( *s1 && tolower(*s1) == tolower(*s2) ) { s1++; s2++; } return((int)tolower(*s1)-(int)tolower(*s2)); } /* #] StrICmp : #[ StrHICmp : */ int StrHICmp(UBYTE *s1, UBYTE *s2) { while ( *s1 && tolower(*s1) == *s2 ) { s1++; s2++; } return((int)tolower(*s1)-(int)(*s2)); } /* #] StrHICmp : #[ StrICont : */ int StrICont(UBYTE *s1, UBYTE *s2) { while ( *s1 && tolower(*s1) == tolower(*s2) ) { s1++; s2++; } if ( *s1 == 0 ) return(0); return((int)tolower(*s1)-(int)tolower(*s2)); } /* #] StrICont : #[ CmpArray : */ int CmpArray(WORD *t1, WORD *t2, WORD n) { int i,x; for ( i = 0; i < n; i++ ) { if ( ( x = (int)(t1[i]-t2[i]) ) != 0 ) return(x); } return(0); } /* #] CmpArray : #[ ConWord : */ int ConWord(UBYTE *s1, UBYTE *s2) { while ( *s1 && ( tolower(*s1) == tolower(*s2) ) ) { s1++; s2++; } if ( *s1 == 0 ) return(1); return(0); } /* #] ConWord : #[ StrLen : */ int StrLen(UBYTE *s) { int i = 0; while ( *s ) { s++; i++; } return(i); } /* #] StrLen : #[ NumToStr : */ void NumToStr(UBYTE *s, LONG x) { UBYTE *t, str[24]; ULONG xx; t = str; if ( x < 0 ) { *s++ = '-'; xx = -x; } else xx = x; do { *t++ = xx % 10 + '0'; xx /= 10; } while ( xx ); while ( t > str ) *s++ = *--t; *s = 0; } /* #] NumToStr : #[ WriteString : Writes a characterstring to the various outputs. The action may depend on the flags involved. The type of output is given by type, the string by str and the number of characters in it by num */ void WriteString(int type, UBYTE *str, int num) { int error = 0; if ( num > 0 && str[num-1] == 0 ) { num--; } else if ( num <= 0 || str[num-1] != LINEFEED ) { AddLineFeed(str,num); } /*[15apr2004 mt]:*/ if(type == EXTERNALCHANNELOUT){ if(WriteFile(0,str,num) != num) error = 1; }else /*:[15apr2004 mt]*/ if ( AM.silent == 0 || type == ERROROUT ) { if ( type == INPUTOUT ) { if ( !AM.FileOnlyFlag && WriteFile(AM.StdOut,(UBYTE *)" ",4) != 4 ) error = 1; if ( AC.LogHandle >= 0 && WriteFile(AC.LogHandle,(UBYTE *)" ",4) != 4 ) error = 1; } if ( !AM.FileOnlyFlag && WriteFile(AM.StdOut,str,num) != num ) error = 1; if ( AC.LogHandle >= 0 && WriteFile(AC.LogHandle,str,num) != num ) error = 1; } if ( error ) Terminate(-1); } /* #] WriteString : #[ WriteUnfinString : Writes a characterstring to the various outputs. The action may depend on the flags involved. The type of output is given by type, the string by str and the number of characters in it by num */ void WriteUnfinString(int type, UBYTE *str, int num) { int error = 0; /*[15apr2004 mt]:*/ if(type == EXTERNALCHANNELOUT){ if(WriteFile(0,str,num) != num) error = 1; }else /*:[15apr2004 mt]*/ if ( AM.silent == 0 || type == ERROROUT ) { if ( type == INPUTOUT ) { if ( !AM.FileOnlyFlag && WriteFile(AM.StdOut,(UBYTE *)" ",4) != 4 ) error = 1; if ( AC.LogHandle >= 0 && WriteFile(AC.LogHandle,(UBYTE *)" ",4) != 4 ) error = 1; } if ( !AM.FileOnlyFlag && WriteFile(AM.StdOut,str,num) != num ) error = 1; if ( AC.LogHandle >= 0 && WriteFile(AC.LogHandle,str,num) != num ) error = 1; } if ( error ) Terminate(-1); } /* #] WriteUnfinString : #[ AddToString : */ UBYTE *AddToString(UBYTE *outstring, UBYTE *extrastring, int par) { UBYTE *s = extrastring, *t, *newstring; int n, nn; while ( *s ) { s++; } n = s-extrastring; if ( outstring == 0 ) { s = extrastring; t = outstring = (UBYTE *)Malloc1(n+1,"AddToString"); NCOPY(t,s,n) *t++ = 0; return(outstring); } else { t = outstring; while ( *t ) t++; nn = t - outstring; t = newstring = (UBYTE *)Malloc1(n+nn+2,"AddToString"); s = outstring; NCOPY(t,s,nn) if ( par == 1 ) *t++ = ','; s = extrastring; NCOPY(t,s,n) *t = 0; M_free(outstring,"AddToString"); return(newstring); } } /* #] AddToString : #[ strDup1 : string duplication with message passing for Malloc1, allowing this routine to give a more detailed error message if there is not enough memory. */ UBYTE *strDup1(UBYTE *instring, char *ifwrong) { UBYTE *s = instring, *to; while ( *s ) s++; to = s = (UBYTE *)Malloc1((s-instring)+1,ifwrong); while ( *instring ) *to++ = *instring++; *to = 0; return(s); } /* #] strDup1 : #[ EndOfToken : */ /** * Skips over alphanumeric characters to find the end of the token. * * @note This function does not handle formal names (e.g., `[x+a]`). * To handle them, use `SkipAName` instead. * * @param[in] s Pointer to a null-terminated input buffer. * @return Pointer to the first non-alphanumeric character (i.e., the * character immediately after the token), or the null * terminator if the token reaches the end of the string. */ UBYTE *EndOfToken(UBYTE *s) { UBYTE c; while ( ( c = (UBYTE)(FG.cTable[*s]) ) == 0 || c == 1 ) s++; return(s); } /* #] EndOfToken : #[ ToToken : */ /** * Skips over non-alphanumeric characters to find the start of a token. * * @note This function does not handle formal names (e.g., `[x+a]`). * To handle them, consider simply skipping whitespace, e.g., by using * `SkipSpaces`. * * @param[in] s Pointer to a null-terminated input buffer. * @return Pointer to the first alphanumeric character (i.e., the start * of the token), or the null terminator if none is found. */ UBYTE *ToToken(UBYTE *s) { UBYTE c; while ( *s && ( c = (UBYTE)(FG.cTable[*s]) ) != 0 && c != 1 ) s++; return(s); } /* #] ToToken : #[ SkipField : */ /** * Skips from `s` to the end of a declaration field * (e.g., `x`, `1+2*[x+a]`, or `f({x,[x+a]},1)`). * * @param[in] s Pointer to a null-terminated input buffer. * @param[in] level Number of parentheses that still have to be closed. * @return Pointer to the character after the field, which is either * a comma at level 0 or the null terminator. */ UBYTE *SkipField(UBYTE *s, int level) { while ( *s ) { if ( *s == ',' && level == 0 ) return(s); if ( *s == '(' ) level++; else if ( *s == ')' ) { level--; if ( level < 0 ) level = 0; } else if ( *s == '[' ) { SKIPBRA1(s) } else if ( *s == '{' ) { SKIPBRA2(s) } s++; } return(s); } /* #] SkipField : #[ ReadSnum : WORD ReadSnum(p) Reads a number that should fit in a word. The number should be unsigned and a negative return value indicates an irregularity. */ WORD ReadSnum(UBYTE **p) { LONG x = 0; UBYTE *s; s = *p; if ( FG.cTable[*s] == 1 ) { do { x = ( x << 3 ) + ( x << 1 ) + ( *s++ - '0' ); if ( x > MAXPOSITIVE ) return(-1); } while ( FG.cTable[*s] == 1 ); *p = s; return((WORD)x); } else return(-1); } /* #] ReadSnum : #[ NumCopy : Adds the decimal representation of a number to a string. */ UBYTE *NumCopy(WORD y, UBYTE *to) { UBYTE *s; WORD i = 0, j; UWORD x; if ( y < 0 ) { *to++ = '-'; } x = WordAbs(y); s = to; do { *s++ = (UBYTE)((x % 10)+'0'); i++; } while ( ( x /= 10 ) != 0 ); *s-- = '\0'; j = ( i - 1 ) >> 1; while ( j >= 0 ) { i = to[j]; to[j] = s[-j]; s[-j] = (UBYTE)i; j--; } return(s+1); } /* #] NumCopy : #[ LongCopy : Adds the decimal representation of a number to a string. */ char *LongCopy(LONG y, char *to) { char *s; WORD i = 0, j; ULONG x; if ( y < 0 ) { *to++ = '-'; } x = LongAbs(y); s = to; do { *s++ = (x % 10)+'0'; i++; } while ( ( x /= 10 ) != 0 ); *s-- = '\0'; j = ( i - 1 ) >> 1; while ( j >= 0 ) { i = to[j]; to[j] = s[-j]; s[-j] = (char)i; j--; } return(s+1); } /* #] LongCopy : #[ LongLongCopy : Adds the decimal representation of a number to a string. Bugfix feb 2003. y was not pointer! */ char *LongLongCopy(off_t *y, char *to) { /* * This code fails to print the maximum negative value on systems with two's * complement. To fix this, we need the unsigned version of off_t with the * same size, but unfortunately it is undefined. On the other hand, if a * system is configured with a 64-bit off_t, in practice one never reaches * 2^63 ~ 10^18 as of 2016. If one really reach such a big number, then it * would be the time to move on a 128-bit off_t. */ off_t x = *y; char *s; WORD i = 0, j; if ( x < 0 ) { x = -x; *to++ = '-'; } s = to; do { *s++ = (x % 10)+'0'; i++; } while ( ( x /= 10 ) != 0 ); *s-- = '\0'; j = ( i - 1 ) >> 1; while ( j >= 0 ) { i = to[j]; to[j] = s[-j]; s[-j] = (char)i; j--; } return(s+1); } /* #] LongLongCopy : #[ MakeDate : Routine produces a string with the date and time of the run */ #if defined(ANSI) || defined(mBSD) #else static char notime[] = ""; #endif UBYTE *MakeDate(void) { #if defined(ANSI) || defined(mBSD) time_t tp; time(&tp); return((UBYTE *)ctime(&tp)); #else return((UBYTE *)notime); #endif } /* #] MakeDate : #[ set_in : Returns 1 if ch is in set ; 0 if ch is not in set: */ int set_in(UBYTE ch, set_of_char set) { set += ch/8; switch (ch % 8){ case 0: return(set->bit_0); case 1: return(set->bit_1); case 2: return(set->bit_2); case 3: return(set->bit_3); case 4: return(set->bit_4); case 5: return(set->bit_5); case 6: return(set->bit_6); case 7: return(set->bit_7); }/*switch (ch % 8)*/ return(-1); }/*set_in*/ /* #] set_in : #[ set_set : sets ch into set; returns *set: */ one_byte set_set(UBYTE ch, set_of_char set) { one_byte tmp=(one_byte)set; set += ch/8; switch (ch % 8){ case 0: set->bit_0=1;break; case 1: set->bit_1=1;break; case 2: set->bit_2=1;break; case 3: set->bit_3=1;break; case 4: set->bit_4=1;break; case 5: set->bit_5=1;break; case 6: set->bit_6=1;break; case 7: set->bit_7=1;break; } return(tmp); }/*set_set*/ /* #] set_set : #[ set_del : deletes ch from set; returns *set: */ one_byte set_del(UBYTE ch, set_of_char set) { one_byte tmp=(one_byte)set; set += ch/8; switch (ch % 8){ case 0: set->bit_0=0;break; case 1: set->bit_1=0;break; case 2: set->bit_2=0;break; case 3: set->bit_3=0;break; case 4: set->bit_4=0;break; case 5: set->bit_5=0;break; case 6: set->bit_6=0;break; case 7: set->bit_7=0;break; } return(tmp); }/*set_del*/ /* #] set_del : #[ set_sub : returns *set = set1\set2. This function may be usd for initialising, set_sub(a,a,a) => now a is empty set : */ one_byte set_sub(set_of_char set, set_of_char set1, set_of_char set2) { one_byte tmp=(one_byte)set; int i=0,j=0; while(j=0,i++<32) while(j<9) switch (j++){ case 0: set->bit_0=(set1->bit_0&&(!set2->bit_0));break; case 1: set->bit_1=(set1->bit_1&&(!set2->bit_1));break; case 2: set->bit_2=(set1->bit_2&&(!set2->bit_2));break; case 3: set->bit_3=(set1->bit_3&&(!set2->bit_3));break; case 4: set->bit_4=(set1->bit_4&&(!set2->bit_4));break; case 5: set->bit_5=(set1->bit_5&&(!set2->bit_5));break; case 6: set->bit_6=(set1->bit_6&&(!set2->bit_6));break; case 7: set->bit_7=(set1->bit_7&&(!set2->bit_7));break; case 8: set++;set1++;set2++; }; return(tmp); }/*set_sub*/ /* #] set_sub : #] Strings : #[ Mixed : #[ iniTools : */ void iniTools(void) { #ifdef MALLOCPROTECT if ( mprotectInit() ) exit(0); #endif return; } /* #] iniTools : #[ Malloc1 : Malloc routine with built in error checking, and a more detailed error message. Gives the user some idea of what is happening. */ #ifdef MALLOCDEBUG INILOCK(MallocLock) #endif void *Malloc1(LONG size, const char *messageifwrong) { void *mem; #ifdef MALLOCDEBUG char *t, *u; int i; LOCK(MallocLock); if ( size == 0 ) { MesPrint("%wAsking for 0 bytes in Malloc1"); } #endif #ifdef WITHSTATS nummallocs++; #endif if ( ( size & 7 ) != 0 ) { size = size - ( size&7 ) + 8; } #ifdef MALLOCDEBUG size += 2*BANNER; #endif mem = (void *)M_alloc(size); if ( mem == 0 ) { #ifndef MALLOCDEBUG MLOCK(ErrorMessageLock); #endif MesPrint("Attempted to allocate %l bytes.", size); MesPrint("@No memory while allocating %s", (UBYTE *)messageifwrong); #ifndef MALLOCDEBUG MUNLOCK(ErrorMessageLock); #else UNLOCK(MallocLock); #endif Terminate(-1); } #ifdef MALLOCDEBUG mallocsizes[nummalloclist] = size; mallocstrings[nummalloclist] = (char *)messageifwrong; malloclist[nummalloclist++] = mem; if ( AC.MemDebugFlag && filelist ) MesPrint("%wMem1 at 0x%x: %l bytes. %s",mem,size,messageifwrong); { int i = nummalloclist-1; while ( --i >= 0 ) { if ( (char *)mem < (((char *)malloclist[i]) + mallocsizes[i]) && (char *)(malloclist[i]) < ((char *)mem + size) ) { if ( filelist ) MesPrint("This memory overlaps with the block at 0x%x" ,malloclist[i]); } } } #ifdef MALLOCDEBUGOUTPUT printf ("Malloc1: %s, allocated %li bytes at %.8lx\n",messageifwrong,size,(unsigned long)mem); fflush (stdout); #endif t = (char *)mem; u = t + size; for ( i = 0; i < (int)BANNER; i++ ) { *t++ = FILLVALUE; *--u = FILLVALUE; } mem = (void *)t; M_check(); /* MUNLOCK(ErrorMessageLock); */ UNLOCK(MallocLock); #endif /* if ( size > 500000000L ) { MLOCK(ErrorMessageLock); MesPrint("Malloc1: %s, allocated %l bytes\n",messageifwrong,size); MUNLOCK(ErrorMessageLock); } */ return(mem); } /* #] Malloc1 : #[ M_free : */ void M_free(void *x, const char *where) { #ifdef MALLOCDEBUG char *t = (char *)x; int i, j, k; LONG size = 0; x = (void *)(((char *)x)-BANNER); /* MLOCK(ErrorMessageLock); */ if ( AC.MemDebugFlag ) MesPrint("%wFreeing 0x%x: %s",x,where); LOCK(MallocLock); for ( i = nummalloclist-1; i >= 0; i-- ) { if ( x == malloclist[i] ) { size = mallocsizes[i]; for ( j = i+1; j < nummalloclist; j++ ) { malloclist[j-1] = malloclist[j]; mallocsizes[j-1] = mallocsizes[j]; mallocstrings[j-1] = mallocstrings[j]; } nummalloclist--; break; } } if ( i < 0 ) { unsigned int xx = ((ULONG)x); printf("Error returning non-allocated address: 0x%x from %s\n" ,xx,where); /* MUNLOCK(ErrorMessageLock); */ UNLOCK(MallocLock); exit(-1); } else { for ( k = 0, j = 0; k < (int)BANNER; k++ ) { if ( *--t != FILLVALUE ) j++; } if ( j ) { LONG *tt = (LONG *)x; MesPrint("%w!!!!! Banner has been written in !!!!!: %x %x %x %x", tt[0],tt[1],tt[2],tt[3]); } t += size; for ( k = 0, j = 0; k < (int)BANNER; k++ ) { if ( *--t != FILLVALUE ) j++; } if ( j ) { LONG *tt = (LONG *)x; MesPrint("%w!!!!! Tail has been written in !!!!!: %x %x %x %x", tt[0],tt[1],tt[2],tt[3]); } M_check(); /* MUNLOCK(ErrorMessageLock); */ UNLOCK(MallocLock); } #else DUMMYUSE(where); #endif #ifdef WITHSTATS numfrees++; #endif if ( x ) { #ifdef MALLOCDEBUGOUTPUT printf ("M_free: %s, memory freed at %.8lx\n",where,(unsigned long)x); fflush(stdout); #endif #ifdef MALLOCPROTECT mprotectFree((void *)x); #else free(x); #endif } } /* #] M_free : #[ M_check : */ #ifdef MALLOCDEBUG void M_check1() { MesPrint("Checking Malloc"); M_check(); } void M_check() { int i,j,k,error = 0; char *t; LONG *tt; for ( i = 0; i < nummalloclist; i++ ) { t = (char *)(malloclist[i]); for ( k = 0, j = 0; k < (int)BANNER; k++ ) { if ( *t++ != FILLVALUE ) j++; } if ( j ) { tt = (LONG *)(malloclist[i]); MesPrint("%w!!!!! Banner %d (%s) has been written in !!!!!: %x %x %x %x", i,mallocstrings[i],tt[0],tt[1],tt[2],tt[3]); tt[0] = tt[1] = tt[2] = tt[3] = 0; error = 1; } t = (char *)(malloclist[i]) + mallocsizes[i]; for ( k = 0, j = 0; k < (int)BANNER; k++ ) { if ( *--t != FILLVALUE ) j++; } if ( j ) { tt = (LONG *)t; MesPrint("%w!!!!! Tail %d (%s) has been written in !!!!!: %x %x %x %x", i,mallocstrings[i],tt[0],tt[1],tt[2],tt[3]); tt[0] = tt[1] = tt[2] = tt[3] = 0; error = 1; } if ( ( mallocstrings[i][0] == ' ' ) || ( mallocstrings[i][0] == '#' ) ) { MesPrint("%w!!!!! Funny mallocstring"); error = 1; } } if ( error ) { M_print(); /* MUNLOCK(ErrorMessageLock); */ UNLOCK(MallocLock); Terminate(-1); } } void M_print() { int i; MesPrint("We have the following memory allocations left:"); for ( i = 0; i < nummalloclist; i++ ) { MesPrint("0x%x: %l bytes. number %d: '%s'",malloclist[i],mallocsizes[i],i,mallocstrings[i]); } } #else void M_check1(void) {} void M_print(void) {} #endif /* #] M_check : #[ TermMalloc : */ /** * Provides memory for one term (or one small polynomial) * This means that the memory is limited to a buffer of size AM.MaxTer * plus a few extra words. * In parallel versions, each worker has its own memory pool. * * The way we use the memory is by: * term = TermMalloc(BHEAD0); * and later we free it by * TermFree(BHEAD term); * * Layout: * We have a list of available pointers to buffers: AT.TermMemHeap * Its size is AT.TermMemMax * We take from the top (indicated by AT.TermMemTop). * When we run out of buffers we assign new ones (doubling the amount) * and we have to extend the AT.TermMemHeap array. * Important: * There is no checking that the returned memory is legal, ie is * memory that was handed out earlier. */ #define TERMMEMSTARTNUM 16 #define TERMEXTRAWORDS 10 void TermMallocAddMemory(PHEAD0) { WORD *newbufs; int i, extra; if ( AT.TermMemMax == 0 ) extra = TERMMEMSTARTNUM; else extra = AT.TermMemMax; if ( AT.TermMemHeap ) M_free(AT.TermMemHeap,"TermMalloc"); newbufs = (WORD *)Malloc1(extra*(AM.MaxTer+TERMEXTRAWORDS*sizeof(WORD)),"TermMalloc"); AT.TermMemHeap = (WORD **)Malloc1((extra+AT.TermMemMax)*sizeof(WORD *),"TermMalloc"); for ( i = 0; i < extra; i++ ) { AT.TermMemHeap[i] = newbufs + i*(AM.MaxTer/sizeof(WORD)+TERMEXTRAWORDS); } #ifdef TERMMALLOCDEBUG DebugHeap2 = (WORD **)Malloc1((extra+AT.TermMemMax)*sizeof(WORD *),"TermMalloc"); for ( i = 0; i < AT.TermMemMax; i++ ) { DebugHeap2[i] = DebugHeap1[i]; } for ( i = 0; i < extra; i++ ) { DebugHeap2[i+AT.TermMemMax] = newbufs + i*(AM.MaxTer/sizeof(WORD)+TERMEXTRAWORDS); } if ( DebugHeap1 ) M_free(DebugHeap1,"TermMalloc"); DebugHeap1 = DebugHeap2; #endif AT.TermMemTop = extra; AT.TermMemMax += extra; #ifdef TERMMALLOCDEBUG MesPrint("AT.TermMemMax is now %l",AT.TermMemMax); #endif } #ifndef MEMORYMACROS WORD *TermMalloc2(PHEAD char *text) { if ( AT.TermMemTop <= 0 ) TermMallocAddMemory(BHEAD0); #ifdef TERMMALLOCDEBUG MesPrint("TermMalloc: %s, %d",text,(AT.TermMemMax-AT.TermMemTop)); #endif #ifdef MALLOCDEBUGOUTPUT MesPrint("TermMalloc: %s, %l/%l (%x)",text,AT.TermMemTop,AT.TermMemMax,AT.TermMemHeap[AT.TermMemTop-1]); #endif DUMMYUSE(text); return(AT.TermMemHeap[--AT.TermMemTop]); } void TermFree2(PHEAD WORD *TermMem, char *text) { #ifdef TERMMALLOCDEBUG int i; for ( i = 0; i < AT.TermMemMax; i++ ) { if ( TermMem == DebugHeap1[i] ) break; } if ( i >= AT.TermMemMax ) { MesPrint(" ERROR: TermFree called with an address not given by TermMalloc."); Terminate(-1); } #endif DUMMYUSE(text); AT.TermMemHeap[AT.TermMemTop++] = TermMem; #ifdef TERMMALLOCDEBUG MesPrint("TermFree: %s, %d",text,(AT.TermMemMax-AT.TermMemTop)); #endif #ifdef MALLOCDEBUGOUTPUT MesPrint("TermFree: %s, %l/%l (%x)",text,AT.TermMemTop,AT.TermMemMax,TermMem); #endif } #endif /* #] TermMalloc : #[ NumberMalloc : */ /** * Provides memory for one Long number * This means that the memory is limited to a buffer of size AM.MaxTal * In parallel versions, each worker has its own memory pool. * * The way we use the memory is by: * num = NumberMalloc(BHEAD0); Number = AT.NumberMemHeap[num]; * and later we free it by * NumberFree(BHEAD num); * * Layout: * We have a list of available pointers to buffers: AT.NumberMemHeap * Its size is AT.NumberMemMax * We take from the top (indicated by AT.NumberMemTop). * When we run out of buffers we assign new ones (doubling the amount) * and we have to extend the AT.NumberMemHeap array. * Important: * There is no checking on the returned memory!!!! */ #define NUMBERMEMSTARTNUM 16 #define NUMBEREXTRAWORDS 10L #ifdef TERMMALLOCDEBUG UWORD **DebugHeap3, **DebugHeap4; #endif void NumberMallocAddMemory(PHEAD0) { UWORD *newbufs; WORD extra; int i; if ( AT.NumberMemMax == 0 ) extra = NUMBERMEMSTARTNUM; else extra = AT.NumberMemMax; if ( AT.NumberMemHeap ) M_free(AT.NumberMemHeap,"NumberMalloc"); newbufs = (UWORD *)Malloc1(extra*(AM.MaxTal+NUMBEREXTRAWORDS)*sizeof(UWORD),"NumberMalloc"); AT.NumberMemHeap = (UWORD **)Malloc1((extra+AT.NumberMemMax)*sizeof(UWORD *),"NumberMalloc"); for ( i = 0; i < extra; i++ ) { AT.NumberMemHeap[i] = newbufs + i*(LONG)(AM.MaxTal+NUMBEREXTRAWORDS); } #ifdef TERMMALLOCDEBUG DebugHeap4 = (UWORD **)Malloc1((extra+AT.NumberMemMax)*sizeof(WORD *),"NumberMalloc"); for ( i = 0; i < AT.NumberMemMax; i++ ) { DebugHeap4[i] = DebugHeap3[i]; } for ( i = 0; i < extra; i++ ) { DebugHeap4[i+AT.NumberMemMax] = newbufs + i*(LONG)(AM.MaxTal+NUMBEREXTRAWORDS); } if ( DebugHeap3 ) M_free(DebugHeap3,"NumberMalloc"); DebugHeap3 = DebugHeap4; #endif AT.NumberMemTop = extra; AT.NumberMemMax += extra; /* MesPrint("AT.NumberMemMax is now %l",AT.NumberMemMax); */ } #ifndef MEMORYMACROS UWORD *NumberMalloc2(PHEAD char *text) { if ( AT.NumberMemTop <= 0 ) NumberMallocAddMemory(BHEAD text); #ifdef MALLOCDEBUGOUTPUT if ( (AT.NumberMemMax-AT.NumberMemTop) > 10 ) MesPrint("NumberMalloc: %s, %l/%l (%x)",text,AT.NumberMemTop,AT.NumberMemMax,AT.NumberMemHeap[AT.NumberMemTop-1]); #endif DUMMYUSE(text); return(AT.NumberMemHeap[--AT.NumberMemTop]); } void NumberFree2(PHEAD UWORD *NumberMem, char *text) { #ifdef TERMMALLOCDEBUG int i; for ( i = 0; i < AT.NumberMemMax; i++ ) { if ( NumberMem == DebugHeap3[i] ) break; } if ( i >= AT.NumberMemMax ) { MesPrint(" ERROR: NumberFree called with an address not given by NumberMalloc."); Terminate(-1); } #endif DUMMYUSE(text); AT.NumberMemHeap[AT.NumberMemTop++] = NumberMem; #ifdef MALLOCDEBUGOUTPUT if ( (AT.NumberMemMax-AT.NumberMemTop) > 10 ) MesPrint("NumberFree: %s, %l/%l (%x)",text,AT.NumberMemTop,AT.NumberMemMax,NumberMem); #endif } #endif /* #] NumberMalloc : #[ CacheNumberMalloc : Similar to NumberMalloc */ void CacheNumberMallocAddMemory(PHEAD0) { UWORD *newbufs; WORD extra; int i; if ( AT.CacheNumberMemMax == 0 ) extra = NUMBERMEMSTARTNUM; else extra = AT.CacheNumberMemMax; if ( AT.CacheNumberMemHeap ) M_free(AT.CacheNumberMemHeap,"NumberMalloc"); newbufs = (UWORD *)Malloc1(extra*(AM.MaxTal+NUMBEREXTRAWORDS)*sizeof(UWORD),"CacheNumberMalloc"); AT.CacheNumberMemHeap = (UWORD **)Malloc1((extra+AT.NumberMemMax)*sizeof(UWORD *),"CacheNumberMalloc"); for ( i = 0; i < extra; i++ ) { AT.CacheNumberMemHeap[i] = newbufs + i*(LONG)(AM.MaxTal+NUMBEREXTRAWORDS); } AT.CacheNumberMemTop = extra; AT.CacheNumberMemMax += extra; } #ifndef MEMORYMACROS UWORD *CacheNumberMalloc2(PHEAD char *text) { if ( AT.CacheNumberMemTop <= 0 ) CacheNumberMallocAddMemory(BHEAD0); #ifdef MALLOCDEBUGOUTPUT MesPrint("NumberMalloc: %s, %l/%l (%x)",text,AT.NumberMemTop,AT.NumberMemMax,AT.NumberMemHeap[AT.NumberMemTop-1]); #endif DUMMYUSE(text); return(AT.CacheNumberMemHeap[--AT.CacheNumberMemTop]); } void CacheNumberFree2(PHEAD UWORD *NumberMem, char *text) { DUMMYUSE(text); AT.CacheNumberMemHeap[AT.CacheNumberMemTop++] = NumberMem; #ifdef MALLOCDEBUGOUTPUT MesPrint("NumberFree: %s, %l/%l (%x)",text,AT.NumberMemTop,AT.NumberMemMax,NumberMem); #endif } #endif /* #] CacheNumberMalloc : #[ FromList : Returns the next object in a list. If the list has been exhausted we double it (like a realloc) If the list has not been initialized yet we start with 12 elements. */ void *FromList(LIST *L) { void *newlist; int i, *old, *newL; if ( L->num >= L->maxnum || L->lijst == 0 ) { if ( L->maxnum == 0 ) L->maxnum = 12; else if ( L->lijst ) L->maxnum *= 2; newlist = Malloc1(L->maxnum * L->size,L->message); if ( L->lijst ) { i = ( L->num * L->size ) / sizeof(int); old = (int *)L->lijst; newL = (int *)newlist; while ( --i >= 0 ) *newL++ = *old++; if ( L->lijst ) M_free(L->lijst,"L->lijst FromList"); } L->lijst = newlist; } return( ((char *)(L->lijst)) + L->size * (L->num)++ ); } /* #] FromList : #[ From0List : Same as FromList, but we zero excess variables. */ void *From0List(LIST *L) { void *newlist; int i, *old, *newL; if ( L->num >= L->maxnum || L->lijst == 0 ) { if ( L->maxnum == 0 ) L->maxnum = 12; else if ( L->lijst ) L->maxnum *= 2; newlist = Malloc1(L->maxnum * L->size,L->message); i = ( L->num * L->size ) / sizeof(int); old = (int *)(L->lijst); newL = (int *)newlist; while ( --i >= 0 ) *newL++ = *old++; i = ( L->maxnum - L->num ) / sizeof(int); while ( --i >= 0 ) *newL++ = 0; if ( L->lijst ) M_free(L->lijst,"L->lijst From0List"); L->lijst = newlist; } return( ((char *)(L->lijst)) + L->size * (L->num)++ ); } /* #] From0List : #[ FromVarList : Returns the next object in a list of variables. If the list has been exhausted we double it (like a realloc) If the list has not been initialized yet we start with 12 elements. We allow at most MAXVARIABLES elements! */ void *FromVarList(LIST *L) { void *newlist; int i, *old, *newL; if ( L->num >= L->maxnum || L->lijst == 0 ) { if ( L->maxnum == 0 ) L->maxnum = 12; else if ( L->lijst ) { L->maxnum *= 2; if ( L == &(AP.DollarList) ) { if ( L->maxnum > MAXDOLLARVARIABLES ) L->maxnum = MAXDOLLARVARIABLES; if ( L->num >= MAXDOLLARVARIABLES ) { MesPrint("!!!More than %l objects in list of $-variables", MAXDOLLARVARIABLES); Terminate(-1); } } else { if ( L->maxnum > MAXVARIABLES ) L->maxnum = MAXVARIABLES; if ( L->num >= MAXVARIABLES ) { MesPrint("!!!More than %l objects in list of variables", MAXVARIABLES); Terminate(-1); } } } newlist = Malloc1(L->maxnum * L->size,L->message); if ( L->lijst ) { i = ( L->num * L->size ) / sizeof(int); old = (int *)(L->lijst); newL = (int *)newlist; while ( --i >= 0 ) *newL++ = *old++; if ( L->lijst ) M_free(L->lijst,"L->lijst from VarList"); } L->lijst = newlist; } return( ((char *)(L->lijst)) + L->size * ((L->num)++) ); } /* #] FromVarList : #[ DoubleList : */ int DoubleList(void ***lijst, int *oldsize, int objectsize, char *nameoftype) { void **newlist; LONG i, newsize, fullsize; void **to, **from; static LONG maxlistsize = (LONG)(MAXPOSITIVE); if ( *lijst == 0 ) { if ( *oldsize > 0 ) newsize = *oldsize; else newsize = 100; } else newsize = *oldsize * 2; if ( newsize > maxlistsize ) { if ( *oldsize == maxlistsize ) { MesPrint("No memory for extra space in %s",nameoftype); return(-1); } newsize = maxlistsize; } fullsize = ( newsize * objectsize + sizeof(void *)-1 ) & (-sizeof(void *)); newlist = (void **)Malloc1(fullsize,nameoftype); if ( *lijst ) { /* Now some punning. DANGEROUS CODE in principle */ to = newlist; from = *lijst; i = (*oldsize * objectsize)/sizeof(void *); /* #ifdef MALLOCDEBUG if ( filelist ) MesPrint(" oldsize: %l, objectsize: %d, fullsize: %l" ,*oldsize,objectsize,fullsize); #endif */ while ( --i >= 0 ) *to++ = *from++; } if ( *lijst ) M_free(*lijst,"DoubleLList"); *lijst = newlist; *oldsize = newsize; return(0); /* int error; LONG lsize = *oldsize; maxlistsize = (LONG)(MAXPOSITIVE); error = DoubleLList(lijst,&lsize,objectsize,nameoftype); *oldsize = lsize; maxlistsize = (LONG)(MAXLONG); return(error); */ } /* #] DoubleList : #[ DoubleLList : */ int DoubleLList(void ***lijst, LONG *oldsize, int objectsize, char *nameoftype) { void **newlist; LONG i, newsize, fullsize; void **to, **from; static LONG maxlistsize = (LONG)(MAXLONG); if ( *lijst == 0 ) { if ( *oldsize > 0 ) newsize = *oldsize; else newsize = 100; } else newsize = *oldsize * 2; if ( newsize > maxlistsize ) { if ( *oldsize == maxlistsize ) { MesPrint("No memory for extra space in %s",nameoftype); return(-1); } newsize = maxlistsize; } fullsize = ( newsize * objectsize + sizeof(void *)-1 ) & (-sizeof(void *)); newlist = (void **)Malloc1(fullsize,nameoftype); if ( *lijst ) { /* Now some punning. DANGEROUS CODE in principle */ to = newlist; from = *lijst; i = (*oldsize * objectsize)/sizeof(void *); /* #ifdef MALLOCDEBUG if ( filelist ) MesPrint(" oldsize: %l, objectsize: %d, fullsize: %l" ,*oldsize,objectsize,fullsize); #endif */ while ( --i >= 0 ) *to++ = *from++; } if ( *lijst ) M_free(*lijst,"DoubleLList"); *lijst = newlist; *oldsize = newsize; return(0); } /* #] DoubleLList : #[ DoubleBuffer : */ #define DODOUBLE(x) { x *s, *t, *u; if ( *start ) { \ oldsize = *(x **)stop - *(x **)start; newsize = 2*oldsize; \ t = u = (x *)Malloc1(newsize*sizeof(x),text); s = *(x **)start; \ for ( i = 0; i < oldsize; i++ ) {*t++ = *s++;} M_free(*start,"double"); } \ else { newsize = 100; u = (x *)Malloc1(newsize*sizeof(x),text); } \ *start = (void *)u; *stop = (void *)(u+newsize); } void DoubleBuffer(void **start, void **stop, int size, char *text) { LONG oldsize, newsize, i; if ( size == sizeof(char) ) DODOUBLE(char) else if ( size == sizeof(short) ) DODOUBLE(short) else if ( size == sizeof(int) ) DODOUBLE(int) else if ( size == sizeof(LONG) ) DODOUBLE(LONG) else if ( size % sizeof(int) == 0 ) DODOUBLE(int) else { MesPrint("---Cannot handle doubling buffers of size %d",size); Terminate(-1); } } /* #] DoubleBuffer : #[ ExpandBuffer : */ #define DOEXPAND(x) { x *newbuffer, *t, *m; \ t = newbuffer = (x *)Malloc1((newsize+2)*type,"ExpandBuffer"); \ if ( *buffer ) { m = (x *)*buffer; i = *oldsize; \ while ( --i >= 0 ) {*t++ = *m++;} M_free(*buffer,"ExpandBuffer"); \ } *buffer = newbuffer; *oldsize = newsize; } void ExpandBuffer(void **buffer, LONG *oldsize, int type) { LONG newsize, i; if ( *oldsize <= 0 ) { newsize = 100; } else newsize = 2*(*oldsize); if ( type == sizeof(char) ) DOEXPAND(char) else if ( type == sizeof(short) ) DOEXPAND(short) else if ( type == sizeof(int) ) DOEXPAND(int) else if ( type == sizeof(LONG) ) DOEXPAND(LONG) else if ( type == sizeof(POSITION) ) DOEXPAND(POSITION) else { MesPrint("---Cannot handle expanding buffers with objects of size %d",type); Terminate(-1); } } /* #] ExpandBuffer : #[ iexp : Raises the long integer y to the power p. Returnvalue is long, regardless of overflow. */ LONG iexp(LONG x, int p) { int sign; ULONG y; ULONG ux; if ( x == 0 ) return(0); if ( p == 0 ) return(1); sign = x < 0 ? -1 : 1; if ( sign < 0 && ( p & 1 ) == 0 ) sign = 1; ux = LongAbs(x); if ( ux == 1 ) return(sign); if ( p < 0 ) return(0); y = 1; while ( p ) { if ( ( p & 1 ) != 0 ) y *= ux; p >>= 1; ux = ux*ux; } if ( sign < 0 ) y = -y; return ULongToLong(y); } /* #] iexp : #[ ToGeneral : Convert a fast argument to a general argument Input in r, output in m. If par == 0 we need the argument header also. */ void ToGeneral(WORD *r, WORD *m, WORD par) { WORD *mm = m, j, k; if ( par ) m++; else { m[1] = 0; m += ARGHEAD + 1; } j = -*r++; k = 3; /* JV: Bugfix 1-feb-2016. Old code assumed FUNHEAD to be 2 */ if ( j >= FUNCTION ) { *m++ = j; *m++ = FUNHEAD; FILLFUN(m) } else { switch ( j ) { case SYMBOL: *m++ = j; *m++ = 4; *m++ = *r++; *m++ = 1; break; case SNUMBER: if ( *r > 0 ) { *m++ = *r; *m++ = 1; *m++ = 3; } else if ( *r == 0 ) { m--; } else { *m++ = -*r; *m++ = 1; *m++ = -3; } goto MakeSize; case MINVECTOR: k = -k; /* fall through */ case INDEX: case VECTOR: *m++ = INDEX; *m++ = 3; *m++ = *r++; break; } } *m++ = 1; *m++ = 1; *m++ = k; MakeSize: *mm = m-mm; if ( !par ) mm[ARGHEAD] = *mm-ARGHEAD; } /* #] ToGeneral : #[ ToFast : Checks whether an argument can be converted to fast notation If this can be done it does it. Important: m should be allowed to be equal to r! Return value is 1 if conversion took place. If there was conversion the answer is in m. If there was no conversion m hasn't been touched. */ int ToFast(WORD *r, WORD *m) { WORD i; if ( *r == ARGHEAD ) { *m++ = -SNUMBER; *m++ = 0; return(1); } if ( *r != r[ARGHEAD]+ARGHEAD ) return(0); /* > 1 term */ r += ARGHEAD; if ( *r == 4 ) { if ( r[2] != 1 || r[1] <= 0 ) return(0); *m++ = -SNUMBER; *m = ( r[3] < 0 ) ? -r[1] : r[1]; return(1); } i = *r - 1; if ( r[i-1] != 1 || r[i-2] != 1 ) return(0); if ( r[i] != 3 ) { if ( r[i] == -3 && r[2] == *r-4 && r[2] == 3 && r[1] == INDEX && r[3] < MINSPEC ) {} else return(0); } else if ( r[2] != *r - 4 ) return(0); r++; if ( *r >= FUNCTION ) { if ( r[1] <= FUNHEAD ) { *m++ = -*r; return(1); } } else if ( *r == SYMBOL ) { if ( r[1] == 4 && r[3] == 1 ) { *m++ = -SYMBOL; *m++ = r[2]; return(1); } } else if ( *r == INDEX ) { if ( r[1] == 3 ) { if ( r[2] >= MINSPEC ) { if ( r[2] >= 0 && r[2] < AM.OffsetIndex ) *m++ = -SNUMBER; else *m++ = -INDEX; } else { if ( r[5] == -3 ) *m++ = -MINVECTOR; else *m++ = -VECTOR; } *m++ = r[2]; return(1); } } return(0); } /* #] ToFast : #[ ToPolyFunGeneral : Routine forces a polyratfun into general notation if needed. If no action was needed, the return value is zero. A positive return value indicates how many arguments were converted. The new term overwrite the old. */ WORD ToPolyFunGeneral(PHEAD WORD *term) { WORD *t = term+1, *tt, *to, *to1, *termout, *tstop, *tnext; WORD numarg, i, change = 0; tstop = term + *term; tstop -= ABS(tstop[-1]); termout = to = AT.WorkPointer; to++; while ( t < tstop ) { /* go through the subterms */ if ( *t == AR.PolyFun ) { tt = t+FUNHEAD; tnext = t + t[1]; numarg = 0; while ( tt < tnext ) { numarg++; NEXTARG(tt); } if ( numarg == 2 ) { /* this needs attention */ tt = t + FUNHEAD; to1 = to; i = FUNHEAD; NCOPY(to,t,i); while ( tt < tnext ) { /* Do the arguments */ if ( *tt > 0 ) { i = *tt; NCOPY(to,tt,i); } else if ( *tt == -SYMBOL ) { to1[1] += 6+ARGHEAD; to1[2] |= MUSTCLEANPRF; change++; *to++ = 8+ARGHEAD; *to++ = 0; FILLARG(to); *to++ = 8; *to++ = SYMBOL; *to++ = 4; *to++ = tt[1]; *to++ = 1; *to++ = 1; *to++ = 1; *to++ = 3; tt += 2; } else if ( *tt == -SNUMBER ) { if ( tt[1] > 0 ) { to1[1] += 2+ARGHEAD; to1[2] |= MUSTCLEANPRF; change++; *to++ = 4+ARGHEAD; *to++ = 0; FILLARG(to); *to++ = 4; *to++ = tt[1]; *to++ = 1; *to++ = 3; tt += 2; } else if ( tt[1] < 0 ) { to1[1] += 2+ARGHEAD; to1[2] |= MUSTCLEANPRF; change++; *to++ = 4+ARGHEAD; *to++ = 0; FILLARG(to); *to++ = 4; *to++ = -tt[1]; *to++ = 1; *to++ = -3; tt += 2; } else { MLOCK(ErrorMessageLock); MesPrint("Internal error: Zero in PolyRatFun"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } t = tnext; continue; } } i = t[1]; NCOPY(to,t,i) } if ( change ) { tt = term + *term; while ( t < tt ) *to++ = *t++; *termout = to - termout; t = term; i = *termout; tt = termout; NCOPY(t,tt,i) AT.WorkPointer = term + *term; } return(change); } /* #] ToPolyFunGeneral : #[ IsLikeVector : Routine determines whether a function argument is like a vector. Returnvalue: 1: is vector or index 0: is not vector or index -1: may be an index */ int IsLikeVector(WORD *arg) { WORD *sstop, *t, *tstop; if ( *arg < 0 ) { if ( *arg == -VECTOR || *arg == -INDEX ) return(1); if ( *arg == -SNUMBER && arg[1] >= 0 && arg[1] < AM.OffsetIndex ) return(-1); return(0); } sstop = arg + *arg; arg += ARGHEAD; while ( arg < sstop ) { t = arg + *arg; tstop = t - ABS(t[-1]); arg++; while ( arg < tstop ) { if ( *arg == INDEX ) return(1); arg += arg[1]; } arg = t; } return(0); } /* #] IsLikeVector : #[ AreArgsEqual : */ int AreArgsEqual(WORD *arg1, WORD *arg2) { int i; if ( *arg2 != *arg1 ) return(0); if ( *arg1 > 0 ) { i = *arg1; while ( --i > 0 ) { if ( arg1[i] != arg2[i] ) return(0); } return(1); } else if ( *arg1 <= -FUNCTION ) return(1); else if ( arg1[1] == arg2[1] ) return(1); return(0); } /* #] AreArgsEqual : #[ CompareArgs : */ int CompareArgs(WORD *arg1, WORD *arg2) { int i1,i2; if ( *arg1 > 0 ) { if ( *arg2 < 0 ) return(-1); i1 = *arg1-ARGHEAD; arg1 += ARGHEAD; i2 = *arg2-ARGHEAD; arg2 += ARGHEAD; while ( i1 > 0 && i2 > 0 ) { if ( *arg1 != *arg2 ) return((int)(*arg1)-(int)(*arg2)); i1--; i2--; arg1++; arg2++; } return(i1-i2); } else if ( *arg2 > 0 ) return(1); else { if ( *arg1 != *arg2 ) { if ( *arg1 < *arg2 ) return(-1); else return(1); } if ( *arg1 <= -FUNCTION ) return(0); return((int)(arg1[1])-(int)(arg2[1])); } } /* #] CompareArgs : #[ CompArg : returns 1 if arg1 comes first, -1 if arg2 comes first, 0 if equal */ int CompArg(WORD *s1, WORD *s2) { GETIDENTITY WORD *st1, *st2, x[7]; int k; if ( *s1 < 0 ) { if ( *s2 < 0 ) { if ( *s1 <= -FUNCTION && *s2 <= -FUNCTION ) { if ( *s1 > *s2 ) return(-1); if ( *s1 < *s2 ) return(1); return(0); } if ( *s1 > *s2 ) return(1); if ( *s1 < *s2 ) return(-1); if ( *s1 <= -FUNCTION ) return(0); s1++; s2++; if ( *s1 > *s2 ) return(1); if ( *s1 < *s2 ) return(-1); return(0); } x[1] = AT.comsym[3]; x[2] = AT.comnum[1]; x[3] = AT.comnum[3]; x[4] = AT.comind[3]; x[5] = AT.comind[6]; x[6] = AT.comfun[1]; if ( *s1 == -SYMBOL ) { AT.comsym[3] = s1[1]; st1 = AT.comsym+8; s1 = AT.comsym; } else if ( *s1 == -SNUMBER ) { if ( s1[1] < 0 ) { AT.comnum[1] = -s1[1]; AT.comnum[3] = -3; } else { AT.comnum[1] = s1[1]; AT.comnum[3] = 3; } st1 = AT.comnum+4; s1 = AT.comnum; } else if ( *s1 == -INDEX || *s1 == -VECTOR ) { AT.comind[3] = s1[1]; AT.comind[6] = 3; st1 = AT.comind+7; s1 = AT.comind; } else if ( *s1 == -MINVECTOR ) { AT.comind[3] = s1[1]; AT.comind[6] = -3; st1 = AT.comind+7; s1 = AT.comind; } else if ( *s1 <= -FUNCTION ) { AT.comfun[1] = -*s1; st1 = AT.comfun+FUNHEAD+4; s1 = AT.comfun; } /* Symmetrize during compilation of id statement when properorder needs this one. Code added 10-nov-2001 */ else if ( *s1 == -ARGWILD ) { return(-1); } else { goto argerror; } st2 = s2 + *s2; s2 += ARGHEAD; goto docompare; } else if ( *s2 < 0 ) { x[1] = AT.comsym[3]; x[2] = AT.comnum[1]; x[3] = AT.comnum[3]; x[4] = AT.comind[3]; x[5] = AT.comind[6]; x[6] = AT.comfun[1]; if ( *s2 == -SYMBOL ) { AT.comsym[3] = s2[1]; st2 = AT.comsym+8; s2 = AT.comsym; } else if ( *s2 == -SNUMBER ) { if ( s2[1] < 0 ) { AT.comnum[1] = -s2[1]; AT.comnum[3] = -3; st2 = AT.comnum+4; } else if ( s2[1] == 0 ) { st2 = AT.comnum+4; s2 = st2; } else { AT.comnum[1] = s2[1]; AT.comnum[3] = 3; st2 = AT.comnum+4; } s2 = AT.comnum; } else if ( *s2 == -INDEX || *s2 == -VECTOR ) { AT.comind[3] = s2[1]; AT.comind[6] = 3; st2 = AT.comind+7; s2 = AT.comind; } else if ( *s2 == -MINVECTOR ) { AT.comind[3] = s2[1]; AT.comind[6] = -3; st2 = AT.comind+7; s2 = AT.comind; } else if ( *s2 <= -FUNCTION ) { AT.comfun[1] = -*s2; st2 = AT.comfun+FUNHEAD+4; s2 = AT.comfun; } /* Symmetrize during compilation of id statement when properorder needs this one. Code added 10-nov-2001 */ else if ( *s2 == -ARGWILD ) { return(1); } else { goto argerror; } st1 = s1 + *s1; s1 += ARGHEAD; goto docompare; } else { x[1] = AT.comsym[3]; x[2] = AT.comnum[1]; x[3] = AT.comnum[3]; x[4] = AT.comind[3]; x[5] = AT.comind[6]; x[6] = AT.comfun[1]; st1 = s1 + *s1; st2 = s2 + *s2; s1 += ARGHEAD; s2 += ARGHEAD; docompare: while ( s1 < st1 && s2 < st2 ) { if ( ( k = CompareTerms(BHEAD s1,s2,(WORD)2) ) != 0 ) { AT.comsym[3] = x[1]; AT.comnum[1] = x[2]; AT.comnum[3] = x[3]; AT.comind[3] = x[4]; AT.comind[6] = x[5]; AT.comfun[1] = x[6]; return(-k); } s1 += *s1; s2 += *s2; } AT.comsym[3] = x[1]; AT.comnum[1] = x[2]; AT.comnum[3] = x[3]; AT.comind[3] = x[4]; AT.comind[6] = x[5]; AT.comfun[1] = x[6]; if ( s1 < st1 ) return(1); if ( s2 < st2 ) return(-1); } return(0); argerror: MesPrint("Illegal type of short function argument in Normalize"); Terminate(-1); return(0); } /* #] CompArg : #[ TimeWallClock : */ #ifdef HAVE_CLOCK_GETTIME #include /* for clock_gettime() */ #else #ifdef HAVE_GETTIMEOFDAY #include /* for gettimeofday() */ #else #include /* for ftime() */ #endif #endif /** * Returns the wall-clock time. * * @param par If zero, the wall-clock time will be reset to 0. * @return The wall-clock time in centiseconds. */ LONG TimeWallClock(WORD par) { /* * NOTE: this function is not thread-safe. Operations on tp are not atomic. */ #ifdef HAVE_CLOCK_GETTIME struct timespec ts; clock_gettime(CLOCK_MONOTONIC, &ts); if ( par ) { return(((LONG)(ts.tv_sec)-AM.OldSecTime)*100 + ((LONG)(ts.tv_nsec / 1000000)-AM.OldMilliTime)/10); } else { AM.OldSecTime = (LONG)(ts.tv_sec); AM.OldMilliTime = (LONG)(ts.tv_nsec / 1000000); return(0L); } #else #ifdef HAVE_GETTIMEOFDAY struct timeval t; LONG sec, msec; gettimeofday(&t, NULL); sec = (LONG)t.tv_sec; msec = (LONG)(t.tv_usec/1000); if ( par ) { return (sec-AM.OldSecTime)*100 + (msec-AM.OldMilliTime)/10; } else { AM.OldSecTime = sec; AM.OldMilliTime = msec; return(0L); } #else struct timeb tp; ftime(&tp); if ( par ) { return(((LONG)(tp.time)-AM.OldSecTime)*100 + ((LONG)(tp.millitm)-AM.OldMilliTime)/10); } else { AM.OldSecTime = (LONG)(tp.time); AM.OldMilliTime = (LONG)(tp.millitm); return(0L); } #endif #endif } /* #] TimeWallClock : #[ TimeChildren : */ LONG TimeChildren(WORD par) { if ( par ) return(Timer(1)-AM.OldChildTime); AM.OldChildTime = Timer(1); return(0L); } /* #] TimeChildren : #[ TimeCPU : */ /** * Returns the CPU time. * * @param par If zero, the CPU time will be reset to 0. * @return The CPU time in milliseconds. */ LONG TimeCPU(WORD par) { GETIDENTITY if ( par ) return(Timer(0)-AR.OldTime); AR.OldTime = Timer(0); return(0L); } /* #] TimeCPU : #[ Timer : */ #if defined(WINDOWS) LONG Timer(int par) { #ifndef WITHPTHREADS static int initialized = 0; static HANDLE hProcess; FILETIME ftCreate, ftExit, ftKernel, ftUser; DUMMYUSE(par); if ( !initialized ) { hProcess = OpenProcess(PROCESS_QUERY_INFORMATION, FALSE, GetCurrentProcessId()); } if ( GetProcessTimes(hProcess, &ftCreate, &ftExit, &ftKernel, &ftUser) ) { PFILETIME pftKernel = &ftKernel; /* to avoid strict-aliasing rule warnings */ PFILETIME pftUser = &ftUser; __int64 t = *(__int64 *)pftKernel + *(__int64 *)pftUser; /* in 100 nsec. */ return (LONG)(t / 10000); /* in msec. */ } return 0; #else LONG lResult = 0; HANDLE hThread; FILETIME ftCreate, ftExit, ftKernel, ftUser; DUMMYUSE(par); hThread = OpenThread(THREAD_QUERY_INFORMATION, FALSE, GetCurrentThreadId()); if ( hThread ) { if ( GetThreadTimes(hThread, &ftCreate, &ftExit, &ftKernel, &ftUser) ) { PFILETIME pftKernel = &ftKernel; /* to avoid strict-aliasing rule warnings */ PFILETIME pftUser = &ftUser; __int64 t = *(__int64 *)pftKernel + *(__int64 *)pftUser; /* in 100 nsec. */ lResult = (LONG)(t / 10000); /* in msec. */ } CloseHandle(hThread); } return lResult; #endif } #elif defined(UNIX) #include #include #ifdef WITHPOSIXCLOCK #include /* And include -lrt in the link statement (on blade02) */ #endif LONG Timer(int par) { #ifdef WITHPOSIXCLOCK /* Only to be used in combination with WITHPTHREADS This clock seems to be supported by the standard. The getrusage clock returns according to the standard only the combined time of the whole process. But in older versions of Linux LinuxThreads is used which gives a separate id to each thread and individual timings. In NPTL we get, according to the standard, one combined timing. To get individual timings we need to use clock_gettime(CLOCK_THREAD_CPUTIME_ID, &timing) with timing of the time struct timespec { time_t tv_sec; Seconds. long tv_nsec; Nanoseconds. }; */ struct timespec t; if ( par == 0 ) { if ( clock_gettime(CLOCK_THREAD_CPUTIME_ID, &t) ) { MesPrint("Error in getting timing information"); } return (LONG)t.tv_sec * 1000 + (LONG)t.tv_nsec / 1000000; } return(0); #else struct rusage rusage; if ( par == 1 ) { getrusage(RUSAGE_CHILDREN,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } else { getrusage(RUSAGE_SELF,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } #endif } #elif defined(SUN) #define _TIME_T_ #include #include LONG Timer(int par) { struct rusage rusage; if ( par == 1 ) { getrusage(RUSAGE_CHILDREN,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } else { getrusage(RUSAGE_SELF,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } } #elif defined(RS6K) #include #include LONG Timer(int par) { struct rusage rusage; if ( par == 1 ) { getrusage(RUSAGE_CHILDREN,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } else { getrusage(RUSAGE_SELF,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } } #elif defined(ANSI) LONG Timer(int par) { #ifdef ALPHA /* clock_t t,tikken = clock(); */ /* MesPrint("ALPHA-clock = %l",(LONG)tikken); */ /* t = tikken % CLOCKS_PER_SEC; */ /* tikken /= CLOCKS_PER_SEC; */ /* tikken *= 1000; */ /* tikken += (t*1000)/CLOCKS_PER_SEC; */ /* return((LONG)tikken); */ /* #define _TIME_T_ */ #include #include struct rusage rusage; if ( par == 1 ) { getrusage(RUSAGE_CHILDREN,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } else { getrusage(RUSAGE_SELF,&rusage); return(((LONG)(rusage.ru_utime.tv_sec)+(LONG)(rusage.ru_stime.tv_sec))*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } #else #ifdef DEC_STATION clock_t tikken = clock(); return((LONG)tikken/1000); #else clock_t t, tikken = clock(); t = tikken % CLK_TCK; tikken /= CLK_TCK; tikken *= 1000; tikken += (t*1000)/CLK_TCK; return(tikken); #endif #endif } #elif defined(VMS) #include void times(tbuffer_t *buffer); LONG Timer(int par) { tbuffer_t buffer; if ( par == 1 ) { return(0); } else { times(&buffer); return(buffer.proc_user_time * 10); } } #elif defined(mBSD) #ifdef MICROTIME /* There is only a CP time clock in microseconds here This can cause problems with AO.wrap around */ #else #ifdef mBSD2 #include #include #include LONG pretime = 0; #else #define _TIME_T_ #include #include #endif #endif LONG Timer(int par) { #ifdef MICROTIME LONG t; if ( par == 1 ) { return(0); } t = clock(); if ( ( AO.wrapnum & 1 ) != 0 ) t ^= 0x80000000; if ( t < 0 ) { t ^= 0x80000000; warpnum++; AO.wrap += 2147584; } return(AO.wrap+(t/1000)); #else #ifdef mBSD2 struct tms buffer; LONG ret; ULONG a1, a2, a3, a4; if ( par == 1 ) { return(0); } times(&buffer); a1 = (ULONG)buffer.tms_utime; a2 = a1 >> 16; a3 = a1 & 0xFFFFL; a3 *= 1000; a2 = 1000*a2 + (a3 >> 16); a3 &= 0xFFFFL; a4 = a2/CLK_TCK; a2 %= CLK_TCK; a3 += a2 << 16; ret = (LONG)((a4 << 16) + a3 / CLK_TCK); /* ret = ((LONG)buffer.tms_utime * 1000)/CLK_TCK; */ return(ret); #else #ifdef REALTIME struct timeval tp; struct timezone tzp; if ( par == 1 ) { return(0); } gettimeofday(&tp,&tzp); */ return(tp.tv_sec*1000+tp.tv_usec/1000); #else struct rusage rusage; if ( par == 1 ) { getrusage(RUSAGE_CHILDREN,&rusage); return((rusage.ru_utime.tv_sec+rusage.ru_stime.tv_sec)*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } else { getrusage(RUSAGE_SELF,&rusage); return((rusage.ru_utime.tv_sec+rusage.ru_stime.tv_sec)*1000 +(rusage.ru_utime.tv_usec/1000+rusage.ru_stime.tv_usec/1000)); } #endif #endif #endif } #endif /* #] Timer : #[ Crash : Routine for debugging purposes */ int Crash(void) { int retval; #ifdef DEBUGGING int *zero = 0; retval = *zero; #else retval = 0; #endif return(retval); } /* #] Crash : #[ TestTerm : */ /** * Tests the consistency of the term. * Returns 0 when the term is OK. Any nonzero value is trouble. * In the current version the testing isn't 100% complete. * For instance, we don't check the validity of the symbols nor * do we check the range of their powers. Etc. * This should be extended when the need is there. * * @param term: the term to be tested */ int TestTerm(WORD *term) { int errorcode = 0, coeffsize; WORD *t, *tt, *tstop, *endterm, *targ, *targstop, *funstop, *argterm; endterm = term + *term; coeffsize = ABS(endterm[-1]); if ( coeffsize >= *term ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Coefficient too big."); MUNLOCK(ErrorMessageLock); errorcode = 1; goto finish; } if ( ( coeffsize < 3 ) || ( ( coeffsize & 1 ) != 1 ) ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Wrong size coefficient."); MUNLOCK(ErrorMessageLock); errorcode = 2; goto finish; } t = term+1; tstop = endterm - coeffsize; while ( t < tstop ) { switch ( *t ) { case SYMBOL: case DOTPRODUCT: case INDEX: case VECTOR: case DELTA: case HAAKJE: break; case SNUMBER: case LNUMBER: MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. L or S number"); MUNLOCK(ErrorMessageLock); errorcode = 3; goto finish; break; case EXPRESSION: case SUBEXPRESSION: case DOLLAREXPRESSION: /* MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Expression survives."); MUNLOCK(ErrorMessageLock); errorcode = 4; goto finish; */ break; case SETSET: case MINVECTOR: case SETEXP: case ARGFIELD: MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal subterm."); MUNLOCK(ErrorMessageLock); errorcode = 5; goto finish; break; case ARGWILD: break; default: if ( *t <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal subterm number."); MUNLOCK(ErrorMessageLock); errorcode = 6; goto finish; } /* This is a regular function. */ if ( *t-FUNCTION >= NumFunctions ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal function number"); MUNLOCK(ErrorMessageLock); errorcode = 7; goto finish; } funstop = t + t[1]; if ( funstop > tstop ) goto subtermsize; if ( t[2] != 0 ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Dirty flag nonzero."); MUNLOCK(ErrorMessageLock); errorcode = 8; goto finish; } targ = t + FUNHEAD; if ( targ > funstop ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal function size."); MUNLOCK(ErrorMessageLock); errorcode = 9; goto finish; } if ( functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { } else { while ( targ < funstop ) { if ( *targ < 0 ) { if ( *targ <= -(FUNCTION+NumFunctions) ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal function number in argument."); MUNLOCK(ErrorMessageLock); errorcode = 10; goto finish; } if ( *targ <= -FUNCTION ) { targ++; } else { if ( ( *targ != -SYMBOL ) && ( *targ != -VECTOR ) && ( *targ != -MINVECTOR ) && ( *targ != -SNUMBER ) && ( *targ != -ARGWILD ) && ( *targ != -INDEX ) ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal object in argument."); MUNLOCK(ErrorMessageLock); errorcode = 11; goto finish; } targ += 2; } } else if ( ( *targ < ARGHEAD ) || ( targ+*targ > funstop ) ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal size of argument."); MUNLOCK(ErrorMessageLock); errorcode = 12; goto finish; } else if ( targ[1] != 0 ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Dirty flag in argument."); MUNLOCK(ErrorMessageLock); errorcode = 13; goto finish; } else { targstop = targ + *targ; argterm = targ + ARGHEAD; while ( argterm < targstop ) { if ( ( *argterm < 4 ) || ( argterm + *argterm > targstop ) ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal termsize in argument."); MUNLOCK(ErrorMessageLock); errorcode = 14; goto finish; } if ( TestTerm(argterm) != 0 ) { MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Called from TestTerm."); MUNLOCK(ErrorMessageLock); errorcode = 15; goto finish; } argterm += *argterm; } targ = targstop; } } } break; } tt = t + t[1]; if ( tt > tstop ) { subtermsize: MLOCK(ErrorMessageLock); MesPrint("TestTerm: Internal inconsistency in term. Illegal subterm size."); MUNLOCK(ErrorMessageLock); errorcode = 100; goto finish; } t = tt; } return(errorcode); finish: return(errorcode); } /* #] TestTerm : #[ DistrN : */ int DistrN(int n, int *cpl, int ncpl, int *scratch) { /* Divides n objects over ncpl bins (cpl), each time returning one of those distributions until there are no more after which the routine returns the value zero (otherwise one). The array scratch (size n) is kept for the intermediate information. The whole starts with scratch[0] == -2; */ int i, j; if ( ncpl == 0 ) { if ( scratch[0] == -2 ) { scratch[0] = 0; return(1); } else return(0); } if ( scratch[0] == ncpl-1 ) { return(0); } else if ( scratch[0] == -2 ) { for ( i = 0; i < n; i++ ) scratch[i] = 0; } else { j = n-1; while ( j >= 0 ) { scratch[j]++; if ( scratch[j] < ncpl ) break; j--; } j++; while ( j < n ) { scratch[j] = scratch[j-1]; j++; } } for ( i = 0; i < ncpl; i++ ) cpl[i] = 0; for ( i = 0; i < n; i++ ) { cpl[scratch[i]]++; } return(1); } /* #] DistrN : #] Mixed : */ form-5.0.1/sources/extcmd.c0000644000175100017510000014307715217035721011275 /** @file extcmd.c * * The system that takes care of communication with external programs. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Documentation : This module is written by M.Tentyukov as a part of implementation of interaction between FORM and external processes, first release 09.04.2004. A part of this code is copied from the DIANA project, which was written by M. Tentyukov and published under the GPL version 2 as published by the Free Software Foundation. This file is completely re-written by M.Tentyukov in May 2006. Since the interface was changed, the public function were changed, also. A new public functions were added: initPresetExternalChannels() (see comments just before this function in the present file) and setKillModeForExternalChannel (a pointer, not a function). If a macro WITHEXTERNALCHANNEL is not defined, all public functions are stubs returning failure. The idea is to start an external command swallowing its stdin and stdout. This can be done by means of the function int openExternalChannel(cmd,daemonize,shellname,stderrname), where cmd is a command to run, daemonize: if !=0 then start the command in the "daemon" mode, shellname: if !=NULL, execute the command in a subshell, stderrname: if != NULL, redirect stderr of the command to this file. The function returns some small positive integer number (the descriptor of a newly created external channel), or -1 on failure. After the command is started, it becomes a _current_ opened external channel. The buffer can be sent to its stdin by a function int writeBufToExtChannel(buf, n) (here buf is a pointer to the buffer, n is the length in bytes; the function returns 0 in success, or -1 on failure), or one character can be read from its stdout by means of the function int getcFromExtChannel(). The latter returns the character casted to integer, or something <0. This can be -2 (if there is no current external channel) or EOF, if the external program closes its stdout, or if the external program outputs a string coinciding with a _terminator_. By default, the terminator if an empty line. For the current external channel it can be set by means of the function int setTerminatorForExternalChannel(newterminator). The function returns 0 in success, or !0 if something is wrong (no current channel, too long terminator). After getcFromExtChannel() returns EOF, the current channel becomes undefined. Any further attempts to read information by getcFromExtChannel() result in -2. To set (re-set) a current channel, the function int selectExternalChannel(n) can be used. This function accepts the valid external channel descriptor (returned by openExternalChannel) and returns the descriptor of a previous current channel (0, if there was no current channel, or -1, if the external channel descriptor is invalid). If n == 0, the function undefine the current external channel. The function int closeExternalChannel(n) destroys the opened external channel with the descriptor n. It returns 0 in success, or -1 on failure. If the corresponding external channel was the current one, the current channel becomes undefined. If n==0, the function closes the current external channel. The function int getCurrentExternalChannel(void) returns the descriptor if the current external channel, or 0 , if there is no current external channel. The function void closeAllExternalChannels(void) destroys all opened external channels. List of all public functions: int openExternalChannel(UBYTE *cmd,int daemonize,UBYTE *shellname, UBYTE * stderrname); int initPresetExternalChannels(UBYTE *theline, int thetimeout); int setTerminatorForExternalChannel(char *newterminator); int setKillModeForExternalChannel(int signum, int sentToWholeGroup); int closeExternalChannel(int n); int selectExternalChannel(int n); int writeBufToExtChannel(char *buf,int n); int getcFromExtChannel(void); int getCurrentExternalChannel(void); void closeAllExternalChannels(void); ATTENTION! Four of them: 1 setTerminatorForExternalChannel 2 setKillModeForExternalChannel 3 writeBufToExtChannel 4 getcFromExtChannel are NOT functions, but variables (pointers) of a corrsponding type. They are initialised by proper values to avoid repeated error checking. All public functions are independent of realization hidden in this module. All other functions may have a returned type/parameters type local w.r.t. this module; they are not declared outside of this file. #] Documentation : #[ Selftest initializing: */ /* Uncomment to get a self-consistent program: #define SELFTEST 1 */ #ifdef SELFTEST #define WITHEXTERNALCHANNEL 1 #ifdef _MSC_VER #define FORM_INLINE __inline #else #define FORM_INLINE inline #endif /* From form3.h: */ typedef unsigned char UBYTE; /*The following variables should be defined in variable.h:*/ extern int (*writeBufToExtChannel)(char *buffer, size_t n); extern int (*getcFromExtChannel)(); extern int (*setTerminatorForExternalChannel)(char *buffer); extern int (*setKillModeForExternalChannel)(int signum, int sentToWholeGroup); #else /*ifdef SELFTEST*/ #include "form3.h" #endif /*ifdef SELFTEST ... else*/ /* pid_t getExternalChannelPid(void); */ /* #] Selftest initializing: #[ Includes : */ #ifdef WITHEXTERNALCHANNEL #include #ifndef _MSC_VER #include #endif #include #include #ifndef _MSC_VER #include #include #endif #include #include #include /* #] Includes : #[ FailureFunctions: */ /*Non-initialized variant of public functions:*/ int writeBufToExtChannelFailure(char *buf, size_t count) { DUMMYUSE(buf); DUMMYUSE(count); return(-1); }/*writeBufToExtChannelFailure*/ int setTerminatorForExternalChannelFailure(char *newTerminator) { DUMMYUSE(newTerminator); return(-1); }/*setTerminatorForExternalChannelFailure*/ int setKillModeForExternalChannelFailure(int signum, int sentToWholeGroup) { DUMMYUSE(signum); DUMMYUSE(sentToWholeGroup); return(-1); }/*setKillModeForExternalChannelFailure*/ int getcFromExtChannelFailure(void) { return(-2); }/*getcFromExtChannelFailure*/ int (*writeBufToExtChannel)(char *buffer, size_t n) = &writeBufToExtChannelFailure; int (*setTerminatorForExternalChannel)(char *buffer) = &setTerminatorForExternalChannelFailure; int (*setKillModeForExternalChannel)(int signum, int sentToWholeGroup) = &setKillModeForExternalChannelFailure; int (*getcFromExtChannel)(void) = &getcFromExtChannelFailure; #endif /* #] FailureFunctions: #[ Stubs : */ #ifndef WITHEXTERNALCHANNEL /*Stubs for public functions:*/ int openExternalChannel(UBYTE *cmd, int daemonize, UBYTE *shellname, UBYTE *stderrname) { DUMMYUSE(cmd); DUMMYUSE(daemonize); DUMMYUSE(shellname); DUMMYUSE(stderrname); return(-1); }; int initPresetExternalChannels(UBYTE *theline, int thetimeout) { DUMMYUSE(theline); DUMMYUSE(thetimeout); return(-1); }; int closeExternalChannel(int n) { DUMMYUSE(n); return(-1); }; int selectExternalChannel(int n) { DUMMYUSE(n); return(-1); }; int getCurrentExternalChannel(void) { return(0); }; void closeAllExternalChannels(void) {}; #else /*ifndef WITHEXTERNALCHANNEL*/ /* #] Stubs : #[ Local types : */ /*First argument for the function signal:*/ #ifndef INTSIGHANDLER typedef void (*mysighandler_t)(int); #else /* Sometimes, this nonsense may occurs:*/ /*typedef int (*mysighandler_t)(int);*/ #endif /*Input IO buffer size increment -- each time the buffer is expired it will be increased by this value (in bytes):*/ #define DELTA_EXT_BUF 128 /*Re-allocatable array containing External Channel handlers increased each time by this value:*/ #define DELTA_EXT_LIST 8 /*How many times I/O routines may attempt to continue their work in some failures:*/ #define MAX_FAILS_IO 2 /*The external channel handler structure:*/ typedef struct ExternalChannel { pid_t pid; /*PID of the external process*/ pid_t gpid; /*process group ID of the external process. If <=0, not used, if >0, the kill signals is sent to the whole group */ FILE *frec; /*stdout of the external process*/ char *INbuf; /*External channel buffer*/ char *IBfill; /*Position in INbuf from which the next input character will be read*/ char *IBfull; /*End of read INbuf*/ char *IBstop; /*end of allocated space for INbuf*/ char *terminator;/* Terminator - when extern. program outputs ONLY this string, it is assumed that the answer is ready, and getcFromExtChannel returns EOF. Should not be longer then the minimal buffer!*/ /*Info fields, not changable after creating a channel:*/ char *cmd; /*the command*/ char *shellname; char *stderrname;/*filename to redirect stderr, or NULL*/ int fsend; /*stdin of the external process*/ int killSignal; /*signal to kill*/ int daemonize;/*0 --neither setsid nor daemonize, !=0 -- full daemonization*/ } EXTHANDLE; static EXTHANDLE *externalChannelsList=0; /*Here integers are better than pointers: */ static int externalChannelsListStop=0; static int externalChannelsListFill=0; /*"current" external channel:*/ static EXTHANDLE *externalChannelsListTop=0; /* #] Local types : #[ Selftest functions : */ #ifdef SELFTEST /*For malloc prototype:*/ #include /*StrLen, Malloc1, M_free and strDup1 are defined in tools.c -- here only emulation:*/ int StrLen(char *pattern) { register char *p=(char*)pattern; while(*p)p++; return((int) ((p-(char*)pattern)) ); }/*StrLen*/ void *Malloc1(int l, char *c) { return(malloc(l)); } void M_free(void *p,char *c) { return(free(p)); } char *strDup1(UBYTE *instring, char *ifwrong) { UBYTE *s = instring, *to; while ( *s ) s++; to = s = (UBYTE *)Malloc1((s-instring)+1,ifwrong); while ( *instring ) *to++ = *instring++; *to = 0; return(s); } /*PutPreVar from pre.c -- just ths stub:*/ int PutPreVar(UBYTE *a,UBYTE *b,UBYTE *c,int i) { return(0); } #endif /* #] Selftest functions : #[ Local functions : */ /*Initialize one cell of handler:*/ static FORM_INLINE void extHandlerInit(EXTHANDLE *h) { h->pid=-1; h->gpid=-1; h->fsend=0; h->killSignal=SIGKILL; h->daemonize=1; h->frec=NULL; h->INbuf=h->IBfill=h->IBfull=h->IBstop= h->terminator=h->cmd=h->shellname=h->stderrname=NULL; }/*extHandlerInit*/ /* Copies each field of handler:*/ static FORM_INLINE void extHandlerSwallowCopy(EXTHANDLE *to, EXTHANDLE *from) { to->pid=from->pid; to->gpid=from->gpid; to->fsend=from->fsend; to->killSignal=from->killSignal; to->daemonize=from->daemonize; to->frec=from->frec; to->INbuf=from->INbuf; to->IBfill=from->IBfill; to->IBfull=from->IBfull; to->IBstop=from->IBstop; to->terminator=from->terminator; to->cmd=from->cmd; to->shellname=from->shellname; to->stderrname=from->stderrname; }/*extHandlerSwallow*/ /*Allocates memory for fields of handler which have no fixed storage size and initializes some fields:*/ static FORM_INLINE void extHandlerAlloc(EXTHANDLE *h, char *cmd, char *shellname, char *stderrname) { h->IBfill=h->IBfull=h->INbuf= Malloc1(DELTA_EXT_BUF,"External channel buffer"); h->IBstop=h->INbuf+DELTA_EXT_BUF; /*Initialize a terminator:*/ *(h->terminator=Malloc1(DELTA_EXT_BUF,"External channel terminator"))='\n'; (h->terminator)[1]='\0';/*By default the terminator is '\n'*/ /*Deep copy all strings:*/ if(cmd!=NULL) h->cmd=(char *)strDup1((UBYTE *)cmd,"External channel command"); else/*cmd cannot be NULL! If this is NULL then force it to be something special*/ h->cmd=(char *)strDup1((UBYTE *)"/","External channel command"); if(shellname!=NULL) h->shellname= (char *)strDup1((UBYTE *)shellname,"External channel shell name"); if(stderrname!=NULL) h->stderrname= (char *)strDup1((UBYTE *)stderrname,"External channel stderr name"); }/*extHandlerAlloc*/ /*Disallocates dynamically allocated fields of a handler:*/ static FORM_INLINE void extHandlerFree(EXTHANDLE *h) { if(h->stderrname) M_free(h->stderrname,"External channel stderr name"); if(h->shellname) M_free(h->shellname,"External channel shell name"); if(h->cmd) M_free(h->cmd,"External channel command"); if(h->terminator)M_free(h->terminator,"External channel terminator"); if(h->INbuf)M_free(h->INbuf,"External channel buffer"); extHandlerInit(h); }/*extHandlerFree*/ /* Closes all descriptors, kills the external process, frees all internal fields, BUT does NOT free the main container:*/ static void destroyExternalChannel(EXTHANDLE *h) { /*Note, this function works in parallel mode correctly, see comments below.*/ /*Note, for slaves in a parallel mode h->pid == 0:*/ if( (h->pid > 0) && (h->killSignal > 0) ){ int chstatus; if( h->gpid > 0) chstatus=kill(-h->gpid,h->killSignal); else chstatus=kill(h->pid,h->killSignal); if(chstatus==0) /*If the process will not be killed by this signal, FORM hangs up here!:*/ waitpid(h->pid, &chstatus, 0); }/*if( (h->pid > 0) && (h->killSignal > 0) )*/ /*Note, for slaves in a parallel mode h->frec == h->fsend == 0:*/ if(h->frec) fclose(h->frec); if( h->fsend > 0) close(h->fsend); extHandlerFree(h); /*Does not do "free(h)"!*/ }/*destroyExternalChannel*/ /*Wrapper to the read() syscall, to handle possible interrupts by unblocked signals:*/ static FORM_INLINE ssize_t read2b(int fd, char *buf, size_t count) { ssize_t res; if( (res=read(fd,buf,count)) <1 )/*EOF or read is interrupted by a signal?:*/ while( (errno == EINTR)&&(res <1) ) /*The call was interrupted by a signal before any data was read, try again:*/ res=read(fd,buf,count); return (res); }/*read2b*/ /*Wrapper to the write() syscall, to handle possible interrupts by unblocked signals:*/ static FORM_INLINE ssize_t writeFromb(int fd, char *buf, size_t count) { ssize_t res; if( (res=write(fd,buf,count)) <1 )/*Is write interrupted by a signal?:*/ while( (errno == EINTR)&&(res <1) ) /*The call was interrupted by a signal before any data was written, try again:*/ res=write(fd,buf,count); return (res); }/*writeFromb*/ /* Read one (binary) PID from the file descriptor fd:*/ static FORM_INLINE pid_t readpid(int fd) { pid_t tmp; if(read2b(fd,(char*)&tmp,sizeof(pid_t))!=sizeof(pid_t)) return (pid_t)-1; return tmp; }/*readpid*/ /* Writeone (binary) PID to the file descriptor fd:*/ static FORM_INLINE pid_t writepid(int fd, pid_t thepid) { if(writeFromb(fd,(char*)&thepid,sizeof(pid_t))!=sizeof(pid_t)) return (pid_t)-1; return (pid_t)0; }/*readpid*/ /*Wrtites exactly count bytes from the buffer buf into the descriptor fd, independently on nonblocked signals and the MPU/buffer hits. Returns 0 or -1: */ static FORM_INLINE int writexactly(int fd, char *buf, size_t count) { ssize_t i; int j=0,n=0; for(;;){ if( (i=writeFromb(fd, buf+j, count-j)) < 0 ) return(-1); j+=i; if ( ((size_t)j) == count ) break; if(i==0)n++; else n=0; if(n>MAX_FAILS_IO)return (-1); }/*for(;;)*/ return (0); }/*writexactly*/ /* Set the FD_CLOEXEC flag of desc if value is nonzero, or clear the flag if value is 0. Return 0 on success, or -1 on error with errno set. */ static int set_cloexec_flag(int desc, int value) { int oldflags = fcntl (desc, F_GETFD, 0); /* If reading the flags failed, return error indication now.*/ if (oldflags < 0) return (oldflags); /* Set just the flag we want to set. */ if (value != 0) oldflags |= FD_CLOEXEC; else oldflags &= ~FD_CLOEXEC; /* Store modified flag word in the descriptor. */ return (fcntl(desc, F_SETFD, oldflags)); }/*set_cloexec_flag*/ /* Adds the integer fd to the array fifo of length top+1 so that the array is ascendantly ordered. It is supposed that all 0 -- top-1 elements in the array are already ordered:*/ static void pushDescriptor(int *fifo, int top, int fd) { if ( top == 0 ) { fifo[top] = fd; } else { int ins=top-1; if( fifo[ins]<=fd ) fifo[top]=fd; else{ /*Find the position:*/ while( (ins>=0)&&(fifo[ins]>fd) )ins--; /*Move all elements starting from the position to the right:*/ for(ins++;top>ins; top--) fifo[top]=fifo[top-1]; /*Put the element:*/ fifo[ins]=fd; } } }/*pushDescriptor*/ /*Close all descriptors greater or equal than startFrom except those listed in the ascendantly ordered array usedFd of length top:*/ static FORM_INLINE void closeAllDescriptors(int startFrom, int *usedFd, int top) { int n,maxfd; for(n=0;n ' '); if(*cmd != '\0') *cmd++ = '\0'; n++; }/*if(*cmd != '\0')*/ }/*while(*cmd != '\0')*/ argv[n]=NULL; if(n==0)return -1; return n; }/*parseline*/ /*Reads positive decimal number (not bigger than maxnum) from the string and returns it; the pointer *b is set to the next non-converted character:*/ static LONG str2i(char *str, char **b, LONG maxnum) { LONG n=0; /*Eat trailing spaces:*/ while(*str<=' ')if(*str++ == '\0')return(-1); (*b)=str; while (*str>='0'&&*str<='9') if( (n=10*n + *str++ - '0')>maxnum ) return(-1); if((*b)==str)/*No single number!*/ return(-1); (*b)=str; return(n); } /*Converts long integer to a decimal representation. For portability reasons we cannot use LongCopy from tools.c since theoretically LONG may be smaller than pid_t:*/ static char *l2s(LONG x, char *to) { char *s; int i = 0, j; s = to; do { *s++ = (x % 10)+'0'; i++; } while ( ( x /= 10 ) != 0 ); *s-- = '\0'; j = ( i - 1 ) >> 1; while ( j >= 0 ) { i = to[j]; to[j] = s[-j]; s[-j] = (char)i; j--; } return(s+1); } /*like strcat() but returns the pointer to the end of the resulting string:*/ static FORM_INLINE char *addStr(char *to, char *from) { while( (*to++ = *from++)!='\0' ); return(to-1); }/*addStr*/ /*Try to write (atomically) short buffer (of length count) to fd. timeout is a timeout in millisecs. Returns number of written bytes or -1:*/ static FORM_INLINE ssize_t writeSome(int fd, char *buf, size_t count, int timeout) { ssize_t res = 0; fd_set wfds; struct timeval tv; int nrep=5;/*five attempts it interrupted by a non-blocking signal*/ int flags = fcntl(fd, F_GETFL,0); /*Add O_NONBLOCK:*/ fcntl(fd,F_SETFL, flags | O_NONBLOCK); /* important -- in order to avoid blocking of short receiver buffer*/ do{ FD_ZERO(&wfds); FD_SET(fd, &wfds); /* Wait up to timeout. */ tv.tv_sec =timeout /1000; tv.tv_usec = (timeout % 1000)*1000; nrep--; switch(select(fd+1, NULL, &wfds, NULL, &tv)){ case -1: if((nrep == 0)||( errno != EINTR) ){ perror("select()"); res=-1; nrep=0; }/*else -- A non blocked signal was caught, just repeat*/ break; case 0:/*timeout*/ res=-1; nrep=0; break; default: if( (res=write(fd,buf,count)) <0 )/*Signal?*/ while( (errno == EINTR)&&(res <0) ) res=write(fd,buf,count); nrep=0; }/*switch*/ }while(nrep); /*restore the flags:*/ fcntl(fd,F_SETFL, flags); return (res); }/*writeSome*/ /*Try to read short buffer (of length not more than count) from fd. timeout is a timeout in millisecs. Returns number of written bytes or -1: */ static FORM_INLINE ssize_t readSome(int fd, char *buf, size_t count, int timeout) { ssize_t res = 0; fd_set rfds; struct timeval tv; int nrep=5;/*five attempts it interrupted by a non-blocking signal*/ do{ FD_ZERO(&rfds); FD_SET(fd, &rfds); /* Wait up to timeout. */ tv.tv_sec = timeout/1000; tv.tv_usec = (timeout % 1000)*1000; nrep--; switch(select(fd+1, &rfds, NULL, NULL, &tv)){ case -1: if((nrep == 0)||( errno != EINTR) ){ perror("select()"); res=-1; nrep=0; }/*else -- A non blocked signal was caught, just repeat*/ break; case 0:/*timeout*/ res=-1; nrep=0; break; default: if( (res=read(fd,buf,count)) <0 )/*Signal?*/ while( (errno == EINTR)&&(res <0) ) res=read(fd,buf,count); nrep=0; }/*switch*/ }while(nrep); return (res); }/*readSome*/ /* #] Local functions : #[ Ok functions: */ /*Copies (deep copy) newTerminator to thehandler->terminator. Returns 0 if newTerminator fits to the buffer, or !0 if it does not fit. ATT! In the latter case thehandler->terminator is NOT '\0' terminated! */ int setTerminatorForExternalChannelOk(char *newTerminator) { int i=DELTA_EXT_BUF; /* No problems with externalChannelsListTop are possible since this function may be invoked only when the current channel is defined and externalChannelsListTop is set properly */ char *t=externalChannelsListTop->terminator; for(; i>1; i--) if( (*t++ = *newTerminator++)=='\0' ) break; /*Add trailing '\n', if absent:*/ if( (i == DELTA_EXT_BUF)/*newTerminator == '\0'*/ ||(*(t-2)!='\n') ){ *(t-1)='\n';*t='\0'; } return(i==1); }/*setTerminatorForExternalChannelOk*/ /*Interface to change handler fields "killSignal" and "gpid"*/ int setKillModeForExternalChannelOk(int signum, int sentToWholeGroup) { if(signum<0) return(-1); /* No problems with externalChannelsListTop are possible since this function may be invoked only when the current channel is defined and externalChannelsListTop is set properly */ externalChannelsListTop->killSignal=signum; if(sentToWholeGroup){/*gpid must be >0*/ if(externalChannelsListTop->gpid <= 0) externalChannelsListTop->gpid=-externalChannelsListTop->gpid; }else{/*gpid must be <=0*/ if(externalChannelsListTop->gpid>0) externalChannelsListTop->gpid=-externalChannelsListTop->gpid; } return(0); }/*setKillModeForExternalChannelOk*/ /* #[ getcFromExtChannelOk */ /*Returns one character from the external channel. It the input is expired, returns EOF. If the external process is finished completely, the function closes the channel (and returns EOF). If the external process was finished, the function returns EOF:*/ int getcFromExtChannelOk(void) { mysighandler_t oldPIPE = 0; EXTHANDLE *h; int ret; if (externalChannelsListTop->IBfill < externalChannelsListTop->IBfull) /*in buffer*/ return( *(externalChannelsListTop->IBfill++) ); /*else -- the buffer is empty*/ ret=EOF; h= externalChannelsListTop; #ifdef WITHMPI if ( PF.me == MASTER ){ #endif /* Temporary ignore this signal:*/ /* if compiler fails here, try to change the definition of mysighandler_t on the beginning of this file (just define INTSIGHANDLER).*/ oldPIPE=signal(SIGPIPE,SIG_IGN); #ifdef WITHMPI if( fgets(h->INbuf,h->IBstop - h->INbuf, h->frec) == 0 )/*Fail! EOF?*/ *(h->INbuf)='\0';/*Empty line may not appear here!*/ #else if( (fgets(h->INbuf,h->IBstop - h->INbuf, h->frec) == 0)/*Fail! EOF?*/ ||( *(h->INbuf) == '\0')/*Empty line? This shouldn't be!*/ ){ closeExternalChannel(externalChannelsListTop-externalChannelsList+1); /*Note, this code is only for the sequential mode! */ goto getcFromExtChannelReady; /*Here we assume that fgets is never interrupted by singals*/ }/*if( fgets(h->INbuf,h->IBstop - h->INbuf, h->frec) == 0 )*/ #endif #ifdef WITHMPI }/*if ( PF.me == MASTER */ /*Master broadcasts result to slaves, slaves read it from the master:*/ if( PF_BroadcastString((UBYTE *)h->INbuf) ){/*Fail!*/ MesPrint("Fail broadcasting external channel results"); Terminate(-1); }/*if( PF_BroadcastString((UBYTE *)h->INbuf) )*/ if( *(h->INbuf) == '\0'){/*Empty line? This shouldn't be!*/ closeExternalChannel(externalChannelsListTop-externalChannelsList+1); goto getcFromExtChannelReady; }/*if( *(h->INbuf) == '\0')*/ #endif {/*Block*/ char *t=h->terminator; /*Move IBfull to the end of read line and compare the line with the terminator. Note, by construction the terminator fits to the first read line, see the function setTerminatorForExternalChannel.*/ for(h->IBfull=h->INbuf; *(h->IBfull)!='\0'; (h->IBfull)++) if( *t== *(h->IBfull) ) t++; else break;/*not a terminator*/ /*Continue moving IBfullto the end of read line:*/ while(*(h->IBfull)!='\0')(h->IBfull)++; if( (t-h->terminator) == (h->IBfull-h->INbuf) ){ /*Terminator!*/ /*Reset the channel*/ h->IBfull=h->IBfill=h->INbuf; externalChannelsListTop=0;/*Undefine the current channel*/ writeBufToExtChannel=&writeBufToExtChannelFailure; getcFromExtChannel=&getcFromExtChannelFailure; setTerminatorForExternalChannel=&setTerminatorForExternalChannelFailure; setKillModeForExternalChannel=&setKillModeForExternalChannelFailure; goto getcFromExtChannelReady; }/*if(t == (h->IBfull-h->INbuf) )*/ }/*Block*/ /*Does the buffer have enough capacity?*/ while( *(h->IBfull - 1) != '\n' ){/*Buffer is not enough!*/ /*Extend the buffer:*/ int l= (h->IBstop - h->INbuf)+DELTA_EXT_BUF; char *newbuf=Malloc1(l,"External channel buffer"); /*We wouldn't like to use realloc.*/ /*Copy the buffer:*/ char *n=newbuf,*o=h->INbuf; while( (*n++ = *o++)!='\0' ); /*Att! The order of the following operators is important!:*/ h->IBfull= newbuf+(h->IBfull-h->INbuf); M_free(h->INbuf,"External channel buffer"); h->INbuf = newbuf; h->IBstop = h->INbuf+l; #ifdef WITHMPI if ( PF.me == MASTER ){ (h->IBfull)[1]='\0';/*Will mark (h->IBfull)[1] as '!' for failure*/ if( fgets(h->IBfull,h->IBstop - h->IBfull, h->frec) == 0 ){ /*EOF! No trailing '\n'?*/ /*Mark:*/ (h->IBfull)[0]='\0'; (h->IBfull)[1]='!'; (h->IBfull)[2]='\0'; /*The string "\0!\0" is used as an image of NULL.*/ }/*if( fgets(h->IBfull,h->IBstop - h->IBfull, h->frec) == 0 )*/ }/*if ( PF.me == MASTER )*/ /*Master broadcasts results to slaves, slaves read it from the master:*/ if( PF_BroadcastString((UBYTE *)h->IBfull) ){/*Fail!*/ MesPrint("Fail broadcasting external channel results"); Terminate(-1); }/*if( PF_BroadcastString(h->IBfull) )*/ /*The string "\0!\0" is used as the image of NULL.*/ if( ( (h->IBfull)[0]=='\0' ) &&( (h->IBfull)[1]=='!' ) &&( (h->IBfull)[2]=='\0' ) )/*EOF! No trailing '\n'?*/ break; #else if( fgets(h->IBfull,h->IBstop - h->IBfull, h->frec) == 0 ) /*EOF! No trailing '\n'?*/ break; #endif while( *(h->IBfull)!='\0' )(h->IBfull)++; }/*while( *(h->IBfull - 1) != '\n' )*/ /*In h->INbuf we have a fresh string.*/ ret=*(h->IBfill=h->INbuf); h->IBfill++;/*Next time a new, isn't it?*/ getcFromExtChannelReady: #ifdef WITHMPI if ( PF.me == MASTER ){ #endif signal(SIGPIPE,oldPIPE); #ifdef WITHMPI }/*if ( PF.me == MASTER )*/ #endif return(ret); }/*getcFromExtChannelOk*/ /* #] getcFromExtChannelOk */ /*Writes exactly count bytes from the buffer buf to the external channel thehandler Returns 0 (on success) or -1: */ int writeBufToExtChannelOk(char *buf, size_t count) { int ret; mysighandler_t oldPIPE; #ifdef WITHMPI /*Only master communicates with the external program:*/ if ( PF.me == MASTER ){ #endif /* Temporary ignore this signal:*/ /* if compiler fails here, try to change the definition of mysighandler_t on the beginning of this file (just define INTSIGHANDLER)*/ oldPIPE=signal(SIGPIPE,SIG_IGN); ret=writexactly( externalChannelsListTop->fsend, buf, count); signal(SIGPIPE,oldPIPE); #ifdef WITHMPI }else{ /*Do not wait the master status: this would be too slow!*/ ret=0; } #endif return(ret); }/*writeBufToExtChannel*/ /* #] Ok functions: #[ do_run_cmd : */ /*The function returns PID of the started command*/ static FORM_INLINE pid_t do_run_cmd( int *fdsend, int *fdreceive, int *gpid, /*returns group process ID*/ int ttymode, /* &8 - daemonizeing &16 - setsid()*/ char *cmd, char *argv[], char *stderrname ) { int fdin[2]={-1,-1}, fdout[2]={-1,-1}, fdsig[2]={-1,-1}; /*initialised by -1 for possible rollback at failure, see closepipe() above*/ pid_t childpid,fatherchildpid = (pid_t)0; mysighandler_t oldPIPE=NULL; if( (pipe(fdsig)!=0)/*This pipe will be used by a child to tell the father if fail.*/ ||(pipe(fdin)!=0) ||(pipe(fdout)!=0) )goto fail_do_run_cmd; if((childpid = fork()) == -1){ perror("fork"); goto fail_do_run_cmd; }/*if((childpid = fork()) == -1)*/ if(childpid == 0){/*Child.*/ int fifo[3], top=0; /* To be thread safely we can't rely on ascendant order of opened file descriptors. So we put each of descriptor we have to preserve into the array fifo. Note, in _this_ process there are no any threads but descriptors were created in frame of the parent process which may have multiple threads. */ /*Mark descriptors which will NOT be closed:*/ pushDescriptor(fifo,top++,fdsig[1]); pushDescriptor(fifo,top++,fdin[0]); pushDescriptor(fifo,top++,fdout[1]); /*Close all except stdin, stdout, stderr and placed into fifo:*/ closeAllDescriptors(3,fifo, top); /*Now reopen stdin and stdout.*/ /*thread-safety is not a problem here since there are no any threads up to now:*/ if( (close(0) == -1 )||/* Use fdin as stdin :*/ (dup(fdin[0]) == -1 )|| (close(1)==-1)||/* Use fdout as stdout:*/ (dup(fdout[1]) == -1 ) ) {/*Fail!*/ /*Signal to parent:*/ writepid(fdsig[1],(pid_t)-2); _exit(1); } if(stderrname != NULL){ if( (close(2) != 0 )|| (open(stderrname,O_WRONLY)<0) ) {/*Fail!*/ writepid(fdsig[1],(pid_t)-2); _exit(1); } }/*if(stderrname != NULL)*/ if( ttymode & 16 )/* create a session and sets the process group ID */ setsid(); /* */ if(set_cloexec_flag (fdsig[1], 1)!=0){/*Error?*/ /*Signal to parent:*/ writepid(fdsig[1],(pid_t)-2); _exit(1); }/*if(set_cloexec_flag (fdsig[1], 1)!=0)*/ if( ttymode & 8 ){/*Daemonize*/ int fdsig2[2];/*To check exec() success*/ if( pipe(fdsig2)|| (set_cloexec_flag (fdsig2[1], 1)!=0) ) {/*Error?*/ /*Signal to parent:*/ writepid(fdsig[1],(pid_t)-2); _exit(1); } set_cloexec_flag (fdsig2[0], 1); switch(childpid=fork()){ case 0:/*grandchild*/ /*Execute external command:*/ execvp(cmd, argv); /* Control can reach this point only on error!*/ writepid(fdsig2[1],(pid_t)-2); break; case -1: /* Control can reach this point only on error!*/ /*Inform the father about the failure*/ writepid(fdsig[1],(pid_t)-2); _exit(1);/*The child, just exit, not return*/ default:/*Son of his father*/ close(fdsig2[1]); /*Ignore SIGPIPE (up to the end of the process):*/ signal(SIGPIPE,SIG_IGN); /*Wait on read() while the grandchild close the pipe (on success) or send -2 (if exec() fails).*/ /*There are two possibilities: -1 -- this is ok, the pipe was closed on exec, the program was successfully executed; -2 -- something is wrong, exec failed since the grandchild sends -2 after exec. */ if( readpid(fdsig2[0]) != (pid_t)-1 )/*something is wrong*/ writepid(fdsig[1],(pid_t)-1); else/*ok, send PID of the grandchild to the father:*/ writepid(fdsig[1],childpid); /*Die and free the life space for the grandchild:*/ _exit(0);/*The child, just exit, not return*/ }/*switch(childpid=fork())*/ }else{/*if( ttymode & 8 )*/ execvp(cmd, argv); /* Control can reach this point only on error!*/ writepid(fdsig[1],(pid_t)-2); _exit(2);/*The child, just exit, not return*/ }/*if( ttymode & 8 )...else*/ }else{/* The (grand)father*/ close(fdsig[1]); /*To prevent closing fdsig in rollback:*/ fdsig[1]=-1; close(fdin[0]); close(fdout[1]); *fdsend = fdin[1]; *fdreceive = fdout[0]; /*Get the process group ID.*/ /*Avoid to use getpgid() which is non-standard.*/ if( ttymode & 16)/*setsid() was invoked, the child is a group leader:*/ *gpid=childpid; else/*the child belongs to the same process group as the this process:*/ *gpid=getpgrp();/*if compiler fails here, try getpgrp(0) instead!*/ /* Rationale: getpgrp conform to POSIX.1 while 4.3BSD provides a getpgrp() function that returns the process group ID for a specified process. */ /* Temporary ignore this signal:*/ /* if compiler fails here, try to change the definition of mysighandler_t on the beginning of this file (just define INTSIGHANDLER)*/ oldPIPE=signal(SIGPIPE,SIG_IGN); if( ttymode & 8 ){/*Daemonize*/ /*Read the grandchild PID from the son.*/ fatherchildpid=childpid; if( (childpid=readpid(fdsig[0]))<0 ){ /*Daemonization process fails for some reasons!*/ childpid=fatherchildpid;/*for rollback*/ goto fail_do_run_cmd; } }else{ /*fdsig[1] should be closed on exec and this read operation must fail on success:*/ if( readpid(fdsig[0])!= (pid_t)-1 ) goto fail_do_run_cmd; }/*if( ttymode & 8 ) ... else*/ }/*if(childpid == 0)...else*/ /*Here can be ONLY the father*/ close(fdsig[0]); /*To prevent closing fdsig in rollback after goto fail_flnk_do_runcmd:*/ fdsig[0]=-1; if( ttymode & 8 ){/*Daemonize*/ int i; /*Wait while the father of a grandchild dies:*/ waitpid(fatherchildpid,&i,0); } /*Restore the signal:*/ signal(SIGPIPE,oldPIPE); return(childpid); fail_do_run_cmd: closepipe(&fdout); closepipe(&fdin); closepipe(&fdsig); return((pid_t)-1); }/*do_run_cmd*/ /* #] do_run_cmd : #[ run_cmd : */ /*Starts the command cmd (directly, if shellpath is NULL, or in a subshell), swallowing its stdin and stdout; stderr will be re-directed to stderrname (if !=NULL). Returns PID of the started process. Stdin will be available as fdsend, and stdout will be available as fdreceive:*/ static FORM_INLINE pid_t run_cmd(char *cmd, int *fdsend, int *fdreceive, int *gpid, int daemonize, char *shellpath, char *stderrname ) { char **argv; pid_t thepid; cmd=(char*)strDup1((UBYTE*)cmd, "run_cmd: cmd");/*detouch cmd*/ /* Prepare arguments for execvp:*/ if(shellpath != NULL){/*Run in a subshell.*/ int nopt; /*Allocate space which is definitely enough:*/ argv=Malloc1(StrLen((UBYTE*)shellpath)*sizeof(char*)+2,"run_cmd:argv"); shellpath=(char*)strDup1((UBYTE*)shellpath, "run_cmd: shellpath");/*detouch shellpath*/ /*Parse a shell (e.g., "/bin/sh -c"):*/ nopt=parseline(argv, shellpath); /* and add the command as a shell argument:*/ argv[nopt]=cmd; argv[nopt+1]=NULL; }else{/*Run the command directly:*/ /*Allocate space which is definitely enough:*/ argv=Malloc1(StrLen((UBYTE*)cmd)*sizeof(char*)+1,"run_cmd:argv"); parseline(argv, cmd); } thepid=do_run_cmd( fdsend, fdreceive, gpid, (daemonize)?(8|16):0, argv[0], argv, stderrname ); M_free(argv,"run_cmd:argv"); if(shellpath) M_free(shellpath,"run_cmd:argv"); M_free(cmd, "run_cmd: cmd"); return(thepid); }/*run_cmd*/ /* #] run_cmd : #[ createExternalChannel : */ /*The structure to pass parameters to createExternalChannel and openExternalChannel in case of preset channel (instead of shellname):*/ typedef struct{ int fdin; int fdout; pid_t theppid; }ECINFOSTRUCT; /* Creates a new external channel starting the command cmd (if cmd !=NULL) or using information from (ECINFOSTRUCT *)shellname, if cmd ==NULL:*/ static FORM_INLINE void *createExternalChannel( EXTHANDLE *h, char *cmd, /*Command to run or NULL*/ /*0 --neither setsid nor daemonize, !=0 -- full daemonization:*/ int daemonize, char *shellname,/* The shell (like "/bin/sh -c") or NULL*/ char *stderrname/*filename to redirect stderr or NULL*/ ) { int fdreceive=0; int gpid = 0; ECINFOSTRUCT *psetInfo; #ifdef WITHMPI char statusbuf[2]={'\0','\0'};/*'\0' if run_cmd retuns ok, '!' otherwise.*/ #endif extHandlerInit(h); h->pid=0; if( cmd==NULL ){/*Instead of starting a new command, use preset channel:*/ psetInfo=(ECINFOSTRUCT *)shellname; shellname=NULL; h->killSignal=0; h->daemonize=0; } /*Create a channel:*/ #ifdef WITHMPI if ( PF.me == MASTER ){ #endif if(cmd!=NULL) h->pid=run_cmd (cmd, &(h->fsend), &fdreceive,&gpid,daemonize,shellname,stderrname); else{ gpid=-psetInfo->theppid; h->pid=psetInfo->theppid; h->fsend=psetInfo->fdout; fdreceive=psetInfo->fdin; } #ifdef WITHMPI if(h->pid<0) statusbuf[0]='!';/*Broadcast fail to slaves*/ } /*else: Keep h->pid = 0 and h->fsend = 0 for slaves in parallel mode!*/ /*Master broadcasts status to slaves, slaves read it from the master:*/ if( PF_BroadcastString((UBYTE *)statusbuf) ){/*Fail!*/ h->pid=-1; }else if( statusbuf[0]=='!')/*Master fails*/ h->pid=-1; #endif if(h->pid<0)goto createExternalChannelFails; #ifdef WITHMPI if ( PF.me == MASTER ){ #endif h->gpid=gpid; /*Open stdout of a newly created program as FILE* :*/ if( (h->frec=fdopen(fdreceive,"r")) == 0 )goto createExternalChannelFails; #ifdef WITHMPI } #endif /*Initialize buffers:*/ extHandlerAlloc(h,cmd,shellname,stderrname); return(h); /*Something is wrong?*/ createExternalChannelFails: destroyExternalChannel(h); return(NULL); }/*createExternalChannel*/ /* #] createExternalChannel : #[ openExternalChannel : */ int openExternalChannel(UBYTE *cmd, int daemonize, UBYTE *shellname, UBYTE *stderrname) { EXTHANDLE *h=externalChannelsListTop; int i=0; for(externalChannelsListTop=0;i=externalChannelsListFill)|| (externalChannelsList[n].cmd==0) ) return(-1); externalChannelsListTop=externalChannelsList+n; writeBufToExtChannel=&writeBufToExtChannelOk; getcFromExtChannel=&getcFromExtChannelOk; setTerminatorForExternalChannel=&setTerminatorForExternalChannelOk; setKillModeForExternalChannel=&setKillModeForExternalChannelOk; return(ret); }/*selectExternalChannel*/ /* #] selectExternalChannel : #[ closeExternalChannel : */ /* Destroys the opened external channel with the descriptor n. It returns 0 in success, or -1 on failure. If the corresponding external channel was the current one, the current channel becomes undefined. If n==0, the function closes the current external channel. */ int closeExternalChannel(int n) { if(n==0) n=externalChannelsListTop-externalChannelsList; else n--;/*Count from 0*/ if( (n<0)|| (n>=externalChannelsListFill)|| (externalChannelsList[n].cmd==0) )/*No shuch a channel*/ return(-1); destroyExternalChannel(externalChannelsList+n); /*If the current external channel was destroyed, undefine current channel:*/ if(externalChannelsListTop==externalChannelsList+n){ externalChannelsListTop=NULL; writeBufToExtChannel=&writeBufToExtChannelFailure; getcFromExtChannel=&getcFromExtChannelFailure; setTerminatorForExternalChannel=&setTerminatorForExternalChannelFailure; setKillModeForExternalChannel=&setKillModeForExternalChannelFailure; }/*if(externalChannelsListTop==externalChannelsList+n)*/ return(0); }/*closeExternalChannel*/ /* #] closeExternalChannel : #[ closeAllExternalChannels : */ void closeAllExternalChannels(void) { int i; for(i=0; ipid); return(-1); }/*getExternalChannelPid*/ #endif /* #] getExternalChannelPid : #[ getCurrentExternalChannel : */ int getCurrentExternalChannel(void) { if ( externalChannelsListTop != 0 ) return(externalChannelsListTop-externalChannelsList+1); return(0); }/*getCurrentExternalChannel*/ /* #] getCurrentExternalChannel : #[ Selftest main : */ #ifdef SELFTEST /* This is the example of how all these public functions may be used: */ char buf[1024]; char buf2[1024]; void help(void) { printf("String started with a special letter is a command\n"); printf("Known commands are:\n"); printf("H or ? -- this help\n"); printf("Nn -- start a new command\n"); printf("S -- start a new command in a subshell,daemon,stderr>/dev/null\n"); printf("C# -- destroy channel #\n"); printf("R# -- set a new cahhel(number#) as a current one\n"); printf("K#1 #2 -- set signal for kill and kill mode (0 or !=0)\n"); printf(" ^d to quit\n"); }/*help*/ int main (void) { int i, j, k,last; long long sum = 0; /*openExternalChannel(UBYTE *cmd, int daemonize, UBYTE *shellname, UBYTE *stderrname)*/ help(); printf("Initial channel:%d\n",last=openExternalChannel((UBYTE*)"cat",0,NULL,NULL)); if( ( i = setTerminatorForExternalChannel("qu") ) != 0 ) return 1; printf("Terminator is 'qu'\n"); while ( fgets(buf, 1024, stdin) != NULL ) { if ( *buf == 'N' ) { printf("New channel:%d\n",j=openExternalChannel((UBYTE*)buf+1,0,NULL,NULL)); continue; } else if ( *buf == 'C' ) { int n; sscanf(buf+1,"%d",&n); printf("Destroy last channel:%d\n",closeExternalChannel(n)); continue; } else if ( *buf == 'R' ) { int n = 0; sscanf(buf+1,"%d",&n); printf("Reopen channel %d:%d\n",n,selectExternalChannel(n)); continue; }else if( *buf == 'K' ) { int n=0,g = 0; sscanf(buf+1,"%d %d",&n,&g); printf("setKillMode %d\n",setKillModeForExternalChannel(n,g)); continue; }else if( *buf == 'S' ) { printf("New channel with sh&d&stderr:%d\n", j=openExternalChannel((UBYTE*)buf+1,1,(UBYTE*)"/bin/sh -c",(UBYTE*)"/dev/null")); continue; } else if( ( *buf == 'H' )|| ( *buf == '?' ) ){ help(); continue; } writeBufToExtChannel(buf,k=StrLen(buf)); sum += k; for ( j = 0; ( i = getcFromExtChannel() ) != '\n'; j++) { if ( i == EOF ) { printf("EOF!\n"); break; } buf2[j] = i; } buf2[j] = '\0'; printf("I got:'%s'; pid=%d\n",buf2,getExternalChannelPid()); } printf("Total:%lld bytes\n",sum); closeAllExternalChannels(); return 0; } #endif /*ifdef SELFTEST*/ /* #] Selftest main : */ #endif /*ifndef WITHEXTERNALCHANNEL ... else*/ form-5.0.1/sources/polygcd.cc0000644000175100017510000013236315217035721011611 /** @file polygcd.cc * * Contains the routines for calculating greatest commons divisors of * multivariate polynomials */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ include : */ #include "poly.h" #include "polygcd.h" #include #include #include #include #include //#define DEBUG //#define DEBUGALL #ifdef DEBUG #include "mytime.h" #endif using namespace std; /* #] include : #[ ostream operator : */ #ifdef DEBUG // ostream operator for outputting vectors for debugging purposes template ostream& operator<< (ostream &out, const vector &x) { out<<"{"; for (int i=0; i<(int)x.size(); i++) { if (i>0) out<<","; out<0) return a.integer_lcoeff(); poly c(BHEAD 0, 0, 1); WORD *d = (WORD *)NumberMalloc("polygcd::integer_content"); WORD nc=0; for (int i=0; i a(_a), b(_b); while (b.size() != 0) { a = poly::coefficient_list_divmod(a,b,p,1); swap(a,b); } while (a.back()==0) a.pop_back(); WORD inv; GetModInverses(a.back() + (a.back()<0?p:0), p, &inv, NULL); for (int i=0; i<(int)a.size(); i++) a[i] = (LONG)inv*a[i] % p; #ifdef DEBUGALL cout << "*** [" << thetime() << "] RES : coefficient_list_gcd("<<_a<<","<<_b<<","<=-1 && b.is_dense_univariate()>=-1) { vector coeff = coefficient_list_gcd(poly::to_coefficient_list(a), poly::to_coefficient_list(b), a.modp); res = poly::from_coefficient_list(BHEAD coeff, a.first_variable(), a.modp); } else { res = a; poly rem(b); while (!rem.is_zero()) swap(res%=rem, rem); res /= res.integer_lcoeff(); } #ifdef DEBUG cout << "*** [" << thetime() << "] RES : gcd_Euclidean("< &x, const poly &s) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: gcd_modular_sparse_interpolation(" << origa << "," << origb << "," << x << "," << "," << s <<")" << endl; #endif POLY_GETIDENTITY(origa); // strip multivariate content poly conta(content_multivar(origa,x.back())); poly contb(content_multivar(origb,x.back())); poly gcdconts(gcd_Euclidean(conta,contb)); const poly& a = conta.is_one() ? origa : origa/conta; const poly& b = contb.is_one() ? origb : origb/contb; // for non-monic cases, we need to normalize with the gcd of the lcoeffs of a poly in x[0] // or else the shape fitting does not work. // FIXME: the current implementation still rejects some valid shapes. poly lcgcd(BHEAD 1, a.modp); if (!s.lcoeff_univar(x[0]).is_integer()) { lcgcd = gcd_modular_dense_interpolation(a.lcoeff_univar(x[0]), b.lcoeff_univar(x[0]), x, poly(BHEAD 0)); } // reduce polynomials poly ared(sparse_interpolation_reduce_poly(a,x)); poly bred(sparse_interpolation_reduce_poly(b,x)); poly sred(sparse_interpolation_reduce_poly(s,x)); poly lred(sparse_interpolation_reduce_poly(lcgcd,x)); // set all coefficients to 1 for (int i=1; i c(x.size()-1); vector smul; bool duplicates; do { for (int i=0; i<(int)c.size(); i++) c[i] = 1 + wranf(BHEAD0) % (a.modp-1); smul = sparse_interpolation_get_mul_list(s,x,c); duplicates = false; int fr=0,to=0; for (int i=1; i amul(sparse_interpolation_get_mul_list(a,x,c)); vector bmul(sparse_interpolation_get_mul_list(b,x,c)); vector lmul(sparse_interpolation_get_mul_list(lcgcd,x,c)); vector > > M; vector > V; int maxMsize=0; // create (empty) matrices for (int i=1; i >()); V.push_back(vector()); } M.back().push_back(vector()); V.back().push_back(0); maxMsize = max(maxMsize, (int)M.back().size()); } // generate linear equations for (int numg=0; numg=0; j--) for (int k=j+1; k coeff; for (int i=0; i<(int)V.size(); i++) for (int j=0; j<(int)V[i].size(); j++) coeff.push_back(V[i][j]); // create resulting polynomial poly res(BHEAD 0); int ri=1, i=0; for (int si=1; si &x, const poly &s) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: gcd_modular_dense_interpolation(" << a << "," << b << "," << x << "," << s <<")" << endl; #endif POLY_GETIDENTITY(a); // if univariate, then use Euclidean algorithm if (x.size() == 1) { return gcd_Euclidean(a,b); } // if shape is known, use sparse interpolation if (!s.is_zero()) { poly res = gcd_modular_sparse_interpolation (a,b,x,s); if (!res.is_zero()) return res; // apparently the shape was not correct. continue. } // divide out multivariate content in last variable int X = x.back(); poly conta(content_multivar(a,X)); poly contb(content_multivar(b,X)); poly gcdconts(gcd_Euclidean(conta,contb)); const poly& ppa = conta.is_one() ? a : poly(a/conta); const poly& ppb = contb.is_one() ? b : poly(b/contb); // gcd of leading coefficients poly lcoeffa(ppa.lcoeff_multivar(X)); poly lcoeffb(ppb.lcoeff_multivar(X)); poly gcdlcoeffs(gcd_Euclidean(lcoeffa,lcoeffb)); // calculate the degree bound for each variable int m = MiN(ppa.degree(x[x.size() - 2]),ppb.degree(x[x.size() - 2])); poly res(BHEAD 0); poly oldres(BHEAD 0); poly newshape(BHEAD 0); poly modpoly(BHEAD 1,a.modp); while (true) { // generate random constants and substitute it int c = 1 + wranf(BHEAD0) % (a.modp-1); if (substitute(gcdlcoeffs,X,c).is_zero()) continue; if (substitute(modpoly,X,c).is_zero()) continue; poly amodc(substitute(ppa,X,c)); poly bmodc(substitute(ppb,X,c)); // calculate gcd recursively poly gcdmodc(gcd_modular_dense_interpolation(amodc,bmodc,vector(x.begin(),x.end()-1), newshape)); int n = gcdmodc.degree(x[x.size() - 2]); // normalize gcdmodc = (gcdmodc * substitute(gcdlcoeffs,X,c)) / gcdmodc.integer_lcoeff(); poly simple(poly::simple_poly(BHEAD X,c,1,a.modp)); // (X-c) mod p // if power is smaller, the old one was wrong if ((res.is_zero() && n == m) || n < m) { m = n; res = gcdmodc; newshape = gcdmodc; // set a new shape (interpolation does not change it) modpoly = simple; } else if (n == m) { oldres = res; // equal powers, so interpolate results poly coeff_poly(substitute(modpoly,X,c)); WORD coeff_word = coeff_poly[2+AN.poly_num_vars] * coeff_poly[3+AN.poly_num_vars]; if (coeff_word < 0) coeff_word += a.modp; GetModInverses(coeff_word, a.modp, &coeff_word, NULL); res.setmod(a.modp); // make sure the mod is set before substituting res += poly(BHEAD coeff_word, a.modp, 1) * modpoly * (gcdmodc - substitute(res,X,c)); modpoly *= simple; } // check whether this is the complete gcd if (!res.is_zero() && res == oldres) { poly nres = res / content_multivar(res, X); if (poly::divides(nres,ppa) && poly::divides(nres,ppb)) { #ifdef DEBUG cout << "*** [" << thetime() << "] RES : gcd_modular_dense_interpolation(" << a << "," << b << "," << x << "," << "," << s <<") = " << gcdconts * nres << endl; #endif return gcdconts * nres; } // At this point, the gcd may be too large due to bad luck // TODO: create an efficient fail state that tries to find a smaller // polynomial without interpolating bad ones? newshape = poly(BHEAD 0); // reset the shape, important! } } } /* #] gcd_modular_dense_interpolation : : #[ gcd_modular : */ /** Zippel's Modular GCD Algorithm * * Description * =========== * This method choose a prime number and calls the method * "gcd_modular_dense_interpolation" to calculate the gcd modulo * this prime. It continues choosing more primes and constructs a * final result with the Chinese Remainder Algorithm. * * Notes * ===== * - Necessary condition: icont(a) = icont(b) = 0 * - More efficient methods for the leading coefficient problem * exist, such as Linzip (see: "Algorithms for the Non-monic case * of the Sparse Modular GCD Algorithm" by De Kleine et al) [TODO] */ const poly polygcd::gcd_modular (const poly &origa, const poly &origb, const vector &x) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: gcd_modular(" << origa << "," << origb << "," << x << ")" << endl; #endif POLY_GETIDENTITY(origa); if (origa.is_zero()) return origa.modp==0 ? origb : origb / origb.integer_lcoeff(); if (origb.is_zero()) return origa.modp==0 ? origa : origa / origa.integer_lcoeff(); if (origa==origb) return origa.modp==0 ? origa : origa / origa.integer_lcoeff(); poly ac = integer_content(origa); poly bc = integer_content(origb); const poly& a = ac.is_one() ? origa : poly(origa/ac); const poly& b = bc.is_one() ? origb : poly(origb/bc); poly ic = integer_gcd(ac, bc); poly g = integer_gcd(a.integer_lcoeff(), b.integer_lcoeff()); int pnum=0; poly d(BHEAD 0); poly m1(BHEAD 1); int mindeg=MAXPOSITIVE; while (true) { // choose a prime and solve modulo the prime WORD p = NextPrime(BHEAD pnum++); if (poly(a.integer_lcoeff(),p).is_zero()) continue; if (poly(b.integer_lcoeff(),p).is_zero()) continue; poly c(gcd_modular_dense_interpolation(poly(a,p),poly(b,p),x,poly(d,p))); c = (c * poly(g,p)) / c.integer_lcoeff(); // normalize so that lcoeff(c) = g mod p if (c.is_zero()) { // unlucky choices somewhere, so start all over again d = poly(BHEAD 0); m1 = poly(BHEAD 1); mindeg = MAXPOSITIVE; continue; } if (!(poly(a,p)%c).is_zero()) continue; if (!(poly(b,p)%c).is_zero()) continue; int deg = c.degree(x[0]); if (deg < mindeg) { // small degree, so the old one is wrong d=c; d.modp=a.modp; d.modn=a.modn; m1 = poly(BHEAD p); mindeg=deg; } else if (deg == mindeg) { // same degree, so use Chinese Remainder Algorithm poly newd(BHEAD 0); for (int ci=1,di=1; ci= 0) { newd.termscopy(&c[ci],newd[0],1+AN.poly_num_vars); a2 = poly(BHEAD (UWORD *)&c[ci+1+AN.poly_num_vars],c[ci+c[ci]-1]); ci+=c[ci]; } poly e(chinese_remainder(a1,m1,a2,poly(BHEAD p))); newd.termscopy(&e[2+AN.poly_num_vars], newd[0]+1+AN.poly_num_vars, ABS(e[e[1]])+1); newd[newd[0]] = 2 + AN.poly_num_vars + ABS(e[e[1]]); newd[0] += newd[newd[0]]; } m1 *= poly(BHEAD p); d=newd; } // divide out spurious integer content poly ppd(d / integer_content(d)); // check whether this is the complete gcd if (poly::divides(ppd,a) && poly::divides(ppd,b)) { #ifdef DEBUG cout << "*** [" << thetime() << "] RES : gcd_modular(" << origa << "," << origb << "," << x << ") = " << ic * ppd << endl; #endif return ic * ppd; } #ifdef DEBUG cout << "*** [" << thetime() << "] Retrying modular_gcd with new prime" << endl; #endif } } /* #] gcd_modular : #[ gcd_heuristic_possible : */ /** Heuristic greatest common divisor of multivariate polynomials * * Description * =========== * Checks whether the heuristic seems possible by estimating * * MAX_{terms} (coeff ^ PROD_{i=1..#vars} (pow_i+1)) * * and comparing this with GCD_HEURISTIC_MAX_DIGITS. * * Notes * ===== * - For small polynomials, this consumes time and never triggers. */ bool gcd_heuristic_possible (const poly &a) { POLY_GETIDENTITY(a); double prod_deg = 1; for (int j=0; j &x, int max_tries) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: gcd_heuristic("< 0) { pxi = (UWORD *)&a[i+a[i]-1-na]; nxi = na; } } for (int i=1; i 0) { pxi = (UWORD *)&b[i+b[i]-1-nb]; nxi = nb; } } poly xi(BHEAD pxi,nxi); // Addition of another random factor gives better performance xi = xi*poly(BHEAD 2) + poly(BHEAD 2 + wranf(BHEAD0)%POLYGCD_HEURISTIC_MAX_ADD_RANDOM); // If degree*digits(xi) is too large, throw exception if (max(a.degree(x[0]),b.degree(x[0])) * xi[xi[1]] >= MiN(AM.MaxTal, POLYGCD_HEURISTIC_MAX_DIGITS)) { #ifdef DEBUG cout << "*** [" << thetime() << "] RES : gcd_heuristic("<(x.begin()+1,x.end()),1)); // If a gcd is found, reconstruct the powers of x if (!gamma.is_zero()) { // res is construct is reverse order. idx/len are for reversing // it in the correct order poly res(BHEAD 0), c(BHEAD 0); vector idx, len; for (int power=0; !gamma.is_zero(); power++) { // calculate c = gamma % xi (c and gamma are polynomials, xi is integer) c = gamma; c.coefficients_modulo((UWORD *)&xi[2+AN.poly_num_vars], xi[xi[0]-1], false); // Add the terms c * x^power to res res.check_memory(res[0]+c[0]); res.termscopy(&c[1],res[0],c[0]-1); for (int i=1; i=0; i--) { rev.termscopy(&res[idx[i]], rev[0], len[i]); rev[0] += len[i]; } res = rev; poly ppres = res / integer_content(res); if ((a%ppres).is_zero() && (b%ppres).is_zero()) { #ifdef DEBUG cout << "*** [" << thetime() << "] RES : gcd_heuristic("<,poly> polygcd::full_bracket(const poly &a, const vector& filter) { POLY_GETIDENTITY(a); map,poly> bracket; for (int ai=1; ai varpattern(AN.poly_num_vars); for (int i=0; i 0) varpattern[i] = a[ai + i + 1]; // create monomial poly mon(BHEAD 1); mon.setmod(a.modp); mon[0] = a[ai] + 1; for (int i=0; i 0 && i <= AN.poly_num_vars && varpattern[i - 1]) mon[1+i] = 0; else mon[1+i] = a[ai+i]; map,poly>::iterator i = bracket.find(varpattern); if (i == bracket.end()) { bracket.insert(std::make_pair(varpattern, mon)); } else { i->second += mon; } } return bracket; } const poly polygcd::bracket(const poly &a, const vector& pattern, const vector& filter) { POLY_GETIDENTITY(a); poly bracket(BHEAD 0); for (int ai=1; ai 0 && i <= AN.poly_num_vars && pattern[i - 1]) mon[1+i] = 0; else mon[1+i] = a[ai+i]; bracket += mon; } } return bracket; } const map,int> polygcd::bracket_count(const poly &a, const vector& filter) { POLY_GETIDENTITY(a); map,int> bracket; for (int ai=1; ai varpattern(AN.poly_num_vars); for (int i=0; i 0) varpattern[i] = a[ai + i + 1]; map,int>::iterator i = bracket.find(varpattern); if (i == bracket.end()) { bracket.insert(std::make_pair(varpattern, 0)); } else { i->second++; } } return bracket; } struct BracketInfo { std::vector pattern; int num_terms, dummy = 0; const poly* p; BracketInfo(const std::vector& pattern, int num_terms, const poly* p) : pattern(pattern), num_terms(num_terms), p(p) {} bool operator<(const BracketInfo& rhs) const { return num_terms > rhs.num_terms; } // biggest should be first! }; /* #] bracket : #[ gcd_linear: */ const poly gcd_linear_helper (const poly &a, const poly &b) { POLY_GETIDENTITY(a); for (int i = 0; i < AN.poly_num_vars; i++) if (a.degree(i) == 1) { vector filter(AN.poly_num_vars); filter[i] = 1; // bracket the linear variable map,poly> ba = polygcd::full_bracket(a, filter); poly subgcd(BHEAD 1); if (ba.size() == 2) subgcd = polygcd::gcd_linear(ba.begin()->second, (++ba.begin())->second); else subgcd = ba.begin()->second; poly linfac = a / subgcd; if (poly::divides(linfac,b)) return linfac * polygcd::gcd_linear(subgcd, b / linfac); return polygcd::gcd_linear(subgcd, b); } return poly(BHEAD 0); } /** Performs a faster, recursive gcd algorithm if one of the variables in one of the polynomials is linear. If no terms are linear, fall back to Zippel's method. */ const poly polygcd::gcd_linear (const poly &a, const poly &b) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: gcd_linear("< 0) return poly(BHEAD 1,a.modp,a.modn); return poly(integer_gcd(integer_content(a),integer_content(b)),0,1); } poly h = gcd_linear_helper(a, b); if (!h.is_zero()) return h; h = gcd_linear_helper(b, a); if (!h.is_zero()) return h; vector xa = a.all_variables(); vector xb = b.all_variables(); vector used(AN.poly_num_vars,0); for (int i=0; i<(int)xa.size(); i++) used[xa[i]]++; for (int i=0; i<(int)xb.size(); i++) used[xb[i]]++; vector x; for (int i=0; i 0) return poly(BHEAD 1,a.modp,a.modn); return poly(integer_gcd(integer_content(a),integer_content(b)),0,1); } // Generate a list of variables of a and b vector xa = a.all_variables(); vector xb = b.all_variables(); vector used(AN.poly_num_vars,0); for (int i=0; i<(int)xa.size(); i++) used[xa[i]]++; for (int i=0; i<(int)xb.size(); i++) used[xb[i]]++; vector x; for (int i=0; i bracketinfo; if (!diva) { map,int> ba = bracket_count(ppa, used); for(map,int>::iterator it = ba.begin(); it != ba.end(); it++) bracketinfo.push_back(BracketInfo(it->first, it->second, &ppa)); } if (!divb) { map,int> bb = bracket_count(ppb, used); for(map,int>::iterator it = bb.begin(); it != bb.end(); it++) bracketinfo.push_back(BracketInfo(it->first, it->second, &ppb)); } // sort so that the smallest bracket will be last sort(bracketinfo.begin(), bracketinfo.end()); if (res.is_zero()) { res = bracket(*bracketinfo.back().p, bracketinfo.back().pattern, used); bracketinfo.pop_back(); } while (bracketinfo.size() > 0) { poly subpoly(bracket(*bracketinfo.back().p, bracketinfo.back().pattern, used)); if (!poly::divides(res,subpoly)) { // if we can filter out more variables, call gcd again if (res.all_variables() != subpoly.all_variables()) res = gcd(subpoly,res); else res = gcd_linear(subpoly,res); } bracketinfo.pop_back(); } } if (res.is_zero() || !poly::divides(res,ppa) || !poly::divides(res,ppb)) { MesPrint("Bad gcd found."); std::cout << "Bad gcd:" << res << " for " << ppa << " " << ppb << std::endl; Terminate(1); } } res *= gcdconts * poly(BHEAD res.sign()); #ifdef DEBUG cout << "*** [" << thetime() << "] RES : gcd("<. */ /* #] License : */ #define LINEFEED '\n' #define CARRIAGERETURN 0x0D #define WITHPIPE #define WITHSYSTEM /*[13jul2005 mt]:*/ /*With SAFESIGNAL defined, write() and read() syscalls are wrapped by the errno checkup*/ /*#define SAFESIGNAL*/ /*:[13jul2005 mt]*/ /*[29apr2004 mt]:*/ #define WITHEXTERNALCHANNEL /* */ #define TRAPSIGNALS /*:[29apr2004 mt]*/ #define P_term(code) exit((int)(code<0?-code:code)) #define SEPARATOR '/' #define ALTSEPARATOR '/' #define PATHSEPARATOR ':' #define WITH_ENV #define WITH_ALARM form-5.0.1/sources/dict.c0000644000175100017510000007372715217035721010740 /** @file dict.c * * Contains the code pertaining to dictionaries * Commands are: * #opendictionary name * #closedictionary * #selectdictionary name * There can be several dictionaries, but only one can be active. * Defining elements is done with * #add object: "replacement" * Replacements are strings when a dictionary is for output translation. * Objects can be * 1: a number (rational) * 2: a variable * 3: * ^ * 4: a function with arguments */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : ratio.c Data setup: AO.Dictionaries Array of pointers to DICTIONARY AO.NumDictionaries AO.SizeDictionaries AO.CurrentDictionary AO.CurDictNumbers AO.CurDictVariables AO.CurDictSpecials AP.OpenDictionary */ #include "form3.h" /* #] Includes : #[ TransformRational: Tries to transform the rational number a according to the rules of the current dictionary. Whatever cannot be translated goes to the regular output. Options for AO.CurDictNumbers are: DICT_ALLNUMBERS, DICT_RATIONALONLY, DICT_INTEGERONLY, DICT_NONUMBERS */ void TransformRational(UWORD *a, WORD na) { DICTIONARY *dict; WORD i, j, nb, i1, i2; UWORD *b; if ( AO.CurrentDictionary <= 0 ) goto NoAction; dict = AO.Dictionaries[AO.CurrentDictionary-1]; if ( na < 0 ) na = -na; switch ( AO.CurDictNumbers ) { case DICT_NONUMBERS: goto NoAction; case DICT_INTEGERONLY: if ( a[na] != 1 ) goto NoAction; if ( na > 1 ) { for ( i = 1; i < na; i++ ) { if ( a[na+i] != 0 ) goto NoAction; } } Numeratoronly:; for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_INTEGERNUMBER ) { if ( dict->elements[i]->size == na ) { for ( j = 0; j < na; j++ ) { if ( (UWORD)(dict->elements[i]->lhs[j]) != a[j] ) break; } if ( j == na ) { /* Got it */ TokenToLine((UBYTE *)(dict->elements[i]->rhs)); return; } } } } goto NotFound; case DICT_RATIONALONLY: nb = 2*na; for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_RATIONALNUMBER ) { if ( dict->elements[i]->size == nb+2 ) { for ( j = 0; j < nb; j++ ) { if ( (UWORD)(dict->elements[i]->lhs[j+1]) != a[j] ) break; } if ( j == nb ) { /* Got it */ TokenToLine((UBYTE *)(dict->elements[i]->rhs)); return; } } } } goto NotFound; case DICT_ALLNUMBERS: /* First fish for rationals */ nb = 2*na; for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_RATIONALNUMBER ) { if ( dict->elements[i]->size == nb+2 ) { for ( j = 0; j < nb; j++ ) { if ( (UWORD)(dict->elements[i]->lhs[j+1]) != a[j] ) break; } if ( j == nb ) { /* Got it */ TokenToLine((UBYTE *)(dict->elements[i]->rhs)); return; } } } } /* Now look for element[j1]/element[j2] */ nb = na; b = a+na; while ( b[nb-1] == 0 ) nb--; if ( nb == 1 && b[0] == 1 ) goto Numeratoronly; while ( a[na-1] == 0 ) na--; for ( i1 = dict->numelements-1; i1 >= 0; i1-- ) { if ( dict->elements[i1]->type == DICT_INTEGERNUMBER ) { if ( dict->elements[i1]->size == na ) { for ( j = 0; j < na; j++ ) { if ( (UWORD)(dict->elements[i1]->lhs[j]) != a[j] ) break; } if ( j == na ) break; } } } for ( i2 = dict->numelements-1; i2 >= 0; i2-- ) { if ( dict->elements[i2]->type == DICT_INTEGERNUMBER ) { if ( dict->elements[i2]->size == nb ) { for ( j = 0; j < nb; j++ ) { if ( (UWORD)(dict->elements[i2]->lhs[j]) != b[j] ) break; } if ( j == nb ) break; } } } if ( i1 < 0 ) { if ( i2 < 0 ) goto NotFound; else { /* number/replacement[i2] */ LongToLine(a,na); if ( na > 1 || ( AO.DoubleFlag & 4 ) == 4 ) { if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || AC.OutputMode == CMODE ) { if ( ( AO.DoubleFlag & 2 ) == 2 ) { AddToLine((UBYTE *)".Q0/"); } else if ( ( AO.DoubleFlag & 1 ) == 1 ) { AddToLine((UBYTE *)".D0/"); } else { AddToLine((UBYTE *)"/"); } } } else AddToLine((UBYTE *)("/")); TokenToLine((UBYTE *)(dict->elements[i2]->rhs)); } } else if ( i2 < 0 ) { /* replacement[i1]/number */ TokenToLine((UBYTE *)(dict->elements[i1]->rhs)); AddToLine((UBYTE *)("/")); LongToLine((UWORD *)(b),nb); if ( nb > 1 || ( AO.DoubleFlag & 4 ) == 4 ) { if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || AC.OutputMode == CMODE ) { if ( ( AO.DoubleFlag & 2 ) == 2 ) { AddToLine((UBYTE *)".Q0"); } else if ( ( AO.DoubleFlag & 1 ) == 1 ) { AddToLine((UBYTE *)".D0"); } } } } else { /* replacement[i1]/replacement[i2] */ TokenToLine((UBYTE *)(dict->elements[i1]->rhs)); AddToLine((UBYTE *)("/")); TokenToLine((UBYTE *)(dict->elements[i2]->rhs)); } break; default: MesPrint("Illegal code in TransformRational: %d",AO.CurDictNumbers); Terminate(-1); } return; NotFound: if ( na != 1 || a[1] != 1 ) { if ( AO.CurDictNumberWarning ) { MesPrint(">>>>>>>>Could not translate coefficient with dictionary %s<<<<<<<<<<<<",dict->name); } } NoAction: RatToLine(a,na); return; } /* #] TransformRational: #[ IsMultiplySign: */ UBYTE *IsMultiplySign(void) { DICTIONARY *dict; int i; if ( AO.CurrentDictionary <= 0 ) return(0); dict = AO.Dictionaries[AO.CurrentDictionary-1]; if ( dict->characters == 0 ) return(0); for ( i = dict->numelements-1; i >= 0; i-- ) { if ( ( dict->elements[i]->type == DICT_SPECIALCHARACTER ) && ( dict->elements[i]->lhs[0] == (WORD)('*') ) ) return((UBYTE *)(dict->elements[i]->rhs)); } return(0); } /* #] IsMultiplySign: #[ IsExponentSign: */ UBYTE *IsExponentSign(void) { DICTIONARY *dict; int i; if ( AO.CurrentDictionary <= 0 ) return(0); dict = AO.Dictionaries[AO.CurrentDictionary-1]; if ( dict->characters == 0 ) return(0); for ( i = dict->numelements-1; i >= 0; i-- ) { if ( ( dict->elements[i]->type == DICT_SPECIALCHARACTER ) && ( dict->elements[i]->lhs[0] == (WORD)('^') ) ) return((UBYTE *)(dict->elements[i]->rhs)); } return(0); } /* #] IsExponentSign: #[ FindSymbol : */ UBYTE *FindSymbol(WORD num) { if ( AO.CurrentDictionary > 0 ) { DICTIONARY *dict = AO.Dictionaries[AO.CurrentDictionary-1]; int i; if ( dict->variables > 0 && AO.CurDictVariables == DICT_DOVARIABLES ) { for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_SYMBOL && dict->elements[i]->lhs[0] == num ) return((UBYTE *)(dict->elements[i]->rhs)); } } } return(VARNAME(symbols,num)); } /* #] FindSymbol : #[ FindVector : */ UBYTE *FindVector(WORD num) { if ( AO.CurrentDictionary > 0 ) { DICTIONARY *dict = AO.Dictionaries[AO.CurrentDictionary-1]; int i; if ( dict->variables > 0 && AO.CurDictVariables == DICT_DOVARIABLES ) { for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_VECTOR && dict->elements[i]->lhs[0] == num ) return((UBYTE *)(dict->elements[i]->rhs)); } } } num -= AM.OffsetVector; return(VARNAME(vectors,num)); } /* #] FindVector : #[ FindIndex : */ UBYTE *FindIndex(WORD num) { if ( AO.CurrentDictionary > 0 ) { DICTIONARY *dict = AO.Dictionaries[AO.CurrentDictionary-1]; int i; if ( dict->variables > 0 && AO.CurDictVariables == DICT_DOVARIABLES ) { for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_INDEX && dict->elements[i]->lhs[0] == num ) return((UBYTE *)(dict->elements[i]->rhs)); } } } num -= AM.OffsetIndex; return(VARNAME(indices,num)); } /* #] FindIndex : #[ FindFunction : */ UBYTE *FindFunction(WORD num) { if ( AO.CurrentDictionary > 0 ) { DICTIONARY *dict = AO.Dictionaries[AO.CurrentDictionary-1]; int i; if ( dict->variables > 0 && AO.CurDictVariables == DICT_DOVARIABLES ) { for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_FUNCTION && dict->elements[i]->lhs[0] == num ) return((UBYTE *)(dict->elements[i]->rhs)); } } } num -= FUNCTION; return(VARNAME(functions,num)); } /* #] FindFunction : #[ FindFunWithArgs : */ UBYTE *FindFunWithArgs(WORD *t) { if ( AO.CurrentDictionary > 0 ) { DICTIONARY *dict = AO.Dictionaries[AO.CurrentDictionary-1]; int i, j; if ( dict->funwith > 0 && AO.CurDictFunWithArgs == DICT_DOFUNWITHARGS ) { for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_FUNCTION_WITH_ARGUMENTS && (WORD)(dict->elements[i]->lhs[0]) == t[0] && (WORD)(dict->elements[i]->lhs[1]) == t[1] ) { for ( j = 2; j < t[1]; j++ ) { if ( (WORD)(dict->elements[i]->lhs[j]) != t[j] ) break; } if ( j >= t[1] ) return((UBYTE *)(dict->elements[i]->rhs)); } } } } return(0); } /* #] FindFunWithArgs : #[ FindExtraSymbol : The extra symbol is constructed in the WorkSpace. This way we do not have to worry about Malloc and freeing the object later. The input value num is already the number of the extra symbol. We do NOT need num = MAXVARIABLES-num; */ UBYTE *FindExtraSymbol(WORD num) { GETIDENTITY; UBYTE *out = (UBYTE *)(AT.WorkPointer); *out = 0; if ( AO.CurrentDictionary > 0 ) { DICTIONARY *dict = AO.Dictionaries[AO.CurrentDictionary-1]; int i; if ( dict->ranges > 0 && AO.CurDictVariables == DICT_DOVARIABLES ) { for ( i = dict->numelements-1; i >= 0; i-- ) { if ( dict->elements[i]->type == DICT_RANGE && num >= dict->elements[i]->lhs[0] && num <= dict->elements[i]->lhs[1] ) { /* Now we have to translate the rhs %# gives the number %@ gives the number as its position in the range */ UBYTE *r = (UBYTE *)(dict->elements[i]->rhs); while ( *r ) { if ( *r == (UBYTE)'%' && ( r[1] == (UBYTE)'#' || r[1] == (UBYTE)'@' ) ) { if ( r[1] == (UBYTE)'#' ) { out = NumCopy(num,out); } else { out = NumCopy(num-dict->elements[i]->lhs[0]+1,out); } r += 2; } else { *out++ = *r++; } } *out = 0; return((UBYTE *)(AT.WorkPointer)); } } } } out = StrCopy((UBYTE *)AC.extrasym,out); if ( AC.extrasymbols == 0 ) { out = NumCopy(num,out); out = StrCopy((UBYTE *)"_",out); } else if ( AC.extrasymbols == 1 ) { out = AddArrayIndex(num,out); } return((UBYTE *)(AT.WorkPointer)); } /* #] FindExtraSymbol : #[ FindDictionary : */ int FindDictionary(UBYTE *name) { int i; for ( i = 0; i < AO.NumDictionaries; i++ ) { if ( StrCmp(AO.Dictionaries[i]->name,name) == 0 ) return(i+1); } return(0); } /* #] FindDictionary : #[ AddDictionary : */ int AddDictionary(UBYTE *name) { DICTIONARY *dict; /* First make space for the pointer in the list. */ if ( AO.NumDictionaries >= AO.SizeDictionaries-1 ) { DICTIONARY **d; int i; if ( AO.SizeDictionaries <= 0 ) AO.SizeDictionaries = 10; else AO.SizeDictionaries = 2*AO.SizeDictionaries; d = (DICTIONARY **)Malloc1(AO.SizeDictionaries*sizeof(DICTIONARY *),"Dictionaries"); for ( i = 0; i < AO.NumDictionaries; i++ ) d[i] = AO.Dictionaries[i]; if ( AO.Dictionaries != 0 ) M_free(AO.Dictionaries,"Dictionaries"); AO.Dictionaries = d; } /* Now create an empty dictionary. */ dict = (DICTIONARY *)Malloc1(sizeof(DICTIONARY),"Dictionary"); AO.Dictionaries[AO.NumDictionaries++] = dict; dict->elements = 0; dict->name = strDup1(name,"DictionaryName"); dict->sizeelements = 0; dict->numelements = 0; dict->numbers = 0; dict->variables = 0; dict->characters = 0; dict->funwith = 0; dict->gnumelements = 0; dict->ranges = 0; return(AO.NumDictionaries); } /* #] AddDictionary : #[ AddToDictionary : To be called from #add left:right */ int AddToDictionary(DICTIONARY *dict,UBYTE *left,UBYTE *right) { GETIDENTITY CBUF *C = cbuf+AC.cbufnum; WORD *w = AT.WorkPointer; WORD *OldWork = AT.WorkPointer; WORD *s, oldnumrhs = C->numrhs, oldnumlhs = C->numlhs; WORD *ow, *ww, *mm, oldEside, *where = 0, type, number, range[3]; LONG oldcpointer; int error = 0, sizelhs, sizerhs, i, retcode; UBYTE *r; DICTIONARY_ELEMENT *new; WORD power = (WORD)('^'), times = (WORD)('*'); if ( ( left[0] == '^' && left[1] == 0 ) || ( left[0] == '*' && left[1] == '*' && left[2] == 0 ) ) { type = DICT_SPECIALCHARACTER; number = 1; where = &power; goto TestDouble; } else if ( left[0] == '*' && left[1] == 0 ) { type = DICT_SPECIALCHARACTER; number = 1; where = × goto TestDouble; } else if ( left[0] == '(' ) { /* range of extra symbols */ WORD x1 = 0, x2 = 0; r = left+1; while ( FG.cTable[*r] == 1 ) x1 = 10*x1 + *r++ - '0'; if ( *r == ',' ) { r++; while ( FG.cTable[*r] == 1 ) x2 = 10*x2 + *r++ - '0'; } else x2 = x1; number = 2; if ( *r != ')' ) { MesPrint("&Illegal range specification in LHS of %#add instruction."); return(1); } type = DICT_RANGE; if ( x1 <= 0 || x2 <= 0 || x1 > x2 ) { MesPrint("&Illegal range in LHS of %#add instruction."); return(1); } range[0] = x1; range[1] = x2; range[2] = 0; where = range; goto TestDouble; } /* Translate the left part. Determine type. We follow the code in CoIdExpression and then veto what we do not like. Just make sure to pop what needs to be popped in the compiler buffer. */ AC.ProtoType = w; *w++ = SUBEXPRESSION; *w++ = SUBEXPSIZE; *w++ = C->numrhs+1; *w++ = 1; *w++ = AC.cbufnum; FILLSUB(w) AC.WildC = w; AC.NwildC = 0; AT.WorkPointer = s = w + 4*AM.MaxWildcards + 8; /* Now read the LHS */ oldcpointer = AddLHS(AC.cbufnum) - C->Buffer; if ( ( retcode = CompileAlgebra(left,LHSIDE,AC.ProtoType) ) < 0 ) { error = 1; } else AC.ProtoType[2] = retcode; AT.WorkPointer = s; if ( AC.NwildC && SortWild(w,AC.NwildC) ) error = 1; OldWork[1] = AC.WildC-OldWork; w = AC.WildC; AT.WorkPointer = w; s = C->rhs[C->numrhs]; /* We have the expression in the compiler buffers. The main level is at lhs[numlhs] The partial lhs (including ProtoType) is in OldWork (in WorkSpace) We need to load the result at w after the prototype Because these sort routines don't use the WorkSpace there should not be a conflict */ if ( !error && *s == 0 ) { IllLeft:MesPrint("&Illegal LHS in dictionary"); AC.lhdollarflag = 0; return(1); } if ( !error && *(s+*s) != 0 ) { MesPrint("&LHS in dictionary should be one term only"); return(1); } if ( error == 0 ) { if ( NewSort(BHEAD0) || NewSort(BHEAD0) ) { if ( !error ) error = 1; return(error); } AN.RepPoint = AT.RepCount + 1; ow = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); mm = s; ww = ow; i = *mm; while ( --i >= 0 ) {*ww++ = *mm++;} AT.WorkPointer = ww; AC.lhdollarflag = 0; oldEside = AR.Eside; AR.Eside = LHSIDE; AR.Cnumlhs = C->numlhs; if ( Generator(BHEAD ow,C->numlhs) ) { AR.Eside = oldEside; LowerSortLevel(); LowerSortLevel(); goto IllLeft; } AR.Eside = oldEside; AT.WorkPointer = w; if ( EndSort(BHEAD w,0) < 0 ) { LowerSortLevel(); goto IllLeft; } if ( *w == 0 || *(w+*w) != 0 ) { MesPrint("&LHS must be one term"); AC.lhdollarflag = 0; return(1); } LowerSortLevel(); } AT.WorkPointer = w + *w; AC.DumNum = 0; /* Everything is now after OldWork. We can pop the compilerbuffer. Next test for illegal things like a coefficient At this point we have: w = the term of the LHS */ C->Pointer = C->Buffer + oldcpointer; C->numrhs = oldnumrhs; C->numlhs = oldnumlhs; AC.lhdollarflag = 0; /* Test for undesirables. 1: wildcards 2: sign 3: more than one term 4: composite terms */ if ( AC.ProtoType[1] != SUBEXPSIZE ) { MesPrint("& Currently no wildcards allowed in dictionaries."); return(1); } if ( w[w[0]-1] < 0 ) { MesPrint("& Currently no sign allowed in dictionaries."); return(1); } if ( w[w[0]] != 0 ) { MesPrint("& More than one term in dictionary element."); return(1); } if ( w[0] == w[w[0]-1]+1 ) { /* Only coefficient */ WORD *numer, *denom; WORD nsize, dsize; nsize = dsize = (w[w[0]-1]-1)/2; numer = w+1; denom = numer+nsize; while ( numer[nsize-1] == 0 ) nsize--; while ( denom[dsize-1] == 0 ) dsize--; if ( dsize == 1 && denom[0] == 1 ) { type = DICT_INTEGERNUMBER; number = nsize; where = numer; } else { type = DICT_RATIONALNUMBER; number = w[0]; where = w; } } else { s = w + w[0]-1; if ( s[0] != 3 || s[-1] != 1 || s[-2] != 1 ) { Compositeness:; MesPrint("& Currently no composite objects allowed in dictionaries."); return(1); } if ( w[0] != w[2]+4 ) goto Compositeness; s = w+1; switch ( *s ) { case SYMBOL: if ( s[1] != 4 || s[3] != 1 ) goto Compositeness; type = DICT_SYMBOL; number = 1; where = s+2; break; case INDEX: if ( s[1] != 3 ) goto Compositeness; if ( s[2] < 0 ) type = DICT_VECTOR; else type = DICT_INDEX; number = 1; where = s+2; break; default: if ( *s < FUNCTION ) { MesPrint("& Illegal object in dictionary."); return(1); } if ( s[1] == FUNHEAD ) { type = DICT_FUNCTION; number = 1; where = s; break; } else { type = DICT_FUNCTION_WITH_ARGUMENTS; number = s[1]; where = s; } break; } } TestDouble:; /* Create a new element */ if ( dict->numelements >= dict->sizeelements ) { DICTIONARY_ELEMENT **d; if ( dict->sizeelements <= 0 ) dict->sizeelements = 10; else dict->sizeelements *= 2; d = (DICTIONARY_ELEMENT **)Malloc1( sizeof(DICTIONARY_ELEMENT *)*dict->sizeelements,"Dictionary elements"); for ( i = 0; i < dict->numelements; i++ ) d[i] = dict->elements[i]; if ( dict->elements ) M_free(dict->elements,"Dictionary elements"); dict->elements = d; } sizelhs = number+1; sizerhs = 1; r = right; while ( *r++ ) sizerhs++; sizerhs = (sizerhs+sizeof(WORD)-1)/sizeof(WORD)+1; new = (DICTIONARY_ELEMENT *)Malloc1(sizeof(DICTIONARY_ELEMENT) +sizeof(WORD)*(sizelhs+sizerhs),"Dictionary element"); new->lhs = (WORD *)(new+1); new->rhs = new->lhs+sizelhs; new->type = type; new->size = number; for ( i = 0; i < number; i++ ) new->lhs[i] = where[i]; new->lhs[i] = 0; r = (UBYTE *)(new->rhs); while ( *right ) { if ( *right == '\\' && ( right[1] == '`' || right[1] == '\'' ) ) right++; *r++ = *right++; } *r = 0; dict->elements[dict->numelements++] = new; switch ( type ) { case DICT_INTEGERNUMBER: case DICT_RATIONALNUMBER: dict->numbers++; break; case DICT_SYMBOL: case DICT_VECTOR: case DICT_INDEX: case DICT_FUNCTION: dict->variables++; break; case DICT_FUNCTION_WITH_ARGUMENTS: dict->funwith++; break; case DICT_SPECIALCHARACTER: dict->characters++; break; case DICT_RANGE: dict->ranges++; break; } AT.WorkPointer = OldWork; return(0); } /* #] AddToDictionary : #[ UseDictionary : */ int UseDictionary(UBYTE *name,UBYTE *options) { int i; for ( i = 0; i < AO.NumDictionaries; i++ ) { if ( StrCmp(AO.Dictionaries[i]->name,name) == 0 ) { AO.CurrentDictionary = i+1; if ( SetDictionaryOptions(options) < 0 ) { AO.CurrentDictionary = 0; return(-1); } else { /* Now test whether what is requested is really there? */ return(0); } } } MesPrint("@There is no dictionary with the name %s",name); exit(-1); } /* #] UseDictionary : #[ SetDictionaryOptions : */ int SetDictionaryOptions(UBYTE *options) { UBYTE *opt, *s, c; int retval = 0; s = options; AO.CurDictNumbers = DICT_ALLNUMBERS; AO.CurDictVariables = DICT_DOVARIABLES; AO.CurDictSpecials = DICT_DOSPECIALS; AO.CurDictFunWithArgs = DICT_DOFUNWITHARGS; AO.CurDictNumberWarning = 0; AO.CurDictNotInFunctions= 0; AO.CurDictInDollars = DICT_NOTINDOLLARS; while ( *s ) { opt = s; while ( *s && *s != ',' ) s++; c = *s; *s = 0; if ( opt[0] == '$' && opt[1] == 0 ) { AO.CurDictInDollars = DICT_INDOLLARS; } else if ( StrICmp(opt,(UBYTE *)"nonumbers") == 0 ) { AO.CurDictNumbers = DICT_NONUMBERS; } else if ( StrICmp(opt,(UBYTE *)"integersonly") == 0 ) { AO.CurDictNumbers = DICT_INTEGERONLY; } else if ( StrICmp(opt,(UBYTE *)"rationalsonly") == 0 ) { AO.CurDictNumbers = DICT_RATIONALONLY; } else if ( StrICmp(opt,(UBYTE *)"allnumbers") == 0 ) { AO.CurDictNumbers = DICT_ALLNUMBERS; } else if ( StrICmp(opt,(UBYTE *)"novariables") == 0 ) { AO.CurDictVariables = DICT_NOVARIABLES; } else if ( StrICmp(opt,(UBYTE *)"numbersonly") == 0 ) { AO.CurDictNumbers = DICT_ALLNUMBERS; AO.CurDictVariables = DICT_NOVARIABLES; AO.CurDictSpecials = DICT_NOSPECIALS; AO.CurDictFunWithArgs = DICT_NOFUNWITHARGS; } else if ( StrICmp(opt,(UBYTE *)"variablesonly") == 0 ) { AO.CurDictNumbers = DICT_NONUMBERS; AO.CurDictVariables = DICT_DOVARIABLES; AO.CurDictSpecials = DICT_NOSPECIALS; AO.CurDictFunWithArgs = DICT_NOFUNWITHARGS; } else if ( StrICmp(opt,(UBYTE *)"nospecials") == 0 ) { AO.CurDictSpecials = DICT_NOSPECIALS; } else if ( StrICmp(opt,(UBYTE *)"specialsonly") == 0 ) { AO.CurDictNumbers = DICT_NONUMBERS; AO.CurDictVariables = DICT_NOVARIABLES; AO.CurDictSpecials = DICT_DOSPECIALS; AO.CurDictFunWithArgs = DICT_NOFUNWITHARGS; } else if ( StrICmp(opt,(UBYTE *)"nofunwithargs") == 0 ) { AO.CurDictFunWithArgs = DICT_NOFUNWITHARGS; } else if ( StrICmp(opt,(UBYTE *)"funwithargsonly") == 0 ) { AO.CurDictNumbers = DICT_NONUMBERS; AO.CurDictVariables = DICT_NOVARIABLES; AO.CurDictSpecials = DICT_NOSPECIALS; AO.CurDictFunWithArgs = DICT_DOFUNWITHARGS; } else if ( StrICmp(opt,(UBYTE *)"warnings") == 0 || StrICmp(opt,(UBYTE *)"warning") == 0 ) { AO.CurDictNumberWarning = 1; } else if ( StrICmp(opt,(UBYTE *)"nowarnings") == 0 || StrICmp(opt,(UBYTE *)"nowarning") == 0 ) { AO.CurDictNumberWarning = 0; } else if ( StrICmp(opt,(UBYTE *)"infunctions") == 0 ) { AO.CurDictNotInFunctions= 0; } else if ( StrICmp(opt,(UBYTE *)"notinfunctions") == 0 ) { AO.CurDictNotInFunctions= 1; } else { MesPrint("@ Unrecognized option in %#SetDictionary: %s",opt); retval = -1; } *s = c; if ( c == ',' ) s++; } return(retval); } /* #] SetDictionaryOptions : #[ UnSetDictionary : */ void UnSetDictionary(void) { AO.CurrentDictionary = 0; AO.CurDictNumbers = -1; AO.CurDictVariables = -1; AO.CurDictSpecials = -1; AO.CurDictFunWithArgs = -1; AO.CurDictFunWithArgs = -1; AO.CurDictNumberWarning = -1; AO.CurDictNotInFunctions= -1; } /* #] UnSetDictionary : #[ RemoveDictionary : Mostly needed for .clear */ void RemoveDictionary(DICTIONARY *dict) { int i; if ( dict == 0 ) return; for ( i = 0; i < AO.NumDictionaries; i++ ) { if ( AO.Dictionaries[i] == dict ) { for (i++; i < AO.NumDictionaries; i++ ) { AO.Dictionaries[i-1] = AO.Dictionaries[i]; } AO.NumDictionaries--; goto removeit; } } MesPrint("@ Dictionary not found in RemoveDictionary"); exit(-1); removeit:; for ( i = 0; i < dict->numelements; i++ ) M_free(dict->elements[i],"Dictionary element"); for ( i = 0; i < dict->numelements; i++ ) dict->elements[i] = 0; if ( dict->elements ) M_free(dict->elements,"Dictionary elements"); if ( dict->name ) { M_free(dict->name,"DictionaryName"); dict->name = 0; } dict->sizeelements = 0; dict->numelements = 0; dict->numbers = 0; dict->variables = 0; dict->characters = 0; dict->funwith = 0; dict->gnumelements = 0; dict->ranges = 0; } /* #] RemoveDictionary : #[ ShrinkDictionary : To be called after a .store to restore the dictionary to the state it had at the last .global We do not make the elements array shorter. */ void ShrinkDictionary(DICTIONARY *dict) { while ( dict->numelements > dict->gnumelements ) { dict->numelements--; M_free(dict->elements[dict->numelements],"Dictionary element"); dict->elements[dict->numelements] = 0; } } /* #] ShrinkDictionary : #[ DoPreOpenDictionary : */ int DoPreOpenDictionary(UBYTE *s) { UBYTE *name; int dict; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' ) s++; name = s; s = SkipAName(s); if ( *s != 0 && *s != ';' ) { MesPrint("@proper syntax is #opendictionary name"); return(-1); } *s = 0; if ( AP.OpenDictionary > 0 ) { MesPrint("@you cannot nest #opendictionary instructions"); MesPrint("@dictionary %s is open already", AO.Dictionaries[AP.OpenDictionary-1]->name); return(-1); } if ( AO.CurrentDictionary > 0 ) { MesPrint("@before opening a dictionary you have to first close the selected dictionary"); return(-1); } /* Do we have this dictionary already? */ dict = FindDictionary(name); if ( dict == 0 ) dict = AddDictionary(name); AP.OpenDictionary = dict; return(0); } /* #] DoPreOpenDictionary : #[ DoPreCloseDictionary : */ int DoPreCloseDictionary(UBYTE *s) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' ) s++; if ( AP.OpenDictionary == 0 && AO.CurrentDictionary == 0 ) { MesPrint("@you have neither an open, nor a selected dictionary"); return(-1); } AP.OpenDictionary = 0; AO.CurrentDictionary = 0; AO.CurDictNotInFunctions = 0; return(0); } /* #] DoPreCloseDictionary : #[ DoPreUseDictionary : */ int DoPreUseDictionary(UBYTE *s) { UBYTE *options, c, *ss, *sss, *name; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' ) s++; if ( AP.OpenDictionary > 0 ) { MesPrint("@before selecting a dictionary you have to first close the open dictionary"); return(-1); } name = s; s = SkipAName(s); ss = s; while ( *s && *s != '(' ) s++; c = *ss; *ss = 0; if ( c == 0 ) { options = ss; } else { options = s+1; SKIPBRA3(s) if ( *s != ')' ) { MesPrint("@Irregular end of %#UseDictionary instruction"); return(-1); } sss = s; s++; while ( *s == ' ' || *s == '\t' || *s == ';' ) s++; *sss = 0; if ( *s ) { MesPrint("@Irregular end of %#UseDictionary instruction"); return(-1); } } return(UseDictionary(name,options)); } /* #] DoPreUseDictionary : #[ DoPreAdd : Syntax: #add left :right #add left : "right" Adds to the currently open dictionary */ int DoPreAdd(UBYTE *s) { UBYTE *left, *right; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' ) s++; if ( AP.OpenDictionary == 0 ) { MesPrint("@there is no open dictionary to add to"); return(-1); } /* Scan to the : and mark the left and right parts. */ left = s; while ( *s && *s != ':' ) { if ( *s == '[' ) { SKIPBRA1(s) s++; } else if ( *s == '{' ) { SKIPBRA2(s) s++; } else if ( *s == '(' ) { SKIPBRA3(s) s++; } else if ( *s == ']' || *s == '}' || *s == ')' ) { MesPrint("@unmatched brackets in #add instruction"); return(-1); } else s++; } if ( *s == 0 ) { MesPrint("@Missing : in #add instruction"); return(-1); } *s++ = 0; right = s; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '"' && s[1] ) { right = s+1; s = s+2; while ( *s ) s++; while ( s[-1] != '"' ) s--; if ( s <= right ) { MesPrint("@Irregular use of double quotes in #add instruction"); return(-1); } s[-1] = 0; } return(AddToDictionary(AO.Dictionaries[AP.OpenDictionary-1],left,right)); } /* #] DoPreAdd : #[ DictToBytes : */ LONG DictToBytes(DICTIONARY *dict,UBYTE *buf) { int numelements = dict->numelements, sizeelement, i, j, x; UBYTE *s1, *s2 = buf; DICTIONARY_ELEMENT *e; /* First copy the struct */ s1 = (UBYTE *)dict; j = sizeof(DICTIONARY); NCOPY(s2,s1,j) /* Now the elements. Put a size indicator in front of each of them. */ for ( i = 0; i < numelements; i++ ) { e = dict->elements[i]; sizeelement = sizeof(DICTIONARY_ELEMENT)+(e->size+1)*sizeof(WORD); s1 = (UBYTE *)e->rhs; x = 0; while ( *s1 ) { s1++; x++; } x /= sizeof(WORD); sizeelement += (x+1) * sizeof(WORD); s1 = (UBYTE *)(&sizeelement); j = sizeof(WORD); NCOPY(s2,s1,j) s1 = (UBYTE *)e; j = sizeof(DICTIONARY_ELEMENT); NCOPY(s2,s1,j) s1 = (UBYTE *)e->lhs; j = (e->size+1)*(sizeof(WORD)); NCOPY(s2,s1,j) s1 = (UBYTE *)e->rhs; j = (x+1)*(sizeof(WORD)); NCOPY(s2,s1,j) } return(s2-buf); } /* #] DictToBytes : #[ DictFromBytes : */ DICTIONARY *DictFromBytes(UBYTE *buf) { DICTIONARY *dict = Malloc1(sizeof(DICTIONARY),"Dictionary"); UBYTE *s1, *s2; int i, j, sizeelement; DICTIONARY_ELEMENT *e; /* First read the dictionary itself */ s1 = buf; s2 = (UBYTE *)dict; j = sizeof(DICTIONARY); NCOPY(s2,s1,j) /* Allocate the elements array: */ dict->elements = (DICTIONARY_ELEMENT **)Malloc1( sizeof(DICTIONARY_ELEMENT *)*dict->sizeelements,"dictionary elements"); for ( i = 0; i < dict->numelements; i++ ) { s2 = (UBYTE *)(&sizeelement); j = sizeof(WORD); NCOPY(s2,s1,j) e = (DICTIONARY_ELEMENT *)Malloc1(sizeelement*sizeof(UBYTE),"dictionary element"); dict->elements[i] = e; j = sizeelement; s2 = (UBYTE *)e; NCOPY(s2,s1,j) e->lhs = (WORD *)(e+1); e->rhs = e->lhs + e->size+1; } return(dict); } /* #] DictFromBytes : */ form-5.0.1/sources/float.c0000644000175100017510000022206015217035721011104 /** @file float.c * * This file contains numerical routines that deal with floating point numbers. * We use the GMP for arbitrary precision floating point arithmetic. * The functions of the type sin, cos, ln, sqrt etc are handled by the * mpfr library. The reason that for MZV's and the general notation we use * the GMP (mpf_) is because the contents of the structs have been frozen * and can be used for storage in a Form function float_. With mpfr_ this * is not safely possible. All mpfr_ related code is in the file evaluate.c. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : float.c */ #include "form3.h" #include #include #define WITHCUTOFF #define GMPSPREAD (GMP_LIMB_BITS/BITSINWORD) void Form_mpf_init(mpf_t t); void Form_mpf_clear(mpf_t t); void Form_mpf_set_prec_raw(mpf_t t,ULONG newprec); void FormtoZ(mpz_t z,UWORD *a,WORD na); void ZtoForm(UWORD *a,WORD *na,mpz_t z); long FloatToInteger(UWORD *out, mpf_t floatin, long *bitsused); void IntegerToFloat(mpf_t result, UWORD *formlong, int longsize); int FloatToRat(UWORD *ratout, WORD *nratout, mpf_t floatin); int AddFloats(PHEAD WORD *fun3, WORD *fun1, WORD *fun2); int MulFloats(PHEAD WORD *fun3, WORD *fun1, WORD *fun2); int DivFloats(PHEAD WORD *fun3, WORD *fun1, WORD *fun2); int AddRatToFloat(PHEAD WORD *outfun, WORD *infun, UWORD *formrat, WORD nrat); int MulRatToFloat(PHEAD WORD *outfun, WORD *infun, UWORD *formrat, WORD nrat); void SimpleDelta(mpf_t sum, int m); void SimpleDeltaC(mpf_t sum, int m); void SingleTable(mpf_t *tabl, int N, int m, int pow); void DoubleTable(mpf_t *tabout, mpf_t *tabin, int N, int m, int pow); void EndTable(mpf_t sum, mpf_t *tabin, int N, int m, int pow); void deltaMZV(mpf_t, WORD *, int); void deltaEuler(mpf_t, WORD *, int); void deltaEulerC(mpf_t, WORD *, int); void CalculateMZVhalf(mpf_t, WORD *, int); void CalculateMZV(mpf_t, WORD *, int); void CalculateEuler(mpf_t, WORD *, int); int ExpandMZV(WORD *term, WORD level); int ExpandEuler(WORD *term, WORD level); int PackFloat(WORD *,mpf_t); int UnpackFloat(mpf_t, WORD *); void RatToFloat(mpf_t result, UWORD *formrat, int ratsize); /* #] Includes : #[ Some GMP float info : From gmp.h: typedef struct { int _mp_prec; Max precision, in number of `mp_limb_t's. Set by mpf_init and modified by mpf_set_prec. The area pointed to by the _mp_d field contains `prec' + 1 limbs. int _mp_size; abs(_mp_size) is the number of limbs the last field points to. If _mp_size is negative this is a negative number. mp_exp_t _mp_exp; Exponent, in the base of `mp_limb_t'. mp_limb_t *_mp_d; Pointer to the limbs. } __mpf_struct; typedef __mpf_struct mpf_t[1]; Currently: sizeof(int) = 4 sizeof(mpf_t) = 24 sizeof(mp_limb_t) = 8, sizeof(mp_exp_t) = 8, sizeof a pointer is 8. If any of this changes in the future we would have to change the PackFloat and UnpackFloat routines. Our float_ function is packed with the 4 arguments: -SNUMBER _mp_prec -SNUMBER _mp_size exponent which can be -SNUMBER or a regular term the limbs as n/1 in regular term format, or just an -SNUMBER. During normalization the sign is taken away from the second argument and put as the sign of the complete term. This is easier for the WriteInnerTerm routine in sch.c Wildcarding of functions excludes matches with float_ Float_ always ends up inside the bracket, just like poly(rat)fun. From mpfr.h The formats here are different. This has, among others, to do with the rounding. The result is that we need different aux variables when working with mpfr and we need a different conversion routine to float. It also means that we need to treat the mzv_ etc functions completely separately. For now we try to develop that in the file Evaluate.c. At a later stage we may merge the two files. Originally we had the sqrt in float.c but it seems better to put it in Evaluate.c #] Some GMP float info : #[ Low Level : In the low level routines we interact directly with the content of the GMP structs. This can be done safely, because their layout is documented. We pay particular attention to the init and clear routines, because they involve malloc/free calls. #[ Explanations : We need a number of facilities inside Form to deal with floating point numbers, taking into account that they are only meant for sporadic use. 1: We need a special function float_ who's arguments contain a limb representation of the mpf_t of the gmp. 2: Some functions may return a floating point number. This is then in the form of an occurrence of the function float_. 3: We need a print routine to print this float_. 4: We need routines for conversions: a: (long) int to float. b: rat to float. c: float to rat (if possible) d: float to integer (with rounding toward zero). 5: We need calculational operations for add, sub, mul, div, exp. 6: We need service routines to pack and unpack the function float_. 7: The coefficient should be pulled inside float_. 8: Float_ cannot occur inside PolyRatFun. 9: We need to be able to treat float_ as the coefficient during sorting. 10: For now, we need the functions mzvf_ and eulerf_ for the evaluation of mzv's and euler sums. 11: We need a setting for the default precision. 12: We need a special flag for the dirty field of arguments to avoid the normalization of the argument with the limbs. Alternatively, the float_ should be not a regular function, but get a status < FUNCTION. Just like SNUMBER, LNUMBER etc. Note that we can keep this thread-safe. The only routine that is not thread-safe is the print routine, but that is in accordance with all other print routines in Form. When called from MesPrint it needs to be protected by a lock, as is done standard inside Form. #] Explanations : #[ Form_mpf_init : */ void Form_mpf_init(mpf_t t) { mp_limb_t *d; int i, prec; if ( t->_mp_d ) { M_free(t->_mp_d,"Form_mpf_init"); t->_mp_d = 0; } prec = (AC.DefaultPrecision + 8*sizeof(mp_limb_t)-1)/(8*sizeof(mp_limb_t)) + 1; t->_mp_prec = prec; t->_mp_size = 0; t->_mp_exp = 0; d = (mp_limb_t *)Malloc1(prec*sizeof(mp_limb_t),"Form_mpf_init"); if ( d == 0 ) { MesPrint("Fatal error in Malloc1 call in Form_mpf_init. Trying to allocate %ld bytes.", prec*sizeof(mp_limb_t)); Terminate(-1); } t->_mp_d = d; for ( i = 0; i < prec; i++ ) d[i] = 0; } /* #] Form_mpf_init : #[ Form_mpf_clear : */ void Form_mpf_clear(mpf_t t) { if ( t->_mp_d ) { M_free(t->_mp_d,"Form_mpf_init"); t->_mp_d = 0; } t->_mp_prec = 0; t->_mp_size = 0; t->_mp_exp = 0; } /* #] Form_mpf_clear : #[ Form_mpf_empty : */ void Form_mpf_empty(mpf_t t) { int i; for ( i = 0; i < t->_mp_prec; i++ ) t->_mp_d[i] = 0; t->_mp_size = 0; t->_mp_exp = 0; } /* #] Form_mpf_empty : #[ Form_mpf_set_prec_raw : */ void Form_mpf_set_prec_raw(mpf_t t,ULONG newprec) { ULONG newpr = (newprec + 8*sizeof(mp_limb_t)-1)/(8*sizeof(mp_limb_t)) + 1; if ( newpr <= (ULONG)(t->_mp_prec) ) { int i, used = ABS(t->_mp_size) ; if ( newpr > (ULONG)used ) { for ( i = used; i < (int)newpr; i++ ) t->_mp_d[i] = 0; } if ( t->_mp_size < 0 ) newpr = -newpr; t->_mp_size = newpr; } else { /* We can choose here between "forget about it" or making a new malloc. If the program is well designed, we should never get here though. For now we choose the "forget it" option. */ MesPrint("Trying too big a precision %ld in Form_mpf_set_prec_raw.",newprec); MesPrint("Old maximal precision is %ld.", (size_t)(t->_mp_prec-1)*sizeof(mp_limb_t)*8); Terminate(-1); } } /* #] Form_mpf_set_prec_raw : #[ PackFloat : Puts an object of type mpf_t inside a function float_ float_(prec, nlimbs, exp, limbs); Complication: the limbs and the exponent are long's. That means two times the size of a Form (U)WORD. To save space we could split the limbs in two because Form stores coefficients as rationals with equal space for numerator and denominator. Hence for each limb we could put the most significant UWORD in the numerator and the least significant limb in the denominator. This gives a problem with the compilation and subsequent potential normalization of the 'fraction'. Hence for now we take the wasteful approach. At a later stage we can try to veto normalization of FLOATFUN. Caution: gmp/fmp is little endian and Form is big endian. Zero is represented by zero limbs (and zero exponent). */ int PackFloat(WORD *fun,mpf_t infloat) { WORD *t, nlimbs, num, nnum; mp_limb_t *d = infloat->_mp_d; /* Pointer to the limbs. */ int i; long e = infloat->_mp_exp; t = fun; *t++ = FLOATFUN; t++; FILLFUN(t); *t++ = -SNUMBER; *t++ = infloat->_mp_prec; *t++ = -SNUMBER; *t++ = infloat->_mp_size; /* Now the exponent which is a signed long */ if ( e < 0 ) { e = -e; if ( ( e >> (BITSINWORD-1) ) == 0 ) { *t++ = -SNUMBER; *t++ = -e; } else { *t++ = ARGHEAD+6; *t++ = 0; FILLARG(t); *t++ = 6; *t++ = (UWORD)e; *t++ = (UWORD)(e >> BITSINWORD); *t++ = 1; *t++ = 0; *t++ = -5; } } else { if ( ( e >> (BITSINWORD-1) ) == 0 ) { *t++ = -SNUMBER; *t++ = e; } else { *t++ = ARGHEAD+6; *t++ = 0; FILLARG(t); *t++ = 6; *t++ = (UWORD)e; *t++ = (UWORD)(e >> BITSINWORD); *t++ = 1; *t++ = 0; *t++ = 5; } } /* and now the limbs. Note that the number of active limbs could be less than prec+1 in which case we copy the smaller number. */ nlimbs = infloat->_mp_size < 0 ? -infloat->_mp_size: infloat->_mp_size; if ( nlimbs == 0 ) { *t++ = -SNUMBER; *t++ = 0; } else if ( nlimbs == 1 && (ULONG)(*d) < ((ULONG)1)<<(BITSINWORD-1) ) { *t++ = -SNUMBER; *t++ = (UWORD)(*d); } else { if ( d[nlimbs-1] < ((ULONG)1)< 1 ) { *t++ = (UWORD)(*d); *t++ = (UWORD)(((ULONG)(*d))>>BITSINWORD); d++; num -= 2; } if ( num == 1 ) { *t++ = (UWORD)(*d); } *t++ = 1; for ( i = 1; i < nnum; i++ ) *t++ = 0; *t++ = 2*nnum+1; /* the sign is hidden in infloat->_mp_size */ } fun[1] = t-fun; return(fun[1]); } /* #] PackFloat : #[ UnpackFloat : Takes the arguments of a function float_ and puts it inside an mpf_t. For notation see commentary for PutInFloat. We should make a new allocation for the limbs if the precision exceeds the present precision of outfloat, or when outfloat has not been initialized yet. The return value is -1 if the contents of the FLOATFUN cannot be converted. Otherwise the return value is the number of limbs. */ int UnpackFloat(mpf_t outfloat,WORD *fun) { UWORD *t; WORD *f; int num, i; mp_limb_t *d; /* Very first step: check whether we can use float_: */ GETIDENTITY if ( AT.aux_ == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal attempt at using a float_ function without proper startup."); MesPrint("Please use %#StartFloat first."); MUNLOCK(ErrorMessageLock); Terminate(-1); } /* Check first the number and types of the arguments There should be 4. -SNUMBER,-SNUMBER,-SNUMBER or a long number. + the limbs, either -SNUMBER or Long number in the form of a Form rational. */ if ( TestFloat(fun) == 0 ) goto Incorrect; f = fun + FUNHEAD + 2; if ( ABS(f[1]) > f[-1]+1 ) goto Incorrect; if ( f[1] > outfloat->_mp_prec+1 || outfloat->_mp_d == 0 ) { /* We need to make a new allocation. Unfortunately we cannot use Malloc1 because that is not recognised by gmp and hence we cannot clear with mpf_clear. Maybe we can do something about it by making our own mpf_init and mpf_clear? */ if ( outfloat->_mp_d != 0 ) free(outfloat->_mp_d); outfloat->_mp_d = (mp_limb_t *)malloc((f[1]+1)*sizeof(mp_limb_t)); } num = f[1]; outfloat->_mp_size = num; if ( num < 0 ) { num = -num; } f += 2; if ( *f == -SNUMBER ) { outfloat->_mp_exp = (mp_exp_t)(f[1]); f += 2; } else { f += ARGHEAD+6; if ( f[-1] == -5 ) { outfloat->_mp_exp = -(mp_exp_t)((((ULONG)(f[-4]))<_mp_exp = (mp_exp_t)((((ULONG)(f[-4]))<_mp_d; if ( outfloat->_mp_size == 0 ) { for ( i = 0; i < outfloat->_mp_prec; i++ ) *d++ = 0; return(0); } else if ( *f == -SNUMBER ) { *d++ = (mp_limb_t)f[1]; for ( i = 0; i < outfloat->_mp_prec; i++ ) *d++ = 0; return(0); } num = (*f-ARGHEAD-2)/2; /* 2*number of limbs in the argument */ t = (UWORD *)(f+ARGHEAD+1); while ( num > 1 ) { *d++ = (mp_limb_t)((((ULONG)(t[1]))<_mp_d; i <= outfloat->_mp_prec; i++ ) *d++ = 0; return(0); Incorrect: return(-1); } /* #] UnpackFloat : #[ TestFloat : Tells whether the function (with its arguments) is a legal float_. We assume, as in the whole float library that one limb is 2 WORDs. */ int TestFloat(WORD *fun) { WORD *fstop, *f, num, nnum, i; fstop = fun+fun[1]; f = fun + FUNHEAD; num = 0; /* Count arguments */ while ( f < fstop ) { num++; NEXTARG(f); } if ( num != 4 ) return(0); f = fun + FUNHEAD; if ( *f != -SNUMBER ) return(0); if ( f[1] < 0 ) return(0); f += 2; if ( *f != -SNUMBER ) return(0); num = ABS(f[1]); /* number of limbs */ f += 2; if ( *f == -SNUMBER ) { f += 2; } else { if ( *f != ARGHEAD+6 ) return(0); if ( ABS(f[ARGHEAD+5]) != 5 ) return(0); if ( f[ARGHEAD+3] != 1 ) return(0); if ( f[ARGHEAD+4] != 0 ) return(0); f += *f; } if ( num == 0 ) return(1); if ( *f == -SNUMBER ) { if ( num != 1 ) return(0); } else { nnum = (ABS(f[*f-1])-1)/2; if ( ( *f != 4*num+2+ARGHEAD ) && ( *f != 4*num+ARGHEAD ) ) return(0); if ( ( nnum != 2*num ) && ( nnum != 2*num-1 ) ) return(0); f += ARGHEAD+nnum+1; if ( f[0] != 1 ) return(0); for ( i = 1; i < nnum; i++ ) { if ( f[i] != 0 ) return(0); } } return(1); } /* #] TestFloat : #[ FormtoZ : Converts a Form long integer to a GMP long integer. typedef struct { int _mp_alloc; Number of *limbs* allocated and pointed to by the _mp_d field. int _mp_size; abs(_mp_size) is the number of limbs the last field points to. If _mp_size is negative this is a negative number. mp_limb_t *_mp_d;Pointer to the limbs. } __mpz_struct; typedef __mpz_struct mpz_t[1]; */ void FormtoZ(mpz_t z,UWORD *a,WORD na) { int nlimbs, sgn = 1; mp_limb_t *d; UWORD *b = a; WORD nb = na; if ( nb == 0 ) { z->_mp_size = 0; z->_mp_d[0] = 0; return; } if ( nb < 0 ) { sgn = -1; nb = -nb; } nlimbs = (nb+1)/2; if ( mpz_cmp_si(z,0L) <= 1 ) { mpz_set_ui(z,10000000); } if ( z->_mp_alloc <= nlimbs ) { mpz_t zz; mpz_init(zz); while ( z->_mp_alloc <= nlimbs ) { mpz_mul(zz,z,z); mpz_set(z,zz); } mpz_clear(zz); } z->_mp_size = sgn*nlimbs; d = z->_mp_d; while ( nb > 1 ) { *d++ = (((mp_limb_t)(b[1]))<_mp_d; int nlimbs = ABS(z->_mp_size), i; UWORD j; if ( nlimbs == 0 ) { *na = 0; return; } *na = 0; for ( i = 0; i < nlimbs-1; i++ ) { *a++ = (UWORD)(*d); *a++ = (UWORD)((*d++)>>BITSINWORD); *na += 2; } *na += 1; *a++ = (UWORD)(*d); j = (UWORD)((*d)>>BITSINWORD); if ( j != 0 ) { *a = j; *na += 1; } if ( z->_mp_size < 0 ) *na = -*na; } /* #] ZtoForm : #[ FloatToInteger : Converts a GMP float to a long Form integer. */ long FloatToInteger(UWORD *out, mpf_t floatin, long *bitsused) { mpz_t z; WORD nout, nx; UWORD x; mpz_init(z); mpz_set_f(z,floatin); ZtoForm(out,&nout,z); mpz_clear(z); x = out[nout-1]; nx = 0; while ( x ) { nx++; x >>= 1; } *bitsused = (nout-1)*BITSINWORD + nx; return(nout); } /* #] FloatToInteger : #[ IntegerToFloat : Converts a Form long integer to a gmp float of default size. We assume that sizeof(unsigned long int) = 2*sizeof(UWORD). */ void IntegerToFloat(mpf_t result, UWORD *formlong, int longsize) { mpz_t z; mpz_init(z); FormtoZ(z,formlong,longsize); mpf_set_z(result,z); mpz_clear(z); } /* #] IntegerToFloat : #[ RatToFloat : Converts a Form rational to a gmp float of default size. */ void RatToFloat(mpf_t result, UWORD *formrat, int ratsize) { GETIDENTITY int nnum, nden; UWORD *num, *den; int sgn = 0; if ( ratsize < 0 ) { ratsize = -ratsize; sgn = 1; } nnum = nden = (ratsize-1)/2; num = formrat; den = formrat+nnum; while ( num[nnum-1] == 0 ) { nnum--; } while ( den[nden-1] == 0 ) { nden--; } IntegerToFloat(aux2,num,nnum); IntegerToFloat(aux3,den,nden); mpf_div(result,aux2,aux3); if ( sgn > 0 ) mpf_neg(result,result); } /* #] RatToFloat : #[ FloatFunToRat : */ WORD FloatFunToRat(PHEAD UWORD *ratout,WORD *in) { WORD oldin = in[0], nratout; in[0] = FLOATFUN; UnpackFloat(aux4,in); FloatToRat(ratout,&nratout,aux4); in[0] = oldin; return(nratout); } /* #] FloatFunToRat : #[ FloatToRat : Converts a gmp float to a Form rational. The algorithm we use is 'repeated fractions' of the style n0+1/(n1+1/(n2+1/(n3+.....))) The moment we get an n that is very large we should have the proper fraction Main problem: what if the sequence keeps going? (there are always rounding errors) We need a cutoff with an error condition. Basically the product n0*n1*n2*... is an underlimit on the number of digits in the answer. We can put a limit on this. A return value of zero means that everything went fine. */ int FloatToRat(UWORD *ratout, WORD *nratout, mpf_t floatin) { GETIDENTITY WORD *out = AT.WorkPointer; WORD s; /* the sign. */ UWORD *a, *b, *c, *d, *mc; WORD na, nb, nc, nd, i; int nout; LONG oldpWorkPointer = AT.pWorkPointer; long bitsused = 0, totalbitsused = 0, totalbits = AC.DefaultPrecision-AC.MaxWeight-1; int retval = 0, startnul; WantAddPointers(AC.DefaultPrecision); /* Horrible overkill */ AT.pWorkSpace[AT.pWorkPointer++] = out; a = NumberMalloc("FloatToRat"); b = NumberMalloc("FloatToRat"); s = mpf_sgn(floatin); if ( s < 0 ) mpf_neg(floatin,floatin); Form_mpf_empty(aux1); Form_mpf_empty(aux2); Form_mpf_empty(aux3); mpf_trunc(aux1,floatin); /* This should now be an integer */ mpf_sub(aux2,floatin,aux1); /* and this >= 0 */ if ( mpf_sgn(aux1) == 0 ) { *out++ = 0; startnul = 1; } else { nout = FloatToInteger((UWORD *)out,aux1,&totalbitsused); out += nout; startnul = 0; } AT.pWorkSpace[AT.pWorkPointer++] = out; if ( mpf_sgn(aux2) ) { for(;;) { mpf_ui_div(aux3,1,aux2); mpf_trunc(aux1,aux3); mpf_sub(aux2,aux3,aux1); if ( mpf_sgn(aux1) == 0 ) { *out++ = 0; } else { nout = FloatToInteger((UWORD *)out,aux1,&bitsused); out += nout; } if ( bitsused > (totalbits-totalbitsused)/2 ) { break; } if ( mpf_sgn(aux2) == 0 ) { /*if ( startnul == 1 )*/ AT.pWorkSpace[AT.pWorkPointer++] = out; break; } totalbitsused += bitsused; AT.pWorkSpace[AT.pWorkPointer++] = out; } /* For |floatin| << 1, we have startnul = 1 and hit the precision guard already on the first continued-fraction step. The resulting float is therefore close to the rational 0/1 and we can immediately return. */ if ( startnul == 1 && AT.pWorkPointer == oldpWorkPointer + 2 ) { *ratout++ = 0; *ratout++ = 1; *ratout = *nratout = 3; goto ret; } /* At this point we have the function with the repeated fraction. Now we should work out the fraction. Form code would be: repeat id dum_(?a,x1?,x2?) = dum_(?a,x1+1/x2); id dum_(x?) = x; We have to work backwards. This is why we made a list of pointers in AT.pWorkSpace Now we need the long integers a and b. Note that by construction there should never be a GCD! */ out = (WORD *)(AT.pWorkSpace[--AT.pWorkPointer]); na = 1; a[0] = 1; c = (UWORD *)(AT.pWorkSpace[--AT.pWorkPointer]); nc = nb = ((UWORD *)out)-c; for ( i = 0; i < nb; i++ ) b[i] = c[i]; mc = c = NumberMalloc("FloatToRat"); while ( AT.pWorkPointer > oldpWorkPointer ) { d = (UWORD *)(AT.pWorkSpace[--AT.pWorkPointer]); nd = (UWORD *)(AT.pWorkSpace[AT.pWorkPointer+1])-d; /* This is the x1 in the formula */ if ( nd == 1 && *d == 0 ) break; c = a; a = b; b = c; nc = na; na = nb; nb = nc; /* 1/x2 */ MulLong(d,nd,a,na,mc,&nc); AddLong(mc,nc,b,nb,b,&nb); } NumberFree(mc,"FloatToRat"); if ( startnul == 0 ) { c = a; a = b; b = c; nc = na; na = nb; nb = nc; } } else { c = (UWORD *)(AT.pWorkSpace[oldpWorkPointer]); na = (UWORD *)out - c; for ( i = 0; i < na; i++ ) a[i] = c[i]; b[0] = 1; nb = 1; } /* Now we have the fraction in a/b. Create the rational and add the sign. */ d = ratout; if ( na == nb ) { *nratout = (2*na+1)*s; for ( i = 0; i < na; i++ ) *d++ = a[i]; for ( i = 0; i < nb; i++ ) *d++ = b[i]; } else if ( na < nb ) { *nratout = (2*nb+1)*s; for ( i = 0; i < na; i++ ) *d++ = a[i]; for ( ; i < nb; i++ ) *d++ = 0; for ( i = 0; i < nb; i++ ) *d++ = b[i]; } else { *nratout = (2*na+1)*s; for ( i = 0; i < na; i++ ) *d++ = a[i]; for ( i = 0; i < nb; i++ ) *d++ = b[i]; for ( ; i < na; i++ ) *d++ = 0; } *d = (UWORD)(*nratout); NumberFree(b,"FloatToRat"); NumberFree(a,"FloatToRat"); AT.pWorkPointer = oldpWorkPointer; /* Just for check we go back to float */ if ( s < 0 ) mpf_neg(floatin,floatin); /* { WORD n = *nratout; RatToFloat(aux1,ratout,n); mpf_sub(aux2,floatin,aux1); gmp_printf("Diff is %.*Fe\n",40,aux2); } */ ret: return(retval); } /* #] FloatToRat : #[ ZeroTable : */ void ZeroTable(mpf_t *tab, int N) { int i, j; for ( i = 0; i < N; i++ ) { for ( j = 0; j < tab[i]->_mp_prec; j++ ) tab[i]->_mp_d[j] = 0; } } /* #] ZeroTable : #[ ReadFloat : Used by the compiler. It reads a floating point number and outputs it at AT.WorkPointer as if it were a float_ function with its arguments. The call enters with s[-1] == TFLOAT. */ SBYTE *ReadFloat(SBYTE *s) { GETIDENTITY SBYTE *ss, c; ss = s; while ( *ss > 0 ) ss++; c = *ss; *ss = 0; gmp_sscanf((char *)s,"%Ff",aux1); if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); Terminate(-1); } PackFloat(AT.WorkPointer,aux1); *ss = c; return(ss); } /* #] ReadFloat : #[ CheckFloat : For the tokenizer. Tests whether the input string can be a float. */ UBYTE *CheckFloat(UBYTE *ss, int *spec) { GETIDENTITY UBYTE *s = ss; int gotdot = 0; /* A single dot is not a valid float */ if ( *s == '.' && FG.cTable[s[-1]] != 1 && FG.cTable[s[1]] != 1 ) return(ss); while ( FG.cTable[s[-1]] == 1 ) s--; /* This cannot be a valid float */ if ( *s != '.' && FG.cTable[*s] != 1 ) return(ss); *spec = 0; while ( FG.cTable[*s] == 1 ) s++; if ( *s == '.' ) { gotdot = 1; s++; while ( FG.cTable[*s] == 1 ) s++; } /* Now we have had the mantissa part, which may be zero. Check for an exponent. */ if ( *s == 'e' || *s == 'E' ) { s++; if ( *s == '-' || *s == '+' ) s++; if ( FG.cTable[*s] == 1 ) { s++; while ( FG.cTable[*s] == 1 ) s++; } else { return(ss); } } else if ( gotdot == 0 ) return(ss); /* No radix point and no exponent */ if ( AT.aux_ == 0 ) { /* no floating point system */ *spec = -1; return(s); } return(s); } /* #] CheckFloat : #] Low Level : #[ Float Routines : #[ SetFloatPrecision : Sets the default precision (in bits) of the floats and allocate buffer space for an output string. The buffer is used by PrintFloat (decimal output) and Strictrounding (binary or decimal output), so it must accommodate the larger space requirement: exponent: up to 12 chars. mantissa: prec + a little bit extra */ int SetFloatPrecision(WORD prec) { if ( prec <= 0 ) { MesPrint("&Illegal value for number of bits for floating point constants: %d",prec); return(-1); } else { AC.DefaultPrecision = prec; if ( AO.floatspace != 0 ) M_free(AO.floatspace,"floatspace"); AO.floatsize = (prec+20)*sizeof(char); AO.floatspace = (UBYTE *)Malloc1(AO.floatsize,"floatspace"); mpf_set_default_prec(prec); return(0); } } /* #] SetFloatPrecision : #[ PrintFloat : Print the float_ function with its arguments as a floating point number with numdigits digits. If however we use rawfloat as a format option it prints it as a regular Form function and it should never come here because the print routines in sch.c should intercept it. The buffer AO.floatspace is allocated when the precision of the floats is set in the routine SetFloatPrecision. */ int PrintFloat(WORD *fun,int numdigits) { GETIDENTITY UBYTE *s1, *s2; int n = 0; int prec = (AC.DefaultPrecision-AC.MaxWeight-1)*log10(2.0); if ( numdigits > prec || numdigits == 0 ) { numdigits = prec; } /* GMP's gmp_snprintf always prints a non-zero number before the decimal point, so we ask for one digit less. */ if ( UnpackFloat(aux4,fun) == 0 ) n = gmp_snprintf((char *)(AO.floatspace),AO.floatsize,"%.*Fe",numdigits-1,aux4); if ( n > 0 ) { int n1, n2 = n; s1 = AO.floatspace+n; while ( s1 > AO.floatspace && s1[-1] != 'e' && s1[-1] != 'E' && s1[-1] != '.' ) { s1--; n2--; } if ( s1 > AO.floatspace && s1[-1] != '.' ) { s1--; n2--; s2 = s1; n1 = n2; while ( s1[-1] == '0' ) { s1--; n1--; } if ( s1[-1] == '.' ) { s1++; n1++; } n -= (n2-n1); while ( n1 < n ) { *s1++ = *s2++; n1++; } *s1 = 0; } if ( AC.OutputMode == FORTRANMODE ) { s1 = AO.floatspace+n; while ( s1 > AO.floatspace && *s1 != 'e' && *s1 != 'E' ) { s1--; } if ( ( AO.DoubleFlag & 2 ) == 2 ) { *s1 = 'Q'; } /* Quadruple precision fortran */ else if ( ( AO.DoubleFlag & 1 ) == 1 ) { *s1 = 'D'; } /* Double precision fortran */ else { *s1 = 'E'; } /* Single precision fortran */ } if ( AC.OutputMode == MATHEMATICAMODE ) { s1 = AO.floatspace+n; s2 = s1+2; *s2-- = 0; while ( s1 > AO.floatspace && *s1 != 'e' && *s1 != 'E' ) { *s2-- = *s1--; } *s2-- = '^'; *s2 = '*'; /* Replace 'e' by '^*' */ n++; } } return(n); } /* #] PrintFloat : #[ AddFloats : */ int AddFloats(PHEAD WORD *fun3, WORD *fun1, WORD *fun2) { int retval = 0; if ( UnpackFloat(aux1,fun1) == 0 && UnpackFloat(aux2,fun2) == 0 ) { mpf_add(aux1,aux1,aux2); PackFloat(fun3,aux1); } else { retval = -1; } return(retval); } /* #] AddFloats : #[ MulFloats : */ int MulFloats(PHEAD WORD *fun3, WORD *fun1, WORD *fun2) { int retval = 0; if ( UnpackFloat(aux1,fun1) == 0 && UnpackFloat(aux2,fun2) == 0 ) { mpf_mul(aux1,aux1,aux2); PackFloat(fun3,aux1); } else { retval = -1; } return(retval); } /* #] MulFloats : #[ DivFloats : */ int DivFloats(PHEAD WORD *fun3, WORD *fun1, WORD *fun2) { int retval = 0; if ( UnpackFloat(aux1,fun1) == 0 && UnpackFloat(aux2,fun2) == 0 ) { mpf_div(aux1,aux1,aux2); PackFloat(fun3,aux1); } else { retval = -1; } return(retval); } /* #] DivFloats : #[ AddRatToFloat : Note: this can be optimized, because often the rat is rather simple. */ int AddRatToFloat(PHEAD WORD *outfun, WORD *infun, UWORD *formrat, WORD nrat) { int retval = 0; if ( UnpackFloat(aux2,infun) == 0 ) { RatToFloat(aux1,formrat,nrat); mpf_add(aux2,aux2,aux1); PackFloat(outfun,aux2); } else retval = -1; return(retval); } /* #] AddRatToFloat : #[ MulRatToFloat : Note: this can be optimized, because often the rat is rather simple. */ int MulRatToFloat(PHEAD WORD *outfun, WORD *infun, UWORD *formrat, WORD nrat) { int retval = 0; if ( UnpackFloat(aux2,infun) == 0 ) { RatToFloat(aux1,formrat,nrat); mpf_mul(aux2,aux2,aux1); PackFloat(outfun,aux2); } else retval = -1; return(retval); } /* #] MulRatToFloat : #[ SetupMZVTables : */ void SetupMZVTables(void) { /* Sets up a table of N+1 mpf_t floats with variable precision. It assumes that each next element needs one bit less. Initializes all of them. We take some extra space, to have one limb overflow everywhere. Because the depth of the MZV's can get close to the weight and each deeper sum goes one higher, we make the tablesize a bit bigger. This may not be needed if we fiddle with the sum boundaries. */ #ifdef WITHPTHREADS int i, Nw, id, totnum; size_t N; mpf_t *a; Nw = AC.DefaultPrecision; N = (size_t)Nw; totnum = AM.totalnumberofthreads; for ( id = 0; id < totnum; id++ ) { AB[id]->T.mpf_tab1 = (void *)Malloc1((N+2)*sizeof(mpf_t),"mpftab1"); a = (mpf_t *)AB[id]->T.mpf_tab1; for ( i = 0; i <=Nw; i++ ) { /* As explained in the comment above, we could make this variable precision using mpf_init2. */ mpf_init(a[i]); } AB[id]->T.mpf_tab2 = (void *)Malloc1((N+2)*sizeof(mpf_t),"mpftab2"); a = (mpf_t *)AB[id]->T.mpf_tab2; for ( i = 0; i <=Nw; i++ ) { mpf_init(a[i]); } } #else int i, Nw; size_t N; Nw = AC.DefaultPrecision; N = (size_t)Nw; AT.mpf_tab1 = (void *)Malloc1((N+2)*sizeof(mpf_t),"mpftab1"); for ( i = 0; i <= Nw; i++ ) { /* As explained in the comment above, we could make this variable precision using mpf_init2. */ mpf_init(mpftab1[i]); } AT.mpf_tab2 = (void *)Malloc1((N+2)*sizeof(mpf_t),"mpftab2"); for ( i = 0; i <= Nw; i++ ) { mpf_init(mpftab2[i]); } #endif AS.delta_1 = (void *)Malloc1(sizeof(mpf_t),"delta1"); mpf_init(mpfdelta1); SimpleDelta(mpfdelta1,1); /* this can speed up things. delta1 = ln(2) */ } /* #] SetupMZVTables : #[ SetupMPFTables : Allocates the aux variables */ void SetupMPFTables(void) { #ifdef WITHPTHREADS int id, totnum; mpf_t *a; #ifdef WITHSORTBOTS totnum = MaX(2*AM.totalnumberofthreads-3,AM.totalnumberofthreads); #endif for ( id = 0; id < totnum; id++ ) { /* We work here with a[0] etc because the aux1 etc contain B which in the current routine would be AB[0] only */ AB[id]->T.aux_ = (void *)Malloc1(sizeof(mpf_t)*8,"AB[id]->T.aux_"); a = (mpf_t *)AB[id]->T.aux_; mpf_inits(a[0],a[1],a[2],a[3],a[4],a[5],a[6],a[7],(mpf_ptr)0); if ( AB[id]->T.indi1 ) M_free(AB[id]->T.indi1,"indi1"); AB[id]->T.indi1 = (WORD *)Malloc1(sizeof(WORD)*AC.MaxWeight*2,"indi1"); AB[id]->T.indi2 = AB[id]->T.indi1 + AC.MaxWeight; } #else AT.aux_ = (void *)Malloc1(sizeof(mpf_t)*8,"AT.aux_"); mpf_inits(aux1,aux2,aux3,aux4,aux5,auxjm,auxjjm,auxsum,(mpf_ptr)0); if ( AT.indi1 ) M_free(AT.indi1,"indi1"); AT.indi1 = (WORD *)Malloc1(sizeof(WORD)*AC.MaxWeight*2,"indi1"); AT.indi2 = AT.indi1 + AC.MaxWeight; #endif } /* #] SetupMPFTables : #[ ClearMZVTables : */ void ClearMZVTables(void) { #ifdef WITHPTHREADS int i, id, totnum; mpf_t *a; totnum = AM.totalnumberofthreads; for ( id = 0; id < totnum; id++ ) { if ( AB[id]->T.mpf_tab1 ) { /* We work here with a[0] etc because the aux1, mpftab1 etc contain B which in the current routine would be AB[0] only */ a = (mpf_t *)AB[id]->T.mpf_tab1; for ( i = 0; i <=AC.DefaultPrecision; i++ ) { mpf_clear(a[i]); } M_free(AB[id]->T.mpf_tab1,"mpftab1"); AB[id]->T.mpf_tab1 = 0; } if ( AB[id]->T.mpf_tab2 ) { a = (mpf_t *)AB[id]->T.mpf_tab2; for ( i = 0; i <=AC.DefaultPrecision; i++ ) { mpf_clear(a[i]); } M_free(AB[id]->T.mpf_tab2,"mpftab2"); AB[id]->T.mpf_tab2 = 0; } } #ifdef WITHSORTBOTS totnum = MaX(2*AM.totalnumberofthreads-3,AM.totalnumberofthreads); #endif for ( id = 0; id < totnum; id++ ) { if ( AB[id]->T.aux_ ) { a = (mpf_t *)AB[id]->T.aux_; mpf_clears(a[0],a[1],a[2],a[3],a[4],a[5],a[6],a[7],(mpf_ptr)0); M_free(AB[id]->T.aux_,"AB[id]->T.aux_"); AB[id]->T.aux_ = 0; } if ( AB[id]->T.indi1 ) { M_free(AB[id]->T.indi1,"indi1"); AB[id]->T.indi1 = 0; } } #else int i; if ( AT.mpf_tab1 ) { for ( i = 0; i <= AC.DefaultPrecision; i++ ) { mpf_clear(mpftab1[i]); } M_free(AT.mpf_tab1,"mpftab1"); AT.mpf_tab1 = 0; } if ( AT.mpf_tab2 ) { for ( i = 0; i <= AC.DefaultPrecision; i++ ) { mpf_clear(mpftab2[i]); } M_free(AT.mpf_tab2,"mpftab2"); AT.mpf_tab2 = 0; } if ( AT.aux_ ) { mpf_clears(aux1,aux2,aux3,aux4,aux5,auxjm,auxjjm,auxsum,(mpf_ptr)0); M_free(AT.aux_,"AT.aux_"); AT.aux_ = 0; } if ( AT.indi1 ) { M_free(AT.indi1,"indi1"); AT.indi1 = 0; } #endif if ( AO.floatspace ) { M_free(AO.floatspace,"floatspace"); AO.floatspace = 0; AO.floatsize = 0; } if ( AS.delta_1 ) { mpf_clear(mpfdelta1); M_free(AS.delta_1,"delta1"); AS.delta_1 = 0; } } /* #] ClearMZVTables : #[ CoToFloat : */ int CoToFloat(UBYTE *s) { GETIDENTITY if ( AT.aux_ == 0 ) { MesPrint("&Illegal attempt to convert to float_ without activating floating point numbers."); MesPrint("&Forgotten %#startfloat instruction?"); return(1); } while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s ) { MesPrint("&Illegal argument(s) in ToFloat statement: '%s'",s); return(1); } Add2Com(TYPETOFLOAT); return(0); } /* #] CoToFloat : #[ CoToRat : */ int CoToRat(UBYTE *s) { GETIDENTITY if ( AT.aux_ == 0 ) { MesPrint("&Illegal attempt to convert from float_ without activating floating point numbers."); MesPrint("&Forgotten %#startfloat instruction?"); return(1); } while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s ) { MesPrint("&Illegal argument(s) in ToRat statement: '%s'",s); return(1); } Add2Com(TYPETORAT); return(0); } /* #] CoToRat : #[ CoStrictRounding : Syntax: StrictRounding [precision][base] - precision: number of digits to round to (optional) - base: 'd' for decimal (base 10) or 'b' for binary (base 2) If no arguments are provided, uses default precision with binary base. */ int CoStrictRounding(UBYTE *s) { GETIDENTITY WORD x; int base; if ( AT.aux_ == 0 ) { MesPrint("&Illegal attempt for strict rounding without activating floating point numbers."); MesPrint("&Forgotten %#startfloat instruction?"); return(1); } while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == 0 ) { /* No subkey, which means round to default precision */ x = AC.DefaultPrecision - AC.MaxWeight - 1; base = 2; } else if ( FG.cTable[*s] == 1 ) { /* number */ ParseNumber(x,s) if ( tolower(*s) == 'd' ) { base = 10; s++; } /* decimal base */ else if ( tolower(*s) == 'b' ){ base = 2; s++; } /* binary base */ else goto IllPar; /* invalid base specification */ } else { goto IllPar; } while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; /* Check for invalid arguments */ if ( *s ) { IllPar: MesPrint("&Illegal argument(s) in StrictRounding statement: '%s'",s); return(1); } Add4Com(TYPESTRICTROUNDING,x,base); return(0); } /* #] CoStrictRounding : #[ CoChop : LHS notation of the chop statement: TYPECHOP, length, FLOATFUN, ... where FLOATFUN, ... represents the threshold of the chop statement in the notation of a float_ function with its arguments. */ int CoChop(UBYTE *s) { GETIDENTITY UBYTE *ss, c; WORD *w, *OldWork; int spec, pow = 1; unsigned long x; if ( AT.aux_ == 0 ) { MesPrint("&Illegal attempt to chop a float_ without activating floating point numbers."); MesPrint("&Forgotten %#startfloat instruction?"); return(1); } if ( *s == 0 ) { MesPrint("&Chop needs a number (float, rational or power) as an argument."); return(1); } /* Create TYPECHOP header */ w = OldWork = AT.WorkPointer; *w++ = TYPECHOP; w++; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; /* The argument of chop can be 1: a floating-point number 2: an integer, rational number or power */ if ( FG.cTable[*s] == 1 || *s == '.' ) { /* 1: Attempt to parse as floating-point number */ ss = CheckFloat(s, &spec); if ( ss > s ) { /* CheckFloat found a valid float */ AT.WorkPointer = w; /* Reads the floating point number and outputs it at AT.WorkPointer as if it were a float_ function with its arguments. */ ReadFloat((SBYTE *)s); s = ss; w += w[1]; } else { /* 2: CheckFloat didn't find a float, we now try for rationals and powers */ /* Parse the integer part (numerator for rationals) */ if ( FG.cTable[*s] == 1 ) { ParseNumber(x,s) mpf_set_ui(aux1,x); } while ( *s == ' ' || *s == '\t' ) s++; /* Check for rational number or power*/ if ( *s == '/' || *s == '^' ) { c = *s; s++; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '-' ) { s++; pow = -1; } /* negative power */ /* Parse the denominator or power */ if ( FG.cTable[*s] == 1 ) { ParseNumber(x,s) if ( c == '/' ) { /* rational */ if ( x == 0 ) { MesPrint("&Division by zero in chop statement."); return(1); } /* Perform the division */ mpf_div_ui(aux1, aux1,x); } else { /* Power */ mpf_pow_ui(aux1,aux1,x); if ( pow == -1 ) { mpf_ui_div(aux1,(unsigned long) 1, aux1); } } } } /* Put aux1 in the notation of a float_ function */ PackFloat(w, aux1); w += w[1]; } } if ( *s ) { MesPrint("&Illegal argument(s) in Chop statement: '%s'.",s); return(1); } AT.WorkPointer = OldWork; AT.WorkPointer[1] = w - AT.WorkPointer; /* Set total length */ AddNtoL(AT.WorkPointer[1],AT.WorkPointer); /* Add the LHS to the compiler buffer */ return(0); } /* #] CoChop : #[ ToFloat : Converts the coefficient to floating point if it is still a rat. */ int ToFloat(PHEAD WORD *term, WORD level) { WORD *t, *tstop, nsize, nsign = 3; t = term+*term; nsize = ABS(t[-1]); tstop = t - nsize; if ( t[-1] < 0 ) { nsign = -nsign; } if ( nsize == 3 && t[-2] == 1 && t[-3] == 1 ) { /* Could be float */ t = term + 1; while ( t < tstop ) { if ( ( *t == FLOATFUN ) && ( t+t[1] == tstop ) ) { return(Generator(BHEAD term,level)); } t += t[1]; } } RatToFloat(aux4,(UWORD *)tstop,nsize); PackFloat(tstop,aux4); tstop += tstop[1]; *tstop++ = 1; *tstop++ = 1; *tstop++ = nsign; *term = tstop - term; AT.WorkPointer = tstop; return(Generator(BHEAD term,level)); } /* #] ToFloat : #[ ToRat : Tries to convert the coefficient to rational if it is still a float. */ int ToRat(PHEAD WORD *term, WORD level) { WORD *tstop, *t, nsize, nsign, ncoef; /* 1: find the float which should be at the end. */ tstop = term + *term; nsize = ABS(tstop[-1]); nsign = tstop[-1] < 0 ? -1: 1; tstop -= nsize; t = term+1; while ( t < tstop ) { if ( *t == FLOATFUN && t + t[1] == tstop && TestFloat(t) && nsize == 3 && tstop[0] == 1 && tstop[1] == 1 ) break; t += t[1]; } if ( t < tstop ) { /* Now t points at the float_ function and everything is correct. The result can go straight over the float_ function. */ UnpackFloat(aux4,t); // If aux4 is zero, the term vanishes if ( mpf_sgn(aux4) == 0 ) return(0); if ( FloatToRat((UWORD *)t,&ncoef,aux4) == 0 ) { // Check if the resulting rational is zero if ( t[0] == 0 && t[1] == 1 && ncoef == 3 ) return(0); t += ABS(ncoef); t[-1] = ncoef*nsign; *term = t - term; } } return(Generator(BHEAD term,level)); } /* #] ToRat : #[ StrictRounding : Rounds floating point numbers to a specified precision in a given base (decimal or binary). */ int StrictRounding(PHEAD WORD *term, WORD level, WORD prec, WORD base) { WORD *t,*tstop; int sign,size,maxprec = AC.DefaultPrecision-AC.MaxWeight-1; /* maxprec is in bits */ if ( base == 2 && prec > maxprec ) { prec = maxprec; } if ( base == 10 && prec > (int)(maxprec*log10(2.0)) ) { prec = maxprec*log10(2.0); } /* Find the float which should be at the end. */ tstop = term + *term; size = ABS(tstop[-1]); sign = tstop[-1] < 0 ? -1: 1; tstop -= size; t = term+1; while ( t < tstop ) { if ( *t == FLOATFUN && t + t[1] == tstop && TestFloat(t) && size == 3 && tstop[0] == 1 && tstop[1] == 1) { break; } t += t[1]; } if ( t < tstop ) { /* Now t points at the float_ function and everything is correct. The result can go straight over the float_ function. */ char *s; mp_exp_t exp; /* Extract the floating point value */ UnpackFloat(aux4,t); /* Convert to string: - Format as MeN with M the mantissa and N the exponent - the generated string by mpf_get_str is the fraction/mantissa with an implicit radix point immediately to the left of the first digit. The applicable exponent is written in exp. */ s = (char *)AO.floatspace; *s++ = '.'; mpf_get_str(s,&exp, base, prec, aux4); while ( *s != 0 ) s++; *s++ = 'e'; snprintf(s,AO.floatsize-(s-(char *)AO.floatspace),"%ld",exp); /* Negative base values are used to specify that the exponent is in decimal */ mpf_set_str(aux4,(char *)AO.floatspace,-base); /* Pack the rounded floating point value back into the term */ PackFloat(t,aux4); t+=t[1]; *t++ = 1; *t++ = 1; *t++ = 3*sign; *term = t - term; } return(Generator(BHEAD term,level)); } /* #] StrictRounding : #[ Chop : Removes terms with a floating point number smaller than a given threshold. Search for a FLOATFUN and compares its absolute value against the threshold specified in the chop statement. This threshold can be obtained from the LHS of the chop statement in the compiler buffer. */ int Chop(PHEAD WORD *term, WORD level) { WORD *tstop, *t, nsize, *threshold; CBUF *C = cbuf+AM.rbufnum; /* Find the float which should be at the end. */ tstop = term + *term; nsize = ABS(tstop[-1]); tstop -= nsize; t = term+1; while ( t < tstop ) { if ( *t == FLOATFUN && t + t[1] == tstop && TestFloat(t) && nsize == 3 && tstop[0] == 1 && tstop[1] == 1 ) break; t += t[1]; } if ( t < tstop ) { /* Get threshold value from compiler buffer */ threshold = C->lhs[level]; threshold += 2; /* Skip TYPECHOP header */ UnpackFloat(aux5, threshold); /* Extract float and compute its absolute value */ UnpackFloat(aux4, t); mpf_abs(aux4, aux4); /* Remove if < threshold */ if ( mpf_cmp(aux4, aux5) < 0 ) return(0); } return(Generator(BHEAD term,level)); } /* #] Chop : #] Float Routines : #[ Sorting : We need a method to see whether two terms need addition that could involve floating point numbers. 1: if PolyWise is active, we do not need anything, because Poly(Rat)Fun and floating point are mutually exclusive. 2: This means that there should be only interference in AddCoef. and the AddRat parts in MergePatches, MasterMerge, SortBotMerge and PF_GetLoser. The compare routine(s) should recognise the float_ and give off a code (SortFloatMode) inside the AT struct: 0: no float_ 1: float_ in term1 only 2: float_ in term2 only 3: float_ in both terms Be careful: we have several compare routines, because various codes use their own routines and we just set a variable with its address. Currently we have Compare1, CompareSymbols and CompareHSymbols. Only Compare1 should be active for this. The others should make sure that the proper variable is always zero. Remember: the sign of the coefficient is in the last word of the term. We need two routines: 1: AddWithFloat for SplitMerge which sorts by pointer. 2: MergeWithFloat for MergePatches etc which keeps terms as much as possible in their location. The routines start out the same, because AT.SortFloatMode, set in Compare1, tells more or less what should be done. The difference is in where we leave the result. In the future we may want to add a feature that makes the result zero if the sum comes within a certain distance of the numerical accuracy, like for instance 5% of the number of bits. #[ AddWithFloat : */ int AddWithFloat(PHEAD WORD **ps1, WORD **ps2) { GETBIDENTITY SORTING *S = AT.SS; WORD *coef1, *coef2, size1, size2, *fun1, *fun2, *fun3; WORD *s1,*s2,sign3,j,jj, *t1, *t2, i; s1 = *ps1; s2 = *ps2; coef1 = s1+*s1; size1 = coef1[-1]; coef1 -= ABS(coef1[-1]); coef2 = s2+*s2; size2 = coef2[-1]; coef2 -= ABS(coef2[-1]); if ( AT.SortFloatMode == 3 ) { fun1 = s1+1; while ( fun1 < coef1 && fun1[0] != FLOATFUN ) fun1 += fun1[1]; fun2 = s2+1; while ( fun2 < coef2 && fun2[0] != FLOATFUN ) fun2 += fun2[1]; UnpackFloat(aux1,fun1); if ( size1 < 0 ) mpf_neg(aux1,aux1); UnpackFloat(aux2,fun2); if ( size2 < 0 ) mpf_neg(aux2,aux2); } else if ( AT.SortFloatMode == 1 ) { fun1 = s1+1; while ( fun1 < coef1 && fun1[0] != FLOATFUN ) fun1 += fun1[1]; UnpackFloat(aux1,fun1); if ( size1 < 0 ) mpf_neg(aux1,aux1); fun2 = coef2; RatToFloat(aux2,(UWORD *)coef2,size2); } else if ( AT.SortFloatMode == 2 ) { fun2 = s2+1; while ( fun2 < coef2 && fun2[0] != FLOATFUN ) fun2 += fun2[1]; fun1 = coef1; RatToFloat(aux1,(UWORD *)coef1,size1); UnpackFloat(aux2,fun2); if ( size2 < 0 ) mpf_neg(aux2,aux2); } else { MLOCK(ErrorMessageLock); MesPrint("Illegal value %d for AT.SortFloatMode in AddWithFloat.",AT.SortFloatMode); MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } mpf_add(aux3,aux1,aux2); sign3 = mpf_sgn(aux3); if ( sign3 < 0 ) mpf_neg(aux3,aux3); fun3 = TermMalloc("AddWithFloat"); PackFloat(fun3,aux3); /* Now we have to calculate where the sumterm fits. If we are sloppy, we can be faster, but run the risk to need the extension space, even when it is not needed. At slightly lower speed (ie first creating the result in scribble space) we are better off. This is why we use TermMalloc. The new term will have a rational coefficient of 1,1,+-3. The size will be (fun1 or fun2 - term) + fun3 +3; */ if ( AT.SortFloatMode == 3 ) { if ( fun1[1] == fun3[1] ) { Over1: i = fun3[1]; t1 = fun1; t2 = fun3; NCOPY(t1,t2,i); *t1++ = 1; *t1++ = 1; *t1++ = sign3 < 0 ? -3: 3; *s1 = t1-s1; goto Finished; } else if ( fun2[1] == fun3[1] ) { Over2: i = fun3[1]; t1 = fun2; t2 = fun3; NCOPY(t1,t2,i); *t1++ = 1; *t1++ = 1; *t1++ = sign3 < 0 ? -3: 3; *s2 = t1-s2; *ps1 = s2; goto Finished; } else if ( fun1[1] >= fun3[1] ) goto Over1; else if ( fun2[1] >= fun3[1] ) goto Over2; } else if ( AT.SortFloatMode == 1 ) { if ( fun1[1] >= fun3[1] ) goto Over1; else if ( fun3[1]+3 <= ABS(size2) ) goto Over2; } else if ( AT.SortFloatMode == 2 ) { if ( fun2[1] >= fun3[1] ) goto Over2; else if ( fun3[1]+3 <= ABS(size1) ) goto Over1; } /* Does not fit. Go to extension space. */ jj = fun1-s1; j = jj+fun3[1]+3; /* space needed */ if ( (S->sFill + j) >= S->sTop2 ) { GarbHand(); s1 = *ps1; /* new position of the term after the garbage collection */ fun1 = s1+jj; } t1 = S->sFill; for ( i = 0; i < jj; i++ ) *t1++ = s1[i]; i = fun3[1]; s1 = fun3; NCOPY(t1,s1,i); *t1++ = 1; *t1++ = 1; *t1++ = sign3 < 0 ? -3: 3; *ps1 = S->sFill; **ps1 = t1-*ps1; S->sFill = t1; Finished: *ps2 = 0; TermFree(fun3,"AddWithFloat"); AT.SortFloatMode = 0; if ( **ps1 > AM.MaxTer/((LONG)(sizeof(WORD))) ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex after addition in sort. MaxTermSize = %10l", AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } return(1); } /* #] AddWithFloat : #[ MergeWithFloat : Note that we always park the result on top of term1. This makes life easier, because the original AddRat in MergePatches does this as well. */ int MergeWithFloat(PHEAD WORD **interm1, WORD **interm2) { GETBIDENTITY WORD *coef1, *coef2, size1, size2, *fun1, *fun2, *fun3, *tt; WORD sign3,jj, *t1, *t2, i, *term1 = *interm1, *term2 = *interm2; int retval = 0; coef1 = term1+*term1; size1 = coef1[-1]; coef1 -= ABS(size1); coef2 = term2+*term2; size2 = coef2[-1]; coef2 -= ABS(size2); if ( AT.SortFloatMode == 3 ) { fun1 = term1+1; while ( fun1 < coef1 && fun1[0] != FLOATFUN ) fun1 += fun1[1]; fun2 = term2+1; while ( fun2 < coef2 && fun2[0] != FLOATFUN ) fun2 += fun2[1]; UnpackFloat(aux1,fun1); if ( size1 < 0 ) mpf_neg(aux1,aux1); UnpackFloat(aux2,fun2); if ( size2 < 0 ) mpf_neg(aux2,aux2); } else if ( AT.SortFloatMode == 1 ) { fun1 = term1+1; while ( fun1 < coef1 && fun1[0] != FLOATFUN ) fun1 += fun1[1]; UnpackFloat(aux1,fun1); if ( size1 < 0 ) mpf_neg(aux1,aux1); fun2 = coef2; RatToFloat(aux2,(UWORD *)coef2,size2); } else if ( AT.SortFloatMode == 2 ) { fun2 = term2+1; while ( fun2 < coef2 && fun2[0] != FLOATFUN ) fun2 += fun2[1]; fun1 = coef1; RatToFloat(aux1,(UWORD *)coef1,size1); UnpackFloat(aux2,fun2); if ( size2 < 0 ) mpf_neg(aux2,aux2); } else { MLOCK(ErrorMessageLock); MesPrint("Illegal value %d for AT.SortFloatMode in MergeWithFloat.",AT.SortFloatMode); MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } mpf_add(aux3,aux1,aux2); sign3 = mpf_sgn(aux3); /* Now check whether we can park the result on top of one of the input terms. */ if ( sign3 < 0 ) mpf_neg(aux3,aux3); fun3 = TermMalloc("MergeWithFloat"); PackFloat(fun3,aux3); if ( AT.SortFloatMode == 3 ) { if ( fun1[1] + ABS(size1) == fun3[1] + 3 ) { OnTopOf1: t1 = fun3; t2 = fun1; for ( i = 0; i < fun3[1]; i++ ) *t2++ = *t1++; *t2++ = 1; *t2++ = 1; *t2++ = sign3 < 0 ? -3: 3; retval = 1; } else if ( fun1[1] + ABS(size1) > fun3[1] + 3 ) { Shift1: t2 = term1 + *term1; tt = t2; *--t2 = sign3 < 0 ? -3: 3; *--t2 = 1; *--t2 = 1; t1 = fun3 + fun3[1]; for ( i = 0; i < fun3[1]; i++ ) *--t2 = *--t1; t1 = fun1; while ( t1 > term1 ) *--t2 = *--t1; *t2 = tt-t2; term1 = t2; retval = 1; } else { /* Here we have to move term1 to the left to make room. */ jj = fun3[1]-fun1[1]+3-ABS(size1); /* This is positive */ Over1: t2 = term1-jj; t1 = term1; while ( t1 < fun1 ) *t2++ = *t1++; term1 -= jj; *term1 += jj; for ( i = 0; i < fun3[1]; i++ ) *t2++ = fun3[i]; *t2++ = 1; *t2++ = 1; *t2++ = sign3 < 0 ? -3: 3; retval = 1; } } else if ( AT.SortFloatMode == 1 ) { if ( fun1[1] + ABS(size1) == fun3[1] + 3 ) goto OnTopOf1; else if ( fun1[1] + ABS(size1) > fun3[1] + 3 ) goto Shift1; else { jj = fun3[1]-fun1[1]+3-ABS(size1); /* This is positive */ goto Over1; } } else { /* Can only be 2, based on previous tests */ if ( fun3[1] + 3 == ABS(size1) ) goto OnTopOf1; else if ( fun3[1] + 3 < ABS(size1) ) goto Shift1; else { jj = fun3[1]+3-ABS(size1); /* This is positive */ goto Over1; } } *interm1 = term1; TermFree(fun3,"MergeWithFloat"); AT.SortFloatMode = 0; return(retval); } /* #] MergeWithFloat : #] Sorting : #[ MZV : The functions here allow the arbitrary precision calculation of MZV's and Euler sums. They are called when the functions mzv_ and/or euler_ are used and the evaluate statement is applied. The output is in a float_ function. The expand statement tries to express the functions in terms of a basis. The bases are the 'standard basis for the euler sums and the pushdown bases from the datamine, unless otherwise specified. #[ SimpleDelta : */ void SimpleDelta(mpf_t sum, int m) { long s = 1; long prec = AC.DefaultPrecision; unsigned long xprec = (unsigned long)prec, x; int j, jmax, n; mpf_t jm,jjm; mpf_init(jm); mpf_init(jjm); if ( m < 0 ) { s = -1; m = -m; } /* We will loop until 1/2^j/j^m is smaller than the default precision. Just running to prec is however overkill, specially when m is large. We try to estimate a better value. jmax = prec - ((log2(prec)-1)*m). Hence we need the leading bit of prec. We are still overshooting a bit. */ n = 0; x = xprec; while ( x ) { x >>= 1; n++; } /* We have now n = floor(log2(x))+1. */ n--; jmax = (int)((int)xprec - (n-1)*m); /* For small prec and large m, the estimate can be wrong and even be negative, so we increase jmax until jmax + m*log2(jmax) > prec */ if ( jmax < 0 ) jmax = 1; do { n = 0; x = (unsigned long)jmax; while (x) { x >>= 1; n++; } n--; // floor(log2(jmax)) jmax++; } while ( jmax + m * n <= prec ); mpf_set_ui(sum,0); for ( j = 1; j <= jmax; j++ ) { #ifdef WITHCUTOFF xprec--; mpf_set_prec_raw(jm,xprec); mpf_set_prec_raw(jjm,xprec); #endif mpf_set_ui(jm,1L); mpf_div_ui(jjm,jm,(unsigned long)j); mpf_pow_ui(jm,jjm,(unsigned long)m); mpf_div_2exp(jjm,jm,(unsigned long)j); if ( s == -1 && j%2 == 1 ) mpf_sub(sum,sum,jjm); else mpf_add(sum,sum,jjm); } mpf_clear(jjm); mpf_clear(jm); } /* #] SimpleDelta : #[ SimpleDeltaC : */ void SimpleDeltaC(mpf_t sum, int m) { long s = 1; long prec = AC.DefaultPrecision; unsigned long xprec = (unsigned long)prec, x; int j, jmax, n; mpf_t jm,jjm; mpf_init(jm); mpf_init(jjm); if ( m < 0 ) { s = -1; m = -m; } /* We will loop until 1/2^j/j^m is smaller than the default precision. Just running to prec is however overkill, specially when m is large. We try to estimate a better value. jmax = prec - ((log2(prec)-1)*m). Hence we need the leading bit of prec. We are still overshooting a bit. */ n = 0; x = xprec; while ( x ) { x >>= 1; n++; } /* We have now n = floor(log2(x))+1. */ n--; jmax = (int)((int)xprec - (n-1)*m); /* For small prec and large m, the estimate can be wrong and even be negative, so we increase jmax until jmax + m*log2(jmax) > prec */ if ( jmax < 0 ) jmax = 1; do { n = 0; x = (unsigned long)jmax; while (x) { x >>= 1; n++; } n--; // floor(log2(jmax)) jmax++; } while ( jmax + m * n <= prec ); if ( s < 0 ) jmax /= 2; mpf_set_si(sum,0L); for ( j = 1; j <= jmax; j++ ) { #ifdef WITHCUTOFF xprec--; mpf_set_prec_raw(jm,xprec); mpf_set_prec_raw(jjm,xprec); #endif mpf_set_ui(jm,1L); mpf_div_ui(jjm,jm,(unsigned long)j); mpf_pow_ui(jm,jjm,(unsigned long)m); if ( s == -1 ) mpf_div_2exp(jjm,jm,2*(unsigned long)j); else mpf_div_2exp(jjm,jm,(unsigned long)j); mpf_add(sum,sum,jjm); } mpf_clear(jjm); mpf_clear(jm); } /* #] SimpleDeltaC : #[ SingleTable : */ void SingleTable(mpf_t *tabl, int N, int m, int pow) { /* Creates a table T(1,...,N) with T(i) = sum_(j,i,N,[sign_(j)]/2^j/j^m) To make this table we have two options: 1: run the sum backwards with the potential problem that the precision is difficult to manage. 2: run the sum forwards. Take sum_(j,1,i-1,...) and later subtract. When doing Euler sums we may need also 1/4^j pow: 1 -> 1/2^j 2 -> 1/4^j */ GETIDENTITY long s = 1; int j; #ifdef WITHCUTOFF long prec = mpf_get_default_prec(); #endif mpf_t jm,jjm; mpf_init(jm); mpf_init(jjm); if ( pow < 1 || pow > 2 ) { MLOCK(ErrorMessageLock); MesPrint("Wrong parameter pow in SingleTable: %d\n",pow); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( m < 0 ) { m = -m; s = -1; } mpf_set_si(auxsum,0L); for ( j = N; j > 0; j-- ) { #ifdef WITHCUTOFF mpf_set_prec_raw(jm,prec-j); mpf_set_prec_raw(jjm,prec-j); #endif mpf_set_ui(jm,1L); mpf_div_ui(jjm,jm,(unsigned long)j); mpf_pow_ui(jm,jjm,(unsigned long)m); mpf_div_2exp(jjm,jm,pow*(unsigned long)j); if ( pow == 2 ) mpf_add(auxsum,auxsum,jjm); else if ( s == -1 && j%2 == 1 ) mpf_sub(auxsum,auxsum,jjm); else mpf_add(auxsum,auxsum,jjm); /* And now copy auxsum to tablelement j */ mpf_set(tabl[j],auxsum); } mpf_clear(jjm); mpf_clear(jm); } /* #] SingleTable : #[ DoubleTable : */ void DoubleTable(mpf_t *tabout, mpf_t *tabin, int N, int m, int pow) { GETIDENTITY long s = 1; #ifdef WITHCUTOFF long prec = mpf_get_default_prec(); #endif int j; mpf_t jm,jjm; mpf_init(jm); mpf_init(jjm); if ( pow < -1 || pow > 2 ) { MLOCK(ErrorMessageLock); MesPrint("Wrong parameter pow in DoubleTable: %d\n",pow); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( m < 0 ) { m = -m; s = -1; } mpf_set_ui(auxsum,0L); for ( j = N; j > 0; j-- ) { #ifdef WITHCUTOFF mpf_set_prec_raw(jm,prec-j); mpf_set_prec_raw(jjm,prec-j); #endif mpf_set_ui(jm,1L); mpf_div_ui(jjm,jm,(unsigned long)j); mpf_pow_ui(jm,jjm,(unsigned long)m); if ( pow == -1 ) { mpf_mul_2exp(jjm,jm,(unsigned long)j); mpf_mul(jm,jjm,tabin[j+1]); } else if ( pow > 0 ) { mpf_div_2exp(jjm,jm,pow*(unsigned long)j); mpf_mul(jm,jjm,tabin[j+1]); } else { mpf_mul(jm,jm,tabin[j+1]); } if ( pow == 2 ) mpf_add(auxsum,auxsum,jm); else if ( s == -1 && j%2 == 1 ) mpf_sub(auxsum,auxsum,jm); else mpf_add(auxsum,auxsum,jm); /* And now copy auxsum to tablelement j */ mpf_set(tabout[j],auxsum); } mpf_clear(jjm); mpf_clear(jm); } /* #] DoubleTable : #[ EndTable : */ void EndTable(mpf_t sum, mpf_t *tabin, int N, int m, int pow) { long s = 1; #ifdef WITHCUTOFF long prec = mpf_get_default_prec(); #endif int j; mpf_t jm,jjm; mpf_init(jm); mpf_init(jjm); if ( pow < -1 || pow > 2 ) { MLOCK(ErrorMessageLock); MesPrint("Wrong parameter pow in EndTable: %d\n",pow); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( m < 0 ) { m = -m; s = -1; } mpf_set_si(sum,0L); for ( j = N; j > 0; j-- ) { #ifdef WITHCUTOFF mpf_set_prec_raw(jm,prec-j); mpf_set_prec_raw(jjm,prec-j); #endif mpf_set_ui(jm,1L); mpf_div_ui(jjm,jm,(unsigned long)j); mpf_pow_ui(jm,jjm,(unsigned long)m); if ( pow == -1 ) { mpf_mul_2exp(jjm,jm,(unsigned long)j); mpf_mul(jm,jjm,tabin[j+1]); } else if ( pow > 0 ) { mpf_div_2exp(jjm,jm,pow*(unsigned long)j); mpf_mul(jm,jjm,tabin[j+1]); } else { mpf_mul(jm,jm,tabin[j+1]); } if ( s == -1 && j%2 == 1 ) mpf_sub(sum,sum,jm); else mpf_add(sum,sum,jm); } mpf_clear(jjm); mpf_clear(jm); } /* #] EndTable : #[ deltaMZV : */ void deltaMZV(mpf_t result, WORD *indexes, int depth) { GETIDENTITY /* Because all sums go roughly like 1/2^j we need about depth steps. */ /* MesPrint("deltaMZV(%a)",depth,indexes); */ if ( depth == 1 ) { if ( indexes[0] == 1 ) { mpf_set(result,mpfdelta1); return; } SimpleDelta(result,indexes[0]); } else if ( depth == 2 ) { if ( indexes[0] == 1 && indexes[1] == 1 ) { mpf_pow_ui(result,mpfdelta1,2); mpf_div_2exp(result,result,1); } else { SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+1,indexes[0],1); EndTable(result,mpftab1,AC.DefaultPrecision-AC.MaxWeight,indexes[1],0); }; } else if ( depth > 2 ) { mpf_t *mpftab3; int d; /* Check first whether this is a power of delta1 = ln(2) */ for ( d = 0; d < depth; d++ ) { if ( indexes[d] != 1 ) break; } if ( d == depth ) { /* divide by fac_(depth) */ mpf_pow_ui(result,mpfdelta1,depth); for ( d = 2; d <= depth; d++ ) { mpf_div_ui(result,result,(unsigned long)d); } } else { d = depth-1; SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+d,*indexes,1); d--; indexes++; for(;;) { DoubleTable(mpftab2,mpftab1,AC.DefaultPrecision-AC.MaxWeight+d,*indexes,0); d--; indexes++; if ( d == 0 ) { EndTable(result,mpftab2,AC.DefaultPrecision-AC.MaxWeight,*indexes,0); break; } mpftab3 = (mpf_t *)AT.mpf_tab1; AT.mpf_tab1 = AT.mpf_tab2; AT.mpf_tab2 = (void *)mpftab3; } } } else if ( depth == 0 ) { mpf_set_ui(result,1L); } } /* #] deltaMZV : #[ deltaEuler : Regular Euler delta with - signs, but everywhere 1/2^j */ void deltaEuler(mpf_t result, WORD *indexes, int depth) { GETIDENTITY int m; #ifdef DEBUG int i; printf(" deltaEuler("); for ( i = 0; i < depth; i++ ) { if ( i != 0 ) printf(","); printf("%d",indexes[i]); } printf(") = "); #endif if ( depth == 1 ) { SimpleDelta(result,indexes[0]); } else if ( depth == 2 ) { SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+1,indexes[0],1); m = indexes[1]; if ( indexes[0] < 0 ) m = -m; EndTable(result,mpftab1,AC.DefaultPrecision-AC.MaxWeight,m,0); } else if ( depth > 2 ) { int d; mpf_t *mpftab3; d = depth-1; SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+d,*indexes,1); d--; indexes++; m = *indexes; if ( indexes[-1] < 0 ) m = -m; for(;;) { DoubleTable(mpftab2,mpftab1,AC.DefaultPrecision-AC.MaxWeight+d,m,0); d--; indexes++; m = *indexes; if ( indexes[-1] < 0 ) m = -m; if ( d == 0 ) { EndTable(result,mpftab2,AC.DefaultPrecision-AC.MaxWeight,m,0); break; } mpftab3 = (mpf_t *)AT.mpf_tab1; AT.mpf_tab1 = AT.mpf_tab2; AT.mpf_tab2 = (void *)mpftab3; } } else if ( depth == 0 ) { mpf_set_ui(result,1L); } #ifdef DEBUG gmp_printf("%.*Fe\n",40,result); #endif } /* #] deltaEuler : #[ deltaEulerC : Conjugate Euler delta without - signs, but possibly 1/4^j When there is a - in the string we have 1/4. */ void deltaEulerC(mpf_t result, WORD *indexes, int depth) { GETIDENTITY int m; #ifdef DEBUG int i; printf(" deltaEulerC("); for ( i = 0; i < depth; i++ ) { if ( i != 0 ) printf(","); printf("%d",indexes[i]); } printf(") = "); #endif mpf_set_ui(result,0); if ( depth == 1 ) { if ( indexes[0] == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal index in depth=1 deltaEulerC: %d\n",indexes[0]); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( indexes[0] < 0 ) SimpleDeltaC(result,indexes[0]); else SimpleDelta(result,indexes[0]); } else if ( depth == 2 ) { int par; m = indexes[0]; if ( m < 0 ) SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+depth,-m,2); else SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+depth, m,1); m = indexes[1]; if ( m < 0 ) { m = -m; par = indexes[0] < 0 ? 0: 1; } else { par = indexes[0] < 0 ? -1: 0; } EndTable(result,mpftab1,AC.DefaultPrecision-AC.MaxWeight,m,par); } else if ( depth > 2 ) { int d, par; mpf_t *mpftab3; d = depth-1; m = indexes[0]; ZeroTable(mpftab1,AC.DefaultPrecision+1); if ( m < 0 ) SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+d+1,-m,2); else SingleTable(mpftab1,AC.DefaultPrecision-AC.MaxWeight+d+1, m,1); d--; indexes++; m = indexes[0]; if ( m < 0 ) { m = -m; par = indexes[-1] < 0 ? 0: 1; } else { par = indexes[-1] < 0 ? -1: 0; } for(;;) { ZeroTable(mpftab2,AC.DefaultPrecision-AC.MaxWeight+d); DoubleTable(mpftab2,mpftab1,AC.DefaultPrecision-AC.MaxWeight+d,m,par); d--; indexes++; m = indexes[0]; if ( m < 0 ) { m = -m; par = indexes[-1] < 0 ? 0: 1; } else { par = indexes[-1] < 0 ? -1: 0; } if ( d == 0 ) { mpf_set_ui(result,0); EndTable(result,mpftab2,AC.DefaultPrecision-AC.MaxWeight,m,par); break; } mpftab3 = (mpf_t *)AT.mpf_tab1; AT.mpf_tab1 = AT.mpf_tab2; AT.mpf_tab2 = (void *)mpftab3; } } else if ( depth == 0 ) { mpf_set_ui(result,1L); } #ifdef DEBUG gmp_printf("%.*Fe\n",40,result); #endif } /* #] deltaEulerC : #[ CalculateMZVhalf : This routine is mainly for support when large numbers of MZV's have to be calculated at the same time. */ void CalculateMZVhalf(mpf_t result, WORD *indexes, int depth) { int i; if ( depth < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal depth in CalculateMZVhalf: %d",depth); MUNLOCK(ErrorMessageLock); Terminate(-1); } for ( i = 0; i < depth; i++ ) { if ( indexes[i] <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal index[%d] in CalculateMZVhalf: %d",i,indexes[i]); MUNLOCK(ErrorMessageLock); Terminate(-1); } } deltaMZV(result,indexes,depth); } /* #] CalculateMZVhalf : #[ CalculateMZV : */ void CalculateMZV(mpf_t result, WORD *indexes, int depth) { GETIDENTITY int num1, num2 = 0, i, j = 0; if ( depth < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal depth in CalculateMZV: %d",depth); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( indexes[0] == 1 ) { MLOCK(ErrorMessageLock); MesPrint("Divergent MZV in CalculateMZV"); MUNLOCK(ErrorMessageLock); Terminate(-1); } /* MesPrint("calculateMZV(%a)",depth,indexes); */ for ( i = 0; i < depth; i++ ) { if ( indexes[i] <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal index[%d] in CalculateMZV: %d",i,indexes[i]); MUNLOCK(ErrorMessageLock); Terminate(-1); } AT.indi1[i] = indexes[i]; } num1 = depth; i = 0; deltaMZV(result,indexes,depth); for(;;) { if ( AT.indi1[0] > 1 ) { AT.indi1[0] -= 1; for ( j = num2; j > 0; j-- ) AT.indi2[j] = AT.indi2[j-1]; AT.indi2[0] = 1; num2++; } else { AT.indi2[0] += 1; for ( j = 1; j < num1; j++ ) AT.indi1[j-1] = AT.indi1[j]; num1--; if ( num1 == 0 ) break; } deltaMZV(aux1,AT.indi1,num1); deltaMZV(aux2,AT.indi2,num2); mpf_mul(aux3,aux1,aux2); mpf_add(result,result,aux3); } deltaMZV(aux3,AT.indi2,num2); mpf_add(result,result,aux3); } /* #] CalculateMZV : #[ CalculateEuler : There is a problem of notation here. Basically there are two notations. 1: Z(m1,m2,m3) = sum_(j3,1,inf,sign_(m3)/j3^abs_(m3)* sum_(j2,j3+1,inf,sign_(m2)/j2^abs_(m2)* sum_(j1,j2+1,inf,sign_(m1)/j1^abs_(m1)))) See Broadhurst,1996 2: L(m1,m2,m3) = sum_(j1,1,inf,sign_(m1)* sum_(j2,1,inf,sign_(m2)* sum_(j3,1,inf,sign_(m3) /j3^abs_(m3) /(j2+j3)^abs_(m2) /(j1+j2+j3)^abs_(m1) ))) See Borwein, Bradley, Broadhurst and Lisonek, 1999 The L corresponds with the H of the datamine up to sign_(m1*m2*m3) The algorithm follows 2, but the more common notation is 1. Hence we start with a conversion. */ void CalculateEuler(mpf_t result, WORD *Zindexes, int depth) { GETIDENTITY int s1, num1, num2, i, j; WORD *indexes = AT.WorkPointer; for ( i = 0; i < depth; i++ ) indexes[i] = Zindexes[i]; for ( i = 0; i < depth-1; i++ ) { if ( Zindexes[i] < 0 ) { for ( j = i+1; j < depth; j++ ) indexes[j] = -indexes[j]; } } if ( depth < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal depth in CalculateEuler: %d\n",depth); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( indexes[0] == 1 ) { MLOCK(ErrorMessageLock); MesPrint("Divergent Euler sum in CalculateEuler\n"); MUNLOCK(ErrorMessageLock); Terminate(-1); } for ( i = 0, j = 0; i < depth; i++ ) { if ( indexes[i] == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal index[%d] in CalculateEuler: %d\n",i,indexes[i]); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( indexes[i] < 0 ) j = 1; AT.indi1[i] = indexes[i]; } if ( j == 0 ) { CalculateMZV(result,indexes,depth); return; } num1 = depth; AT.indi2[0] = 0; num2 = 0; deltaEuler(result,AT.indi1,depth); s1 = 0; for(;;) { s1++; if ( AT.indi1[0] > 1 ) { AT.indi1[0] -= 1; for ( j = num2; j > 0; j-- ) AT.indi2[j] = AT.indi2[j-1]; AT.indi2[0] = 1; num2++; } else if ( AT.indi1[0] < -1 ) { AT.indi1[0] += 1; for ( j = num2; j > 0; j-- ) AT.indi2[j] = AT.indi2[j-1]; AT.indi2[0] = 1; num2++; } else if ( AT.indi1[0] == -1 ) { for ( j = num2; j > 0; j-- ) AT.indi2[j] = AT.indi2[j-1]; AT.indi2[0] = -1; num2++; for ( j = 1; j < num1; j++ ) AT.indi1[j-1] = AT.indi1[j]; num1--; } else { AT.indi2[0] = AT.indi2[0] < 0 ? AT.indi2[0]-1: AT.indi2[0]+1; for ( j = 1; j < num1; j++ ) AT.indi1[j-1] = AT.indi1[j]; num1--; } if ( num1 == 0 ) break; deltaEuler(aux1,AT.indi1,num1); deltaEulerC(aux2,AT.indi2,num2); mpf_mul(aux3,aux1,aux2); if ( (depth+num1+num2+s1)%2 == 0 ) mpf_add(result,result,aux3); else mpf_sub(result,result,aux3); } deltaEulerC(aux3,AT.indi2,num2); if ( (depth+num2+s1)%2 == 0 ) mpf_add(result,result,aux3); else mpf_sub(result,result,aux3); } /* #] CalculateEuler : #[ ExpandMZV : */ int ExpandMZV(WORD *term, WORD level) { DUMMYUSE(term); DUMMYUSE(level); return(0); } /* #] ExpandMZV : #[ ExpandEuler : */ int ExpandEuler(WORD *term, WORD level) { DUMMYUSE(term); DUMMYUSE(level); return(0); } /* #] ExpandEuler : #[ EvaluateEuler : There are various steps here: 1: locate an Euler function. 2: evaluate it into a float. 3: convert the coefficient to a float and multiply. 4: Put the new term together. 5: Restart to see whether there are more Euler functions. The compiler should check that there is no conflict between the evaluate command and a potential polyfun or polyratfun. Yet, when reading in expressions there can be a conflict. Hence the Normalize routine should check as well. par == MZV: MZV par == EULER: Euler par == MZVHALF: MZV sums in 1/2 rather than 1. -> deltaMZV. par == ALLMZVFUNCTIONS: all of the above. */ int EvaluateEuler(PHEAD WORD *term, WORD level, WORD par) { WORD *t, *tstop, *tt, *tnext, sumweight, depth, first = 1, *newterm, i; WORD *oldworkpointer = AT.WorkPointer, nsize, *indexes; int retval; tstop = term + *term; tstop -= ABS(tstop[-1]); if ( AT.WorkPointer < term+*term ) AT.WorkPointer = term + *term; /* Step 1. We also need to verify that the argument we find is legal */ t = term+1; while ( t < tstop ) { if ( ( *t == par ) || ( ( par == ALLMZVFUNCTIONS ) && ( *t == MZV || *t == EULER || *t == MZVHALF ) ) ) { /* all arguments should be small integers */ indexes = AT.WorkPointer; sumweight = 0; depth = 0; tnext = t + t[1]; tt = t + FUNHEAD; while ( tt < tnext ) { if ( *tt != -SNUMBER ) goto nextfun; if ( tt[1] == 0 ) goto nextfun; indexes[depth] = tt[1]; sumweight += ABS(tt[1]); depth++; tt += 2; } /* euler sum without arguments, i.e. mzv_(), euler_() or mzvhalf_() */ if ( depth == 0) goto nextfun; if ( sumweight > AC.MaxWeight ) { MLOCK(ErrorMessageLock); MesPrint("Error: Weight of Euler/MZV sum greater than %d.",AC.MaxWeight); MesPrint("Please increase the maximum weight in %#startfloat."); MUNLOCK(ErrorMessageLock); Terminate(-1); } /* Step 2: evaluate: */ AT.WorkPointer += depth; if ( first ) { if ( *t == MZV ) CalculateMZV(aux4,indexes,depth); else if ( *t == EULER ) CalculateEuler(aux4,indexes,depth); else if ( *t == MZVHALF ) CalculateMZVhalf(aux4,indexes,depth); first = 0; } else { if ( *t == MZV ) CalculateMZV(aux5,indexes,depth); else if ( *t == EULER ) CalculateEuler(aux5,indexes,depth); else if ( *t == MZVHALF ) CalculateMZVhalf(aux5,indexes,depth); mpf_mul(aux4,aux4,aux5); } *t = 0; } nextfun: t += t[1]; } if ( first == 1 ) return(Generator(BHEAD term,level)); /* Step 3: Now the regular coefficient, if it is not 1/1. We have two cases: size +- 3, or bigger. */ nsize = term[*term-1]; if ( nsize < 0 ) { mpf_neg(aux4,aux4); nsize = -nsize; } if ( nsize == 3 ) { if ( tstop[0] != 1 ) { mpf_mul_ui(aux4,aux4,(ULONG)((UWORD)tstop[0])); } if ( tstop[1] != 1 ) { mpf_div_ui(aux4,aux4,(ULONG)((UWORD)tstop[1])); } } else { RatToFloat(aux5,(UWORD *)tstop,nsize); mpf_mul(aux4,aux4,aux5); } /* Now we have to locate possible other float_ functions. */ t = term+1; while ( t < tstop ) { if ( *t == FLOATFUN ) { UnpackFloat(aux5,t); mpf_mul(aux4,aux4,aux5); } t += t[1]; } /* Now we should compose the new term in the WorkSpace. */ t = term+1; newterm = AT.WorkPointer; tt = newterm+1; while ( t < tstop ) { if ( *t == 0 || *t == FLOATFUN ) t += t[1]; else { i = t[1]; NCOPY(tt,t,i); } } PackFloat(tt,aux4); tt += tt[1]; *tt++ = 1; *tt++ = 1; *tt++ = 3; *newterm = tt-newterm; AT.WorkPointer = tt; retval = Generator(BHEAD newterm,level); AT.WorkPointer = oldworkpointer; return(retval); } /* #] EvaluateEuler : #] MZV : #[ Functions : #[ CoEvaluate : Current subkeys: mzv_, euler_ and sqrt_. */ int CoEvaluate(UBYTE *s) { GETIDENTITY UBYTE *subkey, c; WORD numfun, type; int error = 0; if ( AT.aux_ == 0 ) { MesPrint("&Illegal attempt to evaluate a function without activating floating point numbers."); MesPrint("&Forgotten %#startfloat instruction?"); return(1); } while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == 0 ) { /* No subkey, which means all functions. */ Add3Com(TYPEEVALUATE,ALLFUNCTIONS); /* The MZV, EULER and MZVHALF are done separately */ Add3Com(TYPEEVALUATE,ALLMZVFUNCTIONS); return(0); } while ( *s ) { subkey = s; while ( FG.cTable[*s] == 0 ) s++; if ( *s == '2' ) s++; /* cases li2_ and atan2_ */ if ( *s == '_' ) s++; c = *s; *s = 0; /* We still need provisions for pi_ and possibly other constants. */ if ( ( ( type = GetName(AC.varnames,subkey,&numfun,NOAUTO) ) != CFUNCTION ) || ( functions[numfun].spec != 0 ) ) { if ( type == CSYMBOL ) { Add4Com(TYPEEVALUATE,SYMBOL,numfun); break; } /* This cannot work. */ MesPrint("&%s should be a built in function that can be evaluated numerically.",s); return(1); } else { switch ( numfun+FUNCTION ) { case MZV: case EULER: case MZVHALF: /* The following functions are treated in evaluate.c */ case SQRTFUNCTION: case LNFUNCTION: case EXPFUNCTION: case SINFUNCTION: case COSFUNCTION: case TANFUNCTION: case ASINFUNCTION: case ACOSFUNCTION: case ATANFUNCTION: case ATAN2FUNCTION: case SINHFUNCTION: case COSHFUNCTION: case TANHFUNCTION: case ASINHFUNCTION: case ACOSHFUNCTION: case ATANHFUNCTION: case LI2FUNCTION: case LINFUNCTION: case AGMFUNCTION: case GAMMAFUN: /* At a later stage we can add more functions from mpfr here mpfr_(number,arg(s)) */ Add3Com(TYPEEVALUATE,numfun+FUNCTION); break; default: MesPrint("&%s should be a built in function that can be evaluated numerically.",s); error = 1; break; } } *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; } return(error); } /* #] CoEvaluate : #] Functions : */ form-5.0.1/sources/evaluate.c0000644000175100017510000005022015217035721011602 /** @file evaluate.c * * Evaluation of functions for the floating-point system, by interfacing with MPFR. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ includes : */ #include "form3.h" #include #include #define EXTRAPRECISION 4 #define RND MPFR_RNDN #define auxr1 (((mpfr_t *)(AT.auxr_))[0]) #define auxr2 (((mpfr_t *)(AT.auxr_))[1]) #define auxr3 (((mpfr_t *)(AT.auxr_))[2]) #define auxr4 (((mpfr_t *)(AT.auxr_))[3]) #define auxr5 (((mpfr_t *)(AT.auxr_))[4]) mpf_t ln2; int PackFloat(WORD *,mpf_t); int UnpackFloat(mpf_t,WORD *); void RatToFloat(mpf_t, UWORD *, int); void FormtoZ(mpz_t,UWORD *,WORD); /* #] includes : #[ mpfr_ : #[ IntegerToFloatr : Converts a Form long integer to a mpfr_ float of default size. We assume that sizeof(unsigned long int) = 2*sizeof(UWORD). */ void IntegerToFloatr(mpfr_t result, UWORD *formlong, int longsize) { mpz_t z; mpz_init(z); FormtoZ(z,formlong,longsize); mpfr_set_z(result,z,RND); mpz_clear(z); } /* #] IntegerToFloatr : #[ RatToFloatr : Converts a Form rational to a gmp float of default size. */ void RatToFloatr(mpfr_t result, UWORD *formrat, int ratsize) { GETIDENTITY int nnum, nden; UWORD *num, *den; int sgn = 0; if ( ratsize < 0 ) { ratsize = -ratsize; sgn = 1; } nnum = nden = (ratsize-1)/2; num = formrat; den = formrat+nnum; while ( nnum > 1 && num[nnum-1] == 0 ) { nnum--; } while ( nden > 1 && den[nden-1] == 0 ) { nden--; } IntegerToFloatr(auxr4,num,nnum); IntegerToFloatr(auxr5,den,nden); mpfr_div(result,auxr4,auxr5,RND); if ( sgn > 0 ) mpfr_neg(result,result,RND); } /* #] RatToFloatr : #[ SetfFloatPrecision : The AC.DefaultPrecision is in bits. prec is in limbs. fprec is NOT in bits for mpfr_ which is slightly less than in mpf_ We also set the auxr1,auxr2,auxr3,auxr4,auxr5 variables. */ void SetfFloatPrecision(LONG prec) { /* mpfr_prec_t fprec = prec * mp_bits_per_limb - EXTRAPRECISION; */ mpfr_prec_t fprec = prec + 1; mpfr_set_default_prec(fprec); #ifdef WITHPTHREADS int totnum = AM.totalnumberofthreads, id; mpfr_t *a; #ifdef WITHSORTBOTS totnum = MaX(2*AM.totalnumberofthreads-3,AM.totalnumberofthreads); #endif for ( id = 0; id < totnum; id++ ) { AB[id]->T.auxr_ = (void *)Malloc1(sizeof(mpfr_t)*5,"AB[id]->T.auxr_"); a = (mpfr_t *)AB[id]->T.auxr_; /* We work here with a[0] etc because the aux1 etc contain B which in the current routine would be AB[0] only */ mpfr_inits2(fprec,a[0],a[1],a[2],a[3],a[4],(mpfr_ptr)0); } #else AT.auxr_ = (void *)Malloc1(sizeof(mpfr_t)*5,"AT.auxr_"); mpfr_inits2(fprec,auxr1,auxr2,auxr3,auxr4,auxr5,(mpfr_ptr)0); #endif } /* #] SetfFloatPrecision : #[ ClearfFloat : */ void ClearfFloat(void) { #ifdef WITHPTHREADS int totnum = AM.totalnumberofthreads, id; mpfr_t *a; #ifdef WITHSORTBOTS totnum = MaX(2*AM.totalnumberofthreads-3,AM.totalnumberofthreads); #endif if ( AB[0]->T.auxr_ ) { for ( id = 0; id < totnum; id++ ) { a = (mpfr_t *)AB[id]->T.auxr_; mpfr_clears(a[0],a[1],a[2],a[3],a[4],(mpfr_ptr)0); M_free(AB[id]->T.auxr_,"AB[id]->T.auxr_"); AB[id]->T.auxr_ = 0; } } #else if ( AT.auxr_ ) { mpfr_clears(auxr1,auxr2,auxr3,auxr4,auxr5,(mpfr_ptr)0); M_free(AT.auxr_,"AT.auxr_"); AT.auxr_ = 0; } #endif } /* #] ClearfFloat : #[ GetFloatArgument : Convert an argument to an mpfr float if possible. Return value: 0: was converted successfully. -1: could not convert. Note: arguments with more than one term should be evaluated first inside an Argument environment. If there is still more than one term remaining we get the code: "could not convert". par tells which argument we need. If it is negative it should also be the last argument. */ int GetFloatArgument(PHEAD mpfr_t f_out,WORD *fun,int par) { WORD *term, *tn, *t, *tstop, first, ncoef, *arg, *argp, abspar; arg = fun+FUNHEAD; abspar = ABS(par); while ( arg < fun+fun[1] && abspar > 1 ) { abspar--; NEXTARG(arg) } if ( arg >= fun+fun[1] || abspar!= 1 ) return(-1); if ( par < 0 ) { argp = arg; NEXTARG(argp); if ( argp != fun+fun[1] ) return(-1); } if ( *arg < 0 ) { if ( *arg == -SNUMBER ) { mpfr_set_si(f_out,(LONG)(arg[1]),RND); } else if ( *arg == -SYMBOL && ( arg[1] == PISYMBOL ) ) { mpfr_const_pi(f_out,RND); } else if ( *arg == -INDEX && arg[1] >= 0 && arg[1] < AM.OffsetIndex ) { mpfr_set_ui(f_out,(ULONG)(arg[1]),RND); } else { return(-1); } return(0); } else if ( arg[0] != arg[ARGHEAD]+ARGHEAD ) { /* more than one term */ return(-1); } term = arg+ARGHEAD; tn = term+*term; tstop = tn-ABS(tn[-1]); t = term+1; first = 1; while ( t <= tstop ) { if ( t == tstop ) { /* Fraction */ if ( first ) RatToFloatr(f_out,(UWORD *)tstop,tn[-1]); else { RatToFloatr(auxr4,(UWORD *)tstop,tn[-1]); mpfr_mul(f_out,f_out,auxr4,RND); } return(0); } else if ( *t == FLOATFUN ) { if ( t+t[1] != tstop ) return(-1); if ( UnpackFloat(aux5,t) < 0 ) return(-1); if ( first ) { mpfr_set_f(f_out,aux5,RND); first = 0; } else { mpfr_set_f(auxr4,aux5,RND); mpfr_mul(f_out,f_out,auxr4,RND); } first = 0; if ( tn[-1] < 0 ) { /* change sign */ ncoef = -tn[-1]; mpfr_neg(f_out,f_out,RND); } else ncoef = tn[-1]; if ( ncoef == 3 && tn[-2] == 1 && tn[-3] == 1 ) return(0); /* If the argument was properly normalized we are not supposed to come here. */ MLOCK(ErrorMessageLock); MesPrint("Unnormalized argument in GetFloatArgument: %a",*term,term); MUNLOCK(ErrorMessageLock); Terminate(-1); } else if ( t[0] == SYMBOL && t[1] == 4 && t[2] == PISYMBOL && t[3] == 1 ) { if ( first ) { mpfr_const_pi(f_out,RND); first = 0; } else { mpfr_const_pi(auxr5,RND); mpfr_mul(f_out,f_out,auxr5,RND); } } else { /* This we do not / cannot do */ return(-1); } t += t[1]; } return(0); } /* #] GetFloatArgument : #[ GetPiArgument : Tests for sin,cos,tan whether the argument is a simple multiple of pi or can be reduced to such. Return value: -1: the answer is no. 0-23: we have 0, 1/12*pi_,...,23/12*pi_ With success most values can be worked out by simple means. */ int GetPiArgument(PHEAD WORD *arg) { UWORD *coef, *co, *tco, twelve, *numer, *denom, *c, *d; WORD i, ii, i2, iflip, nc, nd, *t, *tn, *tstop; int rem; /* One: determine whether there is a rational coefficient and a pi_: */ if ( *arg == -SNUMBER && arg[1] == 0 ) return(0); if ( *arg == -SYMBOL && arg[1] == PISYMBOL ) return(12); if ( *arg < 0 ) return(-1); if ( arg[ARGHEAD] != *arg-ARGHEAD ) return(-1); t = arg+ARGHEAD+1; tn = arg+*arg; tstop = tn - ABS(tn[-1]); if ( *t != SYMBOL || t[1] != 4 || t[2] != PISYMBOL || t[3] != 1 || t+t[1] != tstop ) return(-1); /* The denominator must be a divisor of 12 1: copy the coefficient */ co = coef = NumberMalloc("GetPiArgument"); tco = (UWORD *)tstop; i = tn[-1]; if ( i < 0 ) { i = -i; iflip = 1; } else iflip = 0; ii = (i-1)/2; twelve = 12; NCOPY(co,tco,i); co = coef; Mully(BHEAD co,&ii,&twelve,1); /* Now the denominator should be 1 */ i = ii; i2 = i-1; numer = co; denom = numer + i; if ( i > 1 ) { while ( i2 > 0 ) { if ( denom[i2--] != 0 ) { NumberFree(co,"GetPiArgument"); return(-1); } } } if ( *denom != 1 ) { NumberFree(co,"GetPiArgument"); return(-1); } /* Now we need the numerator modulus 24. */ if ( i == 1 ) { rem = *numer % 24; } else { c = NumberMalloc("GetPiArgument"); d = NumberMalloc("GetPiArgument"); twelve *= 2; DivLong(numer,i,&twelve,1,c,&nc,d,&nd); rem = *d % 24; NumberFree(d,"GetPiArgument"); NumberFree(c,"GetPiArgument"); } NumberFree(co,"GetPiArgument"); if ( iflip && rem != 0 ) rem = 24-rem; return(rem); } /* #] GetPiArgument : #[ EvaluateFun : What we need to do is: 1: look for a function to be treated. 2: make sure its argument is treatable. 3: call the proper mpfr_ function. 4: accumulate the result. For some functions we have to insert 'smart' shortcuts as is the case with sin_(pi_) or sin_(pi_/6) of sqrt(4/9) etc. Otherwise we may have to insert a value for pi_ first. There are several types of arguments: a: (short) integers. b: rationals. c: floats. We accumulate the result(s) in auxr2. The argument comes in aux5 and a result in auxr3 which then gets multiplied into auxr2. In the end we have to combine auxr2 with whatever coefficient existed already. When the float system is started we need for aux only 3 variables per thread. auxr1-auxr3. This should be done separately. The main problem is the conversion of mpfr_t to float_ and/or mpf_t and back. */ int EvaluateFun(PHEAD WORD *term, WORD level, WORD *pars) { WORD *t, *tstop, *tt, *tnext, *newterm, i; WORD *oldworkpointer = AT.WorkPointer, nsize, nsgn, nsgn2; int retval = 0, first = 1, pimul; tstop = term + *term; tstop -= ABS(tstop[-1]); if ( AT.WorkPointer < term+*term ) AT.WorkPointer = term + *term; t = term+1; mpfr_set_ui(auxr2,1L,RND); while ( t < tstop ) { if ( pars[2] == *t ) { /* have to do this one if possible */ TestArgument: /* There must be a single argument, except for the AGM or atan2 functions */ tnext = t+t[1]; tt = t+FUNHEAD; NEXTARG(tt); if( *t == SYMBOL) { for ( WORD* ti = t+2; ti < t+t[1]; ti+=2 ) { if( ( *ti == PISYMBOL || *ti == EESYMBOL || *ti == EMSYMBOL ) && ( pars[2] == ALLFUNCTIONS || pars[3] == *ti ) ) { if ( *ti == PISYMBOL ) mpfr_const_pi(auxr3,RND); else if ( *ti == EESYMBOL ) { mpfr_set_ui(auxr3,1,RND); mpfr_exp(auxr3,auxr3,RND); } else if ( *ti == EMSYMBOL ) mpfr_const_euler(auxr3,RND); if ( ti[1] != 1 ) mpfr_pow_si(auxr3,auxr3,ti[1],RND); mpfr_mul(auxr2,auxr2,auxr3,RND); ti[1] = 0; first = 0; } } goto nextfun; } if ( tt != tnext && *t != AGMFUNCTION && *t != ATAN2FUNCTION) goto nextfun; if ( *t == SINFUNCTION ) { pimul = GetPiArgument(BHEAD t+FUNHEAD); if ( pimul >= 0 && pimul < 24 ) { if ( pimul == 0 || pimul == 12 ) goto getout; if ( pimul > 12 ) { pimul = 24-pimul; nsgn = -1; } else nsgn = 1; if ( pimul > 6 ) pimul = 12-pimul; switch ( pimul ) { case 1: label1: mpfr_sqrt_ui(auxr3,3L,RND); mpfr_sub_ui(auxr3,auxr3,1L,RND); mpfr_sqrt_ui(auxr1,2L,RND); mpfr_div_ui(auxr1,auxr1,4L,RND); mpfr_mul(auxr3,auxr3,auxr1,RND); if ( nsgn < 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case 2: label2: mpfr_div_ui(auxr2,auxr2,2L,RND); if ( nsgn < 0 ) mpfr_neg(auxr2,auxr2,RND); break; case 3: label3: mpfr_sqrt_ui(auxr3,2L,RND); mpfr_div_ui(auxr3,auxr3,2L,RND); if ( nsgn < 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case 4: label4: mpfr_sqrt_ui(auxr3,3L,RND); mpfr_div_ui(auxr3,auxr3,2L,RND); if ( nsgn < 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case 5: label5: mpfr_sqrt_ui(auxr3,3L,RND); mpfr_add_ui(auxr3,auxr3,1L,RND); mpfr_sqrt_ui(auxr1,2L,RND); mpfr_div_ui(auxr1,auxr1,4L,RND); mpfr_mul(auxr3,auxr3,auxr1,RND); if ( nsgn < 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case 6: label6: if ( nsgn < 0 ) mpfr_neg(auxr2,auxr2,RND); break; } *t = 0; first = 0; goto nextfun; } } else if ( *t == COSFUNCTION ) { pimul = GetPiArgument(BHEAD t+FUNHEAD); if ( pimul >= 0 && pimul < 24 ) { if ( pimul > 12 ) pimul = 24-pimul; if ( pimul > 6 ) { pimul = 12-pimul; nsgn = -1; } else nsgn = 1; if ( pimul == 6 ) goto getout; switch ( pimul ) { case 0: goto label6; case 1: goto label5; case 2: goto label4; case 3: goto label3; case 4: goto label2; case 5: goto label1; } } } else if ( *t == TANFUNCTION ) { pimul = GetPiArgument(BHEAD t+FUNHEAD); if ( pimul >= 0 && pimul < 24 ) { if ( pimul == 6 || pimul == 18 ) goto nextfun; if ( pimul == 0 || pimul == 12 ) goto getout; if ( pimul > 12 ) { pimul = 24-pimul; nsgn = -1; } else nsgn = 1; if ( pimul > 6 ) { pimul = 12-pimul; nsgn = -nsgn; } switch ( pimul ) { case 1: mpfr_sqrt_ui(auxr3,3L,RND); mpfr_sub_ui(auxr3,auxr3,2L,RND); if ( nsgn > 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case 2: mpfr_sqrt_ui(auxr3,3L,RND); mpfr_div_ui(auxr3,auxr3,3L,RND); if ( nsgn < 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case 3: break; case 4: mpfr_sqrt_ui(auxr3,3L,RND); if ( nsgn < 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case 5: mpfr_sqrt_ui(auxr3,3L,RND); mpfr_add_ui(auxr3,auxr3,2L,RND); if ( nsgn < 0 ) mpfr_neg(auxr3,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; } *t = 0; first = 0; goto nextfun; } } if ( *t == AGMFUNCTION || *t == ATAN2FUNCTION ) { if ( GetFloatArgument(BHEAD auxr1,t,1) < 0 ) goto nextfun; if ( GetFloatArgument(BHEAD auxr3,t,-2) < 0 ) goto nextfun; } else if ( GetFloatArgument(BHEAD auxr1,t,-1) < 0 ) goto nextfun; nsgn = mpfr_sgn(auxr1); switch ( *t ) { case SQRTFUNCTION: if ( nsgn < 0 ) goto nextfun; if ( nsgn == 0 ) goto getout; else mpfr_sqrt(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case LNFUNCTION: if ( nsgn <= 0 ) goto nextfun; if ( mpfr_cmp_ui(auxr1,1L) == 0 ) goto getout; else mpfr_log(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case EXPFUNCTION: mpfr_exp(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case LI2FUNCTION: /* should be between -1 and +1 */ if ( nsgn == 0 ) goto getout; mpfr_abs(auxr3,auxr1,RND); if ( mpfr_cmp_ui(auxr3,1L) > 0 ) goto nextfun; mpfr_li2(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case GAMMAFUN: /* We cannot do this when the argument is a non-positive integer */ if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] <= 0 ) goto nextfun; if ( t[FUNHEAD] == t[1]-FUNHEAD && ABS(t[t[1]-1]) == t[FUNHEAD]-ARGHEAD-1 && t[t[1]-1] < 0 ) { nsize = (-t[t[1]-1]-1)/2; if ( t[t[1]-1-nsize] == 1 ) { for ( i = 1; i < nsize; i++ ) { if ( t[t[1]-1-nsize+i] != 0 ) break; } if ( i >= nsize ) goto nextfun; } } mpfr_gamma(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case AGMFUNCTION: nsgn = mpfr_sgn(auxr1); nsgn2 = mpfr_sgn(auxr3); if ( nsgn == 0 || nsgn2 == 0) goto getout; if ( nsgn < 0 || nsgn2 < 0 ) goto nextfun; mpfr_agm(auxr3,auxr1,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case SINHFUNCTION: if ( nsgn == 0 ) goto getout; mpfr_sinh(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case COSHFUNCTION: mpfr_cosh(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case TANHFUNCTION: if ( nsgn == 0 ) goto getout; mpfr_tanh(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case ASINHFUNCTION: if ( nsgn == 0 ) goto getout; mpfr_asinh(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case ACOSHFUNCTION: if ( mpfr_cmp_ui(auxr1,1L) < 0 ) goto nextfun; if ( mpfr_cmp_ui(auxr1,1L) == 0 ) goto getout; mpfr_acosh(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case ATANHFUNCTION: if ( nsgn == 0 ) goto getout; mpfr_abs(auxr3,auxr1,RND); if ( mpfr_cmp_ui(auxr3,1L) >= 0 ) goto nextfun; mpfr_atanh(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case ASINFUNCTION: if ( nsgn == 0 ) goto getout; mpfr_abs(auxr3,auxr1,RND); if ( mpfr_cmp_ui(auxr3,1L) > 0 ) goto nextfun; mpfr_asin(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case ACOSFUNCTION: if ( mpfr_cmp_ui(auxr1,1L) == 0 ) goto getout; mpfr_abs(auxr3,auxr1,RND); if ( mpfr_cmp_ui(auxr3,1L) > 0 ) goto nextfun; mpfr_acos(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case ATANFUNCTION: if ( nsgn == 0 ) goto getout; mpfr_atan(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case ATAN2FUNCTION: nsgn = mpfr_sgn(auxr1); nsgn2 = mpfr_sgn(auxr3); // We follow the conventions of mpfr here: if ( nsgn == 0 && nsgn2 >= 0) goto getout; mpfr_atan2(auxr3,auxr1,auxr3,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case SINFUNCTION: mpfr_sin(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case COSFUNCTION: mpfr_cos(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; case TANFUNCTION: mpfr_tan(auxr3,auxr1,RND); mpfr_mul(auxr2,auxr2,auxr3,RND); break; default: goto nextfun; break; } first = 0; *t = 0; goto nextfun; } else if ( pars[2] == ALLFUNCTIONS ) { /* Now we have to test whether this is one of our functions */ if ( t[1] == FUNHEAD ) goto nextfun; switch ( *t ) { case SQRTFUNCTION: case LNFUNCTION: case LI2FUNCTION: case LINFUNCTION: case EXPFUNCTION: case ASINFUNCTION: case ACOSFUNCTION: case ATANFUNCTION: case ATAN2FUNCTION: case SINHFUNCTION: case COSHFUNCTION: case TANHFUNCTION: case ASINHFUNCTION: case ACOSHFUNCTION: case ATANHFUNCTION: case SINFUNCTION: case COSFUNCTION: case TANFUNCTION: case AGMFUNCTION: case SYMBOL: goto TestArgument; case MZV: case EULER: case MZVHALF: default: goto nextfun; } } else goto nextfun; nextfun: t += t[1]; } if ( first == 1 ) return(Generator(BHEAD term,level)); mpfr_get_f(aux4,auxr2,RND); /* Step 3: Now the regular coefficient, if it is not 1/1. We have two cases: size +- 3, or bigger. */ nsize = term[*term-1]; if ( nsize < 0 ) { nsize = -nsize; nsgn = -1; } else nsgn = 1; if ( aux4->_mp_size < 0 ) { aux4->_mp_size = -aux4->_mp_size; nsgn = -nsgn; } if ( nsize == 3 ) { if ( tstop[0] != 1 ) { mpf_mul_ui(aux4,aux4,(ULONG)((UWORD)tstop[0])); } if ( tstop[1] != 1 ) { mpf_div_ui(aux4,aux4,(ULONG)((UWORD)tstop[1])); } } else { RatToFloat(aux5,(UWORD *)tstop,nsize); mpf_mul(aux4,aux4,aux5); } /* Now we have to locate possible other float_ functions. Note possible incompatibilities between the mpf and mpfr formats. */ t = term+1; while ( t < tstop ) { if ( *t == FLOATFUN ) { UnpackFloat(aux5,t); mpf_mul(aux4,aux4,aux5); } t += t[1]; } /* Now we should compose the new term in the WorkSpace. */ t = term+1; newterm = AT.WorkPointer; tt = newterm+1; while ( t < tstop ) { if ( *t == 0 || *t == FLOATFUN ) t += t[1]; else { i = t[1]; NCOPY(tt,t,i); } } PackFloat(tt,aux4); tt += tt[1]; *tt++ = 1; *tt++ = 1; *tt++ = 3*nsgn; *newterm = tt-newterm; AT.WorkPointer = tt; retval = Generator(BHEAD newterm,level); getout: AT.WorkPointer = oldworkpointer; return(retval); } /* #] EvaluateFun : #] mpfr_ : */ form-5.0.1/sources/startup.c0000644000175100017510000017643515217035721011517 /** @file startup.c * * This file contains the main program. * It also deals with the very early stages of the startup of FORM * and the final stages when the program attempts some cleanup. * Here is the routine that analyses the command tail. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ includes : */ #include "form3.h" #include "inivar.h" #ifdef TRAPSIGNALS #include "portsignals.h" #else #include #endif #ifdef ENABLE_BACKTRACE #include #ifdef LINUX #include #include #endif #endif /* * A macro for translating the contents of `x' into a string after expanding. */ #define STRINGIFY(x) STRINGIFY__(x) #define STRINGIFY__(x) #x /* * FORMNAME = "FORM" or "TFORM" or "ParFORM". */ #if defined(WITHPTHREADS) #define FORMNAME "TFORM" #elif defined(WITHMPI) #define FORMNAME "ParFORM" #else #define FORMNAME "FORM" #endif /* * VERSIONSTR is the version information printed in the header line. */ #ifdef HAVE_CONFIG_H /* We have also version.h. */ #include "version.h" #ifndef REPO_VERSION #define REPO_VERSION STRINGIFY(REPO_MAJOR_VERSION) "." STRINGIFY(REPO_MINOR_VERSION) "." STRINGIFY(REPO_PATCH_VERSION) #endif #ifndef REPO_DATE /* The build date, instead of the repo date. */ #define REPO_DATE __DATE__ #endif #ifdef REPO_REVISION #define VERSIONSTR FORMNAME " " REPO_VERSION " (" REPO_DATE ", " REPO_REVISION ")" #else #define VERSIONSTR FORMNAME " " REPO_VERSION " (" REPO_DATE ")" #endif #define MAJORVERSION REPO_MAJOR_VERSION #define MINORVERSION REPO_MINOR_VERSION #define PATCHVERSION REPO_PATCH_VERSION #else /* * Otherwise, form3.h defines MAJORVERSION, MINORVERSION, PATCHVERSION * and PRODUCTIONDATE, possibly BETAVERSION. */ #ifdef BETAVERSION #define VERSIONSTR__ STRINGIFY(MAJORVERSION) "." STRINGIFY(MINORVERSION) "." STRINGIFY(PATCHVERSION) "Beta" #else #define VERSIONSTR__ STRINGIFY(MAJORVERSION) "." STRINGIFY(MINORVERSION) "." STRINGIFY(PATCHVERSION) #endif #define VERSIONSTR FORMNAME " " VERSIONSTR__ " (" PRODUCTIONDATE ")" #endif /* #] includes : #[ PrintHeader : */ /** * Prints build information. * * @note As a configure-time assumption, the C and C++ compilers are from * the same vendor and have the same version. */ static void PrintBuildInfo(void) { #if defined(__INTEL_LLVM_COMPILER) MesPrint("Compiler: Intel LLVM oneAPI %d",__INTEL_LLVM_COMPILER); #elif defined(__INTEL_COMPILER) MesPrint("Compiler: Intel Classic %d",__INTEL_COMPILER); #elif defined(__clang__) && defined(__apple_build_version__) MesPrint("Compiler: Apple Clang %d.%d.%d (build %d)",__clang_major__,__clang_minor__,__clang_patchlevel__,__apple_build_version__); #elif defined(__clang__) MesPrint("Compiler: Clang %d.%d.%d",__clang_major__,__clang_minor__,__clang_patchlevel__); #elif defined(__GNUC__) MesPrint("Compiler: GCC %d.%d.%d",__GNUC__,__GNUC_MINOR__,__GNUC_PATCHLEVEL__); #elif defined(_MSC_VER) MesPrint("Compiler: MSVC %d",_MSC_VER); #else MesPrint("Compiler: Unknown"); #endif #if defined(__x86_64__) || defined(_M_X64) MesPrint("Architecture: x86_64"); #elif defined(__i386__) || defined(_M_IX86) MesPrint("Architecture: x86 (32-bit)"); #elif defined(__aarch64__) || defined(_M_ARM64) MesPrint("Architecture: arm64"); #elif defined(__arm__) || defined(_M_ARM) MesPrint("Architecture: arm (32-bit)"); #else MesPrint("Architecture: Unknown"); #endif } /** * Prints the header line of the output. * * @param par Controls the output mode * (0: default, * 1: including runtime information, * 2: including verbose version information). */ static void PrintHeader(int par) { #ifdef WITHMPI if ( PF.me == MASTER && !AM.silent ) { #else if ( !AM.silent ) { #endif char buffer1[250], buffer2[80], *s = buffer1, *t = buffer2; WORD length, n; for ( n = 0; n < 250; n++ ) buffer1[n] = ' '; /* * NOTE: we expect that the compiler optimizes strlen("string literal") * to just a number. */ if ( strlen(VERSIONSTR) <= 100 ) { strcpy(s,VERSIONSTR); s += strlen(VERSIONSTR); *s = 0; } else { /* * Truncate when it is too long. */ strncpy(s,VERSIONSTR,97); s[97] = '.'; s[98] = '.'; s[99] = ')'; s[100] = '\0'; s += 100; } /* By now we omit the message about 32/64 bits. It should all be 64. s += snprintf(s,250-(s-buffer1)," %d-bits",(WORD)(sizeof(WORD)*16)); *s = 0; */ if ( par == 1 ) { #if defined(WITHPTHREADS) || defined(WITHMPI) #if defined(WITHPTHREADS) int nworkers = AM.totalnumberofthreads-1; #elif defined(WITHMPI) int nworkers = PF.numtasks-1; #endif s += snprintf(s,250-(s-buffer1)," %d worker",nworkers); *s = 0; /* while ( *s ) s++; */ if ( nworkers != 1 ) { *s++ = 's'; *s = '\0'; } #endif snprintf(t,80-(t-buffer2),"Run: %s",MakeDate()); while ( *t ) t++; /* * Align the date to the right, if it fits in a line. */ length = (s-buffer1) + (t-buffer2); if ( length+2 <= AC.LineLength ) { for ( n = AC.LineLength-length; n > 0; n-- ) *s++ = ' '; *s = 0; strcat(s,buffer2); while ( *s ) s++; } else { *s = 0; strcat(s," "); while ( *s ) s++; *s = 0; strcat(s,buffer2); while ( *s ) s++; } } /* * If the header information doesn't fit in a line, we need to extend * the line length temporarily. */ length = s-buffer1; if ( length <= AC.LineLength ) { MesPrint("%s",buffer1); } else { WORD oldLineLength = AC.LineLength; AC.LineLength = length; MesPrint("%s",buffer1); AC.LineLength = oldLineLength; } if ( par == 2 ) { PrintFeatureList(); PrintBuildInfo(); } } #ifdef WINDOWS PrintDeprecation("the native Windows version", "issues/623"); #endif #if BITSINWORD == 16 PrintDeprecation("the 32-bit version", "issues/624"); #endif #ifdef WITHMPI PrintDeprecation("the MPI version (ParFORM)", "issues/625"); #endif if ( AC.CheckpointFlag ) { PrintDeprecation("the checkpoint mechanism", "issues/626"); } } /* #] PrintHeader : #[ DoTail : Routine reads the command tail and handles the commandline options. It sets the flags for later actions and stored pathnames for the setup file, include/prc/sub directories etc. Finally the name of the program is passed on. Note that we do not support interactive use yet. This will come to pass in the distant future when we can couple STedi to FORM. Routine made 23-feb-1993 by J.Vermaseren */ #ifdef WITHINTERACTION static UBYTE deflogname[] = "formsession.log"; #endif #define TAKEPATH(x) if(s[1]== '=' ){x=s+2;} else{x=*argv++;argc--;} int DoTail(int argc, UBYTE **argv) { int errorflag = 0, onlyversion = 1; UBYTE *s, *t, *copy; int threadnum = 0; argc--; argv++; AM.ClearStore = 0; AM.TimeLimit = 0; AM.LogType = -1; AM.HoldFlag = AM.qError = AM.Interact = AM.FileOnlyFlag = 0; AM.InputFileName = AM.LogFileName = AM.IncDir = AM.TempDir = AM.TempSortDir = AM.SetupDir = AM.SetupFile = AM.Path = 0; AM.FromStdin = 0; /* Always use MultiRun, "-M" option is now ignored. */ AM.MultiRun = 1; if ( argc < 1 ) { onlyversion = 0; goto printversion; } while ( argc >= 1 ) { s = *argv++; argc--; if ( *s == '-' || ( *s == '/' && ( argc > 0 || AM.Interact ) ) ) { s++; switch (*s) { case 'c': /* Error checking only */ AM.qError = 1; break; case 'C': /* Next arg is filename of log file */ TAKEPATH(AM.LogFileName) break; case 'D': case 'd': /* Next arg is define preprocessor var. */ t = copy = strDup1(*argv,"Dotail"); while ( *t && *t != '=' ) t++; if ( *t == 0 ) { if ( PutPreVar(copy,(UBYTE *)"1",0,0) < 0 ) return(-1); } else { *t++ = 0; if ( PutPreVar(copy,t,0,0) < 0 ) return(-1); t[-1] = '='; } M_free(copy,"-d prevar"); argv++; argc--; break; case 'f': /* Output only to regular log file */ AM.FileOnlyFlag = 1; AM.LogType = 0; break; case 'F': /* Output only to log file. Further like L. */ AM.FileOnlyFlag = 1; AM.LogType = 1; break; case 'h': /* For old systems: wait for key before exit */ AM.HoldFlag = 1; break; case 'i': if ( StrCmp(s, (UBYTE *)"ignore-deprecation") == 0 ) { AM.IgnoreDeprecation = 1; break; } #ifdef WITHINTERACTION /* Interactive session (not used yet) */ AM.Interact = 1; break; #else goto IllegalOption; #endif case 'I': /* Next arg is dir for inc/prc/sub files */ TAKEPATH(AM.IncDir) break; case 'l': /* Make regular log file */ if ( s[1] == 'l' ) AM.LogType = 1; /*compatibility! */ else AM.LogType = 0; break; case 'L': /* Make log file with only final statistics */ AM.LogType = 1; break; case 'M': /* Multirun. Name of tempfiles will contain PID */ /* This option is now ignored. We always use MultiRun. */ /* AM.MultiRun = 1; */ break; case 'm': /* Read number of threads */ case 'w': /* Read number of workers */ t = s++; threadnum = 0; while ( *s >= '0' && *s <= '9' ) threadnum = 10*threadnum + *s++ - '0'; if ( *s ) { #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Illegal value for option m or w: %s\n",t); errorflag++; } /* if ( threadnum == 1 ) threadnum = 0; */ threadnum++; break; case 'W': /* Print the wall-clock time on the master. */ AM.ggWTimeStatsFlag = 1; break; /* case 'n': Reserved for number of slaves without MPI */ case 'p': #ifdef WITHEXTERNALCHANNEL /*There are two possibilities: -p|-pipe*/ if(s[1]=='i'){ if( (s[2]=='p')&&(s[3]=='e')&&(s[4]=='\0') ){ argc--; /*Initialize pre-set external channels, see the file extcmd.c:*/ if(initPresetExternalChannels(*argv++,AX.timeout)<1){ #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Error initializing preset external channels\n"); errorflag++; } AX.timeout=-1;/*This indicates that preset channels are initialized from cmdline*/ }else{ #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Illegal option in call of FORM: %s\n",s); errorflag++; } }else #else if ( s[1] ) { if ( ( s[1]=='i' ) && ( s[2] == 'p' ) && (s[3] == 'e' ) && ( s[4] == '\0' ) ){ #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Illegal option: Pipes not supported on this system.\n"); } else { #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Illegal option: %s\n",s); } errorflag++; } else #endif { /* Next arg is a path variable like in environment */ TAKEPATH(AM.Path) } break; case 'q': /* Quiet option. Only output. Same as -si */ AM.silent = 1; break; case 'R': /* recover from saved snapshot */ AC.CheckpointFlag = -1; break; case 's': /* Next arg is dir with form.set to be used */ if ( ( s[1] == 'o' ) && ( s[2] == 'r' ) && ( s[3] == 't' ) ) { if(s[4]== '=' ) { AM.TempSortDir = s+5; } else { AM.TempSortDir = *argv++; argc--; } } else if ( s[1] == 'i' ) { /* compatibility: silent/quiet */ AM.silent = 1; } else { TAKEPATH(AM.SetupDir) } break; case 'S': /* Next arg is setup file */ TAKEPATH(AM.SetupFile) break; case 't': /* Next arg is directory for temp files */ if ( s[1] == 's' ) { s++; AM.havesortdir = 1; TAKEPATH(AM.TempSortDir) } else { TAKEPATH(AM.TempDir) } break; case 'T': /* Print the total size used at end of job */ AM.PrintTotalSize = 1; break; case 'v': /* Print version information */ AC.FinalStats = 0; if ( s[1] == 'v' ) { /* verbose version information */ PrintHeader(2); return(1); } printversion:; PrintHeader(0); if ( onlyversion ) return(1); goto NoFile; case 'y': /* Preprocessor dumps output. No compilation. */ AP.PreDebug = PREPROONLY; break; case 'z': /* The number following is a time limit in sec. */ t = s++; AM.TimeLimit = 0; while ( *s >= '0' && *s <= '9' ) AM.TimeLimit = 10*AM.TimeLimit + *s++ - '0'; break; case 'Z': /* Removes the .str file on crash, no matter its contents */ AM.ClearStore = 1; break; case '\0': /* "-" to use STDIN for the input. */ #ifdef WITHMPI /* At the moment, ParFORM doesn't implement STDIN broadcasts. */ if ( PF.me == MASTER ) printf("Sorry, reading STDIN as input is currently not supported by ParFORM\n"); errorflag++; #endif AM.FromStdin = 1; AC.NoShowInput = 1; // disable input echoing by default break; default: if ( FG.cTable[*s] == 1 ) { AM.SkipClears = 0; t = s; while ( FG.cTable[*t] == 1 ) AM.SkipClears = 10*AM.SkipClears + *t++ - '0'; if ( *t != 0 ) { #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Illegal numerical option in call of FORM: %s\n",s); errorflag++; } } else { IllegalOption: #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Illegal option in call of FORM: %s\n",s); errorflag++; } break; } } else if ( argc == 0 && !AM.Interact ) AM.InputFileName = argv[-1]; else { #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("Illegal option in call of FORM: %s\n",s); errorflag++; } } AM.totalnumberofthreads = threadnum; if ( AM.InputFileName ) { if ( AM.FromStdin ) { printf("STDIN and the input filename cannot be specified simultaneously\n"); errorflag++; } s = AM.InputFileName; while ( *s ) s++; if ( s < AM.InputFileName+4 || s[-4] != '.' || s[-3] != 'f' || s[-2] != 'r' || s[-1] != 'm' ) { t = (UBYTE *)Malloc1((s-AM.InputFileName)+5,"adding .frm"); s = AM.InputFileName; AM.InputFileName = t; while ( *s ) *t++ = *s++; *t++ = '.'; *t++ = 'f'; *t++ = 'r'; *t++ = 'm'; *t = 0; } if ( AM.LogType >= 0 && AM.LogFileName == 0 ) { AM.LogFileName = strDup1(AM.InputFileName,"name of logfile"); s = AM.LogFileName; while ( *s ) s++; s[-3] = 'l'; s[-2] = 'o'; s[-1] = 'g'; } } #ifdef WITHINTERACTION else if ( AM.Interact ) { if ( AM.LogType >= 0 ) { /* We may have to do better than just taking a name. It is not unique! This will be left for later. */ AM.LogFileName = deflogname; } } #endif else if ( AM.FromStdin ) { /* Do nothing. */ } else { NoFile: #ifdef WITHMPI if ( PF.me == MASTER ) #endif printf("No filename specified in call of FORM\n"); errorflag++; } if ( AM.Path == 0 ) AM.Path = (UBYTE *)getenv("FORMPATH"); if ( AM.Path ) { /* * AM.Path is taken from argv or getenv. Reallocate it to avoid invalid * frees when AM.Path has to be changed. */ AM.Path = strDup1(AM.Path,"DoTail Path"); } return(errorflag); } /* #] DoTail : #[ OpenInput : Major task here after opening is to skip the proper number of .clear instructions if so desired without using interpretation */ int OpenInput(void) { int oldNoShowInput = AC.NoShowInput; UBYTE c; if ( !AM.Interact ) { if ( AM.FromStdin ) { if ( OpenStream(0,INPUTSTREAM,0,PRENOACTION) == 0 ) { Error0("Cannot open STDIN"); return(-1); } } else { if ( OpenStream(AM.InputFileName,FILESTREAM,0,PRENOACTION) == 0 ) { Error1("Cannot open file",AM.InputFileName); return(-1); } if ( AC.CurrentStream->inbuffer <= 0 ) { Error1("No input in file",AM.InputFileName); return(-1); } } AC.NoShowInput = 1; while ( AM.SkipClears > 0 ) { c = GetInput(); if ( c == ENDOFINPUT ) { Error0("Not enough .clear instructions in input file"); } if ( c == '\\' ) { c = GetInput(); if ( c == ENDOFINPUT ) Error0("Not enough .clear instructions in input file"); continue; } if ( c == ' ' || c == '\t' ) continue; if ( c == '.' ) { c = GetInput(); if ( tolower(c) == 'c' ) { c = GetInput(); if ( tolower(c) == 'l' ) { c = GetInput(); if ( tolower(c) == 'e' ) { c = GetInput(); if ( tolower(c) == 'a' ) { c = GetInput(); if ( tolower(c) == 'r' ) { c = GetInput(); if ( FG.cTable[c] > 2 ) { AM.SkipClears--; } } } } } } while ( c != '\n' && c != '\r' && c != ENDOFINPUT ) { c = GetInput(); if ( c == '\\' ) c = GetInput(); } } else if ( c == '\n' || c == '\r' ) continue; else { while ( ( c = GetInput() ) != '\n' && c != '\r' ) { if ( c == ENDOFINPUT ) { Error0("Not enough .clear instructions in input file"); } } } } AC.NoShowInput = oldNoShowInput; } if ( AM.LogFileName ) { #ifdef WITHMPI if ( PF.me != MASTER ) { /* * Only the master writes to the log file. On slaves, we need * a dummy handle, without opening the file. */ extern FILES **filelist; /* in tools.c */ int i = CreateHandle(); RWLOCKW(AM.handlelock); filelist[i] = (FILES *)123; /* Must be nonzero to prevent a reuse in CreateHandle. */ UNRWLOCK(AM.handlelock); AC.LogHandle = i; } else #endif if ( AC.CheckpointFlag != -1 ) { if ( ( AC.LogHandle = CreateLogFile((char *)(AM.LogFileName)) ) < 0 ) { Error1("Cannot create logfile",AM.LogFileName); return(-1); } } else { if ( ( AC.LogHandle = OpenAddFile((char *)(AM.LogFileName)) ) < 0 ) { Error1("Cannot re-open logfile",AM.LogFileName); return(-1); } } } return(0); } /* #] OpenInput : #[ ReserveTempFiles : Order of preference: a: if there is a path in the commandtail, take that. b: if none, try in the form.set file. c: if still none, try in the environment for the variable FORMTMP d: if still none, try the current directory. The parameter indicates action in the case of multithreaded running. par = 0 : We just run on a single processor. Keep everything normal. par = 1 : Multithreaded running startup phase 1. par = 2 : Multithreaded running startup phase 2. */ UBYTE *emptystring = (UBYTE *)"."; UBYTE *defaulttempfilename = (UBYTE *)"xformxxx.str"; /* This is the length of the above default, but with 7 spaces for PID digits instead of the "xxx". (Previously FORM used 5 digits and this value was 14) */ #define DEFAULTFNAMELENGTH 16 void ReserveTempFiles(int par) { GETIDENTITY SETUPPARAMETERS *sp; UBYTE *s, *t, *tenddir, *tenddir2, c; int i = 0; WORD j; if ( par == 0 || par == 1 ) { if ( AM.TempDir == 0 ) { sp = GetSetupPar((UBYTE *)"tempdir"); if ( ( sp->flags & USEDFLAG ) != USEDFLAG ) { AM.TempDir = (UBYTE *)getenv("FORMTMP"); if ( AM.TempDir == 0 ) AM.TempDir = emptystring; } else AM.TempDir = (UBYTE *)(sp->value); } if ( AM.TempSortDir == 0 ) { if ( AM.havesortdir ) { sp = GetSetupPar((UBYTE *)"tempsortdir"); AM.TempSortDir = (UBYTE *)(sp->value); } else { AM.TempSortDir = (UBYTE *)getenv("FORMTMPSORT"); if ( AM.TempSortDir == 0 ) AM.TempSortDir = AM.TempDir; } } /* We have now in principle a path but we will use its first element only. Later that should become more complicated. Then we will use a path and when one device is full we can continue on the next one. */ s = AM.TempDir; i = 200; /* Some extra for VMS */ while ( *s && *s != PATHSEPARATOR ) { if ( *s == '\\' ) s++; s++; i++; } FG.fnamesize = sizeof(UBYTE)*(i+DEFAULTFNAMELENGTH); FG.fname = (char *)Malloc1(FG.fnamesize,"name for temporary files"); s = AM.TempDir; t = (UBYTE *)FG.fname; while ( *s && *s != PATHSEPARATOR ) { if ( *s == '\\' ) s++; *t++ = *s++; } if ( (char *)t > FG.fname && t[-1] != SEPARATOR && t[-1] != ALTSEPARATOR ) *t++ = SEPARATOR; *t = 0; tenddir = t; FG.fnamebase = t-(UBYTE *)(FG.fname); s = AM.TempSortDir; i = 200; /* Some extra for VMS */ while ( *s && *s != PATHSEPARATOR ) { if ( *s == '\\' ) s++; s++; i++; } FG.fname2size = sizeof(UBYTE)*(i+DEFAULTFNAMELENGTH); FG.fname2 = (char *)Malloc1(FG.fname2size,"name for sort files"); s = AM.TempSortDir; t = (UBYTE *)FG.fname2; while ( *s && *s != PATHSEPARATOR ) { if ( *s == '\\' ) s++; *t++ = *s++; } if ( (char *)t > FG.fname2 && t[-1] != SEPARATOR && t[-1] != ALTSEPARATOR ) *t++ = SEPARATOR; *t = 0; tenddir2 = t; FG.fname2base = t-(UBYTE *)(FG.fname2); t = tenddir; s = defaulttempfilename; #ifdef WITHMPI { int iii; iii = snprintf((char*)t,FG.fnamesize-((char*)t-FG.fname),"%d",PF.me); t+= iii; s+= iii; /* in case defaulttmpfilename is too short */ } #endif while ( *s ) *t++ = *s++; *t = 0; /* There are problems when running many FORM jobs at the same time from make or minos. If they start up simultaneously, occasionally they can make the same .str file. We prevent this with first trying a file that contains the digits of the pid. If this file has already been taken we fall back on the old scheme. The whole is controlled with the -M (MultiRun) parameter in the command tail. */ if ( AM.MultiRun ) { int num = ((int)GetPID())%10000000; t += 4; *t = 0; t[-1] = 'r'; t[-2] = 't'; t[-3] = 's'; t[-4] = '.'; t[-5] = (UBYTE)('0' + num%10); t[-6] = (UBYTE)('0' + (num/10)%10); t[-7] = (UBYTE)('0' + (num/100)%10); t[-8] = (UBYTE)('0' + (num/1000)%10); t[-9] = (UBYTE)('0' + (num/10000)%10); t[-10] = (UBYTE)('0' + (num/100000)%10); t[-11] = (UBYTE)('0' + num/1000000); if ( ( AC.StoreHandle = CreateFile((char *)FG.fname) ) < 0 ) { t[-5] = 'x'; t[-6] = 'x'; t[-7] = 'x'; t[-8] = 'x'; t[-9] = 'x'; t[-10] = 'x'; t[-11] = 'x'; goto classic; } } else { classic:; for(;;) { if ( ( AC.StoreHandle = OpenFile((char *)FG.fname) ) < 0 ) { if ( ( AC.StoreHandle = CreateFile((char *)FG.fname) ) >= 0 ) break; } else CloseFile(AC.StoreHandle); c = t[-5]; if ( c == 'x' ) t[-5] = '0'; else if ( c == '9' ) { t[-5] = '0'; c = t[-6]; if ( c == 'x' ) t[-6] = '0'; else if ( c == '9' ) { t[-6] = '0'; c = t[-7]; if ( c == 'x' ) t[-7] = '0'; else if ( c == '9' ) { /* Note that we tried 1111 names! */ MesPrint("Name space for temp files exhausted"); t[-7] = 0; MesPrint("Please remove files of the type %s or try a different directory" ,FG.fname); Terminate(-1); } else t[-7] = (UBYTE)(c+1); } else t[-6] = (UBYTE)(c+1); } else t[-5] = (UBYTE)(c+1); } } /* Now we should make sure that the tempsortdir cq tempsortfilename makes it into a similar construction. */ s = tenddir; t = tenddir2; while ( *s ) *t++ = *s++; *t = 0; /* Now we should assign a name to the main sort file and the two stage 4 files. */ AM.S0->file.name = (char *)Malloc1(sizeof(char)*(i+DEFAULTFNAMELENGTH),"name for temporary files"); s = (UBYTE *)AM.S0->file.name; t = (UBYTE *)FG.fname2; i = 1; while ( *t ) { *s++ = *t++; i++; } s[-2] = 'o'; *s = 0; } /* Try to create the sort file already, so we can Terminate earlier if this fails. */ #ifdef WITHPTHREADS if ( par <= 1 ) { #endif if ( ( AM.S0->file.handle = CreateFile((char *)AM.S0->file.name) ) < 0 ) { MesPrint("Could not create sort file: %s", AM.S0->file.name); Terminate(-1); }; /* Close and clean up the test file */ CloseFile(AM.S0->file.handle); AM.S0->file.handle = -1; remove(AM.S0->file.name); #ifdef WITHPTHREADS } #endif /* With the stage4 and scratch file names we have to be a bit more careful. They are to be allocated after the threads are initialized when there are threads of course. */ if ( par == 0 ) { s = (UBYTE *)((void *)(FG.fname2)); i = 0; while ( *s ) { s++; i++; } /* +1 for null terminator */ s = (UBYTE *)Malloc1(sizeof(char)*(i+1),"name for stage4 file a"); AR.FoStage4[1].name = (char *)s; t = (UBYTE *)FG.fname2; while ( *t ) *s++ = *t++; s[-2] = '4'; s[-1] = 'a'; *s = 0; s = (UBYTE *)((void *)(FG.fname)); i = 0; while ( *s ) { s++; i++; } /* +1 for null terminator */ s = (UBYTE *)Malloc1(sizeof(char)*(i+1),"name for stage4 file b"); AR.FoStage4[0].name = (char *)s; t = (UBYTE *)FG.fname; while ( *t ) *s++ = *t++; s[-2] = '4'; s[-1] = 'b'; *s = 0; for ( j = 0; j < 3; j++ ) { /* +1 for null terminator */ s = (UBYTE *)Malloc1(sizeof(char)*(i+1),"name for scratch file"); AR.Fscr[j].name = (char *)s; t = (UBYTE *)FG.fname; while ( *t ) *s++ = *t++; s[-2] = 'c'; s[-1] = (UBYTE)('0'+j); *s = 0; } } #ifdef WITHPTHREADS else if ( par == 2 ) { size_t tname; s = (UBYTE *)((void *)(FG.fname2)); i = 0; while ( *s ) { s++; i++; } /* +1 for null terminator, +10 for 32bit int, +1 for "." */ tname = sizeof(char)*(i+12); s = (UBYTE *)Malloc1(tname,"name for stage4 file a"); snprintf((char *)s,tname,"%s.%d",FG.fname2,AT.identity); s[i-2] = '4'; s[i-1] = 'a'; AR.FoStage4[1].name = (char *)s; s = (UBYTE *)((void *)(FG.fname)); i = 0; while ( *s ) { s++; i++; } /* +1 for null terminator, +10 for 32bit int, +1 for "." */ tname = sizeof(char)*(i+12); s = (UBYTE *)Malloc1(tname,"name for stage4 file b"); snprintf((char *)s,tname,"%s.%d",FG.fname,AT.identity); s[i-2] = '4'; s[i-1] = 'b'; AR.FoStage4[0].name = (char *)s; if ( AT.identity == 0 ) { for ( j = 0; j < 3; j++ ) { /* +1 for null terminator */ s = (UBYTE *)Malloc1(sizeof(char)*(i+1),"name for scratch file"); AR.Fscr[j].name = (char *)s; t = (UBYTE *)FG.fname; while ( *t ) *s++ = *t++; s[-2] = 'c'; s[-1] = (UBYTE)('0'+j); *s = 0; } } } #endif } /* #] ReserveTempFiles : #[ StartVariables : */ #ifdef WITHPTHREADS ALLPRIVATES *DummyPointer = 0; #endif void StartVariables(void) { int i, ii; PUTZERO(AM.zeropos); StartPrepro(); /* The module counter: */ AC.CModule=0; #ifdef WITHPTHREADS /* We need a value in AB because in the startup some routines may call AB[0]. */ AB = (ALLPRIVATES **)&DummyPointer; #endif /* separators used to delimit arguments in #call and #do, by default ',' and '|': Be sure, it is en empty set: */ set_sub(AC.separators,AC.separators,AC.separators); set_set(',',AC.separators); set_set('|',AC.separators); AM.BracketFactors[0] = 8; AM.BracketFactors[1] = SYMBOL; AM.BracketFactors[2] = 4; AM.BracketFactors[3] = FACTORSYMBOL; AM.BracketFactors[4] = 1; AM.BracketFactors[5] = 1; AM.BracketFactors[6] = 1; AM.BracketFactors[7] = 3; AM.SkipClears = 0; AC.Cnumpows = 0; AC.OutputMode = 72; AC.OutputSpaces = NORMALFORMAT; AC.LineLength = 79; AM.gIsFortran90 = AC.IsFortran90 = ISNOTFORTRAN90; AM.gFortran90Kind = AC.Fortran90Kind = 0; AM.gCnumpows = 0; AC.exprfillwarning = 0; AM.gLineLength = 79; AM.OutBufSize = 80; AM.MaxStreamSize = MAXFILESTREAMSIZE; AP.MaxPreAssignLevel = 4; AC.iBufferSize = 512; AP.pSize = 128; AP.MaxPreIfLevel = 10; AP.cComChar = AP.ComChar = '*'; AP.firstnamespace = 0; AP.lastnamespace = 0; AP.fullnamesize = 127; AP.fullname = (UBYTE *)Malloc1((AP.fullnamesize+1)*sizeof(UBYTE),"AP.fullname"); AM.OffsetVector = -2*WILDOFFSET+MINSPEC; AC.cbufList.num = 0; AM.hparallelflag = AM.gparallelflag = AC.parallelflag = AC.mparallelflag = PARALLELFLAG; #ifdef WITHMPI if ( PF.numtasks < 2 ) AM.hparallelflag |= NOPARALLEL_NPROC; #endif AC.tablefilling = 0; AC.models = 0; AC.nummodels = 0; AC.ModelLevel = 0; AC.modelspace = 0; AM.resetTimeOnClear = 1; AM.gnumextrasym = AM.ggnumextrasym = 0; AM.havesortdir = 0; AM.SpectatorFiles = 0; AM.NumSpectatorFiles = 0; AM.SizeForSpectatorFiles = 0; /* Information for the lists of variables. Part of error message and size: */ AP.ProcList.message = "procedure"; AP.ProcList.size = sizeof(PROCEDURE); AP.LoopList.message = "doloop"; AP.LoopList.size = sizeof(DOLOOP); AP.PreVarList.message = "PreVariable"; AP.PreVarList.size = sizeof(PREVAR); AC.SymbolList.message = "symbol"; AC.SymbolList.size = sizeof(struct SyMbOl); AC.IndexList.message = "index"; AC.IndexList.size = sizeof(struct InDeX); AC.VectorList.message = "vector"; AC.VectorList.size = sizeof(struct VeCtOr); AC.FunctionList.message = "function"; AC.FunctionList.size = sizeof(struct FuNcTiOn); AC.SetList.message = "set"; AC.SetList.size = sizeof(struct SeTs); AC.SetElementList.message = "set element"; AC.SetElementList.size = sizeof(WORD); AC.ExpressionList.message = "expression"; AC.ExpressionList.size = sizeof(struct ExPrEsSiOn); AC.cbufList.message = "compiler buffer"; AC.cbufList.size = sizeof(CBUF); AC.ChannelList.message = "channel buffer"; AC.ChannelList.size = sizeof(CHANNEL); AP.DollarList.message = "$-variable"; AP.DollarList.size = sizeof(struct DoLlArS); AC.DubiousList.message = "ambiguous variable"; AC.DubiousList.size = sizeof(struct DuBiOuS); AC.TableBaseList.message = "list of tablebases"; AC.TableBaseList.size = sizeof(DBASE); AC.TestValue = 0; AC.InnerTest = 0; AC.AutoSymbolList.message = "autosymbol"; AC.AutoSymbolList.size = sizeof(struct SyMbOl); AC.AutoIndexList.message = "autoindex"; AC.AutoIndexList.size = sizeof(struct InDeX); AC.AutoVectorList.message = "autovector"; AC.AutoVectorList.size = sizeof(struct VeCtOr); AC.AutoFunctionList.message = "autofunction"; AC.AutoFunctionList.size = sizeof(struct FuNcTiOn); AC.PotModDolList.message = "potentially modified dollar"; AC.PotModDolList.size = sizeof(WORD); AC.ModOptDolList.message = "moduleoptiondollar"; AC.ModOptDolList.size = sizeof(MODOPTDOLLAR); AO.FortDotChar = '_'; AO.ErrorBlock = 0; AC.firstconstindex = 1; AO.Optimize.mctsconstant.fval = 1.0; AO.Optimize.horner = O_MCTS; AO.Optimize.hornerdirection = O_FORWARDORBACKWARD; AO.Optimize.method = O_GREEDY; AO.Optimize.mctstimelimit = 0; AO.Optimize.mctsnumexpand = 1000; AO.Optimize.mctsnumkeep = 10; AO.Optimize.mctsnumrepeat = 1; AO.Optimize.greedytimelimit = 0; AO.Optimize.greedyminnum = 10; AO.Optimize.greedymaxperc = 5; AO.Optimize.printstats = 0; AO.Optimize.debugflags = 0; AO.OptimizeResult.code = NULL; AO.inscheme = 0; AO.schemenum = 0; AO.wpos = 0; AO.wpoin = 0; AO.wlen = 0; AM.dollarzero = 0; AC.doloopstack = 0; AC.doloopstacksize = 0; AC.dolooplevel = 0; /* Set up the main name trees: */ AC.varnames = MakeNameTree(); AC.exprnames = MakeNameTree(); AC.dollarnames = MakeNameTree(); AC.autonames = MakeNameTree(); AC.activenames = &(AC.varnames); AP.preError = 0; /* Initialize the compiler: */ inictable(); AM.rbufnum = inicbufs(); /* Regular compiler buffer */ #ifndef WITHPTHREADS AT.ebufnum = inicbufs(); /* Buffer for extras during execution */ AT.fbufnum = inicbufs(); /* Buffer for caching in factorization */ AT.allbufnum = inicbufs(); /* Buffer for id,all */ AT.aebufnum = inicbufs(); /* Buffer for id,all */ AN.tryterm = 0; #else AS.MasterSort = 0; #endif AM.dbufnum = inicbufs(); /* Buffer for dollar variables */ AM.sbufnum = inicbufs(); /* Subterm buffer for polynomials and optimization */ AC.ffbufnum = inicbufs(); /* Buffer number for user defined factorizations */ AM.zbufnum = inicbufs(); /* For very special values */ { CBUF *C = cbuf+AM.zbufnum; WORD one[5] = {4,1,1,3,0}; WORD zero = 0; AddRHS(AM.zbufnum,1); AM.zerorhs = C->numrhs; AddNtoC(AM.zbufnum,1,&zero,17); AddRHS(AM.zbufnum,1); AM.onerhs = C->numrhs; AddNtoC(AM.zbufnum,5,one,17); } AP.inside.inscbuf = inicbufs(); /* For the #inside instruction */ /* Enter the built in objects */ AC.Symbols = &(AC.SymbolList); AC.Indices = &(AC.IndexList); AC.Vectors = &(AC.VectorList); AC.Functions = &(AC.FunctionList); AC.vetofilling = 0; AddDollar((UBYTE *)"$",DOLUNDEFINED,0,0); cbuf[AM.dbufnum].mnumlhs = cbuf[AM.dbufnum].numlhs; cbuf[AM.dbufnum].mnumrhs = cbuf[AM.dbufnum].numrhs; AddSymbol((UBYTE *)"i_",-MAXPOWER,MAXPOWER,VARTYPEIMAGINARY,0); AddSymbol((UBYTE *)"pi_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); /* coeff_ should have the number COEFFSYMBOL and den_ the number DENOMINATOR and the three should be in this order! */ AddSymbol((UBYTE *)"coeff_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"num_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"den_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"xarg_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"dimension_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"factor_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"sep_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"ee_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); AddSymbol((UBYTE *)"em_",-MAXPOWER,MAXPOWER,VARTYPENONE,0); i = BUILTINSYMBOLS; /* update this in ftypes.h when we add new symbols */ /* Next we add a number of dummy symbols for ensuring that the user defined symbols start at a fixed given number FIRSTUSERSYMBOL We do want to give them unique names though that the user cannot access. */ { char dumstr[20]; for ( ; i < FIRSTUSERSYMBOL; i++ ) { snprintf(dumstr,20,":%d:",i); AddSymbol((UBYTE *)dumstr,-MAXPOWER,MAXPOWER,VARTYPENONE,0); } } AddIndex((UBYTE *)"iarg_",4,0); AddVector((UBYTE *)"parg_",VARTYPENONE,0); AM.NumFixedFunctions = sizeof(fixedfunctions)/sizeof(struct fixedfun); for ( i = 0; i < AM.NumFixedFunctions; i++ ) { ii = AddFunction((UBYTE *)fixedfunctions[i].name ,fixedfunctions[i].commu ,fixedfunctions[i].tensor ,fixedfunctions[i].complx ,fixedfunctions[i].symmetric ,0,-1,-1); if ( fixedfunctions[i].tensor == GAMMAFUNCTION ) functions[ii].flags |= COULDCOMMUTE; } /* Next we add a number of dummy functions for ensuring that the user defined functions start at a fixed given number FIRSTUSERFUNCTION. We do want to give them unique names though that the user cannot access. */ { char dumstr[20]; for ( ; i < FIRSTUSERFUNCTION-FUNCTION; i++ ) { snprintf(dumstr,20,"::%d::",i); AddFunction((UBYTE *)dumstr,0,0,0,0,0,-1,-1); } } AM.NumFixedSets = sizeof(fixedsets)/sizeof(struct fixedset); for ( i = 0; i < AM.NumFixedSets; i++ ) { ii = AddSet((UBYTE *)fixedsets[i].name,fixedsets[i].dimension); Sets[ii].type = fixedsets[i].type; } AM.RepMax = MAXREPEAT; #ifndef WITHPTHREADS AT.RepCount = (int *)Malloc1((LONG)((AM.RepMax+3)*sizeof(int)),"repeat buffers"); AN.RepPoint = AT.RepCount; AT.RepTop = AT.RepCount + AM.RepMax; AN.polysortflag = 0; AN.subsubveto = 0; #endif AC.NumWildcardNames = 0; AC.WildcardBufferSize = 50; AC.WildcardNames = (UBYTE *)Malloc1((LONG)AC.WildcardBufferSize,"argument list names"); #ifndef WITHPTHREADS AT.WildArgTaken = (WORD *)Malloc1((LONG)AC.WildcardBufferSize*sizeof(WORD)/2 ,"argument list names"); AT.WildcardBufferSize = AC.WildcardBufferSize; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); AT.nfac = AT.nBer = 0; AT.factorials = 0; AT.bernoullis = 0; AR.wranfia = 0; AR.wranfcall = 0; AR.wranfnpair1 = NPAIR1; AR.wranfnpair2 = NPAIR2; AR.wranfseed = 0; AT.NormData = Malloc1(sizeof(*(AT.NormData)), "NormData pointers"); AT.NormDataSize = 1; AT.NormData[0] = AllocNormData(); AT.NormDepth = 0; #endif AM.atstartup = 1; AM.oldnumextrasymbols = strDup1((UBYTE *)"OLDNUMEXTRASYMBOLS_","oldnumextrasymbols"); PutPreVar((UBYTE *)"VERSION_",(UBYTE *)STRINGIFY(MAJORVERSION),0,0); PutPreVar((UBYTE *)"SUBVERSION_",(UBYTE *)STRINGIFY(MINORVERSION),0,0); PutPreVar((UBYTE *)"SUBSUBVERSION_",(UBYTE *)STRINGIFY(PATCHVERSION),0,0); PutPreVar((UBYTE *)"DATE_",(UBYTE *)MakeDate(),0,0); PutPreVar((UBYTE *)"random_",(UBYTE *)"________",0,0); PutPreVar((UBYTE *)"optimminvar_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"optimmaxvar_",(UBYTE *)("0"),0,0); PutPreVar(AM.oldnumextrasymbols,(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"optimvalue_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"optimscheme_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"tolower_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"toupper_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"takeleft_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"takeright_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"keepleft_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"keepright_",(UBYTE *)("0"),0,0); PutPreVar((UBYTE *)"SYSTEMERROR_",(UBYTE *)("0"),0,0); /* Next are the flags to control diagram generation filters */ #define STR2(x) #x #define STR(x) STR2(x) PutPreVar((UBYTE *)"TOPOLOGIESONLY_" ,(UBYTE*)(STR(TOPOLOGIESONLY)) ,0,0); PutPreVar((UBYTE *)"WITHOUTNODES_" ,(UBYTE*)(STR(WITHOUTNODES)) ,0,0); PutPreVar((UBYTE *)"WITHEDGES_" ,(UBYTE*)(STR(WITHEDGES)) ,0,0); PutPreVar((UBYTE *)"WITHBLOCKS_" ,(UBYTE*)(STR(WITHBLOCKS)) ,0,0); PutPreVar((UBYTE *)"WITHONEPISETS_" ,(UBYTE*)(STR(WITHONEPISETS)) ,0,0); PutPreVar((UBYTE *)"WITHSYMMETRIZEI_",(UBYTE*)(STR(WITHSYMMETRIZEI)),0,0); PutPreVar((UBYTE *)"WITHSYMMETRIZEF_",(UBYTE*)(STR(WITHSYMMETRIZEF)),0,0); // This is not an "option" preprocessor var but is set by "external" particle definitions // PutPreVar((UBYTE *)"CHECKEXTERN_" ,(UBYTE*)(STR(CHECKEXTERN)) ,0,0); PutPreVar((UBYTE *)"ONEPI_" ,(UBYTE*)(STR(ONEPARTI)) ,0,0); PutPreVar((UBYTE *)"ONEPR_" ,(UBYTE*)(STR(ONEPARTR)) ,0,0); PutPreVar((UBYTE *)"ONSHELL_" ,(UBYTE*)(STR(ONSHELL)) ,0,0); PutPreVar((UBYTE *)"OFFSHELL_" ,(UBYTE*)(STR(OFFSHELL)) ,0,0); PutPreVar((UBYTE *)"NOSIGMA_" ,(UBYTE*)(STR(NOSIGMA)) ,0,0); PutPreVar((UBYTE *)"SIGMA_" ,(UBYTE*)(STR(SIGMA)) ,0,0); PutPreVar((UBYTE *)"NOSNAIL_" ,(UBYTE*)(STR(NOSNAIL)) ,0,0); PutPreVar((UBYTE *)"SNAIL_" ,(UBYTE*)(STR(SNAIL)) ,0,0); PutPreVar((UBYTE *)"NOTADPOLE_" ,(UBYTE*)(STR(NOTADPOLE)) ,0,0); PutPreVar((UBYTE *)"TADPOLE_" ,(UBYTE*)(STR(TADPOLE)) ,0,0); PutPreVar((UBYTE *)"SIMPLE_" ,(UBYTE*)(STR(SIMPLE)) ,0,0); PutPreVar((UBYTE *)"NOTSIMPLE_" ,(UBYTE*)(STR(NOTSIMPLE)) ,0,0); PutPreVar((UBYTE *)"BIPART_" ,(UBYTE*)(STR(BIPART)) ,0,0); PutPreVar((UBYTE *)"NONBIPART_" ,(UBYTE*)(STR(NONBIPART)) ,0,0); PutPreVar((UBYTE *)"CYCLI_" ,(UBYTE*)(STR(CYCLI)) ,0,0); PutPreVar((UBYTE *)"CYCLR_" ,(UBYTE*)(STR(CYCLR)) ,0,0); PutPreVar((UBYTE *)"FLOOP_" ,(UBYTE*)(STR(FLOOP)) ,0,0); PutPreVar((UBYTE *)"NOTFLOOP_" ,(UBYTE*)(STR(NOTFLOOP)) ,0,0); { char buf[41]; /* up to 128-bit */ LONG pid; #ifndef WITHMPI pid = GetPID(); #else pid = ( PF.me == MASTER ) ? GetPID() : (LONG)0; pid = PF_BroadcastNumber(pid); #endif LongCopy(pid,buf); PutPreVar((UBYTE *)"PID_",(UBYTE *)buf,0,0); } AM.atstartup = 0; AP.MaxPreTypes = 10; AP.NumPreTypes = 0; AP.PreTypes = (int *)Malloc1(sizeof(int)*(AP.MaxPreTypes+1),"preprocessor types"); AP.inside.buffer = 0; AP.inside.size = 0; AC.SortType = AC.lSortType = AM.gSortType = SORTLOWFIRST; #ifdef WITHPTHREADS #else AR.SortType = AC.SortType; #endif AC.LogHandle = -1; AC.SetList.numtemp = AC.SetList.num; AC.SetElementList.numtemp = AC.SetElementList.num; GetName(AC.varnames,(UBYTE *)"exp_",&AM.expnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"denom_",&AM.denomnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"fac_",&AM.facnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"invfac_",&AM.invfacnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"sum_",&AM.sumnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"sump_",&AM.sumpnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"term_",&AM.termfunnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"match_",&AM.matchfunnum,NOAUTO); GetName(AC.varnames,(UBYTE *)"count_",&AM.countfunnum,NOAUTO); AM.termfunnum += FUNCTION; AM.matchfunnum += FUNCTION; AM.countfunnum += FUNCTION; AC.ThreadStats = AM.gThreadStats = AM.ggThreadStats = 1; AC.FinalStats = AM.gFinalStats = AM.ggFinalStats = 1; AC.StatsFlag = AM.gStatsFlag = AM.ggStatsFlag = 1; AC.ThreadsFlag = AM.gThreadsFlag = AM.ggThreadsFlag = 1; AC.ThreadBalancing = AM.gThreadBalancing = AM.ggThreadBalancing = 1; AC.ThreadSortFileSynch = AM.gThreadSortFileSynch = AM.ggThreadSortFileSynch = 0; AC.ProcessStats = AM.gProcessStats = AM.ggProcessStats = 1; AC.OldParallelStats = AM.gOldParallelStats = AM.ggOldParallelStats = 0; AC.OldFactArgFlag = AM.gOldFactArgFlag = AM.ggOldFactArgFlag = NEWFACTARG; AC.OldGCDflag = AM.gOldGCDflag = AM.ggOldGCDflag = 1; AC.OldPRFSignFlag = 0; AC.WTimeStatsFlag = AM.gWTimeStatsFlag = AM.ggWTimeStatsFlag = 0; AM.gcNumDollars = AP.DollarList.num; AC.SizeCommuteInSet = AM.gSizeCommuteInSet = 0; #ifdef WITHFLOAT AC.MaxWeight = AM.gMaxWeight = AM.ggMaxWeight = MAXWEIGHT; AC.DefaultPrecision = AM.gDefaultPrecision = AM.ggDefaultPrecision = DEFAULTPRECISION; #endif AC.CommuteInSet = 0; AM.PrintTotalSize = 0; AO.NoSpacesInNumbers = AM.gNoSpacesInNumbers = AM.ggNoSpacesInNumbers = 0; AO.IndentSpace = AM.gIndentSpace = AM.ggIndentSpace = INDENTSPACE; AO.BlockSpaces = 0; AO.OptimizationLevel = 0; PUTZERO(AS.MaxExprSize); PUTZERO(AC.StoreFileSize); #ifdef WITHPTHREADS AC.inputnumbers = 0; AC.pfirstnum = 0; AC.numpfirstnum = AC.sizepfirstnum = 0; #endif AC.MemDebugFlag = 1; #ifdef WITHEXTERNALCHANNEL AX.currentExternalChannel=0; AX.killSignal=SIGKILL; AX.killWholeGroup=1; AX.daemonize=1; AX.currentPrompt=0; AX.timeout=1000;/*One second to initialize preset channels*/ AX.shellname=strDup1((UBYTE *)"/bin/sh -c","external channel shellname"); AX.stderrname=strDup1((UBYTE *)"/dev/null","external channel stderrname"); #endif } /* #] StartVariables : #[ StartMore : */ void StartMore(void) { #ifdef WITHEXTERNALCHANNEL /*If env.variable "FORM_PIPES" is defined, we have to initialize corresponding pre-set external channels, see file extcmd.c.*/ /*This line must be after all setup settings: in future, timeout could be changed at setup.*/ if(AX.timeout>=0)/*if AX.timeout<0, this was done by cmdline option -pipe*/ initPresetExternalChannels((UBYTE*)getenv("FORM_PIPES"),AX.timeout); #endif #ifdef WITHMPI /* Define preprocessor variable PARALLELTASK_ as a process number, 0 is the master Define preprocessor variable NPARALLELTASKS_ as a total number of processes */ { UBYTE buf[32]; snprintf((char*)buf,32,"%d",PF.me); PutPreVar((UBYTE *)"PARALLELTASK_",buf,0,0); snprintf((char*)buf,32,"%d",PF.numtasks); PutPreVar((UBYTE *)"NPARALLELTASKS_",buf,0,0); } #else PutPreVar((UBYTE *)"PARALLELTASK_",(UBYTE *)"0",0,0); PutPreVar((UBYTE *)"NPARALLELTASKS_",(UBYTE *)"1",0,0); #endif PutPreVar((UBYTE *)"NAME_",AM.InputFileName ? AM.InputFileName : (UBYTE *)"STDIN",0,0); } /* #] StartMore : #[ IniVars : This routine initializes the parameters that may change during the run. */ void IniVars(void) { #ifdef WITHPTHREADS GETIDENTITY #else WORD *t; #endif WORD *fi, i, one = 1; CBUF *C = cbuf+AC.cbufnum; #ifdef WITHPTHREADS UBYTE buf[32]; snprintf((char*)buf,32,"%d",AM.totalnumberofthreads); PutPreVar((UBYTE *)"NTHREADS_",buf,0,1); #else PutPreVar((UBYTE *)"NTHREADS_",(UBYTE *)"1",0,1); #endif AC.ShortStats = 0; AC.WarnFlag = 1; AR.SortType = AC.SortType = AC.lSortType = AM.gSortType; AC.OutputMode = 72; AC.OutputSpaces = NORMALFORMAT; AR.Eside = 0; AC.DumNum = 0; AC.ncmod = AM.gncmod = 0; AC.modmode = AM.gmodmode = 0; AC.npowmod = AM.gnpowmod = 0; AC.halfmod = 0; AC.nhalfmod = 0; AC.modinverses = 0; AC.lPolyFun = AM.gPolyFun = 0; AC.lPolyFunInv = AM.gPolyFunInv = 0; AC.lPolyFunType = AM.gPolyFunType = 0; AC.lPolyFunExp = AM.gPolyFunExp = 0; AC.lPolyFunVar = AM.gPolyFunVar = 0; AC.lPolyFunPow = AM.gPolyFunPow = 0; #ifdef WITHFLINT AC.FlintPolyFlag = 1; #else AC.FlintPolyFlag = 0; #endif AC.DirtPow = 0; AC.lDefDim = AM.gDefDim = 4; AC.lDefDim4 = AM.gDefDim4 = 0; AC.lUnitTrace = AM.gUnitTrace = 4; AC.NamesFlag = AM.gNamesFlag = 0; AC.CodesFlag = AM.gCodesFlag = 0; /* Printing a backtrace on crash is on by default for both normal and debug modes if FORM has been compiled with backtrace support. */ #ifdef ENABLE_BACKTRACE AC.PrintBacktraceFlag = 1; #else AC.PrintBacktraceFlag = 0; #endif /* Human-readable statistics are off by default */ AC.HumanStatsFlag = 0; AC.extrasymbols = AM.gextrasymbols = AM.ggextrasymbols = 0; AC.extrasym = (UBYTE *)Malloc1(2*sizeof(UBYTE),"extrasym"); AM.gextrasym = (UBYTE *)Malloc1(2*sizeof(UBYTE),"extrasym"); AM.ggextrasym = (UBYTE *)Malloc1(2*sizeof(UBYTE),"extrasym"); AC.extrasym[0] = AM.gextrasym[0] = AM.ggextrasym[0] = 'Z'; AC.extrasym[1] = AM.gextrasym[1] = AM.ggextrasym[1] = 0; AC.TokensWriteFlag = AM.gTokensWriteFlag = 0; AC.SetupFlag = 0; AC.LineLength = AM.gLineLength = 79; AC.NwildC = 0; AC.OutputMode = 0; AM.gOutputMode = 0; AC.OutputSpaces = NORMALFORMAT; AM.gOutputSpaces = NORMALFORMAT; AC.OutNumberType = RATIONALMODE; AM.gOutNumberType = RATIONALMODE; #ifdef WITHZLIB AR.gzipCompress = GZIPDEFAULT; AR.FoStage4[0].ziobuffer = 0; AR.FoStage4[1].ziobuffer = 0; #ifdef WITHZSTD /* Zstd compression is on by default, if we have compiled with it */ ZWRAP_useZSTDcompression(1); #endif #endif AR.BracketOn = 0; AC.bracketindexflag = 0; AT.bracketindexflag = 0; AT.bracketinfo = 0; AO.IsBracket = 0; AM.gfunpowers = AC.funpowers = COMFUNPOWERS; AC.parallelflag = AM.gparallelflag; AC.properorderflag = AM.gproperorderflag = PROPERORDERFLAG; AC.ProcessBucketSize = AC.mProcessBucketSize = AM.gProcessBucketSize; AC.ThreadBucketSize = AM.gThreadBucketSize; AC.ShortStatsMax = 0; AM.gShortStatsMax = 0; AM.ggShortStatsMax = 0; GlobalSymbols = NumSymbols; GlobalIndices = NumIndices; GlobalVectors = NumVectors; GlobalFunctions = NumFunctions; GlobalSets = NumSets; GlobalSetElements = NumSetElements; AC.modpowers = (UWORD *)0; i = AM.OffsetIndex; fi = AC.FixIndices; if ( i > 0 ) do { *fi++ = one; } while ( --i >= 0 ); AR.sLevel = -1; AM.Ordering[0] = 5; AM.Ordering[1] = 6; AM.Ordering[2] = 7; AM.Ordering[3] = 0; AM.Ordering[4] = 1; AM.Ordering[5] = 2; AM.Ordering[6] = 3; AM.Ordering[7] = 4; for ( i = 8; i < 15; i++ ) AM.Ordering[i] = i; AM.gUniTrace[0] = AC.lUniTrace[0] = SNUMBER; AM.gUniTrace[1] = AC.lUniTrace[1] = AM.gUniTrace[2] = AC.lUniTrace[2] = 4; AM.gUniTrace[3] = AC.lUniTrace[3] = 1; #ifdef WITHPTHREADS AS.Balancing = 0; #else AT.MinVecArg[0] = 7+ARGHEAD; AT.MinVecArg[ARGHEAD] = 7; AT.MinVecArg[1+ARGHEAD] = INDEX; AT.MinVecArg[2+ARGHEAD] = 3; AT.MinVecArg[3+ARGHEAD] = 0; AT.MinVecArg[4+ARGHEAD] = 1; AT.MinVecArg[5+ARGHEAD] = 1; AT.MinVecArg[6+ARGHEAD] = -3; t = AT.FunArg; *t++ = 4+ARGHEAD+FUNHEAD; for ( i = 1; i < ARGHEAD; i++ ) *t++ = 0; *t++ = 4+FUNHEAD; *t++ = 0; *t++ = FUNHEAD; for ( i = 2; i < FUNHEAD; i++ ) *t++ = 0; *t++ = 1; *t++ = 1; *t++ = 3; #ifdef WITHMPI AS.printflag = 0; #endif AT.comsym[0] = 8; AT.comsym[1] = SYMBOL; AT.comsym[2] = 4; AT.comsym[3] = 0; AT.comsym[4] = 1; AT.comsym[5] = 1; AT.comsym[6] = 1; AT.comsym[7] = 3; AT.comnum[0] = 4; AT.comnum[1] = 1; AT.comnum[2] = 1; AT.comnum[3] = 3; AT.comfun[0] = FUNHEAD+4; AT.comfun[1] = FUNCTION; AT.comfun[2] = FUNHEAD; AT.comfun[3] = 0; #if FUNHEAD == 4 AT.comfun[4] = 0; #endif AT.comfun[FUNHEAD+1] = 1; AT.comfun[FUNHEAD+2] = 1; AT.comfun[FUNHEAD+3] = 3; AT.comind[0] = 7; AT.comind[1] = INDEX; AT.comind[2] = 3; AT.comind[3] = 0; AT.comind[4] = 1; AT.comind[5] = 1; AT.comind[6] = 3; AT.locwildvalue[0] = SUBEXPRESSION; AT.locwildvalue[1] = SUBEXPSIZE; for ( i = 2; i < SUBEXPSIZE; i++ ) AT.locwildvalue[i] = 0; AT.mulpat[0] = TYPEMULT; AT.mulpat[1] = SUBEXPSIZE+3; AT.mulpat[2] = 0; AT.mulpat[3] = SUBEXPRESSION; AT.mulpat[4] = SUBEXPSIZE; AT.mulpat[5] = 0; AT.mulpat[6] = 1; for ( i = 7; i < SUBEXPSIZE+5; i++ ) AT.mulpat[i] = 0; AT.proexp[0] = SUBEXPSIZE+4; AT.proexp[1] = EXPRESSION; AT.proexp[2] = SUBEXPSIZE; AT.proexp[3] = -1; AT.proexp[4] = 1; for ( i = 5; i < SUBEXPSIZE+1; i++ ) AT.proexp[i] = 0; AT.proexp[SUBEXPSIZE+1] = 1; AT.proexp[SUBEXPSIZE+2] = 1; AT.proexp[SUBEXPSIZE+3] = 3; AT.proexp[SUBEXPSIZE+4] = 0; AT.dummysubexp[0] = SUBEXPRESSION; AT.dummysubexp[1] = SUBEXPSIZE+4; for ( i = 2; i < SUBEXPSIZE; i++ ) AT.dummysubexp[i] = 0; AT.dummysubexp[SUBEXPSIZE] = WILDDUMMY; AT.dummysubexp[SUBEXPSIZE+1] = 4; AT.dummysubexp[SUBEXPSIZE+2] = 0; AT.dummysubexp[SUBEXPSIZE+3] = 0; AT.inprimelist = -1; AT.sizeprimelist = 0; AT.primelist = 0; AT.LeaveNegative = 0; AT.TrimPower = 0; AN.SplitScratch = 0; AN.SplitScratchSize = AN.InScratch = 0; AN.SplitScratch1 = 0; AN.SplitScratchSize1 = AN.InScratch1 = 0; AN.idfunctionflag = 0; #endif AO.OutputLine = AO.OutFill = BufferForOutput; AO.FactorMode = 0; C->Pointer = C->Buffer; AP.PreOut = 0; AP.ComChar = AP.cComChar; AC.cbufnum = AM.rbufnum; /* Select the default compiler buffer */ AC.HideLevel = 0; AP.PreAssignFlag = 0; } /* #] IniVars : #[ Signal handlers : */ /*[28apr2004 mt]:*/ #ifdef TRAPSIGNALS static int exitInProgress = 0; static int trappedTerminate = 0; /*INTSIGHANDLER : some systems require a signal handler to return an integer, so define the macro INTSIGHANDLER if compiler fails:*/ #ifdef INTSIGHANDLER static int onErrSig(int i) #else static void onErrSig(int i) #endif { if (exitInProgress){ signal(i,SIG_DFL);/* Use default behaviour*/ raise (i);/*reproduce trapped signal*/ #ifdef INTSIGHANDLER return(i); #else return; #endif } trappedTerminate = 1; /*[13jul2005 mt]*//*TerminateImpl(-1) on signal is here:*/ Terminate(-1); } #ifdef INTSIGHANDLER static void setNewSig(int i, int (*handler)(int)) #else static void setNewSig(int i, void (*handler)(int)) #endif { if(! (i 0 ) Terminate(0); else Terminate(-1); } if ( DoSetups() ) Terminate(-2); #ifdef WITHMPI /* It is messy if all errors in OpenInput() on slaves are printed. */ AS.printflag = 0; #endif if ( OpenInput() ) Terminate(-3); #ifdef WITHMPI AS.printflag = -1; #endif if ( TryEnvironment() ) Terminate(-2); if ( TryFileSetups() ) Terminate(-2); if ( MakeSetupAllocs() ) Terminate(-2); StartMore(); InitRecovery(); CheckRecoveryFile(); if ( AM.totalnumberofthreads == 0 ) AM.totalnumberofthreads = 1; AS.MultiThreaded = 0; #ifdef WITHPTHREADS if ( AM.totalnumberofthreads > 1 ) AS.MultiThreaded = 1; ReserveTempFiles(1); StartAllThreads(AM.totalnumberofthreads); IniFbufs(); #else ReserveTempFiles(0); IniFbuffer(AT.fbufnum); #endif if ( !AM.FromStdin ) PrintHeader(1); IniVars(); Globalize(1); #ifdef WITH_ALARM if ( AM.TimeLimit > 0 ) alarm(AM.TimeLimit); #endif #ifdef WITHFLINT flint_check_version(); #endif TimeCPU(0); TimeChildren(0); TimeWallClock(0); PreProcessor(); Terminate(0); return(0); } /* #] main : #[ CleanUp : if par < 0 we have to keep the storage file. when par > 0 we ran into a .clear statement. In that case we keep the zero level input and the log file. */ void CleanUp(WORD par) { GETIDENTITY int i; if ( FG.fname ) { #ifdef WITHPTHREADS if ( B ) { #endif CleanUpSort(0); for ( i = 0; i < 3; i++ ) { if ( AR.Fscr[i].handle >= 0 ) { if ( AR.Fscr[i].name ) { /* If there are more threads referring to the same file only the one with the name is the owner of the file. */ CloseFile(AR.Fscr[i].handle); remove(AR.Fscr[i].name); } AR.Fscr[i].handle = - 1; AR.Fscr[i].POfill = 0; } } #ifdef WITHPTHREADS } #endif if ( par > 0 ) { /* Close all input levels above the lowest? */ } if ( AC.StoreHandle >= 0 && par <= 0 ) { #ifdef TRAPSIGNALS if ( trappedTerminate ) { /* We don't throw .str if it has contents */ POSITION pos; PUTZERO(pos); SeekFile(AC.StoreHandle,&pos,SEEK_END); if ( ISNOTZEROPOS(pos) ) { CloseFile(AC.StoreHandle); goto dontremove; } } CloseFile(AC.StoreHandle); #ifdef WITHPTHREADS if ( B ) #endif if ( par >= 0 || AR.StoreData.Handle < 0 || AM.ClearStore ) { remove(FG.fname); } dontremove:; #else CloseFile(AC.StoreHandle); #ifdef WITHPTHREADS if ( B ) #endif if ( par >= 0 || AR.StoreData.Handle < 0 || AM.ClearStore > 0 ) { remove(FG.fname); } #endif } } ClearSpectators(CLEARMODULE); /* Remove recovery file on exit if everything went well */ if ( par == 0 ) { DeleteRecoveryFile(); } /* Now the final message concerning the total time */ if ( AC.LogHandle >= 0 && par <= 0 ) { WORD lh = AC.LogHandle; AC.LogHandle = -1; #ifdef WITHMPI if ( PF.me == MASTER ) /* Only the master opened the real file. */ #endif CloseFile(lh); } } /* #] CleanUp : #[ TerminateImpl : */ static int firstterminate = 1; void TerminateImpl(int errorcode, const char* file, int line, const char* function) { #ifdef WITHMPI if ( errorcode && firstterminate && !PF.notMyFault ) { #else if ( errorcode && firstterminate ) { #endif firstterminate = 0; MLOCK(ErrorMessageLock); #ifdef WITHPTHREADS MesPrint("Program terminating in thread %w at &"); #elif defined(WITHMPI) MesPrint("Program terminating in process %w at &"); #else MesPrint("Program terminating at &"); #endif MesPrint("Terminate called from %s:%d (%s)", file, line, function); if ( AC.PrintBacktraceFlag ) { #ifdef ENABLE_BACKTRACE void *stack[64]; int stacksize, stop = 0; stacksize = backtrace(stack, sizeof(stack)/sizeof(stack[0])); /* First check whether eu-addr2line is available */ if ( !system("command -v eu-addr2line > /dev/null 2>&1") ) { MesPrint("Backtrace:"); for (int i = 0; i < stacksize && !stop; i++) { FILE *fp; char cmd[512]; // Leave an initial space cmd[0] = ' '; MesPrint("%#%2d:%", i); snprintf(cmd+1, sizeof(cmd)-1, "eu-addr2line -s --pretty-print -f -i '%p' --pid=%d\n", stack[i], getpid()); fp = popen(cmd+1, "r"); while ( fgets(cmd+1, sizeof(cmd)-1, fp) != NULL ) { MesPrint("%s", cmd); /* Don't show functions lower than "main" (or thread equivalent) */ if ( strstr(cmd, " main ") || strstr(cmd, " RunThread ") || strstr(cmd, " RunSortBot ") ) { stop = 1; } } pclose(fp); } } #ifdef LINUX else if ( !system("command -v addr2line > /dev/null 2>&1") ) { /* Get the executable path. */ char exe_path[PATH_MAX]; { ssize_t len = readlink("/proc/self/exe", exe_path, sizeof(exe_path) - 1); if ( len != -1 ) { exe_path[len] = '\0'; } else { goto backtrace_fallback; } } /* Assume PIE binary and get the base address. */ uintptr_t base_address = 0; { char line[256]; FILE *maps = fopen("/proc/self/maps", "r"); if ( !maps ) { goto backtrace_fallback; } /* See the format used by nommu_region_show() in fs/proc/nommu.c of the Linux source. */ if ( fgets(line, sizeof(line), maps) ) { sscanf(line, "%" SCNxPTR "-", &base_address); } else { fclose(maps); goto backtrace_fallback; } fclose(maps); } char **strings; strings = backtrace_symbols(stack, stacksize); MesPrint("Backtrace:"); for ( int i = 0; i < stacksize && !stop; i++ ) { FILE *fp; char cmd[PATH_MAX + 512]; // Leave an initial space cmd[0] = ' '; uintptr_t addr = (uintptr_t)stack[i] - base_address; MesPrint("%#%2d:%", i); snprintf(cmd+1, sizeof(cmd)-1, "addr2line -e \"%s\" -i -p -s -f -C 0x%" PRIxPTR, exe_path, addr); fp = popen(cmd+1, "r"); while ( fgets(cmd+1, sizeof(cmd)-1, fp) != NULL ) { MesPrint("%s", cmd); /* Don't show functions lower than "main" */ if ( strstr(cmd, " main ") || strstr(cmd, " RunThread ") || strstr(cmd, " RunSortBot ") ) { stop = 1; } } pclose(fp); } free(strings); } #endif else { /* eu-addr2line not found */ #ifdef LINUX backtrace_fallback: ; #endif char **strings; strings = backtrace_symbols(stack, stacksize); MesPrint("Backtrace:"); for ( int i = 0; i < stacksize && !stop; i++ ) { char *p = strings[i]; while ( *p && *p != '(' ) p++; MesPrint("%#%2d: %s\n", i, p); /* Don't show functions lower than "main" (or thread equivalent) */ if ( strstr(p, "(main+") || strstr(p, "(RunThread+") || strstr(p, "(RunSortBot+") ) { stop = 1; } } #ifdef LINUX MesPrint("Please install addr2line or eu-addr2line for readable stack information."); #else MesPrint("Please install eu-addr2line for readable stack information."); #endif free(strings); } #else MesPrint("FORM compiled without backtrace support."); #endif } /* if ( AC.PrintBacktraceFlag) { */ MUNLOCK(ErrorMessageLock); #ifdef WITHMPI PF_PreTerminate(errorcode); #endif Crash(); } #ifdef TRAPSIGNALS exitInProgress=1; #endif #ifdef WITHEXTERNALCHANNEL /* This function can be called from the error handler, so it is better to clean up all started processes before any activity: */ closeAllExternalChannels(); AX.currentExternalChannel=0; /*[08may2006 mt]:*/ AX.killSignal=SIGKILL; AX.killWholeGroup=1; AX.daemonize=1; /*:[08may2006 mt]*/ if(AX.currentPrompt){ M_free(AX.currentPrompt,"external channel prompt"); AX.currentPrompt=0; } /*[08may2006 mt]:*/ if(AX.shellname){ M_free(AX.shellname,"external channel shellname"); AX.shellname=0; } if(AX.stderrname){ M_free(AX.stderrname,"external channel stderrname"); AX.stderrname=0; } /*:[08may2006 mt]*/ #endif #ifdef WITHPTHREADS if ( !WhoAmI() && !errorcode ) { TerminateAllThreads(); } #endif if ( AC.FinalStats ) { if ( AM.PrintTotalSize ) { MesPrint("Max. space for expressions: %19p bytes",&(AS.MaxExprSize)); } PrintRunningTime(); } #ifdef WITHMPI if ( AM.HoldFlag && PF.me == MASTER ) { WriteFile(AM.StdOut,(UBYTE *)("Hit any key "),12); PF_FlushStdOutBuffer(); getchar(); } #else if ( AM.HoldFlag ) { WriteFile(AM.StdOut,(UBYTE *)("Hit any key "),12); getchar(); } #endif #ifdef WITHMPI PF_Terminate(errorcode); #endif /* We are about to terminate the program. If we are using flint, call the cleanup function. This keeps valgrind happy. */ #ifdef WITHFLINT flint_final_cleanup_master(); #endif CleanUp(errorcode); M_print(); #ifdef VMS P_term(errorcode? 0: 1); #else P_term(errorcode); #endif } /* #] TerminateImpl : #[ PrintDeprecation : */ /** * Prints a deprecation warning for a given feature. * * @param feature The name of the deprecated feature. * @param issue The associated issue, e.g., "issues/700". */ void PrintDeprecation(const char *feature, const char *issue) { #ifdef WITHMPI if ( PF.me != MASTER ) return; #endif if ( AM.IgnoreDeprecation ) return; UBYTE *e = (UBYTE *)getenv("FORM_IGNORE_DEPRECATION"); if ( e && e[0] && StrCmp(e, (UBYTE *)"0") && StrICmp(e, (UBYTE *)"false") && StrICmp(e, (UBYTE *)"no") ) return; MesPrint("DeprecationWarning: We are considering deprecating %s.", feature); MesPrint("If you want this support to continue, leave a comment at:"); MesPrint(""); MesPrint(" https://github.com/form-dev/form/%s", issue); MesPrint(""); MesPrint("Otherwise, it will be discontinued in the future."); MesPrint("To suppress this warning, use the -ignore-deprecation command line option or"); MesPrint("set the environment variable FORM_IGNORE_DEPRECATION=1."); } /* #] PrintDeprecation : #[ PrintRunningTime : */ void PrintRunningTime(void) { #if (defined(WITHPTHREADS) && (defined(WITHPOSIXCLOCK) || defined(WINDOWS))) || defined(WITHMPI) LONG mastertime; LONG workertime; LONG wallclocktime; LONG totaltime; #if defined(WITHPTHREADS) if ( AB[0] != 0 ) { workertime = GetWorkerTimes(); #else workertime = PF_GetSlaveTimes(); /* must be called on all processors */ if ( PF.me == MASTER ) { #endif mastertime = AM.SumTime + TimeCPU(1); wallclocktime = TimeWallClock(1); totaltime = mastertime+workertime; if ( !AM.silent ) { MesPrint(" %l.%2i sec + %l.%2i sec: %l.%2i sec out of %l.%2i sec", mastertime/1000,(WORD)((mastertime%1000)/10), workertime/1000,(WORD)((workertime%1000)/10), totaltime/1000,(WORD)((totaltime%1000)/10), wallclocktime/100,(WORD)(wallclocktime%100)); } } #else LONG mastertime = AM.SumTime + TimeCPU(1); LONG wallclocktime = TimeWallClock(1); if ( !AM.silent ) { MesPrint(" %l.%2i sec out of %l.%2i sec", mastertime/1000,(WORD)((mastertime%1000)/10), wallclocktime/100,(WORD)(wallclocktime%100)); } #endif } /* #] PrintRunningTime : #[ GetRunningTime : */ LONG GetRunningTime(void) { #if defined(WITHPTHREADS) && (defined(WITHPOSIXCLOCK) || defined(WINDOWS)) LONG mastertime; if ( AB[0] != 0 ) { /* #if ( defined(APPLE64) || defined(APPLE32) ) mastertime = AM.SumTime + TimeCPU(1); return(mastertime); #else */ LONG workertime = GetWorkerTimes(); mastertime = AM.SumTime + TimeCPU(1); return(mastertime+workertime); /* #endif */ } else { return(AM.SumTime + TimeCPU(1)); } #elif defined(WITHMPI) LONG mastertime, t = 0; LONG workertime = PF_GetSlaveTimes(); /* must be called on all processors */ if ( PF.me == MASTER ) { mastertime = AM.SumTime + TimeCPU(1); t = mastertime + workertime; } return PF_BroadcastNumber(t); /* must be called on all processors */ #else return(AM.SumTime + TimeCPU(1)); #endif } /* #] GetRunningTime : */ form-5.0.1/sources/opera.c0000644000175100017510000016775415217035721011127 /** @file opera.c * * Contains the 'operations' * These are the trace routines, the contractions of the Levi-Civita tensors * and the tensor to vector/vector to tensor routines. * The trace and contraction routines are done in a special way * (see commentary with the FIXEDGLOBALS struct) */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : opera.c */ #include "form3.h" /* int hulp; */ /* #] Includes : #[ Operations : #[ EpfFind : WORD EpfFind(term,params) Searches for a pair of Levi-Civita tensors that should be contracted. If a match is found its settings are recorded in AT.TMout. type indicates the number of indices that is searched for, unless all are searched for (type = 0). number is the number of tensors that should survive contraction. */ int EpfFind(PHEAD WORD *term, WORD *params) { GETBIDENTITY WORD *t, *m, *r, n1 = 0, n2, min = -1, count, fac; WORD *c1 = 0, *c2 = 0, sgn = 1; WORD *tstop, *mstop; UWORD *facto = (UWORD *)AT.WorkPointer; WORD ncoef,nfac; WORD number, type; if ( ( AT.WorkPointer = (WORD *)(facto + AM.MaxTal) ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } number = params[3]; type = params[4]; t = term; GETSTOP(t,tstop); t++; if ( !type ) { while ( *t != LEVICIVITA && t < tstop ) t += t[1]; if ( t >= tstop ) return(0); m = t; while ( *m == LEVICIVITA && m < tstop ) { n1++; m += m[1]; } AllLev: if ( n1 <= (number+1) || n1 <= 1 ) return(0); mstop = m; m = t + t[1]; do { while ( m[1] == t[1] ) { m += FUNHEAD; r = t+FUNHEAD; count = fac = n1 = n2 = t[1] - FUNHEAD; while ( n1 && n2 ) { if ( *m > *r ) { r++; n2--; } else if ( *m < *r ) { m++; n1--; } else { if ( *m >= AM.OffsetIndex && ( ( *m >= AM.IndDum && AC.lDefDim == fac ) || ( *m < AM.IndDum && indices[*m-AM.OffsetIndex].dimension == fac ) ) ) { count--; } r++; m++; n1--; n2--; } } m += n1; if ( min < 0 || count < min ) { c1 = t; c2 = m - fac - FUNHEAD; min = count; } if ( m >= mstop ) break; } t += t[1]; } while ( ( m = t + t[1] ) < mstop ); } else { fac = type + FUNHEAD; while ( *t != LEVICIVITA && t < tstop ) t += t[1]; while ( *t == LEVICIVITA && t < tstop && t[1] != fac ) t += t[1]; if ( t >= tstop ) return(0); m = t; while ( *m == LEVICIVITA && m < tstop && m[1] == fac ) { n1++; m += m[1]; } goto AllLev; } /* We have now the two tensors that give the minimum contraction in c1 and c2. Prepare the AT.TMout array; */ if ( min < 0 ) return(0); /* No matching pair! */ t = c1; mstop = c2; fac = t[1] - FUNHEAD; m = AT.TMout; *m++ = 3 + (min*2); /* The full length */ *m++ = CONTRACT; if ( number < 0 ) *m++ = 1; else *m++ = 0; n1 = n2 = t[1] - FUNHEAD; r = c1 + FUNHEAD; c1 = m; m = c2 + FUNHEAD; c2 = c1 + min; while ( n1 && n2 ) { if ( *m > *r ) { *c1++ = *r++; n2--; } else if ( *m < *r ) { *c2++ = *m++; n1--; } else { if ( *m < AM.OffsetIndex || ( *m < AM.IndDum && ( indices[*m-AM.OffsetIndex].dimension != fac ) ) || ( *m >= AM.IndDum && AC.lDefDim != fac ) ) { *c1++ = *r++; *c2++ = *m++; } else { if ( ( n1 ^ n2 ) & 1 ) sgn = -sgn; r++; m++; } n1--; n2--; } } if ( n1 ) { NCOPY(c2,m,n1); } else if ( n2 ) { NCOPY(c1,r,n2); } fac -= min; m = t + t[1]; while ( m < mstop ) *t++ = *m++; m += m[1]; while ( m < tstop ) *t++ = *m++; *t++ = SUBEXPRESSION; *t++ = SUBEXPSIZE; *t++ = -1; *t++ = 1; *t++ = DUMMYBUFFER; FILLSUB(t) r = term; r += *r - 1; mstop = r; ncoef = REDLENG(*r); tstop = t; while ( m < mstop ) *t++ = *m++; if ( Factorial(BHEAD fac,facto,&nfac) || Mully(BHEAD (UWORD *)tstop,&ncoef,facto,nfac) ) { MLOCK(ErrorMessageLock); MesCall("EpfFind"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } tstop += (ABS(ncoef))*2; if ( sgn < 0 ) ncoef = -ncoef; ncoef *= 2; *tstop++ = (ncoef<0)?(ncoef-1):(ncoef+1); *term = WORDDIF(tstop,term); return(1); } /* #] EpfFind : #[ EpfCon : WORD EpfCon(term,params,num,level) Contraction of two strings of indices/vectors. They come from LeviCivita tensors that are being contracted. term is the term with the subterm to be replaced. params is the full indicator: Length, number, raise, parameters. Length is the length of the parameter field. number is the number of the operation. raise tells whether level should be raised afterwards. the parameters are the two strings. level is the id level. The factorial has been multiplied in already. */ int EpfCon(PHEAD WORD *term, WORD *params, WORD num, WORD level) { GETBIDENTITY WORD *kron, *perm, *termout, *tstop, size2; WORD *m, *t, sizes, sgn = 0, i; sizes = *params - 3; kron = AT.WorkPointer; perm = (AT.WorkPointer += sizes); termout = (AT.WorkPointer += sizes); AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } params += 2; if ( !(*params++) ) level--; size2 = sizes>>1; if ( !size2 ) goto DoOnce; while ( ( sgn = EpfGen(size2,params,kron,perm,sgn) ) != 0 ) { DoOnce: t = term; GETSTOP(t,tstop); m = termout; tstop -= SUBEXPSIZE; while ( t < tstop ) *m++ = *t++; if ( t[2] != num || *t != SUBEXPRESSION ) { MLOCK(ErrorMessageLock); MesPrint("Serious error in EpfCon"); MUNLOCK(ErrorMessageLock); return(-1); } tstop += SUBEXPSIZE; if ( sizes ) { *m++ = DELTA; *m++ = sizes + 2; t = kron; i = sizes; if ( i ) { NCOPY(m,t,i); } } t = tstop; tstop = term + *term; while ( t < tstop ) *m++ = *t++; *termout = WORDDIF(m,termout); m--; if ( sgn < 0 ) *m = - *m; if ( *termout ) { *AN.RepPoint = 1; AR.expchanged = 1; AT.WorkPointer = termout + *termout; if ( Generator(BHEAD termout,level) < 0 ) goto EpfCall; } } AT.WorkPointer = kron; return(0); EpfCall: if ( AM.tracebackflag ) { MLOCK(ErrorMessageLock); MesCall("EpfCon"); MUNLOCK(ErrorMessageLock); } return(-1); } /* #] EpfCon : #[ EpfGen : WORD EpfGen(number,inlist,kron,perm,sgn) */ WORD EpfGen(WORD number, WORD *inlist, WORD *kron, WORD *perm, WORD sgn) { WORD i, *in2, k, a; if ( !sgn ) { in2 = inlist + number; number *= 2; for ( i = 1; i < number; i += 2 ) { *perm++ = i; *perm++ = i; *kron++ = *inlist++; *kron++ = *in2++; } if ( number <= 0 ) return(0); else return(1); } number *= 2; i = number - 1; while ( ( i -= 2 ) >= 0 ) { if ( ( k = perm[i] ) != i ) { sgn = -sgn; a = kron[i]; kron[i] = kron[k]; kron[k] = a; } if ( ( k = ( perm[i] += 2 ) ) < number ) { a = kron[i]; kron[i] = kron[k]; kron[k] = a; sgn = - sgn; for ( k = i + 2; k < number; k += 2 ) perm[k] = k; return(sgn); } } return(0); } /* #] EpfGen : #[ Trick : WORD Trick(in,t) This routine implements the identity: g_(j,mu)*g_(j,nu)*g_(j,ro)=e_(mu,nu,ro,si)*g5_(j)*g_(j,si) +d_(mu,nu)*g_(j,ro)-d_(mu,ro)*g_(j,nu)+d_(nu,ro)*g_(j,mu) which is for 4 dimensions only! Note that z->gamm = 1 if there is no g5 present. */ WORD Trick(WORD *in, TRACES *t) { WORD n, n1; n = t->stap; n1 = t->step1; switch ( t->eers[n] ) { case 0: { WORD *p; p = t->pepf + t->mepf[n]; *p++ = *in++; *p++ = *in++; *p++ = *in; *p = ++(t->mdum); (t->mepf[n1]) += 4; *in = t->mdum; t->gamm = - t->gamm; t->eers[n] = 5; break; } case 4: { WORD *p; p = t->pdel + t->mdel[n]; (t->mepf[n1]) -= 4; (t->mdum)--; *p++ = *in++; *p = *in++; *in = *(t->pepf + t->mepf[n] + 2); (t->mdel[n1]) += 2; t->gamm = - t->gamm; break; } case 3: { t->sign1 = - t->sign1; *(t->pdel + t->mdel[n] + 1) = in[2]; in[2] = in[1]; break; } case 2: { t->sign1 = - t->sign1; in[2] = in[0]; *(t->pdel + t->mdel[n]) = in[1]; break; } case 1: { in[2] = *(t->pdel + t->mdel[n] + 1); (t->mdel[n1]) -= 2; break; } default: { return(0); } } return(--(t->eers[n])); } /* #] Trick : #[ Trace4no : WORD Trace4no(number,kron,t) Takes the trace of a string of gamma matrices in 4 dimensions. There is no test for indices or vectors that are the same. The four dimensions refer to the contraction in the algebra: g_(i,a,b,c) = e_(a,b,c,d)*g_(i,5_,d) + g_(i,a)*d_(b,c) - g_(i,b)*d_(a,c) + g_(i,c)*d_(a,b) This simplifies life very much and leads to shorter expressions than in the n dimensional case. Parameters: number: the number of vectors/indices in inlist. inlist: the indices/vectors in the string. kron: the output delta's. gamma5: the potential gamma5 in front. t: the struct for scratch manipulations. stack: the space to put all scratch arrays in. The return value is zero if there are no more terms, 1 if a term was generated with a positive sign and -1 if a term was generated with a negative sign. The value of one is increased to two if the first 4 values in kron should be interpreted as a Levi-Civita tensor. Note that kron should have more places reserved than the number of indices in inlist, because it will contain dummy indices temporarily. In principle there can be 'number*1/4' extra dummies. */ int Trace4no(WORD number, WORD *kron, TRACES *t) { WORD i; WORD *p, *m; WORD *stop, oldsign; int retval; if ( !t->sgn ) { /* Startup */ if ( ( number < 0 ) || ( number & 1 ) ) return(0); if ( number <= 2 ) { if ( t->gamma5 == GAMMA5 ) return(0); if ( number == 2 ) { *kron++ = *t->inlist; *kron++ = t->inlist[1]; } return(1); } t->sgn = 1; { WORD nhalf = number >> 1; WORD ndouble = number * 2; p = t->eers; t->eers = p; p += nhalf; t->mepf = p; p += nhalf; t->mdel = p; p += nhalf; t->pdel = p; p += number + nhalf; t->pepf = p; p += ndouble; t->e4 = p; p += number; t->e3 = p; p += ndouble; t->nt3 = p; p += nhalf; t->nt4 = p; p += nhalf; t->j3 = p; p += ndouble; t->j4 = p; } t->mepf[0] = 0; t->mdel[0] = 0; t->mdum = AM.mTraceDum; t->kstep = -2; t->step1 = 0; t->sign1 = 1; t->lc3 = -1; t->lc4 = -1; t->gamm = 1; do { t->stap = (t->step1)++; t->kstep += 2; t->eers[t->stap] = 0; t->mepf[t->step1] = t->mepf[t->stap]; t->mdel[t->step1] = t->mdel[t->stap]; CallTrick: while ( !Trick(t->inlist+t->kstep,t) ) { t->kstep -= 2; t->step1 = (t->stap)--; if ( t->stap < 0 ) { return(0); } } } while ( t->kstep < (number-4) ); /* Take now the trace of the leftover matrices. If gamma5 causes the term to vanish there will be a renewed call to Trick for its next term. */ t->sign2 = t->sign1; if ( ( t->gamma5 == GAMMA7 ) && ( t->gamm == -1 ) ) { t->sign2 = - t->sign2; } else if ( ( t->gamma5 == GAMMA5 ) && ( t->gamm == 1 ) ) { goto CallTrick; } else if ( ( t->gamma5 == GAMMA1 ) && ( t->gamm == -1 ) ) { goto CallTrick; } p = t->pdel + t->mdel[t->step1]; *p++ = t->inlist[t->kstep+2]; *p++ = t->inlist[t->kstep+3]; /* Now the trace has been expressed in terms of Levi-Civita tensors and Kronecker delta's. The Levi-Civita tensors are in t->pepf and there are t->mepf[step1] elements in this array. The Kronecker delta's are in t->pdel and there are t->mdel[step1] elements in this array. Next we rake the Levi-Civita tensors together such that there is an optimal use of the contractions. */ { WORD ae; ae = t->mepf[t->step1]; t->ad = t->mdel[t->step1]+2; t->a4 = 0; t->a3 = 0; while ( ( ae -= 4 ) >= 0 ) { if ( t->pepf[ae] > AM.mTraceDum && t->pepf[ae] <= t->mdum ) { p = t->e3 + t->a3; m = t->pepf + ae; for ( i = 0; i < 3; i++ ) { p[3] = m[3-i]; *p++ = m[i-4]; } t->a3 += 6; ae -= 4; } else { p = t->e4 + t->a4; m = t->pepf + ae; for ( i = 0; i < 4; i++ ) *p++ = *m++; t->a4 += 4; } } } /* Now e3 contains pairs of LeviCivita tensors that have three indices each and a3 is the total number of indices. e4 contains individual tensors with 4 indices. Some indices may be contracted with Kronecker delta's. Contract the e3 tensors first. */ while ( t->a3 > 0 ) { t->nt3[++(t->lc3)] = 0; while ( ( t->nt3[t->lc3] = EpfGen(3,t->e3+t->a3-6, t->pdel+t->ad,t->j3+6*t->lc3,oldsign = t->nt3[t->lc3]) ) == 0 ) { if ( oldsign < 0 ) t->sign2 = - t->sign2; (t->lc3)--; NextE3: if ( t->lc3 < 0 ) goto CallTrick; t->ad -= 6; t->a3 += 6; } if ( oldsign ) { if ( oldsign != t->nt3[t->lc3] ) t->sign2 = - t->sign2; } else if ( t->nt3[t->lc3] < 0 ) t->sign2 = - t->sign2; t->a3 -= 6; t->ad += 6; } /* Contract the e4 tensors. */ while ( t->a4 > 4 ) { t->nt4[++(t->lc4)] = 0; while ( ( t->nt4[t->lc4] = EpfGen(4,t->e4+t->a4-8, t->pdel+t->ad,t->j4+8*t->lc4,oldsign = t->nt4[t->lc4]) ) == 0 ) { if ( oldsign < 0 ) t->sign2 = - t->sign2; (t->lc4)--; NextE4: if ( t->lc4 < 0 ) goto NextE3; t->ad -= 8; t->a4 += 8; } if ( oldsign ) { if ( oldsign != t->nt4[t->lc4] ) t->sign2 = - t->sign2; } else if ( t->nt4[t->lc4] < 0 ) t->sign2 = - t->sign2; t->a4 -= 8; t->ad += 8; } /* Finally the extra dummy indices can be eliminated. Note that there are currently t->ad words in t->pdel forming t->ad / 2 Kronecker delta's. We are however not allowed to alter anything in these arrays, so the results should be copied to kron. */ m = kron; if ( t->a4 == 4 ) { p = t->e4; *m++ = *p++; *m++ = *p++; *m++ = *p++; *m++ = *p++; retval = 2; } else retval = 1; if ( t->sign2 < 0 ) retval = - retval; p = t->pdel; for ( i = 0; i < t->ad; i++ ) *m++ = *p++; p = kron; if ( t->a4 == 4 ) { /* Test for dummies in the last position of the e_. */ stop = p + t->ad + 4; p += 3; while ( *p >= AM.mTraceDum && *p <= t->mdum ) { m = p + 1; do { if ( *m == *p ) { *p = m[1]; *m = *--stop; m[1] = *--stop; break; } else if ( m[1] == *p ) { *p = *m; *m = *--stop; m[1] = *--stop; break; } else m += 2; } while ( m < stop ); } p++; } else stop = p + t->ad; while ( p < (stop-2) ) { while ( *p >= AM.mTraceDum && *p <= t->mdum ) { m = p + 2; do { if ( *m == *p ) { *p = m[1]; *m = *--stop; m[1] = *--stop; break; } else if ( m[1] == *p ) { *p = *m; *m = *--stop; m[1] = *--stop; break; } else m += 2; } while ( m < stop ); } p++; while ( *p >= AM.mTraceDum && *p <= t->mdum ) { m = p + 1; do { if ( *m == *p ) { *p = m[1]; *m = *--stop; m[1] = *--stop; break; } else if ( m[1] == *p ) { *p = *m; *m = *--stop; m[1] = *--stop; break; } else m += 2; } while ( m < stop ); } p++; } return(retval); } if ( number <= 2 ) return(0); else { goto NextE4; } } /* #] Trace4no : #[ Trace4 : WORD Trace4(term,params,num,level) Generates traces of the string of gamma matrices in 'instring'. The difference with the routine tracen ( for n dimensions ) lies in the treatment of gamma 5 and the specific form of the Chisholm identities. The identities used here are g(mu)*g(a1)*...*g(an)*g(mu)= n=odd: -2*g(an)*...*g(a1) ( reversed order ) n=even: 2*g(an)*g(a1)*...*g(a(n-1)) +2*g(a(n-1))*...*g(a1)*g(an) There is a special case for n=2 : 4*d(a1,a2)*gi The main difference with the old fortran version lies in the recursion that is used here. That cleans up the variables very much. The contents of the AT.TMout array are: length,type,gamma5,gamma's The space for the vectors in t is at most 14 * number. The condition params[5] == 0 corresponds to finding gamma6*gamma7 during the pick up of the matrices. */ int Trace4(PHEAD WORD *term, WORD *params, WORD num, WORD level) { GETBIDENTITY TRACES *t; WORD *p, *m, number, i; WORD *OldW; WORD j, minimum, minimum2, *min, *stopper; int ret; OldW = AT.WorkPointer; if ( AN.numtracesctack >= AN.intracestack ) { number = AN.intracestack + 2; t = (TRACES *)Malloc1(number*sizeof(TRACES),"TRACES-struct"); if ( AN.tracestack ) { for ( i = 0; i < AN.intracestack; i++ ) { t[i] = AN.tracestack[i]; } M_free(AN.tracestack,"TRACES-struct"); } AN.tracestack = t; AN.intracestack = number; } number = *params - 6; if ( number < 0 || ( number & 1 ) || !params[5] ) return(0); t = AN.tracestack + AN.numtracesctack; AN.numtracesctack++; t->finalstep = ( params[2] & 16 ) ? 1 : 0; t->gamma5 = params[3]; if ( t->finalstep && t->gamma5 != GAMMA1 ) { MLOCK(ErrorMessageLock); MesPrint("Gamma5 not allowed in this option of the trace command"); MUNLOCK(ErrorMessageLock); AN.numtracesctack--; SETERROR(-1) } t->inlist = AT.WorkPointer; t->accup = t->accu = t->inlist + number; t->perm = t->accu + (number*2); t->eers = t->perm + number; if ( ( AT.WorkPointer += 19 * number ) >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } t->num = num; t->level = level; p = t->inlist; m = params+6; for ( i = 0; i < number; i++ ) *p++ = *m++; t->termp = term; t->factor = params[4]; t->allsign = params[5]; if ( number >= 10 || ( t->gamma5 != GAMMA1 && number > 4 ) ) { /* The next code should `normal order' the string We need the lexicographic smallest string, taking also the reverse strings into account. */ minimum = 0; min = t->inlist; stopper = min + number; for ( i = 1; i < number; i++ ) { p = min; m = t->inlist + i; for ( j = 0; j < number; j++ ) { if ( *p < *m ) break; if ( *p > *m ) { min = t->inlist+i; minimum = i; break; } p++; m++; if ( m >= stopper ) m = t->inlist; if ( p >= stopper ) p = t->inlist; } } p = min; min = m = AT.WorkPointer; i = number; while ( --i >= 0 ) { *m++ = *p++; if ( p >= stopper ) p = t->inlist; } p = t->inlist; m = min; i = number; while ( --i >= 0 ) *p++ = *m++; p = t->inlist; m = stopper; while ( p < m ) { /* reverse string */ i = *p; *p++ = *--m; *m = i; } minimum2 = 0; for ( i = 0; i < number; i++ ) { p = min; m = t->inlist + i; for ( j = 0; j < number; j++ ) { if ( *p < *m ) break; if ( *p > *m ) { m = t->inlist + i; p = min; j = number; while ( --j >= 0 ) { *p++ = *m++; if ( m >= stopper ) m = t->inlist; } minimum2 = i; break; } p++; m++; if ( m >= stopper ) m = t->inlist; } } minimum ^= minimum2; if ( ( minimum & 1 ) != 0 ) { if ( t->gamma5 == GAMMA5 ) t->allsign = - t->allsign; else if ( t->gamma5 != GAMMA1 ) t->gamma5 = GAMMA6 + GAMMA7 - t->gamma5; } p = min; m = t->inlist; i = number; while ( --i >= 0 ) *m++ = *p++; /* Now the trace is in normal order */ } ret = Trace4Gen(BHEAD t,number); AT.WorkPointer = OldW; AN.numtracesctack--; return(ret); } /* #] Trace4 : #[ Trace4Gen : WORD Trace4Gen(t,number) The recursive breakdown of a trace in 4 dimensions. We test first whether the trace has zero or two gamma's left. This case can be done quickly. Next we test whether we can eliminate adjacent objects that are the same. Then we test for Chisholm identities (I). First for identities with an odd number of gamma matrices (II), then for those with an even number of matrices (III). The special thing here is the demand that the contraction be between indices with 4 dimensions only. Then there is a scan for objects that are the same, not regarding their type (IV). This is exactly the same as in n dimensions. Finally we have a string left in which all objects are different (V). This case is treated by the routine Trace4no (no stands for no objects are the same). In case I we have one d_ of which the result of the contraction has not yet been fixed. Case II gives just a reordering of the matrices and a factor -2. Case III gives two terms: one for the anti commutation, such that the number of intermediate matrices becomes odd and the other from the Chisholm rule for an odd number of matrices. Both have a factor 2. Case IV gives m+1 terms when m is the number of matrices inbetween. We take the shortest path. The sign alternates and all terms have a factor two, except for the last one. */ int Trace4Gen(PHEAD TRACES *t, WORD number) { GETBIDENTITY WORD *termout, *stop; WORD *p, *m, oldval; WORD *pold, *mold, diff, *oldstring, cp; /* #[ Special cases : */ if ( number <= 2 ) { /* Special cases */ if ( t->gamma5 == GAMMA5 ) return(0); termout = AT.WorkPointer; p = t->termp; stop = p + *p; m = termout; p++; if ( p < stop ) do { if ( *p == SUBEXPRESSION && p[2] == t->num ) { oldstring = p; p = t->termp; do { *m++ = *p++; } while ( p < oldstring ); p += p[1]; *m++ = AC.lUniTrace[0]; *m++ = AC.lUniTrace[1]; *m++ = AC.lUniTrace[2]; *m++ = AC.lUniTrace[3]; if ( number == 2 || t->accup > t->accu ) { oldstring = m; *m++ = DELTA; *m++ = 4; if ( number == 2 ) { *m++ = t->inlist[0]; *m++ = t->inlist[1]; } if ( t->accup > t->accu ) { pold = p; p = t->accu; while ( p < t->accup ) *m++ = *p++; oldstring[1] = WORDDIF(m,oldstring); p = pold; } } if ( t->factor ) { *m++ = SNUMBER; *m++ = 4; *m++ = 2; *m++ = t->factor; } do { *m++ = *p++; } while ( p < stop ); *termout = WORDDIF(m,termout); if ( t->allsign < 0 ) m[-1] = -m[-1]; if ( ( AT.WorkPointer = m ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } *AN.RepPoint = 1; AR.expchanged = 1; if ( *termout ) { *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,t->level) ) goto TracCall; } AT.WorkPointer= termout; return(0); } p += p[1]; } while ( p < stop ); return(0); } /* #] Special cases : #[ Adjacent objects : */ p = t->inlist; stop = p + number - 1; if ( *p == *stop ) { /* First and last of string */ oldval = *p; *(t->accup)++ = *p; *(t->accup)++ = *p; m = p+1; while ( m < stop ) *p++ = *m++; if ( t->gamma5 != GAMMA1 ) { if ( t->gamma5 == GAMMA5 ) t->allsign = - t->allsign; else if ( t->gamma5 == GAMMA6 ) t->gamma5 = GAMMA7; else if ( t->gamma5 == GAMMA7 ) t->gamma5 = GAMMA6; } if ( Trace4Gen(BHEAD t,number-2) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; if ( t->gamma5 != GAMMA1 ) { if ( t->gamma5 == GAMMA5 ) t->allsign = - t->allsign; else if ( t->gamma5 == GAMMA6 ) t->gamma5 = GAMMA7; else if ( t->gamma5 == GAMMA7 ) t->gamma5 = GAMMA6; } while ( p > t->inlist ) *--m = *--p; *p = *stop = oldval; t->accup -= 2; return(0); } do { if ( *p == p[1] ) { /* Adjacent in string */ oldval = *p; pold = p; m = p+2; *(t->accup)++ = *p; *(t->accup)++ = *p; while ( m <= stop ) *p++ = *m++; if ( Trace4Gen(BHEAD t,number-2) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; while ( p > pold ) *--m = *--p; *p++ = oldval; *p++ = oldval; t->accup -= 2; return(0); } p++; } while ( p < stop ); /* #] Adjacent objects : #[ Odd Contraction : */ p = t->inlist; stop = p + number; do { if ( *p >= AM.OffsetIndex && ( ( *p < WILDOFFSET + AM.OffsetIndex && indices[*p-AM.OffsetIndex].dimension == 4 ) || ( *p >= WILDOFFSET + AM.OffsetIndex && AC.lDefDim == 4 ) ) ) { m = p+2; while ( m < stop ) { if ( *p == *m ) { pold = p; mold = m; oldval = *p; (t->factor)++; t->allsign = - t->allsign; *p++ = *--m; m--; while ( m > p ) { diff = *p; *p++ = *m; *m-- = diff; } p = mold - 1; m = mold + 1; while ( m < stop ) *p++ = *m++; if ( Trace4Gen(BHEAD t,number-2) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; m--; while ( m > mold ) *m-- = *--p; p = pold; *m-- = oldval; *m-- = *p; *p++ = oldval; while ( m > p ) { diff = *p; *p++ = *m; *m-- = diff; } t->allsign = - t->allsign; (t->factor)--; return(0); } m += 2; } } p++; } while ( p < stop ); /* #] Odd Contraction : #[ Even Contraction : First the case with two matrices inbetween. */ p = t->inlist; stop = p + number; do { if ( *p >= AM.OffsetIndex && ( ( *p < WILDOFFSET + AM.OffsetIndex && indices[*p-AM.OffsetIndex].dimension == 4 ) || ( *p >= WILDOFFSET + AM.OffsetIndex && AC.lDefDim == 4 ) ) ) { m = p+3; if ( m >= stop ) m -= number; if ( *p == *m ) { WORD oldfactor, old5; oldstring = AT.WorkPointer; AT.WorkPointer += number; oldfactor = t->allsign; old5 = t->gamma5; if ( m < p ) cp = (WORDDIF(m,t->inlist) + 1 ) & 1; else cp = 0; if ( cp && ( t->gamma5 != GAMMA1 ) ) { if ( t->gamma5 == GAMMA5 ) t->allsign = -t->allsign; else if ( t->gamma5 == GAMMA6 ) t->gamma5 = GAMMA7; else if ( t->gamma5 == GAMMA7 ) t->gamma5 = GAMMA6; } mold = m; p = oldstring; m = t->inlist; while ( m < stop ) *p++ = *m++; /* Rotate the string */ m = mold + 1; p = t->inlist; while ( m < stop ) *p++ = *m++; m = oldstring; if ( !cp && ((WORDDIF(stop,p))&1) != 0 && ( t->gamma5 != GAMMA1 ) ) { if ( t->gamma5 == GAMMA5 ) t->allsign = -t->allsign; else if ( t->gamma5 == GAMMA6 ) t->gamma5 = GAMMA7; else if ( t->gamma5 == GAMMA7 ) t->gamma5 = GAMMA6; } while ( p < stop ) *p++ = *m++; t->factor += 2; m = p - 3; p = t->inlist; oldval = number - 4; while ( oldval > 0 ) { if ( *p >= AM.OffsetIndex && ( ( *p < WILDOFFSET + AM.OffsetIndex && indices[*p-AM.OffsetIndex].dimension ) || ( *p >= WILDOFFSET + AM.OffsetIndex && AC.lDefDim ) ) ) { if ( *p == *m ) { *p = m[1]; break; } else if ( *p == m[1] ) { *p = *m; break; } } p++; oldval--; } if ( oldval <= 0 ) { *(t->accup)++ = *m++; *(t->accup)++ = *m++; } if ( Trace4Gen(BHEAD t,number-4) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; t->factor -= 2; if ( oldval <= 0 ) t->accup -= 2; t->gamma5 = old5; t->allsign = oldfactor; AT.WorkPointer = p = oldstring; m = t->inlist; while ( m < stop ) *m++ = *p++; return(0); } } p++; } while ( p < stop ); /* The case with at least 4 matrices inbetween. */ p = t->inlist; stop = p + number; do { if ( *p >= AM.OffsetIndex && ( ( *p < WILDOFFSET + AM.OffsetIndex && indices[*p-AM.OffsetIndex].dimension == 4 ) || ( *p >= WILDOFFSET + AM.OffsetIndex && AC.lDefDim == 4 ) ) ) { m = p+5; while ( m < stop ) { if ( *p == *m ) { WORD *pex, *mex; pold = p; mold = m; oldval = *p; /* g_(1,mu)*g_(1,a1)*...*g_(1,aj)*g_(1,an)*g_(1,mu) -> first: 2*g_(1,an)*g_(1,a1)*...*g_(1,aj) */ (t->factor)++; /* The variable hulp seems unnecessary *p = hulp = m[-1]; */ *p = m[-1]; p = m - 1; m++; while ( m < stop ) *p++ = *m++; if ( Trace4Gen(BHEAD t,number-2) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; pex = p; mex = m; p = pold; m = mold - 2; while ( m > p ) { diff = *p; *p++ = *m; *m-- = diff; } /* and then: 2*g_(1,aj)*...*g_(1,a1)*g_(1,an) */ if ( Trace4Gen(BHEAD t,number-2) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; p = pold; m = mold - 2; while ( m > p ) { diff = *p; *p++ = *m; *m-- = diff; } m = mex; p = pex; m--; while ( m > mold ) *m-- = *--p; m = mold; *m-- = oldval; p = pold; *m = *p; *p = oldval; (t->factor)--; return(0); } m += 2; } } p++; } while ( p < stop ); /* #] Even Contraction : #[ Same Objects : */ p = t->inlist; stop = p + number - 1; diff = 2; do { p = t->inlist; while ( p <= stop ) { m = p + diff; if ( m > stop ) m -= number; if ( *p == *m ) { WORD oldfactor, c, old5; oldfactor = t->allsign; old5 = t->gamma5; cp = (WORDDIF(m,t->inlist)) & 1; if ( !cp && ( t->gamma5 != GAMMA1 ) ) { if ( t->gamma5 == GAMMA5 ) t->allsign = -t->allsign; else if ( t->gamma5 == GAMMA6 ) t->gamma5 = GAMMA7; else if ( t->gamma5 == GAMMA7 ) t->gamma5 = GAMMA6; } oldstring = AT.WorkPointer; AT.WorkPointer += number; mold = m; oldval = *p; p = oldstring; m = t->inlist; while ( m <= stop ) *p++ = *m++; /* Rotate the string */ m = mold + 1; p = t->inlist; while ( m <= stop ) *p++ = *m++; m = oldstring; while ( p <= stop ) *p++ = *m++; (t->factor)++; p -= diff + 1; m = stop; *(t->accup) = oldval; t->accup += 2; m--; while ( m > p ) { c = t->accup[-1]; t->accup[-1] = *m; *m = c; if ( Trace4Gen(BHEAD t,number-2) ) goto Trac4Call; t = AN.tracestack + AN.numtracesctack - 1; m--; t->allsign = - t->allsign; } c = t->accup[-1]; t->accup[-1] = *m; *m = c; (t->factor)--; if ( Trace4Gen(BHEAD t,number-2) ) goto Trac4Call; t = AN.tracestack + AN.numtracesctack - 1; t->accup -= 2; t->allsign = oldfactor; AT.WorkPointer = p = oldstring; m = t->inlist; while ( m <= stop ) *m++ = *p++; t->gamma5 = old5; return(0); } p++; } } while ( ++diff <= (number>>1) ); /* #] Same Objects : #[ All Different : Here we have a string with all different objects. */ t->sgn = 0; termout = AT.WorkPointer; for(;;) { if ( t->finalstep == 0 ) diff = Trace4no(number,t->accup,t); else diff = TraceNno(number,t->accup,t); /* while ( ( diff = Trace4no(number,t->accup,t) ) != 0 ) */ if ( diff == 0 ) break; p = t->termp; stop = p + *p; m = termout; p++; if ( p < stop ) do { if ( *p == SUBEXPRESSION && p[2] == t->num ) { oldstring = p; p = t->termp; do { *m++ = *p++; } while ( p < oldstring ); p += p[1]; pold = p; *m++ = AC.lUniTrace[0]; *m++ = AC.lUniTrace[1]; *m++ = AC.lUniTrace[2]; *m++ = AC.lUniTrace[3]; *m++ = SNUMBER; *m++ = 4; *m++ = 2; *m++ = t->factor; p = t->accup; oldval = number; if ( diff == 2 || diff == -2 ) { *m++ = LEVICIVITA; *m++ = 4+FUNHEAD; *m++ = DIRTYFLAG; FILLFUN3(m) *m++ = *p++; *m++ = *p++; *m++ = *p++; *m++ = *p++; oldval -= 4; } if ( oldval > 0 || t->accup > t->accu ) { oldstring = m; *m++ = DELTA; *m++ = oldval + 2; if ( oldval > 0 ) NCOPY(m,p,oldval); if ( t->accup > t->accu ) { p = t->accu; while ( p < t->accup ) *m++ = *p++; oldstring[1] = WORDDIF(m,oldstring); } } p = pold; do { *m++ = *p++; } while ( p < stop ); *termout = WORDDIF(m,termout); if ( ( diff ^ t->allsign ) < 0 ) m[-1] = - m[-1]; if ( ( AT.WorkPointer = m ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } if ( *termout ) { *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,t->level) ) { AT.WorkPointer = termout; goto TracCall; } t = AN.tracestack + AN.numtracesctack - 1; } break; } p += p[1]; } while ( p < stop ); } AT.WorkPointer = termout; return(0); /* #] All Different : */ Trac4Call: AT.WorkPointer = oldstring; TracCall: if ( AM.tracebackflag ) { MLOCK(ErrorMessageLock); MesCall("Trace4Gen"); MUNLOCK(ErrorMessageLock); } return(-1); } /* #] Trace4Gen : #[ TraceNno : WORD TraceNno(number,kron,t) Routine takes the trace in N dimensions of a string of gamma matrices. It is assumed that there are no contractions and no vectors that are the same. For the treatment of those cases there are special routines, that call this routine as a final stage. The calling routine must reserve 'number' WORDs for perm and kron each. kron and perm may not be altered during the generation! */ WORD TraceNno(WORD number, WORD *kron, TRACES *t) { WORD i, j, a, *p; if ( !t->sgn ) { if ( !number || ( number & 1 ) ) return(0); p = t->inlist; for ( i = 0; i < number; i++ ) { t->perm[i] = i; *kron++ = *p++; } t->sgn = 1; return(1); } else { i = number - 3; while ( i > 0 ) { a = kron[i]; p = t->perm + i; for ( j = i + 1; j <= *p; j++ ) kron[j-1] = kron[j]; kron[(*p)++] = a; if ( *p < number ) { a = kron[*p]; j = *p; while ( j >= (i+1) ) { kron[j] = kron[j-1]; j--; } kron[i] = a; number -= 2; for ( j = i+2; j < number; j += 2 ) t->perm[j] = j; t->sgn = - t->sgn; return(t->sgn); } i -= 2; } } return(0); } /* #] TraceNno : #[ TraceN : WORD TraceN(term,params,num,level) */ int TraceN(PHEAD WORD *term, WORD *params, WORD num, WORD level) { GETBIDENTITY TRACES *t; WORD *p, *m, number, i; WORD *OldW; int ret; if ( params[3] != GAMMA1 ) { MLOCK(ErrorMessageLock); MesPrint("Gamma5 not allowed in n-trace"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } OldW = AT.WorkPointer; if ( AN.numtracesctack >= AN.intracestack ) { number = AN.intracestack + 2; t = (TRACES *)Malloc1(number*sizeof(TRACES),"TRACES-struct"); if ( AN.tracestack ) { for ( i = 0; i < AN.intracestack; i++ ) { t[i] = AN.tracestack[i]; } M_free(AN.tracestack,"TRACES-struct"); } AN.tracestack = t; AN.intracestack = number; } number = *params - 6; if ( number < 0 || ( number & 1 ) || !params[5] ) return(0); t = AN.tracestack + AN.numtracesctack; AN.numtracesctack++; t->inlist = AT.WorkPointer; t->accup = t->accu = t->inlist + number; t->perm = t->accu + number; if ( ( AT.WorkPointer += 3 * number ) >= AT.WorkTop ) { AN.numtracesctack--; MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } t->num = num; t->level = level; p = t->inlist; m = params+6; for ( i = 0; i < number; i++ ) *p++ = *m++; t->termp = term; t->factor = params[4]; t->allsign = params[5]; ret = TraceNgen(BHEAD t,number); AT.WorkPointer = OldW; AN.numtracesctack--; return(ret); } /* #] TraceN : #[ TraceNgen : WORD TraceNgen(t,number) This routine is a simplified version of Trace4Gen. We know here only three cases: Adjacent objects, same objects and all different. The other difference lies of course in the struct which is now not of type TRACES, but of type TRACES. */ int TraceNgen(PHEAD TRACES *t, WORD number) { GETBIDENTITY WORD *termout, *stop; WORD *p, *m, oldval; WORD *pold, *mold, diff, *oldstring; /* #[ Special cases : */ if ( number <= 2 ) { /* Special cases */ termout = AT.WorkPointer; p = t->termp; stop = p + *p; m = termout; p++; if ( p < stop ) do { if ( *p == SUBEXPRESSION && p[2] == t->num ) { oldstring = p; p = t->termp; do { *m++ = *p++; } while ( p < oldstring ); p += p[1]; *m++ = AC.lUniTrace[0]; *m++ = AC.lUniTrace[1]; *m++ = AC.lUniTrace[2]; *m++ = AC.lUniTrace[3]; if ( number == 2 || t->accup > t->accu ) { oldstring = m; *m++ = DELTA; *m++ = 4; if ( number == 2 ) { *m++ = t->inlist[0]; *m++ = t->inlist[1]; } if ( t->accup > t->accu ) { pold = p; p = t->accu; while ( p < t->accup ) *m++ = *p++; oldstring[1] = WORDDIF(m,oldstring); p = pold; } } if ( t->factor ) { *m++ = SNUMBER; *m++ = 4; *m++ = 2; *m++ = t->factor; } do { *m++ = *p++; } while ( p < stop ); *termout = WORDDIF(m,termout); if ( t->allsign < 0 ) m[-1] = -m[-1]; if ( ( AT.WorkPointer = m ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } if ( *termout ) { *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,t->level) ) goto TracCall; } AT.WorkPointer= termout; return(0); } p += p[1]; } while ( p < stop ); return(0); } /* #] Special cases : #[ Adjacent objects : */ p = t->inlist; stop = p + number - 1; if ( *p == *stop ) { /* First and last of string */ oldval = *p; *(t->accup)++ = *p; *(t->accup)++ = *p; m = p+1; while ( m < stop ) *p++ = *m++; if ( TraceNgen(BHEAD t,number-2) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; while ( p > t->inlist ) *--m = *--p; *p = *stop = oldval; t->accup -= 2; return(0); } do { if ( *p == p[1] ) { /* Adjacent in string */ oldval = *p; pold = p; m = p+2; *(t->accup)++ = *p; *(t->accup)++ = *p; while ( m <= stop ) *p++ = *m++; if ( TraceNgen(BHEAD t,number-2) ) goto TracCall; t = AN.tracestack + AN.numtracesctack - 1; while ( p > pold ) *--m = *--p; *p++ = oldval; *p++ = oldval; t->accup -= 2; return(0); } p++; } while ( p < stop ); /* #] Adjacent objects : #[ Same Objects : */ p = t->inlist; stop = p + number - 1; diff = 2; do { p = t->inlist; while ( p <= stop ) { m = p + diff; if ( m > stop ) m -= number; if ( *p == *m ) { WORD oldfactor, c; oldstring = AT.WorkPointer; AT.WorkPointer += number; mold = m; oldval = *p; p = oldstring; m = t->inlist; while ( m <= stop ) *p++ = *m++; /* Rotate the string */ { m = mold + 1; p = t->inlist; while ( m <= stop ) *p++ = *m++; m = oldstring; while ( p <= stop ) *p++ = *m++; } oldfactor = t->allsign; (t->factor)++; p -= diff + 1; m = stop; if ( oldval >= ( AM.OffsetIndex + WILDOFFSET ) || ( oldval >= AM.OffsetIndex && indices[oldval-AM.OffsetIndex].dimension ) ) { m--; /* We distinguish 4 cases: m-p=1 Use g_(1,mu,a,mu) = (2-d_(mu,mu))*g_(1,a) m-p=2 Use g_(1,mu,a,b,mu) = 4*d_(a,b)+(d_(mu,mu)-4)*g_(1,a,b) m-p=3 Use g_(1,mu,a,b,c,mu) = -2*g_(1,c,b,a) -(d_(mu,mu)-4)*g_(1,a,b,c) m-p>3 Reduce down to m-p=3 with the old technique */ while ( m > (p+3) ) { c = *p; *p = *m; *m = c; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; m--; t->allsign = - t->allsign; } switch ( WORDDIF(m,p) ) { case 1: c = *p; *p = *m; *m = c; if ( oldval < ( AM.OffsetIndex + WILDOFFSET ) && indices[oldval-AM.OffsetIndex].nmin4 != -NMIN4SHIFT ) { t->allsign = - t->allsign; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; (t->factor)--; *(t->accup)++ = SUMMEDIND; *(t->accup)++ = indices[oldval-AM.OffsetIndex].nmin4; } else { if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->allsign = - t->allsign; (t->factor)--; *(t->accup)++ = oldval; *(t->accup)++ = oldval; } if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->accup -= 2; break; case 2: { WORD one, two; one = *p = p[1]; two = p[1] = *m; (t->factor)++; /* 4 */ *(t->accup)++ = *p; /* d_(a,b) */ *(t->accup)++ = *m; if ( TraceNgen(BHEAD t,number-4) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; *p = one; p[1] = two; t->accup -= 2; if ( oldval < ( AM.OffsetIndex + WILDOFFSET ) && indices[oldval-AM.OffsetIndex].nmin4 != -NMIN4SHIFT ) { t->factor -= 2; *(t->accup)++ = SUMMEDIND; *(t->accup)++ = indices[oldval-AM.OffsetIndex].nmin4; } else { t->allsign = - t->allsign; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->allsign = - t->allsign; t->factor -= 2; *(t->accup)++ = oldval; *(t->accup)++ = oldval; } if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->accup -= 2; } break; default: c = *p; *p = *m; *m = c; c = m[-1]; m[-1] = m[-2]; m[-2] = c; t->allsign = - t->allsign; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; m--; c = *p; *p = *m; *m = c; (t->factor)--; if ( oldval < ( AM.OffsetIndex + WILDOFFSET ) && indices[oldval-AM.OffsetIndex].nmin4 != -NMIN4SHIFT ) { *(t->accup)++ = SUMMEDIND; *(t->accup)++ = indices[oldval-AM.OffsetIndex].nmin4; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->accup -= 2; t->allsign = - t->allsign; } else { *(t->accup)++ = oldval; *(t->accup)++ = oldval; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->accup -= 2; t->allsign = - t->allsign; t->factor += 2; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->factor -= 2; } break; } } else { *(t->accup) = oldval; t->accup += 2; m--; while ( m > p ) { c = t->accup[-1]; t->accup[-1] = *m; *m = c; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; m--; t->allsign = - t->allsign; } c = t->accup[-1]; t->accup[-1] = *m; *m = c; (t->factor)--; if ( TraceNgen(BHEAD t,number-2) ) goto TracnCall; t = AN.tracestack + AN.numtracesctack - 1; t->accup -= 2; } t->allsign = oldfactor; p = oldstring; m = t->inlist; while ( m <= stop ) *m++ = *p++; AT.WorkPointer = oldstring; return(0); } p++; } diff++; } while ( diff <= (number>>1) ); /* #] Same Objects : #[ All Different : Here we have a string with all different objects. */ t->sgn = 0; termout = AT.WorkPointer; while ( ( diff = TraceNno(number,t->accup,t) ) != 0 ) { p = t->termp; stop = p + *p; m = termout; p++; if ( p < stop ) do { if ( *p == SUBEXPRESSION && p[2] == t->num ) { oldstring = p; p = t->termp; do { *m++ = *p++; } while ( p < oldstring ); p += p[1]; pold = p; *m++ = AC.lUniTrace[0]; *m++ = AC.lUniTrace[1]; *m++ = AC.lUniTrace[2]; *m++ = AC.lUniTrace[3]; *m++ = SNUMBER; *m++ = 4; *m++ = 2; *m++ = t->factor; p = t->accup; oldval = number; oldstring = m; *m++ = DELTA; *m++ = oldval + 2; NCOPY(m,p,oldval); if ( t->accup > t->accu ) { p = t->accu; while ( p < t->accup ) *m++ = *p++; oldstring[1] = WORDDIF(m,oldstring); } p = pold; do { *m++ = *p++; } while ( p < stop ); *termout = WORDDIF(m,termout); if ( ( diff ^ t->allsign ) < 0 ) m[-1] = - m[-1]; if ( ( AT.WorkPointer = m ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } if ( *termout ) { *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,t->level) ) { AT.WorkPointer = termout; goto TracCall; } t = AN.tracestack + AN.numtracesctack - 1; } break; } p += p[1]; } while ( p < stop ); } AT.WorkPointer = termout; return(0); /* #] All Different : */ TracnCall: AT.WorkPointer = oldstring; TracCall: if ( AM.tracebackflag ) { MLOCK(ErrorMessageLock); MesCall("TraceNGen"); MUNLOCK(ErrorMessageLock); } return(-1); } /* #] TraceNgen : #[ Traces : WORD Traces(term,params,num,level) The contents of the AT.TMout array are: length,type,subtype,gamma5,factor,sign,gamma's */ int Traces(PHEAD WORD *term, WORD *params, WORD num, WORD level) { GETBIDENTITY switch ( AT.TMout[2] ) { /* Subtype gives dimension */ case 0: return(TraceN(BHEAD term,params,num,level)); case 4: return(Trace4(BHEAD term,params,num,level)); case 12: return(Trace4(BHEAD term,params,num,level)); case 20: return(Trace4(BHEAD term,params,num,level)); default: return(0); } } /* #] Traces : #[ TraceFind : WORD TraceFind(term,params) */ int TraceFind(PHEAD WORD *term, WORD *params) { GETBIDENTITY WORD *p, *m, *to; WORD *termout, *stop, *stop2, number = 0; WORD first = 1; WORD type, spinline, sp; type = params[3]; spinline = params[4]; if ( spinline < 0 ) { /* $ variable. Evaluate */ sp = DolToIndex(BHEAD -spinline); if ( AN.ErrorInDollar || sp < 0 ) { MLOCK(ErrorMessageLock); MesPrint("$%s does not have an index value in trace statement in module %l", DOLLARNAME(Dollars,-spinline),AC.CModule); MUNLOCK(ErrorMessageLock); return(0); } spinline = sp; } to = AT.TMout; to++; *to++ = TAKETRACE; *to++ = type; *to++ = GAMMA1; *to++ = 0; /* Powers of two */ *to++ = 1; /* sign */ p = term; m = p + *p - 1; stop = m - ABS(*m); termout = m = AT.WorkPointer; m++; p++; while ( p < stop ) { stop2 = p + p[1]; if ( *p == GAMMA && p[FUNHEAD] == spinline ) { if ( first ) { *m++ = SUBEXPRESSION; *m++ = SUBEXPSIZE; *m++ = -1; *m++ = 1; *m++ = DUMMYBUFFER; FILLSUB(m) first = 0; } p += FUNHEAD+1; while ( p < stop2 ) { if ( *p == GAMMA5 ) { if ( AT.TMout[3] == GAMMA5 ) AT.TMout[3] = GAMMA1; else if ( AT.TMout[3] == GAMMA1 ) AT.TMout[3] = GAMMA5; else if ( AT.TMout[3] == GAMMA7 ) AT.TMout[5] = -AT.TMout[5]; if ( number & 1 ) AT.TMout[5] = - AT.TMout[5]; p++; } else if ( *p == GAMMA6 ) { if ( number & 1 ) goto F7; F6: if ( AT.TMout[3] == GAMMA6 ) (AT.TMout[4])++; else if ( AT.TMout[3] == GAMMA1 ) AT.TMout[3] = GAMMA6; else if ( AT.TMout[3] == GAMMA5 ) AT.TMout[3] = GAMMA6; else if ( AT.TMout[3] == GAMMA7 ) AT.TMout[5] = 0; p++; } else if ( *p == GAMMA7 ) { if ( number & 1 ) goto F6; F7: if ( AT.TMout[3] == GAMMA7 ) (AT.TMout[4])++; else if ( AT.TMout[3] == GAMMA1 ) AT.TMout[3] = GAMMA7; else if ( AT.TMout[3] == GAMMA5 ) { AT.TMout[3] = GAMMA7; AT.TMout[5] = -AT.TMout[5]; } else if ( AT.TMout[3] == GAMMA6 ) AT.TMout[5] = 0; p++; } else { *to++ = *p++; number++; } } } else { while ( p < stop2 ) *m++ = *p++; } } if ( first ) return(0); AT.TMout[0] = WORDDIF(to,AT.TMout); to = term; to += *to; while ( p < to ) *m++ = *p++; *termout = WORDDIF(m,termout); to = term; p = termout; do { *to++ = *p++; } while ( p < m ); AT.WorkPointer = term + *term; return(1); } /* #] TraceFind : #[ Chisholm : WORD Chisholm(term,level,num) Routines for reorganizing traces. The command Chisholm,1; will collect the gamma matrices in spinline 1 and see whether they have an index in common with another gamma matrix. If this is the case the identity g_(2,mu)*Tr[g_(1,mu)*S(2)] = S(2)+SR(2) is applied (SR is the reversed string). */ int Chisholm(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD *t, *r, *m, *s, *tt, *rr; WORD *mat, *matpoint, *termout, *rdo; CBUF *C = cbuf+AM.rbufnum; WORD i, j, num = C->lhs[level][2], gam5; WORD norm = 0, k, *matp; /* #[ Find : Find possible matrices */ mat = matpoint = AT.WorkPointer; t = term; r = t + *t - 1; r -= ABS(*r); t++; i = 0; gam5 = GAMMA1; while ( t < r ) { if ( *t == GAMMA && t[FUNHEAD] == num ) { m = t + t[1]; t += FUNHEAD+1; while ( t < m ) { if ( *t >= 0 || *t < MINSPEC ) i++; else { if ( gam5 == GAMMA1 ) gam5 = *t; else if ( gam5 == GAMMA5 ) { if ( *t == GAMMA5 ) gam5 = GAMMA1; else if ( *t != GAMMA1 ) gam5 = *t; } } *matpoint++ = *t++; } } else t += t[1]; } if ( ( i & 1 ) != 0 ) return(0); /* odd trace */ /* #] Find : #[ Test : Test for contracted index This code should be modified. We have to check for all possible matches if C->lhs[level][3] == 1 and the trace contains a gamma5, gamma6 or gamma7. Then we normalize by the number of possible contractions (norm) and do all of them. This way the Levi-Civita tensors have a maximum chance of cancelling each other. This option is activated with `contract' and `symmetrize'. Defaults are that they are on, but they can be switched off with nocontract and nosymmetrize. */ s = mat; while ( s < matpoint ) { /* if ( *s < AM.OffsetIndex || ( *s < ( AM.OffsetIndex + WILDOFFSET ) && indices[*s-AM.OffsetIndex].dimension == 0 ) ) { */ if ( *s < AM.OffsetIndex || ( *s < ( AM.OffsetIndex + WILDOFFSET ) && indices[*s-AM.OffsetIndex].dimension != 4 ) || ( ( AC.lDefDim != 4 ) && ( *s >= ( AM.OffsetIndex + WILDOFFSET ) ) ) ) { s++; continue; } t = term+1; while ( t < r ) { if ( *t == GAMMA && t[FUNHEAD] != num ) { m = t + t[1]; t += FUNHEAD+1; while ( t < m ) { if ( *t == *s ) { norm++; } t++; } } else t += t[1]; } s++; } if ( norm == 0 ) return(Generator(BHEAD term,level)); /* No Action */ /* #] Test : #[ Do : Process the string tt: The subterm t: The matrix s: The matrix in the relevant string Cycle the string in mat so that s is at the end. Copy the part till the critical GAMMA. Copy inside the critical string, copy S, copy tail inside string. Important to remember where S is so that we can reverse it later. Add term UnitTrace/2/norm. Copy rest of term. Continue execution with S. Reverse S. Continue execution with SR. */ if ( C->lhs[level][3] == 0 /* || gam5 == GAMMA1 */ ) norm = 1; matp = matpoint; for ( k = 0; k < norm; k++ ) { matpoint = matp; s = mat; while ( s < matpoint ) { /* if ( *s < AM.OffsetIndex || ( *s < ( AM.OffsetIndex + WILDOFFSET ) && indices[*s-AM.OffsetIndex].dimension == 0 ) ) { */ if ( *s < AM.OffsetIndex || ( *s < ( AM.OffsetIndex + WILDOFFSET ) && indices[*s-AM.OffsetIndex].dimension != 4 ) ) { s++; continue; } t = term+1; while ( t < r ) { if ( *t == GAMMA && t[FUNHEAD] != num ) { tt = t; m = t + t[1]; t += FUNHEAD+1; while ( t < m ) { if ( *t == *s ) { i = WORDDIF(t,tt); m = mat; while ( m <= s ) *matpoint++ = *m++; t = mat; while ( m < matpoint ) *t++ = *m++; termout = t; m = termout + 1; t = term + 1; while ( t < tt ) { if ( *t != GAMMA || t[FUNHEAD] != num ) { j = t[1]; NCOPY(m,t,j); } else t += t[1]; } tt += tt[1]; rdo = m; j = i; while ( --j >= 0 ) *m++ = *t++; matpoint = m; s = mat; while ( s < termout ) *m++ = *s++; m--; t++; while ( t < tt ) *m++ = *t++; rdo[1] = WORDDIF(m,rdo); *m++ = AC.lUniTrace[0]; *m++ = AC.lUniTrace[1]; *m++ = AC.lUniTrace[2]; *m++ = AC.lUniTrace[3]; *m++ = SNUMBER; *m++ = 4; *m++ = 2*norm; *m++ = -1; while ( t < r ) { if ( *t != GAMMA || t[FUNHEAD] != num ) { j = t[1]; NCOPY(m,t,j); } else t += t[1]; } rr = term + *term; while ( t < rr ) *m++ = *t++; *termout = WORDDIF(m,termout); rr = m; t = termout; j = *termout; NCOPY(m,t,j); AT.WorkPointer = m; if ( Generator(BHEAD t,level) ) goto ChisCall; j = WORDDIF(termout,mat)-1; t = matpoint; m = t + j; AT.WorkPointer = rr; while ( m > t ) { i = *--m; *m = *t; *t++ = i; } if ( Generator(BHEAD termout,level) ) goto ChisCall; AT.WorkPointer = mat; goto NextK; } t++; } } else t += t[1]; } s++; } NextK:; } return(0); /* #] Do : */ ChisCall: if ( AM.tracebackflag ) { MLOCK(ErrorMessageLock); MesCall("Chisholm"); MUNLOCK(ErrorMessageLock); } return(-1); } /* #] Chisholm : #[ TenVecFind : WORD TenVecFind(term,params) */ int TenVecFind(PHEAD WORD *term, WORD *params) { GETBIDENTITY WORD *t, *w, *m, *tstop; WORD i, mode, thevector, thetensor, spectator; thetensor = params[3]; thevector = params[4]; mode = params[5]; if ( thetensor < 0 ) { /* $-expression */ thetensor = DolToTensor(BHEAD -thetensor); if ( thetensor < FUNCTION ) { if ( thevector > 0 ) { thetensor = DolToTensor(BHEAD thevector); if ( thetensor < FUNCTION ) { MLOCK(ErrorMessageLock); MesPrint("$%s should have been a tensor in module %l" ,DOLLARNAME(Dollars,params[4]),AC.CModule); MUNLOCK(ErrorMessageLock); return(-1); } thevector = DolToVector(BHEAD -params[3]); if ( thevector >= 0 ) { MLOCK(ErrorMessageLock); MesPrint("$%s should have been a vector in module %l" ,DOLLARNAME(Dollars,-params[3]),AC.CModule); MUNLOCK(ErrorMessageLock); return(-1); } } else { MLOCK(ErrorMessageLock); MesPrint("$%s should have been a tensor in module %l" ,DOLLARNAME(Dollars,-params[3]),AC.CModule); MUNLOCK(ErrorMessageLock); return(-1); } } } if ( thevector > 0 ) { /* $-expression */ thevector = DolToVector(BHEAD thevector); if ( thevector >= 0 ) { MLOCK(ErrorMessageLock); MesPrint("$%s should have been a vector in module %l" ,DOLLARNAME(Dollars,params[4]),AC.CModule); MUNLOCK(ErrorMessageLock); return(-1); } } if ( ( mode & 1 ) != 0 ) { /* Vector to tensor */ GETSTOP(term,tstop); t = term + 1; while ( t < tstop ) { if ( *t == DOTPRODUCT ) { i = t[1] - 2; t += 2; while ( i > 0 ) { spectator = 0; if ( t[2] < 0 ) {} else if ( *t == thevector && t[1] == thevector ) { if ( ( mode & 2 ) == 0 ) spectator = thevector; } else if ( *t == thevector ) spectator = t[1]; else if ( t[1] == thevector ) spectator = *t; if ( spectator ) { if ( ( mode & 8 ) == 0 ) goto match; w = SetElements + Sets[params[6]].first; m = SetElements + Sets[params[6]].last; while ( w < m ) { if ( *w == spectator ) break; w++; } if ( w >= m ) goto match; } t += 3; i -= 3; } } else if ( *t == VECTOR ) { i = t[1] - 2; t += 2; while ( i > 0 ) { if ( *t == thevector ) goto match; t += 2; i -= 2; } } else if ( *t == thetensor ) t += t[1]; else if ( *t >= FUNCTION ) { if ( functions[*t-FUNCTION].spec > 0 ) { w = t + t[1]; t += FUNHEAD; while ( t < w ) { if ( *t == thevector ) goto match; t++; } } else if ( ( mode & 4 ) != 0 ) { w = t + t[1]; t += FUNHEAD; while ( t < w ) { if ( *t == -VECTOR && t[1] == thevector ) goto match; else if ( *t > 0 ) t += *t; else if ( *t <= -FUNCTION ) t++; else t += 2; } } else t += t[1]; } else t += t[1]; } } else { /* Tensor to Vector */ GETSTOP(term,tstop); t = term+1; while ( t < tstop ) { if ( *t == thetensor ) goto match; t += t[1]; } } return(0); match: AT.TMout[0] = 5; AT.TMout[1] = TENVEC; AT.TMout[2] = thetensor; AT.TMout[3] = thevector; AT.TMout[4] = mode; if ( ( mode & 8 ) != 0 ) { AT.TMout[0] = 6; AT.TMout[5] = params[6]; } return(1); } /* #] TenVecFind : #[ TenVec : WORD TenVec(term,params,num,level) */ int TenVec(PHEAD WORD *term, WORD *params, WORD num, WORD level) { GETBIDENTITY WORD *t, *m, *w, *termout, *tstop, *outlist, *ou, *ww, *mm; WORD i, j, k, x, mode, thevector, thetensor, DumNow, spectator; DUMMYUSE(num); thetensor = params[2]; thevector = params[3]; mode = params[4]; termout = AT.WorkPointer; DumNow = AR.CurDum = DetCurDum(BHEAD term); if ( ( mode & 1 ) != 0 ) { /* Vector to tensor */ AT.WorkPointer += *term; ou = outlist = AT.WorkPointer; GETSTOP(term,tstop); t = term + 1; m = termout + 1; while ( t < tstop ) { if ( *t == DOTPRODUCT ) { i = t[1] - 2; w = m; *m++ = *t++; *m++ = *t++; while ( i > 0 ) { spectator = 0; if ( t[2] < 0 ) { *m++ = *t++; *m++ = *t++; *m++ = *t++; } else if ( *t == thevector && t[1] == thevector ) { if ( ( mode & 2 ) == 0 ) spectator = thevector; else { *m++ = *t++; *m++ = *t++; *m++ = *t++; } } else if ( *t == thevector ) spectator = t[1]; else if ( t[1] == thevector ) spectator = *t; else { *m++ = *t++; *m++ = *t++; *m++ = *t++; } if ( spectator ) { if ( ( mode & 8 ) == 0 ) goto noveto; ww = SetElements + Sets[params[5]].first; mm = SetElements + Sets[params[5]].last; while ( ww < mm ) { if ( *ww == spectator ) break; ww++; } if ( ww < mm ) { *m++ = *t++; *m++ = *t++; *m++ = *t++; } else { noveto: if ( spectator == thevector ) { for ( j = 0; j < t[2]; j++ ) { *ou++ = ++AR.CurDum; *ou++ = AR.CurDum; } t += 3; } else { for ( j = 0; j < t[2]; j++ ) *ou++ = spectator; t += 3; }} } i -= 3; } w[1] = WORDDIF(m,w); if ( w[1] == 2 ) m = w; } else if ( *t == VECTOR ) { i = t[1] - 2; w = m; *m++ = *t++; *m++ = *t++; while ( i > 0 ) { if ( *t == thevector ) { *ou++ = t[1]; t += 2; } else { *m++ = *t++; *m++ = *t++; } i -= 2; } w[1] = WORDDIF(m,w); if ( w[1] == 2 ) m = w; } else if ( *t == thetensor ) { i = t[1] - FUNHEAD; t += FUNHEAD; NCOPY(ou,t,i); } else if ( *t >= FUNCTION ) { if ( functions[*t-FUNCTION].spec > 0 ) { w = t + t[1]; i = FUNHEAD; NCOPY(m,t,i); while ( t < w ) { if ( *t == thevector ) { *m++ = ++AR.CurDum; *ou++ = AR.CurDum; t++; } else *m++ = *t++; } } else if ( ( mode & 4 ) != 0 ) { w = t + t[1]; i = FUNHEAD; NCOPY(m,t,i); while ( t < w ) { if ( *t == -VECTOR && t[1] == thevector ) { *m++ = -INDEX; *m++ = ++AR.CurDum; *ou++ = AR.CurDum; t += 2; } else if ( *t > 0 ) { i = *t; NCOPY(m,t,i); } else if ( *t <= -FUNCTION ) *m++ = *t++; else { *m++ = *t++; *m++ = *t++; } } } else goto docopy; } else { docopy: i = t[1]; NCOPY(m,t,i); } } i = WORDDIF(ou,outlist); if ( i > 0 ) { for ( j = 1; j < i; j++ ) { if ( outlist[j-1] > outlist[j] ) { x = outlist[j-1]; outlist[j-1] = outlist[j]; outlist[j] = x; for ( k = j-1; k > 0; k-- ) { if ( outlist[k-1] <= outlist[k] ) break; x = outlist[k-1]; outlist[k-1] = outlist[k]; outlist[k] = x; } } } *m++ = thetensor; *m++ = FUNHEAD + i; *m++ = DIRTYSYMFLAG; FILLFUN3(m) ou = outlist; NCOPY(m,ou,i); } w = term + *term; while ( t < w ) *m++ = *t++; } else { /* Tensor to Vector */ GETSTOP(term,tstop); t = term+1; m = termout+1; while ( t < tstop ) { if ( *t != thetensor ) { i = t[1]; NCOPY(m,t,i); } else { i = t[1] - FUNHEAD; t += FUNHEAD; if ( i > 0 ) { w = m; m += 2; while ( --i >= 0 ) { *m++ = thevector; *m++ = *t++; } *w = DELTA; w[1] = WORDDIF(m,w); } } } w = term + *term; while ( t < w ) *m++ = *t++; } *termout = WORDDIF(m,termout); AT.WorkPointer = m; *AT.TMout = 0; if ( Generator(BHEAD termout,level) ) goto fromTenVec; AR.CurDum = DumNow; AT.WorkPointer = termout; return(0); fromTenVec: if ( AM.tracebackflag ) { MLOCK(ErrorMessageLock); MesCall("TenVec"); MUNLOCK(ErrorMessageLock); } return(-1); } /* #] TenVec : #] Operations : */ form-5.0.1/sources/compiler.c0000644000175100017510000022245415217035721011620 /** @file compiler.c * * The heart of the compiler. * It contains the tables of statements. * It finds the statements in the tables and calls the proper routines. * For algebraic expressions it runs the compilation by first calling * the tokenizer, splitting things into subexpressions and generating * the code. There is a system for recognizing already existing * subexpressions. This economizes on the length of the output. * * Note: the compiler of FORM doesn't attempt to normalize the input. * Hence x+1 and 1+x are different objects during compilation. * Similarly (a+b-b) will not be simplified to (a). */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ includes : */ #include "form3.h" #include "comtool.h" /* com1commands are the commands of which only part of the word has to be present. The order is rather important here. com2commands are the commands that must have their whole word match. here we can do a binary search. {[( */ static KEYWORD com1commands[] = { {"also", (TFUN)CoIdOld, STATEMENT, PARTEST} ,{"abrackets", (TFUN)CoAntiBracket, TOOUTPUT, PARTEST} ,{"antisymmetrize", (TFUN)CoAntiSymmetrize, STATEMENT, PARTEST} ,{"antibrackets", (TFUN)CoAntiBracket, TOOUTPUT, PARTEST} ,{"brackets", (TFUN)CoBracket, TOOUTPUT, PARTEST} ,{"cfunctions", (TFUN)CoCFunction, DECLARATION, PARTEST|WITHAUTO} ,{"commuting", (TFUN)CoCFunction, DECLARATION, PARTEST|WITHAUTO} ,{"compress", (TFUN)CoCompress, DECLARATION, PARTEST} ,{"ctensors", (TFUN)CoCTensor, DECLARATION, PARTEST|WITHAUTO} ,{"cyclesymmetrize",(TFUN)CoCycleSymmetrize, STATEMENT, PARTEST} ,{"dimension", (TFUN)CoDimension, DECLARATION, PARTEST} ,{"discard", (TFUN)CoDiscard, STATEMENT, PARTEST} ,{"functions", (TFUN)CoNFunction, DECLARATION, PARTEST|WITHAUTO} ,{"format", (TFUN)CoFormat, TOOUTPUT, PARTEST} ,{"fixindex", (TFUN)CoFixIndex, DECLARATION, PARTEST} ,{"global", (TFUN)CoGlobal, DEFINITION, PARTEST} ,{"gfactorized", (TFUN)CoGlobalFactorized, DEFINITION, PARTEST} ,{"globalfactorized",(TFUN)CoGlobalFactorized,DEFINITION, PARTEST} ,{"goto", (TFUN)CoGoTo, STATEMENT, PARTEST} ,{"indexes", (TFUN)CoIndex, DECLARATION, PARTEST|WITHAUTO} ,{"indices", (TFUN)CoIndex, DECLARATION, PARTEST|WITHAUTO} ,{"identify", (TFUN)CoId, STATEMENT, PARTEST} ,{"idnew", (TFUN)CoIdNew, STATEMENT, PARTEST} ,{"idold", (TFUN)CoIdOld, STATEMENT, PARTEST} ,{"local", (TFUN)CoLocal, DEFINITION, PARTEST} ,{"lfactorized", (TFUN)CoLocalFactorized, DEFINITION, PARTEST} ,{"localfactorized",(TFUN)CoLocalFactorized, DEFINITION, PARTEST} ,{"load", (TFUN)CoLoad, DECLARATION, PARTEST} ,{"label", (TFUN)CoLabel, STATEMENT, PARTEST} ,{"modulus", (TFUN)CoModulus, DECLARATION, PARTEST} ,{"multiply", (TFUN)CoMultiply, STATEMENT, PARTEST} ,{"nfunctions", (TFUN)CoNFunction, DECLARATION, PARTEST|WITHAUTO} ,{"nprint", (TFUN)CoNPrint, TOOUTPUT, PARTEST} ,{"ntensors", (TFUN)CoNTensor, DECLARATION, PARTEST|WITHAUTO} ,{"nwrite", (TFUN)CoNWrite, DECLARATION, PARTEST} ,{"print", (TFUN)CoPrint, MIXED, 0} ,{"redefine", (TFUN)CoRedefine, STATEMENT, 0} ,{"rcyclesymmetrize",(TFUN)CoRCycleSymmetrize,STATEMENT, PARTEST} ,{"symbols", (TFUN)CoSymbol, DECLARATION, PARTEST|WITHAUTO} ,{"save", (TFUN)CoSave, DECLARATION, PARTEST} ,{"symmetrize", (TFUN)CoSymmetrize, STATEMENT, PARTEST} ,{"tensors", (TFUN)CoCTensor, DECLARATION, PARTEST|WITHAUTO} ,{"unittrace", (TFUN)CoUnitTrace, DECLARATION, PARTEST} ,{"vectors", (TFUN)CoVector, DECLARATION, PARTEST|WITHAUTO} ,{"write", (TFUN)CoWrite, DECLARATION, PARTEST} }; static KEYWORD com2commands[] = { {"antiputinside", (TFUN)CoAntiPutInside, STATEMENT, PARTEST} ,{"apply", (TFUN)CoApply, STATEMENT, PARTEST} ,{"aputinside", (TFUN)CoAntiPutInside, STATEMENT, PARTEST} ,{"argexplode", (TFUN)CoArgExplode, STATEMENT, PARTEST} ,{"argimplode", (TFUN)CoArgImplode, STATEMENT, PARTEST} ,{"argtoextrasymbol",(TFUN)CoArgToExtraSymbol,STATEMENT, PARTEST} ,{"argument", (TFUN)CoArgument, STATEMENT, PARTEST} ,{"assign", (TFUN)CoAssign, STATEMENT, PARTEST} ,{"auto", (TFUN)CoAuto, DECLARATION, PARTEST} ,{"autodeclare", (TFUN)CoAuto, DECLARATION, PARTEST} ,{"break", (TFUN)CoBreak, STATEMENT, PARTEST} ,{"canonicalize", (TFUN)CoCanonicalize, STATEMENT, PARTEST} ,{"case", (TFUN)CoCase, STATEMENT, PARTEST} ,{"chainin", (TFUN)CoChainin, STATEMENT, PARTEST} ,{"chainout", (TFUN)CoChainout, STATEMENT, PARTEST} ,{"chisholm", (TFUN)CoChisholm, STATEMENT, PARTEST} #ifdef WITHFLOAT ,{"chop", (TFUN)CoChop, STATEMENT, PARTEST} #endif ,{"clearflag", (TFUN)CoClearUserFlag, STATEMENT, PARTEST} ,{"cleartable", (TFUN)CoClearTable, DECLARATION, PARTEST} ,{"collect", (TFUN)CoCollect, SPECIFICATION,PARTEST} ,{"commuteinset", (TFUN)CoCommuteInSet, DECLARATION, PARTEST} ,{"contract", (TFUN)CoContract, STATEMENT, PARTEST} ,{"copyspectator", (TFUN)CoCopySpectator, DEFINITION, PARTEST} ,{"createall", (TFUN)CoCreateAll, STATEMENT, PARTEST} ,{"createspectator",(TFUN)CoCreateSpectator, DECLARATION, PARTEST} ,{"ctable", (TFUN)CoCTable, DECLARATION, PARTEST} ,{"deallocatetable",(TFUN)CoDeallocateTable, DECLARATION, PARTEST} ,{"default", (TFUN)CoDefault, STATEMENT, PARTEST} ,{"delete", (TFUN)CoDelete, SPECIFICATION,PARTEST} ,{"denominators", (TFUN)CoDenominators, STATEMENT, PARTEST} ,{"disorder", (TFUN)CoDisorder, STATEMENT, PARTEST} ,{"do", (TFUN)CoDo, STATEMENT, PARTEST} ,{"drop", (TFUN)CoDrop, SPECIFICATION,PARTEST} ,{"dropcoefficient",(TFUN)CoDropCoefficient, STATEMENT, PARTEST} ,{"dropsymbols", (TFUN)CoDropSymbols, STATEMENT, PARTEST} ,{"else", (TFUN)CoElse, STATEMENT, PARTEST} ,{"elseif", (TFUN)CoElseIf, STATEMENT, PARTEST} ,{"emptyspectator", (TFUN)CoEmptySpectator, SPECIFICATION,PARTEST} ,{"endargument", (TFUN)CoEndArgument, STATEMENT, PARTEST} ,{"enddo", (TFUN)CoEndDo, STATEMENT, PARTEST} ,{"endif", (TFUN)CoEndIf, STATEMENT, PARTEST} ,{"endinexpression",(TFUN)CoEndInExpression, STATEMENT, PARTEST} ,{"endinside", (TFUN)CoEndInside, STATEMENT, PARTEST} ,{"endmodel", (TFUN)CoEndModel, DECLARATION, PARTEST} ,{"endrepeat", (TFUN)CoEndRepeat, STATEMENT, PARTEST} ,{"endswitch", (TFUN)CoEndSwitch, STATEMENT, PARTEST} ,{"endterm", (TFUN)CoEndTerm, STATEMENT, PARTEST} ,{"endwhile", (TFUN)CoEndWhile, STATEMENT, PARTEST} #ifdef WITHFLOAT ,{"evaluate", (TFUN)CoEvaluate, STATEMENT, PARTEST} #endif ,{"exit", (TFUN)CoExit, STATEMENT, PARTEST} ,{"extrasymbols", (TFUN)CoExtraSymbols, DECLARATION, PARTEST} ,{"factarg", (TFUN)CoFactArg, STATEMENT, PARTEST} ,{"factdollar", (TFUN)CoFactDollar, STATEMENT, PARTEST} ,{"factorize", (TFUN)CoFactorize, TOOUTPUT, PARTEST} ,{"fill", (TFUN)CoFill, DECLARATION, PARTEST} ,{"fillexpression", (TFUN)CoFillExpression, DECLARATION, PARTEST} ,{"frompolynomial", (TFUN)CoFromPolynomial, STATEMENT, PARTEST} ,{"funpowers", (TFUN)CoFunPowers, DECLARATION, PARTEST} ,{"hide", (TFUN)CoHide, SPECIFICATION,PARTEST} ,{"if", (TFUN)CoIf, STATEMENT, PARTEST} ,{"ifmatch", (TFUN)CoIfMatch, STATEMENT, PARTEST} ,{"ifnomatch", (TFUN)CoIfNoMatch, STATEMENT, PARTEST} ,{"ifnotmatch", (TFUN)CoIfNoMatch, STATEMENT, PARTEST} ,{"inexpression", (TFUN)CoInExpression, STATEMENT, PARTEST} ,{"inparallel", (TFUN)CoInParallel, SPECIFICATION,PARTEST} ,{"inside", (TFUN)CoInside, STATEMENT, PARTEST} ,{"insidefirst", (TFUN)CoInsideFirst, DECLARATION, PARTEST} ,{"intohide", (TFUN)CoIntoHide, SPECIFICATION,PARTEST} ,{"keep", (TFUN)CoKeep, SPECIFICATION,PARTEST} ,{"makeinteger", (TFUN)CoMakeInteger, STATEMENT, PARTEST} ,{"many", (TFUN)CoMany, STATEMENT, PARTEST} ,{"merge", (TFUN)CoMerge, STATEMENT, PARTEST} ,{"metric", (TFUN)CoMetric, DECLARATION, PARTEST} ,{"model", (TFUN)CoModel, DECLARATION, PARTEST} ,{"moduleoption", (TFUN)CoModuleOption, ATENDOFMODULE,PARTEST} ,{"multi", (TFUN)CoMulti, STATEMENT, PARTEST} ,{"multibracket", (TFUN)CoMultiBracket, STATEMENT, PARTEST} ,{"ndrop", (TFUN)CoNoDrop, SPECIFICATION,PARTEST} ,{"nfactorize", (TFUN)CoNFactorize, TOOUTPUT, PARTEST} ,{"nhide", (TFUN)CoNoHide, SPECIFICATION,PARTEST} ,{"nintohide", (TFUN)CoNoIntoHide, SPECIFICATION,PARTEST} ,{"normalize", (TFUN)CoNormalize, STATEMENT, PARTEST} ,{"notinparallel", (TFUN)CoNotInParallel, SPECIFICATION,PARTEST} ,{"nskip", (TFUN)CoNoSkip, SPECIFICATION,PARTEST} ,{"ntable", (TFUN)CoNTable, DECLARATION, PARTEST} ,{"nunfactorize", (TFUN)CoNUnFactorize, TOOUTPUT, PARTEST} ,{"nunhide", (TFUN)CoNoUnHide, SPECIFICATION,PARTEST} ,{"off", (TFUN)CoOff, DECLARATION, PARTEST} ,{"on", (TFUN)CoOn, DECLARATION, PARTEST} ,{"once", (TFUN)CoOnce, STATEMENT, PARTEST} ,{"only", (TFUN)CoOnly, STATEMENT, PARTEST} ,{"particle", (TFUN)CoParticle, DECLARATION, PARTEST} ,{"polyfun", (TFUN)CoPolyFun, DECLARATION, PARTEST} ,{"polyratfun", (TFUN)CoPolyRatFun, DECLARATION, PARTEST} ,{"pophide", (TFUN)CoPopHide, SPECIFICATION,PARTEST} ,{"print[]", (TFUN)CoPrintB, TOOUTPUT, PARTEST} ,{"printtable", (TFUN)CoPrintTable, MIXED, PARTEST} ,{"processbucketsize",(TFUN)CoProcessBucket, DECLARATION, PARTEST} ,{"propercount", (TFUN)CoProperCount, DECLARATION, PARTEST} ,{"pushhide", (TFUN)CoPushHide, SPECIFICATION,PARTEST} ,{"putinside", (TFUN)CoPutInside, STATEMENT, PARTEST} ,{"ratio", (TFUN)CoRatio, STATEMENT, PARTEST} ,{"removespectator",(TFUN)CoRemoveSpectator, SPECIFICATION,PARTEST} ,{"renumber", (TFUN)CoRenumber, STATEMENT, PARTEST} ,{"repeat", (TFUN)CoRepeat, STATEMENT, PARTEST} ,{"replaceloop", (TFUN)CoReplaceLoop, STATEMENT, PARTEST} ,{"select", (TFUN)CoSelect, STATEMENT, PARTEST} ,{"set", (TFUN)CoSet, DECLARATION, PARTEST} ,{"setexitflag", (TFUN)CoSetExitFlag, STATEMENT, PARTEST} ,{"setflag", (TFUN)CoSetUserFlag, STATEMENT, PARTEST} ,{"shuffle", (TFUN)CoMerge, STATEMENT, PARTEST} ,{"skip", (TFUN)CoSkip, SPECIFICATION,PARTEST} ,{"sort", (TFUN)CoSort, STATEMENT, PARTEST} ,{"splitarg", (TFUN)CoSplitArg, STATEMENT, PARTEST} ,{"splitfirstarg", (TFUN)CoSplitFirstArg, STATEMENT, PARTEST} ,{"splitlastarg", (TFUN)CoSplitLastArg, STATEMENT, PARTEST} #ifdef WITHFLOAT ,{"strictrounding", (TFUN)CoStrictRounding, STATEMENT, PARTEST} #endif ,{"stuffle", (TFUN)CoStuffle, STATEMENT, PARTEST} ,{"sum", (TFUN)CoSum, STATEMENT, PARTEST} ,{"switch", (TFUN)CoSwitch, STATEMENT, PARTEST} ,{"table", (TFUN)CoTable, DECLARATION, PARTEST} ,{"tablebase", (TFUN)CoTableBase, DECLARATION, PARTEST} ,{"tb", (TFUN)CoTableBase, DECLARATION, PARTEST} ,{"term", (TFUN)CoTerm, STATEMENT, PARTEST} ,{"testuse", (TFUN)CoTestUse, STATEMENT, PARTEST} ,{"threadbucketsize",(TFUN)CoThreadBucket, DECLARATION, PARTEST} #ifdef WITHFLOAT ,{"tofloat", (TFUN)CoToFloat, STATEMENT, PARTEST} #endif ,{"topolynomial", (TFUN)CoToPolynomial, STATEMENT, PARTEST} #ifdef WITHFLOAT ,{"torat", (TFUN)CoToRat, STATEMENT, PARTEST} ,{"torational", (TFUN)CoToRat, STATEMENT, PARTEST} #endif ,{"tospectator", (TFUN)CoToSpectator, STATEMENT, PARTEST} ,{"totensor", (TFUN)CoToTensor, STATEMENT, PARTEST} ,{"tovector", (TFUN)CoToVector, STATEMENT, PARTEST} ,{"trace4", (TFUN)CoTrace4, STATEMENT, PARTEST} ,{"tracen", (TFUN)CoTraceN, STATEMENT, PARTEST} ,{"transform", (TFUN)CoTransform, STATEMENT, PARTEST} ,{"tryreplace", (TFUN)CoTryReplace, STATEMENT, PARTEST} ,{"unfactorize", (TFUN)CoUnFactorize, TOOUTPUT, PARTEST} ,{"unhide", (TFUN)CoUnHide, SPECIFICATION,PARTEST} ,{"vertex", (TFUN)CoVertex, DECLARATION, PARTEST} ,{"while", (TFUN)CoWhile, STATEMENT, PARTEST} }; int alfatable1[27]; #define OPTION0 1 #define OPTION1 2 #define OPTION2 3 typedef struct SuBbUf { WORD subexpnum; WORD buffernum; } SUBBUF; SUBBUF *subexpbuffers = 0; SUBBUF *topsubexpbuffers = 0; LONG insubexpbuffers = 0; #define REDUCESUBEXPBUFFERS { if ( (topsubexpbuffers-subexpbuffers) > 256 ) {\ M_free(subexpbuffers,"subexpbuffers");\ subexpbuffers = (SUBBUF *)Malloc1(256*sizeof(SUBBUF),"subexpbuffers");\ topsubexpbuffers = subexpbuffers+256; } insubexpbuffers = 0; } #if BITSINWORD == 32 #define PUTNUMBER128(t,n) { if ( n >= 2097152 ) { \ *t++ = ((n/128)/128)/128; *t++ = ((n/128)/128)%128; *t++ = (n/128)%128; *t++ = n%128; } \ else if ( n >= 16384 ) { \ *t++ = n/(128*128); *t++ = (n/128)%128; *t++ = n%128; } \ else if ( n >= 128 ) { *t++ = n/128; *t++ = n%128; } \ else *t++ = n; } #define PUTNUMBER100(t,n) { if ( n >= 1000000 ) { \ *t++ = ((n/100)/100)/100; *t++ = ((n/100)/100)%100; *t++ = (n/100)%100; *t++ = n%100; } \ else if ( n >= 10000 ) { \ *t++ = n/10000; *t++ = (n/100)%100; *t++ = n%100; } \ else if ( n >= 100 ) { *t++ = n/100; *t++ = n%100; } \ else *t++ = n; } #elif BITSINWORD == 16 #define PUTNUMBER128(t,n) { if ( n >= 16384 ) { \ *t++ = n/(128*128); *t++ = (n/128)%128; *t++ = n%128; } \ else if ( n >= 128 ) { *t++ = n/128; *t++ = n%128; } \ else *t++ = n; } #define PUTNUMBER100(t,n) { if ( n >= 10000 ) { \ *t++ = n/10000; *t++ = (n/100)%100; *t++ = n%100; } \ else if ( n >= 100 ) { *t++ = n/100; *t++ = n%100; } \ else *t++ = n; } #else #error Only 64-bit and 32-bit platforms are supported. #endif /* )]} #] includes : #[ Compiler : #[ inictable : Routine sets the table for 1-st characters that allow a faster start in the search in table 1 which should be sequential. Search in table 2 can be binary. */ void inictable(void) { KEYWORD *k = com1commands; int i, j, ksize; ksize = sizeof(com1commands)/sizeof(KEYWORD); j = 0; alfatable1[0] = 0; for ( i = 0; i < 26; i++ ) { while ( j < ksize && k[j].name[0] == 'a'+i ) j++; alfatable1[i+1] = j; } } /* #] inictable : #[ findcommand : Checks whether a command is in the command table. If so a pointer to the table element is returned. If not we return 0. Note that when a command is not in the table, we have to test whether it is an id command without id. It should then have the structure pattern = rhs. This should be done in the calling routine. */ KEYWORD *findcommand(UBYTE *in) { int hi, med, lo, i; UBYTE *s, c; s = in; while ( FG.cTable[*s] <= 1 ) s++; if ( s > in && *s == '[' && s[1] == ']' ) s += 2; if ( *s ) { c = *s; *s = 0; } else c = 0; /* First do a binary search in the second table */ lo = 0; hi = sizeof(com2commands)/sizeof(KEYWORD)-1; do { med = ( hi + lo ) / 2; i = StrICmp(in,(UBYTE *)com2commands[med].name); if ( i == 0 ) { if ( c ) *s = c; return(com2commands+med); } if ( i < 0 ) hi = med-1; else lo = med+1; } while ( hi >= lo ); /* Now do a 'hashed' search in the first table. It is sequential. */ i = tolower(*in) - 'a'; med = alfatable1[i]; hi = alfatable1[i+1]; while ( med < hi ) { if ( StrICont(in,(UBYTE *)com1commands[med].name) == 0 ) { if ( c ) *s = c; return(com1commands+med); } med++; } if ( c ) *s = c; /* Unrecognized. Too bad! */ return(0); } /* #] findcommand : #[ ParenthesesTest : */ int ParenthesesTest(UBYTE *sin) { WORD L1 = 0, L2 = 0, L3 = 0; UBYTE *s = sin; while ( *s ) { if ( *s == '[' ) L1++; else if ( *s == ']' ) { L1--; if ( L1 < 0 ) { MesPrint("&Unmatched []"); return(1); } } s++; } if ( L1 > 0 ) { MesPrint("&Unmatched []"); return(1); } s = sin; while ( *s ) { if ( *s == '[' ) SKIPBRA1(s) else if ( *s == '(' ) { L2++; s++; } else if ( *s == ')' ) { L2--; s++; if ( L2 < 0 ) { MesPrint("&Unmatched ()"); return(1); } } else s++; } if ( L2 > 0 ) { MesPrint("&Unmatched ()"); return(1); } s = sin; while ( *s ) { if ( *s == '[' ) SKIPBRA1(s) else if ( *s == '[' ) SKIPBRA4(s) else if ( *s == '{' ) { L3++; s++; } else if ( *s == '}' ) { L3--; s++; if ( L3 < 0 ) { MesPrint("&Unmatched {}"); return(1); } } else s++; } if ( L3 > 0 ) { MesPrint("&Unmatched {}"); return(1); } return(0); } /* #] ParenthesesTest : #[ SkipAName : */ /** * Skips a name and gives a pointer to the character after the name. * If there is not a proper name, it emits a compiler message and then returns * a null pointer. * This function supports formal names (e.g., `[x+a]`) and $-variables * in addition to ordinary identifiers. * * @note The brackets are assumed to be matched already. * * @param[in] s Pointer to a null-terminated input string that starts * with a name. * @return Pointer to the character after the name, or a null pointer * if the name is invalid. */ UBYTE *SkipAName(UBYTE *s) { UBYTE *t = s; if ( *s == '[' ) { SKIPBRA1(s) /* In principle the brackets match already, so the `if ( *s == 0 )' code is not really needed, but you never know how the program is extended later. */ if ( *s == 0 ) { MesPrint("&Illegal name: '%s'",t); return(0); } s++; } else if ( FG.cTable[*s] == 0 || *s == '_' || *s == '$' ) { if ( *s == '$' ) s++; while ( FG.cTable[*s] <= 1 ) s++; if ( *s == '_' ) s++; } else { MesPrint("&Illegal name: '%s'",t); return(0); } return(s); } /* #] SkipAName : #[ IsRHS : */ UBYTE *IsRHS(UBYTE *s, UBYTE c) { while ( *s && *s != c ) { if ( *s == '[' ) { SKIPBRA1(s); if ( *s != ']' ) { MesPrint("&Unmatched []"); return(0); } } else if ( *s == '{' ) { SKIPBRA2(s); if ( *s != '}' ) { MesPrint("&Unmatched {}"); return(0); } } else if ( *s == '(' ) { SKIPBRA3(s); if ( *s != ')' ) { MesPrint("&Unmatched ()"); return(0); } } else if ( *s == ')' ) { MesPrint("&Unmatched ()"); return(0); } else if ( *s == '}' ) { MesPrint("&Unmatched {}"); return(0); } else if ( *s == ']' ) { MesPrint("&Unmatched []"); return(0); } s++; } return(s); } /* #] IsRHS : #[ IsIdStatement : */ int IsIdStatement(UBYTE *s) { DUMMYUSE(s); return(0); } /* #] IsIdStatement : #[ CompileAlgebra : Returns either the number of the main level RHS (>= 0) or an error code (< 0) */ int CompileAlgebra(UBYTE *s, int leftright, WORD *prototype) { GETIDENTITY int error; WORD *oldproto = AC.ProtoType; AC.ProtoType = prototype; if ( AC.TokensWriteFlag ) { MesPrint("To tokenize: %s",s); error = tokenize(s,leftright); MesPrint(" The contents of the token buffer are:"); WriteTokens(AC.tokens); } else error = tokenize(s,leftright); if ( error == 0 ) { AR.Eside = leftright; AC.CompileLevel = 0; if ( leftright == LHSIDE ) { AC.DumNum = AR.CurDum = 0; } error = CompileSubExpressions(AC.tokens); REDUCESUBEXPBUFFERS } else { AC.ProtoType = oldproto; return(-1); } AC.ProtoType = oldproto; if ( error < 0 ) return(-1); else if ( leftright == LHSIDE ) return(cbuf[AC.cbufnum].numlhs); else return(cbuf[AC.cbufnum].numrhs); } /* #] CompileAlgebra : #[ CompileStatement : */ int CompileStatement(UBYTE *in) { KEYWORD *k; UBYTE *s; int error1 = 0, error2; /* A.iStatement = */ s = in; if ( *s == 0 ) return(0); if ( *s == '$' ) { k = findcommand((UBYTE *)"assign"); } else { if ( ( k = findcommand(s) ) == 0 && IsIdStatement(s) == 0 ) { MesPrint("&Unrecognized statement %s",s); return(1); } if ( k == 0 ) { /* Id statement without id. Note: id must be in table */ k = com1commands + alfatable1['i'-'a']; while ( k->name[1] != 'd' || k->name[2] ) k++; } else { while ( FG.cTable[*s] <= 1 ) s++; if ( s > in && *s == '[' && s[1] == ']' ) s += 2; /* The next statement is rather mysterious It is undone in DoPrint and CoMultiply, but it also causes effects in other (wrong) statements like dimension -4; or Trace4 -1; The code in pre.c (LoadStatement) has been changed 8-sep-2009 to force a comma after the keyword. This means that the 'mysterious' line is automatically inactive. Hence it is taken out. if ( *s == '+' || *s == '-' ) s++; */ if ( *s == ',' ) s++; } } /* First the test on the order of the statements. This is relatively new (2.2c) and may cause some problems with old programs. Hence the first error message should explain! */ if ( AP.PreAssignFlag == 0 && AM.OldOrderFlag == 0 ) { if ( AP.PreInsideLevel ) { if ( k->type != STATEMENT && k->type != MIXED ) { MesPrint("&Only executable and print statements are allowed in an %#inside/%#endinside construction"); return(-1); } } else { if ( ( AC.compiletype == DECLARATION || AC.compiletype == SPECIFICATION ) && ( k->type == STATEMENT || k->type == DEFINITION || k->type == TOOUTPUT ) ) { if ( AC.tablecheck == 0 ) { AC.tablecheck = 1; if ( TestTables() ) error1 = 1; } } if ( k->type == MIXED ) { if ( AC.compiletype <= DEFINITION ) { AC.compiletype = STATEMENT; } } else if ( k->type > AC.compiletype ) { /* * We intentionally do NOT update "compiletype" for: * - Format statements (type = TOOUTPUT) * - ModuleOption statements (type = ATENDOFMODULE) * with sum/maximum/minimum/local (i.e., $-variable-related options) * * This relaxes the ordering constraint, allowing statements with * type >= the current "compiletype" to follow. */ if ( StrCmp((UBYTE *)(k->name),(UBYTE *)"format") == 0 ) goto NoUpdateCompileType; if ( StrCmp((UBYTE *)(k->name),(UBYTE *)"moduleoption") == 0 ) { UBYTE *ss = s; SkipSpaces(&ss); if ( ConsumeOption(&ss,"sum") || ConsumeOption(&ss,"maximum") || ConsumeOption(&ss,"minimum") || ConsumeOption(&ss,"local") ) goto NoUpdateCompileType; } AC.compiletype = k->type; NoUpdateCompileType: ; } else if ( k->type < AC.compiletype ) { switch ( k->type ) { case DECLARATION: MesPrint("&Declaration out of order"); MesPrint("& %s",in); break; case DEFINITION: MesPrint("&Definition out of order"); MesPrint("& %s",in); break; case SPECIFICATION: MesPrint("&Specification out of order"); MesPrint("& %s",in); break; case STATEMENT: MesPrint("&Statement out of order"); break; case TOOUTPUT: MesPrint("&Output control statement out of order"); MesPrint("& %s",in); break; } AC.compiletype = k->type; if ( AC.firstctypemessage == 0 ) { MesPrint("&Proper order inside a module is:"); MesPrint("Declarations, specifications, definitions, statements, output control statements"); AC.firstctypemessage = 1; } error1 = 1; } } } /* Now we execute the tests that are prescribed by the flags. */ if ( AC.AutoDeclareFlag && ( ( k->flags & WITHAUTO ) == 0 ) ) { MesPrint("&Illegal type of auto-declaration"); return(1); } if ( ( ( k->flags & PARTEST ) != 0 ) && ParenthesesTest(s) ) return(1); error2 = (*k->func)(s); if ( error2 == 0 ) return(error1); return(error2); } /* #] CompileStatement : #[ TestTables : */ int TestTables(void) { FUNCTIONS f = functions; TABLES t; WORD j; int error = 0, i; LONG x; i = NumFunctions + FUNCTION - MAXBUILTINFUNCTION - 1; f = f + MAXBUILTINFUNCTION - FUNCTION + 1; if ( AC.MustTestTable > 0 ) { while ( i > 0 ) { if ( ( t = f->tabl ) != 0 && t->strict > 0 && !t->sparse ) { for ( x = 0, j = 0; x < t->totind; x++ ) { if ( t->tablepointers[TABLEEXTENSION*x] < 0 ) j++; } if ( j > 0 ) { if ( j > 1 ) { MesPrint("&In table %s there are %d unfilled elements", AC.varnames->namebuffer+f->name,j); } else { MesPrint("&In table %s there is one unfilled element", AC.varnames->namebuffer+f->name); } error = 1; } } i--; f++; } AC.MustTestTable--; } return(error); } /* #] TestTables : #[ CompileSubExpressions : Now we attack the subexpressions from inside out. We try to see whether we had any of them already. We have to worry about adding the wildcard sum parameter to the prototype. */ int CompileSubExpressions(SBYTE *tokens) { GETIDENTITY SBYTE *fill = tokens, *s = tokens, *t; WORD number[MAXNUMSIZE], *oldwork, *w1, *w2; int level, num, i, sumlevel = 0, sumtype = SYMTOSYM; int retval, error = 0; /* Eliminate all subexpressions. They are marked by LPARENTHESIS,RPARENTHESIS */ AC.CompileLevel++; while ( *s != TENDOFIT ) { if ( *s == TFUNOPEN ) { if ( fill < s ) *fill = TENDOFIT; t = fill - 1; while ( t >= tokens && t[0] >= 0 ) t--; if ( t >= tokens && *t == TFUNCTION ) { t++; i = 0; while ( *t >= 0 ) i = 128*i + *t++; if ( i == AM.sumnum || i == AM.sumpnum ) { t = s + 1; if ( *t == TSYMBOL || *t == TINDEX ) { t++; i = 0; while ( *t >= 0 ) i = 128*i + *t++; if ( s[1] == TINDEX ) { i += AM.OffsetIndex; sumtype = INDTOIND; } else sumtype = SYMTOSYM; sumlevel = i; } } } *fill++ = *s++; } else if ( *s == TFUNCLOSE ) { sumlevel = 0; *fill++ = *s++; } else if ( *s == LPARENTHESIS ) { /* We must make an exception here. If the subexpression is just an integer, whatever its length, we should try to keep it. This is important when we have a function with an integer argument. In particular this is relevant for the MZV program. */ t = s; level = 0; while ( level >= 0 ) { s++; if ( *s == LPARENTHESIS ) level++; else if ( *s == RPARENTHESIS ) level--; else if ( *s == TENDOFIT ) { MesPrint("&Unbalanced subexpression parentheses"); return(-1); } } t++; *s = TENDOFIT; if ( sumlevel > 0 ) { /* Inside sum. Add wildcard to prototype */ oldwork = w1 = AT.WorkPointer; w2 = AC.ProtoType; i = w2[1]; while ( --i >= 0 ) *w1++ = *w2++; oldwork[1] += 4; *w1++ = sumtype; *w1++ = 4; *w1++ = sumlevel; *w1++ = sumlevel; w2 = AC.ProtoType; AT.WorkPointer = w1; AC.ProtoType = oldwork; num = CompileSubExpressions(t); AC.ProtoType = w2; AT.WorkPointer = oldwork; } else num = CompileSubExpressions(t); if ( num < 0 ) return(-1); /* Note that the subexpression code should always fit. We had two parentheses and at least two bytes contents. There cannot be more than 2^21 subexpressions or we get outside this minimum. Ignoring this might lead to really rare and hard to find errors, years from now. */ if ( insubexpbuffers >= MAXSUBEXPRESSIONS ) { MesPrint("&More than %d subexpressions inside one expression",(WORD)MAXSUBEXPRESSIONS); Terminate(-1); } if ( subexpbuffers+insubexpbuffers >= topsubexpbuffers ) { DoubleBuffer((void **)((void *)(&subexpbuffers)) ,(void **)((void *)(&topsubexpbuffers)),sizeof(SUBBUF),"subexpbuffers"); } subexpbuffers[insubexpbuffers].subexpnum = num; subexpbuffers[insubexpbuffers].buffernum = AC.cbufnum; num = insubexpbuffers++; *fill++ = TSUBEXP; i = 0; do { number[i++] = num & 0x7F; num >>= 7; } while ( num ); while ( --i >= 0 ) *fill++ = (SBYTE)(number[i]); s++; } else if ( *s == TEMPTY ) s++; else *fill++ = *s++; } *fill = TENDOFIT; /* At this stage there are no more subexpressions. Hence we can do the basic compilation. */ if ( AC.CompileLevel == 1 && AC.ToBeInFactors ) { error = CodeFactors(tokens); } AC.CompileLevel--; retval = CodeGenerator(tokens); if ( error < 0 ) return(error); return(retval); } /* #] CompileSubExpressions : #[ CodeGenerator : This routine does the real code generation. It returns the number of the rhs subexpression. At this point we do not have to worry about subexpressions, sets, setelements, simple vs complicated function arguments simple vs complicated powers etc. The variable 'first' indicates whether we are starting a new term The major complication are the set elements of type set[n]. We have marked them as TSETNUM,n,Ttype,setnum They go into SETSET,size,subterm,relocation list in which the subterm should be ready to become a regular subterm in which the sets have been replaced by their element The relocation list consists of pairs of numbers: 1: offset in the subterm, 2: the symbol n. Note that such a subterm can be a whole function with its arguments. We use the variable inset to indicate that we have something going. The relocation list is collected in the top of the WorkSpace. */ static UWORD *CGscrat7 = 0; int CodeGenerator(SBYTE *tokens) { GETIDENTITY SBYTE *s = tokens, c; int i, sign = 1, first = 1, deno = 1, error = 0, minus, n, needarg, numexp, cc; int base, sumlevel = 0, sumtype = SYMTOSYM, firstsumarg, inset = 0; int funflag = 0, settype, x1, x2, mulflag = 0; WORD *t, *v, *r, *term, nnumerator, ndenominator, *oldwork, x3, y, nin; WORD *w1, *w2, *tsize = 0, *relo = 0; UWORD *numerator, *denominator, *innum; CBUF *C; POSITION position; WORD TMproto[SUBEXPSIZE]; /* #ifdef WITHPTHREADS RENUMBER renumber; #endif */ RENUMBER renumber; if ( AC.TokensWriteFlag ) WriteTokens(tokens); if ( CGscrat7 == 0 ) CGscrat7 = (UWORD *)Malloc1((AM.MaxTal+2)*sizeof(WORD),"CodeGenerator"); AddRHS(AC.cbufnum,0); C = cbuf + AC.cbufnum; numexp = C->numrhs; C->NumTerms[numexp] = 0; C->numdum[numexp] = 0; oldwork = AT.WorkPointer; numerator = (UWORD *)(AT.WorkPointer); denominator = numerator + 2*AM.MaxTal; innum = denominator + 2*AM.MaxTal; term = (WORD *)(innum + 2*AM.MaxTal); AT.WorkPointer = term + AM.MaxTer/sizeof(WORD); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; cc = 0; t = term+1; numerator[0] = denominator[0] = 1; nnumerator = ndenominator = 1; while ( *s != TENDOFIT ) { if ( *s == TPLUS || *s == TMINUS ) { if ( first || mulflag ) { if ( *s == TMINUS ) sign = -sign; } else { *term = t-term; C->NumTerms[numexp]++; if ( cc && sign ) C->CanCommu[numexp]++; CompleteTerm(term,numerator,denominator,nnumerator,ndenominator,sign); first = 1; cc = 0; t = term + 1; deno = 1; numerator[0] = denominator[0] = 1; nnumerator = ndenominator = 1; if ( *s == TMINUS ) sign = -1; else sign = 1; } s++; } else { mulflag = first = 0; c = *s++; switch ( c ) { case TSYMBOL: x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } if ( *s == TWILDCARD ) { s++; x1 += 2*MAXPOWER; } *t++ = SYMBOL; *t++ = 4; *t++ = x1; if ( inset ) *relo = 2; TryPower: if ( *s == TPOWER ) { s++; if ( *s == TMINUS ) { s++; deno = -deno; } c = *s++; base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = base*x2 + *s++; } if ( c == TSYMBOL ) { if ( *s == TWILDCARD ) s++; x2 += 2*MAXPOWER; } *t++ = deno*x2; } else *t++ = deno; fin: deno = 1; if ( inset ) { while ( relo < AT.WorkTop ) *t++ = *relo++; inset = 0; tsize[1] = t - tsize; } break; case TINDEX: x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } *t++ = INDEX; *t++ = 3; if ( *s == TWILDCARD ) { s++; x1 += WILDOFFSET; } if ( inset ) { *t++ = x1; *relo = 2; } else *t++ = x1 + AM.OffsetIndex; if ( t[-1] > AM.IndDum ) { x1 = t[-1] - AM.IndDum; if ( x1 > C->numdum[numexp] ) C->numdum[numexp] = x1; } goto fin; case TGENINDEX: *t++ = INDEX; *t++ = 3; *t++ = AC.DumNum+WILDOFFSET; deno = 1; break; case TVECTOR: x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } dovector: if ( inset == 0 ) x1 += AM.OffsetVector; if ( *s == TWILDCARD ) { s++; x1 += WILDOFFSET; } if ( inset ) *relo = 2; if ( *s == TDOT ) { /* DotProduct ? */ s++; if ( *s == TSETNUM || *s == TSETDOL ) { settype = ( *s == TSETDOL ); s++; x2 = 0; while ( *s >= 0 ) { x2 = x2*128 + *s++; } if ( settype ) x2 = -x2; if ( inset == 0 ) { tsize = t; *t++ = SETSET; *t++ = 0; relo = AT.WorkTop; } inset += 2; *--relo = x2; *--relo = 3; } if ( *s != TVECTOR && *s != TDUBIOUS ) { MesPrint("&Illegally formed dotproduct"); error = 1; } s++; x2 = 0; while ( *s >= 0 ) { x2 = x2*128 + *s++; } if ( inset < 2 ) x2 += AM.OffsetVector; if ( *s == TWILDCARD ) { s++; x2 += WILDOFFSET; } *t++ = DOTPRODUCT; *t++ = 5; *t++ = x1; *t++ = x2; goto TryPower; } else if ( *s == TFUNOPEN ) { s++; if ( *s == TSETNUM || *s == TSETDOL ) { settype = ( *s == TSETDOL ); s++; x2 = 0; while ( *s >= 0 ) { x2 = x2*128 + *s++; } if ( settype ) x2 = -x2; if ( inset == 0 ) { tsize = t; *t++ = SETSET; *t++ = 0; relo = AT.WorkTop; } inset += 2; *--relo = x2; *--relo = 3; } if ( *s == TINDEX || *s == TDUBIOUS ) { s++; x2 = 0; while ( *s >= 0 ) { x2 = x2*128 + *s++; } if ( inset < 2 ) x2 += AM.OffsetIndex; if ( *s == TWILDCARD ) { s++; x2 += WILDOFFSET; } *t++ = VECTOR; *t++ = 4; *t++ = x1; *t++ = x2; if ( t[-1] > AM.IndDum ) { x2 = t[-1] - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } } else if ( *s == TGENINDEX ) { *t++ = VECTOR; *t++ = 4; *t++ = x1; *t++ = AC.DumNum + WILDOFFSET; } else if ( *s == TNUMBER || *s == TNUMBER1 ) { base = ( *s == TNUMBER ) ? 100: 128; s++; x2 = 0; while ( *s >= 0 ) { x2 = x2*base + *s++; } if ( x2 >= AM.OffsetIndex && inset < 2 ) { MesPrint("&Fixed index in vector greater than %d", AM.OffsetIndex); return(-1); } *t++ = VECTOR; *t++ = 4; *t++ = x1; *t++ = x2; } else if ( *s == TVECTOR || ( *s == TMINUS && s[1] == TVECTOR ) ) { if ( *s == TMINUS ) { s++; sign = -sign; } s++; x2 = 0; while ( *s >= 0 ) { x2 = x2*128 + *s++; } if ( inset < 2 ) x2 += AM.OffsetVector; if ( *s == TWILDCARD ) { s++; x2 += WILDOFFSET; } *t++ = DOTPRODUCT; *t++ = 5; *t++ = x1; *t++ = x2; *t++ = deno; } else { MesPrint("&Illegal argument for vector"); return(-1); } if ( *s != TFUNCLOSE ) { MesPrint("&Illegal argument for vector"); return(-1); } s++; } else { if ( AC.DumNum ) { *t++ = VECTOR; *t++ = 4; *t++ = x1; *t++ = AC.DumNum + WILDOFFSET; } else { *t++ = INDEX; *t++ = 3; *t++ = x1; } } goto fin; case TDELTA: if ( *s != TFUNOPEN ) { MesPrint("&d_ needs two arguments"); error = -1; } v = t; *t++ = DELTA; *t++ = 4; needarg = 2; x3 = x1 = -1; goto dotensor; case TFUNCTION: x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } if ( x1 == AM.sumnum || x1 == AM.sumpnum ) sumlevel = x1; x1 += FUNCTION; if ( x1 == FIRSTBRACKET ) { if ( s[0] == TFUNOPEN && s[1] == TEXPRESSION ) { doexpr: s += 2; *t++ = x1; *t++ = FUNHEAD+2; *t++ = 0; if ( x1 == AR.PolyFun && AR.PolyFunType == 2 && AR.Eside != LHSIDE ) t[-1] |= MUSTCLEANPRF; FILLFUN3(t) x2 = 0; while ( *s >= 0 ) { x2 = x2*128 + *s++; } *t++ = -EXPRESSION; *t++ = x2; /* The next code is added to facilitate parallel processing We need to call GetTable here to make sure all processors have the same numbering of all variables. */ if ( Expressions[x2].status == STOREDEXPRESSION ) { TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = x2; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; PUTZERO(position); /* if ( ( #ifdef WITHPTHREADS renumber = #endif GetTable(x2,&position,0) ) == 0 ) { error = 1; MesPrint("&Problems getting information about stored expression %s(1)" ,EXPRNAME(x2)); } #ifdef WITHPTHREADS M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); #endif */ if ( ( renumber = GetTable(x2,&position,0) ) == 0 ) { error = 1; MesPrint("&Problems getting information about stored expression %s(1)" ,EXPRNAME(x2)); } if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); AR.StoreData.dirtyflag = 1; } if ( *s != TFUNCLOSE ) { if ( x1 == FIRSTBRACKET ) MesPrint("&Problems with argument of FirstBracket_"); else if ( x1 == FIRSTTERM ) MesPrint("&Problems with argument of FirstTerm_"); else if ( x1 == CONTENTTERM ) MesPrint("&Problems with argument of FirstTerm_"); else if ( x1 == TERMSINEXPR ) MesPrint("&Problems with argument of TermsIn_"); else if ( x1 == SIZEOFFUNCTION ) MesPrint("&Problems with argument of SizeOf_"); else if ( x1 == NUMFACTORS ) MesPrint("&Problems with argument of NumFactors_"); else MesPrint("&Problems with argument of FactorIn_"); error = 1; while ( *s != TENDOFIT && *s != TFUNCLOSE ) s++; } if ( *s == TFUNCLOSE ) s++; goto fin; } } else if ( x1 == TERMSINEXPR || x1 == SIZEOFFUNCTION || x1 == FACTORIN || x1 == NUMFACTORS || x1 == FIRSTTERM || x1 == CONTENTTERM ) { if ( s[0] == TFUNOPEN && s[1] == TEXPRESSION ) goto doexpr; if ( s[0] == TFUNOPEN && s[1] == TDOLLAR ) { s += 2; *t++ = x1; *t++ = FUNHEAD+2; *t++ = 0; FILLFUN3(t) x2 = 0; while ( *s >= 0 ) { x2 = x2*128 + *s++; } *t++ = -DOLLAREXPRESSION; *t++ = x2; if ( *s != TFUNCLOSE ) { if ( x1 == TERMSINEXPR ) MesPrint("&Problems with argument of TermsIn_"); else if ( x1 == SIZEOFFUNCTION ) MesPrint("&Problems with argument of SizeOf_"); else if ( x1 == NUMFACTORS ) MesPrint("&Problems with argument of NumFactors_"); else MesPrint("&Problems with argument of FactorIn_"); error = 1; while ( *s != TENDOFIT && *s != TFUNCLOSE ) s++; } if ( *s == TFUNCLOSE ) s++; goto fin; } } x3 = x1; if ( inset && ( t-tsize == 2 ) ) x1 -= FUNCTION; if ( *s == TWILDCARD ) { x1 += WILDOFFSET; s++; } if ( functions[x3-FUNCTION].commute ) cc = 1; if ( *s != TFUNOPEN ) { *t++ = x1; *t++ = FUNHEAD; *t++ = 0; if ( x1 == AR.PolyFun && AR.PolyFunType == 2 && AR.Eside != LHSIDE ) t[-1] |= MUSTCLEANPRF; FILLFUN3(t) sumlevel = 0; goto fin; } v = t; *t++ = x1; *t++ = FUNHEAD; *t++ = DIRTYFLAG; if ( x1 == AR.PolyFun && AR.PolyFunType == 2 && AR.Eside != LHSIDE ) t[-1] |= MUSTCLEANPRF; FILLFUN3(t) needarg = -1; if ( !inset && functions[x3-FUNCTION].spec >= TENSORFUNCTION ) { dotensor: do { if ( needarg == 0 ) { if ( x1 >= 0 ) { x3 = x1; if ( x3 >= FUNCTION+WILDOFFSET ) x3 -= WILDOFFSET; MesPrint("&Too many arguments in function %s", VARNAME(functions,(x3-FUNCTION)) ); } else MesPrint("&d_ needs exactly two arguments"); error = -1; needarg--; } else if ( needarg > 0 ) needarg--; s++; c = *s++; if ( c == TMINUS && *s == TVECTOR ) { sign = -sign; c = *s++; } base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = base*x2 + *s++; } if ( *s == TWILDCARD && c != TNUMBER ) { x2 += WILDOFFSET; s++; } if ( c == TSETNUM || c == TSETDOL ) { if ( c == TSETDOL ) x2 = -x2; if ( inset == 0 ) { w1 = t; t += 2; w2 = t; while ( w1 > v ) *--w2 = *--w1; tsize = v; relo = AT.WorkTop; *v++ = SETSET; *v++ = 0; } inset = 2; *--relo = x2; *--relo = t - v; c = *s++; x2 = 0; while ( *s >= 0 ) x2 = 128*x2 + *s++; switch ( c ) { case TINDEX: *t++ = x2; if ( t[-1]+AM.OffsetIndex > AM.IndDum ) { x2 = t[-1]+AM.OffsetIndex - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } break; case TVECTOR: *t++ = x2; break; case TNUMBER1: if ( x2 >= 0 && x2 < AM.OffsetIndex ) { *t++ = x2; break; } /* fall through */ default: MesPrint("&Illegal type of set inside tensor"); error = 1; *t++ = x2; break; } } else { switch ( c ) { case TINDEX: if ( inset < 2 ) *t++ = x2 + AM.OffsetIndex; else *t++ = x2; if ( x2+AM.OffsetIndex > AM.IndDum ) { x2 = x2+AM.OffsetIndex - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } break; case TGENINDEX: *t++ = AC.DumNum + WILDOFFSET; break; case TVECTOR: if ( inset < 2 ) *t++ = x2 + AM.OffsetVector; else *t++ = x2; break; case TWILDARG: *t++ = FUNNYWILD; *t++ = x2; /* v[2] = 0; */ break; case TDOLLAR: *t++ = FUNNYDOLLAR; *t++ = x2; break; case TDUBIOUS: if ( inset < 2 ) *t++ = x2 + AM.OffsetVector; else *t++ = x2; break; case TSGAMMA: /* Special gamma's */ if ( x3 != GAMMA ) { MesPrint("&5_,6_,7_ can only be used inside g_"); error = -1; } *t++ = -x2; break; case TNUMBER: case TNUMBER1: if ( x2 >= AM.OffsetIndex && inset < 2 ) { MesPrint("&Value of constant index in tensor too large"); error = -1; } *t++ = x2; break; default: MesPrint("&Illegal object in tensor"); error = -1; break; }} if ( inset >= 2 ) inset = 1; } while ( *s == TCOMMA ); } else { dofunction: firstsumarg = 1; do { unsigned int ux2; s++; c = *s++; if ( c == TMINUS && ( *s == TVECTOR || *s == TNUMBER || *s == TNUMBER1 || *s == TSUBEXP ) ) { minus = 1; c = *s++; } else minus = 0; base = ( c == TNUMBER ) ? 100: 128; ux2 = 0; while ( *s >= 0 ) { ux2 = base*ux2 + *s++; } x2 = ux2; /* may cause an implementation-defined behaviour */ /* !!!!!!!! What if it does not fit? */ if ( firstsumarg ) { firstsumarg = 0; if ( sumlevel > 0 ) { if ( c == TSYMBOL ) { sumlevel = x2; sumtype = SYMTOSYM; } else if ( c == TINDEX ) { sumlevel = x2+AM.OffsetIndex; sumtype = INDTOIND; if ( sumlevel > AM.IndDum ) { x2 = sumlevel - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } } } } if ( *s == TWILDCARD ) { if ( c == TSYMBOL ) x2 += 2*MAXPOWER; else if ( c != TNUMBER ) x2 += WILDOFFSET; s++; } switch ( c ) { case TSYMBOL: *t++ = -SYMBOL; *t++ = x2; break; case TDOLLAR: *t++ = -DOLLAREXPRESSION; *t++ = x2; break; case TEXPRESSION: *t++ = -EXPRESSION; *t++ = x2; /* The next code is added to facilitate parallel processing We need to call GetTable here to make sure all processors have the same numbering of all variables. */ if ( Expressions[x2].status == STOREDEXPRESSION ) { TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = x2; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; PUTZERO(position); /* if ( ( #ifdef WITHPTHREADS renumber = #endif GetTable(x2,&position,0) ) == 0 ) { error = 1; MesPrint("&Problems getting information about stored expression %s(2)" ,EXPRNAME(x2)); } #ifdef WITHPTHREADS M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); #endif */ if ( ( renumber = GetTable(x2,&position,0) ) == 0 ) { error = 1; MesPrint("&Problems getting information about stored expression %s(2)" ,EXPRNAME(x2)); } if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); AR.StoreData.dirtyflag = 1; } break; case TINDEX: *t++ = -INDEX; *t++ = x2 + AM.OffsetIndex; if ( t[-1] > AM.IndDum ) { x2 = t[-1] - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } break; case TGENINDEX: *t++ = -INDEX; *t++ = AC.DumNum + WILDOFFSET; break; case TVECTOR: if ( minus ) *t++ = -MINVECTOR; else *t++ = -VECTOR; *t++ = x2 + AM.OffsetVector; break; case TSGAMMA: /* Special gamma's */ MesPrint("&5_,6_,7_ can only be used inside g_"); error = -1; *t++ = -INDEX; *t++ = -x2; break; case TDUBIOUS: *t++ = -SYMBOL; *t++ = x2; break; case TFUNCTION: *t++ = -x2-FUNCTION; break; case TSET: *t++ = -SETSET; *t++ = x2; break; case TWILDARG: *t++ = -ARGWILD; *t++ = x2; break; case TSETDOL: x2 = -x2; /* fall through */ case TSETNUM: if ( inset == 0 ) { w1 = t; t += 2; w2 = t; while ( w1 > v ) *--w2 = *--w1; tsize = v; relo = AT.WorkTop; *v++ = SETSET; *v++ = 0; inset = 1; } *--relo = x2; *--relo = t-v+1; c = *s++; x2 = 0; while ( *s >= 0 ) x2 = 128*x2 + *s++; switch ( c ) { case TFUNCTION: (*relo)--; *t++ = -x2-1; break; case TSYMBOL: *t++ = -SYMBOL; *t++ = x2; break; case TINDEX: *t++ = -INDEX; *t++ = x2; if ( x2+AM.OffsetIndex > AM.IndDum ) { x2 = x2+AM.OffsetIndex - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } break; case TVECTOR: *t++ = -VECTOR; *t++ = x2; break; case TNUMBER1: *t++ = -SNUMBER; *t++ = x2; break; default: MesPrint("&Internal error 435"); error = 1; *t++ = -SYMBOL; *t++ = x2; break; } break; case TSUBEXP: w2 = AC.ProtoType; i = w2[1]; w1 = t; *t++ = i+ARGHEAD+4; *t++ = 1; FILLARG(t); *t++ = i + 4; while ( --i >= 0 ) *t++ = *w2++; w1[ARGHEAD+3] = subexpbuffers[x2].subexpnum; w1[ARGHEAD+5] = subexpbuffers[x2].buffernum; if ( sumlevel > 0 ) { w1[0] += 4; w1[ARGHEAD] += 4; w1[ARGHEAD+2] += 4; *t++ = sumtype; *t++ = 4; *t++ = sumlevel; *t++ = sumlevel; } *t++ = 1; *t++ = 1; if ( minus ) *t++ = -3; else *t++ = 3; break; case TNUMBER: case TNUMBER1: if ( minus ) x2 = UnsignedToInt(-IntAbs(x2)); *t++ = -SNUMBER; *t++ = x2; break; default: MesPrint("&Illegal object in function"); error = -1; break; } } while ( *s == TCOMMA ); } if ( *s != TFUNCLOSE ) { MesPrint("&Illegal argument field for function. Expected )"); return(-1); } s++; sumlevel = 0; v[1] = t-v; /* if ( *v == AM.termfunnum && ( v[1] != FUNHEAD+2 || v[FUNHEAD] != -DOLLAREXPRESSION ) ) { MesPrint("&The function term_ can only have one argument with a single $-expression"); error = 1; } */ goto fin; case TDUBIOUS: x1 = 0; while ( *s >= 0 ) x1 = 128*x1 + *s++; if ( *s == TWILDCARD ) s++; if ( *s == TDOT ) goto dovector; if ( *s == TFUNOPEN ) { x1 += FUNCTION; cc = 1; v = t; *t++ = x1; *t++ = FUNHEAD; *t++ = DIRTYFLAG; if ( x1 == AR.PolyFun && AR.PolyFunType == 2 && AR.Eside != LHSIDE ) t[-1] |= MUSTCLEANPRF; FILLFUN3(t) needarg = -1; goto dofunction; } *t++ = SYMBOL; *t++ = 4; *t++ = 0; if ( inset ) *relo = 2; goto TryPower; case TSUBEXP: x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } if ( *s == TPOWER ) { s++; c = *s++; base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = base*x2 + *s++; } if ( *s == TWILDCARD ) { x2 += 2*MAXPOWER; s++; } else if ( c == TSYMBOL ) x2 += 2*MAXPOWER; } else x2 = 1; r = AC.ProtoType; n = r[1] - 5; r += 5; *t++ = SUBEXPRESSION; *t++ = r[-4]; *t++ = subexpbuffers[x1].subexpnum; *t++ = x2*deno; *t++ = subexpbuffers[x1].buffernum; NCOPY(t,r,n); if ( cbuf[subexpbuffers[x1].buffernum].CanCommu[subexpbuffers[x1].subexpnum] ) cc = 1; deno = 1; break; case TMULTIPLY: mulflag = 1; break; case TDIVIDE: mulflag = 1; deno = -deno; break; case TEXPRESSION: cc = 1; x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } v = t; *t++ = EXPRESSION; *t++ = SUBEXPSIZE; *t++ = x1; *t++ = deno; *t++ = 0; FILLSUB(t) /* Here we had some erroneous code before. It should be after the reading of the parameters as it is now (after 15-jan-2007). Thomas Hahn noticed this and reported it. */ if ( *s == TFUNOPEN ) { do { s++; c = *s++; base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = base*x2 + *s++; } switch ( c ) { case TSYMBOL: *t++ = SYMBOL; *t++ = 4; *t++ = x2; *t++ = 1; break; case TINDEX: *t++ = INDEX; *t++ = 3; *t++ = x2+AM.OffsetIndex; if ( t[-1] > AM.IndDum ) { x2 = t[-1] - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } break; case TVECTOR: *t++ = INDEX; *t++ = 3; *t++ = x2+AM.OffsetVector; break; case TFUNCTION: *t++ = x2+FUNCTION; *t++ = 2; break; case TNUMBER: case TNUMBER1: if ( x2 >= AM.OffsetIndex || x2 < 0 ) { MesPrint("&Index as argument of expression has illegal value"); error = -1; } *t++ = INDEX; *t++ = 3; *t++ = x2; break; case TSETDOL: x2 = -x2; /* fall through */ case TSETNUM: if ( inset == 0 ) { w1 = t; t += 2; w2 = t; while ( w1 > v ) *--w2 = *--w1; tsize = v; relo = AT.WorkTop; *v++ = SETSET; *v++ = 0; inset = 1; } *--relo = x2; *--relo = t-v+2; c = *s++; x2 = 0; while ( *s >= 0 ) x2 = 128*x2 + *s++; switch ( c ) { case TFUNCTION: *relo -= 2; *t++ = -x2-1; break; case TSYMBOL: *t++ = SYMBOL; *t++ = 4; *t++ = x2; *t++ = 1; break; case TINDEX: *t++ = INDEX; *t++ = 3; *t++ = x2; if ( x2+AM.OffsetIndex > AM.IndDum ) { x2 = x2+AM.OffsetIndex - AM.IndDum; if ( x2 > C->numdum[numexp] ) C->numdum[numexp] = x2; } break; case TVECTOR: *t++ = VECTOR; *t++ = 3; *t++ = x2; break; case TNUMBER1: *t++ = SNUMBER; *t++ = 4; *t++ = x2; *t++ = 1; break; default: MesPrint("&Internal error 435"); error = 1; *t++ = SYMBOL; *t++ = 4; *t++ = x2; *t++ = 1; break; } break; default: MesPrint("&Argument of expression can only be symbol, index, vector or function"); error = -1; break; } } while ( *s == TCOMMA ); if ( *s != TFUNCLOSE ) { MesPrint("&Illegal object in argument field for expression"); error = -1; while ( *s != TFUNCLOSE ) s++; } s++; } r = AC.ProtoType; n = r[1]; if ( n > SUBEXPSIZE ) { *t++ = WILDCARDS; *t++ = n+2; NCOPY(t,r,n); } /* Code added for parallel processing. This is different from the other occurrences to test immediately for renumbering. Here we have to read the parameters first. */ if ( Expressions[x1].status == STOREDEXPRESSION ) { v[1] = t-v; AT.TMaddr = v; PUTZERO(position); /* if ( ( #ifdef WITHPTHREADS renumber = #endif GetTable(x1,&position,0) ) == 0 ) { error = 1; MesPrint("&Problems getting information about stored expression %s(3)" ,EXPRNAME(x1)); } #ifdef WITHPTHREADS M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); #endif */ if ( ( renumber = GetTable(x1,&position,0) ) == 0 ) { error = 1; MesPrint("&Problems getting information about stored expression %s(3)" ,EXPRNAME(x1)); } if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); AR.StoreData.dirtyflag = 1; } if ( *s == LBRACE ) { /* This should be one term that should be inserted FROMBRAC size+2 ( term ) Because this term should have been translated already we can copy it from the 'subexpression' */ s++; if ( *s != TSUBEXP ) { MesPrint("&Internal error 23"); Terminate(-1); } s++; x2 = 0; while ( *s >= 0 ) { x2 = 128*x2 + *s++; } r = cbuf[subexpbuffers[x2].buffernum].rhs[subexpbuffers[x2].subexpnum]; *t++ = FROMBRAC; *t++ = *r+2; n = *r; NCOPY(t,r,n); if ( *r != 0 ) { MesPrint("&Object between [] in expression should be a single term"); error = -1; } if ( *s != RBRACE ) { MesPrint("&Internal error 23b"); Terminate(-1); } s++; } if ( *s == TPOWER ) { s++; c = *s++; base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = base*x2 + *s++; } if ( *s == TWILDCARD || c == TSYMBOL ) { x2 += 2*MAXPOWER; s++; } v[3] = x2; } v[1] = t - v; deno = 1; break; case TNUMBER: if ( *s == 0 ) { s++; if ( *s == TPOWER ) { s++; if ( *s == TMINUS ) { s++; deno = -deno; } c = *s++; base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = x2*base + *s++; } if ( x2 == 0 ) { error = -1; MesPrint("&Encountered 0^0 during compilation"); } if ( deno < 0 ) { error = -1; MesPrint("&Division by zero during compilation (0 to the power negative number)"); } } else if ( deno < 0 ) { error = -1; MesPrint("&Division by zero during compilation"); } sign = 0; break; /* term is zero */ } y = *s++; if ( *s >= 0 ) { y = 100*y + *s++; } innum[0] = y; nin = 1; while ( *s >= 0 ) { y = *s++; x2 = 100; if ( *s >= 0 ) { y = 100*y + *s++; x2 = 10000; } Product(innum,&nin,(WORD)x2); if ( y ) AddLong(innum,nin,(UWORD *)(&y),(WORD)1,innum,&nin); } docoef: if ( *s == TPOWER ) { s++; if ( *s == TMINUS ) { s++; deno = -deno; } c = *s++; base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = x2*base + *s++; } if ( x2 == 0 ) { innum[0] = 1; nin = 1; } else if ( RaisPow(BHEAD innum,&nin,x2) ) { error = -1; innum[0] = 1; nin = 1; } } if ( deno > 0 ) { Simplify(BHEAD innum,&nin,denominator,&ndenominator); for ( i = 0; i < nnumerator; i++ ) CGscrat7[i] = numerator[i]; MulLong(innum,nin,CGscrat7,nnumerator,numerator,&nnumerator); } else if ( deno < 0 ) { Simplify(BHEAD innum,&nin,numerator,&nnumerator); for ( i = 0; i < ndenominator; i++ ) CGscrat7[i] = denominator[i]; MulLong(innum,nin,CGscrat7,ndenominator,denominator,&ndenominator); } deno = 1; break; case TNUMBER1: if ( *s == 0 ) { s++; sign = 0; break; /* term is zero */ } y = *s++; if ( *s >= 0 ) { y = 128*y + *s++; } if ( inset == 0 ) { innum[0] = y; nin = 1; while ( *s >= 0 ) { y = *s++; x2 = 128; if ( *s >= 0 ) { y = 128*y + *s++; x2 = 16384; } Product(innum,&nin,(WORD)x2); if ( y ) AddLong(innum,nin,(UWORD *)&y,(WORD)1,innum,&nin); } goto docoef; } *relo = 2; *t++ = SNUMBER; *t++ = 4; *t++ = y; goto TryPower; #ifdef WITHFLOAT case TFLOAT: { WORD *w; s = ReadFloat(s); i = AT.WorkPointer[1]; w = AT.WorkPointer; NCOPY(t,w,i); /* Power? */ } break; #endif case TDOLLAR: { WORD *powplace; x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } if ( AR.Eside != LHSIDE ) { *t++ = SUBEXPRESSION; *t++ = SUBEXPSIZE; *t++ = x1; } else { *t++ = DOLLAREXPRESSION; *t++ = SUBEXPSIZE; *t++ = x1; } powplace = t; t++; *t++ = AM.dbufnum; FILLSUB(t) /* Now we have to test for factors of dollars with [ ] and [ [ ]] */ if ( *s == LBRACE ) { int bracelevel = 1; s++; while ( bracelevel > 0 ) { if ( *s == RBRACE ) { bracelevel--; s++; } else if ( *s == TNUMBER ) { s++; x2 = 0; while ( *s >= 0 ) { x2 = 100*x2 + *s++; } *t++ = DOLLAREXPR2; *t++ = 3; *t++ = -x2-1; CloseBraces: while ( bracelevel > 0 ) { if ( *s != RBRACE ) { ErrorBraces: error = -1; MesPrint("&Improper use of [] in $-variable."); return(error); } else { s++; bracelevel--; } } } else if ( *s == TDOLLAR ) { s++; x1 = 0; while ( *s >= 0 ) { x1 = x1*128 + *s++; } *t++ = DOLLAREXPR2; *t++ = 3; *t++ = x1; if ( *s == RBRACE ) goto CloseBraces; else if ( *s == LBRACE ) { s++; bracelevel++; } } else goto ErrorBraces; } } /* Finally we can continue with the power */ if ( *s == TPOWER ) { s++; if ( *s == TMINUS ) { s++; deno = -deno; } c = *s++; base = ( c == TNUMBER ) ? 100: 128; x2 = 0; while ( *s >= 0 ) { x2 = base*x2 + *s++; } if ( c == TSYMBOL ) { if ( *s == TWILDCARD ) s++; x2 += 2*MAXPOWER; } *powplace = deno*x2; } else *powplace = deno; deno = 1; /* if ( inset ) { while ( relo < AT.WorkTop ) *t++ = *relo++; inset = 0; tsize[1] = t - tsize; } */ } break; case TSETNUM: inset = 1; tsize = t; relo = AT.WorkTop; *t++ = SETSET; *t++ = 0; x1 = 0; while ( *s >= 0 ) x1 = x1*128 + *s++; *--relo = x1; *--relo = 0; break; case TSETDOL: inset = 1; tsize = t; relo = AT.WorkTop; *t++ = SETSET; *t++ = 0; x1 = 0; while ( *s >= 0 ) x1 = x1*128 + *s++; *--relo = -x1; *--relo = 0; break; case TFUNOPEN: MesPrint("&Illegal use of function arguments"); error = -1; funflag = 1; deno = 1; break; case TFUNCLOSE: if ( funflag == 0 ) MesPrint("&Illegal use of function arguments"); error = -1; funflag = 0; deno = 1; break; case TSGAMMA: MesPrint("&Illegal use special gamma symbols 5_, 6_, 7_"); error = -1; funflag = 0; deno = 1; break; case TCONJUGATE: MesPrint("&Complex conjugate operator (%#) is not implemented"); error = -1; deno = 1; break; default: MesPrint("&Internal error in code generator. Unknown object: %d",c); error = -1; deno = 1; break; } } } if ( mulflag ) { MesPrint("&Irregular end of statement."); error = 1; } if ( !first && error == 0 ) { *term = t-term; C->NumTerms[numexp]++; if ( cc && sign ) C->CanCommu[numexp]++; error = CompleteTerm(term,numerator,denominator,nnumerator,ndenominator,sign); } AT.WorkPointer = oldwork; if ( error ) return(-1); AddToCB(C,0) if ( AC.CompileLevel > 0 && AR.Eside != LHSIDE ) { /* See whether we have this one already */ error = InsTree(AC.cbufnum,C->numrhs); if ( error < (C->numrhs) ) { C->Pointer = C->rhs[C->numrhs--]; return(error); } } return(C->numrhs); OverWork: MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* #] CodeGenerator : #[ CompleteTerm : Completes the term Puts it in the buffer */ int CompleteTerm(WORD *term, UWORD *numer, UWORD *denom, WORD nnum, WORD nden, int sign) { int nsize, i; WORD *t; if ( sign == 0 ) return(0); /* Term is zero */ if ( nnum >= nden ) nsize = nnum; else nsize = nden; t = term + *term; for ( i = 0; i < nnum; i++ ) *t++ = numer[i]; for ( ; i < nsize; i++ ) *t++ = 0; for ( i = 0; i < nden; i++ ) *t++ = denom[i]; for ( ; i < nsize; i++ ) *t++ = 0; *t++ = (2*nsize+1)*sign; *term = t - term; AddNtoC(AC.cbufnum,*term,term,7); return(0); } /* #] CompleteTerm : #[ CodeFactors : This routine does the part of reading in in terms of factors. If there is more than one term at this level we have only one factor. In that case any expression should first be unfactorized. Then the whole expression gets read as a new subexpression and finally we generate factor_*subexpression. If the whole has only multiplications we have factors. Then the nasty thing is powers of objects and in particular powers of factorized expressions or dollars. For a power we generate a new subexpression of the type 1+factor_+...+factor_^(power-1) with which we multiply. WE HAVE NOT YET WORRIED ABOUT SETS */ int CodeFactors(SBYTE *tokens) { GETIDENTITY EXPRESSIONS e = Expressions + AR.CurExpr; int nfactor = 1, nparenthesis, i, last = 0, error = 0; SBYTE *t, *startobject, *tt, *s1, *out, *outtokens; WORD nexp, subexp = 0, power, pow, x2, powfactor, first; /* First scan the number of factors */ t = tokens; while ( *t != TENDOFIT ) { if ( *t >= 0 ) { while ( *t >= 0 ) t++; continue; } if ( *t == LPARENTHESIS || *t == LBRACE || *t == TSETOPEN || *t == TFUNOPEN ) { nparenthesis = 0; t++; while ( nparenthesis >= 0 ) { if ( *t == LPARENTHESIS || *t == LBRACE || *t == TSETOPEN || *t == TFUNOPEN ) nparenthesis++; else if ( *t == RPARENTHESIS || *t == RBRACE || *t == TSETCLOSE || *t == TFUNCLOSE ) nparenthesis--; t++; } continue; } else if ( ( *t == TPLUS || *t == TMINUS ) && ( t > tokens ) && ( t[-1] != TPLUS && t[-1] != TMINUS ) ) { if ( t[-1] >= 0 || t[-1] == RPARENTHESIS || t[-1] == RBRACE || t[-1] == TSETCLOSE || t[-1] == TFUNCLOSE ) { subexp = CodeGenerator(tokens); if ( subexp < 0 ) error = -1; if ( insubexpbuffers >= MAXSUBEXPRESSIONS ) { MesPrint("&More than %d subexpressions inside one expression",(WORD)MAXSUBEXPRESSIONS); Terminate(-1); } if ( subexpbuffers+insubexpbuffers >= topsubexpbuffers ) { DoubleBuffer((void **)((void *)(&subexpbuffers)) ,(void **)((void *)(&topsubexpbuffers)),sizeof(SUBBUF),"subexpbuffers"); } subexpbuffers[insubexpbuffers].subexpnum = subexp; subexpbuffers[insubexpbuffers].buffernum = AC.cbufnum; subexp = insubexpbuffers++; t = tokens; *t++ = TSYMBOL; *t++ = FACTORSYMBOL; *t++ = TMULTIPLY; *t++ = TSUBEXP; PUTNUMBER128(t,subexp) *t++ = TENDOFIT; e->numfactors = 1; e->vflags |= ISFACTORIZED; return(subexp); } } else if ( ( *t == TMULTIPLY || *t == TDIVIDE ) && t > tokens ) { nfactor++; } else if ( *t == TEXPRESSION ) { t++; nexp = 0; while ( *t >= 0 ) { nexp = nexp*128 + *t++; } if ( *t == LBRACE ) continue; if ( ( AS.Oldvflags[nexp] & ISFACTORIZED ) != 0 ) { nfactor += AS.OldNumFactors[nexp]; } else { nfactor++; } continue; } else if ( *t == TDOLLAR ) { t++; nexp = 0; while ( *t >= 0 ) { nexp = nexp*128 + *t++; } if ( *t == LBRACE ) continue; if ( Dollars[nexp].nfactors > 0 ) { nfactor += Dollars[nexp].nfactors; } else { nfactor++; } continue; } t++; } /* Now the real pass. nfactor is a not so reliable measure for the space we need. */ outtokens = (SBYTE *)Malloc1(((t-tokens)+(nfactor+2)*25)*sizeof(SBYTE),"CodeFactors"); out = outtokens; t = tokens; first = 1; powfactor = 1; while ( *t == TPLUS || *t == TMINUS ) { if ( *t == TMINUS ) first = -first; t++; } if ( first < 0 ) { *out++ = TMINUS; *out++ = TSYMBOL; *out++ = FACTORSYMBOL; *out++ = TPOWER; *out++ = TNUMBER; PUTNUMBER100(out,powfactor) powfactor++; } startobject = t; power = 1; while ( *t != TENDOFIT ) { if ( *t >= 0 ) { while ( *t >= 0 ) t++; continue; } if ( *t == LPARENTHESIS || *t == LBRACE || *t == TSETOPEN || *t == TFUNOPEN ) { nparenthesis = 0; t++; while ( nparenthesis >= 0 ) { if ( *t == LPARENTHESIS || *t == LBRACE || *t == TSETOPEN || *t == TFUNOPEN ) nparenthesis++; else if ( *t == RPARENTHESIS || *t == RBRACE || *t == TSETCLOSE || *t == TFUNCLOSE ) nparenthesis--; t++; } continue; } else if ( ( *t == TMULTIPLY || *t == TDIVIDE ) && ( t > tokens ) ) { if ( t[-1] >= 0 || t[-1] == RPARENTHESIS || t[-1] == RBRACE || t[-1] == TSETCLOSE || t[-1] == TFUNCLOSE ) { dolast: if ( startobject ) { /* apparently power is 1 or -1 */ *out++ = TPLUS; if ( power < 0 ) { *out++ = TNUMBER; *out++ = 1; *out++ = TDIVIDE; } s1 = startobject; while ( s1 < t ) *out++ = *s1++; *out++ = TMULTIPLY; *out++ = TSYMBOL; *out++ = FACTORSYMBOL; *out++ = TPOWER; *out++ = TNUMBER; PUTNUMBER100(out,powfactor) powfactor++; } if ( last ) { startobject = 0; break; } startobject = t+1; if ( *t == TDIVIDE ) power = -1; if ( *t == TMULTIPLY ) power = 1; } } else if ( *t == TPOWER ) { pow = 1; tt = t+1; while ( ( *tt == TMINUS ) || ( *tt == TPLUS ) ) { if ( *tt == TMINUS ) pow = -pow; tt++; } if ( *tt == TSYMBOL ) { tt++; while ( *tt >= 0 ) tt++; t = tt; continue; } tt++; x2 = 0; while ( *tt >= 0 ) { x2 = 100*x2 + *tt++; } /* We have an object in startobject till t. The power is power*pow*x2 */ power = power*pow*x2; if ( power < 0 ) { pow = -power; power = -1; } else if ( power == 0 ) { t = tt; startobject = tt; continue; } else { pow = power; power = 1; } *out++ = TPLUS; if ( pow > 1 ) { subexp = GenerateFactors(pow,1); if ( subexp < 0 ) { error = -1; subexp = 0; } *out++ = TSUBEXP; PUTNUMBER128(out,subexp); } *out++ = TSYMBOL; *out++ = FACTORSYMBOL; *out++ = TPOWER; *out++ = TNUMBER; PUTNUMBER100(out,powfactor) powfactor += pow; if ( power > 0 ) *out++ = TMULTIPLY; else *out++ = TDIVIDE; s1 = startobject; while ( s1 < t ) *out++ = *s1++; startobject = 0; t = tt; continue; } else if ( *t == TEXPRESSION ) { startobject = t; t++; nexp = 0; while ( *t >= 0 ) { nexp = nexp*128 + *t++; } if ( *t == LBRACE ) continue; if ( *t == LPARENTHESIS ) { nparenthesis = 0; t++; while ( nparenthesis >= 0 ) { if ( *t == LPARENTHESIS ) nparenthesis++; else if ( *t == RPARENTHESIS ) nparenthesis--; t++; } } if ( ( AS.Oldvflags[nexp] & ISFACTORIZED ) == 0 ) continue; if ( *t == TPOWER ) { pow = 1; tt = t+1; while ( ( *tt == TMINUS ) || ( *tt == TPLUS ) ) { if ( *tt == TMINUS ) pow = -pow; tt++; } if ( *tt != TNUMBER ) { MesPrint("Internal problems(1) in CodeFactors"); return(-1); } tt++; x2 = 0; while ( *tt >= 0 ) { x2 = 100*x2 + *tt++; } /* We have an object in startobject till t. The power is power*pow*x2 */ dopower: power = power*pow*x2; if ( power < 0 ) { pow = -power; power = -1; } else if ( power == 0 ) { t = tt; startobject = tt; continue; } else { pow = power; power = 1; } *out++ = TPLUS; if ( pow > 1 ) { subexp = GenerateFactors(pow,AS.OldNumFactors[nexp]); if ( subexp < 0 ) { error = -1; subexp = 0; } *out++ = TSUBEXP; PUTNUMBER128(out,subexp) *out++ = TMULTIPLY; } i = powfactor-1; if ( i > 0 ) { *out++ = TSYMBOL; *out++ = FACTORSYMBOL; if ( i > 1 ) { *out++ = TPOWER; *out++ = TNUMBER; PUTNUMBER100(out,i) } *out++ = TMULTIPLY; } powfactor += AS.OldNumFactors[nexp]*pow; s1 = startobject; while ( s1 < t ) *out++ = *s1++; startobject = 0; t = tt; continue; } else { tt = t; pow = 1; x2 = 1; goto dopower; } } else if ( *t == TDOLLAR ) { startobject = t; t++; nexp = 0; while ( *t >= 0 ) { nexp = nexp*128 + *t++; } if ( *t == LBRACE ) continue; if ( Dollars[nexp].nfactors == 0 ) continue; if ( *t == TPOWER ) { pow = 1; tt = t+1; while ( ( *tt == TMINUS ) || ( *tt == TPLUS ) ) { if ( *tt == TMINUS ) pow = -pow; tt++; } if ( *tt != TNUMBER ) { MesPrint("Internal problems(2) in CodeFactors"); return(-1); } tt++; x2 = 0; while ( *tt >= 0 ) { x2 = 100*x2 + *tt++; } /* We have an object in startobject till t. The power is power*pow*x2 */ dopowerd: power = power*pow*x2; if ( power < 0 ) { pow = -power; power = -1; } else if ( power == 0 ) { t = tt; startobject = tt; continue; } else { pow = power; power = 1; } if ( pow > 1 ) { subexp = GenerateFactors(pow,1); if ( subexp < 0 ) { error = -1; subexp = 0; } } for ( i = 1; i <= Dollars[nexp].nfactors; i++ ) { s1 = startobject; *out++ = TPLUS; while ( s1 < t ) *out++ = *s1++; *out++ = LBRACE; *out++ = TNUMBER; PUTNUMBER128(out,i) *out++ = RBRACE; *out++ = TMULTIPLY; *out++ = TSYMBOL; *out++ = FACTORSYMBOL; *out++ = TPOWER; *out++ = TNUMBER; PUTNUMBER100(out,powfactor) powfactor += pow; if ( pow > 1 ) { *out++ = TSUBEXP; PUTNUMBER128(out,subexp) } } startobject = 0; t = tt; continue; } else { tt = t; pow = 1; x2 = 1; goto dopowerd; } } t++; } if ( last == 0 ) { last = 1; goto dolast; } *out = TENDOFIT; e->numfactors = powfactor-1; e->vflags |= ISFACTORIZED; subexp = CodeGenerator(outtokens); if ( subexp < 0 ) error = -1; if ( insubexpbuffers >= MAXSUBEXPRESSIONS ) { MesPrint("&More than %d subexpressions inside one expression",(WORD)MAXSUBEXPRESSIONS); Terminate(-1); } if ( subexpbuffers+insubexpbuffers >= topsubexpbuffers ) { DoubleBuffer((void **)((void *)(&subexpbuffers)) ,(void **)((void *)(&topsubexpbuffers)),sizeof(SUBBUF),"subexpbuffers"); } subexpbuffers[insubexpbuffers].subexpnum = subexp; subexpbuffers[insubexpbuffers].buffernum = AC.cbufnum; subexp = insubexpbuffers++; M_free(outtokens,"CodeFactors"); s1 = tokens; *s1++ = TSUBEXP; PUTNUMBER128(s1,subexp); *s1++ = TENDOFIT; if ( error < 0 ) return(-1); else return(subexp); } /* #] CodeFactors : #[ GenerateFactors : Generates an expression of the type 1+factor_+factor_^2+...+factor_^(n-1) (this is if inc=1) Returns the subexpression pointer of it. */ WORD GenerateFactors(WORD n,WORD inc) { int subexp; int i, error = 0; SBYTE *s; SBYTE *tokenbuffer = (SBYTE *)Malloc1(8*n*sizeof(SBYTE),"GenerateFactors"); s = tokenbuffer; *s++ = TNUMBER; *s++ = 1; for ( i = inc; i < n*inc; i += inc ) { *s++ = TPLUS; *s++ = TSYMBOL; *s++ = FACTORSYMBOL; if ( i > 1 ) { *s++ = TPOWER; *s++ = TNUMBER; PUTNUMBER100(s,i) } } *s++ = TENDOFIT; subexp = CodeGenerator(tokenbuffer); if ( subexp < 0 ) error = -1; M_free(tokenbuffer,"GenerateFactors"); if ( insubexpbuffers >= MAXSUBEXPRESSIONS ) { MesPrint("&More than %d subexpressions inside one expression",(WORD)MAXSUBEXPRESSIONS); Terminate(-1); } if ( subexpbuffers+insubexpbuffers >= topsubexpbuffers ) { DoubleBuffer((void **)((void *)(&subexpbuffers)) ,(void **)((void *)(&topsubexpbuffers)),sizeof(SUBBUF),"subexpbuffers"); } subexpbuffers[insubexpbuffers].subexpnum = subexp; subexpbuffers[insubexpbuffers].buffernum = AC.cbufnum; subexp = insubexpbuffers++; if ( error < 0 ) return(error); return(subexp); } /* #] GenerateFactors : #] Compiler : */ form-5.0.1/sources/grccparam.h0000644000175100017510000002107615217035721011747 #ifdef GRCC_PARAM_H #else #define GRCC_PARAM_H /* #[ License : */ /* * Copyright (C) 2023-2026 T. Kaneko * When using this file you are requested to refer to the publication * Comput.Phys.Commun. 92 (1995) 127-152 * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /*============================================================== * Parameters */ /* #define GRCC_NAMESPACE */ #define GRCC_MAXNCPLG 4 #define GRCC_MAXLEGS 10 #define GRCC_MAXMPARTICLES 50 #define GRCC_MAXMINTERACT 500 #define GRCC_MAXSUBPROCS 500 #define GRCC_MAXNODES 20 #define GRCC_MAXEDGES 100 #define GRCC_MAXNSTACK 50 #define GRCC_MAXESTACK 50 #define GRCC_MAXGROUP 1000 #define GRCC_MAXPSLIST 500 #define GRCC_MAXMPARTICLES2 (2*GRCC_MAXMPARTICLES-1) #define GRCC_MAXFLINES GRCC_MAXEDGES #define GRCC_FRACERROR (1.0e-10) /* Standard and error message destination */ #define GRCC_Stdout stdout #define GRCC_Stderr stdout #ifndef NOFORM #define GRCC_ABORT() Terminate(-1); #else #define GRCC_ABORT() exit(1) #endif /*--------------------------------------------------------------- * Constants */ /* model definition */ #define GRCC_DEFBYNAME 1 /* define interactions by particle name */ #define GRCC_DEFBYCODE 2 /* define interactions by particle code */ /* types of particles */ #define GRCC_PT_Undef 0 #define GRCC_PT_Scalar 1 #define GRCC_PT_Dirac 2 #define GRCC_PT_Majorana 3 #define GRCC_PT_Vector 4 #define GRCC_PT_Ghost 5 #define GRCC_PT_Size 6 #define GRCC_PTS_Undef "undef" #define GRCC_PTS_Scalar "scalar" #define GRCC_PTS_Dirac "dirac" #define GRCC_PTS_Majorana "majorana" #define GRCC_PTS_Vector "vector" #define GRCC_PTS_Ghost "ghost" #define GRCC_PT_Table { GRCC_PTS_Undef, GRCC_PTS_Scalar, GRCC_PTS_Dirac, GRCC_PTS_Majorana, GRCC_PTS_Vector, GRCC_PTS_Ghost} #define GRCC_PT_GTable { "Undef", "Scalar", "Fermion", "Majorana", "Vector", "Ghost"} /* for mgraph generation */ #define GRCC_AT_Vertex 0 #define GRCC_AT_External -1 #define GRCC_AT_Initial -2 #define GRCC_AT_Final -3 #define GRCC_AT_NdStr(x) ((x)>=GRCC_AT_Vertex ?"Vertex": \ ((x)==GRCC_AT_External ?"External": \ ((x)==GRCC_AT_Final ?"Final": \ ((x)==GRCC_AT_Initial ?"Initial":"Undef")))) /* graph generation */ #define GRCC_MGraph 0 /* mgraph (topology) generation */ #define GRCC_AGraph 1 /* agraph generation */ /* options for graph greneration */ #define GRCC_OPT_Step 0 #define GRCC_OPT_Outgrf 1 #define GRCC_OPT_Outgrp 2 #define GRCC_OPT_1PI 3 #define GRCC_OPT_NoSelfLoop 4 #define GRCC_OPT_NoTadpole 5 #define GRCC_OPT_No1PtBlock 6 #define GRCC_OPT_No2PtL1PI 7 #define GRCC_OPT_NoExtSelf 8 #define GRCC_OPT_NoAdj2PtV 9 #define GRCC_OPT_Block 10 #define GRCC_OPT_NoMultiEdge 11 #define GRCC_OPT_SymmInitial 12 #define GRCC_OPT_SymmFinal 13 #define GRCC_OPT_Size 14 typedef unsigned long ULong; typedef struct { const char *name; const char *mean; int defaultv; int DUMMYPADDING; } OptDef; typedef struct { const char *name; const char *cname; const char *mean; } OptQGDef; typedef struct { const char *name; int index; int sign; } OptQGRef; /*--------------------------------------------------------------- * QGRAF options */ #define GRCC_QGRAF_OPT_ONEPI 0 #define GRCC_QGRAF_OPT_ONSHELL 1 #define GRCC_QGRAF_OPT_NOSIGMA 2 #define GRCC_QGRAF_OPT_NOSNAIL 3 #define GRCC_QGRAF_OPT_NOTADPOLE 4 #define GRCC_QGRAF_OPT_SIMPLE 5 #define GRCC_QGRAF_OPT_BIPART 6 #define GRCC_QGRAF_OPT_CYCLI 7 #define GRCC_QGRAF_OPT_FLOOP 8 //TODO what does this do? Does it work? //#define GRCC_QGRAF_OPT_TOPOL 9 #ifdef GRCC_QGRAF_OPT_TOPOL #define GRCC_QGRAF_OPT_Size 10 #else #define GRCC_QGRAF_OPT_Size 9 #endif /*--------------------------------------------------------------- * Conversion of * eind : index (ed) of EGraph.edges[ed] * sind : value (v) of EGraph.nodes[nd]->edges[j]) */ #define I2Vedge(eind, sign) (((sign<=0)?(-1):(1))*((eind)+1)) #define V2Iedge(sind) (abs(sind)-1) #define V2Ileg(sind) ((sind)<0 ? 0 : 1) /*--------------------------------------------------------------- * data types for model definition */ typedef struct { const char *name; /* name of the model */ int defpart; /* particle is defined by name or code */ /* GRCC_DEFBYNAME or GRCC_DEFBYCODE */ int ncouple; /* No. of coupling constants */ const char *cnamlist[GRCC_MAXNCPLG]; /* Names of coupling constants */ } MInput; typedef struct { const char *name; /* name of particle */ const char *aname; /* name of anti-particle */ int pcode; /* code of particle */ int acode; /* code of anti-particle */ const char *ptypen; /* type : 'GRCC_PTS_Scalar' etc */ int ptypec; /* type : 'GRCC_PT_Scalar' etc */ int extonly; /* only as external particle */ } PInput; typedef struct { const char *name; /* name of interaction */ int icode; /* code of interaction */ int nplistn; /* the number of legs */ const char *plistn[GRCC_MAXLEGS]; /* list of particle names */ int plistc[GRCC_MAXLEGS]; /* list of particle codes */ int cvallist[GRCC_MAXNCPLG]; /* coupling constants */ } IInput; /*--------------------------------------------------------------- * data type for node class input */ typedef struct { /* used as input to MGraph() and SProcess() */ int cldeg; int clnum; int cltyp; int cmind; int cmaxd; /* used as input to SProcess() */ int ptcl; int cple; } NCInput; /*--------------------------------------------------------------- * data types for process definition */ typedef struct { long ninitl; /* the number of initial particles */ const char *initln[GRCC_MAXNODES]; /* list of initial particles (name) */ int initlc[GRCC_MAXNODES]; /* list of final particles (code) */ long nfinal; /* the number of final particles */ const char *finaln[GRCC_MAXNODES]; /* list of final particles (name) */ int finalc[GRCC_MAXNODES]; /* list of final particles (code) */ int coupl[GRCC_MAXNCPLG]; /* list of orders of c. consts */ } FGInput; /* class of node : input for SProcess */ typedef struct { int cdeg; /* degree of each node */ int ctyp; /* type : GRCC_AT_xxx */ int cnum; /* the number of nodes in the class */ int cple; /* total order of c.c. of each node */ /* = 0 for external particle */ const char *pname; /* particle name defined in the model */ /* = NULL for vertex */ long pcode; /* particle code defined in the model */ /* = 0 for vertex */ /* long = int + padding */ } PGInput; /*--------------------------------------------------------------- * minimum input data to EGraph */ typedef struct { int extloop; /* external/loop */ int intrct; /* particl/interaction */ } DNode; typedef int DEdge[2]; /* {node0, node1} */ typedef struct { int nnodes; int nedges; DNode *nodes; DEdge *edges; } DGraph; /*--------------------------------------------------------------- */ #endif form-5.0.1/sources/declare.h0000644000175100017510000021001715217035721011402 #ifndef __FDECLARE__ #define __FDECLARE__ /** @file declare.h * * Contains macros and function declarations. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Macro's : */ #define MaX(x,y) ((x) > (y) ? (x): (y)) #define MiN(x,y) ((x) < (y) ? (x): (y)) #define ABS(x) ( (x) < 0 ? -(x): (x) ) #define SGN(x) ( (x) > 0 ? 1 : (x) < 0 ? -1 : 0 ) #define REDLENG(x) ((((x)<0)?((x)+1):((x)-1))/2) #define INCLENG(x) (((x)<0)?(((x)*2)-1):(((x)*2)+1)) #define GETCOEF(x,y) x += *x;y = x[-1];x -= ABS(y);y=REDLENG(y) #define GETSTOP(x,y) y=x+(*x)-1;y -= ABS(*y)-1 #define StuffAdd(x,y) (((x)<0?-1:1)*(y)+((y)<0?-1:1)*(x)) #define EXCHN(t1,t2,n) { WORD a,i; for(i=0;inextchar[(stream)->isnextchar++]=c) #ifdef WITHRETURN #define AddLineFeed(s,n) { (s)[(n)++] = CARRIAGERETURN; (s)[(n)++] = LINEFEED; } #else #define AddLineFeed(s,n) { (s)[(n)++] = LINEFEED; } #endif #define TryRecover(x) Terminate(-1) #define UngetChar(c) { pushbackchar = c; } #define ParseNumber(x,s) {(x)=0;while(*(s)>='0'&&*(s)<='9')(x)=10*(x)+*(s)++ -'0';} #define ParseSign(sgn,s) {(sgn)=0;while(*(s)=='-'||*(s)=='+'){\ if ( *(s)++ == '-' ) sgn ^= 1;}} #define ParseSignedNumber(x,s) { int sgn; ParseSign(sgn,s)\ ParseNumber(x,s) if ( sgn ) x = -x; } /* (n) is necessary here, since the macro is sometimes passed dereferenced pointers for n */ #define NCOPY(s,t,n) { while ( (n)-- > 0 ) { *s++ = *t++; } } #define NCOPYI(s,t,n) { while ( (n)-- > 0 ) { *s++ = *t++; } } #define NCOPYB(s,t,n) { while ( (n)-- > 0 ) { *s++ = *t++; } } #define NCOPYI32(s,t,n) { while ( (n)-- > 0 ) { *s++ = *t++; } } #define WCOPY(s,t,n) { int nn=n; WORD *ss=(WORD *)s, *tt=(WORD *)t; while ( (nn)-- > 0 ) { *ss++ = *tt++; } } /* Use memmove not memcpy: we can't guarantee that s, t do not overlap */ /* Using memmove produces no measurable performance improvement or regression. */ /*#define NCOPY(s,t,n) { memmove(s,t,(n)*sizeof(*s)); s+=n; t+=n; n=0; } #define NCOPYI(s,t,n) { NCOPY(s,t,n); } #define NCOPYB(s,t,n) { NCOPY(s,t,n); } #define NCOPYI32(s,t,n) { NCOPY(s,t,n); } #define WCOPY(s,t,n) { int nn=n; WORD *ss=(WORD *)s, *tt=(WORD *)t; NCOPY(ss,tt,nn); }*/ #define NeedNumber(x,s,err) { int sgn = 1; \ while ( *s == ' ' || *s == '\t' || *s == '-' || *s == '+' ) { \ if ( *s == '-' ) {sgn = -sgn;} s++; } \ if ( chartype[*s] != 1 ) goto err; \ ParseNumber(x,s) \ if ( sgn < 0 ) {(x) = -(x);} while ( *s == ' ' || *s == '\t' ) s++;\ } #define SKIPBLANKS(s) { while ( *(s) == ' ' || *(s) == '\t' ) (s)++; } #define FLUSHCONSOLE if ( AP.InOutBuf > 0 ) CharOut(LINEFEED) #define SKIPBRA1(s) { int lev1=0; s++; while(*s) { if(*s=='['){lev1++;} \ else {if(*s==']'&&--lev1<0){break;}} s++;} } #define SKIPBRA2(s) { int lev2=0; s++; while(*s) { if(*s=='{'){lev2++;} \ else {if(*s=='}'&&--lev2<0){break;} \ else {if(*s=='['){SKIPBRA1(s)}}} s++;} } #define SKIPBRA3(s) { int lev3=0; s++; while(*s) { if(*s=='('){lev3++;} \ else {if(*s==')'&&--lev3<0){break;} \ else {if(*s=='{'){SKIPBRA2(s)} \ else {if(*s=='['){SKIPBRA1(s)}}}} s++;} } #define SKIPBRA4(s) { int lev4=0; s++; while(*s) { if(*s=='('){lev4++;} \ else {if(*s==')'&&--lev4<0){break;} \ else {if(*s=='['){SKIPBRA1(s)}}} s++;} } #define SKIPBRA5(s) { int lev5=0; s++; while(*s) { if(*s=='{'){lev5++;} \ else {if(*s=='}'&&--lev5<0){break;} \ else {if(*s=='('){SKIPBRA4(s)} \ else {if(*s=='['){SKIPBRA1(s)}}}} s++;} } /* #define CYCLE1(a,i) {WORD iX,jX; iX=*a; for(jX=1;jXPointer>=c->Top) \ {DoubleCbuffer(c-cbuf,c->Pointer,21);} \ *(c->Pointer)++ = wx; #define EXCHINOUT { FILEHANDLE *ffFi = AR.outfile; \ AR.outfile = AR.infile; AR.infile = ffFi; } #define BACKINOUT { FILEHANDLE *ffFi = AR.outfile; POSITION posi; \ AR.outfile = AR.infile; AR.infile = ffFi; \ SetEndScratch(AR.infile,&posi); } #define CopyArg(to,from) { if ( *from > 0 ) { int ica = *from; NCOPY(to,from,ica) } \ else if ( *from <= -FUNCTION ) *to++ = *from++; \ else { *to++ = *from++; *to++ = *from++; } } #if ARGHEAD > 2 #define FILLARG(w) { int i = ARGHEAD-2; while ( --i >= 0 ) *w++ = 0; } #define COPYARG(w,t) { int i = ARGHEAD-2; while ( --i >= 0 ) *w++ = *t++; } #define ZEROARG(w) { int i; for ( i = 2; i < ARGHEAD; i++ ) w[i] = 0; } #else #define FILLARG(w) #define COPYARG(w,t) #define ZEROARG(w) #endif #if FUNHEAD > 2 #define FILLFUN(w) { *w++ = 0; FILLFUN3(w) } #define COPYFUN(w,t) { *w++ = *t++; COPYFUN3(w,t) } #else #define FILLFUN(w) #define COPYFUN(w,t) #endif #if FUNHEAD > 3 #define FILLFUN3(w) { int ie = FUNHEAD-3; while ( --ie >= 0 ) *w++ = 0; } #define COPYFUN3(w,t) { int ie = FUNHEAD-3; while ( --ie >= 0 ) *w++ = *t++; } #else #define COPYFUN3(w,t) #define FILLFUN3(w) #endif #if SUBEXPSIZE > 5 #define FILLSUB(w) { int ie = SUBEXPSIZE-5; while ( --ie >= 0 ) *w++ = 0; } #define COPYSUB(w,ww) { int ie = SUBEXPSIZE-5; while ( --ie >= 0 ) *w++ = *ww++; } #else #define FILLSUB(w) #define COPYSUB(w,ww) #endif #if EXPRHEAD > 4 #define FILLEXPR(w) { int ie = EXPRHEAD-4; while ( --ie >= 0 ) *w++ = 0; } #else #define FILLEXPR(w) #endif #define NEXTARG(x) if(*x>0) x += *x; else if(*x <= -FUNCTION)x++; else x += 2; #define COPY1ARG(s1,t1) { int ica; if ( (ica=*t1) > 0 ) { NCOPY(s1,t1,ica) } \ else if(*t1<=-FUNCTION){*s1++=*t1++;} else{*s1++=*t1++;*s1++=*t1++;} } /** * Fills a buffer by zero in the range [begin,end). * * @param w The buffer. * @param begin The index for the beginning of the range. * @param end The index for the end of the range (exclusive). */ #define ZeroFillRange(w,begin,end) do { \ int tmp_i; \ for ( tmp_i = begin; tmp_i < end; tmp_i++ ) { (w)[tmp_i] = 0; } \ } while (0) #define TABLESIZE(a,b) (((WORD)sizeof(a))/((WORD)sizeof(b))) #define WORDDIF(x,y) (WORD)(x-y) #define wsizeof(a) ((WORD)sizeof(a)) #define VARNAME(type,num) (AC.varnames->namebuffer+type[num].name) #define DOLLARNAME(type,num) (AC.dollarnames->namebuffer+type[num].name) #define EXPRNAME(num) (AC.exprnames->namebuffer+Expressions[num].name) #define PREV(x) prevorder?prevorder:x #define Terminate(x) do { TerminateImpl(x, __FILE__, __LINE__, __FUNCTION__); } while(0) #define SETERROR(x) { Terminate(-1); return(-1); } /* use this macro to avoid the unused parameter warning */ #define DUMMYUSE(x) (void)(x); #ifdef _FILE_OFFSET_BITS #if _FILE_OFFSET_BITS==64 /*:[19mar2004 mt]*/ #define ADDPOS(pp,x) (pp).p1 = ((pp).p1+(off_t)(x)) #define SETBASELENGTH(ss,x) (ss).p1 = (off_t)(x) #define SETBASEPOSITION(pp,x) (pp).p1 = (off_t)(x) #define ISEQUALPOSINC(pp1,pp2,x) ( (pp1).p1 == ((pp2).p1+(off_t)(x)) ) #define ISGEPOSINC(pp1,pp2,x) ( (pp1).p1 >= ((pp2).p1+(off_t)(x)) ) #define DIVPOS(pp,n) ( (pp).p1/(off_t)(n) ) #define MULPOS(pp,n) (pp).p1 *= (off_t)(n) #else #define ADDPOS(pp,x) (pp).p1 = ((pp).p1+(x)) #define SETBASELENGTH(ss,x) (ss).p1 = (x) #define SETBASEPOSITION(pp,x) (pp).p1 = (x) #define ISEQUALPOSINC(pp1,pp2,x) ( (pp1).p1 == ((pp2).p1+(LONG)(x)) ) #define ISGEPOSINC(pp1,pp2,x) ( (pp1).p1 >= ((pp2).p1+(LONG)(x)) ) #define DIVPOS(pp,n) ( (pp).p1/(n) ) #define MULPOS(pp,n) (pp).p1 *= (n) #endif #else #define ADDPOS(pp,x) (pp).p1 = ((pp).p1+(LONG)(x)) #define SETBASELENGTH(ss,x) (ss).p1 = (LONG)(x) #define SETBASEPOSITION(pp,x) (pp).p1 = (LONG)(x) #define ISEQUALPOSINC(pp1,pp2,x) ( (pp1).p1 == ((pp2).p1+(LONG)(x)) ) #define ISGEPOSINC(pp1,pp2,x) ( (pp1).p1 >= ((pp2).p1+(LONG)(x)) ) #define DIVPOS(pp,n) ( (pp).p1/(LONG)(n) ) #define MULPOS(pp,n) (pp).p1 *= (LONG)(n) #endif #define DIFPOS(ss,pp1,pp2) (ss).p1 = ((pp1).p1-(pp2).p1) #define DIFBASE(pp1,pp2) ((pp1).p1-(pp2).p1) #define ADD2POS(pp1,pp2) (pp1).p1 += (pp2).p1 #define PUTZERO(pp) (pp).p1 = 0 #define BASEPOSITION(pp) ((pp).p1) #define SETSTARTPOS(pp) (pp).p1 = -2 #define NOTSTARTPOS(pp) ( (pp).p1 > -2 ) #define ISMINPOS(pp) ( (pp).p1 == -1 ) #define ISEQUALPOS(pp1,pp2) ( (pp1).p1 == (pp2).p1 ) #define ISNOTEQUALPOS(pp1,pp2) ( (pp1).p1 != (pp2).p1 ) #define ISLESSPOS(pp1,pp2) ( (pp1).p1 < (pp2).p1 ) #define ISGEPOS(pp1,pp2) ( (pp1).p1 >= (pp2).p1 ) #define ISNOTZEROPOS(pp) ( (pp).p1 != 0 ) #define ISZEROPOS(pp) ( (pp).p1 == 0 ) #define ISPOSPOS(pp) ( (pp).p1 > 0 ) #define ISNEGPOS(pp) ( (pp).p1 < 0 ) extern void TELLFILE(int,POSITION *); #define TOLONG(x) ((LONG)(x)) #define Add2Com(x) { WORD cod[2]; cod[0] = x; cod[1] = 2; AddNtoL(2,cod); } #define Add3Com(x1,x2) { WORD cod[3]; cod[0] = x1; cod[1] = 3; cod[2] = x2; AddNtoL(3,cod); } #define Add4Com(x1,x2,x3) { WORD cod[4]; cod[0] = x1; cod[1] = 4; \ cod[2] = x2; cod[3] = x3; AddNtoL(4,cod); } #define Add5Com(x1,x2,x3,x4) { WORD cod[5]; cod[0] = x1; cod[1] = 5; \ cod[2] = x2; cod[3] = x3; cod[4] = x4; AddNtoL(5,cod); } /* The temporary variable ppp is to avoid a compiler warning about strict aliassing */ #define WantAddPointers(x) while((AT.pWorkPointer+(x))>AR.pWorkSize){WORD ***ppp=&AT.pWorkSpace;\ ExpandBuffer((void **)ppp,&AR.pWorkSize,(int)(sizeof(WORD *)));} #define WantAddLongs(x) while((AT.lWorkPointer+(x))>AR.lWorkSize){LONG **ppp=&AT.lWorkSpace;\ ExpandBuffer((void **)ppp,&AR.lWorkSize,sizeof(LONG));} #define WantAddPositions(x) while((AT.posWorkPointer+(x))>AR.posWorkSize){POSITION **ppp=&AT.posWorkSpace;\ ExpandBuffer((void **)ppp,&AR.posWorkSize,sizeof(POSITION));} /* inline in form3.h (or config.h). */ #define FORM_INLINE inline /* Macro's for memory management. This can be done by routines, but that would be slower. Inline routines could do this, but we don't want to leave this to the friendliness of the compiler(s). The routines can be found in the file tools.c */ #define MEMORYMACROS #ifdef MEMORYMACROS #define TermMalloc(x) ( (AT.TermMemTop <= 0 ) ? TermMallocAddMemory(BHEAD0), AT.TermMemHeap[--AT.TermMemTop]: AT.TermMemHeap[--AT.TermMemTop] ) #define NumberMalloc(x) ( (AT.NumberMemTop <= 0 ) ? NumberMallocAddMemory(BHEAD0), AT.NumberMemHeap[--AT.NumberMemTop]: AT.NumberMemHeap[--AT.NumberMemTop] ) #define CacheNumberMalloc(x) ( (AT.CacheNumberMemTop <= 0 ) ? CacheNumberMallocAddMemory(BHEAD0), AT.CacheNumberMemHeap[--AT.CacheNumberMemTop]: AT.CacheNumberMemHeap[--AT.CacheNumberMemTop] ) #define TermFree(TermMem,x) AT.TermMemHeap[AT.TermMemTop++] = (WORD *)(TermMem) #define NumberFree(NumberMem,x) AT.NumberMemHeap[AT.NumberMemTop++] = (UWORD *)(NumberMem) #define CacheNumberFree(NumberMem,x) AT.CacheNumberMemHeap[AT.CacheNumberMemTop++] = (UWORD *)(NumberMem) #else #define TermMalloc(x) TermMalloc2(BHEAD (char *)(x)) #define NumberMalloc(x) NumberMalloc2(BHEAD (char *)(x)) #define CacheNumberMalloc(x) CacheNumberMalloc2(BHEAD (char *)(x)) #define TermFree(x,y) TermFree2(BHEAD (WORD *)(x),(char *)(y)) #define NumberFree(x,y) NumberFree2(BHEAD (UWORD *)(x),(char *)(y)) #define CacheNumberFree(x,y) CacheNumberFree2(BHEAD (UWORD *)(x),(char *)(y)) #endif /* * Macros for checking nesting levels in the compiler, used as follows: * * AC.IfSumCheck[AC.IfLevel] = NestingChecksum(); * AC.IfLevel++; * * AC.IfLevel--; * if ( AC.IfSumCheck[AC.IfLevel] != NestingChecksum() ) { * MesNesting(); * } * * Note that NestingChecksum() also contains AC.IfLevel and so in this case * using increment/decrement operators on it in the left-hand side may be * confusing. */ #define NestingChecksum() (AC.IfLevel + AC.RepLevel + AC.arglevel + AC.insidelevel + AC.termlevel + AC.inexprlevel + AC.dolooplevel +AC.SwitchLevel) #define MesNesting() MesPrint("&Illegal nesting of if, repeat, argument, inside, term, inexpression and do") #define MarkPolyRatFunDirty(T) {if(*T&&AR.PolyFunType==2){WORD *TP,*TT;TT=T+*T;TT-=ABS(TT[-1]);\ TP=T+1;while(TP= AP.MaxPreAssignLevel ) { int i; \ LONG *ap = (LONG *)Malloc1(2*AP.MaxPreAssignLevel*sizeof(LONG *),"PreAssignStack"); \ for ( i = 0; i < AP.MaxPreAssignLevel; i++ ) ap[i] = AP.PreAssignStack[i]; \ M_free(AP.PreAssignStack,"PreAssignStack"); \ AP.MaxPreAssignLevel *= 2; AP.PreAssignStack = ap; \ } \ *AT.WorkPointer++ = AP.PreContinuation; AP.PreContinuation = 0; \ AP.PreAssignStack[AP.PreAssignLevel] = AC.iPointer - AC.iBuffer; } #define POPPREASSIGNLEVEL if ( AP.PreAssignLevel > 0 ) { GETIDENTITY \ AC.iPointer = AC.iBuffer + AP.PreAssignStack[AP.PreAssignLevel--]; \ AP.PreContinuation = *--AT.WorkPointer; \ *AC.iPointer = 0; } #ifdef WITHFLOAT /* The following macro's are needed to avoid problems with the compilers and gmp.h. For the C++ files we need the Form include files to be inside and extern C {} environment, but then the structs.h needs gmp.h to recognise the mpf_t datatype. This causes no end of problems. Hence we collect the sensitive objects as (void *) and cast them to something usable with the macro's below. This way the gmp.h file needs to be included only in a very limited number of .c files. */ #define mpftab1 ((mpf_t *)(AT.mpf_tab1)) #define mpftab2 ((mpf_t *)(AT.mpf_tab2)) #define mpfaux_ ((mpf_t *)(AT.aux_)) #define aux1 (((mpf_t *)(AT.aux_))[0]) #define aux2 (((mpf_t *)(AT.aux_))[1]) #define aux3 (((mpf_t *)(AT.aux_))[2]) #define aux4 (((mpf_t *)(AT.aux_))[3]) #define aux5 (((mpf_t *)(AT.aux_))[4]) #define auxjm (((mpf_t *)(AT.aux_))[5]) #define auxjjm (((mpf_t *)(AT.aux_))[6]) #define auxsum (((mpf_t *)(AT.aux_))[7]) #define mpfdelta1 (((mpf_t *)(AS.delta_1))[0]) #endif /* MesPrint("P-level popped to %d with %d",AP.PreAssignLevel,(WORD)(AC.iPointer - AC.iBuffer)); #] Macro's : #[ Inline functions : */ /* * The following three functions give the unsigned absolute value of a signed * integer even for the most negative integer. This is beyond the scope of * the standard abs() function and its family, whose return-values are signed. * In short, we should not use the unary minus operator with signed numbers * unless we are sure that there are no integer overflows. Instead, we rely on * two well-defined operations: (i) signed-to-unsigned conversion and * (ii) unary minus of unsigned operands. * * See also: * https://stackoverflow.com/a/4536188 (Unary minus and signed-to-unsigned conversion) * https://stackoverflow.com/q/8026694 (C: unary minus operator behavior with unsigned operands) * https://stackoverflow.com/q/1610947 (Why does stdlib.h's abs() family of functions return a signed value?) * https://blog.regehr.org/archives/226 (A Guide to Undefined Behavior in C and C++, Part 2) */ static inline unsigned int IntAbs(int x) { if ( x >= 0 ) return (unsigned int)x; return(-((unsigned int)x)); } static inline UWORD WordAbs(WORD x) { if ( x >= 0 ) return (UWORD)x; return(-((UWORD)x)); } static inline ULONG LongAbs(LONG x) { if ( x >= 0 ) return (ULONG)x; return(-((ULONG)x)); } /* * The following functions provide portable unsigned-to-signed conversions * (to avoid the implementation-defined behaviour), which is expected to be * optimized to a no-op. * * See also: * https://stackoverflow.com/a/13208789 (Efficient unsigned-to-signed cast avoiding implementation-defined behavior) */ static inline int UnsignedToInt(unsigned int x) { extern void TerminateImpl(int, const char*, int, const char*) NORETURN; if ( x <= INT_MAX ) return((int)x); if ( x >= (unsigned int)INT_MIN ) return((int)(x - (unsigned int)INT_MIN) + INT_MIN); Terminate(1); return(0); } static inline WORD UWordToWord(UWORD x) { extern void TerminateImpl(int, const char*, int, const char*) NORETURN; if ( x <= WORD_MAX_VALUE ) return((WORD)x); if ( x >= (UWORD)WORD_MIN_VALUE ) return((WORD)(x - (UWORD)WORD_MIN_VALUE) + WORD_MIN_VALUE); Terminate(1); return(0); } static inline LONG ULongToLong(ULONG x) { extern void TerminateImpl(int, const char*, int, const char*) NORETURN; if ( x <= LONG_MAX_VALUE ) return((LONG)x); if ( x >= (ULONG)LONG_MIN_VALUE ) return((LONG)(x - (ULONG)LONG_MIN_VALUE) + LONG_MIN_VALUE); Terminate(1); return(0); } /* #] Inline functions : #[ Thread objects : */ /** * NOTE: We have replaced LOCK(ErrorMessageLock) and UNLOCK(ErrorMessageLock) * by MLOCK(ErrorMessageLock) and MUNLOCK(ErrorMessageLock). They are used * for the synchronised output in ParFORM. * (TU 28 May 2011) */ #ifdef WITHPTHREADS #define EXTERNLOCK(x) extern pthread_mutex_t x; #define INILOCK(x) pthread_mutex_t x = PTHREAD_MUTEX_INITIALIZER; #define EXTERNRWLOCK(x) extern pthread_rwlock_t x; #define INIRWLOCK(x) pthread_rwlock_t x = PTHREAD_RWLOCK_INITIALIZER; #define INIRECLOCK(x) do { pthread_mutexattr_t attrib; \ pthread_mutexattr_init(&attrib); \ pthread_mutexattr_settype(&attrib, PTHREAD_MUTEX_RECURSIVE); \ pthread_mutex_init(&(x), &attrib); \ pthread_mutexattr_destroy(&attrib); \ } while(0) #ifdef DEBUGGINGLOCKS #include #define LOCK(x) while ( pthread_mutex_trylock(&(x)) == EBUSY ) {} #define RWLOCKR(x) while ( pthread_rwlock_tryrdlock(&(x)) == EBUSY ) {} #define RWLOCKW(x) while ( pthread_rwlock_trywrlock(&(x)) == EBUSY ) {} #else #define LOCK(x) pthread_mutex_lock(&(x)) #define RWLOCKR(x) pthread_rwlock_rdlock(&(x)) #define RWLOCKW(x) pthread_rwlock_wrlock(&(x)) #endif #define UNLOCK(x) pthread_mutex_unlock(&(x)) #define UNRWLOCK(x) pthread_rwlock_unlock(&(x)) #define MLOCK(x) LOCK(x) #define MUNLOCK(x) UNLOCK(x) #define GETBIDENTITY #define GETIDENTITY int identity = WhoAmI(); ALLPRIVATES *B = AB[identity]; #else #define EXTERNLOCK(x) #define INILOCK(x) #define LOCK(x) #define UNLOCK(x) #define EXTERNRWLOCK(x) #define INIRWLOCK(x) #define RWLOCKR(x) #define RWLOCKW(x) #define UNRWLOCK(x) #ifdef WITHMPI #define MLOCK(x) do { if ( PF.me != MASTER ) PF_MLock(); } while (0) #define MUNLOCK(x) do { if ( PF.me != MASTER ) PF_MUnlock(); } while (0) #else #define MLOCK(x) #define MUNLOCK(x) #endif #define GETIDENTITY #define GETBIDENTITY #endif /* #] Thread objects : #[ Declarations : */ #ifdef TERMMALLOCDEBUG extern WORD **DebugHeap1, **DebugHeap2; #endif /** * All functions (well, nearly all) are declared here. */ extern void StartVariables(void); extern void setSignalHandlers(void); extern UBYTE *CodeToLine(WORD,UBYTE *); extern UBYTE *AddArrayIndex(WORD ,UBYTE *); extern INDEXENTRY *FindInIndex(WORD,FILEDATA *,WORD,WORD); extern INDEXENTRY *NextFileIndex(POSITION *); extern WORD *PasteTerm(PHEAD WORD,WORD *,WORD *,WORD,WORD); extern UBYTE *StrCopy(UBYTE *,UBYTE *); extern UBYTE *WrtPower(UBYTE *,WORD); extern int AccumGCD(PHEAD UWORD *,WORD *,UWORD *,WORD); extern void AddArgs(PHEAD WORD *,WORD *,WORD *); extern int AddCoef(PHEAD WORD **,WORD **); extern int AddLong(UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern int AddPLon(UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern int AddPoly(PHEAD WORD **,WORD **); extern int AddRat(PHEAD UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern void AddToLine(UBYTE *); extern int AddWild(PHEAD WORD,WORD,WORD); extern int BigLong(UWORD *,WORD,UWORD *,WORD); extern int BinomGen(PHEAD WORD *,WORD,WORD **,WORD,WORD,WORD,WORD,WORD,UWORD *,WORD); extern int CheckWild(PHEAD WORD,WORD,WORD,WORD *); extern int Chisholm(PHEAD WORD *,WORD); extern int CleanExpr(WORD); extern void CleanUp(WORD); extern void ClearWild(PHEAD0); extern int CompareFunctions(WORD *,WORD *); extern int Commute(WORD *,WORD *); extern WORD DetCommu(WORD *); extern WORD DoesCommu(WORD *); extern int CompArg(WORD *,WORD *); extern WORD CompCoef(WORD *, WORD *); extern int CompGroup(PHEAD WORD,WORD **,WORD *,WORD *,WORD); extern WORD Compare1(PHEAD WORD *,WORD *,WORD); extern WORD CountDo(WORD *,WORD *); extern WORD CountFun(WORD *,WORD *); extern WORD DimensionSubterm(WORD *); extern WORD DimensionTerm(WORD *); extern WORD DimensionExpression(PHEAD WORD *); extern int Deferred(PHEAD WORD *,WORD); extern int DeleteStore(WORD); extern WORD DetCurDum(PHEAD WORD *); extern void DetVars(WORD *,WORD); extern int Distribute(DISTRIBUTE *,WORD); extern int DivLong(UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *,UWORD *,WORD *); extern int DivRat(PHEAD UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern int Divvy(PHEAD UWORD *,WORD *,UWORD *,WORD); extern int DoDelta(WORD *); extern int DoDelta3(PHEAD WORD *,WORD); extern int TestPartitions(WORD *, PARTI *); extern int DoPartitions(PHEAD WORD *,WORD); extern int CoCanonicalize(UBYTE *); extern int DoCanonicalize(PHEAD WORD *, WORD *); extern int GenDiagrams(PHEAD WORD *,WORD); extern int DoTopologyCanonicalize(PHEAD WORD *,WORD,WORD,WORD *); extern int DoShattering(PHEAD WORD *,WORD *,WORD *,WORD); extern int DoTableExpansion(WORD *,WORD); extern int DoDistrib(PHEAD WORD *,WORD); extern int DoShuffle(WORD *,WORD,WORD,WORD); extern int DoPermutations(PHEAD WORD *,WORD); extern int Shuffle(WORD *, WORD *, WORD *); extern int FinishShuffle(WORD *); extern int DoStuffle(WORD *,WORD,WORD,WORD); extern int Stuffle(WORD *, WORD *, WORD *); extern int FinishStuffle(WORD *); extern WORD *StuffRootAdd(WORD *, WORD *, WORD *); extern int TestUse(WORD *,WORD); extern DBASE *FindTB(UBYTE *); extern int CheckTableDeclarations(DBASE *); extern void Apply(WORD *,WORD); extern int ApplyExec(WORD *,int,WORD); extern void ApplyReset(WORD); extern void TableReset(void); extern void ReWorkT(WORD *,WORD *,WORD); extern WORD GetIfDollarNum(WORD *, WORD *); extern int FindVar(WORD *,WORD *); extern int DoIfStatement(PHEAD WORD *,WORD *); extern int DoOnePow(PHEAD WORD *,WORD,WORD,WORD *,WORD *,WORD,WORD *); extern void DoRevert(WORD *,WORD *); extern int DoSumF1(PHEAD WORD *,WORD *,WORD,WORD); extern int DoSumF2(PHEAD WORD *,WORD *,WORD,WORD); extern int DoTheta(PHEAD WORD *); extern LONG EndSort(PHEAD WORD *,int); extern int EntVar(WORD,UBYTE *,WORD,WORD,WORD,WORD); extern int EpfCon(PHEAD WORD *,WORD *,WORD,WORD); extern int EpfFind(PHEAD WORD *,WORD *); extern WORD EpfGen(WORD,WORD *,WORD *,WORD *,WORD); extern int EqualArg(WORD *,WORD,WORD); extern int Factorial(PHEAD WORD,UWORD *,WORD *); extern int Bernoulli(WORD,UWORD *,WORD *); extern int FactorIn(PHEAD WORD *,WORD); extern int FactorInExpr(PHEAD WORD *,WORD); extern int FindAll(PHEAD WORD *,WORD *,WORD,WORD *); extern WORD FindMulti(PHEAD WORD *,WORD *); extern int FindOnce(PHEAD WORD *,WORD *); extern int FindOnly(PHEAD WORD *,WORD *); extern int FindRest(PHEAD WORD *,WORD *); extern void FindSpecial(WORD *); extern WORD FindrNumber(WORD,VARRENUM *); extern void FiniLine(void); extern int FiniTerm(PHEAD WORD *,WORD *,WORD *,WORD,WORD); extern int FlushOut(POSITION *,FILEHANDLE *,int); extern void FunLevel(PHEAD WORD *); extern void AdjustRenumScratch(PHEAD0); extern void GarbHand(void); extern int GcdLong(PHEAD UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern int LcmLong(PHEAD UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern void GCD(UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern ULONG GCD2(ULONG,ULONG); extern int Generator(PHEAD WORD *,WORD); extern int GetBinom(UWORD *,WORD *,WORD,WORD); extern WORD GetFromStore(WORD *,POSITION *,RENUMBER,WORD *,WORD); extern int GetLong(UBYTE *,UWORD *,WORD *); extern WORD GetMoreTerms(WORD *); extern int GetMoreFromMem(WORD *,WORD **); extern WORD GetOneTerm(PHEAD WORD *,FILEHANDLE *,POSITION *,int); extern RENUMBER GetTable(WORD,POSITION *,WORD); extern WORD GetTerm(PHEAD WORD *); extern int Glue(PHEAD WORD *,WORD *,WORD *,WORD); extern int InFunction(PHEAD WORD *,WORD *); extern void IniLine(WORD); extern void IniVars(void); extern int InsertTerm(PHEAD WORD *,WORD,WORD,WORD *,WORD *,WORD); extern void LongToLine(UWORD *,WORD); extern int MakeDirty(WORD *,WORD *,WORD); extern void MarkDirty(WORD *,WORD); extern void PolyFunDirty(PHEAD WORD *); extern void PolyFunClean(PHEAD WORD *); extern int MakeModTable(void); extern int MatchE(PHEAD WORD *,WORD *,WORD *,WORD); extern int MatchCy(PHEAD WORD *,WORD *,WORD *,WORD); extern int FunMatchCy(PHEAD WORD *,WORD *,WORD *,WORD); extern int FunMatchSy(PHEAD WORD *,WORD *,WORD *,WORD); extern int MatchArgument(PHEAD WORD *,WORD *); extern int MatchFunction(PHEAD WORD *,WORD *,WORD *); extern int MergePatches(WORD); extern int MesCerr(char *, UBYTE *); extern int MesComp(char *, UBYTE *, UBYTE *); extern int Modulus(WORD *); extern void MoveDummies(PHEAD WORD *,WORD); extern int MulLong(UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern int MulRat(PHEAD UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern int Mully(PHEAD UWORD *,WORD *,UWORD *,WORD); extern int MultDo(PHEAD WORD *,WORD *); extern int NewSort(PHEAD0); extern int ExtraSymbol(WORD,WORD,WORD,WORD *,WORD *); extern int Normalize(PHEAD WORD *); extern int BracketNormalize(PHEAD WORD *); extern void DropCoefficient(PHEAD WORD *); extern void DropSymbols(PHEAD WORD *); extern int PutInside(PHEAD WORD *, WORD *); extern void OpenTemp(void); extern void Pack(UWORD *,WORD *,UWORD *,WORD ); extern LONG PasteFile(PHEAD WORD,WORD *,POSITION *,WORD **,RENUMBER,WORD *,WORD); extern int Permute(PERM *,WORD); extern int PermuteP(PERMP *,WORD); extern int PolyFunMul(PHEAD WORD *); extern int PopVariables(void); extern int PrepPoly(PHEAD WORD *,WORD); extern int Processor(void); extern int Product(UWORD *,WORD *,WORD); extern void PrtLong(UWORD *,WORD,UBYTE *); extern void PrtTerms(void); extern void PrintDeprecation(const char *,const char *); extern void PrintFeatureList(void); extern void PrintRunningTime(void); extern LONG GetRunningTime(void); extern int PutBracket(PHEAD WORD *); extern LONG PutIn(FILEHANDLE *,POSITION *,WORD *,WORD **,int); extern int PutInStore(INDEXENTRY *,WORD); extern WORD PutOut(PHEAD WORD *,POSITION *,FILEHANDLE *,WORD); extern UWORD Quotient(UWORD *,WORD *,WORD); extern int RaisPow(PHEAD UWORD *,WORD *,UWORD); extern void RaisPowCached (PHEAD WORD, WORD, UWORD **, WORD *); extern WORD RaisPowMod (WORD, WORD, WORD); extern int NormalModulus(UWORD *,WORD *); extern int MakeInverses(void); extern int GetModInverses(WORD,WORD,WORD *,WORD *); extern int GetLongModInverses(PHEAD UWORD *, WORD, UWORD *, WORD, UWORD *, WORD *, UWORD *, WORD *); extern void RatToLine(UWORD *,WORD); extern int RatioFind(PHEAD WORD *,WORD *); extern int RatioGen(PHEAD WORD *,WORD *,WORD,WORD); extern WORD ReNumber(PHEAD WORD *); extern WORD ReadSnum(UBYTE **); extern WORD Remain10(UWORD *,WORD *); extern WORD Remain4(UWORD *,WORD *); extern int ResetScratch(void); extern int ResolveSet(PHEAD WORD *,WORD *,WORD *); extern int RevertScratch(void); extern int ScanFunctions(PHEAD WORD *,WORD *,WORD); extern void SeekScratch(FILEHANDLE *,POSITION *); extern void SetEndScratch(FILEHANDLE *,POSITION *); extern void SetEndHScratch(FILEHANDLE *,POSITION *); extern int SetFileIndex(void); extern int Sflush(FILEHANDLE *); extern int Simplify(PHEAD UWORD *,WORD *,UWORD *,WORD *); extern int SortWild(WORD *,WORD); extern FILE *LocateBase(char **,char **,char *); extern LONG SplitMerge(PHEAD WORD **,LONG); extern int StoreTerm(PHEAD WORD *); extern void SubPLon(UWORD *,WORD,UWORD *,WORD,UWORD *,WORD *); extern void Substitute(PHEAD WORD *,WORD *,WORD); extern int SymFind(PHEAD WORD *,WORD *); extern int SymGen(PHEAD WORD *,WORD *,WORD,WORD); extern WORD Symmetrize(PHEAD WORD *,WORD *,WORD,WORD,WORD); extern int FullSymmetrize(PHEAD WORD *,int); extern int TakeModulus(UWORD *,WORD *,UWORD *,WORD,WORD); extern int TakeNormalModulus(UWORD *,WORD *,UWORD *,WORD,WORD); extern void TalToLine(UWORD); extern int TenVec(PHEAD WORD *,WORD *,WORD,WORD); extern int TenVecFind(PHEAD WORD *,WORD *); extern int TermRenumber(WORD *,RENUMBER,WORD); extern void TestDrop(void); extern void PutInVflags(WORD); extern int TestMatch(PHEAD WORD *,WORD *); extern WORD TestSub(PHEAD WORD *,WORD); extern LONG TimeCPU(WORD); extern LONG TimeChildren(WORD); extern LONG TimeWallClock(WORD); extern LONG Timer(int); extern int GetTimerInfo(LONG **,LONG **); extern void WriteTimerInfo(LONG *,LONG *); extern LONG GetWorkerTimes(void); extern int ToStorage(EXPRESSIONS,POSITION *); extern void TokenToLine(UBYTE *); extern int Trace4(PHEAD WORD *,WORD *,WORD,WORD); extern int Trace4Gen(PHEAD TRACES *,WORD); extern int Trace4no(WORD,WORD *,TRACES *); extern int TraceFind(PHEAD WORD *,WORD *); extern int TraceN(PHEAD WORD *,WORD *,WORD,WORD); extern int TraceNgen(PHEAD TRACES *,WORD); extern WORD TraceNno(WORD,WORD *,TRACES *); extern int Traces(PHEAD WORD *,WORD *,WORD,WORD); extern WORD Trick(WORD *,TRACES *); extern int TryDo(PHEAD WORD *,WORD *,WORD); extern void UnPack(UWORD *,WORD,WORD *,WORD *); extern int VarStore(UBYTE *,WORD,WORD,WORD); extern WORD WildFill(PHEAD WORD *,WORD *,WORD *); extern int WriteAll(void); extern int WriteOne(UBYTE *,int,int,WORD); extern void WriteArgument(WORD *); extern int WriteExpression(WORD *,LONG); extern int WriteInnerTerm(WORD *,WORD); extern void WriteLists(void); extern void WriteSetup(void); extern void WriteStats(POSITION *,WORD,WORD); extern int WriteSubTerm(WORD *,WORD); extern int WriteTerm(WORD *,WORD *,WORD,WORD,WORD); extern int execarg(PHEAD WORD *,WORD); extern int execterm(PHEAD WORD *,WORD); extern void SpecialCleanup(PHEAD0); extern void SetMods(void); extern void UnSetMods(void); /*---------------------------------------------------------------------*/ extern int DoExecute(WORD,WORD); extern void SetScratch(FILEHANDLE *,POSITION *); extern void Warning(char *); extern void HighWarning(char *); extern int SpareTable(TABLES); extern UBYTE *strDup1(UBYTE *,char *); extern void *Malloc1(LONG,const char *); extern int DoTail(int,UBYTE **); extern int OpenInput(void); extern int PutPreVar(UBYTE *,UBYTE *,UBYTE *,int); extern void Error0(char *); extern void Error1(char *,UBYTE *); extern void Error2(char *,char *,UBYTE *); extern UBYTE ReadFromStream(STREAM *); extern UBYTE GetFromStream(STREAM *); extern UBYTE LookInStream(STREAM *); extern STREAM *OpenStream(UBYTE *,int,int,int); extern int LocateFile(UBYTE **,int); extern STREAM *CloseStream(STREAM *); extern void PositionStream(STREAM *,LONG); extern int ReverseStatements(STREAM *); extern int ProcessOption(UBYTE *,UBYTE *,int); extern int DoSetups(void); extern void TerminateImpl(int, const char *,int, const char *) NORETURN; extern NAMENODE *GetNode(NAMETREE *,UBYTE *); extern int AddName(NAMETREE *,UBYTE *,WORD,WORD,int *); extern int GetName(NAMETREE *,UBYTE *,WORD *,int); extern UBYTE *GetFunction(UBYTE *,WORD *); extern UBYTE *GetNumber(UBYTE *,WORD *); extern int GetLastExprName(UBYTE *,WORD *); extern int GetAutoName(UBYTE *,WORD *); extern int GetVar(UBYTE *,WORD *,WORD *,int,int); extern int MakeDubious(NAMETREE *,UBYTE *,WORD *); extern int GetOName(NAMETREE *,UBYTE *,WORD *,int); extern void DumpTree(NAMETREE *); extern void DumpNode(NAMETREE *,WORD,WORD); extern void LinkTree(NAMETREE *,WORD,WORD); extern void CopyTree(NAMETREE *,NAMETREE *,WORD,WORD); extern int CompactifyTree(NAMETREE *,WORD); extern NAMETREE *MakeNameTree(void); extern void FreeNameTree(NAMETREE *); extern int AddExpression(UBYTE *,int,int); extern int AddSymbol(UBYTE *,int,int,int,int); extern int AddDollar(UBYTE *,WORD,WORD *,LONG); extern int ReplaceDollar(WORD,WORD,WORD *,LONG); extern int DollarRaiseLow(UBYTE *,LONG); extern int AddVector(UBYTE *,int,int); extern int AddDubious(UBYTE *); extern int AddIndex(UBYTE *,int,int); extern UBYTE *DoDimension(UBYTE *,int *,int *); extern int AddFunction(UBYTE *,int,int,int,int,int,int,int); extern int CoCommuteInSet(UBYTE *); extern int CoFunction(UBYTE *,int,int); extern int TestName(UBYTE *); extern int AddSet(UBYTE *,WORD); extern int DoElements(UBYTE *,SETS,UBYTE *); extern int DoTempSet(UBYTE *,UBYTE *); extern int NameConflict(int,UBYTE *); extern int OpenFile(char *); extern int OpenAddFile(char *); extern int ReOpenFile(char *); extern int CreateFile(char *); extern int CreateLogFile(char *); extern void CloseFile(int); extern int CopyFile(char *, char *); extern int CreateHandle(void); extern LONG ReadFile(int,UBYTE *,LONG); extern LONG ReadPosFile(PHEAD FILEHANDLE *,UBYTE *,LONG,POSITION *); extern LONG WriteFileToFile(int,UBYTE *,LONG); extern void SeekFile(int,POSITION *,int); extern LONG TellFile(int); extern void FlushFile(int); extern int GetPosFile(int,fpos_t *); extern int SetPosFile(int,fpos_t *); extern void SynchFile(int); extern void TruncateFile(int); extern int GetChannel(char *,int); extern int GetAppendChannel(char *); extern int CloseChannel(char *); extern void inictable(void); extern KEYWORD *findcommand(UBYTE *); extern int inicbufs(void); extern void StartFiles(void); extern UBYTE *MakeDate(void); extern void PreProcessor(void); extern void *FromList(LIST *); extern void *From0List(LIST *); extern void *FromVarList(LIST *); extern int DoubleList(void ***,int *,int,char *); extern int DoubleLList(void ***,LONG *,int,char *); extern void DoubleBuffer(void **,void **,int,char *); extern void ExpandBuffer(void **,LONG *,int); extern LONG iexp(LONG,int); extern int IsLikeVector(WORD *); extern int AreArgsEqual(WORD *,WORD *); extern int CompareArgs(WORD *,WORD *); extern UBYTE *SkipField(UBYTE *,int); extern int StrCmp(UBYTE *,UBYTE *); extern int StrICmp(UBYTE *,UBYTE *); extern int StrHICmp(UBYTE *,UBYTE *); extern int StrICont(UBYTE *,UBYTE *); extern int CmpArray(WORD *,WORD *,WORD); extern int ConWord(UBYTE *,UBYTE *); extern int StrLen(UBYTE *); extern UBYTE *GetPreVar(UBYTE *,int); extern void ToGeneral(WORD *,WORD *,WORD); extern WORD ToPolyFunGeneral(PHEAD WORD *); extern int ToFast(WORD *,WORD *); extern SETUPPARAMETERS *GetSetupPar(UBYTE *); extern int RecalcSetups(void); extern int AllocSetups(void); extern SORTING *AllocSort(LONG,LONG,LONG,LONG,int,int,LONG,int); extern void AllocSortFileName(SORTING *); extern UBYTE *LoadInputFile(UBYTE *,int); extern UBYTE GetInput(void); extern void ClearPushback(void); extern UBYTE GetChar(int); extern void CharOut(UBYTE); extern void UnsetAllowDelay(void); extern void PopPreVars(int); extern void IniModule(int); extern void IniSpecialModule(int); extern int ModuleInstruction(int *,int *); extern int PreProInstruction(void); extern int LoadInstruction(int); extern int LoadStatement(int); extern KEYWORD *FindKeyWord(UBYTE *,KEYWORD *,int); extern KEYWORD *FindInKeyWord(UBYTE *,KEYWORD *,int); extern int DoDefine(UBYTE *); extern int DoRedefine(UBYTE *); extern int TheDefine(UBYTE *,int); extern int TheUndefine(UBYTE *); extern int ClearMacro(UBYTE *); extern int DoUndefine(UBYTE *); extern int DoInclude(UBYTE *); extern int DoReverseInclude(UBYTE *); extern int Include(UBYTE *,int); /*[14apr2004 mt]:*/ extern int DoExternal(UBYTE *); extern int DoToExternal(UBYTE *); extern int DoFromExternal(UBYTE *); extern int DoPrompt(UBYTE *); extern int DoSetExternal(UBYTE *); /*[10may2006 mt]:*/ extern int DoSetExternalAttr(UBYTE *); /*:[10may2006 mt]*/ extern int DoRmExternal(UBYTE *); /*:[14apr2004 mt]*/ extern int DoFactDollar(UBYTE *); extern WORD GetDollarNumber(UBYTE **,DOLLARS); extern int DoSetRandom(UBYTE *); extern int DoOptimize(UBYTE *); extern int DoClearOptimize(UBYTE *); extern int DoSkipExtraSymbols(UBYTE *); extern int DoTimeOutAfter(UBYTE *); extern int DoMessage(UBYTE *); extern int DoPreOut(UBYTE *); extern int DoPreAppend(UBYTE *); extern int DoPreCreate(UBYTE *); extern int DoPreAssign(UBYTE *); extern int DoPreBreak(UBYTE *); extern int DoPreDefault(UBYTE *); extern int DoPreSwitch(UBYTE *); extern int DoPreEndSwitch(UBYTE *); extern int DoPreCase(UBYTE *); extern int DoPreShow(UBYTE *); extern int DoPreExchange(UBYTE *); extern int DoSystem(UBYTE *); extern int DoPipe(UBYTE *); extern void StartPrepro(void); extern int DoIfdef(UBYTE *,int); extern int DoIfydef(UBYTE *); extern int DoIfndef(UBYTE *); extern int DoElse(UBYTE *); extern int DoElseif(UBYTE *); extern int DoEndif(UBYTE *); extern int DoTerminate(UBYTE *); extern int DoIf(UBYTE *); extern int DoCall(UBYTE *); extern int DoDebug(UBYTE *); extern int DoContinueDo(UBYTE *); extern int DoDo(UBYTE *); extern int DoBreakDo(UBYTE *); extern int DoEnddo(UBYTE *); extern int DoEndprocedure(UBYTE *); extern int DoInside(UBYTE *); extern int DoEndInside(UBYTE *); extern int DoProcedure(UBYTE *); extern int DoPrePrintTimes(UBYTE *); extern int DoPreWrite(UBYTE *); extern int DoPreClose(UBYTE *); extern int DoPreRemove(UBYTE *); extern int DoPreSortReallocate(UBYTE *); extern int DoCommentChar(UBYTE *); extern int DoPrcExtension(UBYTE *); extern int DoPreReset(UBYTE *); extern void WriteString(int,UBYTE *,int); extern void WriteUnfinString(int,UBYTE *,int); extern UBYTE *AddToString(UBYTE *,UBYTE *,int); extern UBYTE *PreCalc(void); extern UBYTE *PreEval(UBYTE *,LONG *); extern void NumToStr(UBYTE *,LONG); extern int PreCmp(int,int,UBYTE *,int,int,UBYTE *,int); extern int PreEq(int,int,UBYTE *,int,int,UBYTE *,int); extern UBYTE *pParseObject(UBYTE *,int *,LONG *); extern UBYTE *PreIfEval(UBYTE *,int *); extern int EvalPreIf(UBYTE *); extern int PreLoad(PRELOAD *,UBYTE *,UBYTE *,int,char *); extern int PreSkip(UBYTE *,UBYTE *,int); extern UBYTE *EndOfToken(UBYTE *); extern void SetSpecialMode(int,int); extern void MakeGlobal(void); extern int ExecModule(int); extern int ExecStore(void); extern void FullCleanUp(void); extern int DoExecStatement(void); extern int DoPipeStatement(void); extern int DoPolyfun(UBYTE *); extern int DoPolyratfun(UBYTE *); extern int CompileStatement(UBYTE *); extern UBYTE *ToToken(UBYTE *); extern int GetDollar(UBYTE *); extern void MesWork(void) NORETURN; extern int MesPrint(const char *,...); extern int MesCall(char *); extern UBYTE *NumCopy(WORD,UBYTE *); extern char *LongCopy(LONG,char *); extern char *LongLongCopy(off_t *,char *); extern void ReserveTempFiles(int); extern void PrintTerm(WORD *,char *); extern void PrintTermC(WORD *,char *); extern void PrintSubTerm(WORD *,char *); extern void PrintWords(WORD *,LONG); extern void PrintSeq(WORD *,char *); extern int ExpandTripleDots(int); extern LONG ComPress(WORD **,LONG *); extern void StageSort(FILEHANDLE *); #define M_alloc(x) malloc((size_t)(x)) extern void M_free(void *,const char *); extern void ClearWildcardNames(void); extern int AddWildcardName(UBYTE *); extern int GetWildcardName(UBYTE *); extern void Globalize(int); extern void ResetVariables(int); extern void AddToPreTypes(int); extern void MessPreNesting(int); extern LONG GetStreamPosition(STREAM *); extern WORD *DoubleCbuffer(int,WORD *,int); extern WORD *AddLHS(int); extern WORD *AddRHS(int,int); extern int AddNtoL(int,WORD *); extern int AddNtoC(int,int,WORD *,int); extern void DoubleIfBuffers(void); extern STREAM *CreateStream(UBYTE *); extern int setonoff(UBYTE *,int *,int,int); extern int DoPrint(UBYTE *,int); extern int SetExpr(UBYTE *,int,int); extern void AddToCom(int,WORD *); extern int Add2ComStrings(int,WORD *,UBYTE *,UBYTE *); extern int DoSymmetrize(UBYTE *,int); extern int DoArgument(UBYTE *,int); extern int ArgFactorize(PHEAD WORD *,WORD *); extern WORD *TakeArgContent(PHEAD WORD *, WORD *); extern WORD *MakeInteger(PHEAD WORD *,WORD *,WORD *); extern WORD *MakeMod(PHEAD WORD *,WORD *,WORD *); extern WORD FindArg(PHEAD WORD *); extern int InsertArg(PHEAD WORD *,WORD *,int); extern int CleanupArgCache(PHEAD WORD); extern int ArgSymbolMerge(WORD *, WORD *); extern int ArgDotproductMerge(WORD *, WORD *); extern void SortWeights(LONG *,LONG *,WORD); extern int DoBrackets(UBYTE *,int); extern int DoPutInside(UBYTE *,int); extern WORD *CountComp(UBYTE *,WORD *); extern int CoAntiBracket(UBYTE *); extern int CoAntiSymmetrize(UBYTE *); extern int DoArgPlode(UBYTE *,int); extern int CoArgExplode(UBYTE *); extern int CoArgImplode(UBYTE *); extern int CoArgument(UBYTE *); extern int CoInside(UBYTE *); extern int ExecInside(UBYTE *); extern int CoInExpression(UBYTE *); extern int CoInParallel(UBYTE *); extern int CoNotInParallel(UBYTE *); extern int DoInParallel(UBYTE *,int); extern int CoEndInExpression(UBYTE *); extern int CoBracket(UBYTE *); extern int CoPutInside(UBYTE *); extern int CoAntiPutInside(UBYTE *); extern int CoMultiBracket(UBYTE *); extern int CoCFunction(UBYTE *); extern int CoCTensor(UBYTE *); extern int CoCollect(UBYTE *); extern int CoCompress(UBYTE *); extern int CoContract(UBYTE *); extern int CoCycleSymmetrize(UBYTE *); extern int CoDelete(UBYTE *); extern int CoTableBase(UBYTE *); extern int CoApply(UBYTE *); extern int CoDenominators(UBYTE *); extern int CoDimension(UBYTE *); extern int CoDiscard(UBYTE *); extern int CoDisorder(UBYTE *); extern int CoDrop(UBYTE *); extern int CoDropCoefficient(UBYTE *); extern int CoDropSymbols(UBYTE *); extern int CoElse(UBYTE *); extern int CoElseIf(UBYTE *); extern int CoEndArgument(UBYTE *); extern int CoEndInside(UBYTE *); extern int CoEndIf(UBYTE *); extern int CoEndRepeat(UBYTE *); extern int CoEndTerm(UBYTE *); extern int CoEndWhile(UBYTE *); extern int CoExit(UBYTE *); extern int CoFactArg(UBYTE *); extern int CoFactDollar(UBYTE *); extern int CoFactorize(UBYTE *); extern int CoNFactorize(UBYTE *); extern int CoUnFactorize(UBYTE *); extern int CoNUnFactorize(UBYTE *); extern int DoFactorize(UBYTE *,int); extern int CoFill(UBYTE *); extern int CoFillExpression(UBYTE *); extern int CoFixIndex(UBYTE *); extern int CoFormat(UBYTE *); extern int CoGlobal(UBYTE *); extern int CoGlobalFactorized(UBYTE *); extern int CoGoTo(UBYTE *); extern int CoId(UBYTE *); extern int CoIdNew(UBYTE *); extern int CoIdOld(UBYTE *); extern int CoIf(UBYTE *); extern int CoIfMatch(UBYTE *); extern int CoIfNoMatch(UBYTE *); extern int CoIndex(UBYTE *); extern int CoInsideFirst(UBYTE *); extern int CoKeep(UBYTE *); extern int CoLabel(UBYTE *); extern int CoLoad(UBYTE *); extern int CoLocal(UBYTE *); extern int CoLocalFactorized(UBYTE *); extern int CoMany(UBYTE *); extern int CoMerge(UBYTE *); extern int CoStuffle(UBYTE *); extern int CoMetric(UBYTE *); extern int CoModOption(UBYTE *); extern int CoModuleOption(UBYTE *); extern int CoModulus(UBYTE *); extern int CoMulti(UBYTE *); extern int CoMultiply(UBYTE *); extern int CoNFunction(UBYTE *); extern int CoNPrint(UBYTE *); extern int CoNTensor(UBYTE *); extern int CoNWrite(UBYTE *); extern int CoNoDrop(UBYTE *); extern int CoNoSkip(UBYTE *); extern int CoNormalize(UBYTE *); extern int CoMakeInteger(UBYTE *); extern int CoFlags(UBYTE *,int); extern int CoOff(UBYTE *); extern int CoOn(UBYTE *); extern int CoOnce(UBYTE *); extern int CoOnly(UBYTE *); extern int CoOptimizeOption(UBYTE *); extern int CoPolyFun(UBYTE *); extern int CoPolyRatFun(UBYTE *); extern int CoPrint(UBYTE *); extern int CoPrintB(UBYTE *); extern int CoProperCount(UBYTE *); extern int CoUnitTrace(UBYTE *); extern int CoRCycleSymmetrize(UBYTE *); extern int CoRatio(UBYTE *); extern int CoRedefine(UBYTE *); extern int CoRenumber(UBYTE *); extern int CoRepeat(UBYTE *); extern int CoSave(UBYTE *); extern int CoSelect(UBYTE *); extern int CoSet(UBYTE *); extern int CoSetExitFlag(UBYTE *); extern int CoSkip(UBYTE *); extern int CoProcessBucket(UBYTE *); extern int CoPushHide(UBYTE *); extern int CoPopHide(UBYTE *); extern int CoHide(UBYTE *); extern int CoIntoHide(UBYTE *); extern int CoNoIntoHide(UBYTE *); extern int CoNoHide(UBYTE *); extern int CoUnHide(UBYTE *); extern int CoNoUnHide(UBYTE *); extern int CoSort(UBYTE *); extern int CoSplitArg(UBYTE *); extern int CoSplitFirstArg(UBYTE *); extern int CoSplitLastArg(UBYTE *); extern int CoSum(UBYTE *); extern int CoSymbol(UBYTE *); extern int CoSymmetrize(UBYTE *); extern int DoTable(UBYTE *,int); extern int CoTable(UBYTE *); extern int CoTerm(UBYTE *); extern int CoNTable(UBYTE *); extern int CoCTable(UBYTE *); extern void EmptyTable(TABLES); extern int CoToTensor(UBYTE *); extern int CoToVector(UBYTE *); extern int CoTrace4(UBYTE *); extern int CoTraceN(UBYTE *); extern int CoChisholm(UBYTE *); extern int CoTransform(UBYTE *); extern int CoClearTable(UBYTE *); extern int DoChain(UBYTE *,int); extern int CoChainin(UBYTE *); extern int CoChainout(UBYTE *); extern int CoTryReplace(UBYTE *); extern int CoVector(UBYTE *); extern int CoWhile(UBYTE *); extern int CoWrite(UBYTE *); extern int CoAuto(UBYTE *); extern int CoSwitch(UBYTE *); extern int CoCase(UBYTE *); extern int CoBreak(UBYTE *); extern int CoDefault(UBYTE *); extern int CoEndSwitch(UBYTE *); extern int CoTBaddto(UBYTE *); extern int CoTBaudit(UBYTE *); extern int CoTBcleanup(UBYTE *); extern int CoTBcreate(UBYTE *); extern int CoTBenter(UBYTE *); extern int CoTBhelp(UBYTE *); extern int CoTBload(UBYTE *); extern int CoTBoff(UBYTE *); extern int CoTBon(UBYTE *); extern int CoTBopen(UBYTE *); extern int CoTBreplace(UBYTE *); extern int CoTBuse(UBYTE *); extern int CoTestUse(UBYTE *); extern int CoThreadBucket(UBYTE *); extern int AddComString(int,WORD *,UBYTE *,int); extern int CompileAlgebra(UBYTE *,int,WORD *); extern int IsIdStatement(UBYTE *); extern UBYTE *IsRHS(UBYTE *,UBYTE); extern int ParenthesesTest(UBYTE *); extern int tokenize(UBYTE *,WORD); extern void WriteTokens(SBYTE *); extern int simp1token(SBYTE *); extern int simpwtoken(SBYTE *); extern int simp2token(SBYTE *); extern int simp3atoken(SBYTE *,int); extern int simp3btoken(SBYTE *,int); extern int simp4token(SBYTE *); extern int simp5token(SBYTE *,int); extern int simp6token(SBYTE *,int); extern UBYTE *SkipAName(UBYTE *); extern int TestTables(void); extern int GetLabel(UBYTE *); extern int CoIdExpression(UBYTE *,int); extern int CoAssign(UBYTE *); extern int DoExpr(UBYTE *,int,int); extern int CompileSubExpressions(SBYTE *); extern int CodeGenerator(SBYTE *); extern int CompleteTerm(WORD *,UWORD *,UWORD *,WORD,WORD,int); extern int CodeFactors(SBYTE *s); extern WORD GenerateFactors(WORD,WORD); extern int InsTree(int,int); extern int FindTree(int,WORD *); extern void RedoTree(CBUF *,int); extern void ClearTree(int); extern int CatchDollar(int); extern int AssignDollar(PHEAD WORD *,WORD); extern UBYTE *WriteDollarToBuffer(WORD,WORD); extern UBYTE *WriteDollarFactorToBuffer(WORD,WORD,WORD); extern void AddToDollarBuffer(UBYTE *); extern int PutTermInDollar(WORD *,WORD); extern void TermAssign(WORD *); extern void WildDollars(PHEAD WORD *); extern LONG numcommute(WORD *,LONG *); extern int FullRenumber(PHEAD WORD *,WORD); extern int Lus(WORD *,WORD,WORD,WORD,WORD,WORD); extern int FindLus(int,int,int); extern int CoReplaceLoop(UBYTE *); extern int CoFindLoop(UBYTE *); extern int DoFindLoop(UBYTE *,int); extern int CoFunPowers(UBYTE *); extern int SortTheList(int *,int); extern int MatchIsPossible(WORD *,WORD *); extern int StudyPattern(WORD *); extern WORD DolToTensor(PHEAD WORD); extern WORD DolToFunction(PHEAD WORD); extern WORD DolToVector(PHEAD WORD); extern WORD DolToNumber(PHEAD WORD); extern WORD DolToSymbol(PHEAD WORD); extern WORD DolToIndex(PHEAD WORD); extern LONG DolToLong(PHEAD WORD); extern int DollarFactorize(PHEAD WORD); extern int CoPrintTable(UBYTE *); extern int CoDeallocateTable(UBYTE *); extern void CleanDollarFactors(DOLLARS); extern WORD *TakeDollarContent(PHEAD WORD *,WORD **); extern WORD *MakeDollarInteger(PHEAD WORD *,WORD **); extern WORD *MakeDollarMod(PHEAD WORD *,WORD **); extern int GetDolNum(PHEAD WORD *, WORD *); extern void AddPotModdollar(WORD); // Returns 1 if the ModOptdollar type implies a thread-local copy when running // in TFORM (WITHPTHREADS), and 0 otherwise. static inline int DollarLocalCopy(WORD type) { if ( type == MODLOCAL ) { return 1; } if ( type == MODMIN ) { return 1; } if ( type == MODMAX ) { return 1; } return 0; } extern int Optimize(WORD, int); extern int ClearOptimize(void); extern int TakeLongRoot(UWORD *,WORD *,WORD); extern int TakeRatRoot(UWORD *,WORD *,WORD); extern int MakeRational(WORD ,WORD , WORD *, WORD *); extern int MakeLongRational(PHEAD UWORD *,WORD ,UWORD *,WORD ,UWORD *,WORD *); extern void ClearTableTree(TABLES); extern int InsTableTree(TABLES,WORD *); extern void RedoTableTree(TABLES,int); extern int FindTableTree(TABLES,WORD *,int); extern void finishcbuf(WORD); extern void clearcbuf(WORD); extern void CleanUpSort(int); extern FILEHANDLE *AllocFileHandle(WORD,char *); extern void DeAllocFileHandle(FILEHANDLE *); extern void LowerSortLevel(void); extern WORD *PolyRatFunSpecial(PHEAD WORD *, WORD *); extern void SimpleSplitMergeRec(WORD *,WORD,WORD *); extern void SimpleSplitMerge(WORD *,WORD); extern WORD BinarySearch(WORD *,WORD,WORD); extern int InsideDollar(PHEAD WORD *,WORD); extern DOLLARS DolToTerms(PHEAD WORD); extern WORD EvalDoLoopArg(PHEAD WORD *,WORD); extern int SetExprCases(int,int,int); extern int TestSelect(WORD *,WORD *); extern void SubsInAll(PHEAD0); extern void TransferBuffer(int,int,int); extern int TakeIDfunction(PHEAD WORD *); extern int MakeSetupAllocs(void); extern NORMDATA *AllocNormData(void); extern int TryFileSetups(void); extern void ExchangeExpressions(int,int); extern void ExchangeDollars(int,int); extern int GetFirstBracket(WORD *,int); extern int GetFirstTerm(WORD *,int,int); extern int GetContent(WORD *,int); extern int CleanupTerm(WORD *); extern WORD ContentMerge(PHEAD WORD *,WORD *); extern UBYTE *PreIfDollarEval(UBYTE *,int *); extern LONG TermsInDollar(WORD); extern LONG SizeOfDollar(WORD); extern LONG TermsInExpression(WORD); extern LONG SizeOfExpression(WORD); extern WORD *TranslateExpression(UBYTE *); extern int IsSetMember(WORD *,WORD); extern int IsMultipleOf(WORD *,WORD *); extern int TwoExprCompare(WORD *,WORD *,int); extern void UpdatePositions(void); extern void M_check(void); extern void M_print(void); extern void M_check1(void); extern void PrintTime(UBYTE *); extern POSITION *FindBracket(WORD,WORD *); extern void PutBracketInIndex(PHEAD WORD *,POSITION *); extern void ClearBracketIndex(WORD); extern void OpenBracketIndex(WORD); extern int DoNoParallel(UBYTE *); extern int DoParallel(UBYTE *); extern int DoModSum(UBYTE *); extern int DoModMax(UBYTE *); extern int DoModMin(UBYTE *); extern int DoModLocal(UBYTE *); extern UBYTE *DoModDollar(UBYTE *,int); extern int DoProcessBucket(UBYTE *); extern int DoinParallel(UBYTE *); extern int DonotinParallel(UBYTE *); extern int FlipTable(FUNCTIONS,int); extern int ChainIn(PHEAD WORD *,WORD); extern int ChainOut(PHEAD WORD *,WORD); extern int ArgumentImplode(PHEAD WORD *,WORD *); extern int ArgumentExplode(PHEAD WORD *,WORD *); extern int DenToFunction(WORD *,WORD); extern WORD HowMany(PHEAD WORD *,WORD *); extern void RemoveDollars(void); extern LONG CountTerms1(PHEAD0); extern LONG TermsInBracket(PHEAD WORD *,WORD); extern int Crash(void); extern char *str_dup(char *); extern void convertblock(INDEXBLOCK *,INDEXBLOCK *,int); extern void convertnamesblock(NAMESBLOCK *,NAMESBLOCK *,int); extern void convertiniinfo(INIINFO *,INIINFO *,int); extern int ReadIndex(DBASE *); extern int WriteIndexBlock(DBASE *,MLONG); extern int WriteNamesBlock(DBASE *,MLONG); extern int WriteIndex(DBASE *); extern int WriteIniInfo(DBASE *); extern int ReadIniInfo(DBASE *); extern int AddToIndex(DBASE *,MLONG); extern DBASE *GetDbase(char *,MLONG); extern DBASE *OpenDbase(char *); extern char *ReadObject(DBASE *,MLONG,char *); extern char *ReadijObject(DBASE *,MLONG,MLONG,char *); extern int ExistsObject(DBASE *,MLONG,char *); extern int DeleteObject(DBASE *,MLONG,char *); extern int WriteObject(DBASE *,MLONG,char *,char *,MLONG); extern MLONG AddObject(DBASE *,MLONG,char *,char *); extern DBASE *NewDbase(char *,MLONG); extern void FreeTableBase(DBASE *); extern int ComposeTableNames(DBASE *); extern int PutTableNames(DBASE *); extern MLONG AddTableName(DBASE *,char *,TABLES); extern MLONG GetTableName(DBASE *,char *); extern MLONG FindTableNumber(DBASE *,char *); extern int TryEnvironment(void); #ifdef WITHZLIB extern int SetupOutputGZIP(FILEHANDLE *); extern int PutOutputGZIP(FILEHANDLE *); extern int FlushOutputGZIP(FILEHANDLE *); extern int SetupAllInputGZIP(SORTING *); extern LONG FillInputGZIP(FILEHANDLE *,POSITION *,UBYTE *,LONG,int); extern void ClearSortGZIP(FILEHANDLE *f); #endif #ifdef WITHPTHREADS extern void BeginIdentities(void); extern int WhoAmI(void); extern int StartAllThreads(int); extern void StartHandleLock(void); extern void TerminateAllThreads(void); extern int GetAvailableThread(void); extern int ConditionalGetAvailableThread(void); extern int BalanceRunThread(PHEAD int,WORD *,WORD); extern void WakeupThread(int,int); extern int MasterWait(void); extern int InParallelProcessor(void); extern int ThreadsProcessor(EXPRESSIONS,WORD,WORD); extern int MasterMerge(void); extern int PutToMaster(PHEAD WORD *); extern void SetWorkerFiles(void); extern int MakeThreadBuckets(int,int); extern int SendOneBucket(int); extern int LoadOneThread(int,int,THREADBUCKET *,int); extern void *RunSortBot(void *); extern void MasterWaitAllSortBots(void); extern int SortBotMerge(PHEAD0); extern int SortBotOut(PHEAD WORD *); extern void DefineSortBotTree(void); extern int SortBotMasterMerge(void); extern int SortBotWait(int); extern void StartIdentity(void); extern void FinishIdentity(void *); extern int SetIdentity(int *); extern ALLPRIVATES *InitializeOneThread(int); extern void FinalizeOneThread(int); extern void ClearAllThreads(void); extern void *RunThread(void *); extern void IAmAvailable(int); extern int ThreadWait(int); extern int ThreadClaimedBlock(int); extern int GetThread(int); extern int UpdateOneThread(int); extern void MasterWaitAll(void); extern void MasterWaitAllBlocks(void); extern int MasterWaitThread(int); extern void WakeupMasterFromThread(int,int); extern int LoadReadjusted(void); extern int IniSortBlocks(int); extern int UpdateSortBlocks(int); extern int TreatIndexEntry(PHEAD LONG); extern WORD GetTerm2(PHEAD WORD *); extern void SetHideFiles(void); #endif extern int CopyExpression(FILEHANDLE *,FILEHANDLE *); extern int set_in(UBYTE, set_of_char); extern one_byte set_set(UBYTE, set_of_char); extern one_byte set_del(UBYTE, set_of_char); extern one_byte set_sub (set_of_char, set_of_char, set_of_char); extern int DoPreAddSeparator(UBYTE *); extern int DoPreRmSeparator(UBYTE *); /*See the file extcmd.c*/ extern int openExternalChannel(UBYTE *,int,UBYTE *,UBYTE *); extern int initPresetExternalChannels(UBYTE *, int); extern int closeExternalChannel(int); extern int selectExternalChannel(int); extern int getCurrentExternalChannel(void); extern void closeAllExternalChannels(void); typedef int (*WRITEBUFTOEXTCHANNEL)(char *,size_t); typedef int (*GETCFROMEXTCHANNEL)(void); typedef int (*SETTERMINATORFOREXTERNALCHANNEL)(char *); typedef int (*SETKILLMODEFOREXTERNALCHANNEL)(int,int); typedef LONG (*WRITEFILE)(int,UBYTE *,LONG); typedef WORD (*GETTERM)(PHEAD WORD *); #define CompareTerms ((COMPARE)AR.CompareRoutine) #define FiniShuffle AN.SHvar.finishuf #define DoShtuffle ((DO_UFFLE)AN.SHvar.do_uffle) extern UBYTE *defineChannel(UBYTE*, HANDLERS*); extern int writeToChannel(int,UBYTE *,HANDLERS*); #ifdef WITHEXTERNALCHANNEL extern LONG WriteToExternalChannel(int,UBYTE *,LONG); #endif extern int writeBufToExtChannelOk(char *,size_t); extern int getcFromExtChannelOk(void); extern int setKillModeForExternalChannelOk(int,int); extern int setTerminatorForExternalChannelOk(char *); extern int getcFromExtChannelFailure(void); extern int setKillModeForExternalChannelFailure(int,int); extern int setTerminatorForExternalChannelFailure(char *); extern int writeBufToExtChannelFailure(char *,size_t); extern int ReleaseTB(void); extern int SymbolNormalize(WORD *); extern int TestFunFlag(PHEAD WORD *); extern WORD CompareSymbols(PHEAD WORD *,WORD *,WORD); extern WORD CompareHSymbols(PHEAD WORD *,WORD *,WORD); extern WORD NextPrime(PHEAD WORD); extern WORD Moebius(PHEAD WORD); extern UWORD wranf(PHEAD0); extern UWORD iranf(PHEAD UWORD); extern void iniwranf(PHEAD0); extern UBYTE *PreRandom(UBYTE *); extern WORD *PolyNormPoly(PHEAD WORD); extern WORD *EvaluateGcd(PHEAD WORD *); extern int TreatPolyRatFun(PHEAD WORD *); extern int ReadSaveHeader(void); extern LONG ReadSaveIndex(FILEINDEX *); extern LONG ReadSaveExpression(UBYTE *,UBYTE *,LONG *,LONG *); extern UBYTE *ReadSaveTerm32(UBYTE *,UBYTE *,UBYTE **,UBYTE *,UBYTE *,int); extern LONG ReadSaveVariables(UBYTE *,UBYTE *,LONG *,LONG *,INDEXENTRY *,LONG *); extern LONG WriteStoreHeader(WORD); extern void InitRecovery(void); extern int CheckRecoveryFile(void); extern void DeleteRecoveryFile(void); extern char *RecoveryFilename(void); extern int DoRecovery(int *); extern void DoCheckpoint(int); extern void NumberMallocAddMemory(PHEAD0); extern void CacheNumberMallocAddMemory(PHEAD0); extern void TermMallocAddMemory(PHEAD0); #ifndef MEMORYMACROS extern WORD *TermMalloc2(PHEAD char *text); extern void TermFree2(PHEAD WORD *term,char *text); extern UWORD *NumberMalloc2(PHEAD char *text); extern UWORD *CacheNumberMalloc2(PHEAD char *text); extern void NumberFree2(PHEAD UWORD *NumberMem,char *text); extern void CacheNumberFree2(PHEAD UWORD *NumberMem,char *text); #endif extern void ExprStatus(EXPRESSIONS); extern void iniTools(void); extern int TestTerm(WORD *); extern int RunTransform(PHEAD WORD *term, WORD *params); extern int RunEncode(PHEAD WORD *fun, WORD *args, WORD *info); extern int RunDecode(PHEAD WORD *fun, WORD *args, WORD *info); extern int RunReplace(PHEAD WORD *fun, WORD *args, WORD *info); extern int RunImplode(WORD *fun, WORD *args); extern int RunExplode(PHEAD WORD *fun, WORD *args); extern int TestArgNum(int n, int totarg, WORD *args); extern WORD PutArgInScratch(WORD *arg,UWORD *scrat); extern UBYTE *ReadRange(UBYTE *s, WORD *out, int par); extern int FindRange(PHEAD WORD *,WORD *,WORD *,WORD); extern int RunPermute(PHEAD WORD *fun, WORD *args, WORD *info); extern int RunReverse(PHEAD WORD *fun, WORD *args); extern int RunCycle(PHEAD WORD *fun, WORD *args, WORD *info); extern int RunAddArg(PHEAD WORD *fun, WORD *args); extern int RunMulArg(PHEAD WORD *fun, WORD *args); extern int RunIsLyndon(PHEAD WORD *fun, WORD *args, int par); extern WORD RunToLyndon(PHEAD WORD *fun, WORD *args, int par); extern int RunDropArg(PHEAD WORD *fun, WORD *args); extern int RunSelectArg(PHEAD WORD *fun, WORD *args); extern int RunDedup(PHEAD WORD *fun, WORD *args); extern int RunZtoHArg(PHEAD WORD *fun, WORD *args); extern int RunHtoZArg(PHEAD WORD *fun, WORD *args); extern int NormPolyTerm(PHEAD WORD *); extern WORD ComparePoly(WORD *, WORD *, WORD); extern int ConvertToPoly(PHEAD WORD *, WORD *,WORD *,WORD); extern int LocalConvertToPoly(PHEAD WORD *, WORD *, WORD,WORD); extern int ConvertFromPoly(PHEAD WORD *, WORD *, WORD, WORD, WORD, WORD); extern int FindSubterm(WORD *); extern int FindLocalSubterm(PHEAD WORD *, WORD); extern void PrintSubtermList(int,int); extern void PrintExtraSymbol(int,WORD *,int); extern int FindSubexpression(WORD *); extern void UpdateMaxSize(void); extern int CoToPolynomial(UBYTE *); extern int CoFromPolynomial(UBYTE *); extern int CoArgToExtraSymbol(UBYTE *); extern int CoExtraSymbols(UBYTE *); extern UBYTE *GetDoParam(UBYTE *, WORD **, int); extern WORD *GetIfDollarFactor(UBYTE **, WORD *); extern int CoDo(UBYTE *); extern int CoEndDo(UBYTE *); extern int ExtraSymFun(PHEAD WORD *,WORD); extern int PruneExtraSymbols(WORD); extern int IniFbuffer(WORD); extern void IniFbufs(void); extern int GCDfunction(PHEAD WORD *,WORD); extern WORD *GCDfunction3(PHEAD WORD *,WORD *); extern int ReadPolyRatFun(PHEAD WORD *); extern int FromPolyRatFun(PHEAD WORD *, WORD **, WORD **); extern WORD *PolyDiv(PHEAD WORD *,WORD *,char *); extern void GCDclean(PHEAD WORD *, WORD *); extern WORD *TakeSymbolContent(PHEAD WORD *,WORD *); extern int GCDterms(PHEAD WORD *,WORD *,WORD *); extern WORD *PutExtraSymbols(PHEAD WORD *,WORD,int *); extern WORD *TakeExtraSymbols(PHEAD WORD *,WORD); extern WORD *MultiplyWithTerm(PHEAD WORD *, WORD *,WORD); extern WORD *TakeContent(PHEAD WORD *, WORD *); extern int MergeSymbolLists(PHEAD WORD *, WORD *, int); extern int MergeDotproductLists(PHEAD WORD *, WORD *, int); extern WORD *CreateExpression(PHEAD WORD); extern int DIVfunction(PHEAD WORD *,WORD,int); extern WORD *MULfunc(PHEAD WORD *, WORD *); extern WORD *ConvertArgument(PHEAD WORD *,int *); extern int ExpandRat(PHEAD WORD *); extern int InvPoly(PHEAD WORD *,WORD,WORD); extern WORD TestDoLoop(PHEAD WORD *,WORD); extern WORD TestEndDoLoop(PHEAD WORD *,WORD); extern WORD *poly_gcd(PHEAD WORD *, WORD *, WORD); extern WORD *poly_div(PHEAD WORD *, WORD *, WORD); extern WORD *poly_rem(PHEAD WORD *, WORD *, WORD); extern WORD *poly_inverse(PHEAD WORD *, WORD *); extern WORD *poly_mul(PHEAD WORD *, WORD *); extern WORD *poly_ratfun_add(PHEAD WORD *, WORD *); extern int poly_ratfun_normalize(PHEAD WORD *); extern int poly_factorize_argument(PHEAD WORD *, WORD *); extern WORD *poly_factorize_dollar(PHEAD WORD *); extern int poly_factorize_expression(EXPRESSIONS); extern int poly_unfactorize_expression(EXPRESSIONS); extern void poly_free_poly_vars(PHEAD const char *); #ifdef WITHFLINT extern void flint_final_cleanup_thread(void); extern void flint_final_cleanup_master(void); extern WORD* flint_div(PHEAD WORD *, WORD *, const WORD); extern int flint_factorize_argument(PHEAD WORD *, WORD *); extern WORD* flint_factorize_dollar(PHEAD WORD *); extern WORD* flint_gcd(PHEAD WORD *, WORD *, const WORD); extern WORD* flint_inverse(PHEAD WORD *, WORD *); extern WORD* flint_mul(PHEAD WORD *, WORD *); extern WORD* flint_ratfun_add(PHEAD WORD *, WORD *); extern int flint_ratfun_normalize(PHEAD WORD *); extern WORD* flint_rem(PHEAD WORD *, WORD *, const WORD); extern void flint_check_version(void); #endif extern void optimize_print_code (int); #ifdef WITHPTHREADS extern void find_Horner_MCTS_expand_tree(void); extern void find_Horner_MCTS_expand_tree_threaded(void); extern void optimize_expression_given_Horner(void); extern void optimize_expression_given_Horner_threaded(void); #endif extern int DoPreAdd(UBYTE *s); extern int DoPreUseDictionary(UBYTE *s); extern int DoPreCloseDictionary(UBYTE *s); extern int DoPreOpenDictionary(UBYTE *s); extern void RemoveDictionary(DICTIONARY *dict); extern void UnSetDictionary(void); extern int SetDictionaryOptions(UBYTE *options); extern int AddToDictionary(DICTIONARY *dict,UBYTE *left,UBYTE *right); extern int AddDictionary(UBYTE *name); extern int FindDictionary(UBYTE *name); extern UBYTE *IsExponentSign(void); extern UBYTE *IsMultiplySign(void); extern void TransformRational(UWORD *a, WORD na); extern void WriteDictionary(DICTIONARY *); extern void ShrinkDictionary(DICTIONARY *); extern void MultiplyToLine(void); extern UBYTE *FindSymbol(WORD num); extern UBYTE *FindVector(WORD num); extern UBYTE *FindIndex(WORD num); extern UBYTE *FindFunction(WORD num); extern UBYTE *FindFunWithArgs(WORD *t); extern UBYTE *FindExtraSymbol(WORD num); extern LONG DictToBytes(DICTIONARY *dict,UBYTE *buf); extern DICTIONARY *DictFromBytes(UBYTE *buf); extern int CoCreateSpectator(UBYTE *inp); extern int CoToSpectator(UBYTE *inp); extern int CoRemoveSpectator(UBYTE *inp); extern int CoEmptySpectator(UBYTE *inp); extern int CoCopySpectator(UBYTE *inp); extern int PutInSpectator(WORD *,WORD); extern void ClearSpectators(WORD); extern WORD GetFromSpectator(WORD *,WORD); extern void FlushSpectators(void); extern WORD *PreGCD(PHEAD WORD *, WORD *,int); extern int InvPoly(PHEAD WORD *,WORD,WORD); extern int ReadFromScratch(FILEHANDLE *,POSITION *,UBYTE *,POSITION *); extern int AddToScratch(FILEHANDLE *,POSITION *,UBYTE *,POSITION *,int); extern int DoPreAppendPath(UBYTE *); extern int DoPrePrependPath(UBYTE *); extern int DoSwitch(PHEAD WORD *, WORD *); extern int DoEndSwitch(PHEAD WORD *, WORD *); extern SWITCHTABLE *FindCase(WORD, WORD); extern void SwitchSplitMergeRec(SWITCHTABLE *, WORD, SWITCHTABLE *); extern void SwitchSplitMerge(SWITCHTABLE *, WORD); extern int DoubleSwitchBuffers(void); extern int DistrN(int, int *, int, int *); extern int DoNamespace(UBYTE *); extern int DoEndNamespace(UBYTE *); extern int DoUse(UBYTE *); extern UBYTE *SkipName(UBYTE *); extern UBYTE *ConstructName(UBYTE *,UBYTE); extern int DoSetUserFlag(UBYTE *); extern int DoClearUserFlag(UBYTE *); VERTEX *CreateVertex(MODEL *); UBYTE *ReadParticle(UBYTE *, VERTEX *,MODEL *, int); int CoModel(UBYTE *); int CoParticle(UBYTE *); int CoVertex(UBYTE *); int CoEndModel(UBYTE *); int LoadModel(MODEL *); int CoSetUserFlag(UBYTE *); int CoClearUserFlag(UBYTE *); int CoCreateAllLoops(UBYTE *); int CoCreateAllPaths(UBYTE *); int CoCreateAll(UBYTE *); int AllLoops(PHEAD WORD *,WORD); LONG StartLoops(PHEAD WORD *,WORD,LONG,WORD,WORD *,WORD,WORD *,WORD); LONG GenLoops(PHEAD WORD *,WORD,LONG,WORD,WORD *,WORD,WORD *,WORD); void LoopOutput(PHEAD WORD *,WORD,WORD *,WORD); int AllPaths(PHEAD WORD *,WORD); LONG GenPaths(PHEAD WORD *,WORD,LONG,WORD,WORD *,WORD,WORD *,WORD); void PathOutput(PHEAD WORD *,WORD,WORD *,WORD); #ifdef WITHFLOAT int DoStartFloat(UBYTE *); int DoEndFloat(UBYTE *); int SetFloatPrecision(WORD); void SetupMZVTables(void); void SetupMPFTables(void); void ClearMZVTables(void); int EvaluateEuler(PHEAD WORD *,WORD,WORD); int EvaluateSqrt(PHEAD WORD *,WORD,WORD); int CoEvaluate(UBYTE *); int PrintFloat(WORD *fun,int numdigits); int CoToRat(UBYTE *); int CoToFloat(UBYTE *); int CoChop(UBYTE *); int ToRat(PHEAD WORD *,WORD); int ToFloat(PHEAD WORD *,WORD); int Chop(PHEAD WORD *, WORD); WORD FloatFunToRat(PHEAD UWORD *,WORD *); int AddWithFloat(PHEAD WORD **,WORD **); int MergeWithFloat(PHEAD WORD **,WORD **); void ClearfFloat(void); int TestFloat(WORD *); SBYTE *ReadFloat(SBYTE *); UBYTE *CheckFloat(UBYTE *,int *); void SetfFloatPrecision(LONG); int EvaluateFun(PHEAD WORD *, WORD, WORD *); int CoStrictRounding(UBYTE *); int StrictRounding(PHEAD WORD *, WORD, WORD, WORD); #endif /* #] Declarations : */ #endif form-5.0.1/sources/wildcard.c0000644000175100017510000017540315217035721011600 /** @file wildcard.c * * Contains the functions that deal with the wildcards. * During the pattern matching there are two steps: * 1: check that a wildcard substitution is correct (if there was already * an assignment for this variable, it is the same; it is part of the * proper set; it is the proper type of variables, etc.) * 2: make the assignment * In addition we have to be able to clear assignments. * During execution we have to make the actual replacements (WildFill) */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : wildcard.c */ #include "form3.h" #define DEBUG(x) /* #define DEBUG(x) x #] Includes : #[ Wildcards : #[ WildFill : WORD WildFill(to,from,sub) Takes the term in from and puts it into to while making wildcard substitutions. The return value is the number of words put in to. The length as the first word of from is not copied. There are two possible algorithms: 1: For each element in `from': scan sub. 2: For each wildcard in sub replace elements in term. The original algorithm used 1: */ WORD WildFill(PHEAD WORD *to, WORD *from, WORD *sub) { GETBIDENTITY WORD i, j, *s, *t, *m, len, dflag, odirt, adirt; WORD *r, *u, *v, *w, *z, *zst, *zz, *subs, *accu, na, dirty = 0, *tstop; WORD *temp = 0, *uu, *oldcpointer, sgn; WORD subcount, setflag, *setlist = 0, si; accu = oldcpointer = AR.CompressPointer; t = sub; t += sub[1]; s = sub + SUBEXPSIZE; i = 0; while ( s < t && *s != FROMBRAC ) { i++; s += s[1]; } if ( !i ) { /* No wildcards -> done quickly */ j = i = *from; NCOPY(to,from,i); if ( dirty ) AN.WildDirt = dirty; return(j); } sgn = 0; subs = sub + SUBEXPSIZE; t = from; GETSTOP(t,r); t++; m = to + 1; if ( t < r ) do { uu = u = t + t[1]; setflag = 0; ReSwitch: switch ( *t ) { case SYMBOL: /* #[ SYMBOLS : */ z = accu; *m++ = *t++; *m++ = *t++; v = m; while ( t < u ) { *m = *t; for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) goto sspow; } s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == SYMTOSYM ) { *m = s[3]; dirty = 1; break; } else if ( *s == SYMTONUM ) { dirty = 1; zst = z; *z++ = SNUMBER; *z++ = 4; *z++ = s[3]; w = z; *z++ = *++t; if ( ABS(*t) >= 2*MAXPOWER) { DoPow: s = subs; for ( j = 0; j < i; j++ ) { if ( ( *s == SYMTONUM ) && ( ABS(*t) - 2*MAXPOWER ) == s[2] ) { dirty = 1; *w = s[3]; if ( *t < 0 ) *w = -*w; break; } if ( ( *s == SYMTOSYM ) && ( ABS(*t) - 2*MAXPOWER ) == s[2] ) { dirty = 1; zz = z; while ( --zz >= zst ) { zz[1+FUNHEAD+ARGHEAD] = *zz; } w += 1+FUNHEAD+ARGHEAD; *zst = EXPONENT; zst[2] = DIRTYFLAG; zst[FUNHEAD+ARGHEAD] = WORDDIF(z,zst)+4; zst[1+FUNHEAD] = 1; zst[FUNHEAD] = WORDDIF(z,zst)+4+ARGHEAD; z += FUNHEAD+ARGHEAD+1; *w = 1; /* exponent -> 1 */ *z++ = 1; *z++ = 1; *z++ = 3; if ( *t > 0 ) { *z++ = -SYMBOL; *z++ = s[3]; } else { *z++ = ARGHEAD+8; *z++ = 1; *z++ = 8; *z++ = SYMBOL; *z++ = 4; *z++ = s[3]; *z++ = 1; *z++ = 1; *z++ = 1; *z++ = -3; } zst[1] = WORDDIF(z,zst); break; } if ( *s == SYMTOSUB && ( ABS(*t) - 2*MAXPOWER ) == s[2] ) { MakeExp: dirty = 1; zz = z; while ( --zz >= zst ) { zz[1+FUNHEAD+ARGHEAD] = *zz; } w += 1+FUNHEAD+ARGHEAD; *zst = EXPONENT; zst[2] = DIRTYFLAG; zst[FUNHEAD+ARGHEAD] = WORDDIF(z,zst)+4; zst[1+FUNHEAD] = 1; zst[FUNHEAD] = WORDDIF(z,zst)+4+ARGHEAD; z += FUNHEAD+ARGHEAD+1; *w = 1; /* exponent -> 1 */ *z++ = 1; *z++ = 1; *z++ = 3; *z++ = 4+SUBEXPSIZE+ARGHEAD; *z++ = 1; *z++ = 4+SUBEXPSIZE; *z++ = SUBEXPRESSION; *z++ = SUBEXPSIZE; *z++ = s[3]; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = 1; *z++ = 1; *z++ = *t > 0 ? 3: -3; zst[1] = WORDDIF(z,zst); break; } s += s[1]; } } if ( !*w ) z = w - 3; t++; goto Seven; } else if ( *s == SYMTOSUB ) { dirty = 1; zst = z; *z++ = SUBEXPRESSION; *z++ = SUBEXPSIZE; *z++ = s[3]; w = z; *z++ = *++t; *z++ = AT.ebufnum; FILLSUB(z) goto DoPow; } } s += s[1]; } sspow: s = subs; *++m = *++t; for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) { t++; m++; goto Seven; } } for ( j = 0; j < i; j++ ) { if ( ( ABS(*t) - 2*MAXPOWER ) == s[2] ) { if ( *s == SYMTONUM ) { dirty = 1; *m = s[3]; if ( *t < 0 ) *m = -*m; break; } else if ( *s == SYMTOSYM ) { dirty = 1; *z++ = EXPONENT; if ( *t < 0 ) *z++ = FUNHEAD+ARGHEAD+10; else *z++ = 4+FUNHEAD; *z++ = 0; FILLFUN3(z) *z++ = -SYMBOL; *z++ = m[-1]; if ( *t < 0 ) { *z++ = ARGHEAD+8; *z++ = 0; *z++ = 8; *z++ = SYMBOL; *z++ = 4; *z++ = s[3]; *z++ = 1; *z++ = 1; *z++ = 1; *z = -3; } else { *z++ = -SYMBOL; *z++ = s[3]; } m -= 2; break; } else if ( *s == SYMTOSUB ) { zst = z; *z++ = SYMBOL; *z++ = 4; *z++ = *--m; w = z; *z++ = *t; goto MakeExp; } } s += s[1]; } t++; if ( *m ) m++; else m--; Seven:; } j = WORDDIF(m,v); if ( !j ) m -= 2; else v[-1] = j + 2; s = accu; while ( s < z ) *m++ = *s++; break; /* #] SYMBOLS : */ case DOTPRODUCT: /* #[ DOTPRODUCTS : */ *m++ = *t++; *m++ = *t++; v = m; z = accu; while ( t < u ) { *m = *t; subcount = 0; /* Process the first vector of the DOTPRODUCT */ for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) goto ss2; } s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == VECTOVEC ) { *m = s[3]; dirty = 1; break; } if ( *s == VECTOMIN ) { *m = s[3]; dirty = 1; if ( ( ABS(t[2]) - 2*MAXPOWER ) < 0 ) { /* The power is a number */ sgn += t[2]; } else { /* The power is a wildcard. Put a -, resolve later. */ sgn++; } break; } if ( *s == VECTOSUB ) { *m = s[3]; dirty = 1; subcount = 1; break; } } s += s[1]; } ss2: *++m = *++t; s = subs; /* Process the second vector of the DOTPRODUCT */ for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) goto ss3; } for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == VECTOVEC ) { *m = s[3]; dirty = 1; break; } if ( *s == VECTOMIN ) { *m = s[3]; dirty = 1; if ( ( ABS(t[1]) - 2*MAXPOWER ) < 0 ) { /* The power is a number */ sgn += t[1]; } else { /* The power is a wildcard. Put a -, resolve later. */ sgn++; } break; } if ( *s == VECTOSUB ) { *m = s[3]; dirty = 1; subcount += 2; break; } } s += s[1]; } ss3: *++m = *++t; /* Process the power */ if ( ( ABS(*t) - 2*MAXPOWER ) < 0 ) goto RegPow; s = subs; for ( j = 0; j < i; j++ ) { if ( ( ABS(*t) - 2*MAXPOWER ) == s[2] ) { if ( *s == SYMTONUM ) { *m = s[3]; /* Since the power is a wildcard, sgn is 0,1,2 depending whether there were 0,1,2 VECTOMIN in the DOTPRODUCT. Multiply by the power, which is positive currently. */ sgn *= *m; /* Now flip the sign of the power, if the wildcard came with a - */ if ( *t < 0 ) *m = -*m; dirty = 1; break; } if ( *s <= SYMTOSUB ) { /* Here we put together a power function with the proper arguments. Note that a p?.q? resolves to a single power. */ m -= 2; *z++ = EXPONENT; w = z; if ( subcount == 0 ) { *z++ = 17+FUNHEAD+2*ARGHEAD; *z++ = DIRTYFLAG; FILLFUN3(z) *z++ = 9+ARGHEAD; *z++ = 0; FILLARG(z) *z++ = 9; *z++ = DOTPRODUCT; *z++ = 5; *z++ = *m; *z++ = m[1]; *z++ = 1; *z++ = 1; *z++ = 1; *z++ = 3; if ( *s == SYMTOSYM ) { *z++ = 8+ARGHEAD; *z++ = 0; FILLARG(z) *z++ = 8; *z++ = SYMBOL; *z++ = 4; *z++ = s[3]; *z++ = 1; } else { *z++ = 4+SUBEXPSIZE+ARGHEAD; *z++ = 1; FILLARG(z) *z++ = 4+SUBEXPSIZE; *z++ = SUBEXPRESSION; *z++ = SUBEXPSIZE; *z++ = s[3]; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) } *z++ = 1; *z++ = 1; *z++ = ( s[2] > 0 ) ? 3: -3; } else if ( subcount == 3 ) { *z++ = 20+2*SUBEXPSIZE+FUNHEAD+2*ARGHEAD; *z++ = DIRTYFLAG; FILLFUN3(z) *z++ = 12+2*SUBEXPSIZE+ARGHEAD; *z++ = 1; *z++ = 12+2*SUBEXPSIZE; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = *m + 1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = ++AR.CurDum; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = m[1] + 1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = AR.CurDum; *z++ = 1; *z++ = 1; *z++ = 3; } else { if ( subcount == 2 ) { j = *m; *m = m[1]; m[1] = j; } *z++ = 16+SUBEXPSIZE+FUNHEAD+2*ARGHEAD; *z++ = DIRTYFLAG; FILLFUN3(z) *z++ = 8+SUBEXPSIZE+ARGHEAD; *z++ = 1; *z++ = 8+SUBEXPSIZE; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = *m + 1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = m[1]; *z++ = 1; *z++ = 1; *z++ = 3; } if ( *s == SYMTOSYM ) { if ( s[2] > 0 ) { *z++ = -SYMBOL; *z++ = s[3]; t++; *w = z-w+1; goto NextDot; } *z++ = 8+ARGHEAD; *z++ = 0; *z++ = 8; *z++ = SYMBOL; *z++ = 4; *z++ = s[3]; *z++ = 1; } else { *z++ = 4+SUBEXPSIZE+ARGHEAD; *z++ = 1; *z++ = 4+SUBEXPSIZE; *z++ = SUBEXPRESSION; *z++ = SUBEXPSIZE; *z++ = s[3]; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) } *z++ = 1; *z++ = 1; *z++ = ( s[2] > 0 ) ? 3: -3; t++; *w = z-w+1; goto NextDot; } } s += s[1]; } RegPow: if ( *m ) m++; else { m -= 2; subcount = 0; } t++; if ( subcount ) { m -= 3; if ( subcount == 3 ) { if ( m[2] < 0 ) { j = (-m[2]) * (2*SUBEXPSIZE+8); *z++ = DENOMINATOR; *z++ = j + 8 + FUNHEAD + ARGHEAD; *z++ = DIRTYFLAG; FILLFUN3(z) *z++ = j + 8 + ARGHEAD; *z++ = 1; *z++ = j + 8; while ( m[2] < 0 ) { (m[2])++; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = *m + 1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = ++AR.CurDum; *z++ = SUBEXPRESSION; *z++ = 8+SUBEXPSIZE; *z++ = m[1] + 1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = AR.CurDum; *z++ = SYMTOSYM; /* Needed to avoid */ *z++ = 4; /* problems with */ *z++ = 1000; /* conversion to */ *z++ = 1000; /* square of subexp*/ } *z++ = 1; *z++ = 1; *z++ = 3; } else { while ( m[2] > 0 ) { (m[2])--; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = *m + 1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = ++AR.CurDum; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = m[1] + 1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = AR.CurDum; } } } else { if ( subcount == 2 ) { j = *m; *m = m[1]; m[1] = j; } if ( m[2] < 0 ) { *z++ = DENOMINATOR; *z++ = 8+SUBEXPSIZE+FUNHEAD+ARGHEAD; *z++ = DIRTYFLAG; FILLFUN3(z) *z++ = 8+SUBEXPSIZE+ARGHEAD; *z++ = 1; *z++ = 8+SUBEXPSIZE; } *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = *m + 1; *z++ = ABS(m[2]); *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = m[1]; if ( m[2] < 0 ) { *z++ = 1; *z++ = 1; *z++ = 3; } } } NextDot:; } if ( m <= v ) m = v - 2; else v[-1] = WORDDIF(m,v) + 2; if ( z > accu ) { j = WORDDIF(z,accu); z = accu; NCOPY(m,z,j); } break; /* #] DOTPRODUCTS : */ case SETSET: /* #[ SETS : */ temp = accu + (((AR.ComprTop - accu)>>1)&(-2)); if ( ResolveSet(BHEAD t,temp,sub) ) { Terminate(-1); } setlist = t + 2 + t[3]; setflag = t[1] - 2 - t[3]; /* Number of elements * 2 */ t = temp; u = t + t[1]; goto ReSwitch; /* #] SETS : */ case VECTOR: /* #[ VECTORS : */ *m++ = *t++; *m++ = *t++; v = m; z = accu; while ( t < u ) { *m = *t; for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) goto ss4; } s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == INDTOIND || *s == VECTOVEC ) { *m = s[3]; dirty = 1; break; } if ( *s == VECTOMIN ) { *m = s[3]; dirty = 1; sgn++; break; } else if ( *s == VECTOSUB ) { *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = s[3]+1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = VECTOVEC; *z++ = 4; *z++ = FUNNYVEC; *z++ = *++t; m--; s = subs; for ( j = 0; j < i; j++ ) { if ( z[-1] == s[2] ) { if ( *s == INDTOIND || *s == VECTOVEC ) { z[-1] = s[3]; break; } if ( *s == INDTOSUB || *s == VECTOSUB ) { z[-1] = ++AR.CurDum; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = s[3]+1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) if ( *s == INDTOSUB ) *z++ = INDTOIND; else *z++ = VECTOSUB; *z++ = 4; *z++ = FUNNYVEC; *z++ = AR.CurDum; break; } } s += s[1]; } dirty = 1; break; } else if ( *s == INDTOSUB ) { *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = s[3]+1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; m -= 2; *z++ = m[1]; dirty = 1; t++; break; } } s += s[1]; } ss4: m++; t++; } if ( m <= v ) m = v-2; else v[-1] = WORDDIF(m,v)+2; if ( z > accu ) { j = WORDDIF(z,accu); z = accu; NCOPY(m,z,j); } break; /* #] VECTORS : */ case INDEX: /* #[ INDEX : */ *m++ = *t++; *m++ = *t++; v = m; z = accu; while ( t < u ) { *m = *t; for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) goto ss5; } s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == INDTOIND || *s == VECTOVEC ) { *m = s[3]; dirty = 1; break; } if ( *s == VECTOMIN ) { *m = s[3]; dirty = 1; sgn++; break; } else if ( *s == VECTOSUB || *s == INDTOSUB ) { *z++ = SUBEXPRESSION; *z++ = SUBEXPSIZE; *z++ = s[3]; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) m--; dirty = 1; break; } } s += s[1]; } ss5: m++; t++; } if ( m <= v ) m = v-2; else v[-1] = WORDDIF(m,v)+2; if ( z > accu ) { j = WORDDIF(z,accu); z = accu; NCOPY(m,z,j); } break; /* #] INDEX : */ case DELTA: case LEVICIVITA: case GAMMA: /* #[ SPECIALS : */ v = m; *m++ = *t++; *m++ = *t++; #if FUNHEAD > 2 if ( t[-2] != DELTA ) *m++ = *t++; #endif Tensors: COPYFUN3(m,t) z = accu; while ( t < u ) { *m = *t; for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) goto ss6; } s = subs; if ( *m == FUNNYWILD ) { CBUF *C = cbuf+AT.ebufnum; t++; for ( j = 0; j < i; j++ ) { if ( *s == ARGTOARG && *t == s[2] ) { v[2] |= DIRTYFLAG; if ( s[3] < 0 ) { /* empty */ t++; break; } w = C->rhs[s[3]]; DEBUG(MesPrint("Thread %w(a): s[3] = %d, w=(%d,%d,%d,%d)",s[3],w[0],w[1],w[2],w[3]);) j = *w++; if ( j > 0 ) { NCOPY(m,w,j); } else { while ( *w ) { if ( *w == -INDEX || *w == -VECTOR || *w == -MINVECTOR || ( *w == -SNUMBER && w[1] >= 0 && w[1] < AM.OffsetIndex ) ) { if ( *w == -MINVECTOR ) sgn++; w++; *m++ = *w++; } else { MLOCK(ErrorMessageLock); DEBUG(MesPrint("Thread %w(aa): *w = %d",*w);) MesPrint("Illegal substitution of argument field in tensor"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } } } t++; break; } s += s[1]; } } else { for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == INDTOIND || *s == VECTOVEC ) { *m = s[3]; dirty = 1; break; } if ( *s == VECTOMIN ) { *m = s[3]; dirty = 1; sgn++; break; } else if ( *s == VECTOSUB || *s == INDTOSUB ) { *m = ++AR.CurDum; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = s[3]+1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = AR.CurDum; dirty = 1; break; } } s += s[1]; } if ( j < i && *v != DELTA ) v[2] |= DIRTYFLAG; ss6: m++; t++; } } v[1] = WORDDIF(m,v); if ( z > accu ) { j = WORDDIF(z,accu); z = accu; NCOPY(m,z,j); } break; /* #] SPECIALS : */ case SUBEXPRESSION: /* #[ SUBEXPRESSION : */ dirty = 1; tstop = t + t[1]; *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; if ( t[-1] >= 2*MAXPOWER || t[-1] <= -2*MAXPOWER ) { s = subs; for ( j = 0; j < i; j++ ) { if ( *s == SYMTONUM && ( ABS(t[-1]) - 2*MAXPOWER ) == s[2] ) { m[-1] = s[3]; if ( t[-1] < 0 ) m[-1] = -m[-1]; break; } s += s[1]; } } *m++ = *t++; COPYSUB(m,t) while ( t < tstop ) { for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] - 2 ) goto ss7; } s = subs; for ( j = 0; j < i; j++ ) { if ( s[2] == t[2] ) { if ( ( *s <= SYMTOSUB && *t <= SYMTOSUB ) || ( *s == *t && *s < FROMBRAC ) || ( *s == VECTOVEC && ( *t == VECTOSUB || *t == VECTOMIN ) ) || ( *s == VECTOSUB && ( *t == VECTOVEC || *t == VECTOMIN ) ) || ( *s == VECTOMIN && ( *t == VECTOSUB || *t == VECTOVEC ) ) || ( *s == INDTOIND && *t == INDTOSUB ) || ( *s == INDTOSUB && *t == INDTOIND ) ) { WORD *vv = m; /* *t = *s; Wrong!!! Overwrites compiler buffer */ j = t[1]; NCOPY(m,t,j); vv[0] = s[0]; vv[3] = s[3]; goto sr7; } } s += s[1]; } ss7: j = t[1]; NCOPY(m,t,j); sr7:; } break; /* #] SUBEXPRESSION : */ case EXPRESSION: /* #[ EXPRESSION : */ dirty = 1; tstop = t + t[1]; v = m; *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; s = subs; for ( j = 0; j < i; j++ ) { if ( ( ABS(t[-1]) - 2*MAXPOWER ) == s[2] ) { if ( *s == SYMTONUM ) { m[-1] = s[3]; if ( t[-1] < 0 ) m[-1] = -m[-1]; break; } else if ( *s <= SYMTOSUB ) { MLOCK(ErrorMessageLock); MesPrint("Wildcard power of expression should be a number"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } } s += s[1]; } *m++ = *t++; COPYSUB(m,t) while ( t < tstop && *t != WILDCARDS ) { j = t[1]; NCOPY(m,t,j); } if ( t < tstop && *t == WILDCARDS ) { *m++ = *t; s = sub; j = s[1]; *m++ = j+2; NCOPY(m,s,j); t += t[1]; } if ( t < tstop && *t == FROMBRAC ) { w = m; *m++ = *t; *m++ = t[1]; if ( WildFill(BHEAD m,t+2,sub) < 0 ) { MLOCK(ErrorMessageLock); MesCall("WildFill"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } m += *m; w[1] = m - w; t += t[1]; } while ( t < tstop ) { j = t[1]; NCOPY(m,t,j); } v[1] = m-v; break; /* #] EXPRESSION : */ default: /* #[ FUNCTIONS : */ if ( *t >= FUNCTION ) { dflag = 0; na = 0; *m = *t; for ( si = 0; si < setflag; si += 2 ) { if ( t == temp + setlist[si] ) { dflag = DIRTYFLAG; goto ss8; } } s = subs; for ( j = 0; j < i; j++ ) { if ( *s == FUNTOFUN && *t == s[2] ) { *m = s[3]; dirty = 1; dflag = DIRTYFLAG; break; } s += s[1]; } ss8: v = m; if ( *t >= FUNCTION && functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { if ( *m < FUNCTION || functions[*m-FUNCTION].spec < TENSORFUNCTION ) { MLOCK(ErrorMessageLock); MesPrint("Illegal wildcarding of regular function to tensorfunction"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } m++; t++; *m++ = *t++; *m++ = *t++ | dflag; goto Tensors; } m++; t++; *m++ = *t++; *m++ = *t++ | dflag; COPYFUN3(m,t) z = accu; while ( t < u ) { /* do an argument */ if ( *t < 0 ) { /* #[ Simple arguments : */ CBUF *C = cbuf+AT.ebufnum; for ( si = 0; si < setflag; si += 2 ) { if ( *t <= -FUNCTION ) { if ( t == temp + setlist[si] ) { v[2] |= DIRTYFLAG; goto ss10; } } else { if ( t == temp + setlist[si]-1 ) { v[2] |= DIRTYFLAG; goto ss9; } } } if ( *t == -ARGWILD ) { s = subs; for ( j = 0; j < i; j++ ) { if ( *s == ARGTOARG && s[2] == t[1] ) break; s += s[1]; } v[2] |= DIRTYFLAG; w = C->rhs[s[3]]; DEBUG(MesPrint("Thread %w(b): s[3] = %d, w=(%d,%d,%d,%d)",s[3],w[0],w[1],w[2],w[3]);) if ( *w == 0 ) { w++; while ( *w ) { if ( *w > 0 ) j = *w; else if ( *w <= -FUNCTION ) j = 1; else j = 2; NCOPY(m,w,j); } } else { j = *w++; while ( --j >= 0 ) { if ( *w < MINSPEC ) *m++ = -VECTOR; else if ( *w >= 0 && *w < AM.OffsetIndex ) *m++ = -SNUMBER; else *m++ = -INDEX; *m++ = *w++; } } t += 2; dirty = 1; if ( ( *v == NUMARGSFUN || *v == NUMTERMSFUN ) && t >= u && m == v + FUNHEAD ) { m = v; *m++ = SNUMBER; *m++ = 3; *m++ = 0; break; } } else if ( *t <= -FUNCTION ) { *m = *t; s = subs; for ( j = 0; j < i; j++ ) { if ( -*t == s[2] ) { if ( *s == FUNTOFUN ) { *m = -s[3]; dirty = 1; v[2] |= DIRTYFLAG; break; } } s += s[1]; } m++; t++; } else if ( *t == -SYMBOL ) { *m++ = *t++; *m = *t; s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] && *s <= SYMTOSUB ) { dirty = 1; v[2] |= DIRTYFLAG; if ( AR.PolyFunType == 2 && v[0] == AR.PolyFun ) v[2] |= MUSTCLEANPRF; if ( *s == SYMTOSYM ) *m = s[3]; else if ( *s == SYMTONUM ) { m[-1] = -SNUMBER; *m = s[3]; } else if ( *s == SYMTOSUB ) { ToSub: m--; w = C->rhs[s[3]]; DEBUG(MesPrint("Thread %w(c): s[3] = %d, w=(%d,%d,%d,%d)",s[3],w[0],w[1],w[2],w[3]);) s = m; m += 2; while ( *w ) { j = *w; NCOPY(m,w,j); } *s = WORDDIF(m,s); s[1] = 0; *m = 0; if ( t[-1] == -MINVECTOR ) { w = s+2; while ( *w ) { w += *w; w[-1] = -w[-1]; } } if ( ToFast(s,s) ) { if ( *s <= -FUNCTION ) m = s; else m = s + 1; } else m--; } break; } s += s[1]; } m++; t++; } else if ( *t == -INDEX ) { *m++ = *t++; *m = *t; s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == INDTOIND || *s == VECTOVEC ) { *m = s[3]; if ( *m < MINSPEC ) m[-1] = -VECTOR; else if ( *m >= 0 && *m < AM.OffsetIndex ) m[-1] = -SNUMBER; else m[-1] = -INDEX; } else if ( *s == VECTOSUB || *s == INDTOSUB ) { m[-1] = -INDEX; *m = ++AR.CurDum; *z++ = SUBEXPRESSION; *z++ = 4+SUBEXPSIZE; *z++ = s[3]+1; *z++ = 1; *z++ = AT.ebufnum; FILLSUB(z) *z++ = INDTOIND; *z++ = 4; *z++ = FUNNYVEC; *z++ = AR.CurDum; } v[2] |= DIRTYFLAG; dirty = 1; break; } s += s[1]; } m++; t++; } else if ( *t == -VECTOR || *t == -MINVECTOR ) { *m++ = *t++; *m = *t; s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] ) { if ( *s == VECTOVEC ) *m = s[3]; else if ( *s == VECTOMIN ) { *m = s[3]; if ( t[-1] == -VECTOR ) m[-1] = -MINVECTOR; else m[-1] = -VECTOR; } else if ( *s == VECTOSUB ) goto ToSub; dirty = 1; v[2] |= DIRTYFLAG; break; } s += s[1]; } m++; t++; } else if ( *t == -SNUMBER ) { *m++ = *t++; *m = *t; s = subs; for ( j = 0; j < i; j++ ) { if ( *t == s[2] && *s >= NUMTONUM && *s <= NUMTOSUB ) { dirty = 1; v[2] |= DIRTYFLAG; if ( *s == NUMTONUM ) *m = s[3]; else if ( *s == NUMTOSYM ) { m[-1] = -SYMBOL; *m = s[3]; } else if ( *s == NUMTOIND ) { m[-1] = -INDEX; *m = s[3]; } else if ( *s == NUMTOSUB ) goto ToSub; break; } s += s[1]; } m++; t++; } else { ss9: *m++ = *t++; ss10: *m++ = *t++; } na = WORDDIF(z,accu); /* #] Simple arguments : */ } else { w = m; zz = t; NEXTARG(zz) odirt = AN.WildDirt; AN.WildDirt = 0; AR.CompressPointer = accu + na; for ( j = 0; j < ARGHEAD; j++ ) *m++ = *t++; j = 0; adirt = 0; while ( t < zz ) { /* do a term */ if ( ( len = WildFill(BHEAD m,t,sub) ) < 0 ) { MLOCK(ErrorMessageLock); MesCall("WildFill"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( AN.WildDirt ) { adirt = AN.WildDirt; AN.WildDirt = 0; } m += len; t += *t; } *w = WORDDIF(m,w); /* Fill parameter length */ if ( adirt ) { dirty = w[1] = 1; v[2] |= DIRTYFLAG; if ( AR.PolyFunType == 2 && v[0] == AR.PolyFun ) v[2] |= MUSTCLEANPRF; AN.WildDirt = adirt; } else { AN.WildDirt = odirt; } if ( ToFast(w,w) ) { if ( *w <= -FUNCTION ) { if ( *w == NUMARGSFUN || *w == NUMTERMSFUN ) { *w = -SNUMBER; w[1] = 0; m = w + 2; } else m = w+1; } else m = w+2; } AR.CompressPointer = oldcpointer; } } v[1] = WORDDIF(m,v); /* Fill function length */ s = accu; NCOPY(m,s,na); /* Now some code to speed up a few special cases */ if ( v[0] == EXPONENT ) { if ( v[1] == FUNHEAD+4 && v[FUNHEAD] == -SYMBOL && v[FUNHEAD+2] == -SNUMBER && v[FUNHEAD+3] < MAXPOWER && v[FUNHEAD+3] > -MAXPOWER ) { v[0] = SYMBOL; v[1] = 4; v[2] = v[FUNHEAD+1]; v[3] = v[FUNHEAD+3]; m = v+4; } else if ( v[1] == FUNHEAD+ARGHEAD+11 && v[FUNHEAD] == ARGHEAD+9 && v[FUNHEAD+ARGHEAD] == 9 && v[FUNHEAD+ARGHEAD+1] == DOTPRODUCT && v[FUNHEAD+ARGHEAD+8] == 3 && v[FUNHEAD+ARGHEAD+7] == 1 && v[FUNHEAD+ARGHEAD+6] == 1 && v[FUNHEAD+ARGHEAD+5] == 1 && v[FUNHEAD+ARGHEAD+9] == -SNUMBER && v[FUNHEAD+ARGHEAD+10] < MAXPOWER && v[FUNHEAD+ARGHEAD+10] > -MAXPOWER ) { v[0] = DOTPRODUCT; v[1] = 5; v[2] = v[FUNHEAD+ARGHEAD+3]; v[3] = v[FUNHEAD+ARGHEAD+4]; v[4] = v[FUNHEAD+ARGHEAD+10]; m = v+5; } } } else { while ( t < u ) *m++ = *t++; } /* #] FUNCTIONS : */ } t = uu; } while ( t < r ); t = from; /* Copy coefficient */ t += *t; if ( r < t ) do { *m++ = *r++; } while ( r < t ); if ( ( sgn & 1 ) != 0 ) m[-1] = -m[-1]; *to = WORDDIF(m,to); if ( dirty ) AN.WildDirt = dirty; return(*to); } /* #] WildFill : #[ ResolveSet : WORD ResolveSet(from,to,subs) The set syntax is: SET,length,subterm,where,whichmember[,where,whichmember] setlength is 2*n+1 with n the number of set substitutions. length = setlength + subtermlength + 2 At `where' is the number of the set and `whichmember' is the number of the element. This is still a symbol/dollar and we have to find the substitution in the wildcards. The output is the subterm in which the setelements have been substituted. This is ready for further wildcard substitutions. */ int ResolveSet(PHEAD WORD *from, WORD *to, WORD *subs) { GETBIDENTITY WORD *m, *s, *w, j, i, ii, i3, flag, num; DOLLARS d = 0; #ifdef WITHPTHREADS int nummodopt, dtype = -1; #endif m = to; /* pointer in output */ s = from + 2; w = s + s[1]; while ( s < w ) *m++ = *s++; j = (from[1] - WORDDIF(w,from) ) >> 1; m = subs + subs[1]; subs += SUBEXPSIZE; s = subs; i = 0; while ( s < m ) { i++; s += s[1]; } m = to; if ( *m >= FUNCTION && functions[*m-FUNCTION].spec >= TENSORFUNCTION ) flag = 0; else flag = 1; while ( --j >= 0 ) { if ( w[1] >= 0 ) { s = subs; for ( ii = 0; ii < i; ii++ ) { if ( *s == SYMTONUM && s[2] == w[1] ) { num = s[3]; goto GotOne; } s += s[1]; } MLOCK(ErrorMessageLock); MesPrint(" Unresolved setelement during substitution"); MUNLOCK(ErrorMessageLock); return(-1); } else { /* Dollar ! */ d = Dollars - w[1]; #ifdef WITHPTHREADS if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( -w[1] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif if ( d->type == DOLNUMBER || d->type == DOLTERMS ) { if ( d->where[0] == 4 && d->where[3] == 3 && d->where[2] == 1 && d->where[1] > 0 && d->where[4] == 0 ) { num = d->where[1]; goto GotOne; } } else if ( d->type == DOLINDEX ) { if ( d->index > 0 && d->index < AM.OffsetIndex ) { num = d->index; goto GotOne; } } else if ( d->type == DOLARGUMENT ) { if ( d->where[0] == -SNUMBER && d->where[1] > 0 ) { num = d->where[1]; goto GotOne; } } else if ( d->type == DOLWILDARGS ) { if ( d->where[0] == 1 && d->where[1] > 0 && d->where[1] < AM.OffsetIndex ) { num = d->where[1]; goto GotOne; } if ( d->where[0] == 0 && d->where[1] < 0 && d->where[3] == 0 ) { if ( ( d->where[1] == -SNUMBER && d->where[2] > 0 ) || ( d->where[1] == -INDEX && d->where[2] > 0 && d->where[2] < AM.OffsetIndex ) ) { num = d->where[2]; goto GotOne; } } } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("Unusable type of variable $%s in set substitution", AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); return(-1); } GotOne:; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif ii = m[*w]; if ( ii >= 2*MAXPOWER ) i3 = ii - 2*MAXPOWER; else if ( ii <= -2*MAXPOWER ) i3 = -ii - 2*MAXPOWER; else i3 = ( ii >= 0 ) ? ii: -ii - 1; if ( num > ( Sets[i3].last - Sets[i3].first ) || num <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Array bound check during set substitution"); MesPrint(" value is %d",num); MUNLOCK(ErrorMessageLock); return(-1); } m[*w] = (SetElements+Sets[i3].first)[num-1]; if ( Sets[i3].type == CSYMBOL && m[*w] > MAXPOWER ) { if ( ii >= 2*MAXPOWER ) m[*w] -= 2*MAXPOWER; else if ( ii <= -2*MAXPOWER ) m[*w] = -(m[*w] - 2*MAXPOWER); else { m[*w] -= MAXPOWER; if ( m[*w] < MAXPOWER ) m[*w] -= 2*MAXPOWER; if ( flag ) MakeDirty(m,m+*w,1); } } else if ( Sets[i3].type == CSYMBOL ) { if ( ii >= 2*MAXPOWER ) m[*w] += 2*MAXPOWER; else if ( ii <= -2*MAXPOWER ) m[*w] = -m[*w] - 2*MAXPOWER; else if ( ii < 0 ) m[*w] = - m[*w]; } else if ( ii < 0 ) m[*w] = - m[*w]; w += 2; } m = to; if ( *m >= FUNCTION && functions[*m-FUNCTION].spec >= TENSORFUNCTION ) { w = from + 2 + from[3]; if ( *w == 0 ) { /* We had function -> tensor */ m = from + 2 + FUNHEAD; s = to + FUNHEAD; while ( m < w ) { if ( *m == -INDEX || *m == -VECTOR ) {} else if ( *m == -ARGWILD ) { *s++ = FUNNYWILD; } else { MLOCK(ErrorMessageLock); MesPrint("Illegal argument in tensor after set substitution"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } *s++ = m[1]; m += 2; } to[1] = WORDDIF(s,to); } } return(0); } /* #] ResolveSet : #[ ClearWild : void ClearWild() Clears the current wildcard settings and makes them ready for CheckWild and AddWild. */ void ClearWild(PHEAD0) { GETBIDENTITY WORD n, nn, *w; n = (AN.WildValue[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; /* Number of wildcards */ AN.NumWild = nn = n; if ( n > 0 ) { w = AT.WildMask; do { *w++ = 0; } while ( --n > 0 ); w = AN.WildValue; do { if ( *w == SYMTONUM ) *w = SYMTOSYM; w += w[1]; } while ( --nn > 0 ); } } /* #] ClearWild : #[ AddWild : WORD AddWild(oldnumber,type,newnumber) Adds a wildcard assignment. Extra parameter in AN.argaddress; */ int AddWild(PHEAD WORD oldnumber, WORD type, WORD newnumber) { GETBIDENTITY WORD *w, *m, n, k, i = -1; CBUF *C = cbuf+AT.ebufnum; WORD eattensor = type & EATTENSOR; type = type & ~EATTENSOR; DEBUG(WORD *mm;) AN.WildReserve = 0; m = AT.WildMask; w = AN.WildValue; n = AN.NumWild; if ( n <= 0 ) { return(-1); } if ( type <= SYMTOSUB ) { do { if ( w[2] == oldnumber && *w <= SYMTOSUB ) { if ( n > 1 && w[4] == SETTONUM ) i = w[7]; *w = type; if ( *m != 2 ) *m = 1; if ( type != SYMTOSUB ) { if ( type == SYMTONUM ) AN.MaskPointer = m; w[3] = newnumber; goto FlipOn; } m = AddRHS(AT.ebufnum,1); w[3] = C->numrhs; w = AN.argaddress; DEBUG(mm = m;) n = *w - ARGHEAD; w += ARGHEAD; while ( (m + n + 10) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,4); while ( --n >= 0 ) *m++ = *w++; *m++ = 0; C->rhs[C->numrhs+1] = m; DEBUG(MesPrint("Thread %w(d): m=(%d,%d,%d,%d)(%d)",mm[0],mm[1],mm[2],mm[3],C->numrhs);) C->Pointer = m; goto FlipOn; } m++; w += w[1]; } while ( --n > 0 ); } else if ( type == ARGTOARG ) { do { if ( w[2] == oldnumber && *w == ARGTOARG ) { *m = 1; m = AddRHS(AT.ebufnum,1); w[3] = C->numrhs; w = AN.argaddress; DEBUG(mm=m;) if ( eattensor ) { n = newnumber; *m++ = n; w = AN.argaddress; } else { while ( --newnumber >= 0 ) { NEXTARG(w) } n = WORDDIF(w,AN.argaddress); w = AN.argaddress; *m++ = 0; } while ( (m + n + 10) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,5); DEBUG(if ( mm != m-1 ) MesPrint("Thread %w(e): Alarm!"); mm = m-1;) while ( --n >= 0 ) *m++ = *w++; *m++ = 0; C->rhs[C->numrhs+1] = m; C->Pointer = m; DEBUG(MesPrint("Thread %w(e): w=(%d,%d,%d,%d)(%d)",mm[0],mm[1],mm[2],mm[3],C->numrhs);) return(0); } m++; w += w[1]; } while ( --n > 0 ); } else if ( type == ARLTOARL ) { do { if ( w[2] == oldnumber && *w == ARGTOARG ) { WORD **a; *m = 1; m = AddRHS(AT.ebufnum,1); w[3] = C->numrhs; DEBUG(mm=m;) a = (WORD **)(AN.argaddress); n = 0; k = newnumber; while ( --newnumber >= 0 ) { w = *a++; if ( *w > 0 ) n += *w; else if ( *w <= -FUNCTION ) n++; else n += 2; } *m++ = 0; while ( (m + n + 10) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,6); DEBUG(if ( mm != m-1 ) MesPrint("Thread %w(f): Alarm!"); mm = m-1;) a = (WORD **)(AN.argaddress); while ( --k >= 0 ) { w = *a++; if ( *w > 0 ) { n = *w; NCOPY(m,w,n); } else if ( *w <= -FUNCTION ) *m++ = *w++; else { *m++ = *w++; *m++ = *w++; } } *m++ = 0; C->rhs[C->numrhs+1] = m; DEBUG(MesPrint("Thread %w(f): w=(%d,%d,%d,%d)(%d)",mm[0],mm[1],mm[2],mm[3],C->numrhs);) C->Pointer = m; return(0); } m++; w += w[1]; } while ( --n > 0 ); } else if ( type == VECTOSUB || type == INDTOSUB ) { WORD *ss, *sstop, *tt, *ttstop, j, *v1, *v2 = 0; do { if ( w[2] == oldnumber && ( *w == type || ( type == VECTOSUB && ( *w == VECTOVEC || *w == VECTOMIN ) ) || ( type == INDTOSUB && *w == INDTOIND ) ) ) { if ( n > 1 && w[4] == SETTONUM ) i = w[7]; *w = type; *m = 1; m = AddRHS(AT.ebufnum,1); w[3] = C->numrhs; w = AN.argaddress; n = *w - ARGHEAD; w += ARGHEAD; while ( (m + n + 10) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,7); while ( --n >= 0 ) *m++ = *w++; *m++ = 0; C->rhs[C->numrhs+1] = m; C->Pointer = m; m = AddRHS(AT.ebufnum,1); w = AN.argaddress; n = *w - ARGHEAD; w += ARGHEAD; while ( (m + n + 10) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,8); sstop = w + n; while ( w < sstop ) { /* Run over terms */ tt = w + *w; ttstop = tt - ABS(tt[-1]); ss = m; m++; w++; while ( w < ttstop ) { /* Subterms */ if ( *w != INDEX ) { j = w[1]; NCOPY(m,w,j); } else { v1 = m; *m++ = *w++; *m++ = j = *w++; j -= 2; while ( --j >= 0 ) { if ( *w >= MINSPEC ) *m++ = *w++; else v2 = w++; } j = WORDDIF(m,v1); if ( j != v1[1] ) { if ( j <= 2 ) m -= 2; else v1[1] = j; *m++ = VECTOR; *m++ = 4; *m++ = *v2; *m++ = FUNNYVEC; } } } while ( w < tt ) *m++ = *w++; *ss = WORDDIF(m,ss); } *m++ = 0; C->rhs[C->numrhs+1] = m; C->Pointer = m; if ( m > C->Top ) { MLOCK(ErrorMessageLock); MesPrint("Internal problems with extra compiler buffer"); MUNLOCK(ErrorMessageLock); Terminate(-1); } goto FlipOn; } m++; w += w[1]; } while ( --n > 0 ); } else { do { if ( w[2] == oldnumber && ( *w == type || ( type == VECTOVEC && ( *w == VECTOMIN || *w == VECTOSUB ) ) || ( type == VECTOMIN && ( *w == VECTOVEC || *w == VECTOSUB ) ) || ( type == INDTOIND && *w == INDTOSUB ) ) ) { if ( n > 1 && w[4] == SETTONUM ) i = w[7]; *w = type; w[3] = newnumber; *m = 1; goto FlipOn; } m++; w += w[1]; } while ( --n > 0 ); } MLOCK(ErrorMessageLock); MesPrint("Bug in AddWild."); MUNLOCK(ErrorMessageLock); return(-1); FlipOn: if ( i >= 0 ) { m = AT.WildMask; w = AN.WildValue; n = AN.NumWild; while ( --n >= 0 ) { if ( w[2] == i && *w == SYMTONUM ) { *m = 2; return(0); } m++; w += w[1]; } MLOCK(ErrorMessageLock); MesPrint(" Bug in AddWild with passing set[i]"); MUNLOCK(ErrorMessageLock); /* For the moment we want to crash here. That is easier with debugging. */ #ifdef WITHPTHREADS { WORD *s = 0; *s++ = 1; } #endif Terminate(-1); } return(0); } /* #] AddWild : #[ CheckWild : WORD CheckWild(oldnumber,type,newnumber,newval) Tests whether a wildcard assignment is allowed. A return value of zero means that it is allowed (nihil obstat). If the variable has been assigned already its existing assignment is returned in AN.oldvalue and AN.oldtype, which are global variables. Note the special problem with name?set[i]. Here we have to pass an extra assignment. This cannot be done via globals as we call CheckWild sometimes twice before calling AddWild. Trick: Check the assignment of the number and if OK put it in place, but don't alter the used flag (if needed). Then AddWild can alter the used flag but the value is there. As long as this trick is `hanging' we turn on the flag: `AN.WildReserve' which is either turned off by AddWild or by a failing call to CheckWild. With ARGTOARG the tensors give the number of arguments or-ed with EATTENSOR which is at least 8192. */ int CheckWild(PHEAD WORD oldnumber, WORD type, WORD newnumber, WORD *newval) { GETBIDENTITY WORD *w, *m, *s, n, old2, inset; WORD n2, oldval, dirty, i, j; int notflag = 0, retblock = 0; CBUF *C = cbuf+AT.ebufnum; WORD eattensor = type & EATTENSOR; type = type & ~EATTENSOR; m = AT.WildMask; w = AN.WildValue; n = AN.NumWild; if ( n <= 0 ) { AN.oldtype = -1; AN.WildReserve = 0; return(-1); } switch ( type ) { case SYMTONUM : *newval = newnumber; do { if ( w[2] == oldnumber && *w <= SYMTOSUB ) { old2 = *w; if ( !*m ) goto TestSet; AN.MaskPointer = m; if ( *w == SYMTONUM && w[3] == newnumber ) { return(0); } AN.oldtype = old2; AN.oldvalue = w[3]; goto NoMatch; } m++; w += w[1]; } while ( --n > 0 ); break; case SYMTOSYM : *newval = newnumber; do { if ( w[2] == oldnumber && *w <= SYMTOSUB ) { old2 = *w; if ( *w == SYMTOSYM ) { if ( !*m ) goto TestSet; if ( newnumber >= 0 && (w+4) < AN.WildStop && ( w[4] == FROMSET || w[4] == SETTONUM ) && w[7] >= 0 ) goto TestSet; if ( w[3] == newnumber ) return(0); } else { if ( !*m ) goto TestSet; } goto NoM; } m++; w += w[1]; } while ( --n > 0 ); break; case SYMTOSUB : /* Now newval contains the pointer to the argument. */ { /* Search for vector or index nature. If so: reject. */ WORD *ss, *sstop, *tt, *ttstop; ss = newval; sstop = ss + *ss; ss += ARGHEAD; while ( ss < sstop ) { tt = ss + *ss; ttstop = tt - ABS(tt[-1]); ss++; while ( ss < ttstop ) { if ( *ss == INDEX ) goto NoMatch; ss += ss[1]; } ss = tt; } } do { if ( w[2] == oldnumber && *w <= SYMTOSUB ) { old2 = *w; if ( *w == SYMTONUM || *w == SYMTOSYM ) { if ( !*m ) { s = w + w[1]; if ( s >= AN.WildStop || *s != SETTONUM ) goto TestSet; } } else if ( *w == SYMTOSUB ) { if ( !*m ) { s = w + w[1]; if ( s >= AN.WildStop || *s != SETTONUM ) goto TestSet; } n = *newval - 2; newval += 2; m = C->rhs[w[3]]; if ( (C->rhs[w[3]+1] - m - 1) == n ) { while ( n > 0 ) { if ( *m != *newval ) { m++; newval++; break; } m++; newval++; n--; } if ( n <= 0 ) return(0); } } AN.oldtype = old2; AN.oldvalue = w[3]; goto NoMatch; } m++; w += w[1]; } while ( --n > 0 ); break; case ARGTOARG : do { if ( w[2] == oldnumber && *w == ARGTOARG ) { if ( !*m ) return(0); /* nihil obstat */ m = C->rhs[w[3]]; if ( eattensor ) { n = newnumber; if ( *m != 0 ) { if ( n == *m ) { m++; while ( --n >= 0 ) { if ( *m != *newval ) { m++; newval++; break; } m++; newval++; } if ( n < 0 ) return(0); } } else { m++; while ( --n >= 0 ) { if ( *newval != m[1] || ( *m != -INDEX && *m != -VECTOR && *m != -SNUMBER ) ) break; m += 2; newval++; } if ( n < 0 && *m == 0 ) return(0); } } else { i = newnumber; if ( *m != 0 ) { /* Tensor field */ if ( *m == i ) { m++; while ( --i >= 0 ) { if ( *m != newval[1] || ( *newval != -VECTOR && *newval != -INDEX && *newval != -SNUMBER ) ) break; newval += 2; m++; } if ( i < 0 ) return(0); } } else { m++; s = newval; while ( --i >= 0 ) { NEXTARG(s) } n = WORDDIF(s,newval); while ( --n >= 0 ) { if ( *m != *newval ) { m++; newval++; break; } m++; newval++; } if ( n < 0 && *m == 0 ) return(0); } } AN.oldtype = *w; AN.oldvalue = w[3]; goto NoMatch; } m++; w += w[1]; } while ( --n > 0 ); break; case ARLTOARL : do { if ( w[2] == oldnumber && *w == ARGTOARG ) { WORD **a; if ( !*m ) return(0); /* nihil obstat */ m = C->rhs[w[3]]; i = newnumber; a = (WORD **)newval; if ( *m != 0 ) { /* Tensor field */ if ( *m == i ) { m++; while ( --i >= 0 ) { s = *a++; if ( *m != s[1] || ( *s != -VECTOR && *s != -INDEX && *s != -SNUMBER ) ) break; m++; } if ( i < 0 ) return(0); } } else { m++; while ( --i >= 0 ) { s = *a++; if ( *s > 0 ) { n = *s; while ( --n >= 0 ) { if ( *s != *m ) { s++; m++; break; } s++; m++; } if ( n >= 0 ) break; } else if ( *s <= -FUNCTION ) { if ( *s != *m ) { s++; m++; break; } s++; m++; } else { if ( *s != *m ) { s++; m++; break; } s++; m++; if ( *s != *m ) { s++; m++; break; } s++; m++; } } if ( i < 0 && *m == 0 ) return(0); } AN.oldtype = *w; AN.oldvalue = w[3]; goto NoMatch; } m++; w += w[1]; } while ( --n > 0 ); break; case VECTOSUB : case INDTOSUB : /* Now newval contains the pointer to the argument(s). */ { /* Search for vector or index nature. If not so: reject. */ WORD *ss, *sstop, *tt, *ttstop, count, jt; ss = newval; sstop = ss + *ss; ss += ARGHEAD; while ( ss < sstop ) { tt = ss + *ss; ttstop = tt - ABS(tt[-1]); ss++; count = 0; while ( ss < ttstop ) { if ( *ss == INDEX ) { jt = ss[1] - 2; ss += 2; while ( --jt >= 0 ) { if ( *ss < MINSPEC ) count++; ss++; } } else ss += ss[1]; } if ( count != 1 ) goto NoMatch; ss = tt; } } do { if ( w[2] == oldnumber ) { old2 = *w; if ( ( type == VECTOSUB && ( *w == VECTOVEC || *w == VECTOMIN ) ) || ( type == INDTOSUB && *w == INDTOIND ) ) { if ( !*m ) goto TestSet; AN.oldtype = old2; AN.oldvalue = w[3]; goto NoMatch; } else if ( *w == type ) { if ( !*m ) goto TestSet; if ( type != INDTOIND && type != INDTOSUB ) { /* Prevent double index */ n = *newval - 2; newval += 2; m = C->rhs[w[3]]; if ( (C->rhs[w[3]+1] - m - 1) == n ) { while ( n > 0 ) { if ( *m != *newval ) { m++; newval++; break; } m++; newval++; n--; } if ( n <= 0 ) return(0); } } AN.oldtype = old2; AN.oldvalue = w[3]; goto NoMatch; } } m++; w += w[1]; } while ( --n > 0 ); break; default : *newval = newnumber; do { if ( w[2] == oldnumber ) { if ( *w == type ) { old2 = *w; if ( !*m ) goto TestSet; if ( newnumber >= 0 && (w+4) < AN.WildStop && ( w[4] == FROMSET || w[4] == SETTONUM ) && w[7] >= 0 ) goto TestSet; if ( newnumber < 0 && *w == VECTOVEC && (w+4) < AN.WildStop && ( w[4] == FROMSET || w[4] == SETTONUM ) && w[7] >= 0 ) goto TestSet; /* The next statement kills multiple indices -> vector */ if ( *w == INDTOIND && w[3] < 0 ) goto NoMatch; if ( w[3] == newnumber ) { if ( *w != FUNTOFUN || newnumber < FUNCTION || functions[newnumber-FUNCTION].spec == functions[oldnumber-FUNCTION].spec ) return(0); } AN.oldtype = old2; AN.oldvalue = w[3]; goto NoMatch; } else if ( ( type == VECTOVEC && ( *w == VECTOSUB || *w == VECTOMIN ) ) || ( type == INDTOIND && *w == INDTOSUB ) ) { if ( *m ) goto NoMatch; old2 = *w; goto TestSet; } else if ( type == VECTOMIN && ( *w == VECTOSUB || *w == VECTOVEC ) ) { if ( *m ) goto NoMatch; old2 = *w; goto TestSet; } } m++; w += w[1]; if ( n > 1 && ( *w == FROMSET || *w == SETTONUM ) ) { n--; m++; w += w[1]; } } while ( --n > 0 ); break; } AN.oldtype = -1; AN.oldvalue = -1; AN.WildReserve = 0; MLOCK(ErrorMessageLock); MesPrint("Inconsistency in Wildcard prototype."); MUNLOCK(ErrorMessageLock); return(-1); NoMatch: AN.WildReserve = 0; return(1+retblock); /* Here we test the compatibility with a set specification. */ TestSet: dirty = *m; oldval = w[3]; w += w[1]; if ( w < AN.WildStop && ( *w == FROMSET || *w == SETTONUM ) ) { WORD k; s = w; j = w[2]; n2 = w[3]; /* if SETTONUM: x?j[n2] if FROMSET: x?j?n2 or x?j and n2 = -WOLDOFFSET. */ if ( j > WILDOFFSET ) { j -= 2*WILDOFFSET; notflag = 1; /* ??????? */ AN.oldtype = -1; AN.oldvalue = -1; } if ( j < AM.NumFixedSets ) { /* special set */ retblock = 1; switch ( j ) { case POS_: if ( type != SYMTONUM || newnumber <= 0 ) goto NoMnot; break; case POS0_: if ( type != SYMTONUM || newnumber < 0 ) goto NoMnot; break; case NEG_: if ( type != SYMTONUM || newnumber >= 0 ) goto NoMnot; break; case NEG0_: if ( type != SYMTONUM || newnumber > 0 ) goto NoMnot; break; case EVEN_: if ( type != SYMTONUM || ( newnumber & 1 ) != 0 ) goto NoMnot; break; case ODD_: if ( type != SYMTONUM || ( newnumber & 1 ) == 0 ) goto NoMnot; break; case Z_: if ( type != SYMTONUM ) goto NoMnot; break; case SYMBOL_: if ( type != SYMTOSYM ) goto NoMnot; break; case FIXED_: if ( type != INDTOIND || newnumber >= AM.OffsetIndex || newnumber < 0 ) goto NoMnot; break; case INDEX_: if ( type != INDTOIND || newnumber < 0 ) goto NoMnot; break; case Q_: if ( type == SYMTONUM ) break; if ( type == SYMTOSUB ) { WORD *ss, *sstop; ss = newval; sstop = ss + *ss; ss += ARGHEAD; if ( ss >= sstop ) break; if ( ss + *ss < sstop ) goto NoMnot; if ( ABS(sstop[-1]) == ss[0]-1 ) break; } goto NoMnot; case DUMMYINDEX_: if ( type != INDTOIND || newnumber < AM.IndDum || newnumber >= AM.IndDum+MAXDUMMIES ) goto NoMnot; break; case VECTOR_: if ( type != VECTOVEC ) goto NoMnot; break; default: goto NoMnot; } Mnot: if ( notflag ) goto NoM; return(0); NoMnot: if ( !notflag ) goto NoM; return(0); } else if ( Sets[j].type == CRANGE ) { if ( ( type == SYMTONUM ) || ( type == INDTOIND && ( newnumber > 0 && newnumber <= AM.OffsetIndex ) ) ) { if ( Sets[j].first < MAXPOWER ) { if ( newnumber >= Sets[j].first ) goto NoMnot; } else if ( Sets[j].first < 3*MAXPOWER ) { if ( newnumber+2*MAXPOWER > Sets[j].first ) goto NoMnot; } if ( Sets[j].last > -MAXPOWER ) { if ( newnumber <= Sets[j].last ) goto NoMnot; } else if ( Sets[j].last > -3*MAXPOWER ) { if ( newnumber-2*MAXPOWER < Sets[j].last ) goto NoMnot; } goto Mnot; } goto NoMnot; } /* Now we have to determine which set element */ w = SetElements + Sets[j].first; m = SetElements + Sets[j].last; if ( w == m ) { /* The set is empty! This is not a match unless we have !{}, in which case it is. */ if ( notflag ) return 0; AN.oldtype = old2; AN.oldvalue = oldval; goto NoMatch; } if ( ( Sets[j].flags & ORDEREDSET ) == ORDEREDSET ) { /* We search first and ask questions later */ i = BinarySearch(w,Sets[j].last-Sets[j].first,newnumber); if ( i < 0 ) { /* no matter what, it is not in the set. */ goto NoMnot; } else { /* We can set the proper parameters now to make only the checks for the given set element. After that we jump into the appropriate loop. */ w = m = SetElements + i; i++; if ( Sets[j].type == -1 || Sets[j].type == CNUMBER ) { goto insideloop1; } else { goto insideloop2; } } } i = 1; if ( Sets[j].type == -1 || Sets[j].type == CNUMBER ) { do { insideloop1: if ( notflag ) { switch ( type ) { case SYMTOSYM: if ( Sets[j].type == CNUMBER ) {} else { if ( *w == newnumber ) goto NoMatch; } break; case SYMTONUM: case INDTOIND: if ( *w == newnumber ) goto NoMatch; break; default: break; } } else if ( type != SYMTONUM && type != INDTOIND && type != SYMTOSYM ) goto NoMatch; else if ( type == SYMTOSYM && Sets[j].type == CNUMBER ) goto NoMatch; else if ( *w == newnumber ) { if ( *s == SETTONUM ) { if ( n2 == oldnumber && type <= SYMTOSUB ) goto NoMatch; m = AT.WildMask; w = AN.WildValue; n = AN.NumWild; while ( --n >= 0 ) { if ( w[2] == n2 && *w <= SYMTOSUB ) { if ( !*m ) { *w = SYMTONUM; w[3] = i; AN.WildReserve = 1; return(0); } if ( *w != SYMTONUM ) goto NoMatch; if ( w[3] == i ) return(0); i = w[3]; j = (SetElements + Sets[j].first)[i]; if ( j == n2 ) return(0); goto NoMatch; } m++; w += w[1]; } } else if ( n2 >= 0 ) { *newval = *(w - Sets[j].first + Sets[n2].first); if ( *newval > MAXPOWER ) *newval -= 2*MAXPOWER; if ( dirty && *newval != oldval ) { *newval = oldval; goto NoMatch; } } return(0); } i++; } while ( ++w < m ); } else { do { insideloop2: inset = *w; if ( notflag ) { switch ( type ) { case SYMTONUM: case SYMTOSYM: if ( ( type == SYMTOSYM && *w == newnumber ) || ( type == SYMTONUM && *w-2*MAXPOWER == newnumber ) ) { goto NoMatch; } /* fall through */ case SYMTOSUB: if ( *w < 0 ) { WORD *mm = AT.WildMask, *mmm, *part; WORD *ww = AN.WildValue; WORD nn = AN.NumWild; k = -*w; while ( --nn >= 0 ) { if ( *mm && ww[2] == k && ww[0] == type ) { if ( type != SYMTOSUB ) { if ( ww[3] == newnumber ) goto NoMatch; } else { mmm = C->rhs[ww[3]]; nn = *newval-2; part = newval+2; if ( (C->rhs[ww[3]+1]-mmm-1) == nn ) { while ( --nn >= 0 ) { if ( *mmm != *part ) { mmm++; part++; break; } mmm++; part++; } if ( nn < 0 ) goto NoMatch; } } break; } mm++; ww += ww[1]; } } break; case VECTOMIN: if ( type == VECTOMIN ) { if ( inset >= AM.OffsetVector ) { i++; continue; } inset += WILDMASK; } /* fall through */ case VECTOVEC: if ( inset == newnumber ) goto NoMatch; /* fall through */ case VECTOSUB: if ( inset - WILDOFFSET >= AM.OffsetVector ) { WORD *mm = AT.WildMask, *mmm, *part; WORD *ww = AN.WildValue; WORD nn = AN.NumWild; k = inset - WILDOFFSET; while ( --nn >= 0 ) { if ( *mm && ww[2] == k && ww[0] == type ) { if ( type == VECTOVEC ) { if ( ww[3] == newnumber ) goto NoMatch; } else { mmm = C->rhs[ww[3]]; nn = *newval-2; part = newval+2; if ( (C->rhs[ww[3]+1]-mmm-1) == nn ) { while ( --nn >= 0 ) { if ( *mmm != *part ) { mmm++; part++; break; } mmm++; part++; } if ( nn < 0 ) goto NoMatch; } } break; } mm++; ww += ww[1]; } } break; case INDTOIND: if ( *w == newnumber ) goto NoMatch; /* fall through */ case INDTOSUB: if ( *w - (WORD)WILDMASK >= AM.OffsetIndex ) { WORD *mm = AT.WildMask, *mmm, *part; WORD *ww = AN.WildValue; WORD nn = AN.NumWild; k = *w - WILDMASK; while ( --nn >= 0 ) { if ( *mm && ww[2] == k && ww[0] == type ) { if ( type == INDTOIND ) { if ( ww[3] == newnumber ) goto NoMatch; } else { mmm = C->rhs[ww[3]]; nn = *newval-2; part = newval+2; if ( (C->rhs[ww[3]+1]-mmm-1) == nn ) { while ( --nn >= 0 ) { if ( *mmm != *part ) { mmm++; part++; break; } mmm++; part++; } if ( nn < 0 ) goto NoMatch; } } break; } mm++; ww += ww[1]; } } break; case FUNTOFUN: if ( *w == newnumber ) goto NoMatch; if ( ( type == FUNTOFUN && ( k = *w - WILDMASK ) > FUNCTION ) ) { WORD *mm = AT.WildMask; WORD *ww = AN.WildValue; WORD nn = AN.NumWild; while ( --nn >= 0 ) { if ( *mm && ww[2] == k && ww[0] == type ) { if ( ww[3] == newnumber ) goto NoMatch; break; } mm++; ww += ww[1]; } } default: break; } } else { if ( type == VECTOMIN ) { if ( inset >= AM.OffsetVector ) { i++; continue; } inset += WILDMASK; } if ( ( inset == newnumber && type != SYMTONUM ) || ( type == SYMTONUM && inset-2*MAXPOWER == newnumber ) ) { if ( *s == SETTONUM ) { if ( n2 == oldnumber && type <= SYMTOSUB ) goto NoMatch; m = AT.WildMask; w = AN.WildValue; n = AN.NumWild; while ( --n >= 0 ) { if ( w[2] == n2 && *w <= SYMTOSUB ) { if ( !*m ) { *w = SYMTONUM; w[3] = i; AN.WildReserve = 1; return(0); } if ( *w != SYMTONUM ) goto NoMatch; if ( w[3] == i ) return(0); i = w[3]; j = (SetElements + Sets[j].first)[i]; if ( j == n2 ) return(0); goto NoMatch; } m++; w += w[1]; } } else if ( n2 >= 0 ) { *newval = *(w - Sets[j].first + Sets[n2].first); if ( *newval > MAXPOWER ) *newval -= 2*MAXPOWER; if ( dirty && *newval != oldval ) { *newval = oldval; goto NoMatch; } } return(0); } } i++; } while ( ++w < m ); } if ( notflag ) return(0); AN.oldtype = old2; AN.oldvalue = oldval; goto NoMatch; } else { return(0); } NoM: AN.oldtype = old2; AN.oldvalue = w[3]; goto NoMatch; } /* #] CheckWild : #] Wildcards : #[ DenToFunction : Renames the denominator function into a function with the given number. For the syntax see Denominators,function; */ int DenToFunction(WORD *term, WORD numfun) { int action = 0; WORD *t, *tstop, *tnext, *arg, *argstop, *targ; t = term+1; tstop = term + *term; tstop -= ABS(tstop[-1]); while ( t < tstop ) { if ( *t == DENOMINATOR ) { *t = numfun; t[2] |= DIRTYFLAG; action = 1; } tnext = t + t[1]; if ( *t >= FUNCTION && functions[*t-FUNCTION].spec <= 0 ) { arg = t + FUNHEAD; while ( arg < tnext ) { if ( *arg > 0 ) { targ = arg + ARGHEAD; argstop = arg + *arg; while ( targ < argstop ) { if ( DenToFunction(targ,numfun) ) { arg[1] |= DIRTYFLAG; t[2] |= DIRTYFLAG; action = 1; } targ += *targ; } arg = argstop; } else if ( *arg <= -FUNCTION ) arg++; else arg += 2; } } t = tnext; } return(action); } /* #] DenToFunction : */ form-5.0.1/sources/polygcd.h0000644000175100017510000000711715217035721011451 #pragma once /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #include #include class poly; // polynomial class class gcd_heuristic_failed {}; // class for throwing exceptions // whether or not to use the heuristic before Zippel's algorithm #define POLYGCD_USE_HEURISTIC // maximum number of words in a coefficient for gcd_heuristic to continue const int POLYGCD_HEURISTIC_MAX_DIGITS = 1000; // maximum number of retries after the heuristic has failed const int POLYGCD_HEURISTIC_MAX_TRIES = 10; // a fudge factor, which improves efficiency const int POLYGCD_HEURISTIC_MAX_ADD_RANDOM = 10; // maximum cached power in substitute_last and sparse_interpolation_get_mul_list const int POLYGCD_RAISPOWMOD_CACHE_SIZE = 1000; namespace polygcd { // functions to call the gcd routines const poly integer_gcd (const poly &a, const poly &b); const poly integer_content (const poly &a); const poly gcd (const poly &a, const poly &b); const poly content_univar (const poly &a, int x); const poly content_multivar (const poly &a, int x); const std::vector coefficient_list_gcd (const std::vector &a, const std::vector &b, WORD p); // internal functions const poly gcd_heuristic (const poly &a, const poly &b, const std::vector &x, int max_tries=POLYGCD_HEURISTIC_MAX_TRIES); const poly gcd_Euclidean (const poly &a, const poly &b); const poly gcd_modular (const poly &a, const poly &b, const std::vector &x); const poly gcd_modular_dense_interpolation (const poly &a, const poly &b, const std::vector &x, const poly &s); const poly gcd_modular_sparse_interpolation (const poly &a, const poly &b, const std::vector &x, const poly &s); const std::vector sparse_interpolation_get_mul_list (const poly &a, const std::vector &x, const std::vector &c); void sparse_interpolation_mul_poly (poly &a, const std::vector &m); const poly sparse_interpolation_reduce_poly (const poly &a, const std::vector &x); const poly sparse_interpolation_fix_poly (const poly &a, int x); const poly chinese_remainder (const poly &a1, const poly &m1, const poly &a2, const poly &m2); const poly substitute(const poly &a, int x, int c); const std::map,poly> full_bracket(const poly &a, const std::vector& filter); const poly bracket(const poly &a, const std::vector& pattern, const std::vector& filter); const std::map,int> bracket_count(const poly &a, const std::vector& filter); const poly gcd_linear (const poly &a, const poly &b); } form-5.0.1/sources/flintwrap.cc0000644000175100017510000002173015217035721012151 /** @file flintwrap.cc * * Contains functions to call FLINT interface from the rest of FORM. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ extern "C" { #include "form3.h" } #include #include "flintinterface.h" /* #[ flint_final_cleanup_thread : */ void flint_final_cleanup_thread(void) { flint::cleanup(); } /* #] flint_final_cleanup_thread : #[ flint_final_cleanup_master : */ void flint_final_cleanup_master(void) { flint::cleanup_master(); } /* #] flint_final_cleanup_master : #[ flint_div : */ WORD* flint_div(PHEAD WORD *a, WORD *b, const WORD must_fit_term) { // Extract expressions vector e; e.reserve(2); e.push_back(a); e.push_back(b); const bool with_arghead = false; const bool sort_vars = false; const flint::var_map_t var_map = flint::get_variables(e, with_arghead, sort_vars); const bool return_rem = false; if ( var_map.size() > 1 ) { return flint::divmod_mpoly(BHEAD a, b, return_rem, must_fit_term, var_map, sort_vars); } else { return flint::divmod_poly(BHEAD a, b, return_rem, must_fit_term, var_map); } } /* #] flint_div : #[ flint_factorize_argument : */ int flint_factorize_argument(PHEAD WORD *argin, WORD *argout) { const bool with_arghead = true; const bool sort_vars = true; const flint::var_map_t var_map = flint::get_variables(vector(1,argin), with_arghead, sort_vars); const bool is_fun_arg = true; if ( var_map.size() > 1 ) { flint::factorize_mpoly(BHEAD argin, argout, with_arghead, is_fun_arg, var_map, sort_vars); } else { flint::factorize_poly(BHEAD argin, argout, with_arghead, is_fun_arg, var_map); } return 0; } /* #] flint_factorize_argument : #[ flint_factorize_dollar : */ WORD* flint_factorize_dollar(PHEAD WORD *argin) { const bool with_arghead = false; const bool sort_vars = true; const flint::var_map_t var_map = flint::get_variables(vector(1,argin), with_arghead, sort_vars); const bool is_fun_arg = false; if ( var_map.size() > 1 ) { return flint::factorize_mpoly(BHEAD argin, NULL, with_arghead, is_fun_arg, var_map, sort_vars); } else { return flint::factorize_poly(BHEAD argin, NULL, with_arghead, is_fun_arg, var_map); } } /* #] flint_factorize_dollar : #[ flint_gcd : */ WORD* flint_gcd(PHEAD WORD *a, WORD *b, const WORD must_fit_term) { // Extract expressions vector e; e.reserve(2); e.push_back(a); e.push_back(b); const bool with_arghead = false; const bool sort_vars = true; const flint::var_map_t var_map = flint::get_variables(e, with_arghead, sort_vars); if ( var_map.size() > 1 ) { return flint::gcd_mpoly(BHEAD a, b, must_fit_term, var_map, sort_vars); } else { return flint::gcd_poly(BHEAD a, b, must_fit_term, var_map); } } /* #] flint_gcd : #[ flint_inverse : */ WORD* flint_inverse(PHEAD WORD *a, WORD *b) { // Extract expressions vector e; e.reserve(2); e.push_back(a); e.push_back(b); const flint::var_map_t var_map = flint::get_variables(e, false, false); if ( var_map.size() > 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint_inverse: error: only univariate polynomials are supported."); MUNLOCK(ErrorMessageLock); Terminate(-1); } return flint::inverse_poly(BHEAD a, b, var_map); } /* #] flint_inverse : #[ flint_mul : */ WORD* flint_mul(PHEAD WORD *a, WORD *b) { // Extract expressions vector e; e.reserve(2); e.push_back(a); e.push_back(b); const bool with_arghead = false; const bool sort_vars = false; const flint::var_map_t var_map = flint::get_variables(e, with_arghead, sort_vars); if ( var_map.size() > 1 ) { return flint::mul_mpoly(BHEAD a, b, var_map, sort_vars); } else { return flint::mul_poly(BHEAD a, b, var_map); } } /* #] flint_mul : #[ flint_ratfun_add : */ WORD* flint_ratfun_add(PHEAD WORD *t1, WORD *t2) { if ( AR.PolyFunExp == 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint_ratfun_add: PolyFunExp unimplemented."); MUNLOCK(ErrorMessageLock); Terminate(-1); } WORD *oldworkpointer = AT.WorkPointer; // Extract expressions: the num and den of both prf vector e; e.reserve(4); for (WORD *t=t1+FUNHEAD; t 1 ) { flint::ratfun_add_mpoly(BHEAD t1, t2, oldworkpointer, var_map, sort_vars); } else { flint::ratfun_add_poly(BHEAD t1, t2, oldworkpointer, var_map); } return oldworkpointer; } /* #] flint_ratfun_add : #[ flint_ratfun_normalize : */ int flint_ratfun_normalize(PHEAD WORD *term) { // The length of the coefficient const WORD ncoeff = (term + *term)[-1]; // The end of the term data, before the coefficient: const WORD *tstop = term + *term - ABS(ncoeff); // Search the term for multiple PolyFun or one dirty one. unsigned num_polyratfun = 0; for (WORD *t = term+1; t < tstop; t += t[1]) { if (*t == AR.PolyFun) { // Found one! num_polyratfun++; if ((t[2] & MUSTCLEANPRF) != 0) { // Dirty, increment again to force normalisation for single PolyFun num_polyratfun++; } if (num_polyratfun > 1) { // We're not counting all occurrences, just determinining if there // is something to be done. break; } } } if (num_polyratfun <= 1) { // There is nothing to do, return early return 0; } // When there are polyratfun with only one argument: rename them temporarily to TMPPOLYFUN. for (WORD *t = term+1; t < tstop; t += t[1]) { if (*t == AR.PolyFun && (t[1] == FUNHEAD+t[FUNHEAD] || t[1] == FUNHEAD+2 ) ) { *t = TMPPOLYFUN; } } // Extract all variables in the polyfuns // Collect pointers to each relevant argument vector e; e.reserve(4); // There could be more than 4 args in principle, but 4 is probably common. for (WORD *t=term+1; t 1 ) { flint::ratfun_normalize_mpoly(BHEAD term, var_map, sort_vars); } else { flint::ratfun_normalize_poly(BHEAD term, var_map); } // Undo renaming of single-argument PolyFun const WORD *new_tstop = term + *term - ABS((term + *term)[-1]); for (WORD *t=term+1; t e; e.reserve(2); e.push_back(a); e.push_back(b); const bool with_arghead = false; const bool sort_vars = false; const flint::var_map_t var_map = flint::get_variables(e, with_arghead, sort_vars); const bool return_rem = true; if ( var_map.size() > 1 ) { return flint::divmod_mpoly(BHEAD a, b, return_rem, must_fit_term, var_map, sort_vars); } else { return flint::divmod_poly(BHEAD a, b, return_rem, must_fit_term, var_map); } } /* #] flint_rem : #[ flint_check_version : */ /** * Checks the FLINT library version at runtime. * * This function should be called at startup. * The program will terminate if a known buggy version of FLINT is detected. */ void flint_check_version(void) { bool ok = true; std::stringstream ss(flint_version); int major, minor, patch; char dot1, dot2; if ( ss >> major >> dot1 >> minor >> dot2 >> patch ) { if ( dot1 != '.' || dot2 != '.' || major < 0 || minor < 0 || patch < 0 ) { ok = false; } else if ( major * 10000 + minor * 100 + patch < 30200 ) { // flint < 3.2.0: https://github.com/form-dev/form/issues/679 ok = false; } } else { ok = false; } if ( !ok ) { MesPrint("Bad FLINT version detected at runtime: %s",flint_version); Terminate(-2); } } /* #] flint_check_version : */ form-5.0.1/sources/notation.c0000644000175100017510000007063515217035721011643 /** @file notation.c * * Contains the functions that deal with the rewriting and manipulation * of expressions/terms in polynomial representation. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include "form3.h" /* #] Includes : #[ NormPolyTerm : Brings a term to normal form. This routine knows objects of the following types: SYMBOL HAAKJE SNUMBER LNUMBER The SNUMBER and LNUMBER are worked into the coefficient. One of the essences here is that everything can be done in place. */ int NormPolyTerm(PHEAD WORD *term) { WORD *tcoef, ncoef, *tstop, *tfill, *t, *tt; int equal, i; WORD *r1, *r2, *r3, *r4, *r5, *rfirst, rv; WORD *lnum, nnum; /* Scratch, originally for factorials */ /* One: find the coefficient */ tcoef = term+*term; ncoef = tcoef[-1]; tstop = tcoef - ABS(tcoef[-1]); tfill = t = term + 1; rfirst = 0; if ( t >= tstop ) { return(*term); } while ( t < tstop ) { switch ( *t ) { case SYMBOL: if ( rfirst == 0 ) { /* Here we only need to sort 1: assume no equals. Bubble. */ rfirst = t; r2 = rfirst+4; tt = r3 = t + t[1]; equal = 0; while ( r2 < r3 ) { r1 = r2 - 2; if ( *r2 > *r1 ) { r2 += 2; continue; } if ( *r2 == *r1 ) { r2 += 2; equal = 1; continue; } rv = *r1; *r1 = *r2; *r2 = rv; r1 -= 2; r2 -= 2; r4 = r2 + 2; while ( r1 > t ) { if ( *r2 >= *r1 ) { r2 = r4; break; } rv = *r1; *r1 = *r2; *r2 = rv; r1 -= 2; r2 -= 2; } } /* 2: hunt down the equal objects postpone eliminating zero powers. */ if ( equal ) { r1 = t+2; r2 = r1+2; while ( r2 < r3 ) { if ( *r1 == *r2 ) { r1[1] += r2[1]; r4 = r2+2; while ( r4 < r3 ) *r2++ = *r4++; t[1] -= 2; r2 = r1 + 2; r3 -= 2; } } } } else { /* Here we only need to insert */ r1 = t + 2; tt = r3 = t + t[1]; while ( r1 < r3 ) { r2 = rfirst+2; r4 = rfirst + rfirst[1]; while ( r2 < r4 ) { if ( *r1 == *r2 ) { r2[1] += r1[1]; break; } else if ( *r2 > *r1 ) { r5 = r4; while ( r5 > r2 ) { r5[1] = r5[-1]; r5[0] = r5[-2]; r5 -= 2; } rfirst[1] += 2; *r2 = *r1; r2[1] = r1[1]; break; } r2 += 2; } if ( r2 == r4 ) { rfirst[1] += 2; *r2++ = *r1++; *r2++ = *r1++; } else r1 += 2; } } t = tt; break; case HAAKJE: /* Here we skip brackets */ t += t[1]; break; case SNUMBER: if ( t[2] < 0 ) { t[2] = -t[2]; if ( t[3] & 1 ) ncoef = -ncoef; } else if ( t[2] == 0 ) { if ( t[3] < 0 ) goto NormInf; goto NormZero; } lnum = TermMalloc("lnum"); lnum[0] = t[2]; nnum = 1; if ( t[3] && RaisPow(BHEAD (UWORD *)lnum,&nnum,(UWORD)(ABS(t[3]))) ) goto FromNorm; ncoef = REDLENG(ncoef); if ( t[3] < 0 ) { if ( Divvy(BHEAD (UWORD *)tstop,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; } else if ( t[3] > 0 ) { if ( Mully(BHEAD (UWORD *)tstop,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; } ncoef = INCLENG(ncoef); t += t[1]; TermFree(lnum,"lnum"); break; case LNUMBER: ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)tstop,&ncoef,(UWORD *)(t+3),t[2]) ) goto FromNorm; ncoef = INCLENG(ncoef); t += t[1]; break; default: MLOCK(ErrorMessageLock); MesPrint("Illegal code in NormPolyTerm"); MUNLOCK(ErrorMessageLock); Terminate(-1); break; } } /* Now we try to eliminate objects to the power zero. */ if ( rfirst ) { r2 = rfirst+2; r3 = rfirst + rfirst[1]; while ( r2 < r3 ) { if ( r2[1] == 0 ) { r1 = r2 + 2; while ( r1 < r3 ) { r1[-2] = r1[0]; r1[-1] = r1[1]; r1 += 2; } r3 -= 2; rfirst[1] -= 2; } else { r2 += 2; } } if ( rfirst[1] < 4 ) rfirst = 0; } /* Finally we put the term together */ if ( rfirst ) { i = rfirst[1]; NCOPY(tfill,rfirst,i) } i = ABS(ncoef)-1; NCOPY(tfill,tstop,i) *tfill++ = ncoef; *term = tfill - term; return(*term); NormZero: *term = 0; return(0); NormInf: MLOCK(ErrorMessageLock); MesPrint("0^0 in NormPolyTerm"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); FromNorm: MLOCK(ErrorMessageLock); MesCall("NormPolyTerm"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); } /* #] NormPolyTerm : #[ ComparePoly : */ /** * Compares two terms. The answer is: * 0 equal ( with exception of the coefficient ) * >0 term1 comes first. * <0 term2 comes first. * This routine should not return an error condition. * * The address of this routine is to be put in AR.CompareRoutine when we * want to use it for sorting. * This makes all existing code work properly and we can just replace the * routine on a thread by thread basis (each thread has its own AR struct). * Don't forget to put the old routine back afterwards! * * @param term1 First input term * @param term2 Second input term * @param level Not used for polynomials * @return 0 equal ( with exception of the coefficient if level == 0. ) * >0 term1 comes first. * <0 term2 comes first. */ #ifdef WITHCOMPAREPOLY WORD ComparePoly(WORD *term1, WORD *term2, WORD level) { WORD *t1, *t2, *t3, *t4, *tstop1, *tstop2; tstop1 = term1 + *term1; tstop1 -= ABS(tstop1[-1]); tstop2 = term2 + *term2; tstop2 -= ABS(tstop2[-1]); t1 = term1+1; t2 = term2+1; while ( t1 < tstop1 && t2 < tstop2 ) { if ( *t1 == *t2 ) { if ( *t1 == HAAKJE ) { if ( t1[2] != t2[2] ) return(t2[2]-t1[2]); t1 += t1[1]; t2 += t2[1]; } else { /* must be type SYMBOL */ t3 = t1 + t1[1]; t4 = t2 + t2[1]; t1 += 2; t2 += 2; while ( t1 < t3 && t2 < t4 ) { if ( *t1 != *t2 ) return(*t2-*t1); if ( t1[1] != t2[1] ) return(t2[1]-t1[1]); t1 += 2; t2 += 2; } if ( t1 < t3 ) return(-1); if ( t2 < t4 ) return(1); } } else return(*t2-*t1); } if ( t1 < tstop1 ) return(-1); if ( t2 < tstop2 ) return(1); return(0); } #endif /* #] ComparePoly : #[ ConvertToPoly : */ /** * Converts a generic term to polynomial notation in which there are * only symbols and brackets. * During conversion there will be only symbols. Brackets are stripped. * Objects that need 'translation' are put inside a special compiler * buffer and represented by a symbol. The numbering of the extra * symbols is down from the maximum. In principle there can be a * problem when running into the already assigned ones. * The output overwrites the input. * comlist is the compiler code. Used for the various options */ static int FirstWarnConvertToPoly = 1; int ConvertToPoly(PHEAD WORD *term, WORD *outterm, WORD *comlist, WORD par) { WORD *tout, *tstop, ncoef, *t, *r, *tt, *ttwo = 0; int i, action = 0; tt = term + *term; ncoef = ABS(tt[-1]); tstop = tt - ncoef; tout = outterm+1; t = term + 1; if ( comlist[2] == DOALL ) { while ( t < tstop ) { if ( *t == SYMBOL ) { r = t+2; t += t[1]; while ( r < t ) { if ( r[1] > 0 ) { *tout++ = SYMBOL; *tout++ = 4; *tout++ = r[0]; *tout++ = r[1]; } else { tout[1] = SYMBOL; tout[2] = 4; tout[3] = r[0]; tout[4] = -1; i = FindSubterm(tout+1); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = -r[1]; action = 1; } r += 2; } } else if ( *t == DOTPRODUCT ) { r = t + 2; t += t[1]; while ( r < t ) { tout[1] = DOTPRODUCT; tout[2] = 5; tout[3] = r[0]; tout[4] = r[1]; if ( r[2] < 0 ) { tout[5] = -1; } else { tout[5] = 1; } i = FindSubterm(tout+1); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = ABS(r[2]); r += 3; action = 1; } } else if ( *t == VECTOR ) { r = t + 2; t += t[1]; while ( r < t ) { tout[1] = VECTOR; tout[2] = 4; tout[3] = r[0]; tout[4] = r[1]; i = FindSubterm(tout+1); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; r += 2; action = 1; } } else if ( *t == INDEX ) { r = t + 2; t += t[1]; while ( r < t ) { tout[1] = INDEX; tout[2] = 3; tout[3] = r[0]; i = FindSubterm(tout+1); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; r++; action = 1; } } else if ( *t == HAAKJE) { if ( par ) { tout[0] = 1; tout[1] = 1; tout[2] = 3; *outterm = (tout+3)-outterm; if ( NormPolyTerm(BHEAD outterm) < 0 ) return(-1); tout = outterm + *outterm; tout -= 3; i = t[1]; NCOPY(tout,t,i); ttwo = tout-1; } else { t += t[1]; } } else if ( *t >= FUNCTION ) { i = FindSubterm(t); t += t[1]; *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; action = 1; } else { if ( FirstWarnConvertToPoly ) { MLOCK(ErrorMessageLock); MesPrint("Illegal object in conversion to polynomial notation"); MUNLOCK(ErrorMessageLock); FirstWarnConvertToPoly = 0; } return(-1); } } NCOPY(tout,tstop,ncoef) if ( ttwo ) { WORD hh = *ttwo; *ttwo = tout-ttwo; if ( ( i = NormPolyTerm(BHEAD ttwo) ) >= 0 ) i = action; tout = ttwo + *ttwo; *ttwo = hh; *outterm = tout - outterm; } else { *outterm = tout-outterm; if ( ( i = NormPolyTerm(BHEAD outterm) ) >= 0 ) i = action; } } else if ( comlist[2] == ONLYFUNCTIONS ) { while ( t < tstop ) { if ( *t >= FUNCTION ) { if ( comlist[1] == 3 ) { i = FindSubterm(t); t += t[1]; *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; action = 1; } else { for ( i = 3; i < comlist[1]; i++ ) { if ( *t == comlist[i] ) break; } if ( i < comlist[1] ) { i = FindSubterm(t); t += t[1]; *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; action = 1; } else { i = t[1]; NCOPY(tout,t,i); } } } else { i = t[1]; NCOPY(tout,t,i); } } NCOPY(tout,tstop,ncoef) *outterm = tout-outterm; Normalize(BHEAD outterm); i = action; } else { MLOCK(ErrorMessageLock); MesPrint("Illegal internal code in conversion to polynomial notation"); MUNLOCK(ErrorMessageLock); i = -1; } return(i); } /* #] ConvertToPoly : #[ LocalConvertToPoly : */ /** * Converts a generic term to polynomial notation in which there are * only symbols and brackets. * During conversion there will be only symbols. Brackets are stripped. * Objects that need 'translation' are put inside a special compiler * buffer and represented by a symbol. The numbering of the extra * symbols is down from the maximum. In principle there can be a * problem when running into the already assigned ones. * This uses the FindTree for searching in the global tree and * then looks further in the AT.ebufnum. This allows fully parallel * processing. Hence we need no locks. Cannot be used in the same * module as ConvertToPoly. */ int LocalConvertToPoly(PHEAD WORD *term, WORD *outterm, WORD startebuf, WORD par) { WORD *tout, *tstop, ncoef, *t, *r, *tt, *ttwo = 0; int i, action = 0; tt = term + *term; ncoef = ABS(tt[-1]); tstop = tt - ncoef; tout = outterm+1; t = term + 1; while ( t < tstop ) { if ( *t == SYMBOL ) { r = t+2; t += t[1]; while ( r < t ) { if ( r[1] > 0 ) { *tout++ = SYMBOL; *tout++ = 4; *tout++ = r[0]; *tout++ = r[1]; } else { tout[1] = SYMBOL; tout[2] = 4; tout[3] = r[0]; tout[4] = -1; i = FindLocalSubterm(BHEAD tout+1,startebuf); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = -r[1]; action = 1; } r += 2; } } else if ( *t == DOTPRODUCT ) { r = t + 2; t += t[1]; while ( r < t ) { tout[1] = DOTPRODUCT; tout[2] = 5; tout[3] = r[0]; tout[4] = r[1]; if ( r[2] < 0 ) { tout[5] = -1; } else { tout[5] = 1; } i = FindLocalSubterm(BHEAD tout+1,startebuf); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = ABS(r[2]); r += 3; action = 1; } } else if ( *t == VECTOR ) { r = t + 2; t += t[1]; while ( r < t ) { tout[1] = VECTOR; tout[2] = 4; tout[3] = r[0]; tout[4] = r[1]; i = FindLocalSubterm(BHEAD tout+1,startebuf); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; r += 2; action = 1; } } else if ( *t == INDEX ) { r = t + 2; t += t[1]; while ( r < t ) { tout[1] = INDEX; tout[2] = 3; tout[3] = r[0]; i = FindLocalSubterm(BHEAD tout+1,startebuf); *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; r++; action = 1; } } else if ( *t == HAAKJE) { if ( par ) { tout[0] = 1; tout[1] = 1; tout[2] = 3; *outterm = (tout+3)-outterm; if ( NormPolyTerm(BHEAD outterm) < 0 ) return(-1); tout = outterm + *outterm; tout -= 3; i = t[1]; NCOPY(tout,t,i); ttwo = tout-1; } else { t += t[1]; } } else if ( *t >= FUNCTION ) { i = FindLocalSubterm(BHEAD t,startebuf); t += t[1]; *tout++ = SYMBOL; *tout++ = 4; *tout++ = MAXVARIABLES-i; *tout++ = 1; action = 1; } else { if ( FirstWarnConvertToPoly ) { MLOCK(ErrorMessageLock); MesPrint("Illegal object in conversion to polynomial notation"); MUNLOCK(ErrorMessageLock); FirstWarnConvertToPoly = 0; } return(-1); } } NCOPY(tout,tstop,ncoef) if ( ttwo ) { WORD hh = *ttwo; *ttwo = tout-ttwo; if ( ( i = NormPolyTerm(BHEAD ttwo) ) >= 0 ) i = action; tout = ttwo + *ttwo; *ttwo = hh; *outterm = tout - outterm; } else { *outterm = tout-outterm; if ( ( i = NormPolyTerm(BHEAD outterm) ) >= 0 ) i = action; } return(i); } /* #] LocalConvertToPoly : #[ ConvertFromPoly : Converts a generic term from polynomial notation to the original in which the extra symbols have been replaced by their values. The output is in outterm. We only deal with the extra symbols in the range from < i <= to The output has to be sent to TestSub because it may contain subexpressions when extra symbols have been replaced. */ int ConvertFromPoly(PHEAD WORD *term, WORD *outterm, WORD from, WORD to, WORD offset, WORD par) { WORD *tout, *tstop, *tstop1, ncoef, *t, *r, *tt; int i; /* first = 1; */ tt = term + *term; tout = outterm+1; ncoef = ABS(tt[-1]); tstop = tt - ncoef; /* r = t = term + 1; while ( t < tstop ) { if ( *t == SYMBOL ) { tstop1 = t + t[1]; tt = t + 2; while ( tt < tstop1 ) { if ( ( *tt < MAXVARIABLES - to ) || ( *tt >= MAXVARIABLES - from ) ) { tt += 2; } else break; } if ( tt >= tstop1 ) { t = tstop1; continue; } while ( r < t ) *tout++ = *r++; t += 2; first = 0; while ( t < tstop1 ) { if ( ( *t < MAXVARIABLES - to ) || ( *t >= MAXVARIABLES - from ) ) { *tout++ = SYMBOL; *tout++ = 4; *tout++ = *t++; *tout++ = *t++; } else { *tout++ = SUBEXPRESSION; *tout++ = SUBEXPSIZE; *tout++ = MAXVARIABLES - *t++ + offset; *tout++ = *t++; if ( par ) *tout++ = AT.ebufnum; else *tout++ = AM.sbufnum; FILLSUB(tout) } } r = t; } else { t += t[1]; } } if ( first ) { i = *term; t = term; NCOPY(outterm,t,i); return(*term); } while ( r < t ) *tout++ = *r++; NCOPY(tout,tstop,ncoef) *outterm = tout-outterm; */ t = term + 1; while ( t < tstop ) { if ( *t == SYMBOL ) { tstop1 = t + t[1]; tt = t + 2; while ( tt < tstop1 ) { if ( ( *tt < MAXVARIABLES - to ) || ( *tt >= MAXVARIABLES - from ) ) { tt += 2; } else { *tout++ = SUBEXPRESSION; *tout++ = SUBEXPSIZE; *tout++ = MAXVARIABLES - *tt++ + offset; *tout++ = *tt++; if ( par ) *tout++ = AT.ebufnum; else *tout++ = AM.sbufnum; FILLSUB(tout) } } r = tout; t += 2; *tout++ = SYMBOL; *tout++ = 0; while ( t < tstop1 ) { if ( ( *t < MAXVARIABLES - to ) || ( *t >= MAXVARIABLES - from ) ) { *tout++ = *t++; *tout++ = *t++; } else { t += 2; } } r[1] = tout - r; if ( r[1] <= 2 ) tout = r; } else { i = t[1]; NCOPY(tout,t,i) } } NCOPY(tout,tstop,ncoef) *outterm = tout-outterm; return(*outterm); } /* #] ConvertFromPoly : #[ FindSubterm : In this routine we look up a variable. If we don't find it we will enter it in the subterm compiler buffer Searching is by tree structure. Adding changes the tree. Notice that in TFORM we should be in sequential mode. */ int FindSubterm(WORD *subterm) { WORD old[5], *ss, *term; int number; CBUF *C = cbuf + AM.sbufnum; LONG oldCpointer; term = subterm-1; ss = subterm+subterm[1]; /* Convert to proper term */ old[0] = *term; old[1] = ss[0]; old[2] = ss[1]; old[3] = ss[2]; old[4] = ss[3]; ss[0] = 1; ss[1] = 1; ss[2] = 3; ss[3] = 0; *term = subterm[1]+4; /* We may have to add the term to the compiler buffer and then to the tree. This cannot be done in parallel and hence we have to set a lock. */ LOCK(AM.sbuflock); oldCpointer = C->Pointer-C->Buffer; /* Offset of course !!!!!*/ AddRHS(AM.sbufnum,1); AddNtoC(AM.sbufnum,*term,term,8); AddToCB(C,0) /* See whether we have this one already. If not, insert it in the tree. */ number = InsTree(AM.sbufnum,C->numrhs); /* Restore old values and return what is needed. */ if ( number < (C->numrhs) ) { /* It existed already */ C->Pointer = oldCpointer + C->Buffer; C->numrhs--; } else { GETIDENTITY WORD dim = DimensionSubterm(subterm); if ( dim == -MAXPOSITIVE ) { /* Give error message but continue */ WORD *old = AN.currentTerm; AN.currentTerm = term; MLOCK(ErrorMessageLock); MesPrint("Dimension out of range in %t"); MUNLOCK(ErrorMessageLock); AN.currentTerm = old; } /* Store the dimension */ C->dimension[number] = dim; } UNLOCK(AM.sbuflock); *term = old[0]; ss[0] = old[1]; ss[1] = old[2]; ss[2] = old[3]; ss[3] = old[4]; return(number); } /* #] FindSubterm : #[ FindLocalSubterm : In this routine we look up a variable. If we don't find it we will enter it in the subterm compiler buffer Searching is by tree structure. Adding changes the tree. Notice that in TFORM we should be in sequential mode. */ int FindLocalSubterm(PHEAD WORD *subterm, WORD startebuf) { WORD old[5], *ss, *term, i, j, *t1, *t2; int number; CBUF *C = cbuf + AT.ebufnum; term = subterm-1; ss = subterm+subterm[1]; /* Convert to proper term */ old[0] = *term; old[1] = ss[0]; old[2] = ss[1]; old[3] = ss[2]; old[4] = ss[3]; ss[0] = 1; ss[1] = 1; ss[2] = 3; ss[3] = 0; *term = subterm[1]+4; /* First see whether we have this one already in the global buffer. */ number = FindTree(AM.sbufnum,term); if ( number > 0 ) goto wearehappy; /* Now look whether it is in the ebufnum between startebuf and numrhs Note however that we need an offset of (numxsymbol-startebuf) */ for ( i = startebuf+1; i <= C->numrhs; i++ ) { t1 = C->rhs[i]; t2 = term; if ( *t1 == *t2 ) { j = *t1; while ( *t1 == *t2 && j > 0 ) { t1++; t2++; j--; } if ( j <= 0 ) { number = i-startebuf+numxsymbol; goto wearehappy; } } } /* Now we have to add it to cbuf[AT.ebufnum] */ AddRHS(AT.ebufnum,1); AddNtoC(AT.ebufnum,*term,term,9); AddToCB(C,0) number = C->numrhs-startebuf+numxsymbol; wearehappy: *term = old[0]; ss[0] = old[1]; ss[1] = old[2]; ss[2] = old[3]; ss[3] = old[4]; return(number); } /* #] FindLocalSubterm : #[ PrintSubtermList : Prints all the expressions in the subterm compiler buffer. The format is such that they give definitions of the temporary variables of which the contents are stored in this buffer. These variables have the names Z_123 etc. */ void PrintSubtermList(int from,int to) { UBYTE buffer[80], *out, outbuffer[300]; int first, i, ii, inc = 1; WORD *term; CBUF *C = cbuf + AM.sbufnum; /* if ( to < from ) inc = -1; if ( to == from ) inc = 0; */ if ( from <= to ) { inc = 1; to += inc; } else { inc = -1; to += inc; } AO.OutFill = AO.OutputLine = outbuffer; AO.OutStop = AO.OutputLine+AC.LineLength; AO.IsBracket = 0; AO.OutSkip = 3; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { TokenToLine((UBYTE *)" "); AO.OutSkip = 7; } else if ( ( AO.Optimize.debugflags & 1 ) == 1 ) {} else if ( AO.OutSkip > 0 ) { for ( i = 0; i < AO.OutSkip; i++ ) TokenToLine((UBYTE *)" "); } i = from; do { if ( ( AO.Optimize.debugflags & 1 ) == 1 ) { TokenToLine((UBYTE *)"id "); for ( ii = 3; ii < AO.OutSkip; ii++ ) TokenToLine((UBYTE *)" "); } /* if ( AC.OutputMode == NORMALFORMAT ) { TokenToLine((UBYTE *)"id "); } */ else if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) {} else { TokenToLine((UBYTE *)" "); } out = StrCopy((UBYTE *)AC.extrasym,buffer); if ( AC.extrasymbols == 0 ) { out = NumCopy(i,out); out = StrCopy((UBYTE *)"_",out); } else if ( AC.extrasymbols == 1 ) { out = AddArrayIndex(i,out); } out = StrCopy((UBYTE *)"=",out); TokenToLine(buffer); term = C->rhs[i]; first = 1; if ( *term == 0 ) { out = StrCopy((UBYTE *)"0",buffer); if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE ) { out = StrCopy((UBYTE *)";",out); } TokenToLine(buffer); } else { while ( *term ) { if ( WriteInnerTerm(term,first) ) Terminate(-1); term += *term; first = 0; } if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE ) { out = StrCopy((UBYTE *)";",buffer); TokenToLine(buffer); } } /* There is a problem with FiniLine because it prepares for a continuation line in fortran mode. But the next statement should start on a blank line. */ /* FiniLine(); if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { AO.OutFill = AO.OutputLine; TokenToLine((UBYTE *)" "); AO.OutSkip = 7; } */ if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { AO.OutSkip = 6; FiniLine(); AO.OutSkip = 7; } else { FiniLine(); } i += inc; } while ( i != to ); } /* #] PrintSubtermList : #[ PrintExtraSymbol : Prints the definition of extra symbol num as the contents of the expression in terms. The parameter par has three options: EXTRASYMBOL num is interpreted as the number of an extra symbol REGULARSYMBOL num is interpreted as the number of a symbol. It could still be an extra symbol. EXPRESSIONNUMBER num is the number of an expression. terms contains the rhs expression. */ void PrintExtraSymbol(int num, WORD *terms,int par) { UBYTE buffer[80], *out, outbuffer[300]; int first, i; WORD *term; AO.OutFill = AO.OutputLine = outbuffer; AO.OutStop = AO.OutputLine+AC.LineLength; AO.IsBracket = 0; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { TokenToLine((UBYTE *)" "); AO.OutSkip = 7; } else if ( ( AO.Optimize.debugflags & 1 ) == 1 ) { TokenToLine((UBYTE *)"id "); for ( i = 3; i < AO.OutSkip; i++ ) TokenToLine((UBYTE *)" "); } else if ( AO.OutSkip > 0 ) { for ( i = 0; i < AO.OutSkip; i++ ) TokenToLine((UBYTE *)" "); } out = buffer; switch ( par ) { case REGULARSYMBOL: if ( num >= MAXVARIABLES-cbuf[AM.sbufnum].numrhs ) { num = MAXVARIABLES-num; } else { out = StrCopy(FindSymbol(num),out); /* out = StrCopy(VARNAME(symbols,num),out); */ break; } /* fall through */ case EXTRASYMBOL: out = StrCopy(FindExtraSymbol(num),out); /* out = StrCopy((UBYTE *)AC.extrasym,out); if ( AC.extrasymbols == 0 ) { out = NumCopy(num,out); out = StrCopy((UBYTE *)"_",out); } else if ( AC.extrasymbols == 1 ) { out = AddArrayIndex(num,out); } */ break; case EXPRESSIONNUMBER: out = StrCopy(EXPRNAME(num),out); break; default: MesPrint("Illegal option in PrintExtraSymbol"); Terminate(-1); } out = StrCopy((UBYTE *)"=",out); TokenToLine(buffer); term = terms; first = 1; if ( *term == 0 ) { out = StrCopy((UBYTE *)"0",buffer); TokenToLine(buffer); } else { while ( *term ) { if ( WriteInnerTerm(term,first) ) Terminate(-1); term += *term; first = 0; } } if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE ) { out = StrCopy((UBYTE *)";",buffer); TokenToLine(buffer); } FiniLine(); } /* #] PrintExtraSymbol : #[ FindSubexpression : In this routine we look up a subexpression. If we don't find it we will enter it in the subterm compiler buffer Searching is by tree structure. Adding changes the tree. Notice that in TFORM we should be in sequential mode. */ int FindSubexpression(WORD *subexpr) { WORD *term; int number; CBUF *C = cbuf + AM.sbufnum; LONG oldCpointer; term = subexpr; while ( *term ) term += *term; number = term - subexpr; /* We may have to add the subexpression to the tree. This requires a lock. */ LOCK(AM.sbuflock); oldCpointer = C->Pointer-C->Buffer; /* Offset of course !!!!!*/ AddRHS(AM.sbufnum,1); /* Add the terms to the compiler buffer. Paste on a zero. */ AddNtoC(AM.sbufnum,number,subexpr,10); AddToCB(C,0) /* See whether we have this one already. If not, insert it in the tree. */ number = InsTree(AM.sbufnum,C->numrhs); /* Restore old values and return what is needed. */ if ( number < (C->numrhs) ) { /* It existed already */ C->Pointer = oldCpointer + C->Buffer; C->numrhs--; } else { GETIDENTITY WORD dim = DimensionExpression(BHEAD subexpr); /* Store the dimension */ C->dimension[number] = dim; } UNLOCK(AM.sbuflock); return(number); } /* #] FindSubexpression : #[ ExtraSymFun : */ int ExtraSymFun(PHEAD WORD *term,WORD level) { WORD *oldworkpointer = AT.WorkPointer; WORD *termout, *t1, *t2, *t3, *tstop, *tend, i; int retval = 0; tend = termout = term + *term; tstop = tend - ABS(tend[-1]); t3 = t1 = term+1; t2 = termout+1; /* First refind the function(s). There is at least one. */ while ( t1 < tstop ) { if ( *t1 == EXTRASYMFUN && t1[1] == FUNHEAD+2 ) { if ( t1[FUNHEAD] == -SNUMBER && t1[FUNHEAD+1] <= numxsymbol && t1[FUNHEAD+1] > 0 ) { i = t1[FUNHEAD+1]; } else if ( t1[FUNHEAD] == -SYMBOL && t1[FUNHEAD+1] < MAXVARIABLES && t1[FUNHEAD+1] >= MAXVARIABLES-numxsymbol ) { i = MAXVARIABLES - t1[FUNHEAD+1]; } else goto nocase; while ( t3 < t1 ) *t2++ = *t3++; /* Now inset the rhs pointer */ *t2++ = SUBEXPRESSION; *t2++ = SUBEXPSIZE; *t2++ = i; *t2++ = 1; *t2++ = AM.sbufnum; FILLSUB(t2) t3 = t1 = t1 + t1[1]; } else if ( *t1 == EXTRASYMFUN && t1[1] == FUNHEAD ) { while ( t3 < t1 ) *t2++ = *t3++; t3 = t1 = t1 + t1[1]; } else { nocase:; t1 = t1 + t1[1]; } } while ( t3 < tend ) *t2++ = *t3++; *termout = t2 - termout; AT.WorkPointer = t2; if ( AT.WorkPointer >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); AT.WorkPointer = oldworkpointer; return(-1); } retval = Generator(BHEAD termout,level); AT.WorkPointer = oldworkpointer; if ( retval < 0 ) { MLOCK(ErrorMessageLock); MesCall("ExtraSymFun"); MUNLOCK(ErrorMessageLock); } return(retval); } /* #] ExtraSymFun : #[ PruneExtraSymbols : */ int PruneExtraSymbols(WORD downto) { CBUF *C = cbuf + AM.sbufnum; if ( downto < C->numrhs && downto >= 0 ) { /* !!!!! */ ClearTree(AM.sbufnum); C->numrhs = downto; if ( downto == 0 ) { C->Pointer = C->Buffer; } else { WORD *w = C->rhs[downto], i; while ( *w ) w += *w; C->Pointer = w+1; for ( i = 1; i <= downto; i++ ) { InsTree(AM.sbufnum,i); } } } return(0); } /* #] PruneExtraSymbols : */ form-5.0.1/sources/comtool.h0000644000175100017510000000600515217035721011457 /** @file comtool.h * * Utility routines for the compiler. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #ifndef FORM_COMTOOL_H_ #define FORM_COMTOOL_H_ /* #[ Includes : */ #include "form3.h" /* #] Includes : #[ Inline functions : */ /** * Skips over whitespace characters in the buffer, including commas, * which are treated as whitespace characters in the FORM compiler. * * @note To avoid skipping commas, use `SKIPBLANKS(s)` instead. * * @param[in,out] s Pointer to the current position in the buffer. The buffer * must be null-terminated. On return, the pointer is * advanced to the first non-whitespace character, or the * null terminator if none is found. */ static inline void SkipSpaces(UBYTE **s) { const char *p = (const char *)*s; while ( *p == ' ' || *p == ',' || *p == '\t' ) p++; *s = (UBYTE *)p; } /** * Checks whether the next token in the buffer is the given keyword, * ignoring case. If found, the keyword is consumed and the pointer is advanced * to the first non-whitespace character following the keyword. * * @param[in,out] s Pointer to the current position in the buffer. * The buffer must be null-terminated. On return, * the pointer is advanced if the keyword is found. * @param opt Case-insensitive keyword. * @return 1 if the keyword is found, otherwise 0. */ static inline int ConsumeOption(UBYTE **s, const char *opt) { const char *p = (const char *)*s; while ( *p && *opt && tolower(*p) == tolower(*opt) ) { p++; opt++; } /* Check if `opt` ended. */ if ( !*opt ) { /* Check if `*p` is a word boundary. */ UINT c = FG.cTable[(unsigned char)*p]; if ( c != 0 && c != 1 && *p != '_' && *p != '$' ) { /* Consume the option. Skip the trailing whitespace. */ *s = (UBYTE *)p; SkipSpaces(s); return(1); } } return(0); } /* #] Inline functions : */ #endif /* FORM_COMTOOL_H_ */ form-5.0.1/sources/index.c0000644000175100017510000004735415217035721011121 /** @file index.c * * The routines that deal with bracket indexing * It creates the bracket index and it can find the brackets using * the index. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : index.c */ #include "form3.h" /* #] Includes : #[ syntax and use : The indexing of brackets is not automatic! It should only be used when one intends to use the contents of individual brackets. This is done with the addition of a + sign to the bracket statement: B+ a,b,c; or AB+ a,b,c; It does require resources! The index is kept in memory and is removed once the expression is treated and passed on to the output with different or no brackets. The index is limited to a given amount of space. Hence if there are too many brackets we will skip some in the index. Skipping goes by space occupied by the contents. We take the two adjacent bracket(s) with the least space together and represent them by the first one only. This gives a new spot. The expression struct has two pointers: bracketinfo for using. newbracketinfo for making new index. #] syntax and use : #[ FindBracket : */ POSITION *FindBracket(WORD nexp, WORD *bracket) { GETIDENTITY BRACKETINDEX *bi; BRACKETINFO *bracketinfo; EXPRESSIONS e = &(Expressions[nexp]); LONG hi, low, med; int i; WORD oldsorttype = AR.SortType, *t1, *t2, j, bsize, *term, *p, *pstop, *pp; WORD *tstop, *cp, a[4], *bracketh; FILEHANDLE *fi; POSITION auxpos, toppos; switch ( e->status ) { case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: fi = AR.hidefile; break; default: fi = AR.infile; break; } if ( AT.bracketinfo ) bracketinfo = AT.bracketinfo; else bracketinfo = e->bracketinfo; hi = bracketinfo->indexfill; low = 0; if ( hi <= 0 ) return(0); /* The next code is needed for a problem with sorting when there are only functions outside the bracket. This gives ordinarily the wrong sorting. We solve that by taking HAAKJE along with the outside while running the Compare. But this means that we need to copy bracket. */ bracketh = TermMalloc("FindBracket"); i = *bracket; p = bracket; pp = bracketh; NCOPY(pp,p,i) pp -= 3; *pp++ = HAAKJE; *pp++ = 3; *pp++ = 0; *pp++ = 1; *pp++ = 1; *pp++ = 3; *bracketh += 3; AT.fromindex = 1; AR.SortType = bracketinfo->SortType; bi = bracketinfo->indexbuffer + hi - 1; if ( *bracketh == 7 ) { if ( bracketinfo->bracketbuffer[bi->bracket] == 7 ) i = 0; else i = -1; } else if ( bracketinfo->bracketbuffer[bi->bracket] == 7 ) i = 1; else i = CompareTerms(BHEAD bracketh,bracketinfo->bracketbuffer+bi->bracket,0); if ( i < 0 ) { AR.SortType = oldsorttype; AT.fromindex = 0; TermFree(bracketh,"FindBracket"); return(0); } else if ( i == 0 ) med = hi-1; else { for (;;) { med = (hi+low)/2; bi = bracketinfo->indexbuffer + med; if ( *bracketh == 7 ) { if ( bracketinfo->bracketbuffer[bi->bracket] == 7 ) i = 0; else i = -1; } else if ( bracketinfo->bracketbuffer[bi->bracket] == 7 ) i = 1; else i = CompareTerms(BHEAD bracketh,bracketinfo->bracketbuffer+bi->bracket,0); if ( i == 0 ) { break; } if ( i > 0 ) { if ( low == med ) { /* no occurrence */ AR.SortType = oldsorttype; AT.fromindex = 0; TermFree(bracketh,"FindBracket"); return(0); } hi = med; } else if ( i < 0 ) { if ( low == med ) break; low = med; } }} /* The bracket is now either bi itself or between bi and the next one or it is not present at all. */ AN.theposition = AS.OldOnFile[nexp]; ADD2POS(AN.theposition,bi->start); /* The seek will have to move closer to the actual read so that we can place a lock around the two. if ( fi->handle >= 0 ) SeekFile(fi->handle,&AN.theposition,SEEK_SET); else SetScratch(fi,&AN.theposition); */ /* Put the bracket in the compress buffer as if it were the last term read. Have a look at AR.CompressPointer. (set it right) */ term = AT.WorkPointer; t1 = bracketinfo->bracketbuffer+bi->bracket; j = *t1; /* Note that in the bracketbuffer, the bracket sits with HAAKJE. The next is (hopefully) a bug fix. Originally the code read bsize = j but that overcounts one. We have the part outside the bracket and the coefficient which is 1,1,3. But we also have the length indicator. Where we use the variable bsize we do not include the length indicator, and we have the part outside plus 7,3,0 which is also three words. */ bsize = j-1; t2 = AR.CompressPointer; NCOPY(t2,t1,j) if ( i == 0 ) { /* We found the proper bracket already */ AR.SortType = oldsorttype; AT.fromindex = 0; TermFree(bracketh,"FindBracket"); return(&AN.theposition); } /* Here we have to skip to the bracket if it exists (!) Let us first look whether the expression is in memory. If not we have to make a buffer to increase speed.. */ if ( fi->handle < 0 ) { p = (WORD *)((UBYTE *)(fi->PObuffer) + BASEPOSITION(AS.OldOnFile[nexp]) + BASEPOSITION(bi->start)); pstop = (WORD *)((UBYTE *)(fi->PObuffer) + BASEPOSITION(AS.OldOnFile[nexp]) + BASEPOSITION(bi->next)); while ( p < pstop ) { /* Check now: if size or part from previous term < size of bracket we have to setup the bracket again and test. Otherwise, skip immediately to the next term. */ if ( *p <= -bsize ) { /* no change of bracket */ p++; p += *p + 1; } else if ( *p < 0 ) { /* changes bracket */ pp = p; t2 = AR.CompressPointer; t1 = t2 - *p++ + 1; j = *p++; NCOPY(t1,p,j) t2++; while ( *t2 != HAAKJE ) t2 += t2[1]; t2 += t2[1]; a[1] = t2[0]; a[2] = t2[1]; a[3] = t2[2]; *t2++ = 1; *t2++ = 1; *t2++ = 3; *AR.CompressPointer = t2 - AR.CompressPointer; bsize = *AR.CompressPointer - 1; if ( *bracketh == 7 ) { if ( AR.CompressPointer[0] == 7 ) i = 0; else i = -1; } else if ( AR.CompressPointer[0] == 7 ) i = 1; else i = CompareTerms(BHEAD bracketh,AR.CompressPointer,0); t2[-3] = a[1]; t2[-2] = a[2]; t2[-1] = a[3]; if ( i == 0 ) { SETBASEPOSITION(AN.theposition,(pp-fi->PObuffer)*sizeof(WORD)); fi->POfill = pp; goto found; } if ( i > 0 ) break; /* passed what was possible */ } else { /* no compression. We have to check! */ WORD *oldworkpointer = AT.WorkPointer, *t3, *t4; t2 = p + 1; while ( *t2 != HAAKJE ) t2 += t2[1]; t2 += t2[1]; /* Here we need to copy the term. Modifying has proven to be NOT threadsafe. */ t3 = oldworkpointer; t4 = p; while ( t4 < t2 ) *t3++ = *t4++; *t3++ = 1; *t3++ = 1; *t3++ = 3; *oldworkpointer = t3 - oldworkpointer; bsize = *oldworkpointer - 1; AT.WorkPointer = t3; t3 = oldworkpointer; if ( *bracketh == 7 ) { if ( t3[0] == 7 ) i = 0; else i = -1; } else if ( t3[0] == 7 ) i = 1; else { i = CompareTerms(BHEAD bracketh,t3,0); } AT.WorkPointer = oldworkpointer; if ( i == 0 ) { SETBASEPOSITION(AN.theposition,(p-fi->PObuffer)*sizeof(WORD)); fi->POfill = p; goto found; } if ( i > 0 ) break; /* passed what was possible */ p += *p; } } AR.SortType = oldsorttype; AT.fromindex = 0; TermFree(bracketh,"FindBracket"); return(0); /* Bracket does not exist */ } else { /* In this case we can work with the old representation without HAAKJE. We stop searching when we reach toppos and we do not call Compare. */ toppos = AS.OldOnFile[nexp]; ADD2POS(toppos,bi->next); cp = AR.CompressPointer; for(;;) { auxpos = AN.theposition; GetOneTerm(BHEAD term,fi,&auxpos,0); if ( *term == 0 ) { AR.SortType = oldsorttype; AT.fromindex = 0; return(0); /* Bracket does not exist */ } tstop = term + *term; tstop -= ABS(tstop[-1]); t1 = term + 1; while ( *t1 != HAAKJE && t1 < tstop ) t1 += t1[1]; i = *bracket-4; if ( t1-term == *bracket-3 ) { t1 = term + 1; t2 = bracket+1; while ( i > 0 && *t1 == *t2 ) { t1++; t2++; i--; } if ( i <= 0 ) { AR.CompressPointer = cp; goto found; } } AR.CompressPointer = cp; AN.theposition = auxpos; /* Now check whether we passed the 'point' */ if ( ISGEPOS(AN.theposition,toppos) ) { AR.SortType = oldsorttype; AR.CompressPointer = cp; AT.fromindex = 0; TermFree(bracketh,"FindBracket"); return(0); /* Bracket does not exist */ } } } found: AR.SortType = oldsorttype; AT.fromindex = 0; TermFree(bracketh,"FindBracket"); return(&AN.theposition); } /* #] FindBracket : #[ PutBracketInIndex : Call via if ( AR.BracketOn ) PutBracketInIndex(BHEAD term); This means that there should be a bracket somewhere Note that the brackets come in in proper order. DON'T forget AR.SortType to be put into e->bracketinfo->SortType */ void PutBracketInIndex(PHEAD WORD *term, POSITION *newpos) { GETBIDENTITY BRACKETINDEX *bi, *b1, *b2, *b3; BRACKETINFO *b; POSITION thepos; EXPRESSIONS e = Expressions + AR.CurExpr; LONG hi, i, average; WORD *t, *tstop, *t1, *t2, *oldt, oldsize, a[4]; if ( ( b = e->newbracketinfo ) == 0 ) return; DIFPOS(thepos,*newpos,e->onfile); tstop = term + *term; tstop -= ABS(tstop[-1]); t = term+1; while ( *t != HAAKJE && t < tstop ) t += t[1]; if ( t >= tstop ) return; /* no ticket, no laundry */ t += t[1]; /* include HAAKJE for the sorting */ a[0] = t[0]; a[1] = t[1]; a[2] = t[2]; oldt = t; oldsize = *term; *t++ = 1; *t++ = 1; *t++ = 3; *term = t - term; AT.fromindex = 1; /* Check now with the last bracket in the buffer. If it is the same we can abort. */ hi = b->indexfill; if ( hi > 0 ) { bi = b->indexbuffer + hi - 1; bi->next = thepos; if ( *term == 7 ) { if ( b->bracketbuffer[bi->bracket] == 7 ) i = 0; else i = -1; } else if ( b->bracketbuffer[bi->bracket] == 7 ) i = 1; else i = CompareTerms(BHEAD term,b->bracketbuffer+bi->bracket,0); if ( i == 0 ) { /* still the same bracket */ bi->termsinbracket++; goto bracketdone; } if ( i > 0 ) { /* We have a problem */ /* There is a special case in which we have only functions and term is contained completely in the bracket */ /* t = term + 1; tstop = term + *term - 3; while ( t < tstop && *t > HAAKJE ) t += t[1]; if ( t < tstop ) goto problems; */ for ( i = 1; i < *term - 3; i++ ) { if ( term[i] != b->bracketbuffer[bi->bracket+i] ) break; } if ( i < *term - 3 ) { /* problems:; */ *term = oldsize; oldt[0] = a[0]; oldt[1] = a[1]; oldt[2] = a[2]; MLOCK(ErrorMessageLock); MesPrint("Error!!!! Illegal bracket sequence detected in PutBracketInIndex"); #ifdef WITHPTHREADS MesPrint("Worker = %w"); #endif PrintTerm(term,"term into index"); PrintTerm(b->bracketbuffer+bi->bracket,"Last in index"); MUNLOCK(ErrorMessageLock); AT.fromindex = 0; Terminate(-1); } i = -1; } } /* If there is room for more brackets, we add this one. */ if ( b->bracketfill+*term >= b->bracketbuffersize && ( b->bracketbuffersize < AM.MaxBracketBufferSize || ( e->vflags & ISFACTORIZED ) != 0 ) ) { /* Enlarge bracket buffer */ WORD *oldbracketbuffer = b->bracketbuffer; i = MaX(b->bracketbuffersize * 2, b->bracketfill+*term+1); if ( i > AM.MaxBracketBufferSize && ( e->vflags & ISFACTORIZED ) == 0 ) i = AM.MaxBracketBufferSize; if ( i > b->bracketfill+*term ) { b->bracketbuffersize = i; b->bracketbuffer = (WORD *)Malloc1(b->bracketbuffersize*sizeof(WORD), "new bracket buffer"); t1 = b->bracketbuffer; t2 = oldbracketbuffer; i = b->bracketfill; NCOPY(t1,t2,i) if ( oldbracketbuffer ) M_free(oldbracketbuffer,"old bracket buffer"); } } if ( b->bracketfill+*term < b->bracketbuffersize ) { if ( b->indexfill >= b->indexbuffersize ) { /* Enlarge index */ BRACKETINDEX *oldindexbuffer = b->indexbuffer; b->indexbuffersize *= 2; b->indexbuffer = (BRACKETINDEX *) Malloc1(b->indexbuffersize*sizeof(BRACKETINDEX),"new bracket index"); b1 = b->indexbuffer; b2 = oldindexbuffer; i = b->indexfill; NCOPY(b1,b2,i) if ( oldindexbuffer ) M_free(oldindexbuffer,"old bracket index"); } } else { /* We have too many brackets in the buffer. Try to improve. This is the interesting algorithm. We try to eliminate about 1/4 to 1/2 of the brackets from the index. This should be done by size of the bracket contents to make the searching as fast as possible. But! Do not touch the last bracket. Note that we are always filling from the back. Algorithm: Throw away every second bracket, unless b1+b2 is much longer than average. How much is something we can tune. */ average = DIVPOS(thepos,b->indexfill+1); if ( average <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Problems with bracket buffer. Increase MaxBracketBufferSize in form.set"); MesPrint("Current size is %l",AM.MaxBracketBufferSize*sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } average *= 4; /* 2*2: one 2 for much longer, one 2 because we have pairs */ t2 = b->bracketbuffer; b3 = b1 = b->indexbuffer; bi = b->indexbuffer + b->indexfill; b2 = b1+1; while ( b2+2 < bi ) { if ( DIFBASE(b2->next,b1->start) > average ) { t1 = b->bracketbuffer + b1->bracket; b1->bracket = t2 - b->bracketbuffer; i = *t1; NCOPY(t2,t1,i) *b3++ = *b1; t1 = b->bracketbuffer + b2->bracket; b2->bracket = t2 - b->bracketbuffer; i = *t1; NCOPY(t2,t1,i) *b3++ = *b2; if ( b3 <= b1 ) { PUTZERO(b1->start); PUTZERO(b1->next); b1->bracket = 0; b1->termsinbracket = 0; } if ( b3 <= b2 ) { PUTZERO(b2->start); PUTZERO(b2->next); b2->bracket = 0; b2->termsinbracket = 0; } } else { t1 = b->bracketbuffer + b1->bracket; b1->bracket = t2 - b->bracketbuffer; i = *t1; NCOPY(t2,t1,i) b1->next = b2->next; b1->termsinbracket += b2->termsinbracket; *b3++ = *b1; if ( b3 <= b1 ) { PUTZERO(b1->start); PUTZERO(b1->next); b1->bracket = 0; b1->termsinbracket = 0; } PUTZERO(b2->start); PUTZERO(b2->next); b2->bracket = 0; b2->termsinbracket = 0; } b1 += 2; b2 += 2; } while ( b1 < bi ) { t1 = b->bracketbuffer + b1->bracket; b1->bracket = t2 - b->bracketbuffer; i = *t1; NCOPY(t2,t1,i) *b3++ = *b1; if ( b3 <= b1 ) { PUTZERO(b1->start); PUTZERO(b1->next); b1->bracket = 0; b1->termsinbracket = 0; } b1++; } b->indexfill = b3 - b->indexbuffer; b->bracketfill = t2 - b->bracketbuffer; } bi = b->indexbuffer + b->indexfill; b->indexfill++; bi->bracket = b->bracketfill; bi->start = thepos; bi->next = thepos; bi->termsinbracket = 1; /* Copy the bracket into the buffer */ t1 = term; t2 = b->bracketbuffer + bi->bracket; i = *t1; b->bracketfill += i; NCOPY(t2,t1,i) bracketdone: *term = oldsize; oldt[0] = a[0]; oldt[1] = a[1]; oldt[2] = a[2]; AT.fromindex = 0; } /* #] PutBracketInIndex : #[ ClearBracketIndex : */ void ClearBracketIndex(WORD numexp) { BRACKETINFO *b; if ( numexp >= 0 ) { b = Expressions[numexp].bracketinfo; Expressions[numexp].bracketinfo = 0; } else if ( numexp == -1 ) { GETIDENTITY b = AT.bracketinfo; AT.bracketinfo = 0; } else { numexp = -numexp-2; b = Expressions[numexp].newbracketinfo; Expressions[numexp].newbracketinfo = 0; } if ( b == 0 ) return; b->indexfill = b->indexbuffersize = 0; b->bracketfill = b->bracketbuffersize = 0; M_free(b->bracketbuffer,"ClearBracketBuffer"); M_free(b->indexbuffer,"ClearIndexBuffer"); M_free(b,"BracketInfo"); } /* #] ClearBracketIndex : #[ OpenBracketIndex : Note: This routine is thread-safe */ void OpenBracketIndex(WORD nexpr) { EXPRESSIONS e = Expressions + nexpr; BRACKETINFO *bi; LONG i; bi = (BRACKETINFO *)Malloc1(sizeof(BRACKETINFO),"BracketInfo"); e->newbracketinfo = bi; /* i = 20*AM.MaxTer/sizeof(WORD); if ( i < 1000 ) i = 1000; */ i = 2000; bi->bracketbuffer = (WORD *)Malloc1(i*sizeof(WORD),"Bracket Buffer"); bi->bracketbuffersize = i; bi->bracketfill = 0; i = 50; bi->indexbuffer = (BRACKETINDEX *)Malloc1(i*sizeof(BRACKETINDEX),"Bracket Index"); bi->indexbuffersize = i; bi->indexfill = 0; bi->SortType = AC.SortType; } /* #] OpenBracketIndex : #[ PutInside : Puts a term, or a bracket determined part of a term inside a function. AT.WorkPointer points at term+*term */ int PutInside(PHEAD WORD *term, WORD *code) { WORD *from, *to, *oldbuf, *tStop, *t, *tt, oldon, oldact, inc, argsize, *termout; int i, ii, error; if ( code[1] == 4 && ( code[2] == 0 || code[2] == 1 ) ) { /* Put all inside. Move the term by 1+FUNHEAD+ARGHEAD */ from = term+*term; to = from+1+ARGHEAD+FUNHEAD; i = ii = *term; to[0] = 1; to[1] = 1; to[2] = 3; while ( --i >= 0 ) *--to = *--from; to = term; *to++ = term[0]+4+ARGHEAD+FUNHEAD; *to++ = code[3]; *to++ = ii+FUNHEAD+ARGHEAD; *to++ = 1; /* set dirty flags, because there could be a fast notation */ FILLFUN3(to) *to++ = ii+ARGHEAD; *to++ = 1; FILLARG(to) return(0); } /* First we save the old bracket variables. Then we set variables to influence the PutBracket routine and call it. After that we set the values back and sort out the results by placing the inside of the bracket inside the function. */ termout = AT.WorkPointer; oldbuf = AT.BrackBuf; oldon = AR.BracketOn; oldact = AT.PolyAct; AR.BracketOn = -code[2]; AT.BrackBuf = code+4; AT.PolyAct = 0; error = PutBracket(BHEAD term); AT.PolyAct = oldact; AT.BrackBuf = oldbuf; AR.BracketOn = oldon; if ( error ) return(error); i = *termout; from = termout; to = term; NCOPY(to,from,i); tStop = term +*term; tStop -= tStop[-1]; t = term+1; while ( t < tStop && *t != HAAKJE ) t += t[1]; from = term + *term; inc = FUNHEAD+ARGHEAD-t[1]+1; tt = t + t[1]; argsize = from-tt+1; to = from + inc; to[0] = 1; to[1] = 1; to[2] = 3; while ( from > tt ) *--to = *--from; *--to = argsize; *t++ = code[3]; *t++ = argsize+FUNHEAD+ARGHEAD; *t++ = 1; FILLFUN3(t); *t++ = argsize+ARGHEAD; *t++ = 1; FILLARG(t); *term += inc+3; AT.WorkPointer = term+*term; if ( Normalize(BHEAD term) ) error = 1; return(error); } /* #] PutInside : */ /* The next routines are for indexing the local output files in a parallel sort. This indexing is needed to get a fast determination of the splitting terms needed to divide the terms evenly over the processors. Actually this method works well for ParFORM, but may not work well for TFORM. #[ PutTermInIndex : Puts a term in the term index. Action: if the index hasn't reached its full size if there is room, put the term if there is no room: extend the buffer, put the term else check if the last term has a number of the type skip*m+1 if no, overwrite the last term if yes, check whether there is room for one more term yes: add the term no: drop all even terms, compress the list, multiply skip by 2, and add this term. int PutTermInIndex(WORD *term,POSITION *position) { return(0); } #] PutTermInIndex : */ form-5.0.1/sources/execute.c0000644000175100017510000022757115217035721011455 /** @file execute.c * * The routines that start the execution phase of a module. * It also contains the routines for placing the bracket subterm. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : execute.c */ #include "form3.h" /* #] Includes : #[ DoExecute : #[ CleanExpr : par == 1 after .store or .clear par == 0 after .sort */ int CleanExpr(WORD par) { GETIDENTITY WORD j, n, i; POSITION length; EXPRESSIONS e_in, e_out, e; int numhid = 0; NAMENODE *node; n = NumExpressions; j = 0; e_in = e_out = Expressions; if ( n > 0 ) { do { e_in->vflags &= ~( TOBEFACTORED | TOBEUNFACTORED ); if ( par ) { if ( e_in->renumlists ) { if ( e_in->renumlists != AN.dummyrenumlist ) M_free(e_in->renumlists,"Renumber-lists"); e_in->renumlists = 0; } if ( e_in->renum ) { M_free(e_in->renum,"Renumber"); e_in->renum = 0; } } if ( e_in->status == HIDDENLEXPRESSION || e_in->status == HIDDENGEXPRESSION ) numhid++; switch ( e_in->status ) { case SPECTATOREXPRESSION: case LOCALEXPRESSION: case HIDDENLEXPRESSION: if ( par ) { AC.exprnames->namenode[e_in->node].type = CDELETE; AC.DidClean = 1; if ( e_in->status != HIDDENLEXPRESSION ) ClearBracketIndex(e_in-Expressions); break; } /* fall through */ case GLOBALEXPRESSION: case HIDDENGEXPRESSION: if ( par ) { #ifdef WITHMPI /* * Broadcast the global expression from the master to the all workers. */ if ( PF_BroadcastExpr(e_in, e_in->status == HIDDENGEXPRESSION ? AR.hidefile : AR.outfile) ) return -1; if ( PF.me == MASTER ) { #endif e = e_in; i = n-1; while ( --i >= 0 ) { e++; if ( e_in->status == HIDDENGEXPRESSION ) { if ( e->status == HIDDENGEXPRESSION || e->status == HIDDENLEXPRESSION ) break; } else { if ( e->status == GLOBALEXPRESSION || e->status == LOCALEXPRESSION ) break; } } #ifdef WITHMPI } else { /* * On the slaves, the broadcast expression is sitting at the end of the file. */ e = e_in; i = -1; } #endif if ( i >= 0 ) { DIFPOS(length,e->onfile,e_in->onfile); } else { FILEHANDLE *f = e_in->status == HIDDENGEXPRESSION ? AR.hidefile : AR.outfile; if ( f->handle < 0 ) { SETBASELENGTH(length,TOLONG(f->POfull) - TOLONG(f->PObuffer) - BASEPOSITION(e_in->onfile)); } else { SeekFile(f->handle,&(f->filesize),SEEK_SET); DIFPOS(length,f->filesize,e_in->onfile); } } if ( ToStorage(e_in,&length) ) { return(MesCall("CleanExpr")); } e_in->status = STOREDEXPRESSION; if ( e_in->status != HIDDENGEXPRESSION ) ClearBracketIndex(e_in-Expressions); } /* fall through */ case SKIPLEXPRESSION: case DROPLEXPRESSION: case DROPHLEXPRESSION: case DROPGEXPRESSION: case DROPHGEXPRESSION: case STOREDEXPRESSION: case DROPSPECTATOREXPRESSION: if ( e_out != e_in ) { node = AC.exprnames->namenode + e_in->node; node->number = e_out - Expressions; e_out->onfile = e_in->onfile; e_out->size = e_in->size; e_out->printflag = 0; if ( par ) e_out->status = STOREDEXPRESSION; else e_out->status = e_in->status; e_out->name = e_in->name; e_out->node = e_in->node; e_out->renum = e_in->renum; e_out->renumlists = e_in->renumlists; e_out->counter = e_in->counter; e_out->hidelevel = e_in->hidelevel; e_out->inmem = e_in->inmem; e_out->bracketinfo = e_in->bracketinfo; e_out->newbracketinfo = e_in->newbracketinfo; e_out->numdummies = e_in->numdummies; e_out->numfactors = e_in->numfactors; e_out->vflags = e_in->vflags; e_out->uflags = e_in->uflags; e_out->sizeprototype = e_in->sizeprototype; } #ifdef PARALLELCODE e_out->partodo = 0; #endif e_out++; j++; break; case DROPPEDEXPRESSION: break; default: AC.exprnames->namenode[e_in->node].type = CDELETE; AC.DidClean = 1; break; } e_in++; } while ( --n > 0 ); } UpdateMaxSize(); NumExpressions = j; if ( numhid == 0 && AR.hidefile->PObuffer ) { if ( AR.hidefile->handle >= 0 ) { CloseFile(AR.hidefile->handle); remove(AR.hidefile->name); AR.hidefile->handle = -1; } AR.hidefile->POfull = AR.hidefile->POfill = AR.hidefile->PObuffer; PUTZERO(AR.hidefile->POposition); } FlushSpectators(); return(0); } /* #] CleanExpr : #[ PopVariables : Pops the local variables from the tables. The Expressions are reprocessed and their tables are compactified. */ int PopVariables(void) { GETIDENTITY WORD i, j; int retval; UBYTE *s; retval = CleanExpr(1); ResetVariables(1); if ( AC.DidClean ) CompactifyTree(AC.exprnames,EXPRNAMES); AC.CodesFlag = AM.gCodesFlag; AC.NamesFlag = AM.gNamesFlag; AC.StatsFlag = AM.gStatsFlag; #ifdef WITHFLOAT AC.MaxWeight = AM.gMaxWeight; AC.DefaultPrecision = AM.gDefaultPrecision; #endif AC.OldFactArgFlag = AM.gOldFactArgFlag; AC.TokensWriteFlag = AM.gTokensWriteFlag; AC.extrasymbols = AM.gextrasymbols; if ( AC.extrasym ) { M_free(AC.extrasym,"extrasym"); AC.extrasym = 0; } i = 1; s = AM.gextrasym; while ( *s ) { s++; i++; } AC.extrasym = (UBYTE *)Malloc1(i*sizeof(UBYTE),"extrasym"); for ( j = 0; j < i; j++ ) AC.extrasym[j] = AM.gextrasym[j]; AO.NoSpacesInNumbers = AM.gNoSpacesInNumbers; AO.IndentSpace = AM.gIndentSpace; AC.lUnitTrace = AM.gUnitTrace; AC.lDefDim = AM.gDefDim; AC.lDefDim4 = AM.gDefDim4; if ( AC.halfmod ) { if ( AC.ncmod == AM.gncmod && AC.modmode == AM.gmodmode ) { j = ABS(AC.ncmod); while ( --j >= 0 ) { if ( AC.cmod[j] != AM.gcmod[j] ) break; } if ( j >= 0 ) { M_free(AC.halfmod,"halfmod"); AC.halfmod = 0; AC.nhalfmod = 0; } } else { M_free(AC.halfmod,"halfmod"); AC.halfmod = 0; AC.nhalfmod = 0; } } if ( AC.modinverses ) { if ( AC.ncmod == AM.gncmod && AC.modmode == AM.gmodmode ) { j = ABS(AC.ncmod); while ( --j >= 0 ) { if ( AC.cmod[j] != AM.gcmod[j] ) break; } if ( j >= 0 ) { M_free(AC.modinverses,"modinverses"); AC.modinverses = 0; } } else { M_free(AC.modinverses,"modinverses"); AC.modinverses = 0; } } AN.ncmod = AC.ncmod = AM.gncmod; AC.npowmod = AM.gnpowmod; AC.modmode = AM.gmodmode; if ( ( ( AC.modmode & INVERSETABLE ) != 0 ) && ( AC.modinverses == 0 ) ) MakeInverses(); AC.funpowers = AM.gfunpowers; AC.lPolyFun = AM.gPolyFun; AC.lPolyFunInv = AM.gPolyFunInv; AC.lPolyFunType = AM.gPolyFunType; AC.lPolyFunExp = AM.gPolyFunExp; AR.PolyFunVar = AC.lPolyFunVar = AM.gPolyFunVar; AC.lPolyFunPow = AM.gPolyFunPow; AC.parallelflag = AM.gparallelflag; AC.ProcessBucketSize = AC.mProcessBucketSize = AM.gProcessBucketSize; AC.properorderflag = AM.gproperorderflag; AC.ThreadBucketSize = AM.gThreadBucketSize; AC.ThreadStats = AM.gThreadStats; AC.FinalStats = AM.gFinalStats; AC.OldGCDflag = AM.gOldGCDflag; AC.WTimeStatsFlag = AM.gWTimeStatsFlag; AC.ThreadsFlag = AM.gThreadsFlag; AC.ThreadBalancing = AM.gThreadBalancing; AC.ThreadSortFileSynch = AM.gThreadSortFileSynch; AC.ProcessStats = AM.gProcessStats; AC.OldParallelStats = AM.gOldParallelStats; AC.IsFortran90 = AM.gIsFortran90; AC.SizeCommuteInSet = AM.gSizeCommuteInSet; PruneExtraSymbols(AM.gnumextrasym); if ( AC.Fortran90Kind ) { M_free(AC.Fortran90Kind,"Fortran90 Kind"); AC.Fortran90Kind = 0; } if ( AM.gFortran90Kind ) { AC.Fortran90Kind = strDup1(AM.gFortran90Kind,"Fortran90 Kind"); } if ( AC.ThreadsFlag && AM.totalnumberofthreads > 1 ) AS.MultiThreaded = 1; { UWORD *p, *m; p = AM.gcmod; m = AC.cmod; j = ABS(AC.ncmod); NCOPY(m,p,j); p = AM.gpowmod; m = AC.powmod; j = AC.npowmod; NCOPY(m,p,j); if ( AC.DirtPow ) { if ( MakeModTable() ) { MesPrint("===No printing in powers of generator"); } AC.DirtPow = 0; } } { WORD *p, *m; p = AM.gUniTrace; m = AC.lUniTrace; j = 4; NCOPY(m,p,j); } AC.Cnumpows = AM.gCnumpows; AC.OutputMode = AM.gOutputMode; AC.OutputSpaces = AM.gOutputSpaces; AC.OutNumberType = AM.gOutNumberType; AR.SortType = AC.SortType = AM.gSortType; AC.ShortStatsMax = AM.gShortStatsMax; /* Now we have to clean up the commutation properties */ for ( i = 0; i < NumFunctions; i++ ) functions[i].flags &= ~COULDCOMMUTE; if ( AC.CommuteInSet ) { WORD *g, *gg; g = AC.CommuteInSet; while ( *g ) { gg = g+1; g += *g; while ( gg < g ) { if ( *gg <= GAMMASEVEN && *gg >= GAMMA ) { functions[GAMMA-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMAI-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMAFIVE-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMASIX-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMASEVEN-FUNCTION].flags |= COULDCOMMUTE; } else { functions[*gg-FUNCTION].flags |= COULDCOMMUTE; } } } } /* Clean up the dictionaries. */ for ( i = AO.NumDictionaries-1; i >= AO.gNumDictionaries; i-- ) { RemoveDictionary(AO.Dictionaries[i]); M_free(AO.Dictionaries[i],"Dictionary"); } for( ; i >= 0; i-- ) { ShrinkDictionary(AO.Dictionaries[i]); } AO.NumDictionaries = AO.gNumDictionaries; return(retval); } /* #] PopVariables : #[ MakeGlobal : */ void MakeGlobal(void) { WORD i, j, *pp, *mm; UWORD *p, *m; UBYTE *s; Globalize(0); AM.gCodesFlag = AC.CodesFlag; AM.gNamesFlag = AC.NamesFlag; AM.gStatsFlag = AC.StatsFlag; #ifdef WITHFLOAT AM.gMaxWeight = AC.MaxWeight; AM.gDefaultPrecision = AC.DefaultPrecision; #endif AM.gOldFactArgFlag = AC.OldFactArgFlag; AM.gextrasymbols = AC.extrasymbols; if ( AM.gextrasym ) { M_free(AM.gextrasym,"extrasym"); AM.gextrasym = 0; } i = 1; s = AC.extrasym; while ( *s ) { s++; i++; } AM.gextrasym = (UBYTE *)Malloc1(i*sizeof(UBYTE),"extrasym"); for ( j = 0; j < i; j++ ) AM.gextrasym[j] = AC.extrasym[j]; AM.gTokensWriteFlag= AC.TokensWriteFlag; AM.gNoSpacesInNumbers = AO.NoSpacesInNumbers; AM.gIndentSpace = AO.IndentSpace; AM.gUnitTrace = AC.lUnitTrace; AM.gDefDim = AC.lDefDim; AM.gDefDim4 = AC.lDefDim4; AM.gncmod = AC.ncmod; AM.gnpowmod = AC.npowmod; AM.gmodmode = AC.modmode; AM.gCnumpows = AC.Cnumpows; AM.gOutputMode = AC.OutputMode; AM.gOutputSpaces = AC.OutputSpaces; AM.gOutNumberType = AC.OutNumberType; AM.gfunpowers = AC.funpowers; AM.gPolyFun = AC.lPolyFun; AM.gPolyFunInv = AC.lPolyFunInv; AM.gPolyFunType = AC.lPolyFunType; AM.gPolyFunExp = AC.lPolyFunExp; AM.gPolyFunVar = AC.lPolyFunVar; AM.gPolyFunPow = AC.lPolyFunPow; AM.gparallelflag = AC.parallelflag; AM.gProcessBucketSize = AC.ProcessBucketSize; AM.gproperorderflag = AC.properorderflag; AM.gThreadBucketSize = AC.ThreadBucketSize; AM.gThreadStats = AC.ThreadStats; AM.gFinalStats = AC.FinalStats; AM.gOldGCDflag = AC.OldGCDflag; AM.gWTimeStatsFlag = AC.WTimeStatsFlag; AM.gThreadsFlag = AC.ThreadsFlag; AM.gThreadBalancing = AC.ThreadBalancing; AM.gThreadSortFileSynch = AC.ThreadSortFileSynch; AM.gProcessStats = AC.ProcessStats; AM.gOldParallelStats = AC.OldParallelStats; AM.gIsFortran90 = AC.IsFortran90; AM.gSizeCommuteInSet = AC.SizeCommuteInSet; AM.gnumextrasym = (cbuf+AM.sbufnum)->numrhs; if ( AM.gFortran90Kind ) { M_free(AM.gFortran90Kind,"Fortran 90 Kind"); AM.gFortran90Kind = 0; } if ( AC.Fortran90Kind ) { AM.gFortran90Kind = strDup1(AC.Fortran90Kind,"Fortran 90 Kind"); } p = AM.gcmod; m = AC.cmod; i = ABS(AC.ncmod); NCOPY(p,m,i); p = AM.gpowmod; m = AC.powmod; i = AC.npowmod; NCOPY(p,m,i); pp = AM.gUniTrace; mm = AC.lUniTrace; i = 4; NCOPY(pp,mm,i); AM.gSortType = AC.SortType; AM.gShortStatsMax = AC.ShortStatsMax; if ( AO.CurrentDictionary > 0 || AP.OpenDictionary > 0 ) { Warning("You cannot have an open or selected dictionary at a .global. Dictionary closed."); AP.OpenDictionary = 0; AO.CurrentDictionary = 0; } AO.gNumDictionaries = AO.NumDictionaries; for ( i = 0; i < AO.NumDictionaries; i++ ) { AO.Dictionaries[i]->gnumelements = AO.Dictionaries[i]->numelements; } if ( AM.NumSpectatorFiles > 0 ) { for ( i = 0; i < AM.SizeForSpectatorFiles; i++ ) { if ( AM.SpectatorFiles[i].name != 0 ) AM.SpectatorFiles[i].flags |= GLOBALSPECTATORFLAG; } } } /* #] MakeGlobal : #[ TestDrop : */ void TestDrop(void) { EXPRESSIONS e; WORD j; for ( j = 0, e = Expressions; j < NumExpressions; j++, e++ ) { switch ( e->status ) { case SKIPLEXPRESSION: e->status = LOCALEXPRESSION; break; case UNHIDELEXPRESSION: e->status = LOCALEXPRESSION; ClearBracketIndex(j); e->bracketinfo = e->newbracketinfo; e->newbracketinfo = 0; break; case HIDELEXPRESSION: e->status = HIDDENLEXPRESSION; break; case SKIPGEXPRESSION: e->status = GLOBALEXPRESSION; break; case UNHIDEGEXPRESSION: e->status = GLOBALEXPRESSION; ClearBracketIndex(j); e->bracketinfo = e->newbracketinfo; e->newbracketinfo = 0; break; case HIDEGEXPRESSION: e->status = HIDDENGEXPRESSION; break; case DROPLEXPRESSION: case DROPGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case DROPSPECTATOREXPRESSION: e->status = DROPPEDEXPRESSION; ClearBracketIndex(j); e->bracketinfo = e->newbracketinfo; e->newbracketinfo = 0; if ( e->replace >= 0 ) { Expressions[e->replace].replace = REGULAREXPRESSION; AC.exprnames->namenode[e->node].number = e->replace; e->replace = REGULAREXPRESSION; } else { AC.exprnames->namenode[e->node].type = CDELETE; AC.DidClean = 1; } break; case LOCALEXPRESSION: case GLOBALEXPRESSION: ClearBracketIndex(j); e->bracketinfo = e->newbracketinfo; e->newbracketinfo = 0; break; case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: break; case INTOHIDELEXPRESSION: ClearBracketIndex(j); e->bracketinfo = e->newbracketinfo; e->newbracketinfo = 0; e->status = HIDDENLEXPRESSION; break; case INTOHIDEGEXPRESSION: ClearBracketIndex(j); e->bracketinfo = e->newbracketinfo; e->newbracketinfo = 0; e->status = HIDDENGEXPRESSION; break; default: ClearBracketIndex(j); e->bracketinfo = 0; break; } if ( e->replace == NEWLYDEFINEDEXPRESSION ) e->replace = REGULAREXPRESSION; } } /* #] TestDrop : #[ PutInVflags : */ void PutInVflags(WORD nexpr) { EXPRESSIONS e = Expressions + nexpr; POSITION *old; WORD *oldw; int i; restart:; if ( AS.OldOnFile == 0 ) { AS.NumOldOnFile = 20; AS.OldOnFile = (POSITION *)Malloc1(AS.NumOldOnFile*sizeof(POSITION),"file pointers"); } else if ( nexpr >= AS.NumOldOnFile ) { old = AS.OldOnFile; AS.OldOnFile = (POSITION *)Malloc1(2*AS.NumOldOnFile*sizeof(POSITION),"file pointers"); for ( i = 0; i < AS.NumOldOnFile; i++ ) AS.OldOnFile[i] = old[i]; AS.NumOldOnFile = 2*AS.NumOldOnFile; M_free(old,"process file pointers"); } if ( AS.OldNumFactors == 0 ) { AS.NumOldNumFactors = 20; AS.OldNumFactors = (WORD *)Malloc1(AS.NumOldNumFactors*sizeof(WORD),"numfactors pointers"); AS.Oldvflags = (WORD *)Malloc1(AS.NumOldNumFactors*sizeof(WORD),"vflags pointers"); AS.Olduflags = (WORD *)Malloc1(AS.NumOldNumFactors*sizeof(WORD),"uflags pointers"); } else if ( nexpr >= AS.NumOldNumFactors ) { oldw = AS.OldNumFactors; AS.OldNumFactors = (WORD *)Malloc1(2*AS.NumOldNumFactors*sizeof(WORD),"numfactors pointers"); for ( i = 0; i < AS.NumOldNumFactors; i++ ) AS.OldNumFactors[i] = oldw[i]; M_free(oldw,"numfactors pointers"); oldw = AS.Oldvflags; AS.Oldvflags = (WORD *)Malloc1(2*AS.NumOldNumFactors*sizeof(WORD),"vflags pointers"); for ( i = 0; i < AS.NumOldNumFactors; i++ ) AS.Oldvflags[i] = oldw[i]; M_free(oldw,"vflags pointers"); oldw = AS.Olduflags; AS.Olduflags = (WORD *)Malloc1(2*AS.NumOldNumFactors*sizeof(WORD),"uflags pointers"); for ( i = 0; i < AS.NumOldNumFactors; i++ ) AS.Olduflags[i] = oldw[i]; M_free(oldw,"uflags pointers"); AS.NumOldNumFactors = 2*AS.NumOldNumFactors; } /* The next is needed when we Load a .sav file with lots of expressions. */ if ( nexpr >= AS.NumOldOnFile || nexpr >= AS.NumOldNumFactors ) goto restart; AS.OldOnFile[nexpr] = e->onfile; AS.OldNumFactors[nexpr] = e->numfactors; AS.Oldvflags[nexpr] = e->vflags; AS.Olduflags[nexpr] = e->uflags; } /* #] PutInVflags : #[ DoExecute : */ int DoExecute(WORD par, WORD skip) { GETIDENTITY int RetCode = 0; int i, oldmultithreaded = AS.MultiThreaded; #ifdef PARALLELCODE int j; #endif SpecialCleanup(BHEAD0); if ( skip ) goto skipexec; if ( AC.IfLevel > 0 ) { MesPrint(" %d endif statement(s) missing",AC.IfLevel); RetCode = 1; } if ( AC.WhileLevel > 0 ) { MesPrint(" %d endwhile statement(s) missing",AC.WhileLevel); RetCode = 1; } if ( AC.arglevel > 0 ) { MesPrint(" %d endargument statement(s) missing",AC.arglevel); RetCode = 1; } if ( AC.termlevel > 0 ) { MesPrint(" %d endterm statement(s) missing",AC.termlevel); RetCode = 1; } if ( AC.insidelevel > 0 ) { MesPrint(" %d endinside statement(s) missing",AC.insidelevel); RetCode = 1; } if ( AC.inexprlevel > 0 ) { MesPrint(" %d endinexpression statement(s) missing",AC.inexprlevel); RetCode = 1; } if ( AC.NumLabels > 0 ) { for ( i = 0; i < AC.NumLabels; i++ ) { if ( AC.Labels[i] < 0 ) { MesPrint(" -->Label %s missing",AC.LabelNames[i]); RetCode = 1; } } } if ( AC.SwitchLevel > 0 ) { MesPrint(" %d endswitch statement(s) missing",AC.SwitchLevel); RetCode = 1; } if ( AC.dolooplevel > 0 ) { MesPrint(" %d enddo statement(s) missing",AC.dolooplevel); RetCode = 1; } if ( AP.OpenDictionary > 0 ) { MesPrint(" Dictionary %s has not been closed.", AO.Dictionaries[AP.OpenDictionary-1]->name); AP.OpenDictionary = 0; RetCode = 1; } if ( RetCode ) return(RetCode); AR.Cnumlhs = cbuf[AM.rbufnum].numlhs; if ( ( AS.ExecMode = par ) == GLOBALMODULE ) AS.ExecMode = 0; #ifdef PARALLELCODE /* Now check whether we have either the regular parallel flag or the mparallel flag set. Next check whether any of the expressions has partodo set. If any of the above we need to check what the dollar status is. */ AC.partodoflag = -1; if ( NumPotModdollars >= 0 ) { for ( i = 0; i < NumExpressions; i++ ) { if ( Expressions[i].partodo ) { AC.partodoflag = 1; break; } } } #ifdef WITHMPI if ( AC.partodoflag > 0 && PF.numtasks < 3 ) { AC.partodoflag = 0; } #endif if ( AC.partodoflag > 0 || ( NumPotModdollars > 0 && AC.mparallelflag == PARALLELFLAG ) ) { if ( NumPotModdollars > NumModOptdollars ) { AC.mparallelflag |= NOPARALLEL_DOLLAR; #ifdef WITHPTHREADS AS.MultiThreaded = 0; #endif AC.partodoflag = 0; } else { for ( i = 0; i < NumPotModdollars; i++ ) { for ( j = 0; j < NumModOptdollars; j++ ) if ( PotModdollars[i] == ModOptdollars[j].number ) break; if ( j >= NumModOptdollars ) { AC.mparallelflag |= NOPARALLEL_DOLLAR; #ifdef WITHPTHREADS AS.MultiThreaded = 0; #endif AC.partodoflag = 0; break; } switch ( ModOptdollars[j].type ) { case MODSUM: case MODMAX: case MODMIN: case MODLOCAL: break; default: AC.mparallelflag |= NOPARALLEL_DOLLAR; AS.MultiThreaded = 0; AC.partodoflag = 0; break; } } } } else if ( ( AC.mparallelflag & NOPARALLEL_USER ) != 0 ) { #ifdef WITHPTHREADS AS.MultiThreaded = 0; #endif AC.partodoflag = 0; } if ( AC.partodoflag == 0 ) { for ( i = 0; i < NumExpressions; i++ ) { Expressions[i].partodo = 0; } } else if ( AC.partodoflag == -1 ) { AC.partodoflag = 0; } #endif #ifdef WITHMPI /* * Check RHS expressions. */ if ( AC.RhsExprInModuleFlag && (AC.mparallelflag == PARALLELFLAG || AC.partodoflag) ) { if (PF.rhsInParallel) { PF.mkSlaveInfile=1; if(PF.me != MASTER){ PF.slavebuf.PObuffer=(WORD *)Malloc1(AM.ScratSize*sizeof(WORD),"PF inbuf"); PF.slavebuf.POsize=AM.ScratSize*sizeof(WORD); PF.slavebuf.POfull = PF.slavebuf.POfill = PF.slavebuf.PObuffer; PF.slavebuf.POstop= PF.slavebuf.PObuffer+AM.ScratSize; PUTZERO(PF.slavebuf.POposition); }/*if(PF.me != MASTER)*/ } else { AC.mparallelflag |= NOPARALLEL_RHS; AC.partodoflag = 0; for ( i = 0; i < NumExpressions; i++ ) { Expressions[i].partodo = 0; } } } /* * Set $-variables with MODSUM to zero on the slaves. */ if ( (AC.mparallelflag == PARALLELFLAG || AC.partodoflag) && PF.me != MASTER ) { for ( i = 0; i < NumModOptdollars; i++ ) { if ( ModOptdollars[i].type == MODSUM ) { DOLLARS d = Dollars + ModOptdollars[i].number; d->type = DOLZERO; if ( d->where && d->where != &AM.dollarzero ) M_free(d->where, "old content of dollar"); d->where = &AM.dollarzero; d->size = 0; CleanDollarFactors(d); } } } #endif AR.SortType = AC.SortType; #ifdef WITHMPI if ( PF.me == MASTER ) #endif { if ( AC.SetupFlag ) WriteSetup(); if ( AC.NamesFlag || AC.CodesFlag ) WriteLists(); } if ( par == GLOBALMODULE ) MakeGlobal(); if ( RevertScratch() ) return(-1); if ( AC.ncmod ) SetMods(); /* Warn if the module has to run in sequential mode due to some problems. */ #ifdef WITHMPI if ( PF.me == MASTER ) #endif { if ( !AC.ThreadsFlag || AC.mparallelflag & NOPARALLEL_USER ) { /* The user switched off the parallel execution explicitly. */ } else if ( AC.mparallelflag & NOPARALLEL_DOLLAR ) { if ( AC.WarnFlag >= 1 ) { /* Warning */ int i, j, k, n; UBYTE *s, *s1; s = strDup1((UBYTE *)"","NOPARALLEL_DOLLAR s"); n = 0; j = NumPotModdollars; for ( i = 0; i < j; i++ ) { for ( k = 0; k < NumModOptdollars; k++ ) if ( ModOptdollars[k].number == PotModdollars[i] ) break; if ( k >= NumModOptdollars ) { /* global $-variable */ if ( n > 0 ) s = AddToString(s,(UBYTE *)", ",0); s = AddToString(s,(UBYTE *)"$",0); s = AddToString(s,DOLLARNAME(Dollars,PotModdollars[i]),0); n++; } } s1 = strDup1((UBYTE *)"This module is forced to run in sequential mode due to $-variable","NOPARALLEL_DOLLAR s1"); if ( n != 1 ) s1 = AddToString(s1,(UBYTE *)"s",0); s1 = AddToString(s1,(UBYTE *)": ",0); s1 = AddToString(s1,s,0); Warning((char *)s1); M_free(s,"NOPARALLEL_DOLLAR s"); M_free(s1,"NOPARALLEL_DOLLAR s1"); } } else if ( AC.mparallelflag & NOPARALLEL_RHS ) { HighWarning("This module is forced to run in sequential mode due to RHS expression names"); } else if ( AC.mparallelflag & NOPARALLEL_CONVPOLY ) { HighWarning("This module is forced to run in sequential mode due to conversion to extra symbols"); } else if ( AC.mparallelflag & NOPARALLEL_SPECTATOR ) { HighWarning("This module is forced to run in sequential mode due to tospectator/copyspectator"); } else if ( AC.mparallelflag & NOPARALLEL_TBLDOLLAR ) { HighWarning("This module is forced to run in sequential mode due to $-variable assignments in tables"); } else if ( AC.mparallelflag & NOPARALLEL_NPROC ) { HighWarning("This module is forced to run in sequential mode because there is only one processor"); } } /* Now the actual execution */ #ifdef WITHMPI /* * Turn on AS.printflag to print runtime errors occurring on slaves. */ AS.printflag = 1; #endif if ( AP.preError == 0 && ( Processor() || WriteAll() ) ) RetCode = -1; #ifdef WITHMPI AS.printflag = 0; #endif /* That was it. Next is cleanup. */ if ( AC.ncmod ) UnSetMods(); AS.MultiThreaded = oldmultithreaded; TableReset(); /*[28sep2005 mt]:*/ #ifdef WITHMPI /* Combine and then broadcast modified dollar variables. */ if ( NumPotModdollars > 0 ) { RetCode = PF_CollectModifiedDollars(); if ( RetCode ) return RetCode; RetCode = PF_BroadcastModifiedDollars(); if ( RetCode ) return RetCode; } /* Broadcast the list of objects converted to symbols in AM.sbufnum. */ if ( AC.topolynomialflag & TOPOLYNOMIALFLAG ) { RetCode = PF_BroadcastCBuf(AM.sbufnum); if ( RetCode ) return RetCode; } /* * Broadcast AR.expflags, which may be used on the slaves in the next module * via ZERO_ or UNCHANGED_. It also broadcasts several flags of each expression. */ RetCode = PF_BroadcastExpFlags(); if ( RetCode ) return RetCode; /* * Clean the hide file on the slaves, which was used for RHS expressions * broadcast from the master at the beginning of the module. */ if ( PF.me != MASTER && AR.hidefile->PObuffer ) { if ( AR.hidefile->handle >= 0 ) { CloseFile(AR.hidefile->handle); AR.hidefile->handle = -1; remove(AR.hidefile->name); } AR.hidefile->POfull = AR.hidefile->POfill = AR.hidefile->PObuffer; PUTZERO(AR.hidefile->POposition); } #endif #ifdef WITHPTHREADS for ( j = 0; j < NumModOptdollars; j++ ) { if ( ModOptdollars[j].dstruct ) { //Here we must collect global maximum or minimum dollar values, for //MODMAX and MODMIN cases, and put them in the global dollar variable. //Then we clean up. if ( ModOptdollars[j].type == MODMAX || ModOptdollars[j].type == MODMIN ) { const WORD globalnumber = ModOptdollars[j].number; const DOLLARS gd = Dollars + globalnumber; // If the global dollar is DOLZERO, convert it into DOLNUMBER. // Note that parts of the code rely on the trailing zero. if ( gd->type == DOLZERO ) { gd->type = DOLNUMBER; if ( ! gd->where || gd->where == &(AM.dollarzero) ) { gd->size = MINALLOC; gd->where = (WORD*)Malloc1(gd->size*sizeof(WORD), "dollar contents"); } gd->where[0] = 4; gd->where[1] = 0; gd->where[2] = 1; gd->where[3] = 3; gd->where[4] = 0; } for ( i = 0; i < AM.totalnumberofthreads; i++ ) { const DOLLARS ld = &(ModOptdollars[j].dstruct[i]); // This can happen when a thread doesn't obtain a dollar value, // for instance if it did not process any terms. if ( ld->type == DOLUNDEFINED ) continue; if ( ld->type != DOLZERO && ld->type != DOLNUMBER ) { MLOCK(ErrorMessageLock); MesPrint("Illegal dollar variable type in MODMIN/MODMAX case: %d", ld->type); MUNLOCK(ErrorMessageLock); Terminate(-1); } // If the thread value is DOLZERO, convert it to DOLNUMBER: if ( ld->type == DOLZERO ) { ld->type = DOLNUMBER; if ( ! ld->where || ld->where == &(AM.dollarzero) ) { ld->size = MINALLOC; ld->where = (WORD*)Malloc1(ld->size*sizeof(WORD), "dollar contents"); } ld->where[0] = 4; ld->where[1] = 0; ld->where[2] = 1; ld->where[3] = 3; ld->where[4] = 0; } // If the global dollar is DOLUNDEFINED, just take the thread value. This comes // after the above "continue" if the local dollar is DOLUNDEFINED: thus, if the // global and all local dollars are DOLUNDEFINED, the final global dollar will // still be DOLUNDEFINED. if ( gd->type == DOLUNDEFINED ) { gd->type = ld->type; if ( ! gd->where || gd->where == &(AM.dollarzero) ) { gd->size = MINALLOC; gd->where = (WORD*)Malloc1(gd->size*sizeof(WORD), "dollar contents"); } for ( int v = 0; v < 5; v++ ) { gd->where[v] = ld->where[v]; } continue; } // MODMIN and MODMAX are supposed to work only for "short integers". Thus // the term data should be "4 N 1 +-3". Use CompCoef to make the comparison: const WORD cmp = CompCoef(gd->where, ld->where); if ( ( ModOptdollars[j].type == MODMAX && cmp < 0 ) || ( ModOptdollars[j].type == MODMIN && cmp > 0 ) ) { // Update the global value: for ( int v = 0; v < 5; v++ ) { gd->where[v] = ld->where[v]; } if ( gd->where[4] != 0 ) { // The loop above should have put a trailing zero after the coeff // size. If not, there is probably a bug somewhere else... MLOCK(ErrorMessageLock); MesPrint("Missing trailing zero in MODMIN/MODMAX global dollar %d", globalnumber); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } // If the global dollar is 0, convert it into DOLZERO: if ( gd->where[1] == 0 ) { gd->type = DOLZERO; if ( gd->where && gd->where != &(AM.dollarzero) ) { M_free(gd->where, "dollar contents"); } gd->size = 0; gd->where = &(AM.dollarzero); } } // Now clean up the thread-local variables for ( i = 0; i < AM.totalnumberofthreads; i++ ) { if ( ModOptdollars[j].dstruct[i].size > 0 ) { CleanDollarFactors(&(ModOptdollars[j].dstruct[i])); if ( ModOptdollars[j].dstruct[i].where && ModOptdollars[j].dstruct[i].where != &(AM.dollarzero) ) { M_free(ModOptdollars[j].dstruct[i].where,"Local dollar value"); } } } /* Now clean up the whole array. */ M_free(ModOptdollars[j].dstruct,"Local DOLLARS"); ModOptdollars[j].dstruct = 0; } } #endif /*:[28sep2005 mt]*/ /* @@@@@@@@@@@@@@@ Now follows the code to invalidate caches for all objects in the PotModdollars. There are NumPotModdollars of them and PotModdollars is an array of WORD. */ /* Cleanup: */ #ifdef JV_IS_WRONG /* Giving back this memory gives way too much activity with Malloc1 Better to keep it and just put the number of used objects to zero (JV) If you put the lijst equal to NULL, please also make maxnum = 0 */ if ( ModOptdollars ) M_free(ModOptdollars, "ModOptdollars pointer"); if ( PotModdollars ) M_free(PotModdollars, "PotModdollars pointer"); /* ModOptdollars changed to AC.ModOptDolList.lijst because AIX C compiler complained. MF 30/07/2003. */ AC.ModOptDolList.lijst = NULL; /* PotModdollars changed to AC.PotModDolList.lijst because AIX C compiler complained. MF 30/07/2003. */ AC.PotModDolList.lijst = NULL; #endif NumPotModdollars = 0; NumModOptdollars = 0; skipexec: /* Clean up the switch information. We keep the switch array and heap. */ if ( AC.SwitchInArray > 0 ) { for ( i = 0; i < AC.SwitchInArray; i++ ) { SWITCH *sw = AC.SwitchArray + i; if ( sw->table ) M_free(sw->table,"Switch table"); sw->table = 0; sw->defaultcase.ncase = 0; sw->defaultcase.value = 0; sw->defaultcase.compbuffer = 0; sw->endswitch.ncase = 0; sw->endswitch.value = 0; sw->endswitch.compbuffer = 0; sw->typetable = 0; sw->maxcase = 0; sw->mincase = 0; sw->numcases = 0; sw->tablesize = 0; sw->caseoffset = 0; sw->iflevel = 0; sw->whilelevel = 0; sw->nestingsum = 0; } AC.SwitchInArray = 0; AC.SwitchLevel = 0; } #ifdef PARALLELCODE AC.numpfirstnum = 0; #endif AC.DidClean = 0; AC.PolyRatFunChanged = 0; TestDrop(); if ( par == STOREMODULE || par == CLEARMODULE ) { ClearOptimize(); if ( par == STOREMODULE && PopVariables() ) RetCode = -1; if ( AR.infile->handle >= 0 ) { CloseFile(AR.infile->handle); remove(AR.infile->name); AR.infile->handle = -1; } AR.infile->POfill = AR.infile->PObuffer; PUTZERO(AR.infile->POposition); AR.infile->POfull = AR.infile->PObuffer; if ( AR.outfile->handle >= 0 ) { CloseFile(AR.outfile->handle); remove(AR.outfile->name); AR.outfile->handle = -1; } AR.outfile->POfull = AR.outfile->POfill = AR.outfile->PObuffer; PUTZERO(AR.outfile->POposition); if ( AR.hidefile->handle >= 0 ) { CloseFile(AR.hidefile->handle); remove(AR.hidefile->name); AR.hidefile->handle = -1; } AR.hidefile->POfull = AR.hidefile->POfill = AR.hidefile->PObuffer; PUTZERO(AR.hidefile->POposition); AC.HideLevel = 0; if ( par == CLEARMODULE ) { if ( DeleteStore(0) < 0 ) { MesPrint("Cannot restart the storage file"); RetCode = -1; } else RetCode = 0; CleanUp(1); ResetVariables(2); AM.gProcessBucketSize = AM.hProcessBucketSize; AM.gparallelflag = PARALLELFLAG; AM.gnumextrasym = AM.ggnumextrasym; PruneExtraSymbols(AM.ggnumextrasym); IniVars(); } ClearSpectators(par); } else { if ( CleanExpr(0) ) RetCode = -1; if ( AC.DidClean ) CompactifyTree(AC.exprnames,EXPRNAMES); ResetVariables(0); CleanUpSort(-1); } clearcbuf(AC.cbufnum); if ( AC.MultiBracketBuf != 0 ) { for ( i = 0; i < MAXMULTIBRACKETLEVELS; i++ ) { if ( AC.MultiBracketBuf[i] ) { M_free(AC.MultiBracketBuf[i],"bracket buffer i"); AC.MultiBracketBuf[i] = 0; } } AC.MultiBracketLevels = 0; M_free(AC.MultiBracketBuf,"multi bracket buffer"); AC.MultiBracketBuf = 0; } if ( AC.SortReallocateFlag ) { /* Reallocate the sort buffers to reduce resident set usage */ /* AT.SS is the same as AT.S0 here */ SORTING* S = AT.S0; M_free(S->lBuffer, "SortReallocate lBuffer+sBuffer"); S->lBuffer = Malloc1(sizeof(*(S->lBuffer))*(S->LargeSize+S->SmallEsize), "SortReallocate lBuffer+sBuffer"); S->lTop = S->lBuffer+S->LargeSize; S->sBuffer = S->lTop; if ( S->LargeSize == 0 ) { S->lBuffer = 0; S->lTop = 0; } S->sTop = S->sBuffer + S->SmallSize; S->sTop2 = S->sBuffer + S->SmallEsize; S->sHalf = S->sBuffer + (LONG)((S->SmallSize+S->SmallEsize)>>1); #ifdef WITHPTHREADS /* We have to re-set the pointers into master lBuffer in the SortBlocks */ UpdateSortBlocks(AM.totalnumberofthreads-1); /* The SortBots do not have a real sort buffer to reallocate. */ /* AB[0] has been reallocated above already. */ for ( i = 1; i < AM.totalnumberofthreads; i++ ) { SORTING* S = AB[i]->T.S0; M_free(S->lBuffer, "SortReallocate lBuffer+sBuffer"); S->lBuffer = Malloc1(sizeof(*(S->lBuffer))*(S->LargeSize+S->SmallEsize), "SortReallocate lBuffer+sBuffer"); S->lTop = S->lBuffer+S->LargeSize; S->sBuffer = S->lTop; if ( S->LargeSize == 0 ) { S->lBuffer = 0; S->lTop = 0; } S->sTop = S->sBuffer + S->SmallSize; S->sTop2 = S->sBuffer + S->SmallEsize; S->sHalf = S->sBuffer + (LONG)((S->SmallSize+S->SmallEsize)>>1); } #endif } if ( AC.SortReallocateFlag == 2 ) { /* The Flag was set for a single module by the preprocessor #sortreallocate, so turn it off again. */ AC.SortReallocateFlag = 0; } return(RetCode); } /* #] DoExecute : #[ PutBracket : Routine uses the bracket info to split a term into two pieces: 1: the part outside the bracket, and 2: the part inside the bracket. These parts are separated by a subterm of type HAAKJE. This subterm looks like: HAAKJE,3,level The level is used for nestings of brackets. The print routines cannot handle this yet (31-Mar-1988). The Bracket selector is in AT.BrackBuf in the form of a regular term, but without coefficient. When AR.BracketOn < 0 we have a socalled antibracket. The main effect is an exchange of the inner and outer part and where the coefficient goes. Routine recoded to facilitate b p1,p2; etc for dotproducts and tensors 15-oct-1991 */ int PutBracket(PHEAD WORD *termin) { GETBIDENTITY WORD *t, *t1, *b, i, j, *lastfun; WORD *t2, *s1, *s2; WORD *bStop, *bb, *bf, *tStop; WORD *term1,*term2, *m1, *m2, *tStopa; WORD *bbb = 0, *bind, *binst = 0, bwild = 0, *bss = 0, *bns = 0, bset = 0; term1 = AT.WorkPointer+1; term2 = (WORD *)(((UBYTE *)(term1)) + AM.MaxTer); if ( ( (WORD *)(((UBYTE *)(term2)) + AM.MaxTer) ) > AT.WorkTop ) { MesWork(); } if ( AR.BracketOn < 0 ) { t2 = term1; t1 = term2; /* AntiBracket */ } else { t1 = term1; t2 = term2; /* Regular bracket */ } b = AT.BrackBuf; bStop = b+*b; b++; while ( b < bStop ) { if ( *b == INDEX ) { bwild = 1; bbb = b+2; binst = b + b[1]; } if ( *b == SETSET ) { bset = 1; bss = b+2; bns = b + b[1]; } b += b[1]; } t = termin; tStopa = t + *t; i = *(t + *t -1); i = ABS(i); if ( AR.PolyFun && AT.PolyAct ) tStop = termin + AT.PolyAct; #ifdef WITHFLOAT else if ( AT.FloatPos ) tStop = termin + AT.FloatPos; #endif else tStop = tStopa - i; t++; if ( AR.BracketOn < 0 ) { lastfun = 0; while ( t < tStop && *t >= FUNCTION && functions[*t-FUNCTION].commute ) { b = AT.BrackBuf+1; while ( b < bStop ) { if ( *b == *t ) { lastfun = t; while ( t < tStop && *t >= FUNCTION && functions[*t-FUNCTION].commute ) t += t[1]; goto NextNcom1; } b += b[1]; } if ( bset ) { b = bss; while ( b < bns ) { if ( b[1] == CFUNCTION ) { /* Set of functions */ SETS set = Sets+b[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { lastfun = t; while ( t < tStop && *t >= FUNCTION && functions[*t-FUNCTION].commute ) t += t[1]; goto NextNcom1; } } } b += 2; } } if ( bwild && *t >= FUNCTION && functions[*t-FUNCTION].spec ) { s1 = t + t[1]; s2 = t + FUNHEAD; while ( s2 < s1 ) { bind = bbb; while ( bind < binst ) { if ( *bind == *s2 ) { lastfun = t; while ( t < tStop && *t >= FUNCTION && functions[*t-FUNCTION].commute ) t += t[1]; goto NextNcom1; } bind++; } s2++; } } t += t[1]; } NextNcom1: s1 = termin + 1; if ( lastfun ) { while ( s1 < lastfun ) *t2++ = *s1++; while ( s1 < t ) *t1++ = *s1++; } else { while ( s1 < t ) *t2++ = *s1++; } } else { lastfun = t; while ( t < tStop && *t >= FUNCTION && functions[*t-FUNCTION].commute ) { b = AT.BrackBuf+1; while ( b < bStop ) { if ( *b == *t ) { lastfun = t + t[1]; goto NextNcom; } b += b[1]; } if ( bset ) { b = bss; while ( b < bns ) { if ( b[1] == CFUNCTION ) { /* Set of functions */ SETS set = Sets+b[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { lastfun = t + t[1]; goto NextNcom; } } } b += 2; } } if ( bwild && *t >= FUNCTION && functions[*t-FUNCTION].spec ) { s1 = t + t[1]; s2 = t + FUNHEAD; while ( s2 < s1 ) { bind = bbb; while ( bind < binst ) { if ( *bind == *s2 ) { lastfun = t + t[1]; goto NextNcom; } bind++; } s2++; } } NextNcom: t += t[1]; } s1 = termin + 1; while ( s1 < lastfun ) *t1++ = *s1++; while ( s1 < t ) *t2++ = *s1++; } /* Now we have only commuting functions left. Move the b pointer to them. */ b = AT.BrackBuf + 1; while ( b < bStop && *b >= FUNCTION && ( *b < FUNCTION || functions[*b-FUNCTION].commute ) ) { b += b[1]; } bf = b; while ( t < tStop && ( bf < bStop || bwild || bset ) ) { b = bf; while ( b < bStop && *b != *t ) { b += b[1]; } i = t[1]; if ( *t >= FUNCTION ) { /* We are in function territory */ if ( b < bStop && *b == *t ) goto FunBrac; if ( bset ) { b = bss; while ( b < bns ) { if ( b[1] == CFUNCTION ) { /* Set of functions */ SETS set = Sets+b[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) goto FunBrac; } } b += 2; } } if ( bwild && *t >= FUNCTION && functions[*t-FUNCTION].spec ) { s1 = t + t[1]; s2 = t + FUNHEAD; while ( s2 < s1 ) { bind = bbb; while ( bind < binst ) { if ( *bind == *s2 ) goto FunBrac; bind++; } s2++; } } NCOPY(t2,t,i); continue; FunBrac: NCOPY(t1,t,i); continue; } /* We have left: DELTA, INDEX, VECTOR, DOTPRODUCT, SYMBOL */ if ( *t == DELTA ) { if ( b < bStop && *b == DELTA ) { b += b[1]; NCOPY(t1,t,i); } else { NCOPY(t2,t,i); } } else if ( *t == INDEX ) { if ( bwild ) { m1 = t1; m2 = t2; *t1++ = *t; t1++; *t2++ = *t; t2++; bind = bbb; j = t[1] -2; t += 2; while ( --j >= 0 ) { while ( *bind < *t && bind < binst ) bind++; if ( *bind == *t && bind < binst ) { *t1++ = *t++; } else if ( bset ) { WORD *b3 = bss; while ( b3 < bns ) { if ( b3[1] == CVECTOR ) { SETS set = Sets+b3[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { *t1++ = *t++; goto nextind; } } } b3 += 2; } *t2++ = *t++; } else *t2++ = *t++; nextind:; } m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else if ( bset ) { m1 = t1; m2 = t2; *t1++ = *t; t1++; *t2++ = *t; t2++; j = t[1] -2; t += 2; while ( --j >= 0 ) { WORD *b3 = bss; while ( b3 < bns ) { if ( b3[1] == CVECTOR ) { SETS set = Sets+b3[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { *t1++ = *t++; goto nextind2; } } } b3 += 2; } *t2++ = *t++; nextind2:; } m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else { NCOPY(t2,t,i); } } else if ( *t == VECTOR ) { if ( ( b < bStop && *b == VECTOR ) || bwild ) { if ( b < bStop && *b == VECTOR ) { bb = b + b[1]; b += 2; } else bb = b; j = t[1] - 2; m1 = t1; m2 = t2; *t1++ = *t; *t2++ = *t; t1++; t2++; t += 2; while ( j > 0 ) { j -= 2; while ( b < bb && ( *b < *t || ( *b == *t && b[1] < t[1] ) ) ) b += 2; if ( b < bb && ( *t == *b && t[1] == b[1] ) ) { *t1++ = *t++; *t1++ = *t++; goto nextvec; } else if ( bwild ) { bind = bbb; while ( bind < binst ) { if ( *t == *bind || t[1] == *bind ) { *t1++ = *t++; *t1++ = *t++; goto nextvec; } bind++; } } if ( bset ) { WORD *b3 = bss; while ( b3 < bns ) { if ( b3[1] == CVECTOR ) { SETS set = Sets+b3[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { *t1++ = *t++; *t1++ = *t++; goto nextvec; } } } b3 += 2; } } *t2++ = *t++; *t2++ = *t++; nextvec:; } m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else if ( bset ) { m1 = t1; *t1++ = *t; t1++; m2 = t2; *t2++ = *t; t2++; s2 = t + i; t += 2; while ( t < s2 ) { WORD *b3 = bss; while ( b3 < bns ) { if ( b3[1] == CVECTOR ) { SETS set = Sets+b3[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { *t1++ = *t++; *t1++ = *t++; goto nextvec2; } } } b3 += 2; } *t2++ = *t++; *t2++ = *t++; nextvec2:; } m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else { NCOPY(t2,t,i); } } else if ( *t == DOTPRODUCT ) { if ( ( b < bStop && *b == *t ) || bwild ) { m1 = t1; *t1++ = *t; t1++; m2 = t2; *t2++ = *t; t2++; if ( b >= bStop || *b != *t ) { bb = b; s1 = b; } else { s1 = b + b[1]; bb = b + 2; } s2 = t + i; t += 2; while ( t < s2 && ( bb < s1 || bwild || bset ) ) { while ( bb < s1 && ( *bb < *t || ( *bb == *t && bb[1] < t[1] ) ) ) bb += 3; if ( bb < s1 && *bb == *t && bb[1] == t[1] ) { *t1++ = *t++; *t1++ = *t++; *t1++ = *t++; bb += 3; goto nextdot; } else if ( bwild ) { bind = bbb; while ( bind < binst ) { if ( *bind == *t || *bind == t[1] ) { *t1++ = *t++; *t1++ = *t++; *t1++ = *t++; goto nextdot; } bind++; } } if ( bset ) { WORD *b3 = bss; while ( b3 < bns ) { if ( b3[1] == CVECTOR ) { SETS set = Sets+b3[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t || SetElements[i] == t[1] ) { *t1++ = *t++; *t1++ = *t++; *t1++ = *t++; goto nextdot; } } } b3 += 2; } } *t2++ = *t++; *t2++ = *t++; *t2++ = *t++; nextdot:; } while ( t < s2 ) *t2++ = *t++; m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else if ( bset ) { m1 = t1; *t1++ = *t; t1++; m2 = t2; *t2++ = *t; t2++; s2 = t + i; t += 2; while ( t < s2 ) { WORD *b3 = bss; while ( b3 < bns ) { if ( b3[1] == CVECTOR ) { SETS set = Sets+b3[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t || SetElements[i] == t[1] ) { *t1++ = *t++; *t1++ = *t++; *t1++ = *t++; goto nextdot2; } } } b3 += 2; } *t2++ = *t++; *t2++ = *t++; *t2++ = *t++; nextdot2:; } m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else { NCOPY(t2,t,i); } } else if ( *t == SYMBOL ) { if ( b < bStop && *b == *t ) { m1 = t1; *t1++ = *t; t1++; m2 = t2; *t2++ = *t; t2++; s1 = b + b[1]; bb = b+2; s2 = t + i; t += 2; while ( bb < s1 && t < s2 ) { while ( bb < s1 && *bb < *t ) bb += 2; if ( bb >= s1 ) { if ( bset ) goto TrySymbolSet; break; } if ( *bb == *t ) { *t1++ = *t++; *t1++ = *t++; } else if ( bset ) { WORD *bbb; TrySymbolSet: bbb = bss; while ( bbb < bns ) { if ( bbb[1] == CSYMBOL ) { /* Set of symbols */ SETS set = Sets+bbb[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { *t1++ = *t++; *t1++ = *t++; goto NextSymbol; } } } bbb += 2; } *t2++ = *t++; *t2++ = *t++; } else { *t2++ = *t++; *t2++ = *t++; } NextSymbol:; } while ( t < s2 ) *t2++ = *t++; m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else if ( bset ) { WORD *bbb; m1 = t1; *t1++ = *t; t1++; m2 = t2; *t2++ = *t; t2++; s2 = t + i; t += 2; while ( t < s2 ) { bbb = bss; while ( bbb < bns ) { if ( bbb[1] == CSYMBOL ) { /* Set of symbols */ SETS set = Sets+bbb[0]; WORD i; for ( i = set->first; i < set->last; i++ ) { if ( SetElements[i] == *t ) { *t1++ = *t++; *t1++ = *t++; goto NextSymbol2; } } } bbb += 2; } *t2++ = *t++; *t2++ = *t++; NextSymbol2:; } m1[1] = WORDDIF(t1,m1); if ( m1[1] == 2 ) t1 = m1; m2[1] = WORDDIF(t2,m2); if ( m2[1] == 2 ) t2 = m2; } else { NCOPY(t2,t,i); } } else { NCOPY(t2,t,i); } } if ( ( i = WORDDIF(tStop,t) ) > 0 ) NCOPY(t2,t,i); if ( AR.BracketOn < 0 ) { s1 = t1; t1 = t2; t2 = s1; } do { *t2++ = *t++; } while ( t < (WORD *)tStopa ); t = AT.WorkPointer; i = WORDDIF(t1,term1); *t++ = 4 + i + WORDDIF(t2,term2); t += i; *t++ = HAAKJE; *t++ = 3; *t++ = 0; /* This feature won't be used for a while */ i = WORDDIF(t2,term2); t1 = term2; if ( i > 0 ) NCOPY(t,t1,i); AT.WorkPointer = t; return(0); } /* #] PutBracket : #[ SpecialCleanup : */ void SpecialCleanup(PHEAD0) { GETBIDENTITY if ( AT.previousEfactor ) M_free(AT.previousEfactor,"Efactor cache"); AT.previousEfactor = 0; } /* #] SpecialCleanup : #[ SetMods : */ #ifndef WITHPTHREADS void SetMods(void) { int i, n; if ( AN.cmod != 0 ) M_free(AN.cmod,"AN.cmod"); n = ABS(AN.ncmod); AN.cmod = (UWORD *)Malloc1(sizeof(WORD)*n,"AN.cmod"); for ( i = 0; i < n; i++ ) AN.cmod[i] = AC.cmod[i]; } #endif /* #] SetMods : #[ UnSetMods : */ #ifndef WITHPTHREADS void UnSetMods(void) { if ( AN.cmod != 0 ) M_free(AN.cmod,"AN.cmod"); AN.cmod = 0; } #endif /* #] UnSetMods : #] DoExecute : #[ Expressions : #[ ExchangeExpressions : */ void ExchangeExpressions(int num1, int num2) { GETIDENTITY WORD node1, node2, namesize, TMproto[SUBEXPSIZE]; INDEXENTRY *ind; EXPRESSIONS e1, e2; LONG a; SBYTE *s1, *s2; int i; e1 = Expressions + num1; e2 = Expressions + num2; node1 = e1->node; node2 = e2->node; AC.exprnames->namenode[node1].number = num2; AC.exprnames->namenode[node2].number = num1; a = e1->name; e1->name = e2->name; e2->name = a; namesize = e1->namesize; e1->namesize = e2->namesize; e2->namesize = namesize; e1->node = node2; e2->node = node1; if ( e1->status == STOREDEXPRESSION ) { /* Find the name in the index and replace by the new name */ TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = num1; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; ind = FindInIndex(num1,&AR.StoreData,0,0); s1 = (SBYTE *)(AC.exprnames->namebuffer+e1->name); i = e1->namesize; s2 = ind->name; NCOPY(s2,s1,i); *s2 = 0; SeekFile(AR.StoreData.Handle,&(e1->onfile),SEEK_SET); if ( WriteFile(AR.StoreData.Handle,(UBYTE *)ind, (LONG)(sizeof(INDEXENTRY))) != sizeof(INDEXENTRY) ) { MesPrint("File error while exchanging expressions"); Terminate(-1); } FlushFile(AR.StoreData.Handle); } if ( e2->status == STOREDEXPRESSION ) { /* Find the name in the index and replace by the new name */ TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = num2; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; ind = FindInIndex(num1,&AR.StoreData,0,0); s1 = (SBYTE *)(AC.exprnames->namebuffer+e2->name); i = e2->namesize; s2 = ind->name; NCOPY(s2,s1,i); *s2 = 0; SeekFile(AR.StoreData.Handle,&(e2->onfile),SEEK_SET); if ( WriteFile(AR.StoreData.Handle,(UBYTE *)ind, (LONG)(sizeof(INDEXENTRY))) != sizeof(INDEXENTRY) ) { MesPrint("File error while exchanging expressions"); Terminate(-1); } FlushFile(AR.StoreData.Handle); } } /* #] ExchangeExpressions : #[ GetFirstBracket : */ int GetFirstBracket(WORD *term, int num) { /* Gets the first bracket of the expression 'num' Puts it in term. If no brackets the answer is one. Routine should be thread-safe */ GETIDENTITY POSITION position, oldposition; RENUMBER renumber; FILEHANDLE *fi; WORD type, *oldcomppointer, oldonefile, numword; WORD *t, *tstop; oldcomppointer = AR.CompressPointer; type = Expressions[num].status; if ( type == STOREDEXPRESSION ) { WORD TMproto[SUBEXPSIZE]; TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = num; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; PUTZERO(position); if ( ( renumber = GetTable(num,&position,0) ) == 0 ) { MesCall("GetFirstBracket"); SETERROR(-1) } if ( GetFromStore(term,&position,renumber,&numword,num) < 0 ) { MesCall("GetFirstBracket"); SETERROR(-1) } /* #ifdef WITHPTHREADS */ if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); /* #endif */ } else { /* Active expression */ oldonefile = AR.GetOneFile; if ( type == HIDDENLEXPRESSION || type == HIDDENGEXPRESSION ) { AR.GetOneFile = 2; fi = AR.hidefile; } else { AR.GetOneFile = 0; fi = AR.infile; } if ( fi->handle >= 0 ) { PUTZERO(oldposition); /* SeekFile(fi->handle,&oldposition,SEEK_CUR); */ } else { SETBASEPOSITION(oldposition,fi->POfill-fi->PObuffer); } position = AS.OldOnFile[num]; if ( GetOneTerm(BHEAD term,fi,&position,1) < 0 || ( GetOneTerm(BHEAD term,fi,&position,1) < 0 ) ) { MLOCK(ErrorMessageLock); MesCall("GetFirstBracket"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( fi->handle >= 0 ) { /* SeekFile(fi->handle,&oldposition,SEEK_SET); if ( ISNEGPOS(oldposition) ) { MLOCK(ErrorMessageLock); MesPrint("File error"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } */ } else { fi->POfill = fi->PObuffer+BASEPOSITION(oldposition); } AR.GetOneFile = oldonefile; } AR.CompressPointer = oldcomppointer; if ( *term ) { tstop = term + *term; tstop -= ABS(tstop[-1]); t = term + 1; while ( t < tstop ) { if ( *t == HAAKJE ) break; t += t[1]; } if ( t >= tstop ) { term[0] = 4; term[1] = 1; term[2] = 1; term[3] = 3; } else { *t++ = 1; *t++ = 1; *t++ = 3; *term = t - term; } } else { term[0] = 4; term[1] = 1; term[2] = 1; term[3] = 3; } return(*term); } /* #] GetFirstBracket : #[ GetFirstTerm : */ /** * Gets the first term of an expression. Routine should be thread safe. * * @param[out] term Pointer to the buffer where the term should be written. * @param[in] num The expression number from which to get the term. * @param[in] pre Denotes a pre-processor call (1) or not (0). Used to * determine the correct source file for the expression. * @return First WORD of term, a negative value denotes an error. */ int GetFirstTerm(WORD *term, int num, int pre) { GETIDENTITY POSITION position, oldposition; RENUMBER renumber; FILEHANDLE *fi; WORD type, *oldcomppointer, oldonefile, numword; oldcomppointer = AR.CompressPointer; type = Expressions[num].status; if ( type == STOREDEXPRESSION ) { WORD TMproto[SUBEXPSIZE]; TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = num; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; PUTZERO(position); if ( ( renumber = GetTable(num,&position,0) ) == 0 ) { MesCall("GetFirstTerm"); SETERROR(-1) } if ( GetFromStore(term,&position,renumber,&numword,num) < 0 ) { MesCall("GetFirstTerm"); SETERROR(-1) } /* #ifdef WITHPTHREADS */ if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); /* #endif */ } else { /* Active expression */ oldonefile = AR.GetOneFile; if ( type == HIDDENLEXPRESSION || type == HIDDENGEXPRESSION ) { AR.GetOneFile = 2; fi = AR.hidefile; } else { AR.GetOneFile = 0; if ( Expressions[num].replace == NEWLYDEFINEDEXPRESSION ) { /* During execution, if the expression has already been processed it will be in the outfile. If it has not, the usage is illegal according to the manual, though no error is given. */ if ( pre == 0 ) { fi = AR.outfile; } /* During preprocessing, the expression certainly has not been processed yet. Print an error and terminate. */ else { MesPrint("&isnumerical: expression is not yet defined!"); SETERROR(-1); } } else { /* During execution, we should use the definition as stored at the end of the previous module. This is in the infile. */ if ( pre == 0 ) { fi = AR.infile; } /* During preprocessing, this function is called before the RevertScratch at the beginning of this module's execution. Thus the expressions are in the outfile of the previous module. */ else { fi = AR.outfile; } } } if ( fi->handle >= 0 ) { PUTZERO(oldposition); /* SeekFile(fi->handle,&oldposition,SEEK_CUR); */ } else { SETBASEPOSITION(oldposition,fi->POfill-fi->PObuffer); } position = AS.OldOnFile[num]; if ( GetOneTerm(BHEAD term,fi,&position,1) < 0 || ( GetOneTerm(BHEAD term,fi,&position,1) < 0 ) ) { MLOCK(ErrorMessageLock); MesCall("GetFirstTerm"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( fi->handle >= 0 ) { /* SeekFile(fi->handle,&oldposition,SEEK_SET); if ( ISNEGPOS(oldposition) ) { MLOCK(ErrorMessageLock); MesPrint("File error"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } */ } else { fi->POfill = fi->PObuffer+BASEPOSITION(oldposition); } AR.GetOneFile = oldonefile; } AR.CompressPointer = oldcomppointer; return(*term); } /* #] GetFirstTerm : #[ GetContent : */ int GetContent(WORD *content, int num) { /* Gets the content of the expression 'num' Puts it in content. Routine should be thread-safe The content is defined as the term that will make the expression 'num' with integer coefficients, no GCD and all common factors taken out, all negative powers removed when we divide the expression by this content. */ GETIDENTITY POSITION position, oldposition; RENUMBER renumber; FILEHANDLE *fi; WORD type, *oldcomppointer, oldonefile, numword, *term, i; WORD *cbuffer = TermMalloc("GetContent"); WORD *oldworkpointer = AT.WorkPointer; oldcomppointer = AR.CompressPointer; type = Expressions[num].status; if ( type == STOREDEXPRESSION ) { WORD TMproto[SUBEXPSIZE]; TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = num; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; PUTZERO(position); if ( ( renumber = GetTable(num,&position,0) ) == 0 ) goto CalledFrom; if ( GetFromStore(cbuffer,&position,renumber,&numword,num) < 0 ) goto CalledFrom; for(;;) { term = oldworkpointer; AR.CompressPointer = oldcomppointer; if ( GetFromStore(term,&position,renumber,&numword,num) < 0 ) goto CalledFrom; if ( *term == 0 ) break; /* 'merge' the two terms */ if ( ContentMerge(BHEAD cbuffer,term) < 0 ) goto CalledFrom; } /* #ifdef WITHPTHREADS */ if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); /* #endif */ } else { /* Active expression */ oldonefile = AR.GetOneFile; if ( type == HIDDENLEXPRESSION || type == HIDDENGEXPRESSION ) { AR.GetOneFile = 2; fi = AR.hidefile; } else { AR.GetOneFile = 0; if ( Expressions[num].replace == NEWLYDEFINEDEXPRESSION ) fi = AR.outfile; else fi = AR.infile; } if ( fi->handle >= 0 ) { PUTZERO(oldposition); /* SeekFile(fi->handle,&oldposition,SEEK_CUR); */ } else { SETBASEPOSITION(oldposition,fi->POfill-fi->PObuffer); } position = AS.OldOnFile[num]; if ( GetOneTerm(BHEAD cbuffer,fi,&position,1) < 0 ) goto CalledFrom; AR.CompressPointer = oldcomppointer; if ( GetOneTerm(BHEAD cbuffer,fi,&position,1) < 0 ) goto CalledFrom; /* Now go through the terms. For each term we have to test whether what is in cbuffer is also in that term. If not, we have to remove it from cbuffer. Additionally we have to accumulate the GCD of the numerators and the LCM of the denominators. This is all done in the routine ContentMerge. */ for(;;) { term = oldworkpointer; AR.CompressPointer = oldcomppointer; if ( GetOneTerm(BHEAD term,fi,&position,1) < 0 ) goto CalledFrom; if ( *term == 0 ) break; /* 'merge' the two terms */ if ( ContentMerge(BHEAD cbuffer,term) < 0 ) goto CalledFrom; } if ( fi->handle < 0 ) { fi->POfill = fi->PObuffer+BASEPOSITION(oldposition); } AR.GetOneFile = oldonefile; } AR.CompressPointer = oldcomppointer; for ( i = 0; i < *cbuffer; i++ ) content[i] = cbuffer[i]; TermFree(cbuffer,"GetContent"); AT.WorkPointer = oldworkpointer; return(*content); CalledFrom: MLOCK(ErrorMessageLock); MesCall("GetContent"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] GetContent : #[ CleanupTerm : Removes noncommuting objects from the term */ int CleanupTerm(WORD *term) { WORD *tstop, *t, *tfill, *tt; GETSTOP(term,tstop); t = term+1; while ( t < tstop ) { if ( *t >= FUNCTION && ( functions[*t-FUNCTION].commute || *t == DENOMINATOR ) ) { tfill = t; tt = t + t[1]; tstop = term + *term; while ( tt < tstop ) *tfill++ = *tt++; *term = tfill - term; tstop -= ABS(tfill[-1]); } else { t += t[1]; } } return(0); } /* #] CleanupTerm : #[ ContentMerge : */ WORD ContentMerge(PHEAD WORD *content, WORD *term) { GETBIDENTITY WORD *cstop, csize, crsize, sign = 1, numsize, densize, i, tnsize, tdsize; UWORD *num, *den, *tnum, *tden; WORD *outfill, *outb = TermMalloc("ContentMerge"), *ct; WORD *t, *tstop, tsize, trsize, *told; WORD *t1, *t2, *c1, *c2, i1, i2, *out1; WORD didsymbol = 0, diddotp = 0, tfirst; cstop = content + *content; csize = cstop[-1]; if ( csize < 0 ) { sign = -sign; csize = -csize; } cstop -= csize; numsize = densize = crsize = (csize-1)/2; num = NumberMalloc("ContentMerge"); den = NumberMalloc("ContentMerge"); for ( i = 0; i < numsize; i++ ) num[i] = (UWORD)(cstop[i]); for ( i = 0; i < densize; i++ ) den[i] = (UWORD)(cstop[i+crsize]); while ( num[numsize-1] == 0 ) numsize--; while ( den[densize-1] == 0 ) densize--; /* First we do the coefficient */ tstop = term + *term; tsize = tstop[-1]; if ( tsize < 0 ) tsize = -tsize; /* else { sign = 1; } */ tstop = tstop - tsize; tnsize = tdsize = trsize = (tsize-1)/2; tnum = (UWORD *)tstop; tden = (UWORD *)(tstop + trsize); while ( tnum[tnsize-1] == 0 ) tnsize--; while ( tden[tdsize-1] == 0 ) tdsize--; GcdLong(BHEAD num, numsize, tnum, tnsize, num, &numsize); if ( LcmLong(BHEAD den, densize, tden, tdsize, den, &densize) ) goto CalledFrom; outfill = outb + 1; ct = content + 1; t = term + 1; while ( ct < cstop ) { switch ( *ct ) { case SYMBOL: didsymbol = 1; t = term+1; while ( t < tstop && *t != *ct ) t += t[1]; if ( t >= tstop ) break; t1 = t+2; t2 = t+t[1]; c1 = ct+2; c2 = ct+ct[1]; out1 = outfill; *outfill++ = *ct; outfill++; while ( c1 < c2 && t1 < t2 ) { if ( *c1 == *t1 ) { if ( t1[1] <= c1[1] ) { *outfill++ = *t1++; *outfill++ = *t1++; c1 += 2; } else { *outfill++ = *c1++; *outfill++ = *c1++; t1 += 2; } } else if ( *c1 < *t1 ) { if ( c1[1] < 0 ) { *outfill++ = *c1++; *outfill++ = *c1++; } else { c1 += 2; } } else { if ( t1[1] < 0 ) { *outfill++ = *t1++; *outfill++ = *t1++; } else t1 += 2; } } while ( c1 < c2 ) { if ( c1[1] < 0 ) { *outfill++ = c1[0]; *outfill++ = c1[1]; } c1 += 2; } while ( t1 < t2 ) { if ( t1[1] < 0 ) { *outfill++ = t1[0]; *outfill++ = t1[1]; } t1 += 2; } out1[1] = outfill - out1; if ( out1[1] == 2 ) outfill = out1; break; case DOTPRODUCT: diddotp = 1; t = term+1; while ( t < tstop && *t != *ct ) t += t[1]; if ( t >= tstop ) break; t1 = t+2; t2 = t+t[1]; c1 = ct+2; c2 = ct+ct[1]; out1 = outfill; *outfill++ = *ct; outfill++; while ( c1 < c2 && t1 < t2 ) { if ( *c1 == *t1 && c1[1] == t1[1] ) { if ( t1[2] <= c1[2] ) { *outfill++ = *t1++; *outfill++ = *t1++; *outfill++ = *t1++; c1 += 3; } else { *outfill++ = *c1++; *outfill++ = *c1++; *outfill++ = *c1++; t1 += 3; } } else if ( *c1 < *t1 || ( *c1 == *t1 && c1[1] < t1[1] ) ) { if ( c1[2] < 0 ) { *outfill++ = *c1++; *outfill++ = *c1++; *outfill++ = *c1++; } else { c1 += 3; } } else { if ( t1[2] < 0 ) { *outfill++ = *t1++; *outfill++ = *t1++; *outfill++ = *t1++; } else t1 += 3; } } while ( c1 < c2 ) { if ( c1[2] < 0 ) { *outfill++ = c1[0]; *outfill++ = c1[1]; *outfill++ = c1[1]; } c1 += 3; } while ( t1 < t2 ) { if ( t1[2] < 0 ) { *outfill++ = t1[0]; *outfill++ = t1[1]; *outfill++ = t1[1]; } t1 += 3; } out1[1] = outfill - out1; if ( out1[1] == 2 ) outfill = out1; break; case INDEX: t = term+1; while ( t < tstop && *t != *ct ) t += t[1]; if ( t >= tstop ) break; t1 = t+2; t2 = t+t[1]; c1 = ct+2; c2 = ct+ct[1]; out1 = outfill; *outfill++ = *ct; outfill++; while ( c1 < c2 && t1 < t2 ) { if ( *c1 == *t1 ) { *outfill++ = *c1++; t1 += 1; } else if ( *c1 < *t1 ) { c1 += 1; } else { t1 += 1; } } out1[1] = outfill - out1; if ( out1[1] == 2 ) outfill = out1; break; case VECTOR: case DELTA: t = term+1; while ( t < tstop && *t != *ct ) t += t[1]; if ( t >= tstop ) break; t1 = t+2; t2 = t+t[1]; c1 = ct+2; c2 = ct+ct[1]; out1 = outfill; *outfill++ = *ct; outfill++; while ( c1 < c2 && t1 < t2 ) { if ( *c1 == *t1 && c1[1] && t1[1] ) { *outfill++ = *c1++; *outfill++ = *c1++; t1 += 2; } else if ( *c1 < *t1 || ( *c1 == *t1 && c1[1] < t1[1] ) ) { c1 += 2; } else { t1 += 2; } } out1[1] = outfill - out1; if ( out1[1] == 2 ) outfill = out1; break; case GAMMA: default: /* Functions */ told = t; t = term+1; while ( t < tstop ) { if ( *t != *ct ) { t += t[1]; continue; } if ( ct[1] != t[1] ) { t += t[1]; continue; } if ( ct[2] != t[2] ) { t += t[1]; continue; } t1 = t; t2 = ct; i1 = t1[1]; i2 = t2[1]; while ( i1 > 0 ) { if ( *t1 != *t2 ) break; t1++; t2++; i1--; } if ( i1 != 0 ) { t += t[1]; continue; } t1 = t; for ( i = 0; i < i2; i++ ) { *outfill++ = *t++; } /* Mark as 'used'. The flags must be different! */ t1[2] |= SUBTERMUSED1; ct[2] |= SUBTERMUSED2; t = told; break; } break; } ct += ct[1]; } if ( diddotp == 0 ) { t = term+1; while ( t < tstop && *t != DOTPRODUCT ) t += t[1]; if ( t < tstop ) { /* now we need the negative powers */ tfirst = 1; told = outfill; for ( i = 2; i < t[1]; i += 3 ) { if ( t[i+2] < 0 ) { if ( tfirst ) { *outfill++ = DOTPRODUCT; *outfill++ = 0; tfirst = 0; } *outfill++ = t[i]; *outfill++ = t[i+1]; *outfill++ = t[i+2]; } } if ( outfill > told ) told[1] = outfill-told; } } if ( didsymbol == 0 ) { t = term+1; while ( t < tstop && *t != SYMBOL ) t += t[1]; if ( t < tstop ) { /* now we need the negative powers */ tfirst = 1; told = outfill; for ( i = 2; i < t[1]; i += 2 ) { if ( t[i+1] < 0 ) { if ( tfirst ) { *outfill++ = SYMBOL; *outfill++ = 0; tfirst = 0; } *outfill++ = t[i]; *outfill++ = t[i+1]; } } if ( outfill > told ) told[1] = outfill-told; } } /* Now put the coefficient back. */ if ( numsize < densize ) { for ( i = numsize; i < densize; i++ ) num[i] = 0; numsize = densize; } else if ( densize < numsize ) { for ( i = densize; i < numsize; i++ ) den[i] = 0; densize = numsize; } for ( i = 0; i < numsize; i++ ) *outfill++ = num[i]; for ( i = 0; i < densize; i++ ) *outfill++ = den[i]; csize = numsize+densize+1; if ( sign < 0 ) csize = -csize; *outfill++ = csize; *outb = outfill-outb; NumberFree(den,"ContentMerge"); NumberFree(num,"ContentMerge"); for ( i = 0; i < *outb; i++ ) content[i] = outb[i]; TermFree(outb,"ContentMerge"); /* Now we have to 'restore' the term to its original. We do not restore the content, because if anything was used the new content overwrites the old. 6-mar-2018 JV */ t = term + 1; while ( t < tstop ) { if ( *t >= FUNCTION ) t[2] &= ~SUBTERMUSED1; t += t[1]; } return(*content); CalledFrom: MLOCK(ErrorMessageLock); MesCall("GetContent"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] ContentMerge : #[ TermsInExpression : */ LONG TermsInExpression(WORD num) { LONG x = Expressions[num].counter; if ( x >= 0 ) return(x); return(-1); } /* #] TermsInExpression : #[ SizeOfExpression : */ LONG SizeOfExpression(WORD num) { LONG x = (LONG)(DIVPOS(Expressions[num].size,sizeof(WORD))); if ( x >= 0 ) return(x); return(-1); } /* #] SizeOfExpression : #[ UpdatePositions : */ void UpdatePositions(void) { EXPRESSIONS e = Expressions; POSITION *old; WORD *oldw; int i; if ( NumExpressions > 0 && ( AS.OldOnFile == 0 || AS.NumOldOnFile < NumExpressions ) ) { if ( AS.OldOnFile ) { old = AS.OldOnFile; AS.OldOnFile = (POSITION *)Malloc1(NumExpressions*sizeof(POSITION),"file pointers"); for ( i = 0; i < AS.NumOldOnFile; i++ ) AS.OldOnFile[i] = old[i]; AS.NumOldOnFile = NumExpressions; M_free(old,"process file pointers"); } else { AS.OldOnFile = (POSITION *)Malloc1(NumExpressions*sizeof(POSITION),"file pointers"); AS.NumOldOnFile = NumExpressions; } } if ( NumExpressions > 0 && ( AS.OldNumFactors == 0 || AS.NumOldNumFactors < NumExpressions ) ) { if ( AS.OldNumFactors ) { oldw = AS.OldNumFactors; AS.OldNumFactors = (WORD *)Malloc1(NumExpressions*sizeof(WORD),"numfactors pointers"); for ( i = 0; i < AS.NumOldNumFactors; i++ ) AS.OldNumFactors[i] = oldw[i]; M_free(oldw,"numfactors pointers"); oldw = AS.Oldvflags; AS.Oldvflags = (WORD *)Malloc1(NumExpressions*sizeof(WORD),"vflags pointers"); for ( i = 0; i < AS.NumOldNumFactors; i++ ) AS.Oldvflags[i] = oldw[i]; M_free(oldw,"vflags pointers"); oldw = AS.Olduflags; AS.Olduflags = (WORD *)Malloc1(NumExpressions*sizeof(WORD),"uflags pointers"); for ( i = 0; i < AS.NumOldNumFactors; i++ ) AS.Olduflags[i] = oldw[i]; M_free(oldw,"uflags pointers"); AS.NumOldNumFactors = NumExpressions; } else { AS.OldNumFactors = (WORD *)Malloc1(NumExpressions*sizeof(WORD),"numfactors pointers"); AS.Oldvflags = (WORD *)Malloc1(NumExpressions*sizeof(WORD),"vflags pointers"); AS.Olduflags = (WORD *)Malloc1(NumExpressions*sizeof(WORD),"uflags pointers"); AS.NumOldNumFactors = NumExpressions; } } for ( i = 0; i < NumExpressions; i++ ) { AS.OldOnFile[i] = e[i].onfile; AS.OldNumFactors[i] = e[i].numfactors; AS.Oldvflags[i] = e[i].vflags; AS.Olduflags[i] = e[i].uflags; } } /* #] UpdatePositions : #[ CountTerms1 : LONG CountTerms1() Counts the terms in the current deferred bracket Is mainly an adaptation of the routine Deferred in proces.c */ LONG CountTerms1(PHEAD0) { GETBIDENTITY POSITION oldposition, startposition; WORD *t, *m, *mstop, decr, i, *oldwork, retval; WORD *oldipointer = AR.CompressPointer; WORD oldGetOneFile = AR.GetOneFile, olddeferflag = AR.DeferFlag; LONG numterms = 0; AR.GetOneFile = 1; oldwork = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); AR.DeferFlag = 0; startposition = AR.DefPosition; /* Store old position */ if ( AR.infile->handle >= 0 ) { PUTZERO(oldposition); /* SeekFile(AR.infile->handle,&oldposition,SEEK_CUR); */ } else { SETBASEPOSITION(oldposition,AR.infile->POfill-AR.infile->PObuffer); AR.infile->POfill = (WORD *)((UBYTE *)(AR.infile->PObuffer) +BASEPOSITION(startposition)); } /* Look in the CompressBuffer where the bracket contents start */ t = m = AR.CompressBuffer; t += *t; mstop = t - ABS(t[-1]); m++; while ( *m != HAAKJE && m < mstop ) m += m[1]; if ( m >= mstop ) { /* No deferred action! */ numterms = 1; AR.DeferFlag = olddeferflag; AT.WorkPointer = oldwork; AR.GetOneFile = oldGetOneFile; return(numterms); } mstop = m + m[1]; decr = WORDDIF(mstop,AR.CompressBuffer)-1; m = AR.CompressBuffer; t = AR.CompressPointer; i = *m; NCOPY(t,m,i); AR.TePos = 0; AN.TeSuOut = 0; /* Status: First bracket content starts at mstop. Next term starts at startposition. Decompression information is in AR.CompressPointer. The outside of the bracket runs from AR.CompressBuffer+1 to mstop. */ AR.CompressPointer = oldipointer; for(;;) { numterms++; retval = GetOneTerm(BHEAD AT.WorkPointer,AR.infile,&startposition,0); if ( retval >= 0 ) AR.CompressPointer = oldipointer; if ( retval <= 0 ) break; t = AR.CompressPointer; if ( *t < (1 + decr + ABS(*(t+*t-1))) ) break; t++; m = AR.CompressBuffer+1; while ( m < mstop ) { if ( *m != *t ) goto Thatsit; m++; t++; } } Thatsit:; /* Finished. Reposition the file, restore information and return. */ AT.WorkPointer = oldwork; if ( AR.infile->handle >= 0 ) { /* SeekFile(AR.infile->handle,&oldposition,SEEK_SET); */ } else { AR.infile->POfill = AR.infile->PObuffer + BASEPOSITION(oldposition); } AR.DeferFlag = olddeferflag; AR.GetOneFile = oldGetOneFile; return(numterms); } /* #] CountTerms1 : #[ TermsInBracket : LONG TermsInBracket(term,level) The function TermsInBracket_() Syntax: TermsInBracket_() : The current bracket in a Keep Brackets TermsInBracket_(bracket) : This bracket in the current expression TermsInBracket_(expression,bracket) : This bracket in the given expression All other specifications don't have any effect. */ #define CURRENTBRACKET 1 #define BRACKETCURRENTEXPR 2 #define BRACKETOTHEREXPR 3 #define NOBRACKETACTIVE 4 LONG TermsInBracket(PHEAD WORD *term, WORD level) { WORD *t, *tstop, *b, *tt, *n1, *n2; int type = 0, i, num; LONG numterms = 0; WORD *bracketbuffer = AT.WorkPointer; t = term; GETSTOP(t,tstop); t++; b = bracketbuffer; while ( t < tstop ) { if ( *t != TERMSINBRACKET ) { t += t[1]; continue; } if ( t[1] == FUNHEAD || ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] == 0 ) ) { if ( AC.ComDefer == 0 ) { type = NOBRACKETACTIVE; } else { type = CURRENTBRACKET; } *b = 0; break; } if ( t[FUNHEAD] == -EXPRESSION ) { if ( t[FUNHEAD+2] < 0 ) { if ( ( t[FUNHEAD+2] <= -FUNCTION ) && ( t[1] == FUNHEAD+3 ) ) { type = BRACKETOTHEREXPR; *b++ = FUNHEAD+4; *b++ = -t[FUNHEAD+2]; *b++ = FUNHEAD; for ( i = 2; i < FUNHEAD; i++ ) *b++ = 0; *b++ = 1; *b++ = 1; *b++ = 3; break; } else if ( ( t[FUNHEAD+2] > -FUNCTION ) && ( t[1] == FUNHEAD+4 ) ) { type = BRACKETOTHEREXPR; tt = t + FUNHEAD+2; switch ( *tt ) { case -SYMBOL: *b++ = 8; *b++ = SYMBOL; *b++ = 4; *b++ = tt[1]; *b++ = 1; *b++ = 1; *b++ = 1; *b++ = 3; break; case -SNUMBER: if ( tt[1] == 1 ) { *b++ = 4; *b++ = 1; *b++ = 1; *b++ = 3; } else goto IllBraReq; break; default: goto IllBraReq; } break; } } else if ( ( t[FUNHEAD+2] == (t[1]-FUNHEAD-2) ) && ( t[FUNHEAD+2+ARGHEAD] == (t[FUNHEAD+2]-ARGHEAD) ) ) { type = BRACKETOTHEREXPR; tt = t + FUNHEAD + ARGHEAD; num = *tt; for ( i = 0; i < num; i++ ) *b++ = *tt++; break; } } else { if ( t[FUNHEAD] < 0 ) { if ( ( t[FUNHEAD] <= -FUNCTION ) && ( t[1] == FUNHEAD+1 ) ) { type = BRACKETCURRENTEXPR; *b++ = FUNHEAD+4; *b++ = -t[FUNHEAD+2]; *b++ = FUNHEAD; for ( i = 2; i < FUNHEAD; i++ ) *b++ = 0; *b++ = 1; *b++ = 1; *b++ = 3; *b = 0; break; } else if ( ( t[FUNHEAD] > -FUNCTION ) && ( t[1] == FUNHEAD+2 ) ) { type = BRACKETCURRENTEXPR; tt = t + FUNHEAD+2; switch ( *tt ) { case -SYMBOL: *b++ = 8; *b++ = SYMBOL; *b++ = 4; *b++ = tt[1]; *b++ = 1; *b++ = 1; *b++ = 1; *b++ = 3; break; case -SNUMBER: if ( tt[1] == 1 ) { *b++ = 4; *b++ = 1; *b++ = 1; *b++ = 3; } else goto IllBraReq; break; default: goto IllBraReq; } break; } } else if ( ( t[FUNHEAD] == (t[1]-FUNHEAD) ) && ( t[FUNHEAD+ARGHEAD] == (t[FUNHEAD]-ARGHEAD) ) ) { type = BRACKETCURRENTEXPR; tt = t + FUNHEAD + ARGHEAD; num = *tt; for ( i = 0; i < num; i++ ) *b++ = *tt++; break; } else { IllBraReq:; MLOCK(ErrorMessageLock); MesPrint("Illegal bracket request in termsinbracket_ function."); MUNLOCK(ErrorMessageLock); Terminate(-1); } } t += t[1]; } AT.WorkPointer = b; if ( AT.WorkPointer + *term +4 > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MesPrint("Called from termsinbracket_ function."); MUNLOCK(ErrorMessageLock); return(-1); } /* We are now in the position to look for the bracket */ switch ( type ) { case CURRENTBRACKET: /* The code here should be rather similar to when we pick up the contents of the bracket. In our case we only count the terms though. */ numterms = CountTerms1(BHEAD0); break; case BRACKETCURRENTEXPR: /* Not implemented yet. */ MLOCK(ErrorMessageLock); MesPrint("termsinbracket_ function currently only handles Keep Brackets."); MUNLOCK(ErrorMessageLock); return(-1); case BRACKETOTHEREXPR: MLOCK(ErrorMessageLock); MesPrint("termsinbracket_ function currently only handles Keep Brackets."); MUNLOCK(ErrorMessageLock); return(-1); case NOBRACKETACTIVE: numterms = 1; break; } /* Now we have the number in numterms. We replace the function by it. */ n1 = term; n2 = AT.WorkPointer; tstop = n1 + *n1; while ( n1 < t ) *n2++ = *n1++; i = numterms >> BITSINWORD; if ( i == 0 ) { *n2++ = LNUMBER; *n2++ = 4; *n2++ = 1; *n2++ = (WORD)(numterms & WORDMASK); } else { *n2++ = LNUMBER; *n2++ = 5; *n2++ = 2; *n2++ = (WORD)(numterms & WORDMASK); *n2++ = i; } n1 += n1[1]; while ( n1 < tstop ) *n2++ = *n1++; AT.WorkPointer[0] = n2 - AT.WorkPointer; AT.WorkPointer = n2; if ( Generator(BHEAD n1,level) < 0 ) { AT.WorkPointer = bracketbuffer; MLOCK(ErrorMessageLock); MesPrint("Called from termsinbracket_ function."); MUNLOCK(ErrorMessageLock); return(-1); } /* Finished. Reset things and return. */ AT.WorkPointer = bracketbuffer; return(numterms); } /* #] TermsInBracket : LONG TermsInBracket(term,level) #] Expressions : */ form-5.0.1/sources/poly.h0000644000175100017510000001717215217035721010775 #pragma once /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ extern "C" { #include "form3.h" } #include #include #include // for debugging // #define POLY_MOVE_DEBUG // macros for tform #ifndef WITHPTHREADS #define POLY_GETIDENTITY(X) #define POLY_STOREIDENTITY #else #define POLY_GETIDENTITY(X) ALLPRIVATES *B = (X).Bpointer #define POLY_STOREIDENTITY Bpointer = B #endif // maximum size of the hash table used for multiplication and division const int POLY_MAX_HASH_SIZE = MiN(1<<20, MAXPOSITIVE); class poly { public: // variables #ifdef WITHPTHREADS ALLPRIVATES *Bpointer; #endif WORD *terms; LONG size_of_terms; WORD modp,modn; // constructors/destructor poly (PHEAD int, WORD=-1, WORD=1); poly (PHEAD const UWORD *, WORD, WORD=-1, WORD=1); poly (const poly &, WORD=-1, WORD=1); ~poly (); // operators poly& operator+= (const poly&); poly& operator-= (const poly&); poly& operator*= (const poly&); poly& operator/= (const poly&); poly& operator%= (const poly&); const poly operator+ (const poly&) const; const poly operator- (const poly&) const; const poly operator* (const poly&) const; const poly operator/ (const poly&) const; const poly operator% (const poly&) const; bool operator== (const poly&) const; bool operator!= (const poly&) const; poly& operator= (const poly &); WORD& operator[] (int); const WORD& operator[] (int) const; #if __cplusplus >= 201103L // support move semantics poly (poly &&, WORD=-1, WORD=1) noexcept; poly& operator= (poly &&) noexcept; #endif // memory management void termscopy (const WORD *, int, int); void check_memory(int); void expand_memory(int); // check type of polynomial bool is_zero () const; bool is_one () const; bool is_integer () const; bool is_monomial () const; int is_dense_univariate () const; // properties int sign () const; int degree (int) const; int total_degree () const; int first_variable () const; int number_of_terms () const; const std::vector all_variables () const; const poly integer_lcoeff () const; const poly lcoeff_univar (int) const; const poly lcoeff_multivar (int) const; const poly coefficient (int, int) const; const poly derivative (int) const; // modulo calculus void setmod(WORD, WORD=1); void coefficients_modulo (UWORD *, WORD, bool); // simple polynomials static const poly simple_poly (PHEAD int, int=0, int=1, int=0, int=1); static const poly simple_poly (PHEAD int, const poly&, int=1, int=0, int=1); // conversion from/to form notation static void get_variables (PHEAD const std::vector &, bool, bool); static const poly argument_to_poly (PHEAD WORD *, bool, bool, poly *den=NULL); static void poly_to_argument (const poly &, WORD *, bool); static void poly_to_argument_with_den (const poly &, WORD, const UWORD *, WORD *, bool); int size_of_form_notation () const; int size_of_form_notation_with_den (WORD) const; const poly & normalize (); // operations for coefficient lists static const poly from_coefficient_list (PHEAD const std::vector &, int, WORD); static const std::vector to_coefficient_list (const poly &); static const std::vector coefficient_list_divmod (const std::vector &, const std::vector &, WORD, int); // string output for debugging const std::string to_string() const; // monomials static int monomial_compare (PHEAD const WORD *, const WORD *); WORD last_monomial_index () const; WORD* last_monomial () const; int compare_degree_vector(const poly &) const; std::vector degree_vector() const; int compare_degree_vector(const std::vector &) const; // (internal) mathematical operations static void add (const poly &, const poly &, poly &); static void sub (const poly &, const poly &, poly &); static void mul (const poly &, const poly &, poly &); static void div (const poly &, const poly &, poly &); static void mod (const poly &, const poly &, poly &); static void divmod (const poly &, const poly &, poly &, poly &, bool only_divides); static bool divides (const poly &, const poly &); static void mul_one_term (const poly &, const poly &, poly &); static void mul_univar (const poly &, const poly &, poly &, int); static void mul_heap (const poly &, const poly &, poly &); static void divmod_one_term (const poly &, const poly &, poly &, poly &, bool); static void divmod_univar (const poly &, const poly &, poly &, poly &, int, bool); static void divmod_heap (const poly &, const poly &, poly &, poly &, bool, bool, bool&); static void push_heap (PHEAD WORD **, int); static void pop_heap (PHEAD WORD **, int); }; // comparison class for monomials (for std::sort) class monomial_larger { public: #ifndef WITHPTHREADS monomial_larger() {} #else ALLPRIVATES *B; monomial_larger(ALLPRIVATES *b): B(b) {} #endif bool operator()(const WORD *a, const WORD *b) { return poly::monomial_compare(BHEAD a, b) > 0; } }; // stream operator std::ostream& operator<< (std::ostream &, const poly &); // inline function definitions #if __cplusplus >= 201103L inline poly::poly (poly &&a, WORD modp, WORD modn) noexcept { #ifdef POLY_MOVE_DEBUG std::cout << "poly move ctor" << std::endl; #endif POLY_GETIDENTITY(a); POLY_STOREIDENTITY; terms = a.terms; size_of_terms = a.size_of_terms; this->modp = a.modp; this->modn = a.modn; if (modp != -1) { setmod(modp,modn); } a.terms = nullptr; a.size_of_terms = -1; } inline poly& poly::operator= (poly &&a) noexcept { #ifdef POLY_MOVE_DEBUG std::cout << "poly move assign" << std::endl; #endif if (this != &a) { WORD *old_terms = terms; LONG old_size_of_terms = size_of_terms; terms = a.terms; size_of_terms = a.size_of_terms; modp = a.modp; modn = a.modn; a.terms = old_terms; a.size_of_terms = old_size_of_terms; } return *this; } #endif /* Checks whether the terms array is large enough to add another * term (of size AM.MaxTal) to the polynomials. In case not, it is * expanded. */ inline void poly::check_memory (int i) { POLY_GETIDENTITY(*this); if (i + 3 + AN.poly_num_vars + AM.MaxTal >= size_of_terms) expand_memory(i + AM.MaxTal); // Used to be i+2 but there should also be space for a trailing zero } // indexing operators inline WORD& poly::operator[] (int i) { return terms[i]; } inline const WORD& poly::operator[] (int i) const { return terms[i]; } /* Copies "num" WORD-sized terms from the pointer "source" to the * current polynomial at index "dest" */ inline void poly::termscopy (const WORD *source, int dest, int num) { #ifdef POLY_MOVE_DEBUG std::cout << "poly termscopy: num=" << num << std::endl; #endif memcpy (terms+dest, source, num*sizeof(WORD)); } form-5.0.1/sources/fwin.h0000644000175100017510000000264315217035721010752 /** @file fwin.h * * Settings for Windows computers. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #define LINEFEED '\n' #define CARRIAGERETURN 0x0D #define WITHRETURN #define WITHSYSTEM #define P_term(code) exit((int)(code<0?-code:code)) #define SEPARATOR '\\' #define ALTSEPARATOR '/' #define PATHSEPARATOR ';' #define WITH_ENV form-5.0.1/sources/polyfact.h0000644000175100017510000001017615217035721011630 #pragma once /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #include #include // First prime modulo which factorization is tried. Too small results // in more unsuccessful attempts; too large is slower. const int POLYFACT_FIRST_PRIME = 17; // Fraction of [1,p) that is used for substitutions of variables. Too // small results in more unsuccessful attempts; too large is slower. const int POLYFACT_IDEAL_FRACTION = 5; // Number of ideals that are tried before failure due to unlucky // choices is accepted. const int POLYFACT_MAX_IDEAL_TRIES = 3; // Number of confirmations for the minimal number of factors before // Hensel lifting is started. const int POLYFACT_NUM_CONFIRMATIONS = 3; // Maximum number of equations for predetermination of coefficients // for multivariate Hensel lifting const int POLYFACT_MAX_PREDETERMINATION = 10000; class poly; class factorized_poly { /* Class for representing a factorized polynomial * The polynomial is given by: PRODUCT(factor[i] ^ power[i]) */ public: std::vector factor; std::vector power; void add_factor(const poly &f, int p=1); const std::string tostring () const; friend std::ostream& operator<< (std::ostream &out, const poly &p); }; std::ostream& operator<< (std::ostream &out, const factorized_poly &a); namespace polyfact { // factorization routine const factorized_poly factorize (const poly &a); // methods for squarefree factorization const factorized_poly squarefree_factors (const poly &a); const factorized_poly squarefree_factors_Yun (const poly &a); const factorized_poly squarefree_factors_modp (const poly &a); // methods for choosing suitable reductions const std::vector factorize_squarefree (const poly &a, const std::vector &x); WORD choose_prime (const poly &a, const std::vector &x, WORD p=0); WORD choose_prime_power (const poly &a, WORD p); const std::vector choose_ideal (const poly &a, int p, const factorized_poly &lc, const std::vector &x); // methods for univariate factorization const std::vector > Berlekamp_Qmatrix (const poly &a); const std::vector Berlekamp_find_factors (const poly &a, const std::vector > &Q); const std::vector combine_factors (const poly &a, const std::vector &f); // methods for Hensel lifting const std::vector extended_gcd_Euclidean_lifted (const poly &a, const poly &b); const std::vector solve_Diophantine_univariate (const std::vector &a, const poly &b); const std::vector solve_Diophantine_multivariate (const std::vector &a, const poly &b, const std::vector &x, const std::vector &c, int d); const std::vector lift_coefficients (const poly &a, const std::vector &f); const std::vector lift_variables (const poly &a, const std::vector &f, const std::vector &x, const std::vector &c, const std::vector &lc); void predetermine (int dep, const std::vector > &state, std::vector > > &terms, std::vector &term, int sumdeg=0); } form-5.0.1/sources/portsignals.h0000644000175100017510000000504415217035721012352 #ifndef PORTSIGNAL_H #define PORTSIGNAL_H /** @file portsignals.h * * Contains definitions for signals used/intercepted in FORM. * * Some systems (especially LINUX) have not enough * signals available so some of the (!documented!) signals * are not defined. This file contains the definition of all * signals used in the program. * If the signal is not defined we define it as unused (>NSIG). * * The include of signal.h must be first, before we try to define * undefined signals. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #include #define FATAL_SIG_ERROR 4 #ifndef NSIG /* The value of NSIG must be enough to fall outside the range of defined signals */ #define NSIG (1024) #endif #ifndef SIGSEGV #define SIGSEGV (NSIG+1) #endif #ifndef SIGFPE #define SIGFPE (NSIG+2) #endif #ifndef SIGILL #define SIGILL (NSIG+3) #endif #ifndef SIGEMT #define SIGEMT (NSIG+4) #endif #ifndef SIGSYS #define SIGSYS (NSIG+5) #endif #ifndef SIGPIPE #define SIGPIPE (NSIG+6) #endif #ifndef SIGLOST #define SIGLOST (NSIG+7) #endif #ifndef SIGXCPU #define SIGXCPU (NSIG+8) #endif #ifndef SIGXFSZ #define SIGXFSZ (NSIG+9) #endif #ifndef SIGTERM #define SIGTERM (NSIG+10) #endif #ifndef SIGINT #define SIGINT (NSIG+11) #endif #ifndef SIGQUIT #define SIGQUIT (NSIG+12) #endif #ifndef SIGHUP #define SIGHUP (NSIG+13) #endif #ifndef SIGALRM #define SIGALRM (NSIG+14) #endif #ifndef SIGVTALRM #define SIGVTALRM (NSIG+15) #endif #ifndef SIGPROF #define SIGPROF (NSIG+16) #endif #endif form-5.0.1/sources/grcc.h0000644000175100017510000012727215217035721010733 #pragma once /* #[ License : */ /* * Copyright (C) 2023-2026 T. Kaneko * When using this file you are requested to refer to the publication * Comput.Phys.Commun. 92 (1995) 127-152 * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #include #include #include #include #define CHECK //============================================================== extern "C" { #include "grccparam.h" } //============================================================== // Name space of this library // See 'grccparam.h' for #define #ifdef GRCC_NAMESPACE namespace Grcc { #endif //============================================================== // Common types // #define True 1 #define False 0 typedef int Bool; //============================================================== // Big integer (may be replaced by suitable one) #define BigInt long #define ToBigInt(x) ((BigInt) (x)) //============================================================== // Macro functions #define Real(x) ((double) (x)) #define Abs(x) (((x) >= 0)? (x): (-x)) #define Sign(x) (((x) >= 0)? (1): (-1)) #define Max(x, y) ((x) > (y) ? (x) : (y)) #define Min(x, y) ((x) < (y) ? (x) : (y)) #define Second(t) ((double)(*(t)=(double)(clock()/((double)CLOCKS_PER_SEC)))) #define isATExternal(x) ((x)==GRCC_AT_Initial||(x)==GRCC_AT_Final||(x)==GRCC_AT_External) //============================================================== // types and classes typedef int Edge2n[2]; // pair of nodes expressing an edge class Assign; class AStack; class EEdge; class EGraph; class ENode; class Interaction; class MGraph; class MNodeClass; class MCEdge; class MCOpi; class MCBridge; class MCBlock; class MConn; class Model; class MOrbits; class Options; class Output; class Particle; class PNodeClass; class Process; class SGroup; class SProcess; class DCGraph; //============================================================== // type of output functions typedef Bool OutEGB(EGraph *, void *); typedef void OutEG(EGraph *, void *); typedef void ErExit(const char *msg, void *); //============================================================== class Options { public: Model *model; Process *proc; SProcess *sproc; Output *out; // for output OutEGB *outmg; // call back function of mgraph OutEGB *endmg; // call back function of end of mgraph OutEG *outag; // call back function of agraph void *argmg; // additional argument to outmg void *argemg; // additional argument to endmg void *argag; // additional argument to outag //switches for graph generation OptQGRef qgref[2*GRCC_QGRAF_OPT_Size]; // array of reference to QG-options int values[GRCC_OPT_Size]; // array of options int qgopt[GRCC_QGRAF_OPT_Size]; // array of QGRAF options int nqgopt; // effective length of qgref int DUMMYPADDING; // measuring time double time0; double time1; //------------------ Options(void); ~Options(void); void setDefaultValues(void); void setOldDefaultValues(void); void setValue(int ind, int val); int getValue(int ind); void setQGrafOpt(int *qgopt); void print(void); void setOutputF(Bool outgrf, const char *fname); void setOutputP(Bool outgrp, const char *fname); void printLevel(int l); void printModel(void); void setOutMG(OutEGB *omg, void *pt); void setOutAG(OutEG *oag, void *pt); void setEndMG(OutEGB *omg, void *pt); void setErExit(ErExit *ere, void *pt); const OptDef *getDef(void); const OptDef *getOldDef(void); const OptQGDef *getQGDef(void); void begin(Model *mdl); void end(void); void beginProc(Process *prc); void endProc(void); void beginSubProc(SProcess *sprc); void endSubProc(void); void newMGraph(MGraph *mgr); void newAGraph(EGraph *egr); void outModel(void); }; //============================================================== class Output { public: Options *opt; Model *model; Process *proc; SProcess *sproc; char *outgrf; FILE *outgrfp; char *outgrp; FILE *outgrpp; int procId; Bool outproc; Output(Options *optn); ~Output(void); void setOutgrf(const char *fname); void setOutgrp(const char *fname); Bool outBeginF(Model *mdl, Bool pr); Bool outBeginP(Model *mdl, Bool pr); void outEndF(void); void outEndP(void); void outProcBeginF(Process *prc); void outProcBeginP(Process *prc); void outProcBegin0(int next, int couple, int loop); void outSProcBeginF(SProcess *sprc); void outSProcBeginP(SProcess *sprc); void outProcEndF(void); void outProcEndP(void); void outEGraphF(EGraph *egraph); void outEGraphP(EGraph *egraph); void outModelF(void); void outModelP(void); }; //============================================================== class Fraction { public: BigInt num, den; double ratio; Fraction() { num = 0; den = 1; }; Fraction(BigInt n, BigInt d); void print(const char *msg); void setValue(BigInt n, BigInt d); void setValue(Fraction &f); void add(BigInt n, BigInt d); void add(Fraction f); void sub(Fraction f); BigInt gcd(BigInt n0, BigInt n1); void normal(void); Bool isEq(Fraction f); }; //************************************************************** // Model //============================================================== //-------------------------------------------------------------- class Particle { public: Model *mdl; // the model char *name; // the name of the particle char *aname; // the name of the anti-particle int id; // id of this particle int ptype; // the type of partice : GRCC_PT_Scalar, etc. int neutral; // True if particle==anti-particle int pcode; // Particle code int acode; // Anti-particle code int cmindeg; // min(leg of connectable interactions) int cmaxdeg; // max(leg of connectable interactions) int extonly; // can appear only as external particle //----------------------------- Particle(Model *modl, int pid, PInput *pinp); ~Particle(void); char *particleName(int p); int particleCode(int p); char *interactionName(int p); char *aparticle(void); void prParticle(void); int isNeutral(void); const char *typeName(void); const char *typeGName(void); }; //-------------------------------------------------------------- class Interaction { public: Model *mdl; // the model char *name; // the name of the interaction int *plist; // the list of particle codes int *clist; // the orders of coupling constants int *slist; // the sorted list of particle codes int id; // id of this interaction int csum; // the total orders of coupling constants int nlegs; // the number of legs int loop; // the number of loops int icode; // user defined interaction code int nplist; // the list of particle codes int nclist; // the orders of coupling constants int nslist; // the sorted list of particle codes //----------------------------- Interaction(Model *modl, int iid, const char* nam, int icode, int *cpl, int nlgs, int *plst, int csm, int lp); ~Interaction(void); void prInteraction(void); }; //-------------------------------------------------------------- class Model { public: char *name; // the name of this model char **cnlist; // the list of coupling constant names int ncouple; // the number of coupling consants. int nParticles; // the number of particles Particle **particles; // the list of particles int pdef; // the def. of partcls is ended // list of particles and anti-p. without Undef. int nallPart; int allPart[GRCC_MAXMPARTICLES2]; // list of particles and anti-p. without ones of extloop=True int nintPart; int intPart[GRCC_MAXMPARTICLES2]; int nInteracts; // the number of interactions. Interaction **interacts; // the list of interactions int vdef; // the definition of interaction is ended int maxnlegs; // maximum number of legs of an interaction int maxcpl; // maximum number of coupling const. int maxloop; // maximum number of loops inside an intr. // classification of interactions int *cplgcp; // coupling constants int *cplglg; // degree int *cplgnvl; // number of vertices int **cplgvl; // list of vertices int ncplgcp; // the number of classes int defpart; // GRCC_DEFBYNAME or GRCC_DEFBYCODE // methods Model(MInput *minp); ~Model(void); void prModel(void); void addParticle(PInput *pinp); void addParticleEnd(void); void addInteraction(IInput *iinp); void addInteractionEnd(void); int findParticleName(const char *name); int findParticleCode(int pcd); int findInteractionName(const char *name); int findInteractionCode(int icd); char *particleName(int p); int particleCode(int p); int normalParticle(int pt); int antiParticle(int pt); int *allParticles(int *len); int findMClass(const int cpl, const int dgr); void prParticleArray(int n, int *a, const char *msg); static void printMInput(MInput *min); static void printPInput(PInput *pin); static void printIInput(IInput *iin); }; //************************************************************** // Process //=============================================================== class PNodeClass { public: SProcess *sproc; int *deg; // The degree of each node int *type; // The type of the class : GRCC_AT_xxx int *particle; // The particle code of external node. int *couple; // The orders of coupling constans int *cmindeg; // min(deg of connectable vertex) int *cmaxdeg; // max(deg of connectable vertex) int *count; // The number of nodes in the class int *cl2nd; // cl2nd[class] <= nd < cl2nd[class+1] = set of nodes int *nd2cl; // nd2cl[node] = class int *cl2mcl; // cl2mcl[class] = class defined in the model. int nnodes; int nclass; PNodeClass(SProcess *sprc, int nnods, int nclss, NCInput *cls); PNodeClass(SProcess *sprc, int nnods, int nclss, int *dgs, int *typ, int *ptcl, int *cpl, int *cnt, int *cmind, int *cmaxd); ~PNodeClass(void); void prPNodeClass(void); void prElem(int e); }; //=============================================================== class SProcess { // In sprocess the number of nodes and edges are fixed. // A node is considered as // (degree, total order of coupling constants), // which pair of data defines a class of nodes. public: Model *model; // model Process *proc; // mother process Options *opt; // options PNodeClass *pnclass; // list of classes (cpl and deg is determined) AStack *astack; MGraph *mgraph; EGraph *egraph; Assign *agraph; int *cl2nd; // (code of nodes in the class[c]) // = [cl2nd[c], ..., cl2nd[c+1]-1] int *nd2cl; // node nd is in the class pnclass[nd2cl[nd]] int nclass; // the number of classes int ninitl; // the number of initial particles int nfinal; // the number of final particles int nvert; // the number of vertices int clist[GRCC_MAXNCPLG]; // coupling constans of the process int id; // sprocess id int loop; // the number of loops int nNodes; // the number of nodes int nEdges; // the number of edges int nExtern; // the number of external particles int ncouple; // the number of coupling constants int tCouple; // the total coupling constants int DUMMYPADDING; BigInt mgrcount; // count generated mgraph BigInt agrcount; // count generated agraph BigInt extperm; // count generated agraph // the results of the graph generation BigInt nMGraphs; // the number of generated M-graphs BigInt nMOPI; // the number of 1PI M-graphs Fraction wMGraphs; // the weighted sum of M-graphs Fraction wMOPI; // the weighted sum of 1PI M-graphs BigInt nAGraphs; // the number of generated A-graphs BigInt nAOPI; // the number of 1PI A-graphs Fraction wAGraphs; // the weighted sum of A-graphs Fraction wAOPI; // the weighted sum of 1PI A-graphs // methods SProcess(Model *mdl, Process *prc, Options *opts, int sid, int *clst, int ncls, NCInput *cls); SProcess(Model *mdl, Process *prc, Options *opts, int sid, int *clst, int ncls, int *cdeg, int *ctyp, int *ptcl, int *cpl, int *cnum, int *cmind, int *cmaxd); ~SProcess(void); void prSProcess(void); BigInt generate(void); void assign(MGraph *mgr); int toMNodeClass(int *ctyp, int *cldeg, int *clnum, int *cmind, int *cmaxd); PNodeClass *match(MGraph *mgr); void endMGraph(MGraph *mgr); void endAGraph(EGraph *egr); void resultMGraph(BigInt nmgraphs, Fraction mwsum, BigInt nmopi, Fraction mwopi); void resultAGraph(BigInt nagraphs, Fraction awsum, BigInt naopi, Fraction awopi); }; //=============================================================== class Process { public: Model *model; // model used for this process Options *opt; // options BigInt mgrcount; // count generated mgraph BigInt agrcount; // count generated agraph int *initlPart; // list of ids of initial particles int *finalPart; // list of ids of final particles int id; // process id int ninitl; // the number of initial particles int nfinal; // the number of final particles int ctotal; // the total number of coupling constants int nExtern; // the number of external particles int loop; // the number of external particles int maxnlegs; // the maximum possible degree of node int clist[GRCC_MAXNCPLG]; // coupling constans of the process // table of sprocesses int nSubproc; // the number of sprocesses SProcess *sptbl[GRCC_MAXSUBPROCS]; // the table of sprocesses SProcess *sproc; // the current sprocess // stack for the assignment; AStack *astack; // the number of graphs BigInt ngraphs; BigInt nopi; BigInt wgraphs; BigInt wopi; // the results of the graph generation BigInt nMGraphs; // the number of generated M-graphs BigInt nMOPI; // the number of 1PI M-graphs Fraction wMGraphs; // the weighted sum of M-graphs Fraction wMOPI; // the weighted sum of 1PI M-graphs BigInt nAGraphs; // the number of generated A-graphs BigInt nAOPI; // the number of 1PI A-graphs Fraction wAGraphs; // the weighted sum of A-graphs Fraction wAOPI; // the weighted sum of 1PI A-graphs double sec; Process(int pid, Model *model, Options *opt, int nin, int *initlPart, int nfin, int *finalPart, int *coupling); Process(int pid, Model *model, Options *opt, FGInput *fgi); ~Process(void); void prProcess(void); void outProcP(FILE *fp); void prProcessP(const char *fname); void mkSProcess(void); }; //************************************************************** // classes for EGraph //============================================================== // Constants #define GRCC_ED_Undef 0 #define GRCC_ED_Deleted 1 #define GRCC_ED_Extern 2 #define GRCC_ED_Back 3 #define GRCC_ED_Bridge 4 #define GRCC_ED_Inloop 5 #define GRCC_ED_Size 6 #define GRCC_ED_NAMES {"Undef", "Deleted", "Extern", "Back_Edge", "Bridge", "In_Loop"} #define GRCC_ND_Undef 0 #define GRCC_ND_Deleted 1 #define GRCC_ND_Initial 2 #define GRCC_ND_Final 3 #define GRCC_ND_CPoint 4 #define GRCC_ND_VBlock 5 #define GRCC_ND_Inblock 6 #define GRCC_ND_Size 7 #define GRCC_ND_NAMES {"Undef", "Deleted", "Init", "Final", "CPoint", "VBlock", "In_Block"} //-------------------------------------------------------------- class ENode { public: EGraph *egraph; int *edges; // list of edges // the value is \pm [(edge index)+1] int id; // id of the enode int maxdeg; // maximum degree int deg; // degree int extloop; // loop inside this node or AT_Initial etc. int ndtype; // type of the node int intrct; // assigned interaction/particle (ext.) // used in EGraph::biconn() int *klow; int visited; int DUMMYPADDING; //-------------------------------- // functions ENode(void); ENode(EGraph *egrph, int loops, int sdeg); ~ENode(void); void initAss(EGraph *egrph, int nid, int sdg); void setId(EGraph *egrph, const int nid); void copy(ENode *en); void setExtern(int typ, int pt); void setType(int typ); void print(void); }; //-------------------------------------------------------------- class EEdge { // momentum is printed like: ("%s%d", (enode.ext)?"Q":"p", enode.momn) public: EGraph *egraph; // egraph int id; // id int ext; int ptcl; // assigned particle (agraph) int deleted; // deleted edge, if true int nodes[2]; // nodes of bothsides int nlegs[2]; // nodes of both side (agraph) // for biconn int *emom; // external momenta int *lmom; // loop momenta int *extMom; // set of external momenta. // momentum obtain in searchME ULong momset; // set of momenta in bit string (leaf --> root) int momdir; // direction (leg=0 --> leg=1) Bool cut; int visited; int conid; // connected component int edtype; // type int opicomp; // id of 1PI component int dir; // direction of momentum int DUMMYPADDING; //-------------------------------- // functions EEdge(void); EEdge(EGraph *egrph, int nedges, int nloops); ~EEdge(void); void copy(EEdge *ee); void setId(EGraph *egrph, const int eid); void print(void); void setType(int typ); void setLMom(int k, int dir); void setEMom(int nedges, int *extn, int dir); }; //-------------------------------------------------------------- // type of fermion lines typedef enum {FL_Open, FL_Closed} FLType; //-------------------------------------------------------------- class EFLine { public: int elist[GRCC_MAXNODES]; // list of (\pm [(edge index)+1]) FLType ftype; int fkind; int nlist; EFLine(void); void print(const char *msg); }; //-------------------------------------------------------------- class EGraph { public: Options *opt; // table of options Model *model; Process *proc; SProcess *sproc; MGraph *mgraph; MConn *econn; ENode **nodes; EEdge **edges; // edges[nEdges+1]: index starts from 1 BigInt mId; // id of mgraph BigInt aId; // id of agraph in the same mgraph BigInt sId; // sequential no. of agraph BigInt gSubId; // ??? Bool assigned; // mgraph (False) or agraph (True) int fsign; BigInt nsym, esym; // symmetry factor with symm. ext. BigInt nsym1; // symmetry factor without symm. ext. BigInt extperm; // the order of group of symm. ext. BigInt multp; // multiplicity of graph in symm. ext. int pId; int sNodes; // memory size int sEdges; // memory size int sMaxdeg; // memory size int sLoops; // memory size int nNodes; int nEdges; int nExtern; int maxdeg; // maximum value of degree of nodes int nLoops; int totalc; // total order of coupling constants // biconnect int nopicomp; int opi2plp; int nopi2p; int nadj2ptv; // the no. of edges connecting 2point vertices int DUMMYPADDING; int *bidef; int *bilow; int *extMom; int bconn; int bicount; int loopm; int opiCount; // Fermion lines EFLine *flines[GRCC_MAXFLINES]; int nFlines; int DUMMYPADDING1; //-------------------------- // functions EGraph(int nnodes, int nedges, int mxdeg); ~EGraph(void); void copy(EGraph *eg); void print(void); void printPy(FILE *fp, long mId); void fromDGraph(DGraph *dg); void fromMGraph(MGraph *mgraph); Bool optQGrafM(Options *opt); Bool optQGrafA(Options *opt); Bool isOptE(void); ENode *setExtern(int n0, int pt, int ndtp); Bool isExternal(int nd) { return (nodes[nd]->extloop < 0); }; Bool isFermion(int nd); void setExtLoop(int nd, int val); void endSetExtLoop(void); int connComp(void); int connVisit(int nd, int ncc); void biconnE(void); void biinitE(void); void bisearchE(int nd, int *extlst, int *intlst, int *opiext, int *opiloop); int findRoot(void); int dirEdge(int n, int e); void extMomConsv(void); int cmpMom(int *lm0, int *em0, int *lm1, int *em1); int groupLMom(int *grp, int *ed2gr); void chkMomConsv(void); void prFLines(void); void getFLines(void); int fltrace(int fk, int nd0, int *fl); void addFLine(const FLType ft, int fk, int nfl, int *fl); int legParticle(int ed, int lg); }; //************************************************************** // Symmetry group of graphs //=============================================================== class SGroup { public: BigInt size; // # of allocated elements BigInt nelem; // # of saved elements int **elem; // saved elements int nnodes; // # of nodes. int neclass; // # of classes int eclass[GRCC_MAXNODES]; // table of classes int cgen; // counter for the generation int csav; // counter for the saved elements int permg[GRCC_MAXNODES]; // resulting permutation int perms[GRCC_MAXNODES]; // curr. elem of saved ones. int pgr[GRCC_MAXNODES]; // work int pgq[GRCC_MAXNODES]; // work int psr[GRCC_MAXNODES]; // work int psq[GRCC_MAXNODES]; // work //------------------------------- // functions SGroup(void); ~SGroup(void); void print(void); void newGroup(int nelm, int nclss, int *clss); void clearGroup(void); void delGroup(void); int *genNext(void); void addGroup(int *p); BigInt nElem(void); int *nextElem(void); }; //************************************************************** // MGraph //============================================================== // class of nodes for MGraph class MNode { public: int id; // node id int deg; // degree(node) = the number of legs int clss; // initial class number in which the node belongs int extloop; int cmindeg; int cmaxdeg; int freelg; // the number of free legs int visited; MNode(int id, int clss, NCInput *mgi); MNode(int id, int deg, int extloop, int clss, int cmind, int cmaxd); }; //=============================================================== // class of scalar graph expressed by matrix form // // Input : the classified set of nodes. // Output : control passed to 'EGraph(self)' class MGraph { public: // initial conditions Options *opt; // options // symmetry group SGroup *group; // symmetry group MOrbits *orbits; // Orbits of nodes with respect to symmetry group MNode **nodes; // table of MNode object BigInt mId; // process/sprocess ID int *clist; // list of initial classes int pId; // process/sprocess ID int nNodes; // the number of nodes int nEdges; // the number of edges int nLoops; // the number of loops int nExtern; // the number of external nodes int nClasses; // the number of initial classes int mindeg; // minimum value of degree of nodes int maxdeg; // maximum value of degree of nodes // the current graph int **adjMat; // adjacency matrix MNodeClass *curcl; // the current 'MNodeClass' object EGraph *egraph; BigInt nsym; // symmetry factor from nodes BigInt esym; // symmetry factor from edges // generated set of graphs BigInt cDiag; // the total number of generated graphs BigInt c1PI; // the total number of 1PI graphs BigInt cNoTadpole; // the total number of graphs without tadpoles BigInt cNoTadBlock; // the total number of graphs without tad-blocks BigInt c1PINoTadBlock; // the total number of 1PI graphs without tad-blocks Fraction wscon; // weighted sum of graphs Fraction wsopi; // weighted sum of 1PI graphs // measures of efficiency BigInt ngen; // generated graph before check BigInt ngconn; // generated connected graph before check BigInt nCallRefine; BigInt discardRefine; BigInt discardDisc; BigInt discardIso; // for options Bool opi; Bool opiloop; Bool extself; Bool selfloop; Bool multiedge; Bool tadpole; Bool tadblock; Bool block; Bool bipart; int DUMMYPADDING1; // table of n edge-connected components MConn *mconn; // work space for isomorphism int **modmat; // permutated adjacency matrix // work space for biconnected component int *bidef; int *bilow; int *bicol; int bicount; int DUMMYPADDING2; //---------- // functions MGraph(int pid, int ncl, NCInput *mgi, Options *opt); MGraph(int pid, int ncl, int *cldeg, int *clnum, int *clexl, int *cmind, int *cmaxd, Options *opt); ~MGraph(void); void init(void); BigInt generate(void); Bool isExternal(int nd) { return (nodes[nd]->extloop < 0); }; void printAdjMat(MNodeClass *cl); void print(void); void printPy(FILE *fp, long mId); Bool isConnected(void); Bool visit(int nd); Bool isIsomorphic(MNodeClass *cl); void permMat(int size, int *perm, int **mat0, int **mat1); int compMat(int size, int **mat0, int **mat1); MNodeClass *refineClass(MNodeClass *cl); void bisearchME(int nd, int pd, int ned, int col, MCOpi *mopi, MCBlock *mblk, ULong *momset, int *next, int *nart); void biconnME(void); Bool isOptM(void); void connectClass(MNodeClass *cl); void connectNode(int sc, int ss, MNodeClass *cl); void connectLeg(int sc, int sn, int tc, int ts, MNodeClass *cl); void newGraph(MNodeClass *cl); }; //=============================================================== // class of node-classes for MGraph //-------------------------------------------------------------- class MNodeClass { public: int clmat[GRCC_MAXNODES][GRCC_MAXNODES]; // matrix used for classification int clist[GRCC_MAXNODES]; // the number of nodes in each class int ndcl[GRCC_MAXNODES]; // node --> class int flist[GRCC_MAXNODES+1]; // the first node in each class int clord[GRCC_MAXNODES]; // ordering of classes int cmindeg[GRCC_MAXNODES]; // min(deg of connectable node) int cmaxdeg[GRCC_MAXNODES]; // max(deg of connectable node) int nNodes; // the number of nodes int nClasses; // the number of classes int maxdeg; // maximal value of degree(node) int flg0; int flg1; int flg2; MNodeClass(int nnodes, int nclasses); ~MNodeClass(void); void init(int *cl, int mxdeg, int **adjmat); void copy(MNodeClass* mnc); int clCmp(int nd0, int nd1, int cn); void printMat(void); void mkFlist(void); void mkNdCl(void); void mkClMat(int **adjmat); void incMat(int nd, int td, int val); int cmpMNCArray(int *a0, int *a1, int ma); void reorder(MGraph *mg); }; //=============================================================== // class of an edge //-------------------------------------------------------------- class MCEdge { public: Edge2n nodes; // nodes at the both size of the edge (leaf --> root) ULong momset; // set of momenta in bit string int momdir; // set of momenta in bit string int DUMMYPADDING; MCEdge(void); ~MCEdge(void); }; //=============================================================== // class of 1PI component //-------------------------------------------------------------- class MCOpi { public: int *nodes; // array of nodes in int nnodes; // # nodes in the 1PI component int nlegs; // # leg (bridges) of the 1PI component int next; // # external particles of the 1PI comp. int nedges; // # edges in the 1PI comp. int loop; // # loops in the 1PI comp. int ctloop; // # loops in the counter terms in the OP comp. int mom0lg; // # leg (bridges) with 0 momentum int DUMMYPADDING; MCOpi(void); ~MCOpi(void); void init(void); }; //=============================================================== // class of bridge //-------------------------------------------------------------- class MCBridge { public: Edge2n nodes; // nodes at the both size of the bridge int next; // # momenta of ext. particles flowing on the bridge MCBridge(void); ~MCBridge(void); }; //=============================================================== // class of block //-------------------------------------------------------------- class MCBlock { public: Edge2n *edges; // array of edges in the block int nmedges; // # edges in the block int nartps; // # articulation points of the block int loop; // # loop in the block int DUMMYPADDING; MCBlock(void); ~MCBlock(void); void init(void); }; //=============================================================== // class of table of MConn //-------------------------------------------------------------- class MConn { public: // 2-edge connected components MCEdge *cedges; // table of edges MCOpi *opics; // table of n-edge-connected components MCBridge *bridges; // table of bridges MCBlock *blocks; // table of blocks int *articuls; // buffer for nodes for articulation points int *opisp; // buffer for nodes in 1PI components int *opistk; // stack of nodes for 1PI components. Edge2n *blksp; // buffer for edges in blocks Edge2n *blkstk; // stack of edges for blocks int snodes; // # nodes int sedges; // # edges // opi components (edge-connected) int nopic; // # 1PI components (n1PIComps) int nlpopic; // # looped 1PI components (n1PIComps) int nctopic; // # 1PI components of one counter term. // edges int nbacked; // # back edges // bridges int nbridges; // # bridges int ne0bridges; // # bridges whose next=0 int ne1bridges; // # bridges whose next=1 int nselfloops; int nmultiedges; // blocks (node-connected) int nblocks; // # blocks int na1blocks; // # bridges whose next=0 int narticuls; // # articulation points int neblocks; // # effective looped blocks // indices to work spaces int nopisp; // # used in opisp int opistkptr; // # stack pointer of opistk int nblksp; // # used in blksp int blkstkptr; // # stack pointer of tlkstk int DUMMYPADDING; MConn(int nnod, int nedg); ~MConn(void); void init(void); void initCEdges(MGraph *); void pushNode(int nd); void pushEdge(int n0, int n1); void addCEdge(int n0, int n1, ULong momset); void addOPIc(MCOpi *mopi, int stp); void addBridge(int n0, int n1, int nex, int nextot); void addArtic(int nd, int mul); void addBlock(MCBlock *eblk, int stp); void addBlockSelf(int nd, int mul); void print(void); void prEdges(void); }; //=============================================================== // class of orbits of nodes //-------------------------------------------------------------- class MOrbits { // Usage // 1. node ==> orbit // (class) = nd2or[(node)] // // 2. class ==> nodes // for (c = 0; c < nClass; c++) { // for (j = flist[c]; j < flist[c+1]; j++) { // (node) = or2nd[c]; // } // } public: int nOrbits; int nNodes; int nd2or[GRCC_MAXNODES]; int or2nd[GRCC_MAXNODES]; int flist[GRCC_MAXNODES+1]; MOrbits(void); ~MOrbits(void); void print(void); // construction of orbits void initPerm(int nnodes); void fromPerm(int *perm); void toOrbits(void); }; //************************************************************** // Particle assignment //=============================================================== typedef int CheckPt[2]; typedef enum { AS_UnAssLegs, AS_Assigned, AS_Assigned0, AS_AssExt, AS_Impossible } NCandSt; //=============================================================== class NCand { // List of candidates for the assignment of interactions to a vertex public: int deg; // degree of the node NCandSt st; // status int nilist; // length of the list int ilist[GRCC_MAXMINTERACT]; // list of candidates //======== NCand(const NCandSt sta, const int dega, const int nilst, int *ilst); ~NCand(void); // print void prNCand(const char* msg); }; //=============================================================== class ECand { // List of candidates for the assignment of particles to an edge public: Bool det; // determined or not int nplist; // size of the list of candidates int plist[GRCC_MAXMPARTICLES2]; // list of candidates ECand(int dt, int nplist, int *plst); ~ECand(void); // print void prECand(const char *msg); }; //=============================================================== class ANode { // Connection information of a node to others // // (this node) -- (adjacent edge) -- (next node) // (n0, j) e n1 // // e = (aedges[j], aelegs[j]) // n1 = anodes[j] public: int deg; // degree of the node int nlegs; // the number of legs already assigned int *anodes; // anodes[j] = (next node of leg j) int *aedges; // aedges[j] = (next edge of leg j) int *aelegs; // aelegs[j] = (leg of the next edge) NCand *cand; // candidate list ANode(int dg); ~ANode(void); int newleg(void); // get a new leg }; //=============================================================== class AEdge { // Connection information of an edge // (self) ==> nodes [(nodes[0], nlegs[0]), (nodes[1], nlegs[1])] // particle 'ptcl' flows from leg=0 to 1. public: ECand *cand; // candidate int nodes[2]; // nodes of both sides of the edge int nlegs[2]; // nodes of both sides of the edge int ptcl; // particle defined in the model int DUMMYPADDING; AEdge(int n0, int l0, int n1, int l1); ~AEdge(void); }; //=============================================================== class Assign { // Class for particle/interaction assignment. public: EGraph *egraph; // EGraph object MGraph *mgraph; // MGraph object SProcess *sproc; // Sub-process object Process *proc; // Process object Model *model; // Model object Options *opt; // Option object AStack *astack; // Stack for saving candidates PNodeClass *pnclass; // class of nodes MOrbits *orbits; // orbits of nodes by symmetry group int nNodes; // the number of nodes int nEdges; // the number of edges int nExtern; // the number of external particles. int nETotal; // the total number of edges BigInt nAGraphs; // the number of assigned graphs Fraction wAGraphs; // the weighted sum of graphs BigInt nAOPI; // the number of assigned 1PI Fraction wAOPI; // the weighted sum of 1PI ANode **nodes; // table of nodes AEdge **edges; // table of edges CheckPt checkpoint0; // save stack pointers int cplleft[GRCC_MAXNCPLG]; // coupling constants left //=========================================== Assign(SProcess *sprc, MGraph *mgr, PNodeClass *pnc); ~Assign(void); //=========================================== // print lists of candidates void prCand(const char *msg); // check void checkAG(const char *msg); //=========================================== // control of assignment // entry point of assignment Bool assignAllVertices(void); // select a source node for assignment Bool selectVertex(void); Bool selectVertexSimp(int lastv); // select a source leg of the node for assignment Bool selectLeg(int v, int lastlg); // assign a vertex a interaction Bool assignVertex(int v); // assignment procedure is finished. Needs check. Bool allAssigned(void); //=========================================== // Input and output // Input from mgraph Bool fromMGraph(void); // add an edge void addEdge(int n0, int n1, int nplist, int *plist); // connect nodes and edges. void connect(int n0, int l0, int eg, int el, int n1, int l1); // Output to egraph Bool fillEGraph(int aid, BigInt nsym, BigInt esym, BigInt nsym1); // reorder legs in accordance with the interaction definition int *reordLeg(int n, int *reord, int *plist, int *used); //=========================================== // direction of particle on an edge and at (node, leg) // convert particle code // at node-leg ('n', 'ln') <==> edge at ('n', 'ln') int getLegParticle(int n, int ln); // convert particle 'pt' on the edge to ('n', 'ln') int legEdgeParticle(int n, int ln, int pt); // convert candidate list at ('v', 'lg') into in-coming direction int legPart(int v, int lg, int nplst, int *plst, int *rlist, const int size); // convert candidate list at ('v', 'lg') into in-coming direction int candPart(int v, int ln, int *plist, const int size); //=========================================== // assignment // find a vertex to be assigned int selUnAssVertex(void); int selUnAssVertexSimp(int lastv); // find a leg of the vertex to be assigned int selUnAssLeg(int v, int lastlg); // assign the interaction 'ia' to the vertex 'v'. NCandSt assignIVertex(int v, int ia); // assign particle 'pt' the the leg 'ln' of the node 'n'. Bool assignPLeg(int n, int ln, int pt); Bool isOrdPLeg(int n, int ln, int pt); Bool detEdge(int e); //=========================================== // canndidates // construct lists of assigned / unassigned particles at a node Bool candPartClassify(int v, int *npdass, int *pdass, int *npuass, int *puass, const int size); // update candidate list for a vertex 'v'. Bool updateCandNode(int v); //=========================================== // filter Bool checkOrderCpl(void); Bool isOrdLegs(void); Bool isIsomorphic(MNodeClass *cl, BigInt *nsym, BigInt *esym, BigInt *nsym1); int cmpPermGraph(int *p, MNodeClass *cl); int cmpNodes(int nd0, int nd1, MNodeClass *cn); BigInt edgeSym(void); void saveCouple(int *sav); void restoreCouple(int *sav); Bool subCouple(int *cpl); #ifdef CHECK //=========================================== // check Bool checkCand(const char *msg); void checkNode(int n, const char *msg); #endif }; //************************************************************** // Stack of candidate lists //=============================================================== class NStack { // Stack for backtracking method for a node. public: int noden; int deg; NCandSt st; int nilist; int ilist[GRCC_MAXMINTERACT]; NStack() { }; ~NStack() { }; void print(const char *msg); }; //=============================================================== class EStack { // Stack for backtracking method for an edge. public: int edgen; int det; int nplist; int plist[GRCC_MAXMPARTICLES2]; EStack() { }; ~EStack() { }; void print(const char *msg); }; //=============================================================== class AStack { // Stack for backtracking method for an edge. public: Assign *agraph; NStack **nStack; // stack for nodes int nStackP; // stack pointer for nodes int nSize; // stack size EStack **eStack; // stack for edges int eStackP; // stack pointer for edges int eSize; // stack size AStack(int nSize, int eSize); ~AStack(void); void setAGraph(Assign *ag); void checkPoint(CheckPt sav); void restore(CheckPt sav); void restoreMsg(CheckPt sav, const char *msg); void prStack(void); void pushNode(int n); void pushEdge(int e); private: void restoreNode(int spr); void restoreEdge(int spr); }; //============================================================== // end of namespace Grcc #ifdef GRCC_NAMESPACE } #endif form-5.0.1/sources/reshuf.c0000644000175100017510000024133315217035721011277 /** @file reshuf.c * * Mixed routines: * Routines for relabelling dummy indices. * The multiply command * The distrib_ function * The tryreplace statement */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #define NEWCODE /* #[ Includes : reshuf.c */ #include "form3.h" /* #] Includes : #[ Reshuf : Routines to rearrange dummy indices, so that a: The notation becomes reasonably unique (the perfect job may consume very much time). b: The value of AR.CurDum is reset. Also some routines are needed to aid in the reading of stored expressions. Also in those expressions there can be dummy indices, and there should be no conflict with the already existing dummies. #[ ReNumber : Reads the term, tests for dummies, and puts them in order. Note that this is kind of a first order approximation. There is quite some room to make this routine 'smart' First order: First index will be lowest, second will be next etc. Second order: Functions with more than one index and symmetry properties have some look ahead to see which index is the first to find its partner. Third order: Take the ordering of the functions into account. Fourth order: Try all permutations and see which one gives the 'minimal' term. Currently we use only the first order. We need a scratch array for the numbers we find, and one for the addresses at which these numbers are. We can use the space for the Scrat arrays. There are 13 of those and each is AM.MaxTal UWORDs long. */ WORD ReNumber(PHEAD WORD *term) { GETBIDENTITY WORD *d, *e, **p, **f; WORD n, i, j, old; AN.DumFound = AN.RenumScratch; AN.DumPlace = AN.PoinScratch; AN.DumFunPlace = AN.FunScratch; AN.NumFound = 0; FunLevel(BHEAD term); d = AN.RenumScratch; p = AN.PoinScratch; f = AN.FunScratch; /* Now the first level sorting. */ i = AN.IndDum; n = AN.NumFound; while ( --n >= 0 ) { if ( *d > 0 ) { old = **p; **p = ++i; if ( *f ) **f |= DIRTYSYMFLAG; e = d; e++; for ( j = 1; j <= n; j++ ) { if ( *e && *(p[j]) == old ) { *(p[j]) = i; if ( f[j] ) *(f[j]) |= DIRTYSYMFLAG; *e = 0; } e++; } } p++; d++; f++; } return(i); } /* #] ReNumber : #[ FunLevel : Does one term in determining where the dummies are. Made to work recursively for functions. */ void FunLevel(PHEAD WORD *term) { GETBIDENTITY WORD *t, *tstop, *r, *fun; WORD *m; t = r = term; r += *r; tstop = r - ABS(r[-1]); t++; if ( t < tstop ) do { r = t + t[1]; switch ( *t ) { case SYMBOL: case DOTPRODUCT: break; case VECTOR: t += 3; do { if ( *t > AN.IndDum ) { if ( AN.NumFound >= AN.MaxRenumScratch ) AdjustRenumScratch(BHEAD0); AN.NumFound++; *AN.DumFound++ = *t; *AN.DumPlace++ = t; *AN.DumFunPlace++ = 0; } t += 2; } while ( t < r ); break; case SUBEXPRESSION: /* Still must hunt down the wildcards(?) */ break; case GAMMA: t += FUNHEAD-2; /* fall through */ case DELTA: case INDEX: t += 2; while ( t < r ) { if ( *t > AN.IndDum ) { if ( AN.NumFound >= AN.MaxRenumScratch ) AdjustRenumScratch(BHEAD0); AN.NumFound++; *AN.DumFound++ = *t; *AN.DumPlace++ = t; *AN.DumFunPlace++ = 0; } t++; } break; case HAAKJE: case EXPRESSION: case SNUMBER: case LNUMBER: break; default: if ( *t < FUNCTION ) { MLOCK(ErrorMessageLock); MesPrint("Unexpected code in ReNumber"); MUNLOCK(ErrorMessageLock); Terminate(-1); } fun = t+2; if ( *t >= FUNCTION && functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { t += FUNHEAD; while ( t < r ) { if ( *t > AN.IndDum ) { if ( AN.NumFound >= AN.MaxRenumScratch ) AdjustRenumScratch(BHEAD0); AN.NumFound++; *AN.DumFound++ = *t; *AN.DumPlace++ = t; *AN.DumFunPlace++ = fun; } t++; } break; } t += FUNHEAD; while ( t < r ) { if ( *t > 0 ) { /* General function. Enter 'recursion'. */ m = t + *t; t += ARGHEAD; while ( t < m ) { FunLevel(BHEAD t); t += *t; } } else { if ( *t == -INDEX ) { t++; if ( *t > AN.IndDum ) { if ( AN.NumFound >= AN.MaxRenumScratch ) AdjustRenumScratch(BHEAD0); AN.NumFound++; *AN.DumFound++ = *t; *AN.DumPlace++ = t; *AN.DumFunPlace++ = fun; } t++; } else if ( *t <= -FUNCTION ) t++; else t += 2; } } break; } t = r; } while ( t < tstop ); } /* #] FunLevel : #[ DetCurDum : We look for indices in the range AM.IndDum to AM.IndDum+MAXDUMMIES. The maximum value is returned. */ WORD DetCurDum(PHEAD WORD *t) { GETBIDENTITY WORD maxval = AN.IndDum; WORD maxtop = AM.IndDum + WILDOFFSET; WORD *tstop, *m, *r, i; tstop = t + *t - 1; tstop -= ABS(*tstop); t++; while ( t < tstop ) { if ( *t == VECTOR ) { m = t + 3; t += t[1]; while ( m < t ) { if ( *m > maxval && *m < maxtop ) maxval = *m; m += 2; } } else if ( *t == DELTA || *t == INDEX ) { m = t + 2; Singles: t += t[1]; while ( m < t ) { if ( *m > maxval && *m < maxtop ) maxval = *m; m++; } } else if ( *t >= FUNCTION ) { if ( functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { m = t + FUNHEAD; goto Singles; } r = t + FUNHEAD; t += t[1]; while ( r < t ) { /* The arguments */ if ( *r < 0 ) { if ( *r <= -FUNCTION ) r++; else if ( *r == -INDEX ) { if ( r[1] > maxval && r[1] < maxtop ) maxval = r[1]; r += 2; } else r += 2; } else { m = r + ARGHEAD; r += *r; while ( m < r ) { /* Terms in the argument */ i = DetCurDum(BHEAD m); if ( i > maxval && i < maxtop ) maxval = i; m += *m; } } } } else { t += t[1]; } } return(maxval); } /* #] DetCurDum : #[ FullRenumber : Does a full renumbering. May be slow if there are many indices. par = 1 Goes with a factorial! par = 0 All single exchanges only till there is no more improvement. Notice that there is a hole in the defense with respect to arguments inside functions inside functions. */ int FullRenumber(PHEAD WORD *term, WORD par) { GETBIDENTITY WORD *d, **p, **f, *w, *t, *best, *stac, *perm, a, *termtry; WORD n, i, j, k, ii; WORD *oldworkpointer = AT.WorkPointer; n = ReNumber(BHEAD term) - AM.IndDum; if ( n <= 1 ) return(0); Normalize(BHEAD term); if ( *term == 0 ) return(0); n = ReNumber(BHEAD term) - AM.IndDum; d = AN.RenumScratch; p = AN.PoinScratch; f = AN.FunScratch; if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; k = AN.NumFound; best = w = AT.WorkPointer; t = term; for ( i = *term; i > 0; i-- ) *w++ = *t++; AT.WorkPointer = w; Normalize(BHEAD best); AT.WorkPointer = w = best + *best; stac = w+100; perm = stac + n + 1; termtry = perm + n + 1; for ( i = 1; i <= n; i++ ) perm[i] = i + AM.IndDum; for ( i = 1; i <= n; i++ ) stac[i] = i; for ( i = 0; i < k; i++ ) d[i] = *(p[i]) - AM.IndDum; if ( par == 0 ) { /* All single exchanges */ for ( i = 1; i < n; i++ ) { for ( j = i+1; j <= n; j++ ) { a = perm[j]; perm[j] = perm[i]; perm[i] = a; for ( ii = 0; ii < k; ii++ ) { *(p[ii]) = perm[d[ii]]; if ( f[ii] ) *(f[ii]) |= DIRTYSYMFLAG; } t = term; w = termtry; for ( ii = 0; ii < *term; ii++ ) *w++ = *t++; AT.WorkPointer = w; if ( Normalize(BHEAD termtry) == 0 ) { if ( *termtry == 0 ) goto Return0; if ( ( ii = CompareTerms(BHEAD termtry,best,0) ) > 0 ) { t = termtry; w = best; for ( ii = 0; ii < *termtry; ii++ ) *w++ = *t++; i = 0; break; /* restart from beginning */ } else if ( ii == 0 && CompCoef(termtry,best) != 0 ) goto Return0; } /* if no success, set back */ a = perm[j]; perm[j] = perm[i]; perm[i] = a; } } } else if ( par == 1 ) { /* all permutations */ j = n-1; for(;;) { if ( stac[j] == n ) { a = perm[j]; perm[j] = perm[n]; perm[n] = a; stac[j] = j; j--; if ( j <= 0 ) break; continue; } if ( j != stac[j] ) { a = perm[j]; perm[j] = perm[stac[j]]; perm[stac[j]] = a; } (stac[j])++; a = perm[j]; perm[j] = perm[stac[j]]; perm[stac[j]] = a; { for ( i = 0; i < k; i++ ) { *(p[i]) = perm[d[i]]; if ( f[i] ) *(f[i]) |= DIRTYSYMFLAG; } t = term; w = termtry; for ( i = 0; i < *term; i++ ) *w++ = *t++; AT.WorkPointer = w; if ( Normalize(BHEAD termtry) == 0 ) { if ( *termtry == 0 ) goto Return0; if ( ( ii = CompareTerms(BHEAD termtry,best,0) ) > 0 ) { t = termtry; w = best; for ( i = 0; i < *termtry; i++ ) *w++ = *t++; } else if ( ii == 0 && CompCoef(termtry,best) != 0 ) goto Return0; } } if ( j < n-1 ) { j = n-1; } } } t = term; w = best; n = *best; for ( i = 0; i < n; i++ ) *t++ = *w++; AT.WorkPointer = oldworkpointer; return(0); Return0: *term = 0; AT.WorkPointer = oldworkpointer; return(0); } /* #] FullRenumber : #[ MoveDummies : Routine shifts the dummy indices by an amount 'shift'. It is an adaptation of DetCurDum. Needed for = ...*expression^power*... in which expression contains dummy indices. Note that this code should have been in ver1 already and has always been missing. Routine made 29-jan-2007. */ void MoveDummies(PHEAD WORD *term, WORD shift) { GETBIDENTITY WORD maxval = AN.IndDum; WORD maxtop = AM.IndDum + WILDOFFSET; WORD *tstop, *m, *r; tstop = term + *term - 1; tstop -= ABS(*tstop); term++; while ( term < tstop ) { if ( *term == VECTOR ) { m = term + 3; term += term[1]; while ( m < term ) { if ( *m > maxval && *m < maxtop ) *m += shift; m += 2; } } else if ( *term == DELTA || *term == INDEX ) { m = term + 2; Singles: term += term[1]; while ( m < term ) { if ( *m > maxval && *m < maxtop ) *m += shift; m++; } } else if ( *term >= FUNCTION ) { if ( functions[*term-FUNCTION].spec >= TENSORFUNCTION ) { m = term + FUNHEAD; goto Singles; } r = term + FUNHEAD; term += term[1]; while ( r < term ) { /* The arguments */ if ( *r < 0 ) { if ( *r <= -FUNCTION ) r++; else if ( *r == -INDEX ) { if ( r[1] > maxval && r[1] < maxtop ) r[1] += shift; r += 2; } else r += 2; } else { m = r + ARGHEAD; r += *r; while ( m < r ) { /* Terms in the argument */ MoveDummies(BHEAD m,shift); m += *m; } } } } else { term += term[1]; } } } /* #] MoveDummies : #[ AdjustRenumScratch : Extends the buffer for number of dummies that can be found in a term. Originally we had a fixed buffer at size 300 in the AN struct. Thomas Hahn ran out of that. Hence we have now made it a dynamical buffer. Note that the pointers used in FunLevel need adjustment as well. */ void AdjustRenumScratch(PHEAD0) { GETBIDENTITY WORD newsize; int i; WORD **newpoin, *newnum; if ( AN.MaxRenumScratch == 0 ) newsize = 100; else newsize = AN.MaxRenumScratch*2; if ( newsize > MAXPOSITIVE/2 ) newsize = MAXPOSITIVE/2+1; newpoin = (WORD **)Malloc1(newsize*sizeof(WORD *),"PoinScratch"); for ( i = 0; i < AN.NumFound; i++ ) newpoin[i] = AN.PoinScratch[i]; for ( ; i < newsize; i++ ) newpoin[i] = 0; if ( AN.PoinScratch ) M_free(AN.PoinScratch,"PoinScratch"); AN.PoinScratch = newpoin; AN.DumPlace = newpoin + AN.NumFound; newpoin = (WORD **)Malloc1(newsize*sizeof(WORD *),"FunScratch"); for ( i = 0; i < AN.NumFound; i++ ) newpoin[i] = AN.FunScratch[i]; for ( ; i < newsize; i++ ) newpoin[i] = 0; if ( AN.FunScratch ) M_free(AN.FunScratch,"FunScratch"); AN.FunScratch = newpoin; AN.DumFunPlace = newpoin + AN.NumFound; newnum = (WORD *)Malloc1(newsize*sizeof(WORD),"RenumScratch"); for ( i = 0; i < AN.NumFound; i++ ) newnum[i] = AN.RenumScratch[i]; for ( ; i < newsize; i++ ) newnum[i] = 0; if ( AN.RenumScratch ) M_free(AN.RenumScratch,"RenumScratch"); AN.RenumScratch = newnum; AN.DumFound = newnum + AN.NumFound; AN.MaxRenumScratch = newsize; } /* #] AdjustRenumScratch : #] Reshuf : #[ Count : #[ CountDo : This function executes the counting action in a count operation. The return value is the count of the term. Input is the term and a pointer to the instruction. */ WORD CountDo(WORD *term, WORD *instruct) { WORD *m, *r, i, j, count = 0; WORD *stopper, *tstop, *r1 = 0, *r2 = 0; m = instruct; stopper = m + m[1]; instruct += 3; tstop = term + *term; tstop -= ABS(tstop[-1]); term++; while ( term < tstop ) { switch ( *term ) { case SYMBOL: i = term[1] - 2; term += 2; while ( i > 0 ) { m = instruct; while ( m < stopper ) { if ( *m == SYMBOL && m[2] == *term ) { count += m[3] * term[1]; } m += m[1]; } term += 2; i -= 2; } break; case DOTPRODUCT: i = term[1] - 2; term += 2; while ( i > 0 ) { m = instruct; while ( m < stopper ) { if ( *m == DOTPRODUCT && (( m[2] == *term && m[3] == term[1]) || ( m[2] == term[1] && m[3] == *term )) ) { count += m[4] * term[2]; break; } m += m[1]; } m = instruct; while ( m < stopper ) { if ( *m == VECTOR && m[2] == *term && ( m[3] & DOTPBIT ) != 0 ) { count += m[m[1]-1] * term[2]; } m += m[1]; } m = instruct; while ( m < stopper ) { if ( *m == VECTOR && m[2] == term[1] && ( m[3] & DOTPBIT ) != 0 ) { count += m[m[1]-1] * term[2]; } m += m[1]; } term += 3; i -= 3; } break; case INDEX: j = 1; goto VectInd; case VECTOR: j = 2; VectInd: i = term[1] - 2; term += 2; while ( i > 0 ) { m = instruct; while ( m < stopper ) { if ( *m == VECTOR && m[2] == *term && ( m[3] & VECTBIT ) != 0 ) { count += m[m[1]-1]; } m += m[1]; } term += j; i -= j; } break; default: if ( *term >= FUNCTION ) { i = *term; m = instruct; while ( m < stopper ) { if ( *m == FUNCTION && m[2] == i ) count += m[3]; m += m[1]; } if ( functions[i-FUNCTION].spec >= TENSORFUNCTION ) { i = term[1] - FUNHEAD; term += FUNHEAD; while ( i > 0 ) { if ( *term < 0 ) { m = instruct; while ( m < stopper ) { if ( *m == VECTOR && m[2] == *term && ( m[3] & FUNBIT ) != 0 ) { count += m[m[1]-1]; } m += m[1]; } } term++; i--; } } else { r = term + term[1]; term += FUNHEAD; while ( term < r ) { if ( ( *term == -INDEX || *term == -VECTOR || *term == -MINVECTOR ) && term[1] < MINSPEC ) { m = instruct; while ( m < stopper ) { if ( *m == VECTOR && term[1] == m[2] && ( m[3] & SETBIT ) != 0 ) { r1 = SetElements + Sets[m[4]].first; r2 = SetElements + Sets[m[4]].last; while ( r1 < r2 ) { if ( *r1 == i ) { count += m[m[1]-1]; goto NextFF; } r1++; } } m += m[1]; } NextFF: term += 2; } else { NEXTARG(term) } } } break; } else { term += term[1]; } break; } } return(count); } /* #] CountDo : #[ CountFun : This is the count function. The return value is the count of the term. Input is the term and a pointer to the count function. */ WORD CountFun(WORD *term, WORD *countfun) { WORD *m, *r, i, j, count = 0, *instruct, *stopper, *tstop; m = countfun; stopper = m + m[1]; instruct = countfun + FUNHEAD; tstop = term + *term; tstop -= ABS(tstop[-1]); term++; while ( term < tstop ) { switch ( *term ) { case SYMBOL: i = term[1] - 2; term += 2; while ( i > 0 ) { m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( *m == -SYMBOL && m[1] == *term && m[2] == -SNUMBER && ( m + 2 ) < stopper ) { count += m[3] * term[1]; m += 4; } else { NEXTARG(m) } } term += 2; i -= 2; } break; case DOTPRODUCT: i = term[1] - 2; term += 2; while ( i > 0 ) { m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( *m == 9+ARGHEAD && m[ARGHEAD] == 9 && m[ARGHEAD+1] == DOTPRODUCT && m[ARGHEAD+9] == -SNUMBER && ( m + ARGHEAD+9 ) < stopper && (( m[ARGHEAD+3] == *term && m[ARGHEAD+4] == term[1]) || ( m[ARGHEAD+3] == term[1] && m[ARGHEAD+4] == *term )) ) { count += m[ARGHEAD+10] * term[2]; m += ARGHEAD+11; } else { NEXTARG(m) } } m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( ( *m == -VECTOR || *m == -MINVECTOR ) && m[1] == *term && m[2] == -SNUMBER && ( m+2 ) < stopper ) { count += m[3] * term[2]; m += 4; } NEXTARG(m) } m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( ( *m == -VECTOR || *m == -MINVECTOR ) && m[1] == term[1] && m[2] == -SNUMBER && ( m+2 ) < stopper ) { count += m[3] * term[2]; m += 4; } NEXTARG(m) } term += 3; i -= 3; } break; case INDEX: j = 1; goto VectInd; case VECTOR: j = 2; VectInd: i = term[1] - 2; term += 2; while ( i > 0 ) { m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( ( *m == -VECTOR || *m == -MINVECTOR ) && m[1] == *term && m[2] == -SNUMBER && (m+2) < stopper ) { count += m[3]; m += 4; } NEXTARG(m) } term += j; i -= j; } break; default: if ( *term >= FUNCTION ) { i = *term; m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( *m == -i && m[1] == -SNUMBER && (m+1) < stopper ) { count += m[2]; m += 3; } NEXTARG(m) } if ( functions[i-FUNCTION].spec >= TENSORFUNCTION ) { i = term[1] - FUNHEAD; term += FUNHEAD; while ( i > 0 ) { if ( *term < 0 ) { m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( ( *m == -VECTOR || *m == -INDEX || *m == -MINVECTOR ) && m[1] == *term && m[2] == -SNUMBER && (m+2) < stopper ) { count += m[3]; m += 4; } else { NEXTARG(m) } } } term++; i--; } } else { r = term + term[1]; term += FUNHEAD; while ( term < r ) { if ( ( *term == -INDEX || *term == -VECTOR || *term == -MINVECTOR ) && term[1] < MINSPEC ) { m = instruct; while ( m < stopper ) { if ( *m == -SNUMBER ) { NEXTARG(m) continue; } if ( *m == -VECTOR && m[1] == term[1] && m[2] == -SNUMBER && (m+2) < stopper ) { count += m[3]; m += 4; } else { NEXTARG(m) } } term += 2; } else { NEXTARG(term) } } } break; } else { term += term[1]; } break; } } return(count); } /* #] CountFun : #] Count : #[ DimensionSubterm : */ WORD DimensionSubterm(WORD *subterm) { WORD *r, *rstop, dim, i; LONG x = 0; rstop = subterm + subterm[1]; if ( *subterm == SYMBOL ) { r = subterm + 2; while ( r < rstop ) { if ( *r <= NumSymbols && *r > -MAXPOWER ) { dim = symbols[*r].dimension; if ( dim == MAXPOSITIVE ) goto undefined; x += dim * r[1]; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; r += 2; } else if ( *r <= MAXVARIABLES ) { /* Here we have an extra symbol. Store dimension in the compiler buffer */ i = MAXVARIABLES - *r; dim = cbuf[AM.sbufnum].dimension[i]; if ( dim == MAXPOSITIVE ) goto undefined; if ( dim == -MAXPOSITIVE ) goto outofrange; x += dim * r[1]; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; r += 2; } else { r += 2; } } } else if ( *subterm == DOTPRODUCT ) { r = subterm + 2; while ( r < rstop ) { dim = vectors[*r-AM.OffsetVector].dimension; if ( dim == MAXPOSITIVE ) goto undefined; x += dim * r[2]; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; dim = vectors[r[1]-AM.OffsetVector].dimension; if ( dim == MAXPOSITIVE ) goto undefined; x += dim * r[2]; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; r += 3; } } else if ( *subterm == VECTOR ) { r = subterm + 2; while ( r < rstop ) { dim = vectors[*r-AM.OffsetVector].dimension; if ( dim == MAXPOSITIVE ) goto undefined; x += dim; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; r += 2; } } else if ( *subterm == INDEX ) { r = subterm + 2; while ( r < rstop ) { if ( *r < 0 ) { dim = vectors[*r-AM.OffsetVector].dimension; if ( dim == MAXPOSITIVE ) goto undefined; x += dim; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; } r++; } } else if ( *subterm >= FUNCTION ) { dim = functions[*subterm-FUNCTION].dimension; if ( dim == MAXPOSITIVE ) goto undefined; x += dim; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; if ( functions[*subterm-FUNCTION].spec > 0 ) { /* tensor */ r = subterm + FUNHEAD; while ( r < rstop ) { if ( *r < MINSPEC ) { dim = vectors[*r-AM.OffsetVector].dimension; if ( dim == MAXPOSITIVE ) goto undefined; x += dim; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; } r++; } } } return((WORD)x); undefined: return((WORD)MAXPOSITIVE); outofrange: return(-(WORD)MAXPOSITIVE); } /* #] DimensionSubterm : #[ DimensionTerm : Returns the dimension of the given term. If there is any variable of which the dimension is not defined we return the code for undefined which is MAXPOSITIVE When the value is out of range we return -MAXPOSITIVE */ WORD DimensionTerm(WORD *term) { WORD *t, *tstop, dim; LONG x = 0; tstop = term + *term; tstop -= ABS(tstop[-1]); t = term+1; while ( t < tstop ) { dim = DimensionSubterm(t); if ( dim == MAXPOSITIVE ) goto undefined; if ( dim == -MAXPOSITIVE ) goto outofrange; x += dim; if ( x >= MAXPOSITIVE || x <= -MAXPOSITIVE ) goto outofrange; t += t[1]; } return((WORD)x); undefined: return((WORD)MAXPOSITIVE); outofrange: return(-(WORD)MAXPOSITIVE); } /* #] DimensionTerm : #[ DimensionExpression : Returns the dimension of the given expression. If there is any variable of which the dimension is not defined we return the code for undefined which is MAXPOSITIVE When the value is out of range we return -MAXPOSITIVE When the value is not consistent we return -MAXPOSITIVE. */ WORD DimensionExpression(PHEAD WORD *expr) { WORD dim, *term, *old, x = 0; int first = 1; term = expr; while ( *term ) { dim = DimensionTerm(term); if ( dim == MAXPOSITIVE ) goto undefined; if ( dim == -MAXPOSITIVE ) goto outofrange; if ( first ) { x = dim; } else if ( x != dim ) { old = AN.currentTerm; MLOCK(ErrorMessageLock); MesPrint("Dimension is not the same in the terms of the expression"); term = expr; while ( *term ) { AN.currentTerm = term; MesPrint(" %T"); } MUNLOCK(ErrorMessageLock); AN.currentTerm = old; return(-(WORD)MAXPOSITIVE); } term += *term; } return((WORD)x); undefined: return((WORD)MAXPOSITIVE); outofrange: old = AN.currentTerm; AN.currentTerm = term; MLOCK(ErrorMessageLock); MesPrint("Dimension out of range in %t in subexpression"); MUNLOCK(ErrorMessageLock); AN.currentTerm = old; return(-(WORD)MAXPOSITIVE); } /* #] DimensionExpression : #[ Multiply Term : #[ MultDo : */ int MultDo(PHEAD WORD *term, WORD *pattern) { GETBIDENTITY WORD *t, *r, i; t = term + *term; if ( pattern[2] > 0 ) { /* Left multiply */ i = *term - 1; } else { /* Right multiply */ i = ABS(t[-1]); } *term += SUBEXPSIZE; r = t + SUBEXPSIZE; do { *--r = *--t; } while ( --i > 0 ); r = pattern + 3; i = r[1]; while ( --i >= 0 ) *t++ = *r++; AT.WorkPointer = term + *term; return(0); } /* #] MultDo : #] Multiply Term : #[ Try Term(s) : #[ TryDo : */ int TryDo(PHEAD WORD *term, WORD *pattern, WORD level) { GETBIDENTITY WORD *t, *r, *m, i, j; ReNumber(BHEAD term); Normalize(BHEAD term); m = r = term + *term; m++; i = pattern[2]; t = pattern + 3; NCOPY(m,t,i) j = *term - 1; t = term + 1; NCOPY(m,t,j) *r = WORDDIF(m,r); AT.WorkPointer = m; if ( ( j = Normalize(BHEAD r) ) == 0 || j == 1 ) { if ( *r == 0 ) return(0); ReNumber(BHEAD r); Normalize(BHEAD r); if ( *r == 0 ) return(0); if ( ( i = CompareTerms(BHEAD term,r,0) ) < 0 ) { *AN.RepPoint = 1; AR.expchanged = 1; return(Generator(BHEAD r,level)); } if ( i == 0 && CompCoef(term,r) != 0 ) { return(0); } } AT.WorkPointer = r; return(Generator(BHEAD term,level)); } /* #] TryDo : #] Try Term(s) : #[ Distribute : #[ DoDistrib : The routine that generates the terms ordered by a distrib_ function. The presence of a replaceable distrib_ function has been sensed in the routine TestSub and has been passed on to Generator. It is then Generator that calls this function in a way that is similar to calling the trace routines, except for that for the trace routines and the Levi-Civita tensors the arguments are put in temporary storage and here we leave them inside the term, because there is no knowing how long the field will be. */ int DoDistrib(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD *t, *m, *r = 0, *stop, *tstop, *termout, *endhead, *starttail, *parms; WORD i, j, k, n, nn, ntype, fun1 = 0, fun2 = 0, typ1 = 0, typ2 = 0; WORD *arg, *oldwork, *mf, ktype = 0, atype = 0; WORD sgn, dirtyflag; AN.TeInFun = AR.TePos = 0; t = term; tstop = t + *t; stop = tstop - ABS(tstop[-1]); t++; while ( t < stop ) { r = t + t[1]; if ( *t == DISTRIBUTION && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] >= -2 && t[FUNHEAD+1] <= 2 && t[FUNHEAD+2] == -SNUMBER && t[FUNHEAD+4] <= -FUNCTION && t[FUNHEAD+5] <= -FUNCTION ) { WORD *ttt = t+FUNHEAD+6, *tttstop = t+t[1]; while ( ttt < tttstop ) { if ( *ttt == -DOLLAREXPRESSION ) break; NEXTARG(ttt); } if ( ttt >= tttstop ) { fun1 = -t[FUNHEAD+4]; fun2 = -t[FUNHEAD+5]; typ1 = functions[fun1-FUNCTION].spec; typ2 = functions[fun2-FUNCTION].spec; if ( typ1 > 0 || typ2 > 0 ) { m = t + FUNHEAD+6; r = t + t[1]; while ( m < r ) { if ( *m != -INDEX && *m != -VECTOR && *m != -MINVECTOR ) break; m += 2; } if ( m < r ) { MLOCK(ErrorMessageLock); MesPrint("Incompatible function types and arguments in distrib_"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } } break; } } t = r; } dirtyflag = t[2]; ntype = t[FUNHEAD+1]; n = t[FUNHEAD+3]; /* t points at the distrib_ function to be expanded. fun1,fun2 and typ1,typ2 are the two functions and their types. ntype indicates the action: 0: Make all possible divisions: 2^nargs 1: fun1 should get n arguments: nargs! / ( n! (nargs-n)! ) 2: fun2 should get n arguments: nargs! / ( n! (nargs-n)! ) The distinction between 1 and two is for noncommuting objects. 3: fun1 should get n arguments. Super symmetric option. 4: fun2 idem The super symmetric option involves: a: arguments get sorted b: identical arguments are seen as such. Hence not all their distributions are taken into account. It is as if after the distrib there is a symmetrize fun1; symmetrize fun2; c: Hence if the occurrence of each argument is a,b,c,... and their occurrence in fun1 is a1,b1,c1,... and in fun2 is a2,b2,c2,... then each term is generated (a1+a2)!/a1!/a2! (b1+b2)!/b1!/b2! (c1+c2)!/c1!/c2! ... times. d: We have to make an array of occurrences and positions. e: Then we sort the arguments indirectly. f: Next we generate the argument lists in the same way as we generate powers of expressions with binomials. Hence we need a third array to keep track of the `powers' */ endhead = t; starttail = r; parms = m = t + FUNHEAD+6; i = 0; while ( m < r ) { /* Count arguments */ i++; NEXTARG(m); } oldwork = AT.WorkPointer; arg = AT.WorkPointer + 1; arg[-1] = 0; termout = arg + i; switch ( ntype ) { case 0: ktype = 1; atype = n < 0 ? 1: 0; n = 0; break; case 1: ktype = 1; atype = 0; break; case 2: ktype = 0; atype = 0; break; case -1: ktype = 1; atype = 1; break; case -2: ktype = 0; atype = 1; break; } do { /* All distributions with n elements. We generate the array arg with all possible 1 and 0 patterns. 1 means in fun1 and 0 means in fun2. */ if ( n > i ) return(0); /* 0 elements */ for ( j = 0; j < n; j++ ) arg[j] = 1; for ( j = n; j < i; j++ ) arg[j] = 0; for(;;) { sgn = 0; t = term; m = termout; while ( t < endhead ) *m++ = *t++; mf = m; *m++ = fun1; *m++ = FUNHEAD; *m++ = dirtyflag; #if FUNHEAD > 3 k = FUNHEAD -3; while ( k-- > 0 ) *m++ = 0; #endif r = parms; for ( k = 0; k < i; k++ ) { if ( arg[k] == ktype ) { if ( *r <= -FUNCTION ) *m++ = *r++; else if ( *r < 0 ) { if ( typ1 > 0 ) { if ( *r == -MINVECTOR ) sgn ^= 1; r++; *m++ = *r++; } else { *m++ = *r++; *m++ = *r++; } } else { nn = *r; NCOPY(m,r,nn); } } else { NEXTARG(r) } } mf[1] = WORDDIF(m,mf); mf = m; *m++ = fun2; *m++ = FUNHEAD; *m++ = dirtyflag; #if FUNHEAD > 3 k = FUNHEAD -3; while ( k-- > 0 ) *m++ = 0; #endif r = parms; for ( k = 0; k < i; k++ ) { if ( arg[k] != ktype ) { if ( *r <= -FUNCTION ) *m++ = *r++; else if ( *r < 0 ) { if ( typ2 > 0 ) { if ( *r == -MINVECTOR ) sgn ^= 1; r++; *m++ = *r++; } else { *m++ = *r++; *m++ = *r++; } } else { nn = *r; NCOPY(m,r,nn); } } else { NEXTARG(r) } } mf[1] = WORDDIF(m,mf); #ifndef NUOVO if ( atype == 0 ) { WORD k1,k2; for ( k = 0; k < i-1; k++ ) { if ( arg[k] == 0 ) continue; k1 = 1; k2 = k; while ( k < i-1 && EqualArg(parms,k,k+1) ) { k++; k1++; } while ( k2 <= k && arg[k2] == 1 ) k2++; k2 = k-k2+1; /* Now we need k1!/(k2! (k1-k2)!) */ if ( k2 != k1 && k2 != 0 ) { if ( GetBinom((UWORD *)m+3,m+2,k1,k2) ) { MLOCK(ErrorMessageLock); MesCall("DoDistrib"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } m[1] = ( m[2] < 0 ? -m[2]: m[2] ) + 3; *m = LNUMBER; m += m[1]; } } } #endif r = starttail; while ( r < tstop ) *m++ = *r++; if ( atype ) { /* antisymmetric field */ k = n; nn = 0; for ( j = 0; j < i && k > 0; j++ ) { if ( arg[j] == 1 ) k--; else nn += k; } sgn ^= nn & 1; } if ( sgn ) m[-1] = -m[-1]; *termout = WORDDIF(m,termout); AT.WorkPointer = m; if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,level) ) Terminate(-1); #ifndef NUOVO { WORD k1; j = i - 1; k = 0; redok: while ( arg[j] == 1 && j >= 0 ) { j--; k++; } while ( arg[j] == 0 && j >= 0 ) j--; if ( j < 0 ) break; k1 = j; arg[j] = 0; while ( !atype && EqualArg(parms,j,j+1) ) { j++; if ( j >= i - k - 1 ) { j = k1; k++; goto redok; } arg[j] = 0; } while ( k >= 0 ) { j++; arg[j] = 1; k--; } j++; while ( j < i ) { arg[j] = 0; j++; } } #else j = i - 1; k = 0; while ( arg[j] == 1 && j >= 0 ) { j--; k++; } while ( arg[j] == 0 && j >= 0 ) j--; if ( j < 0 ) break; arg[j] = 0; while ( k >= 0 ) { j++; arg[j] = 1; k--; } j++; while ( j < i ) { arg[j] = 0; j++; } #endif } } while ( ntype == 0 && ++n <= i ); AT.WorkPointer = oldwork; return(0); } /* #] DoDistrib : #[ EqualArg : Returns 1 if the arguments in the field are identical. */ int EqualArg(WORD *parms, WORD num1, WORD num2) { WORD *t1, *t2; WORD i; t1 = parms; while ( --num1 >= 0 ) { NEXTARG(t1); } t2 = parms; while ( --num2 >= 0 ) { NEXTARG(t2); } if ( *t1 != *t2 ) return(0); if ( *t1 < 0 ) { if ( *t1 <= -FUNCTION || t1[1] == t2[1] ) return(1); return(0); } i = *t1; while ( --i >= 0 ) { if ( *t1 != *t2 ) return(0); t1++; t2++; } return(1); } /* #] EqualArg : #[ DoDelta3 : */ int DoDelta3(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD *t, *m, *m1, *m2, *stopper, *tstop, *termout, *dels, *taken; WORD *ic, *jc, *factors; WORD num, num2, i, j, k, knum, a; AN.TeInFun = AR.TePos = 0; tstop = term + *term; stopper = tstop - ABS(tstop[-1]); t = term+1; while ( ( *t != DELTA3 || ((t[1]-FUNHEAD) & 1 ) != 0 ) && t < stopper ) t += t[1]; if ( t >= stopper ) { MLOCK(ErrorMessageLock); MesPrint("Internal error with dd_ function"); MUNLOCK(ErrorMessageLock); Terminate(-1); } m1 = t; m2 = t + t[1]; num = t[1] - FUNHEAD; if ( num == 0 ) { termout = t = AT.WorkPointer; m = term; while ( m < m1 ) *t++ = *m++; m = m2; while ( m < tstop ) *t++ = *m++; *termout = WORDDIF(t,termout); AT.WorkPointer = t; *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,level) ) { MLOCK(ErrorMessageLock); MesCall("Do dd_"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } AT.WorkPointer = termout; return(0); } t += FUNHEAD; /* Step 1: sort the arguments */ for ( i = 1; i < num; i++ ) { if ( t[i] < t[i-1] ) { a = t[i]; t[i] = t[i-1]; t[i-1] = a; j = i - 1; while ( j > 0 ) { if ( t[j] >= t[j-1] ) break; a = t[j]; t[j] = t[j-1]; t[j-1] = a; j--; } } } /* Step 2: Order them by occurrence In 'taken' we have the array with the number of occurrences. in 'dels' is the type of object. */ m = taken = AT.WorkPointer; for ( i = 0; i < num; i++ ) *m++ = 0; dels = m; knum = 0; for ( i = 0; i < num; knum++ ) { *m++ = t[i]; i++; taken[knum] = 1; while ( i < num ) { if ( t[i] != t[i-1] ) break; i++; (taken[knum])++; } } for ( i = 0; i < knum; i++ ) *m++ = taken[i]; ic = m; num2 = num/2; jc = ic + num2; factors = jc + num2; termout = factors + num2; /* The recursion has num/2 steps */ k = 0; while ( k >= 0 ) { if ( k >= num2 ) { t = termout; m = term; while ( m < m1 ) *t++ = *m++; *t++ = DELTA; *t++ = num+2; for ( i = 0; i < num2; i++ ) { *t++ = dels[ic[i]]; *t++ = dels[jc[i]]; } for ( i = 0; i < num2; i++ ) { if ( ic[i] == jc[i] ) { j = 1; while ( i < num2-1 && ic[i] == ic[i+1] && ic[i] == jc[i+1] ) { i++; j++; } for ( a = 1; a < j; a++ ) { *t++ = SNUMBER; *t++ = 4; *t++ = 2*a+1; *t++ = 1; } for ( a = 0; a+1+i < num2; a++ ) { if ( ic[a+i] != ic[a+i+1] ) break; } if ( a > 0 ) { if ( GetBinom((UWORD *)(t+3),t+2,2*j+a,a) ) { MLOCK(ErrorMessageLock); MesCall("Do dd_"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } t[1] = ( t[2] < 0 ? -t[2]: t[2] ) + 3; *t = LNUMBER; t += t[1]; } } else if ( factors[i] != 1 ) { *t++ = SNUMBER; *t++ = 4; *t++ = factors[i]; *t++ = 1; } } for ( i = 0; i < num2-1; i++ ) { if ( ic[i] == jc[i] ) continue; j = 1; while ( i < num2-1 && jc[i] == jc[i+1] && ic[i] == ic[i+1] ) { i++; j++; } for ( a = 0; a+i < num2-1; a++ ) { if ( ic[i+a] != ic[i+a+1] ) break; } if ( a > 0 ) { if ( GetBinom((UWORD *)(t+3),t+2,j+a,a) ) { MLOCK(ErrorMessageLock); MesCall("Do dd_"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } t[1] = ( t[2] < 0 ? -t[2]: t[2] ) + 3; *t = LNUMBER; t += t[1]; } } m = m2; while ( m < tstop ) *t++ = *m++; *termout = WORDDIF(t,termout); AT.WorkPointer = t; *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,level) ) { MLOCK(ErrorMessageLock); MesCall("Do dd_"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } k--; if ( k >= 0 ) goto nextj; else break; } for ( ic[k] = 0; ic[k] < knum; ic[k]++ ) { if ( taken[ic[k]] > 0 ) break; } if ( k > 0 && ic[k-1] == ic[k] ) jc[k] = jc[k-1]; else jc[k] = ic[k]; for ( ; jc[k] < knum; jc[k]++ ) { if ( taken[jc[k]] <= 0 ) continue; if ( ic[k] == jc[k] ) { if ( taken[jc[k]] <= 1 ) continue; /* factors[k] = taken[ic[k]]; if ( ( factors[k] & 1 ) == 0 ) (factors[k])--; */ taken[ic[k]] -= 2; } else { factors[k] = taken[jc[k]]; (taken[ic[k]])--; (taken[jc[k]])--; } k++; goto nextk; /* This is the simulated recursion */ nextj:; (taken[ic[k]])++; (taken[jc[k]])++; } k--; if ( k >= 0 ) goto nextj; nextk:; } AT.WorkPointer = taken; return(0); } /* #] DoDelta3 : #[ TestPartitions : Checks whether the function in tfun is a partitions_ function that can be expanded. If it can a number of relevant objects is inside the struct parti. This test is not entirely trivial because there are many restrictions w.r.t. the arguments. Syntax (still to be implemented) partitions_(number_of_partition_entries,[function,number,]^nope,arguments) [function,number,]: can be f,3 for a partition of 3 arguments f,0 for the remaining arguments (should be last) num1,f,num2 with num1 effectively a number of partitions but this counts as num1 entries. 0,f,num2: all partitions have num2 arguments. No number of partition entries needed. If num2 does not divide the number of arguments there will be no action. */ int TestPartitions(WORD *tfun, PARTI *parti) { WORD *tnext = tfun + tfun[1]; WORD *t, *tt; WORD argcount = 0, sum = 0, i, ipart, argremain; WORD tensorflag = 0; parti->psize = parti->nfun = parti->args = parti->nargs = 0; parti->numargs = parti->numpart = parti->where = 0; tt = t = tfun + FUNHEAD; while ( t < tnext ) { argcount++; NEXTARG(t); } if ( argcount < 1 ) goto No; t = tt; if ( *t != -SNUMBER ) goto No; if ( t[1] == 0 ) { t += 2; if ( *t <= -FUNCTION && t[1] == -SNUMBER && t[2] > 0 ) { if ( functions[-*t-FUNCTION].spec > 0 ) tensorflag = 1; if ( argcount-3 < 0 ) goto No; if ( ( (argcount-3) % t[2] ) != 0 ) goto No; } else goto No; parti->numpart = (argcount-3)/t[2]; parti->numargs = argcount - 3; parti->psize = (WORD *)Malloc1((parti->numpart*2+parti->numargs*2+2) *sizeof(WORD),"partitions"); parti->nfun = parti->psize + parti->numpart; parti->args = parti->nfun + parti->numpart; parti->nargs = parti->args + parti->numargs; for ( i = 0; i < parti->numpart; i++ ) { parti->psize[i] = t[2]; parti->nfun[i] = -t[0]; } t += 3; } else if ( t[1] > 0 ) { /* Number of partitions */ /* We can have sequences of function,number for one partition or number1,function,number2 for number1 partitions of size number2. The last partition can have number=0. It must be a single partition and it will take all remaining arguments. If any of the functions is a tensor, all arguments must be either vector or index. */ parti->numpart = t[1]; t += 2; ipart = sum = 0; argremain = argcount - 1; /* At this point is seems better to make an allocation already that may be too big. The alternative is having to pass this code twice. */ parti->psize = (WORD *)Malloc1((argcount*4+2)*sizeof(WORD),"partitions"); parti->nfun = parti->psize+argcount; parti->args = parti->nfun+argcount; parti->nargs = parti->args+argcount; while ( ipart < parti->numpart ) { if ( *t <= -FUNCTION && t[1] == -SNUMBER && t[2] >= 0 ) { if ( functions[-*t-FUNCTION].spec > 0 ) tensorflag = 1; if ( t[2] == 0 ) { if ( ipart+1 != parti->numpart ) goto WhatAPity; argremain -= 2; parti->nfun[ipart] = -*t; parti->psize[ipart++] = argremain-sum; ipart++; sum = argremain; } else { parti->nfun[ipart] = -*t; parti->psize[ipart++] = t[2]; argremain -= 2; sum += t[2]; } t += 3; } else if ( *t == -SNUMBER && t[1] > 0 && ipart+t[1] <= parti->numpart && t[2] <= -FUNCTION && t[3] == -SNUMBER && t[4] > 0 ) { if ( functions[-t[2]-FUNCTION].spec > 0 ) tensorflag = 1; argremain -= 3; for ( i = 0; i < t[1]; i++ ) { parti->nfun[ipart] = -t[2]; parti->psize[ipart++] = t[4]; sum += t[4]; } if ( sum > argremain ) goto WhatAPity; t += 5; } else goto WhatAPity; } if ( sum != argremain ) goto WhatAPity; parti->numargs = argremain; } else goto No; /* Now load the offsets of the arguments and check if needed whether OK with tensor */ for ( i = 0; i < parti->numargs; i++ ) { parti->args[i] = t - tfun; if ( tensorflag && ( *t != -VECTOR && *t != -INDEX ) ) goto WhatAPity; NEXTARG(t); } return(1); WhatAPity: M_free(parti->psize,"partitions"); parti->psize = parti->nfun = parti->args = parti->nargs = 0; parti->numargs = parti->numpart = parti->where = 0; No: return(0); } /* #] TestPartitions : #[ DoPartitions : As we have only one AT.partitions we need to copy it locally if we keep needing it. */ int DoPartitions(PHEAD WORD *term, WORD level) { WORD x, i, j, im, *fun, ndiff, siz, tensorflag = 0; PARTI part = AT.partitions; WORD *array, **j3, **j3fill, **j3where; WORD a, pfill, *j2, *j2fill, j3size, ncoeff, ncoeffnum, nfac, ncoeff2, ncoeff3, n; UWORD *coeff, *coeffnum, *cfac, *coeff2, *coeff3, *c; /* Make AT.partitions ready for future use (if there is another function) */ AT.partitions.psize = AT.partitions.nfun = AT.partitions.args = AT.partitions.nargs = 0; AT.partitions.numargs = AT.partitions.numpart = AT.partitions.where = 0; /* Start with bubble sorting the list of arguments. And the list of partitions. */ fun = term + part.where; if ( functions[*fun-FUNCTION].spec > 0 ) tensorflag = 1; for ( i = 1; i < part.numargs; i++ ) { for ( j = i-1; j >= 0; j-- ) { if ( CompArg(fun+part.args[j+1],fun+part.args[j]) >= 0 ) break; x = part.args[j+1]; part.args[j+1] = part.args[j]; part.args[j] = x; } } for ( i = 1; i < part.numpart; i++ ) { for ( j = i-1; j >= 0; j-- ) { if ( part.psize[j+1] < part.psize[j] ) break; if ( part.psize[j+1] == part.psize[j] && part.nfun[j+1] <= part.nfun[j] ) break; x = part.psize[j+1]; part.psize[j+1] = part.psize[j]; part.psize[j] = x; x = part.nfun[j+1]; part.nfun[j+1] = part.nfun[j]; part.nfun[j] = x; } } /* Now we have the partitions sorted from high to low and the arguments have been sorted the regular way arguments are sorted in a symmetrize. The important thing is that identical arguments are adjacent. Assign the numbers (identical arguments have identical numbers). */ ndiff = 1; part.nargs[0] = ndiff; for ( i = 1; i < part.numargs; i++ ) { if ( CompArg(fun+part.args[i],fun+part.args[i-1]) != 0 ) ndiff++; part.nargs[i] = ndiff; } part.nargs[part.numargs] = 0; coeffnum = NumberMalloc("partitionsn"); coeff = NumberMalloc("partitions"); coeff2 = NumberMalloc("partitions2"); coeff3 = NumberMalloc("partitions3"); cfac = NumberMalloc("partitions!"); ncoeffnum = 1; coeffnum[0] = 1; /* The numerator of the coefficient will be n1!*n2!*...*n(ndiff)! We compute it only once. */ j = 0; for ( i = 1; i <= ndiff; i++ ) { n = 0; while ( part.nargs[j] == i ) { n++; j++; } if ( n > 1 ) { /* 1! needs no attention */ if ( Factorial(BHEAD n, cfac, &nfac) ) Terminate(-1); if ( MulLong(coeffnum,ncoeffnum,cfac,nfac,coeff2,&ncoeff2) ) Terminate(-1); c = coeffnum; coeffnum = coeff2; coeff2 = c; n = ncoeffnum; ncoeffnum = ncoeff2; ncoeff2 = n; } } /* Now comes the part where we have to make sure that a: we generate all partitions. b: we generate only different partitions. c: we get the proper combinatorics factor. Method: Suppose the largest partition needs n objects and there are m partitions. We allocate m arrays of n 'digits'. Make in the smaller partitions the appropriate leading digits zero. Divide the largest numbers (of the arguments) over the partitions as leftmost digits (after possible zeroes). The arrays, seen as numbers, should be such that each is less or equal to its left neighbour. Take the next largest numbers, etc. This generates unique partitions and all of them. Because we have a formula for the multiplicity, this should do it. The general case. At a later stage we might put in a more economical version for special cases. */ siz = part.psize[0]; j3size = 2*(part.numpart+1)+2*(part.numargs+1); array = (WORD *)Malloc1((part.numpart+1)*siz*sizeof(WORD),"parts"); j3 = (WORD **)Malloc1(j3size*sizeof(WORD *),"parts3"); j2 = (WORD *)Malloc1((part.numpart+part.numargs+2)*sizeof(WORD),"parts2"); j3fill = j3+(part.numpart+1); j3where = j3fill+(part.numpart+1); for ( i = 0; i < j3size; i++ ) j3[i] = 0; j2fill = j2+(part.numpart+1); for ( i = 0; i < part.numargs; i++ ) j2fill[i] = 0; for ( i = 0; i < part.numpart; i++ ) { j3[i] = array+i*siz; for ( j = 0; j < siz; j++ ) j3[i][j] = 0; j3fill[i] = j3[i]+(siz-part.psize[i]); j2[i] = part.psize[i]; /* Number of places still available */ } j3[part.numpart] = array+part.numpart*siz; j2[part.numpart] = 0; /* Now comes a complicated two-level recursion in a and pfill. */ a = part.numargs-1; pfill = 0; /* We start putting the last number in part.nargs in the first partition in array. For backtracking we need to know where we put this number. Hence j3where. */ while ( a < part.numargs ) { while ( j2[pfill] <= 0 ) { pfill++; while ( pfill >= part.numpart ) { /* we have to pop */ a++; if ( a >= part.numargs ) goto Done; pfill = j2fill[a]; j2[pfill]++; j3where[a][0] = 0; j3fill[pfill]--; pfill++; } } j3where[a] = j3fill[pfill]; *(j3fill[pfill])++ = part.nargs[a]; j2[pfill]--; j2fill[a] = pfill; /* Now test whether this is allowed. */ if ( pfill > 0 && part.psize[pfill] == part.psize[pfill-1] && part.nfun[pfill] == part.nfun[pfill-1] ) { /* First check whether allowed */ for ( im = 0; im < siz; im++ ) { if ( j3[pfill-1][im] < j3[pfill][im] ) break; if ( j3[pfill-1][im] > j3[pfill][im] ) im = siz; } if ( im < siz ) { /* not ordered. undo and raise pfill */ pfill = j2fill[a]; j2[pfill]++; j3where[a][0] = 0; j3fill[pfill]--; pfill++; continue; /* Note that j2[part.numpart] = 0 */ } } a--; if ( a < 0 ) { /* Solution */ /* #[ Solution : Now we compose the output term. The input term contains three parts: head, partitions_, tail. partitions_ starts at term+part.where. We first put the function parts and worry about the coefficient later. */ WORD *t, *to, *twhere = term+part.where, *t2, *tend = term+*term, *termout; WORD num, jj, *targ, *tfun; t2 = twhere+twhere[1]; to = termout = AT.WorkPointer; if ( termout + *term + part.numpart*FUNHEAD + AM.MaxTal >= AT.WorkTop ) { MesWork(); } for ( i = 0; i < ncoeffnum; i++ ) coeff[i] = coeffnum[i]; ncoeff = ncoeffnum; t = term; while ( t < twhere ) *to++ = *t++; /* Now the partitions */ for ( i = 0; i < part.numpart; i++ ) { tfun = to; *to++ = part.nfun[i]; to++; FILLFUN(to); for ( j = 1; j <= part.psize[i]; j++ ) { num = j3[i][siz-j]; /* now we need an argument with this number */ for ( jj = num-1; jj < part.numargs; jj++ ) { if ( part.nargs[jj] == num ) break; } targ = part.args[jj]+twhere; if ( *targ < 0 ) { if ( tensorflag ) targ++; else if ( *targ > -FUNCTION ) *to++ = *targ++; *to++ = *targ++; } else { jj = *targ; NCOPY(to,targ,jj); } } tfun[1] = to - tfun; } /* Now the denominators of the coefficient First identical functions/partitions */ j = 1; n = 1; while ( j < part.numpart ) { for ( im = 0; im < siz; im++ ) { if ( part.nfun[j-1] != part.nfun[j] ) break; if ( j3[j-1][im] < j3[j][im] ) break; if ( j3[j-1][im] > j3[j][im] ) im = 2*siz+2; } if ( im == siz ) { n++; j++; continue; } if ( n > 1 ) { div1: if ( Factorial(BHEAD n, cfac, &nfac) ) Terminate(-1); if ( DivLong(coeff,ncoeff,cfac,nfac,coeff2,&ncoeff2,coeff3,&ncoeff3) ) Terminate(-1); c = coeff; coeff = coeff2; coeff2 = c; n = ncoeff; ncoeff = ncoeff2; ncoeff2 = n; } n = 1; j++; } if ( n > 1 ) goto div1; /* Now identical elements inside the partitions */ for ( i = 0; i < part.numpart; i++ ) { j = 0; while ( j3[i][j] == 0 ) j++; n = 1; j++; while ( j < siz ) { if ( j3[i][j-1] == j3[i][j] ) { n++; j++; } else { if ( n > 1 ) { div2: if ( Factorial(BHEAD n, cfac, &nfac) ) Terminate(-1); if ( DivLong(coeff,ncoeff,cfac,nfac,coeff2,&ncoeff2,coeff3,&ncoeff3) ) Terminate(-1); c = coeff; coeff = coeff2; coeff2 = c; n = ncoeff; ncoeff = ncoeff2; ncoeff2 = n; } n = 1; j++; } } if ( n > 1 ) goto div2; } /* And put this inside the term. Normalize will take care of it. */ if ( ncoeff != 1 || coeff[0] > 1 ) { if ( ncoeff == 1 && coeff[0] <= MAXPOSITIVE ) { *to++ = SNUMBER; *to++ = 4; *to++ = (WORD)(coeff[0]); *to++ = 1; } else { *to++ = LNUMBER; *to++ = ncoeff+3; *to++ = ncoeff; for ( i = 0; i < ncoeff; i++ ) *to++ = ((WORD *)coeff)[i]; } } /* And the tail */ while ( t2 < tend ) *to++ = *t2++; *termout = to-termout; AT.WorkPointer = to; if ( Generator(BHEAD termout,level) ) Terminate(-1); AT.WorkPointer = termout; /* #] Solution : Now we can pop all a with the lowest value and one more. */ a = 0; while ( part.nargs[a] == 1 ) { pfill = j2fill[a]; j2[pfill]++; j3where[a][0] = 0; j3fill[pfill]--; a++; } if ( a < part.numargs ) { pfill = j2fill[a]; j2[pfill]++; j3where[a][0] = 0; j3fill[pfill]--; a++; } a--; pfill++; } else if ( part.nargs[a] == part.nargs[a+1] ) {} else { pfill = 0; } } Done: M_free(j2,"parts2"); M_free(j3,"parts3"); M_free(array,"parts"); NumberFree(cfac,"partitions!"); NumberFree(coeff3,"partitions3"); NumberFree(coeff2,"partitions2"); NumberFree(coeff,"partitions"); NumberFree(coeffnum,"partitionsn"); M_free(part.psize,"partitions"); part.psize = part.nfun = part.args = part.nargs = 0; part.numargs = part.numpart = part.where = 0; return(0); } /* #] DoPartitions : #] Distribute : #[ DoPermutations : Routine replaces the function perm_(f,args) by occurrences of f with all permutations of the args. This should always fit! */ int DoPermutations(PHEAD WORD *term, WORD level) { PERMP perm; WORD *oldworkpointer = AT.WorkPointer, *termout = AT.WorkPointer; WORD *t, *tstop, *tt, *ttstop, odd = 0; WORD *args[MAXMATCH], nargs, i, first, skip, *to, *from; /* Find function and count arguments. Check for odd/even */ tstop = term+*term; tstop -= ABS(tstop[-1]); t = term+1; while ( t < tstop ) { if ( *t == PERMUTATIONS ) { if ( t[1] >= FUNHEAD+1 && t[FUNHEAD] <= -FUNCTION ) { odd = 0; skip = 1; } else if ( t[1] >= FUNHEAD+3 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+2] <= -FUNCTION ) { if ( t[FUNHEAD+1] % 2 == 1 ) odd = -1; else odd = 0; skip = 3; } else { t += t[1]; continue; } tt = t+FUNHEAD+skip; ttstop = t + t[1]; nargs = 0; while ( tt < ttstop ) { NEXTARG(tt); nargs++; } tt = t+FUNHEAD+skip; if ( nargs > MAXMATCH ) { MLOCK(ErrorMessageLock); MesPrint("Too many arguments in function perm_. %d! is way too big",(WORD)MAXMATCH); MUNLOCK(ErrorMessageLock); SETERROR(-1) } i = 0; while ( tt < ttstop ) { args[i++] = tt; NEXTARG(tt); } perm.n = nargs; perm.sign = 0; perm.objects = args; first = 1; while ( (first = PermuteP(&perm,first) ) == 0 ) { /* Compose the output term */ to = termout; from = term; while ( from < t ) *to++ = *from++; *to++ = -t[FUNHEAD+skip-1]; *to++ = t[1] - skip; for ( i = 2; i < FUNHEAD; i++ ) *to++ = t[i]; for ( i = 0; i < nargs; i++ ) { from = args[i]; COPY1ARG(to,from); } from = t+t[1]; tstop = term + *term; while ( from < tstop ) *to++ = *from++; if ( odd && ( ( perm.sign & 1 ) != 0 ) ) to[-1] = -to[-1]; *termout = to - termout; AT.WorkPointer = to; if ( Generator(BHEAD termout,level) ) Terminate(-1); AT.WorkPointer = oldworkpointer; } return(0); } t += t[1]; } return(0); } /* #] DoPermutations : #[ DoShuffle : Merges the arguments of all occurrences of function fun into a single occurrence of fun. The opposite of Distrib_ Syntax: Shuffle[,once|all],fun; Shuffle[,once|all],$fun; The expansion of the dollar should give a single function. The dollar is indicated as usual with a negative value. option = 1 (once): generate identical results only once option = 0 (all): generate identical results with combinatorics (default) */ /* We use the Shuffle routine which has a large amount of combinatorics. It doesn't have grouped combinatorics as in (0,1,2)*(0,1,3) where the groups (0,1) also cause double terms. */ int DoShuffle(WORD *term, WORD level, WORD fun, WORD option) { GETIDENTITY SHvariables SHback, *SH = &(AN.SHvar); WORD *t1, *t2, *tstop, ncoef, n = fun, *to, *from; int i, error; LONG k; UWORD *newcombi; if ( n < 0 ) { if ( ( n = DolToFunction(BHEAD -n) ) == 0 ) { MLOCK(ErrorMessageLock); MesPrint("$-variable in merge statement did not evaluate to a function."); MUNLOCK(ErrorMessageLock); return(1); } } if ( AT.WorkPointer + 3*(*term) + AM.MaxTal > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } tstop = term + *term; ncoef = tstop[-1]; tstop -= ABS(ncoef); t1 = term + 1; while ( t1 < tstop ) { if ( ( *t1 == n ) && ( t1+t1[1] < tstop ) && ( t1[1] > FUNHEAD ) ) { t2 = t1 + t1[1]; if ( t2 >= tstop ) { return(Generator(BHEAD term,level)); } while ( t2 < tstop ) { if ( ( *t2 == n ) && ( t2[1] > FUNHEAD ) ) break; t2 += t2[1]; } if ( t2 < tstop ) break; } t1 += t1[1]; } if ( t1 >= tstop ) { return(Generator(BHEAD term,level)); } *AN.RepPoint = 1; /* Now we have two occurrences of the function. Back up all relevant variables and load all the stuff that needs to be passed on. */ SHback = AN.SHvar; SH->finishuf = &FinishShuffle; SH->do_uffle = &DoShuffle; SH->outterm = AT.WorkPointer; AT.WorkPointer += *term; SH->stop1 = t1 + t1[1]; SH->stop2 = t2 + t2[1]; SH->thefunction = n; SH->option = option; SH->level = level; SH->incoef = tstop; SH->nincoef = ncoef; if ( AN.SHcombi == 0 || AN.SHcombisize == 0 ) { AN.SHcombisize = 200; AN.SHcombi = (UWORD *)Malloc1(AN.SHcombisize*sizeof(UWORD),"AN.SHcombi"); SH->combilast = 0; SHback.combilast = 0; } else { SH->combilast += AN.SHcombi[SH->combilast]+1; if ( SH->combilast >= AN.SHcombisize - 100 ) { newcombi = (UWORD *)Malloc1(2*AN.SHcombisize*sizeof(UWORD),"AN.SHcombi"); for ( k = 0; k < AN.SHcombisize; k++ ) newcombi[k] = AN.SHcombi[k]; M_free(AN.SHcombi,"AN.SHcombi"); AN.SHcombi = newcombi; AN.SHcombisize *= 2; } } AN.SHcombi[SH->combilast] = 1; AN.SHcombi[SH->combilast+1] = 1; i = t1-term; to = SH->outterm; from = term; NCOPY(to,from,i) SH->outfun = to; for ( i = 0; i < FUNHEAD; i++ ) { *to++ = t1[i]; } error = Shuffle(t1+FUNHEAD,t2+FUNHEAD,to); AT.WorkPointer = SH->outterm; AN.SHvar = SHback; if ( error ) { MesCall("DoShuffle"); return(-1); } return(0); } /* #] DoShuffle : #[ Shuffle : How to make shuffles: We have two lists of arguments. We have to make a single shuffle of them. All combinations. Doubles should have as much as possible a combinatorics factor. Sometimes this is very difficult as in: (0,1,2)x(0,1,3) = -> (0,1) is a repeated pattern and the factor on that is difficult Simple way: (without combinatorics) repeat id f0(?c)*f(x1?,?a)*f(x2?,?b) = +f0(?c,x1)*f(?a)*f(x2,?b) +f0(?c,x2)*f(x1,?a)*f(?b); Refinement: if ( x1 == x2 ) check how many more there are of the same. --> (n1,x) and (n2,x) id f0(?c)*f1((n1,x),?b)*f2((n2,x),?c) = +binom_(n1+n2,n1)*f0(?c,(n1+n2,x))*f1(?a)*f2(?b) +sum_(j,0,n1-1,binom_(n2+j,j)*f0(?c,(j+n2,x)) *f1((n1-j),?a)*f2(?b))*force2 +sum_(j,0,n2-1,binom_(n1+j,j)*f0(?c,(j+n1,x)) *f1(?a)*f2((n2-j),?b))*force1 The force operation can be executed directly The next question is how to program this: recursively or linearly which would require simulation of a recursion. Recursive is clearest but we need to pass a number of arguments from the calling routine to the final routine. This is done with AN.SHvar. We need space for the accumulation of the combinatoric factors. */ int Shuffle(WORD *from1, WORD *from2, WORD *to) { GETIDENTITY WORD *t, *fr, *next1, *next2, na, *fn1, *fn2, *tt; int i, n, n1, n2, j; LONG combilast; SHvariables *SH = &(AN.SHvar); if ( from1 == SH->stop1 && from2 == SH->stop2 ) { return(FiniShuffle(to)); } else if ( from1 == SH->stop1 ) { i = SH->stop2 - from2; t = to; tt = from2; NCOPY(t,tt,i) return(FiniShuffle(t)); } else if ( from2 == SH->stop2 ) { i = SH->stop1 - from1; t = to; tt = from1; NCOPY(t,tt,i) return(FiniShuffle(t)); } /* Compare lead arguments */ if ( AreArgsEqual(from1,from2) ) { /* First find out how many of each */ next1 = from1; n1 = 1; NEXTARG(next1) while ( ( next1 < SH->stop1 ) && AreArgsEqual(from1,next1) ) { n1++; NEXTARG(next1) } next2 = from2; n2 = 1; NEXTARG(next2) while ( ( next2 < SH->stop2 ) && AreArgsEqual(from2,next2) ) { n2++; NEXTARG(next2) } combilast = SH->combilast; /* +binom_(n1+n2,n1)*f0(?c,(n1+n2,x))*f1(?a)*f2(?b) */ t = to; n = n1 + n2; while ( --n >= 0 ) { fr = from1; CopyArg(t,fr) } if ( GetBinom((UWORD *)(t),&na,n1+n2,n1) ) goto shuffcall; if ( combilast + AN.SHcombi[combilast] + na + 2 >= AN.SHcombisize ) { /* We need more memory in this stack. Fortunately this is the only place where we have to do this, because the other factors are definitely smaller. Layout: size, LongInteger, size, LongInteger, ..... We start pointing at the last one. */ UWORD *combi = (UWORD *)Malloc1(2*AN.SHcombisize*2,"AN.SHcombi"); LONG jj; for ( jj = 0; jj < AN.SHcombisize; jj++ ) combi[jj] = AN.SHcombi[jj]; AN.SHcombisize *= 2; M_free(AN.SHcombi,"AN.SHcombi"); AN.SHcombi = combi; } if ( MulLong((UWORD *)(AN.SHcombi+combilast+1),AN.SHcombi[combilast], (UWORD *)(t),na, (UWORD *)(AN.SHcombi+combilast+AN.SHcombi[combilast]+2), (WORD *)(AN.SHcombi+combilast+AN.SHcombi[combilast]+1)) ) goto shuffcall; SH->combilast = combilast + AN.SHcombi[combilast] + 1; if ( next1 >= SH->stop1 ) { fr = next2; i = SH->stop2 - fr; NCOPY(t,fr,i) if ( FiniShuffle(t) ) goto shuffcall; } else if ( next2 >= SH->stop2 ) { fr = next1; i = SH->stop1 - fr; NCOPY(t,fr,i) if ( FiniShuffle(t) ) goto shuffcall; } else { if ( Shuffle(next1,next2,t) ) goto shuffcall; } SH->combilast = combilast; /* +sum_(j,0,n1-1,binom_(n2+j,j)*f0(?c,(j+n2,x)) *f1((n1-j),?a)*f2(?b))*force2 */ if ( next2 < SH->stop2 ) { t = to; n = n2; while ( --n >= 0 ) { fr = from1; CopyArg(t,fr) } for ( j = 0; j < n1; j++ ) { if ( GetBinom((UWORD *)(t),&na,n2+j,j) ) goto shuffcall; if ( MulLong((UWORD *)(AN.SHcombi+combilast+1),AN.SHcombi[combilast], (UWORD *)(t),na, (UWORD *)(AN.SHcombi+combilast+AN.SHcombi[combilast]+2), (WORD *)(AN.SHcombi+combilast+AN.SHcombi[combilast]+1)) ) goto shuffcall; SH->combilast = combilast + AN.SHcombi[combilast] + 1; if ( j > 0 ) { fr = from1; CopyArg(t,fr) } fn2 = next2; tt = t; CopyArg(tt,fn2) if ( fn2 >= SH->stop2 ) { n = n1-j; while ( --n >= 0 ) { fr = from1; CopyArg(tt,fr) } fr = next1; i = SH->stop1 - fr; NCOPY(tt,fr,i) if ( FiniShuffle(tt) ) goto shuffcall; } else { n = j; fn1 = from1; while ( --n >= 0 ) { NEXTARG(fn1) } if ( Shuffle(fn1,fn2,tt) ) goto shuffcall; } SH->combilast = combilast; } } /* +sum_(j,0,n2-1,binom_(n1+j,j)*f0(?c,(j+n1,x)) *f1(?a)*f2((n2-j),?b))*force1 */ if ( next1 < SH->stop1 ) { t = to; n = n1; while ( --n >= 0 ) { fr = from1; CopyArg(t,fr) } for ( j = 0; j < n2; j++ ) { if ( GetBinom((UWORD *)(t),&na,n1+j,j) ) goto shuffcall; if ( MulLong((UWORD *)(AN.SHcombi+combilast+1),AN.SHcombi[combilast], (UWORD *)(t),na, (UWORD *)(AN.SHcombi+combilast+AN.SHcombi[combilast]+2), (WORD *)(AN.SHcombi+combilast+AN.SHcombi[combilast]+1)) ) goto shuffcall; SH->combilast = combilast + AN.SHcombi[combilast] + 1; if ( j > 0 ) { fr = from1; CopyArg(t,fr) } fn1 = next1; tt = t; CopyArg(tt,fn1) if ( fn1 >= SH->stop1 ) { n = n2-j; while ( --n >= 0 ) { fr = from1; CopyArg(tt,fr) } fr = next2; i = SH->stop2 - fr; NCOPY(tt,fr,i) if ( FiniShuffle(tt) ) goto shuffcall; } else { n = j; fn2 = from2; while ( --n >= 0 ) { NEXTARG(fn2) } if ( Shuffle(fn1,fn2,tt) ) goto shuffcall; } SH->combilast = combilast; } } } else { /* Argument from first list */ t = to; fr = from1; CopyArg(t,fr) if ( fr >= SH->stop1 ) { fr = from2; i = SH->stop2 - fr; NCOPY(t,fr,i) if ( FiniShuffle(t) ) goto shuffcall; } else { if ( Shuffle(fr,from2,t) ) goto shuffcall; } /* Argument from second list */ t = to; fr = from2; CopyArg(t,fr) if ( fr >= SH->stop2 ) { fr = from1; i = SH->stop1 - fr; NCOPY(t,fr,i) if ( FiniShuffle(t) ) goto shuffcall; } else { if ( Shuffle(from1,fr,t) ) goto shuffcall; } } return(0); shuffcall: MesCall("Shuffle"); return(-1); } /* #] Shuffle : #[ FinishShuffle : The complications here are: 1: We want to save space. We put the output term in 'out' straight on top of what we produced thusfar. We have to copy the early piece because once the term goes back to Generator, Normalize can change it in situ 2: There can be other occurrence of the function between the two that we did. For shuffles that isn't likely, but we use this routine also for the stuffles and there it can happen. */ int FinishShuffle(WORD *fini) { GETIDENTITY WORD *t, *t1, *oldworkpointer = AT.WorkPointer, *tcoef, ntcoef, *out; int i; SHvariables *SH = &(AN.SHvar); SH->outfun[1] = fini - SH->outfun; if ( functions[SH->outfun[0]-FUNCTION].symmetric != 0 ) SH->outfun[2] |= DIRTYSYMFLAG; out = fini; i = fini - SH->outterm; t = SH->outterm; NCOPY(fini,t,i) t = SH->stop1; t1 = t + t[1]; while ( t1 < SH->stop2 ) { t = t1; t1 = t + t[1]; } t1 = SH->stop1; while ( t1 < t ) *fini++ = *t1++; t = SH->stop2; while ( t < SH->incoef ) *fini++ = *t++; tcoef = fini; ntcoef = SH->nincoef; i = ABS(ntcoef); NCOPY(fini,t,i); ntcoef = REDLENG(ntcoef); Mully(BHEAD (UWORD *)tcoef,&ntcoef, (UWORD *)(AN.SHcombi+SH->combilast+1),AN.SHcombi[SH->combilast]); ntcoef = INCLENG(ntcoef); fini = tcoef + ABS(ntcoef); if ( ( ( SH->option & 2 ) != 0 ) && ( ( SH->option & 256 ) != 0 ) ) ntcoef = -ntcoef; fini[-1] = ntcoef; i = *out = fini - out; /* Now check whether we have to do more */ AT.WorkPointer = out + *out; if ( ( SH->option & 1 ) == 1 ) { if ( Generator(BHEAD out,SH->level) ) goto Finicall; } else { if ( DoShtuffle(out,SH->level,SH->thefunction,SH->option) ) goto Finicall; } AT.WorkPointer = oldworkpointer; return(0); Finicall: AT.WorkPointer = oldworkpointer; MesCall("FinishShuffle"); return(-1); } /* #] FinishShuffle : #[ DoStuffle : Stuffling is a variation of shuffling. In the stuffling we insist that the arguments are (short) integers. nonzero. The stuffle sum is x st y = sig_(x)*sig_(y)*(abs(x)+abs(y)) The way we do this is: 1: count the arguments in each function: n1, n2 2: take the minimum minval = min(n1,n2). 3: for ( j = 0; j <= min; j++ ) take j elements in each of the lists. 4: the j+1 groups of remaining arguments have to each be shuffled 5: the j selected pairs have to be stuffle added. We can use many of the shuffle things. Considering the recursive nature of the generation we actually don't need to know n1, n2, minval. */ int DoStuffle(WORD *term, WORD level, WORD fun, WORD option) { GETIDENTITY SHvariables SHback, *SH = &(AN.SHvar); WORD *t1, *t2, *tstop, *t1stop, *t2stop, ncoef, n = fun, *to, *from; WORD *r1, *r2; int i, error; LONG k; UWORD *newcombi; #ifdef NEWCODE WORD *rr1, *rr2, i1, i2; #endif if ( n < 0 ) { if ( ( n = DolToFunction(BHEAD -n) ) == 0 ) { MLOCK(ErrorMessageLock); MesPrint("$-variable in merge statement did not evaluate to a function."); MUNLOCK(ErrorMessageLock); return(1); } } if ( AT.WorkPointer + 3*(*term) + AM.MaxTal > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } tstop = term + *term; ncoef = tstop[-1]; tstop -= ABS(ncoef); t1 = term + 1; retry1:; while ( t1 < tstop ) { if ( ( *t1 == n ) && ( t1+t1[1] < tstop ) && ( t1[1] > FUNHEAD ) ) { t2 = t1 + t1[1]; if ( t2 >= tstop ) { return(Generator(BHEAD term,level)); } retry2:; while ( t2 < tstop ) { if ( ( *t2 == n ) && ( t2[1] > FUNHEAD ) ) break; t2 += t2[1]; } if ( t2 < tstop ) break; } t1 += t1[1]; } if ( t1 >= tstop ) { return(Generator(BHEAD term,level)); } /* Next we have to check that the arguments are of the correct type At the same time we can count them. */ #ifndef NEWCODE t1stop = t1 + t1[1]; r1 = t1 + FUNHEAD; while ( r1 < t1stop ) { if ( *r1 != -SNUMBER ) break; if ( r1[1] == 0 ) break; r1 += 2; } if ( r1 < t1stop ) { t1 = t2; goto retry1; } t2stop = t2 + t2[1]; r2 = t2 + FUNHEAD; while ( r2 < t2stop ) { if ( *r2 != -SNUMBER ) break; if ( r2[1] == 0 ) break; r2 += 2; } if ( r2 < t2stop ) { t2 = t2 + t2[1]; goto retry2; } #else t1stop = t1 + t1[1]; r1 = t1 + FUNHEAD; while ( r1 < t1stop ) { if ( *r1 == -SNUMBER ) { if ( r1[1] == 0 ) break; r1 += 2; continue; } else if ( *r1 == -SYMBOL ) { if ( ( symbols[r1[1]].complex & VARTYPEROOTOFUNITY ) != VARTYPEROOTOFUNITY ) break; r1 += 2; continue; } if ( *r1 > 0 && *r1 == r1[ARGHEAD]+ARGHEAD ) { if ( ABS(r1[r1[0]-1]) == r1[0]-ARGHEAD-1 ) {} else if ( r1[ARGHEAD+1] == SYMBOL ) { rr1 = r1 + ARGHEAD + 3; i1 = rr1[-1]-2; while ( i1 > 0 ) { if ( ( symbols[*rr1].complex & VARTYPEROOTOFUNITY ) != VARTYPEROOTOFUNITY ) break; i1 -= 2; rr1 += 2; } if ( i1 > 0 ) break; } else break; rr1 = r1+*r1-1; i1 = (ABS(*rr1)-1)/2; while ( i1 > 1 ) { if ( rr1[-1] ) break; i1--; rr1--; } if ( i1 > 1 || rr1[-1] != 1 ) break; r1 += *r1; } else break; } if ( r1 < t1stop ) { t1 = t2; goto retry1; } t2stop = t2 + t2[1]; r2 = t2 + FUNHEAD; while ( r2 < t2stop ) { if ( *r2 == -SNUMBER ) { if ( r2[1] == 0 ) break; r2 += 2; continue; } else if ( *r2 == -SYMBOL ) { if ( ( symbols[r2[1]].complex & VARTYPEROOTOFUNITY ) != VARTYPEROOTOFUNITY ) break; r2 += 2; continue; } if ( *r2 > 0 && *r2 == r2[ARGHEAD]+ARGHEAD ) { if ( ABS(r2[r2[0]-1]) == r2[0]-ARGHEAD-1 ) {} else if ( r2[ARGHEAD+1] == SYMBOL ) { rr2 = r2 + ARGHEAD + 3; i2 = rr2[-1]-2; while ( i2 > 0 ) { if ( ( symbols[*rr2].complex & VARTYPEROOTOFUNITY ) != VARTYPEROOTOFUNITY ) break; i2 -= 2; rr2 += 2; } if ( i2 > 0 ) break; } else break; rr2 = r2+*r2-1; i2 = (ABS(*rr2)-1)/2; while ( i2 > 1 ) { if ( rr2[-1] ) break; i2--; rr2--; } if ( i2 > 1 || rr2[-1] != 1 ) break; r2 += *r2; } else break; } if ( r2 < t2stop ) { t2 = t2 + t2[1]; goto retry2; } #endif /* OK, now we got two objects that can be used. */ *AN.RepPoint = 1; SHback = AN.SHvar; SH->finishuf = &FinishStuffle; SH->do_uffle = &DoStuffle; SH->outterm = AT.WorkPointer; AT.WorkPointer += *term; SH->ststop1 = t1 + t1[1]; SH->ststop2 = t2 + t2[1]; SH->thefunction = n; SH->option = option; SH->level = level; SH->incoef = tstop; SH->nincoef = ncoef; if ( AN.SHcombi == 0 || AN.SHcombisize == 0 ) { AN.SHcombisize = 200; AN.SHcombi = (UWORD *)Malloc1(AN.SHcombisize*sizeof(UWORD),"AN.SHcombi"); SH->combilast = 0; SHback.combilast = 0; } else { SH->combilast += AN.SHcombi[SH->combilast]+1; if ( SH->combilast >= AN.SHcombisize - 100 ) { newcombi = (UWORD *)Malloc1(2*AN.SHcombisize*sizeof(UWORD),"AN.SHcombi"); for ( k = 0; k < AN.SHcombisize; k++ ) newcombi[k] = AN.SHcombi[k]; M_free(AN.SHcombi,"AN.SHcombi"); AN.SHcombi = newcombi; AN.SHcombisize *= 2; } } AN.SHcombi[SH->combilast] = 1; AN.SHcombi[SH->combilast+1] = 1; i = t1-term; to = SH->outterm; from = term; NCOPY(to,from,i) SH->outfun = to; for ( i = 0; i < FUNHEAD; i++ ) { *to++ = t1[i]; } error = Stuffle(t1+FUNHEAD,t2+FUNHEAD,to); AT.WorkPointer = SH->outterm; AN.SHvar = SHback; if ( error ) { MesCall("DoStuffle"); return(-1); } return(0); } /* #] DoStuffle : #[ Stuffle : The way to generate the stuffles 1: select an argument in the first list (for(j1=0;j1ststop1 and SH->ststop2 at these arguments. 4: generate all shuffles of the arguments in front. 5: Then put the stuffle sum of arg(j1) and arg(j2) 6: Then continue calling Stuffle 7: Once one gets exhausted, we can clean up the list and call FinishShuffle 8: if ( ( SH->option & 2 ) != 0 ) the stuffle sum is negative. */ int Stuffle(WORD *from1, WORD *from2, WORD *to) { GETIDENTITY WORD *t, *tf, *next1, *next2, *st1, *st2, *save1, *save2; SHvariables *SH = &(AN.SHvar); int i, retval; /* First the special cases (exhausted list(s)): */ save1 = SH->stop1; save2 = SH->stop2; if ( from1 >= SH->ststop1 && from2 == SH->ststop2 ) { SH->stop1 = SH->ststop1; SH->stop2 = SH->ststop2; retval = FinishShuffle(to); SH->stop1 = save1; SH->stop2 = save2; return(retval); } else if ( from1 >= SH->ststop1 ) { i = SH->ststop2 - from2; t = to; tf = from2; NCOPY(t,tf,i) SH->stop1 = SH->ststop1; SH->stop2 = SH->ststop2; retval = FinishShuffle(t); SH->stop1 = save1; SH->stop2 = save2; return(retval); } else if ( from2 >= SH->ststop2 ) { i = SH->ststop1 - from1; t = to; tf = from1; NCOPY(t,tf,i) SH->stop1 = SH->ststop1; SH->stop2 = SH->ststop2; retval = FinishShuffle(t); SH->stop1 = save1; SH->stop2 = save2; return(retval); } /* Now the case that we have no stuffle sums. */ SH->stop1 = SH->ststop1; SH->stop2 = SH->ststop2; SH->finishuf = &FinishShuffle; if ( Shuffle(from1,from2,to) ) goto stuffcall; SH->finishuf = &FinishStuffle; /* Now we have to select a pair, one from 1 and one from 2. */ #ifndef NEWCODE st1 = from1; next1 = st1+2; /* <----- */ #else st1 = next1 = from1; NEXTARG(next1) #endif while ( next1 <= SH->ststop1 ) { #ifndef NEWCODE st2 = from2; next2 = st2+2; /* <----- */ #else next2 = st2 = from2; NEXTARG(next2) #endif while ( next2 <= SH->ststop2 ) { SH->stop1 = st1; SH->stop2 = st2; if ( st1 == from1 && st2 == from2 ) { t = to; #ifndef NEWCODE *t++ = -SNUMBER; *t++ = StuffAdd(st1[1],st2[1]); #else t = StuffRootAdd(st1,st2,t); #endif SH->option ^= 256; if ( Stuffle(next1,next2,t) ) goto stuffcall; SH->option ^= 256; } else if ( st1 == from1 ) { i = st2-from2; t = to; tf = from2; NCOPY(t,tf,i) #ifndef NEWCODE *t++ = -SNUMBER; *t++ = StuffAdd(st1[1],st2[1]); #else t = StuffRootAdd(st1,st2,t); #endif SH->option ^= 256; if ( Stuffle(next1,next2,t) ) goto stuffcall; SH->option ^= 256; } else if ( st2 == from2 ) { i = st1-from1; t = to; tf = from1; NCOPY(t,tf,i) #ifndef NEWCODE *t++ = -SNUMBER; *t++ = StuffAdd(st1[1],st2[1]); #else t = StuffRootAdd(st1,st2,t); #endif SH->option ^= 256; if ( Stuffle(next1,next2,t) ) goto stuffcall; SH->option ^= 256; } else { if ( Shuffle(from1,from2,to) ) goto stuffcall; } #ifndef NEWCODE st2 = next2; next2 += 2; /* <----- */ #else st2 = next2; NEXTARG(next2) #endif } #ifndef NEWCODE st1 = next1; next1 += 2; /* <----- */ #else st1 = next1; NEXTARG(next1) #endif } SH->stop1 = save1; SH->stop2 = save2; return(0); stuffcall:; MesCall("Stuffle"); return(-1); } /* #] Stuffle : #[ FinishStuffle : The program only comes here from the Shuffle routine. It should add the stuffle sum and then call Stuffle again. */ int FinishStuffle(WORD *fini) { GETIDENTITY SHvariables *SH = &(AN.SHvar); #ifdef NEWCODE WORD *next1 = SH->stop1, *next2 = SH->stop2; fini = StuffRootAdd(next1,next2,fini); #else *fini++ = -SNUMBER; *fini++ = StuffAdd(SH->stop1[1],SH->stop2[1]); #endif SH->option ^= 256; #ifdef NEWCODE NEXTARG(next1) NEXTARG(next2) if ( Stuffle(next1,next2,fini) ) goto stuffcall; #else if ( Stuffle(SH->stop1+2,SH->stop2+2,fini) ) goto stuffcall; #endif SH->option ^= 256; return(0); stuffcall:; MesCall("FinishStuffle"); return(-1); } /* #] FinishStuffle : #[ StuffRootAdd : Makes the stuffle sum of two arguments. The arguments can be of one of three types: 1: -SNUMBER,num 2: -SYMBOL,symbol 3: Numerical (long) argument. 4: Generic argument with (only) symbols that are roots of unity and a coefficient. We have excluded the case that both t1 and t2 are of type 1: The output should be written to 'to' and the new fill position should be the return value. `to' is inside the workspace. The stuffle sum is sig_(t2)*t1+sig_(t1)*t2 or sig_(t1)*sig_(t2)*(abs_(t1)+abs_(t2)) */ #ifdef NEWCODE WORD *StuffRootAdd(WORD *t1, WORD *t2, WORD *to) { int type1, type2, type3, sgn, sgn1, sgn2, sgn3, pow, root, nosymbols, i; WORD *tt1, *tt2, it1, it2, *t3, *r, size1, size2, size3; WORD scratch[2]; LONG x; if ( *t1 == -SNUMBER ) { type1 = 1; if ( t1[1] < 0 ) sgn1 = -1; else sgn1 = 1; } else if ( *t1 == -SYMBOL ) { type1 = 2; sgn1 = 1; } else if ( ABS(t1[*t1-1]) == *t1-ARGHEAD-1 ) { type1 = 3; if ( t1[*t1-1] < 0 ) sgn1 = -1; else sgn1 = 1; } else { type1 = 4; if ( t1[*t1-1] < 0 ) sgn1 = -1; else sgn1 = 1; } if ( *t2 == -SNUMBER ) { type2 = 1; if ( t2[1] < 0 ) sgn2 = -1; else sgn2 = 1; } else if ( *t2 == -SYMBOL ) { type2 = 2; sgn2 = 1; } else if ( ABS(t2[*t2-1]) == *t2-ARGHEAD-1 ) { type2 = 3; if ( t2[*t2-1] < 0 ) sgn2 = -1; else sgn2 = 1; } else { type2 = 4; if ( t2[*t2-1] < 0 ) sgn2 = -1; else sgn2 = 1; } if ( type1 > type2 ) { t3 = t1; t1 = t2; t2 = t3; type3 = type1; type1 = type2; type2 = type3; sgn3 = sgn1; sgn1 = sgn2; sgn2 = sgn3; } nosymbols = 1; sgn3 = 1; switch ( type1 ) { case 1: if ( type2 == 1 ) { x = sgn2 * t1[1]; x += sgn1 * t2[1]; if ( x > MAXPOSITIVE || x < -(MAXPOSITIVE+1) ) { if ( x < 0 ) { sgn1 = -3; x = -x; } else sgn1 = 3; *to++ = ARGHEAD+4; *to++ = 0; FILLARG(to) *to++ = 4; *to++ = (UWORD)x; *to++ = 1; *to++ = sgn1; } else { *to++ = -SNUMBER; *to++ = (WORD)x; } } else if ( type2 == 2 ) { *to++ = ARGHEAD+8; *to++ = 0; FILLARG(to) *to++ = 8; *to++ = SYMBOL; *to++ = 4; *to++ = t2[1]; *to++ = 1; *to++ = ABS(t1[1])+1; *to++ = 1; *to++ = 3*sgn1; } else if ( type2 == 3 ) { tt1 = (WORD *)scratch; tt1[0] = ABS(t1[1]); size1 = 1; tt2 = t2+ARGHEAD+1; size2 = (ABS(t2[*t2-1])-1)/2; t3 = to; *to++ = 0; *to++ = 0; FILLARG(to) *to++ = 0; goto DoCoeffi; } else { /* t1 is (short) numeric, t2 has the symbol(s). */ tt1 = (WORD *)scratch; tt1[0] = ABS(t1[1]); size1 = 1; tt2 = t2+ARGHEAD+1; tt2 += tt2[1]; size2 = (ABS(t2[*t2-1])-1)/2; t3 = to; i = tt2 - t2; r = t2; NCOPY(to,r,i) nosymbols = 0; goto DoCoeffi; } break; case 2: if ( type2 == 2 ) { if ( t1[1] == t2[1] ) { if ( ( symbols[t1[1]].maxpower == 4 ) && ( ( symbols[t1[1]].complex & VARTYPEMINUS ) == VARTYPEMINUS ) ) { *to++ = -SNUMBER; *to++ = -2; } else if ( symbols[t1[1]].maxpower == 2 ) { *to++ = -SNUMBER; *to++ = 2; } else { *to++ = ARGHEAD+8; *to++ = 0; FILLARG(to) *to++ = 8; *to++ = SYMBOL; *to++ = 4; *to++ = t1[1]; *to++ = 2; *to++ = 2; *to++ = 1; *to++ = 3; } } else { *to++ = ARGHEAD+10; *to++ = 0; FILLARG(to) *to++ = 10; *to++ = SYMBOL; *to++ = 6; if ( t1[1] < t2[1] ) { *to++ = t1[1]; *to++ = 1; *to++ = t2[1]; *to++ = 1; } else { *to++ = t2[1]; *to++ = 1; *to++ = t1[1]; *to++ = 1; } *to++ = 2; *to++ = 1; *to++ = 3; } } else if ( type2 == 3 ) { t3 = to; *to++ = 0; *to++ = 0; FILLARG(to) *to++ = 0; *to++ = SYMBOL; *to++ = 4; *to++ = t1[1]; *to++ = 1; tt1 = scratch; tt1[1] = 1; size1 = 1; tt2 = t2+ARGHEAD+1; size2 = (ABS(t2[*t2-1])-1)/2; nosymbols = 0; goto DoCoeffi; } else { tt1 = scratch; tt1[0] = 1; size1 = 1; t3 = to; *to++ = 0; *to++ = 0; FILLARG(to) *to++ = 0; *to++ = SYMBOL; *to++ = 0; tt2 = t2 + ARGHEAD+3; it2 = tt2[-1]-2; while ( it2 > 0 ) { if ( *tt2 == t1[1] ) { pow = tt2[1]+1; root = symbols[*tt2].maxpower; if ( pow >= root ) pow -= root; if ( ( symbols[*tt2].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { if ( ( root & 1 ) == 0 && pow >= root/2 ) { pow -= root/2; sgn3 = -sgn3; } } if ( pow != 0 ) { *to++ = *tt2; *to++ = pow; } tt2 += 2; it2 -= 2; break; } else if ( t1[1] < *tt2 ) { *to++ = t1[1]; *to++ = 1; break; } else { *to++ = *tt2++; *to++ = *tt2++; it2 -= 2; if ( it2 <= 0 ) { *to++ = t1[1]; *to++ = 1; } } } while ( it2 > 0 ) { *to++ = *tt2++; *to++ = *tt2++; it2 -= 2; } if ( (to - t3) > ARGHEAD+3 ) { t3[ARGHEAD+2] = (to-t3)-ARGHEAD-1; /* size of the SYMBOL field */ nosymbols = 0; } else { to = t3+ARGHEAD+1; /* no SYMBOL field */ } size2 = (ABS(t2[*t2-1])-1)/2; goto DoCoeffi; } break; case 3: if ( type2 == 3 ) { /* Both are numeric */ tt1 = t1+ARGHEAD+1; size1 = (ABS(t1[*t1-1])-1)/2; tt2 = t2+ARGHEAD+1; size2 = (ABS(t2[*t2-1])-1)/2; t3 = to; *to++ = 0; *to++ = 0; FILLARG(to) *to++ = 0; goto DoCoeffi; } else { /* t1 is (long) numeric, t2 has the symbol(s). */ tt1 = t1+ARGHEAD+1; size1 = (ABS(t1[*t1-1])-1)/2; tt2 = t2+ARGHEAD+1; tt2 += tt2[1]; size2 = (ABS(t2[*t2-1])-1)/2; t3 = to; i = tt2 - t2; r = t2; NCOPY(to,r,i) nosymbols = 0; goto DoCoeffi; } break; case 4: /* Both have roots of unity 1: Merge the lists and simplify if possible */ tt1 = t1+ARGHEAD+3; it1 = tt1[-1]-2; tt2 = t2+ARGHEAD+3; it2 = tt2[-1]-2; t3 = to; *to++ = 0; *to++ = 0; FILLARG(to) *to++ = 0; *to++ = SYMBOL; *to++ = 0; while ( it1 > 0 && it2 > 0 ) { if ( *tt1 == *tt2 ) { pow = tt1[1]+tt2[1]; root = symbols[*tt1].maxpower; if ( pow >= root ) pow -= root; if ( ( symbols[*tt1].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { if ( ( root & 1 ) == 0 && pow >= root/2 ) { pow -= root/2; sgn3 = -sgn3; } } if ( pow != 0 ) { *to++ = *tt1; *to++ = pow; } tt1 += 2; tt2 += 2; it1 -= 2; it2 -= 2; } else if ( *tt1 < *tt2 ) { *to++ = *tt1++; *to++ = *tt1++; it1 -= 2; } else { *to++ = *tt2++; *to++ = *tt2++; it2 -= 2; } } while ( it1 > 0 ) { *to++ = *tt1++; *to++ = *tt1++; it1 -= 2; } while ( it2 > 0 ) { *to++ = *tt2++; *to++ = *tt2++; it2 -= 2; } if ( (to - t3) > ARGHEAD+3 ) { t3[ARGHEAD+2] = (to-t3)-ARGHEAD-1; /* size of the SYMBOL field */ nosymbols = 0; } else { to = t3+ARGHEAD+1; /* no SYMBOL field */ } size1 = (ABS(t1[*t1-1])-1)/2; size2 = (ABS(t2[*t2-1])-1)/2; /* Now tt1 and tt2 are pointing at their coefficients. sgn1 is the sign of 1, sgn2 is the sign of 2 and sgn3 is an extra overall sign. */ DoCoeffi: if ( AddLong((UWORD *)tt1,size1,(UWORD *)tt2,size2,(UWORD *)to,&size3) ) { MLOCK(ErrorMessageLock); MesPrint("Called from StuffRootAdd"); MUNLOCK(ErrorMessageLock); Terminate(-1); } sgn = sgn1*sgn2*sgn3; if ( nosymbols && size3 == 1 ) { if ( (UWORD)(to[0]) <= MAXPOSITIVE && sgn > 0 ) { sgn1 = to[0]; to = t3; *to++ = -SNUMBER; *to++ = sgn1; } else if ( (UWORD)(to[0]) <= (MAXPOSITIVE+1) && sgn < 0 ) { sgn1 = to[0]; to = t3; *to++ = -SNUMBER; *to++ = -sgn1; } else goto genericcoef; } else { genericcoef: to += size3; sgn = sgn*(2*size3+1); *to++ = 1; while ( size3 > 1 ) { *to++ = 0; size3--; } *to++ = sgn; t3[0] = to - t3; t3[ARGHEAD] = t3[0] - ARGHEAD; } break; } return(to); } #endif /* #] StuffRootAdd : */ form-5.0.1/sources/features.cc0000644000175100017510000001033615217035721011761 /** @file features.cc * * Utility code for printing available features. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ // #[ Includes : extern "C" { #include "form3.h" } #include #include #include #ifdef WITHFLINT #include #endif #ifdef WITHGMP #include #endif #ifdef WITHMPFR #include #endif #ifdef WITHZLIB #include #endif #ifdef WITHZSTD #include #endif // #] Includes : // #[ PrintFeatureList : /** * Prints a list of strings in multiple columns to fit within the line length. * * @param lines List of strings to print. */ static void PrintMulticolumn(const std::vector& lines) { const std::size_t n_lines = lines.size(); if ( n_lines == 0 ) return; const std::size_t line_len = AC.LineLength > 0 ? AC.LineLength : 79; constexpr std::size_t max_cols = 6; constexpr std::size_t col_spacing = 2; std::vector col_lens(max_cols); for ( std::size_t n_cols = max_cols; n_cols >= 2; n_cols-- ) { const std::size_t n_rows = (n_lines - 1) / n_cols + 1; // Check whether `n_cols` columns fit within the line length. // Columns are filled top-to-bottom, then left-to-right. std::fill(col_lens.begin(),col_lens.begin()+n_cols,0); std::size_t total_len = 0; for ( std::size_t j = 0; j < n_cols; j++ ) { for ( std::size_t i = 0; i < n_rows; i++ ) { const std::size_t k = i + j * n_rows; if ( k >= n_lines ) break; col_lens[j] = std::max(col_lens[j],lines[k].size()); } total_len += col_lens[j]; } total_len += (n_cols - 1) * col_spacing; if ( total_len > line_len ) continue; // Output using `n_cols` columns. std::string line; line.reserve(line_len); for ( std::size_t i = 0; i < n_rows; i++ ) { line.clear(); for ( std::size_t j = 0; j < n_cols; j++ ) { const std::size_t k = i + j * n_rows; if ( k >= n_lines ) break; line += lines[k]; if ( j < n_cols - 1 ) { line += std::string(col_lens[j]-lines[k].size()+col_spacing,' '); } } MesPrint("%s",line.c_str()); } return; } // Fallback to a single column. for ( const auto& f : lines ) { MesPrint("%s",f.c_str()); } } /** * Prints the list of available features. */ void PrintFeatureList(void) { std::vector feature_list = { #ifdef ENABLE_BACKTRACE "+backtrace", #else "-backtrace", #endif #ifdef DEBUGGING "+debugging", #else "-debugging", #endif #ifdef WITHFLINT "+flint=" + std::string(flint_version), #else "-flint", #endif #ifdef WITHFLOAT "+float", #else "-float", #endif #ifdef WITHGMP "+gmp=" + std::string(gmp_version), #else "-gmp", #endif #ifdef WITHMPFR "+mpfr=" + std::string(mpfr_get_version()), #else "-mpfr", #endif #ifdef WITHMPI "+mpi", #else "-mpi", #endif #ifdef UNIX "+posix", #else "-posix", #endif #ifdef WITHPTHREADS "+pthreads", #else "-pthreads", #endif #ifdef WINDOWS "+windows", #else "-windows", #endif #ifdef WITHZLIB "+zlib=" + std::string(zlibVersion()), #else "-zlib", #endif #ifdef WITHZSTD "+zstd=" + std::string(ZSTD_versionString()), #else "-zstd", #endif }; PrintMulticolumn(feature_list); } // #] PrintFeatureList : form-5.0.1/sources/checkpoint.c0000644000175100017510000026740015217035721012135 /* #[ Explanations : */ /** @file checkpoint.c * * Contains all functions that deal with the recovery mechanism controlled and * activated by the On Checkpoint switch. * * The main function are DoCheckpoint, DoRecovery, and DoSnapshot. If the * checkpoints are activated DoCheckpoint is called every time a module is * finished executing. If the conditions for the creation of a recovery * snapshot are met DoCheckpoint calls DoSnapshot. DoRecovery is called once * when FORM starts up with the command line argument -R. Most of the other * code contains debugging facilities that are only compiled if the macro * PRINTDEBUG is defined. * * The recovery mechanism is atomic, i.e. only if everything went well, the * final recovery file is created (and the older one overwritten) in a single * step (copying). If some errors occur, a warning is issued and the program * continues without having created a new recovery file. The only situation in * which the creation of the recovery data leads to a termination of the * running program is if not enough disk or memory space is left. * * For ParFORM each slave creates its own recovery file, sends it to the * master and then it deletes the recovery file. The master stores all the * recovery files and on recovery it feeds these files to the slaves. It is * nearly impossible to recover after some MPI fault so ParFORM terminates * on any recovery failure. * * DoRecovery and DoSnapshot do the loading and saving of the recovery data, * respectively. Every change in one functions needs to be accompanied by the * appropriate change in the other function. The structure of both functions is * quite similar. They handle the relevant global structs one after the other * and then care about the copying of the hide and scratch files. * * The names of the recovery, scratch and hide files are hard-coded in the * variables in fold "filenames and system commands". * * If the global structs AM,AP,AC,AR are changed, DoRecovery and DoSnapshot * usually also have to be changed. Some structs are read/written as a whole * (AP,AC), some are read/written only partly as a selection of their * individual elements (AM,AR). If AM or AR have been changed by adding or * removing an element that is important for the runtime status, then the * reading/writing statements have to be added to or removed from DoRecovery * and DoSnapshot. If AP or AC are changed, then for non-pointer variables (in * the case of a struct it also means that none of its elements is a pointer) * nothing has to be changed in the functions here. If pointers are involved, * extra code has to be added (or removed). See the comments of DoRecovery and * DoSnapshot. * */ /* #] Explanations : #[ License : * * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : #[ Includes : */ #include "form3.h" #include /* #define PRINTDEBUG */ /* #define PRINTTIMEMARKS */ /* #] Includes : #[ filenames and system commands : */ /** * BaseName of recovery files */ #ifdef WITHMPI #define BASENAME_FMT "%c%04dFORMrecv" /** * The basenames for ParFORM will be created from BASENAME_FMT by means of * sprintf(BaseName,BASENAME_FMT,(PF.me == MASTER)?'m':'s',PF.me); * in InitRecovery(). Here just reserve the space: */ static char BaseName[] = BASENAME_FMT; #else static char *BaseName = "FORMrecv"; #endif /** * filename for the recovery file */ static char *recoveryfile = 0; /** * filename for the intermediate recovery file. only if the write is * completely successful, this file will be moved/renamed to the one * named by recoveryfile. this offers atomicity for the snapshot generation. */ static char *intermedfile = 0; /** * filename of sort file copy */ static char *sortfile = 0; /** * filename of hide file copy */ static char *hidefile = 0; /** * filename of store file copy */ static char *storefile = 0; /** * >0 if at least once the respective file has been created. * Checked by DeleteRecoveryFile(). */ static int done_snapshot = 0; #ifdef WITHMPI /** * The position at which BASENAME_FMT should be applied. * Initialized in InitRecovery(). */ static int PF_fmt_pos; /** * Returns the contents of recoveryfile or intermedfile but with the renaming * specified by the arguments. */ static const char *PF_recoveryfile(char prefix, int id, int intermed) { /* * Assume that InitRecovery() has been already called, namely * recoveryfile, intermedfile and PF_fmt_pos are already initialized. */ static char *tmp_recovery = NULL; static char *tmp_intermed = NULL; char *tmp, c; if ( tmp_recovery == NULL ) { if ( PF.numtasks > 9999 ) { /* see BASENAME_FMT */ MesPrint("Checkpoint: too many number of processors."); Terminate(-1); } tmp_recovery = (char *)Malloc1(strlen(recoveryfile) + strlen(intermedfile) + 2, "PF_recoveryfile"); tmp_intermed = tmp_recovery + strlen(recoveryfile) + 1; strcpy(tmp_recovery, recoveryfile); strcpy(tmp_intermed, intermedfile); } tmp = intermed ? tmp_intermed : tmp_recovery; c = tmp[PF_fmt_pos + 13]; /* The magic number 13 comes from BASENAME_FMT. */ sprintf(tmp + PF_fmt_pos, BASENAME_FMT, prefix, id); tmp[PF_fmt_pos + 13] = c; return tmp; } #endif /* #] filenames and system commands : #[ CheckRecoveryFile : */ /** * Checks whether a snapshot/recovery file exists. * Returns 1 if it exists, 0 otherwise. */ #ifdef WITHMPI /** * The master has all the recovery files. It checks whether these files * exist and sends proper files to slaves. On any error PF_CheckRecoveryFile() * returns -1 which leads to the program termination. */ static int PF_CheckRecoveryFile() { int i,ret=0; FILE *fd; /* Check if the recovery file for the master exists. */ if ( PF.me == MASTER ) { if ( (fd = fopen(recoveryfile, "r")) ) { fclose(fd); PF_BroadcastNumber(1); } else { PF_BroadcastNumber(0); return 0; } } else { if ( !PF_BroadcastNumber(0) ) return 0; } /* Now the main part. */ if (PF.me == MASTER){ /*We have to have recovery files for the master and all the slaves:*/ for(i=1; i 0 ) { if ( AC.CheckpointFlag != -1 ) { /* recovery file exists but recovery option is not given */ #ifdef WITHMPI if ( PF.me == MASTER ) { #endif MesPrint("The recovery file %s exists, but the recovery option -R has not been given!", RecoveryFilename()); MesPrint("FORM will be terminated to avoid unintentional loss of data."); MesPrint("Delete the recovery file manually, if you want to start FORM without recovery."); #ifdef WITHMPI } if(PF.me != MASTER) remove(RecoveryFilename()); #endif Terminate(-1); } } else { if ( AC.CheckpointFlag == -1 ) { /* recovery option given but recovery file does not exist */ #ifdef WITHMPI if ( PF.me == MASTER ) #endif MesPrint("Option -R for recovery has been given, but the recovery file %s does not exist!", RecoveryFilename()); Terminate(-1); } } return(ret); } /* #] CheckRecoveryFile : #[ DeleteRecoveryFile : */ /** * Deletes the recovery files. It is called by CleanUp() in the case of a * successful completion. */ void DeleteRecoveryFile(void) { if ( done_snapshot ) { remove(recoveryfile); #ifdef WITHMPI if( PF.me == MASTER){ int i; for(i=1; i> 4); UBYTE l = (UBYTE)(*((UBYTE*)p) & 0x0F); if ( h > 9 ) h += 55; else h += 48; if ( l > 9 ) l += 55; else l += 48; printf("%c%c ", h, l); } static void print_STR(UBYTE *p) { if ( p ) { MesPrint("%s", (char*)p); } else { MesPrint("NULL"); } } static void print_WORDB(WORD *buf, WORD *top) { LONG size = top-buf; int i; while ( size > 0 ) { if ( size > MAXPOSITIVE ) i = MAXPOSITIVE; else i = size; size -= i; MesPrint("%a",i,buf); buf += i; } } static void print_VOIDP(void *p, size_t size) { int i; if ( p ) { while ( size > 0 ) { if ( size > MAXPOSITIVE ) i = MAXPOSITIVE; else i = size; size -= i; MesPrint("%b",i,(UBYTE *)p); p = ((UBYTE *)p)+i; } } else { MesPrint("NULL"); } } static void print_CHARS(UBYTE *p, size_t size) { int i; while ( size > 0 ) { if ( size > MAXPOSITIVE ) i = MAXPOSITIVE; else i = size; size -= i; MesPrint("%C",i,(char *)p); p += i; } } static void print_WORDV(WORD *p, size_t size) { int i; if ( p ) { while ( size > 0 ) { if ( size > MAXPOSITIVE ) i = MAXPOSITIVE; else i = size; size -= i; MesPrint("%a",i,p); p += i; } } else { MesPrint("NULL"); } } static void print_INTV(int *p, size_t size) { int iarray[8]; WORD i = 0; if ( p ) { while ( size > 0 ) { if ( i >= 8 ) { MesPrint("%I",i,iarray); i = 0; } iarray[i++] = *p++; size--; } if ( i > 0 ) MesPrint("%I",i,iarray); } else { MesPrint("NULL"); } } static void print_LONGV(LONG *p, size_t size) { LONG larray[8]; WORD i = 0; if ( p ) { while ( size > 0 ) { if ( i >= 8 ) { MesPrint("%I",i,larray); i = 0; } larray[i++] = *p++; size--; } if ( i > 0 ) MesPrint("%I",i,larray); } else { MesPrint("NULL"); } } static void print_PRELOAD(PRELOAD *l) { if ( l->size ) { print_CHARS(l->buffer, l->size); } MesPrint("%ld", l->size); } static void print_PREVAR(PREVAR *l) { MesPrint("%s", l->name); print_STR(l->value); if ( l->nargs ) print_STR(l->argnames); MesPrint("%d", l->nargs); MesPrint("%d", l->wildarg); } static void print_DOLLARS(DOLLARS l) { print_VOIDP(l->where, l->size); MesPrint("%ld", l->size); MesPrint("%ld", l->name); MesPrint("%s", AC.dollarnames->namebuffer+l->name); MesPrint("%d", l->type); MesPrint("%d", l->node); MesPrint("%d", l->index); MesPrint("%d", l->zero); MesPrint("%d", l->numdummies); MesPrint("%d", l->nfactors); } static void print_LIST(LIST *l) { print_VOIDP(l->lijst, l->size); MesPrint("%s", l->message); MesPrint("%d", l->num); MesPrint("%d", l->maxnum); MesPrint("%d", l->size); MesPrint("%d", l->numglobal); MesPrint("%d", l->numtemp); MesPrint("%d", l->numclear); } static void print_DOLOOP(DOLOOP *l) { print_PRELOAD(&(l->p)); print_STR(l->name); if ( l->type != NUMERICALLOOP ) { print_STR(l->vars); } print_STR(l->contents); if ( l->type != LISTEDLOOP && l->type != NUMERICALLOOP ) { print_STR(l->dollarname); } MesPrint("%l", l->startlinenumber); MesPrint("%l", l->firstnum); MesPrint("%l", l->lastnum); MesPrint("%l", l->incnum); MesPrint("%d", l->type); MesPrint("%d", l->NoShowInput); MesPrint("%d", l->errorsinloop); MesPrint("%d", l->firstloopcall); } static void print_PROCEDURE(PROCEDURE *l) { if ( l->loadmode != 1 ) { print_PRELOAD(&(l->p)); } print_STR(l->name); MesPrint("%d", l->loadmode); } static void print_NAMETREE(NAMETREE *t) { int i; for ( i=0; inodefill; ++i ) { MesPrint("%l %d %d %d %d %d %d\n", t->namenode[i].name, t->namenode[i].parent, t->namenode[i].left, t->namenode[i].right, t->namenode[i].balance, t->namenode[i].type, t->namenode[i].number ); } print_CHARS(t->namebuffer, t->namefill); MesPrint("%l", t->namesize); MesPrint("%l", t->namefill); MesPrint("%l", t->nodesize); MesPrint("%l", t->nodefill); MesPrint("%l", t->oldnamefill); MesPrint("%l", t->oldnodefill); MesPrint("%l", t->globalnamefill); MesPrint("%l", t->globalnodefill); MesPrint("%l", t->clearnamefill); MesPrint("%l", t->clearnodefill); MesPrint("%d", t->headnode); } void print_CBUF(CBUF *c) { int i; print_WORDV(c->Buffer, c->BufferSize); /* MesPrint("%x", c->Buffer); MesPrint("%x", c->lhs); MesPrint("%x", c->rhs); */ for ( i=0; inumlhs; ++i ) { if ( c->lhs[i]) MesPrint("%d", *(c->lhs[i])); } for ( i=0; inumrhs; ++i ) { if ( c->rhs[i]) MesPrint("%d", *(c->rhs[i])); } MesPrint("%l", *c->CanCommu); MesPrint("%l", *c->NumTerms); MesPrint("%d", *c->numdum); for ( i=0; iMaxTreeSize; ++i ) { MesPrint("%d %d %d %d %d", c->boomlijst[i].parent, c->boomlijst[i].left, c->boomlijst[i].right, c->boomlijst[i].value, c->boomlijst[i].blnce); } } static void print_STREAM(STREAM *t) { print_CHARS(t->buffer, t->inbuffer); MesPrint("%l", (LONG)(t->pointer-t->buffer)); print_STR(t->FoldName); print_STR(t->name); if ( t->type == PREVARSTREAM || t->type == DOLLARSTREAM ) { print_STR(t->pname); } MesPrint("%l", (LONG)t->fileposition); MesPrint("%l", (LONG)t->linenumber); MesPrint("%l", (LONG)t->prevline); MesPrint("%l", t->buffersize); MesPrint("%l", t->bufferposition); MesPrint("%l", t->inbuffer); MesPrint("%d", t->previous); MesPrint("%d", t->handle); switch ( t->type ) { case FILESTREAM: MesPrint("%d == FILESTREAM", t->type); break; case PREVARSTREAM: MesPrint("%d == PREVARSTREAM", t->type); break; case PREREADSTREAM: MesPrint("%d == PREREADSTREAM", t->type); break; case PIPESTREAM: MesPrint("%d == PIPESTREAM", t->type); break; case PRECALCSTREAM: MesPrint("%d == PRECALCSTREAM", t->type); break; case DOLLARSTREAM: MesPrint("%d == DOLLARSTREAM", t->type); break; case PREREADSTREAM2: MesPrint("%d == PREREADSTREAM2", t->type); break; case EXTERNALCHANNELSTREAM: MesPrint("%d == EXTERNALCHANNELSTREAM", t->type); break; case PREREADSTREAM3: MesPrint("%d == PREREADSTREAM3", t->type); break; default: MesPrint("%d == UNKNOWN", t->type); } } static void print_M() { MesPrint("%%%% M_const"); MesPrint("%d", *AM.gcmod); MesPrint("%d", *AM.gpowmod); print_STR(AM.TempDir); print_STR(AM.TempSortDir); print_STR(AM.IncDir); print_STR(AM.InputFileName); print_STR(AM.LogFileName); print_STR(AM.OutBuffer); print_STR(AM.Path); print_STR(AM.SetupDir); print_STR(AM.SetupFile); MesPrint("--MARK 1"); MesPrint("%l", (LONG)BASEPOSITION(AM.zeropos)); #ifdef WITHPTHREADS MesPrint("%l", AM.ThreadScratSize); MesPrint("%l", AM.ThreadScratOutSize); #endif MesPrint("%l", AM.MaxTer); MesPrint("%l", AM.CompressSize); MesPrint("%l", AM.ScratSize); MesPrint("%l", AM.SizeStoreCache); MesPrint("%l", AM.MaxStreamSize); MesPrint("%l", AM.SIOsize); MesPrint("%l", AM.SLargeSize); MesPrint("%l", AM.SSmallEsize); MesPrint("%l", AM.SSmallSize); MesPrint("--MARK 2"); MesPrint("%l", AM.STermsInSmall); MesPrint("%l", AM.MaxBracketBufferSize); MesPrint("%l", AM.hProcessBucketSize); MesPrint("%l", AM.gProcessBucketSize); MesPrint("%l", AM.shmWinSize); MesPrint("%l", AM.OldChildTime); MesPrint("%l", AM.OldSecTime); MesPrint("%l", AM.OldMilliTime); MesPrint("%l", AM.WorkSize); MesPrint("%l", AM.gThreadBucketSize); MesPrint("--MARK 3"); MesPrint("%l", AM.ggThreadBucketSize); MesPrint("%d", AM.FileOnlyFlag); MesPrint("%d", AM.Interact); MesPrint("%d", AM.MaxParLevel); MesPrint("%d", AM.OutBufSize); MesPrint("%d", AM.SMaxFpatches); MesPrint("%d", AM.SMaxPatches); MesPrint("%d", AM.StdOut); MesPrint("%d", AM.ginsidefirst); MesPrint("%d", AM.gDefDim); MesPrint("%d", AM.gDefDim4); MesPrint("--MARK 4"); MesPrint("%d", AM.NumFixedSets); MesPrint("%d", AM.NumFixedFunctions); MesPrint("%d", AM.rbufnum); MesPrint("%d", AM.dbufnum); MesPrint("%d", AM.SkipClears); MesPrint("%d", AM.gfunpowers); MesPrint("%d", AM.gStatsFlag); MesPrint("%d", AM.gNamesFlag); MesPrint("%d", AM.gCodesFlag); MesPrint("%d", AM.gTokensWriteFlag); MesPrint("%d", AM.gSortType); MesPrint("%d", AM.gproperorderflag); MesPrint("--MARK 5"); MesPrint("%d", AM.hparallelflag); MesPrint("%d", AM.gparallelflag); MesPrint("%d", AM.totalnumberofthreads); MesPrint("%d", AM.gSizeCommuteInSet); MesPrint("%d", AM.gThreadStats); MesPrint("%d", AM.ggThreadStats); MesPrint("%d", AM.gFinalStats); MesPrint("%d", AM.ggFinalStats); MesPrint("%d", AM.gThreadsFlag); MesPrint("%d", AM.ggThreadsFlag); MesPrint("%d", AM.gThreadBalancing); MesPrint("%d", AM.ggThreadBalancing); MesPrint("%d", AM.gThreadSortFileSynch); MesPrint("%d", AM.ggThreadSortFileSynch); MesPrint("%d", AM.gProcessStats); MesPrint("%d", AM.ggProcessStats); MesPrint("%d", AM.gOldParallelStats); MesPrint("%d", AM.ggOldParallelStats); MesPrint("%d", AM.gWTimeStatsFlag); MesPrint("%d", AM.ggWTimeStatsFlag); MesPrint("%d", AM.maxFlevels); MesPrint("--MARK 6"); MesPrint("%d", AM.resetTimeOnClear); MesPrint("%d", AM.gcNumDollars); MesPrint("%d", AM.MultiRun); MesPrint("%d", AM.gNoSpacesInNumbers); MesPrint("%d", AM.ggNoSpacesInNumbers); MesPrint("%d", AM.MaxTal); MesPrint("%d", AM.IndDum); MesPrint("%d", AM.DumInd); MesPrint("%d", AM.WilInd); MesPrint("%d", AM.gncmod); MesPrint("%d", AM.gnpowmod); MesPrint("%d", AM.gmodmode); MesPrint("--MARK 7"); MesPrint("%d", AM.gUnitTrace); MesPrint("%d", AM.gOutputMode); MesPrint("%d", AM.gCnumpows); MesPrint("%d", AM.gOutputSpaces); MesPrint("%d", AM.gOutNumberType); MesPrint("%d %d %d %d", AM.gUniTrace[0], AM.gUniTrace[1], AM.gUniTrace[2], AM.gUniTrace[3]); MesPrint("%d", AM.MaxWildcards); MesPrint("%d", AM.mTraceDum); MesPrint("%d", AM.OffsetIndex); MesPrint("%d", AM.OffsetVector); MesPrint("%d", AM.RepMax); MesPrint("%d", AM.LogType); MesPrint("%d", AM.ggStatsFlag); MesPrint("%d", AM.gLineLength); MesPrint("%d", AM.qError); MesPrint("--MARK 8"); MesPrint("%d", AM.FortranCont); MesPrint("%d", AM.HoldFlag); MesPrint("%d %d %d %d %d", AM.Ordering[0], AM.Ordering[1], AM.Ordering[2], AM.Ordering[3], AM.Ordering[4]); MesPrint("%d %d %d %d %d", AM.Ordering[5], AM.Ordering[6], AM.Ordering[7], AM.Ordering[8], AM.Ordering[9]); MesPrint("%d %d %d %d %d", AM.Ordering[10], AM.Ordering[11], AM.Ordering[12], AM.Ordering[13], AM.Ordering[14]); MesPrint("%d", AM.silent); MesPrint("%d", AM.tracebackflag); MesPrint("%d", AM.expnum); MesPrint("%d", AM.denomnum); MesPrint("%d", AM.facnum); MesPrint("%d", AM.invfacnum); MesPrint("%d", AM.sumnum); MesPrint("%d", AM.sumpnum); MesPrint("--MARK 9"); MesPrint("%d", AM.OldOrderFlag); MesPrint("%d", AM.termfunnum); MesPrint("%d", AM.matchfunnum); MesPrint("%d", AM.countfunnum); MesPrint("%d", AM.gPolyFun); MesPrint("%d", AM.gPolyFunInv); MesPrint("%d", AM.gPolyFunType); MesPrint("%d", AM.gPolyFunExp); MesPrint("%d", AM.gPolyFunVar); MesPrint("%d", AM.gPolyFunPow); MesPrint("--MARK 10"); MesPrint("%d", AM.dollarzero); MesPrint("%d", AM.atstartup); MesPrint("%d", AM.exitflag); MesPrint("%d", AM.NumStoreCaches); MesPrint("%d", AM.gIndentSpace); MesPrint("%d", AM.ggIndentSpace); MesPrint("%d", AM.gShortStatsMax); MesPrint("%d", AM.ggShortStatsMax); MesPrint("--MARK 11"); MesPrint("%d", AM.FromStdin); MesPrint("%d", AM.IgnoreDeprecation); MesPrint("%%%% END M_const"); /* fflush(0); */ } static void print_P() { int i; MesPrint("%%%% P_const"); print_LIST(&AP.DollarList); for ( i=0; iname); MesPrint("%l", (LONG)(AR.outfile-AR.Fscr)); MesPrint("%s", AR.outfile->name); MesPrint("%l", AR.hidefile-AR.Fscr); MesPrint("%s", AR.hidefile->name); for ( i=0; i<3; ++i ) { MesPrint("FSCR %d", i); print_WORDB(AR.Fscr[i].PObuffer, AR.Fscr[i].POfull); } /* ... */ MesPrint("%l", AR.OldTime); MesPrint("%l", AR.InInBuf); MesPrint("%l", AR.InHiBuf); MesPrint("%l", AR.pWorkSize); MesPrint("%l", AR.lWorkSize); MesPrint("%l", AR.posWorkSize); MesPrint("%d", AR.NoCompress); MesPrint("%d", AR.gzipCompress); MesPrint("%d", AR.Cnumlhs); #ifdef WITHPTHREADS MesPrint("%d", AR.exprtodo); #endif MesPrint("%d", AR.GetFile); MesPrint("%d", AR.KeptInHold); MesPrint("%d", AR.BracketOn); MesPrint("%d", AR.MaxBracket); MesPrint("%d", AR.CurDum); MesPrint("%d", AR.DeferFlag); MesPrint("%d", AR.TePos); MesPrint("%d", AR.sLevel); MesPrint("%d", AR.Stage4Name); MesPrint("%d", AR.GetOneFile); MesPrint("%d", AR.PolyFun); MesPrint("%d", AR.PolyFunInv); MesPrint("%d", AR.PolyFunType); MesPrint("%d", AR.PolyFunExp); MesPrint("%d", AR.PolyFunVar); MesPrint("%d", AR.PolyFunPow); MesPrint("%d", AR.Eside); MesPrint("%d", AR.MaxDum); MesPrint("%d", AR.level); MesPrint("%d", AR.expchanged); MesPrint("%d", AR.expflags); MesPrint("%d", AR.CurExpr); MesPrint("%d", AR.SortType); MesPrint("%d", AR.ShortSortCount); MesPrint("%%%% END R_const"); /* fflush(0); */ } #endif /* ifdef PRINTDEBUG */ /* #] Debugging : #[ Cached file operation functions : */ #define CACHED_SNAPSHOT #define CACHE_SIZE 4096 #ifdef CACHED_SNAPSHOT unsigned char cache_buffer[CACHE_SIZE]; size_t cache_fill = 0; size_t fwrite_cached(const void *ptr, size_t size, size_t nmemb, FILE *fd) { size_t fullsize = size*nmemb; if ( fullsize+cache_fill >= CACHE_SIZE ) { size_t overlap = CACHE_SIZE-cache_fill; memcpy(cache_buffer+cache_fill, (unsigned char*)ptr, overlap); if ( fwrite(cache_buffer, 1, CACHE_SIZE, fd) != CACHE_SIZE ) return 0; fullsize -= overlap; if ( fullsize >= CACHE_SIZE ) { cache_fill = fullsize % CACHE_SIZE; if ( cache_fill ) memcpy(cache_buffer, (unsigned char*)ptr+overlap+fullsize-cache_fill, cache_fill); if ( fwrite((unsigned char*)ptr+overlap, 1, fullsize-cache_fill, fd) != fullsize-cache_fill ) return 0; } else { memcpy(cache_buffer, (unsigned char*)ptr+overlap, fullsize); cache_fill = fullsize; } } else { memcpy(cache_buffer+cache_fill, (unsigned char*)ptr, fullsize); cache_fill += fullsize; } return nmemb; } size_t flush_cache(FILE *fd) { if ( cache_fill ) { size_t retval = fwrite(cache_buffer, 1, cache_fill, fd); if ( retval != cache_fill ) { cache_fill = 0; return 0; } cache_fill = 0; } return 1; } #else size_t fwrite_cached(const void *ptr, size_t size, size_t nmemb, FILE *fd) { return fwrite(ptr, size, nmemb, fd); } size_t flush_cache(FILE *fd) { DUMMYUSE(fd) return 1; } #endif /* #] Cached file operation functions : #[ Helper Macros : */ /* some helper macros to streamline the code in DoSnapshot() and DoRecovery() */ /* freeing memory */ #define R_FREE(ARG) \ if ( ARG ) M_free(ARG, #ARG); #define R_FREE_NAMETREE(ARG) \ R_FREE(ARG->namenode); \ R_FREE(ARG->namebuffer); \ R_FREE(ARG); #define R_FREE_STREAM(ARG) \ R_FREE(ARG.buffer); \ R_FREE(ARG.FoldName); \ R_FREE(ARG.name); /* reading a single variable */ #define R_SET(VAR,TYPE) \ VAR = *((TYPE*)p); p = (unsigned char*)p + sizeof(TYPE); /* general buffer */ #define R_COPY_B(VAR,SIZE,CAST) \ VAR = (CAST)Malloc1(SIZE,#VAR); \ memcpy(VAR, p, SIZE); p = (unsigned char*)p + SIZE; #define S_WRITE_B(BUF,LEN) \ if ( fwrite_cached(BUF, 1, LEN, fd) != (size_t)(LEN) ) return(__LINE__); #define S_FLUSH_B \ if ( flush_cache(fd) != 1 ) return(__LINE__); /* character strings */ #define R_COPY_S(VAR,CAST) \ if ( VAR ) { \ VAR = (CAST)Malloc1(strlen(p)+1,"R_COPY_S"); \ strcpy((char*)VAR, p); p = (unsigned char*)p + strlen(p) + 1; \ } #define S_WRITE_S(STR) \ if ( STR ) { \ l = strlen((char*)STR) + 1; \ if ( fwrite_cached(STR, 1, l, fd) != (size_t)l ) return(__LINE__); \ } /* LIST */ #define R_COPY_LIST(ARG) \ if ( ARG.maxnum ) { \ R_COPY_B(ARG.lijst, ARG.size*ARG.maxnum, void*) \ } #define S_WRITE_LIST(LST) \ if ( LST.maxnum ) { \ S_WRITE_B((char*)LST.lijst, LST.maxnum*LST.size) \ } /* NAMETREE */ #define R_COPY_NAMETREE(ARG) \ R_COPY_B(ARG, sizeof(NAMETREE), NAMETREE*); \ if ( ARG->namenode ) { \ R_COPY_B(ARG->namenode, ARG->nodesize*sizeof(NAMENODE), NAMENODE*); \ } \ if ( ARG->namebuffer ) { \ R_COPY_B(ARG->namebuffer, ARG->namesize, UBYTE*); \ } #define S_WRITE_NAMETREE(ARG) \ S_WRITE_B(ARG, sizeof(NAMETREE)); \ if ( ARG->namenode ) { \ S_WRITE_B(ARG->namenode, ARG->nodesize*sizeof(struct NaMeNode)); \ } \ if ( ARG->namebuffer ) { \ S_WRITE_B(ARG->namebuffer, ARG->namesize); \ } /* DOLLAR */ #define S_WRITE_DOLLAR(ARG) \ if ( ARG.size && ARG.where && ARG.where != &(AM.dollarzero) ) { \ S_WRITE_B(ARG.where, ARG.size*sizeof(WORD)) \ } /* Printing time marks with ANNOUNCE macro */ #ifdef PRINTTIMEMARKS time_t announce_time; #define ANNOUNCE(str) time(&announce_time); MesPrint("TIMEMARK %s %s", ctime(&announce_time), #str); #else #define ANNOUNCE(str) #endif /* #] Helper Macros : #[ DoRecovery : */ /** * Reads from the recovery file and restores all necessary variables and * states in FORM, so that the execution can recommence in preprocessor() as * if no restart of FORM had occurred. * * The recovery file is read into memory as a whole. The pointer p then points * into this memory at the next non-processed data. The macros by which * variables are restored, like R_SET, automatically increase p appropriately. * * If something goes wrong, the function returns with a non-zero value. * * Allocated memory that would be lost when overwriting the global structs with * data from the file is freed first. A major part of the code deals with the * restoration of pointers. The idiom we use is to memorize the original * pointer value (org), allocate new memory and copy the data from the file * into this memory, calculate the offset between the old pointer value * and the new allocated memory position (ofs), and then correct all affected * pointers (+=ofs). * * We rely on the fact that several variables (especially in AM) are already * assigned the correct values by the startup functions. That means, in * principle, that a change in the setup files between snapshot creation and * recovery will be noticed. */ int DoRecovery(int *moduletype) { GETIDENTITY FILE *fd; POSITION pos; void *buf, *p; LONG size, l; int i, j; UBYTE *org; char *namebufout, *namebufhide; LONG ofs; void *oldAMdollarzero; LIST PotModDolListBackup; LIST ModOptDolListBackup; WORD oldLogHandle; MesPrint("Recovering ... %"); fflush(0); if ( !(fd = fopen(recoveryfile, "r")) ) return(__LINE__); /* load the complete recovery file into a buffer */ if ( fread(&pos, sizeof(POSITION), 1, fd) != 1 ) return(__LINE__); size = BASEPOSITION(pos) - sizeof(POSITION); buf = Malloc1(size, "recovery buffer"); if ( fread(buf, size, 1, fd) != 1 ) return(__LINE__); /* pointer p will go through the buffer in the following */ p = buf; /* read moduletype */ R_SET(*moduletype, int); /*#[ AM : */ /* only certain elements will be restored. the rest of AM should have gotten * the correct values at startup. */ R_SET(AM.hparallelflag, int); R_SET(AM.gparallelflag, int); R_SET(AM.gCodesFlag, int); R_SET(AM.gNamesFlag, int); R_SET(AM.gStatsFlag, int); R_SET(AM.gTokensWriteFlag, int); R_SET(AM.gNoSpacesInNumbers, int); R_SET(AM.gIndentSpace, WORD); R_SET(AM.gUnitTrace, WORD); R_SET(AM.gDefDim, int); R_SET(AM.gDefDim4, int); R_SET(AM.gncmod, WORD); R_SET(AM.gnpowmod, WORD); R_SET(AM.gmodmode, WORD); R_SET(AM.gOutputMode, WORD); R_SET(AM.gCnumpows, WORD); R_SET(AM.gOutputSpaces, WORD); R_SET(AM.gOutNumberType, WORD); R_SET(AM.gfunpowers, int); R_SET(AM.gPolyFun, WORD); R_SET(AM.gPolyFunInv, WORD); R_SET(AM.gPolyFunType, WORD); R_SET(AM.gPolyFunExp, WORD); R_SET(AM.gPolyFunVar, WORD); R_SET(AM.gPolyFunPow, WORD); R_SET(AM.gProcessBucketSize, LONG); R_SET(AM.OldChildTime, LONG); R_SET(AM.OldSecTime, LONG); R_SET(AM.OldMilliTime, LONG); R_SET(AM.gproperorderflag, int); R_SET(AM.gThreadBucketSize, LONG); R_SET(AM.gSizeCommuteInSet, int); R_SET(AM.gThreadStats, int); R_SET(AM.gFinalStats, int); R_SET(AM.gThreadsFlag, int); R_SET(AM.gThreadBalancing, int); R_SET(AM.gThreadSortFileSynch, int); R_SET(AM.gProcessStats, int); R_SET(AM.gOldParallelStats, int); R_SET(AM.gSortType, int); R_SET(AM.gShortStatsMax, WORD); R_SET(AM.gIsFortran90, int); R_SET(oldAMdollarzero, void*); R_FREE(AM.gFortran90Kind); R_SET(AM.gFortran90Kind,UBYTE *); R_COPY_S(AM.gFortran90Kind,UBYTE *); R_COPY_S(AM.gextrasym,UBYTE *); R_COPY_S(AM.ggextrasym,UBYTE *); R_SET(AM.PrintTotalSize,int); R_SET(AM.fbuffersize,int); R_SET(AM.gOldFactArgFlag,int); R_SET(AM.ggOldFactArgFlag,int); R_SET(AM.gnumextrasym,int); R_SET(AM.ggnumextrasym,int); R_SET(AM.NumSpectatorFiles,int); R_SET(AM.SizeForSpectatorFiles,int); R_SET(AM.gOldGCDflag,int); R_SET(AM.ggOldGCDflag,int); R_SET(AM.gWTimeStatsFlag, int); R_FREE(AM.Path); R_SET(AM.Path,UBYTE *); R_COPY_S(AM.Path,UBYTE *); R_SET(AM.FromStdin, BOOL); R_SET(AM.IgnoreDeprecation, BOOL); #ifdef PRINTDEBUG print_M(); #endif /*#] AM : */ /*#[ AC : */ /* #[ AC free pointers */ /* AC will be overwritten by data from the recovery file, therefore * dynamically allocated memory must be freed first. */ R_FREE_NAMETREE(AC.dollarnames); R_FREE_NAMETREE(AC.exprnames); R_FREE_NAMETREE(AC.varnames); for ( i=0; ibuffers); R_FREE(T->mm); R_FREE(T->flags); R_FREE(T->prototype); R_FREE(T->tablepointers); if ( T->sparse ) { R_FREE(T->boomlijst); R_FREE(T->argtail); } if ( T->spare ) { R_FREE(T->spare->buffers); R_FREE(T->spare->mm); R_FREE(T->spare->flags); R_FREE(T->spare->tablepointers); if ( T->spare->sparse ) { R_FREE(T->spare->boomlijst); } R_FREE(T->spare); } R_FREE(T); } } R_FREE(AC.FunctionList.lijst); for ( i=0; isymb.lo); R_FREE(Expressions[i].renum); } if ( Expressions[i].bracketinfo ) { R_FREE(Expressions[i].bracketinfo->indexbuffer); R_FREE(Expressions[i].bracketinfo->bracketbuffer); R_FREE(Expressions[i].bracketinfo); } if ( Expressions[i].newbracketinfo ) { R_FREE(Expressions[i].newbracketinfo->indexbuffer); R_FREE(Expressions[i].newbracketinfo->bracketbuffer); R_FREE(Expressions[i].newbracketinfo); } if ( Expressions[i].renumlists != AN.dummyrenumlist ) { R_FREE(Expressions[i].renumlists); } R_FREE(Expressions[i].inmem); } R_FREE(AC.ExpressionList.lijst); R_FREE(AC.IndexList.lijst); R_FREE(AC.SetElementList.lijst); R_FREE(AC.SetList.lijst); R_FREE(AC.SymbolList.lijst); R_FREE(AC.VectorList.lijst); for ( i=0; itablepointers ) { if ( tabl->sparse ) { R_COPY_B(tabl->tablepointers, tabl->reserved*sizeof(WORD)*(tabl->numind+TABLEEXTENSION), WORD*); } else { R_COPY_B(tabl->tablepointers, TABLEEXTENSION*sizeof(WORD)*(tabl->totind), WORD*); } } org = (UBYTE*)tabl->prototype; #ifdef WITHPTHREADS R_COPY_B(tabl->prototype, tabl->prototypeSize, WORD**); ofs = (UBYTE*)tabl->prototype - org; for ( j=0; jprototype[j] ) { tabl->prototype[j] = (WORD*)((UBYTE*)tabl->prototype[j] + ofs); } } if ( tabl->pattern ) { tabl->pattern = (WORD**)((UBYTE*)tabl->pattern + ofs); for ( j=0; jpattern[j] ) { tabl->pattern[j] = (WORD*)((UBYTE*)tabl->pattern[j] + ofs); } } } #else ofs = tabl->pattern - tabl->prototype; R_COPY_B(tabl->prototype, tabl->prototypeSize, WORD*); if ( tabl->pattern ) { tabl->pattern = tabl->prototype + ofs; } #endif R_COPY_B(tabl->mm, tabl->numind*(LONG)sizeof(MINMAX), MINMAX*); R_COPY_B(tabl->flags, tabl->numind*(LONG)sizeof(WORD), WORD*); if ( tabl->sparse ) { R_COPY_B(tabl->boomlijst, tabl->MaxTreeSize*(LONG)sizeof(COMPTREE), COMPTREE*); R_COPY_S(tabl->argtail,UBYTE*); } R_COPY_B(tabl->buffers, tabl->bufferssize*(LONG)sizeof(WORD), WORD*); if ( tabl->spare ) { TABLES spare; R_COPY_B(spare, sizeof(struct TaBlEs), TABLES); tabl->spare = spare; if ( spare->tablepointers ) { if ( spare->sparse ) { R_COPY_B(spare->tablepointers, spare->reserved*sizeof(WORD)*(spare->numind+TABLEEXTENSION), WORD*); } else { R_COPY_B(spare->tablepointers, TABLEEXTENSION*sizeof(WORD)*(spare->totind), WORD*); } } spare->prototype = tabl->prototype; spare->pattern = tabl->pattern; R_COPY_B(spare->mm, spare->numind*(LONG)sizeof(MINMAX), MINMAX*); R_COPY_B(spare->flags, spare->numind*(LONG)sizeof(WORD), WORD*); if ( tabl->sparse ) { R_COPY_B(spare->boomlijst, spare->MaxTreeSize*(LONG)sizeof(COMPTREE), COMPTREE*); spare->argtail = tabl->argtail; } spare->spare = tabl; R_COPY_B(spare->buffers, spare->bufferssize*(LONG)sizeof(WORD), WORD*); } } } AC.FunctionList.message = "function"; R_COPY_LIST(AC.ExpressionList); for ( i=0; irenum ) { R_COPY_B(ex->renum, sizeof(struct ReNuMbEr), RENUMBER); org = (UBYTE*)ex->renum->symb.lo; R_SET(size, size_t); R_COPY_B(ex->renum->symb.lo, size, WORD*); ofs = (UBYTE*)ex->renum->symb.lo - org; ex->renum->symb.start = (WORD*)((UBYTE*)ex->renum->symb.start + ofs); ex->renum->symb.hi = (WORD*)((UBYTE*)ex->renum->symb.hi + ofs); ex->renum->indi.lo = (WORD*)((UBYTE*)ex->renum->indi.lo + ofs); ex->renum->indi.start = (WORD*)((UBYTE*)ex->renum->indi.start + ofs); ex->renum->indi.hi = (WORD*)((UBYTE*)ex->renum->indi.hi + ofs); ex->renum->vect.lo = (WORD*)((UBYTE*)ex->renum->vect.lo + ofs); ex->renum->vect.start = (WORD*)((UBYTE*)ex->renum->vect.start + ofs); ex->renum->vect.hi = (WORD*)((UBYTE*)ex->renum->vect.hi + ofs); ex->renum->func.lo = (WORD*)((UBYTE*)ex->renum->func.lo + ofs); ex->renum->func.start = (WORD*)((UBYTE*)ex->renum->func.start + ofs); ex->renum->func.hi = (WORD*)((UBYTE*)ex->renum->func.hi + ofs); ex->renum->symnum = (WORD*)((UBYTE*)ex->renum->symnum + ofs); ex->renum->indnum = (WORD*)((UBYTE*)ex->renum->indnum + ofs); ex->renum->vecnum = (WORD*)((UBYTE*)ex->renum->vecnum + ofs); ex->renum->funnum = (WORD*)((UBYTE*)ex->renum->funnum + ofs); } if ( ex->bracketinfo ) { R_COPY_B(ex->bracketinfo, sizeof(BRACKETINFO), BRACKETINFO*); R_COPY_B(ex->bracketinfo->indexbuffer, ex->bracketinfo->indexbuffersize*sizeof(BRACKETINDEX), BRACKETINDEX*); R_COPY_B(ex->bracketinfo->bracketbuffer, ex->bracketinfo->bracketbuffersize*sizeof(WORD), WORD*); } if ( ex->newbracketinfo ) { R_COPY_B(ex->newbracketinfo, sizeof(BRACKETINFO), BRACKETINFO*); R_COPY_B(ex->newbracketinfo->indexbuffer, ex->newbracketinfo->indexbuffersize*sizeof(BRACKETINDEX), BRACKETINDEX*); R_COPY_B(ex->newbracketinfo->bracketbuffer, ex->newbracketinfo->bracketbuffersize*sizeof(WORD), WORD*); } #ifdef WITHPTHREADS ex->renumlists = 0; #else ex->renumlists = AN.dummyrenumlist; #endif if ( ex->inmem ) { R_SET(size, size_t); R_COPY_B(ex->inmem, size, WORD*); } } AC.ExpressionList.message = "expression"; R_COPY_LIST(AC.IndexList); AC.IndexList.message = "index"; R_COPY_LIST(AC.SetElementList); AC.SetElementList.message = "set element"; R_COPY_LIST(AC.SetList); AC.SetList.message = "set"; R_COPY_LIST(AC.SymbolList); AC.SymbolList.message = "symbol"; R_COPY_LIST(AC.VectorList); AC.VectorList.message = "vector"; AC.PotModDolList = PotModDolListBackup; AC.ModOptDolList = ModOptDolListBackup; R_COPY_LIST(AC.TableBaseList); for ( i=0; isize * sizeof(WORD); if ( size && d->where && d->where != oldAMdollarzero ) { R_COPY_B(d->where, size, void*); } #ifdef WITHPTHREADS INIRECLOCK(d->pthreadslock); #endif if ( d->nfactors > 1 ) { R_COPY_B(d->factors,sizeof(FACDOLLAR)*d->nfactors,FACDOLLAR*); for ( j = 0; j < d->nfactors; j++ ) { if ( d->factors[j].size > 0 ) { R_COPY_B(d->factors[i].where,sizeof(WORD)*(d->factors[j].size+1),WORD*); } } } } AP.DollarList.message = "$-variable"; R_COPY_LIST(AP.PreVarList); for ( i=0; iname; namebufhide = AR.hidefile->name; R_FREE(AR.outfile->PObuffer); #ifdef WITHZLIB R_FREE(AR.outfile->zsp); R_FREE(AR.outfile->ziobuffer); #endif namebufhide = AR.hidefile->name; R_FREE(AR.hidefile->PObuffer); #ifdef WITHZLIB R_FREE(AR.hidefile->zsp); R_FREE(AR.hidefile->ziobuffer); #endif /* no files should be opened -> nothing to do with handle */ /* #] AR free pointers */ /* outfile */ R_SET(*AR.outfile, FILEHANDLE); org = (UBYTE*)AR.outfile->PObuffer; size = AR.outfile->POfull - AR.outfile->PObuffer; AR.outfile->PObuffer = (WORD*)Malloc1(AR.outfile->POsize, "PObuffer"); if ( size ) { memcpy(AR.outfile->PObuffer, p, size*sizeof(WORD)); p = (unsigned char*)p + size*sizeof(WORD); } ofs = (UBYTE*)AR.outfile->PObuffer - org; AR.outfile->POstop = (WORD*)((UBYTE*)AR.outfile->POstop + ofs); AR.outfile->POfill = (WORD*)((UBYTE*)AR.outfile->POfill + ofs); AR.outfile->POfull = (WORD*)((UBYTE*)AR.outfile->POfull + ofs); AR.outfile->name = namebufout; #ifdef WITHPTHREADS AR.outfile->wPObuffer = AR.outfile->PObuffer; AR.outfile->wPOstop = AR.outfile->POstop; AR.outfile->wPOfill = AR.outfile->POfill; AR.outfile->wPOfull = AR.outfile->POfull; #endif #ifdef WITHZLIB /* zsp and ziobuffer will be allocated when used */ AR.outfile->zsp = 0; AR.outfile->ziobuffer = 0; #endif /* reopen old outfile */ #ifdef WITHMPI if(PF.me==MASTER) #endif if ( AR.outfile->handle >= 0 ) { if ( CopyFile(sortfile, AR.outfile->name) ) { MesPrint("ERROR: Could not copy old output sort file %s!",sortfile); Terminate(-1); } AR.outfile->handle = ReOpenFile(AR.outfile->name); if ( AR.outfile->handle == -1 ) { MesPrint("ERROR: Could not reopen output sort file %s!",AR.outfile->name); Terminate(-1); } SeekFile(AR.outfile->handle, &AR.outfile->POposition, SEEK_SET); } /* hidefile */ R_SET(*AR.hidefile, FILEHANDLE); AR.hidefile->name = namebufhide; if ( AR.hidefile->PObuffer ) { org = (UBYTE*)AR.hidefile->PObuffer; size = AR.hidefile->POfull - AR.hidefile->PObuffer; AR.hidefile->PObuffer = (WORD*)Malloc1(AR.hidefile->POsize, "PObuffer"); if ( size ) { memcpy(AR.hidefile->PObuffer, p, size*sizeof(WORD)); p = (unsigned char*)p + size*sizeof(WORD); } ofs = (UBYTE*)AR.hidefile->PObuffer - org; AR.hidefile->POstop = (WORD*)((UBYTE*)AR.hidefile->POstop + ofs); AR.hidefile->POfill = (WORD*)((UBYTE*)AR.hidefile->POfill + ofs); AR.hidefile->POfull = (WORD*)((UBYTE*)AR.hidefile->POfull + ofs); #ifdef WITHPTHREADS AR.hidefile->wPObuffer = AR.hidefile->PObuffer; AR.hidefile->wPOstop = AR.hidefile->POstop; AR.hidefile->wPOfill = AR.hidefile->POfill; AR.hidefile->wPOfull = AR.hidefile->POfull; #endif } #ifdef WITHZLIB /* zsp and ziobuffer will be allocated when used */ AR.hidefile->zsp = 0; AR.hidefile->ziobuffer = 0; #endif /* reopen old hidefile */ if ( AR.hidefile->handle >= 0 ) { if ( CopyFile(hidefile, AR.hidefile->name) ) { MesPrint("ERROR: Could not copy old hide file %s!",hidefile); Terminate(-1); } AR.hidefile->handle = ReOpenFile(AR.hidefile->name); if ( AR.hidefile->handle == -1 ) { MesPrint("ERROR: Could not reopen hide file %s!",AR.hidefile->name); Terminate(-1); } SeekFile(AR.hidefile->handle, &AR.hidefile->POposition, SEEK_SET); } /* store file */ R_SET(pos, POSITION); if ( ISNOTZEROPOS(pos) ) { CloseFile(AR.StoreData.Handle); R_SET(AR.StoreData, FILEDATA); if ( CopyFile(storefile, FG.fname) ) { MesPrint("ERROR: Could not copy old store file %s!",storefile); Terminate(-1); } AR.StoreData.Handle = (WORD)ReOpenFile(FG.fname); SeekFile(AR.StoreData.Handle, &AR.StoreData.Position, SEEK_SET); } R_SET(AR.DefPosition, POSITION); R_SET(AR.OldTime, LONG); R_SET(AR.InInBuf, LONG); R_SET(AR.InHiBuf, LONG); R_SET(AR.NoCompress, int); R_SET(AR.gzipCompress, int); R_SET(AR.outtohide, int); R_SET(AR.GetFile, WORD); R_SET(AR.KeptInHold, WORD); R_SET(AR.BracketOn, WORD); R_SET(AR.MaxBracket, WORD); R_SET(AR.CurDum, WORD); R_SET(AR.DeferFlag, WORD); R_SET(AR.TePos, WORD); R_SET(AR.sLevel, WORD); R_SET(AR.Stage4Name, WORD); R_SET(AR.GetOneFile, WORD); R_SET(AR.PolyFun, WORD); R_SET(AR.PolyFunInv, WORD); R_SET(AR.PolyFunType, WORD); R_SET(AR.PolyFunExp, WORD); R_SET(AR.PolyFunVar, WORD); R_SET(AR.PolyFunPow, WORD); R_SET(AR.Eside, WORD); R_SET(AR.MaxDum, WORD); R_SET(AR.level, WORD); R_SET(AR.expchanged, WORD); R_SET(AR.expflags, WORD); R_SET(AR.CurExpr, WORD); R_SET(AR.SortType, WORD); R_SET(AR.ShortSortCount, WORD); /* this is usually done in Process(), but sometimes FORM does not end up executing Process() before it uses the AR.CompressPointer, so we need to explicitly set it here. */ AR.CompressPointer = AR.CompressBuffer; #ifdef WITHPTHREADS for ( j = 0; j < AM.totalnumberofthreads; j++ ) { R_SET(AB[j]->R.wranfnpair1, int); R_SET(AB[j]->R.wranfnpair2, int); R_SET(AB[j]->R.wranfcall, int); R_SET(AB[j]->R.wranfseed, ULONG); R_SET(AB[j]->R.wranfia,ULONG*); if ( AB[j]->R.wranfia ) { R_COPY_B(AB[j]->R.wranfia, sizeof(ULONG)*AB[j]->R.wranfnpair2, ULONG*); } } #else R_SET(AR.wranfnpair1, int); R_SET(AR.wranfnpair2, int); R_SET(AR.wranfcall, int); R_SET(AR.wranfseed, ULONG); R_SET(AR.wranfia,ULONG*); if ( AR.wranfia ) { R_COPY_B(AR.wranfia, sizeof(ULONG)*AR.wranfnpair2, ULONG*); } #endif #ifdef PRINTDEBUG print_R(); #endif /*#] AR : */ /*#[ AO :*/ /* We copy all non-pointer variables. */ l = sizeof(A.O) - ((UBYTE *)(&(A.O.NumInBrack))-(UBYTE *)(&A.O)); memcpy(&(A.O.NumInBrack), p, l); p = (unsigned char*)p + l; /* Now the variables in OptimizeResult */ memcpy(&(A.O.OptimizeResult),p,sizeof(OPTIMIZERESULT)); p = (unsigned char*)p + sizeof(OPTIMIZERESULT); if ( A.O.OptimizeResult.codesize > 0 ) { R_COPY_B(A.O.OptimizeResult.code,A.O.OptimizeResult.codesize*sizeof(WORD),WORD *); } R_COPY_S(A.O.OptimizeResult.nameofexpr,UBYTE *); /* And now the dictionaries. We know how many there are. We also know how many elements the array AO.Dictionaries should have. */ if ( AO.SizeDictionaries > 0 ) { AO.Dictionaries = (DICTIONARY **)Malloc1(AO.SizeDictionaries*sizeof(DICTIONARY *), "Dictionaries"); for ( i = 0; i < AO.NumDictionaries; i++ ) { R_SET(l,LONG) AO.Dictionaries[i] = DictFromBytes(p); p = (char *)p + l; } } /*#] AO :*/ #ifdef WITHMPI /*#[ PF : */ {/*Block*/ int numtasks; R_SET(numtasks, int); if(numtasks!=PF.numtasks){ MesPrint("%d number of tasks expected instead of %d; use mpirun -np %d", numtasks,PF.numtasks,numtasks); if(PF.me!=MASTER) remove(RecoveryFilename()); Terminate(-1); } }/*Block*/ R_SET(PF.rhsInParallel, int); R_SET(PF.exprbufsize, int); R_SET(PF.log, int); /*#] PF : */ #endif #ifdef WITHPTHREADS /* read timing information of individual threads */ R_SET(i, int); for ( j=1; jR.OldTime = -(*((LONG*)p+j)); } WriteTimerInfo((LONG*)p,(LONG *)((unsigned char*)p + i*(LONG)sizeof(LONG))); p = (unsigned char*)p + 2*i*(LONG)sizeof(LONG); #endif /* ifdef WITHPTHREADS */ if ( fclose(fd) ) return(__LINE__); M_free(buf,"recovery buffer"); /* cares about data in S_const */ UpdatePositions(); AT.SS = AT.S0; /* Set the checkpoint parameter right for the next checkpoint. */ AC.CheckpointStamp = TimeWallClock(1); done_snapshot = 1; MesPrint("done."); fflush(0); return(0); } /* #] DoRecovery : #[ DoSnapshot : */ /** * Writes all relevant information for a recovery to the recovery file. It * writes first to an intermediate file and then only if everything went well * it renames this intermediate file to the final recovery file. Then it copies * the sort and store files if necessary. * * The data is directly written to file from the structs or struct element. * * No data is changed in the global structs and this function should never crash. * Honorably exception might be: not enough memory for the allocation of the * command strings (usually less than 100 bytes), or not enough disk space for * the recovery file and the copies of the hide/scratch/store files. * * If something goes wrong, the function returns with a non-zero value. */ static int DoSnapshot(int moduletype) { GETIDENTITY FILE *fd; POSITION pos; int i, j; LONG l; WORD *w; void *adr; #ifdef WITHPTHREADS LONG *longp,*longpp; #endif /* ifdef WITHPTHREADS */ MesPrint("Saving recovery point ... %"); fflush(0); #ifdef PRINTTIMEMARKS MesPrint("\n"); #endif if ( !(fd = fopen(intermedfile, "wb")) ) return(__LINE__); /* reserve space in the file for a length field */ if ( fwrite(&pos, 1, sizeof(POSITION), fd) != sizeof(POSITION) ) return(__LINE__); /* write moduletype */ if ( fwrite(&moduletype, 1, sizeof(int), fd) != sizeof(int) ) return(__LINE__); /*#[ AM :*/ /* since most values don't change during execution, AM doesn't need to be * written as a whole. all values will be correctly set when starting up * anyway. only the exceptions need to be taken care of. see MakeGlobal() * and PopVariables() in execute.c. */ ANNOUNCE(AM) S_WRITE_B(&AM.hparallelflag, sizeof(int)); S_WRITE_B(&AM.gparallelflag, sizeof(int)); S_WRITE_B(&AM.gCodesFlag, sizeof(int)); S_WRITE_B(&AM.gNamesFlag, sizeof(int)); S_WRITE_B(&AM.gStatsFlag, sizeof(int)); S_WRITE_B(&AM.gTokensWriteFlag, sizeof(int)); S_WRITE_B(&AM.gNoSpacesInNumbers, sizeof(int)); S_WRITE_B(&AM.gIndentSpace, sizeof(WORD)); S_WRITE_B(&AM.gUnitTrace, sizeof(WORD)); S_WRITE_B(&AM.gDefDim, sizeof(int)); S_WRITE_B(&AM.gDefDim4, sizeof(int)); S_WRITE_B(&AM.gncmod, sizeof(WORD)); S_WRITE_B(&AM.gnpowmod, sizeof(WORD)); S_WRITE_B(&AM.gmodmode, sizeof(WORD)); S_WRITE_B(&AM.gOutputMode, sizeof(WORD)); S_WRITE_B(&AM.gCnumpows, sizeof(WORD)); S_WRITE_B(&AM.gOutputSpaces, sizeof(WORD)); S_WRITE_B(&AM.gOutNumberType, sizeof(WORD)); S_WRITE_B(&AM.gfunpowers, sizeof(int)); S_WRITE_B(&AM.gPolyFun, sizeof(WORD)); S_WRITE_B(&AM.gPolyFunInv, sizeof(WORD)); S_WRITE_B(&AM.gPolyFunType, sizeof(WORD)); S_WRITE_B(&AM.gPolyFunExp, sizeof(WORD)); S_WRITE_B(&AM.gPolyFunVar, sizeof(WORD)); S_WRITE_B(&AM.gPolyFunPow, sizeof(WORD)); S_WRITE_B(&AM.gProcessBucketSize, sizeof(LONG)); S_WRITE_B(&AM.OldChildTime, sizeof(LONG)); S_WRITE_B(&AM.OldSecTime, sizeof(LONG)); S_WRITE_B(&AM.OldMilliTime, sizeof(LONG)); S_WRITE_B(&AM.gproperorderflag, sizeof(int)); S_WRITE_B(&AM.gThreadBucketSize, sizeof(LONG)); S_WRITE_B(&AM.gSizeCommuteInSet, sizeof(int)); S_WRITE_B(&AM.gThreadStats, sizeof(int)); S_WRITE_B(&AM.gFinalStats, sizeof(int)); S_WRITE_B(&AM.gThreadsFlag, sizeof(int)); S_WRITE_B(&AM.gThreadBalancing, sizeof(int)); S_WRITE_B(&AM.gThreadSortFileSynch, sizeof(int)); S_WRITE_B(&AM.gProcessStats, sizeof(int)); S_WRITE_B(&AM.gOldParallelStats, sizeof(int)); S_WRITE_B(&AM.gSortType, sizeof(int)); S_WRITE_B(&AM.gShortStatsMax, sizeof(WORD)); S_WRITE_B(&AM.gIsFortran90, sizeof(int)); adr = &AM.dollarzero; S_WRITE_B(&adr, sizeof(void*)); S_WRITE_B(&AM.gFortran90Kind,sizeof(UBYTE *)); S_WRITE_S(AM.gFortran90Kind); S_WRITE_S(AM.gextrasym); S_WRITE_S(AM.ggextrasym); S_WRITE_B(&AM.PrintTotalSize,sizeof(int)); S_WRITE_B(&AM.fbuffersize,sizeof(int)); S_WRITE_B(&AM.gOldFactArgFlag,sizeof(int)); S_WRITE_B(&AM.ggOldFactArgFlag,sizeof(int)); S_WRITE_B(&AM.gnumextrasym,sizeof(int)); S_WRITE_B(&AM.ggnumextrasym,sizeof(int)); S_WRITE_B(&AM.NumSpectatorFiles,sizeof(int)); S_WRITE_B(&AM.SizeForSpectatorFiles,sizeof(int)); S_WRITE_B(&AM.gOldGCDflag,sizeof(int)); S_WRITE_B(&AM.ggOldGCDflag,sizeof(int)); S_WRITE_B(&AM.gWTimeStatsFlag, sizeof(int)); S_WRITE_B(&AM.Path,sizeof(UBYTE *)); S_WRITE_S(AM.Path); S_WRITE_B(&AM.FromStdin,sizeof(BOOL)); S_WRITE_B(&AM.IgnoreDeprecation,sizeof(BOOL)); /*#] AM :*/ /*#[ AC :*/ /* we write AC as a whole and then write all additional data step by step. * AC.DubiousList doesn't need to be treated, because it should be empty. */ ANNOUNCE(AC) S_WRITE_B(&AC, sizeof(struct C_const)); S_WRITE_NAMETREE(AC.dollarnames); S_WRITE_NAMETREE(AC.exprnames); S_WRITE_NAMETREE(AC.varnames); S_WRITE_LIST(AC.ChannelList); for ( i=0; itablepointers ) { if ( tabl->sparse ) { /* sparse tables. reserved holds number of allocated * elements. the size of an element is numind plus * TABLEEXTENSION times the size of WORD. */ S_WRITE_B(tabl->tablepointers, tabl->reserved*sizeof(WORD)*(tabl->numind+TABLEEXTENSION)); } else { /* matrix like tables. */ S_WRITE_B(tabl->tablepointers, TABLEEXTENSION*sizeof(WORD)*(tabl->totind)); } } S_WRITE_B(tabl->prototype, tabl->prototypeSize); S_WRITE_B(tabl->mm, tabl->numind*(LONG)sizeof(MINMAX)); S_WRITE_B(tabl->flags, tabl->numind*(LONG)sizeof(WORD)); if ( tabl->sparse ) { S_WRITE_B(tabl->boomlijst, tabl->MaxTreeSize*(LONG)sizeof(COMPTREE)); S_WRITE_S(tabl->argtail); } S_WRITE_B(tabl->buffers, tabl->bufferssize*(LONG)sizeof(WORD)); if ( tabl->spare ) { TABLES spare = tabl->spare; S_WRITE_B(spare, sizeof(struct TaBlEs)); if ( spare->tablepointers ) { if ( spare->sparse ) { /* sparse tables */ S_WRITE_B(spare->tablepointers, spare->reserved*sizeof(WORD)*(spare->numind+TABLEEXTENSION)); } else { /* matrix like tables */ S_WRITE_B(spare->tablepointers, TABLEEXTENSION*sizeof(WORD)*(spare->totind)); } } S_WRITE_B(spare->mm, spare->numind*(LONG)sizeof(MINMAX)); S_WRITE_B(spare->flags, spare->numind*(LONG)sizeof(WORD)); if ( spare->sparse ) { S_WRITE_B(spare->boomlijst, spare->MaxTreeSize*(LONG)sizeof(COMPTREE)); } S_WRITE_B(spare->buffers, spare->bufferssize*(LONG)sizeof(WORD)); } } } ANNOUNCE(AC.ExpressionList) S_WRITE_LIST(AC.ExpressionList); for ( i=0; irenum ) { S_WRITE_B(ex->renum, sizeof(struct ReNuMbEr)); /* there is one dynamically allocated buffer for struct ReNuMbEr and * symb.lo points to its beginning. the size of the buffer is not * stored anywhere but we know it is 2*sizeof(WORD)*N, where N is * the number of all vectors, indices, functions and symbols. since * funum points into the buffer at a distance 2N-[Number of * functions] from symb.lo (see GetTable() in store.c), we can * calculate the buffer size by some pointer arithmetic. the size is * then written to the file. */ l = ex->renum->funnum - ex->renum->symb.lo; l += ex->renum->funnum - ex->renum->func.lo; S_WRITE_B(&l, sizeof(size_t)); S_WRITE_B(ex->renum->symb.lo, l); } if ( ex->bracketinfo ) { S_WRITE_B(ex->bracketinfo, sizeof(BRACKETINFO)); S_WRITE_B(ex->bracketinfo->indexbuffer, ex->bracketinfo->indexbuffersize*sizeof(BRACKETINDEX)); S_WRITE_B(ex->bracketinfo->bracketbuffer, ex->bracketinfo->bracketbuffersize*sizeof(WORD)); } if ( ex->newbracketinfo ) { S_WRITE_B(ex->newbracketinfo, sizeof(BRACKETINFO)); S_WRITE_B(ex->newbracketinfo->indexbuffer, ex->newbracketinfo->indexbuffersize*sizeof(BRACKETINDEX)); S_WRITE_B(ex->newbracketinfo->bracketbuffer, ex->newbracketinfo->bracketbuffersize*sizeof(WORD)); } /* don't need to write ex->renumlists */ if ( ex->inmem ) { /* size of the inmem buffer has to be determined. we use the fact * that the end of an expression is marked by a zero. */ w = ex->inmem; while ( *w++ ) ; l = w - ex->inmem; S_WRITE_B(&l, sizeof(size_t)); S_WRITE_B(ex->inmem, l); } } ANNOUNCE(AC.IndexList) S_WRITE_LIST(AC.IndexList); S_WRITE_LIST(AC.SetElementList); S_WRITE_LIST(AC.SetList); S_WRITE_LIST(AC.SymbolList); S_WRITE_LIST(AC.VectorList); ANNOUNCE(AC.TableBaseList) S_WRITE_LIST(AC.TableBaseList); for ( i=0; infactors > 1 ) { S_WRITE_B(&(d->factors),sizeof(FACDOLLAR)*d->nfactors); for ( j = 0; j < d->nfactors; j++ ) { if ( d->factors[j].size > 0 ) { S_WRITE_B(&(d->factors[i].where),sizeof(WORD)*(d->factors[j].size+1)); } } } } S_WRITE_LIST(AP.PreVarList); for ( i=0; iPOfull - AR.outfile->PObuffer; if ( l ) { S_WRITE_B(AR.outfile->PObuffer, l*sizeof(WORD)); } S_WRITE_B(AR.hidefile, sizeof(FILEHANDLE)); l = AR.hidefile->POfull - AR.hidefile->PObuffer; if ( l ) { S_WRITE_B(AR.hidefile->PObuffer, l*sizeof(WORD)); } S_WRITE_B(&AR.StoreData.Fill, sizeof(POSITION)); if ( ISNOTZEROPOS(AR.StoreData.Fill) ) { S_WRITE_B(&AR.StoreData, sizeof(FILEDATA)); } S_WRITE_B(&AR.DefPosition, sizeof(POSITION)); l = TimeCPU(1); l = -l; S_WRITE_B(&l, sizeof(LONG)); ANNOUNCE(AR.InInBuf) S_WRITE_B(&AR.InInBuf, sizeof(LONG)); S_WRITE_B(&AR.InHiBuf, sizeof(LONG)); S_WRITE_B(&AR.NoCompress, sizeof(int)); S_WRITE_B(&AR.gzipCompress, sizeof(int)); S_WRITE_B(&AR.outtohide, sizeof(int)); S_WRITE_B(&AR.GetFile, sizeof(WORD)); S_WRITE_B(&AR.KeptInHold, sizeof(WORD)); S_WRITE_B(&AR.BracketOn, sizeof(WORD)); S_WRITE_B(&AR.MaxBracket, sizeof(WORD)); S_WRITE_B(&AR.CurDum, sizeof(WORD)); S_WRITE_B(&AR.DeferFlag, sizeof(WORD)); S_WRITE_B(&AR.TePos, sizeof(WORD)); S_WRITE_B(&AR.sLevel, sizeof(WORD)); S_WRITE_B(&AR.Stage4Name, sizeof(WORD)); S_WRITE_B(&AR.GetOneFile, sizeof(WORD)); S_WRITE_B(&AR.PolyFun, sizeof(WORD)); S_WRITE_B(&AR.PolyFunInv, sizeof(WORD)); S_WRITE_B(&AR.PolyFunType, sizeof(WORD)); S_WRITE_B(&AR.PolyFunExp, sizeof(WORD)); S_WRITE_B(&AR.PolyFunVar, sizeof(WORD)); S_WRITE_B(&AR.PolyFunPow, sizeof(WORD)); S_WRITE_B(&AR.Eside, sizeof(WORD)); S_WRITE_B(&AR.MaxDum, sizeof(WORD)); S_WRITE_B(&AR.level, sizeof(WORD)); S_WRITE_B(&AR.expchanged, sizeof(WORD)); S_WRITE_B(&AR.expflags, sizeof(WORD)); S_WRITE_B(&AR.CurExpr, sizeof(WORD)); S_WRITE_B(&AR.SortType, sizeof(WORD)); S_WRITE_B(&AR.ShortSortCount, sizeof(WORD)); #ifdef WITHPTHREADS for ( j = 0; j < AM.totalnumberofthreads; j++ ) { S_WRITE_B(&(AB[j]->R.wranfnpair1), sizeof(int)); S_WRITE_B(&(AB[j]->R.wranfnpair2), sizeof(int)); S_WRITE_B(&(AB[j]->R.wranfcall), sizeof(int)); S_WRITE_B(&(AB[j]->R.wranfseed), sizeof(ULONG)); S_WRITE_B(&(AB[j]->R.wranfia),sizeof(ULONG *)); if ( AB[j]->R.wranfia ) { S_WRITE_B(AB[j]->R.wranfia, sizeof(ULONG)*AB[j]->R.wranfnpair2); } } #else S_WRITE_B(&(AR.wranfnpair1), sizeof(int)); S_WRITE_B(&(AR.wranfnpair2), sizeof(int)); S_WRITE_B(&(AR.wranfcall), sizeof(int)); S_WRITE_B(&(AR.wranfseed), sizeof(ULONG)); S_WRITE_B(&(AR.wranfia),sizeof(ULONG *)); if ( AR.wranfia ) { S_WRITE_B(AR.wranfia, sizeof(ULONG)*AR.wranfnpair2); } #endif /*#] AR :*/ /*#[ AO :*/ /* We copy all non-pointer variables. */ ANNOUNCE(AO) l = sizeof(A.O) - ((UBYTE *)(&(A.O.NumInBrack))-(UBYTE *)(&A.O)); S_WRITE_B(&(A.O.NumInBrack),l); /* Now the variables in OptimizeResult */ S_WRITE_B(&(A.O.OptimizeResult),sizeof(OPTIMIZERESULT)); if ( A.O.OptimizeResult.codesize > 0 ) { S_WRITE_B(A.O.OptimizeResult.code,A.O.OptimizeResult.codesize*sizeof(WORD)); } S_WRITE_S(A.O.OptimizeResult.nameofexpr); /* And now the dictionaries. We write each dictionary to a buffer and get the size of that buffer. Then we write the size and the buffer. */ for ( i = 0; i < AO.NumDictionaries; i++ ) { l = DictToBytes(AO.Dictionaries[i],(UBYTE *)(AT.WorkPointer)); S_WRITE_B(&l,sizeof(LONG)); S_WRITE_B(AT.WorkPointer,l); } /*#] AO :*/ /*#[ PF :*/ #ifdef WITHMPI S_WRITE_B(&PF.numtasks, sizeof(int)); S_WRITE_B(&PF.rhsInParallel, sizeof(int)); S_WRITE_B(&PF.exprbufsize, sizeof(int)); S_WRITE_B(&PF.log, sizeof(int)); #endif /*#] PF :*/ #ifdef WITHPTHREADS ANNOUNCE(GetTimerInfo) /* write timing information of individual threads */ i = GetTimerInfo(&longp,&longpp); S_WRITE_B(&i, sizeof(int)); S_WRITE_B(longp, i*(LONG)sizeof(LONG)); S_WRITE_B(&i, sizeof(int)); S_WRITE_B(longpp, i*(LONG)sizeof(LONG)); #endif S_FLUSH_B /* because we will call fwrite() directly in the following code */ /* save length of data at the beginning of the file */ ANNOUNCE(file length) SETBASEPOSITION(pos, (ftell(fd))); fseek(fd, 0, SEEK_SET); if ( fwrite(&pos, 1, sizeof(POSITION), fd) != sizeof(POSITION) ) return(__LINE__); fseek(fd, BASEPOSITION(pos), SEEK_SET); ANNOUNCE(file close) if ( fclose(fd) ) return(__LINE__); #ifdef WITHMPI if ( PF.me == MASTER ) { #endif /* copy store file if necessary */ ANNOUNCE(copy store file) if ( ISNOTZEROPOS(AR.StoreData.Fill) ) { if ( CopyFile(FG.fname, storefile) ) return(__LINE__); } /* copy sort file if necessary */ ANNOUNCE(copy sort file) if ( AR.outfile->handle >= 0 ) { if ( CopyFile(AR.outfile->name, sortfile) ) return(__LINE__); } /* copy hide file if necessary */ ANNOUNCE(copy hide file) if ( AR.hidefile->handle >= 0 ) { if ( CopyFile(AR.hidefile->name, hidefile) ) return(__LINE__); } #ifdef WITHMPI } /* * For ParFORM, the renaming will be performed after the master got * all recovery files from the slaves. */ #else /* make the intermediate file the recovery file */ ANNOUNCE(rename intermediate file) if ( rename(intermedfile, recoveryfile) ) return(__LINE__); done_snapshot = 1; MesPrint("done."); fflush(0); #endif #ifdef PRINTDEBUG print_M(); print_C(); print_P(); print_R(); #endif return(0); } /* #] DoSnapshot : #[ DoCheckpoint : */ /** * Checks whether a snapshot should be done. Calls DoSnapshot() to create the * snapshot. */ void DoCheckpoint(int moduletype) { int error; LONG timestamp = TimeWallClock(1); #ifdef WITHMPI if(PF.me == MASTER){ #endif if ( timestamp - AC.CheckpointStamp >= AC.CheckpointInterval ) { char argbuf[20]; int retvalue = 0; if ( AC.CheckpointRunBefore ) { size_t l, l2; char *str; l = strlen(AC.CheckpointRunBefore); NumToStr((UBYTE*)argbuf, AC.CModule); l2 = strlen(argbuf); str = (char*)Malloc1(l+l2+2, "callbefore"); strcpy(str, AC.CheckpointRunBefore); *(str+l) = ' '; strcpy(str+l+1, argbuf); retvalue = system(str); M_free(str, "callbefore"); if ( retvalue ) { MesPrint("Script returned error -> no recovery file will be created."); } } #ifdef WITHMPI /* Confirm slaves to make snapshots. */ PF_BroadcastNumber(retvalue == 0); #endif if ( retvalue == 0 ) { if ( (error = DoSnapshot(moduletype)) ) { MesPrint("Error creating recovery files: %d", error); } #ifdef WITHMPI { int i; /*get recovery files from slaves:*/ for(i=1; i %s", src, dst); } } done_snapshot = 1; MesPrint("done."); fflush(0); } #endif } if ( AC.CheckpointRunAfter ) { size_t l, l2; char *str; l = strlen(AC.CheckpointRunAfter); NumToStr((UBYTE*)argbuf, AC.CModule); l2 = strlen(argbuf); str = (char*)Malloc1(l+l2+2, "callafter"); strcpy(str, AC.CheckpointRunAfter); *(str+l) = ' '; strcpy(str+l+1, argbuf); retvalue = system(str); M_free(str, "callafter"); if ( retvalue ) { MesPrint("Error calling script after recovery."); } } AC.CheckpointStamp = TimeWallClock(1); } #ifdef WITHMPI else{/* timestamp - AC.CheckpointStamp < AC.CheckpointInterval*/ /* The slaves don't need to make snapshots. */ PF_BroadcastNumber(0); } }/*if(PF.me == MASTER)*/ else{/*Slave*/ int i; /* Check if the slave needs to make a snapshot. */ if ( PF_BroadcastNumber(0) ) { error = DoSnapshot(moduletype); if(error == 0){ FILE *fd; /* * Send the recovery file to the master. Note that no renaming * has been performed and what we have to send is actually sitting * in the intermediate file. */ fd = fopen(intermedfile, "r"); i=PF_SendFile(MASTER, fd);/*if fd==NULL, PF_SendFile seds to a slave the failure tag*/ if(fd == NULL) Terminate(-1); fclose(fd); if(i<=0) Terminate(-1); /*Now the slave need not the recovery file so remove it:*/ remove(intermedfile); } else{ /*send the error tag to the master:*/ PF_SendFile(MASTER,NULL);/*if fd==NULL, PF_SendFile seds to a slave the failure tag*/ Terminate(-1); } done_snapshot = 1; }/*if(tag=PF_DATA_MSGTAG)*/ }/*if(PF.me != MASTER)*/ #endif } /* #] DoCheckpoint : */ form-5.0.1/sources/spectator.c0000644000175100017510000004761515217035721012016 /** @file spectator.c * * File contains the code for the spectator files and their control. * */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ includes : */ #include "form3.h" /* #] includes : #[ Commentary : We use an array of SPECTATOR structs in AM.SpectatorFiles. When a spectator is removed this leaves a hole. This means that we cannot use AM.NumSpectatorFiles but always have to scan up to AM.SizeForSpectatorFiles which is the size of the array. An element is in use when it has a name. This is the name of the expression that is associated with it. There is also the number of the expression, but because the expressions are frequently renumbered at the end of a module, we always search for the spectators by name. The expression number is only valid in the current module. During execution we use the number of the spectator. The FILEHANDLE struct is borrowed from the structs for the scratch files, but we do not keep copies for all workers as with the scratch files. This brings some limitations (but saves much space). Basically the reading can only be done by one master or worker. And because we use the buffer both for writing and for reading we cannot read and write in the same module. Processor can see that an expression is to be filled with a spectator because we replace the compiler buffer number in the prototype by -specnum-1. Of course, after this filling has taken place we should make sure that in the next module there is a nonnegative number there. The input is then obtained from GetFromSpectator instead from GetTerm. This needed an extra argument in ThreadsProcessor. InParallelProcessor can figure it out by itself. ParFORM still needs to be treated for this. The writing is to a single buffer. Hence it needs a lock. It is possible to give all workers their own buffers (at great memory cost) and merge the results when needed. That would be friendlier on ParFORM. We ALWAYS assume that the order of the terms in the spectator file is random. In the first version there is no compression in the file. This could change in later versions because both the writing and the reading are purely sequential. Brackets are not possible. Currently, ParFORM allows use of spectators only in the sequential mode. The parallelization is switched off in modules containing ToSpectator or CopySpectator. Workers never create or access to spectator files. Their file handles are always -1. We leave the parallelization of modules with spectators for future work. #] Commentary : #[ CoCreateSpectator : Syntax: CreateSpectator name_of_expr "filename"; */ int CoCreateSpectator(UBYTE *inp) { UBYTE *p, *q, *filename, c, cc; WORD c1, c2, numexpr = 0, specnum, HadOne = 0; FILEHANDLE *fh; while ( *inp == ',' ) inp++; if ( ( q = SkipAName(inp) ) == 0 || q[-1] == '_' ) { MesPrint("&Illegal name for expression"); return(1); } c = *q; *q = 0; if ( GetVar(inp,&c1,&c2,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { if ( c2 == CEXPRESSION && Expressions[c1].status == DROPSPECTATOREXPRESSION ) { numexpr = c1; Expressions[numexpr].status = SPECTATOREXPRESSION; HadOne = 1; } else { MesPrint("&The name %s has been used already.",inp); *q = c; return(1); } } p = q+1; while ( *p == ',' ) p++; if ( *p != '"' ) goto Syntax; p++; filename = p; while ( *p && *p != '"' ) { if ( *p == '\\' ) p++; p++; } if ( *p != '"' ) goto Syntax; q = p+1; while ( *q && ( *q == ',' || *q == ' ' || *q == '\t' ) ) q++; if ( *q ) goto Syntax; cc = *p; *p = 0; /* Now we need to: create a struct for the spectator file. */ if ( HadOne == 0 ) numexpr = EntVar(CEXPRESSION,inp,SPECTATOREXPRESSION,0,0,0); fh = AllocFileHandle(1,(char *)filename); /* Make sure there is space in the AM.spectatorfiles array */ if ( AM.NumSpectatorFiles >= AM.SizeForSpectatorFiles || AM.SpectatorFiles == 0 ) { int newsize, i; SPECTATOR *newspectators; if ( AM.SizeForSpectatorFiles == 0 ) { newsize = 10; AM.NumSpectatorFiles = AM.SizeForSpectatorFiles = 0; } else newsize = AM.SizeForSpectatorFiles*2; newspectators = (SPECTATOR *)Malloc1(newsize*sizeof(SPECTATOR),"Spectators"); for ( i = 0; i < AM.NumSpectatorFiles; i++ ) newspectators[i] = AM.SpectatorFiles[i]; for ( ; i < newsize; i++ ) { newspectators[i].fh = 0; newspectators[i].name = 0; newspectators[i].exprnumber = -1; newspectators[i].flags = 0; PUTZERO(newspectators[i].position); PUTZERO(newspectators[i].readpos); } AM.SizeForSpectatorFiles = newsize; if ( AM.SpectatorFiles != 0 ) M_free(AM.SpectatorFiles,"Spectators"); AM.SpectatorFiles = newspectators; specnum = AM.NumSpectatorFiles++; } else { for ( specnum = 0; specnum < AM.SizeForSpectatorFiles; specnum++ ) { if ( AM.SpectatorFiles[specnum].name == 0 ) break; } AM.NumSpectatorFiles++; } PUTZERO(AM.SpectatorFiles[specnum].position); AM.SpectatorFiles[specnum].name = (char *)(strDup1(inp,"Spectator expression name")); AM.SpectatorFiles[specnum].fh = fh; AM.SpectatorFiles[specnum].exprnumber = numexpr; *p = cc; return(0); Syntax: MesPrint("&Proper syntax is: CreateSpectator,exprname,\"filename\";"); return(-1); } /* #] CoCreateSpectator : #[ CoToSpectator : */ int CoToSpectator(UBYTE *inp) { UBYTE *q; WORD c1, numexpr; int i; while ( *inp == ',' ) inp++; if ( ( q = SkipAName(inp) ) == 0 || q[-1] == '_' ) { MesPrint("&Illegal name for expression"); return(1); } if ( *q != 0 ) goto Syntax; if ( GetVar(inp,&c1,&numexpr,ALLVARIABLES,NOAUTO) == NAMENOTFOUND || c1 != CEXPRESSION ) { MesPrint("&%s is not a valid expression.",inp); return(1); } if ( Expressions[numexpr].status != SPECTATOREXPRESSION ) { MesPrint("&%s is not an active spectator.",inp); return(1); } for ( i = 0; i < AM.SizeForSpectatorFiles; i++ ) { if ( AM.SpectatorFiles[i].name != 0 ) { if ( StrCmp((UBYTE *)(AM.SpectatorFiles[i].name),(UBYTE *)(inp)) == 0 ) break; } } if ( i >= AM.SizeForSpectatorFiles ) { MesPrint("&Spectator %s not found.",inp); return(1); } if ( ( AM.SpectatorFiles[i].flags & READSPECTATORFLAG ) != 0 ) { MesPrint("&Spectator %s: It is not permitted to read from and write to the same spectator in one module.",inp); return(1); } AM.SpectatorFiles[i].exprnumber = numexpr; Add3Com(TYPETOSPECTATOR,i); #ifdef WITHMPI /* * In ParFORM, ToSpectator has to be executed on the master. */ AC.mparallelflag |= NOPARALLEL_SPECTATOR; #endif return(0); Syntax: MesPrint("&Proper syntax is: ToSpectator,exprname;"); return(-1); } /* #] CoToSpectator : #[ CoRemoveSpectator : */ int CoRemoveSpectator(UBYTE *inp) { UBYTE *q; WORD c1, numexpr; int i; SPECTATOR *sp; while ( *inp == ',' ) inp++; if ( ( q = SkipAName(inp) ) == 0 || q[-1] == '_' ) { MesPrint("&Illegal name for expression"); return(1); } if ( *q != 0 ) goto Syntax; if ( GetVar(inp,&c1,&numexpr,ALLVARIABLES,NOAUTO) == NAMENOTFOUND || c1 != CEXPRESSION ) { MesPrint("&%s is not a valid expression.",inp); return(1); } if ( Expressions[numexpr].status != SPECTATOREXPRESSION ) { MesPrint("&%s is not a spectator.",inp); return(1); } for ( i = 0; i < AM.SizeForSpectatorFiles; i++ ) { if ( AM.SpectatorFiles[i].name != 0 ) { if ( StrCmp((UBYTE *)(AM.SpectatorFiles[i].name),(UBYTE *)(inp)) == 0 ) { break; } } } if ( i >= AM.SizeForSpectatorFiles ) { MesPrint("&Spectator %s not found.",inp); return(1); } sp = AM.SpectatorFiles+i; Expressions[numexpr].status = DROPSPECTATOREXPRESSION; if ( sp->fh->handle != -1 ) { CloseFile(sp->fh->handle); sp->fh->handle = -1; remove(sp->fh->name); } M_free(sp->fh,"Temporary FileHandle"); M_free(sp->name,"Spectator expression name"); PUTZERO(sp->position); PUTZERO(sp->readpos); sp->fh = 0; sp->name = 0; sp->exprnumber = -1; sp->flags = 0; AM.NumSpectatorFiles--; return(0); Syntax: MesPrint("&Proper syntax is: RemoveSpectator,exprname;"); return(-1); } /* #] CoRemoveSpectator : #[ CoEmptySpectator : */ int CoEmptySpectator(UBYTE *inp) { UBYTE *q; WORD c1, numexpr; int i; SPECTATOR *sp; while ( *inp == ',' ) inp++; if ( ( q = SkipAName(inp) ) == 0 || q[-1] == '_' ) { MesPrint("&Illegal name for expression"); return(1); } if ( *q != 0 ) goto Syntax; if ( GetVar(inp,&c1,&numexpr,ALLVARIABLES,NOAUTO) == NAMENOTFOUND || c1 != CEXPRESSION ) { MesPrint("&%s is not a valid expression.",inp); return(1); } if ( Expressions[numexpr].status != SPECTATOREXPRESSION ) { MesPrint("&%s is not a spectator.",inp); return(1); } for ( i = 0; i < AM.SizeForSpectatorFiles; i++ ) { if ( StrCmp((UBYTE *)(AM.SpectatorFiles[i].name),(UBYTE *)(inp)) == 0 ) break; } if ( i >= AM.SizeForSpectatorFiles ) { MesPrint("&Spectator %s not found.",inp); return(1); } sp = AM.SpectatorFiles+i; if ( sp->fh->handle != -1 ) { CloseFile(sp->fh->handle); sp->fh->handle = -1; remove(sp->fh->name); } sp->fh->POfill = sp->fh->POfull = sp->fh->PObuffer; PUTZERO(sp->position); PUTZERO(sp->readpos); return(0); Syntax: MesPrint("&Proper syntax is: EmptySpectator,exprname;"); return(-1); } /* #] CoEmptySpectator : #[ PutInSpectator : We need to use locks! There is only one file. The code was copied (and modified) from PutOut. Here we use no compression. */ int PutInSpectator(WORD *term,WORD specnum) { GETBIDENTITY WORD i, *p, ret; LONG RetCode; SPECTATOR *sp = &(AM.SpectatorFiles[specnum]); FILEHANDLE *fi = sp->fh; if ( ( i = *term ) <= 0 ) return(0); LOCK(fi->pthreadslock); ret = i; p = fi->POfill; do { if ( p >= fi->POstop ) { if ( fi->handle < 0 ) { if ( ( RetCode = CreateFile(fi->name) ) >= 0 ) { fi->handle = (WORD)RetCode; PUTZERO(fi->filesize); PUTZERO(fi->POposition); } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create spectator file %s",fi->name); MUNLOCK(ErrorMessageLock); UNLOCK(fi->pthreadslock); return(-1); } } SeekFile(fi->handle,&(sp->position),SEEK_SET); if ( ( RetCode = WriteFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize) ) != fi->POsize ) { MLOCK(ErrorMessageLock); MesPrint("Error during spectator write. Disk full?"); MesPrint("Attempt to write %l bytes on file %d at position %15p", fi->POsize,fi->handle,&(fi->POposition)); MesPrint("RetCode = %l, Buffer address = %l",RetCode,(LONG)(fi->PObuffer)); MUNLOCK(ErrorMessageLock); UNLOCK(fi->pthreadslock); return(-1); } ADDPOS(fi->filesize,fi->POsize); p = fi->PObuffer; ADDPOS(sp->position,fi->POsize); fi->POposition = sp->position; } *p++ = *term++; } while ( --i > 0 ); fi->POfull = fi->POfill = p; Expressions[AM.SpectatorFiles[specnum].exprnumber].counter++; UNLOCK(fi->pthreadslock); return(ret); } /* #] PutInSpectator : #[ FlushSpectators : */ void FlushSpectators(void) { SPECTATOR *sp = AM.SpectatorFiles; FILEHANDLE *fh; LONG RetCode; int i; LONG size; if ( AM.NumSpectatorFiles <= 0 ) return; for ( i = 0; i < AM.SizeForSpectatorFiles; i++, sp++ ) { if ( sp->name == 0 ) continue; fh = sp->fh; if ( ( sp->flags & READSPECTATORFLAG ) != 0 ) { /* reset for writing */ sp->flags &= ~READSPECTATORFLAG; fh->POfill = fh->PObuffer; if ( fh->handle >= 0 ) { SeekFile(fh->handle,&(sp->position),SEEK_SET); fh->POposition = sp->position; } continue; } if ( fh->POfill <= fh->PObuffer ) continue; /* is clean */ if ( fh->handle < 0 ) { /* File needs to be created */ if ( ( RetCode = CreateFile(fh->name) ) >= 0 ) { PUTZERO(fh->filesize); PUTZERO(fh->POposition); fh->handle = (WORD)RetCode; } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create spectator file %s",fh->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } PUTZERO(sp->position); } SeekFile(fh->handle,&(sp->position),SEEK_SET); size = (fh->POfill - fh->PObuffer)*sizeof(WORD); if ( ( RetCode = WriteFile(fh->handle,(UBYTE *)(fh->PObuffer),size) ) != size ) { MLOCK(ErrorMessageLock); MesPrint("Write error synching spectator file. Disk full?"); MesPrint("Attempt to write %l bytes on file %s at position %15p", size,fh->name,&(sp->position)); MUNLOCK(ErrorMessageLock); Terminate(-1); } fh->POfill = fh->PObuffer; SeekFile(fh->handle,&(sp->position),SEEK_END); fh->POposition = sp->position; } return; } /* #] FlushSpectators : #[ CoCopySpectator : */ int CoCopySpectator(UBYTE *inp) { GETIDENTITY UBYTE *q, c, *exprname, *p; WORD c1, c2, numexpr; int specnum, error = 0; SPECTATOR *sp; while ( *inp == ',' ) inp++; if ( ( q = SkipAName(inp) ) == 0 || q[-1] == '_' ) { MesPrint("&Illegal name for expression"); return(1); } if ( *q == 0 ) goto Syntax; c = *q; *q = 0; if ( GetVar(inp,&c1,&c2,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { MesPrint("&%s is the name of an existing variable.",inp); return(1); } numexpr = EntVar(CEXPRESSION,inp,LOCALEXPRESSION,0,0,0); p = q; exprname = inp; *q = c; while ( *q == ' ' || *q == ',' || *q == '\t' ) q++; if ( *q != '=' ) goto Syntax; q++; while ( *q == ' ' || *q == ',' || *q == '\t' ) q++; inp = q; if ( ( q = SkipAName(inp) ) == 0 || q[-1] == '_' ) { MesPrint("&Illegal name for spectator expression"); return(1); } if ( *q != 0 ) goto Syntax; if ( AM.NumSpectatorFiles <= 0 ) { MesPrint("&CopySpectator: There are no spectator expressions!"); return(1); } sp = AM.SpectatorFiles; for ( specnum = 0; specnum < AM.SizeForSpectatorFiles; specnum++, sp++ ) { if ( sp->name != 0 ) { if ( StrCmp((UBYTE *)(sp->name),(UBYTE *)(inp)) == 0 ) break; } } if ( specnum >= AM.SizeForSpectatorFiles ) { MesPrint("&Spectator %s not found.",inp); return(1); } sp->flags |= READSPECTATORFLAG; PUTZERO(sp->fh->POposition); PUTZERO(sp->readpos); sp->fh->POfill = sp->fh->PObuffer; if ( sp->fh->handle >= 0 ) { SeekFile(sp->fh->handle,&(sp->fh->POposition),SEEK_SET); } /* Now we have: 1: The name of the target expression: numexpr 2: The spectator: sp (or specnum). Time for some action. We need: a: Write a prototype to create the expression b: Signal to Processor that this is a spectator. We do this by giving a negative compiler buffer number. */ { WORD *OldWork, *w; POSITION pos; OldWork = w = AT.WorkPointer; *w++ = TYPEEXPRESSION; *w++ = 3+SUBEXPSIZE; *w++ = numexpr; AC.ProtoType = w; AR.CurExpr = numexpr; /* Block expression numexpr */ *w++ = SUBEXPRESSION; *w++ = SUBEXPSIZE; *w++ = numexpr; *w++ = 1; *w++ = -specnum-1; /* Indicates "spectator" to Processor */ FILLSUB(w) *w++ = 1; *w++ = 1; *w++ = 3; *w++ = 0; SeekScratch(AR.outfile,&pos); Expressions[numexpr].counter = 1; Expressions[numexpr].onfile = pos; Expressions[numexpr].whichbuffer = 0; #ifdef PARALLELCODE Expressions[numexpr].partodo = AC.inparallelflag; #endif OldWork[2] = w - OldWork - 3; AT.WorkPointer = w; if ( PutOut(BHEAD OldWork+2,&pos,AR.outfile,0) < 0 ) { c = *p; *p = 0; MesPrint("&Cannot create expression %s",exprname); *p = c; error = -1; } else { OldWork[2] = 4+SUBEXPSIZE; OldWork[4] = SUBEXPSIZE; OldWork[5] = numexpr; OldWork[SUBEXPSIZE+3] = 1; OldWork[SUBEXPSIZE+4] = 1; OldWork[SUBEXPSIZE+5] = 3; OldWork[SUBEXPSIZE+6] = 0; if ( PutOut(BHEAD OldWork+2,&pos,AR.outfile,0) < 0 || FlushOut(&pos,AR.outfile,0) ) { c = *p; *p = 0; MesPrint("&Cannot create expression %s",exprname); *p = c; error = -1; } AR.outfile->POfull = AR.outfile->POfill; } OldWork[2] = numexpr; /* Seems unnecessary (13-feb-2018) AddNtoL(OldWork[1],OldWork); */ AT.WorkPointer = OldWork; if ( AC.dumnumflag ) Add2Com(TYPEDETCURDUM) } #ifdef WITHMPI /* * In ParFORM, substitutions of spectators has to be done on the master. */ AC.mparallelflag |= NOPARALLEL_SPECTATOR; #endif return(error); Syntax: MesPrint("&Proper syntax is: CopySpectator,exprname=spectatorname;"); return(-1); } /* #] CoCopySpectator : #[ GetFromSpectator : Note that if we did things right, we do not need a lock for the reading. */ WORD GetFromSpectator(WORD *term,WORD specnum) { SPECTATOR *sp = &(AM.SpectatorFiles[specnum]); FILEHANDLE *fh = sp->fh; WORD i, size, *t = term; LONG InIn; if ( fh-> handle < 0 ) { *term = 0; return(0); } /* sp->position marks the 'end' of the file: the point where writing should take place. sp->readpos marks from where to read. fh->POposition marks where the file is currently positioned. Note that when we read, we need to */ if ( ISZEROPOS(sp->readpos) ) { /* we start reading. Fill buffer. */ FillBuffer: SeekFile(fh->handle,&(sp->readpos),SEEK_SET); InIn = ReadFile(fh->handle,(UBYTE *)(fh->PObuffer),fh->POsize); if ( InIn < 0 || ( InIn & 1 ) ) { MLOCK(ErrorMessageLock); MesPrint("Error reading information for %s spectator",sp->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } InIn /= sizeof(WORD); if ( InIn == 0 ) { *term = 0; return(0); } SeekFile(fh->handle,&(sp->readpos),SEEK_CUR); fh->POposition = sp->readpos; fh->POfull = fh->PObuffer+InIn; fh->POfill = fh->PObuffer; } if ( fh->POfill == fh->POfull ) { /* not even the size of the term! */ if ( ISLESSPOS(sp->readpos,sp->position) ) goto FillBuffer; *term = 0; return(0); } size = *fh->POfill++; *t++ = size; for ( i = 1; i < size; i++ ) { if ( fh->POfill >= fh->POfull ) { SeekFile(fh->handle,&(sp->readpos),SEEK_SET); InIn = ReadFile(fh->handle,(UBYTE *)(fh->PObuffer),fh->POsize); if ( InIn < 0 || ( InIn & 1 ) ) { MLOCK(ErrorMessageLock); MesPrint("Error reading information for %s spectator",sp->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } InIn /= sizeof(WORD); if ( InIn == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Reading incomplete information for %s spectator",sp->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } SeekFile(fh->handle,&(sp->readpos),SEEK_CUR); fh->POposition = sp->readpos; fh->POfull = fh->PObuffer+InIn; fh->POfill = fh->PObuffer; } *t++ = *fh->POfill++; } return(size); } /* #] GetFromSpectator : #[ ClearSpectators : Removes all spectators. In case of .store, the ones that are protected by .global stay. */ void ClearSpectators(WORD par) { SPECTATOR *sp = AM.SpectatorFiles; WORD numexpr, c1; int i; if ( AM.NumSpectatorFiles > 0 ) { for ( i = 0; i < AM.SizeForSpectatorFiles; i++, sp++ ) { if ( sp->name == 0 ) continue; if ( ( sp->flags & GLOBALSPECTATORFLAG ) == 1 && par == STOREMODULE ) continue; if ( GetVar((UBYTE *)(sp->name),&c1,&numexpr,ALLVARIABLES,NOAUTO) == NAMENOTFOUND || c1 != CEXPRESSION ) { MesPrint("&%s is not a valid expression.",sp->name); continue; } Expressions[numexpr].status = DROPPEDEXPRESSION; if ( sp->fh->handle != -1 ) { CloseFile(sp->fh->handle); sp->fh->handle = -1; remove(sp->fh->name); } M_free(sp->fh,"Temporary FileHandle"); M_free(sp->name,"Spectator expression name"); PUTZERO(sp->position); sp->fh = 0; sp->name = 0; sp->exprnumber = -1; sp->flags = 0; AM.NumSpectatorFiles--; } } } /* #] ClearSpectators : */ form-5.0.1/sources/comtool.c0000644000175100017510000004311115217035721011451 /** @file comtool.c * * Utility routines for the compiler. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include "form3.h" /* #] Includes : #[ inicbufs : */ /** * Creates a new compiler buffer and returns its ID number. * * @return The ID number for the new compiler buffer. */ int inicbufs(void) { int i, num = AC.cbufList.num; CBUF *C = cbuf; for ( i = 0; i < num; i++, C++ ) { if ( C->Buffer == 0 ) break; } if ( i >= num ) C = (CBUF *)FromList(&AC.cbufList); else num = i; C->BufferSize = 2000; C->Buffer = (WORD *)Malloc1(C->BufferSize*sizeof(WORD),"compiler buffer-1"); C->Pointer = C->Buffer; C->Top = C->Buffer + C->BufferSize; C->maxlhs = 10; C->lhs = (WORD **)Malloc1(C->maxlhs*sizeof(WORD *),"compiler buffer-2"); C->numlhs = 0; C->mnumlhs = 0; C->maxrhs = 25; C->rhs = (WORD **)Malloc1(C->maxrhs*(sizeof(WORD *)+2*sizeof(LONG)+2*sizeof(WORD)),"compiler buffer-3"); C->CanCommu = (LONG *)(C->rhs+C->maxrhs); C->NumTerms = C->CanCommu+C->maxrhs; C->numdum = (WORD *)(C->NumTerms+C->maxrhs); C->dimension = C->numdum + C->maxrhs; C->numrhs = 0; C->mnumrhs = 0; C->rhs[0] = C->rhs[1] = C->Pointer; C->boomlijst = 0; RedoTree(C,C->maxrhs); ClearTree(num); return(num); } /* #] inicbufs : #[ finishcbuf : */ /** * Frees a compiler buffer. * * @param num The ID number for the buffer to be freed. */ void finishcbuf(WORD num) { CBUF *C = cbuf+num; if ( C->Buffer ) M_free(C->Buffer,"compiler buffer-1"); if ( C->rhs ) M_free(C->rhs,"compiler buffer-3"); if ( C->lhs ) M_free(C->lhs,"compiler buffer-2"); if ( C->boomlijst ) M_free(C->boomlijst,"boomlijst"); C->Top = C->Pointer = C->Buffer = 0; C->rhs = C->lhs = 0; C->CanCommu = 0; C->NumTerms = 0; C->BufferSize = 0; C->boomlijst = 0; C->numlhs = C->numrhs = C->maxlhs = C->maxrhs = C->mnumlhs = C->mnumrhs = C->numtree = C->rootnum = C->MaxTreeSize = 0; } /* #] finishcbuf : #[ clearcbuf : */ /** * Clears contents in a compiler buffer. * * @param num The ID number for the buffer to be cleared. */ void clearcbuf(WORD num) { CBUF *C = cbuf+num; if ( C->boomlijst ) M_free(C->boomlijst,"boomlijst"); C->Pointer = C->Buffer; C->numrhs = C->numlhs = 0; C->mnumlhs = 0; C->boomlijst = 0; C->mnumrhs = 0; C->rhs[0] = C->rhs[1] = C->Pointer; C->numtree = C->rootnum = C->MaxTreeSize = 0; RedoTree(C,C->maxrhs); ClearTree(num); } /* #] clearcbuf : #[ DoubleCbuffer : */ /** * Doubles a compiler buffer. * * @param num The ID number for the buffer to be doubled. * @param w The pointer to the end (exclusive) of the current buffer. The * contents in the range of [cbuf[num].Buffer,w) will be kept. */ WORD *DoubleCbuffer(int num, WORD *w,int par) { CBUF *C = cbuf + num; LONG newsize = C->BufferSize*2; WORD *newbuffer = (WORD *)Malloc1(newsize*sizeof(WORD),"compiler buffer-4"); WORD *w1, *w2; LONG offset, j, i; DUMMYUSE(par) /* MLOCK(ErrorMessageLock); MesPrint(" doubleCbuffer: par = %d",par); MUNLOCK(ErrorMessageLock); */ w1 = C->Buffer; w2 = newbuffer; i = w - w1; j = i & 7; while ( --j >= 0 ) *w2++ = *w1++; i >>= 3; while ( --i >= 0 ) { *w2++ = *w1++; *w2++ = *w1++; *w2++ = *w1++; *w2++ = *w1++; *w2++ = *w1++; *w2++ = *w1++; *w2++ = *w1++; *w2++ = *w1++; } offset = newbuffer - C->Buffer; for ( i = 0; i <= C->numlhs; i++ ) C->lhs[i] += offset; for ( i = 1; i <= C->numrhs; i++ ) C->rhs[i] += offset; w1 = C->Buffer; C->Pointer += offset; C->Top = newbuffer + newsize; C->BufferSize = newsize; C->Buffer = newbuffer; M_free(w1,"DoubleCbuffer"); return(w2); } /* #] DoubleCbuffer : #[ AddLHS : */ /** * Adds an LHS to a compiler buffer and returns the pointer to a buffer for the * new LHS. * * @param num The ID number for the buffer to get another LHS. */ WORD *AddLHS(int num) { CBUF *C = cbuf + num; C->numlhs++; if ( C->numlhs >= (C->maxlhs-2) ) { WORD ***ppp = &(C->lhs); /* to avoid compiler warning */ if ( DoubleList((void ***)ppp,&(C->maxlhs),sizeof(WORD *), "statement lists") ) Terminate(-1); } C->lhs[C->numlhs] = C->Pointer; C->lhs[C->numlhs+1] = 0; return(C->Pointer); } /* #] AddLHS : #[ AddRHS : */ /** * Adds an RHS to a compiler buffer and returns the pointer to a buffer for the * new RHS. * * @param num The ID number for the buffer to get another RHS. * @param type If 0, the subexpression tree will be reallocated. */ WORD *AddRHS(int num, int type) { LONG fullsize, *lold, newsize; int i; WORD **old, *wold; CBUF *C; restart:; C = cbuf + num; if ( C->numrhs >= (C->maxrhs-2) ) { if ( C->maxrhs == 0 ) newsize = 100; else newsize = C->maxrhs * 2; if ( newsize > MAXCOMBUFRHS ) newsize = MAXCOMBUFRHS; if ( newsize == C->maxrhs ) { if ( AC.tablefilling ) { TABLES T = functions[AC.tablefilling].tabl; /* We add a compiler buffer, change a few settings and continue. */ if ( T->buffersfill >= T->bufferssize ) { int new1 = 2*T->bufferssize; WORD *nbufs = (WORD *)Malloc1(new1*sizeof(WORD),"Table compile buffers"); for ( i = 0; i < T->buffersfill; i++ ) nbufs[i] = T->buffers[i]; for ( ; i < new1; i++ ) nbufs[i] = 0; M_free(T->buffers,"Table compile buffers"); T->buffers = nbufs; T->bufferssize = new1; } T->buffers[T->buffersfill++] = T->bufnum = inicbufs(); AC.cbufnum = num = T->bufnum; goto restart; } else { MesPrint("@Compiler buffer overflow. Try to make modules smaller"); Terminate(-1); } } old = C->rhs; fullsize = newsize * (sizeof(WORD *) + 2*sizeof(LONG) + 2*sizeof(WORD)); C->rhs = (WORD **)Malloc1(fullsize,"subexpression lists"); for ( i = 0; i < C->maxrhs; i++ ) C->rhs[i] = old[i]; lold = C->CanCommu; C->CanCommu = (LONG *)(C->rhs+newsize); for ( i = 0; i < C->maxrhs; i++ ) C->CanCommu[i] = lold[i]; lold = C->NumTerms; C->NumTerms = (LONG *)(C->rhs+2*newsize); for ( i = 0; i < C->maxrhs; i++ ) C->NumTerms[i] = lold[i]; wold = C->numdum; C->numdum = (WORD *)(C->NumTerms+newsize); for ( i = 0; i < C->maxrhs; i++ ) C->numdum[i] = wold[i]; wold = C->dimension; C->dimension = (WORD *)(C->numdum+newsize); for ( i = 0; i < C->maxrhs; i++ ) C->dimension[i] = wold[i]; if ( old ) M_free(old,"subexpression lists"); C->maxrhs = newsize; if ( type == 0 ) RedoTree(C,C->maxrhs); } C->numrhs++; C->CanCommu[C->numrhs] = 0; C->NumTerms[C->numrhs] = 0; C->numdum[C->numrhs] = 0; C->dimension[C->numrhs] = 0; C->rhs[C->numrhs] = C->Pointer; return(C->Pointer); } /* #] AddRHS : #[ AddNtoL : */ /** * Adds an LHS with the given data to the current compiler buffer. * * @param n The length of the data. * @param array The data to be added. * @return 0 if succeeds. */ int AddNtoL(int n, WORD *array) { int i; CBUF *C = cbuf+AC.cbufnum; #ifdef COMPBUFDEBUG MesPrint("LH: %a",n,array); #endif AddLHS(AC.cbufnum); while ( C->Pointer+n >= C->Top ) DoubleCbuffer(AC.cbufnum,C->Pointer,1); for ( i = 0; i < n; i++ ) *(C->Pointer)++ = *array++; return(0); } /* #] AddNtoL : #[ AddNtoC : Commentary: added the bufnum on 14-sep-2010 to make the whole a bit more flexible (JV). Still to do with AddNtoL. */ /** * Adds the given data to the last LHS/RHS in a compiler buffer. * * @param bufnum The ID number for the buffer where the data will be added. * @param n The length of the data. * @param array The data to be added. * @return 0 if succeeds. */ int AddNtoC(int bufnum, int n, WORD *array,int par) { int i; WORD *w; CBUF *C = cbuf+bufnum; #ifdef COMPBUFDEBUG MesPrint("RH: %a",n,array); #endif while ( C->Pointer+n+1 >= C->Top ) DoubleCbuffer(bufnum,C->Pointer,50+par); w = C->Pointer; for ( i = 0; i < n; i++ ) *w++ = *array++; C->Pointer = w; return(0); } /* #] AddNtoC : #[ InsTree : Routines for balanced tree searching and insertion. Compared to Knuth we have a parent link. This minimizes the number of compares. That is better for anything that is more complicated than just single numbers. There are no provisions for removing elements from the tree. The routines are: void RedoTree(size) Re-allocates the tree space. There will be MaxTreeSize = size elements. void ClearTree() Prunes the tree down to the root element. int InsTree(int,int)Searches for the requested element. If not found it will allocate a new element, balance the tree if necessary and return the called number. If it was in the tree, it returns the tree 'value'. Commentary: added the bufnum on 14-sep-2010 to make the whole a bit more flexible (JV). */ static COMPTREE comptreezero = {0,0,0,0,0,0}; int InsTree(int bufnum, int h) { CBUF *C = cbuf + bufnum; COMPTREE *boomlijst = C->boomlijst, *q = boomlijst + C->rootnum, *p, *s; WORD *v1, *v2, *v3; int ip, iq, is; if ( C->numtree + 1 >= C->MaxTreeSize ) { if ( C->MaxTreeSize == 0 ) { COMPTREE *root; C->MaxTreeSize = 125; C->boomlijst = (COMPTREE *)Malloc1((C->MaxTreeSize+1)*sizeof(COMPTREE), "ClearInsTree"); root = C->boomlijst; C->numtree = 0; C->rootnum = 0; root->left = -1; root->right = -1; root->parent = -1; root->blnce = 0; root->value = -1; root->usage = 0; for ( ip = 1; ip < C->MaxTreeSize; ip++ ) { C->boomlijst[ip] = comptreezero; } } else { is = C->MaxTreeSize * 2; s = (COMPTREE *)Malloc1((is+1)*sizeof(COMPTREE),"InsTree"); for ( ip = 0; ip < C->MaxTreeSize; ip++ ) { s[ip] = C->boomlijst[ip]; } for ( ip = C->MaxTreeSize; ip <= is; ip++ ) { s[ip] = comptreezero; } if ( C->boomlijst ) M_free(C->boomlijst,"InsTree"); C->boomlijst = s; C->MaxTreeSize = is; } boomlijst = C->boomlijst; q = boomlijst + C->rootnum; } if ( q->right == -1 ) { /* First element */ C->numtree++; s = boomlijst+C->numtree; q->right = C->numtree; s->parent = C->rootnum; s->left = s->right = -1; s->blnce = 0; s->value = h; s->usage = 1; return(h); } ip = q->right; while ( ip >= 0 ) { p = boomlijst + ip; v1 = C->rhs[p->value]; v2 = v3 = C->rhs[h]; while ( *v3 ) v3 += *v3; /* find the 0 that indicates end-of-expr */ while ( *v1 == *v2 && v2 < v3 ) { v1++; v2++; } if ( *v1 > *v2 ) { iq = p->right; if ( iq >= 0 ) { ip = iq; } else { C->numtree++; is = C->numtree; p->right = is; s = boomlijst + is; s->parent = ip; s->left = s->right = -1; s->blnce = 0; s->value = h; s->usage = 1; p->blnce++; if ( p->blnce == 0 ) return(h); goto balance; } } else if ( *v1 < *v2 ) { iq = p->left; if ( iq >= 0 ) { ip = iq; } else { C->numtree++; is = C->numtree; s = boomlijst+is; p->left = is; s->parent = ip; s->left = s->right = -1; s->blnce = 0; s->value = h; s->usage = 1; p->blnce--; if ( p->blnce == 0 ) return(h); goto balance; } } else { p->usage++; return(p->value); } } MesPrint("We vallen uit de boom!"); Terminate(-1); return(h); balance:; for (;;) { p = boomlijst + ip; iq = p->parent; if ( iq == C->rootnum ) break; q = boomlijst + iq; if ( ip == q->left ) q->blnce--; else q->blnce++; if ( q->blnce == 0 ) break; if ( q->blnce == -2 ) { if ( p->blnce == -1 ) { /* single rotation */ q->left = p->right; p->right = iq; p->parent = q->parent; q->parent = ip; if ( boomlijst[p->parent].left == iq ) boomlijst[p->parent].left = ip; else boomlijst[p->parent].right = ip; if ( q->left >= 0 ) boomlijst[q->left].parent = iq; q->blnce = p->blnce = 0; } else { /* double rotation */ s = boomlijst + is; q->left = s->right; p->right = s->left; s->right = iq; s->left = ip; if ( p->right >= 0 ) boomlijst[p->right].parent = ip; if ( q->left >= 0 ) boomlijst[q->left].parent = iq; s->parent = q->parent; q->parent = is; p->parent = is; if ( boomlijst[s->parent].left == iq ) boomlijst[s->parent].left = is; else boomlijst[s->parent].right = is; if ( s->blnce > 0 ) { q->blnce = s->blnce = 0; p->blnce = -1; } else if ( s->blnce < 0 ) { p->blnce = s->blnce = 0; q->blnce = 1; } else { p->blnce = s->blnce = q->blnce = 0; } } break; } else if ( q->blnce == 2 ) { if ( p->blnce == 1 ) { /* single rotation */ q->right = p->left; p->left = iq; p->parent = q->parent; q->parent = ip; if ( boomlijst[p->parent].left == iq ) boomlijst[p->parent].left = ip; else boomlijst[p->parent].right = ip; if ( q->right >= 0 ) boomlijst[q->right].parent = iq; q->blnce = p->blnce = 0; } else { /* double rotation */ s = boomlijst + is; q->right = s->left; p->left = s->right; s->left = iq; s->right = ip; if ( p->left >= 0 ) boomlijst[p->left].parent = ip; if ( q->right >= 0 ) boomlijst[q->right].parent = iq; s->parent = q->parent; q->parent = is; p->parent = is; if ( boomlijst[s->parent].left == iq ) boomlijst[s->parent].left = is; else boomlijst[s->parent].right = is; if ( s->blnce < 0 ) { q->blnce = s->blnce = 0; p->blnce = 1; } else if ( s->blnce > 0 ) { p->blnce = s->blnce = 0; q->blnce = -1; } else { p->blnce = s->blnce = q->blnce = 0; } } break; } is = ip; ip = iq; } return(h); } /* #] InsTree : #[ FindTree : Routines for balanced tree searching. Is like InsTree but without the insertions. Returns -1 if the element is not in the tree. The advantage of this routine over InsTree is that this routine can be run in parallel. */ int FindTree(int bufnum, WORD *subexpr) { CBUF *C = cbuf + bufnum; COMPTREE *boomlijst = C->boomlijst, *q = boomlijst + C->rootnum, *p; WORD *v1, *v2, *v3; int ip, iq; ip = q->right; while ( ip >= 0 ) { p = boomlijst + ip; v1 = C->rhs[p->value]; v2 = v3 = subexpr; while ( *v3 ) v3 += *v3; /* find the 0 that indicates end-of-expr */ while ( *v1 == *v2 && v2 < v3 ) { v1++; v2++; } if ( *v1 > *v2 ) { iq = p->right; if ( iq >= 0 ) { ip = iq; } else { return(-1); } } else if ( *v1 < *v2 ) { iq = p->left; if ( iq >= 0 ) { ip = iq; } else { return(-1); } } else { p->usage++; return(p->value); } } return(-1); } /* #] FindTree : #[ RedoTree : */ void RedoTree(CBUF *C, int size) { COMPTREE *newboomlijst; int i; newboomlijst = (COMPTREE *)Malloc1((size+1)*sizeof(COMPTREE),"newboomlijst"); if ( C->boomlijst ) { if ( C->MaxTreeSize > size ) C->MaxTreeSize = size; for ( i = 0; i < C->MaxTreeSize; i++ ) newboomlijst[i] = C->boomlijst[i]; M_free(C->boomlijst,"boomlijst"); } C->boomlijst = newboomlijst; C->MaxTreeSize = size; } /* #] RedoTree : #[ ClearTree : */ void ClearTree(int i) { CBUF *C = cbuf + i; COMPTREE *root = C->boomlijst; if ( root ) { C->numtree = 0; C->rootnum = 0; root->left = -1; root->right = -1; root->parent = -1; root->blnce = 0; root->value = -1; root->usage = 0; } } /* #] ClearTree : #[ IniFbuffer : */ /** * Initialize a factorization cache buffer. * We set the size of the rhs and boomlijst buffers immediately * to their final values. */ int IniFbuffer(WORD bufnum) { CBUF *C = cbuf + bufnum; COMPTREE *root; int i; LONG fullsize; C->maxrhs = AM.fbuffersize; C->MaxTreeSize = AM.fbuffersize; /* * Note that bufnum is a return value of inicbufs(). So C has been already * initialized. (TU 20 Dec 2011) */ if ( C->boomlijst ) M_free(C->boomlijst, "IniFbuffer-tree"); if ( C->rhs ) M_free(C->rhs, "IniFbuffer-rhs"); C->boomlijst = (COMPTREE *)Malloc1((C->MaxTreeSize+1)*sizeof(COMPTREE),"IniFbuffer-tree"); root = C->boomlijst; C->numtree = 0; C->rootnum = 0; root->left = -1; root->right = -1; root->parent = -1; root->blnce = 0; root->value = -1; root->usage = 0; for ( i = 1; i < C->MaxTreeSize; i++ ) { C->boomlijst[i] = comptreezero; } fullsize = (C->maxrhs+1) * (sizeof(WORD *) + 2*sizeof(LONG) + 2*sizeof(WORD)); C->rhs = (WORD **)Malloc1(fullsize,"IniFbuffer-rhs"); C->CanCommu = (LONG *)(C->rhs+C->maxrhs); C->NumTerms = (LONG *)(C->rhs+2*C->maxrhs); C->numdum = (WORD *)(C->NumTerms+C->maxrhs); C->dimension = (WORD *)(C->numdum+C->maxrhs); return(0); } /* #] IniFbuffer : #[ numcommute : Returns the number of non-commuting terms in the expression */ LONG numcommute(WORD *terms, LONG *numterms) { LONG num = 0; WORD *t, *m; *numterms = 0; while ( *terms ) { *numterms += 1; t = terms + 1; GETSTOP(terms,m); while ( t < m ) { if ( *t >= FUNCTION ) { if ( functions[*t-FUNCTION].commute ) { num++; break; } } t += t[1]; } terms = terms + *terms; } return(num); } /* #] numcommute : */ form-5.0.1/sources/tables.c0000644000175100017510000017221515217035721011257 /** @file tables.c * * Contains all functions that deal with the table bases on the 'FORM level' * The low level database routines are in minos.c */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : File contains the routines for the tree structure of sparse tables We insert elements by InsTableTree(T,tp) with T the TABLES element and tp the pointer to the indices. We look for elements with FindTableTree(T,tp,inc) with T the TABLES element, tp the pointer to the indices or the function arguments and inc tells which of these options. The tree is cleared with ClearTableTree(T) and we rebuild the tree after a .store in which we lost a part of the table with RedoTableTree(T,newsize) In T->tablepointers we have the lists of indices for each element. Additionally for each element there is an extension. There are TABLEEXTENSION WORDs reserved for that. The old system had two words One for the element in the rhs of the compile buffer and one for an additional rhs in case the original would be overwritten by a new definition, but the old was fixed by .global and hence it should be possible to restore it. New use (new = 24-sep-2001) rhs1,numCompBuffer1,rhs2,numCompBuffer2,usage Hence TABLEEXTENSION will be 5. Note that for 64 bits the use of the compiler buffer is overdoing it a bit, but it would be too complicated to try to give it special code. */ #include "form3.h" #include "minos.h" #include "comtool.h" /* static UBYTE *sparse = (UBYTE *)"sparse"; */ static UBYTE *tablebase = (UBYTE *)"tablebase"; /* #] Includes : #[ ClearTableTree : */ void ClearTableTree(TABLES T) { COMPTREE *root; if ( T->boomlijst == 0 ) { T->MaxTreeSize = 125; T->boomlijst = (COMPTREE *)Malloc1(T->MaxTreeSize*sizeof(COMPTREE), "ClearTableTree"); } root = T->boomlijst; T->numtree = 0; T->rootnum = 0; root->left = -1; root->right = -1; root->parent = -1; root->blnce = 0; root->value = -1; root->usage = 0; } /* #] ClearTableTree : #[ InsTableTree : int InsTableTree(TABLES T,WORD *,arglist) Searches for the element specified by the list of arguments. If found, it returns -(the offset in T->tablepointers) If not found, it will allocate a new element, balance the tree if necessary and return the number of the element in the boomlijst This number is always > 0, because we start from 1. */ int InsTableTree(TABLES T, WORD *tp) { COMPTREE *boomlijst, *q, *p, *s; WORD *v1, *v2, *v3, xstop; int ip, iq, is; if ( T->numtree + 1 >= T->MaxTreeSize ) { if ( T->MaxTreeSize == 0 ) ClearTableTree(T); else { is = T->MaxTreeSize * 2; s = (COMPTREE *)Malloc1(is*sizeof(COMPTREE),"InsTableTree"); for ( ip = 0; ip < T->MaxTreeSize; ip++ ) { s[ip] = T->boomlijst[ip]; } if ( T->boomlijst ) M_free(T->boomlijst,"InsTableTree"); T->boomlijst = s; T->MaxTreeSize = is; } } boomlijst = T->boomlijst; q = boomlijst + T->rootnum; if ( q->right == -1 ) { /* First element */ T->numtree++; s = boomlijst+T->numtree; q->right = T->numtree; s->parent = T->rootnum; s->left = s->right = -1; s->blnce = 0; s->value = tp - T->tablepointers; s->usage = 0; return(T->numtree); } ip = q->right; if ( T->numind >= 0 ) xstop = T->numind; else xstop = *tp + 1; while ( ip >= 0 ) { p = boomlijst + ip; v1 = T->tablepointers + p->value; v2 = tp; v3 = tp + xstop; while ( *v1 == *v2 && v2 < v3 ) { v1++; v2++; } if ( v2 >= v3 ) return(-p->value); if ( *v1 > *v2 ) { iq = p->right; if ( iq >= 0 ) { ip = iq; } else { T->numtree++; is = T->numtree; p->right = is; s = boomlijst + is; s->parent = ip; s->left = s->right = -1; s->blnce = 0; s->value = tp - T->tablepointers; s->usage = 0; p->blnce++; if ( p->blnce == 0 ) return(T->numtree); goto balance; } } else if ( *v1 < *v2 ) { iq = p->left; if ( iq >= 0 ) { ip = iq; } else { T->numtree++; is = T->numtree; s = boomlijst+is; p->left = is; s->parent = ip; s->left = s->right = -1; s->blnce = 0; s->value = tp - T->tablepointers; s->usage = 0; p->blnce--; if ( p->blnce == 0 ) return(T->numtree); goto balance; } } } MesPrint("Serious problems in InsTableTree!\n"); Terminate(-1); return(0); balance:; for (;;) { p = boomlijst + ip; iq = p->parent; if ( iq == T->rootnum ) break; q = boomlijst + iq; if ( ip == q->left ) q->blnce--; else q->blnce++; if ( q->blnce == 0 ) break; if ( q->blnce == -2 ) { if ( p->blnce == -1 ) { /* single rotation */ q->left = p->right; p->right = iq; p->parent = q->parent; q->parent = ip; if ( boomlijst[p->parent].left == iq ) boomlijst[p->parent].left = ip; else boomlijst[p->parent].right = ip; if ( q->left >= 0 ) boomlijst[q->left].parent = iq; q->blnce = p->blnce = 0; } else { /* double rotation */ s = boomlijst + is; q->left = s->right; p->right = s->left; s->right = iq; s->left = ip; if ( p->right >= 0 ) boomlijst[p->right].parent = ip; if ( q->left >= 0 ) boomlijst[q->left].parent = iq; s->parent = q->parent; q->parent = is; p->parent = is; if ( boomlijst[s->parent].left == iq ) boomlijst[s->parent].left = is; else boomlijst[s->parent].right = is; if ( s->blnce > 0 ) { q->blnce = s->blnce = 0; p->blnce = -1; } else if ( s->blnce < 0 ) { p->blnce = s->blnce = 0; q->blnce = 1; } else { p->blnce = s->blnce = q->blnce = 0; } } break; } else if ( q->blnce == 2 ) { if ( p->blnce == 1 ) { /* single rotation */ q->right = p->left; p->left = iq; p->parent = q->parent; q->parent = ip; if ( boomlijst[p->parent].left == iq ) boomlijst[p->parent].left = ip; else boomlijst[p->parent].right = ip; if ( q->right >= 0 ) boomlijst[q->right].parent = iq; q->blnce = p->blnce = 0; } else { /* double rotation */ s = boomlijst + is; q->right = s->left; p->left = s->right; s->left = iq; s->right = ip; if ( p->left >= 0 ) boomlijst[p->left].parent = ip; if ( q->right >= 0 ) boomlijst[q->right].parent = iq; s->parent = q->parent; q->parent = is; p->parent = is; if ( boomlijst[s->parent].left == iq ) boomlijst[s->parent].left = is; else boomlijst[s->parent].right = is; if ( s->blnce < 0 ) { q->blnce = s->blnce = 0; p->blnce = 1; } else if ( s->blnce > 0 ) { p->blnce = s->blnce = 0; q->blnce = -1; } else { p->blnce = s->blnce = q->blnce = 0; } } break; } is = ip; ip = iq; } return(T->numtree); } /* #] InsTableTree : #[ RedoTableTree : To be used when a sparse table is trimmed due to a .store We rebuild the tree. In the future one could try to become faster at the cost of quite some complexity. We need to keep the first 'size' elements in the boomlijst. Kill all others and reconstruct the tree with the original ordering. This is very complicated! Because .store will either keep the whole table or remove the whole table we should not come here often. Hence we choose the slow solution for now. */ void RedoTableTree(TABLES T, int newsize) { WORD *tp; int i; ClearTableTree(T); for ( i = 0, tp = T->tablepointers; i < newsize; i++ ) { InsTableTree(T,tp); tp += ABS(T->numind)+TABLEEXTENSION; } } /* #] RedoTableTree : #[ FindTableTree : int FindTableTree(TABLES T,WORD *,arglist,int,inc) Searches for the element specified by the list of arguments. If found, it returns the offset in T->tablepointers If not found, it will return -1 The list here is from the list of function arguments. Hence it has pairs of numbers -SNUMBER,index Actually inc says how many numbers there are and the above case is for inc = 2. For inc = 1 we have just a list of indices. */ int FindTableTree(TABLES T, WORD *tp, int inc) { COMPTREE *boomlijst = T->boomlijst, *q = boomlijst + T->rootnum, *p; WORD *v1, *v2, *v3, xstop; int ip, iq; if ( q->right == -1 ) return(-1); ip = q->right; if ( inc > 1 ) tp += inc-1; if ( T->numind >= 0 ) xstop = T->numind; else { /* We have to read the number of arguments first */ if ( *tp <= 0 ) return(-1); /* Cannot be! */ xstop = *tp+1; } while ( ip >= 0 ) { p = boomlijst + ip; v1 = T->tablepointers + p->value; v2 = tp; v3 = v1 + xstop; while ( *v1 == *v2 && v1 < v3 ) { v1++; v2 += inc; } if ( v1 == v3 ) { p->usage++; return(p->value); } if ( *v1 > *v2 ) { iq = p->right; if ( iq >= 0 ) { ip = iq; } else return(-1); } else if ( *v1 < *v2 ) { iq = p->left; if ( iq >= 0 ) { ip = iq; } else return(-1); } } MesPrint("Serious problems in FindTableTree\n"); Terminate(-1); return(-1); } /* #] FindTableTree : #[ DoTableExpansion : */ int DoTableExpansion(WORD *term, WORD level) { GETIDENTITY WORD *t, *tstop, *stopper, *termout, *m, *mm, *tp, *r, xx; WORD numsubexp, numbuf; TABLES T = 0; int i, j, num; AN.TeInFun = AR.TePos = 0; tstop = term + *term; stopper = tstop - ABS(tstop[-1]); t = term+1; while ( t < stopper ) { if ( *t != TABLEFUNCTION ) { t += t[1]; continue; } if ( t[FUNHEAD] > -FUNCTION ) { t += t[1]; continue; } T = functions[-t[FUNHEAD]-FUNCTION].tabl; if ( T == 0 ) { t += t[1]; continue; } if ( T->spare ) T = T->spare; if ( t[1] == FUNHEAD+2 && t[FUNHEAD+1] <= -FUNCTION ) break; if ( t[1] < FUNHEAD+1+2*ABS(T->numind) ) { t += t[1]; continue; } for ( i = 0; i < ABS(T->numind); i++ ) { if ( t[FUNHEAD+1+2*i] != -SYMBOL ) break; } if ( i >= ABS(T->numind) ) break; t += t[1]; } if ( t >= stopper ) { MesPrint("Internal error: Missing table_ function"); Terminate(-1); } /* Table in T. Now collect the numbers of the symbols; */ termout = AT.WorkPointer; if ( T->sparse ) { for ( i = 0; i < T->totind; i++ ) { /* Loop over all table elements */ m = termout + 1; mm = term + 1; while ( mm < t ) *m++ = *mm++; r = m; if ( t[1] == FUNHEAD+2 && t[FUNHEAD+1] <= -FUNCTION ) { *m++ = -t[FUNHEAD+1]; tp = T->tablepointers + (ABS(T->numind)+TABLEEXTENSION)*i; if ( T->numind < 0 ) { xx = tp[0]+1; *m++ = FUNHEAD+xx*2; for ( j = 2; j < FUNHEAD; j++ ) *m++ = 0; for ( j = 0; j < xx; j++ ) { *m++ = -SNUMBER; *m++ = *tp++; } } else { *m++ = FUNHEAD+T->numind*2; for ( j = 2; j < FUNHEAD; j++ ) *m++ = 0; for ( j = 0; j < T->numind; j++ ) { *m++ = -SNUMBER; *m++ = *tp++; } } } else if ( T->numind < 0 ) { tp = T->tablepointers + (ABS(T->numind)+TABLEEXTENSION)*i; xx = tp[0]+1; *m++ = SYMBOL; *m++ = 2+xx*2; mm = t + FUNHEAD+1; for ( j = 0; j < xx; j++, mm += 2, tp++ ) { if ( *tp != 0 ) { *m++ = mm[1]; *m++ = *tp; } } r[1] = m-r; if ( r[1] == 2 ) m = r; } else { *m++ = SYMBOL; *m++ = 2+T->numind*2; mm = t + FUNHEAD+1; tp = T->tablepointers + (T->numind+TABLEEXTENSION)*i; for ( j = 0; j < T->numind; j++, mm += 2, tp++ ) { if ( *tp != 0 ) { *m++ = mm[1]; *m++ = *tp; } } r[1] = m-r; if ( r[1] == 2 ) m = r; } /* The next code replaces this old code *m++ = SUBEXPRESSION; *m++ = SUBEXPSIZE; *m++ = *tp; *m++ = 1; *m++ = T->bufnum; FILLSUB(m); mm = t + t[1]; We had forgotten to take the parameters into account. Hence the subexpression prototype for wildcards was missed Now we slow things down a little bit, but we do not run any risks. There is still one problem. We have not checked that the prototype matches. */ tp = T->tablepointers + (ABS(T->numind)+TABLEEXTENSION)*i +ABS(T->numind); numsubexp = tp[0]; numbuf = tp[1]; r = m; #ifdef WITHPTHREADS tp = T->prototype[identity]; #else tp = T->prototype; #endif for ( j = 0; j < tp[1]; j++ ) *m++ = tp[j]; r[2] = numsubexp; r[4] = numbuf; /* r = m; tp = T->tablepointers + (ABS(T->numind)+TABLEEXTENSION)*i; *m++ = -t[FUNHEAD]; if ( T->numind < 0 ) { xx = tp[0]+1; *m++ = t[1] - xx - T->numind - 1; } else { xx = T->numind; *m++ = t[1] - 1; } for ( j = 2; j < FUNHEAD; j++ ) *m++ = t[j]; for ( j = 0; j < xx; j++ ) { *m++ = -SNUMBER; *m++ = *tp++; } tp = t + FUNHEAD + 1 + 2*T->numind; mm = t + t[1]; while ( tp < mm ) *m++ = *tp++; r[1] = m-r; */ /* From now on is old code */ mm = t + t[1]; while ( mm < tstop ) *m++ = *mm++; *termout = m - termout; AT.WorkPointer = m; if ( Generator(BHEAD termout,level) ) { MesCall("DoTableExpand"); return(-1); } AT.WorkPointer = termout; } } else { for ( i = 0; i < T->totind; i++ ) { #if TABLEEXTENSION == 2 if ( T->tablepointers[i] < 0 ) continue; #else if ( T->tablepointers[TABLEEXTENSION*i] < 0 ) continue; #endif m = termout + 1; mm = term + 1; while ( mm < t ) *m++ = *mm++; r = m; if ( t[1] == FUNHEAD+2 && t[FUNHEAD+1] <= -FUNCTION ) { *m++ = -t[FUNHEAD+1]; *m++ = FUNHEAD+T->numind*2; for ( j = 2; j < FUNHEAD; j++ ) *m++ = 0; tp = T->tablepointers + (T->numind+TABLEEXTENSION)*i; for ( j = 0; j < T->numind; j++ ) { if ( j > 0 ) { num = T->mm[j].mini + ( i % T->mm[j-1].size ) / T->mm[j].size; } else { num = T->mm[j].mini + i / T->mm[j].size; } *m++ = -SNUMBER; *m++ = num; } } else { *m++ = SYMBOL; *m++ = 2+T->numind*2; mm = t + FUNHEAD+1; for ( j = 0; j < T->numind; j++, mm += 2 ) { if ( j > 0 ) { num = T->mm[j].mini + ( i % T->mm[j-1].size ) / T->mm[j].size; } else { num = T->mm[j].mini + i / T->mm[j].size; } if ( num != 0 ) { *m++ = mm[1]; *m++ = num; } } r[1] = m-r; if ( r[1] == 2 ) m = r; } /* The next code replaces this old code *m++ = SUBEXPRESSION; *m++ = SUBEXPSIZE; *m++ = *tp; *m++ = 1; *m++ = T->bufnum; FILLSUB(m); mm = t + t[1]; We had forgotten to take the parameters into account. Hence the subexpression prototype for wildcards was missed Now we slow things down a little bit, but we do not run any risks. There is still one problem. We have not checked that the prototype matches. */ r = m; *m++ = -t[FUNHEAD]; *m++ = t[1] - 1; for ( j = 2; j < FUNHEAD; j++ ) *m++ = t[j]; for ( j = 0; j < T->numind; j++ ) { if ( j > 0 ) { num = T->mm[j].mini + ( i % T->mm[j-1].size ) / T->mm[j].size; } else { num = T->mm[j].mini + i / T->mm[j].size; } *m++ = -SNUMBER; *m++ = num; } tp = t + FUNHEAD + 1 + 2*T->numind; mm = t + t[1]; while ( tp < mm ) *m++ = *tp++; r[1] = m - r; /* From now on is old code */ while ( mm < tstop ) *m++ = *mm++; *termout = m - termout; AT.WorkPointer = m; if ( Generator(BHEAD termout,level) ) { MesCall("DoTableExpand"); return(-1); } } } return(0); } /* #] DoTableExpansion : #[ TableBase : File with all the database related things. We have the routines for the generic database command TableBase,options; TB,options; Options are: Open "File.tbl"; Open for R/W Open "File.tbl", readonly; Open for R Create "File.tbl"; Create for write Load "File.tbl", tablename; Loads stubs of table Load "File.tbl"; Loads stubs of all tables Enter "File.tbl", tablename; Loads whole table Enter "File.tbl"; Loads all tables Audit "File.tbl", options; Print list of contents Replace "File.tbl", tablename; Saves a table (with overwrite) Replace "File.tbl", table element; Saves a table element ,, Cleanup "File.tbl"; Makes tables contingent AddTo "File.tbl" tablename; Add if not yet there. AddTo "File.tbl" table element; Add if not yet there. Delete "File.tbl" tablename; Delete "File.tbl" table element; On/Off substitute; On/Off compress "File.tbl"; id tbl_(f?,?a) = f(?a); When a tbl_ is used, automatically the corresponding element is compiled at the start of the next module. if TB,On,substitute [tablename], use of table RHS (if loaded) if TB,Off,substitute [tablename], use of tbl_(table,...); Still needed: Something like OverLoad to allow loading parts of a table from more than one file. Date stamps needed? In that case we need a touch command as well. If we put all our diagrams inside, we have to go outside the concept of tables. #] TableBase : #[ CoTableBase : To be followed by ,subkey */ static KEYWORD tboptions[] = { {"addto", (TFUN)CoTBaddto, 0, PARTEST} ,{"audit", (TFUN)CoTBaudit, 0, PARTEST} ,{"cleanup", (TFUN)CoTBcleanup, 0, PARTEST} ,{"create", (TFUN)CoTBcreate, 0, PARTEST} ,{"enter", (TFUN)CoTBenter, 0, PARTEST} ,{"help", (TFUN)CoTBhelp, 0, PARTEST} ,{"load", (TFUN)CoTBload, 0, PARTEST} ,{"off", (TFUN)CoTBoff, 0, PARTEST} ,{"on", (TFUN)CoTBon, 0, PARTEST} ,{"open", (TFUN)CoTBopen, 0, PARTEST} ,{"replace", (TFUN)CoTBreplace, 0, PARTEST} ,{"use", (TFUN)CoTBuse, 0, PARTEST} }; static UBYTE *tablebasename = 0; int CoTableBase(UBYTE *s) { UBYTE *option, c, *t; int i,optlistsize = sizeof(tboptions)/sizeof(KEYWORD), error = 0; while ( *s == ' ' ) s++; if ( *s != '"' ) { if ( ( tolower(*s) == 'h' ) && ( tolower(s[1]) == 'e' ) && ( tolower(s[2]) == 'l' ) && ( tolower(s[3]) == 'p' ) && ( FG.cTable[s[4]] > 1 ) ) { CoTBhelp(s); return(0); } proper:; MesPrint("&Proper syntax: TableBase \"filename\" options"); return(1); } s++; tablebasename = s; while ( *s && *s != '"' ) s++; if ( *s != '"' ) goto proper; t = s; s++; *t = 0; while ( *s == ' ' || *s == '\t' || *s == ',' ) s++; option = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; for ( i = 0; i < optlistsize; i++ ) { if ( StrICmp(option,(UBYTE *)(tboptions[i].name)) == 0 ) { *s = c; while ( *s == ',' ) s++; error = (tboptions[i].func)(s); *t = '"'; return(error); } } MesPrint("&Unrecognized option %s in TableBase statement",option); return(1); } /* #] CoTableBase : #[ FlipTable : Flips the table between use as 'stub' and regular use */ int FlipTable(FUNCTIONS f, int type) { TABLES T, TT; T = f->tabl; if ( ( TT = T->spare ) == 0 ) { MesPrint("Error: trying to change mode on a table that has no tablebase"); return(-1); } if ( TT->mode == type ) f->tabl = TT; return(0); } /* #] FlipTable : #[ SpareTable : Creates a spare element for a table. This is used in the table bases. It is a (thus far) empty copy of the TT table. By using FlipTable we can switch between them and alter which version of a table we will be using. Note that this also causes some extra work in the ResetVariables and the Globalize routines. */ int SpareTable(TABLES TT) { TABLES T; T = (TABLES)Malloc1(sizeof(struct TaBlEs),"table"); T->defined = T->mdefined = 0; T->sparse = TT->sparse; T->mm = 0; T->flags = 0; T->numtree = 0; T->rootnum = 0; T->MaxTreeSize = 0; T->boomlijst = 0; T->strict = TT->strict; T->bounds = TT->bounds; T->bufnum = inicbufs(); T->argtail = TT->argtail; T->spare = TT; T->bufferssize = 8; T->buffers = (WORD *)Malloc1(sizeof(WORD)*T->bufferssize,"SpareTable buffers"); T->buffersfill = 0; T->buffers[T->buffersfill++] = T->bufnum; T->mode = 0; T->numind = TT->numind; T->totind = 0; T->prototype = TT->prototype; T->pattern = TT->pattern; T->tablepointers = 0; T->reserved = 0; T->tablenum = 0; T->numdummies = 0; T->mm = (MINMAX *)Malloc1(ABS(T->numind)*sizeof(MINMAX),"table dimensions"); T->flags = (WORD *)Malloc1(ABS(T->numind)*sizeof(WORD),"table flags"); ClearTableTree(T); TT->spare = T; TT->mode = 1; return(0); } /* #] SpareTable : #[ FindTB : Looks for a tablebase with the given name in the active tablebases. */ DBASE *FindTB(UBYTE *name) { DBASE *d; int i; for ( i = 0; i < NumTableBases; i++ ) { d = tablebases+i; if ( d->name && ( StrCmp(name,(UBYTE *)(d->name)) == 0 ) ) { return(d); } } return(0); } /* #] FindTB : #[ CoTBcreate : Creates a new tablebase. Error is when there is already an active tablebase by this name. If a file with the given name exists already, but it does not correspond to an active table base, its contents will be lost. Note that tablebasename is a static variable, defined in CoTableBase */ int CoTBcreate(UBYTE *s) { DUMMYUSE(s); if ( FindTB(tablebasename) != 0 ) { MesPrint("&There is already an open TableBase with the name %s",tablebasename); return(-1); } NewDbase((char *)tablebasename,0); return(0); } /* #] CoTBcreate : #[ CoTBopen : */ int CoTBopen(UBYTE *s) { DBASE *d; MLONG rw = 1; SkipSpaces(&s); if ( *s ) { if ( ConsumeOption(&s,"readonly") != 0 ) { rw = 0; } else { MesPrint("&Invalid option for TableBase open: %s, ignoring", s); } } if ( ( d = FindTB(tablebasename) ) != 0 ) { MesPrint("&There is already an open TableBase with the name %s",tablebasename); return(-1); } d = GetDbase((char *)tablebasename, rw); if ( CheckTableDeclarations(d) ) return(-1); return(0); } /* #] CoTBopen : #[ CoTBaddto : */ int CoTBaddto(UBYTE *s) { GETIDENTITY DBASE *d; UBYTE *tablename, c, *t, elementstring[ELEMENTSIZE+20], *ss, *es; WORD type, funnum, lbrac, first, num, *expr, *w; TABLES T = 0; MLONG basenumber; LONG x; int i, j, error = 0, sum; if ( ( d = FindTB(tablebasename) ) == 0 ) { MesPrint("&No open tablebase with the name %s",tablebasename); return(-1); } if ( ( d->rwmode ) == 0 ) { MesPrint("&Tablebase with the name %s opened in read only mode",tablebasename); return(-1); } AO.DollarOutSizeBuffer = 32; AO.DollarOutBuffer = (UBYTE *)Malloc1(AO.DollarOutSizeBuffer, "TableOutBuffer"); /* Now loop through the names and start adding */ while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; while ( *s ) { tablename = s; if ( ( s = SkipAName(s) ) == 0 ) goto tableabort; c = *s; *s = 0; if ( ( GetVar(tablename,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",tablename); *s = c; goto tableabort; } if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",tablename); *s = c; goto tableabort; } basenumber = AddTableName(d,(char *)tablename,T); if ( T->spare && ( T->mode == 1 ) ) T = T->spare; if ( basenumber < 0 ) basenumber = -basenumber; else if ( basenumber == 0 ) { *s = c; goto tableabort; } *s = c; if ( *s == '(' ) { /* Addition of single element */ s++; es = s; for ( i = 0, w = AT.WorkPointer; i < ABS(T->numind); i++ ) { ParseSignedNumber(x,s); if ( FG.cTable[s[-1]] != 1 || ( *s != ',' && *s != ')' ) ) { MesPrint("&Table arguments in TableBase addto statement should be numbers"); return(1); } *w++ = x; if ( *s == ')' ) break; s++; } if ( *s != ')' || i < ( ABS(T->numind) - 1 ) ) { MesPrint("&Incorrect number of table arguments in TableBase addto statement. Should be %d" ,ABS(T->numind)); error = 1; } c = *s; *s = 0; i = FindTableTree(T,AT.WorkPointer,1); if ( i < 0 ) { MesPrint("&Element %s has not been defined",es); error = 1; *s++ = c; } else if ( ExistsObject(d,basenumber,(char *)es) ) {} else { int dict = AO.CurrentDictionary; AO.CurrentDictionary = 0; sum = i + ABS(T->numind); /* See also commentary below */ AO.DollarInOutBuffer = 1; AO.PrintType = 1; ss = AO.DollarOutBuffer; *ss = 0; AO.OutInBuffer = 1; #if ( TABLEEXTENSION == 2 ) expr = cbuf[T->bufnum].rhs[T->tablepointers[sum]]; #else expr = cbuf[T->tablepointers[sum+1]].rhs[T->tablepointers[sum]]; #endif lbrac = 0; first = 0; while ( *expr ) { if ( WriteTerm(expr,&lbrac,first,PRINTON,0) ) { error = 1; break; } expr += *expr; } AO.OutInBuffer = 0; AddObject(d,basenumber,(char *)es,(char *)(AO.DollarOutBuffer)); *s++ = c; AO.CurrentDictionary = dict; } } else { /* Now we have to start looping through all defined elements of this table. We have to construct the arguments in text format. */ for ( i = 0; i < T->totind; i++ ) { #if ( TABLEEXTENSION == 2 ) if ( !T->sparse && T->tablepointers[i] < 0 ) continue; #else if ( !T->sparse && T->tablepointers[TABLEEXTENSION*i] < 0 ) continue; #endif sum = i * ( ABS(T->numind) + TABLEEXTENSION ); t = elementstring; for ( j = 0; j < ABS(T->numind); j++, sum++ ) { if ( j > 0 ) *t++ = ','; num = T->tablepointers[sum]; t = NumCopy(num,t); if ( ( t - elementstring ) >= ELEMENTSIZE ) { MesPrint("&Table element specification takes more than %ld characters and cannot be handled", (MLONG)ELEMENTSIZE); goto tableabort; } } if ( ExistsObject(d,basenumber,(char *)elementstring) ) { continue; } /* We have the number in basenumber and the element in elementstring. Now we need the rhs. We can use the code from WriteDollarToBuffer. Main complication: in the table compiler buffer there can be brackets. The dollars do not have those...... */ AO.DollarInOutBuffer = 1; AO.PrintType = 1; ss = AO.DollarOutBuffer; *ss = 0; AO.OutInBuffer = 1; #if ( TABLEEXTENSION == 2 ) expr = cbuf[T->bufnum].rhs[T->tablepointers[sum]]; #else expr = cbuf[T->tablepointers[sum+1]].rhs[T->tablepointers[sum]]; #endif lbrac = 0; first = 0; while ( *expr ) { if ( WriteTerm(expr,&lbrac,first,PRINTON,0) ) { error = 1; break; } expr += *expr; } AO.OutInBuffer = 0; AddObject(d,basenumber,(char *)elementstring,(char *)(AO.DollarOutBuffer)); } } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } if ( WriteIniInfo(d) ) goto tableabort; M_free(AO.DollarOutBuffer,"DollarOutBuffer"); AO.DollarOutBuffer = 0; AO.DollarOutSizeBuffer = 0; return(error); tableabort:; M_free(AO.DollarOutBuffer,"DollarOutBuffer"); AO.DollarOutBuffer = 0; AO.DollarOutSizeBuffer = 0; AO.OutInBuffer = 0; return(1); } /* #] CoTBaddto : #[ CoTBenter : Loads the elements of the tables specified into memory and sends them one by one to the compiler as Fill statements. */ int CoTBenter(UBYTE *s) { DBASE *d; MLONG basenumber; UBYTE *arguments, *rhs, *buffer, *t, *u, c, *tablename; LONG size; int i, j, error = 0, error1 = 0, printall = 0; TABLES T = 0; WORD type, funnum; int dict = AO.CurrentDictionary; AO.CurrentDictionary = 0; if ( ( d = FindTB(tablebasename) ) == 0 ) { MesPrint("&No open tablebase with the name %s, check for existence of file or try readonly mode when opening.",tablebasename); error = -1; goto Endofall; } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s == '!' ) { printall = 1; s++; } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s ) { while ( *s ) { tablename = s; if ( ( s = SkipAName(s) ) == 0 ) { error = 1; goto Endofall; } c = *s; *s = 0; if ( ( GetVar(tablename,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",tablename); basenumber = 0; } else if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",tablename); basenumber = 0; } else { basenumber = GetTableName(d,(char *)tablename); } if ( T->spare == 0 ) { SpareTable(T); } if ( basenumber > 0 ) { for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( basenumber != d->iblocks[i]->objects[j].tablenumber ) continue; arguments = (UBYTE *)(d->iblocks[i]->objects[j].element); rhs = (UBYTE *)ReadObject(d,basenumber,(char *)arguments); if ( printall ) { if ( rhs ) { MesPrint("%s(%s) = %s",tablename,arguments,rhs); } else { MesPrint("%s(%s) = 0",tablename,arguments); } } if ( rhs ) { u = rhs; while ( *u ) u++; size = u-rhs; u = arguments; while ( *u ) u++; size += u-arguments; u = tablename; while ( *u ) u++; size += u-tablename; size += 6; buffer = (UBYTE *)Malloc1(size,"TableBase copy"); t = tablename; u = buffer; while ( *t ) *u++ = *t++; *u++ = '('; t = arguments; while ( *t ) *u++ = *t++; *u++ = ')'; *u++ = '='; t = rhs; while ( *t ) *u++ = *t++; if ( t == rhs ) *u++ = '0'; *u++ = 0; *u = 0; M_free(rhs,"rhs in TBenter"); error1 = CoFill(buffer); if ( error1 < 0 ) goto Endofall; if ( error1 != 0 ) error = error1; M_free(buffer,"TableBase copy"); } } } } *s = c; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } } else { s = (UBYTE *)(d->tablenames); basenumber = 0; while ( *s ) { basenumber++; tablename = s; while ( *s ) s++; s++; while ( *s ) s++; s++; if ( ( GetVar(tablename,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",tablename); } else if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",tablename); } if ( T->spare == 0 ) { SpareTable(T); } for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber == basenumber ) { arguments = (UBYTE *)(d->iblocks[i]->objects[j].element); rhs = (UBYTE *)ReadObject(d,basenumber,(char *)arguments); if ( printall ) { if ( rhs ) { MesPrint("%s%s = %s",tablename,arguments,rhs); } else { MesPrint("%s%s = 0",tablename,arguments); } } if ( rhs ) { u = rhs; while ( *u ) u++; size = u-rhs; u = arguments; while ( *u ) u++; size += u-arguments; u = tablename; while ( *u ) u++; size += u-tablename; size += 6; buffer = (UBYTE *)Malloc1(size,"TableBase copy"); t = tablename; u = buffer; while ( *t ) *u++ = *t++; *u++ = '('; t = arguments; while ( *t ) *u++ = *t++; *u++ = ')'; *u++ = '='; t = rhs; while ( *t ) *u++ = *t++; if ( t == rhs ) *u++ = '0'; *u++ = 0; *u = 0; M_free(rhs,"rhs in TBenter"); error1 = CoFill(buffer); if ( error1 < 0 ) goto Endofall; if ( error1 != 0 ) error = error1; M_free(buffer,"TableBase copy"); } } } } } } Endofall:; AO.CurrentDictionary = dict; return(error); } /* #] CoTBenter : #[ CoTestUse : Possibly to be followed by names of tables. We make an array of TABLES structs to be tested in AC.usedtables. Note: only sparse tables are allowed. No arguments means all tables. */ int CoTestUse(UBYTE *s) { GETIDENTITY UBYTE *tablename, c; WORD type, funnum, *w; TABLES T; int error = 0; w = AT.WorkPointer; *w++ = TYPETESTUSE; *w++ = 2; while ( *s ) { tablename = s; if ( ( s = SkipAName(s) ) == 0 ) return(1); c = *s; *s = 0; if ( ( GetVar(tablename,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",tablename); error = 1; } else if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",tablename); error = 1; } *w++ = funnum + FUNCTION; *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; } AT.WorkPointer[1] = w - AT.WorkPointer; /* if ( AT.WorkPointer[1] > 2 ) { AddNtoL(AT.WorkPointer[1],AT.WorkPointer); } */ AddNtoL(AT.WorkPointer[1],AT.WorkPointer); return(error); } /* #] CoTestUse : #[ CheckTableDeclarations : Checks that all tables in a tablebase have identical properties to possible previous declarations. If they have not been declared before, they are declared here. */ int CheckTableDeclarations(DBASE *d) { WORD type, funnum; UBYTE *s, *ss, *t, *command = 0; int k, error = 0, error1, i; TABLES T; LONG commandsize = 0; s = (UBYTE *)(d->tablenames); for ( k = 0; k < d->topnumber; k++ ) { if ( GetVar(s,&type,&funnum,ANYTYPE,NOAUTO) == NAMENOTFOUND ) { /* We have to declare the table */ ss = s; i = 0; while ( *ss ) { ss++; i++; } /* name */ ss++; while ( *ss ) { ss++; i++; } /* tail */ if ( commandsize == 0 ) { commandsize = i + 15; if ( commandsize < 100 ) commandsize = 100; } if ( (i+11) > commandsize ) { if ( command ) { M_free(command,"table command"); command = 0; } commandsize = i+10; } if ( command == 0 ) { command = (UBYTE *)Malloc1(commandsize,"table command"); } t = command; ss = tablebase; while ( *ss ) *t++ = *ss++; *t++ = ','; while ( *s ) *t++ = *s++; s++; while ( *s ) *t++ = *s++; *t++ = ')'; *t = 0; s++; error1 = DoTable(command,1); if ( error1 ) error = error1; } else if ( ( type != CFUNCTION ) || ( ( T = functions[funnum].tabl ) == 0 ) || ( T->sparse == 0 ) ) { MesPrint("&%s has been declared previously, but not as a sparse table.",s); error = 1; while ( *s ) s++; s++; while ( *s ) s++; s++; } else { /* Test dimension and argtail. There should be an exact match. We are not going to rename arguments when reading the elements. */ ss = s; while ( *s ) s++; s++; if ( StrCmp(s,T->argtail) ) { MesPrint("&Declaration of table %s in %s different from previous declaration",ss,d->name); error = 1; } while ( *s ) s++; s++; } } if ( command ) { M_free(command,"table command"); } return(error); } /* #] CheckTableDeclarations : #[ CoTBload : Loads the table stubbs of the specified tables in the indicated tablebase. Syntax: TableBase "tablebasename.tbl" load [tablename(s)]; If no tables are specified all tables are taken. */ int CoTBload(UBYTE *ss) { DBASE *d; UBYTE *s, *name, *t, *r, *command, *arguments, *tail; LONG commandsize; int num, cs, es, ns, ts, i, j, error = 0, error1; if ( ( d = FindTB(tablebasename) ) == 0 ) { MesPrint("&No open tablebase with the name %s",tablebasename); return(-1); } commandsize = 120; command = (UBYTE *)Malloc1(commandsize,"Fill command"); AC.vetofilling = 1; if ( *ss ) { while ( *ss == ',' || *ss == ' ' || *ss == '\t' ) ss++; while ( *ss ) { name = ss; ss = SkipAName(ss); *ss = 0; s = (UBYTE *)(d->tablenames); num = 0; ns = 0; while ( *s ) { num++; if ( StrCmp(s,name) ) { while ( *s ) s++; s++; while ( *s ) s++; s++; num++; continue; } name = s; while ( *s ) s++; ns = s-name; s++; tail = s; while ( *s ) s++; ts = s-tail; s++; tail++; while ( FG.cTable[*tail] == 1 ) tail++; /* Go through all elements */ for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber == num ) { t = arguments = (UBYTE *)(d->iblocks[i]->objects[j].element); while ( *t ) t++; es = t - arguments; cs = 2*es + 2*ns + ts + 10; if ( cs > commandsize ) { commandsize = 2*cs; if ( command ) M_free(command,"Fill command"); command = (UBYTE *)Malloc1(commandsize,"Fill command"); } r = command; t = name; while ( *t ) *r++ = *t++; *r++ = '('; t = arguments; while ( *t ) *r++ = *t++; *r++ = ')'; *r++ = '='; *r++ = 't'; *r++ = 'b'; *r++ = 'l'; *r++ = '_'; *r++ = '('; t = name; while ( *t ) *r++ = *t++; *r++ = ','; t = arguments; while ( *t ) *r++ = *t++; t = tail; while ( *t ) { if ( *t == '?' && r[-1] != ',' ) { t++; if ( FG.cTable[*t] == 0 || *t == '$' || *t == '[' ) { t = SkipAName(t); if ( *t == '[' ) { SKIPBRA1(t); } } else if ( *t == '{' ) { SKIPBRA2(t); } else if ( *t ) { *r++ = *t++; continue; } } else *r++ = *t++; } *r++ = ')'; *r = 0; /* Still to do: replacemode or no replacemode? */ AC.vetotablebasefill = 1; error1 = CoFill(command); AC.vetotablebasefill = 0; if ( error1 < 0 ) goto finishup; if ( error1 != 0 ) error = error1; } } } break; } while ( *ss == ',' || *ss == ' ' || *ss == '\t' ) ss++; } } else { /* do all of them */ s = (UBYTE *)(d->tablenames); num = 0; ns = 0; while ( *s ) { num++; name = s; while ( *s ) s++; ns = s-name; s++; tail = s; while ( *s ) s++; ts = s-tail; s++; tail++; while ( FG.cTable[*tail] == 1 ) tail++; /* Go through all elements */ for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber == num ) { t = arguments = (UBYTE *)(d->iblocks[i]->objects[j].element); while ( *t ) t++; es = t - arguments; cs = 2*es + 2*ns + ts + 10; if ( cs > commandsize ) { commandsize = 2*cs; if ( command ) M_free(command,"Fill command"); command = (UBYTE *)Malloc1(commandsize,"Fill command"); } r = command; t = name; while ( *t ) *r++ = *t++; *r++ = '('; t = arguments; while ( *t ) *r++ = *t++; *r++ = ')'; *r++ = '='; *r++ = 't'; *r++ = 'b'; *r++ = 'l'; *r++ = '_'; *r++ = '('; t = name; while ( *t ) *r++ = *t++; *r++ = ','; t = arguments; while ( *t ) *r++ = *t++; t = tail; while ( *t ) { if ( *t == '?' && r[-1] != ',' ) { t++; if ( FG.cTable[*t] == 0 || *t == '$' || *t == '[' ) { t = SkipAName(t); if ( *t == '[' ) { SKIPBRA1(t); } } else if ( *t == '{' ) { SKIPBRA2(t); } else if ( *t ) { *r++ = *t++; continue; } } else *r++ = *t++; } *r++ = ')'; *r = 0; /* Still to do: replacemode or no replacemode? */ AC.vetotablebasefill = 1; error1 = CoFill(command); AC.vetotablebasefill = 0; if ( error1 < 0 ) goto finishup; if ( error1 != 0 ) error = error1; } } } } } finishup:; AC.vetofilling = 0; if ( command ) M_free(command,"Fill command"); return(error); } /* #] CoTBload : #[ TestUse : Look for tbl_(tablename,arguments) if tablename is encountered, check first whether the element is in use already. If not, check in the tables in AC.usedtables. If the element is not there, add it to AC.usedtables. We need the arguments of TestUse to see for which tables it is to be done */ int TestUse(WORD *term, WORD level) { WORD *tstop, *t, *m, *tstart, tabnum; WORD *funs, numfuns; int error = 0; TABLES T; LONG i; CBUF *C = cbuf+AM.rbufnum; int isp; numfuns = C->lhs[level][1] - 2; funs = C->lhs[level] + 2; GETSTOP(term,tstop); t = term+1; while ( t < tstop ) { if ( *t != TABLESTUB ) { t += t[1]; continue; } tstart = t; m = t + FUNHEAD; t += t[1]; if ( *m >= -FUNCTION ) continue; tabnum = -*m; if ( ( T = functions[tabnum-FUNCTION].tabl ) == 0 ) continue; if ( T->sparse == 0 ) continue; /* Check whether we have to test this one */ if ( numfuns > 0 ) { for ( i = 0; i < numfuns; i++ ) { if ( tabnum == funs[i] ) break; } if ( i >= numfuns && numfuns > 0 ) continue; } /* Test whether the element has been defined already. If not, mark it as used. Note: we only allow sparse tables (for now) */ m++; for ( i = 0; i < ABS(T->numind); i++, m += 2 ) { if ( m >= t || *m != -SNUMBER ) break; } if ( ( i == ABS(T->numind) ) && ( ( isp = FindTableTree(T,tstart+FUNHEAD+1,2) ) >= 0 ) ) { if ( ( T->tablepointers[isp+ABS(T->numind)+4] & ELEMENTLOADED ) == 0 ) { T->tablepointers[isp+ABS(T->numind)+4] |= ELEMENTUSED; } } else { MesPrint("TestUse: Encountered a table element inside tbl_ that does not correspond to a tablebase element"); error = -1; } } return(error); } /* #] TestUse : #[ CoTBaudit : */ int CoTBaudit(UBYTE *s) { DBASE *d; UBYTE *name, *tail; int i, j, error = 0, num; if ( ( d = FindTB(tablebasename) ) == 0 ) { MesPrint("&No open tablebase with the name %s",tablebasename); return(-1); } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; while ( *s ) { /* Get the options here They will mainly involve the sorting of the output. */ s++; } s = (UBYTE *)(d->tablenames); num = 0; while ( *s ) { num++; name = s; while ( *s ) s++; s++; tail = s; while ( *s ) s++; s++; MesPrint("Table,sparse,%s%s)",name,tail); for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber == num ) { MesPrint(" %s(%s)",name,d->iblocks[i]->objects[j].element); } } } } return(error); } /* #] CoTBaudit : #[ CoTBon : */ int CoTBon(UBYTE *s) { DBASE *d; UBYTE *ss, c; int error = 0; if ( ( d = FindTB(tablebasename) ) == 0 ) { MesPrint("&No open tablebase with the name %s",tablebasename); return(-1); } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; while ( *s ) { ss = SkipAName(s); c = *ss; *ss = 0; if ( StrICmp(s,(UBYTE *)("compress")) == 0 ) { d->mode &= ~NOCOMPRESS; } else { MesPrint("&subkey %s not defined in TableBase On statement"); error = 1; } *ss = c; s = ss; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } return(error); } /* #] CoTBon : #[ CoTBoff : */ int CoTBoff(UBYTE *s) { DBASE *d; UBYTE *ss, c; int error = 0; if ( ( d = FindTB(tablebasename) ) == 0 ) { MesPrint("&No open tablebase with the name %s",tablebasename); return(-1); } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; while ( *s ) { ss = SkipAName(s); c = *ss; *ss = 0; if ( StrICmp(s,(UBYTE *)("compress")) == 0 ) { d->mode |= NOCOMPRESS; } else { MesPrint("&subkey %s not defined in TableBase Off statement"); error = 1; } *ss = c; s = ss; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } return(error); } /* #] CoTBoff : #[ CoTBcleanup : */ int CoTBcleanup(UBYTE *s) { DUMMYUSE(s); MesPrint("&TableBase Cleanup statement not yet implemented"); return(1); } /* #] CoTBcleanup : #[ CoTBreplace : */ int CoTBreplace(UBYTE *s) { DUMMYUSE(s); MesPrint("&TableBase Replace statement not yet implemented"); return(1); } /* #] CoTBreplace : #[ CoTBuse : Here the actual table use as determined in TestUse causes the needed table elements to be loaded */ int CoTBuse(UBYTE *s) { GETIDENTITY DBASE *d; MLONG basenumber; UBYTE *arguments, *rhs, *buffer, *t, *u, c, *tablename, *p; LONG size, sum, x; int i, j, error = 0, error1 = 0, k; TABLES T = 0; WORD type, funnum, mode, *w; if ( ( d = FindTB(tablebasename) ) == 0 ) { MesPrint("&No open tablebase with the name %s",tablebasename); return(-1); } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s ) { while ( *s ) { tablename = s; if ( ( s = SkipAName(s) ) == 0 ) return(1); c = *s; *s = 0; if ( ( GetVar(tablename,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",tablename); basenumber = 0; } else if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",tablename); basenumber = 0; } else { basenumber = GetTableName(d,(char *)tablename); } /* if ( T->spare == 0 ) { SpareTable(T); } */ if ( basenumber > 0 ) { for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber != basenumber ) continue; arguments = p = (UBYTE *)(d->iblocks[i]->objects[j].element); /* Now translate the arguments and see whether we need this one.... */ for ( k = 0, w = AT.WorkPointer; k < ABS(T->numind); k++ ) { ParseSignedNumber(x,p); *w++ = x; p++; } sum = FindTableTree(T,AT.WorkPointer,1); if ( sum < 0 ) { MesPrint("Table %s in tablebase %s has not been loaded properly" ,tablename,tablebasename); error = 1; continue; } sum += ABS(T->numind) + 4; mode = T->tablepointers[sum]; if ( ( mode & ELEMENTLOADED ) == ELEMENTLOADED ) { T->tablepointers[sum] &= ~ELEMENTUSED; continue; } if ( ( mode & ELEMENTUSED ) == 0 ) continue; /* We need this one! */ rhs = (UBYTE *)ReadijObject(d,i,j,(char *)arguments); if ( rhs ) { u = rhs; while ( *u ) u++; size = u-rhs; u = arguments; while ( *u ) u++; size += u-arguments; u = tablename; while ( *u ) u++; size += u-tablename; size += 6; buffer = (UBYTE *)Malloc1(size,"TableBase copy"); t = tablename; u = buffer; while ( *t ) *u++ = *t++; *u++ = '('; t = arguments; while ( *t ) *u++ = *t++; *u++ = ')'; *u++ = '='; t = rhs; while ( *t ) *u++ = *t++; if ( t == rhs ) { *u++ = '0'; } *u++ = 0; *u = 0; M_free(rhs,"rhs in TBuse xxx"); error1 = CoFill(buffer); if ( error1 < 0 ) { return(error); } if ( error1 != 0 ) error = error1; M_free(buffer,"TableBase copy"); } T->tablepointers[sum] &= ~ELEMENTUSED; T->tablepointers[sum] |= ELEMENTLOADED; } } } *s = c; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } } else { s = (UBYTE *)(d->tablenames); basenumber = 0; while ( *s ) { basenumber++; tablename = s; while ( *s ) s++; s++; while ( *s ) s++; s++; if ( ( GetVar(tablename,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",tablename); } else if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",tablename); } if ( T->spare && T->mode == 0 ) { MesPrint("In table %s we have a problem with stubb orders in CoTBuse",tablename); error = -1; } /* if ( T->spare == 0 ) { SpareTable(T); } */ for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber == basenumber ) { arguments = p = (UBYTE *)(d->iblocks[i]->objects[j].element); /* Now translate the arguments and see whether we need this one.... */ for ( k = 0, w = AT.WorkPointer; k < ABS(T->numind); k++ ) { ParseSignedNumber(x,p); *w++ = x; p++; } sum = FindTableTree(T,AT.WorkPointer,1); if ( sum < 0 ) { MesPrint("Table %s in tablebase %s has not been loaded properly" ,tablename,tablebasename); error = 1; continue; } sum += ABS(T->numind) + 4; mode = T->tablepointers[sum]; if ( ( mode & ELEMENTLOADED ) == ELEMENTLOADED ) { T->tablepointers[sum] &= ~ELEMENTUSED; continue; } if ( ( mode & ELEMENTUSED ) == 0 ) continue; /* We need this one! */ rhs = (UBYTE *)ReadijObject(d,i,j,(char *)arguments); if ( rhs ) { u = rhs; while ( *u ) u++; size = u-rhs; u = arguments; while ( *u ) u++; size += u-arguments; u = tablename; while ( *u ) u++; size += u-tablename; size += 6; buffer = (UBYTE *)Malloc1(size,"TableBase copy"); t = tablename; u = buffer; while ( *t ) *u++ = *t++; *u++ = '('; t = arguments; while ( *t ) *u++ = *t++; *u++ = ')'; *u++ = '='; t = rhs; while ( *t ) *u++ = *t++; if ( t == rhs ) { *u++ = '0'; } *u++ = 0; *u = 0; M_free(rhs,"rhs in TBuse"); error1 = CoFill(buffer); if ( error1 < 0 ) { return(error); } if ( error1 != 0 ) error = error1; M_free(buffer,"TableBase copy"); } T->tablepointers[sum] &= ~ELEMENTUSED; T->tablepointers[sum] |= ELEMENTLOADED; } } } } } return(error); } /* #] CoTBuse : #[ CoApply : Possibly to be followed by names of tables. */ int CoApply(UBYTE *s) { GETIDENTITY UBYTE *tablename, c; WORD type, funnum, *w; TABLES T; LONG maxtogo = MAXPOSITIVE; int error = 0; w = AT.WorkPointer; if ( FG.cTable[*s] == 1 ) { maxtogo = 0; while ( FG.cTable[*s] == 1 ) { maxtogo = maxtogo*10 + (*s-'0'); s++; } while ( *s == ',' ) s++; if ( maxtogo > MAXPOSITIVE || maxtogo < 0 ) maxtogo = MAXPOSITIVE; } *w++ = TYPEAPPLY; *w++ = 3; *w++ = maxtogo; while ( *s ) { tablename = s; if ( ( s = SkipAName(s) ) == 0 ) return(1); c = *s; *s = 0; if ( ( GetVar(tablename,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",tablename); error = 1; } else if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",tablename); error = 1; } *w++ = funnum + FUNCTION; *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; } AT.WorkPointer[1] = w - AT.WorkPointer; /* if ( AT.WorkPointer[1] > 2 ) { AddNtoL(AT.WorkPointer[1],AT.WorkPointer); } */ AddNtoL(AT.WorkPointer[1],AT.WorkPointer); /* AT.WorkPointer[0] = TYPEAPPLYRESET; AddNtoL(AT.WorkPointer[1],AT.WorkPointer); */ return(error); } /* #] CoApply : #[ CoTBhelp : */ char *helptb[] = { "The TableBase statement is used as follows:" ,"TableBase \"file.tbl\" keyword subkey(s)" ," in which we have" ,"Keyword Subkey(s) Action" ,"open Opens file.tbl for R/W" ,"create Creates file.tbl for R/W. Old contents are lost" ,"load Loads all stubs of all tables" ,"load tablename(s) Loads all stubs the tables mentioned" ,"enter Loads all stubs and rhs of all tables" ,"enter tablename(s) Loads all stubs and rhs of the tables mentioned" ,"audit Prints list of contents" /* ,"replace tablename saves a table (with overwrite)" */ /* ,"replace tableelement saves a table element (with overwrite)" */ /* ,"cleanup makes tables contingent" */ ,"addto tablename adds all elements if not yet there" ,"addto tableelement adds element if not yet there" /* ,"delete tablename removes table from tablebase" */ /* ,"delete tableelement removes element from tablebase" */ ,"on compress elements are stored in gzip format (default)" ,"off compress elements are stored in uncompressed format" ,"use compiles all needed elements" ,"use tablename(s) compiles all needed elements of these tables" ,"" ,"Related commands are:" ,"testuse marks which tbl_ elements occur for all tables" ,"testuse tablename(s) marks which tbl_ elements occur for given tables" ,"apply replaces tbl_ if rhs available" ,"apply tablename(s) replaces tbl_ for given tables if rhs available" ,"" }; int CoTBhelp(UBYTE *s) { int i, ii = sizeof(helptb)/sizeof(char *); DUMMYUSE(s); for ( i = 0; i < ii; i++ ) MesPrint("%s",helptb[i]); return(0); } /* #] CoTBhelp : #[ ReWorkT : Replaces the STUBBS of the functions in the list. This gains one space. Hence we have to be very careful */ void ReWorkT(WORD *term, WORD *funs, WORD numfuns) { WORD *tstop, *tend, *m, *t, *tt, *mm, *mmm, *r, *rr; int i, j; tend = term + *term; tstop = tend - ABS(tend[-1]); m = t = term+1; while ( t < tstop ) { if ( *t == TABLESTUB ) { for ( i = 0; i < numfuns; i++ ) { if ( -t[FUNHEAD] == funs[i] ) break; } if ( numfuns == 0 || i < numfuns ) { /* Hit */ i = t[1] - 1; *m++ = -t[FUNHEAD]; *m++ = i; t += 2; i -= FUNHEAD; if ( m < t ) { for ( j = 0; j < FUNHEAD-2; j++ ) *m++ = *t++; } else { m += FUNHEAD-2; t += FUNHEAD-2; } t++; while ( i-- > 0 ) { *m++ = *t++; } tt = t; mm = m; if ( mm < tt ) { while ( tt < tend ) *mm++ = *tt++; *term = mm - term; tend = term + *term; tstop = tend - ABS(tend[-1]); t = m; } } else { goto inc; } } else if ( *t >= FUNCTION ) { tt = t + t[1]; mm = m; for ( j = 0; j < FUNHEAD; j++ ) { if ( m == t ) { m++; t++; } else *m++ = *t++; } while ( t < tt ) { if ( *t <= -FUNCTION ) { if ( m == t ) { m++; t++; } else *m++ = *t++; } else if ( *t < 0 ) { if ( m == t ) { m += 2; t += 2; } else { *m++ = *t++; *m++ = *t++; } } else { rr = t + *t; mmm = m; for ( j = 0; j < ARGHEAD; j++ ) { if ( m == t ) { m++; t++; } else *m++ = *t++; } while ( t < rr ) { r = t + *t; ReWorkT(t,funs,numfuns); j = *t; if ( m == t ) { m += j; t += j; } else { while ( j-- >= 0 ) *m++ = *t++; } t = r; } *mmm = m-mmm; } } mm[1] = m - mm; t = tt; } else { inc: j = t[1]; if ( m < t ) { while ( j-- >= 0 ) *m++ = *t++; } else { m += j; t += j; } } } if ( m < t ) { while ( t < tend ) *m++ = *t++; *term = m - term; } } /* #] ReWorkT : #[ Apply : */ void Apply(WORD *term, WORD level) { WORD *funs, numfuns; TABLES T; int i, j; CBUF *C = cbuf+AM.rbufnum; /* Point the tables in the proper direction */ numfuns = C->lhs[level][1] - 2; funs = C->lhs[level] + 2; if ( numfuns > 0 ) { for ( i = MAXBUILTINFUNCTION-FUNCTION; i < AC.FunctionList.num; i++ ) { if ( ( T = functions[i].tabl ) != 0 ) { for ( j = 0; j < numfuns; j++ ) { if ( i == (funs[j]-FUNCTION) && T->spare ) { FlipTable(&(functions[i]),0); break; } } } } } else { for ( i = MAXBUILTINFUNCTION-FUNCTION; i < AC.FunctionList.num; i++ ) { if ( ( T = functions[i].tabl ) != 0 ) { if ( T->spare ) FlipTable(&(functions[i]),0); } } } /* Now the replacements everywhere of id tbl_(table,?a) = table(?a); Actually, this has to be done recursively. Note that we actually gain one space. */ ReWorkT(term,funs,numfuns); } /* #] Apply : #[ ApplyExec : Replaces occurrences of tbl_(table,indices,pattern) by the proper rhs of table(indices,pattern). It does this up to maxtogo times in the given term. It starts with the occurrences inside the arguments of functions. If necessary it finishes at groundlevel. An infinite number of tries is indicated by maxtogo = 2^15-1 or 2^31-1. The occurrences are replaced by subexpressions. This allows TestSub to finish the job properly. The main trick here is T = T->spare which turns to the proper rhs. The return value is the number of substitutions that can still be made based on maxtogo. Hence, if the returnvalue is different from maxtogo there was a substitution. */ int ApplyExec(WORD *term, int maxtogo, WORD level) { GETIDENTITY WORD rhsnumber, *Tpattern, *funs, numfuns, funnum; WORD ii, *t, *t1, *w, *p, *m, *m1, *u, *r, tbufnum, csize, wilds; NESTING NN; int i, j, isp, stilltogo; CBUF *C; TABLES T; /* Startup. We need NestPoin for when we have to replace something deep down. */ t = term; m = t + *t; csize = ABS(m[-1]); m -= csize; AT.NestPoin->termsize = t; if ( AT.NestPoin == AT.Nest ) AN.EndNest = t + *t; t++; /* First we look inside function arguments. Also when clean! */ while ( t < m ) { if ( *t < FUNCTION ) { t += t[1]; continue; } if ( functions[*t-FUNCTION].spec > 0 ) { t += t[1]; continue; } AT.NestPoin->funsize = t; r = t + t[1]; t += FUNHEAD; while ( t < r ) { if ( *t < 0 ) { NEXTARG(t); continue; } AT.NestPoin->argsize = t1 = t; u = t + *t; t += ARGHEAD; AT.NestPoin++; while ( t < u ) { /* Now we loop over the terms inside a function argument This defines a recursion and we have to call ApplyExec again. The real problem is when we catch something and we have to insert a subexpression pointer. This may use more or less space and the whole term has to be readjusted. This is why we have the NestPoin variables. They tell us where the sizes of the term, the function and the arguments are sitting, and also where the dirty flags are. This readjusting is of course done in the groundlevel code. Here we worry abound the maxtogo count. */ stilltogo = ApplyExec(t,maxtogo,level); if ( stilltogo != maxtogo ) { if ( stilltogo <= 0 ) { AT.NestPoin--; return(stilltogo); } maxtogo = stilltogo; u = t1 + *t1; m = term + *term - csize; } t += *t; } AT.NestPoin--; } } /* Now we look at the ground level */ C = cbuf+AM.rbufnum; t = term + 1; while ( t < m ) { if ( *t != TABLESTUB ) { t += t[1]; continue; } funnum = -t[FUNHEAD]; if ( ( funnum < FUNCTION ) || ( funnum >= FUNCTION+WILDOFFSET ) || ( ( T = functions[funnum-FUNCTION].tabl ) == 0 ) || ( T->sparse == 0 ) || ( T->spare == 0 ) ) { t += t[1]; continue; } numfuns = C->lhs[level][1] - 3; funs = C->lhs[level] + 3; if ( numfuns > 0 ) { for ( i = 0; i < numfuns; i++ ) { if ( funs[i] == funnum ) break; } if ( i >= numfuns ) { t += t[1]; continue; } } r = t + t[1]; AT.NestPoin->funsize = t + 1; t1 = t; t += FUNHEAD + 1; /* Test whether the table catches Test 1: index arguments and range. isp will be the number of the element in the table. */ T = T->spare; #ifdef WITHPTHREADS Tpattern = T->pattern[identity]; #else Tpattern = T->pattern; #endif p = Tpattern+FUNHEAD+1; for ( i = 0; i < ABS(T->numind); i++, t += 2 ) { if ( *t != -SNUMBER ) break; } if ( i < ABS(T->numind) ) { t = r; continue; } isp = FindTableTree(T,t1+FUNHEAD+1,2); if ( isp < 0 ) { t = r; continue; } rhsnumber = T->tablepointers[isp+ABS(T->numind)]; #if ( TABLEEXTENSION == 2 ) tbufnum = T->bufnum; #else tbufnum = T->tablepointers[isp+ABS(T->numind)+1]; #endif t = t1+FUNHEAD+2; ii = ABS(T->numind); while ( --ii >= 0 ) { *p = *t; t += 2; p += 2; } /* If there are more arguments we have to do some pattern matching. This should be easy. We adapted the pattern, so that the array indices match already. */ #ifdef WITHPTHREADS AN.FullProto = T->prototype[identity]; #else AN.FullProto = T->prototype; #endif AN.WildValue = AN.FullProto + SUBEXPSIZE; AN.WildStop = AN.FullProto+AN.FullProto[1]; ClearWild(BHEAD0); AN.RepFunNum = 0; AN.RepFunList = AN.EndNest; AT.WorkPointer = (WORD *)(((UBYTE *)(AN.EndNest)) + AM.MaxTer/2); /* The RepFunList is after the term but not very relevant. We need because MatchFunction uses it */ if ( AT.WorkPointer + t1[1] >= AT.WorkTop ) { MesWork(); } wilds = 0; w = AT.WorkPointer; *w++ = -t1[FUNHEAD]; *w++ = t1[1] - 1; for ( i = 2; i < FUNHEAD; i++ ) *w++ = t1[i]; t = t1 + FUNHEAD+1; while ( t < r ) *w++ = *t++; t = AT.WorkPointer; AT.WorkPointer = w; if ( MatchFunction(BHEAD Tpattern,t,&wilds) > 0 ) { /* Here we caught one. Now we should worry about: 1: inserting the subexpression pointer with its wildcards 2: NestPoin because we may not be at the lowest level The function starts at t1. */ #ifdef WITHPTHREADS m1 = T->prototype[identity]; #else m1 = T->prototype; #endif m1[2] = rhsnumber; m1[4] = tbufnum; t = t1; j = t[1]; i = m1[1]; if ( j > i ) { j = i - j; NCOPY(t,m1,i); m1 = AN.EndNest; while ( r < m1 ) *t++ = *r++; AN.EndNest = t; *term += j; NN = AT.NestPoin; while ( NN > AT.Nest ) { NN--; NN->termsize[0] += j; NN->funsize[1] += j; NN->argsize[0] += j; NN->funsize[2] |= DIRTYFLAG; NN->argsize[1] |= DIRTYFLAG; } m += j; } else if ( j < i ) { j = i-j; t = AN.EndNest; while ( t >= r ) { t[j] = *t; t--; } t = t1; NCOPY(t,m1,i); AN.EndNest += j; *term += j; NN = AT.NestPoin; while ( NN > AT.Nest ) { NN--; NN->termsize[0] += j; NN->funsize[1] += j; NN->argsize[0] += j; NN->funsize[2] |= DIRTYFLAG; NN->argsize[1] |= DIRTYFLAG; } m += j; } else { NCOPY(t,m1,j); } r = t1 + t1[1]; maxtogo--; if ( maxtogo <= 0 ) return(maxtogo); } t = r; } return(maxtogo); } /* #] ApplyExec : #[ ApplyReset : */ void ApplyReset(WORD level) { WORD *funs, numfuns; TABLES T; int i, j; CBUF *C = cbuf+AM.rbufnum; numfuns = C->lhs[level][1] - 2; funs = C->lhs[level] + 2; if ( numfuns > 0 ) { for ( i = MAXBUILTINFUNCTION-FUNCTION; i < AC.FunctionList.num; i++ ) { if ( ( T = functions[i].tabl ) != 0 ) { for ( j = 0; j < numfuns; j++ ) { if ( i == (funs[j]-FUNCTION) && T->spare ) { FlipTable(&(functions[i]),1); break; } } } } } else { for ( i = MAXBUILTINFUNCTION-FUNCTION; i < AC.FunctionList.num; i++ ) { if ( ( T = functions[i].tabl ) != 0 ) { if ( T->spare ) FlipTable(&(functions[i]),1); } } } } /* #] ApplyReset : #[ TableReset : */ void TableReset(void) { TABLES T; int i; for ( i = MAXBUILTINFUNCTION-FUNCTION; i < AC.FunctionList.num; i++ ) { if ( ( T = functions[i].tabl ) != 0 && T->spare && T->mode == 0 ) { functions[i].tabl = T->spare; } } } /* #] TableReset : #[ LoadTableElement : ????? int LoadTableElement(DBASE *d, TABLE *T, WORD num) { } #] LoadTableElement : #[ ReleaseTB : Releases all TableBases */ int ReleaseTB(void) { DBASE *d; int i; for ( i = NumTableBases - 1; i >= 0; i-- ) { d = tablebases+i; fclose(d->handle); FreeTableBase(d); } return(0); } /* #] ReleaseTB : */ form-5.0.1/sources/minos.c0000644000175100017510000011366615217035721011137 /** @file minos.c * * These are the low level functions for the database part of the * tablebases. These routines have been copied (and then adapted) from * the minos database program. This file goes together with minos.h */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : File contains the lowlevel routines for the management of primitive database-like files. The structures are explained in the file manage.h Original file for minos made by J.Vermaseren, april-1994. Note: the minos primitives for writing are never invoked in parallel. */ #include "form3.h" #include "minos.h" int withoutflush = 0; /* #] Includes : #[ Variables : */ static INDEXBLOCK scratchblock; static NAMESBLOCK scratchnamesblock; #define CFD(y,s,type,x,j) for(x=0,j=0;j<((int)sizeof(type));j++) \ {x=(x<<8)+((*s++)&0x00FF);} y=x; #define CTD(y,s,type,x,j) x=y;for(j=sizeof(type)-1;j>=0;j--){s[j]=x&0xFF; \ x>>=8;} s += sizeof(type); /* #] Variables : #[ Utilities : #[ minosread : */ int minosread(FILE *f,char *buffer,MLONG size) { MLONG x; while ( size > 0 ) { x = fread(buffer,sizeof(char),size,f); if ( x <= 0 ) return(-1); buffer += x; size -= x; } return(0); } /* #] minosread : #[ minoswrite : */ int minoswrite(FILE *f,char *buffer,MLONG size) { MLONG x; while ( size > 0 ) { x = fwrite(buffer,sizeof(char),size,f); if ( x <= 0 ) return(-1); buffer += x; size -= x; } if ( withoutflush == 0 ) fflush(f); return(0); } /* #] minoswrite : #[ str_dup : */ char *str_dup(char *str) { char *s, *t; int i; s = str; while ( *s ) s++; i = s - str + 1; if ( ( s = (char *)Malloc1((size_t)i,"a string copy") ) == 0 ) return(0); t = s; while ( *str ) *t++ = *str++; *t = 0; return(s); } /* #] str_dup : #[ convertblock : */ void convertblock(INDEXBLOCK *in,INDEXBLOCK *out,int mode) { char *s,*t; MLONG i, x; int j; OBJECTS *obj; switch ( mode ) { case TODISK: s = (char *)out; CTD(in->flags,s,MLONG,x,j) CTD(in->previousblock,s,MLONG,x,j) CTD(in->position,s,MLONG,x,j) for ( i = 0, obj = in->objects; i < NUMOBJECTS; i++, obj++ ) { CTD(obj->position,s,MLONG,x,j) CTD(obj->size,s,MLONG,x,j) CTD(obj->date,s,MLONG,x,j) CTD(obj->tablenumber,s,MLONG,x,j) CTD(obj->uncompressed,s,MLONG,x,j) CTD(obj->spare1,s,MLONG,x,j) CTD(obj->spare2,s,MLONG,x,j) CTD(obj->spare3,s,MLONG,x,j) t = obj->element; for ( j = 0; j < ELEMENTSIZE; j++ ) *s++ = *t++; } break; case FROMDISK: s = (char *)in; CFD(out->flags,s,MLONG,x,j) CFD(out->previousblock,s,MLONG,x,j) CFD(out->position,s,MLONG,x,j) for ( i = 0, obj = out->objects; i < NUMOBJECTS; i++, obj++ ) { CFD(obj->position,s,MLONG,x,j) CFD(obj->size,s,MLONG,x,j) CFD(obj->date,s,MLONG,x,j) CFD(obj->tablenumber,s,MLONG,x,j) CFD(obj->uncompressed,s,MLONG,x,j) CFD(obj->spare1,s,MLONG,x,j) CFD(obj->spare2,s,MLONG,x,j) CFD(obj->spare3,s,MLONG,x,j) t = obj->element; for ( j = 0; j < ELEMENTSIZE; j++ ) *t++ = *s++; } break; } } /* #] convertblock : #[ convertnamesblock : */ void convertnamesblock(NAMESBLOCK *in,NAMESBLOCK *out,int mode) { char *s; MLONG x; int j; switch ( mode ) { case TODISK: s = (char *)out; CTD(in->previousblock,s,MLONG,x,j) CTD(in->position,s,MLONG,x,j) for ( j = 0; j < NAMETABLESIZE; j++ ) out->names[j] = in->names[j]; break; case FROMDISK: s = (char *)in; CFD(out->previousblock,s,MLONG,x,j) CFD(out->position,s,MLONG,x,j) for ( j = 0; j < NAMETABLESIZE; j++ ) out->names[j] = in->names[j]; break; } } /* #] convertnamesblock : #[ convertiniinfo : */ void convertiniinfo(INIINFO *in,INIINFO *out,int mode) { char *s; MLONG i, x, *y; int j; switch ( mode ) { case TODISK: s = (char *)out; y = (MLONG *)in; for ( i = sizeof(INIINFO)/sizeof(MLONG); i > 0; i-- ) { CTD(*y,s,MLONG,x,j) y++; } break; case FROMDISK: s = (char *)in; y = (MLONG *)out; for ( i = sizeof(INIINFO)/sizeof(MLONG); i > 0; i-- ) { CFD(*y,s,MLONG,x,j) y++; } break; } } /* #] convertiniinfo : #[ LocateBase : */ FILE *LocateBase(char **name, char **newname, char *iomode) { FILE *handle; int namesize, i; UBYTE *s, *to, *u1, *u2, *indir; if ( ( handle = fopen(*name,iomode) ) != 0 ) { *newname = (char *)strDup1((UBYTE *)(*name),"LocateBase"); return(handle); } namesize = 2; s = (UBYTE *)(*name); while ( *s ) { s++; namesize++; } indir = AM.IncDir; if ( indir ) { s = indir; i = 0; while ( *s ) { s++; i++; } *newname = (char *)Malloc1(namesize+i,"LocateBase"); s = indir; to = (UBYTE *)(*newname); while ( *s ) *to++ = *s++; if ( to > (UBYTE *)(*newname) && to[-1] != SEPARATOR ) *to++ = SEPARATOR; s = (UBYTE *)(*name); while ( *s ) *to++ = *s++; *to = 0; if ( ( handle = fopen(*newname,iomode) ) != 0 ) { return(handle); } M_free(*newname,"LocateBase, incdir/file"); } if ( AM.Path ) { u1 = AM.Path; while ( *u1 ) { u2 = u1; i = 0; while ( *u1 && *u1 != ':' ) { if ( *u1 == '\\' ) u1++; u1++; i++; } *newname = (char *)Malloc1(namesize+i,"LocateBase"); s = u2; to = (UBYTE *)(*newname); while ( s < u1 ) { if ( *s == '\\' ) s++; *to++ = *s++; } if ( to > (UBYTE *)(*newname) && to[-1] != SEPARATOR ) *to++ = SEPARATOR; s = (UBYTE *)(*name); while ( *s ) *to++ = *s++; *to = 0; if ( ( handle = fopen(*newname,iomode) ) != 0 ) { return(handle); } M_free(*newname,"LocateBase Path/file"); if ( *u1 ) u1++; } } /* Error1("LocateBase: Cannot find file",*name); */ return(0); } /* #] LocateBase : #] Utilities : #[ ReadIndex : */ int ReadIndex(DBASE *d) { MLONG i; INDEXBLOCK **ib; NAMESBLOCK **ina; MLONG position, size; /* Allocate the pieces one by one (makes it easier to give it back) */ if ( d->info.numberofindexblocks <= 0 ) return(0); if ( sizeof(INDEXBLOCK)*d->info.numberofindexblocks > MAXINDEXSIZE ) { MesPrint("We need more than %ld bytes for the index.\n",MAXINDEXSIZE); MesPrint("The file %s may not be a proper database\n",d->name); return(-1); } size = sizeof(INDEXBLOCK *)*d->info.numberofindexblocks; if ( ( ib = (INDEXBLOCK **)Malloc1(size,"tb,index") ) == 0 ) return(-1); for ( i = 0; i < d->info.numberofindexblocks; i++ ) { if ( ( ib[i] = (INDEXBLOCK *)Malloc1(sizeof(INDEXBLOCK),"index block") ) == 0 ) { for ( --i; i >= 0; i-- ) M_free(ib[i],"tb,indexblock"); M_free(ib,"tb,index"); return(-1); } } size = sizeof(NAMESBLOCK *)*d->info.numberofnamesblocks; if ( ( ina = (NAMESBLOCK **)Malloc1(size,"tb,indexnames") ) == 0 ) return(-1); for ( i = 0; i < d->info.numberofnamesblocks; i++ ) { if ( ( ina[i] = (NAMESBLOCK *)Malloc1(sizeof(NAMESBLOCK),"index names block") ) == 0 ) { for ( --i; i >= 0; i-- ) M_free(ina[i],"index names block"); M_free(ina,"tb,indexnames"); for ( i = 0; i < d->info.numberofindexblocks; i++ ) M_free(ib[i],"tb,indexblock"); M_free(ib,"tb,index"); return(-1); } } /* Read the index blocks, from the back to the front. The links are only reliable that way. */ position = d->info.lastindexblock; for ( i = d->info.numberofindexblocks - 1; i >= 0; i-- ) { fseek(d->handle,position,SEEK_SET); if ( minosread(d->handle,(char *)(&scratchblock),sizeof(INDEXBLOCK)) ) { MesPrint("Error while reading file %s\n",d->name); thisiswrong: for ( i = 0; i < d->info.numberofnamesblocks; i++ ) M_free(ina[i],"index names block"); M_free(ina,"tb,indexnames"); for ( i = 0; i < d->info.numberofindexblocks; i++ ) M_free(ib[i],"tb,indexblock"); M_free(ib,"tb,index"); return(-1); } convertblock(&scratchblock,ib[i],FROMDISK); if ( ib[i]->position != position || ( ib[i]->previousblock <= 0 && i > 0 ) ) { MesPrint("File %s has inconsistent contents\n",d->name); goto thisiswrong; } position = ib[i]->previousblock; } d->info.firstindexblock = ib[0]->position; for ( i = 0; i < d->info.numberofindexblocks; i++ ) { ib[i]->flags &= MCLEANFLAG; } /* Read the names blocks, from the back to the front. The links are only reliable that way. */ position = d->info.lastnameblock; for ( i = d->info.numberofnamesblocks - 1; i >= 0; i-- ) { fseek(d->handle,position,SEEK_SET); if ( minosread(d->handle,(char *)(&scratchnamesblock),sizeof(NAMESBLOCK)) ) { MesPrint("Error while reading file %s\n",d->name); goto thisiswrong; } convertnamesblock(&scratchnamesblock,ina[i],FROMDISK); if ( ina[i]->position != position || ( ina[i]->previousblock <= 0 && i > 0 ) ) { MesPrint("File %s has inconsistent contents\n",d->name); goto thisiswrong; } position = ina[i]->previousblock; } d->info.firstnameblock = ina[0]->position; /* Give the old info back to the system. */ if ( d->iblocks ) { for ( i = 0; i < d->info.numberofindexblocks; i++ ) { if ( d->iblocks[i] ) M_free(d->iblocks[i],"d->iblocks[i]"); } M_free(d->iblocks,"d->iblocks"); } if ( d->nblocks ) { for ( i = 0; i < d->info.numberofnamesblocks; i++ ) { if ( d->nblocks[i] ) M_free(d->nblocks[i],"d->nblocks[i]"); } M_free(d->nblocks,"d->nblocks"); } /* And substitute the new blocks */ d->iblocks = ib; d->nblocks = ina; return(0); } /* #] ReadIndex : #[ WriteIndexBlock : */ int WriteIndexBlock(DBASE *d,MLONG num) { if ( num >= d->info.numberofindexblocks ) { MesPrint("Illegal number specified for number of index blocks\n"); return(-1); } fseek(d->handle,d->iblocks[num]->position,SEEK_SET); convertblock(d->iblocks[num],&scratchblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchblock),sizeof(INDEXBLOCK)) ) { MesPrint("Error while writing an index block in file %s\n",d->name); MesPrint("File may be unreliable now\n"); return(-1); } return(0); } /* #] WriteIndexBlock : #[ WriteNamesBlock : */ int WriteNamesBlock(DBASE *d,MLONG num) { if ( num >= d->info.numberofnamesblocks ) { MesPrint("Illegal number specified for number of names blocks\n"); return(-1); } fseek(d->handle,d->nblocks[num]->position,SEEK_SET); convertnamesblock(d->nblocks[num],&scratchnamesblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchnamesblock),sizeof(NAMESBLOCK)) ) { MesPrint("Error while writing a names block in file %s\n",d->name); MesPrint("File may be unreliable now\n"); return(-1); } return(0); } /* #] WriteNamesBlock : #[ WriteIndex : Problem here is to get the links right. */ int WriteIndex(DBASE *d) { MLONG i, position; if ( d->iblocks == 0 ) return(0); if ( d->nblocks == 0 ) return(0); for ( i = 0; i < d->info.numberofindexblocks; i++ ) { if ( d->iblocks[i] == 0 ) { MesPrint("Error: unassigned index blocks. Cannot write\n"); return(-1); } } for ( i = 0; i < d->info.numberofnamesblocks; i++ ) { if ( d->nblocks[i] == 0 ) { MesPrint("Error: unassigned names blocks. Cannot write\n"); return(-1); } } d->info.lastindexblock = -1; for ( i = 0; i < d->info.numberofindexblocks; i++ ) { position = d->iblocks[i]->position; if ( position <= 0 ) { fseek(d->handle,0,SEEK_END); position = ftell(d->handle); d->iblocks[i]->position = position; if ( i <= 0 ) d->iblocks[i]->previousblock = -1; else d->iblocks[i]->previousblock = d->iblocks[i-1]->position; } else fseek(d->handle,position,SEEK_SET); convertblock(d->iblocks[i],&scratchblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchblock),sizeof(INDEXBLOCK)) ) { MesPrint("Error while writing index of file %s",d->name); d->iblocks[i]->position = -1; return(-1); } d->info.lastindexblock = position; } d->info.lastnameblock = -1; for ( i = 0; i < d->info.numberofnamesblocks; i++ ) { position = d->nblocks[i]->position; if ( position <= 0 ) { fseek(d->handle,0,SEEK_END); position = ftell(d->handle); d->nblocks[i]->position = position; if ( i <= 0 ) d->nblocks[i]->previousblock = -1; else d->nblocks[i]->previousblock = d->nblocks[i-1]->position; } else fseek(d->handle,position,SEEK_SET); convertnamesblock(d->nblocks[i],&scratchnamesblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchnamesblock),sizeof(NAMESBLOCK)) ) { MesPrint("Error while writing index of file %s",d->name); d->nblocks[i]->position = -1; return(-1); } d->info.lastnameblock = position; } return(0); } /* #] WriteIndex : #[ WriteIniInfo : */ int WriteIniInfo(DBASE *d) { INIINFO inf; fseek(d->handle,0,SEEK_SET); convertiniinfo(&(d->info),&inf,TODISK); if ( minoswrite(d->handle,(char *)(&inf),sizeof(INIINFO)) ) { MesPrint("Error while writing masterindex of file %s",d->name); return(-1); } return(0); } /* #] WriteIniInfo : #[ ReadIniInfo : */ int ReadIniInfo(DBASE *d) { INIINFO inf; fseek(d->handle,0,SEEK_SET); if ( minosread(d->handle,(char *)(&inf),sizeof(INIINFO)) ) { MesPrint("Error while reading masterindex of file %s",d->name); return(-1); } convertiniinfo(&inf,&(d->info),FROMDISK); if ( d->info.entriesinindex < 0 || d->info.numberofindexblocks < 0 || d->info.lastindexblock < 0 ) { MesPrint("The file %s is not a proper database\n",d->name); return(-1); } return(0); } /* #] ReadIniInfo : #[ GetDbase : */ DBASE *GetDbase(char *filename, MLONG rwmode) { FILE *f; DBASE *d; char *newname; if ( rwmode == 0 ) { if ( ( f = LocateBase(&filename,&newname,"rb") ) == 0 ) { MesPrint("&Trying to open non-existent TableBase in readonly mode: %s", filename); Terminate(-1); } } else { if ( ( f = LocateBase(&filename,&newname,"r+b") ) == 0 ) { return(NewDbase(filename,0)); } } /* setbuf(f,0); */ d = (DBASE *)From0List(&(AC.TableBaseList)); d->mode = 0; d->tablenamessize = 0; d->topnumber = 0; d->tablenamefill = 0; d->iblocks = 0; d->nblocks = 0; d->tablenames = 0; d->rwmode = rwmode; d->info.entriesinindex = 0; d->info.numberofindexblocks = 0; d->info.firstindexblock = 0; d->info.lastindexblock = 0; d->info.numberoftables = 0; d->info.numberofnamesblocks = 0; d->info.firstnameblock = 0; d->info.lastnameblock = 0; d->name = str_dup(filename); /* For the moment just for the error messages */ d->handle = f; if ( ReadIniInfo(d) || ReadIndex(d) ) { M_free(d,"index-d"); fclose(f); return(0); } if ( ComposeTableNames(d) < 0 ) { FreeTableBase(d); fclose(f); return(0); } // free allocation from previous str_dup M_free(d->name, "from str_dup"); d->name = str_dup(filename); d->fullname = newname; return(d); } /* #] GetDbase : #[ NewDbase : Creates a new database with 'number' entries in the index. */ DBASE *NewDbase(char *name,MLONG number) { FILE *f; DBASE *d; MLONG numblocks, numnameblocks, i; char *s; /*----------change 10-feb-2003 */ int j, jj; MLONG t = (MLONG)(time(0)); /*-----------------------------*/ if ( number < 0 ) number = 0; if ( ( f = fopen(name,"w+b") ) == 0 ) { MesPrint("Could not create a new file with name %s\n",name); return(0); } numblocks = (number+NUMOBJECTS-1)/NUMOBJECTS; numnameblocks = 1; if ( numblocks <= 0 ) numblocks = 1; if ( numnameblocks <= 0 ) numnameblocks = 1; d = (DBASE *)From0List(&(AC.TableBaseList)); if ( ( d->iblocks = (INDEXBLOCK **)Malloc1(numblocks*sizeof(INDEXBLOCK *), "new database") ) == 0 ) { NumTableBases--; return(0); } d->tablenames = 0; d->tablenamessize = 0; d->topnumber = 0; d->tablenamefill = 0; d->rwmode = 1; d->mode = 0; if ( ( d->nblocks = (NAMESBLOCK **)Malloc1(sizeof(NAMESBLOCK *)*numnameblocks, "new database") ) == 0 ) { M_free(d->iblocks,"new database"); NumTableBases--; return(0); } if ( ( f = fopen(name,"w+b") ) == 0 ) { MesPrint("Could not create new file %s\n",name); NumTableBases--; return(0); } /* setbuf(f,0); */ d->name = str_dup(name); d->fullname = str_dup(name); d->handle = f; d->info.entriesinindex = number; d->info.numberofindexblocks = numblocks; d->info.numberofnamesblocks = numnameblocks; d->info.firstindexblock = 0; d->info.lastindexblock = 0; d->info.numberoftables = 0; d->info.firstnameblock = 0; d->info.lastnameblock = 0; if ( WriteIniInfo(d) ) { getout: fclose(f); remove(d->fullname); if ( d->name ) { M_free(d->name,"name tablebase"); d->name = 0; } if ( d->fullname ) { M_free(d->fullname,"fullname tablebase"); d->fullname = 0; } M_free(d->nblocks,"new database"); M_free(d->iblocks,"new database"); NumTableBases--; return(0); } for ( i = 0; i < numblocks; i++ ) { if ( ( d->iblocks[i] = (INDEXBLOCK *)Malloc1(sizeof(INDEXBLOCK), "index blocks of new database") ) == 0 ) { while ( --i >= 0 ) M_free(d->iblocks[i],"index blocks of new database"); goto getout; } if ( i > 0 ) d->iblocks[i]->previousblock = d->iblocks[i-1]->position; else d->iblocks[i]->previousblock = -1; d->iblocks[i]->position = ftell(f); // Initialise, to keep valgrind happy d->iblocks[i]->flags = -1; /*----------change 10-feb-2003 */ /* Zero things properly. We don't want garbage in the file. */ for ( j = 0; j < NUMOBJECTS; j++ ) { d->iblocks[i]->objects[j].date = t; d->iblocks[i]->objects[j].size = 0; d->iblocks[i]->objects[j].position = -1; d->iblocks[i]->objects[j].tablenumber = 0; d->iblocks[i]->objects[j].uncompressed = 0; d->iblocks[i]->objects[j].spare1 = 0; d->iblocks[i]->objects[j].spare2 = 0; d->iblocks[i]->objects[j].spare3 = 0; for ( jj = 0; jj < ELEMENTSIZE; jj++ ) d->iblocks[i]->objects[j].element[jj] = 0; } convertblock(d->iblocks[i],&scratchblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchblock),sizeof(INDEXBLOCK)) ) { MesPrint("Error while writing new index blocks\n"); goto getout; } } for ( i = 0; i < numnameblocks; i++ ) { if ( ( d->nblocks[i] = (NAMESBLOCK *)Malloc1(sizeof(NAMESBLOCK), "names blocks of new database") ) == 0 ) { while ( --i >= 0 ) { M_free(d->nblocks[i],"names blocks of new database"); } for ( i = 0; i < numblocks; i++ ) M_free(d->iblocks[i],"index blocks of new database"); goto getout; } if ( i > 0 ) d->nblocks[i]->previousblock = d->nblocks[i-1]->position; else d->nblocks[i]->previousblock = -1; d->nblocks[i]->position = ftell(f); s = d->nblocks[i]->names; for ( j = 0; j < NAMETABLESIZE; j++ ) *s++ = 0; convertnamesblock(d->nblocks[i],&scratchnamesblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchnamesblock),sizeof(NAMESBLOCK)) ) { MesPrint("Error while writing new names blocks\n"); for ( i = 0; i < numnameblocks; i++ ) M_free(d->nblocks[i],"names blocks of new database"); for ( i = 0; i < numblocks; i++ ) M_free(d->iblocks[i],"index blocks of new database"); goto getout; } } d->info.firstindexblock = d->iblocks[0]->position; d->info.lastindexblock = d->iblocks[numblocks-1]->position; d->info.firstnameblock = d->nblocks[0]->position; d->info.lastnameblock = d->nblocks[numnameblocks-1]->position; if ( WriteIniInfo(d) ) { for ( i = 0; i < numnameblocks; i++ ) M_free(d->nblocks[i],"names blocks of new database"); for ( i = 0; i < numblocks; i++ ) M_free(d->iblocks[i],"index blocks of new database"); goto getout; } return(d); } /* #] NewDbase : #[ FreeTableBase : */ void FreeTableBase(DBASE *d) { int i, j, *old, *newL; LIST *L; for ( i = 0; i < d->info.numberofnamesblocks; i++ ) M_free(d->nblocks[i],"nblocks[i]"); for ( i = 0; i < d->info.numberofindexblocks; i++ ) M_free(d->iblocks[i],"iblocks[i]"); M_free(d->nblocks,"nblocks"); M_free(d->iblocks,"iblocks"); if ( d->tablenames ) M_free(d->tablenames,"d->tablenames"); if ( d->name ) M_free(d->name,"d->name"); if ( d->fullname ) M_free(d->fullname,"d->fullname"); i = d - tablebases; if ( i < ( NumTableBases - 1 ) ) { L = &(AC.TableBaseList); j = ( ( NumTableBases - i - 1 ) * L->size ) / sizeof(int); old = (int *)d; newL = (int *)(d+1); while ( --j >= 0 ) *newL++ = *old++; j = L->size / sizeof(int); while ( --j >= 0 ) *newL++ = 0; } NumTableBases--; M_free(d,"tb,d"); } /* #] FreeTableBase : #[ ComposeTableNames : The nameblocks are supposed to be in memory. Hence we have to go through them */ int ComposeTableNames(DBASE *d) { MLONG nsize = 0; int i, j, k; char *s, *t, *ss; d->topnumber = 0; i = 0; s = d->nblocks[i]->names; j = NAMETABLESIZE; while ( *s ) { if ( *s ) d->topnumber++; for ( k = 0; k < 2; k++ ) { /* name and argtail */ while ( *s ) { j--; if ( j <= 0 ) { i++; if ( i >= d->info.numberofnamesblocks ) goto gotall; s = d->nblocks[i]->names; j = NAMETABLESIZE; } else s++; } j--; if ( j <= 0 ) { i++; if ( i >= d->info.numberofnamesblocks ) goto gotall; s = d->nblocks[i]->names; j = NAMETABLESIZE; } else s++; } } gotall:; nsize = (d->info.numberofnamesblocks-1)*NAMETABLESIZE + (s-d->nblocks[i]->names)+1; if ( ( d->tablenames = (char *)Malloc1((2*nsize+30)*sizeof(char),"tablenames") ) == 0 ) { return(-1); } t = d->tablenames; d->tablenamessize = 2*nsize+30; d->tablenamefill = nsize-1; for ( k = 0; k < i; k++ ) { ss = d->nblocks[k]->names; for ( j = 0; j < NAMETABLESIZE; j++ ) *t++ = *ss++; } ss = d->nblocks[i]->names; while ( ss < s ) *t++ = *ss++; *t = 0; return(0); } /* #] ComposeTableNames : #[ OpenDbase : */ DBASE *OpenDbase(char *filename) { FILE *f; DBASE *d; char *newname; if ( ( f = LocateBase(&filename,&newname,"r+b") ) == 0 ) { MesPrint("Cannot open file %s\n",filename); return(0); } /* setbuf(f,0); */ d = (DBASE *)From0List(&(AC.TableBaseList)); d->name = filename; /* For the moment just for the error messages */ d->handle = f; if ( ReadIniInfo(d) || ReadIndex(d) ) { M_free(d,"OpenDbase"); fclose(f); return(0); } if ( ComposeTableNames(d) ) { FreeTableBase(d); fclose(f); return(0); } d->name = str_dup(filename); d->fullname = newname; return(d); } /* #] OpenDbase : #[ AddTableName : Adds a name of a table. Writes the namelist to disk. Returns the number of this tablename in the database. If the name was already in the table we return its value in negative. Zero is an error! */ MLONG AddTableName(DBASE *d,char *name,TABLES T) { char *s, *t, *tt; int namesize, tailsize; MLONG newsize, i, num; /* First search for the name in what we have already */ if ( d->tablenames ) { num = 0; s = d->tablenames; while ( *s ) { num++; t = name; while ( ( *s == *t ) && *t ) { s++; t++; } if ( *s == *t ) { return(-num); } while ( *s ) s++; s++; while ( *s ) s++; s++; } } /* This name has to be added */ MesPrint("We add the name %s\n",name); t = name; while ( *t ) { t++; } namesize = t-name; if ( ( t = (char *)(T->argtail) ) != 0 ) { while ( *t ) { t++; } tailsize = t - (char *)(T->argtail); } else { tailsize = 0; } if ( d->tablenames == 0 ) { if ( ComposeTableNames(d) ) { FreeTableBase(d); M_free(d,"AddTableName"); return(0); } } d->info.numberoftables++; while ( ( d->tablenamefill+namesize+tailsize+3 > d->tablenamessize ) || ( d->tablenames == 0 ) ) { newsize = 2*d->tablenamessize + 2*namesize + 2*tailsize + 6; if ( ( t = (char *)Malloc1(newsize*sizeof(char),"AddTableName") ) == 0 ) return(0); tt = t; if ( d->tablenames ) { s = d->tablenames; for ( i = 0; i < d->tablenamefill; i++ ) *t++ = *s++; *t = 0; M_free(d->tablenames,"d->tablenames"); } d->tablenames = tt; d->tablenamessize = newsize; } s = d->tablenames + d->tablenamefill; t = name; while ( *t ) *s++ = *t++; *s++ = 0; t = (char *)(T->argtail); while ( *t ) *s++ = *t++; *s++ = 0; *s = 0; d->tablenamefill = s - d->tablenames; d->topnumber++; /* Now we have to synchronize */ if ( PutTableNames(d) ) return(0); return(d->topnumber); } /* #] AddTableName : #[ GetTableName : Gets a name of a table. Returns the number of this tablename in the database. Zero -> error */ MLONG GetTableName(DBASE *d,char *name) { char *s, *t; MLONG num; /* search for the name in what we have */ if ( d->tablenames ) { num = 0; s = d->tablenames; while ( *s ) { num++; t = name; while ( ( *s == *t ) && *t ) { s++; t++; } if ( *s == *t ) { return(num); } while ( *s ) s++; s++; while ( *s ) s++; s++; } } return(0); } /* #] GetTableName : #[ PutTableNames : Takes the names string in d->tablenames and puts it in the nblocks pieces. Writes what has been changed to disk. */ int PutTableNames(DBASE *d) { NAMESBLOCK **nnew; int i, j, firstdif; MLONG m; char *s, *t; /* Determine how many blocks are needed. */ MLONG numblocks = d->tablenamefill/NAMETABLESIZE + 1; if ( d->info.numberofnamesblocks < numblocks ) { /* We need more blocks. First make sure of the space for nblocks. */ if ( ( nnew = (NAMESBLOCK **)Malloc1(sizeof(NAMESBLOCK *)*numblocks, "new names block") ) == 0 ) { return(-1); } for ( i = 0; i < d->info.numberofnamesblocks; i++ ) { nnew[i] = d->nblocks[i]; } free(d->nblocks); d->nblocks = nnew; for ( ; i < numblocks; i++ ) { if ( ( d->nblocks[i] = (NAMESBLOCK *)Malloc1(sizeof(NAMESBLOCK), "additional names blocks ") ) == 0 ) { FreeTableBase(d); return(-1); } d->nblocks[i]->previousblock = -1; d->nblocks[i]->position = -1; s = d->nblocks[i]->names; for ( j = 0; j < NAMETABLESIZE; j++ ) *s++ = 0; } d->info.numberofnamesblocks = numblocks; } /* Now look till where the new contents agree with the old. */ firstdif = 0; i = 0; t = d->nblocks[i]->names; j = 0; s = d->tablenames; for ( m = 0; m < d->tablenamefill; m++ ) { if ( *s == *t ) { s++; t++; j++; if ( j >= NAMETABLESIZE ) { i++; t = d->nblocks[i]->names; j = 0; } } else { firstdif = i; for ( ; m < d->tablenamefill; m++ ) { *t++ = *s++; j++; if ( j >= NAMETABLESIZE ) { i++; t = d->nblocks[i]->names; j = 0; } } *t = 0; break; } } for ( i = 0; i < d->info.numberofnamesblocks; i++ ) { if ( i == firstdif ) break; if ( d->nblocks[i]->position < 0 ) { firstdif = i; break; } } /* Now we have to (re)write the blocks, starting at firstdif. */ for ( i = firstdif; i < d->info.numberofnamesblocks; i++ ) { if ( i > 0 ) d->nblocks[i]->previousblock = d->nblocks[i-1]->position; else d->nblocks[i]->previousblock = -1; if ( d->nblocks[i]->position < 0 ) { fseek(d->handle,0,SEEK_END); d->nblocks[i]->position = ftell(d->handle); } else fseek(d->handle,d->nblocks[i]->position,SEEK_SET); convertnamesblock(d->nblocks[i],&scratchnamesblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchnamesblock),sizeof(NAMESBLOCK)) ) { MesPrint("Error while writing names blocks\n"); FreeTableBase(d); return(-1); } } d->info.lastnameblock = d->nblocks[d->info.numberofnamesblocks-1]->position; d->info.firstnameblock = d->nblocks[0]->position; return(WriteIniInfo(d)); } /* #] PutTableNames : #[ AddToIndex : */ int AddToIndex(DBASE *d,MLONG number) { MLONG i, oldnumofindexblocks = d->info.numberofindexblocks; MLONG j, newnumofindexblocks, jj; INDEXBLOCK **ib; MLONG t = (MLONG)(time(0)); if ( number == 0 ) return(0); else if ( number < 0 ) { if ( d->info.entriesinindex < -number ) { MesPrint("There are only %ld entries in the index of file %s\n", d->info.entriesinindex,d->name); return(-1); } d->info.entriesinindex += number; dowrite: if ( WriteIniInfo(d) ) { d->info.entriesinindex -= number; MesPrint("File may be corrupted\n"); return(-1); } } else if ( d->info.entriesinindex+number <= NUMOBJECTS*d->info.numberofindexblocks ) { d->info.entriesinindex += number; goto dowrite; } else { d->info.entriesinindex += number; newnumofindexblocks = d->info.numberofindexblocks + ((number - (NUMOBJECTS*d->info.numberofindexblocks - d->info.entriesinindex)) +NUMOBJECTS-1)/NUMOBJECTS; if ( ( ib = (INDEXBLOCK **)Malloc1(sizeof(INDEXBLOCK *)*newnumofindexblocks, "index") ) == 0 ) return(-1); for ( i = 0; i < d->info.numberofindexblocks; i++ ) { ib[i] = d->iblocks[i]; } for ( i = d->info.numberofindexblocks; i < newnumofindexblocks; i++ ) { if ( ( ib[i] = (INDEXBLOCK *)Malloc1(sizeof(INDEXBLOCK),"index block") ) == 0 ) { FreeTableBase(d); return(-1); } if ( i > 0 ) ib[i]->previousblock = ib[i-1]->position; else ib[i]->previousblock = -1; /* Zero things properly. We don't want garbage in the file. */ for ( j = 0; j < NUMOBJECTS; j++ ) { ib[i]->objects[j].date = t; ib[i]->objects[j].size = 0; ib[i]->objects[j].position = -1; ib[i]->objects[j].tablenumber = 0; ib[i]->objects[j].uncompressed = 0; ib[i]->objects[j].spare1 = 0; ib[i]->objects[j].spare2 = 0; ib[i]->objects[j].spare3 = 0; for ( jj = 0; jj < ELEMENTSIZE; jj++ ) ib[i]->objects[j].element[jj] = 0; } fseek(d->handle,0,SEEK_END); ib[i]->position = ftell(d->handle); convertblock(ib[i],&scratchblock,TODISK); if ( minoswrite(d->handle,(char *)(&scratchblock),sizeof(INDEXBLOCK)) ) { MesPrint("Error while writing new index of file %s",d->name); FreeTableBase(d); return(-1); } } d->info.lastindexblock = ib[newnumofindexblocks-1]->position; d->info.firstindexblock = ib[0]->position; d->info.numberofindexblocks = newnumofindexblocks; if ( WriteIniInfo(d) ) { d->info.numberofindexblocks = oldnumofindexblocks; d->info.entriesinindex -= number; MesPrint("File may be corrupted\n"); FreeTableBase(d); return(-1); } M_free(d->iblocks,"AddToIndex"); d->iblocks = ib; } return(0); } /* #] AddToIndex : #[ AddObject : */ MLONG AddObject(DBASE *d,MLONG tablenumber,char *arguments,char *rhs) { MLONG number; number = d->info.entriesinindex; if ( AddToIndex(d,1) ) return(-1); if ( WriteObject(d,tablenumber,arguments,rhs,number) ) return(-1); return(number); } /* #] AddObject : #[ FindTableNumber : */ MLONG FindTableNumber(DBASE *d,char *name) { char *s = d->tablenames, *t, *ss; MLONG num = 0; ss = d->tablenames + d->tablenamefill; while ( s < ss ) { num++; t = name; while ( *s == *t && *t ) { s++; t++; } if ( *s == 0 && *t == 0 ) return(num); while ( *s ) s++; s++; /* Skip also the argument tail */ while ( *s ) s++; s++; } return(-1); /* Name not found */ } /* #] FindTableNumber : #[ WriteObject : */ int WriteObject(DBASE *d,MLONG tablenumber,char *arguments,char *rhs,MLONG number) { char *s, *a; #ifdef WITHZLIB char *buffer = 0; uLongf newsize = 0, oldsize = 0; uLong ssize; int error = 0; #endif MLONG i, j, position, size, n; OBJECTS *obj; if ( ( d->mode & INPUTONLY ) == INPUTONLY ) { MesPrint("Not allowed to write to input\n"); return(-1); } if ( number >= d->info.entriesinindex ) { MesPrint("Reference to non-existing object number %ld\n",number+1); return(0); } j = number/NUMOBJECTS; i = number%NUMOBJECTS; obj = &(d->iblocks[j]->objects[i]); a = arguments; while ( *a ) a++; a++; n = a - arguments; if ( n > ELEMENTSIZE ) { MesPrint("Table element %s has more than %ld characters.\n",arguments, (MLONG)ELEMENTSIZE); return(-1); } s = obj->element; a = arguments; while ( *a ) *s++ = *a++; *s++ = 0; while ( n < ELEMENTSIZE ) { *s++ = 0; n++; } obj->spare1 = obj->spare2 = obj->spare3 = 0; fseek(d->handle,0,SEEK_END); position = ftell(d->handle); s = rhs; while ( *s ) s++; s++; size = s - rhs; #ifdef WITHZLIB if ( ( d->mode & NOCOMPRESS ) == 0 ) { newsize = size + size/1000 + 20; if ( ( buffer = (char *)Malloc1(newsize*sizeof(char),"compress buffer") ) == 0 ) { MesPrint("No compress used for element %s in file %s\n",arguments,d->name); } } else buffer = 0; if ( buffer ) { ssize = size; #ifdef WITHZSTD // Force the use of zlib for compressed Tablebase entries, so that tablebases created // with zstd-supported FORM builds can be used by zstd-unsupported FORM builds. const int old_isUsingZSTDcompression = ZWRAP_isUsingZSTDcompression(); ZWRAP_useZSTDcompression(0); #endif if ( ( error = compress((Bytef *)buffer,&newsize,(Bytef *)rhs,ssize) ) != Z_OK ) { MesPrint("Error = %d\n",error); MesPrint("Due to error no compress used for element %s in file %s\n",arguments,d->name); M_free(buffer,"tb,WriteObject"); buffer = 0; } #ifdef WITHZSTD ZWRAP_useZSTDcompression(old_isUsingZSTDcompression); #endif } if ( buffer ) { rhs = buffer; oldsize = size; size = newsize; } #endif if ( minoswrite(d->handle,rhs,size) ) { MesPrint("Error while writing rhs\n"); return(-1); } obj->position = position; obj->size = size; obj->date = (MLONG)(time(0)); obj->tablenumber = tablenumber; #ifdef WITHZLIB obj->uncompressed = oldsize; if ( buffer ) M_free(buffer,"tb,WriteObject"); #else obj->uncompressed = 0; #endif return(WriteIndexBlock(d,j)); } /* #] WriteObject : #[ ReadObject : Returns a pointer to the proper rhs */ char *ReadObject(DBASE *d,MLONG tablenumber,char *arguments) { OBJECTS *obj; MLONG i, j; char *buffer1, *s, *t; #ifdef WITHZLIB char *buffer2 = 0; uLongf finallength = 0; #endif if ( tablenumber > d->topnumber ) { MesPrint("Reference to non-existing table number in tablebase %s: %ld\n", d->name,tablenumber); return(0); } /* Start looking for the object */ for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber != tablenumber ) continue; s = arguments; t = d->iblocks[i]->objects[j].element; while ( *s == *t && *s ) { s++; t++; } if ( *t == 0 && *s == 0 ) goto foundelement; } } s = d->tablenames; i = 1; while ( *s ) { if ( i == tablenumber ) break; while ( *s ) s++; s++; while ( *s ) s++; s++; i++; } MesPrint("%s(%s) not found in tablebase %s\n",s,arguments,d->name); return(0); foundelement:; obj = &(d->iblocks[i]->objects[j]); fseek(d->handle,obj->position,SEEK_SET); if ( ( buffer1 = (char *)Malloc1(obj->size,"reading rhs buffer1") ) == 0 ) { return(0); } #ifdef WITHZLIB if ( obj->uncompressed > 0 ) { if ( ( buffer2 = (char *)Malloc1(obj->uncompressed,"reading rhs buffer2") ) == 0 ) { return(0); } } else buffer2 = 0; #endif if ( minosread(d->handle,buffer1,obj->size) ) { MesPrint("Could not read rhs %s in file %s\n",arguments,d->name); M_free(buffer1,"tb,ReadObject"); #ifdef WITHZLIB if ( buffer2 ) M_free(buffer2,"tb,ReadObject"); #endif return(0); } #ifdef WITHZLIB if ( buffer2 == 0 ) return(buffer1); finallength = obj->uncompressed; if ( uncompress((Bytef *)buffer2,&finallength,(Bytef *)buffer1,obj->size) != Z_OK ) { MesPrint("Cannot uncompress element %s in file %s\n",arguments,d->name); M_free(buffer1,"tb,ReadObject"); M_free(buffer2,"tb,ReadObject"); return(0); } M_free(buffer1,"tb,ReadObject"); return(buffer2); #else return(buffer1); #endif } /* #] ReadObject : #[ ReadijObject : Returns a pointer to the proper rhs */ char *ReadijObject(DBASE *d,MLONG i,MLONG j,char *arguments) { OBJECTS *obj; char *buffer1; #ifdef WITHZLIB char *buffer2 = 0; uLongf finallength = 0; #endif obj = &(d->iblocks[i]->objects[j]); fseek(d->handle,obj->position,SEEK_SET); if ( ( buffer1 = (char *)Malloc1(obj->size,"reading rhs buffer1") ) == 0 ) { return(0); } #ifdef WITHZLIB if ( obj->uncompressed > 0 ) { if ( ( buffer2 = (char *)Malloc1(obj->uncompressed,"reading rhs buffer2") ) == 0 ) { return(0); } } else buffer2 = 0; #endif if ( minosread(d->handle,buffer1,obj->size) ) { MesPrint("Could not read rhs %s in file %s\n",arguments,d->name); if ( buffer1 ) M_free(buffer1,"rhs buffer1"); #ifdef WITHZLIB if ( buffer2 ) M_free(buffer2,"rhs buffer2"); #endif return(0); } #ifdef WITHZLIB if ( buffer2 == 0 ) return(buffer1); finallength = obj->uncompressed; if ( uncompress((Bytef *)buffer2,&finallength,(Bytef *)buffer1,obj->size) != Z_OK ) { MesPrint("Cannot uncompress element %s in file %s\n",arguments,d->name); if ( buffer1 ) M_free(buffer1,"rhs buffer1"); if ( buffer2 ) M_free(buffer2,"rhs buffer2"); return(0); } M_free(buffer1,"rhs buffer1"); return(buffer2); #else return(buffer1); #endif } /* #] ReadijObject : #[ ExistsObject : Returns 1 if Object exists */ int ExistsObject(DBASE *d,MLONG tablenumber,char *arguments) { MLONG i, j; char *s, *t; if ( tablenumber > d->topnumber ) { MesPrint("Reference to non-existing table number in tablebase %s: %ld\n", d->name,tablenumber); return(0); } /* Start looking for the object */ for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber != tablenumber ) continue; s = arguments; t = d->iblocks[i]->objects[j].element; while ( *s == *t && *s ) { s++; t++; } if ( *t == 0 && *s == 0 ) return(1); } } return(0); } /* #] ExistsObject : #[ DeleteObject : Returns 1 if Object has been deleted. We leave a hole. Actually the object is still there but has been inactivated. It can be reactivated by calling this routine again. */ int DeleteObject(DBASE *d,MLONG tablenumber,char *arguments) { MLONG i, j; char *s, *t; if ( tablenumber > d->topnumber ) { MesPrint("Reference to non-existing table number in tablebase %s: %ld\n", d->name,tablenumber); return(0); } /* Start looking for the object */ for ( i = 0; i < d->info.numberofindexblocks; i++ ) { for ( j = 0; j < NUMOBJECTS; j++ ) { if ( d->iblocks[i]->objects[j].tablenumber != tablenumber ) continue; s = arguments; t = d->iblocks[i]->objects[j].element; while ( *s == *t && *s ) { s++; t++; } if ( *t == 0 && *s == 0 ) { d->iblocks[i]->objects[j].tablenumber = -d->iblocks[i]->objects[j].tablenumber - 1; return(1); } } } return(0); } /* #] DeleteObject : */ form-5.0.1/sources/mytime.h0000644000175100017510000000226315217035721011311 #pragma once /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ double thetime(); std::string thetime_str(); form-5.0.1/sources/flintinterface.cc0000644000175100017510000021604715217035721013147 /** @file flintinterface.cc * * Contains functions which interface with FLINT functions to perform arithmetic with uni- and * multi-variate polynomials and perform factorization. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #ifdef HAVE_CONFIG_H #ifndef CONFIG_H_INCLUDED #define CONFIG_H_INCLUDED #include #endif #endif extern "C" { #include "form3.h" } #include "flintinterface.h" /* #[ Types * Use fixed-size integer types (int32_t, uint32_t, int64_t, uint64_t) except when we refer * specifically to FORM term data, when we use WORD. This code has only been tested on 64bit * systems where WORDs are int32_t, and some functions (fmpz_get_form, fmpz_set_form) require this * to be the case. Enforce this: */ static_assert(sizeof(WORD) == sizeof(int32_t), "flint interface expects 32bit WORD"); static_assert(sizeof(UWORD) == sizeof(uint32_t), "flint interface expects 32bit WORD"); static_assert(BITSINWORD == 32, "flint interface expects 32bit WORD"); static_assert(sizeof(ulong) == sizeof(uint64_t), "flint interface expects ulong is uint64_t"); static_assert(sizeof(slong) == sizeof(int64_t), "flint interface expects slong is int64_t"); /* * Flint functions take arguments or return values which may be "slong" or "ulong" in its * documentation, and these are int64_t and uint64_t respectively. * #] Types */ /* * FLINT's univariate poly has a dense representation. For sufficiently sparse polynomials it is * faster to use mpoly instead, which is sparse. For a density <= this threshold we switch, where * the density defined as is "number of terms" / "maximum degree". */ #define UNIVARIATE_DENSITY_THR 0.02f /* #[ flint::cleanup : */ void flint::cleanup(void) { flint_cleanup(); } /* #] flint::cleanup : #[ flint::cleanup_master : */ void flint::cleanup_master(void) { flint_cleanup_master(); } /* #] flint::cleanup_master : #[ flint::divmod_mpoly : */ WORD* flint::divmod_mpoly(PHEAD const WORD *a, const WORD *b, const bool return_rem, const WORD must_fit_term, const var_map_t &var_map, const bool sort_vars) { flint::mpoly_ctx ctx(var_map.size()); flint::mpoly pa(ctx.d), pb(ctx.d), denpa(ctx.d), denpb(ctx.d); flint::from_argument_mpoly(pa.d, denpa.d, a, false, var_map, ctx.d); flint::from_argument_mpoly(pb.d, denpb.d, b, false, var_map, ctx.d); // The input won't have any symbols with negative powers, but there may be rational // coefficients. Verify this: if ( fmpz_mpoly_is_fmpz(denpa.d, ctx.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::divmod_mpoly: error: denpa is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( fmpz_mpoly_is_fmpz(denpb.d, ctx.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::divmod_mpoly: error: denpb is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } flint::fmpz scale; flint::mpoly div(ctx.d), rem(ctx.d); fmpz_mpoly_quasidivrem(scale.d, div.d, rem.d, pa.d, pb.d, ctx.d); // The quotient must be multiplied by the denominator of the divisor fmpz_mpoly_mul(div.d, div.d, denpb.d, ctx.d); // The overall denominator of both div and rem is given by scale*denpa. This we will pass to // to_argument_mpoly's "denscale" argument which performs the division in the result. We have // already checked denpa is just an fmpz. fmpz_mul(scale.d, scale.d, fmpz_mpoly_term_coeff_ref(denpa.d, 0, ctx.d)); // Determine the size of the output by passing write = false. const bool with_arghead = false; bool write = false; const uint64_t prev_size = 0; const uint64_t out_size = return_rem ? (uint64_t)flint::to_argument_mpoly(BHEAD NULL, with_arghead, must_fit_term, write, prev_size, rem.d, var_map, ctx.d, sort_vars, scale.d) : (uint64_t)flint::to_argument_mpoly(BHEAD NULL, with_arghead, must_fit_term, write, prev_size, div.d, var_map, ctx.d, sort_vars, scale.d) ; WORD* res = (WORD *)Malloc1(sizeof(WORD)*out_size, "flint::divrem_mpoly"); // Write out the result write = true; if ( return_rem ) { (uint64_t)flint::to_argument_mpoly(BHEAD res, with_arghead, must_fit_term, write, prev_size, rem.d, var_map, ctx.d, sort_vars, scale.d); } else { (uint64_t)flint::to_argument_mpoly(BHEAD res, with_arghead, must_fit_term, write, prev_size, div.d, var_map, ctx.d, sort_vars, scale.d); } return res; } /* #] flint::divmod_mpoly : #[ flint::divmod_poly : */ WORD* flint::divmod_poly(PHEAD const WORD *a, const WORD *b, const bool return_rem, const WORD must_fit_term, const var_map_t &var_map) { flint::poly pa, pb, denpa, denpb; flint::from_argument_poly(pa.d, denpa.d, a, false); flint::from_argument_poly(pb.d, denpb.d, b, false); // The input won't have any symbols with negative powers, but there may be rational // coefficients. Verify this: if ( fmpz_poly_length(denpa.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::divmod_poly: error: denpa is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( fmpz_poly_length(denpb.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::divmod_poly: error: denpb is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } flint::fmpz scale; uint64_t scale_power = 0; flint::poly div, rem; // Get the leading coefficient of pb. fmpz_poly_pseudo_divrem returns only the scaling power. fmpz_poly_get_coeff_fmpz(scale.d, pb.d, fmpz_poly_degree(pb.d)); fmpz_poly_pseudo_divrem(div.d, rem.d, (ulong*)&scale_power, pa.d, pb.d); // The quotient must be multiplied by the denominator of the divisor fmpz_poly_mul(div.d, div.d, denpb.d); // The overall denominator of both div and rem is given by scale^scale_power*denpa. This we will // pass to to_argument_poly's "denscale" argument which performs the division in the result. We // have already checked denpa is just an fmpz. fmpz_pow_ui(scale.d, scale.d, scale_power); fmpz_mul(scale.d, scale.d, fmpz_poly_get_coeff_ptr(denpa.d, 0)); // Determine the size of the output by passing write = false. const bool with_arghead = false; bool write = false; const uint64_t prev_size = 0; const uint64_t out_size = return_rem ? (uint64_t)flint::to_argument_poly(BHEAD NULL, with_arghead, must_fit_term, write, prev_size, rem.d, var_map, scale.d) : (uint64_t)flint::to_argument_poly(BHEAD NULL, with_arghead, must_fit_term, write, prev_size, div.d, var_map, scale.d) ; WORD* res = (WORD *)Malloc1(sizeof(WORD)*out_size, "flint::divrem_poly"); // Write out the result write = true; if ( return_rem ) { (uint64_t)flint::to_argument_poly(BHEAD res, with_arghead, must_fit_term, write, prev_size, rem.d, var_map, scale.d); } else { (uint64_t)flint::to_argument_poly(BHEAD res, with_arghead, must_fit_term, write, prev_size, div.d, var_map, scale.d); } return res; } /* #] flint::divmod_poly : #[ flint::factorize_mpoly : */ WORD* flint::factorize_mpoly(PHEAD const WORD *argin, WORD *argout, const bool with_arghead, const bool is_fun_arg, const var_map_t &var_map, const bool sort_vars) { flint::mpoly_ctx ctx(var_map.size()); flint::mpoly arg(ctx.d), den(ctx.d), base(ctx.d); flint::from_argument_mpoly(arg.d, den.d, argin, with_arghead, var_map, ctx.d); // The denominator must be 1: if ( fmpz_mpoly_is_one(den.d, ctx.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::factorize_mpoly error: den != 1"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Now we can factor the mpoly: flint::mpoly_factor arg_fac(ctx.d); fmpz_mpoly_factor(arg_fac.d, arg.d, ctx.d); const int64_t num_factors = fmpz_mpoly_factor_length(arg_fac.d, ctx.d); flint::fmpz overall_constant; fmpz_mpoly_factor_get_constant_fmpz(overall_constant.d, arg_fac.d, ctx.d); // FORM should always have taken the overall constant out in the content. Thus this overall // constant factor should be +- 1 here. Verify this: if ( ! ( fmpz_equal_si(overall_constant.d, 1) || fmpz_equal_si(overall_constant.d, -1) ) ) { MLOCK(ErrorMessageLock); MesPrint("flint::factorize_mpoly error: overall constant factor != +-1"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Construct the output. If argout is not NULL, we write the result there. // Otherwise, allocate memory. // The output is zero-terminated list of factors. If with_arghead, each has an arghead which // contains its size. Otherwise, the factors are zero separated. // We only need to determine the size of the output if we are allocating memory, but we need to // loop through the factors to fix their signs anyway. Do both together in one loop: // Initially 1, for the final trailing 0. uint64_t output_size = 1; // For finding the highest symbol, in FORM's lexicographic ordering vector var_map_inv; var_map_inv.resize(var_map.size()); for ( auto x : var_map ) { var_map_inv[x.second] = x.first; } // Store whether we should flip the factor sign in the ouput: vector base_sign(num_factors, 0); for ( int64_t i = 0; i < num_factors; i++ ) { fmpz_mpoly_factor_get_base(base.d, arg_fac.d, i, ctx.d); const int64_t exponent = fmpz_mpoly_factor_get_exp_si(arg_fac.d, i, ctx.d); // poly_factorize makes sure the highest power of the "highest symbol" (in FORM's // lexicographic ordering) has a positive coefficient. Check this, update overall_constant // of the factorization if necessary. // Store the sign per factor, so that we can flip the signs in the output without re-checking // the individual terms again. uint32_t max_var = 0; // FORM symbols start at 20, 0 is a good initial value. int32_t max_pow = -1; vector base_term_exponents(var_map.size(), 0); for ( int64_t j = 0; j < fmpz_mpoly_length(base.d, ctx.d); j++ ) { fmpz_mpoly_get_term_exp_si((slong*)base_term_exponents.data(), base.d, (slong)j, ctx.d); for ( size_t k = 0; k < var_map.size(); k++ ) { if ( base_term_exponents[k] > 0 && ( var_map_inv[k] > max_var || ( var_map_inv[k] == max_var && base_term_exponents[k] > max_pow ) ) ) { max_var = var_map_inv[k]; max_pow = base_term_exponents[k]; base_sign[i] = fmpz_sgn(fmpz_mpoly_term_coeff_ref(base.d, j, ctx.d)); } } } // If this base's sign will be flipped an odd number of times, there is a contribution to // the overall sign of the whole factorization: if ( ( base_sign[i] == -1 ) && ( exponent % 2 == 1 ) ) { fmpz_neg(overall_constant.d, overall_constant.d); } // Now determine the output size of the factor, if we are allocating the memory if ( argout == NULL ) { const bool write = false; for ( int64_t j = 0; j < exponent; j++ ) { output_size += (uint64_t)flint::to_argument_mpoly(BHEAD NULL, with_arghead, is_fun_arg, write, 0, base.d, var_map, ctx.d, sort_vars); } } } if ( fmpz_sgn(overall_constant.d) == -1 && argout == NULL ) { // Add space for a fast-notation number or a normal-notation number and zero separator output_size += with_arghead ? 2 : 4+1; } // Now make the allocation if necessary: if ( argout == NULL ) { argout = (WORD*)Malloc1(sizeof(WORD)*output_size, "flint::factorize_mpoly"); } // And now comes the actual output: WORD* old_argout = argout; // If the overall sign is negative, first write a full-notation -1. It will be absorbed into the // overall factor in the content by the caller. if ( fmpz_sgn(overall_constant.d) == -1 ) { if ( with_arghead ) { // poly writes in fast notation in this case. Fast notation is expected by the caller, to // properly merge it with the overall factor of the content. *argout++ = -SNUMBER; *argout++ = -1; } else { *argout++ = 4; // term size *argout++ = 1; // numerator *argout++ = 1; // denominator *argout++ = -3; // coeff size, negative number *argout++ = 0; // factor separator } } for ( int64_t i = 0; i < num_factors; i++ ) { fmpz_mpoly_factor_get_base(base.d, arg_fac.d, i, ctx.d); const int64_t exponent = fmpz_mpoly_factor_get_exp_si(arg_fac.d, i, ctx.d); if ( base_sign[i] == -1 ) { fmpz_mpoly_neg(base.d, base.d, ctx.d); } const bool write = true; for ( int64_t j = 0; j < exponent; j++ ) { argout += flint::to_argument_mpoly(BHEAD argout, with_arghead, is_fun_arg, write, argout-old_argout, base.d, var_map, ctx.d, sort_vars); } } // Final trailing zero to denote the end of the factors. *argout++ = 0; return old_argout; } /* #] flint::factorize_mpoly : #[ flint::factorize_poly : */ WORD* flint::factorize_poly(PHEAD const WORD *argin, WORD *argout, const bool with_arghead, const bool is_fun_arg, const var_map_t &var_map) { flint::poly arg, den; flint::from_argument_poly(arg.d, den.d, argin, with_arghead); // The denominator must be 1: if ( fmpz_poly_is_one(den.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::factorize_poly error: den != 1"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Now we can factor the poly: flint::poly_factor arg_fac; fmpz_poly_factor(arg_fac.d, arg.d); // fmpz_poly_factor_t lacks some convenience functions which fmpz_mpoly_factor_t has. // I have worked out how to get the factors by looking at how fmpz_poly_factor_print works. const long num_factors = (arg_fac.d)->num; // Construct the output. If argout is not NULL, we write the result there. // Otherwise, allocate memory. // The output is zero-terminated list of factors. If with_arghead, each has an arghead which // contains its size. Otherwise, the factors are zero separated. if ( argout == NULL ) { // First we need to determine the size of the output. This is the same procedure as the // loop below, but we don't write anything in to_argument_poly (write arg: false). // Initially 1, for the final trailing 0. uint64_t output_size = 1; for ( long i = 0; i < num_factors; i++ ) { fmpz_poly_struct* base = (arg_fac.d)->p + i; const long exponent = (arg_fac.d)->exp[i]; const bool write = false; for ( long j = 0; j < exponent; j++ ) { output_size += (uint64_t)flint::to_argument_poly(BHEAD NULL, with_arghead, is_fun_arg, write, 0, base, var_map); } } argout = (WORD*)Malloc1(sizeof(WORD)*output_size, "flint::factorize_poly"); } WORD* old_argout = argout; for ( long i = 0; i < num_factors; i++ ) { fmpz_poly_struct* base = (arg_fac.d)->p + i; const long exponent = (arg_fac.d)->exp[i]; const bool write = true; for ( long j = 0; j < exponent; j++ ) { argout += flint::to_argument_poly(BHEAD argout, with_arghead, is_fun_arg, write, argout-old_argout, base, var_map); } } *argout = 0; return old_argout; } /* #] flint::factorize_poly : #[ flint::form_sort : */ // Sort terms using form's sorting routines. Uses a custom (faster) compare routine, since here // only symbols can appear. // This is a modified poly_sort from polywrap.cc. void flint::form_sort(PHEAD WORD *terms) { if ( terms[0] < 0 ) { // Fast notation, there is nothing to do return; } const WORD oldsorttype = AR.SortType; AR.SortType = SORTHIGHFIRST; const WORD in_size = terms[0] - ARGHEAD; WORD out_size; if ( NewSort(BHEAD0) ) { Terminate(-1); } AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); // Make sure the symbols are in the right order within the terms for ( WORD i = ARGHEAD; i < terms[0]; i += terms[i] ) { if ( SymbolNormalize(terms+i) < 0 || StoreTerm(BHEAD terms+i) ) { AR.SortType = oldsorttype; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); LowerSortLevel(); Terminate(-1); } } if ( ( out_size = EndSort(BHEAD terms+ARGHEAD, 1) ) < 0 ) { AR.SortType = oldsorttype; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); Terminate(-1); } // Check the final size if ( in_size != out_size ) { MLOCK(ErrorMessageLock); MesPrint("flint::form_sort: error: unexpected sorted arg length change %d->%d", in_size, out_size); MUNLOCK(ErrorMessageLock); Terminate(-1); } AR.SortType = oldsorttype; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); terms[1] = 0; // set dirty flag to zero } /* #] flint::form_sort : #[ flint::from_argument_mpoly : */ // Convert a FORM argument (or 0-terminated list of terms: with_arghead == false) to a // (multi-variate) fmpz_mpoly_t poly. The "denominator" is return in denpoly, and contains the // overall negative-power numeric and symbolic factor. uint64_t flint::from_argument_mpoly(fmpz_mpoly_t poly, fmpz_mpoly_t denpoly, const WORD *args, const bool with_arghead, const var_map_t &var_map, const fmpz_mpoly_ctx_t ctx) { // Some callers re-use their poly, denpoly to avoid calling init/clear unnecessarily. // Make sure they are 0 to begin. fmpz_mpoly_set_si(poly, 0, ctx); fmpz_mpoly_set_si(denpoly, 0, ctx); // First check for "fast notation" arguments: if ( *args == -SNUMBER ) { fmpz_mpoly_set_si(poly, *(args+1), ctx); fmpz_mpoly_set_si(denpoly, 1, ctx); return 2; } if ( *args == -SYMBOL ) { // A "fast notation" SYMBOL has a power and coefficient of 1: vector exponents(var_map.size(), 0); exponents[var_map.at(*(args+1))] = 1; fmpz_mpoly_set_coeff_ui_ui(poly, (ulong)1, (ulong*)exponents.data(), ctx); fmpz_mpoly_set_ui(denpoly, (ulong)1, ctx); return 2; } // Now we can iterate through the terms of the argument. If we have // an ARGHEAD, we already know where to terminate. Otherwise we'll have // to loop until the terminating 0. const WORD* arg_stop = with_arghead ? args+args[0] : (WORD*)UINT64_MAX; uint64_t arg_size = 0; if ( with_arghead ) { arg_size = args[0]; args += ARGHEAD; } // Search for numerical or symbol denominators to create "denpoly". flint::fmpz den_coeff, tmp; fmpz_set_si(den_coeff.d, 1); vector exponents(var_map.size(), 0); vector neg_exponents(var_map.size(), 0); for ( const WORD* term = args; term < arg_stop; term += term[0] ) { const WORD* term_stop = term+term[0]; const WORD coeff_size = (term_stop)[-1]; const WORD* symbol_stop = term_stop - ABS(coeff_size); const WORD* t = term; t++; if ( t == symbol_stop ) { // Just a number, no symbols } else { t++; // this entry is SYMBOL t++; // this entry just has the size of the symbol array, but we can use symbol_stop for ( const WORD* s = t; s < symbol_stop; s += 2 ) { if ( *(s+1) < 0 ) { neg_exponents[var_map.at(*s)] = MaX(neg_exponents[var_map.at(*s)], (uint64_t)(-(*(s+1))) ); } } } // Now check for a denominator in the coefficient: if ( *(symbol_stop+ABS(coeff_size/2)) != 1 ) { flint::fmpz_set_form(tmp.d, (UWORD*)(symbol_stop+ABS(coeff_size/2)), ABS(coeff_size/2)); // Record the LCM of the coefficient denominators: fmpz_lcm(den_coeff.d, den_coeff.d, tmp.d); } if ( !with_arghead && *term_stop == 0 ) { // + 1 for the terminating 0 arg_size = term_stop - args + 1; break; } } // Assemble denpoly. fmpz_mpoly_set_coeff_fmpz_ui(denpoly, den_coeff.d, (ulong*)neg_exponents.data(), ctx); // For the term coefficients flint::fmpz coeff; for ( const WORD* term = args; term < arg_stop; term += term[0] ) { const WORD* term_stop = term+term[0]; const WORD coeff_size = (term_stop)[-1]; const WORD* symbol_stop = term_stop - ABS(coeff_size); const WORD* t = term; fill(exponents.begin(), exponents.end(), 0); t++; // skip over the total size entry if ( t == symbol_stop ) { // Just a number, no symbols } else { t++; // this entry is SYMBOL t++; // this entry just has the size of the symbol array, but we can use symbol_stop for ( const WORD* s = t; s < symbol_stop; s += 2 ) { exponents[var_map.at(*s)] = *(s+1); } } // Now read the coefficient flint::fmpz_set_form(coeff.d, (UWORD*)symbol_stop, coeff_size/2); // Multiply by denominator LCM fmpz_mul(coeff.d, coeff.d, den_coeff.d); // Shift by neg_exponents for ( size_t i = 0; i < var_map.size(); i++ ) { exponents[i] += neg_exponents[i]; } // Read the denominator if there is one, and divide it out of the coefficient if ( *(symbol_stop+ABS(coeff_size/2)) != 1 ) { flint::fmpz_set_form(tmp.d, (UWORD*)(symbol_stop+ABS(coeff_size/2)), ABS(coeff_size/2)); // By construction, this is an exact division fmpz_divexact(coeff.d, coeff.d, tmp.d); } // Push the term to the mpoly, remember to sort when finished! This is much faster than using // fmpz_mpoly_set_coeff_fmpz_ui when the terms arrive in the "wrong order". fmpz_mpoly_push_term_fmpz_ui(poly, coeff.d, (ulong*)exponents.data(), ctx); if ( !with_arghead && *term_stop == 0 ) { break; } } // And now sort the mpoly if necessary: if ( ! fmpz_mpoly_is_canonical(poly, ctx) ) { fmpz_mpoly_sort_terms(poly, ctx); } return arg_size; } /* #] flint::from_argument_mpoly : #[ flint::from_argument_poly : */ // Convert a FORM argument (or 0-terminated list of terms: with_arghead == false) to a // (uni-variate) fmpz_poly_t poly. The "denominator" is return in denpoly, and contains the // overall negative-power numeric and symbolic factor. uint64_t flint::from_argument_poly(fmpz_poly_t poly, fmpz_poly_t denpoly, const WORD *args, const bool with_arghead) { // Some callers re-use their poly, denpoly to avoid calling init/clear unnecessarily. // Make sure they are 0 to begin. fmpz_poly_set_si(poly, 0); fmpz_poly_set_si(denpoly, 0); // First check for "fast notation" arguments: if ( *args == -SNUMBER ) { fmpz_poly_set_si(poly, *(args+1)); fmpz_poly_set_si(denpoly, 1); return 2; } if ( *args == -SYMBOL ) { // A "fast notation" SYMBOL has a power and coefficient of 1: fmpz_poly_set_coeff_si(poly, 1, 1); fmpz_poly_set_si(denpoly, 1); return 2; } // Now we can iterate through the terms of the argument. If we have // an ARGHEAD, we already know where to terminate. Otherwise we'll have // to loop until the terminating 0. const WORD* arg_stop = with_arghead ? args+args[0] : (WORD*)UINT64_MAX; uint64_t arg_size = 0; if ( with_arghead ) { arg_size = args[0]; args += ARGHEAD; } // Search for numerical or symbol denominators to create "denpoly". flint::fmpz den_coeff, tmp; fmpz_set_si(den_coeff.d, 1); uint64_t neg_exponent = 0; for ( const WORD* term = args; term < arg_stop; term += term[0] ) { const WORD* term_stop = term+term[0]; const WORD coeff_size = (term_stop)[-1]; const WORD* symbol_stop = term_stop - ABS(coeff_size); const WORD* t = term; t++; // skip over the total size entry if ( t == symbol_stop ) { // Just a number, no symbols } else { t++; // this entry is SYMBOL t++; // this entry is the size of the symbol array t++; // this is the first (and only) symbol code if ( *t < 0 ) { neg_exponent = MaX(neg_exponent, (uint64_t)(-(*t)) ); } } // Now check for a denominator in the coefficient: if ( *(symbol_stop+ABS(coeff_size/2)) != 1 ) { flint::fmpz_set_form(tmp.d, (UWORD*)(symbol_stop+ABS(coeff_size/2)), ABS(coeff_size/2)); // Record the LCM of the coefficient denominators: fmpz_lcm(den_coeff.d, den_coeff.d, tmp.d); } if ( *term_stop == 0 ) { // + 1 for the terminating 0 arg_size = term_stop - args + 1; break; } } // Assemble denpoly. fmpz_poly_set_coeff_fmpz(denpoly, neg_exponent, den_coeff.d); // For the term coefficients flint::fmpz coeff; for ( const WORD* term = args; term < arg_stop; term += term[0] ) { const WORD* term_stop = term+term[0]; const WORD coeff_size = (term_stop)[-1]; const WORD* symbol_stop = term_stop - ABS(coeff_size); const WORD* t = term; uint64_t exponent = 0; t++; // skip over the total size entry if ( t == symbol_stop ) { // Just a number, no symbols } else { t++; // this entry is SYMBOL t++; // this entry is the size of the symbol array t++; // this is the first (and only) symbol code exponent = *t++; } // Now read the coefficient flint::fmpz_set_form(coeff.d, (UWORD*)symbol_stop, coeff_size/2); // Multiply by denominator LCM fmpz_mul(coeff.d, coeff.d, den_coeff.d); // Shift by neg_exponent exponent += neg_exponent; // Read the denominator if there is one, and divide it out of the coefficient if ( *(symbol_stop+ABS(coeff_size/2)) != 1 ) { flint::fmpz_set_form(tmp.d, (UWORD*)(symbol_stop+ABS(coeff_size/2)), ABS(coeff_size/2)); // By construction, this is an exact division fmpz_divexact(coeff.d, coeff.d, tmp.d); } // Add the term to the poly fmpz_poly_set_coeff_fmpz(poly, exponent, coeff.d); if ( *term_stop == 0 ) { break; } } return arg_size; } /* #] flint::from_argument_poly : #[ flint::fmpz_get_form : */ // Write FORM's long integer representation of an fmpz at a, and put the number of WORDs at na. // na carries the sign of the integer. WORD flint::fmpz_get_form(fmpz_t z, WORD *a) { WORD na = 0; const int32_t sgn = fmpz_sgn(z); if ( sgn == -1 ) { fmpz_neg(z, z); } const int64_t nlimbs = fmpz_size(z); // This works but is UB? //fmpz_get_ui_array(reinterpret_cast(a), nlimbs, z); // Use fixed-size functions to get limb data where possible. These probably cover most real // cases. if ( nlimbs == 1 ) { const uint64_t limb = fmpz_get_ui(z); a[0] = (WORD)(limb & 0xFFFFFFFF); na++; a[1] = (WORD)(limb >> BITSINWORD); if ( a[1] != 0 ) { na++; } } else if ( nlimbs == 2 ) { uint64_t limb_hi = 0, limb_lo = 0; fmpz_get_uiui((ulong*)&limb_hi, (ulong*)&limb_lo, z); a[0] = (WORD)(limb_lo & 0xFFFFFFFF); na++; a[1] = (WORD)(limb_lo >> BITSINWORD); na++; a[2] = (WORD)(limb_hi & 0xFFFFFFFF); na++; a[3] = (WORD)(limb_hi >> BITSINWORD); if ( a[3] != 0 ) { na++; } } else { vector limb_data(nlimbs, 0); fmpz_get_ui_array((ulong*)limb_data.data(), (slong)nlimbs, z); for ( long i = 0; i < nlimbs; i++ ) { a[2*i] = (WORD)(limb_data[i] & 0xFFFFFFFF); na++; a[2*i+1] = (WORD)(limb_data[i] >> BITSINWORD); if ( a[2*i+1] != 0 || i < (nlimbs-1) ) { // The final limb might fit in a single 32bit WORD. Only // increment na if the final WORD is non zero. na++; } } } // And now put the sign in the number of limbs if ( sgn == -1 ) { na = -na; } return na; } /* #] flint::fmpz_get_form : #[ flint::fmpz_set_form : */ // Create an fmpz directly from FORM's long integer representation. fmpz uses 64bit unsigned limbs, // but FORM uses 32bit UWORDs on 64bit architectures so we can't use fmpz_set_ui_array directly. void flint::fmpz_set_form(fmpz_t z, UWORD *a, WORD na) { if ( na == 0 ) { fmpz_zero(z); return; } // Negative na represenents a negative number int32_t sgn = 1; if ( na < 0 ) { sgn = -1; na = -na; } // Remove padding. FORM stores numerators and denominators with equal numbers of limbs but we // don't need to do this within the fmpz. It is not necessary to do this really, the fmpz // doesn't add zero limbs unnecessarily, but we might be able to avoid creating the limb_data // array below. while ( a[na-1] == 0 ) { na--; } // If the number fits in fixed-size fmpz_set functions, we don't need to use additional memory // to convert to uint64_t. These probably cover most real cases. if ( na == 1 ) { fmpz_set_ui(z, (uint64_t)a[0]); } else if ( na == 2 ) { fmpz_set_ui(z, (((uint64_t)a[1])< limb_data(nlimbs, 0); for ( int32_t i = 0; i < nlimbs; i++ ) { if ( 2*i+1 <= na-1 ) { limb_data[i] = (uint64_t)a[2*i] + (((uint64_t)a[2*i+1])< &es, const bool with_arghead, const bool sort_vars) { int32_t num_vars = 0; // We count the total number of terms to determine "density". uint32_t num_terms = 0; // To be used if we sort by highest degree, as the poly code does. vector degrees; var_map_t var_map; // extract all variables for ( size_t ei = 0; ei < es.size(); ei++ ) { WORD *e = es[ei]; // fast notation if ( *e == -SNUMBER ) { num_terms++; } else if ( *e == -SYMBOL ) { num_terms++; if ( !var_map.count(e[1]) ) { var_map[e[1]] = num_vars++; degrees.push_back(1); } } // JD: Here we need to check for non-symbol/number terms in fast notation. else if ( *e < 0 ) { MLOCK(ErrorMessageLock); MesPrint("ERROR: polynomials and polyratfuns must contain symbols only"); MUNLOCK(ErrorMessageLock); Terminate(1); } else { for ( WORD i = with_arghead ? ARGHEAD:0; with_arghead ? i < e[0]:e[i] != 0; i += e[i] ) { num_terms++; const WORD coeff_size = e[i+e[i]-1]; const WORD symbols_size = e[i] - ABS(coeff_size); if ( e[i+1] != SYMBOL && 1 < symbols_size ) { MLOCK(ErrorMessageLock); MesPrint("ERROR: polynomials and polyratfuns must contain symbols only"); MUNLOCK(ErrorMessageLock); Terminate(1); } for ( WORD j = i+3; j < i+symbols_size; j += 2 ) { const WORD symbol = e[j]; const WORD degree = e[j+1]; auto it = var_map.find(symbol); if ( it == var_map.end() ) { var_map[symbol] = num_vars++; degrees.push_back(degree); } else { degrees[it->second] = MaX(degrees[it->second], degree); } } } } } if ( sort_vars ) { // bubble sort variables in decreasing order of degree // (this seems better for factorization) for ( size_t i = 0; i < var_map.size(); i++ ) { for ( size_t j = 0; j+1 < var_map.size(); j++ ) { if ( degrees[j] < degrees[j+1] ) { swap(degrees[j], degrees[j+1]); // Find the map keys associated with the values we want to swap uint32_t j0 = 0; uint32_t j1 = 0; for ( auto x: var_map ) { if ( x.second == j ) { j0 = x.first; } else if ( x.second == j+1 ) { j1 = x.first; } } swap(var_map.at(j0), var_map.at(j1)); } } } } // Otherwise, sort lexicographically in FORM's ordering else { for ( size_t i = 0; i < var_map.size(); i++ ) { for ( size_t j = 0; j+1 < var_map.size(); j++ ) { uint32_t j0 = 0; uint32_t j1 = 0; for ( auto x: var_map ) { if ( x.second == j ) { j0 = x.first; } else if ( x.second == j+1 ) { j1 = x.first; } } if ( j0 > j1 ) { swap(var_map.at(j0), var_map.at(j1)); } } } } if ( var_map.size() == 1 ) { // In the univariate case, if the polynomials are sufficiently sparse force the use of the // multivariate routines, which use a sparse representation, by adding a dummy map entry. if ( (float)num_terms <= UNIVARIATE_DENSITY_THR * (float)degrees[0] ) { // -1 will never be a symbol code. Built-in symbols from 0 to 19, and 20 is the first // user symbol. var_map[-1] = num_vars; } } return var_map; } /* #] flint::get_variables : #[ flint::inverse_poly : */ WORD* flint::inverse_poly(PHEAD const WORD *a, const WORD *b, const var_map_t &var_map) { flint::poly pa, pb, denpa, denpb; flint::from_argument_poly(pa.d, denpa.d, a, false); flint::from_argument_poly(pb.d, denpb.d, b, false); // fmpz_poly_xgcd is undefined if the content of pa and pb are not 1. Take the content out. // fmpz_poly_content gives the non-negative content and fmpz_poly_primitive normalizes to a // non-negative lcoeff, so we need to add the sign to the content if the polys have a negative // lcoeff. We don't need to keep the content of pb, it is a numerical multiple of the modulus. flint::fmpz content_a, resultant; flint::poly inverse, tmp; fmpz_poly_content(content_a.d, pa.d); if ( fmpz_sgn(fmpz_poly_lead(pa.d)) == -1 ) { fmpz_neg(content_a.d, content_a.d); } fmpz_poly_primitive_part(pa.d, pa.d); fmpz_poly_primitive_part(pb.d, pb.d); // Special cases: // Possibly strange that we give 1 for inverse_(x1,1) but here we take MMA's convention. if ( fmpz_poly_is_one(pa.d) && fmpz_poly_is_one(pb.d) ) { fmpz_poly_one(inverse.d); fmpz_one(resultant.d); } else if ( fmpz_poly_is_one(pb.d) ) { fmpz_poly_zero(inverse.d); fmpz_one(resultant.d); } else { // Now use the extended Euclidean algorithm to find inverse, resultant, tmp of the Bezout // identity: inverse*pa + tmp*pb = resultant. Then inverse/resultant is the multiplicative // inverse of pa mod pb. We'll divide by resultant in the denscale argument of to_argument_poly. fmpz_poly_xgcd(resultant.d, inverse.d, tmp.d, pa.d, pb.d); // If the resultant is zero, the inverse does not exist: if ( fmpz_is_zero(resultant.d) ) { MLOCK(ErrorMessageLock); MesPrint("flint::inverse_poly error: inverse does not exist"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } // Multiply inverse by denpa. denpb is a numerical multiple of the modulus, so doesn't matter. // We also need to divide by content_a, which we do in the denscale argument of to_argument_poly // by multiplying resultant by content_a here. fmpz_poly_mul(inverse.d, inverse.d, denpa.d); fmpz_mul(resultant.d, resultant.d, content_a.d); WORD* res; // First determine the result size, and malloc. The result should have no arghead. Here we use // the "scale" argument of to_argument_poly since resultant might not be 1. const bool with_arghead = false; bool write = false; const bool must_fit_term = false; const uint64_t prev_size = 0; const uint64_t res_size = (uint64_t)flint::to_argument_poly(BHEAD NULL, with_arghead, must_fit_term, write, prev_size, inverse.d, var_map, resultant.d); res = (WORD*)Malloc1(sizeof(WORD)*res_size, "flint::inverse_poly"); write = true; flint::to_argument_poly(BHEAD res, with_arghead, must_fit_term, write, prev_size, inverse.d, var_map, resultant.d); return res; } /* #] flint::inverse_poly : #[ flint::mul_mpoly : */ // Return a pointer to a buffer containing the product of the 0-terminated term lists at a and b. // For multi-variate cases. WORD* flint::mul_mpoly(PHEAD const WORD *a, const WORD *b, const var_map_t &var_map, const bool sort_vars) { flint::mpoly_ctx ctx(var_map.size()); flint::mpoly pa(ctx.d), pb(ctx.d), denpa(ctx.d), denpb(ctx.d); flint::from_argument_mpoly(pa.d, denpa.d, a, false, var_map, ctx.d); flint::from_argument_mpoly(pb.d, denpb.d, b, false, var_map, ctx.d); // denpa, denpb must be integers. Negative symbol powers have been converted to extra symbols. if ( fmpz_mpoly_is_fmpz(denpa.d, ctx.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::mul_mpoly: error: denpa is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( fmpz_mpoly_is_fmpz(denpb.d, ctx.d) != 1 ) { MLOCK(ErrorMessageLock); MesPrint("flint::mul_mpoly: error: denpb is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Multiply numerators, store result in pa fmpz_mpoly_mul(pa.d, pa.d, pb.d, ctx.d); // Multiply denominators, store result in denpa, and convert to an fmpz: fmpz_mpoly_mul(denpa.d, denpa.d, denpb.d, ctx.d); flint::fmpz den; fmpz_mpoly_get_fmpz(den.d, denpa.d, ctx.d); WORD* res; // First determine the result size, and malloc. The result should have no arghead. Here we use // the "scale" argument of to_argument_mpoly since den might not be 1. const bool with_arghead = false; bool write = false; const bool must_fit_term = false; const uint64_t prev_size = 0; const uint64_t mul_size = (uint64_t)flint::to_argument_mpoly(BHEAD NULL, with_arghead, must_fit_term, write, prev_size, pa.d, var_map, ctx.d, sort_vars, den.d); res = (WORD*)Malloc1(sizeof(WORD)*mul_size, "flint::mul_mpoly"); write = true; flint::to_argument_mpoly(BHEAD res, with_arghead, must_fit_term, write, prev_size, pa.d, var_map, ctx.d, sort_vars, den.d); return res; } /* #] flint::mul_mpoly : #[ flint::mul_poly : */ // Return a pointer to a buffer containing the product of the 0-terminated term lists at a and b. // For uni-variate cases. WORD* flint::mul_poly(PHEAD const WORD *a, const WORD *b, const var_map_t &var_map) { flint::poly pa, pb, denpa, denpb; flint::from_argument_poly(pa.d, denpa.d, a, false); flint::from_argument_poly(pb.d, denpb.d, b, false); // denpa, denpb must be integers. Negative symbol powers have been converted to extra symbols. if ( fmpz_poly_degree(denpa.d) != 0 ) { MLOCK(ErrorMessageLock); MesPrint("flint::mul_poly: error: denpa is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( fmpz_poly_degree(denpb.d) != 0 ) { MLOCK(ErrorMessageLock); MesPrint("flint::mul_poly: error: denpb is non-constant"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Multiply numerators, store result in pa fmpz_poly_mul(pa.d, pa.d, pb.d); // Multiply denominators, store result in denpa, and convert to an fmpz: fmpz_poly_mul(denpa.d, denpa.d, denpb.d); flint::fmpz den; fmpz_poly_get_coeff_fmpz(den.d, denpa.d, 0); WORD* res; // First determine the result size, and malloc. The result should have no arghead. Here we use // the "scale" argument of to_argument_poly since den might not be 1. const bool with_arghead = false; bool write = false; const bool must_fit_term = false; const uint64_t prev_size = 0; const uint64_t mul_size = (uint64_t)flint::to_argument_poly(BHEAD NULL, with_arghead, must_fit_term, write, prev_size, pa.d, var_map, den.d); res = (WORD*)Malloc1(sizeof(WORD)*mul_size, "flint::mul_poly"); write = true; flint::to_argument_poly(BHEAD res, with_arghead, must_fit_term, write, prev_size, pa.d, var_map, den.d); return res; } /* #] flint::mul_poly : #[ flint::ratfun_add_mpoly : */ // Add the multi-variate FORM rational polynomials at t1 and t2. The result is written at out. void flint::ratfun_add_mpoly(PHEAD const WORD *t1, const WORD *t2, WORD *out, const var_map_t &var_map, const bool sort_vars) { flint::mpoly_ctx ctx(var_map.size()); flint::mpoly gcd(ctx.d), num1(ctx.d), den1(ctx.d), num2(ctx.d), den2(ctx.d); flint::ratfun_read_mpoly(t1, num1.d, den1.d, var_map, ctx.d); flint::ratfun_read_mpoly(t2, num2.d, den2.d, var_map, ctx.d); if ( fmpz_mpoly_cmp(den1.d, den2.d, ctx.d) != 0 ) { fmpz_mpoly_gcd_cofactors(gcd.d, den1.d, den2.d, den1.d, den2.d, ctx.d); fmpz_mpoly_mul(num1.d, num1.d, den2.d, ctx.d); fmpz_mpoly_mul(num2.d, num2.d, den1.d, ctx.d); fmpz_mpoly_add(num1.d, num1.d, num2.d, ctx.d); fmpz_mpoly_mul(den1.d, den1.d, den2.d, ctx.d); fmpz_mpoly_mul(den1.d, den1.d, gcd.d, ctx.d); } else { fmpz_mpoly_add(num1.d, num1.d, num2.d, ctx.d); } // Finally divide out any common factors between the resulting num1, den1: fmpz_mpoly_gcd_cofactors(gcd.d, num1.d, den1.d, num1.d, den1.d, ctx.d); flint::util::fix_sign_fmpz_mpoly_ratfun(num1.d, den1.d, ctx.d); // Result in FORM notation: *out++ = AR.PolyFun; WORD* args_size = out++; WORD* args_flag = out++; *args_flag = 0; // clean prf FILLFUN3(out); // Remainder of funhead, if it is larger than 3 const bool with_arghead = true; const bool must_fit_term = true; const bool write = true; // prev_size + 4, to account for final term size and coeff of "1/1" out += flint::to_argument_mpoly(BHEAD out, with_arghead, must_fit_term, write, out-args_size+4, num1.d, var_map, ctx.d, sort_vars); out += flint::to_argument_mpoly(BHEAD out, with_arghead, must_fit_term, write, out-args_size+4, den1.d, var_map, ctx.d, sort_vars); *args_size = out - args_size + 1; // The +1 is to include the function ID AT.WorkPointer = out; } /* #] flint::ratfun_add_mpoly : #[ flint::ratfun_add_poly : */ // Add the uni-variate FORM rational polynomials at t1 and t2. The result is written at out. void flint::ratfun_add_poly(PHEAD const WORD *t1, const WORD *t2, WORD *out, const var_map_t &var_map) { flint::poly gcd, num1, den1, num2, den2; flint::ratfun_read_poly(t1, num1.d, den1.d); flint::ratfun_read_poly(t2, num2.d, den2.d); if ( fmpz_poly_equal(den1.d, den2.d) == 0 ) { flint::util::simplify_fmpz_poly(den1.d, den2.d, gcd.d); fmpz_poly_mul(num1.d, num1.d, den2.d); fmpz_poly_mul(num2.d, num2.d, den1.d); fmpz_poly_add(num1.d, num1.d, num2.d); fmpz_poly_mul(den1.d, den1.d, den2.d); fmpz_poly_mul(den1.d, den1.d, gcd.d); } else { fmpz_poly_add(num1.d, num1.d, num2.d); } // Finally divide out any common factors between the resulting num1, den1: flint::util::simplify_fmpz_poly(num1.d, den1.d, gcd.d); flint::util::fix_sign_fmpz_poly_ratfun(num1.d, den1.d); // Result in FORM notation: *out++ = AR.PolyFun; WORD* args_size = out++; WORD* args_flag = out++; *args_flag = 0; // clean prf FILLFUN3(out); // Remainder of funhead, if it is larger than 3 const bool with_arghead = true; const bool must_fit_term = true; const bool write = true; // prev_size + 4, to account for final term size and coeff of "1/1" out += flint::to_argument_poly(BHEAD out, with_arghead, must_fit_term, write, out-args_size+4, num1.d, var_map); out += flint::to_argument_poly(BHEAD out, with_arghead, must_fit_term, write, out-args_size+4, den1.d, var_map); *args_size = out - args_size + 1; // The +1 is to include the function ID AT.WorkPointer = out; } /* #] flint::ratfun_add_poly : #[ flint::ratfun_normalize_mpoly : */ // Multiply and simplify occurrences of the multi-variate FORM rational polynomials found in term. // The final term is written in place, with the rational polynomial at the end. void flint::ratfun_normalize_mpoly(PHEAD WORD *term, const var_map_t &var_map, const bool sort_vars) { // The length of the coefficient const WORD ncoeff = (term + *term)[-1]; // The end of the term data, before the coefficient: const WORD *tstop = term + *term - ABS(ncoeff); flint::mpoly_ctx ctx(var_map.size()); flint::mpoly num1(ctx.d), den1(ctx.d), num2(ctx.d), den2(ctx.d), gcd(ctx.d); // Start with "trivial" polynomials, and multiply in the num and den of the prf which appear. flint::fmpz tmpNum, tmpDen; flint::fmpz_set_form(tmpNum.d, (UWORD*)tstop, ncoeff/2); flint::fmpz_set_form(tmpDen.d, (UWORD*)tstop+ABS(ncoeff/2), ABS(ncoeff/2)); fmpz_mpoly_set_fmpz(num1.d, tmpNum.d, ctx.d); fmpz_mpoly_set_fmpz(den1.d, tmpDen.d, ctx.d); // Loop over the occurrences of PolyFun in the term, and multiply in to num1, den1. // s tracks where we are writing the non-PolyFun term data. The final PolyFun will // go at the end. WORD* term_size = term; WORD* s = term + 1; for ( WORD *t = term + 1; t < tstop; ) { if ( *t == AR.PolyFun ) { flint::ratfun_read_mpoly(t, num2.d, den2.d, var_map, ctx.d); // get gcd of num1,den2 and num2,den1 and then assemble fmpz_mpoly_gcd_cofactors(gcd.d, num1.d, den2.d, num1.d, den2.d, ctx.d); fmpz_mpoly_gcd_cofactors(gcd.d, num2.d, den1.d, num2.d, den1.d, ctx.d); fmpz_mpoly_mul(num1.d, num1.d, num2.d, ctx.d); fmpz_mpoly_mul(den1.d, den1.d, den2.d, ctx.d); t += t[1]; } else { // Not a PolyFun, just copy or skip over WORD i = t[1]; if ( s != t ) { NCOPY(s,t,i); } else { t += i; s += i; } } } flint::util::fix_sign_fmpz_mpoly_ratfun(num1.d, den1.d, ctx.d); // Result in FORM notation: WORD* out = s; *out++ = AR.PolyFun; WORD* args_size = out++; WORD* args_flag = out++; *args_flag &= ~MUSTCLEANPRF; const bool with_arghead = true; const bool must_fit_term = true; const bool write = true; out += flint::to_argument_mpoly(BHEAD out, with_arghead, must_fit_term, write, out-term_size, num1.d, var_map, ctx.d, sort_vars); out += flint::to_argument_mpoly(BHEAD out, with_arghead, must_fit_term, write, out-term_size, den1.d, var_map, ctx.d, sort_vars); *args_size = out - args_size + 1; // The +1 is to include the function ID // +3 for the coefficient of 1/1, which is added after the check if ( sizeof(WORD)*(out-term_size+3) > (size_t)AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("flint::ratfun_normalize: output exceeds MaxTermSize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } *out++ = 1; *out++ = 1; *out++ = 3; // the term's coefficient is now 1/1 *term_size = out - term_size; } /* #] flint::ratfun_normalize_mpoly : #[ flint::ratfun_normalize_poly : */ // Multiply and simplify occurrences of the uni-variate FORM rational polynomials found in term. // The final term is written in place, with the rational polynomial at the end. void flint::ratfun_normalize_poly(PHEAD WORD *term, const var_map_t &var_map) { // The length of the coefficient const WORD ncoeff = (term + *term)[-1]; // The end of the term data, before the coefficient: const WORD *tstop = term + *term - ABS(ncoeff); flint::poly num1, den1, num2, den2, gcd; // Start with "trivial" polynomials, and multiply in the num and den of the prf which appear. flint::fmpz tmpNum, tmpDen; flint::fmpz_set_form(tmpNum.d, (UWORD*)tstop, ncoeff/2); flint::fmpz_set_form(tmpDen.d, (UWORD*)tstop+ABS(ncoeff/2), ABS(ncoeff/2)); fmpz_poly_set_fmpz(num1.d, tmpNum.d); fmpz_poly_set_fmpz(den1.d, tmpDen.d); // Loop over the occurrences of PolyFun in the term, and multiply in to num1, den1. // s tracks where we are writing the non-PolyFun term data. The final PolyFun will // go at the end. WORD* term_size = term; WORD* s = term + 1; for ( WORD *t = term + 1; t < tstop; ) { if ( *t == AR.PolyFun ) { flint::ratfun_read_poly(t, num2.d, den2.d); // get gcd of num1,den2 and num2,den1 and then assemble flint::util::simplify_fmpz_poly(num1.d, den2.d, gcd.d); flint::util::simplify_fmpz_poly(num2.d, den1.d, gcd.d); fmpz_poly_mul(num1.d, num1.d, num2.d); fmpz_poly_mul(den1.d, den1.d, den2.d); t += t[1]; } else { // Not a PolyFun, just copy or skip over WORD i = t[1]; if ( s != t ) { NCOPY(s,t,i); } else { t += i; s += i; } } } flint::util::fix_sign_fmpz_poly_ratfun(num1.d, den1.d); // Result in FORM notation: WORD* out = s; *out++ = AR.PolyFun; WORD* args_size = out++; WORD* args_flag = out++; *args_flag &= ~MUSTCLEANPRF; const bool with_arghead = true; const bool must_fit_term = true; const bool write = true; out += flint::to_argument_poly(BHEAD out, with_arghead, must_fit_term, write, out-term_size, num1.d, var_map); out += flint::to_argument_poly(BHEAD out, with_arghead, must_fit_term, write, out-term_size, den1.d, var_map); *args_size = out - args_size + 1; // The +1 is to include the function ID // +3 for the coefficient of 1/1, which is added after the check if ( sizeof(WORD)*(out-term_size+3) > (size_t)AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("flint::ratfun_normalize: output exceeds MaxTermSize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } *out++ = 1; *out++ = 1; *out++ = 3; // the term's coefficient is now 1/1 *term_size = out - term_size; } /* #] flint::ratfun_normalize_poly : #[ flint::ratfun_read_mpoly : */ // Read the multi-variate FORM rational polynomial at a and create fmpz_mpoly_t numerator and // denominator. void flint::ratfun_read_mpoly(const WORD *a, fmpz_mpoly_t num, fmpz_mpoly_t den, const var_map_t &var_map, fmpz_mpoly_ctx_t ctx) { // The end of the arguments: const WORD* arg_stop = a+a[1]; const bool must_normalize = (a[2] & MUSTCLEANPRF) != 0; a += FUNHEAD; if ( a >= arg_stop ) { MLOCK(ErrorMessageLock); MesPrint("ERROR: PolyRatFun cannot have zero arguments"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Polys to collect the "den of the num" and "den of the den". // Input can arrive like this when enabling the PolyRatFun or moving things into it. flint::mpoly den_num(ctx), den_den(ctx); // Read the numerator flint::from_argument_mpoly(num, den_num.d, a, true, var_map, ctx); NEXTARG(a); if ( a < arg_stop ) { // Read the denominator flint::from_argument_mpoly(den, den_den.d, a, true, var_map, ctx); NEXTARG(a); } else { // The denominator is 1 MLOCK(ErrorMessageLock); MesPrint("implement this"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( a < arg_stop ) { MLOCK(ErrorMessageLock); MesPrint("ERROR: PolyRatFun cannot have more than two arguments"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Multiply the num by den_den and den by den_num: fmpz_mpoly_mul(num, num, den_den.d, ctx); fmpz_mpoly_mul(den, den, den_num.d, ctx); if ( must_normalize ) { flint::mpoly gcd(ctx); fmpz_mpoly_gcd_cofactors(gcd.d, num, den, num, den, ctx); } } /* #] flint::ratfun_read_mpoly : #[ flint::ratfun_read_poly : */ // Read the uni-variate FORM rational polynomial at a and create fmpz_mpoly_t numerator and // denominator. void flint::ratfun_read_poly(const WORD *a, fmpz_poly_t num, fmpz_poly_t den) { // The end of the arguments: const WORD* arg_stop = a+a[1]; const bool must_normalize = (a[2] & MUSTCLEANPRF) != 0; a += FUNHEAD; if ( a >= arg_stop ) { MLOCK(ErrorMessageLock); MesPrint("ERROR: PolyRatFun cannot have zero arguments"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Polys to collect the "den of the num" and "den of the den". // Input can arrive like this when enabling the PolyRatFun or moving things into it. flint::poly den_num, den_den; // Read the numerator flint::from_argument_poly(num, den_num.d, a, true); NEXTARG(a); if ( a < arg_stop ) { // Read the denominator flint::from_argument_poly(den, den_den.d, a, true); NEXTARG(a); } else { // The denominator is 1 MLOCK(ErrorMessageLock); MesPrint("implement this"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( a < arg_stop ) { MLOCK(ErrorMessageLock); MesPrint("ERROR: PolyRatFun cannot have more than two arguments"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Multiply the num by den_den and den by den_num: fmpz_poly_mul(num, num, den_den.d); fmpz_poly_mul(den, den, den_num.d); if ( must_normalize ) { flint::poly gcd; flint::util::simplify_fmpz_poly(num, den, gcd.d); } } /* #] flint::ratfun_read_poly : #[ flint::to_argument_mpoly : */ // Convert a fmpz_mpoly_t to a FORM argument (or 0-terminated list of terms: with_arghead==false). // If the caller is building an output term, prev_size contains the size of the term so far, to // check that the output fits in AM.MaxTer if must_fit_term. // All coefficients will be divided by denscale (which might just be 1). // If write is false, we never write to out but only track the total would-be size. This lets this // function be repurposed as a "size of FORM notation" function without duplicating the code. #define IFW(x) { if ( write ) {x;} } uint64_t flint::to_argument_mpoly(PHEAD WORD *out, const bool with_arghead, const bool must_fit_term, const bool write, const uint64_t prev_size, const fmpz_mpoly_t poly, const var_map_t &var_map, const fmpz_mpoly_ctx_t ctx, const bool sort_vars, const fmpz_t denscale) { // out is modified later, keep the pointer at entry const WORD* out_entry = out; // Track the total size written. We could do this with pointer differences, but if // write == false we don't write to or move out to be able to find the size that way. uint64_t ws = 0; // Check there is at least space for ARGHEAD WORDs (the arghead or fast-notation number/symbol) if ( write && must_fit_term && (sizeof(WORD)*(prev_size + ARGHEAD) > (size_t)AM.MaxTer) ) { MLOCK(ErrorMessageLock); MesPrint("flint::to_argument_mpoly: output exceeds MaxTermSize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Create the inverse of var_map, so we don't have to search it for each symbol written vector var_map_inv; var_map_inv.resize(var_map.size()); for ( auto x : var_map ) { var_map_inv[x.second] = x.first; } vector exponents(var_map.size()); const int64_t n_terms = fmpz_mpoly_length(poly, ctx); if ( n_terms == 0 ) { if ( with_arghead ) { IFW(*out++ = -SNUMBER); ws++; IFW(*out++ = 0); ws++; return ws; } else { IFW(*out++ = 0); ws++; return ws; } } // For dividing out denscale flint::fmpz coeff, den, gcd; // The mpoly might be constant or a single symbol with coeff 1. Use fast notation if possible. if ( with_arghead && n_terms == 1 ) { if ( fmpz_mpoly_is_fmpz(poly, ctx) ) { // The mpoly is constant. Use fast notation if the number is an integer and small enough: fmpz_mpoly_get_term_coeff_fmpz(coeff.d, poly, 0, ctx); fmpz_set(den.d, denscale); flint::util::simplify_fmpz(coeff.d, den.d, gcd.d); if ( fmpz_is_one(den.d) && fmpz_fits_si(coeff.d) ) { const int64_t fast_coeff = fmpz_get_si(coeff.d); // While ">=", could work here, FORM does not use fast notation for INT_MIN if ( fast_coeff > INT32_MIN && fast_coeff <= INT32_MAX ) { IFW(*out++ = -SNUMBER); ws++; IFW(*out++ = (WORD)fast_coeff); ws++; return ws; } } } else { fmpz_mpoly_get_term_coeff_fmpz(coeff.d, poly, 0, ctx); fmpz_set(den.d, denscale); flint::util::simplify_fmpz(coeff.d, den.d, gcd.d); if ( fmpz_is_one(coeff.d) && fmpz_is_one(den.d) ) { // The coefficient is one. Now check the symbol powers: fmpz_mpoly_get_term_exp_si((slong*)exponents.data(), poly, 0, ctx); int64_t use_fast = 0; uint32_t fast_symbol = 0; for ( size_t i = 0; i < var_map.size(); i++ ) { if ( exponents[i] == 1 ) fast_symbol = var_map_inv[i]; use_fast += exponents[i]; } // use_fast has collected the total degree. If it is 1, then fast_symbol holds the code if ( use_fast == 1 ) { IFW(*out++ = -SYMBOL); ws++; IFW(*out++ = fast_symbol); ws++; return ws; } } } } WORD *tmp_coeff = (WORD *)NumberMalloc("flint::to_argument_mpoly"); WORD *tmp_den = (WORD *)NumberMalloc("flint::to_argument_mpoly"); WORD* arg_size = 0; WORD* arg_flag = 0; if ( with_arghead ) { IFW(arg_size = out++); ws++; // total arg size IFW(arg_flag = out++); ws++; IFW(*arg_flag = 0); // clean argument } for ( int64_t i = 0; i < n_terms; i++ ) { fmpz_mpoly_get_term_exp_si((slong*)exponents.data(), poly, i, ctx); fmpz_mpoly_get_term_coeff_fmpz(coeff.d, poly, i, ctx); fmpz_set(den.d, denscale); flint::util::simplify_fmpz(coeff.d, den.d, gcd.d); uint32_t num_symbols = 0; for ( size_t j = 0; j < var_map.size(); j++ ) { if ( exponents[j] != 0 ) { num_symbols += 1; } } // Convert the coefficient, write in temporary space const WORD num_size = flint::fmpz_get_form(coeff.d, tmp_coeff); const WORD den_size = flint::fmpz_get_form(den.d, tmp_den); const WORD coeff_size = [num_size, den_size] () -> WORD { WORD size = ABS(num_size) > ABS(den_size) ? ABS(num_size) : ABS(den_size); return size * SGN(num_size) * SGN(den_size); }(); // Now we have the number of symbols and the coeff size, we can determine the output size. // Check it fits if necessary: term size, num,den of "coeff_size", +1 for total coeff size uint64_t current_size = prev_size + ws + 1 + 2*ABS(coeff_size) + 1; if ( num_symbols ) { // symbols header, code,power of each symbol: current_size += 2 + 2*num_symbols; } if ( write && must_fit_term && (sizeof(WORD)*current_size > (size_t)AM.MaxTer) ) { MLOCK(ErrorMessageLock); MesPrint("flint::to_argument_mpoly: output exceeds MaxTermSize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } WORD* term_size = 0; IFW(term_size = out++); ws++; if ( num_symbols ) { IFW(*out++ = SYMBOL); ws++; WORD* symbol_size = 0; IFW(symbol_size = out++); ws++; IFW(*symbol_size = 2); for ( size_t j = 0; j < var_map.size(); j++ ) { if ( exponents[j] != 0 ) { IFW(*out++ = var_map_inv[j]); ws++; IFW(*out++ = exponents[j]); ws++; IFW(*symbol_size += 2); } } } // Copy numerator for ( WORD j = 0; j < ABS(num_size); j++ ) { IFW(*out++ = tmp_coeff[j]); ws++; } for ( WORD j = ABS(num_size); j < ABS(coeff_size); j++ ) { IFW(*out++ = 0); ws++; } // Copy denominator for ( WORD j = 0; j < ABS(den_size); j++ ) { IFW(*out++ = tmp_den[j]); ws++; } for ( WORD j = ABS(den_size); j < ABS(coeff_size); j++ ) { IFW(*out++ = 0); ws++; } IFW(*out = 2*ABS(coeff_size) + 1); // the size of the coefficient IFW(if ( coeff_size < 0 ) { *out = -(*out); }); IFW(out++); ws++; IFW(*term_size = out - term_size); } if ( with_arghead ) { IFW(*arg_size = out - arg_size); if ( write && sort_vars ) { // Sort into form highfirst ordering, if we have potentially re-ordered the variables by // degree, in flint::get_variables. Otherwise, we can rely on FLINT's sorting with // ORD_LEX and the variables ordered in FORM's lexicographic order. flint::form_sort(BHEAD (WORD*)(out_entry)); } } else { // with no arghead, we write a terminating zero IFW(*out++ = 0); ws++; } NumberFree(tmp_coeff, "flint::to_argument_mpoly"); NumberFree(tmp_den, "flint::to_argument_mpoly"); return ws; } // If no denscale argument is supplied, just set it to 1 and call the usual function uint64_t flint::to_argument_mpoly(PHEAD WORD *out, const bool with_arghead, const bool must_fit_term, const bool write, const uint64_t prev_size, const fmpz_mpoly_t poly, const var_map_t &var_map, const fmpz_mpoly_ctx_t ctx, const bool sort_vars) { flint::fmpz tmp; fmpz_set_ui(tmp.d, 1); uint64_t ret = flint::to_argument_mpoly(BHEAD out, with_arghead, must_fit_term, write, prev_size, poly, var_map, ctx, sort_vars, tmp.d); return ret; } /* #] flint::to_argument_mpoly : #[ flint::to_argument_poly : */ // Convert a fmpz_poly_t to a FORM argument (or 0-terminated list of terms: with_arghead==false). // If the caller is building an output term, prev_size contains the size of the term so far, to // check that the output fits in AM.MaxTer if must_fit_term. // All coefficients will be divided by denscale (which might just be 1). // If write is false, we never write to out but only track the total would-be size. This lets this // function be repurposed as a "size of FORM notation" function without duplicating the code. uint64_t flint::to_argument_poly(PHEAD WORD *out, const bool with_arghead, const bool must_fit_term, const bool write, const uint64_t prev_size, const fmpz_poly_t poly, const var_map_t &var_map, const fmpz_t denscale) { // Track the total size written. We could do this with pointer differences, but if // write == false we don't write to or move out to be able to find the size that way. uint64_t ws = 0; // Check there is at least space for ARGHEAD WORDs (the arghead or fast-notation number/symbol) if ( write && must_fit_term && (sizeof(WORD)*(prev_size + ARGHEAD) > (size_t)AM.MaxTer) ) { MLOCK(ErrorMessageLock); MesPrint("flint::to_argument_poly: output exceeds MaxTermSize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Create the inverse of var_map, so we don't have to search it for each symbol written vector var_map_inv; var_map_inv.resize(var_map.size()); for ( auto x : var_map ) { var_map_inv[x.second] = x.first; } const int64_t n_terms = fmpz_poly_length(poly); // The poly is zero if ( n_terms == 0 ) { if ( with_arghead ) { IFW(*out++ = -SNUMBER); ws++; IFW(*out++ = 0); ws++; return ws; } else { IFW(*out++ = 0); ws++; return ws; } } // For dividing out denscale flint::fmpz coeff, den, gcd; // The poly is constant, use fast notation if the coefficient is integer and small enough if ( with_arghead && n_terms == 1 ) { fmpz_poly_get_coeff_fmpz(coeff.d, poly, 0); fmpz_set(den.d, denscale); flint::util::simplify_fmpz(coeff.d, den.d, gcd.d); if ( fmpz_is_one(den.d) && fmpz_fits_si(coeff.d) ) { const long fast_coeff = fmpz_get_si(coeff.d); // While ">=", could work here, FORM does not use fast notation for INT_MIN if ( fast_coeff > INT_MIN && fast_coeff <= INT_MAX ) { IFW(*out++ = -SNUMBER); ws++; IFW(*out++ = (WORD)fast_coeff); ws++; return ws; } } } // The poly might be a single symbol with coeff 1, use fast notation if so. if ( with_arghead && n_terms == 2 ) { if ( fmpz_is_zero(fmpz_poly_get_coeff_ptr(poly, 0)) ) { // The constant term is zero fmpz_poly_get_coeff_fmpz(coeff.d, poly, 1); fmpz_set(den.d, denscale); flint::util::simplify_fmpz(coeff.d, den.d, gcd.d); if ( fmpz_is_one(coeff.d) && fmpz_is_one(den.d) ) { // Single symbol with coeff 1. Use fast notation: IFW(*out++ = -SYMBOL); ws++; IFW(*out++ = var_map_inv[0]); ws++; return ws; } } } WORD *tmp_coeff = (WORD *)NumberMalloc("flint::to_argument_poly"); WORD *tmp_den = (WORD *)NumberMalloc("flint::to_argument_mpoly"); WORD* arg_size = 0; WORD* arg_flag = 0; if ( with_arghead ) { IFW(arg_size = out++); ws++; // total arg size IFW(arg_flag = out++); ws++; IFW(*arg_flag = 0); // clean argument } // In reverse, since we want a "highfirst" output for ( int64_t i = n_terms-1; i >= 0; i-- ) { // fmpz_poly is dense, there might be many zero coefficients: if ( !fmpz_is_zero(fmpz_poly_get_coeff_ptr(poly, i)) ) { fmpz_poly_get_coeff_fmpz(coeff.d, poly, i); fmpz_set(den.d, denscale); flint::util::simplify_fmpz(coeff.d, den.d, gcd.d); // Convert the coefficient, write in temporary space const WORD num_size = flint::fmpz_get_form(coeff.d, tmp_coeff); const WORD den_size = flint::fmpz_get_form(den.d, tmp_den); const WORD coeff_size = [num_size, den_size] () -> WORD { WORD size = ABS(num_size) > ABS(den_size) ? ABS(num_size) : ABS(den_size); return size * SGN(num_size) * SGN(den_size); }(); // Now we have the coeff size, we can determine the output size // Check it fits if necessary: symbol code,power, num,den of "coeff_size", // +1 for total coeff size uint64_t current_size = prev_size + ws + 1 + 2*ABS(coeff_size) + 1; if ( i > 0 ) { // and also symbols header, code,power of the symbol current_size += 4; } if ( write && must_fit_term && (sizeof(WORD)*current_size > (size_t)AM.MaxTer) ) { MLOCK(ErrorMessageLock); MesPrint("flint::to_argument_poly: output exceeds MaxTermSize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } WORD* term_size = 0; IFW(term_size = out++); ws++; if ( i > 0 ) { IFW(*out++ = SYMBOL); ws++; IFW(*out++ = 4); ws++; // The symbol array size, it is univariate IFW(*out++ = var_map_inv[0]); ws++; IFW(*out++ = i); ws++; } // Copy numerator for ( WORD j = 0; j < ABS(num_size); j++ ) { IFW(*out++ = tmp_coeff[j]); ws++; } for ( WORD j = ABS(num_size); j < ABS(coeff_size); j++ ) { IFW(*out++ = 0); ws++; } // Copy denominator for ( WORD j = 0; j < ABS(den_size); j++ ) { IFW(*out++ = tmp_den[j]); ws++; } for ( WORD j = ABS(den_size); j < ABS(coeff_size); j++ ) { IFW(*out++ = 0); ws++; } IFW(*out = 2*ABS(coeff_size) + 1); // the size of the coefficient IFW(if ( coeff_size < 0 ) { *out = -(*out); }); IFW(out++); ws++; IFW(*term_size = out - term_size); } } if ( with_arghead ) { IFW(*arg_size = out - arg_size); } else { // with no arghead, we write a terminating zero IFW(*out++ = 0); ws++; } NumberFree(tmp_coeff, "flint::to_argument_poly"); NumberFree(tmp_den, "flint::to_argument_poly"); return ws; } // If no denscale argument is supplied, just set it to 1 and call the usual function uint64_t flint::to_argument_poly(PHEAD WORD *out, const bool with_arghead, const bool must_fit_term, const bool write, const uint64_t prev_size, const fmpz_poly_t poly, const var_map_t &var_map) { flint::fmpz tmp; fmpz_set_ui(tmp.d, 1); uint64_t ret = flint::to_argument_poly(BHEAD out, with_arghead, must_fit_term, write, prev_size, poly, var_map, tmp.d); return ret; } /* #] flint::to_argument_poly : */ // Utility functions /* #[ flint::util::simplify_fmpz : */ // Divide the GCD out of num and den inline void flint::util::simplify_fmpz(fmpz_t num, fmpz_t den, fmpz_t gcd) { fmpz_gcd(gcd, num, den); if ( !fmpz_is_one(gcd) ) { fmpz_divexact(num, num, gcd); fmpz_divexact(den, den, gcd); } } /* #] flint::util::simplify_fmpz : #[ flint::util::simplify_fmpz_poly : */ // Divide the GCD out of num and den inline void flint::util::simplify_fmpz_poly(fmpz_poly_t num, fmpz_poly_t den, fmpz_poly_t gcd) { fmpz_poly_gcd(gcd, num, den); if ( !fmpz_poly_is_one(gcd) ) { #if __FLINT_RELEASE >= 30100 // This should be faster than fmpz_poly_div, see https://github.com/flintlib/flint/pull/1766 fmpz_poly_divexact(num, num, gcd); fmpz_poly_divexact(den, den, gcd); #else fmpz_poly_div(num, num, gcd); fmpz_poly_div(den, den, gcd); #endif } } /* #] flint::util::simplify_fmpz_poly : #[ flint::util::fix_sign_fmpz_mpoly_ratfun : */ inline void flint::util::fix_sign_fmpz_mpoly_ratfun(fmpz_mpoly_t num, fmpz_mpoly_t den, const fmpz_mpoly_ctx_t ctx) { // Fix sign to align with poly: the leading denominator term should have a positive coeff if ( fmpz_sgn(fmpz_mpoly_term_coeff_ref(den, 0, ctx)) == -1 ) { fmpz_mpoly_neg(num, num, ctx); fmpz_mpoly_neg(den, den, ctx); } } /* #] flint::util::fix_sign_fmpz_mpoly_ratfun : #[ flint::util::fix_sign_fmpz_poly_ratfun : */ inline void flint::util::fix_sign_fmpz_poly_ratfun(fmpz_poly_t num, fmpz_poly_t den) { // Fix sign to align with poly: the leading denominator term should have a positive coeff if ( fmpz_sgn(fmpz_poly_get_coeff_ptr(den, fmpz_poly_degree(den))) == -1 ) { fmpz_poly_neg(num, num); fmpz_poly_neg(den, den); } } /* #] flint::util::fix_sign_fmpz_poly_ratfun : */ form-5.0.1/sources/names.c0000644000175100017510000026163415217035721011114 /** @file names.c * * The complete names administration. * All variables with a name have to pass here to be properly registered, * have structs of the proper type assigned to them etc. * The file also contains the utility routines for maintaining the * balanced trees that make searching for names rather fast. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include "form3.h" /* EXTERNLOCK(dummylock) */ /* #] Includes : #[ GetNode : */ NAMENODE *GetNode(NAMETREE *nametree, UBYTE *name) { NAMENODE *n; int node, newnode, i; if ( nametree->namenode == 0 ) return(0); newnode = nametree->headnode; do { node = newnode; n = nametree->namenode+node; if ( ( i = StrCmp(name,nametree->namebuffer+n->name) ) < 0 ) newnode = n->left; else if ( i > 0 ) newnode = n->right; else { return(n); } } while ( newnode >= 0 ); return(0); } /* #] GetNode : #[ AddName : */ int AddName(NAMETREE *nametree, UBYTE *name, WORD type, WORD number, int *nodenum) { NAMENODE *n, *nn, *nnn; UBYTE *s, *ss, *sss; LONG *c1,*c2, j, newsize; int node, newnode, node3, r, rr = 0, i, retval = 0; if ( nametree->namenode == 0 ) { s = name; i = 1; while ( *s ) { i++; s++; } j = INITNAMESIZE; if ( i > j ) j = i; nametree->namenode = (NAMENODE *)Malloc1(INITNODESIZE*sizeof(NAMENODE), "new nametree in AddName"); nametree->namebuffer = (UBYTE *)Malloc1(j, "new namebuffer in AddName"); nametree->nodesize = INITNODESIZE; nametree->namesize = j; nametree->namefill = i; nametree->nodefill = 1; nametree->headnode = 0; n = nametree->namenode; n->parent = n->left = n->right = -1; n->balance = 0; n->type = type; n->number = number; n->name = 0; s = name; ss = nametree->namebuffer; while ( *s ) *ss++ = *s++; *ss = 0; *nodenum = 0; return(retval); } newnode = nametree->headnode; do { node = newnode; n = nametree->namenode+node; if ( StrCmp(name,nametree->namebuffer+n->name) < 0 ) { newnode = n->left; r = -1; } else { newnode = n->right; r = 1; } } while ( newnode >= 0 ); /* We are at the insertion point. Add the node. */ if ( nametree->nodefill >= nametree->nodesize ) { /* Double allocation */ newsize = nametree->nodesize * 2; if ( newsize > MAXINNAMETREE ) newsize = MAXINNAMETREE; if ( nametree->nodefill >= MAXINNAMETREE ) { MesPrint("!!!More than %l names in one object",(LONG)MAXINNAMETREE); Terminate(-1); } nnn = (NAMENODE *)Malloc1(2*((LONG)newsize*sizeof(NAMENODE)), "extra names in AddName"); c1 = (LONG *)nnn; c2 = (LONG *)nametree->namenode; i = (nametree->nodefill * sizeof(NAMENODE))/sizeof(LONG); while ( --i >= 0 ) *c1++ = *c2++; M_free(nametree->namenode,"nametree->namenode"); nametree->namenode = nnn; nametree->nodesize = newsize; n = nametree->namenode+node; } *nodenum = newnode = nametree->nodefill++; nn = nametree->namenode+newnode; nn->parent = node; if ( r < 0 ) n->left = newnode; else n->right = newnode; nn->left = nn->right = -1; nn->type = type; nn->number = number; nn->balance = 0; i = 1; s = name; while ( *s ) { i++; s++; } while ( nametree->namefill + i >= nametree->namesize ) { /* Double alloc */ sss = (UBYTE *)Malloc1(2*nametree->namesize, "extra names in AddName"); s = sss; ss = nametree->namebuffer; j = nametree->namefill; while ( --j >= 0 ) *s++ = *ss++; M_free(nametree->namebuffer,"nametree->namebuffer"); nametree->namebuffer = sss; nametree->namesize *= 2; } s = nametree->namebuffer+nametree->namefill; nn->name = nametree->namefill; retval = nametree->namefill; nametree->namefill += i; while ( *name ) *s++ = *name++; *s = 0; /* Adjust the balance factors */ while ( node >= 0 ) { n = nametree->namenode + node; if ( newnode == n->left ) rr = -1; else rr = 1; if ( n->balance == -rr ) { n->balance = 0; return(retval); } else if ( n->balance == rr ) break; n->balance = rr; newnode = node; node = n->parent; } if ( node < 0 ) return(retval); /* We have to rebalance the tree. There are two basic operations. n/node is the unbalanced node. newnode is its child. rr is the old balance of n/node. */ nn = nametree->namenode + newnode; if ( nn->balance == -rr ) { /* The difficult case */ if ( rr > 0 ) { node3 = nn->left; nnn = nametree->namenode + node3; nnn->parent = n->parent; n->parent = nn->parent = node3; if ( nnn->right >= 0 ) nametree->namenode[nnn->right].parent = newnode; if ( nnn->left >= 0 ) nametree->namenode[nnn->left].parent = node; n->right = nnn->left; nnn->left = node; nn->left = nnn->right; nnn->right = newnode; if ( nnn->balance > 0 ) { n->balance = -1; nn->balance = 0; } else if ( nnn->balance == 0 ) { n->balance = nn->balance = 0; } else { nn->balance = 1; n->balance = 0; } } else { node3 = nn->right; nnn = nametree->namenode + node3; nnn->parent = n->parent; n->parent = nn->parent = node3; if ( nnn->right >= 0 ) nametree->namenode[nnn->right].parent = node; if ( nnn->left >= 0 ) nametree->namenode[nnn->left].parent = newnode; n->left = nnn->right; nnn->right = node; nn->right = nnn->left; nnn->left = newnode; if ( nnn->balance < 0 ) { n->balance = 1; nn->balance = 0; } else if ( nnn->balance == 0 ) { n->balance = nn->balance = 0; } else { nn->balance = -1; n->balance = 0; } } nnn->balance = 0; if ( nnn->parent >= 0 ) { nn = nametree->namenode + nnn->parent; if ( node == nn->left ) nn->left = node3; else nn->right = node3; } if ( node == nametree->headnode ) nametree->headnode = node3; } else if ( nn->balance == rr ) { /* The easy case */ nn->parent = n->parent; n->parent = newnode; if ( rr > 0 ) { if ( nn->left >= 0 ) nametree->namenode[nn->left].parent = node; n->right = nn->left; nn->left = node; } else { if ( nn->right >= 0 ) nametree->namenode[nn->right].parent = node; n->left = nn->right; nn->right = node; } if ( nn->parent >= 0 ) { nnn = nametree->namenode + nn->parent; if ( node == nnn->left ) nnn->left = newnode; else nnn->right = newnode; } nn->balance = n->balance = 0; if ( node == nametree->headnode ) nametree->headnode = newnode; } #ifdef DEBUGON else { /* Cannot be. Code here for debugging only */ MesPrint("We ran into an impossible case in AddName\n"); DumpTree(nametree); Terminate(-1); } #endif return(retval); } /* #] AddName : #[ GetName : When AutoDeclare is an active statement. If par == WITHAUTO and the variable is not found we have to check: 1: that nametree != AC.exprnames && nametree != AC.dollarnames 2: check that the variable is not in AC.exprnames after all. 3: call GetAutoName and return its values. */ int GetName(NAMETREE *nametree, UBYTE *namein, WORD *number, int par) { NAMENODE *n; int node, newnode, i; UBYTE *s, *t, *u, *name; /* name = ConstructName(namein,0); */ name = namein; if ( nametree->namenode == 0 || nametree->namefill == 0 ) goto NotFound; newnode = nametree->headnode; do { node = newnode; n = nametree->namenode+node; if ( ( i = StrCmp(name,nametree->namebuffer+n->name) ) < 0 ) newnode = n->left; else if ( i > 0 ) newnode = n->right; else { *number = n->number; return(n->type); } } while ( newnode >= 0 ); s = name; while ( *s ) s++; if ( s > name && s[-1] == '_' && nametree == AC.varnames ) { /* The Kronecker delta d_ is very special. It is not really a function. */ if ( s == name+2 && ( *name == 'd' || *name == 'D' ) ) { *number = DELTA-FUNCTION; return(CDELTA); } /* Test for N#_? type variables (summed indices) */ if ( s > name+2 && *name == 'N' ) { t = name+1; i = 0; while ( FG.cTable[*t] == 1 ) i = 10*i + *t++ -'0'; if ( s == t+1 ) { *number = i + AM.IndDum - AM.OffsetIndex; return(CINDEX); } } /* Now test for any built in object */ newnode = nametree->headnode; do { node = newnode; n = nametree->namenode+node; if ( ( i = StrHICmp(name,nametree->namebuffer+n->name) ) < 0 ) newnode = n->left; else if ( i > 0 ) newnode = n->right; else { *number = n->number; return(n->type); } } while ( newnode >= 0 ); /* Now we test for the extra symbols of the type STR###_ The string sits in AC.extrasym and is followed by digits. The name is only legal if the number is in the range 1,...,cbuf[AM.sbufnum].numrhs */ t = name; u = AC.extrasym; while ( *t == *u ) { t++; u++; } if ( *u == 0 && *t != 0 ) { /* potential hit */ WORD x = 0; while ( FG.cTable[*t] == 1 ) { x = 10*x + (*t++ - '0'); } if ( *t == '_' && x > 0 && x <= cbuf[AM.sbufnum].numrhs ) { /* Hit */ *number = MAXVARIABLES-x; return(CSYMBOL); } } } NotFound:; if ( par != WITHAUTO || nametree == AC.autonames ) return(NAMENOTFOUND); return(GetAutoName(name,number)); } /* #] GetName : #[ GetFunction : Gets either a function or a $ that should expand into a function during runtime. In the case of the $ the value in funnum is -dolnum-1. The return value is the position after the name of the function or the $. */ static WORD one = 1; UBYTE *GetFunction(UBYTE *s,WORD *funnum) { int type; WORD numfun; UBYTE *t1, c; if ( *s == '$' ) { t1 = s+1; while ( FG.cTable[*t1] < 2 ) t1++; c = *t1; *t1 = 0; if ( ( type = GetName(AC.dollarnames,s+1,&numfun,NOAUTO) ) == CDOLLAR ) { *funnum = -numfun-2; } else { MesPrint("&%s is undefined",s); numfun = AddDollar(s+1,DOLINDEX,&one,1); *funnum = 0; } } else { t1 = SkipAName(s); c = *t1; *t1 = 0; if ( ( ( type = GetName(AC.varnames,s,&numfun,WITHAUTO) ) != CFUNCTION ) || ( functions[numfun].spec > 0 ) ) { MesPrint("&%s should be a regular function",s); *funnum = 0; if ( type < 0 ) { if ( GetName(AC.exprnames,s,&numfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } *t1 = c; return(t1); } *funnum = numfun+FUNCTION; } *t1 = c; return(t1); } /* #] GetFunction : #[ GetNumber : Gets either a number or a $ that should expand into a number during runtime. In the case of the $ the value in num is -dolnum-2. The return value is the position after the number or the $. */ UBYTE *GetNumber(UBYTE *s,WORD *num) { int type; WORD numfun; UBYTE *t1, c; while ( *s == '+' ) s++; if ( *s == '$' ) { t1 = s+1; while ( FG.cTable[*t1] < 2 ) t1++; c = *t1; *t1 = 0; if ( ( type = GetName(AC.dollarnames,s+1,&numfun,NOAUTO) ) == CDOLLAR ) { *num = -numfun-2; } else { MesPrint("&%s is undefined",s); numfun = AddDollar(s+1,DOLINDEX,&one,1); *num = -1; } } else if ( *s >= '0' && *s <= '9' ) { ULONG x = *s++ - '0'; while ( *s >= '0' && *s <= '9' ) { x = 10*x + (*s++-'0'); } t1 = s; if ( x >= MAXPOSITIVE ) goto illegal; *num = (WORD)x; return(t1); } else { if ( *s == '-' ) { s++; } if ( *s >= '0' && *s <= '9' ) { while ( *s >= '0' && *s <= '9' ) s++; t1 = s; } else { t1 = SkipAName(s); } illegal: *num = -1; MesPrint("&Illegal option in Canonicalize statement. Should be a nonnegative number or $ variable."); return(t1); } *t1 = c; return(t1); } /* #] GetNumber : #[ GetLastExprName : When AutoDeclare is an active statement. If par == WITHAUTO and the variable is not found we have to check: 1: that nametree != AC.exprnames && nametree != AC.dollarnames 2: check that the variable is not in AC.exprnames after all. 3: call GetAutoName and return its values. */ int GetLastExprName(UBYTE *name, WORD *number) { int i; EXPRESSIONS e; for ( i = NumExpressions; i > 0; i-- ) { e = Expressions+i-1; if ( StrCmp(AC.exprnames->namebuffer+e->name,name) == 0 ) { *number = i-1; return(1); } } return(0); } /* #] GetLastExprName : #[ GetOName : Adds the proper offsets, so we do not have to do that in the calling routine. */ int GetOName(NAMETREE *nametree, UBYTE *name, WORD *number, int par) { int retval = GetName(nametree,name,number,par); switch ( retval ) { case CVECTOR: *number += AM.OffsetVector; break; case CINDEX: *number += AM.OffsetIndex; break; case CFUNCTION: *number += FUNCTION; break; default: break; } return(retval); } /* #] GetOName : #[ GetAutoName : This routine gets the automatic declarations */ int GetAutoName(UBYTE *name, WORD *number) { UBYTE *s, c; int type; if ( GetName(AC.exprnames,name,number,NOAUTO) != NAMENOTFOUND ) return(NAMENOTFOUND); s = name; while ( *s ) { s++; } if ( s[-1] == '_' ) { return(NAMENOTFOUND); } while ( s > name ) { c = *s; *s = 0; type = GetName(AC.autonames,name,number,NOAUTO); *s = c; switch(type) { case CSYMBOL: { SYMBOLS sym = ((SYMBOLS)(AC.AutoSymbolList.lijst)) + *number; *number = AddSymbol(name,sym->minpower,sym->maxpower,sym->complex,sym->dimension); return(type); } case CVECTOR: { VECTORS vec = ((VECTORS)(AC.AutoVectorList.lijst)) + *number; *number = AddVector(name,vec->complex,vec->dimension); return(type); } case CINDEX: { INDICES ind = ((INDICES)(AC.AutoIndexList.lijst)) + *number; *number = AddIndex(name,ind->dimension,ind->nmin4); return(type); } case CFUNCTION: { FUNCTIONS fun = ((FUNCTIONS)(AC.AutoFunctionList.lijst)) + *number; *number = AddFunction(name,fun->commute,fun->spec,fun->complex,fun->symmetric,fun->dimension,fun->maxnumargs,fun->minnumargs); return(type); } default: break; } s--; } return(NAMENOTFOUND); } /* #] GetAutoName : #[ GetVar : */ int GetVar(UBYTE *name, WORD *type, WORD *number, int wantedtype, int par) { WORD funnum; int typ; if ( ( typ = GetName(AC.varnames,name,number,par) ) != wantedtype ) { if ( typ != NAMENOTFOUND ) { if ( wantedtype == -1 ) { *type = typ; return(1); } NameConflict(typ,name); MakeDubious(AC.varnames,name,&funnum); return(-1); } if ( ( typ = GetName(AC.exprnames,name,&funnum,par) ) != NAMENOTFOUND ) { if ( typ == wantedtype || wantedtype == -1 ) { *number = funnum; *type = typ; return(1); } NameConflict(typ,name); return(-1); } return(NAMENOTFOUND); } if ( typ == -1 ) { return(0); } *type = typ; return(1); } /* #] GetVar : #[ EntVar : */ int EntVar(WORD type, UBYTE *name, WORD x, WORD y, WORD z, WORD d) { switch ( type ) { case CSYMBOL: return(AddSymbol(name,y,z,x,d)); break; case CINDEX: return(AddIndex(name,x,z)); break; case CVECTOR: return(AddVector(name,x,d)); break; case CFUNCTION: return(AddFunction(name,y,z,x,0,d,-1,-1)); break; case CSET: AC.SetList.numtemp++; return(AddSet(name,d)); break; case CEXPRESSION: return(AddExpression(name,x,y)); break; default: break; } return(-1); } /* #] EntVar : #[ GetDollar : */ int GetDollar(UBYTE *name) { WORD number; if ( GetName(AC.dollarnames,name,&number,NOAUTO) == NAMENOTFOUND ) return(-1); return((int)number); } /* #] GetDollar : #[ DumpTree : */ void DumpTree(NAMETREE *nametree) { if ( nametree->headnode >= 0 && nametree->namebuffer && nametree->namenode ) { DumpNode(nametree,nametree->headnode,0); } } /* #] DumpTree : #[ DumpNode : */ void DumpNode(NAMETREE *nametree, WORD node, WORD depth) { NAMENODE *n; int i; char *name; n = nametree->namenode + node; if ( n->left >= 0 ) DumpNode(nametree,n->left,depth+1); for ( i = 0; i < depth; i++ ) printf(" "); name = (char *)(nametree->namebuffer+n->name); printf("%s(%d): {%d}(%d)(%d)[%d]\n", name,node,n->parent,n->left,n->right,n->balance); if ( n->right >= 0 ) DumpNode(nametree,n->right,depth+1); } /* #] DumpNode : #[ CompactifyTree : */ int CompactifyTree(NAMETREE *nametree,WORD par) { NAMETREE newtree; NAMENODE *n; LONG i, j, ns, k; UBYTE *s; for ( i = 0, j = 0, k = 0, n = nametree->namenode, ns = 0; i < nametree->nodefill; i++, n++ ) { if ( n->type != CDELETE ) { s = nametree->namebuffer+n->name; while ( *s ) { s++; ns++; } j++; } else k++; } if ( k == 0 ) return(0); if ( j == 0 ) { if ( nametree->namebuffer ) M_free(nametree->namebuffer,"nametree->namebuffer"); if ( nametree->namenode ) M_free(nametree->namenode,"nametree->namenode"); nametree->namebuffer = 0; nametree->namenode = 0; nametree->namesize = nametree->namefill = nametree->nodesize = nametree->nodefill = nametree->oldnamefill = nametree->oldnodefill = 0; nametree->globalnamefill = nametree->globalnodefill = nametree->clearnamefill = nametree->clearnodefill = 0; nametree->headnode = -1; return(0); } ns += j; if ( j < 10 ) j = 10; if ( ns < 100 ) ns = 100; newtree.namenode = (NAMENODE *)Malloc1(2*j*sizeof(NAMENODE),"compactify namestree"); newtree.nodefill = 0; newtree.nodesize = 2*j; newtree.namebuffer = (UBYTE *)Malloc1(2*ns,"compactify namestree"); newtree.namefill = 0; newtree.namesize = 2*ns; CopyTree(&newtree,nametree,nametree->headnode,par); newtree.namenode[newtree.nodefill>>1].parent = -1; LinkTree(&newtree,(WORD)0,newtree.nodefill); newtree.headnode = newtree.nodefill >> 1; M_free(nametree->namebuffer,"nametree->namebuffer"); M_free(nametree->namenode,"nametree->namenode"); nametree->namebuffer = newtree.namebuffer; nametree->namenode = newtree.namenode; nametree->namesize = newtree.namesize; nametree->namefill = newtree.namefill; nametree->nodesize = newtree.nodesize; nametree->nodefill = newtree.nodefill; nametree->oldnamefill = newtree.namefill; nametree->oldnodefill = newtree.nodefill; nametree->headnode = newtree.headnode; /* DumpTree(nametree); */ return(0); } /* #] CompactifyTree : #[ CopyTree : */ void CopyTree(NAMETREE *newtree, NAMETREE *oldtree, WORD node, WORD par) { NAMENODE *n, *m; UBYTE *s, *t; n = oldtree->namenode+node; if ( n->left >= 0 ) CopyTree(newtree,oldtree,n->left,par); if ( n->type != CDELETE ) { m = newtree->namenode+newtree->nodefill; m->type = n->type; m->number = n->number; m->name = newtree->namefill; m->left = m->right = -1; m->balance = 0; switch ( n->type ) { case CSYMBOL: if ( par == AUTONAMES ) { autosymbols[n->number].name = newtree->namefill; autosymbols[n->number].node = newtree->nodefill; } else { symbols[n->number].name = newtree->namefill; symbols[n->number].node = newtree->nodefill; } break; case CINDEX : if ( par == AUTONAMES ) { autoindices[n->number].name = newtree->namefill; autoindices[n->number].node = newtree->nodefill; } else { indices[n->number].name = newtree->namefill; indices[n->number].node = newtree->nodefill; } break; case CVECTOR: if ( par == AUTONAMES ) { autovectors[n->number].name = newtree->namefill; autovectors[n->number].node = newtree->nodefill; } else { vectors[n->number].name = newtree->namefill; vectors[n->number].node = newtree->nodefill; } break; case CFUNCTION: if ( par == AUTONAMES ) { autofunctions[n->number].name = newtree->namefill; autofunctions[n->number].node = newtree->nodefill; } else { functions[n->number].name = newtree->namefill; functions[n->number].node = newtree->nodefill; } break; case CSET: Sets[n->number].name = newtree->namefill; Sets[n->number].node = newtree->nodefill; break; case CEXPRESSION: Expressions[n->number].name = newtree->namefill; Expressions[n->number].node = newtree->nodefill; break; case CDUBIOUS: Dubious[n->number].name = newtree->namefill; Dubious[n->number].node = newtree->nodefill; break; case CDOLLAR: Dollars[n->number].name = newtree->namefill; Dollars[n->number].node = newtree->nodefill; break; default: MesPrint("Illegal variable type in CopyTree: %d",n->type); break; } newtree->nodefill++; s = newtree->namebuffer + newtree->namefill; t = oldtree->namebuffer + n->name; while ( *t ) { *s++ = *t++; newtree->namefill++; } *s = 0; newtree->namefill++; } if ( n->right >= 0 ) CopyTree(newtree,oldtree,n->right,par); } /* #] CopyTree : #[ LinkTree : */ void LinkTree(NAMETREE *tree, WORD offset, WORD numnodes) { /* Makes the tree into a binary tree */ int med,numleft,numright,medleft,medright; med = numnodes >> 1; numleft = med; numright = numnodes - med - 1; medleft = numleft >> 1; medright = ( numright >> 1 ) + med + 1; if ( numleft > 0 ) { tree->namenode[offset+med].left = offset+medleft; tree->namenode[offset+medleft].parent = offset+med; } if ( numright > 0 ) { tree->namenode[offset+med].right = offset+medright; tree->namenode[offset+medright].parent = offset+med; } if ( numleft > 0 ) LinkTree(tree,offset,numleft); if ( numright > 0 ) LinkTree(tree,offset+med+1,numright); while ( numleft && numright ) { numleft >>= 1; numright >>= 1; } if ( numleft ) tree->namenode[offset+med].balance = -1; else if ( numright ) tree->namenode[offset+med].balance = 1; } /* #] LinkTree : #[ MakeNameTree : */ NAMETREE *MakeNameTree(void) { NAMETREE *n; n = (NAMETREE *)Malloc1(sizeof(NAMETREE),"new nametree"); n->namebuffer = 0; n->namenode = 0; n->namesize = n->namefill = n->nodesize = n->nodefill = n->oldnamefill = n->oldnodefill = 0; n->globalnamefill = n->globalnodefill = n->clearnamefill = n->clearnodefill = 0; n->headnode = -1; return(n); } /* #] MakeNameTree : #[ FreeNameTree : */ void FreeNameTree(NAMETREE *n) { if ( n ) { if ( n->namebuffer ) M_free(n->namebuffer,"nametree->namebuffer"); if ( n->namenode ) M_free(n->namenode,"nametree->namenode"); M_free(n,"nametree"); } } /* #] FreeNameTree : #[ WildcardNames : */ void ClearWildcardNames(void) { AC.NumWildcardNames = 0; } int AddWildcardName(UBYTE *name) { GETIDENTITY int size = 0, tocopy, i; UBYTE *s = name, *t, *newbuffer; while ( *s ) { s++; size++; } for ( i = 0, t = AC.WildcardNames; i < AC.NumWildcardNames; i++ ) { s = name; while ( ( *s == *t ) && *s ) { s++; t++; } if ( *s == 0 && *t == 0 ) return(i+1); while ( *t ) t++; t++; } tocopy = t - AC.WildcardNames; if ( tocopy + size + 1 > AC.WildcardBufferSize ) { if ( AC.WildcardBufferSize == 0 ) { AC.WildcardBufferSize = size+1; if ( AC.WildcardBufferSize < 100 ) AC.WildcardBufferSize = 100; } else if ( size+1 >= AC.WildcardBufferSize ) { AC.WildcardBufferSize += size+1; } else { AC.WildcardBufferSize *= 2; } newbuffer = (UBYTE *)Malloc1((LONG)AC.WildcardBufferSize,"argument list names"); t = newbuffer; if ( AC.WildcardNames ) { s = AC.WildcardNames; while ( tocopy > 0 ) { *t++ = *s++; tocopy--; } M_free(AC.WildcardNames,"AC.WildcardNames"); } AC.WildcardNames = newbuffer; M_free(AT.WildArgTaken,"AT.WildArgTaken"); AT.WildArgTaken = (WORD *)Malloc1((LONG)AC.WildcardBufferSize*sizeof(WORD)/2 ,"argument list names"); } s = name; while ( *s ) *t++ = *s++; *t = 0; AC.NumWildcardNames++; return(AC.NumWildcardNames); } int GetWildcardName(UBYTE *name) { UBYTE *s, *t; int i; for ( i = 0, t = AC.WildcardNames; i < AC.NumWildcardNames; i++ ) { s = name; while ( ( *s == *t ) && *s ) { s++; t++; } if ( *s == 0 && *t == 0 ) return(i+1); while ( *t ) t++; t++; } return(0); } /* #] WildcardNames : #[ AddSymbol : The actual addition. Special routine for additions 'on the fly' */ int AddSymbol(UBYTE *name, int minpow, int maxpow, int cplx, int dim) { int nodenum, numsymbol = AC.Symbols->num; UBYTE *s = name; SYMBOLS sym = (SYMBOLS)FromVarList(AC.Symbols); bzero(sym,sizeof(struct SyMbOl)); sym->name = AddName(*AC.activenames,name,CSYMBOL,numsymbol,&nodenum); sym->minpower = minpow; sym->maxpower = maxpow; sym->complex = cplx; sym->flags = 0; sym->node = nodenum; sym->dimension= dim; while ( *s ) s++; sym->namesize = (s-name)+1; return(numsymbol); } /* #] AddSymbol : #[ CoSymbol : Symbol declarations. name[#{R|I|C}][([min]:[max])] Note that we know already that the parentheses match properly */ int CoSymbol(UBYTE *s) { int type, error = 0, minpow, maxpow, cplx, sgn, dim; WORD numsymbol; UBYTE *name, *oldc, c, cc; do { minpow = -MAXPOWER; maxpow = MAXPOWER; cplx = 0; dim = 0; name = s; if ( ( s = SkipAName(s) ) == 0 ) { IllForm: MesPrint("&Illegally formed name in symbol statement"); error = 1; s = SkipField(name,0); goto eol; } oldc = s; cc = c = *s; *s = 0; if ( TestName(name) ) { *s = c; goto IllForm; } if ( cc == '#' ) { s++; if ( tolower(*s) == 'r' ) cplx = VARTYPENONE; else if ( tolower(*s) == 'c' ) cplx = VARTYPECOMPLEX; else if ( tolower(*s) == 'i' ) cplx = VARTYPEIMAGINARY; else if ( ( ( *s == '-' || *s == '+' || *s == '=' ) && ( s[1] >= '0' && s[1] <= '9' ) ) || ( *s >= '0' && *s <= '9' ) ) { LONG x; sgn = 0; if ( *s == '-' ) { sgn = VARTYPEMINUS; s++; } else if ( *s == '+' || *s == '=' ) { sgn = 0; s++; } x = *s -'0'; while ( s[1] >= '0' && s[1] <= '9' ) { x = 10*x + (s[1] - '0'); s++; } if ( x >= MAXPOWER || x <= 1 ) { MesPrint("&Illegal value for root of unity %s",name); error = 1; } else { maxpow = x; } cplx = VARTYPEROOTOFUNITY | sgn; } else { MesPrint("&Illegal specification for complexity of symbol %s",name); *oldc = c; error = 1; s = SkipField(s,0); goto eol; } s++; cc = *s; } if ( cc == '{' ) { s++; if ( ( *s == 'd' || *s == 'D' ) && s[1] == '=' ) { s += 2; if ( *s == '-' || *s == '+' || FG.cTable[*s] == 1 ) { ParseSignedNumber(dim,s) if ( dim < -HALFMAX || dim > HALFMAX ) { MesPrint("&Warning: dimension of %s (%d) out of range" ,name,dim); } } if ( *s != '}' ) goto IllDim; else s++; } else { IllDim: MesPrint("&Error: Illegal dimension field for variable %s",name); error = 1; s = SkipField(s,0); goto eol; } cc = *s; } if ( cc == '(' ) { if ( ( cplx & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) { MesPrint("&Root of unity property for %s cannot be combined with power restrictions",name); error = 1; } s++; if ( *s == '-' || *s == '+' || FG.cTable[*s] == 1 ) { ParseSignedNumber(minpow,s) if ( minpow < -MAXPOWER ) { minpow = -MAXPOWER; if ( AC.WarnFlag ) MesPrint("&Warning: minimum power of %s corrected to %d" ,name,-MAXPOWER); } } if ( *s != ':' ) { skippar: error = 1; s = SkipField(s,1); goto eol; } else s++; if ( *s == '-' || *s == '+' || FG.cTable[*s] == 1 ) { ParseSignedNumber(maxpow,s) if ( maxpow > MAXPOWER ) { maxpow = MAXPOWER; if ( AC.WarnFlag ) MesPrint("&Warning: maximum power of %s corrected to %d" ,name,MAXPOWER); } } if ( *s != ')' ) goto skippar; s++; } if ( ( AC.AutoDeclareFlag == 0 && ( ( type = GetName(AC.exprnames,name,&numsymbol,NOAUTO) ) != NAMENOTFOUND ) ) || ( ( type = GetName(*(AC.activenames),name,&numsymbol,NOAUTO) ) != NAMENOTFOUND ) ) { if ( type != CSYMBOL ) error = NameConflict(type,name); else { SYMBOLS sym = (SYMBOLS)(AC.Symbols->lijst) + numsymbol; if ( ( numsymbol == AC.lPolyFunVar ) && ( AC.lPolyFunType > 0 ) && ( AC.lPolyFun != 0 ) && ( minpow > -MAXPOWER || maxpow < MAXPOWER ) ) { MesPrint("&The symbol %s is used by power expansions in the PolyRatFun!",name); error = 1; } sym->complex = cplx; sym->minpower = minpow; sym->maxpower = maxpow; sym->dimension= dim; } } else { AddSymbol(name,minpow,maxpow,cplx,dim); } *oldc = c; eol: while ( *s == ',' ) s++; } while ( *s ); return(error); } /* #] CoSymbol : #[ AddIndex : The actual addition. Special routine for additions 'on the fly' */ int AddIndex(UBYTE *name, int dim, int dim4) { int nodenum, numindex = AC.Indices->num; INDICES ind = (INDICES)FromVarList(AC.Indices); UBYTE *s = name; bzero(ind,sizeof(struct InDeX)); ind->name = AddName(*AC.activenames,name,CINDEX,numindex,&nodenum); ind->type = 0; ind->dimension = dim; ind->flags = 0; ind->nmin4 = dim4; ind->node = nodenum; while ( *s ) s++; ind->namesize = (s-name)+1; return(numindex); } /* #] AddIndex : #[ CoIndex : Index declarations. name[={number|symbol[:othersymbol]}] */ int CoIndex(UBYTE *s) { int type, error = 0, dim, dim4; WORD numindex; UBYTE *name, *oldc, c; do { dim = AC.lDefDim; dim4 = AC.lDefDim4; name = s; if ( ( s = SkipAName(s) ) == 0 ) { IllForm: MesPrint("&Illegally formed name in index statement"); error = 1; s = SkipField(name,0); goto eol; } oldc = s; c = *s; *s = 0; if ( TestName(name) ) { *s = c; goto IllForm; } if ( c == '=' ) { s++; if ( ( s = DoDimension(s,&dim,&dim4) ) == 0 ) { *oldc = c; error = 1; s = SkipField(name,0); goto eol; } } if ( ( AC.AutoDeclareFlag == 0 && ( ( type = GetName(AC.exprnames,name,&numindex,NOAUTO) ) != NAMENOTFOUND ) ) || ( ( type = GetName(*(AC.activenames),name,&numindex,NOAUTO) ) != NAMENOTFOUND ) ) { if ( type != CINDEX ) error = NameConflict(type,name); else { /* reset the dimensions */ indices[numindex].dimension = dim; indices[numindex].nmin4 = dim4; } } else AddIndex(name,dim,dim4); *oldc = c; eol: while ( *s == ',' ) s++; } while ( *s ); return(error); } /* #] CoIndex : #[ DoDimension : */ UBYTE *DoDimension(UBYTE *s, int *dim, int *dim4) { UBYTE c, *t = s; int type, error = 0; WORD numsymbol; NAMETREE **oldtree = AC.activenames; LIST* oldsymbols = AC.Symbols; *dim4 = -NMIN4SHIFT; if ( FG.cTable[*s] == 1 ) { retry: ParseNumber(*dim,s) #if ( BITSINWORD/8 < 4 ) if ( *dim >= (1 << (BITSINWORD-1)) ) goto illeg; #endif *dim4 = *dim - 4; return(s); } else if ( ( (FG.cTable[*s] == 0 ) || ( *s == '[' ) ) && ( s = SkipAName(s) ) != 0 ) { AC.activenames = &(AC.varnames); AC.Symbols = &(AC.SymbolList); c = *s; *s = 0; if ( ( ( type = GetName(AC.exprnames,t,&numsymbol,NOAUTO) ) != NAMENOTFOUND ) || ( ( type = GetName(AC.varnames,t,&numsymbol,WITHAUTO) ) != NAMENOTFOUND ) ) { if ( type != CSYMBOL ) error = NameConflict(type,t); } else { numsymbol = AddSymbol(t,-MAXPOWER,MAXPOWER,0,0); if ( AC.WarnFlag ) MesPrint("&Warning: Implicit declaration of %s as a symbol",t); } *dim = -numsymbol; if ( ( *s = c ) == ':' ) { s++; t = s; if ( ( s = SkipAName(s) ) == 0 ) goto illeg; if ( ( ( type = GetName(AC.exprnames,t,&numsymbol,NOAUTO) ) != NAMENOTFOUND ) || ( ( type = GetName(AC.varnames,t,&numsymbol,WITHAUTO) ) != NAMENOTFOUND ) ) { if ( type != CSYMBOL ) error = NameConflict(type,t); } else { numsymbol = AddSymbol(t,-MAXPOWER,MAXPOWER,0,0); if ( AC.WarnFlag ) MesPrint("&Warning: Implicit declaration of %s as a symbol",t); } *dim4 = -numsymbol-NMIN4SHIFT; } } else if ( *s == '+' && FG.cTable[s[1]] == 1 ) { s++; goto retry; } else { illeg: MesPrint("&Illegal dimension specification. Should be number >= 0, symbol or symbol:symbol"); return(0); } AC.Symbols = oldsymbols; AC.activenames = oldtree; if ( error ) return(0); return(s); } /* #] DoDimension : #[ CoDimension : */ int CoDimension(UBYTE *s) { s = DoDimension(s,&AC.lDefDim,&AC.lDefDim4); if ( s == 0 ) return(1); if ( *s != 0 ) { MesPrint("&Argument of dimension statement should be number >= 0, symbol or symbol:symbol"); return(1); } return(0); } /* #] CoDimension : #[ AddVector : The actual addition. Special routine for additions 'on the fly' */ int AddVector(UBYTE *name, int cplx, int dim) { int nodenum, numvector = AC.Vectors->num; VECTORS v = (VECTORS)FromVarList(AC.Vectors); UBYTE *s = name; bzero(v,sizeof(struct VeCtOr)); v->name = AddName(*AC.activenames,name,CVECTOR,numvector,&nodenum); v->complex = cplx; v->node = nodenum; v->dimension = dim; v->flags = 0; while ( *s ) s++; v->namesize = (s-name)+1; return(numvector); } /* #] AddVector : #[ CoVector : Vector declarations. The descriptor string is "(,%n)" */ int CoVector(UBYTE *s) { int type, error = 0, dim; WORD numvector; UBYTE *name, c, *endname; do { name = s; dim = 0; if ( ( s = SkipAName(s) ) == 0 ) { IllForm: MesPrint("&Illegally formed name in vector statement"); error = 1; s = SkipField(s,0); } else { c = *s; *s = 0, endname = s; if ( TestName(name) ) { *s = c; goto IllForm; } if ( c == '{' ) { s++; if ( ( *s == 'd' || *s == 'D' ) && s[1] == '=' ) { s += 2; if ( *s == '-' || *s == '+' || FG.cTable[*s] == 1 ) { ParseSignedNumber(dim,s) if ( dim < -HALFMAX || dim > HALFMAX ) { MesPrint("&Warning: dimension of %s (%d) out of range" ,name,dim); } } if ( *s != '}' ) goto IllDim; else s++; } else { IllDim: MesPrint("&Error: Illegal dimension field for variable %s",name); error = 1; s = SkipField(s,0); while ( *s == ',' ) s++; continue; } } if ( ( AC.AutoDeclareFlag == 0 && ( ( type = GetName(AC.exprnames,name,&numvector,NOAUTO) ) != NAMENOTFOUND ) ) || ( ( type = GetName(*(AC.activenames),name,&numvector,NOAUTO) ) != NAMENOTFOUND ) ) { if ( type != CVECTOR ) error = NameConflict(type,name); } else AddVector(name,0,dim); *endname = c; } while ( *s == ',' ) s++; } while ( *s ); return(error); } /* #] CoVector : #[ AddFunction : The actual addition. Special routine for additions 'on the fly' */ int AddFunction(UBYTE *name, int comm, int istensor, int cplx, int symprop, int dim, int argmax, int argmin) { int nodenum, numfunction = AC.Functions->num; FUNCTIONS fun = (FUNCTIONS)FromVarList(AC.Functions); UBYTE *s = name; bzero(fun,sizeof(struct FuNcTiOn)); fun->name = AddName(*AC.activenames,name,CFUNCTION,numfunction,&nodenum); fun->commute = comm; fun->spec = istensor; fun->complex = cplx; fun->tabl = 0; fun->flags = 0; fun->node = nodenum; fun->symminfo = 0; fun->symmetric = symprop; fun->dimension = dim; fun->maxnumargs = argmax; fun->minnumargs = argmin; while ( *s ) s++; fun->namesize = (s-name)+1; return(numfunction); } /* #] AddFunction : #[ CoCommuteInSet : Commuting,f1,...,fn; */ int CoCommuteInSet(UBYTE *s) { UBYTE *name, *ss, c, *start = s; WORD number, type, *g, *gg; int error = 0, i, len = StrLen(s), len2 = 0; if ( AC.CommuteInSet != 0 ) { g = AC.CommuteInSet; while ( *g ) g += *g; len2 = g - AC.CommuteInSet; if ( len2+len+3 > AC.SizeCommuteInSet ) { gg = (WORD *)Malloc1((len2+len+3)*sizeof(WORD),"CommuteInSet"); for ( i = 0; i < len2; i++ ) gg[i] = AC.CommuteInSet[i]; gg[len2] = 0; M_free(AC.CommuteInSet,"CommuteInSet"); AC.CommuteInSet = gg; AC.SizeCommuteInSet = len+len2+3; g = AC.CommuteInSet+len2; } } else { AC.SizeCommuteInSet = len+2; g = AC.CommuteInSet = (WORD *)Malloc1((len+3)*sizeof(WORD),"CommuteInSet"); *g = 0; } gg = g++; ss = s-1; for(;;) { while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) { if ( s - start >= len ) break; *s = '}'; s++; *g = 0; *gg = g-gg; if ( *gg < 2 ) { MesPrint("&There should be at least two noncommuting functions or tensors in a commuting statement."); error = 1; } else if ( *gg == 2 ) { gg[2] = gg[1]; gg[3] = 0; gg[0] = 3; } gg = g++; continue; } if ( s > ss ) { if ( *s != '{' ) { MesPrint("&The CommuteInSet statement should have sets enclosed in {}."); error = 1; break; } ss = s; SKIPBRA2(ss) /* Note that parentheses were tested before */ *ss = 0; s++; } name = s; s = SkipAName(s); c = *s; *s = 0; if ( ( type = GetName(AC.varnames,name,&number,NOAUTO) ) != CFUNCTION ) { MesPrint("&%s is not a function or tensor",name); error = 1; } else if ( functions[number].commute == 0 ){ MesPrint("&%s is not a noncommuting function or tensor",name); error = 1; } else { *g++ = number+FUNCTION; functions[number].flags |= COULDCOMMUTE; if ( number+FUNCTION >= GAMMA && number+FUNCTION <= GAMMASEVEN ) { functions[GAMMA-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMAI-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMAFIVE-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMASIX-FUNCTION].flags |= COULDCOMMUTE; functions[GAMMASEVEN-FUNCTION].flags |= COULDCOMMUTE; } } *s = c; } return(error); } /* #] CoCommuteInSet : #[ CoFunction + ...: Function declarations. The second parameter indicates commutation properties. The third parameter tells whether we have a tensor. */ int CoFunction(UBYTE *s, int comm, int istensor) { int type, error = 0, cplx, symtype, dim, argmax, argmin; WORD numfunction, reverseorder = 0, addone; UBYTE *name, *oldc, *par, c, cc; do { symtype = cplx = 0, argmin = argmax = -1; dim = 0; name = s; if ( ( s = SkipAName(s) ) == 0 ) { IllForm: MesPrint("&Illegally formed function/tensor name"); error = 1; s = SkipField(name,0); goto eol; } oldc = s; cc = c = *s; *s = 0; if ( TestName(name) ) { *s = c; goto IllForm; } if ( c == '#' ) { s++; if ( tolower(*s) == 'r' ) cplx = VARTYPENONE; else if ( tolower(*s) == 'c' ) cplx = VARTYPECOMPLEX; else if ( tolower(*s) == 'i' ) cplx = VARTYPEIMAGINARY; else { MesPrint("&Illegal specification for complexity of %s",name); *oldc = c; error = 1; s = SkipField(s,0); goto eol; } s++; cc = *s; } if ( cc == '{' ) { s++; if ( ( *s == 'd' || *s == 'D' ) && s[1] == '=' ) { s += 2; if ( *s == '-' || *s == '+' || FG.cTable[*s] == 1 ) { ParseSignedNumber(dim,s) if ( dim < -HALFMAX || dim > HALFMAX ) { MesPrint("&Warning: dimension of %s (%d) out of range" ,name,dim); } } if ( *s != '}' ) goto IllDim; else s++; } else { IllDim: MesPrint("&Error: Illegal dimension field for variable %s",name); error = 1; s = SkipField(s,0); goto eol; } cc = *s; } if ( cc == '(' ) { s++; if ( *s == '-' ) { reverseorder = REVERSEORDER; s++; } else { reverseorder = 0; } par = s; while ( FG.cTable[*s] == 0 ) s++; cc = *s; *s = 0; if ( s <= par ) { illegsym: *s = cc; MesPrint("&Illegal specification for symmetry of %s",name); *oldc = c; error = 1; s = SkipField(s,1); goto eol; } if ( StrICont(par,(UBYTE *)"symmetric") == 0 ) symtype = SYMMETRIC; else if ( StrICont(par,(UBYTE *)"antisymmetric") == 0 ) symtype = ANTISYMMETRIC; else if ( ( StrICont(par,(UBYTE *)"cyclesymmetric") == 0 ) || ( StrICont(par,(UBYTE *)"cyclic") == 0 ) ) symtype = CYCLESYMMETRIC; else if ( ( StrICont(par,(UBYTE *)"rcyclesymmetric") == 0 ) || ( StrICont(par,(UBYTE *)"rcyclic") == 0 ) || ( StrICont(par,(UBYTE *)"reversecyclic") == 0 ) ) symtype = RCYCLESYMMETRIC; else goto illegsym; *s = cc; if ( *s != ')' || ( s[1] && s[1] != ',' && s[1] != '<' ) ) { Warning("Excess information in symmetric properties currently ignored"); s = SkipField(s,1); } else s++; symtype |= reverseorder; cc = *s; } retry:; if ( cc == '<' ) { s++; addone = 0; if ( *s == '=' ) { addone++; s++; } argmax = 0; while ( FG.cTable[*s] == 1 ) { argmax = 10*argmax + *s++ - '0'; } argmax += addone; par = s; while ( FG.cTable[*s] == 0 ) s++; if ( s > par ) { cc = *s; *s = 0; if ( ( StrICont(par,(UBYTE *)"arguments") == 0 ) || ( StrICont(par,(UBYTE *)"args") == 0 ) ) {} else { Warning("Illegal information in number of arguments properties currently ignored"); } *s = cc; } if ( argmax <= 0 ) { MesPrint("&Error: Cannot have fewer than 0 arguments for variable %s",name); error = 1; } cc = *s; } if ( cc == '>' ) { s++; addone = 1; if ( *s == '=' ) { addone = 0; s++; } argmin = 0; while ( FG.cTable[*s] == 1 ) { argmin = 10*argmin + *s++ - '0'; } argmin += addone; par = s; while ( FG.cTable[*s] == 0 ) s++; if ( s > par ) { cc = *s; *s = 0; if ( ( StrICont(par,(UBYTE *)"arguments") == 0 ) || ( StrICont(par,(UBYTE *)"args") == 0 ) ) {} else { Warning("Illegal information in number of arguments properties currently ignored"); } *s = cc; } cc = *s; } if ( cc == '<' ) goto retry; if ( ( AC.AutoDeclareFlag == 0 && ( ( type = GetName(AC.exprnames,name,&numfunction,NOAUTO) ) != NAMENOTFOUND ) ) || ( ( type = GetName(*(AC.activenames),name,&numfunction,NOAUTO) ) != NAMENOTFOUND ) ) { if ( type != CFUNCTION ) error = NameConflict(type,name); else { /* FUNCTIONS fun = (FUNCTIONS)(AC.Functions->lijst) + numfunction-FUNCTION; */ FUNCTIONS fun = (FUNCTIONS)(AC.Functions->lijst) + numfunction; if ( fun->tabl != 0 ) { MesPrint("&Illegal attempt to change table into function"); error = 1; } fun->complex = cplx; fun->commute = comm; if ( istensor && fun->spec == 0 ) { MesPrint("&Function %s changed to tensor",name); error = 1; } else if ( istensor == 0 && fun->spec > 0 ) { MesPrint("&Tensor %s changed to function",name); error = 1; } else if ( fun->spec == VERTEXFUNCTION ) { MesPrint("&Function or Tensor %s already declared as a Particle",name); error = 1; } fun->spec = istensor; if ( fun->symmetric != symtype ) { fun->symmetric = symtype; AC.SymChangeFlag = 1; } fun->maxnumargs = argmax; fun->minnumargs = argmin; } } else { AddFunction(name,comm,istensor,cplx,symtype,dim,argmax,argmin); } *oldc = c; eol: while ( *s == ',' ) s++; } while ( *s ); return(error); } int CoNFunction(UBYTE *s) { return(CoFunction(s,1,0)); } int CoCFunction(UBYTE *s) { return(CoFunction(s,0,0)); } int CoNTensor(UBYTE *s) { return(CoFunction(s,1,2)); } int CoCTensor(UBYTE *s) { return(CoFunction(s,0,2)); } /* #] CoFunction + ...: #[ DoTable : Syntax: Table [check] [strict|relax] [zerofill] name(:1:2,...,regular arguments); name must be the name of a regular function. the table indices must be the first arguments. The parenthesis indicates 'name' as opposed to the options. We leave behind: a struct tabl in the FUNCTION struct Regular table: an array tablepointers for the pointers to elements of rhs in the compiler struct cbuf[T->bufnum] an array MINMAX T->mm with the minima and maxima a prototype array an offset in the compiler buffer for the pattern to be matched Sparse table: Just the number of dimensions We will keep track of the number of defined elements in totind and in tablepointers we will have numind+1 positions for each element. The first numind elements for the indices and the last one for the element in cbuf[T->bufnum].rhs If the number of dimensions is *, there is not a fixed number of dimensions. Just a maximum. In that case the first index should be the number of other dimensions. This first index does not count in . Complication: to preserve speed we need a prototype and a pattern for each thread when we use WITHPTHREADS. This is because we write into those when looking for the pattern. */ static int nwarntab = 1; int DoTable(UBYTE *s, int par) { GETIDENTITY UBYTE *name, *p, *inp, c; int i, j, k, sparseflag = 0, rflag = 0, checkflag = 0; int error = 0, ret, oldcbufnum, oldEside; WORD funnum, type, *OldWork, *w, *ww, *t, *tt, *flags1, oldnumrhs,oldnumlhs; LONG oldcpointer; MINMAX *mm, *mm1; LONG x, y; TABLES T; CBUF *C; while ( *s == ',' ) s++; do { name = s; if ( ( s = SkipAName(s) ) == 0 ) { IllForm: MesPrint("&Illegal name or option in table declaration"); return(1); } c = *s; *s = 0; if ( TestName(name) ) { *s = c; goto IllForm; } *s = c; if ( *s == '(' ) break; if ( *s != ',' ) { MesPrint("&Illegal definition of table"); return(1); } *s = 0; /* Secondary options */ if ( StrICmp(name,(UBYTE *)("check" )) == 0 ) checkflag = 1; else if ( StrICmp(name,(UBYTE *)("zero" )) == 0 ) checkflag = 2; else if ( StrICmp(name,(UBYTE *)("one" )) == 0 ) checkflag = 3; else if ( StrICmp(name,(UBYTE *)("strict")) == 0 ) rflag = 1; else if ( StrICmp(name,(UBYTE *)("relax" )) == 0 ) rflag = -1; else if ( StrICmp(name,(UBYTE *)("zerofill" )) == 0 ) { rflag = -2; checkflag = 2; } else if ( StrICmp(name,(UBYTE *)("onefill" )) == 0 ) { rflag = -3; checkflag = 3; } else if ( StrICmp(name,(UBYTE *)("sparse")) == 0 ) sparseflag |= 1; else if ( StrICmp(name,(UBYTE *)("base")) == 0 ) sparseflag |= 3; else if ( StrICmp(name,(UBYTE *)("tablebase")) == 0 ) sparseflag |= 3; else { MesPrint("&Illegal option in table definition: '%s'",name); error = 1; } *s++ = ','; while ( *s == ',' ) s++; } while ( *s ); if ( name == s || *s == 0 ) { MesPrint("&Illegal name or option in table declaration"); return(1); } *s = 0; /* *s could only have been a parenthesis */ if ( sparseflag ) { if ( checkflag == 1 ) rflag = 0; else if ( checkflag == 2 ) rflag = -2; else if ( checkflag == 3 ) rflag = -3; else rflag = -1; } if ( ( ret = GetVar(name,&type,&funnum,CFUNCTION,NOAUTO) ) == NAMENOTFOUND ) { if ( par == 0 ) { funnum = EntVar(CFUNCTION,name,0,1,0,0); } else if ( par == 1 || par == 2 ) { funnum = EntVar(CFUNCTION,name,0,0,0,0); } } else if ( ret <= 0 ) { funnum = EntVar(CFUNCTION,name,0,0,0,0); error = 1; } else { if ( par == 2 ) { if ( nwarntab ) { Warning("Table now declares its (commuting) function."); Warning("Earlier definition in Function statement obsolete. Please remove."); nwarntab = 0; } } else { error = 1; MesPrint("&(N)(C)Tables should not be declared previously"); } } if ( functions[funnum].spec > 0 ) { MesPrint("&Tensors cannot become tables"); return(1); } if ( functions[funnum].symmetric > 0 ) { MesPrint("&Functions with nontrivial symmetrization properties cannot become tables"); return(1); } if ( functions[funnum].tabl ) { MesPrint("&Redefinition of an existing table is not allowed."); return(1); } functions[funnum].tabl = T = (TABLES)Malloc1(sizeof(struct TaBlEs),"table"); /* Next we find the size of the table (if it is not sparse) */ T->defined = T->mdefined = 0; T->sparse = sparseflag; T->mm = 0; T->flags = 0; T->numtree = 0; T->rootnum = 0; T->MaxTreeSize = 0; T->boomlijst = 0; T->strict = rflag; T->bounds = checkflag; T->bufnum = inicbufs(); T->argtail = 0; T->spare = 0; T->bufferssize = 8; T->buffers = (WORD *)Malloc1(sizeof(WORD)*T->bufferssize,"Table buffers"); T->buffersfill = 0; T->buffers[T->buffersfill++] = T->bufnum; T->mode = 0; T->numdummies = 0; mm = T->mm; T->numind = 0; if ( rflag > 0 ) AC.MustTestTable++; T->totind = 0; /* Table hasn't been checked */ p = s; *s = '('; if ( sparseflag ) { /* First copy the tail, just in case we will construct a tablebase Note that we keep the ( to indicate a tail The actual arguments can be found after the comma. Before we have the dimension which the tablebase will need for consistency checking. */ inp = p+1; SKIPBRA3(inp) c = *inp; *inp = 0; T->argtail = strDup1(p,"argtail"); *inp = c; /* Now the regular compilation */ inp = p++; if ( *p == '<' ) { WORD inc = 1; p++; if ( *p == '=' ) { inc++; p++; } /* We will use one extra number for telling how many there really are. */ x = 0; while ( *p <= '9' && *p >= '0' ) x = 10*x + (*p++-'0'); x = -x-inc; if ( x == -1 ) { MesPrint("&Maximum number of dimensions in *-table should be at least one."); error = 1; goto FinishUp2; } } else { ParseNumber(x,p) if ( FG.cTable[p[-1]] != 1 || ( *p != ',' && *p != ')' ) ) { p = inp; MesPrint("&First argument in a sparse table must be a number of dimensions"); error = 1; x = 1; } } T->numind = x; T->mm = (MINMAX *)Malloc1(ABS(x)*sizeof(MINMAX),"table dimensions"); T->flags = (WORD *)Malloc1(ABS(x)*sizeof(WORD),"table flags"); mm = T->mm; inp = p; if ( *inp != ')' ) inp++; T->totind = 0; /* At the moment there are this many */ T->tablepointers = 0; T->reserved = 0; } else { T->numind = 0; T->totind = 1; for(;;) { /* Read the dimensions as far as they can be recognized */ inp = ++p; if ( FG.cTable[*p] != 1 && *p != '+' && *p != '-' ) break; ParseSignedNumber(x,p) if ( FG.cTable[p[-1]] != 1 || *p != ':' ) break; p++; ParseSignedNumber(y,p) if ( FG.cTable[p[-1]] != 1 || ( *p != ',' && *p != ')' ) ) { MesPrint("&Illegal dimension field in table declaration"); return(1); } mm1 = (MINMAX *)Malloc1((T->numind+1)*sizeof(MINMAX),"table dimensions"); flags1 = (WORD *)Malloc1((T->numind+1)*sizeof(WORD),"table flags"); for ( i = 0; i < T->numind; i++ ) { mm1[i] = T->mm[i]; flags1[i] = T->flags[i]; } if ( T->mm ) M_free(T->mm,"table dimensions"); if ( T->flags ) M_free(T->flags,"table flags"); T->mm = mm1; T->flags = flags1; mm = T->mm + T->numind; mm->mini = x; mm->maxi = y; T->totind *= mm->maxi-mm->mini+1; T->numind++; if ( *p == ')' ) { inp = p; break; } } w = T->tablepointers = (WORD *)Malloc1(TABLEEXTENSION*sizeof(WORD)*(T->totind),"table pointers"); i = T->totind; for ( i = TABLEEXTENSION*T->totind; i > 0; i-- ) *w++ = -1; /* means: undefined */ for ( i = T->numind-1, x = 1; i >= 0; i-- ) { T->mm[i].size = x; /* Defines increment in this dimension */ x *= T->mm[i].maxi - T->mm[i].mini + 1; } } /* Now we redo the 'function part' and send it to the compiler. The prototype has to be picked up properly. */ AT.WorkPointer++; /* We need one extra word later */ OldWork = AT.WorkPointer; oldcbufnum = AC.cbufnum; AC.cbufnum = T->bufnum; C = cbuf+AC.cbufnum; oldcpointer = C->Pointer - C->Buffer; oldnumlhs = C->numlhs; oldnumrhs = C->numrhs; AddLHS(AC.cbufnum); while ( s >= name ) *--inp = *s--; w = AT.WorkPointer; AC.ProtoType = w; *w++ = SUBEXPRESSION; *w++ = SUBEXPSIZE; *w++ = 0; *w++ = 1; *w++ = AC.cbufnum; FILLSUB(w) AC.WildC = w; AC.NwildC = 0; AT.WorkPointer = w + 4*AM.MaxWildcards; if ( ( ret = CompileAlgebra(inp,LHSIDE,AC.ProtoType) ) < 0 ) { error = 1; goto FinishUp; } if ( AC.NwildC && SortWild(w,AC.NwildC) ) error = 1; w += AC.NwildC; i = w-OldWork; OldWork[1] = i; /* Basically we have to pull this pattern through Generator in case there are functions inside functions, or parentheses. We have to temporarily disable the .tabl to avoid problems with TestSub. Essential: we need to start NewSort twice to avoid the PutOut routines. The ground pattern is sitting in C->numrhs, but it could be that it has subexpressions in it. Hence it has to be worked out as the lhs in id statements (in comexpr.c). */ OldWork[2] = C->numrhs; *w++ = 1; *w++ = 1; *w++ = 3; OldWork[-1] = w-OldWork+1; AT.WorkPointer = w; ww = C->rhs[C->numrhs]; for ( j = 0; j < *ww; j++ ) w[j] = ww[j]; AT.WorkPointer = w+*w; if ( *ww == 0 || ww[*ww] != 0 ) { MesPrint("&Illegal table pattern definition"); AC.lhdollarflag = 0; error = 1; } if ( error ) goto FinishUp; if ( NewSort(BHEAD0) || NewSort(BHEAD0) ) { error = 1; goto FinishUp; } AN.RepPoint = AT.RepCount + 1; AC.lhdollarflag = 0; oldEside = AR.Eside; AR.Eside = LHSIDE; AR.Cnumlhs = C->numlhs; functions[funnum].tabl = 0; if ( Generator(BHEAD w,C->numlhs) ) { functions[funnum].tabl = T; AR.Eside = oldEside; LowerSortLevel(); LowerSortLevel(); goto FinishUp; } functions[funnum].tabl = T; AR.Eside = oldEside; AT.WorkPointer = w; if ( EndSort(BHEAD w,0) < 0 ) { LowerSortLevel(); goto FinishUp; } if ( *w == 0 || *(w+*w) != 0 ) { MesPrint("&Irregular pattern in table definition"); error = 1; goto FinishUp; } LowerSortLevel(); if ( AC.lhdollarflag ) { MesPrint("&Unexpanded dollar variables are not allowed in table definition"); error = 1; goto FinishUp; } AT.WorkPointer = ww = w + *w; if ( ww[-1] != 3 || ww[-2] != 1 || ww[-3] != 1 ) { MesPrint("&Coefficient of pattern in table definition should be 1."); error = 1; goto FinishUp; } AC.DumNum = 0; /* Now we have to allocate space for prototype+pattern In the case of TFORM we need extra pointers, because each worker has its own */ j = *w + ABS(T->numind)*2-3; #ifdef WITHPTHREADS { int n; T->prototypeSize = ((i+j)*sizeof(WORD)+2*sizeof(WORD *)) * AM.totalnumberofthreads; T->prototype = (WORD **)Malloc1(T->prototypeSize,"table prototype"); T->pattern = T->prototype + AM.totalnumberofthreads; t = (WORD *)(T->pattern + AM.totalnumberofthreads); for ( n = 0; n < AM.totalnumberofthreads; n++ ) { T->prototype[n] = t; for ( k = 0; k < i; k++ ) *t++ = OldWork[k]; } T->pattern[0] = t; j--; w++; w[1] += ABS(T->numind)*2; for ( k = 0; k < FUNHEAD; k++ ) *t++ = *w++; j -= FUNHEAD; for ( k = 0; k < ABS(T->numind); k++ ) { *t++ = -SNUMBER; *t++ = 0; j -= 2; } for ( k = 0; k < j; k++ ) *t++ = *w++; if ( sparseflag ) T->pattern[0][1] = t - T->pattern[0]; k = t - T->pattern[0]; for ( n = 1; n < AM.totalnumberofthreads; n++ ) { T->pattern[n] = t; tt = T->pattern[0]; for ( i = 0; i < k; i++ ) *t++ = *tt++; } } #else T->prototypeSize = (i+j)*sizeof(WORD); T->prototype = (WORD *)Malloc1(T->prototypeSize, "table prototype"); T->pattern = T->prototype + i; for ( k = 0; k < i; k++ ) T->prototype[k] = OldWork[k]; t = T->pattern; j--; w++; w[1] += ABS(T->numind)*2; for ( k = 0; k < FUNHEAD; k++ ) *t++ = *w++; j -= FUNHEAD; for ( k = 0; k < ABS(T->numind); k++ ) { *t++ = -SNUMBER; *t++ = 0; j -= 2; } for ( k = 0; k < j; k++ ) *t++ = *w++; if ( sparseflag ) T->pattern[1] = t - T->pattern; #endif /* At this point we can pop the compilerbuffer. */ C->Pointer = C->Buffer + oldcpointer; C->numrhs = oldnumrhs; C->numlhs = oldnumlhs; /* Now check whether wildcards get converted to dollars (for PARALLEL) We give a warning! */ #ifdef WITHPTHREADS t = T->prototype[0]; #else t = T->prototype; #endif tt = t + t[1]; t += SUBEXPSIZE; while ( t < tt ) { if ( *t == LOADDOLLAR ) { Warning("The use of $-variable assignments in tables disables parallel\ execution for the whole program."); AM.hparallelflag |= NOPARALLEL_TBLDOLLAR; AC.mparallelflag |= NOPARALLEL_TBLDOLLAR; AddPotModdollar(t[2]); } t += t[1]; } FinishUp:; AT.WorkPointer = OldWork - 1; AC.cbufnum = oldcbufnum; FinishUp2:; if ( T->sparse ) ClearTableTree(T); if ( ( sparseflag & 2 ) != 0 ) { if ( T->spare == 0 ) { SpareTable(T); } } return(error); } /* #] DoTable : #[ CoTable : */ int CoTable(UBYTE *s) { return(DoTable(s,2)); } /* #] CoTable : #[ CoNTable : */ int CoNTable(UBYTE *s) { return(DoTable(s,0)); } /* #] CoNTable : #[ CoCTable : */ int CoCTable(UBYTE *s) { return(DoTable(s,1)); } /* #] CoCTable : #[ EmptyTable : */ void EmptyTable(TABLES T) { int j; if ( T->sparse ) ClearTableTree(T); if ( T->boomlijst ) M_free(T->boomlijst,"TableTree"); T->boomlijst = 0; for (j = 0; j < T->buffersfill; j++ ) { /* was <= */ finishcbuf(T->buffers[j]); } if ( T->buffers ) M_free(T->buffers,"Table buffers"); finishcbuf(T->bufnum); T->bufnum = inicbufs(); T->bufferssize = 8; T->buffers = (WORD *)Malloc1(sizeof(WORD)*T->bufferssize,"Table buffers"); T->buffersfill = 0; T->buffers[T->buffersfill++] = T->bufnum; T->defined = T->mdefined = 0; T->flags = 0; T->numtree = 0; T->rootnum = 0; T->MaxTreeSize = 0; T->spare = 0; T->reserved = 0; if ( T->spare ) { TABLES TT = T->spare; if ( TT->mm ) M_free(TT->mm,"tableminmax"); if ( TT->flags ) M_free(TT->flags,"tableflags"); if ( TT->tablepointers ) M_free(TT->tablepointers,"tablepointers"); for (j = 0; j < TT->buffersfill; j++ ) { finishcbuf(TT->buffers[j]); } if ( TT->boomlijst ) M_free(TT->boomlijst,"TableTree"); if ( TT->buffers ) M_free(TT->buffers,"Table buffers"); M_free(TT,"table"); SpareTable(T); } else { WORD *w = T->tablepointers; j = T->totind; for ( j = TABLEEXTENSION*T->totind; j > 0; j-- ) *w++ = -1; /* means: undefined */ } } /* #] EmptyTable : #[ AddSet : */ int AddSet(UBYTE *name, WORD dim) { int nodenum, numset = AC.SetList.num; SETS set = (SETS)FromVarList(&AC.SetList); UBYTE *s; if ( name ) { set->name = AddName(AC.varnames,name,CSET,numset,&nodenum); s = name; while ( *s ) s++; set->namesize = (s-name)+1; set->node = nodenum; } else { set->name = 0; set->namesize = 0; set->node = -1; } set->first = set->last = AC.SetElementList.num; /* set has no elements yet */ set->type = -1; /* undefined as of yet */ set->dimension = dim; set->flags = 0; return(numset); } /* #] AddSet : #[ DoElements : Remark (25-mar-2011): If the dimension has been set (dim != MAXPOSITIVE) we want to test dimensions. Numbers count as dimension zero? */ int DoElements(UBYTE *s, SETS set, UBYTE *name) { int type, error = 0, x, sgn, i; WORD numset, *e; UBYTE c, *cname; while ( *s ) { if ( *s == ',' ) { s++; continue; } sgn = 0; while ( *s == '-' || *s == '+' ) { if ( *s == '-' ) sgn ^= 1; s++; } cname = s; if ( FG.cTable[*s] == 0 || *s == '_' || *s == '[' ) { if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Illegal name in set definition"); return(1); } c = *s; *s = 0; if ( ( ( type = GetName(AC.exprnames,cname,&numset,NOAUTO) ) == NAMENOTFOUND ) && ( ( type = GetOName(AC.varnames,cname,&numset,WITHAUTO) ) == NAMENOTFOUND ) ) { DUBIOUSV dv; int nodenum; MesPrint("&%s has not been declared",cname); /* We enter a 'dubious' declaration to cut down on errors */ numset = AC.DubiousList.num; dv = (DUBIOUSV)FromVarList(&AC.DubiousList); dv->name = AddName(AC.varnames,cname,CDUBIOUS,numset,&nodenum); dv->node = nodenum; set->type = type = CDUBIOUS; set->dimension = 0; error = 1; } if ( set->type == -1 ) { if ( type == CSYMBOL ) { for ( i = set->first; i < set->last; i++ ) { SetElements[i] += 2*MAXPOWER; } } set->type = type; } if ( set->type != type && set->type != CDUBIOUS && type != CDUBIOUS ) { if ( set->type != CNUMBER || ( type != CSYMBOL && type != CINDEX ) ) { MesPrint( "&%s has not the same type as the other members of the set" ,cname); error = 1; set->type = CDUBIOUS; } else { if ( type == CSYMBOL ) { for ( i = set->first; i < set->last; i++ ) { SetElements[i] += 2*MAXPOWER; } } set->type = type; } } if ( set->dimension != MAXPOSITIVE ) { /* Dimension check */ switch ( set->type ) { case CSYMBOL: if ( symbols[numset].dimension != set->dimension ) { MesPrint("&Dimension check failed in set %s, symbol %s", VARNAME(Sets,(set-Sets)), VARNAME(symbols,numset)); error = 1; set->dimension = MAXPOSITIVE; } break; case CVECTOR: if ( vectors[numset-AM.OffsetVector].dimension != set->dimension ) { MesPrint("&Dimension check failed in set %s, vector %s", VARNAME(Sets,(set-Sets)), VARNAME(vectors,(numset-AM.OffsetVector))); error = 1; set->dimension = MAXPOSITIVE; } break; case CFUNCTION: if ( functions[numset-FUNCTION].dimension != set->dimension ) { MesPrint("&Dimension check failed in set %s, function %s", VARNAME(Sets,(set-Sets)), VARNAME(functions,(numset-FUNCTION))); error = 1; } break; set->dimension = MAXPOSITIVE; } } if ( sgn ) { if ( type != CVECTOR ) { MesPrint("&Illegal use of - sign in set. Can use only with vector or number"); error = 1; } /* numset = AM.OffsetVector - numset; numset |= SPECMASK; numset = AM.OffsetVector - numset; */ numset -= WILDMASK; } *s = c; if ( name == 0 && *s == '?' ) { s++; switch ( set->type ) { case CSYMBOL: numset = -numset; break; case CVECTOR: numset += WILDOFFSET; break; case CINDEX: numset |= WILDMASK; break; case CFUNCTION: numset |= WILDMASK; break; } AC.wildflag = 1; } /* Now add the element to the set. */ e = (WORD *)FromVarList(&AC.SetElementList); *e = numset; (set->last)++; } else if ( FG.cTable[*s] == 1 ) { ParseNumber(x,s) if ( sgn ) x = -x; if ( x >= MAXPOWER || x <= -MAXPOWER || ( set->type == CINDEX && ( x < 0 || x >= AM.OffsetIndex ) ) ) { MesPrint("&Illegal value for set element: %d",x); if ( AC.firstconstindex ) { MesPrint("&0 <= Fixed indices < ConstIndex(which is %d)", AM.OffsetIndex-1); MesPrint("&For setting ConstIndex, read the chapter on the setup file"); AC.firstconstindex = 0; } error = 1; x = 0; } /* Check what is allowed with the type. */ if ( set->type == -1 ) { if ( x < 0 || x >= AM.OffsetIndex ) { for ( i = set->first; i < set->last; i++ ) { SetElements[i] += 2*MAXPOWER; } set->type = CSYMBOL; } else set->type = CNUMBER; } else if ( set->type == CDUBIOUS ) {} else if ( set->type == CNUMBER && x < 0 ) { for ( i = set->first; i < set->last; i++ ) { SetElements[i] += 2*MAXPOWER; } set->type = CSYMBOL; } else if ( set->type != CSYMBOL && ( x < 0 || ( set->type != CINDEX && set->type != CNUMBER ) ) ) { MesPrint("&Illegal mixture of element types in set"); error = 1; set->type = CDUBIOUS; } /* Allocate an element */ e = (WORD *)FromVarList(&AC.SetElementList); (set->last)++; if ( set->type == CSYMBOL ) *e = x + 2*MAXPOWER; /* else if ( set->type == CINDEX ) *e = x; */ else *e = x; } else { MesPrint("&Illegal object in list of set elements"); return(1); } } if ( error == 0 && ( ( set->flags & ORDEREDSET ) == ORDEREDSET ) ) { /* The set->last-set->first list of numbers must be sorted. Because we plan here potentially thousands of elements we use a simple version of splitmerge. In ordered sets we can search later with a binary search. */ SimpleSplitMerge(SetElements+set->first,set->last-set->first); } return(error); } /* #] DoElements : #[ CoSet : Set declarations. */ int CoSet(UBYTE *s) { int type, error = 0, ordered = 0; UBYTE *name = s, c, *ss; SETS set; WORD numberofset, dim = MAXPOSITIVE; #ifdef WITHFLOAT /*----------------------------------------------------------------*/ { WORD numeq = 0; LONG x; ss = s; while ( *ss && *ss != ':' ) { if ( *ss == '=' ) numeq++; ss++; } if ( *ss == 0 && numeq == 1 ) { /* We have the Set var = value; variety */ while ( FG.cTable[*s] == 0 ) s++; ss = s; c = *s; *s = 0; if ( c != '=' ) { Proper: MesPrint("&Proper syntax for value-set is `Set name = value'"); return(1); } x = 0; s++; while ( *s >= '0' && *s <= '9' ) x = 10*x + (*s++-'0'); if ( *s ) goto Proper; if ( StrICmp(name,(UBYTE *)"maxweight") == 0 ) { AC.tMaxWeight = x; /* Temporary. Made permanent later */ } else if ( StrICmp(name,(UBYTE *)"defaultprecision") == 0 ) { AC.tDefaultPrecision = x; /* Temporary. Made permanent later */ } else { MesPrint("&Illegal subkey in value set: %s",name); return(1); } } } /*----------------------------------------------------------------*/ #endif if ( ( s = SkipAName(s) ) == 0 ) { IllForm:MesPrint("&Illegal name for set"); return(1); } c = *s; *s = 0; if ( TestName(name) ) goto IllForm; if ( ( ( type = GetName(AC.exprnames,name,&numberofset,NOAUTO) ) != NAMENOTFOUND ) || ( ( type = GetName(AC.varnames,name,&numberofset,NOAUTO) ) != NAMENOTFOUND ) ) { if ( type != CSET ) NameConflict(type,name); else { MesPrint("&There is already a set with the name %s",name); } return(1); } if ( c == 0 ) { numberofset = AddSet(name,0); set = Sets + numberofset; return(0); /* empty set */ } *s = c; ss = s; /* ss marks the end of the name */ if ( *s == '(' ) { UBYTE *sss, cc; s++; sss = s; /* Beginning of option */ while ( *s != ',' && *s != ')' && *s ) s++; cc = *s; *s = 0; if ( StrICont(sss,(UBYTE *)"ordered") == 0 ) { ordered = ORDEREDSET; } else { MesPrint("&Error: Illegal option in set definition: %s",sss); error = 1; } *s = cc; if ( *s != ')' ) { MesPrint("&Error: Currently only one option allowed in set definition."); error = 1; while ( *s && *s != ')' ) s++; } s++; } if ( *s == '{' ) { s++; if ( ( *s == 'd' || *s == 'D' ) && s[1] == '=' ) { s += 2; if ( *s == '-' || *s == '+' || FG.cTable[*s] == 1 ) { ParseSignedNumber(dim,s) if ( dim < -HALFMAX || dim > HALFMAX ) { MesPrint("&Warning: dimension of %s (%d) out of range" ,name,dim); } } if ( *s != '}' ) goto IllDim; else s++; } else { IllDim: MesPrint("&Error: Illegal dimension field for set %s",name); error = 1; s = SkipField(s,0); } while ( *s == ',' ) s++; } c = *ss; *ss = 0; numberofset = AddSet(name,dim); *ss = c; set = Sets + numberofset; set->flags |= ordered; if ( *s != ':' ) { MesPrint("&Proper syntax is `Set name:elements'"); return(1); } s++; error = DoElements(s,set,name); AC.SetList.numtemp = AC.SetList.num; AC.SetElementList.numtemp = AC.SetElementList.num; return(error); } /* #] CoSet : #[ DoTempSet : Gets a {} set definition and returns a set number if the set is properly structured. This number refers either to an already existing set, or to a set that is defined here. From and to refer to the contents. They exclude the {}. */ int DoTempSet(UBYTE *from, UBYTE *to) { int i, num, j, sgn; WORD *e, *ep; UBYTE c; int setnum = AddSet(0,MAXPOSITIVE); SETS set = Sets + setnum, setp; set->name = -1; set->type = -1; c = *to; *to = 0; AC.wildflag = 0; while ( *from == ',' ) from++; if ( *from == '<' || *from == '>' ) { set->type = CRANGE; set->first = 3*MAXPOWER; set->last = -3*MAXPOWER; while ( *from == '<' || *from == '>' ) { if ( *from == '<' ) { j = 1; from++; if ( *from == '=' ) { from++; j++; } } else { j = -1; from++; if ( *from == '=' ) { from++; j--; } } sgn = 1; while ( *from == '-' || *from == '+' ) { if ( *from == '-' ) sgn = -sgn; from++; } ParseNumber(num,from) if ( *from && *from != ',' ) { MesPrint("&Illegal number in ranged set definition"); return(-1); } if ( sgn < 0 ) num = -num; if ( num >= MAXPOWER || num <= -MAXPOWER ) { Warning("Value in ranged set too big. Adjusted to infinity."); if ( num > 0 ) num = 3*MAXPOWER; else num = -3*MAXPOWER; } else if ( j == 2 ) num += 2*MAXPOWER; else if ( j == -2 ) num -= 2*MAXPOWER; if ( j > 0 ) set->first = num; else set->last = num; while ( *from == ',' ) from++; } if ( *from ) { MesPrint("&Definition of ranged set contains illegal objects"); return(-1); } } else if ( DoElements(from,set,(UBYTE *)0) != 0 ) { AC.SetElementList.num = set->first; AC.SetList.num--; *to = c; return(-1); } *to = c; /* Now we have to test whether this set exists already. */ num = set->last - set->first; for ( setp = Sets, i = 0; i < AC.SetList.num-1; i++, setp++ ) { if ( num != setp->last - setp->first ) continue; if ( set->type != setp->type ) continue; if ( set->type == CRANGE ) { if ( set->first == setp->first ) return(setp-Sets); } else { e = SetElements + set->first; ep = SetElements + setp->first; j = num; while ( --j >= 0 ) if ( *e++ != *ep++ ) break; if ( j < 0 ) { AC.SetElementList.num = set->first; AC.SetList.num--; return(setp - Sets); } } } return(setnum); } /* #] DoTempSet : #[ CoAuto : To prepare first: Use of the proper pointers in the various declaration routines Proper action in .store and .clear */ int CoAuto(UBYTE *inp) { int retval; AC.Symbols = &(AC.AutoSymbolList); AC.Vectors = &(AC.AutoVectorList); AC.Indices = &(AC.AutoIndexList); AC.Functions = &(AC.AutoFunctionList); AC.activenames = &(AC.autonames); AC.AutoDeclareFlag = WITHAUTO; while ( *inp == ',' ) inp++; retval = CompileStatement(inp); AC.AutoDeclareFlag = 0; AC.Symbols = &(AC.SymbolList); AC.Vectors = &(AC.VectorList); AC.Indices = &(AC.IndexList); AC.Functions = &(AC.FunctionList); AC.activenames = &(AC.varnames); return(retval); } /* #] CoAuto : #[ AddDollar : The actual addition. Special routine for additions 'on the fly' */ int AddDollar(UBYTE *name, WORD type, WORD *start, LONG size) { int nodenum, numdollar = AP.DollarList.num; WORD *s, *t; DOLLARS dol = (DOLLARS)FromVarList(&AP.DollarList); dol->name = AddName(AC.dollarnames,name,CDOLLAR,numdollar,&nodenum); dol->type = type; dol->node = nodenum; dol->zero = 0; dol->numdummies = 0; #ifdef WITHPTHREADS INIRECLOCK(dol->pthreadslock); #endif dol->nfactors = 0; dol->factors = 0; AddRHS(AM.dbufnum,1); AddLHS(AM.dbufnum); if ( start && size > 0 ) { dol->size = size; dol->where = s = (WORD *)Malloc1((size+1)*sizeof(WORD),"$-variable contents"); t = start; while ( --size >= 0 ) *s++ = *t++; *s = 0; } else { dol->where = &(AM.dollarzero); dol->size = 0; } cbuf[AM.dbufnum].rhs[numdollar] = dol->where; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; return(numdollar); } /* #] AddDollar : #[ ReplaceDollar : Replacements of dollar variables can happen at any time. For debugging purposes we should have a tracing facility. Not in use???? */ int ReplaceDollar(WORD number, WORD newtype, WORD *newstart, LONG newsize) { int error = 0; DOLLARS dol = Dollars + number; WORD *s, *t; LONG i; dol->type = newtype; if ( dol->size == newsize && newsize > 0 && newstart ) { s = dol->where; t = newstart; i = newsize; while ( --i >= 0 ) { if ( *s++ != *t++ ) break; } if ( i < 0 ) return(0); } if ( dol->where && dol->where != &(dol->zero) ) { M_free(dol->where,"dollar->where"); dol->where = &(dol->zero); dol->size = 0; } if ( newstart && newsize > 0 ) { dol->size = newsize; dol->where = s = (WORD *)Malloc1((newsize+1)*sizeof(WORD),"$-variable contents"); t = newstart; i = newsize; while ( --i >= 0 ) *s++ = *t++; *s = 0; } return(error); } /* #] ReplaceDollar : #[ AddDubious : This adds a variable of which we do not know the proper type. */ int AddDubious(UBYTE *name) { int nodenum, numdubious = AC.DubiousList.num; DUBIOUSV dub = (DUBIOUSV)FromVarList(&AC.DubiousList); dub->name = AddName(AC.varnames,name,CDUBIOUS,numdubious,&nodenum); dub->node = nodenum; return(numdubious); } /* #] AddDubious : #[ MakeDubious : */ int MakeDubious(NAMETREE *nametree, UBYTE *name, WORD *number) { NAMENODE *n; int node, newnode, i; if ( nametree->namenode == 0 ) return(-1); newnode = nametree->headnode; do { node = newnode; n = nametree->namenode+node; if ( ( i = StrCmp(name,nametree->namebuffer+n->name) ) < 0 ) newnode = n->left; else if ( i > 0 ) newnode = n->right; else { if ( n->type != CDUBIOUS ) { int numdubious = AC.DubiousList.num; FUNCTIONS dub = (FUNCTIONS)FromVarList(&AC.DubiousList); dub->name = n->name; n->number = numdubious; } *number = n->number; return(CDUBIOUS); } } while ( newnode >= 0 ); return(-1); } /* #] MakeDubious : #[ NameConflict : */ static char *nametype[] = { "symbol", "index", "vector", "function", "set", "expression" }; static char *plural[] = { "","n","","","","n" }; int NameConflict(int type, UBYTE *name) { if ( type == NAMENOTFOUND ) { MesPrint("&%s has not been declared",name); } else if ( type != CDUBIOUS ) MesPrint("&%s has been declared as a%s %s already" ,name,plural[type],nametype[type]); return(1); } /* #] NameConflict : #[ AddExpression : */ int AddExpression(UBYTE *name, int x, int y) { int nodenum, numexpr = AC.ExpressionList.num; EXPRESSIONS expr = (EXPRESSIONS)FromVarList(&AC.ExpressionList); UBYTE *s; expr->status = x; expr->printflag = y; PUTZERO(expr->onfile); PUTZERO(expr->size); expr->renum = 0; expr->renumlists = 0; expr->hidelevel = 0; expr->inmem = 0; expr->bracketinfo = expr->newbracketinfo = 0; if ( name ) { expr->name = AddName(AC.exprnames,name,CEXPRESSION,numexpr,&nodenum); expr->node = nodenum; expr->replace = NEWLYDEFINEDEXPRESSION ; s = name; while ( *s ) s++; expr->namesize = (s-name)+1; } else { expr->replace = REDEFINEDEXPRESSION; expr->name = AC.TransEname; expr->node = -1; expr->namesize = 0; } expr->vflags = 0; expr->numdummies = 0; expr->numfactors = 0; #ifdef PARALLELCODE expr->partodo = 0; #endif expr->uflags = 0; return(numexpr); } /* #] AddExpression : #[ GetLabel : */ int GetLabel(UBYTE *name) { int i; LONG newnum; UBYTE **NewLabelNames; int *NewLabel; for ( i = 0; i < AC.NumLabels; i++ ) { if ( StrCmp(name,AC.LabelNames[i]) == 0 ) return(i); } if ( AC.NumLabels >= AC.MaxLabels ) { newnum = 2*AC.MaxLabels; if ( newnum == 0 ) newnum = 10; if ( newnum > 32765 ) newnum = 32765; if ( newnum == AC.MaxLabels ) { MesPrint("&More than 32765 labels in one module. Please simplify."); Terminate(-1); } NewLabelNames = (UBYTE **)Malloc1((sizeof(UBYTE *)+sizeof(int)) *newnum,"Labels"); NewLabel = (int *)(NewLabelNames+newnum); for ( i = 0; i< AC.MaxLabels; i++ ) { NewLabelNames[i] = AC.LabelNames[i]; NewLabel[i] = AC.Labels[i]; } if ( AC.LabelNames ) M_free(AC.LabelNames,"Labels"); AC.LabelNames = NewLabelNames; AC.Labels = NewLabel; AC.MaxLabels = newnum; } i = AC.NumLabels++; AC.LabelNames[i] = strDup1(name,"Labels"); AC.Labels[i] = -1; return(i); } /* #] GetLabel : #[ ResetVariables : Resets the variables. par = 0 The list of temporary sets (after each .sort) par = 1 The list of local variables (after each .store) par = 2 All variables (after each .clear) */ void ResetVariables(int par) { int i, j; TABLES T; switch ( par ) { case 0 : /* Only the sets without a name */ AC.SetList.num = AC.SetList.numtemp; AC.SetElementList.num = AC.SetElementList.numtemp; break; case 2 : for ( i = AC.SymbolList.numclear; i < AC.SymbolList.num; i++ ) AC.varnames->namenode[symbols[i].node].type = CDELETE; AC.SymbolList.num = AC.SymbolList.numglobal = AC.SymbolList.numclear; for ( i = AC.VectorList.numclear; i < AC.VectorList.num; i++ ) AC.varnames->namenode[vectors[i].node].type = CDELETE; AC.VectorList.num = AC.VectorList.numglobal = AC.VectorList.numclear; for ( i = AC.IndexList.numclear; i < AC.IndexList.num; i++ ) AC.varnames->namenode[indices[i].node].type = CDELETE; AC.IndexList.num = AC.IndexList.numglobal = AC.IndexList.numclear; for ( i = AC.FunctionList.numclear; i < AC.FunctionList.num; i++ ) { AC.varnames->namenode[functions[i].node].type = CDELETE; if ( ( T = functions[i].tabl ) != 0 ) { if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); if ( T->prototype ) M_free(T->prototype,"tableprototype"); if ( T->mm ) M_free(T->mm,"tableminmax"); if ( T->flags ) M_free(T->flags,"tableflags"); if ( T->argtail ) M_free(T->argtail,"table arguments"); if ( T->boomlijst ) M_free(T->boomlijst,"TableTree"); for (j = 0; j < T->buffersfill; j++ ) { /* was <= */ finishcbuf(T->buffers[j]); } /*[07apr2004 mt]:*/ /*memory leak*/ if ( T->buffers ) M_free(T->buffers,"Table buffers"); /*:[07apr2004 mt]*/ finishcbuf(T->bufnum); if ( T->spare ) { TABLES TT = T->spare; if ( TT->mm ) M_free(TT->mm,"tableminmax"); if ( TT->flags ) M_free(TT->flags,"tableflags"); if ( TT->tablepointers ) M_free(TT->tablepointers,"tablepointers"); for (j = 0; j < TT->buffersfill; j++ ) { /* was <= */ finishcbuf(TT->buffers[j]); } if ( TT->boomlijst ) M_free(TT->boomlijst,"TableTree"); /*[07apr2004 mt]:*/ /*memory leak*/ if ( TT->buffers )M_free(TT->buffers,"Table buffers"); /*:[07apr2004 mt]*/ M_free(TT,"table"); } M_free(T,"table"); } } AC.FunctionList.num = AC.FunctionList.numglobal = AC.FunctionList.numclear; for ( i = AC.SetList.numclear; i < AC.SetList.num; i++ ) { if ( Sets[i].node >= 0 ) AC.varnames->namenode[Sets[i].node].type = CDELETE; } AC.SetList.numtemp = AC.SetList.num = AC.SetList.numglobal = AC.SetList.numclear; for ( i = AC.DubiousList.numclear; i < AC.DubiousList.num; i++ ) AC.varnames->namenode[Dubious[i].node].type = CDELETE; AC.DubiousList.num = AC.DubiousList.numglobal = AC.DubiousList.numclear; AC.SetElementList.numtemp = AC.SetElementList.num = AC.SetElementList.numglobal = AC.SetElementList.numclear; CompactifyTree(AC.varnames,VARNAMES); AC.varnames->namefill = AC.varnames->globalnamefill = AC.varnames->clearnamefill; AC.varnames->nodefill = AC.varnames->globalnodefill = AC.varnames->clearnodefill; for ( i = AC.AutoSymbolList.numclear; i < AC.AutoSymbolList.num; i++ ) AC.autonames->namenode[ ((SYMBOLS)(AC.AutoSymbolList.lijst))[i].node].type = CDELETE; AC.AutoSymbolList.num = AC.AutoSymbolList.numglobal = AC.AutoSymbolList.numclear; for ( i = AC.AutoVectorList.numclear; i < AC.AutoVectorList.num; i++ ) AC.autonames->namenode[ ((VECTORS)(AC.AutoVectorList.lijst))[i].node].type = CDELETE; AC.AutoVectorList.num = AC.AutoVectorList.numglobal = AC.AutoVectorList.numclear; for ( i = AC.AutoIndexList.numclear; i < AC.AutoIndexList.num; i++ ) AC.autonames->namenode[ ((INDICES)(AC.AutoIndexList.lijst))[i].node].type = CDELETE; AC.AutoIndexList.num = AC.AutoIndexList.numglobal = AC.AutoIndexList.numclear; for ( i = AC.AutoFunctionList.numclear; i < AC.AutoFunctionList.num; i++ ) { AC.autonames->namenode[ ((FUNCTIONS)(AC.AutoFunctionList.lijst))[i].node].type = CDELETE; if ( ( T = ((FUNCTIONS)(AC.AutoFunctionList.lijst))[i].tabl ) != 0 ) { if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); if ( T->prototype ) M_free(T->prototype,"tableprototype"); if ( T->mm ) M_free(T->mm,"tableminmax"); if ( T->flags ) M_free(T->flags,"tableflags"); if ( T->argtail ) M_free(T->argtail,"table arguments"); if ( T->boomlijst ) M_free(T->boomlijst,"TableTree"); for (j = 0; j < T->buffersfill; j++ ) { /* was <= */ finishcbuf(T->buffers[j]); } if ( T->spare ) { TABLES TT = T->spare; if ( TT->mm ) M_free(TT->mm,"tableminmax"); if ( TT->flags ) M_free(TT->flags,"tableflags"); if ( TT->tablepointers ) M_free(TT->tablepointers,"tablepointers"); for (j = 0; j < TT->buffersfill; j++ ) { /* was <= */ finishcbuf(TT->buffers[j]); } if ( TT->boomlijst ) M_free(TT->boomlijst,"TableTree"); M_free(TT,"table"); } M_free(T,"table"); } } AC.AutoFunctionList.num = AC.AutoFunctionList.numglobal = AC.AutoFunctionList.numclear; CompactifyTree(AC.autonames,AUTONAMES); AC.autonames->namefill = AC.autonames->globalnamefill = AC.autonames->clearnamefill; AC.autonames->nodefill = AC.autonames->globalnodefill = AC.autonames->clearnodefill; ReleaseTB(); break; case 1 : for ( i = AC.SymbolList.numglobal; i < AC.SymbolList.num; i++ ) AC.varnames->namenode[symbols[i].node].type = CDELETE; AC.SymbolList.num = AC.SymbolList.numglobal; for ( i = AC.VectorList.numglobal; i < AC.VectorList.num; i++ ) AC.varnames->namenode[vectors[i].node].type = CDELETE; AC.VectorList.num = AC.VectorList.numglobal; for ( i = AC.IndexList.numglobal; i < AC.IndexList.num; i++ ) AC.varnames->namenode[indices[i].node].type = CDELETE; AC.IndexList.num = AC.IndexList.numglobal; for ( i = AC.FunctionList.numglobal; i < AC.FunctionList.num; i++ ) { AC.varnames->namenode[functions[i].node].type = CDELETE; if ( ( T = functions[i].tabl ) != 0 ) { if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); if ( T->prototype ) M_free(T->prototype,"tableprototype"); if ( T->mm ) M_free(T->mm,"tableminmax"); if ( T->flags ) M_free(T->flags,"tableflags"); if ( T->argtail ) M_free(T->argtail,"table arguments"); if ( T->boomlijst ) M_free(T->boomlijst,"TableTree"); for (j = 0; j < T->buffersfill; j++ ) { /* was <= */ finishcbuf(T->buffers[j]); } /*[07apr2004 mt]:*/ /*memory leak*/ if ( T->buffers ) M_free(T->buffers,"Table buffers"); /*:[07apr2004 mt]*/ finishcbuf(T->bufnum); if ( T->spare ) { TABLES TT = T->spare; if ( TT->mm ) M_free(TT->mm,"tableminmax"); if ( TT->flags ) M_free(TT->flags,"tableflags"); if ( TT->tablepointers ) M_free(TT->tablepointers,"tablepointers"); for (j = 0; j < TT->buffersfill; j++ ) { /* was <= */ finishcbuf(TT->buffers[j]); } if ( TT->boomlijst ) M_free(TT->boomlijst,"TableTree"); /*[07apr2004 mt]:*/ /*memory leak*/ if ( TT->buffers ) M_free(TT->buffers,"Table buffers"); /*:[07apr2004 mt]*/ M_free(TT,"table"); } M_free(T,"table"); } } #ifdef TABLECLEANUP { int j; WORD *tp; for ( i = 0; i < AC.FunctionList.numglobal; i++ ) { /* Now, if the table definition is from after the .global while the function is from before, there is a problem. This could be resolved by defining CTable (=Table), Ntable and do away with the previous function definition. */ if ( ( T = functions[i].tabl ) != 0 ) { /* First restore overwritten definitions. */ if ( T->sparse ) { T->totind = T->mdefined; for ( j = 0, tp = T->tablepointers; j < T->totind; j++ ) { tp += ABS(T->numind); #if TABLEEXTENSION == 2 tp[0] = tp[1]; #else tp[0] = tp[2]; tp[1] = tp[3]; tp[4] = tp[5]; #endif tp += TABLEEXTENSION; } RedoTableTree(T,T->totind); if ( T->spare ) { TABLES TT = T->spare; TT->totind = TT->mdefined; for ( j = 0, tp = TT->tablepointers; j < TT->totind; j++ ) { tp += ABS(TT->numind); #if TABLEEXTENSION == 2 tp[0] = tp[1]; #else tp[0] = tp[2]; tp[1] = tp[3]; tp[4] = tp[5]; #endif tp += TABLEEXTENSION; } RedoTableTree(TT,TT->totind); cbuf[TT->bufnum].numlhs = cbuf[TT->bufnum].mnumlhs; cbuf[TT->bufnum].numrhs = cbuf[TT->bufnum].mnumrhs; } } else { for ( j = 0, tp = T->tablepointers; j < T->totind; j++ ) { #if TABLEEXTENSION == 2 tp[0] = tp[1]; #else tp[0] = tp[2]; tp[1] = tp[3]; tp[4] = tp[5]; #endif } T->defined = T->mdefined; } cbuf[T->bufnum].numlhs = cbuf[T->bufnum].mnumlhs; cbuf[T->bufnum].numrhs = cbuf[T->bufnum].mnumrhs; } } } #endif AC.FunctionList.num = AC.FunctionList.numglobal; for ( i = AC.SetList.numglobal; i < AC.SetList.num; i++ ) { if ( Sets[i].node >= 0 ) AC.varnames->namenode[Sets[i].node].type = CDELETE; } AC.SetList.numtemp = AC.SetList.num = AC.SetList.numglobal; for ( i = AC.DubiousList.numglobal; i < AC.DubiousList.num; i++ ) AC.varnames->namenode[Dubious[i].node].type = CDELETE; AC.DubiousList.num = AC.DubiousList.numglobal; AC.SetElementList.numtemp = AC.SetElementList.num = AC.SetElementList.numglobal; CompactifyTree(AC.varnames,VARNAMES); AC.varnames->namefill = AC.varnames->globalnamefill; AC.varnames->nodefill = AC.varnames->globalnodefill; for ( i = AC.AutoSymbolList.numglobal; i < AC.AutoSymbolList.num; i++ ) AC.autonames->namenode[ ((SYMBOLS)(AC.AutoSymbolList.lijst))[i].node].type = CDELETE; AC.AutoSymbolList.num = AC.AutoSymbolList.numglobal; for ( i = AC.AutoVectorList.numglobal; i < AC.AutoVectorList.num; i++ ) AC.autonames->namenode[ ((VECTORS)(AC.AutoVectorList.lijst))[i].node].type = CDELETE; AC.AutoVectorList.num = AC.AutoVectorList.numglobal; for ( i = AC.AutoIndexList.numglobal; i < AC.AutoIndexList.num; i++ ) AC.autonames->namenode[ ((INDICES)(AC.AutoIndexList.lijst))[i].node].type = CDELETE; AC.AutoIndexList.num = AC.AutoIndexList.numglobal; for ( i = AC.AutoFunctionList.numglobal; i < AC.AutoFunctionList.num; i++ ) { AC.autonames->namenode[ ((FUNCTIONS)(AC.AutoFunctionList.lijst))[i].node].type = CDELETE; if ( ( T = ((FUNCTIONS)(AC.AutoFunctionList.lijst))[i].tabl ) != 0 ) { if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); if ( T->prototype ) M_free(T->prototype,"tableprototype"); if ( T->mm ) M_free(T->mm,"tableminmax"); if ( T->flags ) M_free(T->flags,"tableflags"); if ( T->argtail ) M_free(T->argtail,"table arguments"); if ( T->boomlijst ) M_free(T->boomlijst,"TableTree"); for (j = 0; j < T->buffersfill; j++ ) { /* was <= */ finishcbuf(T->buffers[j]); } if ( T->spare ) { TABLES TT = T->spare; if ( TT->mm ) M_free(TT->mm,"tableminmax"); if ( TT->flags ) M_free(TT->flags,"tableflags"); if ( TT->tablepointers ) M_free(TT->tablepointers,"tablepointers"); for (j = 0; j < TT->buffersfill; j++ ) { /* was <= */ finishcbuf(TT->buffers[j]); } if ( TT->boomlijst ) M_free(TT->boomlijst,"TableTree"); M_free(TT,"table"); } M_free(T,"table"); } } AC.AutoFunctionList.num = AC.AutoFunctionList.numglobal; CompactifyTree(AC.autonames,AUTONAMES); AC.autonames->namefill = AC.autonames->globalnamefill; AC.autonames->nodefill = AC.autonames->globalnodefill; break; } } /* #] ResetVariables : #[ RemoveDollars : */ void RemoveDollars(void) { DOLLARS d; CBUF *C = cbuf + AM.dbufnum; int numdollar = AP.DollarList.num; if ( numdollar > 0 ) { while ( numdollar > AM.gcNumDollars ) { numdollar--; d = Dollars + numdollar; if ( d->where && d->where != &(d->zero) && d->where != &(AM.dollarzero) ) { M_free(d->where,"dollar->where"); d->where = &(d->zero); d->size = 0; } AC.dollarnames->namenode[d->node].type = CDELETE; } AP.DollarList.num = AM.gcNumDollars; CompactifyTree(AC.dollarnames,DOLLARNAMES); C->numrhs = C->mnumrhs; C->numlhs = C->mnumlhs; } } /* #] RemoveDollars : #[ Globalize : */ void Globalize(int par) { int i, j; WORD *tp; if ( par == 1 ) { AC.SymbolList.numclear = AC.SymbolList.num; AC.VectorList.numclear = AC.VectorList.num; AC.IndexList.numclear = AC.IndexList.num; AC.FunctionList.numclear = AC.FunctionList.num; AC.SetList.numclear = AC.SetList.num; AC.DubiousList.numclear = AC.DubiousList.num; AC.SetElementList.numclear = AC.SetElementList.num; AC.varnames->clearnamefill = AC.varnames->namefill; AC.varnames->clearnodefill = AC.varnames->nodefill; AC.AutoSymbolList.numclear = AC.AutoSymbolList.num; AC.AutoVectorList.numclear = AC.AutoVectorList.num; AC.AutoIndexList.numclear = AC.AutoIndexList.num; AC.AutoFunctionList.numclear = AC.AutoFunctionList.num; AC.autonames->clearnamefill = AC.autonames->namefill; AC.autonames->clearnodefill = AC.autonames->nodefill; } /* for ( i = AC.FunctionList.numglobal; i < AC.FunctionList.num; i++ ) { */ for ( i = MAXBUILTINFUNCTION-FUNCTION; i < AC.FunctionList.num; i++ ) { /* We need here not only the not-yet-global functions. The already global ones may have obtained extra elements. */ if ( functions[i].tabl ) { TABLES T = functions[i].tabl; if ( T->sparse ) { T->mdefined = T->totind; for ( j = 0, tp = T->tablepointers; j < T->totind; j++ ) { tp += ABS(T->numind); #if TABLEEXTENSION == 2 tp[1] = tp[0]; #else tp[2] = tp[0]; tp[3] = tp[1]; tp[5] = tp[4] & (~ELEMENTUSED); #endif tp += TABLEEXTENSION; } if ( T->spare ) { TABLES TT = T->spare; TT->mdefined = TT->totind; for ( j = 0, tp = TT->tablepointers; j < TT->totind; j++ ) { tp += ABS(TT->numind); #if TABLEEXTENSION == 2 tp[1] = tp[0]; #else tp[2] = tp[0]; tp[3] = tp[1]; tp[5] = tp[4] & (~ELEMENTUSED); #endif tp += TABLEEXTENSION; } cbuf[TT->bufnum].mnumlhs = cbuf[TT->bufnum].numlhs; cbuf[TT->bufnum].mnumrhs = cbuf[TT->bufnum].numrhs; } } else { T->mdefined = T->defined; for ( j = 0, tp = T->tablepointers; j < T->totind; j++ ) { #if TABLEEXTENSION == 2 tp[1] = tp[0]; #else tp[2] = tp[0]; tp[3] = tp[1]; tp[5] = tp[4] & (~ELEMENTUSED); #endif } } cbuf[T->bufnum].mnumlhs = cbuf[T->bufnum].numlhs; cbuf[T->bufnum].mnumrhs = cbuf[T->bufnum].numrhs; } } for ( i = AC.AutoFunctionList.numglobal; i < AC.AutoFunctionList.num; i++ ) { if ( ((FUNCTIONS)(AC.AutoFunctionList.lijst))[i].tabl ) ((FUNCTIONS)(AC.AutoFunctionList.lijst))[i].tabl->mdefined = ((FUNCTIONS)(AC.AutoFunctionList.lijst))[i].tabl->defined; } AC.SymbolList.numglobal = AC.SymbolList.num; AC.VectorList.numglobal = AC.VectorList.num; AC.IndexList.numglobal = AC.IndexList.num; AC.FunctionList.numglobal = AC.FunctionList.num; AC.SetList.numglobal = AC.SetList.num; AC.DubiousList.numglobal = AC.DubiousList.num; AC.SetElementList.numglobal = AC.SetElementList.num; AC.varnames->globalnamefill = AC.varnames->namefill; AC.varnames->globalnodefill = AC.varnames->nodefill; AC.AutoSymbolList.numglobal = AC.AutoSymbolList.num; AC.AutoVectorList.numglobal = AC.AutoVectorList.num; AC.AutoIndexList.numglobal = AC.AutoIndexList.num; AC.AutoFunctionList.numglobal = AC.AutoFunctionList.num; AC.autonames->globalnamefill = AC.autonames->namefill; AC.autonames->globalnodefill = AC.autonames->nodefill; } /* #] Globalize : #[ TestName : */ int TestName(UBYTE *name) { if ( *name == '[' ) { while ( *name ) name++; if ( name[-1] == ']' ) return(0); return(-1); } while ( *name ) { if ( *name == '_' ) return(-1); if ( *name == '$' ) return(-1); name++; } return(0); } /* #] TestName : */ form-5.0.1/sources/optimize.cc0000644000175100017510000041767215217035721012021 /** @file optimize.cc * * experimental routines for the optimization of FORTRAN or C output. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : #[ includes : */ //#define DEBUG //#define DEBUG_MORE //#define DEBUG_MCTS //#define DEBUG_GREEDY #ifdef HAVE_CONFIG_H #ifndef CONFIG_H_INCLUDED #define CONFIG_H_INCLUDED #include #endif #endif #include #include #include #include #include #include #include #include #include #include #ifdef APPLE64 #ifndef HAVE_UNORDERED_MAP #define HAVE_UNORDERED_MAP #endif #ifndef HAVE_UNORDERED_SET #define HAVE_UNORDERED_SET #endif #endif #ifdef HAVE_UNORDERED_MAP #include using std::unordered_map; #elif !defined(HAVE_TR1_UNORDERED_MAP) && defined(HAVE_BOOST_UNORDERED_MAP_HPP) #include using boost::unordered_map; #else #include using std::tr1::unordered_map; #endif #ifdef HAVE_UNORDERED_SET #include using std::unordered_set; #elif !defined(HAVE_TR1_UNORDERED_SET) && defined(HAVE_BOOST_UNORDERED_SET_HPP) #include using boost::unordered_set; #else #include using std::tr1::unordered_set; #endif #if defined(HAVE_BUILTIN_POPCOUNT) static inline int popcount(unsigned int x) { return __builtin_popcount(x); } #elif defined(HAVE_POPCNT) #include static inline int popcount(unsigned int x) { return __popcnt(x); } #else static inline int popcount(unsigned int x) { int count = 0; while (x > 0) { if ((x & 1) == 1) count++; x >>= 1; } return count; } #endif extern "C" { #include "form3.h" } //#ifdef DEBUG #include "mytime.h" //#endif using namespace std; // operators const WORD OPER_ADD = -1; const WORD OPER_MUL = -2; const WORD OPER_COMMA = -3; // class for a node of the MCTS tree class tree_node { public: vector childs; double sum_results; int num_visits; WORD var; bool finished; tree_node (int _var=0): sum_results(0), num_visits(0), var(_var), finished(false) {} tree_node(const tree_node& other): childs(other.childs), sum_results(other.sum_results), num_visits(other.num_visits), var(other.var), finished(other.finished) {} tree_node& operator=(const tree_node& other) { if (this != &other) { childs = other.childs; sum_results = other.sum_results; num_visits = other.num_visits; var = other.var; finished = other.finished; } return *this; } }; // global variables for multithreading WORD *optimize_expr; vector > optimize_best_Horner_schemes; int optimize_num_vars; int optimize_best_num_oper; vector optimize_best_instr; vector optimize_best_vars; // global variables for MCTS bool mcts_factorized, mcts_separated; vector mcts_vars; tree_node mcts_root; int mcts_expr_score; set > > mcts_best_schemes; #ifdef WITHPTHREADS pthread_mutex_t optimize_lock; #endif /* #] includes : #[ print_instr : */ void print_instr (const vector &instr, WORD num) { const WORD *tbegin = &*instr.begin(); const WORD *tend = tbegin+instr.size(); for (const WORD *t=tbegin; t!=tend; t+=*(t+2)) { MesPrint("<%d> %a",num,t[2],t); } } /* #] print_instr : #[ my_random_shuffle : */ /** Random shuffle * * Description * =========== * Randomly permutes elements in the range [fr,to). Functionality is * the same as C++'s "random_shuffle", but it uses Form's "wranf". */ template void my_random_shuffle (PHEAD RandomAccessIterator fr, RandomAccessIterator to) { for (int i=to-fr-1; i>0; --i) swap (fr[i],fr[wranf(BHEAD0) % (i+1)]); } /* #] my_random_shuffle : #[ get_expression : */ static WORD comlist[3] = {TYPETOPOLYNOMIAL,3,DOALL}; /** Get expression * * Description * =========== * Reads an expression from the input file into a buffer (called * optimize_expr). This buffer is used during the optimization * process. Non-symbols are removed by ConvertToPoly and are put in * temporary symbols. * * The return value is the length of the expression in WORDs, or a * negative number if it failed. */ LONG get_expression (int exprnr) { GETIDENTITY; AR.NoCompress = 1; NewSort(BHEAD0); EXPRESSIONS e = Expressions+exprnr; SetScratch(AR.infile,&(e->onfile)); // get header term WORD *term = AT.WorkPointer; GetTerm(BHEAD term); NewSort(BHEAD0); // get terms while (GetTerm(BHEAD term) > 0) { AT.WorkPointer = term + *term; WORD *t1 = term; WORD *t2 = term + *term; if (ConvertToPoly(BHEAD t1,t2,comlist,1) < 0) return -1; int n = *t2; NCOPY(t1,t2,n); AT.WorkPointer = term + *term; if (StoreTerm(BHEAD term)) return -1; } // sort and store in buffer LONG len = EndSort(BHEAD (WORD *)((void *)(&optimize_expr)),2); LowerSortLevel(); AT.WorkPointer = term; return len; } /* #] get_expression : #[ PF_get_expression : */ #ifdef WITHMPI // get_expression for ParFORM LONG PF_get_expression (int exprnr) { LONG len; if (PF.me == MASTER) { len = get_expression(exprnr); } if (PF.numtasks > 1) { PF_BroadcastBuffer(&optimize_expr, &len); } return len; } // replace get_expression called in Optimize #define get_expression PF_get_expression #endif /* #] PF_get_expression : #[ get_brackets : */ /** Get brackets * * Description * =========== * Checks whether the input expression (stored in optimize_expr) * contains brackets. If so, this method replaces terms outside * brackets by powers of SEPERATESYMBOL (equal brackets have equal * powers) and the brackets are returned. If not, the result is * empty. * * Brackets are used for simultaneous optimization. The symbol * SEPARATESYMBOL is always the first one used in a Horner scheme. */ vector > get_brackets () { // check for brackets in expression bool has_brackets = false; for (WORD *t=optimize_expr; *t!=0; t+=*t) { WORD *tend=t+*t; tend-=ABS(*(tend-1)); for (WORD *t1=t+1; t1 > brackets; if (has_brackets) { int exprlen=10; // we need potential space for an empty bracket for (WORD *t=optimize_expr; *t!=0; t+=*t) exprlen += *t; WORD *newexpr = (WORD *)Malloc1(exprlen*sizeof(WORD), "optimize newexpr"); int i=0; int sep_power = 0; for (WORD *t=optimize_expr; *t!=0; t+=*t) { WORD *t1 = t+1; // scan for bracket vector bracket; for (; *t1!=HAAKJE; t1+=*(t1+1)) bracket.insert(bracket.end(), t1, t1+*(t1+1)); if (brackets.size()==0 || bracket!=brackets.back()) { sep_power++; brackets.push_back(bracket); } t1+=*(t1+1); WORD left = t + *t - t1; bool more_symbols = (left != ABS(*(t+*t-1))); // add power of SEPARATESYMBOL newexpr[i++] = 1 + left + (more_symbols ? 2 : 4); newexpr[i++] = SYMBOL; newexpr[i++] = (more_symbols ? *(t1+1) + 2 : 4); newexpr[i++] = SEPARATESYMBOL; newexpr[i++] = sep_power; // add remaining terms if (more_symbols) { t1+=2; left-=2; } while (left-->0) newexpr[i++] = *(t1++); } /* We insert here an empty bracket that is zero. It is used for the case that there is only a single bracket which is outside the notation for trees at a later stage. There may be a problem now in that in the case of sep_power==1 newexpr is bigger than optimize_expr. We have to check that. */ if ( sep_power == 1 ) { WORD *t; vector bracket; bracket.push_back(0); bracket.push_back(0); bracket.push_back(0); bracket.push_back(0); sep_power++; brackets.push_back(bracket); newexpr[i++] = 8; newexpr[i++] = SYMBOL; newexpr[i++] = 4; newexpr[i++] = SEPARATESYMBOL; newexpr[i++] = sep_power; newexpr[i++] = 1; newexpr[i++] = 1; newexpr[i++] = 3; newexpr[i++] = 0; for (t=optimize_expr; *t!=0; t+=*t) {} if ( t-optimize_expr+1 < i ) { // We have to redo this M_free(optimize_expr,"$-sort space"); optimize_expr = (WORD *)Malloc1(i*sizeof(WORD),"$-sort space"); } } else { newexpr[i++] = 0; } memcpy(optimize_expr, newexpr, i*sizeof(WORD)); M_free(newexpr,"optimize newexpr"); // if factorized, replace SEP by FAC and remove brackets if (brackets[0].size()>0 && brackets[0][2]==FACTORSYMBOL) { for (WORD *t=optimize_expr; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (t[1]==SYMBOL) for (int i=3; i >(); } } return brackets; } /* #] get_brackets : #[ count_operators : */ /** Count operators * * Description * =========== * Counts the number of operators in a Form-style expression. */ int count_operators (const WORD *expr, bool print=false) { int n=0; while (*(expr+n)!=0) n+=*(expr+n); int cntpow=0, cntmul=0, cntadd=0, sumpow=0; WORD maxpowfac=1, maxpowsep=1; for (const WORD *t=expr; *t!=0; t+=*t) { if (t!=expr) cntadd++; // new term if (*t==ABS(*(t+*t-1))+1) continue; // only coefficient int cntsym=0; if (t[1]==SYMBOL) for (int i=3; i2) { // (extra)symbol power>2 cntpow++; sumpow += (int)floor(log(t[i+1])/log(2.0)) + popcount(t[i+1]) - 1; } if (t[i+1]==2) cntmul++; // (extra)symbol squared cntsym++; } if (ABS(*(t+*t-1))!=3 || *(t+*t-2)!=1 || *(t+*t-3)!=1) cntsym++; // non +/-1 coefficient if (cntsym > 0) cntmul+=cntsym-1; } cntadd -= maxpowfac-1; cntmul += maxpowfac-1; cntadd -= maxpowsep-1; if (print) MesPrint ("*** STATS: original %lP %lM %lA : %l", cntpow,cntmul,cntadd,sumpow+cntmul+cntadd); return sumpow+cntmul+cntadd; } /** Count operators * * Description * =========== * Counts the number of operators in a vector of instructions */ int count_operators (const vector &instr, bool print=false) { int cntpow=0, cntmul=0, cntadd=0, sumpow=0; const WORD *ebegin = &*instr.begin(); const WORD *eend = ebegin+instr.size(); for (const WORD *e=ebegin; e!=eend; e+=*(e+2)) { for (const WORD *t=e+3; *t!=0; t+=*t) { if (t!=e+3) { if (*(e+1)==OPER_ADD) cntadd++; // new term if (*(e+1)==OPER_MUL) cntmul++; // new term } if (*t == ABS(*(t+*t-1))+1) continue; // only coefficient if (*(t+1)==SYMBOL || *(t+1)==EXTRASYMBOL) { if (*(t+4)==2) cntmul++; // (extra)symbol squared if (*(t+4)>2) { // (extra)symbol power>2 cntpow++; sumpow += (int)floor(log(*(t+4))/log(2.0)) + popcount(*(t+4)) - 1; } } if (ABS(*(t+*t-1))!=3 || *(t+*t-2)!=1 || *(t+*t-3)!=1) cntmul++; // non +/-1 coefficient } } if (print) MesPrint ("*** STATS: optimized %lP %lM %lA : %l", cntpow,cntmul,cntadd,sumpow+cntmul+cntadd); return sumpow+cntmul+cntadd; } /* #] count_operators : #[ occurrence_order : */ /** Occurrence order * * Description * =========== * Extracts all variables from an expression and sorts them with * most occurring first (or last, with rev=true) */ vector occurrence_order (const WORD *expr, bool rev) { // count the number of occurrences of variables map cnt; for (const WORD *t=expr; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; // skip constant term if (t[1] == SYMBOL) for (int i=3; i > cnt_order; for (map::iterator i=cnt.begin(); i!=cnt.end(); i++) cnt_order.push_back(make_pair(i->second, i->first)); sort(cnt_order.rbegin(), cnt_order.rend()); // create resulting order vector order; for (int i=0; i<(int)cnt_order.size(); i++) order.push_back(cnt_order[i].second); if (rev) reverse(order.begin(),order.end()); // add FACTORSYMBOL/SEPARATESYMBOL if (is_fac) order.insert(order.begin(), FACTORSYMBOL); if (is_sep) order.insert(order.begin(), SEPARATESYMBOL); return order; } /* #] occurrence_order : #[ Horner_tree : */ /** Horner tree building * * Description * =========== * Given a Form-style expression (in a buffer in memory), this * builds an expression tree. The tree is determined by a * multivariate Horner scheme, i.e., something of the form: * * 1+y+x*(2+y*(1+y)+x*(3-y*(...))) * * The order of the variables is given to the method "Horner_tree", * which renumbers ad reorders the terms of the expression. Next, * the recursive method "build_Horner_tree" does the actual tree * construction. * * The tree is represented in postfix notation. Tokens are of the * following forms: * * - SNUMBER tokenlength num den coefflength * - SYMBOL tokenlength variable power * - OPER_ADD or OPER_MUL * * Note * ==== * Sets AN.poly_num_vars and allocates AN.poly_vars. The latter * should be freed later. */ /** Get power of variable (helper function for build_Horner_tree) * * Description * =========== * Returns the power of the variable "var", which is at position * "pos" in this term, if it is present. */ WORD getpower (const WORD *term, int var, int pos) { if (*term == ABS(*(term+*term-1))+1) return 0; // constant term if (2*pos+2 >= term[2]) return 0; // too few symbols if (term[2*pos+3] != var) return 0; // incorrect symbol return term[2*pos+4]; // return power } /** Call GcdLong/DivLong with leading zeroes * * Description * =========== * These method remove leading zeroes, so that GcdLong and DivLong * can safely be called. */ void fixarg (UWORD *t, WORD &n) { int an=ABS(n), sn=SGN(n); while (*(t+an-1)==0) an--; n=an*sn; } void GcdLong_fix_args (PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { fixarg(a,na); fixarg(b,nb); GcdLong(BHEAD a,na,b,nb,c,nc); } void DivLong_fix_args(UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc, UWORD *d, WORD *nd) { fixarg(a,na); fixarg(b,nb); DivLong(a,na,b,nb,c,nc,d,nd); } /** Build the Horner tree * * Description * =========== * Constructs the Horner tree. The method processes one variable and * continues recursively until the Horner scheme is completed. * * "terms" is a pointer to the starts of the terms. "numterms" is * the number of terms to be processed. "var" is the next variable * to be processed (index between 0 and #maxvar) and "maxvar" is the * last variable to be processed, so that partial Horner trees can * also be constructed. "pos" is the position that the power of * "var" should be in (one level further in the recursion, "pos" has * increased by 0 or 1 depending on whether the previous power was 0 * or not). The result is written at the pointer "res". * * This method also factors out gcds of the coefficients. The result * should end with "gcd OPER_MUL" at all times, so that one level * higher gcds can be extracted again. */ void build_Horner_tree (const WORD **terms, int numterms, int var, int maxvar, int pos, vector *res) { GETIDENTITY; if (var == maxvar) { // Horner tree is finished, so add remaining terms unfactorized // (note: since only complete Horner schemes seem to be useful, numterms=1 here for (int fr=0; frpush_back(SYMBOL); res->push_back(4); res->push_back(t[i]); res->push_back(t[i+1]); if (!empty) res->push_back(OPER_MUL); empty = false; } // if empty, add a 1, since the result should look like "... coeff *" if (empty) { res->push_back(SNUMBER); res->push_back(5); res->push_back(1); res->push_back(1); res->push_back(3); } // add coefficient res->push_back(SNUMBER); WORD n = ABS(*(t+*t-1)); res->push_back(n+2); for (int i=0; ipush_back(*(t+*t-n+i)); res->push_back(OPER_MUL); if (fr>0) res->push_back(OPER_ADD); } // result should end with gcd of the terms; right now this never // triggers, but if one would allow for incomplete Horner schemes, // one should extract the gcd here if (numterms > 1) { res->push_back(SNUMBER); res->push_back(5); res->push_back(1); res->push_back(1); res->push_back(3); res->push_back(OPER_MUL); } } else { // extract variable "var" and the gcd and proceed recursively WORD nnum = 0, nden = 0, ntmp = 0, ndum = 0; UWORD *num = NumberMalloc("build_Horner_tree"); UWORD *den = NumberMalloc("build_Horner_tree"); UWORD *tmp = NumberMalloc("build_Horner_tree"); UWORD *dum = NumberMalloc("build_Horner_tree"); // previous coefficient for gcd extraction or coefficient multiplication int prev_coeff_idx = -1; for (int fr=0; frat(res->size()-2) / 2; WORD *t1 = &res->at(res->size()-2-2*ABS(n1)); WORD *t2 = fr==0 ? t1 : &res->at(prev_coeff_idx); WORD n2 = fr==0 ? n1 : *(t2+*(t2+1)-1) / 2; if (fr>0) t2+=2; GcdLong_fix_args(BHEAD (UWORD *)t1,n1,(UWORD *)t2,n2,num,&nnum); GcdLong_fix_args(BHEAD (UWORD *)t1+ABS(n1),ABS(n1),(UWORD *)t2+ABS(n2),ABS(n2),den,&nden); // divide out gcds; note: leading zeroes can be added here for (int i=0; i<2; i++) { if (i==1 && fr==0) break; WORD *t = i==0 ? t1 : t2; WORD n = i==0 ? n1 : n2; DivLong_fix_args((UWORD *)t, n, num, nnum, tmp, &ntmp, dum, &ndum); for (int j=0; j0) res->push_back(OPER_ADD); // add the power of "var" WORD nextpow = (to==numterms ? 0 : getpower(terms[to], var, pos)); if (pow-nextpow > 0) { res->push_back(SYMBOL); res->push_back(4); res->push_back(var); res->push_back(pow-nextpow); res->push_back(OPER_MUL); } // add the extracted gcd res->push_back(SNUMBER); WORD n = MaX(ABS(nnum),nden); res->push_back(n*2+3); for (int i=0; ipush_back(num[i]); for (int i=0; ipush_back(0); for (int i=0; ipush_back(den[i]); for (int i=0; ipush_back(0); res->push_back(SGN(nnum)*(2*n+1)); res->push_back(OPER_MUL); prev_coeff_idx = res->size() - ABS(res->at(res->size()-2)) - 3; } else if (AN.poly_vars[var]==FACTORSYMBOL) { // if factorsymbol, multiply overall integer contents if (fr>0) { WORD n1 = res->at(res->size()-2) / 2; WORD *t1 = &res->at(res->size()-2-2*ABS(n1)); WORD *t2 = &res->at(prev_coeff_idx); WORD n2 = *(t2+*(t2+1)-1) / 2; t2+=2; MulRat(BHEAD (UWORD *)t1,n1,(UWORD *)t2,n2,tmp,&ntmp); // replace previous coefficient with 1 n2=ABS(n2); for (int i=0; ipop_back(); // add product res->back() = 2*ABS(ntmp)+3; // adjust size of term res->insert(res->end(), tmp, tmp+2*ABS(ntmp)); // num/den coefficient res->push_back(SGN(ntmp)*(2*ABS(ntmp)+1)); // size of coefficient res->push_back(OPER_MUL); // operator } prev_coeff_idx = res->size() - ABS(res->at(res->size()-2)) - 3; // multiply previous factors with this factor if (fr>0) res->push_back(OPER_MUL); } else { // AN.poly_vars[var]==SEPARATESYMBOL if (fr>0) res->push_back(OPER_COMMA); prev_coeff_idx = -1; } fr=to; } // cleanup NumberFree(dum,"build_Horner_tree"); NumberFree(tmp,"build_Horner_tree"); NumberFree(den,"build_Horner_tree"); NumberFree(num,"build_Horner_tree"); } } /** Term compare (helper function for Horner_tree) * * Description * =========== * Compares two terms of the form "L SYM 4 x n coeff" or "L * coeff". Lower powers of lower-indexed symbols come first. This is * used to sort the terms in correct order. */ bool term_compare (const WORD *a, const WORD *b) { if (*a == ABS(*(a+*a-1))+1) return true; // coefficient comes first if (*b == ABS(*(b+*b-1))+1) return false; if (a[1]!=SYMBOL) return true; if (b[1]!=SYMBOL) return false; for (int i=3; ib[i]; if (a[i+1]!=b[i+1]) return a[i+1] Horner_tree (const WORD *expr, const vector &order) { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: Horner_tree(%a)", thetime_str().c_str(), order.size(), &order[0]); #endif GETIDENTITY; // find the renumbering scheme (new numbers are 0,1,...,#vars-1) map renum; AN.poly_num_vars = order.size(); AN.poly_vars = (WORD *)Malloc1(AN.poly_num_vars*sizeof(WORD), "AN.poly_vars"); for (int i=0; i AT.WorkTop ) { dynamicAlloc = (WORD*)Malloc1(sizeof(*dynamicAlloc)*(sumsize+1), "Horner_tree alloc"); sorted = dynamicAlloc; } else { sorted = AT.WorkPointer; } for (const WORD *t=expr; *t!=0; t+=*t) { memcpy(sorted, t, *t*sizeof(WORD)); if (*t != ABS(*(t+*t-1))+1) { // non-constant term // renumber variables, adding new variables if necessary for (int i=3; i sorted[j+2]) { swap(sorted[j] , sorted[j+2]); swap(sorted[j+1], sorted[j+3]); } } sorted += *sorted; } *sorted = 0; if ( dynamicAlloc ) { sorted = dynamicAlloc; } else { sorted = AT.WorkPointer; } // find pointers to all terms and sort them efficiently vector terms; for (const WORD *t=sorted; *t!=0; t+=*t) terms.push_back(t); sort(terms.rbegin(),terms.rend(),term_compare); // construct the Horner tree vector res; build_Horner_tree(&terms[0], terms.size(), 0, AN.poly_num_vars, 0, &res); // remove leading zeroes in coefficients int j=0; for (int i=0; i<(int)res.size();) { if (res[i]==OPER_ADD || res[i]==OPER_MUL || res[i]==OPER_COMMA) res[j++] = res[i++]; else if (res[i]==SYMBOL) { memmove(&res[j], &res[i], res[i+1]*sizeof(WORD)); i+=res[j+1]; j+=res[j+1]; } else if (res[i]==SNUMBER) { int n = (res[i+1]-2)/2; int dn = 0; while (res[i+1+n-dn]==0 && res[i+1+2*n-dn]==0) dn++; res[j++] = SNUMBER; res[j++] = 2*(n-dn) + 3; memmove(&res[j], &res[i+2], (n-dn)*sizeof(WORD)); j+=n-dn; memmove(&res[j], &res[i+n+2], (n-dn)*sizeof(WORD)); j+=n-dn; res[j++] = SGN(res[i+2*n+2])*(2*(n-dn)+1); i+=2*n+3; } } res.resize(j); if ( dynamicAlloc ) { M_free(dynamicAlloc, "Horner_tree alloc"); } #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: Horner_tree(%a)", thetime_str().c_str(), order.size(), &order[0]); #endif return res; } /* #] Horner_tree : #[ print_tree : */ // print Horner tree (for debugging) void print_tree (const vector &tree) { GETIDENTITY; for (int i=0; i<(int)tree.size();) { if (tree[i]==OPER_ADD) { MesPrint("+%"); i++; } else if (tree[i]==OPER_MUL) { MesPrint("*%"); i++; } else if (tree[i]==OPER_COMMA) { MesPrint(",%"); i++; } else if (tree[i]==SNUMBER) { UBYTE buf[100]; int n = tree[i+tree[i+1]-1]/2; PrtLong((UWORD *)&tree[i+2], n, buf); int l = strlen((char *)buf); buf[l]='/'; n=ABS(n); PrtLong((UWORD *)&tree[i+2+n], n, buf+l+1); MesPrint("%s%",buf); i+=tree[i+1]; } else if (tree[i]==SYMBOL) { if (AN.poly_vars[tree[i+2]] < 10000) MesPrint("%s^%d%", VARNAME(symbols,AN.poly_vars[tree[i+2]]), tree[i+3]); else MesPrint("Z%d^%d%", MAXVARIABLES-AN.poly_vars[tree[i+2]], tree[i+3]); i+=tree[i+1]; } else { MesPrint("error"); exit(1); } MesPrint(" %"); } MesPrint(""); } /* #] print_tree : #[ generate_instructions : */ struct CSEHash { size_t operator()(const vector& n) const { return n[0]; } }; struct CSEEq { bool operator()(const vector& lhs, const vector& rhs) const { if (lhs.size() != rhs.size()) return false; for (unsigned int i = 1; i < lhs.size(); i++) { if (lhs[i] != rhs[i]) return false; } return true; } }; template size_t hash_range(T* array, int size) { size_t hash = 0; for (int i = 0; i < size; i++) { hash ^= array[i] + 0x9e3779b9 + (hash << 6) + (hash >> 2); } return hash; } /** Generate instructions * * Description * =========== * Converts the expression tree to a list of instructions that * directly translate to code. Instructions are of the form: * * expr.nr operator length [operands]+ trailing.zero * * The operands are of the form: * * length [(EXTRA)SYMBOL length variable power] coeff * * This method only generates binary operators. Merging is done * later. The method also checks for common subexpressions and * eliminates them and the flag "do_CSE" is set. * * Implementation details * ====================== * The map "ID" keeps track of which subexpressions already * exist. The key is formatted as one of the following: * * SYMBOL x n * SNUMBER coeff * OPERATOR LHS RHS * * with LHS/RHS formatted as one of the following: * * SNUMBER idx 0 * (EXTRA)SYMBOL x n * * ID[symbol] or ID[operator] equals a subexpression * number. ID[coeff] equals the position of the number in the input. * * The stack s is used the process the postfix expression * tree. Three-word tokens of the form: * * SNUMBER idx.of.coeff 0 * SYMBOL x n * EXTRASYMBOL x 1 * * are pushed onto it. Operators pop two operands and push the * resulting expression. * * (Extra)symbols are 1-indexed, because -X is also needed to * represent -1 times this term. * * There is currently a bug. The notation cannot tell if there is a single * bracket and then ignores the bracket. * * TODO: check if this method performs properly if do_CSE=false */ vector generate_instructions (const vector &tree, bool do_CSE) { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: generate_instructions(cse=%d)", thetime_str().c_str(), do_CSE?1:0); #endif typedef unordered_map, int, CSEHash, CSEEq> csemap; csemap ID; // reserve lots of space, to prevent later rehashes // TODO: what if this is too large? make a parameter? if (do_CSE) { ID.rehash(mcts_expr_score * 2); } // s is a stack of operands to process when you encounter operators // in the postfix expression tree. Operands consist of three WORDs, // formatted as the LHS/RHS of the keys in ID. stack s; vector instr; WORD numinstr = 0; vector x; // process the expression tree for (int i=0; i<(int)tree.size();) { x.clear(); if (tree[i]==SNUMBER) { WORD hash = hash_range(&tree[i], tree[i + 1]); x.push_back(hash); x.push_back(SNUMBER); x.insert(x.end(),&tree[i],&tree[i]+tree[i+1]); int sign = SGN(x.back()); x.back() *= sign; std::pair suc = ID.insert(csemap::value_type(x, i + 1)); s.push(0); s.push(sign * suc.first->second); s.push(SNUMBER); s.push(hash); i+=tree[i+1]; } else if (tree[i]==SYMBOL) { WORD hash = hash_range(&tree[i], tree[i + 1]); if (tree[i+3]>1) { x.push_back(hash); x.push_back(SYMBOL); x.push_back(tree[i+2]+1); // variable (1-indexed) x.push_back(tree[i+3]); // power csemap::iterator it = ID.find(x); if (do_CSE && it != ID.end()) { // already-seen power of a symbol s.push(1); s.push(it->second); s.push(EXTRASYMBOL); } else { //MesPrint("strange"); if (numinstr == MAXPOSITIVE) { MesPrint((char *)"ERROR: too many temporary variables needed in optimization"); Terminate(-1); } // new power greater than 1 of a symbol instr.push_back(numinstr); // expr.nr instr.push_back(OPER_MUL); // operator instr.push_back(9+OPTHEAD); // length total instr.push_back(8); // length operand instr.push_back(SYMBOL); // SYMBOL instr.push_back(4); // length symbol instr.push_back(tree[i+2]); // variable instr.push_back(tree[i+3]); // power instr.push_back(1); // numerator instr.push_back(1); // denominator instr.push_back(3); // length coeff instr.push_back(0); // trailing 0 ID[x] = ++numinstr; s.push(1); s.push(numinstr); s.push(EXTRASYMBOL); } } else { // power of 1 s.push(tree[i+3]); // power s.push(tree[i+2]+1); // variable (1-indexed) s.push(SYMBOL); } s.push(hash); // push hash i+=tree[i+1]; } else { // tree[i]==OPERATOR int oper = tree[i]; i++; x.push_back(0); // placeholder for hash x.push_back(oper); vector hash; hash.push_back(oper); // get two operands from the stack for (int operand=0; operand<2; operand++) { hash.push_back(s.top()); s.pop(); x.push_back(s.top()); s.pop(); x.push_back(s.top()); s.pop(); x.push_back(s.top()); s.pop(); } x[0] = hash_range(&hash[0], 3); // get rid of multiplications by +/-1 if (oper==OPER_MUL) { bool do_continue = false; for (int operand=0; operand<2; operand++) { int idx_oper1 = operand==0 ? 2 : 5; int idx_oper2 = operand==0 ? 5 : 2; // check whether operand 1 equals +/-1 if (x[idx_oper1]==SNUMBER) { int idx = ABS(x[idx_oper1+1])-1; if (tree[idx+2]==1 && tree[idx+3]==1 && ABS(tree[idx+4])==3) { // push +/- other operand and continue s.push(x[idx_oper2+2]); s.push(x[idx_oper2+1]*SGN(x[idx_oper1+1])); s.push(x[idx_oper2]); s.push(hash[1 + (operand + 1) % 2]); do_continue = true; break; } } } if (do_continue) continue; } // check whether this subexpression has been seen before // if not, generate instruction to define it csemap::iterator it = ID.find(x); if (!do_CSE || it == ID.end()) { if (numinstr == MAXPOSITIVE) { MesPrint((char *)"ERROR: too many temporary variables needed in optimization"); Terminate(-1); } instr.push_back(numinstr); // expr.nr. instr.push_back(x[1]); // operator instr.push_back(3); // length ID[x] = ++numinstr; int lenidx = instr.size()-1; for (int j=0; j<2; j++) if (x[3*j+2]==SYMBOL || x[3*j+2]==EXTRASYMBOL) { instr.push_back(8); // length total instr.push_back(x[3*j+2]); // (extra)symbol instr.push_back(4); // length (extra)symbol instr.push_back(ABS(x[3*j+3])-1); // variable (0-indexed) instr.push_back(x[3*j+4]); // power instr.push_back(1); // numerator instr.push_back(1); // denominator instr.push_back(3*SGN(x[3*j+3])); // length coeff instr[lenidx] += 8; } else { // x[3*j+1]==SNUMBER int t = ABS(x[3*j+3])-1; instr.push_back(tree[t+1]-1); // length number instr.insert(instr.end(), &tree[t+2], &tree[t]+tree[t+1]); // digits instr.back() *= SGN(instr.back()) * SGN(x[3*j+3]); instr[lenidx] += tree[t+1]-1; } instr.push_back(0); // trailing 0 instr[lenidx]++; } // push new expression on the stack s.push(1); s.push(ID[x]); s.push(EXTRASYMBOL); s.push(x[0]); // push hash } } #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: generate_instructions(cse=%d) : numoper=%d", thetime_str().c_str(), do_CSE?1:0, count_operators(instr)); #endif return instr; } /* #] generate_instructions : #[ count_operators_cse : */ /** * Count number of operators in a binary tree, while removing CSEs on the fly. * The instruction set is not created, which makes this method slightly faster. * * A hash is created on the fly and is passed through the stack. * TODO: find better hash functions */ int count_operators_cse (const vector &tree) { //MesPrint ("*** [%s] Starting CSEE", thetime_str().c_str()); typedef unordered_map, int, CSEHash, CSEEq> csemap; csemap ID; // reserve lots of space, to prevent later rehashes // TODO: what if this is too large? make a parameter? ID.rehash(mcts_expr_score * 2); // s is a stack of operands to process when you encounter operators // in the postfix expression tree. Operands consist of three WORDs, // formatted as the LHS/RHS of the keys in ID. stack s; int numinstr = 0, numcommas = 0; vector x; // process the expression tree for (int i=0; i<(int)tree.size();) { x.clear(); if (tree[i]==SNUMBER) { WORD hash = hash_range(&tree[i], tree[i + 1]); x.push_back(hash); x.push_back(SNUMBER); x.insert(x.end(),&tree[i],&tree[i]+tree[i+1]); int sign = SGN(x.back()); x.back() *= sign; std::pair suc = ID.insert(csemap::value_type(x, i + 1)); s.push(0); s.push(sign * suc.first->second); s.push(SNUMBER); s.push(hash); i+=tree[i+1]; } else if (tree[i]==SYMBOL) { WORD hash = hash_range(&tree[i], tree[i + 1]); if (tree[i+3]>1) { x.push_back(hash); x.push_back(SYMBOL); x.push_back(tree[i+2]+1); // variable (1-indexed) x.push_back(tree[i+3]); // power csemap::iterator it = ID.find(x); if (it != ID.end()) { // already-seen power of a symbol s.push(1); s.push(it->second); s.push(EXTRASYMBOL); } else { if (tree[i + 3] == 2) numinstr++; else numinstr += (int)floor(log(tree[i+3])/log(2.0)) + popcount(tree[i+3]) - 1; ID[x] = numinstr; s.push(1); s.push(numinstr); s.push(EXTRASYMBOL); } } else { // power of 1 s.push(tree[i+3]); // power s.push(tree[i+2]+1); // variable (1-indexed) s.push(SYMBOL); } s.push(hash); // push hash i+=tree[i+1]; } else { // tree[i]==OPERATOR int oper = tree[i]; i++; x.push_back(0); // placeholder for hash x.push_back(oper); vector hash; hash.push_back(oper); // get two operands from the stack for (int operand=0; operand<2; operand++) { hash.push_back(s.top()); s.pop(); x.push_back(s.top()); s.pop(); x.push_back(s.top()); s.pop(); x.push_back(s.top()); s.pop(); } x[0] = hash_range(&hash[0], 3); // get rid of multiplications by +/-1 if (oper==OPER_MUL) { bool do_continue = false; for (int operand=0; operand<2; operand++) { int idx_oper1 = operand==0 ? 2 : 5; int idx_oper2 = operand==0 ? 5 : 2; // check whether operand 1 equals +/-1 if (x[idx_oper1]==SNUMBER) { int idx = ABS(x[idx_oper1+1])-1; if (tree[idx+2]==1 && tree[idx+3]==1 && ABS(tree[idx+4])==3) { // push +/- other operand and continue s.push(x[idx_oper2+2]); s.push(x[idx_oper2+1]*SGN(x[idx_oper1+1])); s.push(x[idx_oper2]); s.push(hash[1 + (operand + 1) % 2]); do_continue = true; break; } } } if (do_continue) continue; } // check whether this subexpression has been seen before // if not, generate instruction to define it csemap::iterator it = ID.find(x); if (it == ID.end()) { if (numinstr == MAXPOSITIVE) { MesPrint((char *)"ERROR: too many temporary variables needed in optimization"); Terminate(-1); } if (oper == OPER_COMMA) numcommas++; ID[x] = ++numinstr; s.push(1); s.push(numinstr); s.push(EXTRASYMBOL); } else { // push new expression on the stack s.push(1); s.push(it->second); s.push(EXTRASYMBOL); } s.push(x[0]); // push hash } } //MesPrint ("*** [%s] Stopping CSEE", thetime_str().c_str()); return numinstr - numcommas; } /* #] count_operators_cse : #[ count_operators_cse_topdown : */ typedef struct node { const WORD* data; struct node* l; struct node* r; // TODO: add l,r to data? WORD sign; // TODO: use data for this? UWORD hash; node() : l(NULL), r(NULL), sign(1), hash(0) {}; node(const WORD* data) : data(data), l(NULL), r(NULL), sign(1), hash(0) {}; // a minus sign in the tree should only count as a different entry if // it is a compound expression: a = -a, but T+-V != T+V int cmp(const struct node* rhs) const { if (this == rhs) return 0; if (data[0] != rhs->data[0]) return data[0] < rhs->data[0] ? -1 : 1; int mod = data[0] == SNUMBER ? -1 : 0; // don't check sign, for numbers if (data[0] == SYMBOL || data[0] == SNUMBER) { for (int i = 0; i < data[1] + mod; i++) { if (data[i] != rhs->data[i]) return data[i] < rhs->data[i] ? -1 : 1; } } else { int lv = l->cmp(rhs->l); if (lv != 0) return lv; int rv = r->cmp(rhs->r); if (rv != 0) return rv; // TODO: only for ADD operation if (l->sign != rhs->l->sign) return l->sign < rhs->l->sign ? -1 : 1; if (r->sign != rhs->r->sign) return r->sign < rhs->r->sign ? -1 : 1; } return 0; } // less than operator bool operator() (const struct node* lhs, const struct node* rhs) const { return lhs->cmp(rhs) < 0; } void calcHash() { int mod = data[0] == SNUMBER ? -1 : 0; // don't check sign, for numbers if (data[0] == SYMBOL || data[0] == SNUMBER) { hash = hash_range(data, data[1] + mod); } else { if (l->hash == 0) l->calcHash(); if (r->hash == 0) r->calcHash(); // signs only matter for compound expressions size_t newr[] = {(size_t)data[0], l->hash, (size_t)l->sign, r->hash, (size_t)r->sign}; hash = hash_range(newr, 5); } } } NODE; struct NodeHash { size_t operator()(const NODE* n) const { return n->hash; // already computed } }; struct NodeEq { bool operator()(const NODE* lhs, const NODE* rhs) const { return lhs->cmp(rhs) == 0; } }; NODE* buildTree(vector &tree) { //MesPrint ("*** [%s] Starting CSEE topdown", thetime_str().c_str()); // allocate spaces for the tree, cannot be more nodes than tree size NODE* ar = (NODE*)Malloc1(tree.size() * sizeof(NODE), "CSE tree"); NODE* c = 0; unsigned int curIndex = 0; stack st; for (int i=0; i<(int)tree.size();) { c = ar + curIndex; new (c) NODE(&tree[i]); // placement new curIndex++; if (tree[i]==SYMBOL || tree[i] == SNUMBER) { // extract the sign to a new class member if (tree[i] == SNUMBER) { c->sign = SGN(tree[i + tree[i + 1] -1]); } c->calcHash(); st.push(c); i+=tree[i+1]; } else { c->r = st.top(); st.pop(); c->l = st.top(); st.pop(); // filter *1 and *-1 // TODO: also multiply if there are two numbers? if (c->data[0] == OPER_MUL) { NODE* ch[] = {c->r, c->l}; for (int j = 0; j < 2; j++) if (ch[j]->data[0] == SNUMBER && ch[j]->data[1] == 5 && ch[j]->data[2]==1 && ch[j]->data[3]==1) { ch[(j+1)%2]->sign *= ch[j]->sign; // transfer sign c = ch[(j+1)%2]; break; } } c->calcHash(); st.push(c); i++; } } // TODO: reallocate to smaller size? Could save memory //MesPrint("Memory difference: %d vs %d", curIndex, tree.size()); // we want to make the root of the tree the first element // so that we can easily free the array. // we swap the first element with the root // we need to change the pointer in the operator node that has this element as a child // TODO: check performance for (unsigned int i = 0; i < curIndex; i++) { if (ar[i].l == ar) ar[i].l = st.top(); if (ar[i].r == ar) ar[i].r = st.top(); } swap(ar[0], *st.top()); return ar; } int count_operators_cse_topdown (vector &tree) { typedef unordered_set nodeset; nodeset ID; // reserve lots of space, to prevent later rehashes // TODO: what if this is too large? make a parameter? ID.rehash(mcts_expr_score * 2); int numinstr = 0; NODE* root = buildTree(tree); stack stack; stack.push(root); while (!stack.empty()) { NODE* c = stack.top(); stack.pop(); if (c->data[0] == SYMBOL) { if (c->data[3] > 1) { std::pair suc = ID.insert(c); if (suc.second) { // new if (c->data[3] == 2) numinstr++; else numinstr += (int)floor(log(c->data[3])/log(2.0)) + popcount(c->data[3]) - 1; } } } else { if (c->data[0] != SNUMBER) { // operator std::pair suc = ID.insert(c); if (suc.second) { stack.push(c->r); stack.push(c->l); // ignore OPER_COMMA if (c->data[0] == OPER_MUL || c->data[0] == OPER_ADD) numinstr++; } } } } //MesPrint ("*** [%s] Stopping CSEE", thetime_str().c_str()); M_free(root, "CSE tree"); return numinstr; } /* #] count_operators_cse_topdown : #[ simulated_annealing : */ vector simulated_annealing() { float minT = AO.Optimize.saMinT.fval; float maxT = AO.Optimize.saMaxT.fval; float T = maxT; float coolrate = pow(minT / maxT, 1 / (float)AO.Optimize.saIter); GETIDENTITY; // create a valid state where FACTORSYMBOL/SEPARATESYMBOL remains first vector state = occurrence_order(optimize_expr, false); int startindex = 0; if ((state.size() > 0 && state[0] == SEPARATESYMBOL) || (state.size() > 1 && state[1] == FACTORSYMBOL)) startindex++; if (state.size() > 1 && state[1] == FACTORSYMBOL) startindex++; my_random_shuffle(BHEAD state.begin() + startindex, state.end()); // start from random scheme vector tree = Horner_tree(optimize_expr, state); int curscore = count_operators_cse_topdown(tree); // clean poly_vars, that are allocated by Horner_tree AN.poly_num_vars = 0; M_free(AN.poly_vars,"poly_vars"); std::vector best = state; // best state int bestscore = curscore; if (startindex == (int)state.size() || (int)state.size() - startindex < 2) { return best; } for (int o = 0; o < AO.Optimize.saIter; o++) { int inda = iranf(BHEAD state.size() - startindex) + startindex; int indb = iranf(BHEAD state.size() - startindex) + startindex; if (inda == indb) { continue; } swap(state[inda], state[indb]); // swap works best for Horner vector tree = Horner_tree(optimize_expr, state); int newscore = count_operators_cse_topdown(tree); // clean poly_vars, that are allocated by Horner_tree AN.poly_num_vars = 0; M_free(AN.poly_vars,"poly_vars"); if (newscore <= curscore || 2.0 * wranf(BHEAD0) / (float)(UWORD)(-1) < exp((curscore - newscore) / T)) { curscore = newscore; if (curscore < bestscore) { bestscore = curscore; best = state; } } else { swap(state[inda], state[indb]); } #ifdef DEBUG_SA MesPrint("Score at step %d: %d", o, curscore); #endif T *= coolrate; } #ifdef DEBUG_SA MesPrint("Simulated annealing score: %d", bestscore); #endif return best; } /* #] simulated_annealing : #[ printpstree : */ /* // print MCTS tree with LaTeX/pstricks (for analysis) void printpstree_rec (tree_node x, string pre="") { if (x.num_visits==1) { MesPrint("%s\\TR{%d}",pre.c_str(),x.var); } else { MesPrint("%s\\pstree%s{\\TR{%d}}{",pre.c_str(), pre==" "?"[nodesep=0, levelsep=40]":"", x.var); for (int i=0; i<(int)x.childs.size(); i++) if (x.childs[i].num_visits>0) printpstree_rec(x.childs[i], pre+" "); MesPrint("%s}",pre.c_str()); } } void printpstree () { // draw tree with pstricks MesPrint ("\\documentclass{article}"); MesPrint ("\\usepackage{pstricks,pst-node,pst-tree,graphicx}"); MesPrint ("\\begin{document}"); MesPrint ("\\scalebox{0.02}{"); printpstree_rec(mcts_root," "); MesPrint ("}"); MesPrint ("\\end{document}"); } */ /* #] printpstree : #[ find_Horner_MCTS_expand_tree : */ /** Expand MCTS tree * * Description * =========== * This method does one MCTS step: it selects the most-promising * node, expands it, randomly completes the Horner scheme and * backpropagates the results. * * Selection is done according to the UCT formula: * * UCT(i) = + C * sqrt(2*log(N)/n(i)), * * where is the average result of child i, n(i) is the number * of time child i is visited, N=SUM(n(i)) and C is a constant to be * determined experimentally (can be set via mctsconstant). * * A "virtual loss" is added once a node is selected. This is * relevant to avoid duplicate work in the parallel version. * * Notes * ===== * - The method is called from "find_Horner_MCTS" in Form and from * "RunThread" via "find_Horner_MCTS_expand_tree_threaded" in * TForm. * - The code is divided into three functions: "next_MCTS_scheme", * "try_MCTS_scheme" and "update_MCTS_scheme". In this way, the * source code is shared with ParForm; "try_MCTS_scheme" is * assumed to run on workers, while the others are assumed to run * on the master. */ /* #[ next_MCTS_scheme : */ // find a Horner scheme to be used for the next simulation inline static void next_MCTS_scheme (PHEAD vector *porder, vector *pscheme, vector *ppath) { vector &order = *porder; vector &schemev = *pscheme; vector &path = *ppath; int depth = 0, nchild0; float slide_down_factor = 1.0; order.clear(); path.clear(); // MCTS step I: select tree_node *select = &mcts_root; path.push_back(select); nchild0 = select->childs.size(); while (select->childs.size() > 0) { // add virtual loss select->num_visits++; select->sum_results+=mcts_expr_score; //------------------------------------------------------------------- switch ( AO.Optimize.mctsdecaymode ) { case 1: // Based on http://arxiv.org/abs/arXiv:1312.0841 slide_down_factor = 1.0-(1.0*AT.optimtimes)/(1.0*AO.Optimize.mctsnumexpand); break; case 2: // This gives a bit more cleanup time at the end. if ( 2*AT.optimtimes < AO.Optimize.mctsnumexpand ) { slide_down_factor = 1.0*(AO.Optimize.mctsnumexpand-2*AT.optimtimes); slide_down_factor /= 1.0*AO.Optimize.mctsnumexpand; } else { slide_down_factor = 0.0001; } break; case 3: // depth dependent factor combined with case 1 float dd = 1.0-(1.0*depth)/(1.0*nchild0); slide_down_factor = 1.0-(1.0*AT.optimtimes)/(1.0*AO.Optimize.mctsnumexpand); if ( dd <= 0.000001 ) slide_down_factor = 1.0; else slide_down_factor /= dd; if ( slide_down_factor > 1.0 ) slide_down_factor = 1.0; break; } //------------------------------------------------------------------- #ifdef DEBUG_MCTS MesPrint("select %d",select->var); #endif // find most-promising node double best=0; tree_node *next=NULL; for (vector::iterator p=select->childs.begin(); pchilds.end(); p++) { double score; if (p->num_visits >= 1) { // there are results calculated, so select with the UCT formula score = mcts_expr_score / (p->sum_results/p->num_visits) + //------------------------------------------------------------------------- slide_down_factor * //------------------------------------------------------------------------- 2 * AO.Optimize.mctsconstant.fval * sqrt(2*log(select->num_visits) / p->num_visits); #ifdef DEBUG_MCTS printf("%d: %.2lf [x=%.2lf n=%d fin=%i]\n",p->var,score,mcts_expr_score / (p->sum_results/p->num_visits), p->num_visits,p->finished?1:0); fflush(stdout); #endif } else { // no results yet, so select this node by setting score=infinite score = 1e100; #ifdef DEBUG_MCTS printf("%d: inf\n",p->var); fflush(stdout); #endif } // update best candidate if (!p->finished && score>best) { best=score; next=&*p; } } // if no node is found, this node is finished if (next==NULL) { select->finished=true; break; } // traverse down the tree select = next; path.push_back(select); order.push_back(select->var); depth++; } // MCTS step II: expand #ifdef DEBUG_MCTS MesPrint("expand %d",select->var); #endif // variables used so far set var_used; for (int i=0; i<(int)order.size(); i++) var_used.insert(ABS(order[i])-1); // if this a new node, create node and add children if (!select->finished && select->childs.size()==0) { tree_node new_node(select->var); int sign = (order.size() == 0) ? 1 : SGN(order.back()); for (int i=0; i<(int)mcts_vars.size(); i++) if (!var_used.count(mcts_vars[i])) { new_node.childs.push_back(tree_node(sign*(mcts_vars[i]+1))); if (AO.Optimize.hornerdirection==O_FORWARDANDBACKWARD) new_node.childs.push_back(tree_node(-sign*(mcts_vars[i]+1))); } my_random_shuffle(BHEAD new_node.childs.begin(), new_node.childs.end()); // here locking is necessary, since operator=(tree_node) is a // non-atomic operation (using pointers makes this lock obsolete) LOCK(optimize_lock); *select = new_node; UNLOCK(optimize_lock); } // set finished if necessary if (select->childs.size()==0) select->finished = true; // add virtual loss of number of operators in original expression select->num_visits++; select->sum_results+=mcts_expr_score; // MCTS step III: simulation // create complete Horner scheme deque scheme; for (int i=0; i<(int)mcts_vars.size(); i++) if (!var_used.count(mcts_vars[i])) scheme.push_back(mcts_vars[i]); my_random_shuffle(BHEAD scheme.begin(), scheme.end()); for (int i=(int)order.size()-1; i>=0; i--) { if (order[i] > 0) scheme.push_front(order[i]-1); else scheme.push_back(-order[i]-1); } // add FACTORSYMBOL/SEPARATESYMBOL is necessary if (mcts_factorized) scheme.push_front(FACTORSYMBOL); if (mcts_separated) scheme.push_front(SEPARATESYMBOL); // Horner scheme as a vector schemev = vector(scheme.begin(), scheme.end()); } /* #] next_MCTS_scheme : #[ try_MCTS_scheme : */ // count the number of operators in the given Horner scheme inline static void try_MCTS_scheme (PHEAD const vector &scheme, int *pnum_oper) { // do Horner, CSE and count the number of operators vector tree = Horner_tree(optimize_expr, scheme); //vector instr = generate_instructions(tree, true); //int num_oper = count_operators(instr); //int num_oper2 = count_operators_cse(tree); //int num_oper2 = count_operators_cse_topdown(tree); //MesPrint("%d %d", num_oper, num_oper2); int num_oper = count_operators_cse_topdown(tree); // clean poly_vars, that is allocated by Horner_tree AN.poly_num_vars = 0; M_free(AN.poly_vars,"poly_vars"); *pnum_oper = num_oper; } /* #] try_MCTS_scheme : #[ update_MCTS_scheme : */ // update the best score and the search tree inline static void update_MCTS_scheme (int num_oper, const vector &scheme, vector *ppath) { vector &path = *ppath; // update the (global) list of best Horner scheme if ((int)mcts_best_schemes.size() < AO.Optimize.mctsnumkeep || (--mcts_best_schemes.end())->first > num_oper) { // here locking is necessary, for otherwise best_schemes may // become corrupted; lock can be prevented if each thread keeps // track of it's own list and those lists are merged in the end, // but this seems not useful to implement LOCK(optimize_lock); mcts_best_schemes.insert(make_pair(num_oper,scheme)); if ((int)mcts_best_schemes.size() > AO.Optimize.mctsnumkeep) mcts_best_schemes.erase(--mcts_best_schemes.end()); UNLOCK(optimize_lock); } // MCTS step IV: backpropagate // add number of operator and subtract mcts_expr_score, which // behaves as a "virtual loss" for (vector::iterator p=path.begin(); psum_results += num_oper - mcts_expr_score; } /* #] update_MCTS_scheme : */ void find_Horner_MCTS_expand_tree () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: find_Horner_MCTS_expand_tree", thetime_str().c_str()); #endif GETIDENTITY; // the order for the Horner scheme up to the selected node, with signs // indicating forward or backward. vector order; // complete Horner scheme vector scheme; // path to the selected node vector path; // the number of operations obtained by the simulation int num_oper; next_MCTS_scheme(BHEAD &order, &scheme, &path); try_MCTS_scheme(BHEAD scheme, &num_oper); #ifdef DEBUG_MCTS // Actually "order" is needed only for this debug output. MesPrint ("{%a} -> {%a} -> %d", order.size(), &order[0], scheme.size(), &scheme[0], num_oper); #endif update_MCTS_scheme(num_oper, scheme, &path); #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: find_Horner_MCTS_expand_tree(%a-> %d)", thetime_str().c_str(), scheme.size(), &scheme[0], num_oper); #endif } /* #] find_Horner_MCTS_expand_tree : #[ PF_find_Horner_MCTS_expand_tree : */ #ifdef WITHMPI // To remember which task is assigned to each slave. A task is represented by // a pair of a Horner scheme and the selected path for the scheme. // The index range is from 1 to PF.numtasks-1. vector, vector > > PF_opt_MCTS_tasks; // Initialization. void PF_find_Horner_MCTS_expand_tree_master_init () { PF_opt_MCTS_tasks.resize(PF.numtasks); for (int i = 1; i < PF.numtasks; i++) { pair, vector > &p = PF_opt_MCTS_tasks[i]; p.first.clear(); p.second.clear(); } } // Wait for an idle slave and return the process number. int PF_find_Horner_MCTS_expand_tree_master_next () { // Find an idle slave. int next; PF_Receive(PF_ANY_SOURCE, PF_OPT_MCTS_MSGTAG, &next, NULL); // Check if the slave had a task. pair, vector > &p = PF_opt_MCTS_tasks[next]; if (!p.first.empty()) { // If so, update the result. int num_oper; PF_Unpack(&num_oper, 1, PF_INT); update_MCTS_scheme(num_oper, p.first, &p.second); // Clear the task. p.first.clear(); p.second.clear(); } return next; } // The main function on the master. void PF_find_Horner_MCTS_expand_tree_master () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: PF_find_Horner_MCTS_expand_tree_master", thetime_str().c_str()); #endif vector order; vector scheme; vector path; next_MCTS_scheme(BHEAD &order, &scheme, &path); // Find an idle slave. int next = PF_find_Horner_MCTS_expand_tree_master_next(); // Send a new task to the slave. PF_PrepareLongSinglePack(); int len = scheme.size(); PF_LongSinglePack(&len, 1, PF_INT); PF_LongSinglePack(&scheme[0], len, PF_WORD); PF_LongSingleSend(next, PF_OPT_MCTS_MSGTAG); // Remember the task. pair, vector > &p = PF_opt_MCTS_tasks[next]; p.first = scheme; p.second = path; #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: PF_find_Horner_MCTS_expand_tree_master", thetime_str().c_str()); #endif } // Wait for all the slaves to finish their tasks. void PF_find_Horner_MCTS_expand_tree_master_wait () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: PF_find_Horner_MCTS_expand_tree_master_wait", thetime_str().c_str()); #endif // Wait for all the slaves. for (int i = 1; i < PF.numtasks; i++) { int next = PF_find_Horner_MCTS_expand_tree_master_next(); // Send a null task. PF_PrepareLongSinglePack(); int len = 0; PF_LongSinglePack(&len, 1, PF_INT); PF_LongSingleSend(next, PF_OPT_MCTS_MSGTAG); } #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: PF_find_Horner_MCTS_expand_tree_master_wait", thetime_str().c_str()); #endif } // The main function on the slaves. void PF_find_Horner_MCTS_expand_tree_slave () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: PF_find_Horner_MCTS_expand_tree_slave", thetime_str().c_str()); #endif vector scheme; { // Send the first message to the master, which indicates I am idle. PF_PreparePack(); int dummy = 0; PF_Pack(&dummy, 1, PF_INT); PF_Send(MASTER, PF_OPT_MCTS_MSGTAG); } for (;;) { // Get a task from the master. PF_LongSingleReceive(MASTER, PF_OPT_MCTS_MSGTAG, NULL, NULL); // Length of the task. int len; PF_LongSingleUnpack(&len, 1, PF_INT); // No task remains. if (len == 0) break; // Perform the given task. scheme.resize(len); PF_LongSingleUnpack(&scheme[0], len, PF_WORD); int num_oper; try_MCTS_scheme(scheme, &num_oper); // Send the result to the master. PF_PreparePack(); PF_Pack(&num_oper, 1, PF_INT); PF_Send(MASTER, PF_OPT_MCTS_MSGTAG); } #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: PF_find_Horner_MCTS_expand_tree_slave", thetime_str().c_str()); #endif } #endif /* #] PF_find_Horner_MCTS_expand_tree : #[ find_Horner_MCTS : */ /** Find best Horner schemes using MCTS * * Description * =========== * The method governs the MCTS for the best Horner schemes. It does * some pre-processing, calls "find_Horner_MCTS_expand_tree" a * number of times and does some post-processing. */ //vector > find_Horner_MCTS () { void find_Horner_MCTS () { #ifdef WITHMPI if (PF.me != MASTER) { if (PF.numtasks <= 1) return; PF_find_Horner_MCTS_expand_tree_slave(); return; } #endif #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: find_Horner_MCTS", thetime_str().c_str()); #endif GETIDENTITY; LONG start_time = TimeWallClock(1); // initialize the used global variables mcts_expr_score = count_operators(optimize_expr); mcts_root = tree_node(); // extract all symbols from the expression set var_set; for (WORD *t=optimize_expr; *t!=0; t+=*t) if (t[1] == SYMBOL) for (int i=3; i(var_set.begin(), var_set.end()); optimize_num_vars = (int)mcts_vars.size(); // initialize MCTS tree root for (int i=0; i<(int)mcts_vars.size(); i++) { if (AO.Optimize.hornerdirection != O_BACKWARD) mcts_root.childs.push_back(tree_node(+(mcts_vars[i]+1))); if (AO.Optimize.hornerdirection != O_FORWARD) mcts_root.childs.push_back(tree_node(-(mcts_vars[i]+1))); } my_random_shuffle(BHEAD mcts_root.childs.begin(), mcts_root.childs.end()); #if defined(WITHMPI) PF_find_Horner_MCTS_expand_tree_master_init(); #endif // initialize a potential variable mctsconstant scheme. AT.optimtimes = 0; // call expand_tree until it is called "mctsnumexpand" times, the // time limit is reached or the tree is fully finished for (int times=0; times 1) find_Horner_MCTS_expand_tree_threaded(); else #elif defined(WITHMPI) if (PF.numtasks > 1) PF_find_Horner_MCTS_expand_tree_master(); else #endif find_Horner_MCTS_expand_tree(); } // if TForm or ParForm, wait for everyone to finish #ifdef WITHPTHREADS MasterWaitAll(); #endif #ifdef WITHMPI PF_find_Horner_MCTS_expand_tree_master_wait(); #endif #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: find_Horner_MCTS", thetime_str().c_str()); #endif } /* #] find_Horner_MCTS : #[ merge_operators : */ /** Merge operators * * Description * =========== * The input instructions form a binary DAG. This method merges * expressions like * * Z1 = a+b; * Z2 = Z1+c; * * into * * Z2 = a+b+c; * * An instruction is merged iff it only has one parent and the * operator equals its parent's operator. * * This still leaves some freedom: where should the coefficients end * up in cases as: * * Z1 = Z2 + x <=> Z1 = 2*Z2 + x * Z2 = 2*x*y Z2 = x*y * * Both are relevant, e.g. for CSE of the form "2*x" and "2*Z2". The * flag "move_coeff" moves coefficients from LHS-like expressions to * RHS-like expressions. * * Furthermore, this method removes empty equation (Z1=0), that are * introduced by some "optimize_greedy" substitutions. * * Implementation details * ====================== * Expressions are mostly traversed via a stack, so that parents are * evaluated before their children. * * With "move_coeff" set coefficients are moved, but this leads to * some tricky cases, e.g. * * Z1 = Z2 + x * Z2 = 2*y * * Here Z2 reduces to the trivial equation Z2=y, which should be * eliminated. Here the array skip[i] comes in. * * Furthermore in the case * * Z1 = Z2 + x * Z2 = 2*Z3 * Z3 = x*Z4 * Z4 = y*z * * after substituting Z1 = 2*Z3 + x, the parent expression for Z4 * becomes Z3 instead of Z2. This is where renum_par[i] comes in. * * Finally, once a coefficient has been moved, skip_coeff[i] is set * and this coefficient is copied into the new expression anymore. */ vector merge_operators (const vector &all_instr, bool move_coeff) { #ifdef DEBUG_MORE MesPrint ("*** [%s, w=%w] CALL: merge_operators", thetime_str().c_str()); #endif // get starting positions of instructions vector instr; const WORD *tbegin = &*all_instr.begin(); const WORD *tend = tbegin+all_instr.size(); // copy all instructions to temp space. There will be n of them in instr. for (const WORD *t=tbegin; t!=tend; t+=*(t+2)) { instr.push_back(t); } int n = instr.size(); // find parents and number of parents of instructions vector par(n), numpar(n,0); for (int i=0; i 1, increase numpar, // so that this is not merged if (*(t+*t-3)!=1 || *(t+*t-2)!=1 || ABS(*(t+*t-1))!=3) numpar[*(t+3)]++; if (*(t+4)>1) numpar[*(t+3)]++; } } } // determine which instructions to merge stack s; s.push(n-1); vector vis(n,false); while (!s.empty()) { int i=s.top(); s.pop(); if (vis[i]) continue; vis[i]=true; for (const WORD *t=instr[i]+OPTHEAD; *t!=0; t+=*t) if ( *(t+1)==EXTRASYMBOL && *t!=1+ABS(*(t+*t-1)) ) s.push(*(t+3)); // condition: one parent and equal operator as parent if (numpar[i]==1 && *(instr[i]+1)==*(instr[par[i]]+1)) par[i] = par[par[i]]; // The expr into which we subst par[i] to get i else par[i] = i; } // merge instructions into new instructions vector newinstr; // stack of new expressions, all 0-indexed stack new_expr; new_expr.push(n-1); vis = vector(n,false); // skip empty equations (might be introduced by greedy optimizations) vector skip(n,false), skipcoeff(n,false); for (int i=0; i renum_par(n); for (int i=0; i this_expr; this_expr.push(x+1); while (!this_expr.empty()) { // pop from stack, determine expr.nr and sign int i = this_expr.top(); this_expr.pop(); int sign = SGN(i); i = ABS(i)-1; for (const WORD *t=instr[i]+OPTHEAD; *t!=0; t+=*t) { // terms in i // don't copy a term if: // (1) skip=true, since then it's merged into the parent // (2) extrasymbol with parent=x, because its children should be copied // (3) coefficient with skipcoeff=true, since it's already copied bool copy = !skip[i]; if (*t!=1+ABS(*(t+*t-1)) && *(t+1)==EXTRASYMBOL) { if (par[*(t+3)] == x) { // parent of term refers to x. we push it with its sign if no skip is true // and the sign of the expr. this_expr.push(sign * (skip[i]||skipcoeff[i] ? 1 : SGN(*(t+*t-1))) * (1+*(t+3))); if (*(instr[i]+1) == OPER_MUL) sign=1; copy=false; } else { new_expr.push(*(t+3)); } } if (*t == 1+ABS(*(t+*t-1)) && skipcoeff[i]) { copy=false; } if (copy) { // first term, so add header if (first_copy) { newinstr.push_back(renum_par[x]); // expr.nr. newinstr.push_back(*(instr[x]+1)); // operator newinstr.push_back(3); // length OPTHEAD? first_copy=false; } // copy term and adjust sign int thislenidx = newinstr.size(); newinstr.insert(newinstr.end(), t, t+*t); // Put the whole term in newinstr newinstr.back() *= sign; if (*(instr[i]+1) == OPER_MUL) sign=1; newinstr[lenidx] += *t; // check for moving coefficients up // necessary condition: MUL-expression with 1 parent if (move_coeff && *t!=1+ABS(*(t+*t-1)) && *(instr[i]+1)!=OPER_COMMA && *(t+1)==EXTRASYMBOL && numpar[*(t+3)]==1 && *(instr[*(t+3)]+1)==OPER_MUL) { // coefficient is always the first term (that's how Horner+generate works) const WORD *t1 = instr[*(t+3)]+OPTHEAD; const WORD *t2 = t1+*t1; if (*t1 == 1+ABS(*(t1+*t1-1))) { // t1 pointer to a coefficient, so move it // remove old coefficient of 1 WORD *t3 = &*newinstr.end(); // int sign2 = SGN(t3[-1]); // newinstr.erase(newinstr.end()-3, newinstr.end()); // count number of arguments; iff it is 2 move the (extra)symbol too int numargs=0; for (const WORD *tt=t1; *tt!=0; tt+=*tt) { numargs++; } if (numargs==2 && *(t2+4)==1) { // replace (extra)symbol newinstr[newinstr.size()-4] = *(t2+1); newinstr[newinstr.size()-3] = *(t2+2); newinstr[newinstr.size()-2] = *(t2+3); newinstr[newinstr.size()-1] = *(t2+4); sign2 *= SGN(*(t2+*t2-1)); // was t2[7] // ignore this expression from now on skip[*(t+3)]=true; if (*(t2+1)==EXTRASYMBOL) renum_par[*(t+3)] = *(t2+3); } else { // otherwise, ignore coefficient from now on // we need to collect the signs of the terms // first and set them to one. This was forgotten // before. Gave occasional errors. if ( numargs > 2 || ( numargs == 2 && t2[4] > 1 ) ) { for (WORD *tt=(WORD *)t2; *tt!=0; tt+=*tt) { if ( tt[*tt-1] < 0 ) { tt[*tt-1] = -tt[*tt-1]; sign2 = -sign2; } } } skipcoeff[*(t+3)]=true; } // add new coefficient newinstr.insert(newinstr.end(), t1+1, t1+*t1); newinstr.back() *= sign2; newinstr[thislenidx] += ABS(newinstr.back()) - 3; newinstr[lenidx] += ABS(newinstr.back()) - 3; } } } } } // if something has been copied, add trailing zero if (!first_copy) { newinstr.push_back(0); newinstr[lenidx]++; } } // renumber the expressions to 0,1,2,..,; only keep expressions with // skip=false which are their own parent after a renumbering in case // of moved coefficients // find renumber scheme vector renum(n,-1); int next=0; for (int i=0; i sortinstr; for (int i=0; i coeff; vector eqnidxs; bool operator< (const optimization &a) const { if (arg1 != a.arg1) return arg1 < a.arg1; if (arg2 != a.arg2) return arg2 < a.arg2; if (type != a.type) return type < a.type; return coeff < a.coeff; } }; /* #] class Optimization : #[ find_optimizations : */ /** Find optimizations * * Description * =========== * This method find all optimization of the form described in "class * Optimization". It process every equation, looking for possible * optimizations and stores them in a fast-access data structure to * count the total improvement of an optimization. */ vector find_optimizations (const vector &instr) { #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] CALL: find_optimizations", thetime_str().c_str()); #endif // #[ Startup : // the resulting vector of optimizations vector res; // a map to count the improvement of an optimization; the // improvement is stored as a vector with equation numbers map > cnt; // a map to identify coefficients map,int> idx_coeff; const WORD *ebegin = &*instr.begin(); const WORD *eend = ebegin+instr.size(); for (int optim_type=0; optim_type<=4; optim_type++) { cnt.clear(); idx_coeff.clear(); optimization optim; optim.type = optim_type; // #] Startup : // #[ type 0 : find optimizations of the form z=x^n (optim.type==0) if (optim_type == 0) { for (const WORD *e=ebegin; e!=eend; e+=*(e+2)) { if (*(e+1) != OPER_MUL) continue; for (const WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+4) > 1) { optim.arg1 = (*(t+1)==SYMBOL ? 1 : -1) * (*(t+3) + 1); optim.arg2 = *(t+4); cnt[optim].push_back(e-ebegin); } } } } // #] type 0 : // #[ type 1 : find optimizations of the form z=x*y (optim.type==1) if (optim_type == 1) { for (const WORD *e=ebegin; e!=eend; e+=*(e+2)) { if (*(e+1) != OPER_MUL) continue; for (const WORD *t1=e+3; *t1!=0; t1+=*t1) { if (*t1 == ABS(*(t1+*t1-1))+1) continue; int x1 = (*(t1+1)==SYMBOL ? 1 : -1) * (*(t1+3) + 1); for (const WORD *t2=t1+*t1; *t2!=0; t2+=*t2) { if (*t2 == ABS(*(t2+*t2-1))+1) continue; int x2 = (*(t2+1)==SYMBOL ? 1 : -1) * (*(t2+3) + 1); if (*(t1+4) == *(t2+4)) { optim.arg1 = x1; optim.arg2 = x2; if (optim.arg1 > optim.arg2) swap(optim.arg1, optim.arg2); if (*(t1+4) == 1) cnt[optim].push_back(e-ebegin); else { // E=x^n*y^n -> z=x*y; E=z^n is double improvement cnt[optim].push_back(e-ebegin); cnt[optim].push_back(e-ebegin); } } } } } } // #] type 1 : // #[ type 2 : find optimizations of the form z=c*x (optim.type==2) if (optim_type == 2) { for (const WORD *e=ebegin; e!=eend; e+=*(e+2)) { if (*(e+1) == OPER_ADD) { // in ADD-equation for (const WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+4)==1) { if (ABS(*(t+*t-1))==3 && *(t+*t-2)==1 && *(t+*t-3)==1) continue; optim.coeff = vector(t+*t-ABS(*(t+*t-1)), t+*t); optim.coeff.back() = ABS(optim.coeff.back()); optim.arg1 = (*(t+1)==SYMBOL ? 1 : -1) * (*(t+3) + 1); optim.arg2 = 0; cnt[optim].push_back(e-ebegin); } } } else if (*(e+1) == OPER_MUL) { // in MUL-equation optim.coeff.clear(); for (const WORD *t=e+3; *t!=0; t+=*t) if (*t == ABS(*(t+*t-1))+1) { if (ABS(*(t+*t-1))==3 && *(t+*t-2)==1 && *(t+*t-3)==1) continue; optim.coeff = vector(t+*t-ABS(*(t+*t-1)), t+*t); optim.coeff.back() = ABS(optim.coeff.back()); } if (!optim.coeff.empty()) for (const WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+4) != 1) continue; optim.arg1 = (*(t+1)==SYMBOL ? 1 : -1) * (*(t+3) + 1); optim.arg2 = 0; cnt[optim].push_back(e-ebegin); } } } } // #] type 2 : // #[ type 3 : find optimizations of the form z=x+c (optim.type==3) if (optim_type == 3) { for (const WORD *e=ebegin; e!=eend; e+=*(e+2)) { if (*(e+1) != OPER_ADD) continue; optim.coeff.clear(); for (const WORD *t=e+3; *t!=0; t+=*t) if (*t == ABS(*(t+*t-1))+1) { optim.coeff = vector(t+*t-ABS(*(t+*t-1)), t+*t); } if (!optim.coeff.empty()) { for (const WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (ABS(*(t+*t-1))!=3 || *(t+*t-2)!=1 || *(t+*t-3)!=1) continue; if (*(t+*t-1)==-3) optim.coeff.back() *= -1; optim.arg1 = (*(t+1)==SYMBOL ? 1 : -1) * (*(t+3) + 1); optim.arg2 = 0; cnt[optim].push_back(e-ebegin); if (*(t+*t-1)==-3) optim.coeff.back() *= -1; } } } } // #] type 3 : // #[ type 4,5 : find optimizations of the form z=x+y or z=x-y (optim.type==4 or 5) if (optim_type == 4) { for (const WORD *e=ebegin; e!=eend; e+=*(e+2)) { if (*(e+1) != OPER_ADD) continue; for (const WORD *t1=e+3; *t1!=0; t1+=*t1) { if (*t1 == ABS(*(t1+*t1-1))+1) continue; int x1 = (*(t1+1)==SYMBOL ? 1 : -1) * (*(t1+3) + 1); for (const WORD *t2=t1+*t1; *t2!=0; t2+=*t2) { if (*t2 == ABS(*(t2+*t2-1))+1) continue; int x2 = (*(t2+1)==SYMBOL ? 1 : -1) * (*(t2+3) + 1); int sign1 = SGN(*(t1+*t1-1)); int sign2 = SGN(*(t2+*t2-1)); if (BigLong((UWORD *)t1+5, ABS(*(t1+*t1-1))-1, (UWORD *)t2+5, ABS(*(t2+*t2-1))-1) == 0) { optim.type = (sign1 * sign2 == 1 ? 4 : 5); // optimization type optim.arg1 = x1; optim.arg2 = x2; if (optim.arg1 > optim.arg2) { swap(optim.arg1, optim.arg2); } if (ABS(*(t1+*t1-1))==3 && *(t1+*t1-2)==1 && *(t1+*t1-3)==1) cnt[optim].push_back(e-ebegin); else { // E=2x+2y -> z=x+y; E=2z is improvement bby itself cnt[optim].push_back(e-ebegin); cnt[optim].push_back(e-ebegin); } } } } } } // #] type 4,5 : // #[ add : // add optimizations with positive improvement to the result for (map >::iterator i=cnt.begin(); i!=cnt.end(); i++) { int improve = i->second.size() - 1; if (improve > 0) { res.push_back(i->first); res.back().improve = improve; res.back().eqnidxs = i->second; // remove duplicates, that were add to get the correct improvement res.back().eqnidxs.erase(unique(res.back().eqnidxs.begin(), res.back().eqnidxs.end()), res.back().eqnidxs.end()); } } } // #] add : #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: find_optimizations",thetime_str().c_str()); #endif return res; } /* #] find_optimizations : #[ do_optimization : */ /** Do optimization * * Description * =========== * This method performs an optimization. It scans through the * equations of "optim.eqnidxs" and looks in which this optimization * can still be performed (due to other performed optimizations this * isn't always the case). If possible, it substitutes the common * subexpression by a new extra symbol numbered "newid". Finally, * the new extrasymbol is defined accordingly. * * Substitutions may lead to trivial equations of the form "Zi=Zj", * but these are removed in the end of the method. The method returns * whether the substitution has been done once or more (or not). */ bool do_optimization (const optimization optim, vector &instr, int newid) { // #[ Debug code : #ifdef DEBUG_GREEDY if (optim.type==0) MesPrint ("*** [%s, w=%w] CALL: do_optimization(improve=%d, %c%d^%d)", thetime_str().c_str(), optim.improve, optim.arg1>0?'x':'Z', ABS(optim.arg1)-1, optim.arg2); else if (optim.type==1 || optim.type>=4) MesPrint ("*** [%s, w=%w] CALL: do_optimization(improve=%d, %c%d%c%c%d)", thetime_str().c_str(), optim.improve, optim.arg1>0?'x':'Z', ABS(optim.arg1)-1, optim.type==1 ? '*' : optim.type==4 ? '+' : '-', optim.arg2>0?'x':'Z', ABS(optim.arg2)-1); else { WORD n = optim.coeff.back()/2; UBYTE num[BITSINWORD*ABS(n)], den[BITSINWORD*ABS(n)]; PrtLong((UWORD *)&optim.coeff[0], n, num); PrtLong((UWORD *)&optim.coeff[ABS(n)], ABS(n), den); MesPrint ("*** [%s, w=%w] CALL: do_optimization(improve=%d, %c%d%c%s/%s)", thetime_str().c_str(), optim.improve, optim.arg1>0?'x':'Z', ABS(optim.arg1)-1, optim.type==2 ? '*' : '+', num,den); } #endif // #] Debug code : bool substituted = false; WORD *ebegin = &*instr.begin(); // #[ type 0 : substitution of the form z=x^n (optim.type==0) if (optim.type == 0) { int vartypex = optim.arg1>0 ? SYMBOL : EXTRASYMBOL; int varnumx = ABS(optim.arg1) - 1; int n = optim.arg2; for (int i=0; i<(int)optim.eqnidxs.size(); i++) { WORD *e = ebegin + optim.eqnidxs[i]; if (*(e+1) != OPER_MUL) continue; // scan through equation for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+1)==vartypex && *(t+3)==varnumx && *(t+4) % n == 0) { // substitute *(t+1) = EXTRASYMBOL; *(t+3) = newid; *(t+4) /= n; substituted = true; } } } if (!substituted) { #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: do_optimization : res=false", thetime_str().c_str(), optim.improve); #endif return false; } // add extra equation (Tnew = x^n) instr.push_back(newid); // eqn.nr instr.push_back(OPER_MUL); // operator instr.push_back(12); // total length instr.push_back(8); // term length instr.push_back(vartypex); // (extra)symbol instr.push_back(4); // symbol length instr.push_back(varnumx); // symbol id instr.push_back(n); // power instr.push_back(1); instr.push_back(1); // coefficient 1 instr.push_back(3); instr.push_back(0); // trailing 0 } // #] type 0 : // #[ type 1 : substitution of the form z=x*y (optim.type==1) if (optim.type == 1) { int vartypex = optim.arg1>0 ? SYMBOL : EXTRASYMBOL; int varnumx = ABS(optim.arg1) - 1; int vartypey = optim.arg2>0 ? SYMBOL : EXTRASYMBOL; int varnumy = ABS(optim.arg2) - 1; for (int i=0; i<(int)optim.eqnidxs.size(); i++) { WORD *e = ebegin + optim.eqnidxs[i]; if (*(e+1) != OPER_MUL) continue; // scan through equation int powx=0, powy=0; for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+1)==vartypex && *(t+3)==varnumx) powx = *(t+4); if (*(t+1)==vartypey && *(t+3)==varnumy) powy = *(t+4); } // substitute if found if (powx>0 && powy>0 && powx==powy) { WORD sign = 1; WORD *newt = e+3; for (WORD *t=e+3; *t!=0;) { int dt=*t; if (*t == ABS(*(t+*t-1))+1 || (!(*(t+1)==vartypex && *(t+3)==varnumx) && !(*(t+1)==vartypey && *(t+3)==varnumy))) { memmove(newt, t, *t*sizeof(WORD)); newt += dt; } else { sign *= SGN(*(t+*t-1)); } t+=dt; } *newt++ = 8; // term length *newt++ = EXTRASYMBOL; // extrasymbol *newt++ = 4; // symbol length *newt++ = newid; // symbol id *newt++ = powx; // power *newt++ = 1; *newt++ = 1; // coefficient +/-1 *newt++ = 3*sign; *newt++ = 0; // trailing 0 substituted = true; } } if (!substituted) { #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: do_optimization : res=false", thetime_str().c_str(), optim.improve); #endif return false; } // add extra equation (Tnew = x*y) instr.push_back(newid); // eqn.nr instr.push_back(OPER_MUL); // operator instr.push_back(20); // total length instr.push_back(8); // LHS length instr.push_back(vartypex); // (extra)symbol instr.push_back(4); // symbol length instr.push_back(varnumx); // symbol id instr.push_back(1); // power 1 instr.push_back(1); instr.push_back(1); // coefficient 1 instr.push_back(3); instr.push_back(8); // RHS length instr.push_back(vartypey); // (extra)symbol instr.push_back(4); // symbol length instr.push_back(varnumy); // symbol id instr.push_back(1); // power 1 instr.push_back(1); instr.push_back(1); // coefficient 1 instr.push_back(3); instr.push_back(0); // trailing 0 } // #] type 1 : // #[ type 2 : substitution of the form z=c*x (optim.type==2) if (optim.type == 2) { int vartype = optim.arg1>0 ? SYMBOL : EXTRASYMBOL; int varnum = ABS(optim.arg1) - 1; WORD ncoeff = optim.coeff.back(); // scan through equations for (int i=0; i<(int)optim.eqnidxs.size(); i++) { WORD *e = ebegin + optim.eqnidxs[i]; if (*(e+1) == OPER_ADD) { // scan through ADD-equation for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+1)==vartype && ABS(*(t+3))==varnum && *(t+4)==1 && BigLong((UWORD *)&optim.coeff[0],ncoeff-1, (UWORD *)t+*t-ABS(*(t+*t-1)),ABS(*(t+*t-1))-1) == 0) { // substitute int sign = SGN(*(t+*t-1)); WORD *tend = t; while (*tend!=0) tend+=*tend; WORD nmove = tend - t - *t; memmove(t, t+*t, nmove*sizeof(WORD)); t += nmove; *t++ = 8; // term length *t++ = EXTRASYMBOL; // (extra)symbol *t++ = 4; // symbol length *t++ = newid; // symbol id *t++ = 1; // power of 1 *t++ = 1; *t++ = 1; // coefficient of +/-1 *t++ = 3 * sign; *t++ = 0; // trailing 0 substituted = true; break; } } } else if (*(e+1) == OPER_MUL) { bool coeff_match=false, var_match=false; int sign = 1; // scan through MUL-equation for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1 && BigLong((UWORD *)&optim.coeff[0],ncoeff-1, (UWORD *)t+*t-ABS(*(t+*t-1)),ABS(*(t+*t-1))-1) == 0) { coeff_match = true; sign *= SGN(*(t+*t-1)); } else if (*(t+1)==vartype && ABS(*(t+3))==varnum && *(t+4)==1) { var_match = true; sign *= SGN(*(t+*t-1)); } } // substitute if found if (coeff_match && var_match) { WORD *newt = e+3; for (WORD *t=e+3; *t!=0;) { int dt=*t; if (*t!=ABS(*(t+*t-1))+1 && !(*(t+1)==vartype && ABS(*(t+3))==varnum && *(t+4)==1)) { memmove(newt, t, dt*sizeof(WORD)); newt += dt; } t+=dt; } *newt++ = 8; // term length *newt++ = EXTRASYMBOL; // extrasymbol *newt++ = 4; // symbol length *newt++ = newid; // symbol id *newt++ = 1; // power of 1 *newt++ = 1; *newt++ = 1; // coefficient of +/-1 *newt++ = 3 * sign; *newt++ = 0; // trailing 0 substituted = true; } } } if (!substituted) { #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: do_optimization : res=false", thetime_str().c_str(), optim.improve); #endif return false; } // add extra equation (Tnew = c*y) instr.push_back(newid); // eqn.nr instr.push_back(OPER_ADD); // operator instr.push_back(9+ABS(ncoeff)); // total length instr.push_back(5+ABS(ncoeff)); // term length instr.push_back(vartype); // (extra)symbol instr.push_back(4); // symbol length instr.push_back(varnum); // symbol id instr.push_back(1); // power of 1 for (int i=0; i0 ? SYMBOL : EXTRASYMBOL; int varnum = ABS(optim.arg1) - 1; WORD ncoeff = optim.coeff.back(); // scan through equation for (int i=0; i<(int)optim.eqnidxs.size(); i++) { WORD *e = ebegin + optim.eqnidxs[i]; if (*(e+1) != OPER_ADD) continue; int coeff_match=0, var_match=0; for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1 && BigLong((UWORD *)&optim.coeff[0],ABS(ncoeff)-1, (UWORD *)t+*t-ABS(*(t+*t-1)),ABS(*(t+*t-1))-1) == 0) coeff_match = SGN(ncoeff) * SGN(*(t+*t-1)); else if (*(t+1)==vartype && ABS(*(t+3))==varnum && *(t+4)==1) var_match = SGN(*(t+7)); } // substitute if found (x+c and -x-c and matches) if (coeff_match * var_match == 1) { WORD *newt = e+3; for (WORD *t=e+3; *t!=0;) { int dt=*t; if (*t!=ABS(*(t+*t-1))+1 && !(*(t+1)==vartype && ABS(*(t+3))==varnum && *(t+4)==1)) { memmove(newt, t, dt*sizeof(WORD)); newt += dt; } t+=dt; } *newt++ = 8; // term length *newt++ = EXTRASYMBOL; // extrasymbol *newt++ = 4; // symbol length *newt++ = newid; // symbol id *newt++ = 1; // power of 1 *newt++ = 1; *newt++ = 1; // coefficient of +/-1 *newt++ = 3*coeff_match; *newt++ = 0; // trailing zero substituted = true; } } if (!substituted) { #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: do_optimization : res=false", thetime_str().c_str(), optim.improve); #endif return false; } // add extra equation (Tnew = x+c) instr.push_back(newid); // eqn.nr instr.push_back(OPER_ADD); // operator instr.push_back(13+ABS(ncoeff)); // total length instr.push_back(8); // x-term length instr.push_back(vartype); // (extra)symbol instr.push_back(4); // symbol length instr.push_back(varnum); // symbol id instr.push_back(1); // power of 1 instr.push_back(1); instr.push_back(1); // coefficient of 1 instr.push_back(3); instr.push_back(ABS(ncoeff)+1); // c-term length for (int i=0; i= 4) { int vartypex = optim.arg1>0 ? SYMBOL : EXTRASYMBOL; int varnumx = ABS(optim.arg1) - 1; int vartypey = optim.arg2>0 ? SYMBOL : EXTRASYMBOL; int varnumy = ABS(optim.arg2) - 1; // scan through equations for (int i=0; i<(int)optim.eqnidxs.size(); i++) { WORD *e = ebegin + optim.eqnidxs[i]; if (*(e+1) != OPER_ADD) continue; const WORD *coeffx=NULL, *coeffy=NULL; WORD ncoeffx=0,ncoeffy=0; // looks for terms for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; // constant if (*(t+1)==vartypex && *(t+3)==varnumx && *(t+4)==1) { coeffx = t+5; ncoeffx = *(t+*t-1); } if (*(t+1)==vartypey && *(t+3)==varnumy && *(t+4)==1) { coeffy = t+5; ncoeffy = *(t+*t-1); } } // check signs (type=4: x+y and -x-y, type=5: x-y and -x+y) ?????? // check signs (type=4: x+y, type=5: x-y) !!!!!!!!!! if (SGN(ncoeffx) * SGN(ncoeffy) * (optim.type==4 ? 1 : -1) == 1) { // check absolute value of coefficients if (BigLong((UWORD *)coeffx, ABS(ncoeffx)-1, (UWORD *)coeffy, ABS(ncoeffy)-1) == 0) { // substitute vector coeff(coeffx, coeffx+ABS(ncoeffx)); WORD *newt = e+3; /* if ( optim.type == 5 ) { while ( *newt ) newt+=*newt; int i = (newt - e) - 3; MesPrint(" < %a",i,e+3); newt = e+3; } */ for (WORD *t=e+3; *t!=0;) { int dt=*t; if (*t == ABS(*(t+*t-1))+1 || (!(*(t+1)==vartypex && *(t+3)==varnumx) && !(*(t+1)==vartypey && *(t+3)==varnumy))) { memmove(newt, t, dt*sizeof(WORD)); newt += dt; } t+=dt; } *newt++ = 5 + ABS(ncoeffx); // term length *newt++ = EXTRASYMBOL; // extrasymbol *newt++ = 4; // symbol length *newt++ = newid; // symbol id *newt++ = 1; // power of 1 for (int j=0; j %a",i,e+3); } */ } } } if (!substituted) { #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: do_optimization : res=false", thetime_str().c_str(), optim.improve); #endif return false; } /* if ( optim.type == 5 ) MesPrint ("improve=%d, %c%d%c%c%d)", optim.improve, optim.arg1>0?'x':'Z', ABS(optim.arg1)-1, optim.type==1 ? '*' : optim.type==4 ? '+' : '-', optim.arg2>0?'x':'Z', ABS(optim.arg2)-1); */ // add extra equation (Tnew = x+/-y) instr.push_back(newid); // eqn.nr instr.push_back(OPER_ADD); // operator instr.push_back(20); // total length instr.push_back(8); // term length instr.push_back(vartypex); // (extra)symbol instr.push_back(4); // symbol length instr.push_back(varnumx); // symbol id instr.push_back(1); // power of 1 instr.push_back(1); instr.push_back(1); // coefficient of 1 instr.push_back(3); instr.push_back(8); // term length instr.push_back(vartypey); // (extra)symbol instr.push_back(4); // symbol length instr.push_back(varnumy); // symbol id instr.push_back(1); // power of 1 instr.push_back(1); instr.push_back(1); // coefficient of +/-1 instr.push_back(3*(optim.type==4?1:-1)); instr.push_back(0); // trailing 0 } // #] type 4,5 : // #[ trivial : remove trivial equations of the form Zi = +/-Zj vector renum(newid+1, 0); bool do_renum=false; // vector may be moved when it is extended ebegin = &*instr.begin(); for (int i=0; i<(int)optim.eqnidxs.size(); i++) { WORD *e = ebegin + optim.eqnidxs[i]; WORD *t = e+3; if (*t==0) continue; // empty (removed) equation if (*(t+*t)!=0) continue; // more than 1 term if (*t!=8) continue; // term not of correct form if (*(t+4)!=1) continue; // power != 1 if (*(t+5)!=1 || *(t+6)!=1) continue; // coeff != +/-1 // trivial term, so renumber this one renum[*e] = SGN(*(t+7)) * (*(t+3) + 1); do_renum = true; // remove equation *t=0; } // #] trivial : // #[ renumbering : // there are renumberings to be done, so loop through all equations if (do_renum) { WORD *eend = ebegin+instr.size(); for (WORD *e=ebegin; e!=eend; e+=*(e+2)) { for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+1)==EXTRASYMBOL && renum[*(t+3)]!=0) { *(t+*t-1) *= SGN(renum[*(t+3)]); *(t+3) = ABS(renum[*(t+3)]) - 1; } } } } // #] renumbering : #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: do_optimization : res=true", thetime_str().c_str(), optim.improve); #endif return true; } /* #] do_optimization : #[ partial_factorize : */ /** Partial factorization of instructions * * Description * =========== * This method performs partial factorization of instructions. In * particular the following instructions * * Z1 = x*a*b * Z2 = x*c*d*e * Z3 = 2*x + Z1 + Z2 + more * * are replaced by * * Z1 = a*b * Z2 = c*d*e * Z3 = Zj + more * Zi = 2 + Z1 + Z2 * Zj = x*Zi * * Here it is necessary that no other equations refer to Z1 and * Z2. The generation of trivial instructions (Zi=Zj or Zi=x) is * prevented. */ int partial_factorize (vector &instr, int n, int improve) { #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] CALL: partial_factorize (n=%d)", thetime_str().c_str(), n); #endif GETIDENTITY; // get starting positions of instructions vector instr_idx(n); WORD *ebegin = &*instr.begin(); WORD *eend = ebegin+instr.size(); for (WORD *e=ebegin; e!=eend; e+=*(e+2)) { instr_idx[*e] = e - ebegin; } // get reference counts /* * The next construction replaces the vector construction which is * rather costly for valgrind (and maybe also in normal running) */ int nmax = 2*n; WORD *numpar = (WORD *)Malloc1(nmax*sizeof(WORD),"numpar"); for ( int i = 0; i < nmax; i++ ) numpar[i] = 0; // vector numpar(n); for (WORD *e=ebegin; e!=eend; e+=*(e+2)) for (WORD *t=e+3; *t!=0; t+=*t) { if (*t == ABS(*(t+*t-1))+1) continue; if (*(t+1) == EXTRASYMBOL) numpar[*(t+3)]++; } // find factorizable expressions for (int i=0; i cnt; // 1-indexed, <0:EXTRASYMBOL, >0:SYMBOL for (WORD *t=e+3; *t!=0; t+=*t) { if (*t==ABS(*(t+*t-1))+1) continue; // count symbols in t if (*(t+4)==1) cnt[(*(t+1)==SYMBOL ? 1 : -1) * (*(t+3)+1)]++; // count symbols in extrasymbols of t if (*(t+1)==EXTRASYMBOL && *(t+4)==1 && numpar[*(t+3)]==1) { WORD *t2 = &*instr.begin() + instr_idx[*(t+3)]; if (*(t2+1) != OPER_MUL) continue; for (t2+=3; *t2!=0; t2+=*t2) { if (*t2 == ABS(*(t2+*t2-1))+1) continue; if (*(t2+4)==1) cnt[(*(t2+1)==SYMBOL ? 1 : -1) * (*(t2+3)+1)]++; } } } // find most-occurring symbol WORD x=0, best=0; for (map::iterator it=cnt.begin(); it!=cnt.end(); it++) if (it->second > best) { x=it->first; best=it->second; } // occurrence>=2 and occurrence>improve, so factorize if (best>=2 && best>improve) { // initialize new equation (Zi from example above) vector new_eqn; new_eqn.push_back(n); new_eqn.push_back(OPER_ADD); new_eqn.push_back(0); // length WORD dt; WORD *newt=e+3; for (WORD *t=e+3; *t!=0; t+=dt) { dt = *t; bool keep=true; if (*t!=ABS(*(t+*t-1))+1) { // factorized symbol is in t itself if (*(t+4)==1) { WORD y = (*(t+1)==SYMBOL ? 1 : -1) * (*(t+3)+1); if (y==x) { new_eqn.push_back(*t-4); new_eqn.insert(new_eqn.end(), t+5, t+dt); keep=false; } } // look in extrasymbol of t with ref.count=1 if (*(t+1)==EXTRASYMBOL && *(t+4)==1 && numpar[*(t+3)]==1) { WORD *t2 = &*instr.begin() + instr_idx[*(t+3)]; if (*(t2+1) == OPER_MUL) { bool has_x=false; for (t2+=3; *t2!=0; t2+=*t2) { if (*t2 == ABS(*(t2+*t2-1))+1) continue; WORD y = (*(t2+1)==SYMBOL ? 1 : -1) * (*(t2+3)+1); // extrasymbol has factorized symbol if (y==x && *(t2+4)==1) { has_x=true; // copy remaining part WORD *tend=t2+*t2; WORD sign = SGN(*(tend-1)); while (*tend!=0) tend+=*tend; int dt2 = tend - (t2+*t2); memmove(t2, t2+*t2, (dt2+1)*sizeof(WORD)); t2 += dt2; *(t2-1) *= sign; break; } } if (has_x) { // extrasymbol has x, so add it to new equation keep=false; int thisidx=new_eqn.size(); new_eqn.insert(new_eqn.end(), t, t+dt); t2 = &*instr.begin() + instr_idx[*(t+3)] + 3; // if becomes trivial, substitute the term if (*(t2+*t2)==0) { // it's a number if (*t2 == ABS(*(t2+*t2-1))+1) { if (ABS(new_eqn[new_eqn.size()-1])==3 && new_eqn[new_eqn.size()-2]==1 && new_eqn[new_eqn.size()-3]==1) { // original equation has coefficient of +/-1, so replace it WORD sign = SGN(new_eqn.back()); new_eqn.erase(new_eqn.begin()+thisidx, new_eqn.end()); new_eqn.insert(new_eqn.end(), t2, t2+*t2); new_eqn.back() *= sign; *t2 = 0; } else { // two non-trivial coefficients, so multiply them // note: untested code (found no way to trigger it) UWORD *tmp = NumberMalloc("partial_factorize"); WORD ntmp=0; MulRat(BHEAD (UWORD *)t2+*t2-ABS(*(t2+*t2-1)), *(t2+*t2-1), (UWORD *)&*(new_eqn.end()-ABS(new_eqn.back())), new_eqn.back(), tmp, &ntmp); new_eqn.erase(new_eqn.begin()+thisidx, new_eqn.end()); new_eqn.push_back(ABS(ntmp)+1); new_eqn.insert(new_eqn.end(), tmp, tmp+ABS(ntmp)); NumberFree(tmp,"partial_factorize"); *t2 = 0; } } else if (*(t2+4)==1) { // it's a variable new_eqn.back() *= SGN(*(t2+*t2-1)); new_eqn[thisidx+1] = *(t2+1); new_eqn[thisidx+2] = *(t2+2); new_eqn[thisidx+3] = *(t2+3); new_eqn[thisidx+4] = *(t2+4); *t2 = 0; } } } } } } // no x, so copy it if (keep) { memmove(newt, t, dt*sizeof(WORD)); newt += dt; } } // finalize new equation new_eqn.push_back(0); new_eqn[2] = new_eqn.size(); bool empty = newt == e+3; if ( n+1 >= nmax ) { int i, newnmax = nmax*2; WORD *newnumpar = (WORD *)Malloc1(newnmax*sizeof(WORD),"newnumpar"); for ( i = 0; i < n; i++ ) newnumpar[i] = numpar[i]; for ( ; i < newnmax; i++ ) newnumpar[i] = 0; M_free(numpar,"numpar"); numpar = newnumpar; nmax = newnmax; } // numpar.push_back(0); n++; // if original is not empty, add new equation (Zj) to it // otherwise replace it later if (!empty) { *newt++ = 8; *newt++ = EXTRASYMBOL; *newt++ = 4; *newt++ = n; *newt++ = 1; *newt++ = 1; *newt++ = 1; *newt++ = 3; *newt++ = 0; } // add new equation to instructions instr_idx.push_back(instr.size()); instr.insert(instr.end(), new_eqn.begin(), new_eqn.end()); // generate another new equation (Zj=x*Zi) new_eqn.clear(); new_eqn.push_back(n); new_eqn.push_back(OPER_MUL); new_eqn.push_back(20); new_eqn.push_back(8); // add factorized symbol if (x>0) { new_eqn.push_back(SYMBOL); new_eqn.push_back(4); new_eqn.push_back(x-1); new_eqn.push_back(1); } else { new_eqn.push_back(EXTRASYMBOL); new_eqn.push_back(4); new_eqn.push_back(-x-1); new_eqn.push_back(1); } new_eqn.push_back(1); new_eqn.push_back(1); new_eqn.push_back(3); new_eqn.push_back(8); // add new equation (Zi) new_eqn.push_back(EXTRASYMBOL); new_eqn.push_back(4); new_eqn.push_back(n-1); new_eqn.push_back(1); new_eqn.push_back(1); new_eqn.push_back(1); new_eqn.push_back(3); new_eqn.push_back(0); if (!empty) { // add new equation (Zj) to instructions instr_idx.push_back(instr.size()); instr.insert(instr.end(), new_eqn.begin(), new_eqn.end()); if ( n+1 >= nmax ) { int i, newnmax = nmax*2; WORD *newnumpar = (WORD *)Malloc1(newnmax*sizeof(WORD),"newnumpar"); for ( i = 0; i < n; i++ ) newnumpar[i] = numpar[i]; for ( ; i < newnmax; i++ ) newnumpar[i] = 0; M_free(numpar,"numpar"); numpar = newnumpar; nmax = newnmax; } // numpar.push_back(0); n++; } else { // replace e with Zj e = &*instr.begin() + instr_idx[i]; e[1] = OPER_MUL; memcpy(e+3, &new_eqn[3], (new_eqn.size()-3)*sizeof(WORD)); } // decrease i, so this expression is factorized again if possible i--; } } #ifdef DEBUG_GREEDY MesPrint ("*** [%s, w=%w] DONE: partial_factorize (n=%d)", thetime_str().c_str(), n); #endif M_free(numpar,"numpar"); return n; } /* #] partial_factorize : #[ optimize_greedy : */ /** Optimize instructions greedily * * Description * =========== * This method optimizes an expression greedily. It calls * "find_optimizations" to obtain candidates and performs the best * one(s) by calling "do_optimization". * * How many different optimization are done, before * "find_optimization" is called again, is determined by the * settings "greedyminnum" and "greedymaxperc". * * During the optimization process, sequences of zeroes are * introduced in the instructions, since moving all instructions * when one gets optimized, is very costly. Therefore, in the end, * the instructions are "compressed" again to remove these extra * zeroes. */ vector optimize_greedy (vector instr, LONG time_limit) { #ifdef DEBUG int old_num_oper = count_operators(instr); MesPrint ("*** [%s, w=%w] CALL: optimize_greedy(numoper=%d)", thetime_str().c_str(), old_num_oper); #endif LONG start_time = TimeWallClock(1); WORD *ebegin = &*instr.begin(); WORD *eend = ebegin+instr.size(); // store final equation, since it must be the last equation later int final_eqn_idx = 0; int next_eqn = 0; for (WORD *e=ebegin; e!=eend; e+=*(e+2)) { next_eqn = *e + 1; final_eqn_idx = e-ebegin; } // optimize instructions while (TimeWallClock(1)-start_time < time_limit) { int old_next_eqn = next_eqn; // find optimizations vector optim = find_optimizations(instr); // add_eqnidxs contains modified equations, which might have to be updated later again vector add_eqnidxs; // number of optimizations to do int num_do_optims = max(AO.Optimize.greedyminnum, (int)optim.size()*AO.Optimize.greedymaxperc/100); // if best improvement is one, do all optimizations int best_improve=0; for (int i=0; i<(int)optim.size(); i++) best_improve = max(best_improve, optim[i].improve); if (best_improve <= 1) num_do_optims = MAXPOSITIVE; // do a number of optimizations while (optim.size() > 0 && num_do_optims-- > 0) { // find best optimization int best=0; best_improve=0; for (int i=0; i<(int)optim.size(); i++) if (optim[i].improve > best_improve) { best=i; best_improve=optim[i].improve; } // add extra equations for (int i=0; i<(int)add_eqnidxs.size(); i++) optim[best].eqnidxs.push_back(add_eqnidxs[i]); // do optimization, update next_eqn if successful int next_idx = instr.size(); if (do_optimization(optim[best], instr, next_eqn)) { next_eqn++; add_eqnidxs.push_back(next_idx); } optim.erase(optim.begin()+best); } // partially factorize with improve >= best_improve next_eqn = partial_factorize(instr, next_eqn, best_improve); // check whether nothing has changed if (next_eqn == old_next_eqn) break; } // add final equation to the back (must be by definition) instr.push_back(next_eqn); instr.insert(instr.end(), instr.begin()+final_eqn_idx+1, instr.begin()+final_eqn_idx+instr[final_eqn_idx+2]); // removed original final equation instr[final_eqn_idx+3] = 0; // remove extra zeroes WORD *t = &instr[0]; ebegin = &*instr.begin(); eend = ebegin+instr.size(); int de=0; for (WORD *e=ebegin; e!=eend; e+=de) { de = *(e+2); int n=3; while (*(e+n) != 0) n+=*(e+n); n++; memmove (t, e, n*sizeof(WORD)); *(t+2) = n; t += n; } instr.resize(t - &instr[0]); #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: optimize_greedy(numoper=%d) : numoper=%d", thetime_str().c_str(), old_num_oper, count_operators(instr)); #endif return instr; } /* #] optimize_greedy : #[ recycle_variables : */ /** Recycle variables * * Description * =========== * The current input uses many temporary variables. Many of them * become obsolete at some point during the evaluation of the code, * so can be recycled. This method renumbers the temporary * variables, so that they are recycled. Furthermore, the input is * order in depth-first order, so that the instructions can be * performed consecutively. * * Implementation details * ====================== * First, for each subDAG, an estimate for the number of variables * needed is made. This is done by the following recursive formula: * * #vars(x) = max(#vars(ch_i(x)) + i), * * with ch_i(x) the i-th child of x, where the childs are ordered * w.r.t. #vars(ch_i). This formula is exact if the input forms a * tree, and otherwise gives a reasonable estimate. * * Then, the instructions are reordered in a depth-first order with * childs ordered w.r.t. #vars. Next, the times that variables * become obsolete are found. Each LHS of an instruction is * renumbered to the lowest-numbered temporary variable that is * available at that time. */ vector recycle_variables (const vector &all_instr) { #ifdef DEBUG_MORE MesPrint ("*** [%s, w=%w] CALL: recycle_variables", thetime_str().c_str()); #endif // get starting positions of instructions vector instr; const WORD *tbegin = &*all_instr.begin(); const WORD *tend = tbegin+all_instr.size(); for (const WORD *t=tbegin; t!=tend; t+=*(t+2)) instr.push_back(t); int n = instr.size(); // determine with expressions are connected, how many intermediate // are needed (assuming it's a expression tree instead of a DAG) and // sort the leaves such that you need a minimal number of variables vector vars_needed(n); vector vis(n,false); vector > conn(n); stack s; s.push(n); while (!s.empty()) { int i=s.top(); s.pop(); if (i>0) { i--; if (vis[i]) continue; vis[i]=true; s.push(-(i+1)); // find all connections for (const WORD *t=instr[i]+3; *t!=0; t+=*t) if (*t!=1+ABS(*(t+*t-1)) && *(t+1)==EXTRASYMBOL) { int k = *(t+3); conn[i].push_back(k); s.push(k+1); } } else { i=-i-1; // sort the childs w.r.t. needed variables vector > need; for (int j=0; j<(int)conn[i].size(); j++) need.push_back(make_pair(vars_needed[conn[i][j]], conn[i][j])); // keep the comma expression in proper order if (*(instr[i]+1) != OPER_COMMA) sort(need.rbegin(), need.rend()); vars_needed[i] = 1; for (int j=0; j<(int)need.size(); j++) { vars_needed[i] = max(vars_needed[i], need[j].first+j); conn[i][j] = need[j].second; } } } // order the instructions in depth-first order and determine the first // and last occurrences of variables vector order, first(n,0), last(n,0); vis = vector(n,false); s.push(n); while (!s.empty()) { int i=s.top(); s.pop(); if (i>0) { i--; if (vis[i]) continue; vis[i]=true; s.push(-(i+1)); for (int j=(int)conn[i].size()-1; j>=0; j--) s.push(conn[i][j]+1); } else { i=-i-1; first[i] = last[i] = order.size(); order.push_back(i); for (int j=0; j<(int)conn[i].size(); j++) { int k = conn[i][j]; last[k] = max(last[k], first[i]); } } } // find the renumbering to recycled variables, where at any time the // lowest-indexed variable that can be used is chosen int numvar=0; set var; vector renum(n); for (int i=0; i<(int)order.size(); i++) { for (int j=0; j<(int)conn[order[i]].size(); j++) { int k = conn[order[i]][j]; if (last[k] == i) var.insert(renum[k]); } if (var.empty()) var.insert(numvar++); renum[order[i]] = *var.begin(); var.erase(var.begin()); } // put the number of variables used in a preprocessor variable // generate new instructions with the renumbering vector newinstr; for (int i=0; i<(int)order.size(); i++) { int x = order[i]; int j = newinstr.size(); newinstr.insert(newinstr.end(), instr[x], instr[x]+*(instr[x]+2)); newinstr[j] = renum[newinstr[j]]; for (WORD *t=&newinstr[j+3]; *t!=0; t+=*t) if (*t!=1+ABS(*(t+*t-1)) && *(t+1)==EXTRASYMBOL) *(t+3) = renum[*(t+3)]; } #ifdef DEBUG_MORE MesPrint ("*** [%s, w=%w] DONE: recycle_variables", thetime_str().c_str()); #endif return newinstr; } /* #] recycle_variables : #[ optimize_expression_given_Horner : */ /** Optimize expression given a Horner scheme * * Description * =========== * This method picks one Horner scheme from the list of best Horner * schemes, applies this scheme to the expression and then, * depending on optimize.settings, does a common subexpression * elimination (CSE) or performs greedy optimizations. * * CSE is fast, while greedy might be slow. CSE followed by greedy * is faster than greedy alone, but typically results in slightly * worse code (not proven; just observed). */ void optimize_expression_given_Horner () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: optimize_expression_given_Horner", thetime_str().c_str()); #endif GETIDENTITY; // initialize timer LONG start_time = TimeWallClock(1); LONG time_limit = 100 * AO.Optimize.greedytimelimit / (AO.Optimize.horner == O_MCTS ? AO.Optimize.mctsnumkeep : 1); if (time_limit == 0) time_limit=MAXPOSITIVE; // pick a Horner scheme from the list LOCK(optimize_lock); vector Horner_scheme = optimize_best_Horner_schemes.back(); optimize_best_Horner_schemes.pop_back(); UNLOCK(optimize_lock); // if ( ( AO.Optimize.debugflags&2 ) == 2 ) { // MesPrint ("Scheme: %a",Horner_scheme.size(),&(Horner_scheme[0])); // } // apply Horner scheme vector tree = Horner_tree(optimize_expr, Horner_scheme); // generate instructions, eventually with CSE vector instr; if (AO.Optimize.method == O_CSE || AO.Optimize.method == O_CSEGREEDY) instr = generate_instructions(tree, true); else instr = generate_instructions(tree, false); /// eventually do greedy optimizations if (AO.Optimize.method == O_CSEGREEDY || AO.Optimize.method == O_GREEDY) { instr = merge_operators(instr, false); instr = optimize_greedy(instr, time_limit-(TimeWallClock(1)-start_time)); instr = merge_operators(instr, true); instr = optimize_greedy(instr, time_limit-(TimeWallClock(1)-start_time)); } instr = merge_operators(instr, true); // recycle the temporary variables instr = recycle_variables(instr); // determine the quality of the code and possibly update the best code int num_oper = count_operators(instr); LOCK(optimize_lock); if (num_oper < optimize_best_num_oper) { optimize_num_vars = Horner_scheme.size(); optimize_best_num_oper = num_oper; optimize_best_instr = instr; optimize_best_vars = vector(AN.poly_vars, AN.poly_vars+AN.poly_num_vars); } UNLOCK(optimize_lock); // clean poly_vars, that are allocated by Horner_tree AN.poly_num_vars = 0; M_free(AN.poly_vars,"poly_vars"); #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: optimize_expression_given_Horner", thetime_str().c_str()); #endif } /* #] optimize_expression_given_Horner : #[ PF_optimize_expression_given_Horner : */ #ifdef WITHMPI // Initialization. void PF_optimize_expression_given_Horner_master_init () { // Nothing to do for now. } // Wait for an idle slave and return the process number. int PF_optimize_expression_given_Horner_master_next() { // Find an idle slave. int next; PF_LongSingleReceive(PF_ANY_SOURCE, PF_OPT_HORNER_MSGTAG, &next, NULL); return next; } // The main function on the master. void PF_optimize_expression_given_Horner_master () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: PF_optimize_expression_given_Horner_master", thetime_str().c_str()); #endif // pick a Horner scheme from the list vector Horner_scheme = optimize_best_Horner_schemes.back(); optimize_best_Horner_schemes.pop_back(); // Find an idle slave. int next = PF_optimize_expression_given_Horner_master_next(); // Send a new task to the slave. PF_PrepareLongSinglePack(); int len = Horner_scheme.size(); PF_LongSinglePack(&len, 1, PF_INT); PF_LongSinglePack(&Horner_scheme[0], len, PF_WORD); PF_LongSingleSend(next, PF_OPT_HORNER_MSGTAG); #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: PF_optimize_expression_given_Horner_master", thetime_str().c_str()); #endif } // Wait for all the slaves to finish their tasks. void PF_optimize_expression_given_Horner_master_wait () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: PF_optimize_expression_given_Horner_master_wait", thetime_str().c_str()); #endif // Wait for all the slaves. for (int i = 1; i < PF.numtasks; i++) { int next = PF_optimize_expression_given_Horner_master_next(); // Send a null task. PF_PrepareLongSinglePack(); int len = 0; PF_LongSinglePack(&len, 1, PF_INT); PF_LongSingleSend(next, PF_OPT_HORNER_MSGTAG); } // Combine the result from all the slaves. optimize_best_num_oper = INT_MAX; for (int i = 1; i < PF.numtasks; i++) { PF_LongSingleReceive(PF_ANY_SOURCE, PF_OPT_COLLECT_MSGTAG, NULL, NULL); int len; // The first integer is the number of operations. PF_LongSingleUnpack(&len, 1, PF_INT); if (len >= optimize_best_num_oper) continue; // Update the best result. optimize_best_num_oper = len; PF_LongSingleUnpack(&len, 1, PF_INT); optimize_best_instr.resize(len); PF_LongSingleUnpack(&optimize_best_instr[0], len, PF_WORD); PF_LongSingleUnpack(&len, 1, PF_INT); optimize_best_vars.resize(len); PF_LongSingleUnpack(&optimize_best_vars[0], len, PF_WORD); optimize_num_vars = optimize_best_vars.size(); // TODO } #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: PF_optimize_expression_given_Horner_master_wait", thetime_str().c_str()); #endif } // The main function on the slaves. void PF_optimize_expression_given_Horner_slave () { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: PF_optimize_expression_given_Horner_slave", thetime_str().c_str()); #endif optimize_best_Horner_schemes.clear(); optimize_best_num_oper = INT_MAX; int dummy = 0; int len; for (;;) { // Ask the master for the next task. PF_PrepareLongSinglePack(); PF_LongSinglePack(&dummy, 1, PF_INT); PF_LongSingleSend(MASTER, PF_OPT_HORNER_MSGTAG); // Get a task from the master. PF_LongSingleReceive(MASTER, PF_OPT_HORNER_MSGTAG, NULL, NULL); // Length of the task. PF_LongSingleUnpack(&len, 1, PF_INT); // No task remains. if (len == 0) break; // Perform the given task. optimize_best_Horner_schemes.push_back(vector()); vector &Horner_scheme = optimize_best_Horner_schemes.back(); Horner_scheme.resize(len); PF_LongSingleUnpack(&Horner_scheme[0], len, PF_WORD); optimize_expression_given_Horner (); } // Send the result to the master. PF_PrepareLongSinglePack(); PF_LongSinglePack(&optimize_best_num_oper, 1, PF_INT); if (optimize_best_num_oper != INT_MAX) { len = optimize_best_instr.size(); PF_LongSinglePack(&len, 1, PF_INT); PF_LongSinglePack(&optimize_best_instr[0], len, PF_WORD); len = optimize_best_vars.size(); PF_LongSinglePack(&len, 1, PF_INT); PF_LongSinglePack(&optimize_best_vars[0], len, PF_WORD); } PF_LongSingleSend(MASTER, PF_OPT_COLLECT_MSGTAG); #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: PF_optimize_expression_given_Horner_slave", thetime_str().c_str()); #endif } #endif /* #] PF_optimize_expression_given_Horner : #[ generate_output : */ /** Generate output * * Description * =========== * This method prepares the instructions for printing. They are * stored in Form format, so that they can be printed by * "PrintExtraSymbol". The results are stored in the buffer * AO.OptimizeResult. */ void generate_output (const vector &instr, int exprnr, int extraoffset, const vector > &brackets) { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: generate_output", thetime_str().c_str()); #endif GETIDENTITY; vector output; // one-indexed instead of zero-indexed extraoffset++; int num = 0; int maxsize = (int)instr.size(); for (int i=0; ionfile)); if ( GetTerm(BHEAD term) <= 0 ) { MesPrint("Expression %d has problems in scratchfile",exprnr); Terminate(-1); } SeekScratch(AR.outfile,&position); e->onfile = position; if ( PutOut(BHEAD term,&position,AR.outfile,0) < 0 ) { MesPrint("Expression %d has problems in output scratchfile",exprnr); Terminate(-1); } AR.CurExpr = exprnr; NewSort(BHEAD0); // scan for the original expression (marked by *t<0) and give the // terms to Generator WORD *t = AO.OptimizeResult.code; { WORD old = AR.Cnumlhs; AR.Cnumlhs = 0; // We can use the remaining part of the WorkSpace for every term that // goes through Generator. We have WorkSpace problems here if we use // the (modified) AT.WorkPointer every time in the loop. WORD* currentWorkPointer = AT.WorkPointer; while (*t!=0) { bool is_expr = *t < 0; t++; while (*t!=0) { if (is_expr) { memcpy(currentWorkPointer, t, *t*sizeof(WORD)); Generator(BHEAD currentWorkPointer, C->numlhs); } t+=*t; } t++; } AR.Cnumlhs = old; } // final sorting if (EndSort(BHEAD NULL,0) < 0) { LowerSortLevel(); Terminate(-1); } AT.WorkPointer = oldWorkPointer; AR.CurExpr = oldcurexpr; #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: generate_expression", thetime_str().c_str()); #endif return 0; } /* #] generate_expression : #[ optimize_print_code : */ /** Print optimized code * * Description * =========== * This method prints the optimized code via * "PrintExtraSymbol". Depending on the flag, the original * expression is printed (for "Print") or not (for "#Optimize / * #write "%O"). */ void optimize_print_code (int print_expr) { #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: optimize_print_code", thetime_str().c_str()); #endif if ( ( AO.Optimize.debugflags & 1 ) != 0 ) { /* * The next code is for debugging purposes. We may want the statements * in reverse order to substitute them all back. * Jan used a Mathematica program to do this. Here we make that * Format Ox,debugflag=1; * Creates reverse order during printing. * All we have to do is put id in front of the statements. This is done * in PrintExtraSymbol. */ WORD *t = AO.OptimizeResult.code; WORD num = 0; // First we count the number of objects. while (*t!=0) { num++; t++; while (*t!=0) t+=*t; t++; } WORD **tstart = (WORD **)Malloc1(num*sizeof(WORD *),"print objects"); t = AO.OptimizeResult.code; num = 0; // Now we get the addresses while (*t!=0) { tstart[num++] = t; t++; while (*t!=0) t+=*t; t++; } // Flip the addresses int halfnum = num/2; for (int i=0; i 0) PrintExtraSymbol(*t, t+1, EXTRASYMBOL); else if (print_expr) PrintExtraSymbol(-*t-1, t+1, EXPRESSIONNUMBER); } CBUF *C = cbuf + AM.sbufnum; if (C->numrhs >= AO.OptimizeResult.minvar) PrintSubtermList(AO.OptimizeResult.minvar, C->numrhs); } else { // print extra symbols from ConvertToPoly in optimization CBUF *C = cbuf + AM.sbufnum; if (C->numrhs >= AO.OptimizeResult.minvar) PrintSubtermList(AO.OptimizeResult.minvar, C->numrhs); WORD *t = AO.OptimizeResult.code; while (*t!=0) { if (*t > 0) { PrintExtraSymbol(*t, t+1, EXTRASYMBOL); } else if (print_expr) PrintExtraSymbol(-*t-1, t+1, EXPRESSIONNUMBER); t++; while (*t!=0) t+=*t; t++; } } #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: optimize_print_code", thetime_str().c_str()); #endif } /* #] optimize_print_code : #[ Optimize : */ /** Optimization of expression * * Description * =========== * This method takes an input expression and generates optimized * code to calculate its value. The following methods are called to * do so: * * (1) get_expression : to read to expression * * (2) get_brackets : find brackets for simultaneous optimization * * (3) occurrence_order or find_Horner_MCTS : to determine (the) * Horner scheme(s) to use; this depends on AO.optimize.horner * * (4) optimize_expression_given_Horner : to do the optimizations * for each Horner scheme; this method does either CSE or greedy * optimizations dependings on AO.optimize.method * * (5) generate_output : to format the output in Form notation and * store it in a buffer * * (6a) optimize_print_code : to print the expression (for "Print") * or * (6b) generate_expression : to modify the expression (for * "#Optimize") * * On ParFORM, all the processes must call this function at the same * time. Then * * (1) Because only the master can access to the expression to be * optimized, the master broadcast the expression to all the slaves * after reading the expression (PF_get_expression). * * (2) get_brackets reads optimize_expr as the input and it works * also on the slaves. We leave it although the bracket information * is not needed on the slaves (used in (5) on the master). * * (3) and (4) find_Horner_MCTS and optimize_expression_given_Horner * are parallelized. * * (5), (6a) and (6b) are needed only on the master. */ int Optimize (WORD exprnr, int do_print) { #if defined(WITHMPI) && (defined(DEBUG) || defined(DEBUG_MORE) || defined(DEBUG_MCTS) || defined(DEBUG_GREEDY)) // set AS.printflag negative temporary. struct save_printflag { save_printflag() { oldprintflag = AS.printflag; AS.printflag = -1; } ~save_printflag() { AS.printflag = oldprintflag; } int oldprintflag; } save_printflag_; #endif #ifdef DEBUG MesPrint ("*** [%s, w=%w] CALL: Optimize", thetime_str().c_str()); MesPrint ("*** %"); PrintRunningTime(); #endif #ifdef WITHPTHREADS optimize_lock = dummylock; #endif AO.OptimizeResult.minvar = (cbuf + AM.sbufnum)->numrhs + 1; if (get_expression(exprnr) < 0) return -1; vector > brackets = get_brackets(); #ifdef DEBUG #ifdef WITHMPI if (PF.me == MASTER) #endif MesPrint ("*** runtime after preparing the expression: %"); PrintRunningTime(); #endif if (optimize_expr[0]==0 || (optimize_expr[optimize_expr[0]]==0 && optimize_expr[0]==ABS(optimize_expr[optimize_expr[0]-1])+1) || (optimize_expr[optimize_expr[0]]==0 && optimize_expr[0]==8 && optimize_expr[5]==1 && optimize_expr[6]==1 && ABS(optimize_expr[7])==3)) { if (AO.OptimizeResult.code != NULL) M_free(AO.OptimizeResult.code, "optimize output"); // zero terms or one trivial term (number or +/-variable), so no // optimization, so copy expression; special case because without // operators the optimization crashes AO.OptimizeResult.code = (WORD *)Malloc1((optimize_expr[0]+3)*sizeof(WORD), "optimize output"); AO.OptimizeResult.code[0] = -(exprnr+1); memcpy(AO.OptimizeResult.code+1, optimize_expr, (optimize_expr[0]+1)*sizeof(WORD)); AO.OptimizeResult.code[optimize_expr[0]+2] = 0; } else { // find Horner scheme(s) optimize_best_Horner_schemes.clear(); if (AO.Optimize.horner == O_OCCURRENCE) { if (AO.Optimize.hornerdirection != O_BACKWARD) optimize_best_Horner_schemes.push_back(occurrence_order(optimize_expr, false)); if (AO.Optimize.hornerdirection != O_FORWARD) optimize_best_Horner_schemes.push_back(occurrence_order(optimize_expr, true)); } else { if (AO.Optimize.horner == O_SIMULATED_ANNEALING) { optimize_best_Horner_schemes.push_back(simulated_annealing()); } else { mcts_best_schemes.clear(); if ( AO.inscheme ) { optimize_best_Horner_schemes.push_back(vector(AO.schemenum)); for ( int i=0; i < AO.schemenum; i++ ) optimize_best_Horner_schemes[0][i] = AO.inscheme[i]; } else { for ( int i = 0; i < AO.Optimize.mctsnumrepeat; i++ ) find_Horner_MCTS(); // generate results for (set > >::iterator i=mcts_best_schemes.begin(); i!=mcts_best_schemes.end(); i++) { optimize_best_Horner_schemes.push_back(i->second); #ifdef DEBUG_MCTS MesPrint ("{%a} -> %d",i->second.size(), &i->second[0], i->first); #endif } } // clear the tree by making a new empty one. mcts_root = tree_node(); } } #ifdef DEBUG #ifdef WITHMPI if (PF.me == MASTER) #endif MesPrint ("*** runtime after Horner: %"); PrintRunningTime(); #endif #ifdef WITHMPI if (PF.me == MASTER ) { PF_optimize_expression_given_Horner_master_init(); #endif // find best Horner scheme and results optimize_best_num_oper = INT_MAX; int imax = (int)optimize_best_Horner_schemes.size(); for (int i=0; i 1) optimize_expression_given_Horner_threaded(); else #elif defined(WITHMPI) if (PF.numtasks > 1) PF_optimize_expression_given_Horner_master(); else #endif optimize_expression_given_Horner(); } #ifdef WITHMPI PF_optimize_expression_given_Horner_master_wait(); } else { if (PF.numtasks > 1) PF_optimize_expression_given_Horner_slave(); } #endif #ifdef WITHPTHREADS MasterWaitAll(); #endif // format results, then print it (for "Print") or modify // expression (for "#Optimize") #ifdef WITHMPI if (PF.me == MASTER) #endif generate_output(optimize_best_instr, exprnr, cbuf[AM.sbufnum].numrhs, brackets); #ifdef WITHMPI else { // non-null dummy code for slaves if (AO.OptimizeResult.code == NULL) { AO.OptimizeResult.code = (WORD *)Malloc1(sizeof(WORD), "optimize output"); } } #endif } #ifdef WITHMPI if (PF.me == MASTER) { PF_PreparePack(); PF_Pack(&AO.OptimizeResult.minvar, 1, PF_WORD); PF_Pack(&AO.OptimizeResult.maxvar, 1, PF_WORD); } PF_Broadcast(); if (PF.me != MASTER) { PF_Unpack(&AO.OptimizeResult.minvar, 1, PF_WORD); PF_Unpack(&AO.OptimizeResult.maxvar, 1, PF_WORD); } #endif // set preprocessor variables char str[100]; snprintf (str,100,"%d",AO.OptimizeResult.minvar); PutPreVar((UBYTE *)"optimminvar_",(UBYTE *)str,0,1); snprintf (str,100,"%d",AO.OptimizeResult.maxvar); PutPreVar((UBYTE *)"optimmaxvar_",(UBYTE *)str,0,1); if (do_print) { #ifdef WITHMPI if (PF.me == MASTER) #endif optimize_print_code(1); ClearOptimize(); } else { #ifdef WITHMPI if (PF.me == MASTER) #endif generate_expression(exprnr); } #ifdef WITHMPI if (PF.me == MASTER) { #endif if ( AO.Optimize.printstats > 0 ) { char str[20]; MesPrint(""); count_operators(optimize_expr,true); int numop = count_operators(optimize_best_instr,true); snprintf(str,20,"%d",numop); PutPreVar((UBYTE *)"optimvalue_",(UBYTE *)str,0,1); } else { char str[20]; int numop = count_operators(optimize_best_instr,false); snprintf(str,20,"%d",numop); PutPreVar((UBYTE *)"optimvalue_",(UBYTE *)str,0,1); } if ( ( AO.Optimize.schemeflags&1 ) == 1 ) { GETIDENTITY UBYTE *OutScr, *Out, *old1 = AO.OutputLine, *old2 = AO.OutFill; int i, sym; AO.OutputLine = AO.OutFill = (UBYTE *)AT.WorkPointer; FiniLine(); OutScr = (UBYTE *)AT.WorkPointer + ( TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer) ) /2; TokenToLine((UBYTE *)" Scheme selected: "); for ( i = 0; i < optimize_num_vars; i++ ) { Out = OutScr; sym = optimize_best_vars[i]; if ( i > 0 ) TokenToLine((UBYTE *)","); if ( sym < NumSymbols ) { StrCopy(FindSymbol(sym),OutScr); /* StrCopy(VARNAME(symbols,sym),OutScr); */ } else { Out = StrCopy((UBYTE *)AC.extrasym,Out); if ( AC.extrasymbols == 0 ) { Out = NumCopy((MAXVARIABLES-sym),Out); Out = StrCopy((UBYTE *)"_",Out); } else if ( AC.extrasymbols == 1 ) { Out = AddArrayIndex((MAXVARIABLES-sym),Out); } } TokenToLine(OutScr); } TokenToLine((UBYTE *)";"); FiniLine(); AO.OutFill = old2; AO.OutputLine = old1; } { GETIDENTITY UBYTE *OutScr, *Out, *outstring = 0; int i, sym; AO.OutputLine = AO.OutFill = (UBYTE *)AT.WorkPointer; OutScr = (UBYTE *)AT.WorkPointer + ( TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer) ) /2; for ( i = 0; i < optimize_num_vars; i++ ) { Out = OutScr; sym = optimize_best_vars[i]; if ( sym < NumSymbols ) { StrCopy(FindSymbol(sym),OutScr); /* StrCopy(VARNAME(symbols,sym),OutScr); */ } else { Out = StrCopy((UBYTE *)AC.extrasym,Out); if ( AC.extrasymbols == 0 ) { Out = NumCopy((MAXVARIABLES-sym),Out); Out = StrCopy((UBYTE *)"_",Out); } else if ( AC.extrasymbols == 1 ) { Out = AddArrayIndex((MAXVARIABLES-sym),Out); } } outstring = AddToString(outstring,OutScr,1); } if ( outstring == 0 ) { PutPreVar((UBYTE *)"optimscheme_",(UBYTE *)"",0,1); } else { PutPreVar((UBYTE *)"optimscheme_",(UBYTE *)outstring,0,1); M_free(outstring,"AddToString"); } } #ifdef WITHMPI } // synchronize optimvalue_ and optimscheme_ if ( PF.me == MASTER ) { UBYTE *value; int bytes; PF_PrepareLongMultiPack(); value = GetPreVar((UBYTE *)"optimvalue_", WITHERROR); bytes = strlen((char *)value); PF_LongMultiPack(&bytes, 1, PF_INT); PF_LongMultiPack(value, bytes, PF_BYTE); value = GetPreVar((UBYTE *)"optimscheme_", WITHERROR); bytes = strlen((char *)value); PF_LongMultiPack(&bytes, 1, PF_INT); PF_LongMultiPack(value, bytes, PF_BYTE); } PF_LongMultiBroadcast(); if ( PF.me != MASTER ) { static vector prevarbuf; UBYTE *value; int bytes; PF_LongMultiUnpack(&bytes, 1, PF_INT); prevarbuf.reserve(bytes + 1); value = &prevarbuf[0]; PF_LongMultiUnpack(value, bytes, PF_BYTE); value[bytes] = '\0'; // null terminator PutPreVar((UBYTE *)"optimvalue_", value, NULL, 1); PF_LongMultiUnpack(&bytes, 1, PF_INT); prevarbuf.reserve(bytes + 1); value = &prevarbuf[0]; PF_LongMultiUnpack(value, bytes, PF_BYTE); value[bytes] = '\0'; // null terminator PutPreVar((UBYTE *)"optimscheme_", value, NULL, 1); } #endif // cleanup M_free(optimize_expr,"LoadOptim"); #ifdef DEBUG MesPrint ("*** [%s, w=%w] DONE: Optimize", thetime_str().c_str()); #endif return 0; } /* #] Optimize : #[ ClearOptimize : */ /** Optimization of expression * * Description * =========== * Clears the buffers that were used for optimization output. * Clears the expression from the buffers (marks it to be dropped). * Note: we need to use the expression by its name, because numbers * may change if we drop other expressions between when we do the * optimizations and clear the results (in execute.c). Also this is * not 100% safe, because we could overwrite the optimized * expression. But that can be done only in a Local or Global * statement and hence we only have to test there that we might have * to call ClearOptimize first. (in file comexpr.c) */ int ClearOptimize() { char str[20]; WORD numexpr, *w; int error = 0; if ( AO.OptimizeResult.code != NULL ) { M_free(AO.OptimizeResult.code, "optimize output"); AO.OptimizeResult.code = NULL; AO.OptimizeResult.codesize = 0; PutPreVar((UBYTE *)"optimminvar_",(UBYTE *)("0"),0,1); PutPreVar((UBYTE *)"optimmaxvar_",(UBYTE *)("0"),0,1); PruneExtraSymbols(AO.OptimizeResult.minvar-1); cbuf[AM.sbufnum].numrhs = AO.OptimizeResult.minvar-1; AO.OptimizeResult.minvar = AO.OptimizeResult.maxvar = 0; } if ( AO.OptimizeResult.nameofexpr != NULL ) { /* We have to pick up the expression by its name. Numbers may change. Note that this requires that when we overwrite an expression, we check that it is not an optimized expression. See execute.c and comexpr.c */ if ( GetName(AC.exprnames,AO.OptimizeResult.nameofexpr,&numexpr,NOAUTO) != CEXPRESSION ) { MesPrint("@Internal error while clearing optimized expression %s ",AO.OptimizeResult.nameofexpr); Terminate(-1); } M_free(AO.OptimizeResult.nameofexpr, "optimize expression name"); AO.OptimizeResult.nameofexpr = NULL; w = &(Expressions[numexpr].status); *w = SetExprCases(DROP,1,*w); if ( *w < 0 ) error = 1; } snprintf (str,20,"%d",cbuf[AM.sbufnum].numrhs); PutPreVar(AM.oldnumextrasymbols,(UBYTE *)str,0,1); PutPreVar((UBYTE *)"optimvalue_",(UBYTE *)("0"),0,1); PutPreVar((UBYTE *)"optimscheme_",(UBYTE *)("0"),0,1); return(error); } /* #] ClearOptimize : */ form-5.0.1/sources/comexpr.c0000644000175100017510000014755415217035721011472 /** @file comexpr.c * * Compiler routines for statements that involve algebraic expressions. * These involve definitions, id-statements, the multiply statement * and the fill statement. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : compi2.c File contains most of what has to do with compiling expressions. Main supporting file: token.c */ #include "form3.h" static struct id_options { UBYTE *name; int code; int dummy; } IdOptions[] = { {(UBYTE *)"multi", SUBMULTI ,0} ,{(UBYTE *)"many", SUBMANY ,0} ,{(UBYTE *)"only", SUBONLY ,0} ,{(UBYTE *)"once", SUBONCE ,0} ,{(UBYTE *)"ifmatch", SUBAFTER ,0} ,{(UBYTE *)"ifnomatch", SUBAFTERNOT ,0} ,{(UBYTE *)"ifnotmatch", SUBAFTERNOT ,0} ,{(UBYTE *)"disorder", SUBDISORDER ,0} ,{(UBYTE *)"select", SUBSELECT ,0} ,{(UBYTE *)"all", SUBALL ,0} }; /* #] Includes : #[ CoLocal : */ int CoLocal(UBYTE *inp) { return(DoExpr(inp,LOCALEXPRESSION,0)); } /* #] CoLocal : #[ CoGlobal : */ int CoGlobal(UBYTE *inp) { return(DoExpr(inp,GLOBALEXPRESSION,0)); } /* #] CoGlobal : #[ CoLocalFactorized : */ int CoLocalFactorized(UBYTE *inp) { return(DoExpr(inp,LOCALEXPRESSION,1)); } /* #] CoLocalFactorized : #[ CoGlobalFactorized : */ int CoGlobalFactorized(UBYTE *inp) { return(DoExpr(inp,GLOBALEXPRESSION,1)); } /* #] CoGlobalFactorized : #[ DoExpr: */ int DoExpr(UBYTE *inp, int type, int par) { GETIDENTITY int error = 0; UBYTE *p, *q, c; WORD *w, i, j = 0, c1, c2, *OldWork = AT.WorkPointer, osize; WORD jold = 0; POSITION pos; while ( *inp == ',' ) inp++; if ( par ) AC.ToBeInFactors = 1; else AC.ToBeInFactors = 0; p = inp; while ( *p && *p != '=' ) { if ( *p == '(' ) SKIPBRA4(p) else if ( *p == '{' ) SKIPBRA5(p) else if ( *p == '[' ) SKIPBRA1(p) else p++; } if ( *p ) { /* Variety with the = sign */ q = SkipAName(inp); if ( *inp == '$' || q == 0 || q[-1] == '_' ) { MesPrint("&Illegal name for expression"); error = 1; return(error); } else { c = *q; *q = 0; if ( GetVar(inp,&c1,&c2,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { if ( c1 == CEXPRESSION ) { if ( Expressions[c2].status == STOREDEXPRESSION ) { MesPrint("&Illegal attempt to overwrite a stored expression"); error = 1; } else { HighWarning("Expression is replaced by new definition"); if ( AO.OptimizeResult.nameofexpr != NULL && StrCmp(inp,AO.OptimizeResult.nameofexpr) == 0 ) { ClearOptimize(); } if ( Expressions[c2].status != DROPPEDEXPRESSION ) { w = &(Expressions[c2].status); if ( *w == LOCALEXPRESSION || *w == SKIPLEXPRESSION ) *w = DROPLEXPRESSION; else if ( *w == GLOBALEXPRESSION || *w == SKIPGEXPRESSION ) *w = DROPGEXPRESSION; else if ( *w == HIDDENLEXPRESSION ) *w = DROPHLEXPRESSION; else if ( *w == HIDDENGEXPRESSION ) *w = DROPHGEXPRESSION; } AC.TransEname = Expressions[c2].name; j = EntVar(CEXPRESSION,0,type,0,0,0); Expressions[j].node = Expressions[c2].node; Expressions[c2].replace = j; } } else { MesPrint("&name of expression is also name of a variable"); error = 1; j = EntVar(CEXPRESSION,inp,type,0,0,0); } jold = c2; } else { /* Here we have to worry about reuse of the expression in the same module. That will need AS.Oldvflags but that may not be defined or have the proper value. */ j = EntVar(CEXPRESSION,inp,type,0,0,0); jold = j; } *q = c; OldWork = w = AT.WorkPointer; *w++ = TYPEEXPRESSION; *w++ = 3+SUBEXPSIZE; *w++ = j; AC.ProtoType = w; AR.CurExpr = j; /* Block expression j */ *w++ = SUBEXPRESSION; *w++ = SUBEXPSIZE; *w++ = j; *w++ = 1; *w++ = AC.cbufnum; FILLSUB(w) if ( c == '(' ) { while ( *q == ',' || *q == '(' ) { inp = q+1; if ( ( q = SkipAName(inp) ) == 0 ) { MesPrint("&Illegal name for expression argument"); error = 1; q = p - 1; break; } c = *q; *q = 0; if ( GetVar(inp,&c1,&c2,ALLVARIABLES,WITHAUTO) < 0 ) c1 = -1; switch ( c1 ) { case CSYMBOL : *w++ = SYMTOSYM; *w++ = 4; *w++ = c2; *w++ = 0; break; case CINDEX : *w++ = INDTOIND; *w++ = 4; *w++ = c2 + AM.OffsetIndex; *w++ = 0; break; case CVECTOR : *w++ = VECTOVEC; *w++ = 4; *w++ = c2 + AM.OffsetVector; *w++ = 0; break; case CFUNCTION : *w++ = FUNTOFUN; *w++ = 4; *w++ = c2 + FUNCTION; *w++ = 0; break; default : MesPrint("&Illegal expression parameter: %s",inp); error = 1; break; } *q = c; } if ( *q != ')' || q+1 != p ) { MesPrint("&Illegal use of arguments for expression"); error = 1; } AC.ProtoType[1] = w - AC.ProtoType; } else if ( c != '=' ) { /* The dummy accepted L F := RHS; */ MesPrint("&Illegal LHS for expression definition"); error = 1; } *w++ = 1; *w++ = 1; *w++ = 3; *w++ = 0; SeekScratch(AR.outfile,&pos); Expressions[j].counter = 1; Expressions[j].onfile = pos; Expressions[j].whichbuffer = 0; #ifdef PARALLELCODE Expressions[j].partodo = AC.inparallelflag; #endif OldWork[2] = w - OldWork - 3; AT.WorkPointer = w; /* Writing the expression prototype to disk and to the compiler buffer is done only after the RHS has been compiled because we don't know the number of the main level RHS yet. */ } inp = p+1; ClearWildcardNames(); osize = AC.ProtoType[1]; AC.ProtoType[1] = SUBEXPSIZE; PutInVflags(jold); if ( ( i = CompileAlgebra(inp,RHSIDE,AC.ProtoType) ) < 0 ) { AC.ProtoType[1] = osize; error = 1; } else if ( error == 0 ) { AC.ProtoType[1] = osize; AC.ProtoType[2] = i; if ( PutOut(BHEAD OldWork+2,&pos,AR.outfile,0) < 0 ) { MesPrint("&Cannot create expression"); error = -1; } else { Expressions[j].sizeprototype = OldWork[2]; OldWork[2] = 4+SUBEXPSIZE; OldWork[4] = SUBEXPSIZE; OldWork[5] = i; OldWork[SUBEXPSIZE+3] = 1; OldWork[SUBEXPSIZE+4] = 1; OldWork[SUBEXPSIZE+5] = 3; OldWork[SUBEXPSIZE+6] = 0; if ( PutOut(BHEAD OldWork+2,&pos,AR.outfile,0) < 0 || FlushOut(&pos,AR.outfile,0) ) { MesPrint("&Cannot create expression"); error = -1; } AR.outfile->POfull = AR.outfile->POfill; } OldWork[2] = j; /* Seems unnecessary (13-feb-2018) AddNtoL(OldWork[1],OldWork); */ AT.WorkPointer = OldWork; if ( AC.dumnumflag ) Add2Com(TYPEDETCURDUM) } AC.ToBeInFactors = 0; } else { /* Variety in which expressions change property */ /* This code got a major revision because it didn't take hidden expressions into account. (1-jun-2010 JV) */ do { if ( ( q = SkipAName(inp) ) == 0 ) { MesPrint("&Illegal name(s) for expression(s)"); return(1); } c = *q; *q = 0; if ( GetName(AC.exprnames,inp,&c2,NOAUTO) == NAMENOTFOUND ) { MesPrint("&%s is not a valid expression",inp); error = 1; } else { w = &(Expressions[c2].status); if ( type == LOCALEXPRESSION ) { switch ( *w ) { case GLOBALEXPRESSION: *w = LOCALEXPRESSION; break; case SKIPGEXPRESSION: *w = SKIPLEXPRESSION; break; case DROPGEXPRESSION: *w = DROPLEXPRESSION; break; case HIDDENGEXPRESSION: *w = HIDDENLEXPRESSION; break; case HIDEGEXPRESSION: *w = HIDELEXPRESSION; break; case UNHIDEGEXPRESSION: *w = UNHIDELEXPRESSION; break; case INTOHIDEGEXPRESSION: *w = INTOHIDELEXPRESSION; break; case DROPHGEXPRESSION: *w = DROPHLEXPRESSION; break; } } else if ( type == GLOBALEXPRESSION ) { switch ( *w ) { case LOCALEXPRESSION: *w = GLOBALEXPRESSION; break; case SKIPLEXPRESSION: *w = SKIPGEXPRESSION; break; case DROPLEXPRESSION: *w = DROPGEXPRESSION; break; case HIDDENLEXPRESSION: *w = HIDDENGEXPRESSION; break; case HIDELEXPRESSION: *w = HIDEGEXPRESSION; break; case UNHIDELEXPRESSION: *w = UNHIDEGEXPRESSION; break; case INTOHIDELEXPRESSION: *w = INTOHIDEGEXPRESSION; break; case DROPHLEXPRESSION: *w = DROPHGEXPRESSION; break; } } /* old code if ( type != LOCALEXPRESSION || *w != STOREDEXPRESSION ) *w = type; */ } *q = c; inp = q+1; } while ( c == ',' ); if ( c ) { MesPrint("&Illegal object in local or global redefinition"); error = 1; } } return(error); } /* #] DoExpr: #[ CoIdOld : */ int CoIdOld(UBYTE *inp) { AC.idoption = 0; return(CoIdExpression(inp,TYPEIDOLD)); } /* #] CoIdOld : #[ CoId : */ int CoId(UBYTE *inp) { AC.idoption = 0; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoId : #[ CoIdNew : */ int CoIdNew(UBYTE *inp) { AC.idoption = 0; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoIdNew : #[ CoDisorder : */ int CoDisorder(UBYTE *inp) { AC.idoption = SUBDISORDER; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoDisorder : #[ CoMany : */ int CoMany(UBYTE *inp) { AC.idoption = SUBMANY; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoMany : #[ CoMulti : */ int CoMulti(UBYTE *inp) { AC.idoption = SUBMULTI; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoMulti : #[ CoIfMatch : */ int CoIfMatch(UBYTE *inp) { AC.idoption = SUBAFTER; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoIfMatch : #[ CoIfNoMatch : */ int CoIfNoMatch(UBYTE *inp) { AC.idoption = SUBAFTERNOT; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoIfNoMatch : #[ CoOnce : */ int CoOnce(UBYTE *inp) { AC.idoption = SUBONCE; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoOnce : #[ CoOnly : */ int CoOnly(UBYTE *inp) { AC.idoption = SUBONLY; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoOnly : #[ CoSelect : */ int CoSelect(UBYTE *inp) { AC.idoption = SUBSELECT; return(CoIdExpression(inp,TYPEIDNEW)); } /* #] CoSelect : #[ CoIdExpression : First finish dealing with secondary keywords */ int CoIdExpression(UBYTE *inp, int type) { GETIDENTITY int i, j, idhead, error = 0, MinusSign = 0, opt, retcode; WORD *w, *s, *m, *mm, *ww, *FirstWork, *OldWork, c1, numsets = 0, oldnumrhs, *ow, oldEside; UBYTE *p, *pp, c; CBUF *C = cbuf+AC.cbufnum; LONG oldcpointer, x; FirstWork = OldWork = AT.WorkPointer; /* Don't forget to change in StudyPattern if we change/add_to the following setup. if ( type == TYPEIF ) idhead = IDHEAD-1; else */ idhead = IDHEAD; AR.CurExpr = -1; w = AT.WorkPointer; *w++ = type; *w++ = idhead + SUBEXPSIZE; w++; if ( idhead >= IDHEAD ) *w++ = -1; #if IDHEAD > 4 for ( i = 4; i < idhead; i++ ) *w++ = 0; #endif while ( *inp == ',' ) inp++; p = inp; if ( AC.idoption == SUBSELECT ) { p--; goto findsets; } else if ( ( AC.idoption == SUBAFTER ) || ( AC.idoption == SUBAFTERNOT ) ) { while ( *p && *p != '=' && *p != ',' ) { if ( *p == '(' ) SKIPBRA4(p) else if ( *p == '{' ) SKIPBRA5(p) else if ( *p == '[' ) SKIPBRA1(p) else p++; } if ( *p == '=' || *inp != '-' || inp[1] != '>' ) { MesPrint("&Illegal use if if[no]match in id statement"); error = 1; goto AllDone; } if ( *p == 0 ) { MesPrint("&id-statement without = sign"); error = 1; goto AllDone; } inp += 2; pp = inp; goto readlabel; } for(;;) { while ( *p && *p != '=' && *p != ',' ) { if ( *p == '(' ) SKIPBRA4(p) else if ( *p == '{' ) SKIPBRA5(p) else if ( *p == '[' ) SKIPBRA1(p) else p++; } if ( *p == '=' ) break; if ( *p == 0 ) { MesPrint("&id-statement without = sign"); error = 1; goto AllDone; } /* We have either a secondary option or a syntax error */ pp = inp; while ( FG.cTable[*pp] == 0 ) pp++; c = *pp; *pp = 0; i = sizeof(IdOptions)/sizeof(struct id_options); while ( --i >= 0 ) { if ( StrICmp(inp,IdOptions[i].name) == 0 ) break; } if ( i < 0 ) { MesPrint("&Illegal option %s in id-statement",inp); *pp = c; error = 1; p++; inp = p; continue; } opt = IdOptions[i].code; *pp = c; inp = pp+1; switch ( opt ) { case SUBDISORDER: if ( pp != p ) goto IllField; AC.idoption |= SUBDISORDER; p++; inp = p; break; case SUBSELECT: if ( p != pp ) goto IllField; if ( ( AC.idoption & SUBMASK ) != 0 ) { if ( AC.idoption == SUBMULTI && type == TYPEIF ) {} else { MesPrint("&Conflicting options in id-statement"); error = 1; } } findsets:; /* Now we read the sets */ numsets = 0; for(;;) { inp = ++p; while ( *p && *p != '=' && *p != ',' ) { if ( *p == '(' ) SKIPBRA4(p) else if ( *p == '{' ) SKIPBRA5(p) else if ( *p == '[' ) SKIPBRA1(p) else p++; } if ( *p == '=' ) break; if ( *p == 0 ) { MesPrint("&id-statement without = sign"); error = 1; goto AllDone; } /* We have a set at inp. */ if ( *inp == '{' ) { if ( p[-1] != '}' ) { c = *p; *p = 0; MesPrint("&Illegal temporary set: %s",inp); error = 1; *p = c; } else { inp++; c = p[-1]; p[-1] = 0; c1 = DoTempSet(inp,p-1); *w++ = c1; p[-1] = c; numsets++; if ( w[-1] < 0 ) error = 1; } } else { c = *p; *p = 0; if ( GetName(AC.varnames,inp,&c1,NOAUTO) != CSET ) { MesPrint("&%s is not a set",inp); error = 1; } else { if ( c1 < AM.NumFixedSets ) { MesPrint("&Built in sets are not allowed in the select option"); error = 1; } else if ( Sets[c1].type == CRANGE ) { MesPrint("&Ranged sets are not allowed in the select option"); error = 1; } numsets++; *w++ = c1; } *p = c; } } /* Now exchange the positions a bit. Regular stuff at OldWork, numsets sets at FirstWork[idhead] */ OldWork = w; for ( i = 0; i < idhead; i++ ) *w++ = FirstWork[i]; AC.idoption = SUBSELECT; break; case SUBAFTER: case SUBAFTERNOT: if ( type == TYPEIF ) { MesPrint("&The if[no]match->label option is not allowed in an if statement"); error = 1; goto AllDone; } if ( pp[0] != '-' || pp[1] != '>' ) goto IllField; pp += 2; /* points now at the label */ inp = pp; AC.idoption |= opt; readlabel: while ( FG.cTable[*pp] <= 1 ) pp++; if ( pp != p ) { c = *p; *p = 0; MesPrint("&Illegal label %s in if[no]match option of id-statement",inp); *p = c; error = 1; inp = p+1; continue; } c = *p; *p = 0; OldWork[3] = GetLabel(inp); *p++ = c; inp = p; break; case SUBALL: x = 0; if ( *pp == '(' ) { if ( FG.cTable[*inp] == 1 ) { while ( *inp >= '0' && *inp <= '9' ) x = 10*x+*inp++ - '0'; } else { pp++; while ( FG.cTable[*inp] == 0 ) inp++; c = *inp; *inp = 0; if ( StrICont(pp,(UBYTE *)"normalize") != 0 ) goto IllOpt; *inp = c; OldWork[4] |= NORMALIZEFLAG; } if ( *inp != ')' || inp+1 != p ) { c = *inp; *inp = 0; IllOpt: MesPrint("&Illegal ALL option in id-statement: ",pp); *inp++ = c; error = 1; continue; } pp = inp; inp = pp+1; } /* Note that the following statement limits x to */ if ( x > MAXPOSITIVE ) { MesPrint("&Requested maximum number of matches %l in ALL option in id-statement is greater than %l ",x,MAXPOSITIVE); error = 1; } OldWork[5] = x; if ( type != TYPEIDNEW ) { if ( type == TYPEIDOLD ) { MesPrint("&Requested ALL option not allowed in idold/also statement."); error = 1; } else if ( type == TYPEIF ) { MesPrint("&Requested ALL option not allowed in if(match())"); error = 1; } else { MesPrint("&ALL option only allowed in regular id-statement."); error = 1; } } p++; inp = p; AC.idoption = opt; break; default: if ( pp != p ) { IllField: c = *p; *p = 0; MesPrint("&Illegal optionfield %s in id-statement",inp); *p = c; error = 1; inp = p+1; continue; } i = AC.idoption & SUBMASK; if ( i && i != opt ) { MesPrint("&Conflicting options in id-statement"); error = 1; continue; } else AC.idoption |= opt; while ( *p == ',' ) p++; inp = p; break; } } if ( ( AC.idoption & SUBMASK ) == 0 ) AC.idoption |= SUBMULTI; OldWork[2] = AC.idoption; /* Now we have a field till the = sign Now the subexpression prototype */ AC.ProtoType = w; *w++ = SUBEXPRESSION; *w++ = SUBEXPSIZE; *w++ = C->numrhs+1; *w++ = 1; *w++ = AC.cbufnum; FILLSUB(w) AC.WildC = w; AC.NwildC = 0; AT.WorkPointer = s = w + 4*AM.MaxWildcards + 8; /* Now read the LHS */ ClearWildcardNames(); oldcpointer = AddLHS(AC.cbufnum) - C->Buffer; *p = 0; oldnumrhs = C->numrhs; if ( ( retcode = CompileAlgebra(inp,LHSIDE,AC.ProtoType) ) < 0 ) { error = 1; } else AC.ProtoType[2] = retcode; *p = '='; inp = p+1; AT.WorkPointer = s; if ( AC.NwildC && SortWild(w,AC.NwildC) ) error = 1; /* Make the LHS pointers ready */ OldWork[1] = AC.WildC-OldWork; OldWork[idhead+1] = OldWork[1] - idhead; w = AC.WildC; AT.WorkPointer = w; s = C->rhs[C->numrhs]; /* Now check whether wildcards get converted to dollars (for PARALLEL) */ { WORD *tw, *twstop; tw = AC.ProtoType; twstop = tw + tw[1]; tw += SUBEXPSIZE; while ( tw < twstop ) { if ( *tw == LOADDOLLAR ) { AddPotModdollar(tw[2]); } tw += tw[1]; } } /* We have the expression in the compiler buffers. The main level is at lhs[numlhs] The partial lhs (including ProtoType) is in OldWork (in WorkSpace) We need to load the result at w after the prototype Because these sort routines don't use the WorkSpace there should not be a conflict */ if ( !error && *s == 0 ) { IllLeft:MesPrint("&Illegal LHS"); AC.lhdollarflag = 0; return(1); } if ( !error && *(s+*s) != 0 ) { MesPrint("&LHS should be one term only"); return(1); } if ( error == 0 ) { WORD oldpolyfun = AR.PolyFun; if ( NewSort(BHEAD0) || NewSort(BHEAD0) ) { if ( !error ) error = 1; return(error); } AN.RepPoint = AT.RepCount + 1; ow = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); mm = s; ww = ow; i = *mm; while ( --i >= 0 ) {*ww++ = *mm++;} AT.WorkPointer = ww; AC.lhdollarflag = 0; oldEside = AR.Eside; AR.Eside = LHSIDE; AR.Cnumlhs = C->numlhs; AR.PolyFun = 0; if ( Generator(BHEAD ow,C->numlhs) ) { AR.Eside = oldEside; LowerSortLevel(); LowerSortLevel(); AR.PolyFun = oldpolyfun; goto IllLeft; } AR.Eside = oldEside; AT.WorkPointer = w; if ( EndSort(BHEAD w,0) < 0 ) { LowerSortLevel(); AR.PolyFun = oldpolyfun; goto IllLeft; } AR.PolyFun = oldpolyfun; if ( *w == 0 || *(w+*w) != 0 ) { MesPrint("&LHS must be one term"); AC.lhdollarflag = 0; return(1); } LowerSortLevel(); if ( AC.lhdollarflag ) MarkDirty(w,DIRTYFLAG); } AT.WorkPointer = w + *w; AC.DumNum = 0; /* Everything is now after OldWork. We can pop the compilerbuffer. Next test for illegal things like a coefficient At this point we have: w = the term of the LHS */ C->Pointer = C->Buffer + oldcpointer; C->numrhs = oldnumrhs; C->numlhs--; m = w + *w - 3; AC.vectorlikeLHS = 0; if ( !error ) { if ( m[2] != 3 || m[1] != 1 || *m != 1 ) { if ( *m == 1 && m[1] == 1 && m[2] == -3 ) { MinusSign = 1; } else { MesPrint("&Coefficient in LHS"); error = 1; AC.DumNum = 0; *w -= ABS(m[2])-3; } } if ( *w == 7 && w[1] == INDEX && w[3] < 0 ) { if ( ( AC.idoption & SUBMASK ) != 0 && ( AC.idoption & SUBMASK ) != SUBMULTI ) { MesPrint("&Illegal option for substitution of a vector"); error = 1; } AC.DumNum = AM.IndDum; OldWork[2] = ( OldWork[2] - ( OldWork[2] & SUBMASK ) ) | SUBVECTOR; c1 = w[3]; /* We overwrite the LHS */ *w++ = INDTOIND; *w++ = 4; *w++ = AC.DumNum + WILDOFFSET; *w++ = 0; w[0] = 5; w[1] = VECTOR; w[2] = 4; w[3] = c1; w[4] = AC.DumNum + WILDOFFSET; OldWork[idhead+1] = w - OldWork - idhead; AC.vectorlikeLHS = 1; } else { AC.DumNum = 0; *w -= 3; i = OldWork[2] & SUBMASK; m = w + *w; if ( i == 0 || i == SUBMULTI ) { s = w+1; while ( s < m ) { if ( *s == SYMBOL ) { j = s[1]/2; s += 2; while ( --j >= 0 ) { if ( ABS(s[1]) > 2*MAXPOWER ) { OldWork[2] = ( OldWork[2] - i ) | SUBONCE; break; } s += 2; } if ( j >= 0 ) break; } else if ( *s == DOTPRODUCT ) { j = s[1]/3; s += 2; while ( --j >= 0 ) { if ( ABS(s[2]) > 2*MAXPOWER ) { OldWork[2] = ( OldWork[2] - i ) | SUBONCE; break; } else if ( s[1] >= -(2*WILDOFFSET) || s[0] >= -(2*WILDOFFSET) ) { OldWork[2] = ( OldWork[2] - i ) | SUBMANY; i = SUBMANY; } s += 3; } if ( j >= 0 ) break; } else { OldWork[2] = ( OldWork[2] - i ) | SUBMANY; break; } } } if ( ( OldWork[2] & SUBMASK ) == 0 ) OldWork[2] |= SUBMULTI; } if ( ( OldWork[2] & SUBMASK ) == SUBSELECT ) { /* Paste the SETSET information after the pattern. Important note: We will still get function information for the smart patternmatching after it. To distinguish them we need to have that SETSET != m*n+1 in which m is the number of words per function and n the number of functions. Currently (29-may-1997) m = 4. */ *m++ = SETSET; *m++ = numsets+2; s = FirstWork + idhead; while ( --numsets >= 0 ) *m++ = *s++; } else { m = w + *w; } } /* We keep the whole thing in OldWork for the moment. We still have to add the number of the RHS expression. There is also some opportunity now to be smart about the pattern. This is needed for complicated wildcarding with symmetric functions. We do this in a special routine during compile time to make sure that we loose as little time as possible (during running) if there is no need to be smart. */ *m++ = 0; OldWork[1] = m - OldWork; AC.ProtoType = OldWork+idhead; if ( !error ) { if ( StudyPattern(OldWork) ) error = 1; } AT.WorkPointer = OldWork + OldWork[1]; if ( AC.lhdollarflag ) OldWork[4] |= DOLLARFLAG; AC.lhdollarflag = 0; /* Test whether the id/idold configuration is fine. */ if ( type == TYPEIDOLD ) { WORD ci = C->numlhs; while ( ci >= 1 ) { if ( C->lhs[ci][0] == TYPEIDNEW ) { if ( (C->lhs[ci][2] & SUBMASK) == SUBALL ) { MesPrint("&Idold/also cannot follow an id,all statement."); error = 1; } break; } else if ( C->lhs[ci][0] == TYPEDETCURDUM ) { ci--; continue; } else if ( C->lhs[ci][0] == TYPEIDOLD ) { ci--; continue; } else ci = 0; } if ( ci < 1 ) { MesPrint("&Idold/also should follow an id/idnew statement."); error = 1; } } /* Now the right hand side. */ if ( type != TYPEIF ) { if ( ( retcode = CompileAlgebra(inp,RHSIDE,AC.ProtoType) ) < 0 ) error = 1; else { AC.ProtoType[2] = retcode; AC.DumNum = 0; if ( MinusSign ) { /* Flip the sign of the RHS */ w = C->rhs[retcode]; while ( *w ) { w += *w; w[-1] = -w[-1]; } } if ( AC.dumnumflag ) Add2Com(TYPEDETCURDUM) } } /* Actual adding happens only now after numrhs insertion */ if ( !error ) { AddNtoL(OldWork[1],OldWork); } AllDone: AC.lhdollarflag = 0; AT.WorkPointer = FirstWork; return(error); } /* #] CoIdExpression : #[ CoMultiply : */ static WORD mularray[13] = { TYPEMULT, SUBEXPSIZE+3, 0, SUBEXPRESSION, SUBEXPSIZE, 0, 1, 0, 0, 0, 0, 0, 0 }; int CoMultiply(UBYTE *inp) { UBYTE *p; int error = 0, RetCode; mularray[2] = 0; /* right multiply is default */ while ( *inp == ',' ) inp++; /* if ( inp[-1] == '-' || inp[-1] == '+' ) inp--; */ p = SkipField(inp,0); if ( *p ) { *p = 0; if ( StrICont(inp,(UBYTE *)"left") == 0 ) mularray[2] = 1; else if ( StrICont(inp,(UBYTE *)"right") == 0 ) mularray[2] = 0; else { MesPrint("&Illegal option in multiply statement or ; forgotten."); return(1); } *p = ','; inp = p + 1; } ClearWildcardNames(); while ( *inp == ',' ) inp++; AC.ProtoType = mularray+3; mularray[7] = AC.cbufnum; if ( ( RetCode = CompileAlgebra(inp,RHSIDE,AC.ProtoType) ) < 0 ) error = 1; else { mularray[5] = RetCode; AddNtoL(SUBEXPSIZE+3,mularray); if ( AC.dumnumflag ) Add2Com(TYPEDETCURDUM) } return(error); } /* #] CoMultiply : #[ CoFill : Special additions for tablebase-like tables added 12-aug-2002 */ int CoFill(UBYTE *inp) { GETIDENTITY WORD error = 0, x, xx, funnum, type, *oldwp = AT.WorkPointer; int i, oldcbufnum = AC.cbufnum, nofill = 0, numover, redef = 0; WORD *w, *wold, *Tprototype; UBYTE *p = inp, c, *inp1; TABLES T = 0, oldT; LONG newreservation, sum = 0; UBYTE *p1, *p2, *p3, *p4, *fake = 0; int tablestub = 0; if ( AC.exprfillwarning == 1 ) AC.exprfillwarning = 0; /* Read the name of the function and test that it is in the table. */ p1 = inp; if ( ( p = SkipAName(inp) ) == 0 ) return(1); p2 = p; c = *p; *p = 0; if ( ( GetVar(inp,&type,&funnum,CFUNCTION,WITHAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 || ( T->numind > 0 && c != '(' ) ) { MesPrint("&%s should be a table with argument(s)",inp); *p = c; return(1); } oldT = T; *p++ = c; if ( T->numind == 0 ) { if ( c == '(' ) { if ( *p != ')' ) { c = *p; *p = 0; MesPrint("&%s should be a table without arguments",inp); *p = c; return(1); } else { p++; } } else { p--; } sum = 0; p3 = p; goto andagain; } w = oldwp; if ( T->numind < 0 ) { /* Pick up the first index */ ParseSignedNumber(xx,p); if ( FG.cTable[p[-1]] != 1 || *p != ',' || xx < 1 || ( xx > ( -T->numind - 1 ) ) ) { MesPrint("&No valid number of table indices in *-table fill statement."); return(1); } *w++ = xx; p++; } else { xx = T->numind; } for ( sum = 0, i = 0; i < xx; i++ ) { ParseSignedNumber(x,p); if ( FG.cTable[p[-1]] != 1 || ( *p != ',' && *p != ')' ) ) { MesPrint("&Table arguments in fill statement should be numbers"); return(1); } if ( T->sparse ) *w++ = x; else if ( x < T->mm[i].mini || x > T->mm[i].maxi ) { MesPrint("&Value %d for argument %d of table out of bounds",x,i+1); error = 1; nofill = 1; } else sum += ( x - T->mm[i].mini ) * T->mm[i].size; if ( *p == ')' ) break; p++; } p3 = p; if ( T->numind < 0 ) { for ( ; i < ABS(T->numind)-1; i++ ) *w++ = 0; xx = -T->numind; } if ( *p != ')' || i < ( xx - 1 ) ) { MesPrint("&Incorrect number of table arguments in fill statement. Should be %d" ,T->numind); error = 1; nofill = 1; } AT.WorkPointer = w; if ( T->sparse == 0 ) sum *= TABLEEXTENSION; andagain:; AC.cbufnum = T->bufnum; if ( T->sparse ) { i = FindTableTree(T,oldwp,1); if ( i >= 0 ) { sum = i + ABS(T->numind); if ( tablestub == 0 && ( ( T->sparse & 2 ) == 2 ) && ( T->mode != 0 ) && ( AC.vetotablebasefill == 0 ) ) { /* This redefinition does not need a new stub */ functions[funnum].tabl = T = T->spare; tablestub = 1; goto andagain; } redef = 1; goto redef; } if ( T->totind >= T->reserved ) { if ( T->reserved == 0 ) newreservation = 20; else newreservation = T->reserved; while ( T->totind >= newreservation && newreservation < MAXTABLECOMBUF ) newreservation = 2*newreservation; if ( newreservation > MAXTABLECOMBUF ) newreservation = MAXTABLECOMBUF; if ( T->totind >= newreservation ) { MesPrint("@More than %ld elements in sparse table",MAXTABLECOMBUF); AC.cbufnum = oldcbufnum; Terminate(-1); } wold = (WORD *)Malloc1(newreservation*sizeof(WORD)* (ABS(T->numind)+TABLEEXTENSION),"tablepointers"); for ( i = T->reserved*(ABS(T->numind)+TABLEEXTENSION)-1; i >= 0; i-- ) wold[i] = T->tablepointers[i]; if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); T->tablepointers = wold; T->reserved = newreservation; } w = oldwp; for ( sum = T->totind*(ABS(T->numind)+TABLEEXTENSION), i = 0; i < ABS(T->numind); i++ ) { T->tablepointers[sum++] = *w++; } InsTableTree(T,T->tablepointers+sum-ABS(T->numind)); #if TABLEEXTENSION == 2 T->tablepointers[sum+TABLEEXTENSION-1] = -1; /* New element! */ #else T->tablepointers[sum+1] = T->bufnum; T->tablepointers[sum+2] = -1; T->tablepointers[sum+3] = -1; T->tablepointers[sum+4] = 0; T->tablepointers[sum+5] = 0; #endif } else { if ( !nofill && T->tablepointers[sum] >= 0 ) { redef:; if ( AC.vetofilling ) nofill = 1; else { Warning("Table element was already defined. New definition will be used"); } } #if TABLEEXTENSION == 2 T->tablepointers[sum+TABLEEXTENSION-1] = -1; /* New element! */ #else T->tablepointers[sum+1] = T->bufnum; T->tablepointers[sum+2] = -1; T->tablepointers[sum+3] = -1; T->tablepointers[sum+4] = 0; T->tablepointers[sum+5] = 0; #endif } if ( T->numind ) { p++; } if ( *p != '=' ) { MesPrint("&Fill statement misses = sign after the table element"); AC.cbufnum = oldcbufnum; AT.WorkPointer = oldwp; functions[funnum].tabl = oldT; return(1); } if ( tablestub == 0 && T->mode == 1 && AC.vetotablebasefill == 0 ) { /* Here we construct a righthandside from the indices and the wildcards */ int numfake; tablestub = 1; p4 = T->argtail; while ( *p4 ) p4++; numfake = (p4-T->argtail)+(p3-p1)+10; fake = (UBYTE *)Malloc1(numfake*sizeof(UBYTE),"Fill fake rhs"); p = fake; *p++ = 't'; *p++ = 'b'; *p++ = 'l'; *p++ = '_'; *p++ = '('; p4 = p1; while ( p4 < p2 ) *p++ = *p4++; *p++ = ','; p4 = p2+1; while ( p4 < p3 ) *p++ = *p4++; if ( T->argtail ) { p4 = T->argtail + 1; while ( FG.cTable[*p4] == 1 ) p4++; while ( *p4 ) { if ( *p4 == '?' && p[-1] != ',' ) { p4++; if ( FG.cTable[*p4] == 0 || *p4 == '$' || *p4 == '[' ) { p4 = SkipAName(p4); if ( *p4 == '[' ) { SKIPBRA1(p4); } } else if ( *p4 == '{' ) { SKIPBRA2(p4); } else if ( *p4 ) { *p++ = *p4++; continue; } } else *p++ = *p4++; } } *p++ = ')'; *p = 0; inp1 = fake; } else { inp1 = ++p; } c = 0; /* Now we have the indices and p points to the rhs. */ numover = 0; AC.tablefilling = funnum; while ( *inp1 ) { p = SkipField(inp1,0); c = *p; *p = 0; #ifdef WITHPTHREADS Tprototype = T->prototype[0]; #else Tprototype = T->prototype; #endif if ( ( i = CompileAlgebra(inp1,RHSIDE,Tprototype) ) < 0 ) { error = 1; i = 0; } if ( !nofill ) { T->tablepointers[sum] = i; T->tablepointers[sum+1] = T->bufnum; } AC.DumNum = 0; *p = c; if ( T->sparse || c == 0 ) break; inp1 = ++p; #if ( TABLEEXTENSION == 2 ) sum++; #else sum += 2; #endif if ( !nofill && T->tablepointers[sum] >= 0 ) numover++; #if ( TABLEEXTENSION == 2 ) sum++; #else sum += TABLEEXTENSION-2; #endif } if ( AC.exprfillwarning == 1 ) { AC.exprfillwarning = 2; Warning("Use of expressions and/or $variables in Fill statements is potentially very dangerous."); } AC.tablefilling = 0; if ( T->sparse && c != 0 ) { MesPrint("&In sparse tables one can fill only one element at a time"); error = 1; } else if ( numover ) { if ( numover == 1 ) Warning("one element was overwritten. New definition will be used"); else if ( AC.WarnFlag ) MesPrint("&Warning: %d elements were overwritten. New definitions will be used",numover); } if ( T->sparse ) { if ( redef == 0 ) T->totind++; } else T->defined++; /* NumSets = AC.SetList.numtemp; NumSetElements = AC.SetElementList.numtemp; */ if ( fake ) { M_free(fake,"Fill fake rhs"); fake = 0; functions[funnum].tabl = T = T->spare; p = p3; goto andagain; } AC.cbufnum = oldcbufnum; AC.SymChangeFlag = 1; AT.WorkPointer = oldwp; functions[funnum].tabl = oldT; return(error); } /* #] CoFill : #[ CoFillExpression : Syntax: FillExpression table = expression(x1,...,xn); The arguments should have been bracketed. Each corresponds to one of the dimensions of the table. Then the bracket with x1^2*x3^4 will fill the (2,0,4) element of the table (if n=3 of course). Brackets that don't fit will be skipped. It just gives a warning. New option (13-jul-2005) Syntax: FillExpression table = expression(f); The table indices are arguments of the function f which should have been bracketed before. */ int CoFillExpression(UBYTE *inp) { GETIDENTITY UBYTE *p, c; WORD type, funnum, expnum, symnum, numsym = 0, *oldwork = AT.WorkPointer; WORD *brackets, *term, brasize, *b, *m, *w, *pw, *tstop, zero = 0; WORD oldcbuf = AC.cbufnum, curelement = 0; int weneedit, i, j, numzero, pow, numfirst; TABLES T = 0; LONG newreservation, numcommu, sum; POSITION oldposition; FILEHANDLE *fi; CBUF *C; WORD numdummies; AN.IndDum = AM.IndDum; if ( ( p = SkipAName(inp) ) == 0 ) return(1); c = *p; *p = 0; if ( ( GetVar(inp,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",inp); *p = c; return(1); } *p++ = c; if ( T->spare ) T = T->spare; C = cbuf + T->bufnum; if ( c != '=' ) { MesPrint("&No = sign in FillExpression statement"); return(1); } inp = p; if ( ( p = SkipAName(inp) ) == 0 ) return(1); c = *p; *p = 0; if ( ( type = GetName(AC.exprnames,inp,&expnum,NOAUTO) ) == NAMENOTFOUND || c != '(' || ( Expressions[expnum].status != LOCALEXPRESSION && Expressions[expnum].status != SKIPLEXPRESSION && Expressions[expnum].status != DROPLEXPRESSION && Expressions[expnum].status != GLOBALEXPRESSION && Expressions[expnum].status != SKIPGEXPRESSION && Expressions[expnum].status != DROPGEXPRESSION ) ) { MesPrint("&%s should be an active expression with arguments",inp); *p = c; return(1); } if ( Expressions[expnum].inmem ) { MesPrint("&%s cannot be used in a FillExpression statement in the same %n\ module that it has been redefined",inp); *p = c; return(1); } *p++ = c; while ( *p ) { inp = p; if ( ( p = SkipAName(inp) ) == 0 ) return(1); c = *p; *p = 0; if ( GetVar(inp,&type,&symnum,-1,NOAUTO) == NAMENOTFOUND ) { MesPrint("&%s should be a previously declared symbol or function",inp); *p = c; return(1); } else if ( type == CSYMBOL ) { *p++ = c; *AT.WorkPointer++ = symnum; numsym++; } else if ( type == CFUNCTION ) { numsym = -1; *p++ = c; if ( c != ')' ) { MesPrint("&Argument should be a single function or a list of symbols"); return(1); } symnum += FUNCTION; *AT.WorkPointer++ = symnum; } else { MesPrint("&%s should be a previously declared symbol or function",inp); *p = c; return(1); } if ( c == ')' ) break; if ( c != ',' ) { MesPrint("&Illegal separator in FillExpression statement"); goto noway; } } if ( *p ) { MesPrint("&Illegal end of FillExpression statement"); goto noway; } /* We have the number of the table in funnum. The number of the expression in expnum, the table struct in T and either the numbers of the symbols in oldwork (there are numsym of them) or the number of the function in oldwork (just one and numsym = -1). We don't sort them!!!! */ if ( ( numsym > 0 ) && ( ABS(T->numind) != numsym ) ) { MesPrint("&This table needs %d symbols for its array indices"); goto noway; } EXCHINOUT #ifdef WITHMPI /* * The workers can't access to the data of the input expression. We need to * broadcast it to all the workers. */ PF_BroadcastExpr(&Expressions[expnum], AR.infile); if ( PF.me == MASTER ) { /* * Restore the file position on the master. */ POSITION pos; SetEndScratch(AR.infile, &pos); } #endif fi = AR.infile; if ( fi->handle >= 0 ) { PUTZERO(oldposition); SeekFile(fi->handle,&oldposition,SEEK_CUR); SetScratch(fi,&(Expressions[expnum].onfile)); if ( ISNEGPOS(Expressions[expnum].onfile) ) { MesPrint("&File error in FillExpression"); BACKINOUT goto noway; } } else { /* Note: Because everything fits inside memory we never get problems with excessive file sizes. */ SETBASEPOSITION(oldposition,(UBYTE *)(fi->POfill)-(UBYTE *)(fi->PObuffer)); fi->POfill = (WORD *)((UBYTE *)(fi->PObuffer) + BASEPOSITION(Expressions[expnum].onfile)); } pw = AT.WorkPointer; if ( numsym < 0 ) { brackets = pw + 1; } else { brackets = pw + numsym; } brasize = -1; weneedit = 0; /* stands for we need it */ term = (WORD *)(((UBYTE *)(brackets)) + AM.MaxTer); AT.WorkPointer = (WORD *)(((UBYTE *)(term)) + AM.MaxTer); AC.cbufnum = T->bufnum; AC.tablefilling = funnum; if ( GetTerm(BHEAD term) > 0 ) { /* Skip prototype */ while ( GetTerm(BHEAD term) > 0 ) { GETSTOP(term,tstop); w = m = term + 1; while ( m < tstop && *m != HAAKJE ) m += m[1]; if ( *m != HAAKJE ) { MesPrint("&Illegal attempt to put an expression without brackets in a table"); BACKINOUT goto noway; } if ( brasize == m - w ) { b = brackets; while ( *b == *w && w < m ) { b++; w++; } if ( w == m ) { /* Same as current bracket. Copy. */ if ( weneedit ) { m += m[1] - 1; *m = *term - (m-term); AddNtoC(AC.cbufnum,*m,m,3); numdummies = DetCurDum(BHEAD term) - AM.IndDum; if ( numdummies > T->numdummies ) T->numdummies = numdummies; } continue; /* Next term */ } } if ( weneedit ) { AddNtoC(AC.cbufnum,1,&zero,4); /* Terminate old bracket */ numcommu = numcommute(C->rhs[curelement],&(C->NumTerms[curelement])); C->CanCommu[curelement] = numcommu; } b = brackets; w = term + 1; if ( numsym < 0 ) pw = oldwork + 1; else pw = oldwork + numsym; while ( w < m ) *b++ = *w++; brasize = b - brackets; /* Now compute the element. See whether we need it */ if ( numsym < 0 ) { WORD *bb, bnum; if ( *brackets != symnum || brasize != brackets[1] ) { weneedit = 0; continue; /* Cannot work! */ } /* Now count the number of arguments and whether they are numbers */ b = brackets + FUNHEAD; bb = brackets+brackets[1]; i = 0; if ( T->numind < 0 ) { bnum = b[1]+1; if ( bnum > -T->numind ) { weneedit = 0; continue; /* Cannot work! */ } } else bnum = T->numind; while ( b < bb ) { if ( *b != -SNUMBER ) break; i++; b += 2; } if ( b < bb || i != bnum ) { weneedit = 0; continue; /* Cannot work! */ } } else if ( brasize > 0 && ( *brackets != SYMBOL || brackets[1] < brasize || (brackets[1]-2) > numsym*2 ) ) { weneedit = 0; continue; /* Cannot work! */ } numzero = 0; sum = 0; numfirst = 0; if ( numsym > 0 ) { for ( i = 0; i < numsym; i++ ) { if ( brasize > 0 ) { b = brackets + 2; j = brackets[1]-2; while ( j > 0 ) { if ( *b == oldwork[i] ) break; j -= 2; b += 2; } if ( j <= 0 ) { /* it was not there */ numzero++; pow = 0; if ( 2*numzero+brackets[1]-2 > numsym*2 ) { weneedit = 0; goto nextterm; } } else pow = b[1]; } else pow = 0; if ( T->sparse ) { if ( T->numind < 0 ) { if ( i == 0 ) { numfirst = pow; if ( pow > -T->numind ) { weneedit = 0; goto nextterm; } } else if ( i > pow ) { weneedit = 0; goto nextterm; } } *pw++ = pow; } else if ( pow < T->mm[i].mini || pow > T->mm[i].maxi ) { weneedit = 0; goto nextterm; } else sum += ( pow - T->mm[i].mini ) * T->mm[i].size; } } else { WORD xx; b = brackets + FUNHEAD; sum = 0; /* Now scan the arguments of the function. We did check already the number and type of the arguments. */ xx = (brackets[1]-FUNHEAD)/2; for ( i = 0; i < xx; i++ ) { pow = b[1]; b += 2; if ( T->sparse ) { if ( T->numind < 0 ) { if ( i == 0 ) { numfirst = pow; if ( pow >= -T->numind ) { weneedit = 0; goto nextterm; } } } *pw++ = pow; } else if ( pow < T->mm[i].mini || pow > T->mm[i].maxi ) { weneedit = 0; goto nextterm; } else sum += ( pow - T->mm[i].mini ) * T->mm[i].size; } } if ( T->numind < 0 ) { for ( i = numfirst+1; i < -T->numind; i++ ) *pw++ = 0; } weneedit = 1; if ( T->sparse ) { if ( numsym < 0 ) pw = oldwork + 1; else pw = oldwork + ABS(T->numind); i = FindTableTree(T,pw,1); if ( i >= 0 ) { sum = i+ABS(T->numind); /* Wrong!!!! C->rhs[T->tablepointers[sum]] = C->Pointer; */ C->Pointer--; /* Back up over the zero */ goto newentry; } if ( T->totind >= T->reserved ) { if ( T->reserved == 0 ) newreservation = 20; else newreservation = T->reserved; /*---Copied from Fill---------------------------*/ while ( T->totind >= newreservation && newreservation < MAXTABLECOMBUF ) newreservation = 2*newreservation; if ( newreservation > MAXTABLECOMBUF ) newreservation = MAXTABLECOMBUF; if ( T->totind >= newreservation ) { MesPrint("@More than %ld elements in sparse table",MAXTABLECOMBUF); AC.cbufnum = oldcbuf; AT.WorkPointer = oldwork; Terminate(-1); } /*---Copied from Fill---------------------------*/ if ( T->totind >= newreservation ) { MesPrint("@More than %ld elements in sparse table",MAXTABLECOMBUF); AC.cbufnum = oldcbuf; AT.WorkPointer = oldwork; Terminate(-1); } w = (WORD *)Malloc1(newreservation*sizeof(WORD)* (ABS(T->numind)+TABLEEXTENSION),"tablepointers"); for ( i = T->reserved*(ABS(T->numind)+TABLEEXTENSION)-1; i >= 0; i-- ) w[i] = T->tablepointers[i]; if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); T->tablepointers = w; T->reserved = newreservation; } if ( numsym < 0 ) pw = oldwork + 1; else pw = oldwork + numsym; for ( sum = T->totind*(ABS(T->numind)+TABLEEXTENSION), i = 0; i < ABS(T->numind); i++ ) { T->tablepointers[sum++] = *pw++; } InsTableTree(T,T->tablepointers+sum-ABS(T->numind)); (T->totind)++; } #if ( TABLEEXTENSION != 2 ) else { sum *= TABLEEXTENSION; } #endif /* Start a new entry. Copy the element. */ AddRHS(T->bufnum,0); T->tablepointers[sum] = C->numrhs; #if ( TABLEEXTENSION == 2 ) T->tablepointers[sum+TABLEEXTENSION-1] = -1; #else T->tablepointers[sum+1] = T->bufnum; T->tablepointers[sum+2] = -1; T->tablepointers[sum+3] = -1; T->tablepointers[sum+4] = 0; T->tablepointers[sum+5] = 0; #endif newentry: if ( *m == HAAKJE ) { m += m[1] - 1; } else m--; *m = *term - (m-term); AddNtoC(AC.cbufnum,*m,m,5); curelement = T->tablepointers[sum]; nextterm:; } if ( weneedit ) { AddNtoC(AC.cbufnum,1,&zero,6); /* Terminate old bracket */ numcommu = numcommute(C->rhs[curelement],&(C->NumTerms[curelement])); C->CanCommu[curelement] = numcommu; } } if ( fi->handle >= 0 ) { SetScratch(fi,&(oldposition)); } else { fi->POfill = (WORD *)((UBYTE *)(fi->PObuffer) + BASEPOSITION(oldposition)); } BACKINOUT AC.cbufnum = oldcbuf; AC.tablefilling = 0; AT.WorkPointer = oldwork; return(0); noway: BACKINOUT AC.cbufnum = oldcbuf; AC.tablefilling = 0; AT.WorkPointer = oldwork; return(1); } /* #] CoFillExpression : #[ CoPrintTable : Syntax PrintTable [+f] [+s] tablename [>[>] file]; All defined elements are written with individual Fill statements. If a file is specified, the result is written to file only. The flags of the print statement apply as much as possible. We make use of the regular write routines. */ int CoPrintTable(UBYTE *inp) { GETIDENTITY int fflag = 0, sflag = 0, addflag = 0, error = 0, sum, i, j; UBYTE *filename, *p, c, buffer[100], *s, *oldoutputline = AO.OutputLine; WORD type, funnum, *expr, *m, num; TABLES T = 0; WORD oldSkip = AO.OutSkip, oldMode = AC.OutputMode, oldHandle = AC.LogHandle; WORD oldType = AO.PrintType, *oldwork = AT.WorkPointer; UBYTE *oldFill = AO.OutFill, *oldLine = AO.OutputLine; #ifdef WITHMPI if ( PF.me != MASTER ) return 0; #endif /* First the flags */ while ( *inp == '+' ) { inp++; if ( *inp == 'f' || *inp == 'F' ) { fflag = 1; inp++; } else if ( *inp == 's' || *inp == 'S' ) { sflag = PRINTONETERM; inp++; } else { MesPrint("&Illegal + option in PrintTable statement"); error = 1; inp++; } while ( *inp != ',' && *inp && *inp != '+' ) { if ( !error ) { if ( *inp ) { MesPrint("&Illegal + option in PrintTable statement"); inp++; } else { MesPrint("&Unfinished PrintTable statement"); return(1); } error = 1; } inp++; } if ( *inp == ',' ) inp++; } /* Now the name of the table */ if ( ( p = SkipAName(inp) ) == 0 ) return(1); c = *p; *p = 0; if ( ( GetVar(inp,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",inp); *p = c; return(1); } if ( T->spare && T->mode == 1 ) T = T->spare; *p++ = c; /* Check for a filename. Runs to the end of the statement. */ filename = 0; if ( c == '>' ) { if ( *p == '>' ) { addflag = 1; p++; } filename = p; } else filename = 0; if ( filename ) { if ( addflag ) AC.LogHandle = OpenAddFile((char *)filename); else AC.LogHandle = CreateFile((char *)filename); if ( AC.LogHandle < 0 ) { MesPrint("&Cannot open file '%s' properly",filename); error = 1; goto finally; } AO.PrintType = PRINTLFILE; } else if ( fflag && AC.LogHandle >= 0 ) { AO.PrintType = PRINTLFILE; } AO.OutFill = AO.OutputLine = (UBYTE *)AT.WorkPointer; AT.WorkPointer += 2*AC.LineLength; AO.PrintType |= sflag; AC.OutputMode = 0; AO.IsBracket = 0; AO.OutSkip = 0; AR.DeferFlag = 0; AC.outsidefun = 1; if ( AC.LogHandle == oldHandle ) FiniLine(); AO.OutputLine = AO.OutFill = (UBYTE *)Malloc1(AC.LineLength+20,"PrintTable"); AO.OutStop = AO.OutFill + AC.LineLength; for ( i = 0; i < T->totind; i++ ) { if ( !T->sparse && T->tablepointers[i*TABLEEXTENSION] < 0 ) continue; TokenToLine((UBYTE *)"Fill "); TokenToLine((UBYTE *)(VARNAME(functions,funnum))); TokenToLine((UBYTE *)"("); AO.OutSkip = 3; if ( T->sparse ) { sum = i * ( T->numind + TABLEEXTENSION ); for ( j = 0; j < T->numind; j++, sum++ ) { if ( j > 0 ) TokenToLine((UBYTE *)","); num = T->tablepointers[sum]; s = buffer; s = NumCopy(num,s); TokenToLine(buffer); } expr = cbuf[T->bufnum].rhs[T->tablepointers[sum]]; } else { for ( j = 0; j < T->numind; j++ ) { if ( j > 0 ) { TokenToLine((UBYTE *)","); num = T->mm[j].mini + ( i % T->mm[j-1].size ) / T->mm[j].size; } else { num = T->mm[j].mini + i / T->mm[j].size; } s = buffer; s = NumCopy(num,s); TokenToLine(buffer); } expr = cbuf[T->bufnum].rhs[T->tablepointers[TABLEEXTENSION*i]]; } TOKENTOLINE(") =",")="); if ( sflag ) { FiniLine(); if ( AC.OutputSpaces != NOSPACEFORMAT ) TokenToLine((UBYTE *)" "); } m = expr; /* WORD lbrac, first; lbrac = 0; first = 1; while ( *m ) { if ( WriteTerm(m,&lbrac,first,1,0) ) { MesPrint("Error while writing table"); error = 1; goto finally; } first = 0; m += *m; } if ( first ) { TOKENTOLINE(" 0","0") } else if ( lbrac ) { TOKENTOLINE(" )",")") } */ while ( *m ) m += *m; if ( m > expr ) { if ( WriteExpression(expr,(LONG)(m-expr)) ) { error = 1; goto finally; } AO.OutSkip = 0; } else { TokenToLine((UBYTE *)"0"); } TokenToLine((UBYTE *)";"); FiniLine(); } M_free(AO.OutputLine,"PrintTable"); AO.OutputLine = AO.OutFill = oldoutputline; /* Reset the file pointers and parameters if any. Close file if needed. */ finally: AO.OutSkip = oldSkip; AC.OutputMode = oldMode; AC.LogHandle = oldHandle; AO.PrintType = oldType; AO.OutFill = oldFill; AO.OutputLine = oldLine; AT.WorkPointer = oldwork; AC.outsidefun = 0; return(error); } /* #] CoPrintTable : #[ CoAssign : This statement has an easy syntax: $name = expression */ static WORD AssignLHS[14] = { TYPEASSIGN, 3+SUBEXPSIZE, 0, SUBEXPRESSION, SUBEXPSIZE, 0, 1, 0, 0,0,0,0,0 }; int CoAssign(UBYTE *inp) { int error = 0, retcode; UBYTE *name, c; WORD number; if ( *inp != '$' ) { nolhs: MesPrint("&assign statement should have a dollar variable in the LHS"); return(1); } inp++; name = inp; if ( FG.cTable[*inp] != 0 ) goto nolhs; while ( FG.cTable[*inp] < 2 ) inp++; if ( AP.PreAssignFlag == 2 ) { if ( *inp == '_' ) inp++; } if ( ( *inp == ',' && inp[1] != '=' ) && ( *inp != '=' ) ) { MesPrint("&assign statement should have only a dollar variable in the LHS"); return(1); } c = *inp; *inp = 0; if ( GetName(AC.dollarnames,name,&number,NOAUTO) == NAMENOTFOUND ) { number = AddDollar(name,DOLUNDEFINED,0,0); } *inp = c; if ( c == ',' ) inp++; *inp++ = '='; if ( *inp == ',' ) inp++; /* Fake a Prototype and read the RHS */ AssignLHS[7] = AC.cbufnum; retcode = CompileAlgebra(inp,RHSIDE,(AssignLHS+3)); if ( retcode < 0 ) error = 1; AC.DumNum = 0; /* Now add the LHS */ AssignLHS[2] = number; AssignLHS[5] = retcode; AddNtoL(AssignLHS[1],AssignLHS); /* Add to the list of potentially modified dollars (for PARALLEL) */ AddPotModdollar(number); return(error); } /* #] CoAssign : #[ CoDeallocateTable : Syntax: DeallocateTable tablename(s); Should work only for sparse tables. Action: Cleans all definitions of elements of a table as if there have never been any fill statements. */ int CoDeallocateTable(UBYTE *inp) { UBYTE *p, c; TABLES T = 0; WORD type, funnum, i; c = *inp; while ( c ) { while ( *inp == ',' ) inp++; if ( *inp == 0 ) break; if ( ( p = SkipAName(inp) ) == 0 ) return(1); c = *p; *p = 0; if ( ( GetVar(inp,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) || ( T = functions[funnum].tabl ) == 0 ) { MesPrint("&%s should be a previously declared table",inp); *p = c; return(1); } if ( T->sparse == 0 ) { MesPrint("&%s should be a sparse table",inp); *p = c; return(1); } if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); ClearTableTree(T); for (i = 0; i < T->buffersfill; i++ ) { /* was <= */ finishcbuf(T->buffers[i]); } T->bufnum = inicbufs(); T->buffersfill = 0; T->buffers[T->buffersfill++] = T->bufnum; T->tablepointers = 0; T->boomlijst = 0; T->totind = 0; T->reserved = 0; if ( T->spare ) { TABLES TT = T->spare; if ( TT->tablepointers ) M_free(TT->tablepointers,"tablepointers"); ClearTableTree(TT); for (i = 0; i < TT->buffersfill; i++ ) { /* was <= */ finishcbuf(TT->buffers[i]); } TT->bufnum = inicbufs(); TT->buffersfill = 0; TT->buffers[T->buffersfill++] = T->bufnum; TT->tablepointers = 0; TT->boomlijst = 0; TT->totind = 0; TT->reserved = 0; } *p++ = c; inp = p; } return(0); } /* #] CoDeallocateTable : #[ CoFactorCache : */ /** * Reads the FactorCache statement which is like a fill statement for * the factorization cache. Syntax: * FactorCache,expression:factor1,...,factorn; * This statement is mainly for testing purposes, because there are severe * restrictions on the use of the expression (no common GCD, no denominators) * The expression is worked out by FORM and properly normalized and sorted. */ /* int CoFactorCache(UBYTE *inp) { Code to be added in due time We need to read 'expression', get its terms through Generator and sort them. We store the result in the WorkSpace in argument notation. This will be argin. Then we do the same with the sequence of factors. They form argout. The whole is put in the buffer with the call InsertArg(BHEAD argin,argout,1) return(0); } */ /* #] CoFactorCache : */ form-5.0.1/sources/parallel.c0000644000175100017510000041122315217035721011574 /** @file parallel.c * * Message passing library independent functions of parform * * This file contains functions needed for the parallel version of form3 * these functions need no real link to the message passing libraries, they * only need some interface dependent preprocessor definitions (check * parallel.h). So there still need two different objectfiles to be compiled * for mpi and pvm! */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ includes : */ #include "form3.h" #include "vector.h" #include // must come after form3.h /* #define PF_DEBUG_BCAST_LONG #define PF_DEBUG_BCAST_BUF #define PF_DEBUG_BCAST_PREDOLLAR #define PF_DEBUG_BCAST_RHSEXPR #define PF_DEBUG_BCAST_DOLLAR #define PF_DEBUG_BCAST_PREVAR #define PF_DEBUG_BCAST_CBUF #define PF_DEBUG_BCAST_EXPRFLAGS #define PF_DEBUG_REDUCE_DOLLAR */ /* mpi.c */ LONG PF_RealTime(int); int PF_LibInit(int*, char***); int PF_LibTerminate(int); int PF_Probe(int*); int PF_RecvWbuf(WORD*,LONG*,int*); int PF_IRecvRbuf(PF_BUFFER*,int,int); int PF_WaitRbuf(PF_BUFFER *,int,LONG *); int PF_RawSend(int dest, void *buf, LONG l, int tag); LONG PF_RawRecv(int *src,void *buf,LONG thesize,int *tag); int PF_RawProbe(int *src, int *tag, int *bytesize); int PF_RawIsend(int dest, const void *buf, int count, MPI_Datatype type, int tag, MPI_Request *request); int PF_RawWaitAll(int count, MPI_Request *request, MPI_Status *status); int PF_Discard(int *src, int *tag); /* Private functions */ static int PF_WaitAllSlaves(void); static void PF_PackRedefinedPreVars(void); static void PF_UnpackRedefinedPreVars(void); static int PF_Wait4MasterIP(int tag); static int PF_DoOneExpr(void); static int PF_ReadMaster(void);/*reads directly to its scratch!*/ static int PF_Slave2MasterIP(int src);/*both master and slave*/ static int PF_Master2SlaveIP(int dest, EXPRESSIONS e); static int PF_WalkThrough(WORD *t, LONG l, LONG chunk, LONG *count); static int PF_SendChunkIP(FILEHANDLE *curfile, POSITION *position, int to, LONG thesize); static int PF_RecvChunkIP(FILEHANDLE *curfile, int from, LONG thesize); static void PF_ReceiveErrorMessage(int src, int tag); static void PF_CatchErrorMessages(int *src, int *tag); static void PF_CatchErrorMessagesForAll(void); static int PF_ProbeWithCatchingErrorMessages(int *src); static void PF_RaiseRuntimeError(void); static void PF_BroadcastRuntimeError(void); static void PF_PostEndSortBarrier(void); /* Variables */ PARALLELVARS PF; static int PF_processing; /* Flag indicating that parallel processing of terms is in progress */ static LONG PF_goutterms; /* (master) Total out terms at PF_EndSort(), used in PF_Statistics(). */ static POSITION PF_exprsize; /* (master) The size of the expression at PF_EndSort(), used in PF_Processor(). */ /* This will work well only under Linux, see #ifdef PF_WITH_SCHED_YIELD below in PF_WaitAllSlaves(). */ #ifdef PF_WITH_SCHED_YIELD #include #endif #ifdef PF_WITHLOG #define PRINTFBUF(TEXT,TERM,SIZE) { UBYTE lbuf[24]; if(PF.log){ WORD iii;\ NumToStr(lbuf,AC.CModule); \ fprintf(stderr,"[%d|%s] %s : ",PF.me,lbuf,(char*)TEXT);\ if(TERM){ fprintf(stderr,"[%d] ",(int)(*TERM));\ if((SIZE)<500 && (SIZE)>0) for(iii=1;iii<(SIZE);iii++)\ fprintf(stderr,"%d ",TERM[iii]); }\ fprintf(stderr,"\n");\ fflush(stderr); } } #else #define PRINTFBUF(TEXT,TERM,SIZE) {} #endif /** * Swaps the variables \a x and \a y. If sizeof(x) != sizeof(y) then a compilation error * will occur. A set of memcpy calls with constant sizes is expected to be inlined by the optimisation. */ #define SWAP(x, y) \ do { \ char swap_tmp__[sizeof(x) == sizeof(y) ? (int)sizeof(x) : -1]; \ memcpy(swap_tmp__, &y, sizeof(x)); \ memcpy(&y, &x, sizeof(x)); \ memcpy(&x, swap_tmp__, sizeof(x)); \ } while (0) /** * Packs a LONG value \a n to a WORD buffer \a p. */ #define PACK_LONG(p, n) \ do { \ *(p)++ = (UWORD)((ULONG)(n) & (ULONG)WORDMASK); \ *(p)++ = (UWORD)(((ULONG)(n) >> BITSINWORD) & (ULONG)WORDMASK); \ } while (0) /** * Unpacks a LONG value \a n from a WORD buffer \a p. */ #define UNPACK_LONG(p, n) \ do { \ (n) = (LONG)((((ULONG)(p)[1] & (ULONG)WORDMASK) << BITSINWORD) | ((ULONG)(p)[0] & (ULONG)WORDMASK)); \ (p) += 2; \ } while (0) /** * A simple check for unrecoverable errors. */ #define CHECK(condition) _CHECK(condition, __FILE__, __LINE__) #define _CHECK(condition, file, line) __CHECK(condition, file, line) #define __CHECK(condition, file, line) \ do { \ if ( !(condition) ) { \ Error0("Fatal error at " file ":" #line); \ Terminate(-1); \ } \ } while (0) /* * For debugging. */ #define DBGOUT(lv1, lv2, a) do { if ( lv1 >= lv2 ) { printf a; fflush(stdout); } } while (0) /* (AN.ninterms of master) == max(AN.ninterms of slaves) == sum(PF_linterms of slaves) at EndSort(). */ #define DBGOUT_NINTERMS(lv, a) /* #define DBGOUT_NINTERMS(lv, a) DBGOUT(1, lv, a) */ /* #] includes : #[ statistics : #[ variables : (should be part of a struct?) */ static LONG PF_linterms; /* local interms on this proces: PF_Proces */ #define PF_STATS_SIZE 5 static LONG **PF_stats = NULL;/* space for collecting statistics of all procs */ static LONG PF_laststat; /* last realtime when statistics were printed */ static LONG PF_statsinterval;/* timeinterval for printing statistics */ /* #] variables : #[ PF_Statistics : */ /** * Prints statistics every PF_statinterval seconds. * For \a proc = 0 it prints final statistics for EndSort(). * * @param stats the pointer to an array: LONG stats[proc][5] = {cpu,space,in,gen,left}. * @param proc the source process number. * @return 0 if OK, nonzero on error. */ static int PF_Statistics(LONG **stats, int proc) { GETIDENTITY LONG real, cpu; WORD rpart, cpart; int i, j; if ( AT.SS == AM.S0 && PF.me == MASTER ) { real = PF_RealTime(PF_TIME); rpart = (WORD)(real%100); real /= 100; if ( PF_stats == NULL ) { PF_stats = (LONG**)Malloc1(PF.numtasks*sizeof(LONG*),"PF_stats 1"); for ( i = 0; i < PF.numtasks; i++ ) { PF_stats[i] = (LONG*)Malloc1(PF_STATS_SIZE*sizeof(LONG),"PF_stats 2"); for ( j = 0; j < PF_STATS_SIZE; j++ ) PF_stats[i][j] = 0; } } if ( proc > 0 ) for ( i = 0; i < PF_STATS_SIZE; i++ ) PF_stats[proc][i] = stats[0][i]; if ( real >= PF_laststat + PF_statsinterval || proc == 0 ) { LONG sum[PF_STATS_SIZE]; for ( i = 0; i < PF_STATS_SIZE; i++ ) sum[i] = 0; sum[0] = cpu = TimeCPU(1); cpart = (WORD)(cpu%1000); cpu /= 1000; cpart /= 10; if ( AC.OldParallelStats ) MesPrint(""); if ( proc > 0 && AC.StatsFlag && AC.OldParallelStats ) { MesPrint("proc CPU in gen left byte"); MesPrint("%3d : %7l.%2i %10l",0,cpu,cpart,AN.ninterms); } else if ( AC.StatsFlag && AC.OldParallelStats ) { MesPrint("proc CPU in gen out byte"); MesPrint("%3d : %7l.%2i %10l %10l %10l",0,cpu,cpart,AN.ninterms,0,PF_goutterms); } for ( i = 1; i < PF.numtasks; i++ ) { cpart = (WORD)(PF_stats[i][0]%1000); cpu = PF_stats[i][0] / 1000; cpart /= 10; if ( AC.StatsFlag && AC.OldParallelStats ) MesPrint("%3d : %7l.%2i %10l %10l %10l",i,cpu,cpart, PF_stats[i][2],PF_stats[i][3],PF_stats[i][4]); for ( j = 0; j < PF_STATS_SIZE; j++ ) sum[j] += PF_stats[i][j]; } cpart = (WORD)(sum[0]%1000); cpu = sum[0] / 1000; cpart /= 10; if ( AC.StatsFlag && AC.OldParallelStats ) { MesPrint("Sum = %7l.%2i %10l %10l %10l",cpu,cpart,sum[2],sum[3],sum[4]); MesPrint("Real = %7l.%2i %20s (%l) %16s", real,rpart,AC.Commercial,AC.CModule,EXPRNAME(AR.CurExpr)); MesPrint(""); } PF_laststat = real; } } return(0); } /* #] PF_Statistics : #] statistics : #[ sort.c : #[ sort variables : */ /** * A node for the tree of losers in the final sorting on the master. */ typedef struct NoDe { struct NoDe *left; struct NoDe *rght; int lloser; int rloser; int lsrc; int rsrc; } NODE; /* should/could be put in one struct */ static NODE *PF_root; /* root of tree of losers */ static WORD PF_loser; /* this is the last loser */ static WORD **PF_term; /* these point to the active terms */ static WORD **PF_newcpos; /* new coefficients of merged terms */ static WORD *PF_newclen; /* length of new coefficients */ /* preliminary: could also write somewhere else? */ static WORD *PF_WorkSpace; /* used in PF_EndSort() */ static UWORD *PF_ScratchSpace; /* used in PF_GetLoser() */ /* #] sort variables : #[ PF_AllocBuf : */ /** * Allocates one PF_BUFFER struct with \a nbuf cyclic buffers of size \a bsize. * For the first \a free buffers there is no space allocated. * For example, if \a free == 1 then for the first (index 0) buffer there is * no space allocated(!!!) (one can reuse existing space for it) and * actually buff[0], stop[0], fill[0] and full[0] in the returned * PF_BUFFER struct are undefined. * * @param nbufs the number of cyclic buffers for PF_BUFFER struct. * @param bsize the memory allocation size in bytes for each buffer. * @param free the number of the buffers without the memory allocation. * @return the pointer to the PF_BUFFER struct if succeeded. NULL if failed. * * @todo Maybe this should be really hidden in the send/recv routines and pvm/mpi * files, it is only complicated because of nonblocking send/receives! */ static PF_BUFFER *PF_AllocBuf(int nbufs, LONG bsize, WORD free) { PF_BUFFER *buf; UBYTE *p, *stop; LONG allocsize; int i; allocsize = (LONG)(sizeof(PF_BUFFER) + 4*nbufs*sizeof(WORD*) + (nbufs-free)*bsize); allocsize += (LONG)( nbufs * ( 2 * sizeof(MPI_Status) + sizeof(MPI_Request) + sizeof(MPI_Datatype) ) ); allocsize += (LONG)( nbufs * 3 * sizeof(int) ); if ( ( buf = (PF_BUFFER*)Malloc1(allocsize,"PF_AllocBuf") ) == NULL ) return(NULL); p = ((UBYTE *)buf) + sizeof(PF_BUFFER); stop = ((UBYTE *)buf) + allocsize; buf->numbufs = nbufs; buf->active = 0; buf->buff = (WORD**)p; p += buf->numbufs*sizeof(WORD*); buf->fill = (WORD**)p; p += buf->numbufs*sizeof(WORD*); buf->full = (WORD**)p; p += buf->numbufs*sizeof(WORD*); buf->stop = (WORD**)p; p += buf->numbufs*sizeof(WORD*); buf->status = (MPI_Status *)p; p += buf->numbufs*sizeof(MPI_Status); buf->retstat = (MPI_Status *)p; p += buf->numbufs*sizeof(MPI_Status); buf->request = (MPI_Request *)p; p += buf->numbufs*sizeof(MPI_Request); buf->type = (MPI_Datatype *)p; p += buf->numbufs*sizeof(MPI_Datatype); buf->index = (int *)p; p += buf->numbufs*sizeof(int); for ( i = 0; i < buf->numbufs; i++ ) buf->request[i] = MPI_REQUEST_NULL; buf->tag = (int *)p; p += buf->numbufs*sizeof(int); buf->from = (int *)p; p += buf->numbufs*sizeof(int); /* and finally the real bufferspace */ for ( i = free; i < buf->numbufs; i++ ) { buf->buff[i] = (WORD*)p; p += bsize; buf->stop[i] = (WORD*)p; buf->fill[i] = buf->full[i] = buf->buff[i]; } if ( p != stop ) { MesPrint("Error in PF_AllocBuf p = %x stop = %x\n",p,stop); return(NULL); } return(buf); } /* #] PF_AllocBuf : #[ PF_InitTree : */ /** * Initializes the sorting tree on the master. * It allocates bufferspace (if necessary) for * \li pointers to terms in the tree and their coefficients * \li the cyclic receive buffers for nonblocking receives (PF.rbufs) * \li the nodes of the actual tree * * and initializes these with (hopefully) correct values. * * @return the number of nodes in the merge tree if succeeded. -1 if failed. */ static int PF_InitTree(void) { GETIDENTITY PF_BUFFER **rbuf = PF.rbufs; UBYTE *p, *stop; int numrbufs,numtasks = PF.numtasks; int i, j, src, numnodes; int numslaves = numtasks - 1; LONG size; /* #[ the buffers : for the new coefficients and the terms we need one for each slave */ if ( PF_term == NULL ) { size = 2*numtasks*sizeof(WORD*) + sizeof(WORD)* ( numtasks*(1 + AM.MaxTal) + (AM.MaxTer/sizeof(WORD)+1) + 2*(AM.MaxTal+2)); PF_term = (WORD **)Malloc1(size,"PF_term"); stop = ((UBYTE*)PF_term) + size; p = ((UBYTE*)PF_term) + numtasks*sizeof(WORD*); PF_newcpos = (WORD **)p; p += sizeof(WORD*) * numtasks; PF_newclen = (WORD *)p; p += sizeof(WORD) * numtasks; for ( i = 0; i < numtasks; i++ ) { PF_newcpos[i] = (WORD *)p; p += sizeof(WORD)*AM.MaxTal; PF_newclen[i] = 0; } PF_WorkSpace = (WORD *)p; p += AM.MaxTer+sizeof(WORD); PF_ScratchSpace = (UWORD*)p; p += 2*(AM.MaxTal+2)*sizeof(UWORD); if ( p != stop ) { MesPrint("error in PF_InitTree"); return(-1); } } /* #] the buffers : #[ the receive buffers : */ numrbufs = PF.numrbufs; /* this is the size we have in the combined sortbufs for one slave */ size = (AT.SS->sTop2 - AT.SS->lBuffer - 1)/(PF.numtasks - 1); if ( rbuf == NULL ) { if ( ( rbuf = (PF_BUFFER**)Malloc1(numtasks*sizeof(PF_BUFFER*), "Master: rbufs") ) == NULL ) return(-1); if ( (rbuf[0] = PF_AllocBuf(1,0,1) ) == NULL ) return(-1); for ( i = 1; i < numtasks; i++ ) { if (!(rbuf[i] = PF_AllocBuf(numrbufs,sizeof(WORD)*size,1))) return(-1); } } rbuf[0]->buff[0] = AT.SS->lBuffer; rbuf[0]->full[0] = rbuf[0]->fill[0] = rbuf[0]->buff[0]; rbuf[0]->stop[0] = rbuf[1]->buff[0] = rbuf[0]->buff[0] + 1; rbuf[1]->full[0] = rbuf[1]->fill[0] = rbuf[1]->buff[0]; for ( i = 2; i < numtasks; i++ ) { rbuf[i-1]->stop[0] = rbuf[i]->buff[0] = rbuf[i-1]->buff[0] + size; rbuf[i]->full[0] = rbuf[i]->fill[0] = rbuf[i]->buff[0]; } rbuf[numtasks-1]->stop[0] = rbuf[numtasks-1]->buff[0] + size; for ( i = 1; i < numtasks; i++ ) { for ( j = 0; j < rbuf[i]->numbufs; j++ ) { rbuf[i]->full[j] = rbuf[i]->fill[j] = rbuf[i]->buff[j] + AM.MaxTer/sizeof(WORD) + 2; } PF_term[i] = rbuf[i]->fill[rbuf[i]->active]; *PF_term[i] = 0; PF_IRecvRbuf(rbuf[i],rbuf[i]->active,i); } rbuf[0]->active = 0; PF_term[0] = rbuf[0]->buff[0]; PF_term[0][0] = 0; /* PF_term[0] is used for a zero term. */ PF.rbufs = rbuf; /* #] the receive buffers : #[ the actual tree : calculate number of nodes in mergetree and allocate space for them */ if ( numslaves < 3 ) numnodes = 1; else { numnodes = 2; while ( numnodes < numslaves ) numnodes *= 2; numnodes -= 1; } if ( PF_root == NULL ) if ( ( PF_root = (NODE*)Malloc1(sizeof(NODE)*numnodes,"nodes in mergetree") ) == NULL ) return(-1); /* then initialize all the nodes */ src = 1; for ( i = 0; i < numnodes; i++ ) { if ( 2*(i+1) <= numnodes ) { PF_root[i].left = &(PF_root[2*(i+1)-1]); PF_root[i].lsrc = 0; } else { PF_root[i].left = 0; if ( src < numtasks ) PF_root[i].lsrc = src++; else PF_root[i].lsrc = 0; } PF_root[i].lloser = 0; } for ( i = 0; i < numnodes; i++ ) { if ( 2*(i+1)+1 <= numnodes ) { PF_root[i].rght = &(PF_root[2*(i+1)]); PF_root[i].rsrc = 0; } else { PF_root[i].rght = 0; if (src 1. * * @param src the source process. * @return the next term. * * @remark PF_term[0][0] == 0 (see InitTree()), so PF_term[0] can be used to be * the returnvalue for a zero term (== no more terms). */ static WORD *PF_PutIn(int src) { int tag; WORD im, r; WORD *m1, *m2; LONG size; PF_BUFFER *rbuf = PF.rbufs[src]; int a = rbuf->active; int next = a+1 >= rbuf->numbufs ? 0 : a+1 ; WORD *lastterm = PF_term[src]; WORD *term = rbuf->fill[a]; if ( src <= 0 ) return(PF_term[0]); if ( rbuf->full[a] == rbuf->buff[a] + AM.MaxTer/sizeof(WORD) + 2 ) { /* very first term from this src */ tag = PF_WaitRbuf(rbuf,a,&size); if ( tag == PF_RUNTIME_ERROR_MSGTAG ) { PF_ReceiveRuntimeError(); } rbuf->full[a] += size; if ( tag == PF_ENDBUFFER_MSGTAG ) *rbuf->full[a]++ = 0; else if ( rbuf->numbufs > 1 ) { /* post a nonblock. recv. for the next buffer */ rbuf->full[next] = rbuf->buff[next] + AM.MaxTer/sizeof(WORD) + 2; size = (LONG)(rbuf->stop[next] - rbuf->full[next]); PF_IRecvRbuf(rbuf,next,src); } } if ( *term == 0 && term != rbuf->full[a] ) return(PF_term[0]); /* exception is for rare cases when the terms fitted exactly into buffer */ if ( term + *term > rbuf->full[a] || term + 1 >= rbuf->full[a] ) { newterms: m1 = rbuf->buff[next] + AM.MaxTer/sizeof(WORD) + 1; if ( *term < 0 || term == rbuf->full[a] ) { /* copy term and lastterm to the new buffer, so that they end at m1 */ m2 = rbuf->full[a] - 1; while ( m2 >= term ) *m1-- = *m2--; rbuf->fill[next] = term = m1 + 1; m2 = lastterm + *lastterm - 1; while ( m2 >= lastterm ) *m1-- = *m2--; lastterm = m1 + 1; } else { /* copy beginning of term to the next buffer so that it ends at m1 */ m2 = rbuf->full[a] - 1; while ( m2 >= term ) *m1-- = *m2--; rbuf->fill[next] = term = m1 + 1; } if ( rbuf->numbufs == 1 ) { rbuf->full[a] = rbuf->buff[a] + AM.MaxTer/sizeof(WORD) + 2; size = (LONG)(rbuf->stop[a] - rbuf->full[a]); PF_IRecvRbuf(rbuf,a,src); } /* wait for new terms in the next buffer */ rbuf->full[next] = rbuf->buff[next] + AM.MaxTer/sizeof(WORD) + 2; tag = PF_WaitRbuf(rbuf,next,&size); rbuf->full[next] += size; if ( tag == PF_ENDBUFFER_MSGTAG ) { *rbuf->full[next]++ = 0; } else if ( rbuf->numbufs > 1 ) { /* post a nonblock. recv. for active buffer, it is not needed anymore */ rbuf->full[a] = rbuf->buff[a] + AM.MaxTer/sizeof(WORD) + 2; size = (LONG)(rbuf->stop[a] - rbuf->full[a]); PF_IRecvRbuf(rbuf,a,src); } /* now safely make next buffer active */ a = rbuf->active = next; } if ( *term < 0 ) { /* We need to decompress the term */ im = *term; r = term[1] - im + 1; m1 = term + 2; m2 = lastterm - im + 1; while ( ++im <= 0 ) *--m1 = *--m2; *--m1 = r; rbuf->fill[a] = term = m1; if ( term + *term > rbuf->full[a] ) goto newterms; } rbuf->fill[a] += *term; return(term); } /* #] PF_PutIn : #[ PF_GetLoser : */ /** * Finds the 'smallest' of all the PF_terms. Take also care of changing * coefficients and cancelling terms. When the coefficient changes, the new is * sitting in the array PF_newcpos, the length of the new coefficient in * PF_newclen. The original term will be untouched until it is copied to the * output buffer! * * Calling PF_GetLoser() with argument node will return the loser of the * subtree under node when the next term of the stream # PF_loser * (the last "loserstream") is filled into the tree. * PF_loser == 0 means we are just starting and should fill new terms into * all the leaves of the tree. * * @param n the node. * @return the loser of the subtree under the node n. * 0 indicates there are no more terms. * -1 indicates an error. */ static int PF_GetLoser(NODE *n) { GETIDENTITY WORD comp; if ( PF_loser == 0 ) { /* this is for the right initialization of the tree only */ if ( n->left ) n->lloser = PF_GetLoser(n->left); else { n->lloser = n->lsrc; if ( *(PF_term[n->lsrc] = PF_PutIn(n->lsrc)) == 0) n->lloser = 0; } PF_loser = 0; if ( n->rght ) n->rloser = PF_GetLoser(n->rght); else{ n->rloser = n->rsrc; if ( *(PF_term[n->rsrc] = PF_PutIn(n->rsrc)) == 0 ) n->rloser = 0; } PF_loser = 0; } else if ( PF_loser == n->lloser ) { if ( n->left ) n->lloser = PF_GetLoser(n->left); else { n->lloser = n->lsrc; if ( *(PF_term[n->lsrc] = PF_PutIn(n->lsrc)) == 0 ) n->lloser = 0; } } else if ( PF_loser == n->rloser ) { newright: if ( n->rght ) n->rloser = PF_GetLoser(n->rght); else { n->rloser = n->rsrc; if ( *(PF_term[n->rsrc] = PF_PutIn(n->rsrc)) == 0 ) n->rloser = 0; } } if ( n->lloser > 0 && n->rloser > 0 ) { comp = CompareTerms(BHEAD PF_term[n->lloser],PF_term[n->rloser],(WORD)0); if ( comp > 0 ) return(n->lloser); else if (comp < 0 ) return(n->rloser); else { /* #[ terms are equal : */ WORD *lcpos, *rcpos; UWORD *newcpos; WORD lclen, rclen, newclen, newnlen; SORTING *S = AT.SS; if ( S->PolyWise ) { /* #[ Here we work with PolyFun : */ WORD *tt1, *w; WORD r1,r2; WORD *ml = PF_term[n->lloser]; WORD *mr = PF_term[n->rloser]; if ( ( r1 = (int)*PF_term[n->lloser] ) <= 0 ) r1 = 20; if ( ( r2 = (int)*PF_term[n->rloser] ) <= 0 ) r2 = 20; tt1 = ml; ml += S->PolyWise; mr += S->PolyWise; if ( S->PolyFlag == 2 ) { w = poly_ratfun_add(BHEAD ml,mr); if ( *tt1 + w[1] - ml[1] > AM.MaxTer/((LONG)sizeof(WORD)) ) { MesPrint("Term too complex in PolyRatFun addition. MaxTermSize of %10l is too small",AM.MaxTer); Terminate(-1); } AT.WorkPointer = w; } else { w = AT.WorkPointer; if ( w + ml[1] + mr[1] > AT.WorkTop ) { MesPrint("A WorkSpace of %10l is too small",AM.WorkSize); Terminate(-1); } AddArgs(BHEAD ml,mr,w); } r1 = w[1]; if ( r1 <= FUNHEAD || ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 ) ) { goto cancelled; } if ( r1 == ml[1] ) { NCOPY(ml,w,r1); } else if ( r1 < ml[1] ) { r2 = ml[1] - r1; mr = w + r1; ml += ml[1]; while ( --r1 >= 0 ) *--ml = *--mr; mr = ml - r2; r1 = S->PolyWise; while ( --r1 >= 0 ) *--ml = *--mr; *ml -= r2; PF_term[n->lloser] = ml; } else { r2 = r1 - ml[1]; if ( r2 > 2*AM.MaxTal ) MesPrint("warning: new term in polyfun is large"); mr = tt1 - r2; r1 = S->PolyWise; ml = tt1; *ml += r2; PF_term[n->lloser] = mr; NCOPY(mr,ml,r1); r1 = w[1]; NCOPY(mr,w,r1); } PF_newclen[n->rloser] = 0; PF_loser = n->rloser; goto newright; /* #] Here we work with PolyFun : */ } if ( ( lclen = PF_newclen[n->lloser] ) != 0 ) lcpos = PF_newcpos[n->lloser]; else { lcpos = PF_term[n->lloser]; lclen = *(lcpos += *lcpos - 1); lcpos -= ABS(lclen) - 1; } if ( ( rclen = PF_newclen[n->rloser] ) != 0 ) rcpos = PF_newcpos[n->rloser]; else { rcpos = PF_term[n->rloser]; rclen = *(rcpos += *rcpos - 1); rcpos -= ABS(rclen) -1; } lclen = ( (lclen > 0) ? (lclen-1) : (lclen+1) ) >> 1; rclen = ( (rclen > 0) ? (rclen-1) : (rclen+1) ) >> 1; newcpos = PF_ScratchSpace; if ( AddRat(BHEAD (UWORD *)lcpos,lclen,(UWORD *)rcpos,rclen,newcpos,&newnlen) ) return(-1); if ( AN.ncmod != 0 ) { if ( ( AC.modmode & POSNEG ) != 0 ) { NormalModulus(newcpos,&newnlen); } if ( BigLong(newcpos,newnlen,(UWORD *)AC.cmod,ABS(AN.ncmod)) >=0 ) { WORD ii; SubPLon(newcpos,newnlen,(UWORD *)AC.cmod,ABS(AN.ncmod),newcpos,&newnlen); newcpos[newnlen] = 1; for ( ii = 1; ii < newnlen; ii++ ) newcpos[newnlen+ii] = 0; } } if ( newnlen == 0 ) { /* terms cancel, get loser of left subtree and then of right subtree */ cancelled: PF_loser = n->lloser; PF_newclen[n->lloser] = 0; if ( n->left ) n->lloser = PF_GetLoser(n->left); else { n->lloser = n->lsrc; if ( *(PF_term[n->lsrc] = PF_PutIn(n->lsrc)) == 0 ) n->lloser = 0; } PF_loser = n->rloser; PF_newclen[n->rloser] = 0; goto newright; } else { /* keep the left term and get the loser of right subtree */ newnlen *= 2; newclen = ( newnlen > 0 ) ? ( newnlen + 1 ) : ( newnlen - 1 ); if ( newnlen < 0 ) newnlen = -newnlen; PF_newclen[n->lloser] = newclen; lcpos = PF_newcpos[n->lloser]; if ( newclen < 0 ) newclen = -newclen; while ( newclen-- ) *lcpos++ = *newcpos++; PF_loser = n->rloser; PF_newclen[n->rloser] = 0; goto newright; } /* #] terms are equal : */ } } if (n->lloser > 0) return(n->lloser); if (n->rloser > 0) return(n->rloser); return(0); } /* #] PF_GetLoser : #[ PF_EndSort : */ /** * Finishes a master sorting with collecting terms from slaves. * Called by EndSort(). * * If this is not the masterprocess, just initialize the sendbuffers and * return 0, else PF_EndSort() sends the rest of the terms in the sendbuffer * to the next slave and a dummy message to all slaves with tag * PF_ENDSORT_MSGTAG. Then it receives the sorted terms, sorts them using a * recursive 'tree of losers' (PF_GetLoser()) and writes them to the * outputfile. * * @return 1 if the sorting on the master was done. * 0 if EndSort() still must perform a regular sorting because it is not * at the ground level or not on the master or in the sequential mode * or in the InParallel mode. * -1 if an error occurred. * * @remark The slaves will send the sorted terms back to the master in the regular * sorting (after the initialization of the send buffer in PF_EndSort()). * See PutOut() and FlushOut(). * * @remark This function has been changed such that when it returns 1, * AM.S0->TermsLeft is set correctly. But AM.S0->GenTerms is not set: * it will be set after collecting the statistics from the slaves * at the end of PF_Processor(). (TU 30 Jun 2011) */ int PF_EndSort(void) { GETIDENTITY FILEHANDLE *fout = AR.outfile; PF_BUFFER *sbuf=PF.sbuf; SORTING *S = AT.SS; WORD *outterm,*pp; LONG size, noutterms; POSITION position, oldposition; WORD i,cc; int oldgzipCompress; if ( AT.SS != AT.S0 || !PF.parallel ) return 0; if ( PF.me != MASTER ) { /* #[ the slaves have to initialize their sendbuffer : this is a slave and it's PObuffer should be the minimum of the sortiosize on the master and the POsize of our file. First save the original PObuffer and POstop of the outfile */ size = (S->sTop2 - S->lBuffer - 1)/(PF.numtasks - 1); size -= (AM.MaxTer/sizeof(WORD) + 2); if ( fout->POsize < (LONG)(size*sizeof(WORD)) ) size = fout->POsize/sizeof(WORD); if ( sbuf == NULL ) { if ( (sbuf = PF_AllocBuf(PF.numsbufs, size*sizeof(WORD), 1)) == NULL ) return -1; sbuf->active = 0; PF.sbuf = sbuf; } sbuf->buff[0] = fout->PObuffer; sbuf->stop[0] = fout->PObuffer+size; if ( sbuf->stop[0] > fout->POstop ) return -1; for ( i = 0; i < PF.numsbufs; i++ ) sbuf->fill[i] = sbuf->full[i] = sbuf->buff[i]; fout->PObuffer = sbuf->buff[sbuf->active]; fout->POstop = sbuf->stop[sbuf->active]; fout->POsize = size*sizeof(WORD); fout->POfill = fout->POfull = fout->PObuffer; /* #] the slaves have to initialize their sendbuffer : */ return(0); } /* this waits for all slaves to be ready to send terms back */ PF_WaitAllSlaves(); /* Note, the returned value should be 0 on success. */ /* Now collect the terms of all slaves and merge them. PF_GetLoser gives the position of the smallest term, which is the real work. The smallest term needs to be copied to the outbuf: use PutOut. */ PF_InitTree(); if ( AR.PolyFun == 0 ) { S->PolyFlag = 0; } else if ( AR.PolyFunType == 1 ) { S->PolyFlag = 1; } else if ( AR.PolyFunType == 2 ) { if ( AR.PolyFunExp == 2 || AR.PolyFunExp == 3 ) S->PolyFlag = 1; else S->PolyFlag = 2; } *AR.CompressPointer = 0; SeekScratch(fout, &position); oldposition = position; oldgzipCompress = AR.gzipCompress; AR.gzipCompress = 0; noutterms = 0; while ( PF_loser >= 0 ) { if ( (PF_loser = PF_GetLoser(PF_root)) == 0 ) break; outterm = PF_term[PF_loser]; noutterms++; if ( PF_newclen[PF_loser] != 0 ) { /* #[ this is only when new coeff was too long : */ outterm = PF_WorkSpace; pp = PF_term[PF_loser]; cc = *pp; while ( cc-- ) *outterm++ = *pp++; outterm = (outterm[-1] > 0) ? outterm-outterm[-1] : outterm+outterm[-1]; if ( PF_newclen[PF_loser] > 0 ) cc = (WORD)PF_newclen[PF_loser] - 1; else cc = -(WORD)PF_newclen[PF_loser] - 1; pp = PF_newcpos[PF_loser]; while ( cc-- ) *outterm++ = *pp++; *outterm++ = PF_newclen[PF_loser]; *PF_WorkSpace = outterm - PF_WorkSpace; outterm = PF_WorkSpace; *PF_newcpos[PF_loser] = 0; PF_newclen[PF_loser] = 0; /* #] this is only when new coeff was too long : */ } PRINTFBUF("PF_EndSort to PutOut: ",outterm,*outterm); PutOut(BHEAD outterm,&position,fout,1); } if ( FlushOut(&position,fout,0) ) { AR.gzipCompress = oldgzipCompress; return(-1); } S->TermsLeft = PF_goutterms = noutterms; DIFPOS(PF_exprsize, position, oldposition); AR.gzipCompress = oldgzipCompress; return(1); } /* #] PF_EndSort : #] sort.c : #[ proces.c : #[ variables : */ static WORD *PF_CurrentBracket; /* #] variables : #[ PF_GetTerm : */ /** * Replaces GetTerm() on the slaves, which get their terms from the master, * not the infile anymore, is nonblocking and buffered ... * use AR.infile->PObuffer as buffer. For the moment, don't care * about compression, since terms come uncompressed from master. * * To enable keep-brackets when AR.DeferFlag is set, we need to do some * preparation here: * \li copy the part outside brackets to current_bracket * \li skip term if part outside brackets is same as for last term * \li if POfill >= POfull receive new terms as usual * * Different from GetTerm() we use an extra buffer for the part outside brackets: * PF_CurrentBracket. * * @param[out] term the buffer to store the next term. * @return the length of the next term. */ static WORD PF_GetTerm(WORD *term) { assert(PF.me != MASTER); GETIDENTITY FILEHANDLE *fi = AC.RhsExprInModuleFlag && PF.rhsInParallel ? &PF.slavebuf : AR.infile; WORD i; WORD *next, *np, *last, *lp = 0, *nextstop, *tp=term; AN.deferskipped = 0; if ( fi->POfill >= fi->POfull || fi->POfull == fi->PObuffer ) { ReceiveNew: { /* #[ receive new terms from master : */ int src = MASTER, tag; int follow = 0; LONG size,cpu,space = 0; if ( PF.log ) { fprintf(stderr,"[%d] Starting to send to Master\n",PF.me); fflush(stderr); } cpu = TimeCPU(1); PF_PreparePack(); PF_Pack(&cpu ,1,PF_LONG); PF_Pack(&space ,1,PF_LONG); PF_Pack(&PF_linterms ,1,PF_LONG); PF_Pack(&(AM.S0->GenTerms) ,1,PF_LONG); PF_Pack(&(AM.S0->TermsLeft),1,PF_LONG); PF_Pack(&follow ,1,PF_INT ); if ( PF.log ) { fprintf(stderr,"[%d] Now sending with tag = %d\n",PF.me,PF_READY_MSGTAG); fflush(stderr); } PF_Send(MASTER, PF_READY_MSGTAG); if ( PF.log ) { fprintf(stderr,"[%d] returning from send\n",PF.me); fflush(stderr); } size = fi->POstop - fi->PObuffer - 1; tag=PF_RecvWbuf(fi->PObuffer,&size,&src); fi->POfill = fi->PObuffer; /* Get AN.ninterms which sits in the first 2 WORDs. */ { LONG ninterms; UNPACK_LONG(fi->POfill, ninterms); if ( fi->POfill < fi->POfull ) { DBGOUT_NINTERMS(2, ("PF.me=%d AN.ninterms=%d PF_linterms=%d ninterms=%d GET\n", (int)PF.me, (int)AN.ninterms, (int)PF_linterms, (int)ninterms)); AN.ninterms = ninterms - 1; } else { DBGOUT_NINTERMS(2, ("PF.me=%d AN.ninterms=%d PF_linterms=%d ninterms=%d GETEND\n", (int)PF.me, (int)AN.ninterms, (int)PF_linterms, (int)ninterms)); } } fi->POfull = fi->PObuffer + size; if ( tag == PF_ENDSORT_MSGTAG ) *fi->POfull++ = 0; /* #] receive new terms from master : */ } if ( PF_CurrentBracket ) *PF_CurrentBracket = 0; } if ( *fi->POfill == 0 ) { fi->POfill = fi->POfull = fi->PObuffer; *term = 0; goto RegRet; } if ( AR.DeferFlag ) { if ( !PF_CurrentBracket ) { /* #[ alloc space : */ PF_CurrentBracket = (WORD*)Malloc1(AM.MaxTer,"PF_CurrentBracket"); *PF_CurrentBracket = 0; /* #] alloc space : */ } while ( *PF_CurrentBracket ) { /* "for each term in the buffer" */ /* #[ test : bracket & skip if it's equal to the last in PF_CurrentBracket */ next = fi->POfill; nextstop = next + *next; nextstop -= ABS(nextstop[-1]); next++; last = PF_CurrentBracket+1; while ( next < nextstop ) { /* scan the next term and PF_CurrentBracket */ if ( *last == HAAKJE && *next == HAAKJE ) { /* the part outside brackets is equal => skip this term */ PRINTFBUF("PF_GetTerm skips",fi->POfill,*fi->POfill); break; } /* check if the current subterms are equal */ np = next; next += next[1]; lp = last; last += last[1]; while ( np < next ) if ( *lp++ != *np++ ) goto strip; } /* go on to next term */ fi->POfill += *fi->POfill; AN.deferskipped++; /* the usual checks */ if ( fi->POfill >= fi->POfull || fi->POfull == fi->PObuffer ) goto ReceiveNew; if ( *fi->POfill == 0 ) { fi->POfill = fi->POfull = fi->PObuffer; *term = 0; goto RegRet; } /* #] test : */ } /* #[ copy : this term to CurrentBracket and the part outside of bracket to WorkSpace at term */ strip: next = fi->POfill; nextstop = next + *next; nextstop -= ABS(nextstop[-1]); next++; tp++; lp = PF_CurrentBracket + 1; while ( next < nextstop ) { if ( *next == HAAKJE ) { fi->POfill += *fi->POfill; while ( next < fi->POfill ) *lp++ = *next++; *PF_CurrentBracket = lp - PF_CurrentBracket; *lp = 0; *tp++ = 1; *tp++ = 1; *tp++ = 3; *term = WORDDIF(tp,term); PRINTFBUF("PF_GetTerm new brack",PF_CurrentBracket,*PF_CurrentBracket); PRINTFBUF("PF_GetTerm POfill",fi->POfill,*fi->POfill); goto RegRet; } np = next; next += next[1]; while ( np < next ) *tp++ = *lp++ = *np++; } tp = term; /* #] copy : */ } i = *fi->POfill; while ( i-- ) *tp++ = *fi->POfill++; RegRet: PRINTFBUF("PF_GetTerm returns",term,*term); return(*term); } /* #] PF_GetTerm : #[ PF_Deferred : */ /** * Replaces Deferred() on the slaves. * * @param term the term that must be multiplied by the contents of * the current bracket. * @param level the compiler level. * @return 0 if OK, nonzero on error. */ WORD PF_Deferred(WORD *term, WORD level) { GETIDENTITY WORD *bra, *bstop; WORD *tstart; FILEHANDLE *fi = AC.RhsExprInModuleFlag && PF.rhsInParallel ? &PF.slavebuf : AR.infile; WORD *next = fi->POfill; WORD *termout = AT.WorkPointer; WORD *oldwork = AT.WorkPointer; AT.WorkPointer = (WORD *)((UBYTE *)(AT.WorkPointer) + AM.MaxTer); AR.DeferFlag = 0; PRINTFBUF("PF_Deferred (Term) ",term,*term); PRINTFBUF("PF_Deferred (Bracket)",PF_CurrentBracket,*PF_CurrentBracket); bra = bstop = PF_CurrentBracket; if ( *bstop > 0 ) { bstop += *bstop; bstop -= ABS(bstop[-1]); } bra++; while ( *bra != HAAKJE && bra < bstop ) bra += bra[1]; if ( bra >= bstop ) { /* No deferred action! */ AT.WorkPointer = term + *term; if ( Generator(BHEAD term,level) ) goto DefCall; AR.DeferFlag = 1; AT.WorkPointer = oldwork; return(0); } bstop = bra; tstart = bra + bra[1]; bra = PF_CurrentBracket; tstart--; *tstart = bra + *bra - tstart; bra++; /* Status of affairs: First bracket content starts at tstart. Next term starts at next. The outside of the bracket runs from bra = PF_CurrentBracket to bstop. */ for(;;) { if ( InsertTerm(BHEAD term,0,AM.rbufnum,tstart,termout,0) < 0 ) { goto DefCall; } /* call Generator with new composed term */ AT.WorkPointer = termout + *termout; if ( Generator(BHEAD termout,level) ) goto DefCall; AT.WorkPointer = termout; tstart = next + 1; if ( tstart >= fi->POfull ) goto ThatsIt; next += *next; /* compare with current bracket */ while ( bra <= bstop ) { if ( *bra != *tstart ) goto ThatsIt; bra++; tstart++; } /* now bra and tstart should both be a HAAKJE */ bra--; tstart--; if ( *bra != HAAKJE || *tstart != HAAKJE ) goto ThatsIt; tstart += tstart[1]; tstart--; *tstart = next - tstart; bra = PF_CurrentBracket + 1; } ThatsIt: /* AT.WorkPointer = oldwork; */ AR.DeferFlag = 1; return(0); DefCall: MesCall("PF_Deferred"); SETERROR(-1); } /* #] PF_Deferred : #[ PF_Wait4Slave : */ static LONG **PF_W4Sstats = 0; /** * Waits for the slave \a src to accept terms. * * @param src the slave for waiting (can be PF_ANY_SOURCE). * @return the idle slave. */ static int PF_Wait4Slave(int src) { int j, tag, next; tag = PF_ANY_MSGTAG; PF_CatchErrorMessages(&src, &tag); PF_Receive(src, tag, &next, &tag); if ( tag != PF_READY_MSGTAG ) { MesPrint("[%d] PF_Wait4Slave: received MSGTAG %d",(WORD)PF.me,(WORD)tag); return(-1); } if ( PF_W4Sstats == 0 ) { PF_W4Sstats = (LONG**)Malloc1(sizeof(LONG*),""); PF_W4Sstats[0] = (LONG*)Malloc1(PF_STATS_SIZE*sizeof(LONG),""); } PF_Unpack(PF_W4Sstats[0],PF_STATS_SIZE,PF_LONG); PF_Statistics(PF_W4Sstats,next); PF_Unpack(&j,1,PF_INT); if ( j ) { /* actions depending on rest of information in last message */ } return(next); } /* #] PF_Wait4Slave : #[ PF_Wait4SlaveIP : */ /* array of expression numbers for PF_InParallel processor. Each time the master sends expression "i" to the slave "next" it sets partodoexr[next]=i: */ static WORD *partodoexr=NULL; /** * InParallel version of PF_Wait4Slave(). Returns tag as src. * * @param[in,out] src the slave for waiting (can be PF_ANY_SOURCE). * As output, the tag value of the idle slave. * @return the idle slave. */ static int PF_Wait4SlaveIP(int *src) { int j,tag,next; tag = PF_ANY_MSGTAG; PF_CatchErrorMessages(src, &tag); PF_Receive(*src, tag, &next, &tag); *src=tag; if ( PF_W4Sstats == 0 ) { PF_W4Sstats = (LONG**)Malloc1(sizeof(LONG*),""); PF_W4Sstats[0] = (LONG*)Malloc1(PF_STATS_SIZE*sizeof(LONG),""); } PF_Unpack(PF_W4Sstats[0],PF_STATS_SIZE,PF_LONG); if ( tag == PF_DATA_MSGTAG ) AR.CurExpr = partodoexr[next]; PF_Statistics(PF_W4Sstats,next); PF_Unpack(&j,1,PF_INT); if ( j ) { /* actions depending on rest of information in last message */ } return(next); } /* #] PF_Wait4SlaveIP : #[ PF_WaitAllSlaves : */ /** * Waits until all slaves are ready to send terms back to the master. * If some slave is not working, it sends PF_ENDSORT_MSGTAG and waits for the answer. * Messages from slaves will be read only after all slaves are ready, * further in caller function. * * @return 0 if OK, nonzero on error. */ static int PF_WaitAllSlaves(void) { int i, readySlaves, tag, next = PF_ANY_SOURCE; UBYTE *has_sent = 0; has_sent = (UBYTE*)Malloc1(sizeof(UBYTE)*(PF.numtasks + 1),"PF_WaitAllSlaves"); for ( i = 0; i < PF.numtasks; i++ ) has_sent[i] = 0; for ( readySlaves = 1; readySlaves < PF.numtasks; ) { if ( next != PF_ANY_SOURCE) { /*Go to the next slave:*/ do{ /*Note, here readySlaves= PF.numtasks ) next = 1; } while ( has_sent[next] == 1 ); } /* Here PF_ProbeWithCatchingErrorMessages() is BLOCKING function if next = PF_ANY_SOURCE: */ tag = PF_ProbeWithCatchingErrorMessages(&next); /* Here next != PF_ANY_SOURCE */ switch ( tag ) { case PF_BUFFER_MSGTAG: case PF_ENDBUFFER_MSGTAG: /* Slaves are ready to send their results back */ if ( has_sent[next] == 0 ) { has_sent[next] = 1; readySlaves++; } else { /*error?*/ fprintf(stderr,"ERROR next=%d tag=%d\n",next,tag); } /* Note, we do NOT read results here! Messages from these slaves will be read only after all slaves are ready, further in caller function */ break; case 0: /* The slave is not ready. Just go to the next slave. It may appear that there are no more ready slaves, and the master will wait them in infinite loop. Stupid situation - the master can receive buffers from ready slaves! */ #ifdef PF_WITH_SCHED_YIELD /* Relinquish the processor: */ sched_yield(); #endif break; case PF_DATA_MSGTAG: tag=next; next=PF_Wait4SlaveIP(&tag); /* tag must be == PF_DATA_MSGTAG! */ PF_Statistics(PF_stats,0); PF_Slave2MasterIP(next); PF_Master2SlaveIP(next,NULL); if ( has_sent[next] == 0 ) { has_sent[next]=1; readySlaves++; }else{ /*error?*/ fprintf(stderr,"ERROR next=%d tag=%d\n",next,tag); }/*if ( has_sent[next] == 0 )*/ break; case PF_EMPTY_MSGTAG: tag=next; next=PF_Wait4SlaveIP(&tag); /* tag must be == PF_EMPTY_MSGTAG! */ PF_Master2SlaveIP(next,NULL); if ( has_sent[next] == 0 ) { has_sent[next]=1; readySlaves++; }else{ /*error?*/ fprintf(stderr,"ERROR next=%d tag=%d\n",next,tag); }/*if ( has_sent[next] == 0 )*/ break; case PF_READY_MSGTAG: /* idle slave May be only PF_READY_MSGTAG: */ next = PF_Wait4Slave(next); if ( next == -1 ) return(next); /*Cannot be!*/ if ( has_sent[0] == 0 ) { /*Send the last chunk to the slave*/ PF.sbuf->active = 0; has_sent[0] = 1; } else { /* Last chunk was sent, so just send to slave ENDSORT AN.ninterms must be sent because the slave expects it: */ PACK_LONG(PF.sbuf->fill[next], AN.ninterms); /* This will tell to the slave that there are no more terms: */ *(PF.sbuf->fill[next])++ = 0; PF.sbuf->active = next; } /* Send ENDSORT */ PF_ISendSbuf(next,PF_ENDSORT_MSGTAG); break; default: /* Error? Indicates the error. This will force exit from the main loop: */ MesPrint("!!!Unexpected MPI message src=%d tag=%d.", next, tag); readySlaves = PF.numtasks+1; break; } } if ( has_sent ) M_free(has_sent,"PF_WaitAllSlaves"); /* 0 on success (exit from the main loop by loop condition), or -1 if fails (exit from the main loop since readySlaves=PF.numtasks+1): */ return(PF.numtasks-readySlaves); } /* #] PF_WaitAllSlaves : #[ PF_Processor : */ /** * Replaces parts of Processor() on the masters and slaves. * On the master PF_Processor() is responsible for proper distribution of terms * from the input file to the slaves. * On the slaves it calls Generator() for all the terms that this process gets, * but PF_GetTerm() gets terms from the master (not directly from infile). * * @param e The pointer to the current expression. * @param i The index for the current expression. * @param LastExpression The flag indicating whether it is the last expression. * @return 0 if OK, nonzero on error. */ int PF_Processor(EXPRESSIONS e, WORD i, WORD LastExpression) { GETIDENTITY WORD *term = AT.WorkPointer; LONG dd = 0; PF_BUFFER *sb = PF.sbuf; WORD j, *s, next; LONG size, cpu; POSITION position; int k, src, tag; FILEHANDLE *oldoutfile = AR.outfile; if ( ( (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer ) ) > AT.WorkTop ) { MesWork(); } /* For redefine statements. */ if ( AC.numpfirstnum > 0 ) { for ( j = 0; j < AC.numpfirstnum; j++ ) { AC.inputnumbers[j] = -1; } } if ( AC.mparallelflag != PARALLELFLAG ) return(0); PF_processing = 1; if ( PF.me == MASTER ) { /* #[ Master: #[ write prototype to outfile: */ WORD oldBracketOn = AR.BracketOn; WORD *oldBrackBuf = AT.BrackBuf; WORD oldbracketindexflag = AT.bracketindexflag; LONG maxinterms; /* the maximum number of terms in the bucket */ int cmaxinterms; /* a variable controling the transition of maxinterms */ LONG termsinbucket; /* the number of filled terms in the bucket */ LONG ProcessBucketSize = AC.mProcessBucketSize; if ( PF.log && AC.CModule >= PF.log ) MesPrint("[%d] working on expression %s in module %l",PF.me,EXPRNAME(i),AC.CModule); if ( GetTerm(BHEAD term) <= 0 ) { MesPrint("[%d] Expression %d has problems in scratchfile",PF.me,i); return(-1); } term[3] = i; if ( AR.outtohide ) { SeekScratch(AR.hidefile,&position); e->onfile = position; if ( PutOut(BHEAD term,&position,AR.hidefile,0) < 0 ) return(-1); } else { SeekScratch(AR.outfile,&position); e->onfile = position; if ( PutOut(BHEAD term,&position,AR.outfile,0) < 0 ) return(-1); } AR.DeferFlag = 0; /* The master leave the brackets!!! */ AR.Eside = RHSIDE; if ( ( e->vflags & ISFACTORIZED ) != 0 ) { AR.BracketOn = 1; AT.BrackBuf = AM.BracketFactors; AT.bracketindexflag = 1; } if ( AT.bracketindexflag > 0 ) OpenBracketIndex(i); /* #] write prototype to outfile: #[ initialize sendbuffer if necessary: the size of the sendbufs is: MIN(1/PF.numtasks*(AT.SS->sBufsize+AT.SS->lBufsize),AR.infile->POsize) No allocation for extra buffers necessary, just make sb->buf... point to the right places in the sortbuffers. */ NewSort(BHEAD0); /* we need AT.SS to be set for this!!! */ if ( sb == 0 || sb->buff[0] != AT.SS->lBuffer ) { size = (LONG)((AT.SS->sTop2 - AT.SS->lBuffer)/(PF.numtasks)); if ( size > (LONG)(AR.infile->POsize/sizeof(WORD) - 1) ) size = AR.infile->POsize/sizeof(WORD) - 1; if ( sb == 0 ) { if ( ( sb = PF_AllocBuf(PF.numtasks,size*sizeof(WORD),PF.numtasks) ) == NULL ) return(-1); } sb->buff[0] = AT.SS->lBuffer; sb->full[0] = sb->fill[0] = sb->buff[0]; for ( j = 1; j < PF.numtasks; j++ ) { sb->stop[j-1] = sb->buff[j] = sb->buff[j-1] + size; } sb->stop[PF.numtasks-1] = sb->buff[PF.numtasks-1] + size; PF.sbuf = sb; } for ( j = 0; j < PF.numtasks; j++ ) { sb->full[j] = sb->fill[j] = sb->buff[j]; } /* #] initialize sendbuffer if necessary: #[ loop for all terms in infile: */ /* * The initial value of maxinterms is determined by the user given * ProcessBucketSize and the number of terms in the current expression. * We make the initial maxinterms smaller, so that we get the all * workers busy as soon as possible. */ maxinterms = ProcessBucketSize / 100; if ( maxinterms > e->counter / (PF.numtasks - 1) / 4 ) maxinterms = e->counter / (PF.numtasks - 1) / 4; if ( maxinterms < 1 ) maxinterms = 1; cmaxinterms = 0; /* * Copy them always to sb->buff[0]. When that is full, wait for * the next slave to accept terms, exchange sb->buff[0] and * sb->buff[next], send sb->buff[next] to next slave and go on * filling the now empty sb->buff[0]. */ AN.ninterms = 0; termsinbucket = 0; PACK_LONG(sb->fill[0], 1); while ( GetTerm(BHEAD term) ) { AN.ninterms++; dd = AN.deferskipped; if ( AC.CollectFun && *term <= (LONG)(AM.MaxTer/(2*sizeof(WORD))) ) { if ( GetMoreTerms(term) < 0 ) { LowerSortLevel(); return(-1); } } PRINTFBUF("PF_Processor gets",term,*term); if ( termsinbucket >= maxinterms || sb->fill[0] + *term >= sb->stop[0] ) { next = PF_Wait4Slave(PF_ANY_SOURCE); sb->fill[next] = sb->fill[0]; sb->full[next] = sb->full[0]; SWAP(sb->stop[next], sb->stop[0]); SWAP(sb->buff[next], sb->buff[0]); sb->fill[0] = sb->full[0] = sb->buff[0]; sb->active = next; PF_ISendSbuf(next,PF_TERM_MSGTAG); /* Initialize the next bucket. */ termsinbucket = 0; PACK_LONG(sb->fill[0], AN.ninterms); /* * For the "slow startup". We double maxinterms up to ProcessBucketSize * after (hopefully) the all workers got some terms. */ if ( cmaxinterms >= PF.numtasks - 2 ) { maxinterms *= 2; if ( maxinterms >= ProcessBucketSize ) { cmaxinterms = -1; maxinterms = ProcessBucketSize; } } else if ( cmaxinterms >= 0 ) { cmaxinterms++; } } j = *(s = term); NCOPY(sb->fill[0], s, j); termsinbucket++; } /* NOTE: The last chunk will be sent to a slave at EndSort() => PF_EndSort() * => PF_WaitAllSlaves(). */ AN.ninterms += dd; /* #] loop for all terms in infile: #[ Clean up & EndSort: */ if ( LastExpression ) { UpdateMaxSize(); if ( AR.infile->handle >= 0 ) { CloseFile(AR.infile->handle); AR.infile->handle = -1; remove(AR.infile->name); PUTZERO(AR.infile->POposition); } AR.infile->POfill = AR.infile->POfull = AR.infile->PObuffer; } if ( AR.outtohide ) AR.outfile = AR.hidefile; PF.parallel = 1; if ( EndSort(BHEAD AM.S0->sBuffer,0) < 0 ) return(-1); PF.parallel = 0; if ( AR.outtohide ) { AR.outfile = oldoutfile; AR.hidefile->POfull = AR.hidefile->POfill; } UpdateMaxSize(); AR.BracketOn = oldBracketOn; AT.BrackBuf = oldBrackBuf; if ( ( e->vflags & TOBEFACTORED ) != 0 ) poly_factorize_expression(e); else if ( ( ( e->vflags & TOBEUNFACTORED ) != 0 ) && ( ( e->vflags & ISFACTORIZED ) != 0 ) ) poly_unfactorize_expression(e); AT.bracketindexflag = oldbracketindexflag; AR.GetFile = 0; AR.outtohide = 0; /* * NOTE: e->numdummies, e->vflags and AR.exprflags will be updated * after gathering the information from all slaves. */ /* #] Clean up & EndSort: #[ Collect (stats,prepro,...): */ PF_PostEndSortBarrier(); DBGOUT_NINTERMS(1, ("PF.me=%d AN.ninterms=%d ENDSORT\n", (int)PF.me, (int)AN.ninterms)); PF_CatchErrorMessagesForAll(); e->numdummies = 0; for ( k = 1; k < PF.numtasks; k++ ) { PF_LongSingleReceive(PF_ANY_SOURCE, PF_ENDSORT_MSGTAG, &src, &tag); PF_LongSingleUnpack(PF_stats[src], PF_STATS_SIZE, PF_LONG); { WORD numdummies, expchanged; PF_LongSingleUnpack(&numdummies, 1, PF_WORD); PF_LongSingleUnpack(&expchanged, 1, PF_WORD); if ( e->numdummies < numdummies ) e->numdummies = numdummies; AR.expchanged |= expchanged; } /* Now handle redefined preprocessor variables. */ if ( AC.numpfirstnum > 0 ) PF_UnpackRedefinedPreVars(); } /* Broadcast redefined preprocessor variables. */ if ( AC.numpfirstnum > 0 ) { int RetCode = PF_BroadcastRedefinedPreVars(); if ( RetCode ) return RetCode; } if ( ! AC.OldParallelStats ) { /* Now we can calculate AT.SS->GenTerms from the statistics of the slaves. */ LONG genterms = 0; for ( k = 1; k < PF.numtasks; k++ ) { genterms += PF_stats[k][3]; } AT.SS->GenTerms = genterms; WriteStats(&PF_exprsize, STATSPOSTSORT, NOCHECKLOGTYPE); Expressions[AR.CurExpr].size = PF_exprsize; } PF_Statistics(PF_stats,0); /* #] Collect (stats,prepro,...): #[ Update flags : */ if ( AM.S0->TermsLeft ) e->vflags &= ~ISZERO; else e->vflags |= ISZERO; if ( AR.expchanged == 0 ) e->vflags |= ISUNMODIFIED; if ( AM.S0->TermsLeft ) AR.expflags |= ISZERO; if ( AR.expchanged ) AR.expflags |= ISUNMODIFIED; /* #] Update flags : #] Master: */ } else { /* #[ Slave : */ /* #[ Generator Loop & EndSort : loop for all terms to get from master, call Generator for each of them then call EndSort and do cleanup (to be implemented) */ WORD oldBracketOn = AR.BracketOn; WORD *oldBrackBuf = AT.BrackBuf; WORD oldbracketindexflag = AT.bracketindexflag; /* For redefine statements. */ if ( AC.numpfirstnum > 0 ) { for ( j = 0; j < AC.numpfirstnum; j++ ) { AC.inputnumbers[j] = -1; } } SeekScratch(AR.outfile,&position); e->onfile = position; AR.DeferFlag = AC.ComDefer; AR.Eside = RHSIDE; if ( ( e->vflags & ISFACTORIZED ) != 0 ) { AR.BracketOn = 1; AT.BrackBuf = AM.BracketFactors; AT.bracketindexflag = 1; } NewSort(BHEAD0); AR.MaxDum = AM.IndDum; AN.ninterms = 0; PF_linterms = 0; PF.parallel = 1; { FILEHANDLE *fi = AC.RhsExprInModuleFlag && PF.rhsInParallel ? &PF.slavebuf : AR.infile; fi->POfull = fi->POfill = fi->PObuffer; } /* FIXME: AN.ninterms is still broken when AN.deferskipped is non-zero. * It still needs some work, also in PF_GetTerm(). (TU 30 Aug 2011) */ while ( PF_GetTerm(term) ) { PF_linterms++; AN.ninterms++; dd = AN.deferskipped; AT.WorkPointer = term + *term; AN.RepPoint = AT.RepCount + 1; if ( ( e->vflags & ISFACTORIZED ) != 0 && term[1] == HAAKJE ) { StoreTerm(BHEAD term); continue; } if ( AR.DeferFlag ) { AR.CurDum = AN.IndDum = Expressions[AR.CurExpr].numdummies + AM.IndDum; } else { AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); } if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( ( AR.PolyFunType == 2 ) && ( AC.PolyRatFunChanged == 0 ) && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION ) ) { PolyFunClean(BHEAD term); } if ( Generator(BHEAD term,0) ) { LowerSortLevel(); Terminate(-1); } PF_linterms += dd; AN.ninterms += dd; } PF_linterms += dd; AN.ninterms += dd; { /* * EndSort() overrides AR.outfile->PObuffer etc. (See also PF_EndSort()), * but it causes a problem because * (1) PF_EndSort() sets AR.outfile->PObuffer to a send-buffer. * (2) RevertScratch() clears AR.infile, but then swaps buffers of AR.infile * and AR.outfile. * (3) RHS expressions are stored to AR.infile->PObuffer. * (4) Again, PF_EndSort() sets AR.outfile->PObuffer, but now AR.outfile->PObuffer * == AR.infile->PObuffer because of (1) and (2). * (5) The result goes to AR.outfile. This breaks the RHS expressions, * which may be needed for the next expression. * Solution: backup & restore AR.outfile->PObuffer etc. (TU 14 Sep 2011) */ FILEHANDLE *fout = AR.outfile; WORD *oldbuff = fout->PObuffer; WORD *oldstop = fout->POstop; LONG oldsize = fout->POsize; if ( EndSort(BHEAD AM.S0->sBuffer, 0) < 0 ) return -1; fout->PObuffer = oldbuff; fout->POstop = oldstop; fout->POsize = oldsize; fout->POfill = fout->POfull = fout->PObuffer; } AR.BracketOn = oldBracketOn; AT.BrackBuf = oldBrackBuf; AT.bracketindexflag = oldbracketindexflag; /* #] Generator Loop & EndSort : #[ Collect (stats,prepro...) : */ PF_PostEndSortBarrier(); DBGOUT_NINTERMS(1, ("PF.me=%d AN.ninterms=%d PF_linterms=%d ENDSORT\n", (int)PF.me, (int)AN.ninterms, (int)PF_linterms)); PF_PrepareLongSinglePack(); cpu = TimeCPU(1); size = 0; PF_LongSinglePack(&cpu, 1, PF_LONG); PF_LongSinglePack(&size, 1, PF_LONG); PF_LongSinglePack(&PF_linterms, 1, PF_LONG); PF_LongSinglePack(&AM.S0->GenTerms, 1, PF_LONG); PF_LongSinglePack(&AM.S0->TermsLeft, 1, PF_LONG); { WORD numdummies = AR.MaxDum - AM.IndDum; PF_LongSinglePack(&numdummies, 1, PF_WORD); PF_LongSinglePack(&AR.expchanged, 1, PF_WORD); } /* Now handle redefined preprocessor variables. */ if ( AC.numpfirstnum > 0 ) PF_PackRedefinedPreVars(); PF_LongSingleSend(MASTER, PF_ENDSORT_MSGTAG); /* Broadcast redefined preprocessor variables. */ if ( AC.numpfirstnum > 0 ) { int RetCode = PF_BroadcastRedefinedPreVars(); if ( RetCode ) return RetCode; } /* #] Collect (stats,prepro...) : This operation is moved to the beginning of each block, see PreProcessor in pre.c. #] Slave : */ if ( PF.log ) { UBYTE lbuf[24]; NumToStr(lbuf,AC.CModule); fprintf(stderr,"[%d|%s] Endsort,Collect,Broadcast done\n",PF.me,lbuf); fflush(stderr); } } return(0); } /* #] PF_Processor : #] proces.c : #[ startup :, prepro & compile #[ PF_Init : */ /** * All the library independent stuff. * PF_LibInit() should do all library dependent initializations. * * @param argc pointer to the number of arguments. * @param argv pointer to the arguments. * @return 0 if OK, nonzero on error. */ int PF_Init(int *argc, char ***argv) { /* this should definitely be somewhere else ... */ PF_CurrentBracket = 0; PF.numtasks = 0; /* number of tasks, is determined in PF_LibInit ! */ PF.numsbufs = 2; /* might be changed by the environment variable on the master ! */ PF.numrbufs = 2; /* might be changed by the environment variable on the master ! */ int ret = PF_LibInit(argc,argv); if (ret) { return ret; } PF_RealTime(PF_RESET); PF.log = 0; PF.parallel = 0; PF_statsinterval = 10; PF.rhsInParallel=1; PF.exprbufsize=4096;/*in WORDs*/ #ifdef PF_WITHGETENV if ( PF.me == MASTER ) { char *c; /* get these from the environment at the moment should be in setfile/tail */ if ( ( c = getenv("PF_LOG") ) != 0 ) { if ( *c ) PF.log = (int)atoi(c); else PF.log = 1; fprintf(stderr,"[%d] changing PF.log to %d\n",PF.me,PF.log); fflush(stderr); } if ( ( c = (char*)getenv("PF_RBUFS") ) != 0 ) { PF.numrbufs = (int)atoi(c); fprintf(stderr,"[%d] changing numrbufs to: %d\n",PF.me,PF.numrbufs); fflush(stderr); } if ( ( c = (char*)getenv("PF_SBUFS") ) != 0 ) { PF.numsbufs = (int)atoi(c); fprintf(stderr,"[%d] changing numsbufs to: %d\n",PF.me,PF.numsbufs); fflush(stderr); } if ( PF.numsbufs > 10 ) PF.numsbufs = 10; if ( PF.numsbufs < 1 ) PF.numsbufs = 1; if ( PF.numrbufs > 2 ) PF.numrbufs = 2; if ( PF.numrbufs < 1 ) PF.numrbufs = 1; if ( ( c = getenv("PF_STATS") ) ) { UBYTE lbuf[24]; PF_statsinterval = (int)atoi(c); NumToStr(lbuf,PF_statsinterval); fprintf(stderr,"[%d] changing PF_statsinterval to %s\n",PF.me,lbuf); fflush(stderr); if ( PF_statsinterval < 1 ) PF_statsinterval = 10; } } #endif /* #[ Broadcast settings from getenv: could also be done in PF_DoSetup */ if ( PF.me == MASTER ) { PF_PreparePack(); PF_Pack(&PF.log,1,PF_INT); PF_Pack(&PF.numrbufs,1,PF_WORD); PF_Pack(&PF.numsbufs,1,PF_WORD); } PF_Broadcast(); if ( PF.me != MASTER ) { PF_Unpack(&PF.log,1,PF_INT); PF_Unpack(&PF.numrbufs,1,PF_WORD); PF_Unpack(&PF.numsbufs,1,PF_WORD); if ( PF.log ) { fprintf(stderr, "[%d] log=%d rbufs=%d sbufs=%d\n", PF.me, PF.log, PF.numrbufs, PF.numsbufs); fflush(stderr); } } /* #] Broadcast settings from getenv: */ return(0); } /* #] PF_Init : #[ PF_PreTerminate : */ /** * Prepares for termination. * Called by Terminate(). * * @param errorcode an error code. */ void PF_PreTerminate(int errorcode) { if ( errorcode != 0 && PF_processing ) { PF_processing = 0; PF_RaiseRuntimeError(); } } /* #] PF_PreTerminate : #[ PF_Terminate : */ /** * Performs the finalization of ParFORM. * To be called by Terminate(). * * @param errorcode an error code. * @return 0 if OK, nonzero on error. */ int PF_Terminate(int errorcode) { return PF_LibTerminate(errorcode); } /* #] PF_Terminate : #[ PF_GetSlaveTimes : */ /** * Returns the total CPU time of all slaves together. * This function must be called on the master and all slaves. * * @return on the master, the sum of CPU times on all slaves. */ LONG PF_GetSlaveTimes(void) { LONG slavetimes = 0; LONG t = PF.me == MASTER ? 0 : AM.SumTime + TimeCPU(1); int ret = PF_Reduce(&t, &slavetimes, 1, PF_LONG, MPI_SUM, MASTER); CHECK(ret == 0); return slavetimes; } /* #] PF_GetSlaveTimes : #] startup : #[ PF_BroadcastNumber : */ /** * Broadcasts a LONG value from the master to the all slaves. * * @param x the number to be broadcast (set on the master). * @return the synchronised result. */ LONG PF_BroadcastNumber(LONG x) { #ifdef PF_DEBUG_BCAST_LONG if ( PF.me == MASTER ) { MesPrint(">> Broadcast LONG: %l", x); } #endif PF_Bcast(&x, sizeof(LONG)); return x; } /* #] PF_BroadcastNumber : #[ PF_BroadcastBuffer : */ /** * Broadcasts a buffer from the master to all the slaves. * * @param[in,out] buffer on the master, the buffer to be broadcast. On the * slaves, the buffer will be allocated if the length is greater than 0. The * caller must free it. * * @param[in,out] length on the master, the length of the buffer to be * broadcast. On the slaves, it receives the length of transferred buffer. * The actual transfer occurs only if the length is greater than 0. */ void PF_BroadcastBuffer(WORD **buffer, LONG *length) { WORD *p; LONG rest; #ifdef PF_DEBUG_BCAST_BUF if ( PF.me == MASTER ) { MesPrint(">> Broadcast Buffer: length=%l", *length); } #endif /* Initialize the buffer on the slaves. */ if ( PF.me != MASTER ) { *buffer = NULL; } /* Broadcast the length of the buffer. */ *length = PF_BroadcastNumber(*length); if ( *length <= 0 ) return; /* Allocate the buffer on the slaves. */ if ( PF.me != MASTER ) { *buffer = (WORD *)Malloc1(*length * sizeof(WORD), "PF_BroadcastBuffer"); } /* Broadcast the data in the buffer. */ p = *buffer; rest = *length; while ( rest > 0 ) { int l = rest < (LONG)PF.exprbufsize ? (int)rest : PF.exprbufsize; PF_Bcast(p, l * sizeof(WORD)); p += l; rest -= l; } } /* #] PF_BroadcastBuffer : #[ PF_BroadcastString : */ /** * Broadcasts a string from the master to all slaves. * * @param[in,out] str The pointer to a null-terminated string. * @return 0 if OK, nonzero on error. */ int PF_BroadcastString(UBYTE *str) { int clength = 0; /* If string does not fit to the PF_buffer, it will be split into chunks. Next chunk is started at str+clength */ UBYTE *cstr=str; /* Note, compilation is performed INDEPENDENTLY on AC.mparallelflag! No if ( AC.mparallelflag == PARALLELFLAG ) !! */ do { cstr += clength; /*at each step for all slaves and master */ if ( MASTER == PF.me ) { /*Pack str*/ /* initialize buffers */ if ( PF_PreparePack() != 0 ) Terminate(-1); if ( ( clength = PF_PackString(cstr) ) <0 ) Terminate(-1); } PF_Broadcast(); if ( MASTER != PF.me ) { /* Slave - unpack received string For slaves buffers are initialised automatically. */ if ( ( clength = PF_UnpackString(cstr) ) < 0 ) Terminate(-1); } } while ( cstr[clength-1] != '\0' ); return (0); } /* #] PF_BroadcastString : #[ PF_BroadcastPreDollar : */ /** * Broadcasts dollar variables set as a preprocessor variables. * Only the master is able to make an assignment like #$a=g; where g * is an expression: only the master has an access to the expression. * So, the master broadcasts the result to slaves. * * The result is in *dbuffer of the size is *newsize (in number of WORDs), * +1 for trailing zero. For slave newsize and numterms are output * parameters. * * @param[in,out] dbuffer the buffer for a dollar variable. * @param[in,out] newsize the size of the dollar variable in WORDs. * @param[in,out] numterms the number of terms in the dollar variable. * @return 0 if OK, nonzero on error. */ int PF_BroadcastPreDollar(WORD **dbuffer, LONG *newsize, int *numterms) { int err = 0; LONG i; /* Note, compilation is performed INDEPENDENTLY on AC.mparallelflag! No if(AC.mparallelflag==PARALLELFLAG) !! */ if ( MASTER == PF.me ) { /* The problem is that sometimes dollar variables are longer than PF_packbuf! So we split long expression into chunks. There are n filled chunks and one partially filled chunk: */ LONG n = ((*newsize)+1)/PF_maxDollarChunkSize; /* ...and one more chunk for the rest; if the expression fits to the buffer without splitting, the latter will be the only one. PF_maxDollarChunkSize is the maximal number of items fitted to the buffer. It is calculated in PF_LibInit() in mpi.c. PF_maxDollarChunkSize is calculated for the first step, when two fields (numterms and newsize, see below) are already packed. For simplicity, this value is used also for all steps, in despite of it is a bit less than maximally available space. */ WORD *thechunk = *dbuffer; err = PF_PreparePack(); /* initialize buffers */ err |= PF_Pack(numterms,1,PF_INT); err |= PF_Pack(newsize,1,PF_LONG); /* pack the size */ /* Pack and broadcast completely filled chunks. It may happen, this loop is not entered at all: */ for ( i = 0; i < n; i++ ) { err |= PF_Pack(thechunk,PF_maxDollarChunkSize,PF_WORD); err |= PF_Broadcast(); thechunk +=PF_maxDollarChunkSize; PF_PreparePack(); } /* Pack and broadcast the rest: */ if ( ( n = ( (*newsize)+1)%PF_maxDollarChunkSize ) != 0 ) { err |= PF_Pack(thechunk,n,PF_WORD); err |= PF_Broadcast(); } #ifdef PF_DEBUG_BCAST_PREDOLLAR MesPrint(">> Broadcast PreDollar: newsize=%d numterms=%d", (int)*newsize, *numterms); #endif } if ( MASTER != PF.me ) { /* Slave - unpack received buffer */ WORD *thechunk; LONG n, therest, thesize; err |= PF_Broadcast(); err |=PF_Unpack(numterms,1,PF_INT); err |=PF_Unpack(newsize,1,PF_LONG); /* Now we know the buffer size. */ thesize = (*newsize)+1; /* Evaluate the number of completely filled chunks. The last step must be treated separately, so -1: */ n = (thesize/PF_maxDollarChunkSize) - 1; /* Note, here n can be <0, this is ok. */ therest = thesize % PF_maxDollarChunkSize; thechunk = *dbuffer = (WORD*)Malloc1( thesize * sizeof(WORD),"$-buffer slave"); if ( thechunk == NULL ) return(err|4); /* Unpack completely filled chunks and receive the next portion. It may happen, this loop is not entered at all: */ for ( i = 0; i < n; i++ ) { err |= PF_Unpack(thechunk,PF_maxDollarChunkSize,PF_WORD); thechunk += PF_maxDollarChunkSize; err |= PF_Broadcast(); } /* Now the last completely filled chunk: */ if ( n >= 0 ) { err |= PF_Unpack(thechunk,PF_maxDollarChunkSize,PF_WORD); thechunk += PF_maxDollarChunkSize; if ( therest != 0 ) err |= PF_Broadcast(); } /* Unpack the rest (it is already received!): */ if ( therest != 0 ) err |= PF_Unpack(thechunk,therest,PF_WORD); } return (err); } /* #] PF_BroadcastPreDollar : #[ Synchronization of modified dollar variables : #[ Helper functions : #[ dollarlen : */ /** * Returns the size of \a terms in WORDs, not including the null terminator. */ static inline LONG dollarlen(const WORD *terms) { const WORD *p = terms; while ( *p ) p += *p; return p - terms; /* Not including the null terminator. */ } /* #] dollarlen : #[ dollar_mod_type : */ /** * Returns the module option type of a dollar variable specified by \a index. * If no module option is given for the variable, this function returns -1. */ static inline WORD dollar_mod_type(WORD index) { int i; for ( i = 0; i < NumModOptdollars; i++ ) if ( ModOptdollars[i].number == index ) break; if ( i >= NumModOptdollars ) return -1; return ModOptdollars[i].type; } /* #] dollar_mod_type : #] Helper functions : #[ PF_CollectModifiedDollars : */ /* #[ dollar_to_be_collected : */ /** * Returns true if the dollar variable specified by \a index has to be collected * from each slave to the master, i.e., declared as MODSUM, MODMAX or MODMIN. */ static inline int dollar_to_be_collected(WORD index) { switch ( dollar_mod_type(index) ) { case MODSUM: case MODMAX: case MODMIN: return 1; default: return 0; } } /* #] dollar_to_be_collected : #[ copy_dollar : */ /** * Copy the data given by \a type, \a where and \a size to a dollar variable * specified by \a index. */ static inline void copy_dollar(WORD index, WORD type, const WORD *where, LONG size) { DOLLARS d = Dollars + index; CleanDollarFactors(d); if ( type != DOLZERO && where != NULL && where != &AM.dollarzero && where[0] != 0 && size > 0 ) { if ( size > d->size || size < d->size / 4 ) { /* Reallocate if not enough or too much. */ if ( d->where && d->where != &AM.dollarzero ) M_free(d->where, "old content of dollar"); d->where = Malloc1(sizeof(WORD) * size, "copy buffer to dollar"); d->size = size; } d->type = type; WCOPY(d->where, where, size); } else { if ( d->where && d->where != &AM.dollarzero ) M_free(d->where, "old content of dollar"); d->type = DOLZERO; d->where = &AM.dollarzero; d->size = 0; } } /* #] copy_dollar : #[ compare_two_expressions : */ /** * Compares two expressions \a e1 and \a e2 and returns a positive value if * \a e1 > \a e2, a negative value if \a e1 < \a e2, or zero if \a e1 == \a e2. */ static inline int compare_two_expressions(const WORD *e1, const WORD *e2) { GETIDENTITY /* * We consider the cases that * (1) the expression has no term, * (2) the expression has only one term and it is a number, * (3) otherwise. * Assume that the expressions are sorted and all terms are normalized. * The numerators of the coefficients must never be zero. * * Note that TwoExprCompare() is not adequate for our purpose * (as of 6 Aug. 2013), e.g., TwoExprCompare({0}, {4, 1, 1, -1}, LESS) * returns TRUE. */ if ( e1[0] == 0 ) { if ( e2[0] == 0 ) { return(0); } else if ( e2[e2[0]] == 0 && e2[0] == ABS(e2[e2[0] - 1]) + 1 ) { if ( e2[e2[0] - 1] > 0 ) return(-1); else return(+1); } } else if ( e1[e1[0]] == 0 && e1[0] == ABS(e1[e1[0] - 1]) + 1 ) { if ( e2[0] == 0 ) { if ( e1[e1[0] - 1] > 0 ) return(+1); else return(-1); } else if ( e2[e2[0]] == 0 && e2[0] == ABS(e2[e2[0] - 1]) + 1 ) { return(CompCoef((WORD *)e1, (WORD *)e2)); } } /* The expressions are not so simple. Define the order by each term. */ while ( e1[0] && e2[0] ) { int c = CompareTerms(BHEAD (WORD *)e1, (WORD *)e2, 1); if ( c < 0 ) return(-1); else if ( c > 0 ) return(+1); e1 += e1[0]; e2 += e2[0]; } if ( e1[0] ) return(+1); if ( e2[0] ) return(-1); return(0); } /* #] compare_two_expressions : #[ Variables : */ typedef struct { VectorStruct(WORD) buf; LONG size; WORD type; } dollar_buf; /* Buffers used to store data for each variable from each slave. */ static Vector(dollar_buf, dollar_slave_bufs); /* #] Variables : */ /** * Combines modified dollar variables on the all slaves, and store them into * those on the master. * * The potentially modified dollar variables are given in PotModdollars, * and the number of them is given by NumPotModdollars. * * The current module could be executed in parallel only if all potentially * modified variables are listed in ModOptdollars, otherwise the module was * switched to the sequential mode. * * @return 0 if OK, nonzero on error. */ int PF_CollectModifiedDollars(void) { int i, j, ndollars; /* * If the current module was executed in the sequential mode, * there are no modified module on the slaves. */ if ( AC.mparallelflag != PARALLELFLAG && !AC.partodoflag ) return 0; /* * Count the number of (potentially) modified dollar variables, which we need to collect. * Here we need to collect all max/min/sum variables. */ ndollars = 0; for ( i = 0; i < NumPotModdollars; i++ ) { WORD index = PotModdollars[i]; if ( dollar_to_be_collected(index) ) ndollars++; } if ( ndollars == 0 ) return 0; /* No dollars to be collected. */ if ( PF.me == MASTER ) { /* #[ Master : */ int nslaves, nvars; /* Prepare receive buffers. We need ndollars*(PF.numtasks-1) buffers. */ int nbufs = ndollars * (PF.numtasks - 1); VectorReserve(dollar_slave_bufs, nbufs); for ( i = VectorSize(dollar_slave_bufs); i < nbufs; i++ ) { VectorInit(VectorPtr(dollar_slave_bufs)[i].buf); } VectorSize(dollar_slave_bufs) = nbufs; /* Receive data from each slave. */ for ( nslaves = 1; nslaves < PF.numtasks; nslaves++ ) { int src; PF_LongSingleReceive(PF_ANY_SOURCE, PF_DOLLAR_MSGTAG, &src, NULL); nvars = 0; for ( i = 0; i < NumPotModdollars; i++ ) { WORD index = PotModdollars[i]; dollar_buf *b; if ( !dollar_to_be_collected(index) ) continue; b = &VectorPtr(dollar_slave_bufs)[(PF.numtasks - 1) * nvars + (src - 1)]; PF_LongSingleUnpack(&b->type, 1, PF_WORD); if ( b->type != DOLZERO ) { LONG size; WORD *where; PF_LongSingleUnpack(&size, 1, PF_LONG); VectorReserve(b->buf, size + 1); where = VectorPtr(b->buf); PF_LongSingleUnpack(where, size, PF_WORD); where[size] = 0; /* The null terminator is needed. */ b->size = size + 1; /* Including the null terminator. */ /* Note that we don't collect factored stuff for max/min/sum variables. */ } else { VectorReserve(b->buf, 1); VectorPtr(b->buf)[0] = 0; b->size = 0; } nvars++; } } /* * Combine received dollars. The FORM reference manual says maximum/minimum/sum * $-variables must have a numerical value, however, this routine should work also * for non-numerical cases, although the maximum/minimum value for non-numerical * terms has ambiguity. */ nvars = 0; for ( i = 0; i < NumPotModdollars; i++ ) { WORD index = PotModdollars[i]; WORD dtype; DOLLARS d; dollar_buf *b; if ( !dollar_to_be_collected(index) ) continue; d = Dollars + index; b = &VectorPtr(dollar_slave_bufs)[(PF.numtasks - 1) * nvars]; dtype = dollar_mod_type(index); switch ( dtype ) { case MODMAX: case MODMIN: { /* #[ MODMAX & MODMIN : */ int selected = 0; for ( j = 1; j < PF.numtasks - 1; j++ ) { int c = compare_two_expressions(VectorPtr(b[j].buf), VectorPtr(b[selected].buf)); if ( (dtype == MODMAX && c > 0) || (dtype == MODMIN && c < 0) ) selected = j; } b = b + selected; copy_dollar(index, b->type, VectorPtr(b->buf), b->size); /* #] MODMAX & MODMIN : */ break; } case MODSUM: { /* #[ MODSUM : */ GETIDENTITY int err = 0; CBUF *C = cbuf + AM.rbufnum; WORD *oldwork = AT.WorkPointer, *oldcterm = AN.cTerm; WORD olddefer = AR.DeferFlag, oldnumlhs = AR.Cnumlhs, oldnumrhs = C->numrhs; LONG size; WORD type, *dbuf; AN.cTerm = 0; AR.DeferFlag = 0; if ( ((WORD *)((UBYTE *)AT.WorkPointer + AM.MaxTer)) > AT.WorkTop ) { err = -1; goto cleanup; MesWork(); } if ( NewSort(BHEAD0) ) { err = -1; goto cleanup; } if ( NewSort(BHEAD0) ) { LowerSortLevel(); err = -1; goto cleanup; } /* * Sum up the original $-variable in the master and $-variables on all slaves. * Note that $-variables on the slaves are set to zero at the beginning of * the module (See also DoExecute()). */ for ( j = 0; j < PF.numtasks; j++ ) { const WORD *r; for ( r = j == 0 ? Dollars[index].where : VectorPtr(b[j - 1].buf); *r; r += *r ) { WCOPY(AT.WorkPointer, r, *r); AT.WorkPointer += *r; AR.Cnumlhs = 0; if ( Generator(BHEAD oldwork, 0) ) { LowerSortLevel(); LowerSortLevel(); err = -1; goto cleanup; } AT.WorkPointer = oldwork; } } size = EndSort(BHEAD (WORD *)&dbuf, 2); if ( size < 0 ) { LowerSortLevel(); err = -1; goto cleanup; } LowerSortLevel(); /* Find special cases. */ type = DOLTERMS; if ( dbuf[0] == 0 ) { type = DOLZERO; } else if ( dbuf[dbuf[0]] == 0 ) { const WORD *t = dbuf, *w; WORD n, nsize; n = *t; nsize = t[n - 1]; if ( nsize < 0 ) nsize = -nsize; if ( nsize == n - 1 ) { nsize = (nsize - 1) / 2; w = t + 1 + nsize; if ( *w == 1 ) { w++; while ( w < t + n - 1 ) { if ( *w ) break; w++; } if ( w >= t + n - 1 ) type = DOLNUMBER; } else if ( n == 7 && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[1] == INDEX && t[2] == 3 ) { type = DOLINDEX; d->index = t[3]; } } } copy_dollar(index, type, dbuf, dollarlen(dbuf) + 1); M_free(dbuf, "temporary dollar buffer"); cleanup: AR.Cnumlhs = oldnumlhs; C->numrhs = oldnumrhs; AR.DeferFlag = olddefer; AN.cTerm = oldcterm; AT.WorkPointer = oldwork; if ( err ) return err; /* #] MODSUM : */ break; } } if ( d->type == DOLTERMS ) cbuf[AM.dbufnum].CanCommu[index] = numcommute(d->where, &cbuf[AM.dbufnum].NumTerms[index]); cbuf[AM.dbufnum].rhs[index] = d->where; nvars++; #ifdef PF_DEBUG_REDUCE_DOLLAR MesPrint("<< Reduce $-var: %s", AC.dollarnames->namebuffer + d->name); #endif } /* #] Master : */ } else { /* #[ Slave : */ PF_PrepareLongSinglePack(); /* Pack each variable. */ for ( i = 0; i < NumPotModdollars; i++ ) { WORD index = PotModdollars[i]; DOLLARS d; if ( !dollar_to_be_collected(index) ) continue; d = Dollars + index; PF_LongSinglePack(&d->type, 1, PF_WORD); if ( d->type != DOLZERO ) { /* * NOTE: d->size is the allocated buffer size for d->where in WORDs. * So dollarlen(d->where) can be < d->size-1. (TU 15 Dec 2011) */ LONG size = dollarlen(d->where); PF_LongSinglePack(&size, 1, PF_LONG); PF_LongSinglePack(d->where, size, PF_WORD); /* Note that we don't collect factored stuff for max/min/sum variables. */ } } PF_LongSingleSend(MASTER, PF_DOLLAR_MSGTAG); /* #] Slave : */ } return 0; } /* #] PF_CollectModifiedDollars : #[ PF_BroadcastModifiedDollars : */ /* #[ dollar_to_be_broadcast : */ /** * Returns true if the dollar variable specified by \a index has to be broadcast * from the master to the all slaves, i.e., non-local. */ static inline int dollar_to_be_broadcast(WORD index) { switch ( dollar_mod_type(index) ) { case MODLOCAL: return 0; default: return 1; } } /* #] dollar_to_be_broadcast : */ /** * Broadcasts modified dollar variables on the master to the all slaves. * * The potentially modified dollar variables are given in PotModdollars, * and the number of them is given by NumPotModdollars. * * The current module could be executed in parallel only if all potentially * modified variables are listed in ModOptdollars, otherwise the module was * switched to the sequential mode. In either cases, we need to broadcast them. * * @return 0 if OK, nonzero on error. */ int PF_BroadcastModifiedDollars(void) { int i, j, ndollars; /* * Count the number of (potentially) modified dollar variables, which we need to broadcast. * Here we need to broadcast all non-local variables. */ ndollars = 0; for ( i = 0; i < NumPotModdollars; i++ ) { WORD index = PotModdollars[i]; if ( dollar_to_be_broadcast(index) ) ndollars++; } if ( ndollars == 0 ) return 0; /* No dollars to be broadcast. */ if ( PF.me == MASTER ) { /* #[ Master : */ PF_PrepareLongMultiPack(); /* Pack each variable. */ for ( i = 0; i < NumPotModdollars; i++ ) { WORD index = PotModdollars[i]; DOLLARS d; if ( !dollar_to_be_broadcast(index) ) continue; d = Dollars + index; PF_LongMultiPack(&d->type, 1, PF_WORD); if ( d->type != DOLZERO ) { /* * NOTE: d->size is the allocated buffer size for d->where in WORDs. * So dollarlen(d->where) can be < d->size-1. (TU 15 Dec 2011) */ LONG size = dollarlen(d->where); PF_LongMultiPack(&size, 1, PF_LONG); PF_LongMultiPack(d->where, size, PF_WORD); /* ...and the factored stuff. */ PF_LongMultiPack(&d->nfactors, 1, PF_WORD); if ( d->nfactors > 1 ) { for ( j = 0; j < d->nfactors; j++ ) { FACDOLLAR *f = &d->factors[j]; PF_LongMultiPack(&f->type, 1, PF_WORD); PF_LongMultiPack(&f->size, 1, PF_LONG); if ( f->size > 0 ) PF_LongMultiPack(f->where, f->size, PF_WORD); else PF_LongMultiPack(&f->value, 1, PF_WORD); } } } #ifdef PF_DEBUG_BCAST_DOLLAR MesPrint(">> Broadcast $-var: %s", AC.dollarnames->namebuffer + d->name); #endif } /* #] Master : */ } if ( PF_LongMultiBroadcast() ) return -1; if ( PF.me != MASTER ) { /* #[ Slave : */ for ( i = 0; i < NumPotModdollars; i++ ) { WORD index = PotModdollars[i]; DOLLARS d; if ( !dollar_to_be_broadcast(index) ) continue; d = Dollars + index; /* Clear the contents of the dollar variable. */ if ( d->where && d->where != &AM.dollarzero ) M_free(d->where, "old content of dollar"); d->where = &AM.dollarzero; d->size = 0; CleanDollarFactors(d); /* Unpack and store the contents. */ PF_LongMultiUnpack(&d->type, 1, PF_WORD); if ( d->type != DOLZERO ) { LONG size; PF_LongMultiUnpack(&size, 1, PF_LONG); d->size = size + 1; d->where = (WORD *)Malloc1(sizeof(WORD) * d->size, "dollar content"); PF_LongMultiUnpack(d->where, size, PF_WORD); d->where[size] = 0; /* The null terminator is needed. */ /* ...and the factored stuff. */ PF_LongMultiUnpack(&d->nfactors, 1, PF_WORD); if ( d->nfactors > 1 ) { d->factors = (FACDOLLAR *)Malloc1(sizeof(FACDOLLAR) * d->nfactors, "dollar factored stuff"); for ( j = 0; j < d->nfactors; j++ ) { FACDOLLAR *f = &d->factors[j]; PF_LongMultiUnpack(&f->type, 1, PF_WORD); PF_LongMultiUnpack(&f->size, 1, PF_LONG); if ( f->size > 0 ) { f->where = (WORD *)Malloc1(sizeof(WORD) * (f->size + 1), "dollar factor content"); PF_LongMultiUnpack(f->where, f->size, PF_WORD); f->where[f->size] = 0; /* The null terminator is needed. */ f->value = 0; } else { f->where = NULL; PF_LongMultiUnpack(&f->value, 1, PF_WORD); } } } } if ( d->type == DOLTERMS ) cbuf[AM.dbufnum].CanCommu[index] = numcommute(d->where, &cbuf[AM.dbufnum].NumTerms[index]); cbuf[AM.dbufnum].rhs[index] = d->where; } /* #] Slave : */ } return 0; } /* #] PF_BroadcastModifiedDollars : #] Synchronization of modified dollar variables : #[ Synchronization of redefined preprocessor variables : #[ Variables : */ /* A buffer used in receivers. */ static Vector(UBYTE, prevarbuf); /* #] Variables : #[ PF_PackRedefinedPreVars : */ /** * Packs information of redefined preprocessor variables into the long single * pack buffer, with the corresponding value in AC.inputnumbers. * * The potentially redefined preprocessor variables are given in AC.pfirstnum, * and the number of them is given by AC.numpfirstnum. For an actually redefined * variable, the corresponding value in AC.inputnumbers is non-negative. */ static void PF_PackRedefinedPreVars(void) { int i; /* First, pack the number of redefined preprocessor variables. */ int nredefs = 0; for ( i = 0; i < AC.numpfirstnum; i++ ) if ( AC.inputnumbers[i] >= 0 ) nredefs++; PF_LongSinglePack(&nredefs, 1, PF_INT); /* Then, pack each variable. */ for ( i = 0; i < AC.numpfirstnum; i++ ) if ( AC.inputnumbers[i] >= 0) { WORD index = AC.pfirstnum[i]; UBYTE *value = PreVar[index].value; int bytes = strlen((char *)value); PF_LongSinglePack(&index, 1, PF_WORD); PF_LongSinglePack(&bytes, 1, PF_INT); PF_LongSinglePack(value, bytes, PF_BYTE); PF_LongSinglePack(&AC.inputnumbers[i], 1, PF_LONG); } } /* #] PF_PackRedefinedPreVars : #[ PF_UnpackRedefinedPreVars : */ /** * Unpacks information of redefined preprocessor variables from the long single * pack buffer. If the attached value of the input number is greater than * the corresponding current value in AC.inputnumbers, this function updates * the preprocessor variable. * * The potentially redefined preprocessor variables are given in AC.pfirstnum, * and the number of them is AC.numpfirstnum. */ static void PF_UnpackRedefinedPreVars(void) { int i, j; /* Unpack the number of redefined preprocessor variables. */ int nredefs; PF_LongSingleUnpack(&nredefs, 1, PF_INT); if ( nredefs > 0 ) { /* Then unpack each variable. */ for ( i = 0; i < nredefs; i++ ) { WORD index; int bytes; UBYTE *value; LONG inputnumber; PF_LongSingleUnpack(&index, 1, PF_WORD); PF_LongSingleUnpack(&bytes, 1, PF_INT); VectorReserve(prevarbuf, bytes + 1); value = VectorPtr(prevarbuf); PF_LongSingleUnpack(value, bytes, PF_BYTE); value[bytes] = '\0'; /* The null terminator is needed. */ PF_LongSingleUnpack(&inputnumber, 1, PF_LONG); /* Put this variable if it must be updated. */ for ( j = 0; j < AC.numpfirstnum; j++ ) if ( AC.pfirstnum[j] == index ) break; if ( AC.inputnumbers[j] < inputnumber ) { AC.inputnumbers[j] = inputnumber; PutPreVar(PreVar[index].name, value, NULL, 1); } } } } /* #] PF_UnpackRedefinedPreVars : #[ PF_BroadcastRedefinedPreVars : */ /** * Broadcasts preprocessor variables, which were changed by the Redefine statements * in the current module, from the master to the all slaves. * * The potentially redefined preprocessor variables are given in AC.pfirstnum, * and the number of them is given by AC.numpfirstnum. For an actually redefined * variable, the corresponding value in AC.inputnumbers is non-negative. * * @return 0 if OK, nonzero on error. */ int PF_BroadcastRedefinedPreVars(void) { /* * NOTE: Because the compilation is performed on the all processes * independently on AC.mparallelflag, we always have to broadcast redefined * preprocessor variables from the master to the all slaves. */ if ( PF.me == MASTER ) { /* #[ Master : */ int i, nredefs; PF_PrepareLongMultiPack(); /* First, pack the number of redefined preprocessor variables. */ nredefs = 0; for ( i = 0; i < AC.numpfirstnum; i++ ) if ( AC.inputnumbers[i] >= 0 ) nredefs++; PF_LongMultiPack(&nredefs, 1, PF_INT); /* Then, pack each variable. */ for ( i = 0; i < AC.numpfirstnum; i++ ) if ( AC.inputnumbers[i] >= 0) { WORD index = AC.pfirstnum[i]; UBYTE *value = PreVar[index].value; int bytes = strlen((char *)value); PF_LongMultiPack(&index, 1, PF_WORD); PF_LongMultiPack(&bytes, 1, PF_INT); PF_LongMultiPack(value, bytes, PF_BYTE); #ifdef PF_DEBUG_BCAST_PREVAR MesPrint(">> Broadcast PreVar: %s = \"%s\"", PreVar[index].name, value); #endif } /* #] Master : */ } if ( PF_LongMultiBroadcast() ) return -1; if ( PF.me != MASTER ) { /* #[ Slave : */ int i, nredefs; /* Unpack the number of redefined preprocessor variables. */ PF_LongMultiUnpack(&nredefs, 1, PF_INT); if ( nredefs > 0 ) { /* Then unpack each variable and put it. */ for ( i = 0; i < nredefs; i++ ) { WORD index; int bytes; UBYTE *value; PF_LongMultiUnpack(&index, 1, PF_WORD); PF_LongMultiUnpack(&bytes, 1, PF_INT); VectorReserve(prevarbuf, bytes + 1); value = VectorPtr(prevarbuf); PF_LongMultiUnpack(value, bytes, PF_BYTE); value[bytes] = '\0'; /* The null terminator is needed. */ PutPreVar(PreVar[index].name, value, NULL, 1); } } /* #] Slave : */ } return 0; } /* #] PF_BroadcastRedefinedPreVars : #] Synchronization of redefined preprocessor variables : #[ Preprocessor Inside instruction : #[ Variables : */ /* Saved values of AC.RhsExprInModuleFlag, PotModdollars and AC.pfirstnum. */ static WORD oldRhsExprInModuleFlag; static Vector(WORD, oldPotModdollars); static Vector(WORD, oldpfirstnum); /* #] Variables : #[ PF_StoreInsideInfo : */ /* * Saves the current values of AC.RhsExprInModuleFlag, PotModdollars * and AC.pfirstnum. * * Called by DoInside(). * * @return 0 if OK, nonzero on error. */ int PF_StoreInsideInfo(void) { int i; oldRhsExprInModuleFlag = AC.RhsExprInModuleFlag; VectorClear(oldPotModdollars); for ( i = 0; i < NumPotModdollars; i++ ) VectorPushBack(oldPotModdollars, PotModdollars[i]); VectorClear(oldpfirstnum); for ( i = 0; i < AC.numpfirstnum; i++ ) VectorPushBack(oldpfirstnum, AC.pfirstnum[i]); return 0; } /* #] PF_StoreInsideInfo : #[ PF_RestoreInsideInfo : */ /* * Restores the saved values of AC.RhsExprInModuleFlag, PotModdollars * and AC.pfirstnum. * * Called by DoEndInside(). * * @return 0 if OK, nonzero on error. */ int PF_RestoreInsideInfo(void) { int i; AC.RhsExprInModuleFlag = oldRhsExprInModuleFlag; NumPotModdollars = VectorSize(oldPotModdollars); for ( i = 0; i < NumPotModdollars; i++ ) PotModdollars[i] = VectorPtr(oldPotModdollars)[i]; AC.numpfirstnum = VectorSize(oldpfirstnum); for ( i = 0; i < AC.numpfirstnum; i++ ) AC.pfirstnum[i] = VectorPtr(oldpfirstnum)[i]; return 0; } /* #] PF_RestoreInsideInfo : #] Preprocessor Inside instruction : #[ PF_BroadcastCBuf : */ /** * Broadcasts a compiler buffer specified by \a bufnum from the master * to the all slaves. * * @param bufnum The index of the compiler buffer to be broadcast. * @return 0 if OK, nonzero on error. */ int PF_BroadcastCBuf(int bufnum) { CBUF *C = cbuf + bufnum; int i; LONG l; if ( PF.me == MASTER ) { /* #[ Master : */ PF_PrepareLongMultiPack(); /* Pack CBUF struct except pointers. */ PF_LongMultiPack(&C->BufferSize, 1, PF_LONG); PF_LongMultiPack(&C->numlhs, 1, PF_INT); PF_LongMultiPack(&C->numrhs, 1, PF_INT); PF_LongMultiPack(&C->maxlhs, 1, PF_INT); PF_LongMultiPack(&C->maxrhs, 1, PF_INT); PF_LongMultiPack(&C->mnumlhs, 1, PF_INT); PF_LongMultiPack(&C->mnumrhs, 1, PF_INT); PF_LongMultiPack(&C->numtree, 1, PF_INT); PF_LongMultiPack(&C->rootnum, 1, PF_INT); PF_LongMultiPack(&C->MaxTreeSize, 1, PF_INT); /* Now pointers. Pointer, lhs and rhs are packed as offsets. We don't pack Top. */ l = C->Pointer - C->Buffer; PF_LongMultiPack(&l, 1, PF_LONG); PF_LongMultiPack(C->Buffer, l, PF_WORD); for ( i = 0; i < C->numlhs + 1; i++ ) { l = C->lhs[i] - C->Buffer; PF_LongMultiPack(&l, 1, PF_LONG); } for ( i = 0; i < C->numrhs + 1; i++ ) { l = C->rhs[i] - C->Buffer; PF_LongMultiPack(&l, 1, PF_LONG); } PF_LongMultiPack(C->CanCommu, C->numrhs + 1, PF_LONG); PF_LongMultiPack(C->NumTerms, C->numrhs + 1, PF_LONG); PF_LongMultiPack(C->numdum, C->numrhs + 1, PF_WORD); PF_LongMultiPack(C->dimension, C->numrhs + 1, PF_WORD); if ( C->MaxTreeSize > 0 ) PF_LongMultiPack(C->boomlijst, (C->numtree + 1) * (sizeof(COMPTREE) / sizeof(int)), PF_INT); #ifdef PF_DEBUG_BCAST_CBUF MesPrint(">> Broadcast CBuf %d", bufnum); #endif /* #] Master : */ } if ( PF_LongMultiBroadcast() ) return -1; if ( PF.me != MASTER ) { /* #[ Slave : */ /* First, free already allocated buffers. */ finishcbuf(bufnum); /* Unpack CBUF struct except pointers. */ PF_LongMultiUnpack(&C->BufferSize, 1, PF_LONG); PF_LongMultiUnpack(&C->numlhs, 1, PF_INT); PF_LongMultiUnpack(&C->numrhs, 1, PF_INT); PF_LongMultiUnpack(&C->maxlhs, 1, PF_INT); PF_LongMultiUnpack(&C->maxrhs, 1, PF_INT); PF_LongMultiUnpack(&C->mnumlhs, 1, PF_INT); PF_LongMultiUnpack(&C->mnumrhs, 1, PF_INT); PF_LongMultiUnpack(&C->numtree, 1, PF_INT); PF_LongMultiUnpack(&C->rootnum, 1, PF_INT); PF_LongMultiUnpack(&C->MaxTreeSize, 1, PF_INT); /* Allocate new buffers. */ C->Buffer = (WORD *)Malloc1(C->BufferSize * sizeof(WORD), "compiler buffer"); C->Top = C->Buffer + C->BufferSize; C->lhs = (WORD **)Malloc1(C->maxlhs * sizeof(WORD *), "compiler buffer"); C->rhs = (WORD **)Malloc1(C->maxrhs * (sizeof(WORD *) + 2 * sizeof(LONG) + 2 * sizeof(WORD)), "compiler buffer"); C->CanCommu = (LONG *)(C->rhs + C->maxrhs); C->NumTerms = C->CanCommu + C->maxrhs; C->numdum = (WORD *)(C->NumTerms + C->maxrhs); C->dimension = C->numdum + C->maxrhs; if ( C->MaxTreeSize > 0 ) C->boomlijst = (COMPTREE *)Malloc1(C->MaxTreeSize * sizeof(COMPTREE), "compiler buffer"); /* Unpack buffers. */ PF_LongMultiUnpack(&l, 1, PF_LONG); PF_LongMultiUnpack(C->Buffer, l, PF_WORD); C->Pointer = C->Buffer + l; for ( i = 0; i < C->numlhs + 1; i++ ) { PF_LongMultiUnpack(&l, 1, PF_LONG); C->lhs[i] = C->Buffer + l; } for ( i = 0; i < C->numrhs + 1; i++ ) { PF_LongMultiUnpack(&l, 1, PF_LONG); C->rhs[i] = C->Buffer + l; } PF_LongMultiUnpack(C->CanCommu, C->numrhs + 1, PF_LONG); PF_LongMultiUnpack(C->NumTerms, C->numrhs + 1, PF_LONG); PF_LongMultiUnpack(C->numdum, C->numrhs + 1, PF_WORD); PF_LongMultiUnpack(C->dimension, C->numrhs + 1, PF_WORD); if ( C->MaxTreeSize > 0 ) PF_LongMultiUnpack(C->boomlijst, (C->numtree + 1) * (sizeof(COMPTREE) / sizeof(int)), PF_INT); /* #] Slave : */ } return 0; } /* #] PF_BroadcastCBuf : #[ PF_BroadcastExpFlags : */ /** * Broadcasts AR.expflags and several properties of each expression, * e.g., e->vflags, from the master to all slaves. * * @return 0 if OK, nonzero on error. */ int PF_BroadcastExpFlags(void) { WORD i; EXPRESSIONS e; if ( PF.me == MASTER ) { /* #[ Master : */ PF_PrepareLongMultiPack(); PF_LongMultiPack(&AR.expflags, 1, PF_WORD); for ( i = 0; i < NumExpressions; i++ ) { e = &Expressions[i]; PF_LongMultiPack(&e->counter, 1, PF_WORD); PF_LongMultiPack(&e->vflags, 1, PF_WORD); PF_LongMultiPack(&e->uflags, 1, PF_WORD); PF_LongMultiPack(&e->numdummies, 1, PF_WORD); PF_LongMultiPack(&e->numfactors, 1, PF_WORD); #ifdef PF_DEBUG_BCAST_EXPRFLAGS MesPrint(">> Broadcast ExprFlags: %s", AC.exprnames->namebuffer + e->name); #endif } /* #] Master : */ } if ( PF_LongMultiBroadcast() ) return -1; if ( PF.me != MASTER ) { /* #[ Slave : */ PF_LongMultiUnpack(&AR.expflags, 1, PF_WORD); for ( i = 0; i < NumExpressions; i++ ) { e = &Expressions[i]; PF_LongMultiUnpack(&e->counter, 1, PF_WORD); PF_LongMultiUnpack(&e->vflags, 1, PF_WORD); PF_LongMultiUnpack(&e->uflags, 1, PF_WORD); PF_LongMultiUnpack(&e->numdummies, 1, PF_WORD); PF_LongMultiUnpack(&e->numfactors, 1, PF_WORD); } /* #] Slave : */ } return 0; } /* #] PF_BroadcastExpFlags : #[ PF_SetScratch : */ /** * Same as SetScratch() except it always fills the buffer from the given position. * * @param f the file handle. * @param position the position to be loaded into the buffer. */ static void PF_SetScratch(FILEHANDLE *f,POSITION *position) { if( ( f->handle >= 0) && ISGEPOS(*position,f->POposition) && ( ISGEPOSINC(*position,f->POposition,(f->POfull-f->PObuffer)*sizeof(WORD)) ==0 ) )/*position is inside the buffer! SetScratch() will do nothing.*/ f->POfull=f->PObuffer;/*force SetScratch() to re-read the position from the beginning:*/ SetScratch(f,position); } /* #] PF_SetScratch : #[ PF_pushScratch : */ /** * Flushes a scratch file. * * @param f the scratch file to be flushed. * @return 0 if OK, nonzero on error. */ static int PF_pushScratch(FILEHANDLE *f) { LONG size,RetCode; if ( f->handle < 0){ /*Create the file*/ if ( ( RetCode = CreateFile(f->name) ) >= 0 ) { f->handle = (WORD)RetCode; PUTZERO(f->filesize); PUTZERO(f->POposition); } else{ MesPrint("Cannot create scratch file %s",f->name); return(-1); } }/*if ( f->handle < 0)*/ size = (f->POfill-f->PObuffer)*sizeof(WORD); if( size > 0 ){ SeekFile(f->handle,&(f->POposition),SEEK_SET); if ( WriteFile(f->handle,(UBYTE *)(f->PObuffer),size) != size ){ MesPrint("Error while writing to disk. Disk full?"); return(-1); } ADDPOS(f->filesize,size); ADDPOS(f->POposition,size); f->POfill = f->POfull=f->PObuffer; }/*if( size > 0 )*/ return(0); } /* #] PF_pushScratch : #[ Broadcasting RHS expressions : #[ PF_WalkThroughExprMaster : Returns <=0 if the expression is ready, or dl+1; */ static int PF_WalkThroughExprMaster(FILEHANDLE *curfile, int dl) { LONG l=0; for(;;){ if(curfile->POfull-curfile->POfill < dl){ POSITION pos; SeekScratch(curfile,&pos); PF_SetScratch(curfile,&pos); }/*if(curfile->POfull-curfile->POfill < dl)*/ curfile->POfill+=dl; l+=dl; if( l >= PF.exprbufsize){ if( l == PF.exprbufsize){ if( *(curfile->POfill) == 0)/*expression is ready*/ return(0); } l-=PF.exprbufsize; curfile->POfill-=l; return l+1; } dl=*(curfile->POfill); if(dl == 0) return l-PF.exprbufsize; if(dl<0){/*compressed term*/ if(curfile->POfull-curfile->POfill < 1){ POSITION pos; SeekScratch(curfile,&pos); PF_SetScratch(curfile,&pos); }/*if(curfile->POfull-curfile->POfill < 1)*/ dl=*(curfile->POfill+1)+2; }/*if(*(curfile->POfill)<0)*/ }/*for(;;)*/ } /* #] PF_WalkThroughExprMaster : #[ PF_WalkThroughExprSlave : Returns <=0 if the expression is ready, or dl+1; */ static int PF_WalkThroughExprSlave(FILEHANDLE *curfile, LONG *counter, int dl) { LONG l=0; for(;;){ if(curfile->POstop-curfile->POfill < dl){ if(PF_pushScratch(curfile)) return(-PF.exprbufsize-1); } curfile->POfill+=dl; curfile->POfull=curfile->POfill; l+=dl; if( l >= PF.exprbufsize){ if( l == PF.exprbufsize){ /* * This access is valid because PF.exprbufsize+1 WORDs are * broadcasted, this shortcut is not mandatory though. (TU 15 Sep 2011) */ if( *(curfile->POfill) == 0)/*expression is ready*/ return(0); } l-=PF.exprbufsize; curfile->POfill-=l; curfile->POfull=curfile->POfill; return l+1; } dl=*(curfile->POfill); if(dl == 0) return l-PF.exprbufsize; (*counter)++; if(dl<0){/*compressed term*/ if(curfile->POstop-curfile->POfill < 1){ if(PF_pushScratch(curfile)) return(-PF.exprbufsize-1); } /* * This access is always valid because PF.exprbufsize+1 WORDs are * broadcasted. (TU 15 Sep 2011) */ dl=*(curfile->POfill+1)+2; }/*if(*(curfile->POfill)<0)*/ }/*for(;;)*/ } /* #] PF_WalkThroughExprSlave : #[ PF_rhsBCastMaster : */ /** * On the master, broadcasts an expression to the all slaves. * * @param curfile the scratch file in which the expression is stored. * @param e the expression to be broadcasted. * @return 0 if OK, nonzero on error. */ static int PF_rhsBCastMaster(FILEHANDLE *curfile, EXPRESSIONS e) { LONG l=1;/*PF_WalkThroughExpr returns length + 1*/ SetScratch(curfile,&(e->onfile)); do{ /* * We need to broadcast PF.exprbufsize+1 WORDs because PF_WalkThroughExprSlave * may access to an additional 1 WORD. It is better to rewrite the routines * in such a way as to broadcast only PF.exprbufsize WORDs. (TU 15 Sep 2011) */ if ( curfile->POfull - curfile->POfill < PF.exprbufsize + 1 ) { POSITION pos; SeekScratch(curfile,&pos); PF_SetScratch(curfile,&pos); } if ( PF_Bcast(curfile->POfill, (PF.exprbufsize + 1) * sizeof(WORD)) ) return -1; l=PF_WalkThroughExprMaster(curfile,l-1); }while(l>0); if(l<0)/*The tail is extra, decrease POfill*/ curfile->POfill-=l; return(0); } /* #] PF_rhsBCastMaster : #[ PF_rhsBCastSlave : */ /** * On the slave, receives an expression broadcasted from the master. * * @param curfile the scratch file to store the broadcasted expression * (AR.infile or AR.hidefile). * @param e the expression to be broadcasted. * @return 0 if OK, nonzero on error. */ static int PF_rhsBCastSlave(FILEHANDLE *curfile, EXPRESSIONS e) { LONG l=1;/*PF_WalkThroughExpr returns length + 1*/ LONG counter = 0; do{ /* * We need to broadcast PF.exprbufsize+1 WORDs because PF_WalkThroughExprSlave * may access to an additional 1 WORD. It is better to rewrite the routines * in such a way as to broadcast only PF.exprbufsize WORDs. (TU 15 Sep 2011) */ if ( curfile->POstop - curfile->POfill < PF.exprbufsize + 1 ) { if(PF_pushScratch(curfile)) return(-1); } if ( PF_Bcast(curfile->POfill, (PF.exprbufsize + 1) * sizeof(WORD)) ) return(-1); l = PF_WalkThroughExprSlave(curfile, &counter, l - 1); }while(l>0); if(l<0){/*The tail is extra, decrease POfill*/ if(l<-PF.exprbufsize)/*error due to a PF_pushScratch() failure */ return(-1); curfile->POfill-=l; } if ( curfile->handle >= 0 ) { if ( PF_pushScratch(curfile) ) return -1; } curfile->POfull=curfile->POfill; if ( curfile != AR.hidefile ) AR.InInBuf = curfile->POfull-curfile->PObuffer; else AR.InHiBuf = curfile->POfull-curfile->PObuffer; CHECK(counter == e->counter + 1); /* The first term is the prototype. */ return(0); } /* #] PF_rhsBCastSlave : #[ PF_BroadcastExpr : */ /** * Broadcasts an expression from the master to the all slaves. * * @param e The expression to be broadcast. * @param file The file in which the expression is sitting. * @return 0 if OK, nonzero on error. */ int PF_BroadcastExpr(EXPRESSIONS e, FILEHANDLE *file) { if ( PF.me == MASTER ) { if ( PF_rhsBCastMaster(file, e) ) return -1; #ifdef PF_DEBUG_BCAST_RHSEXPR MesPrint(">> Broadcast RhsExpr: %s", AC.exprnames->namebuffer + e->name); #endif } else { POSITION pos; SetEndHScratch(file, &pos); e->onfile = pos; if ( PF_rhsBCastSlave(file, e) ) return -1; } return 0; } /* #] PF_BroadcastExpr : #[ PF_BroadcastRHS : */ /** * Broadcasts expressions appearing in the right-hand side from * the master to the all slaves. * * @return 0 if OK, nonzero on error. */ int PF_BroadcastRHS(void) { int i; for ( i = 0; i < NumExpressions; i++ ) { EXPRESSIONS e = &Expressions[i]; if ( !(e->vflags & ISINRHS) ) continue; switch ( e->status ) { case LOCALEXPRESSION: case SKIPLEXPRESSION: case DROPLEXPRESSION: case GLOBALEXPRESSION: case SKIPGEXPRESSION: case DROPGEXPRESSION: case HIDELEXPRESSION: case HIDEGEXPRESSION: case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: if ( PF_BroadcastExpr(e, AR.infile) ) return -1; break; case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: if ( PF_BroadcastExpr(e, AR.hidefile) ) return -1; break; } } if ( PF.me != MASTER ) UpdatePositions(); return 0; } /* #] PF_BroadcastRHS : #] Broadcasting RHS expressions : #[ InParallel mode : #[ PF_InParallelProcessor : */ /** * Processes expressions in the InParallel mode, i.e., * dividing expressions marked by partodo over the slaves. * * @return 0 if OK, nonzero on error. */ int PF_InParallelProcessor(void) { GETIDENTITY int i, next,tag; EXPRESSIONS e; /* * Skip expressions with zero terms. All the master and slaves need to * change the "partodo" flag. */ if ( PF.numtasks >= 3 ) { for ( i = 0; i < NumExpressions; i++ ) { e = Expressions + i; if ( e->partodo > 0 && e->counter == 0 ) { e->partodo = 0; } } } PF_processing = 1; if(PF.me == MASTER){ if ( PF.numtasks >= 3 ) { partodoexr = (WORD*)Malloc1(sizeof(WORD)*(PF.numtasks+1),"PF_InParallelProcessor"); for ( i = 0; i < NumExpressions; i++ ) { e = Expressions+i; if ( e->partodo <= 0 ) continue; switch(e->status){ case LOCALEXPRESSION: case GLOBALEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: tag=PF_ANY_SOURCE; next=PF_Wait4SlaveIP(&tag); if(next<0) return(-1); if(tag == PF_DATA_MSGTAG){ PF_Statistics(PF_stats,0); if(PF_Slave2MasterIP(next)) return(-1); } if(PF_Master2SlaveIP(next,e)) return(-1); partodoexr[next]=i; break; default: e->partodo = 0; continue; }/*switch(e->status)*/ }/*for ( i = 0; i < NumExpressions; i++ )*/ /*Here some slaves are working, other are waiting on PF_Send. Wait all of them.*/ /*At this point no new slaves may be launched so PF_WaitAllSlaves() does not modify partodoexr[].*/ if(PF_WaitAllSlaves()) return(-1); /**/ if ( AC.CollectFun ) AR.DeferFlag = 0; if(partodoexr){ M_free(partodoexr,"PF_InParallelProcessor"); partodoexr=NULL; }/*if(partodoexr)*/ }/*if ( PF.numtasks >= 3 ) */ else { for ( i = 0; i < NumExpressions; i++ ) { Expressions[i].partodo = 0; } } PF_PostEndSortBarrier(); return(0); }/*if(PF.me == MASTER)*/ /*Slave:*/ if(PF_Wait4MasterIP(PF_EMPTY_MSGTAG)) return(-1); /*master is ready to listen to me*/ do{ WORD *oldwork= AT.WorkPointer; tag=PF_ReadMaster();/*reads directly to its scratch!*/ if(tag<0) return(-1); if(tag == PF_DATA_MSGTAG){ oldwork = AT.WorkPointer; /* For redefine statements. */ if ( AC.numpfirstnum > 0 ) { int j; for ( j = 0; j < AC.numpfirstnum; j++ ) { AC.inputnumbers[j] = -1; } } if(PF_DoOneExpr())/*the processor*/ return(-1); if(PF_Wait4MasterIP(PF_DATA_MSGTAG)) return(-1); if(PF_Slave2MasterIP(PF.me))/*both master and slave*/ return(-1); AT.WorkPointer=oldwork; }/*if(tag == PF_DATA_MSGTAG)*/ }while(tag!=PF_EMPTY_MSGTAG); PF.exprtodo=-1; PF_PostEndSortBarrier(); return(0); }/*PF_InParallelProcessor*/ /* #] PF_InParallelProcessor : #[ PF_Wait4MasterIP : */ static int PF_Wait4MasterIP(int tag) { int follow = 0; LONG cpu,space = 0; if(PF.log){ fprintf(stderr,"[%d] Starting to send to Master\n",PF.me); fflush(stderr); } PF_PreparePack(); cpu = TimeCPU(1); PF_Pack(&cpu ,1,PF_LONG); PF_Pack(&space ,1,PF_LONG); PF_Pack(&PF_linterms ,1,PF_LONG); PF_Pack(&(AM.S0->GenTerms) ,1,PF_LONG); PF_Pack(&(AM.S0->TermsLeft),1,PF_LONG); PF_Pack(&follow ,1,PF_INT ); if(PF.log){ fprintf(stderr,"[%d] Now sending with tag = %d\n",PF.me,tag); fflush(stderr); } PF_Send(MASTER, tag); if(PF.log){ fprintf(stderr,"[%d] returning from send\n",PF.me); fflush(stderr); } return(0); } /* #] PF_Wait4MasterIP : #[ PF_DoOneExpr : */ /** * Processes an expression specified by PF.exprtodo. * * See also "case DOONEEXPRESSION" in RunThread(). * * @return 0 if OK, nonzero on error. */ static int PF_DoOneExpr(void)/*the processor*/ { GETIDENTITY EXPRESSIONS e; int i; WORD *term; POSITION position, outposition; FILEHANDLE *fi, *fout; LONG dd = 0; WORD oldBracketOn = AR.BracketOn; WORD *oldBrackBuf = AT.BrackBuf; WORD oldbracketindexflag = AT.bracketindexflag; e = Expressions + PF.exprtodo; i = PF.exprtodo; AR.CurExpr = i; AR.SortType = AC.SortType; AR.expchanged = 0; if ( ( e->vflags & ISFACTORIZED ) != 0 ) { AR.BracketOn = 1; AT.BrackBuf = AM.BracketFactors; AT.bracketindexflag = 1; } position = AS.OldOnFile[i]; if ( e->status == HIDDENLEXPRESSION || e->status == HIDDENGEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) { AR.GetFile = 2; fi = AR.hidefile; } else { AR.GetFile = 0; fi = AR.infile; } /* PUTZERO(fi->POposition); if ( fi->handle >= 0 ) { fi->POfill = fi->POfull = fi->PObuffer; } */ SetScratch(fi,&position); term = AT.WorkPointer; AR.CompressPointer = AR.CompressBuffer; AR.CompressPointer[0] = 0; AR.KeptInHold = 0; if ( GetTerm(BHEAD term) <= 0 ) { MesPrint("Expression %d has problems in scratchfile",i); Terminate(-1); } if ( AT.bracketindexflag > 0 ) OpenBracketIndex(i); term[3] = i; PUTZERO(outposition); fout = AR.outfile; fout->POfill = fout->POfull = fout->PObuffer; fout->POposition = outposition; if ( fout->handle >= 0 ) { fout->POposition = outposition; } /* The next statement is needed because we need the system to believe that the expression is at position zero for the moment. In this worker, with no memory of other expressions, it is. This is needed for when a bracket index is made because there e->onfile is an offset. Afterwards, when the expression is written to its final location in the masters output e->onfile will get its real value. */ PUTZERO(e->onfile); if ( PutOut(BHEAD term,&outposition,fout,0) < 0 ) return -1; AR.DeferFlag = AC.ComDefer; /* AR.sLevel = AB[0]->R.sLevel;*/ term = AT.WorkPointer; NewSort(BHEAD0); AR.MaxDum = AM.IndDum; AN.ninterms = 0; while ( GetTerm(BHEAD term) ) { SeekScratch(fi,&position); AN.ninterms++; dd = AN.deferskipped; if ( ( e->vflags & ISFACTORIZED ) != 0 && term[1] == HAAKJE ) { StoreTerm(BHEAD term); } else { if ( AC.CollectFun && *term <= (AM.MaxTer/(2*(LONG)sizeof(WORD))) ) { if ( GetMoreTerms(term) < 0 ) { LowerSortLevel(); return(-1); } SeekScratch(fi,&position); } AT.WorkPointer = term + *term; AN.RepPoint = AT.RepCount + 1; if ( AR.DeferFlag ) { AR.CurDum = AN.IndDum = Expressions[PF.exprtodo].numdummies; } else { AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); } if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( ( AR.PolyFunType == 2 ) && ( AC.PolyRatFunChanged == 0 ) && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION ) ) { PolyFunClean(BHEAD term); } if ( Generator(BHEAD term,0) ) { LowerSortLevel(); return(-1); } AN.ninterms += dd; } SetScratch(fi,&position); if ( fi == AR.hidefile ) { AR.InHiBuf = (fi->POfull-fi->PObuffer) -DIFBASE(position,fi->POposition)/sizeof(WORD); } else { AR.InInBuf = (fi->POfull-fi->PObuffer) -DIFBASE(position,fi->POposition)/sizeof(WORD); } } AN.ninterms += dd; if ( EndSort(BHEAD AM.S0->sBuffer,0) < 0 ) return(-1); e->numdummies = AR.MaxDum - AM.IndDum; AR.BracketOn = oldBracketOn; AT.BrackBuf = oldBrackBuf; if ( ( e->vflags & TOBEFACTORED ) != 0 ) poly_factorize_expression(e); else if ( ( ( e->vflags & TOBEUNFACTORED ) != 0 ) && ( ( e->vflags & ISFACTORIZED ) != 0 ) ) poly_unfactorize_expression(e); if ( AM.S0->TermsLeft ) e->vflags &= ~ISZERO; else e->vflags |= ISZERO; if ( AR.expchanged == 0 ) e->vflags |= ISUNMODIFIED; /* if ( AM.S0->TermsLeft ) AR.expflags |= ISZERO; if ( AR.expchanged ) AR.expflags |= ISUNMODIFIED;*/ AR.GetFile = 0; AT.bracketindexflag = oldbracketindexflag; fout->POfull = fout->POfill; return(0); } /* #] PF_DoOneExpr : #[ PF_Slave2MasterIP : */ typedef struct bufIPstruct { LONG i; struct ExPrEsSiOn e; } bufIPstruct_t; static int PF_Slave2MasterIP(int src)/*both master and slave*/ { EXPRESSIONS e; bufIPstruct_t exprData; int i,l; FILEHANDLE *fout=AR.outfile; POSITION pos; /*Here we know the length of data to send in advance: slave has the only one expression in its scratch file, and it sends this information to the master.*/ if(PF.me != MASTER){/*slave*/ e = Expressions + PF.exprtodo; /*Fill in the expression data:*/ memcpy(&(exprData.e), e, sizeof(struct ExPrEsSiOn)); SeekScratch(fout,&pos); exprData.i=BASEPOSITION(pos); /*Send the metadata:*/ if(PF_RawSend(MASTER,&exprData,sizeof(bufIPstruct_t),0)) return(-1); i=exprData.i; SETBASEPOSITION(pos,0); do{ int blen=PF.exprbufsize*sizeof(WORD); if(i0); if ( fout->handle >= 0 ) { /* Now get rid of the file */ CloseFile(fout->handle); fout->handle = -1; remove(fout->name); PUTZERO(fout->POposition); PUTZERO(fout->filesize); fout->POfill = fout->POfull = fout->PObuffer; } /* Now handle redefined preprocessor variables. */ if ( AC.numpfirstnum > 0 ) { PF_PrepareLongSinglePack(); PF_PackRedefinedPreVars(); PF_LongSingleSend(MASTER, PF_MISC_MSGTAG); } return(0); }/*if(PF.me != MASTER)*/ /*Master*/ /*partodoexr[src] is the number of expression.*/ e = Expressions +partodoexr[src]; /*Get metadata:*/ i = PF_ANY_MSGTAG; PF_CatchErrorMessages(&src, &i); if (PF_RawRecv(&src, &exprData,sizeof(bufIPstruct_t),&i)!= sizeof(bufIPstruct_t)) return(-1); /*Fill in the expression data:*/ /* memcpy(e, &(exprData.e), sizeof(struct ExPrEsSiOn)); */ e->counter = exprData.e.counter; e->vflags = exprData.e.vflags; e->uflags = exprData.e.uflags; e->numdummies = exprData.e.numdummies; e->numfactors = exprData.e.numfactors; if ( !(e->vflags & ISZERO) ) AR.expflags |= ISZERO; if ( !(e->vflags & ISUNMODIFIED) ) AR.expflags |= ISUNMODIFIED; SeekScratch(fout,&pos); e->onfile = pos; i=exprData.i; while(i>0){ int blen=PF.exprbufsize*sizeof(WORD); if(i 0 ) { PF_LongSingleReceive(src, PF_MISC_MSGTAG, NULL, NULL); PF_UnpackRedefinedPreVars(); } return(0); } /* #] PF_Slave2MasterIP : #[ PF_Master2SlaveIP : */ static int PF_Master2SlaveIP(int dest, EXPRESSIONS e) { bufIPstruct_t exprData; FILEHANDLE *fi; POSITION pos; int l; LONG ll=0,count=0; WORD *t; if(e==NULL){/*Say to the slave that no more job:*/ if(PF_RawSend(dest,&exprData,sizeof(bufIPstruct_t),PF_EMPTY_MSGTAG)) return(-1); return(0); } memcpy(&(exprData.e), e, sizeof(struct ExPrEsSiOn)); exprData.i=e-Expressions; if ( AC.StatsFlag && AC.OldParallelStats ) { MesPrint(""); MesPrint(" Sending expression %s to slave %d",EXPRNAME(exprData.i),dest); } if(PF_RawSend(dest,&exprData,sizeof(bufIPstruct_t),PF_DATA_MSGTAG)) return(-1); if ( e->status == HIDDENLEXPRESSION || e->status == HIDDENGEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) fi = AR.hidefile; else fi = AR.infile; pos=e->onfile; SetScratch(fi,&pos); do{ l=PF_SendChunkIP(fi, &pos, dest, PF.exprbufsize*sizeof(WORD)); if(l<0) return(-1); t=fi->PObuffer+ (DIFBASE(pos,fi->POposition))/sizeof(WORD); ll=PF_WalkThrough(t,ll,l/sizeof(WORD),&count); ADDPOS(pos,l); }while(ll>-2); return(0); } /* #] PF_Master2SlaveIP : #[ PF_ReadMaster : */ static int PF_ReadMaster(void)/*reads directly to its scratch!*/ { bufIPstruct_t exprData; int tag,m=MASTER; EXPRESSIONS e; FILEHANDLE *fi; POSITION pos; LONG count=0; WORD *t; LONG ll=0; int l; /*Get metadata:*/ tag = PF_ANY_MSGTAG; PF_CatchErrorMessages(&m, &tag); if (PF_RawRecv(&m, &exprData,sizeof(bufIPstruct_t),&tag)!= sizeof(bufIPstruct_t)) return(-1); if(tag == PF_EMPTY_MSGTAG)/*No data, no job*/ return(tag); /*data expected, tag must be == PF_DATA_MSGTAG!*/ PF.exprtodo=exprData.i; e=Expressions + PF.exprtodo; /*Fill in the expression data:*/ /* memcpy(e, &(exprData.e), sizeof(struct ExPrEsSiOn)); */ if ( e->status == HIDDENLEXPRESSION || e->status == HIDDENGEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) fi = AR.hidefile; else fi = AR.infile; SetEndHScratch(fi,&pos); e->onfile=AS.OldOnFile[PF.exprtodo]=pos; do{ l=PF_RecvChunkIP(fi,MASTER,PF.exprbufsize*sizeof(WORD)); if(l<0) return(-1); t=fi->POfull-l/sizeof(WORD); ll=PF_WalkThrough(t,ll,l/sizeof(WORD),&count); }while(ll>-2); /*Now -ll-2 is the number of "extra" elements transferred from the master.*/ fi->POfull-=-ll-2; fi->POfill=fi->POfull; return(PF_DATA_MSGTAG); } /* #] PF_ReadMaster : #[ PF_SendChunkIP : thesize is in bytes. Returns the number of sent bytes or <0 on error: */ static int PF_SendChunkIP(FILEHANDLE *curfile, POSITION *position, int to, LONG thesize) { LONG l=thesize; if( ISLESSPOS(*position,curfile->POposition) || ISGEPOSINC(*position,curfile->POposition, ((curfile->POfull-curfile->PObuffer)*sizeof(WORD)-thesize) ) ){ if(curfile->handle< 0) l=(curfile->POfull-curfile->PObuffer)*sizeof(WORD) - (LONG)(position->p1); else{ PF_SetScratch(curfile,position); if( ISGEPOSINC(*position,curfile->POposition, ((curfile->POfull-curfile->PObuffer)*sizeof(WORD)-thesize) ) ) l=(curfile->POfull-curfile->PObuffer)*sizeof(WORD) - (LONG)position->p1; } } /*Now we are able to sent l bytes from the curfile->PObuffer[position-curfile->POposition]*/ if(PF_RawSend(to,curfile->PObuffer+ (DIFBASE(*position,curfile->POposition))/sizeof(WORD),l,0)) return(-1); return(l); } /* #] PF_SendChunkIP : #[ PF_RecvChunkIP : thesize is in bytes. Returns the number of sent bytes or <0 on error: */ static int PF_RecvChunkIP(FILEHANDLE *curfile, int from, LONG thesize) { LONG receivedBytes; if( (LONG)((curfile->POstop - curfile->POfull)*sizeof(WORD)) < thesize ) if(PF_pushScratch(curfile)) return(-1); /*Now there is enough space from curfile->POfill to curfile->POstop*/ {/*Block:*/ int tag=0; receivedBytes=PF_RawRecv(&from,curfile->POfull,thesize,&tag); }/*:Block*/ if(receivedBytes >= 0 ){ curfile->POfull+=receivedBytes/sizeof(WORD); curfile->POfill=curfile->POfull; }/*if(receivedBytes >= 0 )*/ return(receivedBytes); } /* #] PF_RecvChunkIP : #[ PF_WalkThrough : Returns: >= 0 -- initial offset, -1 -- the first element of t contains the length of the tail of compressed term, <= -2 -- -(d+2), where d is the number of extra transferred elements. Expects: l -- initial offset or -1, chunk -- number of transferred elements (not bytes!) *count -- incremented each time a new term is found */ static int PF_WalkThrough(WORD *t, LONG l, LONG chunk, LONG *count) { if(l<0) /*==-1!*/ l=(*t)+1;/*the first element of t contains the length of the tail of compressed term*/ else{ if(l>=chunk)/*next term is out of the chunk*/ return(l-chunk); t+=l; chunk-=l;/*note, l was less than chunk so chunk >0!*/ l=*t; } /*Main loop:*/ while(l!=0){ if(l>0){/*an offset to the next term*/ if(l0!*/ l=*t; (*count)++; }/*if(l0)*/ else{ /* l<0 */ if(chunk < 2)/*i.e., chunk == 1*/ return(-1);/*the first WORD in the next chunk is length of the tail of the compressed term*/ l=*(t+1)+2;/*+2 since 1. t points to the length field -1, 2. the size of a tail of compressed term is equal to the number of WORDs in this tail*/ } }/*while(l!=0)*/ return(-1-chunk);/* -(2+(chunk-1)), chunk>0 ! */ } /* #] PF_WalkThrough : #] InParallel mode : #[ PF_SendFile : */ #define PF_SNDFILEBUFSIZE 4096 /** * Sends a file to the process specified by \a to. * * @param to the destination process number. * @param fd the file to be sent. * @return the size of sent data in bytes, or -1 on error. */ int PF_SendFile(int to, FILE *fd) { size_t len=0; if(fd == NULL){ if(PF_RawSend(to,&to,sizeof(int),PF_EMPTY_MSGTAG)) return(-1); return(0); } for(;;){ char buf[PF_SNDFILEBUFSIZE]; size_t l; l=fread(buf, 1, PF_SNDFILEBUFSIZE, fd); len+=l; if(l==PF_SNDFILEBUFSIZE){ if(PF_RawSend(to,buf,PF_SNDFILEBUFSIZE,PF_BUFFER_MSGTAG)) return(-1); } else{ if(PF_RawSend(to,buf,l,PF_ENDBUFFER_MSGTAG)) return(-1); break; } }/*for(;;)*/ return(len); } /* #] PF_SendFile : #[ PF_RecvFile : */ /** * Receives a file from the process specified by \a from. * * @param from the source process number. * @param fd the file to save the received data. * @return the size of received data in bytes, or -1 on error. */ int PF_RecvFile(int from, FILE *fd) { size_t len=0; int tag; do{ char buf[PF_SNDFILEBUFSIZE]; int l; l=PF_RawRecv(&from,buf,PF_SNDFILEBUFSIZE,&tag); if(l<0) return(-1); if(tag == PF_EMPTY_MSGTAG) return(-1); if( fwrite(buf,l,1,fd)!=1 ) return(-1); len+=l; }while(tag!=PF_ENDBUFFER_MSGTAG); return(len); } /* #] PF_RecvFile : #[ Synchronised output : #[ Explanations : */ /* * If the master and slaves output statistics or error messages to the same stream * or file (e.g., the standard output or the log file) simultaneously, then * a mixing of their outputs can occur. To avoid this, TFORM uses a lock of * ErrorMessageLock, but there is no locking functionality in the original MPI * specification. We need to synchronise the output from the master and slaves. * * The idea of the synchronised output (by, e.g., MesPrint()) implemented here is * Slaves: * 1. Save the output by WriteFile() (set to PF_WriteFileToFile()) * into some buffers between MLOCK(ErrorMessageLock) and * MUNLOCK(ErrorMessageLock), which call PF_MLock() and PF_MUnlock(), * respectively. The output for AM.StdOut and AC.LogHandle are saved to * the buffers. * 2. At MUNLOCK(ErrorMessageLock), send the output in the buffer to the master, * with PF_STDOUT_MSGTAG or PF_LOG_MSGTAG. * Master: * 1. Receive the buffered output from slaves, and write them by * WriteFileToFile(). * The main problem is how and where the master receives messages from * the slaves (PF_ReceiveErrorMessage()). For this purpose there are three * helper functions: PF_CatchErrorMessages() and PF_CatchErrorMessagesForAll() * which remove messages with PF_STDOUT_MSGTAG or PF_LOG_MSGTAG from the top * of the message queue, and PF_ProbeWithCatchingErrorMessages() which is same as * PF_Probe() except removing these messages. */ /* #] Explanations : #[ Variables : */ static int errorMessageLock = 0; /* (slaves) The lock count. See PF_MLock() and PF_MUnlock(). */ static Vector(UBYTE, stdoutBuffer); /* (slaves) The buffer for AM.StdOut. */ static Vector(UBYTE, logBuffer); /* (slaves) The buffer for AC.LogHandle. */ #define recvBuffer logBuffer /* (master) The buffer for receiving messages. */ /* * If PF_ENABLE_STDOUT_BUFFERING is defined, the master performs the line buffering * (using stdoutBuffer) at PF_WriteFileToFile(). */ #ifndef PF_ENABLE_STDOUT_BUFFERING #ifdef UNIX #define PF_ENABLE_STDOUT_BUFFERING #endif #endif /* #] Variables : #[ PF_MLock : */ /** * A function called by MLOCK(ErrorMessageLock) for slaves. */ void PF_MLock(void) { assert(PF.me != MASTER); if ( errorMessageLock++ > 0 ) return; VectorClear(stdoutBuffer); VectorClear(logBuffer); } /* #] PF_MLock : #[ PF_MUnlock : */ /** * A function called by MUNLOCK(ErrorMessageLock) for slaves. */ void PF_MUnlock(void) { assert(PF.me != MASTER); if ( --errorMessageLock > 0 ) return; if ( !VectorEmpty(stdoutBuffer) ) { PF_RawSend(MASTER, VectorPtr(stdoutBuffer), VectorSize(stdoutBuffer), PF_STDOUT_MSGTAG); } if ( !VectorEmpty(logBuffer) ) { PF_RawSend(MASTER, VectorPtr(logBuffer), VectorSize(logBuffer), PF_LOG_MSGTAG); } } /* #] PF_MUnlock : #[ PF_WriteFileToFile : */ /** * Replaces WriteFileToFile() on the master and slaves. * * It copies the given buffer into internal buffers if called between * MLOCK(ErrorMessageLock) and MUNLOCK(ErrorMessageLock) for slaves and * handle is StdOut or LogHandle, otherwise calls WriteFileToFile(). * * @param handle a file handle that specifies the output. * @param buffer a pointer to the source buffer containing the data to be written. * @param size the size of data to be written in bytes. * @return the actual size of data written to the output in bytes. */ LONG PF_WriteFileToFile(int handle, UBYTE *buffer, LONG size) { if ( PF.me != MASTER && errorMessageLock > 0 ) { if ( handle == AM.StdOut ) { VectorPushBacks(stdoutBuffer, buffer, size); return size; } else if ( handle == AC.LogHandle ) { VectorPushBacks(logBuffer, buffer, size); return size; } } #ifdef PF_ENABLE_STDOUT_BUFFERING /* * On my computer, sometimes a single linefeed "\n" sent to the standard * output is ignored on the execution of mpiexec. A typical example is: * $ cat foo.c * #include * int main() { * write(1, " ", 4); * write(1, "\n", 1); * write(1, " ", 4); * write(1, "123\n", 4); * return 0; * } * or even as a shell script: * $ cat foo.sh * #! bin/sh * printf " " * printf "\n" * printf " " * printf "123\n" * When I ran it on mpiexec * $ while :; do mpiexec -np 1 ./foo.sh; done * I observed the single linefeed (printf "\n") was sometimes ignored. Even * though this phenomenon might be specific to my environment, I added this * code because someone may encounter a similar phenomenon and feel it * frustrating. (TU 16 Jun 2011) * * Phenomenon: * A single linefeed sent to the standard output occasionally ignored * on mpiexec. * * Environment: * openSUSE 11.4 (x86_64) * kernel: 2.6.37.6-0.5-desktop * gcc: 4.5.1 20101208 * mpich2-1.3.2p1 configured with '--enable-shared --with-pm=smpd' * * Solution: * In Unix (in which Uwrite() calls write() system call without any buffering), * we perform the line buffering here. A single linefeed is also buffered. * * XXX: * At the end of the program the buffered output (text without LF) will not be flushed, * i.e., will not be written to the standard output. This is not problematic at a normal run. * The buffer can be explicitly flushed by PF_FlushStdOutBuffer(). */ if ( PF.me == MASTER && handle == AM.StdOut ) { size_t oldsize; /* Assume the newline character is LF (when UNIX is defined). */ if ( (size > 0 && buffer[size - 1] != LINEFEED) || (size == 1 && buffer[0] == LINEFEED) ) { VectorPushBacks(stdoutBuffer, buffer, size); return size; } if ( (oldsize = VectorSize(stdoutBuffer)) > 0 ) { LONG ret; VectorPushBacks(stdoutBuffer, buffer, size); ret = WriteFileToFile(handle, VectorPtr(stdoutBuffer), VectorSize(stdoutBuffer)); VectorClear(stdoutBuffer); if ( ret < 0 ) { return ret; } else if ( ret < (LONG)oldsize ) { return 0; /* This means the buffered output in previous calls is lost. */ } else { return ret - (LONG)oldsize; } } } #endif return WriteFileToFile(handle, buffer, size); } /* #] PF_WriteFileToFile : #[ PF_FlushStdOutBuffer : */ /** * Explicitly Flushes the buffer for the standard output on the master, which is * used if PF_ENABLE_STDOUT_BUFFERING is defined. */ void PF_FlushStdOutBuffer(void) { #ifdef PF_ENABLE_STDOUT_BUFFERING if ( PF.me == MASTER && VectorSize(stdoutBuffer) > 0 ) { WriteFileToFile(AM.StdOut, VectorPtr(stdoutBuffer), VectorSize(stdoutBuffer)); VectorClear(stdoutBuffer); } #endif } /* #] PF_FlushStdOutBuffer : #[ PF_ReceiveErrorMessage : */ /** * Receives an error message from a slave's PF_MUnlock() call, and writes * the message to the corresponding output. * instead of LOCK(ErrorMessageLock) and UNLOCK(ErrorMessageLock). * * @param src the source process. * @param tag the tag value (must be PF_STDOUT_MSGTAG or PF_LOG_MSGTAG or PF_ANY_MSGTAG). */ static void PF_ReceiveErrorMessage(int src, int tag) { assert(PF.me == MASTER); int size; int ret = PF_RawProbe(&src, &tag, &size); CHECK(ret == 0); switch ( tag ) { case PF_STDOUT_MSGTAG: case PF_LOG_MSGTAG: VectorReserve(recvBuffer, size); ret = PF_RawRecv(&src, VectorPtr(recvBuffer), size, &tag); CHECK(ret == size); if ( size > 0 ) { int handle = (tag == PF_STDOUT_MSGTAG) ? AM.StdOut : AC.LogHandle; #ifdef PF_ENABLE_STDOUT_BUFFERING if ( handle == AM.StdOut ) PF_WriteFileToFile(handle, VectorPtr(recvBuffer), size); else #endif WriteFileToFile(handle, VectorPtr(recvBuffer), size); } break; } } /* #] PF_ReceiveErrorMessage : #[ PF_CatchErrorMessages : */ /** * Processes all incoming messages whose tag is PF_STDOUT_MSGTAG * or PF_LOG_MSGTAG. It ensures that the next PF_Receive(src, tag, ...) * will not receive the message with PF_STDOUT_MSGTAG or PF_LOG_MSGTAG. * This function also handles PF_RUNTIME_ERROR_MSGTAG. * * @param[in,out] src the source process. * @param[in,out] tag the tag value. */ static void PF_CatchErrorMessages(int *src, int *tag) { for (;;) { int asrc = *src; int atag = *tag; int ret = PF_RawProbe(&asrc, &atag, NULL); CHECK(ret == 0); if ( atag == PF_STDOUT_MSGTAG || atag == PF_LOG_MSGTAG ) { assert(PF.me == MASTER); PF_ReceiveErrorMessage(asrc, atag); continue; } if ( atag == PF_RUNTIME_ERROR_MSGTAG ) { PF_ReceiveRuntimeError(); } *src = asrc; *tag = atag; break; } } /* #] PF_CatchErrorMessages : #[ PF_CatchErrorMessagesForAll : */ /** * Calls PF_CatchErrorMessages() for all slaves and PF_ANY_MSGTAG. * Note that it is NOT equivalent to PF_CatchErrorMessages() with PF_ANY_SOURCE. */ static void PF_CatchErrorMessagesForAll(void) { assert(PF.me == MASTER); int i; for ( i = 1; i < PF.numtasks; i++ ) { int src = i; int tag = PF_ANY_MSGTAG; PF_CatchErrorMessages(&src, &tag); } } /* #] PF_CatchErrorMessagesForAll : #[ PF_ProbeWithCatchingErrorMessages : */ /** * Same as PF_Probe() except processing incoming messages with PF_STDOUT_MSGTAG * and PF_LOG_MSGTAG. * This function also handles PF_RUNTIME_ERROR_MSGTAG. * * @param[in,out] src the source process. The output value is that of the actual found message. * @return the tag value of the next incoming message if found, * 0 if a nonblocking probe (input src != PF_ANY_SOURCE) did not * find any messages. The negative returned value indicates an error. */ static int PF_ProbeWithCatchingErrorMessages(int *src) { for (;;) { int newsrc = *src; int tag = PF_Probe(&newsrc); if ( tag == PF_STDOUT_MSGTAG || tag == PF_LOG_MSGTAG ) { assert(PF.me == MASTER); PF_ReceiveErrorMessage(newsrc, tag); continue; } if ( tag == PF_RUNTIME_ERROR_MSGTAG ) { PF_ReceiveRuntimeError(); } *src = newsrc; return tag; } } /* #] PF_ProbeWithCatchingErrorMessages : #[ PF_FreeErrorMessageBuffers : */ /** * Frees the buffers allocated for the synchronized output. * * Currently, not used anywhere, but could be used in PF_Terminate(). */ void PF_FreeErrorMessageBuffers(void) { VectorFree(stdoutBuffer); VectorFree(logBuffer); } /* #] PF_FreeErrorMessageBuffers : #] Synchronised output : #[ Handling runtime errors : #[ PF_RaiseRuntimeError : */ /** * Sends a runtime error message to the master if called on a slave, * or broadcasts it to the slaves if called on the master. * Called via PF_PreTerminate() when Terminate() is called with a negative value. */ static void PF_RaiseRuntimeError(void) { if ( PF.me == MASTER ) { PF_BroadcastRuntimeError(); } else { int ret, dummy; ret = PF_RawSend(MASTER, &dummy, 0, PF_RUNTIME_ERROR_MSGTAG); CHECK(ret == 0); int src = MASTER; int tag = PF_RUNTIME_ERROR_MSGTAG; ret = PF_RawRecv(&src, &dummy, 0, &tag); CHECK(ret == 0); } } /* #] PF_RaiseRuntimeError : #[ PF_BroadcastRuntimeError : */ /** * Broadcasts a runtime error message from the master to all slaves * and collects one reply from each slave. */ static void PF_BroadcastRuntimeError(void) { assert(PF.me == MASTER); int ret, dummy; MPI_Request requests[PF.numtasks - 1]; /* * Notify all slaves of program termination by sending PF_RUNTIME_ERROR_MSGTAG. * This must be non-blocking to avoid deadlock if some slaves have already * performed a blocking send. */ for ( int i = 1; i < PF.numtasks; i++ ) { ret = PF_RawIsend(i, &dummy, 0, PF_BYTE, PF_RUNTIME_ERROR_MSGTAG, &requests[i - 1]); CHECK(ret == 0); } /* * Receive exactly one PF_RUNTIME_SYNC_MSGTAG or PF_RUNTIME_ERROR_MSGTAG * message from each slave. */ for ( int i = 1; i < PF.numtasks; i++ ) { retry: int asrc = PF_ANY_SOURCE; // blocking probe int tag = PF_Probe(&asrc); CHECK(tag >= 0); assert(1 <= asrc && asrc < PF.numtasks); switch ( tag ) { case PF_STDOUT_MSGTAG: case PF_LOG_MSGTAG: PF_ReceiveErrorMessage(asrc, tag); goto retry; case PF_RUNTIME_ERROR_MSGTAG: case PF_RUNTIME_SYNC_MSGTAG: ret = PF_RawRecv(&asrc, &dummy, 0, &tag); CHECK(ret == 0); break; default: ret = PF_Discard(&asrc, &tag); CHECK(ret == 0); goto retry; } } ret = PF_RawWaitAll(PF.numtasks - 1, requests, MPI_STATUSES_IGNORE); CHECK(ret == 0); } /* #] PF_BroadcastRuntimeError : #[ PF_PostEndSortBarrier : */ /** * Synchronization after EndSort(). * Ensures that all processes have completed without runtime errors. */ void PF_PostEndSortBarrier(void) { assert(PF_processing); PF_processing = 0; int ret, dummy; /* * Each slave reports either PF_RUNTIME_SYNC_MSGTAG (completed without errors) * or PF_RUNTIME_ERROR_MSGTAG (see PF_RaiseRuntimeError()) * to the master. After collecting one message from each slave, the master sends * PF_RUNTIME_SYNC_MSGTAG to all slaves on success, * or PF_RUNTIME_ERROR_MSGTAG otherwise. * * This matches the behaviour of PF_RaiseRuntimeError() and * PF_ReceiveRuntimeError(). In all cases, each slave sends exactly one * PF_RUNTIME_SYNC_MSGTAG or PF_RUNTIME_ERROR_MSGTAG message to the master, * and the master sends exactly one such message to each slave. */ if ( PF.me == MASTER ) { int error = 0; for ( int i = 1; i < PF.numtasks; i++ ) { retry: int asrc = PF_ANY_SOURCE; // blocking probe int tag = PF_Probe(&asrc); CHECK(tag >= 0); assert(1 <= asrc && asrc < PF.numtasks); switch ( tag ) { case PF_STDOUT_MSGTAG: case PF_LOG_MSGTAG: PF_ReceiveErrorMessage(asrc, tag); goto retry; case PF_RUNTIME_ERROR_MSGTAG: error = 1; ret = PF_RawRecv(&asrc, &dummy, 0, &tag); CHECK(ret == 0); break; case PF_RUNTIME_SYNC_MSGTAG: ret = PF_RawRecv(&asrc, &dummy, 0, &tag); CHECK(ret == 0); break; default: MesPrint("!!!Unexpected MPI message src=%d tag=%d.", asrc, tag); ret = PF_Discard(&asrc, &tag); CHECK(ret == 0); goto retry; } } for ( int i = 1; i < PF.numtasks; i++ ) { ret = PF_RawSend(i, &dummy, 0, error ? PF_RUNTIME_ERROR_MSGTAG : PF_RUNTIME_SYNC_MSGTAG); CHECK(ret == 0); } } else { int tag; ret = PF_RawSend(MASTER, &dummy, 0, PF_RUNTIME_SYNC_MSGTAG); CHECK(ret == 0); int src = MASTER; ret = PF_RawRecv(&src, &dummy, 0, &tag); CHECK(ret == 0); switch ( tag ) { case PF_RUNTIME_SYNC_MSGTAG: break; case PF_RUNTIME_ERROR_MSGTAG: PF.notMyFault = 1; Terminate(-1); break; default: MesPrint("!!!Unexpected MPI message src=%d tag=%d.", src, tag); break; } } } /* #] PF_PostEndSortBarrier : #[ PF_ReceiveRuntimeError : */ /** * Handles a runtime error message received from another process. * It ultimately calls Terminate(-1). */ void PF_ReceiveRuntimeError(void) { PF_processing = 0; PF.notMyFault = 1; if ( PF.me == MASTER ) { PF_BroadcastRuntimeError(); } else { int ret, dummy; int src = MASTER; int tag = PF_RUNTIME_ERROR_MSGTAG; ret = PF_RawRecv(&src, &dummy, 0, &tag); CHECK(ret == 0); ret = PF_RawSend(MASTER, &dummy, 0, PF_RUNTIME_ERROR_MSGTAG); CHECK(ret == 0); } Terminate(-1); } /* #] PF_ReceiveRuntimeError : #] Handling runtime errors : */ form-5.0.1/sources/compress.c0000644000175100017510000004574115217035721011643 /** @file compress.c * * The routines for the use of gzip (de)compression of the information * in the sort file. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #include "form3.h" #ifdef WITHZLIB /* #define GZIPDEBUG Low level routines for dealing with zlib during sorting and handling the scratch files. Work started 5-sep-2005. The .sor file handling was more or less completed on 8-sep-2005 The handling of the scratch files still needs some thinking. Complications are: gzip compression should be per expression, not per buffer. No gzip compression for expressions with a bracket index. Separate decompression buffers for expressions in the rhs. This last one will involve more buffer work and organization. Information about compression should be stored for each expr. (including what method/program was used) Note: Be careful with compression. By far the most compact method is the original problem.... #[ Variables : The following variables are to contain the intermediate buffers for the inflation of the various patches in the sort file. There can be up to MaxFpatches (FilePatches in the setup) and hence we can have that many streams simultaneously. We set this up once and only when needed. (in struct A.N or AB[threadnum].N) Bytef **AN.ziobufnum; Bytef *AN.ziobuffers; */ /* #] Variables : #[ SetupOutputGZIP : Routine prepares a gzip output stream for the given file. */ int SetupOutputGZIP(FILEHANDLE *f) { GETIDENTITY if ( AT.SS != AT.S0 ) return(0); if ( AR.NoCompress == 1 ) return(0); if ( AR.gzipCompress <= 0 ) return(0); if ( f->ziobuffer == 0 ) { /* 1: Allocate a struct for the gzip stream: */ f->zsp = Malloc1(sizeof(z_stream),"output zstream"); /* 2: Allocate the output buffer. */ f->ziobuffer = (Bytef *)Malloc1(f->ziosize*sizeof(char),"output zbuffer"); if ( f->zsp == 0 || f->ziobuffer == 0 ) { MLOCK(ErrorMessageLock); MesCall("SetupOutputGZIP"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } /* 3: Set the default fields: */ f->zsp->zalloc = Z_NULL; f->zsp->zfree = Z_NULL; f->zsp->opaque = Z_NULL; /* 4: Set the output space: */ f->zsp->next_out = f->ziobuffer; f->zsp->avail_out = f->ziosize; f->zsp->total_out = 0; /* 5: Set the input space: */ f->zsp->next_in = (Bytef *)(f->PObuffer); f->zsp->avail_in = (Bytef *)(f->POfill) - (Bytef *)(f->PObuffer); f->zsp->total_in = 0; /* 6: Initiate the deflation */ if ( deflateInit(f->zsp,AR.gzipCompress) != Z_OK ) { MLOCK(ErrorMessageLock); MesPrint("Error from zlib: %s",f->zsp->msg); MesCall("SetupOutputGZIP"); MUNLOCK(ErrorMessageLock); Terminate(-1); } return(0); } /* #] SetupOutputGZIP : #[ PutOutputGZIP : Routine is called when the PObuffer of f is full. The contents of it will be compressed and whenever the output buffer f->ziobuffer is full it will be written and the output buffer will be reset. Upon exit the input buffer will be cleared. */ int PutOutputGZIP(FILEHANDLE *f) { GETIDENTITY int zerror; /* First set the number of bytes in the input */ f->zsp->next_in = (Bytef *)(f->PObuffer); f->zsp->avail_in = (Bytef *)(f->POfill) - (Bytef *)(f->PObuffer); f->zsp->total_in = 0; while ( ( zerror = deflate(f->zsp,Z_NO_FLUSH) ) == Z_OK ) { if ( f->zsp->avail_out == 0 ) { /* ziobuffer is full. Write the output. */ #ifdef GZIPDEBUG { char *s = (char *)((UBYTE *)(f->ziobuffer)+f->ziosize); MLOCK(ErrorMessageLock); MesPrint("%wWriting %l bytes at %10p: %d %d %d %d %d" ,f->ziosize,&(f->POposition),s[-5],s[-4],s[-3],s[-2],s[-1]); MUNLOCK(ErrorMessageLock); } #endif #ifdef ALLLOCK LOCK(f->pthreadslock); #endif if ( f == AR.hidefile ) { LOCK(AS.inputslock); } SeekFile(f->handle,&(f->POposition),SEEK_SET); if ( WriteFile(f->handle,(UBYTE *)(f->ziobuffer),f->ziosize) != f->ziosize ) { if ( f == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif MLOCK(ErrorMessageLock); MesPrint("%wWrite error during compressed sort. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } if ( f == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif ADDPOS(f->filesize,f->ziosize); ADDPOS(f->POposition,f->ziosize); #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch ) { if ( f->handle >= 0 ) SynchFile(f->handle); } #endif /* Reset the output */ f->zsp->next_out = f->ziobuffer; f->zsp->avail_out = f->ziosize; f->zsp->total_out = 0; } else if ( f->zsp->avail_in == 0 ) { /* We compressed everything and it sits in ziobuffer. Finish */ return(0); } else { MLOCK(ErrorMessageLock); MesPrint("%w avail_in = %d, avail_out = %d.",f->zsp->avail_in,f->zsp->avail_out); MUNLOCK(ErrorMessageLock); break; } } MLOCK(ErrorMessageLock); MesPrint("%wError in gzip handling of output. zerror = %d",zerror); MUNLOCK(ErrorMessageLock); return(-1); } /* #] PutOutputGZIP : #[ FlushOutputGZIP : Routine is called to flush a stream. The compression of the input buffer will be completed and the contents of f->ziobuffer will be written. Both buffers will be cleared. */ int FlushOutputGZIP(FILEHANDLE *f) { GETIDENTITY int zerror; /* Set the proper parameters */ f->zsp->next_in = (Bytef *)(f->PObuffer); f->zsp->avail_in = (Bytef *)(f->POfill) - (Bytef *)(f->PObuffer); f->zsp->total_in = 0; while ( ( zerror = deflate(f->zsp,Z_FINISH) ) == Z_OK ) { if ( f->zsp->avail_out == 0 ) { /* Write the output */ #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%wWriting %l bytes at %10p",f->ziosize,&(f->POposition)); MUNLOCK(ErrorMessageLock); #endif #ifdef ALLLOCK LOCK(f->pthreadslock); #endif if ( f == AR.hidefile ) { UNLOCK(AS.inputslock); } SeekFile(f->handle,&(f->POposition),SEEK_SET); if ( WriteFile(f->handle,(UBYTE *)(f->ziobuffer),f->ziosize) != f->ziosize ) { if ( f == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif MLOCK(ErrorMessageLock); MesPrint("%wWrite error during compressed sort. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } if ( f == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif ADDPOS(f->filesize,f->ziosize); ADDPOS(f->POposition,f->ziosize); #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch ) { if ( f->handle >= 0 ) SynchFile(f->handle); } #endif /* Reset the output */ f->zsp->next_out = f->ziobuffer; f->zsp->avail_out = f->ziosize; f->zsp->total_out = 0; } } if ( zerror == Z_STREAM_END ) { /* Write the output */ #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%wWriting %l bytes at %10p",(LONG)(f->zsp->avail_out),&(f->POposition)); MUNLOCK(ErrorMessageLock); #endif #ifdef ALLLOCK LOCK(f->pthreadslock); #endif if ( f == AR.hidefile ) { LOCK(AS.inputslock); } SeekFile(f->handle,&(f->POposition),SEEK_SET); if ( WriteFile(f->handle,(UBYTE *)(f->ziobuffer),f->zsp->total_out) != (LONG)(f->zsp->total_out) ) { if ( f == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif MLOCK(ErrorMessageLock); MesPrint("%wWrite error during compressed sort. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } if ( f == AR.hidefile ) { LOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif ADDPOS(f->filesize,f->zsp->total_out); ADDPOS(f->POposition,f->zsp->total_out); #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch ) { if ( f->handle >= 0 ) SynchFile(f->handle); } #endif #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); { char *s = f->ziobuffer+f->zsp->total_out; MesPrint("%w Last bytes written: %d %d %d %d %d",s[-5],s[-4],s[-3],s[-2],s[-1]); } MesPrint("%w Perceived position in FlushOutputGZIP is %10p",&(f->POposition)); MUNLOCK(ErrorMessageLock); #endif /* Reset the output */ f->zsp->next_out = f->ziobuffer; f->zsp->avail_out = f->ziosize; f->zsp->total_out = 0; if ( ( zerror = deflateEnd(f->zsp) ) == Z_OK ) return(0); MLOCK(ErrorMessageLock); if ( f->zsp->msg ) { MesPrint("%wError in finishing gzip handling of output: %s",f->zsp->msg); } else { MesPrint("%wError in finishing gzip handling of output."); } MUNLOCK(ErrorMessageLock); } else { MLOCK(ErrorMessageLock); MesPrint("%wError in gzip handling of output."); MUNLOCK(ErrorMessageLock); } return(-1); } /* #] FlushOutputGZIP : #[ SetupAllInputGZIP : Routine prepares all gzip input streams for a merge. Problem (29-may-2008): If we never use GZIP compression, this routine will still allocate the array space. This is an enormous amount! It places an effective restriction on the value of SortIOsize */ int SetupAllInputGZIP(SORTING *S) { GETIDENTITY int i, NumberOpened = 0; z_streamp zsp; /* This code was added 29-may-2008 by JV to prevent further processing if there is no compression at all (usually). */ for ( i = 0; i < S->inNum; i++ ) { if ( S->fpincompressed[i] ) break; } if ( i >= S->inNum ) return(0); if ( S->zsparray == 0 ) { S->zsparray = (z_streamp)Malloc1(sizeof(z_stream)*S->MaxFpatches,"input zstreams"); if ( S->zsparray == 0 ) { MLOCK(ErrorMessageLock); MesCall("SetupAllInputGZIP"); MUNLOCK(ErrorMessageLock); Terminate(-1); } /* We add 128 bytes in the hope that if it can happen that it goes outside the buffer during decompression, it does not do damage. */ AN.ziobuffers = (Bytef *)Malloc1(S->MaxFpatches*(S->file.ziosize+128)*sizeof(Bytef),"input raw buffers"); /* This seems to be one of the really stupid errors: We allocate way too much space. Way way way too much. AN.ziobufnum = (Bytef **)Malloc1(S->MaxFpatches*S->file.ziosize*sizeof(Bytef *),"input raw pointers"); */ AN.ziobufnum = (Bytef **)Malloc1(S->MaxFpatches*sizeof(Bytef *),"input raw pointers"); if ( AN.ziobuffers == 0 || AN.ziobufnum == 0 ) { MLOCK(ErrorMessageLock); MesCall("SetupAllInputGZIP"); MUNLOCK(ErrorMessageLock); Terminate(-1); } for ( i = 0 ; i < S->MaxFpatches; i++ ) { AN.ziobufnum[i] = AN.ziobuffers + i * (S->file.ziosize+128); } } for ( i = 0; i < S->inNum; i++ ) { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%wPreparing z-stream %d with compression %d",i,S->fpincompressed[i]); MUNLOCK(ErrorMessageLock); #endif if ( S->fpincompressed[i] ) { zsp = &(S->zsparray[i]); /* 1: Set the default fields: */ zsp->zalloc = Z_NULL; zsp->zfree = Z_NULL; zsp->opaque = Z_NULL; /* 2: Set the output space: */ zsp->next_out = Z_NULL; zsp->avail_out = 0; zsp->total_out = 0; /* 3: Set the input space temporarily: */ zsp->next_in = Z_NULL; zsp->avail_in = 0; zsp->total_in = 0; /* 4: Initiate the inflation */ if ( inflateInit(zsp) != Z_OK ) { MLOCK(ErrorMessageLock); if ( zsp->msg ) MesPrint("%wError from inflateInit: %s",zsp->msg); else MesPrint("%wError from inflateInit"); MesCall("SetupAllInputGZIP"); MUNLOCK(ErrorMessageLock); Terminate(-1); } NumberOpened++; } } return(NumberOpened); } /* #] SetupAllInputGZIP : #[ FillInputGZIP : Routine is called when we need new input in the specified buffer. This buffer is used for the output and we keep reading and uncompressing input till either this buffer is full or the input stream is finished. The return value is the number of bytes in the buffer. */ LONG FillInputGZIP(FILEHANDLE *f, POSITION *position, UBYTE *buffer, LONG buffersize, int numstream) { GETIDENTITY int zerror; LONG readsize, toread = 0; SORTING *S = AT.SS; z_streamp zsp; POSITION pos; if ( S->fpincompressed[numstream] ) { zsp = &(S->zsparray[numstream]); zsp->next_out = (Bytef *)buffer; zsp->avail_out = buffersize; zsp->total_out = 0; if ( zsp->avail_in == 0 ) { /* First loading of the input */ if ( ISGEPOSINC(S->fPatchesStop[numstream],*position,f->ziosize) ) { toread = f->ziosize; } else { DIFPOS(pos,S->fPatchesStop[numstream],*position); toread = (LONG)(BASEPOSITION(pos)); } if ( toread > 0 ) { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w-+Reading %l bytes in stream %d at position %10p; stop at %10p",toread,numstream,position,&(S->fPatchesStop[numstream])); MUNLOCK(ErrorMessageLock); #endif #ifdef ALLLOCK LOCK(f->pthreadslock); #endif SeekFile(f->handle,position,SEEK_SET); readsize = ReadFile(f->handle,(UBYTE *)(AN.ziobufnum[numstream]),toread); SeekFile(f->handle,position,SEEK_CUR); #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); { char *s = AN.ziobufnum[numstream]+readsize; MesPrint("%w read: %l +Last bytes read: %d %d %d %d %d in %s, newpos = %10p",readsize,s[-5],s[-4],s[-3],s[-2],s[-1],f->name,position); } MUNLOCK(ErrorMessageLock); #endif if ( readsize == 0 ) { zsp->next_in = AN.ziobufnum[numstream]; zsp->avail_in = f->ziosize; zsp->total_in = 0; return(zsp->total_out); } if ( readsize < 0 ) { MLOCK(ErrorMessageLock); MesPrint("%wFillInputGZIP: Read error during compressed sort."); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(f->filesize,readsize); ADDPOS(f->POposition,readsize); /* Set the input */ zsp->next_in = AN.ziobufnum[numstream]; zsp->avail_in = readsize; zsp->total_in = 0; } } if ( toread > 0 || zsp->avail_in ) { while ( ( zerror = inflate(zsp,Z_NO_FLUSH) ) == Z_OK ) { if ( zsp->avail_out == 0 ) { /* Finish */ return((LONG)(zsp->total_out)); } if ( zsp->avail_in == 0 ) { if ( ISEQUALPOS(S->fPatchesStop[numstream],*position) ) { /* We finished this stream. Try to terminate. */ zerror = Z_STREAM_END; break; /* if ( ( zerror = inflate(zsp,Z_SYNC_FLUSH) ) == Z_OK ) { return((LONG)(zsp->total_out)); } else break; */ /* #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%wClosing stream %d",numstream); #endif readsize = zsp->total_out; #ifdef GZIPDEBUG if ( readsize > 0 ) { WORD *s = (WORD *)(buffer+zsp->total_out); MesPrint("%w Last words: %d %d %d %d %d",s[-5],s[-4],s[-3],s[-2],s[-1]); } else { MesPrint("%w No words"); } MUNLOCK(ErrorMessageLock); #endif if ( ( zerror = inflateEnd(zsp) ) == Z_OK ) return(readsize); break; */ } /* Read more input */ #ifdef GZIPDEBUG if ( numstream == 0 ) { MLOCK(ErrorMessageLock); MesPrint("%wWant to read in stream 0 at position %10p",position); MUNLOCK(ErrorMessageLock); } #endif if ( ISGEPOSINC(S->fPatchesStop[numstream],*position,f->ziosize) ) { toread = f->ziosize; } else { DIFPOS(pos,S->fPatchesStop[numstream],*position); toread = (LONG)(BASEPOSITION(pos)); } #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w--Reading %l bytes in stream %d at position %10p",toread,numstream,position); MUNLOCK(ErrorMessageLock); #endif #ifdef ALLLOCK LOCK(f->pthreadslock); #endif SeekFile(f->handle,position,SEEK_SET); readsize = ReadFile(f->handle,(UBYTE *)(AN.ziobufnum[numstream]),toread); SeekFile(f->handle,position,SEEK_CUR); #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); { char *s = AN.ziobufnum[numstream]+readsize; MesPrint("%w Last bytes read: %d %d %d %d %d",s[-5],s[-4],s[-3],s[-2],s[-1]); } MUNLOCK(ErrorMessageLock); #endif if ( readsize == 0 ) { zsp->next_in = AN.ziobufnum[numstream]; zsp->avail_in = f->ziosize; zsp->total_in = 0; return(zsp->total_out); } if ( readsize < 0 ) { MLOCK(ErrorMessageLock); MesPrint("%wFillInputGZIP: Read error during compressed sort."); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(f->filesize,readsize); ADDPOS(f->POposition,readsize); /* Reset the input */ zsp->next_in = AN.ziobufnum[numstream]; zsp->avail_in = readsize; zsp->total_in = 0; } else { break; } } } else { zerror = Z_STREAM_END; zsp->total_out = 0; } #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w zerror = %d in stream %d. At position %10p",zerror,numstream,position); MUNLOCK(ErrorMessageLock); #endif if ( zerror == Z_STREAM_END ) { /* Reset the input */ zsp->next_in = Z_NULL; zsp->avail_in = 0; zsp->total_in = 0; /* Make the final call and finish */ #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%wClosing stream %d",numstream); #endif readsize = zsp->total_out; #ifdef GZIPDEBUG if ( readsize > 0 ) { WORD *s = (WORD *)(buffer+zsp->total_out); MesPrint("%w -Last words: %d %d %d %d %d",s[-5],s[-4],s[-3],s[-2],s[-1]); } else { MesPrint("%w No words"); } MUNLOCK(ErrorMessageLock); #endif if ( zsp->zalloc != Z_NULL ) { zerror = inflateEnd(zsp); zsp->zalloc = Z_NULL; } if ( zerror == Z_OK || zerror == Z_STREAM_END ) return(readsize); } MLOCK(ErrorMessageLock); MesPrint("%wFillInputGZIP: Error in gzip handling of input. zerror = %d",zerror); MUNLOCK(ErrorMessageLock); return(-1); } else { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w++Reading %l bytes at position %10p",buffersize,position); MUNLOCK(ErrorMessageLock); #endif #ifdef ALLLOCK LOCK(f->pthreadslock); #endif SeekFile(f->handle,position,SEEK_SET); readsize = ReadFile(f->handle,buffer,buffersize); SeekFile(f->handle,position,SEEK_CUR); #ifdef ALLLOCK UNLOCK(f->pthreadslock); #endif if ( readsize < 0 ) { MLOCK(ErrorMessageLock); MesPrint("%wFillInputGZIP: Read error during uncompressed sort."); MesPrint("%w++Reading %l bytes at position %10p",buffersize,position); MUNLOCK(ErrorMessageLock); } return(readsize); } } /* #] FillInputGZIP : #[ ClearSortGZIP : */ void ClearSortGZIP(FILEHANDLE *f) { if ( f->ziobuffer ) { M_free(f->ziobuffer,"output zbuffer"); M_free(f->zsp,"output zstream"); f->ziobuffer = 0; } } /* #] ClearSortGZIP : */ #endif form-5.0.1/sources/message.c0000644000175100017510000005641215217035721011431 /** @file message.c * * Contains the routines that write messages. * This includes the very important routine MesPrint which is the * FORM equivalent of printf but then with escape sequences that are * relevant for symbolic manipulation. * The FORM statement Print "...." is passed almost literally to MesPrint. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : The static variables for the messages can remain as such also for the parallel version as messages are to be locked to avoid problems with simultaneous messages. */ #include "form3.h" static int iswarning = 0; static char hex[] = {'0','1','2','3','4','5','6','7','8','9', 'A','B','C','D','E','F'}; /* #] Includes : #[ exit : #[ Error0 : */ NORETURN void Error0(char *s) { MesPrint("=== %s",s); Terminate(-1); } /* #] Error0 : #[ Error1 : */ NORETURN void Error1(char *s, UBYTE *t) { MesPrint("@%s %s",s,t); Terminate(-1); } /* #] Error1 : #[ Error2 : */ NORETURN void Error2(char *s1, char *s2, UBYTE *t) { MesPrint("@%s%s %s",s1,s2,t); Terminate(-1); } /* #] Error2 : #[ MesWork : */ NORETURN void MesWork(void) { MesPrint("=== Workspace overflow. %l bytes is not enough.",AM.WorkSize); MesPrint("=== Change parameter WorkSpace in %s",setupfilename); Terminate(-1); } /* #] MesWork : #[ MesPrint : Kind of a printf function for simple messages. The main concern is getting the arguments in a portable way. Note: many compilers have errors when sizeof(WORD) < sizeof(int) %a array of size n WORDs (two parameters, first is int, second WORD *) %b array of size n UBYTEs (two parameters, first is int, second UBYTE *) %C array of size n chars (two parameters, first is int, second char *) %d word; %l long; %L long long *; %s string; %#i unsigned word filled %#d word positioned %#l long word positioned. %#L long long word * positioned. %#s string positioned. %#p position in file. %r The current term in raw format (internal representation) %t The current term (AN.currentTerm) %T The current term (AN.currentTerm) with its sign %w Number of the thread(worker) %$ The next $ in AN.listinprint %x hexadecimal. Takes 8 places. Mainly for debugging. %% % %# # # " ==> " @ " ==> " Preprocessor error & ' --> ' Regular compiler error Each call is terminated with a new line. Put a % at the end of the string to suppress the new line. New feature (7-dec-2011): The & will only work when we do not block it from the execution of the print statement because we need the & also for the tabulator in the print "" statement. */ int MesPrint(const char *fmt, ... ) { GETIDENTITY char Out[MAXLINELENGTH+14], *stopper, *t, *s, *u, c, *carray; UBYTE extrabuffer[MAXLINELENGTH+14]; int w, x, i, specialerror = 0; LONG num, y; WORD *array; UBYTE *oldoutfill = AO.OutputLine, *barray; /*[19apr2004 mt]:*/ LONG (*OldWrite)(int handle, UBYTE *buffer, LONG size) = WriteFile; /*:[19apr2004 mt]*/ va_list ap; va_start(ap,fmt); s = (char *)fmt; #ifdef WITHMPI /* * On slaves, if AS.printflag is * = 0 : print nothing. * > 0 : synchronized output. All text will be sent to the master * in the next MUNLOCK(). * < 0 : normal output. */ if ( PF.me != MASTER && AS.printflag == 0 ) return(0); if ( PF.me == MASTER || AS.printflag < 0 ) #endif FLUSHCONSOLE; /* * MesPrints() never prints a message to an external channel even if * WriteFile is set to &WriteToExternalChannel. */ #ifdef WITHMPI WriteFile = PF.me == MASTER || AS.printflag > 0 ? &PF_WriteFileToFile : &WriteFileToFile; #else WriteFile = &WriteFileToFile; #endif AO.OutputLine = extrabuffer; t = Out; stopper = Out + AC.LineLength; while ( *s ) { if ( ( ( *s == '&' && AO.ErrorBlock == 0 ) || *s == '@' || *s == '#' ) && AC.CurrentStream != 0 ) { u = (char *)AC.CurrentStream->name; while ( *u ) { *t++ = *u++; if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); num = 0; t = Out; } } *t++ = ' '; if ( t+20 >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); num = 0; t = Out; } *t++ = 'L'; *t++ = 'i'; *t++ = 'n'; *t++ = 'e'; *t++ = ' '; if ( *s == '&' ) y = AC.CurrentStream->prevline; else y = AC.CurrentStream->linenumber; t = LongCopy(y,t); if ( !iswarning && ( *s == '&' || *s == '@' ) ) { for ( i = 0; i < NumDoLoops; i++ ) DoLoops[i].errorsinloop = 1; } } if ( ( *s == '&' && AO.ErrorBlock == 0 ) ) { *t++ = ' '; *t++ = '-'; *t++ = '-'; *t++ = '>'; *t++ = ' '; s++; } else if ( *s == '@' || *s == '#' ) { *t++ = ' '; *t++ = '='; *t++ = '='; *t++ = '>'; *t++ = ' '; s++; } /* else if ( *s == '&' && AO.ErrorBlock == 1 ) { } */ else if ( *s != '%' ) { *t++ = *s++; if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); num = 0; t = Out; } } else { s++; if ( *s == 'd' ) { if ( ( w = va_arg(ap, int) ) < 0 ) { *t++ = '-'; w = -w; } t = (char *)NumCopy(w,(UBYTE *)t); } else if ( *s == 'l' ) { if ( ( y = va_arg(ap, LONG) ) < 0 ) { *t++ = '-'; y = -y; } t = LongCopy(y,t); } /* #ifdef __GLIBC_HAVE_LONG_LONG */ else if ( *s == 'p' ) { POSITION *pp; off_t ly; pp = va_arg(ap, POSITION *); ly = BASEPOSITION(*pp); if ( ly < 0 ) { *t++ = '-'; ly = -ly; } /*----change 10-feb-2003 did not have & */ t = LongLongCopy(&(ly),t); } /* #endif */ else if ( *s == 'c' ) { c = (char)(va_arg(ap, int)); *t++ = c; *t = 0; } else if ( *s == 'a' ) { w = va_arg(ap, int); array = va_arg(ap,WORD *); while ( w > 0 ) { t = (char *)NumCopy(*array,(UBYTE *)t); if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); t = Out; *t++ = ' '; } *t++ = ' '; w--; array++; } } else if ( *s == 'b' ) { w = va_arg(ap, int); barray = va_arg(ap,UBYTE *); while ( w > 0 ) { *t++ = hex[((*barray)>>4)&0xF]; *t++ = hex[(*barray)&0xF]; *t = 0; if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); t = Out; *t++ = ' '; } *t++ = ' '; w--; barray++; } } else if ( *s == 'C' ) { w = va_arg(ap, int); carray = va_arg(ap,char *); while ( w > 0 ) { if ( *carray < 32 ) *t++ = '^'; else *t++ = *carray; *t = 0; if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); t = Out; *t++ = ' '; } w--; carray++; } } else if ( *s == 'I' ) { int *iarray; w = va_arg(ap, int); iarray = va_arg(ap,int *); while ( w > 0 ) { t = (char *)LongCopy((LONG)(*iarray),(char *)t); if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); t = Out; *t++ = ' '; } *t++ = ' '; w--; array++; } } else if ( *s == 'E' ) { LONG *larray; w = va_arg(ap, int); larray = va_arg(ap,LONG *); while ( w > 0 ) { t = (char *)LongCopy(*larray,(char *)t); if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); t = Out; *t++ = ' '; } *t++ = ' '; w--; array++; } } else if ( *s == 's' ) { u = va_arg(ap,char *); while ( *u ) { if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); t = Out; } *t++ = *u++; } *t = 0; } else if ( *s == 't' || *s == 'T' ) { WORD oldskip = AO.OutSkip, noleadsign; WORD oldmode = AC.OutputMode; WORD oldbracket = AO.IsBracket; WORD oldlength = AC.LineLength; UBYTE *oldStop = AO.OutStop; if ( AN.currentTerm ) { if ( AC.LineLength > MAXLINELENGTH ) AC.LineLength = MAXLINELENGTH; AO.IsBracket = 0; AO.OutSkip = 1; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; AddToLine((UBYTE *)Out); if ( *s == 'T' ) noleadsign = 1; else noleadsign = 0; if ( WriteInnerTerm(AN.currentTerm,noleadsign) ) Terminate(-1); t = Out; u = (char *)AO.OutputLine; *(AO.OutFill) = 0; while ( u < (char *)(AO.OutFill) ) *t++ = *u++; *t = 0; AO.OutSkip = oldskip; AC.OutputMode = oldmode; AO.IsBracket = oldbracket; AC.LineLength = oldlength; AO.OutStop = oldStop; } } else if ( *s == 'r' ) { WORD oldskip = AO.OutSkip; WORD oldmode = AC.OutputMode; WORD oldbracket = AO.IsBracket; WORD oldlength = AC.LineLength; UBYTE *oldStop = AO.OutStop; if ( AN.currentTerm ) { WORD *tt = AN.currentTerm; if ( AC.LineLength > MAXLINELENGTH ) AC.LineLength = MAXLINELENGTH; AO.IsBracket = 0; AO.OutSkip = 1; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; i = *tt; while ( --i >= 0 ) { t = (char *)NumCopy(*tt,(UBYTE *)t); tt++; if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); num = 0; t = Out; } *t++ = ' '; *t++ = ' '; } *t = 0; AO.OutSkip = oldskip; AC.OutputMode = oldmode; AO.IsBracket = oldbracket; AC.LineLength = oldlength; AO.OutStop = oldStop; } } else if ( *s == '$' ) { /* #[ dollars : */ WORD oldskip = AO.OutSkip; WORD oldmode = AC.OutputMode; WORD oldbracket = AO.IsBracket; WORD oldlength = AC.LineLength; UBYTE *oldStop = AO.OutStop; WORD *term, indsubterm[3], *tt; WORD value[5], first, num; if ( *AN.listinprint != DOLLAREXPRESSION ) { specialerror = 1; } else { DOLLARS d = Dollars + AN.listinprint[1]; #ifdef WITHPTHREADS int nummodopt, dtype; dtype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( AN.listinprint[1] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif AO.IsBracket = 0; AO.OutSkip = 0; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; AddToLine((UBYTE *)Out); if ( d->nfactors >= 1 && AN.listinprint[2] == DOLLAREXPR2 ) { if ( d->type == 0 || ( d->factors == 0 && d->nfactors != 1 ) ) goto dollarzero; num = EvalDoLoopArg(BHEAD AN.listinprint+2,-1); if ( num == 0 ) { value[0] = 4; value[1] = d->nfactors; value[2] = 1; value[3] = 3; value[4] = 0; term = value; goto printterms; } if ( num == 1 && d->nfactors == 1 ) { term = d->where; if ( *term == 0 ) goto dollarzero; goto printterms; } if ( num > d->nfactors ) { MesPrint("\nFactor number for dollar is too large."); Terminate(-1); } term = d->factors[num-1].where; if ( term == 0 ) { if ( d->factors[num-1].value < 0 ) { value[0] = 4; value[1] = -d->factors[num-1].value; value[2] = 1; value[3] = -3; value[4] = 0; } else { value[0] = 4; value[1] = d->factors[num-1].value; value[2] = 1; value[3] = 3; value[4] = 0; } term = value; } goto printterms; } if ( d->type == DOLTERMS || d->type == DOLNUMBER ) { term = d->where; printterms: first = 1; do { if ( AC.LineLength > MAXLINELENGTH ) AC.LineLength = MAXLINELENGTH; AO.IsBracket = 0; AO.OutSkip = 1; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; AddToLine((UBYTE *)Out); if ( WriteInnerTerm(term,first) ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif Terminate(-1); } first = 0; t = Out; u = (char *)AO.OutputLine; *(AO.OutFill) = 0; while ( u < (char *)(AO.OutFill) ) *t++ = *u++; *t = 0; AO.OutSkip = oldskip; AC.OutputMode = oldmode; AO.IsBracket = oldbracket; AC.LineLength = oldlength; AO.OutStop = oldStop; term += *term; } while ( *term ); AO.OutSkip = oldskip; } else if ( d->type == DOLSUBTERM ) { tt = d->where; dosubterm: if ( AC.LineLength > MAXLINELENGTH ) AC.LineLength = MAXLINELENGTH; AO.IsBracket = 0; AO.OutSkip = 1; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; AddToLine((UBYTE *)Out); if ( WriteSubTerm(tt,1) ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif Terminate(-1); } t = Out; u = (char *)AO.OutputLine; *(AO.OutFill) = 0; while ( u < (char *)(AO.OutFill) ) *t++ = *u++; *t = 0; AO.OutSkip = oldskip; AC.OutputMode = oldmode; AO.IsBracket = oldbracket; AC.LineLength = oldlength; AO.OutStop = oldStop; } else if ( d->type == DOLUNDEFINED ) { *t++ = '*'; *t++ = '*'; *t++ = '*'; *t = 0; } else if ( d->type == DOLZERO ) { dollarzero: *t++ = '0'; *t = 0; } else if ( d->type == DOLINDEX ) { tt = indsubterm; *tt = INDEX; tt[1] = 3; tt[2] = d->index; goto dosubterm; } else if ( d->type == DOLARGUMENT ) { if ( AC.LineLength > MAXLINELENGTH ) AC.LineLength = MAXLINELENGTH; AO.IsBracket = 0; AO.OutSkip = 1; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; AddToLine((UBYTE *)Out); WriteArgument(d->where); t = Out; u = (char *)AO.OutputLine; *(AO.OutFill) = 0; while ( u < (char *)(AO.OutFill) ) *t++ = *u++; *t = 0; AO.OutSkip = oldskip; AC.OutputMode = oldmode; AO.IsBracket = oldbracket; AC.LineLength = oldlength; AO.OutStop = oldStop; } else if ( d->type == DOLWILDARGS ) { tt = d->where; if ( *tt == 0 ) { tt++; while ( *tt ) { if ( AC.LineLength > MAXLINELENGTH ) AC.LineLength = MAXLINELENGTH; AO.IsBracket = 0; AO.OutSkip = 1; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; AddToLine((UBYTE *)Out); WriteArgument(tt); NEXTARG(tt); if ( *tt ) TokenToLine((UBYTE *)","); t = Out; u = (char *)AO.OutputLine; *(AO.OutFill) = 0; while ( u < (char *)(AO.OutFill) ) *t++ = *u++; *t = 0; AO.OutSkip = oldskip; AC.OutputMode = oldmode; AO.IsBracket = oldbracket; AC.LineLength = oldlength; AO.OutStop = oldStop; } } else if ( *tt > 0 ) { /* Tensor arguments */ i = *tt++; while ( --i >= 0 ) { indsubterm[0] = INDEX; indsubterm[1] = 3; indsubterm[2] = *tt++; if ( AC.LineLength > MAXLINELENGTH ) AC.LineLength = MAXLINELENGTH; AO.IsBracket = 0; AO.OutSkip = 1; AC.OutputMode = 0; AO.OutFill = AO.OutputLine; AO.OutStop = AO.OutputLine + AC.LineLength; *t = 0; AddToLine((UBYTE *)Out); if ( WriteSubTerm(indsubterm,1) ) Terminate(-1); if ( i > 0 ) TokenToLine((UBYTE *)","); t = Out; u = (char *)AO.OutputLine; *(AO.OutFill) = 0; while ( u < (char *)(AO.OutFill) ) *t++ = *u++; *t = 0; AO.OutSkip = oldskip; AC.OutputMode = oldmode; AO.IsBracket = oldbracket; AC.LineLength = oldlength; AO.OutStop = oldStop; } } } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif AN.listinprint += 2; while ( AN.listinprint[0] == DOLLAREXPR2 ) AN.listinprint += 2; } /* #] dollars : */ } #ifdef WITHPTHREADS else if ( *s == 'W' ) { /* number of the thread with time */ LONG millitime; WORD timepart; t = (char *)NumCopy(identity,(UBYTE *)t); millitime = TimeCPU(1); timepart = (WORD)(millitime%1000); millitime /= 1000; timepart /= 10; *t++ = '('; *t = 0; t = (char *)LongCopy(millitime,(char *)t); *t++ = '.'; *t = 0; t = (char *)NumCopy(timepart,(UBYTE *)t); *t++ = ')'; *t = 0; if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); num = 0; t = Out; } } else if ( *s == 'w' ) { /* number of the thread */ t = (char *)NumCopy(identity,(UBYTE *)t); } #elif defined(WITHMPI) else if ( *s == 'W' ) { /* number of the thread with time */ LONG millitime; WORD timepart; t = (char *)NumCopy(PF.me,(UBYTE *)t); millitime = TimeCPU(1); timepart = (WORD)(millitime%1000); millitime /= 1000; timepart /= 10; *t++ = '('; *t = 0; t = (char *)LongCopy(millitime,(char *)t); *t++ = '.'; *t = 0; t = (char *)NumCopy(timepart,(UBYTE *)t); *t++ = ')'; *t = 0; if ( t >= stopper ) { num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); num = 0; t = Out; } } else if ( *s == 'w' ) { /* number of the thread */ t = (char *)NumCopy(PF.me,(UBYTE *)t); } #else else if ( *s == 'w' ) { } else if ( *s == 'W' ) { } #endif else if ( FG.cTable[(int)*s] == 1 ) { x = *s++ - '0'; while ( FG.cTable[(int)*s] == 1 ) x = 10 * x + *s++ - '0'; if ( *s == 'l' || *s == 'd' ) { if ( *s == 'l' ) { y = va_arg(ap,LONG); } else { y = va_arg(ap,int); } if ( y < 0 ) { y = -y; w = 1; } else w = 0; u = t + x; do { *--u = y%10+'0'; y /= 10; } while ( y && u > t ); if ( w && u > t ) *--u = '-'; while ( --u >= t ) *u = ' '; t += x; } else if ( *s == 's' ) { u = va_arg(ap,char *); i = 0; while ( *u ) { i++; u++; } if ( i > x ) i = x; while ( x > i ) { *t++ = ' '; x--; } t += x; while ( --i >= 0 ) { *--t = *--u; } t += x; } else if ( *s == 'p' ) { POSITION *pp; /*#ifdef __GLIBC_HAVE_LONG_LONG */ off_t ly; /* #else LONG ly; #endif */ pp = va_arg(ap,POSITION *); ly = BASEPOSITION(*pp); u = t + x; do { *--u = ly%10+'0'; ly /= 10; } while ( ly && u > t ); while ( --u >= t ) *u = ' '; t += x; } else if ( *s == 'i' ) { w = va_arg(ap, int); u = t + x; do { *--u = (char)(w%10+'0'); w /= 10; } while ( u > t ); t += x; } else { w = va_arg(ap, int); u = t + x; do { *--u = (char )(w%10+'0'); w /= 10; } while ( w && u > t ); while ( --u >= t ) *u = ' '; t += x; } } else if ( *s == 'x' ) { char ccc; y = va_arg(ap, LONG); i = 2*sizeof(LONG); while ( --i > 0 ) { ccc = ( y >> (i*4) ) & 0xF; if ( ccc ) break; } do { ccc = ( y >> (i*4) ) & 0xF; *t++ = hex[(int)ccc]; } while ( --i >= 0 ); } else if ( *s == '#' ) *t++ = *s; else if ( *s == '%' ) *t++ = *s; else if ( *s == 0 ) { *t++ = 0; break; } else if ( *s == '&' ) { *t++ = *s; } else { *t++ = '%'; s--; } s++; } } num = t - Out; WriteString(ERROROUT,(UBYTE *)Out,num); va_end(ap); if ( specialerror == 1 ) { MesPrint("!!!Wrong object in Print statement!!!"); MesPrint("!!!Object encountered is of a different type as in the format specifier"); } AO.OutputLine = oldoutfill; /*[19apr2004 mt]:*/ WriteFile=OldWrite; /*:[19apr2004 mt]*/ return(-1); } /* #] MesPrint : #[ Warning : */ void Warning(char *s) { iswarning = 1; if ( AC.WarnFlag ) MesPrint("&Warning: %s",s); iswarning = 0; } /* #] Warning : #[ HighWarning : */ void HighWarning(char *s) { iswarning = 1; if ( AC.WarnFlag >= 2 ) MesPrint("&Warning: %s",s); iswarning = 0; } /* #] HighWarning : #[ MesCall : */ int MesCall(char *s) { return(MesPrint((char *)"Called from %s",s)); } /* #] MesCall : #[ MesCerr : */ int MesCerr(char *s, UBYTE *t) { UBYTE *u, c; WORD i = 11; u = t; while ( *u && --i >= 0 ) u--; u++; c = *++t; *t = 0; MesPrint("&Illegal %s: %s",s,u); *t = c; return(-1); } /* #] MesCerr : #[ MesComp : */ int MesComp(char *s, UBYTE *p, UBYTE *q) { UBYTE c; c = *++q; *q = 0; MesPrint("&%s: %s",s,p); *q = c; return(-1); } /* #] MesComp : #[ PrintTerm : */ void PrintTerm(WORD *term, char *where) { UBYTE OutBuf[140]; WORD *t, x; int i; AO.OutFill = AO.OutputLine = OutBuf; t = term; AO.OutSkip = 3; FiniLine(); TokenToLine((UBYTE *)where); TokenToLine((UBYTE *)": "); i = *t; while ( --i >= 0 ) { x = *t++; if ( x < 0 ) { x = -x; TokenToLine((UBYTE *)"-"); } TalToLine((UWORD)(x)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); } /* #] PrintTerm : #[ PrintTermC : */ void PrintTermC(WORD *term, char *where) { UBYTE OutBuf[140]; WORD *t, x; int i; if ( *term >= 0 ) { PrintTerm(term,where); return; } AO.OutFill = AO.OutputLine = OutBuf; t = term; AO.OutSkip = 3; FiniLine(); TokenToLine((UBYTE *)where); TokenToLine((UBYTE *)": "); i = t[1]+2; while ( --i >= 0 ) { x = *t++; if ( x < 0 ) { x = -x; TokenToLine((UBYTE *)"-"); } TalToLine((UWORD)(x)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); } /* #] PrintTermC : #[ PrintSubTerm : */ void PrintSubTerm(WORD *term, char *where) { UBYTE OutBuf[140]; WORD *t; int i; AO.OutFill = AO.OutputLine = OutBuf; t = term; AO.OutSkip = 3; FiniLine(); TokenToLine((UBYTE *)where); TokenToLine((UBYTE *)": "); i = t[1]; while ( --i >= 0 ) { TalToLine((UWORD)(*t++)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); } /* #] PrintSubTerm : #[ PrintWords : */ void PrintWords(WORD *buffer, LONG number) { UBYTE OutBuf[140]; WORD *t; AO.OutFill = AO.OutputLine = OutBuf; t = buffer; AO.OutSkip = 3; FiniLine(); while ( --number >= 0 ) { TalToLine((UWORD)(*t++)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); } /* #] PrintWords : #[ PrintSeq : */ void PrintSeq(WORD *a,char *text) { MesPrint(" %s:",text); while ( *a ) { MesPrint(" %a",a[0],a); a += *a; } } /* #] PrintSeq : #] exit : */ form-5.0.1/sources/flintinterface.h0000644000175100017510000001436315217035721013006 #pragma once /** @file flintinterface.h * * Prototypes for functions in flintinterface.cc */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ extern "C" { #include "form3.h" } #if defined(WINDOWS) // flint.h defines WORD(xx), which conflicts with the one defined in form3.h. #undef WORD #endif #include #if __FLINT_RELEASE >= 30000 #include #endif #include #include #include #include #include #if defined(WINDOWS) // Redefine WORD here to match form3.h. #undef WORD #define WORD FORM_WORD #endif #include #include #include #include #include // The bits of std that are needed: using std::cout; using std::endl; using std::fill; using std::map; using std::swap; using std::string; using std::vector; namespace flint { typedef std::map var_map_t; // Small wrappers around the flint structs to enable RAII init and clear. "d" represents the // data, and this member will be passed to flint functions. class fmpz { public: fmpz_t d; fmpz() { fmpz_init(d); } ~fmpz() { fmpz_clear(d); } void print(const string& text) { cout << text; fmpz_print(d); cout << endl; } }; class poly { public: fmpz_poly_t d; poly() { fmpz_poly_init(d); } ~poly() { fmpz_poly_clear(d); } void print(const string& text) { cout << text; fmpz_poly_print_pretty(d, "x"); cout << endl; } }; class poly_factor { public: fmpz_poly_factor_t d; poly_factor() { fmpz_poly_factor_init(d); } ~poly_factor() { fmpz_poly_factor_clear(d); } }; class mpoly { private: fmpz_mpoly_ctx_struct *ctx; // We need to keep a copy of the context pointer for clearing. public: fmpz_mpoly_t d; explicit mpoly(fmpz_mpoly_ctx_struct *ctx_in) : ctx(ctx_in) { fmpz_mpoly_init(d, ctx); } ~mpoly() { fmpz_mpoly_clear(d, ctx); } void print(const string& text) { cout << text; fmpz_mpoly_print_pretty(d, 0, ctx); cout << endl; } }; class mpoly_factor { private: fmpz_mpoly_ctx_struct *ctx; // We need to keep a copy of the context pointer for clearing. public: fmpz_mpoly_factor_t d; explicit mpoly_factor(fmpz_mpoly_ctx_struct *ctx_in) : ctx(ctx_in) { fmpz_mpoly_factor_init(d, ctx); } ~mpoly_factor() { fmpz_mpoly_factor_clear(d, ctx); } }; class mpoly_ctx { public: fmpz_mpoly_ctx_t d; explicit mpoly_ctx(int64_t nvars) { fmpz_mpoly_ctx_init(d, nvars, ORD_LEX); } ~mpoly_ctx() { fmpz_mpoly_ctx_clear(d); } }; void cleanup(void); void cleanup_master(void); WORD* divmod_mpoly(PHEAD const WORD *, const WORD *, const bool, const WORD, const var_map_t &, const bool); WORD* divmod_poly(PHEAD const WORD *, const WORD *, const bool, const WORD, const var_map_t &); WORD* factorize_mpoly(PHEAD const WORD *, WORD *, const bool, const bool, const var_map_t &, const bool); WORD* factorize_poly(PHEAD const WORD *, WORD *, const bool, const bool, const var_map_t &); void form_sort(PHEAD WORD *); uint64_t from_argument_mpoly(fmpz_mpoly_t, fmpz_mpoly_t, const WORD *, const bool, const var_map_t &, const fmpz_mpoly_ctx_t); uint64_t from_argument_poly(fmpz_poly_t, fmpz_poly_t, const WORD *, const bool); WORD fmpz_get_form(fmpz_t, WORD *); void fmpz_set_form(fmpz_t, UWORD *, WORD); WORD* gcd_mpoly(PHEAD const WORD *, const WORD *, const WORD, const var_map_t &, const bool); WORD* gcd_poly(PHEAD const WORD *, const WORD *, const WORD, const var_map_t &); var_map_t get_variables(const vector &, const bool, const bool); WORD* inverse_poly(PHEAD const WORD *, const WORD *, const var_map_t &); WORD* mul_mpoly(PHEAD const WORD *, const WORD *, const var_map_t &, const bool); WORD* mul_poly(PHEAD const WORD *, const WORD *, const var_map_t &); void ratfun_add_mpoly(PHEAD const WORD *, const WORD *, WORD *, const var_map_t &, const bool); void ratfun_add_poly(PHEAD const WORD *, const WORD *, WORD *, const var_map_t &); void ratfun_normalize_mpoly(PHEAD WORD *, const var_map_t &, const bool); void ratfun_normalize_poly(PHEAD WORD *, const var_map_t &); void ratfun_read_mpoly(const WORD *, fmpz_mpoly_t, fmpz_mpoly_t, const var_map_t &, fmpz_mpoly_ctx_t); void ratfun_read_poly(const WORD *, fmpz_poly_t, fmpz_poly_t); uint64_t to_argument_mpoly(PHEAD WORD *, const bool, const bool, const bool, const uint64_t, const fmpz_mpoly_t, const var_map_t &, const fmpz_mpoly_ctx_t, const bool); uint64_t to_argument_mpoly(PHEAD WORD *, const bool, const bool, const bool, const uint64_t, const fmpz_mpoly_t, const var_map_t &, const fmpz_mpoly_ctx_t, const bool, const fmpz_t); uint64_t to_argument_poly(PHEAD WORD *, const bool, const bool, const bool, const uint64_t, const fmpz_poly_t, const var_map_t &); uint64_t to_argument_poly(PHEAD WORD *, const bool, const bool, const bool, const uint64_t, const fmpz_poly_t, const var_map_t &, const fmpz_t); namespace util { void simplify_fmpz(fmpz_t, fmpz_t, fmpz_t); void simplify_fmpz_poly(fmpz_poly_t, fmpz_poly_t, fmpz_poly_t); void fix_sign_fmpz_mpoly_ratfun(fmpz_mpoly_t, fmpz_mpoly_t, const fmpz_mpoly_ctx_t); void fix_sign_fmpz_poly_ratfun(fmpz_poly_t, fmpz_poly_t); } } form-5.0.1/sources/diagrams.c0000644000175100017510000004726415217035721011601 /** @file diagrams.c * * Contains the wrapper routines for diagram manipulations. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : diagrams.c */ #include "form3.h" static WORD one = 1; /* #] Includes : #[ CoCanonicalize : Syntax: Canonicalize,mainoption,... With the main options currently: Canonicalize,topology,vertexfunction,edgefunction,OutDollar,extraoptions; Canonicalize,polynomial,InDollar,set_or_setname_or_dollar,OutDollar,extraoptions; The vertex function needs to have the format (assume it is called vx): vx(p1,p2,-p3) or vx(-p1,p2,p3,-p4) etc. The external lines have a vertex with only one line. All momenta that form connections should be unique. In principle the - signs are not relevant for the topology, but they may exist already in the remaining part of the diagram. They are also part of the canonical form. The edge function can be used in different ways, depending on the options. The extraoption(s) should be nonnegative integers or $variables that evaluate into nonnegative integers (integers less than 2^31). The Indollar variable contains the polynomial to be canonicalized. The OutDollar variable should be the name of a $-variable (as in $out) which will be filled with a replace_ function. The canonicalization can then be executed in the whole term with the Multiply $out; command. */ int CoCanonicalize(UBYTE *s) { WORD args[10], *a, num; UBYTE *t, c; args[0] = TYPECANONICALIZE; a = args+2; while ( *s == ',' || *s == '\t' || *s == ' ' ) s++; t = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(t,(UBYTE *)("topology")) == 0 ) { *s = c; *a++ = 0; while ( *s == ',' || *s == '\t' || *s == ' ' ) s++; s = GetFunction(s,a); while ( *s == ',' || *s == '\t' || *s == ' ' ) s++; s = GetFunction(s,a+1); if ( *a == 0 || a[1] == 0 ) return(1); a += 2; } else if ( StrICmp(t,(UBYTE *)("polynomial")) == 0 ) { *s = c; *a++ = 1; while ( *s == ',' || *s == '\t' || *s == ' ' ) s++; /* Now get the name of the input $-variable */ if ( *s != '$' ) { MesPrint("&Canonicalize statement needs a $-variable for its input."); return(1); } s++; t = s; while ( FG.cTable[*s] < 2 ) s++; c = *s; *s = 0; if ( GetName(AC.dollarnames,t,&num,NOAUTO) == CDOLLAR ) *a++ = num; else { *a++ = AddDollar(t,DOLINDEX,&one,1); } *s = c; /* Now the set */ if ( *s == '{' ) { t = s+1; SKIPBRA2(s) c = *s; *s = 0; *a++ = DoTempSet(t,s); *s++ = c; } else if ( FG.cTable[*s] == 0 || *s == '[' ) { t = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Illegal name for set in Canonicalize statement: %s",t); return(1); } c = *s; *s = 0; if ( GetName(AC.varnames,t,a,WITHAUTO) == CSET ) { if ( Sets[*a].type != CSYMBOL ) { MesPrint("&In Canonicalize: %s is not a set of symbols.",t); return(1); } } else { MesPrint("&In Canonicalize: %s is not a set.",t); return(1); } *s = c; a++; } else if ( *s == '$' ) { s++; t = s; while ( FG.cTable[*s] < 2 ) s++; c = *s; *s = 0; if ( GetName(AC.dollarnames,t,&num,NOAUTO) == CDOLLAR ) *a++ = -num-2; else { MesPrint("&In Canonicalize: %s is undefined.",t-1); return(1); } *s = c; } else { MesPrint("&In Canonicalize: Illegal third(=set) argument."); return(1); } } else { MesPrint("&Unrecognized option in Canonicalize statement: %s",t); return(1); } /* Now get the name of the output $-variable */ while ( *s == ',' || *s == '\t' || *s == ' ' ) s++; if ( *s != '$' ) { MesPrint("&Canonicalize statement needs a $-variable for its output."); return(1); } s++; t = s; while ( FG.cTable[*s] < 2 ) s++; c = *s; *s = 0; if ( GetName(AC.dollarnames,t,&num,NOAUTO) == CDOLLAR ) *a++ = num; else { *a++ = AddDollar(t,DOLINDEX,&one,1); } *s = c; /* Now the options. At the moment we just do one of them. (the first extra option is relevant to determine the use of the edge function) In the future we may have to be more flexible. */ a[0] = 0; /* default value */ while ( *s == ',' || *s == '\t' || *s == ' ' ) s++; if ( *s != 0 ) { s = GetNumber(s,a); if ( *a == -1 ) return(1); while ( *s == ',' || *s == '\t' || *s == ' ' ) s++; a++; } /* Now complete the args string and put it in the compiler buffer */ args[1] = a-args; AddNtoL(args[1],args); return(0); } /* #] CoCanonicalize : #[ DoCanonicalize : Does the canonicalization. The output term overwrites the input term. */ int DoCanonicalize(PHEAD WORD *term, WORD *params) { WORD args[10]; int i; /* First check whether we need to expand dollars; */ for ( i = 0; i < params[1]; i++ ) args[i] = params[i]; if ( args[2] == 0 ) { /* topology */ for ( i = 3; i < 5; i++ ) { if ( args[i] < 0 ) { /* This is a dollar */ args[i] = DolToFunction(BHEAD -args[i]-2); if ( args[i] == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Value of $-variable in Canonicalize statement should be a function."); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } for ( i = 6; i < args[1]; i++ ) { /* Extra options */ if ( args[i] < 0 ) { /* This is a dollar */ args[i] = DolToNumber(BHEAD -args[i]-2); if ( args[i] < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Value of $-variable in Canonicalize statement should be a nonnegative number < %l.",(LONG)MAXPOSITIVE); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } switch ( args[6] ) { case 1: {/* pass the vertex and edge functions. */ WORD *tstop, *t, *tedge, *te; tstop = term + *term; tstop -= ABS(tstop[-1]); t = term+1; tedge = AT.WorkPointer; te = tedge+1; while ( t < tstop ) { if ( *t != args[3] && *t != args[4] ) { t += t[1]; continue; } for ( i = 0; i < t[1]; i++ ) te[i] = t[i]; te += t[1]; t += t[1]; } *te++ = 1; *te++ = 1; *te++ = 3; tedge[0] = te-tedge; AT.WorkPointer = te; /* DoVertexCanonicalize(BHEAD term,tedge,args[3],args[4],args[5],args[6]); */ AT.WorkPointer = tedge; } break; case 2: {/* pass the edge functions only */ WORD *tstop, *t, *tedge, *te; tstop = term + *term; tstop -= ABS(tstop[-1]); t = term+1; tedge = AT.WorkPointer; te = tedge+1; while ( t < tstop ) { if ( *t != args[4] ) { t += t[1]; continue; } for ( i = 0; i < t[1]; i++ ) te[i] = t[i]; te += t[1]; t += t[1]; } *te++ = 1; *te++ = 1; *te++ = 3; tedge[0] = te-tedge; AT.WorkPointer = te; /* DoEdgeCanonicalize(BHEAD term,tedge,args[5]); */ AT.WorkPointer = tedge; } break; default: { DoTopologyCanonicalize(BHEAD term,args[3],args[4],args+5); } break; } /* Call here the topology canonicalization We will have the arguments: args[3]: The function used as vertex function args[4]: The function used as edge function args[5]: The number of the dollar to be used for the output args[6]: Potentially other options (like saying how to use args[4]). term: The term in which the topology resides. */ } else if ( args[2] == 1 ) { /* polynomial */ WORD *symlist, nsymlist; for ( i = 6; i < args[1]; i++ ) { /* Extra options */ if ( args[i] < 0 ) { /* This is a dollar */ args[i] = DolToNumber(BHEAD -args[i]-2); if ( args[i] < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Value of $-variable in Canonicalize statement should be a nonnegative number < %l.",(LONG)MAXPOSITIVE); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } /* Now we sort out the set. We create a pointer to the list of set elements, and we determine the number of elements in the set. */ symlist = AT.WorkPointer; if ( args[4] < -1 ) { /* Dollar that should expand into a list of symbols */ DOLLARS d = Dollars - args[4] - 2; WORD *ds, *insym; if ( d->type != DOLWILDARGS ) { NoWildArg: MLOCK(ErrorMessageLock); MesPrint("Value of $-variable in Canonicalize statement should be a argument wildcard of symbol arguments."); MUNLOCK(ErrorMessageLock); Terminate(-1); } insym = symlist; ds = d->where+1; while ( *ds ) { if ( *ds != -SYMBOL ) goto NoWildArg; *insym++ = ds[1]; ds += 2; } nsymlist = insym-symlist; } else { /*if ( args[4] >= 0 ) */ WORD *ss, *sy, n; ss = (WORD *)(AC.SetElementList.lijst)+Sets[args[4]].first; nsymlist = n = Sets[args[4]].last-Sets[args[4]].first; sy = symlist = AT.WorkPointer; NCOPY(sy,ss,n); } AT.WorkPointer = symlist+nsymlist; /* Call here the polynomial canonicalization We will have the arguments: args[3]: The number of the dollar to be used for the input symlist: an array of symbols nsymlist: the number of symbols in symlist args[5]: The number of the dollar to be used for the output args[6]: Potentially other options. */ /* DoPolynomialCanonicalize(BHEAD args[3],symlist,nsymlist,args[5],args[6]); */ AT.WorkPointer = symlist; } return(0); } /* #] DoCanonicalize : #[ DoTopologyCanonicalize : term: The term vert: the vertex function edge: the edge function args[0]: the number of the output dollar args[1]: options return value should be zero if all is correct. The external lines connect to an 'external vertex' which has only one line. The vertices are of a type: vertex_(p1,p2,-p3)*vertex_(p3,p4,p5) etc. The edges indicate noninteger powers of the lines: edge_(p1,2) means 1/p1.p1^(2*ep) */ int DoTopologyCanonicalize(PHEAD WORD *term,WORD vert,WORD edge,WORD *args) { int nvert = 0, nvert2, i, ii, jj, flipnames = 0, nparts/*, level, num */; WORD *tstop, *t, *tt, *tend, *td; WORD *oldworkpointer = AT.WorkPointer; WORD *termcopy = TermMalloc("TopologyCanonize1"); WORD *vet= TermMalloc("TopologyCanonize2"); WORD *partition, *environ, *connect, *pparts, *p; /* WORD *pparts; */ WORD momenta[150],flips[50],nmomenta = 0, nflips = 0; /* Step one: the vertices should get a number. We copy the term for this. We need a high number for the vertex function to make sure that it comes after the edge function in the sorting. */ if ( args[0] < args[1] ) { flipnames = 1; } tend = term + *term; tend -= ABS(tend[-1]); t = term+1; tt = termcopy+1; while ( t < tend ) { if ( *t == vert ) { for ( i = FUNHEAD; i < t[1]; i += 2 ) { if ( t[i] == -VECTOR || ( t[i] == -INDEX && t[i+1] < 0 ) ) { momenta[nmomenta++] = -VECTOR; momenta[nmomenta++] = t[i+1]; } else if ( t[i] == -MINVECTOR ) { momenta[nmomenta++] = -MINVECTOR; momenta[nmomenta++] = t[i+1]; } else goto notgoodvertex; momenta[nmomenta++] = nvert; } ii = FUNHEAD; i = t[1]-FUNHEAD; NCOPY(tt,t,ii) if ( flipnames ) tt[-FUNHEAD] = edge; tt[-FUNHEAD+1] += 2; *tt++ = -CNUMBER; *tt++ = nvert++; } else if ( *t == edge && flipnames ) { i = t[1] - 1; *tt++ = vert; t++; } else { notgoodvertex: i = t[1]; } NCOPY(tt,t,i) } while ( t < tend ) *tt++ = *t++; termcopy[0] = tt - termcopy; if ( flipnames ) EXCH(edge,vert) nvert2 = nvert*nvert; /* Sort the momenta. Keep the sign order. */ for ( i = 0; i < nmomenta-3; i+=3 ) { jj = i; while ( jj >= 0 && momenta[jj+4] > momenta[jj+1] ) { EXCH(momenta[jj+5],momenta[jj+2]) EXCH(momenta[jj+4],momenta[jj+1]) EXCH(momenta[jj+3],momenta[jj]) jj -= 3; } } /* Step two: make now the edge functions in the proper notation. */ t = vet+1; for ( i = 0; i < nmomenta; i += 6 ) { if ( momenta[i] == -VECTOR && momenta[i+3] == -MINVECTOR && momenta[i+1] == momenta[i+4] ) { } else if ( momenta[i] == -MINVECTOR && momenta[i+3] == -VECTOR && momenta[i+1] == momenta[i+4] ) { flips[nflips++] = momenta[i+1]; DUMMYUSE(flips[nflips-1]); } else { /* something wrong with the momenta */ MLOCK(ErrorMessageLock); MesPrint("No momentum conservation or wrong momenta in Canonicalize statement"); MUNLOCK(ErrorMessageLock); Terminate(-1); } *t++ = EDGE; *t++ = FUNHEAD+10; FILLFUN(t) *t++ = -SNUMBER; *t++ = momenta[i+2]; *t++ = -SNUMBER; *t++ = momenta[i+5]; *t++ = -VECTOR; *t++ = momenta[i+1]; *t++ = -SNUMBER; *t++ = 0; /* provisional power/color, multiple of ep */ *t++ = -SNUMBER; *t++ = 0; /* provisional power/color, integer */ } tend = t; *t++ = 1; *t++ = 1; *t++ = 3; vet[0] = t-vet; *t = 0; /* Now the powers of the denominators */ tstop = termcopy+*termcopy; tstop -= ABS(tstop[-1]); td = termcopy+1; while ( td < tstop ) { if ( *td == edge && td[1] == FUNHEAD+4 ) { if ( td[FUNHEAD+2] == -SNUMBER && ( td[FUNHEAD] == -VECTOR || td[FUNHEAD] == -INDEX || td[FUNHEAD] == -MINVECTOR ) ) {} else { MLOCK(ErrorMessageLock); MesPrint("Illegal argument in edge function in Canonicalize statement"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = vet+1; while ( tt < tend ) { if ( tt[FUNHEAD+5] == td[FUNHEAD+1] ) { tt[FUNHEAD+7] = td[FUNHEAD+3]; break; } tt += tt[1]; } } else if ( *td == DOTPRODUCT ) break; td += td[1]; } if ( td < tstop ) { tt = vet+1; while ( tt < tend ) { /* tt[FUNHEAD+5] is a vector. We look for dotproducts with twice tt[FUNHEAD+5] */ for ( i = 2; i < td[1]; i += 3 ) { if ( td[i] == tt[FUNHEAD+5] && td[i+1] == tt[FUNHEAD+5] ) { tt[FUNHEAD+9] = td[i+2]; break; } } tt += tt[1]; } } Normalize(BHEAD vet); /* Now we have a term `vet' in the proper notation and we can start. To keep track of the shattering we use an array of 2*nvert. each entry is Number,marker When the marker is zero, the vertices are in the same partition. For the environment we need a matrix that is nvert x nvert At the same time we keep the connectivity matrix, because that will save much time later. The partitions are stored in a matrix as well. This allows them to be treated as a stack. The entries are separated by 0 if they belong to the same part, and by a 1 when they belong to different parts. */ partition = AT.WorkPointer; AT.WorkPointer += 2*nvert2; for ( i = 0; i < nvert; i++ ) { partition[2*i] = i; partition[2*i+1] = 0; } partition[2*i-1] = -1; /* end of the first part which is currently all vertices */ nparts = 1; connect = AT.WorkPointer; AT.WorkPointer += nvert2; for ( i = 0; i < nvert2; i++ ) connect[i] = 0; tstop = vet+*vet; tstop -= ABS(tstop[-1]); t = vet+1; while ( t < tstop ) { if ( *t == EDGE ) { connect[t[FUNHEAD+1]*nvert+t[FUNHEAD+3]]++; connect[t[FUNHEAD+3]*nvert+t[FUNHEAD+1]]++; } t += t[1]; } for ( i = 0; i < nvert; i++ ) { MesPrint("connectivity: %d -- %a",i,nvert,connect+i*nvert); } /* Create the environment matrix and sort it. */ environ = AT.WorkPointer; AT.WorkPointer += nvert2; /* And now the refinement process starts. */ WantAddPointers(nvert+1); for ( i = 0; i < nvert2; i++ ) environ[i] = 0; /* level = 0; */ pparts = partition; while ( nparts < nvert ) { nparts = DoShattering(BHEAD connect,environ,pparts,nvert); if ( nparts < nvert ) { /* raise level and make a copy and split a part */ p = pparts + 2*nvert; /* level++; */ for ( i = 0; i < 2*nvert; i++ ) p[i] = pparts[i]; for ( ii = 0; ii < 2*nvert; ii += 2 ) { if ( p[ii+1] == 0 ) { /* found a part with more than one */ /* num = 2; */ i = ii+2; while ( p[i+1] == 0 ) { /* num++; */ i += 2; } p[ii+1] = -1; pparts = p; break; } } } MesPrint("partition: %d -- %a",nparts,2*nvert,pparts); } /* Just for now */ PutTermInDollar(vet,args[0]); TermFree(vet,"TopologyCanonize2"); TermFree(termcopy,"TopologyCanonize1"); AT.WorkPointer = oldworkpointer; return(0); } /* #] DoTopologyCanonicalize : #[ DoShattering : */ int DoShattering(PHEAD WORD *connect, WORD *environ, WORD *partitions, WORD nvert) { int nparts, i, j, ii, jj, iii, jjj, newmarker; WORD **p = AT.pWorkSpace + AT.pWorkPointer, *part, *endpart; WORD *poin1, *poin2; #ifdef SHATBUG MesPrint("Entering DoShattering. partitions = %a",2*nvert,partitions); #endif restart: /* Determine the number of parts p will be an array with pointers to the parts. We made space for this array in the calling routine and because this routine is not calling any other routines we do not need to raise the pointer in this stack (AT.pWorkPointer). */ nparts = 0; newmarker = 0; part = partitions; endpart = part + 2*nvert; p[0] = part; while ( part < endpart ) { if ( part[1] != 0 ) { p[++nparts] = part+2; } part += 2; } for ( i = 0; i < nparts; i++ ) AT.WorkPointer[i] = (p[i+1]-p[i])/2; #ifdef SHATBUG MesPrint("DoShattering: calculated the pointers"); MesPrint("DoShattering: sizes: %a",nparts,AT.WorkPointer); MesPrint("DoShattering: p[0]: %a, p[1]: %a",6,p[0],6,p[1]); #endif for ( i = 0; i < nparts; i++ ) { if ( AT.WorkPointer[i] > 1 ) { for ( j = 0; j < nparts; j++ ) { /* Shatter part i wrt part j. if there is action, go to restart. */ for ( ii = 0; ii < AT.WorkPointer[i]; ii++ ) { for ( jj = 0; jj < AT.WorkPointer[j]; jj++ ) { environ[ii*AT.WorkPointer[j]+jj] += connect[p[i][2*ii]*nvert+p[j][2*jj]]; } } #ifdef SHATBUG for ( ii = 0; ii < AT.WorkPointer[i]; ii++ ) { MesPrint("Environ(%d,%d): %a",i,j,AT.WorkPointer[j],environ+ii*AT.WorkPointer[j]); } #endif /* Sort the rows internally, then sort the rows wrt each other and finally place new markers. If a new marker, we restart. Don't forget to clean up the environ array. */ for ( ii = 0; ii < nvert; ii++ ) { poin1 = environ+ii*AT.WorkPointer[j]; for ( jj = 0; jj < AT.WorkPointer[j]-1; jj++ ) { jjj = jj; while ( jjj >= 0 && poin1[jjj+1] > poin1[jjj] ) { EXCH(poin1[jjj+1],poin1[jjj]) jjj--; } } } #ifdef SHATBUG for ( ii = 0; ii < AT.WorkPointer[i]; ii++ ) { MesPrint("environ(%d,%d): %a",i,j,AT.WorkPointer[j],environ+ii*AT.WorkPointer[j]); } #endif for ( ii = 0; ii < AT.WorkPointer[i]-1; ii++ ) { poin2 = environ+ii*AT.WorkPointer[j]; poin1 = poin2+AT.WorkPointer[j]; iii = ii; while ( iii >= 0 && ( CmpArray(poin1,poin2,AT.WorkPointer[j]) < 0 ) ) { EXCHN(poin2,poin1,AT.WorkPointer[j]) EXCH(p[i][2*iii+2],p[i][2*iii]) iii--; poin1 = poin2; poin2 = poin1-AT.WorkPointer[j]; } } #ifdef SHATBUG for ( ii = 0; ii < AT.WorkPointer[i]; ii++ ) { MesPrint("environ(%d,%d): %a",i,j,AT.WorkPointer[j],environ+ii*AT.WorkPointer[j]); } MesPrint("partitions = %a",2*nvert,partitions); #endif for ( ii = 0; ii < AT.WorkPointer[i]-1; ii++ ) { poin2 = environ+ii*AT.WorkPointer[j]; poin1 = poin2+AT.WorkPointer[j]; if ( CmpArray(poin1,poin2,AT.WorkPointer[j]) == 0 ) continue; p[i][2*ii+1] = -1; nparts++; newmarker++; } #ifdef SHATBUG MesPrint("partitions = %a",2*nvert,partitions); #endif /* Clear environ. This is probably faster than just clearing the whole array. Maybe in the future a test could be done on nvert to decide how to clear. */ for ( ii = 0; ii < AT.WorkPointer[i]; ii++ ) { for ( jj = 0; jj < AT.WorkPointer[j]; jj++ ) { environ[ii*AT.WorkPointer[j]+jj] = 0; } } if ( newmarker ) { goto restart; } } } } return(nparts); } /* #] DoShattering : */ form-5.0.1/sources/store.c0000644000175100017510000043754215217035721011150 /** @file store.c * * Contains all functions that deal with store-files and the system * independent save-files. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #define HIDEDEBUG #[ Includes : store.c */ #include "form3.h" /* #] Includes : #[ StoreExpressions : #[ OpenTemp : Opens the scratch files for the input -> output operations. */ void OpenTemp(void) { GETIDENTITY if ( AR.outfile->handle >= 0 ) { SeekFile(AR.outfile->handle,&(AR.outfile->filesize),SEEK_SET); AR.outfile->POposition = AR.outfile->filesize; AR.outfile->POfill = AR.outfile->PObuffer; } } /* #] OpenTemp : #[ SeekScratch : */ void SeekScratch(FILEHANDLE *fi, POSITION *pos) { *pos = fi->POposition; ADDPOS(*pos,(TOLONG(fi->POfill)-TOLONG(fi->PObuffer))); } /* #] SeekScratch : #[ SetEndScratch : */ void SetEndScratch(FILEHANDLE *f, POSITION *position) { if ( f->handle < 0 ) { SETBASEPOSITION(*position,(f->POfull-f->PObuffer)*sizeof(WORD)); } else *position = f->filesize; SetScratch(f,position); } /* #] SetEndScratch : #[ SetEndHScratch : */ void SetEndHScratch(FILEHANDLE *f, POSITION *position) { if ( f->handle < 0 ) { SETBASEPOSITION(*position,(f->POfull-f->PObuffer)*sizeof(WORD)); f->POfill = f->POfull; } else { #ifdef HIDEDEBUG POSITION possize; PUTZERO(possize); SeekFile(f->handle,&possize,SEEK_END); MesPrint("SetEndHScratch: filesize(th) = %12p, filesize(ex) = %12p",&(f->filesize), &(possize)); #endif *position = f->filesize; f->POposition = f->filesize; f->POfill = f->POfull = f->PObuffer; } /* SetScratch(f,position); */ } /* #] SetEndHScratch : #[ SetScratch : */ void SetScratch(FILEHANDLE *f, POSITION *position) { GETIDENTITY POSITION possize; LONG size, *whichInInBuf; if ( f == AR.hidefile ) whichInInBuf = &(AR.InHiBuf); else whichInInBuf = &(AR.InInBuf); #ifdef HIDEDEBUG if ( f == AR.hidefile ) MesPrint("In the hide file"); else MesPrint("In the input file"); MesPrint("SetScratch to position %15p",position); MesPrint("POposition = %15p, full = %l, fill = %l" ,&(f->POposition),(f->POfull-f->PObuffer)*sizeof(WORD) ,(f->POfill-f->PObuffer)*sizeof(WORD)); #endif if ( ISLESSPOS(*position,f->POposition) || ISGEPOSINC(*position,f->POposition,(f->POfull-f->PObuffer)*sizeof(WORD)) ) { if ( f->handle < 0 ) { if ( ISEQUALPOSINC(*position,f->POposition, (f->POfull-f->PObuffer)*sizeof(WORD)) ) goto endpos; MesPrint("Illegal position in SetScratch"); Terminate(-1); } possize = *position; LOCK(AS.inputslock); SeekFile(f->handle,&possize,SEEK_SET); if ( ISNOTEQUALPOS(possize,*position) ) { UNLOCK(AS.inputslock); MesPrint("Cannot position file in SetScratch"); Terminate(-1); } #ifdef HIDEDEBUG MesPrint("SetScratch1(%w): position = %12p, size = %l, address = %x",position,f->POsize,f->PObuffer); #endif if ( ( size = ReadFile(f->handle,(UBYTE *)(f->PObuffer),f->POsize) ) < 0 || ( size & 1 ) != 0 ) { UNLOCK(AS.inputslock); MesPrint("Read error in SetScratch"); Terminate(-1); } UNLOCK(AS.inputslock); if ( size == 0 ) { f->PObuffer[0] = 0; } f->POfill = f->PObuffer; f->POposition = *position; #ifdef WORD2 *whichInInBuf = size >> 1; #else *whichInInBuf = size / TABLESIZE(WORD,UBYTE); #endif f->POfull = f->PObuffer + *whichInInBuf; #ifdef HIDEDEBUG MesPrint("SetScratch2: size = %l, InInBuf = %l, fill = %l, full = %l" ,size,*whichInInBuf,(f->POfill-f->PObuffer)*sizeof(WORD) ,(f->POfull-f->PObuffer)*sizeof(WORD)); #endif } else { endpos: DIFPOS(possize,*position,f->POposition); f->POfill = (WORD *)(BASEPOSITION(possize)+(UBYTE *)(f->PObuffer)); *whichInInBuf = f->POfull-f->POfill; } } /* #] SetScratch : #[ RevertScratch : Reverts the input/output directions. This way input comes always from AR.infile */ int RevertScratch(void) { GETIDENTITY FILEHANDLE *f; if ( AR.infile->handle >= 0 && AR.infile->handle != AR.outfile->handle ) { CloseFile(AR.infile->handle); AR.infile->handle = -1; remove(AR.infile->name); } f = AR.infile; AR.infile = AR.outfile; AR.outfile = f; AR.infile->POfull = AR.infile->POfill; AR.infile->POfill = AR.infile->PObuffer; if ( AR.infile->handle >= 0 ) { POSITION scrpos; PUTZERO(scrpos); SeekFile(AR.infile->handle,&scrpos,SEEK_SET); if ( ISNOTZEROPOS(scrpos) ) { return(MesPrint("Error with scratch output.")); } if ( ( AR.InInBuf = ReadFile(AR.infile->handle,(UBYTE *)(AR.infile->PObuffer) ,AR.infile->POsize) ) < 0 || AR.InInBuf & 1 ) { return(MesPrint("Error while reading from scratch file")); } else { AR.InInBuf /= TABLESIZE(WORD,UBYTE); } AR.infile->POfull = AR.infile->PObuffer + AR.InInBuf; } PUTZERO(AR.infile->POposition); AR.outfile->POfill = AR.outfile->POfull = AR.outfile->PObuffer; PUTZERO(AR.outfile->POposition); PUTZERO(AR.outfile->filesize); return(0); } /* #] RevertScratch : #[ ResetScratch : Resets the output scratch file to its beginning in such a way that the write routines can read it. The output buffers are left untouched as they may still be needed for extra declarations. */ int ResetScratch(void) { GETIDENTITY FILEHANDLE *f; if ( AR.infile->handle >= 0 ) { CloseFile(AR.infile->handle); AR.infile->handle = -1; remove(AR.infile->name); PUTZERO(AR.infile->POposition); AR.infile->POfill = AR.infile->POfull = AR.infile->PObuffer; } if ( AR.outfile->handle >= 0 ) { POSITION scrpos; PUTZERO(scrpos); SeekFile(AR.outfile->handle,&scrpos,SEEK_SET); if ( ISNOTZEROPOS(scrpos) ) { return(MesPrint("Error with scratch output.")); } if ( ( AR.InInBuf = ReadFile(AR.outfile->handle,(UBYTE *)(AR.outfile->PObuffer) ,AR.outfile->POsize) ) < 0 || AR.InInBuf & 1 ) { return(MesPrint("Error while reading from scratch file")); } else AR.InInBuf /= TABLESIZE(WORD,UBYTE); AR.outfile->POfull = AR.outfile->PObuffer + AR.InInBuf; } else AR.outfile->POfull = AR.outfile->POfill; AR.outfile->POfill = AR.outfile->PObuffer; PUTZERO(AR.outfile->POposition); f = AR.outfile; AR.outfile = AR.infile; AR.infile = f; return(0); } /* #] ResetScratch : #[ ReadFromScratch : Routine is used to copy files from scratch to hide. */ int ReadFromScratch(FILEHANDLE *fi, POSITION *pos, UBYTE *buffer, POSITION *length) { GETIDENTITY LONG l = BASEPOSITION(*length); if ( fi->handle < 0 ) { memcpy(buffer,fi->POfill,l); } else { SeekFile(fi->handle,pos,SEEK_SET); if ( ReadFile(fi->handle,buffer,l) != l ) { if ( fi == AR.hidefile ) MesPrint("Error reading from hide file."); else MesPrint("Error reading from scratch file."); return(-1); } } return(0); } /* #] ReadFromScratch : #[ AddToScratch : Routine is used to copy files from scratch to hide. */ int AddToScratch(FILEHANDLE *fi, POSITION *pos, UBYTE *buffer, POSITION *length, int withflush) { GETIDENTITY LONG l = BASEPOSITION(*length), avail; DUMMYUSE(pos) fi->POfill = fi->POfull; while ( fi->POfill+l/sizeof(WORD) > fi->POstop ) { avail = (fi->POstop-fi->POfill)*sizeof(WORD); if ( avail > 0 ) { memcpy(fi->POfill,buffer,avail); l -= avail; buffer += avail; } if ( fi->handle < 0 ) { if ( ( fi->handle = (WORD)CreateFile(fi->name) ) < 0 ) { if ( fi == AR.hidefile ) MesPrint("Cannot create hide file %s",fi->name); else MesPrint("Cannot create scratch file %s",fi->name); return(-1); } PUTZERO(fi->POposition); } SeekFile(fi->handle,&(fi->POposition),SEEK_SET); if ( WriteFile(fi->handle,(UBYTE *)fi->PObuffer,fi->POsize) != fi->POsize ) goto writeerror; ADDPOS(fi->POposition,fi->POsize); fi->POfill = fi->POfull = fi->PObuffer; } if ( l > 0 ) { memcpy(fi->POfill,buffer,l); fi->POfill += l/sizeof(WORD); fi->POfull = fi->POfill; } if ( withflush && fi->handle >= 0 && fi->POfill > fi->PObuffer ) { /* flush */ l = (LONG)fi->POfill - (LONG)fi->PObuffer; SeekFile(fi->handle,&(fi->POposition),SEEK_SET); if ( WriteFile(fi->handle,(UBYTE *)fi->PObuffer,l) != l ) goto writeerror; ADDPOS(fi->POposition,fi->POsize); fi->POfill = fi->POfull = fi->PObuffer; } if ( withflush && fi->handle >= 0 ) SETBASEPOSITION(fi->filesize,TellFile(fi->handle)); return(0); writeerror: if ( fi == AR.hidefile ) MesPrint("Error writing to hide file. Disk full?"); else MesPrint("Error writing to scratch file. Disk full?"); return(-1); } /* #] AddToScratch : #[ CoSave : The syntax of the save statement is: save filename save filename expr1 expr2 */ int CoSave(UBYTE *inp) { GETIDENTITY UBYTE *p, c; WORD n = 0, i; WORD error = 0, type, number; WORD exprInStorageFlag = 0; LONG RetCode = 0, wSize; EXPRESSIONS e; INDEXENTRY *ind; INDEXENTRY *indold; WORD TMproto[SUBEXPSIZE]; POSITION scrpos, scrpos1, filesize; int ii, j = sizeof(FILEINDEX)/(sizeof(LONG)); LONG *lo; while ( *inp == ',' ) inp++; p = inp; #ifdef WITHMPI if( PF.me != MASTER) return(0); #endif if ( !*p ) return(MesPrint("No filename in save statement")); if ( FG.cTable[*p] > 1 && ( *p != '.' ) && ( *p != SEPARATOR ) && ( *p != ALTSEPARATOR ) ) return(MesPrint("Illegal filename")); while ( *++p && *p != ',' ) {} c = *p; *p = 0; if ( !AP.preError ) { if ( ( RetCode = CreateFile((char *)inp) ) < 0 ) { return(MesPrint("Cannot open file %s",inp)); } } AO.SaveData.Handle = (WORD)RetCode; PUTZERO(filesize); e = Expressions; n = NumExpressions; if ( c ) { /* There follows a list of expressions */ *p++ = c; inp = p; i = (WORD)(INFILEINDEX); if ( WriteStoreHeader(AO.SaveData.Handle) ) return(MesPrint("Error writing storage file header")); /* PUTZERO(AO.SaveData.Index.number); */ /* PUTZERO(AO.SaveData.Index.next); */ lo = (LONG *)(&AO.SaveData.Index); for ( ii = 0; ii < j; ii++ ) *lo++ = 0; SETBASEPOSITION(AO.SaveData.Position,(LONG)sizeof(STOREHEADER)); ind = AO.SaveData.Index.expression; if ( !AP.preError && WriteFile(AO.SaveData.Handle,(UBYTE *)(&(AO.SaveData.Index)) ,(LONG)sizeof(struct FiLeInDeX))!= (LONG)sizeof(struct FiLeInDeX) ) goto SavWrt; SeekFile(AO.SaveData.Handle,&(filesize),SEEK_END); /* ADDPOS(filesize,sizeof(struct FiLeInDeX)); */ do { /* Scan the list */ if ( !FG.cTable[*p] || *p == '[' ) { p = SkipAName(p); if ( p == 0 ) return(-1); } c = *p; *p = 0; if ( GetVar(inp,&type,&number,CEXPRESSION,NOAUTO) != NAMENOTFOUND ) { if ( e[number].status == STOREDEXPRESSION ) { if ( StrLen(AC.exprnames->namebuffer+e[number].name) > MAXENAME ) { char msg[100]; snprintf(msg, sizeof(msg), "saved expr name over %d char: %s", MAXENAME, AC.exprnames->namebuffer+e[number].name); Warning(msg); } /* Here we have to locate the stored expression, copy its index entry possibly after making a new fileindex and then copy the whole expression. */ if ( AP.preError ) goto NextExpr; TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = number; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; if ( ( indold = FindInIndex(number,&AR.StoreData,0,0) ) != 0 ) { if ( i <= 0 ) { /* AO.SaveData.Index.next = filesize; */ SeekFile(AO.SaveData.Handle,&(AO.SaveData.Index.next),SEEK_END); scrpos = AO.SaveData.Position; SeekFile(AO.SaveData.Handle,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,AO.SaveData.Position) ) goto SavWrt; if ( WriteFile(AO.SaveData.Handle,(UBYTE *)(&(AO.SaveData.Index)) ,(LONG)sizeof(struct FiLeInDeX)) != (LONG)sizeof(struct FiLeInDeX) ) goto SavWrt; i = (WORD)(INFILEINDEX); AO.SaveData.Position = AO.SaveData.Index.next; lo = (LONG *)(&AO.SaveData.Index); for ( ii = 0; ii < j; ii++ ) *lo++ = 0; ind = AO.SaveData.Index.expression; scrpos = AO.SaveData.Position; SeekFile(AO.SaveData.Handle,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,AO.SaveData.Position) ) goto SavWrt; if ( WriteFile(AO.SaveData.Handle,(UBYTE *)(&(AO.SaveData.Index)) ,(LONG)sizeof(struct FiLeInDeX)) != (LONG)sizeof(struct FiLeInDeX) ) goto SavWrt; ADDPOS(filesize,sizeof(struct FiLeInDeX)); } *ind = *indold; /* ind->variables = SeekFile(AO.SaveData.Handle,&(AM.zeropos),SEEK_END); */ ind->variables = filesize; ind->position = ind->variables; ADDPOS(ind->position,DIFBASE(indold->position,indold->variables)); SeekFile(AR.StoreData.Handle,&(indold->variables),SEEK_SET); wSize = TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer); scrpos = ind->length; ADDPOS(scrpos,DIFBASE(ind->position,ind->variables)); ADD2POS(filesize,scrpos); SETBASEPOSITION(scrpos1,wSize); do { if ( ISLESSPOS(scrpos,scrpos1) ) wSize = BASEPOSITION(scrpos); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,wSize) != wSize ) { MesPrint("ReadError"); error = -1; goto EndSave; } if ( WriteFile(AO.SaveData.Handle,(UBYTE *)AT.WorkPointer,wSize) != wSize ) goto SavWrt; ADDPOS(scrpos,-wSize); } while ( ISPOSPOS(scrpos) ); ADDPOS(AO.SaveData.Index.number,1); ind++; } else error = -1; i--; } else { MesPrint("%s is not a stored expression",inp); error = -1; } NextExpr:; } else { MesPrint("%s is not an expression",inp); error = -1; } *p = c; if ( c != ',' && c ) { MesComp("Illegal character",inp,p); error = -1; goto EndSave; } if ( c ) c = *++p; inp = p; } while ( c ); if ( !AP.preError ) { scrpos = AO.SaveData.Position; SeekFile(AO.SaveData.Handle,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,AO.SaveData.Position) ) goto SavWrt; } if ( !AP.preError && WriteFile(AO.SaveData.Handle,(UBYTE *)(&(AO.SaveData.Index)) ,(LONG)sizeof(struct FiLeInDeX)) != (LONG)sizeof(struct FiLeInDeX) ) goto SavWrt; } else if ( !AP.preError ) { /* All stored expressions should be saved. Easy */ /* Make sure there is at least one stored expression: */ if ( n > 0 ) { do { if ( StrLen(AC.exprnames->namebuffer+e->name) > MAXENAME ) { char msg[100]; snprintf(msg, sizeof(msg), "saved expr name over %d char: %s", MAXENAME, AC.exprnames->namebuffer+e->name); Warning(msg); } if ( e->status == STOREDEXPRESSION ) exprInStorageFlag = 1; e++; } while ( --n > 0 ); } if ( exprInStorageFlag ) { wSize = TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer); PUTZERO(scrpos); SeekFile(AR.StoreData.Handle,&scrpos,SEEK_SET); /* Start at the beginning */ scrpos = AR.StoreData.Fill; /* Number of bytes to be copied */ SETBASEPOSITION(scrpos1,wSize); do { if ( ISLESSPOS(scrpos,scrpos1) ) wSize = BASEPOSITION(scrpos); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,wSize) != wSize ) { MesPrint("ReadError"); error = -1; goto EndSave; } if ( WriteFile(AO.SaveData.Handle,(UBYTE *)AT.WorkPointer,wSize) != wSize ) goto SavWrt; ADDPOS(scrpos,-wSize); } while ( ISPOSPOS(scrpos) ); } } EndSave: if ( !AP.preError ) { CloseFile(AO.SaveData.Handle); AO.SaveData.Handle = -1; } return(error); SavWrt: MesPrint("WriteError"); error = -1; goto EndSave; } /* #] CoSave : #[ CoLoad : */ int CoLoad(UBYTE *inp) { GETIDENTITY INDEXENTRY *ind; LONG RetCode; UBYTE *p, c; WORD num, i, error = 0; WORD type, number, silentload = 0; WORD TMproto[SUBEXPSIZE]; POSITION scrpos,firstposition; while ( *inp == ',' ) inp++; p = inp; if ( ( *p == ',' && p[1] == '-' ) || *p == '-' ) { if ( *p == ',' ) p++; p++; if ( *p == 's' || *p == 'S' ) { silentload = 1; while ( *p && ( *p != ',' && *p != '-' && *p != '+' && *p != SEPARATOR && *p != ALTSEPARATOR && *p != '.' ) ) p++; } else if ( *p != ',' ) { return(MesPrint("Illegal option in Load statement")); } while ( *p == ',' ) p++; } inp = p; if ( !*p ) return(MesPrint("No filename in load statement")); if ( FG.cTable[*p] > 1 && ( *p != '.' ) && ( *p != SEPARATOR ) && ( *p != ALTSEPARATOR ) ) return(MesPrint("Illegal filename")); while ( *++p && *p != ',' ) {} c = *p; *p = 0; if ( ( RetCode = OpenFile((char *)inp) ) < 0 ) { return(MesPrint("Cannot open file %s",inp)); } if ( SetFileIndex() ) { MesCall("CoLoad"); SETERROR(-1) } AO.SaveData.Handle = (WORD)(RetCode); #ifdef SYSDEPENDENTSAVE if ( ReadFile(AO.SaveData.Handle,(UBYTE *)(&(AO.SaveData.Index)), (LONG)sizeof(struct FiLeInDeX)) != (LONG)sizeof(struct FiLeInDeX) ) goto LoadRead; #else if ( ReadSaveHeader() ) goto LoadRead; TELLFILE(AO.SaveData.Handle,&firstposition); if ( ReadSaveIndex(&AO.SaveData.Index) ) goto LoadRead; #endif if ( c ) { /* There follows a list of expressions */ *p++ = c; inp = p; do { /* Scan the list */ if ( !FG.cTable[*p] || *p == '[' ) { p = SkipAName(p); if ( p == 0 ) return(-1); } c = *p; *p = 0; if ( GetVar(inp,&type,&number,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { MesPrint("Conflicting name: %s",inp); error = -1; } else { if ( ( num = EntVar(CEXPRESSION,inp,STOREDEXPRESSION,0,0,0) ) >= 0 ) { TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = num; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; SeekFile(AO.SaveData.Handle,&firstposition,SEEK_SET); AO.SaveData.Position = firstposition; if ( ReadSaveIndex(&AO.SaveData.Index) ) goto LoadRead; if ( ( ind = FindInIndex(num,&AO.SaveData,1,0) ) != 0 ) { if ( !error ) { if ( PutInStore(ind,num) ) error = -1; else if ( !AM.silent && silentload == 0 ) MesPrint(" %s loaded",ind->name); } /* !!! Added 1-feb-1998 */ Expressions[num].counter = -1; } else { MesPrint(" %s not found",inp); error = -1; } } else error = -1; } *p = c; if ( c != ',' && c ) { MesComp("Illegal character",inp,p); error = -1; goto EndLoad; } if ( c ) c = *++p; inp = p; } while ( c ); scrpos = AR.StoreData.Position; SeekFile(AR.StoreData.Handle,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,AR.StoreData.Position) ) goto LoadWrt; if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&(AR.StoreData.Index)) ,(LONG)sizeof(struct FiLeInDeX)) != (LONG)sizeof(struct FiLeInDeX) ) goto LoadWrt; } else { /* All saved expressions should be stored. Easy */ i = (WORD)BASEPOSITION(AO.SaveData.Index.number); ind = AO.SaveData.Index.expression; #ifdef SYSDEPENDENTSAVE if ( i > 0 ) { do { if ( GetVar((UBYTE *)(ind->name),&type,&number,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { MesPrint("Conflicting name: %s",ind->name); error = -1; } else { if ( ( num = EntVar(CEXPRESSION,(UBYTE *)(ind->name),STOREDEXPRESSION,0,0,0) ) >= 0 ) { if ( !error ) { if ( PutInStore(ind,num) ) error = -1; else if ( !AM.silent && silentload == 0 ) MesPrint(" %s loaded",ind->name); } } else error = -1; } i--; if ( i == 0 && ISNOTZEROPOS(AO.SaveData.Index.next) ) { SeekFile(AO.SaveData.Handle,&(AO.SaveData.Index.next),SEEK_SET); if ( ReadFile(AO.SaveData.Handle,(UBYTE *)(&(AO.SaveData.Index)), (LONG)sizeof(struct FiLeInDeX)) != (LONG)sizeof(struct FiLeInDeX) ) goto LoadRead; i = (WORD)BASEPOSITION(AO.SaveData.Index.number); ind = AO.SaveData.Index.expression; } else ind++; } while ( i > 0 ); } #else if ( i > 0 ) { do { if ( GetVar((UBYTE *)(ind->name),&type,&number,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { MesPrint("Conflicting name: %s",ind->name); error = -1; } else { if ( ( num = EntVar(CEXPRESSION,(UBYTE *)(ind->name),STOREDEXPRESSION,0,0,0) ) >= 0 ) { if ( !error ) { if ( PutInStore(ind,num) ) error = -1; else if ( !AM.silent && silentload == 0 ) MesPrint(" %s loaded",ind->name); } } else error = -1; } i--; if ( i == 0 && (ISNOTZEROPOS(AO.SaveData.Index.next) || AO.bufferedInd) ) { SeekFile(AO.SaveData.Handle,&(AO.SaveData.Index.next),SEEK_SET); if ( ReadSaveIndex(&AO.SaveData.Index) ) goto LoadRead; i = (WORD)BASEPOSITION(AO.SaveData.Index.number); ind = AO.SaveData.Index.expression; } else ind++; } while ( i > 0 ); } #endif } EndLoad: #ifndef SYSDEPENDENTSAVE if ( AO.powerFlag ) { MesPrint("WARNING: min-/maxpower had to be adjusted!"); } if ( AO.resizeFlag ) { MesPrint("ERROR: could not downsize data!"); return ( -2 ); } #endif CloseFile(AO.SaveData.Handle); AO.SaveData.Handle = -1; SeekFile(AR.StoreData.Handle,&(AC.StoreFileSize),SEEK_END); return(error); LoadWrt: MesPrint("WriteError"); error = -1; goto EndLoad; LoadRead: MesPrint("ReadError"); error = -1; goto EndLoad; } /* #] CoLoad : #[ DeleteStore : Routine deletes the contents of the entire storage file. We close the file and recreate it. If par > 0 we have to remove the expressions from the namelists. */ int DeleteStore(WORD par) { GETIDENTITY char *s; WORD j, n = 0; EXPRESSIONS e_in, e_out; WORD DidClean = 0; if ( AR.StoreData.Handle >= 0 ) { if ( par > 0 ) { n = NumExpressions; j = 0; e_in = e_out = Expressions; if ( n > 0 ) { do { if ( e_in->status == STOREDEXPRESSION ) { NAMENODE *node = GetNode(AC.exprnames, AC.exprnames->namebuffer+e_in->name); node->type = CDELETE; DidClean = 1; } else { if ( e_out != e_in ) { NAMENODE *node; node = GetNode(AC.exprnames, AC.exprnames->namebuffer+e_in->name); node->number = (WORD)(e_out - Expressions); e_out->onfile = e_in->onfile; e_out->prototype = e_in->prototype; e_out->printflag = 0; e_out->status = e_in->status; e_out->name = e_in->name; e_out->inmem = e_in->inmem; e_out->counter = e_in->counter; e_out->numfactors = e_in->numfactors; e_out->numdummies = e_in->numdummies; e_out->compression = e_in->compression; e_out->namesize = e_in->namesize; e_out->whichbuffer = e_in->whichbuffer; e_out->hidelevel = e_in->hidelevel; e_out->node = e_in->node; e_out->replace = e_in->replace; e_out->vflags = e_in->vflags; e_out->uflags = e_in->uflags; #ifdef PARALLELCODE e_out->partodo = e_in->partodo; #endif } e_out++; j++; } e_in++; } while ( --n > 0 ); } NumExpressions = j; if ( DidClean ) CompactifyTree(AC.exprnames,EXPRNAMES); } AR.StoreData.Handle = -1; CloseFile(AC.StoreHandle); AC.StoreHandle = -1; { /* Knock out the storage caches (25-apr-1990!) */ STORECACHE st; st = (STORECACHE)(AT.StoreCache); while ( st ) { SETBASEPOSITION(st->position,-1); SETBASEPOSITION(st->toppos,-1); st = st->next; } #ifdef WITHPTHREADS for ( j = 1; j < AM.totalnumberofthreads; j++ ) { st = (STORECACHE)(AB[j]->T.StoreCache); while ( st ) { SETBASEPOSITION(st->position,-1); SETBASEPOSITION(st->toppos,-1); st = st->next; } } #endif } PUTZERO(AC.StoreFileSize); s = FG.fname; while ( *s ) s++; #ifdef VMS *s = ';'; s[1] = '*'; s[2] = 0; remove(FG.fname); *s = 0; #endif return(AC.StoreHandle = CreateFile(FG.fname)); } else return(0); } /* #] DeleteStore : #[ PutInStore : Copies the expression indicated by ind from a load file to the internal storage file. A return value of zero indicates that everything is OK. */ int PutInStore(INDEXENTRY *ind, WORD num) { GETIDENTITY INDEXENTRY *newind; LONG wSize; #ifndef SYSDEPENDENTSAVE LONG wSizeOut; LONG stage; #endif POSITION scrpos,scrpos1; newind = NextFileIndex(&(Expressions[num].onfile)); *newind = *ind; #ifndef SYSDEPENDENTSAVE SETBASEPOSITION(newind->length, 0); #endif newind->variables = AR.StoreData.Fill; SeekFile(AR.StoreData.Handle,&(newind->variables),SEEK_SET); if ( ISNOTEQUALPOS(newind->variables,AR.StoreData.Fill) ) goto PutErrS; newind->position = newind->variables; #ifdef SYSDEPENDENTSAVE ADDPOS(newind->position,DIFBASE(ind->position,ind->variables)); #endif /* set read position to ind->variables */ scrpos = ind->variables; SeekFile(AO.SaveData.Handle,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,ind->variables) ) goto PutErrS; /* set max size for read-in */ wSize = TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer); #ifdef SYSDEPENDENTSAVE scrpos = ind->length; ADDPOS(scrpos,DIFBASE(ind->position,ind->variables)); ADD2POS(AR.StoreData.Fill,scrpos); #endif SETBASEPOSITION(scrpos1,wSize); #ifndef SYSDEPENDENTSAVE /* prepare look-up table for tensor functions */ if ( ind->nfunctions ) { AO.tensorList = (UBYTE *)Malloc1(MAXSAVEFUNCTION,"PutInStore"); } SETBASEPOSITION(scrpos, DIFBASE(ind->position,ind->variables)); /* copy variables first */ stage = -1; do { wSize = TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer); if ( ISLESSPOS(scrpos,scrpos1) ) wSize = BASEPOSITION(scrpos); wSizeOut = wSize; if ( ReadSaveVariables( (UBYTE *)AT.WorkPointer, (UBYTE *)AT.WorkTop, &wSize, &wSizeOut, ind, &stage) ) { goto PutErrS; } if ( WriteFile(AR.StoreData.Handle, (UBYTE *)AT.WorkPointer, wSizeOut) != wSizeOut ) goto PutErrS; ADDPOS(scrpos,-wSize); ADDPOS(newind->position, wSizeOut); ADDPOS(AR.StoreData.Fill, wSizeOut); } while ( ISPOSPOS(scrpos) ); /* then copy the expression itself */ wSize = TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer); scrpos = ind->length; #endif do { wSize = TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer); if ( ISLESSPOS(scrpos,scrpos1) ) wSize = BASEPOSITION(scrpos); #ifdef SYSDEPENDENTSAVE if ( ReadFile(AO.SaveData.Handle,(UBYTE *)AT.WorkPointer,wSize) != wSize ) goto PutErrS; if ( WriteFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,wSize) != wSize ) goto PutErrS; ADDPOS(scrpos,-wSize); #else wSizeOut = wSize; if ( ReadSaveExpression((UBYTE *)AT.WorkPointer, (UBYTE *)AT.WorkTop, &wSize, &wSizeOut) ) { goto PutErrS; } if ( WriteFile(AR.StoreData.Handle, (UBYTE *)AT.WorkPointer, wSizeOut) != wSizeOut ) goto PutErrS; ADDPOS(scrpos,-wSize); ADDPOS(AR.StoreData.Fill, wSizeOut); ADDPOS(newind->length, wSizeOut); #endif } while ( ISPOSPOS(scrpos) ); /* free look-up table for tensor functions */ if ( ind->nfunctions ) { M_free(AO.tensorList,"PutInStore"); } scrpos = AR.StoreData.Position; SeekFile(AR.StoreData.Handle,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,AR.StoreData.Position) ) goto PutErrS; if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&AR.StoreData.Index),(LONG)sizeof(FILEINDEX)) == (LONG)sizeof(FILEINDEX) ) return(0); PutErrS: return(MesPrint("File error")); } /* #] PutInStore : #[ GetTerm : Gets one term from input scratch stream. Puts it in 'term'. Returns the length of the term. Used by Processor (proces.c) WriteAll (sch.c) WriteOne (sch.c) GetMoreTerms (store.c) ToStorage (store.c) CoFillExpression (comexpr.c) FactorInExpr (factor.c) LoadOpti (optim.c) PF_Processor (parallel.c) ThreadsProcessor (threads.c) In multi thread/processor mode all calls are done by the master. Note however that other routines, used by the threads, can use the same file. Hence we need to be careful about SeekFile and locks. */ WORD GetTerm(PHEAD WORD *term) { GETBIDENTITY WORD *inp, i, j = 0, len; LONG InIn, *whichInInBuf; WORD *r, *m, *mstop = 0, minsiz = 0, *bra = 0, *from; WORD first, *start = 0, testing = 0; FILEHANDLE *fi; AN.deferskipped = 0; if ( AR.GetFile == 2 ) { fi = AR.hidefile; whichInInBuf = &(AR.InHiBuf); } else { fi = AR.infile; whichInInBuf = &(AR.InInBuf); } InIn = *whichInInBuf; from = term; if ( AR.KeptInHold ) { r = AR.CompressBuffer; i = *r; AR.KeptInHold = 0; if ( i <= 0 ) { *term = 0; goto RegRet; } m = term; NCOPY(m,r,i); goto RegRet; } if ( AR.DeferFlag ) { m = AR.CompressBuffer; if ( *m > 0 ) { mstop = m + *m; mstop -= ABS(mstop[-1]); m++; while ( m < mstop ) { if ( *m == HAAKJE ) { testing = 1; mstop = m + m[1]; bra = (WORD *)(((UBYTE *)(term)) + 2*AM.MaxTer); m = AR.CompressBuffer+1; r = bra; while ( m < mstop ) *r++ = *m++; mstop = r; minsiz = WORDDIF(mstop,bra); goto ReStart; /* We have the bracket to be tested in bra till mstop */ } m += m[1]; } } bra = (WORD *)(((UBYTE *)(term)) + 2*AM.MaxTer); mstop = bra+1; *bra = 0; minsiz = 1; testing = 1; } ReStart: first = 0; r = AR.CompressBuffer; if ( fi->handle >= 0 ) { if ( InIn <= 0 ) { ADDPOS(fi->POposition,(fi->POfull-fi->PObuffer)*sizeof(WORD)); LOCK(AS.inputslock); SeekFile(fi->handle,&(fi->POposition),SEEK_SET); InIn = ReadFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize); UNLOCK(AS.inputslock); if ( ( InIn < 0 ) || ( InIn & 1 ) ) { goto GTerr; } #ifdef WORD2 InIn >>= 1; #else InIn /= TABLESIZE(WORD,UBYTE); #endif *whichInInBuf = InIn; if ( !InIn ) { *r = 0; *from = 0; goto RegRet; } fi->POfill = fi->PObuffer; fi->POfull = fi->PObuffer + InIn; } inp = fi->POfill; if ( ( len = i = *inp ) == 0 ) { (*whichInInBuf)--; (fi->POfill)++; *r = 0; *from = 0; goto RegRet; } if ( i < 0 ) { InIn--; inp++; r++; start = term; *term++ = -i + 1; while ( ++i <= 0 ) *term++ = *r++; if ( InIn > 0 ) { i = *inp++; InIn--; *start += i; *(AR.CompressBuffer) = len = *start; } else { first = 1; goto NewIn; } } InIn -= i; if ( InIn < 0 ) { j = (WORD)(- InIn); i -= j; } else j = 0; while ( --i >= 0 ) { *r++ = *term++ = *inp++; } if ( j ) { NewIn: ADDPOS(fi->POposition,(fi->POfull-fi->PObuffer)*sizeof(WORD)); LOCK(AS.inputslock); SeekFile(fi->handle,&(fi->POposition),SEEK_SET); InIn = ReadFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize); UNLOCK(AS.inputslock); if ( ( InIn <= 0 ) || ( InIn & 1 ) ) { goto GTerr; } #ifdef WORD2 InIn >>= 1; #else InIn /= TABLESIZE(WORD,UBYTE); #endif inp = fi->PObuffer; fi->POfull = inp + InIn; if ( first ) { j = *inp++; InIn--; *start += j; *(AR.CompressBuffer) = len = *start; } InIn -= j; while ( --j >= 0 ) { *r++ = *term++ = *inp++; } } fi->POfill = inp; *whichInInBuf = InIn; AR.DefPosition = fi->POposition; ADDPOS(AR.DefPosition,((UBYTE *)(fi->POfill)-(UBYTE *)(fi->PObuffer))); } else { inp = fi->POfill; if ( inp >= fi->POfull ) { *from = 0; goto RegRet; } len = j = *inp; if ( j < 0 ) { inp++; *term++ = *r++ = len = - j + 1 + *inp; while ( ++j <= 0 ) *term++ = *r++; j = *inp++; } else if ( !j ) j = 1; while ( --j >= 0 ) { *r++ = *term++ = *inp++; } fi->POfill = inp; /*%%%%%ADDED 7-apr-2006 for Keep Brackets in bucket */ SETBASEPOSITION(AR.DefPosition,((UBYTE *)(fi->POfill)-(UBYTE *)(fi->PObuffer))); if ( inp > fi->POfull ) { goto GTerr; } } if ( r >= AR.ComprTop ) { MesPrint("CompressSize of %10l is insufficient",AM.CompressSize); Terminate(-1); } AR.CompressPointer = r; *r = 0; /* The next *from is a bug fix that made the program read in forbidden territory. */ if ( testing && *from != 0 ) { WORD jj; r = from; jj = *r - 1 - ABS(*(r+*r-1)); if ( jj < minsiz ) goto strip; r++; m = bra; while ( m < mstop ) { if ( *m != *r ) { strip: r = from; m = r + *r; mstop = m - ABS(m[-1]); r++; while ( r < mstop ) { if ( *r == HAAKJE ) { *r++ = 1; *r++ = 1; *r++ = 3; len = WORDDIF(r,from); *from = len; goto RegRet; } r += r[1]; } goto RegRet; } m++; r++; } term = from; AN.deferskipped++; goto ReStart; } RegRet:; /* #[ debug : */ { UBYTE OutBuf[140]; /* if ( AP.DebugFlag ) { */ if ( ( AP.PreDebug & DUMPINTERMS ) == DUMPINTERMS ) { MLOCK(ErrorMessageLock); AO.OutFill = AO.OutputLine = OutBuf; AO.OutSkip = 3; FiniLine(); r = from; i = *r; TokenToLine((UBYTE *)("Input: ")); if ( i == 0 ) { TokenToLine((UBYTE *)"zero"); } else if ( i < 0 ) { TokenToLine((UBYTE *)"negative!!"); } else { while ( --i >= 0 ) { TalToLine((UWORD)(*r++)); TokenToLine((UBYTE *)" "); } } FiniLine(); MUNLOCK(ErrorMessageLock); } } /* #] debug : */ return(*from); GTerr: MesPrint("Error while reading scratch file in GetTerm"); Terminate(-1); return(-1); } /* #] GetTerm : #[ GetOneTerm : Gets one term from stream AR.infile->handle. Puts it in 'term'. Returns the length of the term. Input is unbuffered. Compression via AR.CompressPointer par is actually in all calls a file handle Routine is called from DoOnePow Get one power of an expression Deferred Get the contents of a bracket GetFirstBracket FindBracket We should do something about the lack of buffering. Maybe a buffer of a few times AM.MaxTer (MaxTermSize*sizeof(WORD)). Each thread will need its own buffer! If par == 0 we use ReadPosFile which can fill the whole buffer. If par == 1 we use ReadFile and do actual read operations. Note: we cannot use ReadPosFile when running in the master thread. */ WORD GetOneTerm(PHEAD WORD *term, FILEHANDLE *fi, POSITION *pos, int par) { GETBIDENTITY WORD i, *p; LONG j, siz; WORD *r, *rr = AR.CompressPointer; int error = 0; r = rr; if ( fi->handle >= 0 ) { #ifdef READONEBYONE #ifdef WITHPTHREADS /* This code needs some investigation. It may be that we should do this always. It may be that even for workers it is no good. We may have to make a variable like AM.ReadDirect with if ( AM.ReadDirect ) par = 1; and a user command like On ReadDirect; */ if ( AT.identity > 0 ) par = 1; #endif #endif /* To be changed: 1: check first whether the term lies completely inside the buffer 2: if not a: use old strategy for AT.identity == 0 (master) b: for workers, position file and read buffer */ if ( par == 0 ) { siz = ReadPosFile(BHEAD fi,(UBYTE *)term,1L,pos); } else { LOCK(AS.inputslock); SeekFile(fi->handle,pos,SEEK_SET); siz = ReadFile(fi->handle,(UBYTE *)term,sizeof(WORD)); UNLOCK(AS.inputslock); ADDPOS(*pos,siz); } if ( siz == sizeof(WORD) ) { p = term; j = i = *term++; if ( ( i > AM.MaxTer/((WORD)sizeof(WORD)) ) || ( -i >= AM.MaxTer/((WORD)sizeof(WORD)) ) ) { error = 1; goto ErrGet; } r++; if ( i < 0 ) { /* Loading a compressed term */ *p = -i + 1; while ( ++i <= 0 ) *term++ = *r++; if ( par == 0 ) { siz = ReadPosFile(BHEAD fi,(UBYTE *)term,1L,pos); } else { LOCK(AS.inputslock); SeekFile(fi->handle,pos,SEEK_SET); siz = ReadFile(fi->handle,(UBYTE *)term,sizeof(WORD)); UNLOCK(AS.inputslock); ADDPOS(*pos,sizeof(WORD)); } if ( siz != sizeof(WORD) ) { error = 2; goto ErrGet; } *p += *term; j = *term; if ( ( j > AM.MaxTer/((WORD)sizeof(WORD)) ) || ( j <= 0 ) ) { error = 3; goto ErrGet; } *rr = *p; /* Write the proper term size to *AR.CompressPointer */ } else { /* Loading a regular term */ if ( !j ) return(0); *rr = i; /* Write the proper term size to *AR.CompressPointer */ j--; } i = (WORD)j; if ( par == 0 ) { siz = ReadPosFile(BHEAD fi,(UBYTE *)term,j,pos); j *= TABLESIZE(WORD,UBYTE); } else { j *= TABLESIZE(WORD,UBYTE); LOCK(AS.inputslock); SeekFile(fi->handle,pos,SEEK_SET); siz = ReadFile(fi->handle,(UBYTE *)term,j); UNLOCK(AS.inputslock); ADDPOS(*pos,j); } if ( siz != j ) { error = 4; goto ErrGet; } while ( --i >= 0 ) *r++ = *term++; if ( r >= AR.ComprTop ) { MLOCK(ErrorMessageLock); MesPrint("CompressSize of %10l is insufficient",AM.CompressSize); MUNLOCK(ErrorMessageLock); Terminate(-1); } AR.CompressPointer = r; *r = 0; return(*p); } error = 5; } else { /* Here the whole expression is in the buffer. */ fi->POfill = (WORD *)((UBYTE *)(fi->PObuffer) + BASEPOSITION(*pos)); p = fi->POfill; if ( p >= fi->POfull ) { *term = 0; return(0); } j = i = *p; if ( i < 0 ) { p++; j = *r++ = *term++ = -i + 1 + *p; while ( ++i <= 0 ) *term++ = *r++; i = *p++; } if ( i == 0 ) { i = 1; *r++ = 0; *term++ = 0; } else { while ( --i >= 0 ) { *r++ = *term++ = *p++; } } fi->POfill = p; SETBASEPOSITION(*pos,(UBYTE *)(fi->POfill)-(UBYTE *)(fi->PObuffer)); if ( p <= fi->POfull ) { if ( r >= AR.ComprTop ) { MLOCK(ErrorMessageLock); MesPrint("CompressSize of %10l is insufficient",AM.CompressSize); MUNLOCK(ErrorMessageLock); Terminate(-1); } AR.CompressPointer = r; *r = 0; return((WORD)j); } error = 6; } ErrGet: MLOCK(ErrorMessageLock); MesPrint("Error while reading scratch file in GetOneTerm (%d)",error); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); } /* #] GetOneTerm : #[ GetMoreTerms : Routine collects more contents of brackets inside a function, indicated by the number in AC.CollectFun. The first term is in term already. We can keep calling GetTerm either till a bracket is finished or till it would make the term too long (> AM.MaxTer/2) In all cases this function makes that the routine GetTerm has a term in 'hold', so the AR.KeptInHold flag must be turned on. */ WORD GetMoreTerms(WORD *term) { GETIDENTITY WORD *t, *r, *m, *h, *tstop, i, inc, same; WORD extra; WORD retval = 0; /* We use 23% as a quasi-random default value. */ extra = ((AM.MaxTer/sizeof(WORD))*((LONG)100-AC.CollectPercentage))/100; if ( extra < 23 ) extra = 23; /* First find the bracket pointer */ t = term + *term; tstop = t - ABS(t[-1]); h = term+1; while ( *h != HAAKJE && h < tstop ) h += h[1]; if ( h >= tstop ) return(retval); inc = FUNHEAD+ARGHEAD+1-h[1]; same = WORDDIF(h,term) + h[1] - 1; r = m = t + inc; tstop = h + h[1]; while ( t > tstop ) *--r = *--t; r--; *r = WORDDIF(m,r); while ( GetTerm(BHEAD m) > 0 ) { r = m + 1; t = m + *m - 1; if ( same > ( i = ( *m - ABS(*t) -1 ) ) ) { /* Must fail */ if ( AC.AltCollectFun && AS.CollectOverFlag == 2 ) AS.CollectOverFlag = 3; break; } t = term+1; i = same; while ( --i >= 0 ) { if ( *r != *t ) { if ( AC.AltCollectFun && AS.CollectOverFlag == 2 ) AS.CollectOverFlag = 3; goto FullTerm; } r++; t++; } if ( ( WORDDIF(m,term) + i + extra ) > (WORD)(AM.MaxTer/sizeof(WORD)) ) { /* 23 = 3 +20. The 20 is to have some extra for substitutions or whatever */ if ( AS.CollectOverFlag == 0 && AC.AltCollectFun == 0 ) { Warning("Bracket contents too long in Collect statement"); Warning("Contents spread over more than one term"); Warning("If possible: increase MaxTermSize in setfile"); AS.CollectOverFlag = 1; } else if ( AC.AltCollectFun ) { AS.CollectOverFlag = 2; } break; } tstop = m + *m; *m -= same; m++; while ( r < tstop ) *m++ = *r++; retval++; if ( extra == 23 ) extra = ((AM.MaxTer/sizeof(WORD))/6); } FullTerm: h[1] = WORDDIF(m,h); if ( AS.CollectOverFlag > 1 ) { *h = AC.AltCollectFun; if ( AS.CollectOverFlag == 3 ) AS.CollectOverFlag = 1; } else *h = AC.CollectFun; h[2] |= DIRTYFLAG; h[FUNHEAD] = h[1] - FUNHEAD; h[FUNHEAD+1] = 0; if ( ToFast(h+FUNHEAD,h+FUNHEAD) ) { if ( h[FUNHEAD] <= -FUNCTION ) { h[1] = FUNHEAD+1; m = h + FUNHEAD+1; } else { h[1] = FUNHEAD+2; m = h + FUNHEAD+2; } } *m++ = 1; *m++ = 1; *m++ = 3; *term = WORDDIF(m,term); AR.KeptInHold = 1; return(retval); } /* #] GetMoreTerms : #[ GetMoreFromMem : */ int GetMoreFromMem(WORD *term, WORD **tpoin) { GETIDENTITY WORD *t, *r, *m, *h, *tstop, i, j, inc, same; LONG extra = 23; /* First find the bracket pointer */ t = term + *term; tstop = t - ABS(t[-1]); h = term+1; while ( *h != HAAKJE && h < tstop ) h += h[1]; if ( h >= tstop ) return(0); inc = FUNHEAD+ARGHEAD+1-h[1]; same = WORDDIF(h,term) + h[1] - 1; r = m = t + inc; tstop = h + h[1]; while ( t > tstop ) *--r = *--t; r--; *r = WORDDIF(m,r); while ( **tpoin ) { r = *tpoin; j = *r; for ( i = 0; i < j; i++ ) m[i] = *r++; *tpoin = r; r = m + 1; t = m + *m - 1; if ( same > ( i = ( *m - ABS(*t) -1 ) ) ) { /* Must fail */ if ( AC.AltCollectFun && AS.CollectOverFlag == 2 ) AS.CollectOverFlag = 3; break; } t = term+1; i = same; while ( --i >= 0 ) { if ( *r != *t ) { if ( AC.AltCollectFun && AS.CollectOverFlag == 2 ) AS.CollectOverFlag = 3; goto FullTerm; } r++; t++; } if ( ( WORDDIF(m,term) + i + extra ) > (LONG)(AM.MaxTer/(2*sizeof(WORD))) ) { /* 23 = 3 +20. The 20 is to have some extra for substitutions or whatever */ if ( AS.CollectOverFlag == 0 && AC.AltCollectFun == 0 ) { Warning("Bracket contents too long in Collect statement"); Warning("Contents spread over more than one term"); Warning("If possible: increase MaxTermSize in setfile"); AS.CollectOverFlag = 1; } else if ( AC.AltCollectFun ) { AS.CollectOverFlag = 2; } break; } tstop = m + *m; *m -= same; m++; while ( r < tstop ) *m++ = *r++; if ( extra == 23 ) extra = ((AM.MaxTer/sizeof(WORD))/6); } FullTerm: h[1] = WORDDIF(m,h); if ( AS.CollectOverFlag > 1 ) { *h = AC.AltCollectFun; if ( AS.CollectOverFlag == 3 ) AS.CollectOverFlag = 1; } else *h = AC.CollectFun; h[2] |= DIRTYFLAG; h[FUNHEAD] = h[1] - FUNHEAD; h[FUNHEAD+1] = 0; if ( ToFast(h+FUNHEAD,h+FUNHEAD) ) { if ( h[FUNHEAD] <= -FUNCTION ) { h[1] = FUNHEAD+1; m = h + FUNHEAD+1; } else { h[1] = FUNHEAD+2; m = h + FUNHEAD+2; } } *m++ = 1; *m++ = 1; *m++ = 3; *term = WORDDIF(m,term); AR.KeptInHold = 1; return(0); } /* #] GetMoreFromMem : #[ GetFromStore : Gets a single term from the storage file at position and puts it at 'to'. The value to be returned is the number of words read. Renumbering is done also. This is controlled by the renumber table, given in 'renumber' This routine should work with a number of cache buffers. The exact number should be definable in form.set. The parameters are: AM.SizeStoreCache (4096) The numbers are the proposed default values. The cache is a pure read cache. */ static int gfs = 0; WORD GetFromStore(WORD *to, POSITION *position, RENUMBER renumber, WORD *InCompState, WORD nexpr) { GETIDENTITY LONG RetCode, num, first = 0; WORD *from, *m; struct StOrEcAcHe sc; STORECACHE s; STORECACHE snext, sold; WORD *r, *rr = AR.CompressPointer; r = rr; gfs++; sc.next = AT.StoreCache; sold = s = ≻ snext = s->next; while ( snext ) { sold = s; s = snext; snext = s->next; if ( BASEPOSITION(s->position) == -1 ) break; if ( ISLESSPOS(*position,s->toppos) && ISGEPOS(*position,s->position) ) { /* Hit */ if ( AT.StoreCache != s ) { sold->next = s->next; s->next = AT.StoreCache->next; AT.StoreCache = s; } from = (WORD *)(((UBYTE *)(s->buffer)) + DIFBASE(*position,s->position)); num = *from; if ( !num ) { return(*to = 0); } *InCompState = (WORD)num; m = to; if ( num < 0 ) { from++; ADDPOS(*position,sizeof(WORD)); *m++ = (WORD)(-num+1); r++; while ( ++num <= 0 ) *m++ = *r++; if ( ISLESSPOS(*position,s->toppos) ) { num = *from++; *to += (WORD)num; ADDPOS(*position,sizeof(WORD)); *InCompState = (WORD)(num + 2); } else { first = 1; goto InNew; } } PastCon:; while ( num > 0 && ISLESSPOS(*position,s->toppos) ) { *r++ = *m++ = *from++; ADDPOS(*position,sizeof(WORD)); num--; } if ( num > 0 ) { InNew: SETBASEPOSITION(s->position,-1); SETBASEPOSITION(s->toppos,-1); LOCK(AM.storefilelock); SeekFile(AR.StoreData.Handle,position,SEEK_SET); RetCode = ReadFile(AR.StoreData.Handle,(UBYTE *)(s->buffer),AM.SizeStoreCache); UNLOCK(AM.storefilelock); if ( RetCode < 0 ) goto PastErr; if ( !RetCode ) return( *to = 0 ); s->position = *position; s->toppos = *position; ADDPOS(s->toppos,RetCode); from = s->buffer; if ( first ) { num = *from++; ADDPOS(*position,sizeof(WORD)); *to += (WORD)num; /* This next line has always been commented, but uncommenting it fixes a rare bug when loading certain save files. */ first = 0; *InCompState = (WORD)(num + 2); } goto PastCon; } goto PastEnd; } } if ( AT.StoreCache ) { /* Fill the last buffer */ s->position = *position; LOCK(AM.storefilelock); SeekFile(AR.StoreData.Handle,position,SEEK_SET); RetCode = ReadFile(AR.StoreData.Handle,(UBYTE *)(s->buffer),AM.SizeStoreCache); UNLOCK(AM.storefilelock); if ( RetCode < 0 ) goto PastErr; if ( !RetCode ) return( *to = 0 ); s->toppos = *position; ADDPOS(s->toppos,RetCode); if ( AT.StoreCache != s ) { sold->next = s->next; s->next = AT.StoreCache->next; AT.StoreCache = s; } m = to; from = s->buffer; num = *from; if ( !num ) { return( *to = 0 ); } *InCompState = (WORD)num; if ( num < 0 ) { *m++ = (WORD)(-num+1); r++; from++; ADDPOS(*position,sizeof(WORD)); while ( ++num <= 0 ) *m++ = *r++; num = *from++; *to += (WORD)num; ADDPOS(*position,sizeof(WORD)); *InCompState = (WORD)(num+2); } goto PastCon; } /* No caching available */ LOCK(AM.storefilelock); SeekFile(AR.StoreData.Handle,position,SEEK_SET); RetCode = ReadFile(AR.StoreData.Handle,(UBYTE *)to,(LONG)sizeof(WORD)); SeekFile(AR.StoreData.Handle,position,SEEK_CUR); UNLOCK(AM.storefilelock); if ( RetCode != sizeof(WORD) ) { *to = 0; return((WORD)RetCode); } if ( !*to ) return(0); m = to; if ( *to < 0 ) { num = *m++; *to = *r++ = (WORD)(-num + 1); while ( ++num <= 0 ) *m++ = *r++; LOCK(AM.storefilelock); SeekFile(AR.StoreData.Handle,position,SEEK_SET); RetCode = ReadFile(AR.StoreData.Handle,(UBYTE *)m,(LONG)sizeof(WORD)); SeekFile(AR.StoreData.Handle,position,SEEK_CUR); UNLOCK(AM.storefilelock); if ( RetCode != sizeof(WORD) ) { MLOCK(ErrorMessageLock); MesPrint("@Error in compression of store file"); MUNLOCK(ErrorMessageLock); return(-1); } num = *m; *to += (WORD)num; *InCompState = (WORD)(num + 2); } else { *InCompState = *to; num = *to - 1; m = to + 1; r = rr + 1; } first = num; num *= wsizeof(WORD); if ( num < 0 ) { MLOCK(ErrorMessageLock); MesPrint("@Error in stored expressions file at position %9p",position); MUNLOCK(ErrorMessageLock); return(-1); } LOCK(AM.storefilelock); SeekFile(AR.StoreData.Handle,position,SEEK_SET); RetCode = ReadFile(AR.StoreData.Handle,(UBYTE *)m,num); SeekFile(AR.StoreData.Handle,position,SEEK_CUR); UNLOCK(AM.storefilelock); if ( RetCode != num ) { MLOCK(ErrorMessageLock); MesPrint("@Error in stored expressions file at position %9p",position); MUNLOCK(ErrorMessageLock); return(-1); } NCOPY(r,m,first); PastEnd: *rr = *to; if ( r >= AR.ComprTop ) { MLOCK(ErrorMessageLock); MesPrint("CompressSize of %10l is insufficient",AM.CompressSize); MUNLOCK(ErrorMessageLock); Terminate(-1); } AR.CompressPointer = r; *r = 0; if ( !TermRenumber(to,renumber,nexpr) ) { MarkDirty(to,DIRTYSYMFLAG); if ( AR.CurDum > AM.IndDum && Expressions[nexpr].numdummies > 0 ) MoveDummies(BHEAD to,AR.CurDum - AM.IndDum); return((WORD)*to); } PastErr: MLOCK(ErrorMessageLock); MesCall("GetFromStore"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] GetFromStore : #[ DetVars : void DetVars(term) Determines which variables are used in term. When par = 1 we are scanning a prototype expression which involves completely different rules. */ void DetVars(WORD *term, WORD par) { GETIDENTITY WORD *stopper; WORD *t, sym; WORD *sarg; stopper = term + *term - 1; stopper = stopper - ABS(*stopper) + 1; term++; if ( par ) { /* Prototype expression */ WORD n; if ( ( n = NumSymbols ) > 0 ) { SYMBOLS tt; tt = symbols; do { (tt++)->flags &= ~INUSE; } while ( --n > 0 ); } if ( ( n = NumIndices ) > 0 ) { INDICES tt; tt = indices; do { (tt++)->flags &= ~INUSE; } while ( --n > 0 ); } if ( ( n = NumVectors ) > 0 ) { VECTORS tt; tt = vectors; do { (tt++)->flags &= ~INUSE; } while ( --n > 0 ); } if ( ( n = NumFunctions ) > 0 ) { FUNCTIONS tt; tt = functions; do { (tt++)->flags &= ~INUSE; } while ( --n > 0 ); } term += SUBEXPSIZE; while ( term < stopper ) { if ( *term == SYMTOSYM || *term == SYMTONUM ) { term += 2; AN.UsedSymbol[*term] = 1; symbols[*term].flags |= INUSE; } else if ( *term == VECTOVEC ) { term += 2; AN.UsedVector[*term-AM.OffsetVector] = 1; vectors[*term-AM.OffsetVector].flags |= INUSE; } else if ( *term == INDTOIND ) { term += 2; sym = indices[*term - AM.OffsetIndex].dimension; if ( sym < 0 ) AN.UsedSymbol[-sym] = 1; AN.UsedIndex[(*term) - AM.OffsetIndex] = 1; sym = indices[*term-AM.OffsetIndex].nmin4; if ( sym < -NMIN4SHIFT ) AN.UsedSymbol[-sym-NMIN4SHIFT] = 1; indices[*term-AM.OffsetIndex].flags |= INUSE; } else if ( *term == FUNTOFUN ) { term += 2; AN.UsedFunction[*term-FUNCTION] = 1; functions[*term-FUNCTION].flags |= INUSE; } term += 2; } } else { while ( term < stopper ) { t = term + term[1]; if ( *term == SYMBOL ) { term += 2; do { AN.UsedSymbol[*term] = 1; term += 2; } while ( term < t ); } else if ( *term == DOTPRODUCT ) { term += 2; do { AN.UsedVector[(*term++) - AM.OffsetVector] = 1; AN.UsedVector[(*term) - AM.OffsetVector] = 1; term += 2; } while ( term < t ); } else if ( *term == VECTOR ) { term += 2; do { AN.UsedVector[(*term++) - AM.OffsetVector] = 1; if ( *term >= AM.OffsetIndex && *term < AM.DumInd ) { sym = indices[*term - AM.OffsetIndex].dimension; if ( sym < 0 ) AN.UsedSymbol[-sym] = 1; AN.UsedIndex[*term - AM.OffsetIndex] = 1; sym = indices[(*term++)-AM.OffsetIndex].nmin4; if ( sym < -NMIN4SHIFT ) AN.UsedSymbol[-sym-NMIN4SHIFT] = 1; } else term++; } while ( term < t ); } else if ( *term == INDEX || *term == LEVICIVITA || *term == GAMMA || *term == DELTA ) { /* Tensors: term += 2; */ if ( *term == INDEX || *term == DELTA ) term += 2; else { Tensors: term += FUNHEAD; } while ( term < t ) { if ( *term >= AM.OffsetIndex && *term < AM.DumInd ) { sym = indices[*term - AM.OffsetIndex].dimension; if ( sym < 0 ) AN.UsedSymbol[-sym] = 1; AN.UsedIndex[(*term) - AM.OffsetIndex] = 1; sym = indices[*term-AM.OffsetIndex].nmin4; if ( sym < -NMIN4SHIFT ) AN.UsedSymbol[-sym-NMIN4SHIFT] = 1; } else if ( *term < (WILDOFFSET+AM.OffsetVector) ) AN.UsedVector[(*term) - AM.OffsetVector] = 1; term++; } } else if ( *term == HAAKJE ) term = t; else { if ( *term > MAXBUILTINFUNCTION ) AN.UsedFunction[(*term)-FUNCTION] = 1; if ( *term >= FUNCTION && functions[*term-FUNCTION].spec >= TENSORFUNCTION && term[1] > FUNHEAD ) goto Tensors; term += FUNHEAD; /* First argument */ while ( term < t ) { sarg = term; NEXTARG(sarg) if ( *term > 0 ) { sarg = term + *term; /* End of argument */ term += ARGHEAD; /* First term in argument */ if ( term < sarg ) { do { DetVars(term,par); term += *term; } while ( term < sarg ); } } else { if ( *term < -MAXBUILTINFUNCTION ) { AN.UsedFunction[-*term-FUNCTION] = 1; } else if ( *term == -SYMBOL ) { AN.UsedSymbol[term[1]] = 1; } else if ( *term == -INDEX ) { if ( term[1] < (WILDOFFSET+AM.OffsetVector) ) { AN.UsedVector[term[1]-AM.OffsetVector] = 1; } else if ( term[1] >= AM.OffsetIndex && term[1] < AM.DumInd ) { sym = indices[term[1] - AM.OffsetIndex].dimension; if ( sym < 0 ) AN.UsedSymbol[-sym] = 1; AN.UsedIndex[term[1] - AM.OffsetIndex] = 1; sym = indices[term[1]-AM.OffsetIndex].nmin4; if ( sym < -NMIN4SHIFT ) AN.UsedSymbol[-sym-NMIN4SHIFT] = 1; } } else if ( *term == -VECTOR || *term == -MINVECTOR ) { AN.UsedVector[term[1]-AM.OffsetVector] = 1; } } term = sarg; /* Next argument */ } term = t; } } } } /* #] DetVars : #[ ToStorage : This routine takes an expression in the scratch buffer (indicated by e) and puts it in the storage file. The necessary actions are: 1: determine the list of the used variables. 2: make an index entry. 3: write the namelists. 4: copy the 'length' bytes of the expression. */ int ToStorage(EXPRESSIONS e, POSITION *length) { GETIDENTITY WORD *w, i, j; WORD *term; INDEXENTRY *indexent; LONG size; POSITION indexpos, scrpos; FILEHANDLE *f; if ( ( indexent = NextFileIndex(&indexpos) ) == 0 ) { MesCall("ToStorage"); SETERROR(-1) } indexent->CompressSize = 0; /* thus far no compression */ f = AR.infile; AR.infile = AR.outfile; AR.outfile = f; if ( e->status == HIDDENGEXPRESSION ) { AR.InHiBuf = 0; f = AR.hidefile; AR.GetFile = 2; } else { AR.InInBuf = 0; f = AR.infile; AR.GetFile = 0; } if ( f->handle >= 0 ) { scrpos = e->onfile; SeekFile(f->handle,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,e->onfile) ) { MesPrint(":::Error in Scratch file"); goto ErrReturn; } f->POposition = e->onfile; f->POfull = f->PObuffer; if ( e->status == HIDDENGEXPRESSION ) AR.InHiBuf = 0; else AR.InInBuf = 0; } else { f->POfill = (WORD *)((UBYTE *)(f->PObuffer)+BASEPOSITION(e->onfile)); } w = AT.WorkPointer; AN.UsedSymbol = w; w += NumSymbols; AN.UsedVector = w; w += NumVectors; AN.UsedIndex = w; w += NumIndices; AN.UsedFunction = w; w += NumFunctions; term = w; w = (WORD *)(((UBYTE *)(w)) + AM.MaxTer); if ( w > AT.WorkTop ) { MesWork(); goto ErrReturn; } w = AN.UsedSymbol; i = NumSymbols + NumVectors + NumIndices + NumFunctions; do { *w++ = 0; } while ( --i > 0 ); if ( GetTerm(BHEAD term) > 0 ) { DetVars(term,1); if ( GetTerm(BHEAD term) ) { do { DetVars(term,0); } while ( GetTerm(BHEAD term) > 0 ); } } j = 0; w = AN.UsedSymbol; i = NumSymbols; while ( --i >= 0 ) { if ( *w++ ) j++; } indexent->nsymbols = j; /* size = j * sizeof(struct SyMbOl); */ j = 0; w = AN.UsedIndex; i = NumIndices; while ( --i >= 0 ) { if ( *w++ ) j++; } indexent->nindices = j; /* size += j * sizeof(struct InDeX); */ j = 0; w = AN.UsedVector; i = NumVectors; while ( --i >= 0 ) { if ( *w++ ) j++; } indexent->nvectors = j; /* size += j * sizeof(struct VeCtOr); */ j = 0; w = AN.UsedFunction; i = NumFunctions; while ( --i >= 0 ) { if ( *w++ ) j++; } indexent->nfunctions = j; /* size += j * sizeof(struct FuNcTiOn); */ indexent->length = *length; indexent->variables = AR.StoreData.Fill; /* indexent->position = AR.StoreData.Fill + size; */ StrCopy(AC.exprnames->namebuffer+e->name,(UBYTE *)(indexent->name)); SeekFile(AR.StoreData.Handle,&(AR.StoreData.Fill),SEEK_SET); AO.wlen = 100000; AO.wpos = (UBYTE *)Malloc1(AO.wlen,"AO.wpos buffer"); AO.wpoin = AO.wpos; { SYMBOLS a; w = AN.UsedSymbol; a = symbols; j = 0; i = indexent->nsymbols; while ( --i >= 0 ) { while ( !*w ) { w++; a++; j++; } a->number = j; if ( VarStore((UBYTE *)a,(WORD)(sizeof(struct SyMbOl)),a->name, a->namesize) ) goto ErrToSto; w++; j++; a++; } } { INDICES a; w = AN.UsedIndex; a = indices; j = 0; i = indexent->nindices; while ( --i >= 0 ) { while ( !*w ) { w++; a++; j++; } a->number = j; if ( VarStore((UBYTE *)a,(WORD)(sizeof(struct InDeX)),a->name, a->namesize) ) goto ErrToSto; w++; j++; a++; } } { VECTORS a; w = AN.UsedVector; a = vectors; j = 0; i = indexent->nvectors; while ( --i >= 0 ) { while ( !*w ) { w++; a++; j++; } a->number = j; if ( VarStore((UBYTE *)a,(WORD)(sizeof(struct VeCtOr)),a->name, a->namesize) ) goto ErrToSto; w++; j++; a++; } } { FUNCTIONS a; w = AN.UsedFunction; a = functions; j = 0; i = indexent->nfunctions; while ( --i >= 0 ) { while ( !*w ) { w++; a++; j++; } a->number = j; if ( VarStore((UBYTE *)a,(WORD)(sizeof(struct FuNcTiOn)),a->name, a->namesize) ) goto ErrToSto; w++; a++; j++; } } if ( VarStore((UBYTE *)0L,(WORD)0,(WORD)0,(WORD)0) ) goto ErrToSto; /* Flush buffer */ TELLFILE(AR.StoreData.Handle,&(indexent->position)); indexent->size = (WORD)DIFBASE(indexent->position,indexent->variables); /* The following code was added when it became apparent (30-jan-2007) that we need provisions for extra space without upsetting existing .sav files. Here we can put as much as we want. Look in GetTable on how to recover numdummies. Forgetting numdummies has been in there from the beginning. */ if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&(e->numdummies)),(LONG)sizeof(WORD)) != sizeof(WORD) ) { MesPrint("Error while writing storage file"); goto ErrReturn; } if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&(e->numfactors)),(LONG)sizeof(WORD)) != sizeof(WORD) ) { MesPrint("Error while writing storage file"); goto ErrReturn; } if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&(e->vflags)),(LONG)sizeof(WORD)) != sizeof(WORD) ) { MesPrint("Error while writing storage file"); goto ErrReturn; } if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&(e->uflags)),(LONG)sizeof(WORD)) != sizeof(WORD) ) { MesPrint("Error while writing storage file"); goto ErrReturn; } TELLFILE(AR.StoreData.Handle,&(indexent->position)); if ( f->handle >= 0 ) { POSITION llength; llength = *length; SeekFile(f->handle,&(e->onfile),SEEK_SET); while ( ISPOSPOS(llength) ) { SETBASEPOSITION(scrpos,AO.wlen); if ( ISLESSPOS(llength,scrpos) ) size = BASEPOSITION(llength); else size = AO.wlen; if ( ReadFile(f->handle,AO.wpos,size) != size ) { MesPrint("Error while reading scratch file"); goto ErrReturn; } if ( WriteFile(AR.StoreData.Handle,AO.wpos,size) != size ) { MesPrint("Error while writing storage file"); goto ErrReturn; } ADDPOS(llength,-size); } } else { WORD *ppp; ppp = (WORD *)((UBYTE *)(f->PObuffer) + BASEPOSITION(e->onfile)); if ( WriteFile(AR.StoreData.Handle,(UBYTE *)ppp,BASEPOSITION(*length)) != BASEPOSITION(*length) ) { MesPrint("Error while writing storage file"); goto ErrReturn; } } ADD2POS(*length,indexent->position); e->onfile = indexpos; /* AR.StoreData.Fill = SeekFile(AR.StoreData.Handle,&(AM.zeropos),SEEK_END); */ AR.StoreData.Fill = *length; SeekFile(AR.StoreData.Handle,&(AR.StoreData.Fill),SEEK_SET); scrpos = AR.StoreData.Position; ADDPOS(scrpos,sizeof(POSITION)); SeekFile(AR.StoreData.Handle,&scrpos,SEEK_SET); if ( WriteFile(AR.StoreData.Handle,((UBYTE *)&(AR.StoreData.Index.number)) ,(LONG)(sizeof(POSITION))) != sizeof(POSITION) ) goto ErrInSto; SeekFile(AR.StoreData.Handle,&indexpos,SEEK_SET); if ( WriteFile(AR.StoreData.Handle,(UBYTE *)indexent,(LONG)(sizeof(INDEXENTRY))) != sizeof(INDEXENTRY) ) goto ErrInSto; FlushFile(AR.StoreData.Handle); SeekFile(AR.StoreData.Handle,&(AC.StoreFileSize),SEEK_END); f = AR.infile; AR.infile = AR.outfile; AR.outfile = f; if ( AO.wpos ) M_free(AO.wpos,"AO.wpos buffer"); AO.wpos = AO.wpoin = 0; return(0); ErrToSto: MesPrint("---Error while storing namelists"); goto ErrReturn; ErrInSto: MesPrint("Error in storage"); ErrReturn: if ( AO.wpos ) M_free(AO.wpos,"AO.wpos buffer"); AO.wpos = AO.wpoin = 0; f = AR.infile; AR.infile = AR.outfile; AR.outfile = f; return(-1); } /* #] ToStorage : #[ NextFileIndex : */ INDEXENTRY *NextFileIndex(POSITION *indexpos) { GETIDENTITY INDEXENTRY *ind; int i, j = sizeof(FILEINDEX)/(sizeof(LONG)); LONG *lo; if ( AR.StoreData.Handle <= 0 ) { if ( SetFileIndex() ) { MesCall("NextFileIndex"); return(0); } SETBASEPOSITION(AR.StoreData.Index.number,1); #ifdef SYSDEPENDENTSAVE SETBASEPOSITION(*indexpos,(2*sizeof(POSITION))); #else SETBASEPOSITION(*indexpos,(2*sizeof(POSITION)+sizeof(STOREHEADER))); #endif return(AR.StoreData.Index.expression); } while ( BASEPOSITION(AR.StoreData.Index.number) >= (LONG)(INFILEINDEX) ) { if ( ISNOTZEROPOS(AR.StoreData.Index.next) ) { SeekFile(AR.StoreData.Handle,&(AR.StoreData.Index.next),SEEK_SET); AR.StoreData.Position = AR.StoreData.Index.next; if ( ReadFile(AR.StoreData.Handle,(UBYTE *)(&AR.StoreData.Index),(LONG)(sizeof(FILEINDEX))) != (LONG)(sizeof(FILEINDEX)) ) goto ErrNextS; } else { PUTZERO(AR.StoreData.Index.number); SeekFile(AR.StoreData.Handle,&(AR.StoreData.Position),SEEK_SET); if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&(AR.StoreData.Fill)),(LONG)(sizeof(POSITION))) != (LONG)(sizeof(POSITION)) ) goto ErrNextS; PUTZERO(AR.StoreData.Index.next); SeekFile(AR.StoreData.Handle,&(AR.StoreData.Fill),SEEK_SET); AR.StoreData.Position = AR.StoreData.Fill; lo = (LONG *)(&AR.StoreData.Index); for ( i = 0; i < j; i++ ) *lo++ = 0; if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&AR.StoreData.Index),(LONG)(sizeof(FILEINDEX))) != (LONG)(sizeof(FILEINDEX)) ) goto ErrNextS; ADDPOS(AR.StoreData.Fill,sizeof(FILEINDEX)); } } *indexpos = AR.StoreData.Position; ADDPOS(*indexpos,(2*sizeof(POSITION)) + BASEPOSITION(AR.StoreData.Index.number) * sizeof(INDEXENTRY)); ind = &AR.StoreData.Index.expression[BASEPOSITION(AR.StoreData.Index.number)]; ADDPOS(AR.StoreData.Index.number,1); return(ind); ErrNextS: MesPrint("Error in storage file"); return(0); } /* #] NextFileIndex : #[ SetFileIndex : */ /** * Reads the next file index and puts it into AR.StoreData.Index. TODO * * @return = 0 everything okay, != 0 an error occurred */ int SetFileIndex(void) { GETIDENTITY int i, j = sizeof(FILEINDEX)/(sizeof(LONG)); LONG *lo; if ( AR.StoreData.Handle < 0 ) { AR.StoreData.Handle = AC.StoreHandle; PUTZERO(AR.StoreData.Index.next); PUTZERO(AR.StoreData.Index.number); #ifdef SYSDEPENDENTSAVE SETBASEPOSITION(AR.StoreData.Fill,sizeof(FILEINDEX)); #else if ( WriteStoreHeader(AR.StoreData.Handle) ) return(MesPrint("Error writing storage file header")); SETBASEPOSITION(AR.StoreData.Fill, (LONG)sizeof(FILEINDEX)+(LONG)sizeof(STOREHEADER)); #endif lo = (LONG *)(&AR.StoreData.Index); for ( i = 0; i < j; i++ ) *lo++ = 0; if ( WriteFile(AR.StoreData.Handle,(UBYTE *)(&AR.StoreData.Index),(LONG)(sizeof(FILEINDEX))) != (LONG)(sizeof(FILEINDEX)) ) return(MesPrint("Error writing storage file")); } else { POSITION scrpos; #ifdef SYSDEPENDENTSAVE PUTZERO(scrpos); #else SETBASEPOSITION(scrpos, (LONG)(sizeof(STOREHEADER))); #endif SeekFile(AR.StoreData.Handle,&scrpos,SEEK_SET); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)(&AR.StoreData.Index),(LONG)(sizeof(FILEINDEX))) != (LONG)(sizeof(FILEINDEX)) ) return(MesPrint("Error reading storage file")); } #ifdef SYSDEPENDENTSAVE PUTZERO(AR.StoreData.Position); #else SETBASEPOSITION(AR.StoreData.Position, (LONG)(sizeof(STOREHEADER))); #endif return(0); } /* #] SetFileIndex : #[ VarStore : The n -= sizeof(WORD); makes that the real length comes in the padding space, provided there is padding space (it seems so). The reading of the information assumes this is the case and hence things work.... */ int VarStore(UBYTE *s, WORD n, WORD name, WORD namesize) { GETIDENTITY UBYTE *t, *u; if ( s ) { n -= sizeof(WORD); t = (UBYTE *)AO.wpoin; /* u = (UBYTE *)AT.WorkTop; */ u = AO.wpos+AO.wlen; while ( n > 0 && t < u ) { *t++ = *s++; n--; } while ( t >= u ) { if ( WriteFile(AR.StoreData.Handle,AO.wpos,AO.wlen) != AO.wlen ) return(-1); t = AO.wpos; while ( n > 0 && t < u ) { *t++ = *s++; n--; } } s = AC.varnames->namebuffer + name; n = namesize; n += sizeof(void *)-1; n &= -(sizeof(void *)); *((WORD *)t) = n; t += sizeof(WORD); while ( n > 0 && t < u ) { if ( namesize > 0 ) { *t++ = *s++; namesize--; } else { *t++ = 0; } n--; } while ( t >= u ) { if ( WriteFile(AR.StoreData.Handle,AO.wpos,AO.wlen) != AO.wlen ) return(-1); t = AO.wpos; while ( n > 0 && t < u ) { if ( namesize > 0 ) { *t++ = *s++; namesize--; } else { *t++ = 0; } n--; } } AO.wpoin = t; } else { LONG size; size = AO.wpoin - AO.wpos; if ( WriteFile(AR.StoreData.Handle,AO.wpos,size) != size ) return(-1); AO.wpoin = AO.wpos; } return(0); } /* #] VarStore : #[ TermRenumber : renumbers the variables inside term according to the information in struct renumber. The search is binary. This avoided having to read/write the expression twice when it was stored. */ int TermRenumber(WORD *term, RENUMBER renumber, WORD nexpr) { WORD *stopper; /*!!! WORD *memterm=term; static LONG ctrap=0; !!!*/ WORD *t, *sarg, n; stopper = term + *term - 1; stopper = stopper - ABS(*stopper) + 1; term++; while ( term < stopper ) { /*!!! ctrap++; !!!*/ if ( *term == SYMBOL ) { t = term + term[1]; term += 2; do { if ( ( n = FindrNumber(*term,&(renumber->symb)) ) < 0 ) goto ErrR; *term = renumber->symnum[n]; term += 2; } while ( term < t ); } else if ( *term == DOTPRODUCT ) { t = term + term[1]; term += 2; do { if ( ( n = FindrNumber(*term,&(renumber->vect)) ) < 0 ) goto ErrR; *term++ = renumber->vecnum[n]; if ( ( n = FindrNumber(*term,&(renumber->vect)) ) < 0 ) goto ErrR; *term = renumber->vecnum[n]; term += 2; } while ( term < t ); } else if ( *term == VECTOR ) { t = term + term[1]; term += 2; do { if ( ( n = FindrNumber(*term,&(renumber->vect)) ) < 0 ) goto ErrR; *term++ = renumber->vecnum[n]; if ( ( *term >= AM.OffsetIndex ) && ( *term < AM.IndDum ) ) { if ( ( n = FindrNumber(*term,&(renumber->indi)) ) < 0 ) goto ErrR; *term++ = renumber->indnum[n]; } else term++; } while ( term < t ); } else if ( *term == INDEX || *term == LEVICIVITA || *term == GAMMA || *term == DELTA ) { Tensors: t = term + term[1]; if ( *term == INDEX || * term == DELTA ) term += 2; else term += FUNHEAD; /* term += 2; */ while ( term < t ) { if ( *term >= AM.OffsetIndex + WILDOFFSET ) { /* Still TOBEDONE */ } else if ( ( *term >= AM.OffsetIndex ) && ( *term < AM.IndDum ) ) { if ( ( n = FindrNumber(*term,&(renumber->indi)) ) < 0 ) goto ErrR; *term = renumber->indnum[n]; } else if ( *term < (WILDOFFSET+AM.OffsetVector) ) { if ( ( n = FindrNumber(*term,&(renumber->vect)) ) < 0 ) goto ErrR; *term = renumber->vecnum[n]; } term++; } } else if ( *term == HAAKJE ) term += term[1]; else { if ( *term > MAXBUILTINFUNCTION ) { if ( ( n = FindrNumber(*term,&(renumber->func)) ) < 0 ) goto ErrR; *term = renumber->funnum[n]; } if ( *term >= FUNCTION && functions[*term-FUNCTION].spec >= TENSORFUNCTION && term[1] > FUNHEAD ) goto Tensors; t = term + term[1]; /* General stopper */ term += FUNHEAD; /* First argument */ while ( term < t ) { sarg = term; NEXTARG(sarg) if ( *term > 0 ) { /* Problem here: Marking the argument as dirty attacks the heap very heavily and costs much computer time. */ *++term = 1; term += ARGHEAD-1; while ( term < sarg ) { if ( TermRenumber(term,renumber,nexpr) ) goto ErrR; term += *term; } } else { if ( *term <= -MAXBUILTINFUNCTION ) { if ( ( n = FindrNumber(-*term,&(renumber->func)) ) < 0 ) goto ErrR; *term = -renumber->funnum[n]; } else if ( *term == -SYMBOL ) { term++; if ( ( n = FindrNumber(*term, &(renumber->symb)) ) < 0 ) goto ErrR; *term = renumber->symnum[n]; } else if ( *term == -INDEX ) { term++; if ( *term >= AM.OffsetIndex + WILDOFFSET ) { /* Still TOBEDONE */ } else if ( ( *term >= AM.OffsetIndex ) && ( *term < AM.IndDum ) ) { if ( ( n = FindrNumber(*term,&(renumber->indi)) ) < 0 ) goto ErrR; *term = renumber->indnum[n]; } else if ( *term < (WILDOFFSET+AM.OffsetVector) ) { if ( ( n = FindrNumber(*term,&(renumber->vect)) ) < 0 ) goto ErrR; *term = renumber->vecnum[n]; } } else if ( *term == -VECTOR || *term == -MINVECTOR ) { term++; if ( ( n = FindrNumber(*term,&(renumber->vect)) ) < 0 ) goto ErrR; *term = renumber->vecnum[n]; } } term = sarg; /* Next argument */ } term = t; } } return(0); ErrR: MesCall("TermRenumber"); SETERROR(-1) } /* #] TermRenumber : #[ FindrNumber : */ WORD FindrNumber(WORD n, VARRENUM *v) { WORD *hi,*med,*lo; hi = v->hi; lo = v->lo; med = v->start; if ( *hi == 0 ) { if ( n != *hi ) { MesPrint("Serious problems coming up in FindrNumber"); return(-1); } return(*hi); } while ( *med != n ) { if ( *med < n ) { if ( med == hi ) goto ErrFindr; lo = med; med = hi - ((WORDDIF(hi,med))/2); } else { if ( med == lo ) goto ErrFindr; hi = med; med = lo + ((WORDDIF(med,lo))/2); } } return(WORDDIF(med,v->lo)); ErrFindr: /* Reconstruction: */ { int i; i = WORDDIF(v->hi,v->lo); MesPrint("FindrNumber: n = %d, list has %d members",n,i); while ( i >= 0 ) { MesPrint("v->lo[%d] = %d",i,v->lo[i]); i--; } hi = v->hi; lo = v->lo; med = v->start; MesPrint("Start with %d,%d,%d",0,WORDDIF(med,v->lo),WORDDIF(hi,v->lo)); while ( *med != n ) { if ( *med < n ) { if ( med == hi ) goto ErrFindr2; lo = med; med = hi - ((WORDDIF(hi,med))/2); } else { if ( med == lo ) goto ErrFindr2; hi = med; med = ((WORDDIF(med,lo))/2) + lo; } MesPrint("New: %d,%d,%d, *med = %d",WORDDIF(lo,v->lo),WORDDIF(med,v->lo),WORDDIF(hi,v->lo),*med); } } return(WORDDIF(med,v->lo)); ErrFindr2: return(MesPrint("Renumbering problems")); } /* #] FindrNumber : #[ FindInIndex : Finds an expression in the storage index if it exists. If found it returns a pointer to the index entry, otherwise zero. par = 0 Search by address (--> f == &AR.StoreData, called by GetTable, CoSave ) par = 1 Search by name (--> f == &AO.SaveData, called by CoLoad ) When comparing parameter fields the parameters of the expression to be searched are in AT.TMaddr. This includes the primary expression and a possible FROMBRAC information. The FROMBRAC is always last. The parameter mode tells whether we should worry about arguments of a stored expression. */ INDEXENTRY *FindInIndex(WORD expr, FILEDATA *f, WORD par, WORD mode) { GETIDENTITY INDEXENTRY *ind; WORD i, hand, *m; WORD *start, *stop, *stop2, *m2, nomatch = 0; POSITION stindex, indexpos, scrpos; LONG number, num; stindex = f->Position; m = AT.TMaddr; stop = m + m[1]; m += SUBEXPSIZE; start = m; while ( m < stop ) { if ( *m == FROMBRAC || *m == WILDCARDS ) break; m += m[1]; } stop = m; if ( !par ) hand = AR.StoreData.Handle; else hand = AO.SaveData.Handle; for(;;) { if ( ( i = (WORD)BASEPOSITION(f->Index.number) ) != 0 ) { indexpos = f->Position; ADDPOS(indexpos,(2*sizeof(POSITION))); ind = f->Index.expression; do { if ( ( !par && ISEQUALPOS(indexpos,Expressions[expr].onfile) ) || ( par && !StrCmp(EXPRNAME(expr),(UBYTE *)(ind->name)) ) ) { nomatch = 1; /* MesPrint("index: position: %8p",&(ind->position)); MesPrint("index: length: %8p",&(ind->length)); MesPrint("index: variables: %8p",&(ind->variables)); MesPrint("index: nsymbols: %d",ind->nsymbols); MesPrint("index: nindices: %d",ind->nindices); MesPrint("index: nvectors: %d",ind->nvectors); MesPrint("index: nfunctions: %d",ind->nfunctions); MesPrint("index: size: %d",ind->size); */ if ( par ) return(ind); scrpos = ind->position; SeekFile(hand,&scrpos,SEEK_SET); if ( ISNOTEQUALPOS(scrpos,ind->position) ) goto ErrGt2; if ( ReadFile(hand,(UBYTE *)AT.WorkPointer,(LONG)sizeof(WORD)) != sizeof(WORD) || !*AT.WorkPointer ) goto ErrGt2; num = *AT.WorkPointer - 1; num *= wsizeof(WORD); if ( *AT.WorkPointer < 0 || ReadFile(hand,(UBYTE *)(AT.WorkPointer+1),num) != num ) goto ErrGt2; m = start; /* start of parameter field to be searched */ m2 = AT.WorkPointer + 1; stop2 = m2 + m2[1]; m2 += SUBEXPSIZE; while ( m < stop && m2 < stop2 ) { if ( *m == SYMBOL ) { if ( *m2 != SYMTOSYM ) break; m2[3] = m[2]; } else if ( *m == INDEX ) { if ( m[2] >= 0 ) { if ( *m2 != INDTOIND ) break; } else { if ( *m2 != VECTOVEC ) break; } m2[3] = m[2]; } else if ( *m >= FUNCTION ) { if ( *m2 != FUNTOFUN ) break; m2[3] = *m; } else {} m += m[1]; m2 += m2[1]; } if ( ( m >= stop && m2 >= stop2 ) || mode == 0 ) { AT.WorkPointer = stop2; return(ind); } } ind++; ADDPOS(indexpos,sizeof(INDEXENTRY)); } while ( --i > 0 ); } f->Position = f->Index.next; #ifndef SYSDEPENDENTSAVE if ( !ISNOTZEROPOS(f->Position) ) ADDPOS(f->Position,sizeof(STOREHEADER)); number = sizeof(struct FiLeInDeX); #endif if ( ISEQUALPOS(f->Position,stindex) && !AO.bufferedInd ) goto ErrGetTab; if ( !par ) { SeekFile(AR.StoreData.Handle,&(f->Position),SEEK_SET); if ( ISNOTEQUALPOS(f->Position,AR.StoreData.Position) ) goto ErrGt2; #ifndef SYSDEPENDENTSAVE if ( ReadFile(f->Handle, (UBYTE *)(&(f->Index)), number) != number ) goto ErrGt2; #endif } else { SeekFile(AO.SaveData.Handle,&(f->Position),SEEK_SET); if ( ISNOTEQUALPOS(f->Position,AO.SaveData.Position) ) goto ErrGt2; #ifndef SYSDEPENDENTSAVE if ( ReadSaveIndex(&f->Index) ) goto ErrGt2; #endif } #ifdef SYSDEPENDENTSAVE number = sizeof(struct FiLeInDeX); if ( ReadFile(f->Handle,(UBYTE *)(&(f->Index)),number) != number ) goto ErrGt2; #endif } ErrGetTab: if ( nomatch ) { MesPrint("Parameters of expression %s don't match." ,EXPRNAME(expr)); } else { MesPrint("Cannot find expression %s",EXPRNAME(expr)); } return(0); ErrGt2: MesPrint("Readerror in IndexSearch"); return(0); } /* #] FindInIndex : #[ GetTable : Locates stored files and constructs the renumbering tables. They are allocated in the WorkSpace. First the expression data are located. The Index is treated as a circularly linked buffer which is paged forwardly. If the indexentry is located (in ind) the two renumber tables have to be constructed. Finally the prototype has to be put in the proper buffer, so that wildcards can be passed. There should be a test with an already existing prototype that is constructed by the pattern matcher. This has not been put in yet. There is a problem with the parallel processing. Feeding in the variables that were erased by a .store could in principle happen in different orders (ParFORM) or simultaneously (TFORM). The proper resolution is to have the compiler call GetTable when a stored expression is encountered. This has been mended in development of TFORM by reading the symbol tables during compilation. See the call to GetTable in the CodeGenerator. Next is the problem of FindInIndex which writes in AR.StoreData Copying this is expensive! This Doesn't work well for TFORM yet.!!!!!!!! e[x1,x2] versus e[x2,x1] messes up. For the rest is the reloading during execution not thread safe. The parameter mode tells whether we should worry about arguments of a stored expression. */ RENUMBER GetTable(WORD expr, POSITION *position, WORD mode) { GETIDENTITY WORD i, j; WORD *w; RENUMBER r; LONG num, nsize, xx; WORD jsym, jind, jvec, jfun; WORD k, type, error = 0, *oldw, *neww, *oldwork = AT.WorkPointer; struct SyMbOl SyM; struct InDeX InD; struct VeCtOr VeC; struct FuNcTiOn FuN; INDEXENTRY *ind; /* Prepare for FindInIndex to put the prototype in the WorkSpace. oldw will point at the "wildcards" */ /* Bug fix. Look also in Generator. #ifndef WITHPTHREADS if ( ( r = Expressions[expr].renum ) != 0 ) { } else { Expressions[expr].renum = r = (RENUMBER)Malloc1(sizeof(struct ReNuMbEr),"Renumber"); } #else r = (RENUMBER)Malloc1(sizeof(struct ReNuMbEr),"Renumber"); #endif */ r = (RENUMBER)Malloc1(sizeof(struct ReNuMbEr),"Renumber"); oldw = AT.WorkPointer + 1 + SUBEXPSIZE; /* The prototype is loaded in the WorkSpace by the Index routine. After all it has to find an occurrence with the proper arguments. This sets the WorkPointer. Hence be careful now. */ LOCK(AM.storefilelock); if ( ( ind = FindInIndex(expr,&AR.StoreData,0,mode) ) == 0 ) { UNLOCK(AM.storefilelock); return(0); } xx = ind->nsymbols+ind->nindices+ind->nvectors+ind->nfunctions; if ( xx == 0 ) { Expressions[expr].renumlists = w = AN.dummyrenumlist; } else { /* #ifndef WITHPTHREADS Expressions[expr].renumlists = #endif */ w = (WORD *)Malloc1(sizeof(WORD)*(xx*2),"VarSpace"); } r->symb.lo = w; r->symb.start = w + ind->nsymbols/2; w += ind->nsymbols; r->symb.hi = w - 1; r->symnum = w; w += ind->nsymbols; r->indi.lo = w; r->indi.start = w + ind->nindices/2; w += ind->nindices; r->indi.hi = w - 1; r->indnum = w; w += ind->nindices; r->vect.lo = w; r->vect.start = w + ind->nvectors/2; w += ind->nvectors; r->vect.hi = w - 1; r->vecnum = w; w += ind->nvectors; r->func.lo = w; r->func.start = w + ind->nfunctions/2; w += ind->nfunctions; r->func.hi = w - 1; r->funnum = w; /* w += ind->nfunctions; */ SeekFile(AR.StoreData.Handle,&(ind->variables),SEEK_SET); *position = ind->position; jsym = ind->nsymbols; jvec = ind->nvectors; jind = ind->nindices; jfun = ind->nfunctions; /* #[ Symbols : */ { SYMBOLS s = &SyM; w = r->symb.lo; j = jsym; for ( i = 0; i < j; i++ ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)s,(LONG)(sizeof(struct SyMbOl))) != sizeof(struct SyMbOl) ) goto ErrGt2; nsize = s->namesize; nsize += sizeof(void *)-1; nsize &= -sizeof(void *); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)(AT.WorkPointer),nsize) != nsize ) goto ErrGt2; *w = s->number; if ( ( s->flags & INUSE ) != 0 ) { /* Find the replacement. It must exist! */ neww = oldw; while ( *neww != SYMTOSYM || neww[2] != *w ) neww += neww[1]; k = neww[3]; } else if ( GetVar((UBYTE *)AT.WorkPointer,&type,&k,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { if ( type != CSYMBOL ) { MesPrint("Error: Conflicting types for %s",(AT.WorkPointer)); error = -1; } else { if ( ( s->complex & (VARTYPEIMAGINARY|VARTYPECOMPLEX) ) != ( symbols[k].complex & (VARTYPEIMAGINARY|VARTYPECOMPLEX) ) ) { MesPrint("Warning: Conflicting complexity for %s",AT.WorkPointer); error = -1; } if ( ( s->complex & (VARTYPEROOTOFUNITY) ) != ( symbols[k].complex & (VARTYPEROOTOFUNITY) ) ) { MesPrint("Warning: Conflicting root of unity properties for %s",AT.WorkPointer); error = -1; } if ( ( s->complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) { if ( s->maxpower != symbols[k].maxpower ) { MesPrint("Warning: Conflicting n in n-th root of unity properties for %s",AT.WorkPointer); error = -1; } } else if ( ( s->minpower != symbols[k].minpower || s->maxpower != symbols[k].maxpower ) && AC.WarnFlag ) { MesPrint("Warning: Conflicting power restrictions for %s",AT.WorkPointer); } } } else { if ( ( k = EntVar(CSYMBOL,(UBYTE *)(AT.WorkPointer),s->complex,s->minpower, s->maxpower,s->dimension) ) < 0 ) goto GetTcall; } *(w+j) = k; w++; } } /* #] Symbols : #[ Indices : */ { INDICES s = &InD; w = r->indi.lo; j = jind; for ( i = 0; i < j; i++ ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)s,(LONG)(sizeof(struct InDeX))) != sizeof(struct InDeX) ) goto ErrGt2; nsize = s->namesize; nsize += sizeof(void *)-1; nsize &= -sizeof(void *); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)(AT.WorkPointer),nsize) != nsize ) goto ErrGt2; *w = s->number + AM.OffsetIndex; if ( s->dimension < 0 ) { /* Relabel the dimension */ s->dimension = -r->symnum[FindrNumber(-s->dimension,&(r->symb))]; if ( s->nmin4 < -NMIN4SHIFT ) { /* Relabel n-4 */ s->nmin4 = -r->symnum[FindrNumber(-s->nmin4-NMIN4SHIFT ,&(r->symb))]-NMIN4SHIFT; } } if ( ( s->flags & INUSE ) != 0 ) { /* Find the replacement. It must exist! */ neww = oldw; while ( *neww != INDTOIND || neww[2] != *w ) neww += neww[1]; k = neww[3] - AM.OffsetIndex; } else if ( s->type == DUMMY ) { /* --------> Here we may have to execute some renumbering */ } else if ( GetVar((UBYTE *)(AT.WorkPointer),&type,&k,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { if ( type != CINDEX ) { MesPrint("Error: Conflicting types for %s",(AT.WorkPointer)); error = -1; } else { if ( s->type != indices[k].type ) { MesPrint("Warning: %s is also a dummy index",(AT.WorkPointer)); error = -1; goto GetTb3; } if ( s->dimension != indices[k].dimension ) { MesPrint("Warning: Conflicting dimensions for %s",(AT.WorkPointer)); error = -1; } } } else { GetTb3: if ( ( k = EntVar(CINDEX,(UBYTE *)(AT.WorkPointer), s->dimension,0,s->nmin4,0) ) < 0 ) goto GetTcall; } *(w+j) = k + AM.OffsetIndex; w++; } } /* #] Indices : #[ Vectors : */ { VECTORS s = &VeC; w = r->vect.lo; j = jvec; for ( i = 0; i < j; i++ ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)s,(LONG)(sizeof(struct VeCtOr))) != sizeof(struct VeCtOr) ) goto ErrGt2; nsize = s->namesize; nsize += sizeof(void *)-1; nsize &= -sizeof(void *); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)(AT.WorkPointer),nsize) != nsize ) goto ErrGt2; *w = s->number + AM.OffsetVector; if ( ( s->flags & INUSE ) != 0 ) { /* Find the replacement. It must exist! */ neww = oldw; while ( *neww != VECTOVEC || neww[2] != *w ) neww += neww[1]; k = neww[3] - AM.OffsetVector; } else if ( GetVar((UBYTE *)(AT.WorkPointer),&type,&k,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { if ( type != CVECTOR ) { MesPrint("Error: Conflicting types for %s",(AT.WorkPointer)); error = -1; } else { if ( ( s->complex & (VARTYPEIMAGINARY|VARTYPECOMPLEX) ) != ( vectors[k].complex & (VARTYPEIMAGINARY|VARTYPECOMPLEX) ) ) { MesPrint("Warning: Conflicting complexity for %s",(AT.WorkPointer)); error = -1; } } } else { if ( ( k = EntVar(CVECTOR,(UBYTE *)(AT.WorkPointer), s->complex,0,0,s->dimension) ) < 0 ) goto GetTcall; } *(w+j) = k + AM.OffsetVector; w++; } } /* #] Vectors : #[ Functions : */ { FUNCTIONS s = &FuN; w = r->func.lo; j = jfun; for ( i = 0; i < j; i++ ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)s,(LONG)(sizeof(struct FuNcTiOn))) != sizeof(struct FuNcTiOn) ) goto ErrGt2; nsize = s->namesize; nsize += sizeof(void *)-1; nsize &= -sizeof(void *); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)(AT.WorkPointer),nsize) != nsize ) goto ErrGt2; *w = s->number + FUNCTION; if ( ( s->flags & INUSE ) != 0 ) { /* Find the replacement. It must exist! */ neww = oldw; while ( *neww != FUNTOFUN || neww[2] != *w ) neww += neww[1]; k = neww[3] - FUNCTION; } else if ( GetVar((UBYTE *)(AT.WorkPointer),&type,&k,ALLVARIABLES,NOAUTO) != NAMENOTFOUND ) { if ( type != CFUNCTION ) { MesPrint("Error: Conflicting types for %s",(AT.WorkPointer)); error = -1; } else { if ( s->complex != functions[k].complex ) { MesPrint("Warning: Conflicting complexity for %s",(AT.WorkPointer)); error = -1; } else if ( s->symmetric != functions[k].symmetric ) { MesPrint("Warning: Conflicting symmetry properties for %s",(AT.WorkPointer)); error = -1; } else if ( ( s->maxnumargs != functions[k].maxnumargs ) || ( s->minnumargs != functions[k].minnumargs ) ) { MesPrint("Warning: Conflicting argument restriction properties for %s",(AT.WorkPointer)); error = -1; } } } else { if ( ( k = EntVar(CFUNCTION,(UBYTE *)(AT.WorkPointer), s->complex,s->commute,s->spec,s->dimension) ) < 0 ) goto GetTcall; functions[k].symmetric = s->symmetric; functions[k].maxnumargs = s->maxnumargs; functions[k].minnumargs = s->minnumargs; } *(w+j) = k + FUNCTION; w++; } } /* #] Functions : Now we skip the prototype. This sets the start position at the first term */ if ( error ) { UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; return(0); } { /* For clarity we look where we are. We want to know: is this position already known? Could we have inserted extra information here? nummystery indicates extra words. We have currently in order (if they exist) numdummies numfactors vflags uflags */ POSITION pos; int nummystery; TELLFILE(AR.StoreData.Handle,&pos); nummystery = DIFBASE(ind->position,pos); /* MesPrint("--> We are at position %8p",&pos); MesPrint("--> The index says at %8p",&(ind->position)); MesPrint("--> There are %d mystery bytes",nummystery); */ if ( nummystery > 0 ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,(LONG)sizeof(WORD)) != sizeof(WORD) ) { UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; return(0); } Expressions[expr].numdummies = *AT.WorkPointer; /* MesPrint("--> numdummies = %d",Expressions[expr].numdummies); */ nummystery -= sizeof(WORD); } else { Expressions[expr].numdummies = 0; } if ( nummystery > 0 ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,(LONG)sizeof(WORD)) != sizeof(WORD) ) { UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; return(0); } if ( ( AS.OldNumFactors == 0 ) || ( AS.NumOldNumFactors < NumExpressions ) ) { WORD *buffer; int capacity = 20; if (capacity < NumExpressions) capacity = NumExpressions * 2; buffer = (WORD *)Malloc1(capacity * sizeof(WORD), "numfactors pointers"); if (AS.OldNumFactors) { WCOPY(buffer, AS.OldNumFactors, AS.NumOldNumFactors); M_free(AS.OldNumFactors, "numfactors pointers"); } AS.OldNumFactors = buffer; buffer = (WORD *)Malloc1(capacity * sizeof(WORD), "vflags pointers"); if (AS.Oldvflags) { WCOPY(buffer, AS.Oldvflags, AS.NumOldNumFactors); M_free(AS.Oldvflags, "vflags pointers"); } AS.Oldvflags = buffer; buffer = (WORD *)Malloc1(capacity * sizeof(WORD), "uflags pointers"); if (AS.Olduflags) { WCOPY(buffer, AS.Olduflags, AS.NumOldNumFactors); M_free(AS.Olduflags, "uflags pointers"); } AS.Olduflags = buffer; AS.NumOldNumFactors = capacity; } AS.OldNumFactors[expr] = Expressions[expr].numfactors = *AT.WorkPointer; /* MesPrint("--> numfactors = %d",Expressions[expr].numfactors); */ nummystery -= sizeof(WORD); } else { Expressions[expr].numfactors = 0; } if ( nummystery > 0 ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,(LONG)sizeof(WORD)) != sizeof(WORD) ) { UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; return(0); } AS.Oldvflags[expr] = Expressions[expr].vflags = *AT.WorkPointer; /* MesPrint("--> vflags = %d",Expressions[expr].vflags); */ nummystery -= sizeof(WORD); } else { Expressions[expr].vflags = 0; } if ( nummystery > 0 ) { if ( ReadFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,(LONG)sizeof(WORD)) != sizeof(WORD) ) { UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; return(0); } AS.Olduflags[expr] = Expressions[expr].uflags = *AT.WorkPointer; /* MesPrint("--> uflags = %d",Expressions[expr].uflags); */ nummystery -= sizeof(WORD); } else { Expressions[expr].uflags = 0; } } SeekFile(AR.StoreData.Handle,&(ind->position),SEEK_SET); if ( ReadFile(AR.StoreData.Handle,(UBYTE *)AT.WorkPointer,(LONG)sizeof(WORD)) != sizeof(WORD) || !*AT.WorkPointer ) { UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; return(0); } num = *AT.WorkPointer - 1; num *= sizeof(WORD); if ( *AT.WorkPointer < 0 || ReadFile(AR.StoreData.Handle,(UBYTE *)(AT.WorkPointer+1),num) != num ) { MesPrint("@Error in stored expressions file at position %10p",*position); UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; return(0); } UNLOCK(AM.storefilelock); ADDPOS(*position,num+sizeof(WORD)); r->startposition = *position; AT.WorkPointer = oldwork; return(r); GetTcall: UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; MesCall("GetTable"); return(0); ErrGt2: UNLOCK(AM.storefilelock); AT.WorkPointer = oldwork; MesPrint("Readerror in GetTable"); return(0); } /* #] GetTable : #[ CopyExpression : Copies from one scratch buffer to another. We assume here that the complete 'from' scratch buffer is taken. We also assume that the 'from' buffer is positioned at the end of the expression. The locks should be placed in the calling routine. We need basically AS.outputslock. */ int CopyExpression(FILEHANDLE *from, FILEHANDLE *to) { POSITION posfrom, poscopy; LONG fullsize,i; WORD *t1, *t2; int RetCode; SeekScratch(from,&posfrom); if ( from->handle < 0 ) { /* input is in memory */ fullsize = (BASEPOSITION(posfrom))/sizeof(WORD); if ( ( to->POstop - to->POfull ) >= fullsize ) { /* Fits inside the buffer of the output. This will be fast. */ t1 = from->PObuffer; t2 = to->POfull; NCOPY(t2,t1,fullsize) to->POfull = to->POfill = t2; goto WriteTrailer; } if ( to->handle < 0 ) { /* First open the file */ if ( ( RetCode = CreateFile(to->name) ) >= 0 ) { to->handle = (WORD)RetCode; PUTZERO(to->filesize); PUTZERO(to->POposition); } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create scratch file %s",to->name); MUNLOCK(ErrorMessageLock); return(-1); } } t1 = from->PObuffer; while ( fullsize > 0 ) { i = to->POstop - to->POfull; if ( i > fullsize ) i = fullsize; fullsize -= i; t2 = to->POfull; NCOPY(t2,t1,i) if ( fullsize > 0 ) { SeekFile(to->handle,&(to->POposition),SEEK_SET); if ( WriteFile(to->handle,((UBYTE *)(to->PObuffer)),to->POsize) != to->POsize ) { MLOCK(ErrorMessageLock); MesPrint("Error while writing to disk. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(to->POposition,to->POsize); /* SeekFile(to->handle,&(to->POposition),SEEK_CUR); */ to->filesize = to->POposition; to->POfill = to->POfull = to->PObuffer; } else { to->POfill = to->POfull = t2; } } goto WriteTrailer; } /* Now the input involves a file. This needs the use of the PObuffer of from. First make sure the tail of the buffer has been written */ if ( ((UBYTE *)(from->POfill)-(UBYTE *)(from->PObuffer)) > 0 ) { if ( WriteFile(from->handle,((UBYTE *)(from->PObuffer)),((UBYTE *)(from->POfill)-(UBYTE *)(from->PObuffer))) != ((UBYTE *)(from->POfill)-(UBYTE *)(from->PObuffer)) ) { MLOCK(ErrorMessageLock); MesPrint("Error while writing to disk. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } SeekFile(from->handle,&(from->POposition),SEEK_CUR); posfrom = from->filesize = from->POposition; from->POfill = from->POfull = from->PObuffer; } /* Now copy the complete contents */ PUTZERO(poscopy); SeekFile(from->handle,&poscopy,SEEK_SET); while ( ISLESSPOS(poscopy,posfrom) ) { fullsize = ReadFile(from->handle,((UBYTE *)(from->PObuffer)),from->POsize); if ( fullsize < 0 || ( fullsize % sizeof(WORD) ) != 0 ) { MLOCK(ErrorMessageLock); MesPrint("Error while reading from disk while copying expression."); MUNLOCK(ErrorMessageLock); return(-1); } fullsize /= sizeof(WORD); from->POfull = from->PObuffer + fullsize; t1 = from->PObuffer; if ( ( to->POstop - to->POfull ) >= fullsize ) { /* Fits inside the buffer of the output. This will be fast. */ t2 = to->POfull; NCOPY(t2,t1,fullsize) to->POfill = to->POfull = t2; } else { if ( to->handle < 0 ) { /* First open the file */ if ( ( RetCode = CreateFile(to->name) ) >= 0 ) { to->handle = (WORD)RetCode; PUTZERO(to->POposition); PUTZERO(to->filesize); } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create scratch file %s",to->name); MUNLOCK(ErrorMessageLock); return(-1); } } while ( fullsize > 0 ) { i = to->POstop - to->POfull; if ( i > fullsize ) i = fullsize; fullsize -= i; t2 = to->POfull; NCOPY(t2,t1,i) if ( fullsize > 0 ) { SeekFile(to->handle,&(to->POposition),SEEK_SET); if ( WriteFile(to->handle,((UBYTE *)(to->PObuffer)),to->POsize) != to->POsize ) { MLOCK(ErrorMessageLock); MesPrint("Error while writing to disk. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(to->POposition,to->POsize); /* SeekFile(to->handle,&(to->POposition),SEEK_CUR); */ to->filesize = to->POposition; to->POfill = to->POfull = to->PObuffer; } else { to->POfill = to->POfull = t2; } } } SeekFile(from->handle,&poscopy,SEEK_CUR); } WriteTrailer: if ( ( to->handle >= 0 ) && ( to->POfill > to->PObuffer ) ) { fullsize = (UBYTE *)(to->POfill) - (UBYTE *)(to->PObuffer); /* PUTZERO(to->POposition); SeekFile(to->handle,&(to->POposition),SEEK_END); */ SeekFile(to->handle,&(to->filesize),SEEK_SET); if ( WriteFile(to->handle,((UBYTE *)(to->PObuffer)),fullsize) != fullsize ) { MLOCK(ErrorMessageLock); MesPrint("Error while writing to disk. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(to->filesize,fullsize); to->POposition = to->filesize; to->POfill = to->POfull = to->PObuffer; } return(0); } /* #] CopyExpression : #[ ExprStatus : */ #ifdef HIDEDEBUG static UBYTE *statusexpr[] = { (UBYTE *)"LOCALEXPRESSION" ,(UBYTE *)"SKIPLEXPRESSION" ,(UBYTE *)"DROPLEXPRESSION" ,(UBYTE *)"DROPPEDEXPRESSION" ,(UBYTE *)"GLOBALEXPRESSION" ,(UBYTE *)"SKIPGEXPRESSION" ,(UBYTE *)"DROPGEXPRESSION" ,(UBYTE *)"UNKNOWN" ,(UBYTE *)"STOREDEXPRESSION" ,(UBYTE *)"HIDDENLEXPRESSION" ,(UBYTE *)"HIDELEXPRESSION" ,(UBYTE *)"DROPHLEXPRESSION" ,(UBYTE *)"UNHIDELEXPRESSION" ,(UBYTE *)"HIDDENGEXPRESSION" ,(UBYTE *)"HIDEGEXPRESSION" ,(UBYTE *)"DROPHGEXPRESSION" ,(UBYTE *)"UNHIDEGEXPRESSION" ,(UBYTE *)"INTOHIDELEXPRESSION" ,(UBYTE *)"INTOHIDEGEXPRESSION" }; void ExprStatus(EXPRESSIONS e) { MesPrint("Expression %s(%d) has status %s(%d,%d). Buffer: %d, Position: %15p", AC.exprnames->namebuffer+e->name,(WORD)(e-Expressions), statusexpr[e->status],e->status,e->hidelevel, e->whichbuffer,&(e->onfile)); } #endif /* #] ExprStatus : #] StoreExpressions : #[ System Independent Saved Expressions : All functions concerned with the system independent reading of save-files are here. They are called by the functions CoLoad, PutInStore, SetFileIndex, FindInIndex. In case no translation (endianness flip, resizing of words, renumbering) has to be done, they just do simple file reading. The function SaveFileHeader() for writing a header with information about the system architecture, FORM version, etc. is also located here. #[ Flip : */ /** * Flips the endianness. This function will be called via function pointers. * See struct O_const and ReadSaveHeader(). * * It is a general version for arbitrary word sizes. * * @param p pointer to data * @param length length of data in bytes */ static void FlipN(UBYTE *p, int length) { UBYTE *q, buf; q = p + length; do { --q; buf = *p; *p = *q; *q = buf; } while ( ++p != q ); } /** * Flips the endianness. This function will be called via function pointers. * See struct O_const and ReadSaveHeader(). * * It is an optimized version for 16 bit (other versions for 32bit and 64bit * do exist). * * @param p pointer to data */ static void Flip16(UBYTE *p) { uint16_t in = *((uint16_t *)p); uint16_t out = (uint16_t)( (((in) >> 8) & UINT16_C(0x00FF)) | (((in) << 8) & UINT16_C(0xFF00)) ); *((uint16_t *)p) = out; } /** @see Flip16() */ static void Flip32(UBYTE *p) { uint32_t in = *((uint32_t *)p); uint32_t out = ( (((in) >> 24) & UINT32_C(0x000000FF)) | (((in) >> 8) & UINT32_C(0x0000FF00)) | \ (((in) << 8) & UINT32_C(0x00FF0000)) | (((in) << 24) & UINT32_C(0xFF000000)) ); *((uint32_t *)p) = out; } /** @see Flip16() */ #ifdef UINT64_C static void Flip64(UBYTE *p) { uint64_t in = *((uint64_t *)p); uint64_t out = ( (((in) >> 56) & UINT64_C(0x00000000000000FF)) | (((in) >> 40) & UINT64_C(0x000000000000FF00)) | \ (((in) >> 24) & UINT64_C(0x0000000000FF0000)) | (((in) >> 8) & UINT64_C(0x00000000FF000000)) | \ (((in) << 8) & UINT64_C(0x000000FF00000000)) | (((in) << 24) & UINT64_C(0x0000FF0000000000)) | \ (((in) << 40) & UINT64_C(0x00FF000000000000)) | (((in) << 56) & UINT64_C(0xFF00000000000000)) ); *((uint64_t *)p) = out; } #else static void Flip64(UBYTE *p) { FlipN(p, 8); } #endif /* UINT64_C */ /** @see Flip16() */ static void Flip128(UBYTE *p) { FlipN(p, 16); } /* #] Flip : #[ Resize : */ /** * Resizes words. This function will be called via function pointers. See * struct O_const and ReadSaveHeader(). * * General version for arbitrary word sizes and big-endian machines. * * @param src pointer to input data * @param dst pointer to output data * @param slen number of bytes of input * @param dlen number of bytes of output */ static void ResizeDataBE(UBYTE *src, int slen, UBYTE *dst, int dlen) { if ( slen > dlen ) { src += slen - dlen; while ( dlen-- ) { *dst++ = *src++; } } else { int i = dlen - slen; while ( i-- ) { *dst++ = 0; } while ( slen-- ) { *dst++ = *src++; } } } /** * The same as ResizeDataBE() but for little-endian machines. */ static void ResizeDataLE(UBYTE *src, int slen, UBYTE *dst, int dlen) { if ( slen > dlen ) { while ( dlen-- ) { *dst++ = *src++; } } else { int i = dlen - slen; while ( slen-- ) { *dst++ = *src++; } while ( i-- ) { *dst++ = 0; } } } /** * Resizes words. This function will be called via function pointers. See * struct O_const and ReadSaveHeader(). * * Specialized version for the specific combination of reading 16bit and * writing 16bit (more versions for other bit-combinations do exist). * * No checking for too big numbers is done. * * @param src pointer to input data * @param dst pointer to output data */ static void Resize16t16(UBYTE *src, UBYTE *dst) { *((int16_t *)dst) = *((int16_t *)src); } /** @see Resize16t16() */ static void Resize16t32(UBYTE *src, UBYTE *dst) { int16_t in = *((int16_t *)src); int32_t out = (int32_t)in; *((int32_t *)dst) = out; } /** @see Resize16t16() */ #ifdef INT64_C static void Resize16t64(UBYTE *src, UBYTE *dst) { int16_t in = *((int16_t *)src); int64_t out = (int64_t)in; *((int64_t *)dst) = out; } #else static void Resize16t64(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 2, dst, 8); } #endif /* INT64_C */ /** @see Resize16t16() */ static void Resize16t128(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 2, dst, 16); } /** @see Resize16t16() */ static void Resize32t32(UBYTE *src, UBYTE *dst) { *((int32_t *)dst) = *((int32_t *)src); } /** @see Resize16t16() */ #ifdef INT64_C static void Resize32t64(UBYTE *src, UBYTE *dst) { int32_t in = *((int32_t *)src); int64_t out = (int64_t)in; *((int64_t *)dst) = out; } #else static void Resize32t64(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 4, dst, 8); } #endif /* INT64_C */ /** @see Resize16t16() */ static void Resize32t128(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 4, dst, 16); } /** @see Resize16t16() */ #ifdef INT64_C static void Resize64t64(UBYTE *src, UBYTE *dst) { *((int64_t *)dst) = *((int64_t *)src); } #else static void Resize64t64(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 8, dst, 8); } #endif /* INT64_C */ /** @see Resize16t16() */ static void Resize64t128(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 8, dst, 16); } /** @see Resize16t16() */ static void Resize128t128(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 16, dst, 16); } /** @see Resize16t16() */ static void Resize32t16(UBYTE *src, UBYTE *dst) { int32_t in = *((int32_t *)src); int16_t out = (int16_t)in; if ( in > (1<<15)-1 || in < -(1<<15)+1 ) AO.resizeFlag |= 1; *((int16_t *)dst) = out; } /** * The same as Resize32t16() but with checking for too big numbers. * * The resizeFlag in struct O_const will be used to signal the result of the * checking. This flag is used by CoLoad(). */ static void Resize32t16NC(UBYTE *src, UBYTE *dst) { int32_t in = *((int32_t *)src); int16_t out = (int16_t)in; *((int16_t *)dst) = out; } #ifdef INT64_C /** @see Resize16t16() */ static void Resize64t16(UBYTE *src, UBYTE *dst) { int64_t in = *((int64_t *)src); int16_t out = (int16_t)in; if ( in > (1<<15)-1 || in < -(1<<15)+1 ) AO.resizeFlag |= 1; *((int16_t *)dst) = out; } /** @see Resize32t16NC() */ static void Resize64t16NC(UBYTE *src, UBYTE *dst) { int64_t in = *((int64_t *)src); int16_t out = (int16_t)in; *((int16_t *)dst) = out; } #else /** @see Resize16t16() */ static void Resize64t16(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 8, dst, 2); } /** @see Resize32t16NC() */ static void Resize64t16NC(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 8, dst, 2); } #endif /* INT64_C */ #ifdef INT64_C /** @see Resize16t16() */ static void Resize64t32(UBYTE *src, UBYTE *dst) { int64_t in = *((int64_t *)src); int32_t out = (int32_t)in; if ( in > (INT64_C(1)<<31)-1 || in < -(INT64_C(1)<<31)+1 ) AO.resizeFlag |= 1; *((int32_t *)dst) = out; } /** @see Resize32t16NC() */ static void Resize64t32NC(UBYTE *src, UBYTE *dst) { int64_t in = *((int64_t *)src); int32_t out = (int32_t)in; *((int32_t *)dst) = out; } #else /** @see Resize16t16() */ static void Resize64t32(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 8, dst, 4); } /** @see Resize32t16NC() */ static void Resize64t32NC(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 8, dst, 4); } #endif /* INT64_C */ /** @see Resize16t16() */ static void Resize128t16(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 16, dst, 2); } /** @see Resize32t16NC() */ static void Resize128t16NC(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 16, dst, 2); } /** @see Resize16t16() */ static void Resize128t32(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 16, dst, 4); } /** @see Resize32t16NC() */ static void Resize128t32NC(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 16, dst, 4); } /** @see Resize16t16() */ static void Resize128t64(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 16, dst, 8); } /** @see Resize32t16NC() */ static void Resize128t64NC(UBYTE *src, UBYTE *dst) { AO.ResizeData(src, 16, dst, 8); } /* #] Resize : #[ CheckPower and RenumberVec : */ /** * Checks the size of exponents. If a checking fails, the powerFlag in struct * O_const will be set. This flag is used by CoLoad(). * * @param p pointer to WORD containing exponent */ static void CheckPower32(UBYTE *p) { if ( *((int32_t *)p) < -MAXPOWER ) { AO.powerFlag |= 0x01; *((int32_t *)p) = -MAXPOWER; } p += sizeof(int32_t); if ( *((int32_t *)p) > MAXPOWER ) { AO.powerFlag |= 0x02; *((int32_t *)p) = MAXPOWER; } } /** * Renumbers vectors by compensating for the different WILDOFFSET on the * involved machines and FORM versions. The WILDOFFSET from the writing * machine is coded in the header of the save-file. * * @param p pointer to WORD containing vector code */ static void RenumberVec32(UBYTE *p) { /* int32_t wildoffset = *((int32_t *)AO.SaveHeader.wildoffset); */ void *dummy = (void *)AO.SaveHeader.wildoffset; /* to remove a warning about strict-aliasing rules in gcc */ int32_t wildoffset = *(int32_t *)dummy; int32_t in = *((int32_t *)p); in = in + 2*wildoffset; in = in - 2*WILDOFFSET; *((int32_t *)p) = in; } /* #] CheckPower and RenumberVec : #[ ResizeCoeff : */ /** * Resizes the coefficients of expressions and terms. The function only * work on uniform data with a word size of 32bit (ReadSaveExpression() * provides for that). The resizing then actually means whether zeros can be * removed when going from 64bit to 32bit, or whether the coefficient size has * to be doubled effectively when going from 32bit to 64bit. Both cases * involve copying of words and a shrinking or growing of the memory used in * @e *bout. * * @param bout input and output buffer for coefficient * @param bend end of input * @param top end of buffer */ static void ResizeCoeff32(UBYTE **bout, UBYTE *bend, UBYTE *top) { int i; int32_t sign; int32_t *in, *p; int32_t *out = (int32_t *)*bout; int32_t *end = (int32_t *)bend; if ( sizeof(WORD) == 2 ) { /* 4 -> 2 */ int32_t len = (end - 1 - out) / 2; int zeros = 2; p = out + len - 1; if ( *p & 0xFFFF0000 ) --zeros; p += len; if ( *p & 0xFFFF0000 ) --zeros; in = end - 1; sign = ( *in-- > 0 ) ? 1 : -1; p = out + 4*len; if ( zeros == 2 ) p -= 2; out = p--; if ( zeros < 2 ) *p-- = *in >> 16; *p-- = *in-- & 0x0000FFFF; for ( i = 1; i < len; ++i ) { *p-- = *in >> 16; *p-- = *in-- & 0x0000FFFF; } if ( zeros < 2 ) *p-- = *in >> 16; *p-- = *in-- & 0x0000FFFF; for ( i = 1; i < len; ++i ) { *p-- = *in >> 16; *p-- = *in-- & 0x0000FFFF; } *out = (out - p) * sign; *bout = (UBYTE *)(out+1); } else { /* 2 -> 4 */ int32_t len = (end - 1 - out) / 2; if ( len == 1 ) { *out = *(uint16_t *)out; ++out; *out = *(uint16_t *)out; ++out; ++out; } else { p = out; *out = *(uint16_t *)out; in = out + 1; for ( i = 1; i < len; ++i ) { /* shift */ *out = (uint32_t)(*(uint16_t *)out) + ((uint32_t)(*(uint16_t *)in) << 16); ++in; if ( ++i == len ) break; /* copy */ ++out; *out = *(uint16_t *)in; ++in; } ++out; *out = *(uint16_t *)in; ++in; for ( i = 1; i < len; ++i ) { /* shift */ *out = (uint32_t)(*(uint16_t *)out) + ((uint32_t)(*(uint16_t *)in) << 16); ++in; if ( ++i == len ) break; /* copy */ ++out; *out = *(uint16_t *)in; ++in; } ++out; if ( *in < 0 ) *out = -(out - p + 1); else *out = out - p + 1; ++out; } if ( out > (int32_t *)top ) { MesPrint("Error in resizing coefficient!"); } *bout = (UBYTE *)out; } } /* #] ResizeCoeff : #[ WriteStoreHeader : */ #define SAVEREVISION 0x02 /** * Writes header with information about system architecture and FORM revision * to an open store file. * * Called by SetFileIndex(). * * @param handle specifies open file to which header will be written * @return = 0 everything okay, != 0 an error occurred */ LONG WriteStoreHeader(WORD handle) { /* template of the STOREHEADER */ static STOREHEADER sh = { { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF }, /* store header mark */ 0, 0, 0, 0, /* sizeof of WORD,LONG,POSITION,void* */ { 0 }, /* endianness check number */ 0, 0, 0, 0, /* sizeof variable structs */ { 0 }, /* maxpower */ { 0 }, /* wildoffset */ SAVEREVISION, /* revision */ { 0 } }; /* reserved */ int endian, i; /* if called for the first time ... */ if ( sh.lenWORD == 0 ) { sh.lenWORD = sizeof(WORD); sh.lenLONG = sizeof(LONG); sh.lenPOS = sizeof(POSITION); sh.lenPOINTER = sizeof(void *); endian = 1; for ( i = 1; i < (int)sizeof(int); ++i ) { endian <<= 8; endian += i+1; } for ( i = 0; i < (int)sizeof(int); ++i ) sh.endianness[i] = ((char *)&endian)[i]; sh.sSym = sizeof(struct SyMbOl); sh.sInd = sizeof(struct InDeX); sh.sVec = sizeof(struct VeCtOr); sh.sFun = sizeof(struct FuNcTiOn); /* *((WORD *)sh.maxpower) = MAXPOWER; *((WORD *)sh.wildoffset) = WILDOFFSET; */ { WORD dumw[8]; UBYTE *dummy; for ( i = 0; i < 8; i++ ) dumw[i] = 0; dummy = (UBYTE *)dumw; dumw[0] = (WORD)MAXPOWER; for ( i = 0; i < 16; i++ ) sh.maxpower[i] = dummy[i]; dumw[0] = (WORD)WILDOFFSET; for ( i = 0; i < 16; i++ ) sh.wildoffset[i] = dummy[i]; } } return ( WriteFile(handle,(UBYTE *)(&sh),(LONG)(sizeof(STOREHEADER))) != (LONG)(sizeof(STOREHEADER)) ); } /* #] WriteStoreHeader : #[ CompactifySizeof : */ /** * Utility function used by ReadSaveHeader() to convert a sizeof into a * convenient array index. * * @param size size in bytes * @return log_2(size) - 1 */ static unsigned int CompactifySizeof(unsigned int size) { switch ( size ) { case 2: return 0; case 4: return 1; case 8: return 2; case 16: return 3; default: MesPrint("Error compactifying size."); return 3; } } /* #] CompactifySizeof : #[ ReadSaveHeader : */ /** * Reads the header in the save file and sets function pointers and flags * according to the information found there. Must be called before any other * ReadSave... function. * * Currently works only for the exchange between 32bit and 64bit machines * (WORD size must be 2 or 4 bytes)! * * It is called by CoLoad(). * * @return = 0 everything okay, != 0 an error occurred */ int ReadSaveHeader(void) { /* Read-only tables of function pointers for conversions. */ static void (*flipJumpTable[4])(UBYTE *) = { Flip16, Flip32, Flip64, Flip128 }; static void (*resizeJumpTable[4][4])(UBYTE *, UBYTE *) = /* "own x saved"-sizes */ { { Resize16t16, Resize32t16, Resize64t16, Resize128t16 }, { Resize16t32, Resize32t32, Resize64t32, Resize128t32 }, { Resize16t64, Resize32t64, Resize64t64, Resize128t64 }, { Resize16t128, Resize32t128, Resize64t128, Resize128t128 } }; static void (*resizeNCJumpTable[4][4])(UBYTE *, UBYTE *) = /* "own x saved"-sizes */ { { Resize16t16, Resize32t16NC, Resize64t16NC, Resize128t16NC }, { Resize16t32, Resize32t32, Resize64t32NC, Resize128t32NC }, { Resize16t64, Resize32t64, Resize64t64, Resize128t64NC }, { Resize16t128, Resize32t128, Resize64t128, Resize128t128 } }; int endian, i; WORD idxW = CompactifySizeof(sizeof(WORD)); WORD idxL = CompactifySizeof(sizeof(LONG)); WORD idxP = CompactifySizeof(sizeof(POSITION)); WORD idxVP = CompactifySizeof(sizeof(void *)); AO.transFlag = 0; AO.powerFlag = 0; AO.resizeFlag = 0; AO.bufferedInd = 0; if ( ReadFile(AO.SaveData.Handle,(UBYTE *)(&AO.SaveHeader), (LONG)sizeof(STOREHEADER)) != (LONG)sizeof(STOREHEADER) ) return(MesPrint("Error reading save file header")); /* check whether save-file has no header. if yes then it is an old version of FORM -> go back to position 0 in file which then contains the first index and skip the rest. */ for ( i = 0; i < 8; ++i ) { if ( AO.SaveHeader.headermark[i] != 0xFF ) { POSITION p; PUTZERO(p); SeekFile(AO.SaveData.Handle, &p, SEEK_SET); return ( 0 ); } } if ( AO.SaveHeader.revision != SAVEREVISION ) { return(MesPrint("Save file header from an old version. Cannot read this file.")); } endian = 1; for ( i = 1; i < (int)sizeof(int); ++i ) { endian <<= 8; endian += i+1; } if ( ((char *)&endian)[0] < ((char *)&endian)[1] ) { /* this machine is big-endian */ AO.ResizeData = ResizeDataBE; } else { /* this machine is little-endian */ AO.ResizeData = ResizeDataLE; } /* set AO.transFlag if ANY conversion has to be done later */ if ( AO.SaveHeader.endianness[0] > AO.SaveHeader.endianness[1] ) { AO.transFlag = ( ((char *)&endian)[0] < ((char *)&endian)[1] ); } else { AO.transFlag = ( ((char *)&endian)[0] > ((char *)&endian)[1] ); } if ( (WORD)AO.SaveHeader.lenWORD != sizeof(WORD) ) AO.transFlag |= 0x02; if ( (WORD)AO.SaveHeader.lenLONG != sizeof(LONG) ) AO.transFlag |= 0x04; if ( (WORD)AO.SaveHeader.lenPOS != sizeof(POSITION) ) AO.transFlag |= 0x08; if ( (WORD)AO.SaveHeader.lenPOINTER != sizeof(void *) ) AO.transFlag |= 0x10; AO.FlipWORD = flipJumpTable[idxW]; AO.FlipLONG = flipJumpTable[idxL]; AO.FlipPOS = flipJumpTable[idxP]; AO.FlipPOINTER = flipJumpTable[idxVP]; /* Works only for machines where WORD is not greater than 32bit ! */ AO.CheckPower = CheckPower32; AO.RenumberVec = RenumberVec32; AO.ResizeWORD = resizeJumpTable[idxW][CompactifySizeof(AO.SaveHeader.lenWORD)]; AO.ResizeNCWORD = resizeNCJumpTable[idxW][CompactifySizeof(AO.SaveHeader.lenWORD)]; AO.ResizeLONG = resizeJumpTable[idxL][CompactifySizeof(AO.SaveHeader.lenLONG)]; AO.ResizePOS = resizeJumpTable[idxP][CompactifySizeof(AO.SaveHeader.lenPOS)]; AO.ResizePOINTER = resizeJumpTable[idxVP][CompactifySizeof(AO.SaveHeader.lenPOINTER)]; { WORD dumw[8]; UBYTE *dummy; for ( i = 0; i < 8; i++ ) dumw[i] = 0; dummy = (UBYTE *)dumw; for ( i = 0; i < 16; i++ ) dummy[i] = AO.SaveHeader.maxpower[i]; AO.mpower = dumw[0]; } return ( 0 ); } /* #] ReadSaveHeader : #[ ReadSaveIndex : */ /** * Reads a FILEINDEX from the open save file specified by AO.SaveData.Handle. * Translations for adjusting endianness and data sizes are done if necessary. * * Depends on the assumption that sizeof(FILEINDEX) is the same everywhere. * If FILEINDEX or INDEXENTRY change, then this functions has to be adjusted. * * Called by CoLoad() and FindInIndex(). * * @param fileind contains the read FILEINDEX after successful return. must * point to allocated, big enough memory. * @return = 0 everything okay, != 0 an error occurred */ LONG ReadSaveIndex(FILEINDEX *fileind) { /* do we need some translation for the FILEINDEX? */ if ( AO.transFlag ) { /* if a translated FILEINDEX can hold less entries than the original FILEINDEX, then we need to buffer the extra entries in this static variable (can happen going from 32bit to 64bit */ static FILEINDEX sbuffer; FILEINDEX buffer; UBYTE *p, *q; int i; /* shortcuts */ int lenW = AO.SaveHeader.lenWORD; int lenL = AO.SaveHeader.lenLONG; int lenP = AO.SaveHeader.lenPOS; /* if we have a buffered FILEINDEX then just return it */ if ( AO.bufferedInd ) { *fileind = sbuffer; AO.bufferedInd = 0; return ( 0 ); } if ( ReadFile(AO.SaveData.Handle, (UBYTE *)fileind, sizeof(FILEINDEX)) != sizeof(FILEINDEX) ) { return ( MesPrint("Error(1) reading stored expression.") ); } /* do we need to flip the endianness? */ if ( AO.transFlag & 1 ) { LONG number; /* padding bytes */ int padp = lenL - ((lenW*5+(MAXENAME + 1)) & (lenL-1)); p = (UBYTE *)fileind; AO.FlipPOS(p); p += lenP; /* next */ AO.FlipPOS(p); /* number */ AO.ResizePOS(p, (UBYTE *)&number); p += lenP; for ( i = 0; i < number; ++i ) { AO.FlipPOS(p); p += lenP; /* position */ AO.FlipPOS(p); p += lenP; /* length */ AO.FlipPOS(p); p += lenP; /* variables */ AO.FlipLONG(p); p += lenL; /* CompressSize */ AO.FlipWORD(p); p += lenW; /* nsymbols */ AO.FlipWORD(p); p += lenW; /* nindices */ AO.FlipWORD(p); p += lenW; /* nvectors */ AO.FlipWORD(p); p += lenW; /* nfunctions */ AO.FlipWORD(p); p += lenW; /* size */ p += padp; } } /* do we need to resize data? */ if ( AO.transFlag > 1 ) { LONG number, maxnumber; int n; /* padding bytes */ int padp = lenL - ((lenW*5+(MAXENAME + 1)) & (lenL-1)); int padq = sizeof(LONG) - ((sizeof(WORD)*5+(MAXENAME + 1)) & (sizeof(LONG)-1)); p = (UBYTE *)fileind; q = (UBYTE *)&buffer; AO.ResizePOS(p, q); /* next */ p += lenP; q += sizeof(POSITION); AO.ResizePOS(p, q); /* number */ p += lenP; number = BASEPOSITION(*((POSITION *)q)); /* if FILEINDEX in file contains more entries than the FILEINDEX in memory can contain, then adjust the numbers and prepare for buffering */ if ( number > (LONG)INFILEINDEX ) { AO.bufferedInd = number-INFILEINDEX; if ( AO.bufferedInd > (WORD)INFILEINDEX ) { /* can happen when reading 32bit and writing >=128bit. Fix: more than one static buffer for FILEINDEX */ return ( MesPrint("Too many index entries.") ); } maxnumber = INFILEINDEX; SETBASEPOSITION(*((POSITION *)q),INFILEINDEX); } else { maxnumber = number; } q += sizeof(POSITION); /* read all INDEXENTRY that fit into the output buffer */ for ( i = 0; i < maxnumber; ++i ) { AO.ResizePOS(p, q); /* position */ p += lenP; q += sizeof(POSITION); AO.ResizePOS(p, q); /* length */ p += lenP; q += sizeof(POSITION); AO.ResizePOS(p, q); /* variables */ p += lenP; q += sizeof(POSITION); AO.ResizeLONG(p, q); /* CompressSize */ p += lenL; q += sizeof(LONG); AO.ResizeWORD(p, q); /* nsymbols */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* nindices */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* nvectors */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* nfunctions */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* size (unchanged!) */ p += lenW; q += sizeof(WORD); n = MAXENAME + 1; NCOPYB(q, p, n) p += padp; q += padq; } /* read all the remaining INDEXENTRY and put them into the static buffer */ if ( AO.bufferedInd ) { sbuffer.next = buffer.next; SETBASEPOSITION(sbuffer.number,AO.bufferedInd); q = (UBYTE *)&sbuffer + sizeof(POSITION) + sizeof(LONG); for ( i = maxnumber; i < number; ++i ) { AO.ResizePOS(p, q); /* position */ p += lenP; q += sizeof(POSITION); AO.ResizePOS(p, q); /* length */ p += lenP; q += sizeof(POSITION); AO.ResizePOS(p, q); /* variables */ p += lenP; q += sizeof(POSITION); AO.ResizeLONG(p, q); /* CompressSize */ p += lenL; q += sizeof(LONG); AO.ResizeWORD(p, q); /* nsymbols */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* nindices */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* nvectors */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* nfunctions */ p += lenW; q += sizeof(WORD); AO.ResizeWORD(p, q); /* size (unchanged!) */ p += lenW; q += sizeof(WORD); n = MAXENAME + 1; NCOPYB(q, p, n) p += padp; q += padq; } } /* copy to output */ p = (UBYTE *)fileind; q = (UBYTE *)&buffer; n = sizeof(FILEINDEX); NCOPYB(p, q, n) } return ( 0 ); } else { return ( ReadFile(AO.SaveData.Handle, (UBYTE *)fileind, sizeof(FILEINDEX)) != sizeof(FILEINDEX) ); } } /* #] ReadSaveIndex : #[ ReadSaveVariables : */ /** * Reads the variables from the open file specified by AO.SaveData.Handle. It * reads the *size bytes and writes them to the *buffer. It is called by * PutInStore(). * * If translation is necessary, the data might shrink or grow in size, then * @e *size is adjusted so that the reading and writing fits into the memory * from the buffer to the top. The actual number of read bytes is returned in * @e *size, the number of written bytes is returned in @e *outsize. * * If the *size is smaller than the actual size of the variables, this function * will be called several times and needs to remember the current position in * the variable structure. The parameter @e stage does this job. When * ReadSaveVariables() is called for the first time, this parameter should * have the value -1. * * The parameter @e ind is used to get the number of variables. * * @param buffer read variables are written into this allocated memory * @param top upper end of allocated memory * @param size number of bytes to read. might return a smaller number * of read bytes if translation was necessary * @param outsize if translation has be done, outsize contains the number * of written bytes * @param ind pointer of INDEXENTRY for the current expression. read-only * @param stage should be -1 for the first call, will be increased by * ReadSaveVariables to memorize the position in the * variable structure * @return = 0 everything okay, != 0 an error occurred */ LONG ReadSaveVariables(UBYTE *buffer, UBYTE *top, LONG *size, LONG *outsize,\ INDEXENTRY *ind, LONG *stage) { /* do we need some translation for the variables? */ if ( AO.transFlag ) { /* counters for the number of already read symbols, indices, ... that need to remain valid between different calls to ReadSaveVariables(). are initialized if stage == -1 */ static WORD numReadSym; static WORD numReadInd; static WORD numReadVec; static WORD numReadFun; POSITION pos; UBYTE *in, *out, *pp = 0, *end, *outbuf; LONG numread; WORD namelen, realnamelen; /* shortcuts */ WORD lenW = AO.SaveHeader.lenWORD; WORD lenL = AO.SaveHeader.lenLONG; WORD lenP = AO.SaveHeader.lenPOINTER; WORD flip = AO.transFlag & 1; /* remember file position in case we have to rewind */ TELLFILE(AO.SaveData.Handle,&pos); /* decide on the position of the in and out buffers. if the input is "bigger" than the output, we resize in-place, i.e. we immediately overwrite the source data by the translated data. in and out buffers start at the same place. if not, we read from the end of the given buffer and write at the beginning. */ if ( (lenW > (WORD)sizeof(WORD)) || ( (lenW == (WORD)sizeof(WORD)) && ( (lenL > (WORD)sizeof(LONG)) || ( (lenL == (WORD)sizeof(LONG)) && lenP > (WORD)sizeof(void *)) ) ) ) { in = out = buffer; end = buffer + *size; } else { /* data will grow roughly by sizeof(WORD)/lenW. the exact value is not important. if reading and writing areas start to overlap, the reading will already be near the end of the data and overwriting doesn't matter. */ LONG newsize = (top - buffer) / (1 + sizeof(WORD)/lenW); end = top; out = buffer; in = end - newsize; if ( *size > newsize ) *size = newsize; } if ( ( numread = ReadFile(AO.SaveData.Handle, in, *size) ) != *size ) { return ( MesPrint("Error(2) reading stored expression.") ); } *size = 0; *outsize = 0; /* first time in ReadSaveVariables(). initialize counters. */ if ( *stage == -1 ) { numReadSym = 0; numReadInd = 0; numReadVec = 0; numReadFun = 0; ++*stage; } while ( in < end ) { /* Symbols */ if ( *stage == 0 ) { if ( ind->nsymbols <= numReadSym ) { ++*stage; continue; } if ( end - in < AO.SaveHeader.sSym ) { goto RSVEnd; } if ( flip ) { pp = in; AO.FlipLONG(pp); pp += lenL; while ( pp < in + AO.SaveHeader.sSym ) { AO.FlipWORD(pp); pp += lenW; } } pp = in + AO.SaveHeader.sSym; AO.ResizeLONG(in, out); in += lenL; out += sizeof(LONG); /* name */ AO.CheckPower(in); AO.ResizeWORD(in, out); in += lenW; if ( *((WORD *)out) == -AO.mpower ) *((WORD *)out) = -MAXPOWER; out += sizeof(WORD); /* minpower */ AO.ResizeWORD(in, out); in += lenW; if ( *((WORD *)out) == AO.mpower ) *((WORD *)out) = MAXPOWER; out += sizeof(WORD); /* maxpower */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* complex */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* number */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* flags */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* node */ AO.ResizeWORD(in, out); in += lenW; /* namesize */ realnamelen = *((WORD *)out); realnamelen += sizeof(void *)-1; realnamelen &= -(sizeof(void *)); out += sizeof(WORD); AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* dimension */ while ( in < pp ) { AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); } namelen = *((WORD *)out-1); /* cares for padding "bug" */ if ( end - in < namelen ) { goto RSVEnd; } *((WORD *)out-1) = realnamelen; *size += AO.SaveHeader.sSym + namelen; *outsize += sizeof(struct SyMbOl) + realnamelen; if ( realnamelen > namelen ) { int j = namelen; NCOPYB(out, in, j); out += realnamelen - namelen; } else { int j = realnamelen; NCOPYB(out, in, j); in += namelen - realnamelen; } ++numReadSym; continue; } /* Indices */ if ( *stage == 1 ) { if ( ind->nindices <= numReadInd ) { ++*stage; continue; } if ( end - in < AO.SaveHeader.sInd ) { goto RSVEnd; } if ( flip ) { pp = in; AO.FlipLONG(pp); pp += lenL; while ( pp < in + AO.SaveHeader.sInd ) { AO.FlipWORD(pp); pp += lenW; } } pp = in + AO.SaveHeader.sInd; AO.ResizeLONG(in, out); in += lenL; out += sizeof(LONG); /* name */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* type */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* dimension */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* number */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* flags */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* nmin4 */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* node */ AO.ResizeWORD(in, out); in += lenW; /* namesize */ realnamelen = *((WORD *)out); realnamelen += sizeof(void *)-1; realnamelen &= -(sizeof(void *)); out += sizeof(WORD); while ( in < pp ) { AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); } namelen = *((WORD *)out-1); /* cares for padding "bug" */ if ( end - in < namelen ) { goto RSVEnd; } *((WORD *)out-1) = realnamelen; *size += AO.SaveHeader.sInd + namelen; *outsize += sizeof(struct InDeX) + realnamelen; if ( realnamelen > namelen ) { int j = namelen; NCOPYB(out, in, j); out += realnamelen - namelen; } else { int j = realnamelen; NCOPYB(out, in, j); in += namelen - realnamelen; } ++numReadInd; continue; } /* Vectors */ if ( *stage == 2 ) { if ( ind->nvectors <= numReadVec ) { ++*stage; continue; } if ( end - in < AO.SaveHeader.sVec ) { goto RSVEnd; } if ( flip ) { pp = in; AO.FlipLONG(pp); pp += lenL; while ( pp < in + AO.SaveHeader.sVec ) { AO.FlipWORD(pp); pp += lenW; } } pp = in + AO.SaveHeader.sVec; AO.ResizeLONG(in, out); in += lenL; out += sizeof(LONG); /* name */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* complex */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* number */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* flags */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* node */ AO.ResizeWORD(in, out); in += lenW; /* namesize */ realnamelen = *((WORD *)out); realnamelen += sizeof(void *)-1; realnamelen &= -(sizeof(void *)); out += sizeof(WORD); AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* dimension */ while ( in < pp ) { AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); } namelen = *((WORD *)out-1); /* cares for padding "bug" */ if ( end - in < namelen ) { goto RSVEnd; } *((WORD *)out-1) = realnamelen; *size += AO.SaveHeader.sVec + namelen; *outsize += sizeof(struct VeCtOr) + realnamelen; if ( realnamelen > namelen ) { int j = namelen; NCOPYB(out, in, j) out += realnamelen - namelen; } else { int j = realnamelen; NCOPYB(out, in, j) in += namelen - realnamelen; } ++numReadVec; continue; } /* Functions */ if ( *stage == 3 ) { if ( ind->nfunctions <= numReadFun ) { ++*stage; continue; } if ( end - in < AO.SaveHeader.sFun ) { goto RSVEnd; } if ( flip ) { pp = in; AO.FlipPOINTER(pp); pp += lenP; AO.FlipLONG(pp); pp += lenL; AO.FlipLONG(pp); pp += lenL; while ( pp < in + AO.SaveHeader.sFun ) { AO.FlipWORD(pp); pp += lenW; } } pp = in + AO.SaveHeader.sFun; outbuf = out; AO.ResizePOINTER(in, out); in += lenP; out += sizeof(void *); /* tabl */ AO.ResizeLONG(in, out); in += lenL; out += sizeof(LONG); /* symminfo */ AO.ResizeLONG(in, out); in += lenL; out += sizeof(LONG); /* name */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* commute */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* complex */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* number */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* flags */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* spec */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* symmetric */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* numargs */ AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* node */ AO.ResizeWORD(in, out); in += lenW; /* namesize */ realnamelen = *((WORD *)out); realnamelen += sizeof(void *)-1; realnamelen &= -(sizeof(void *)); out += sizeof(WORD); AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); /* dimension */ while ( in < pp ) { AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); } namelen = *((WORD *)out-1); /* cares for padding "bug" */ if ( end - in < namelen ) { goto RSVEnd; } *((WORD *)out-1) = realnamelen; *size += AO.SaveHeader.sFun + namelen; *outsize += sizeof(struct FuNcTiOn) + realnamelen; if ( realnamelen > namelen ) { int j = namelen; NCOPYB(out, in, j); out += realnamelen - namelen; } else { int j = realnamelen; NCOPYB(out, in, j); in += namelen - realnamelen; } ++numReadFun; /* we use the information whether a function is tensorial later in ReadSaveTerm */ AO.tensorList[((FUNCTIONS)outbuf)->number+FUNCTION] = (UBYTE)(((FUNCTIONS)outbuf)->spec == TENSORFUNCTION); continue; } /* handle numdummies */ if ( end - in >= lenW ) { if ( flip ) AO.FlipWORD(in); AO.ResizeWORD(in, out); *size += lenW; *outsize += sizeof(WORD); } /* handle numfactors */ if ( end - in >= lenW ) { if ( flip ) AO.FlipWORD(in); AO.ResizeWORD(in, out); *size += lenW; *outsize += sizeof(WORD); } /* handle vflags */ if ( end - in >= lenW ) { if ( flip ) AO.FlipWORD(in); AO.ResizeWORD(in, out); *size += lenW; *outsize += sizeof(WORD); } /* handle uflags */ if ( end - in >= lenW ) { if ( flip ) AO.FlipWORD(in); AO.ResizeWORD(in, out); *size += lenW; *outsize += sizeof(WORD); } return ( 0 ); } RSVEnd: /* we are here because the remaining buffer cannot hold the next struct. we position the file behind the last successfully translated struct and return. */ ADDPOS(pos, *size); SeekFile(AO.SaveData.Handle, &pos, SEEK_SET); return ( 0 ); } else { return ( ReadFile(AO.SaveData.Handle, buffer, *size) != *size ); } } /* #] ReadSaveVariables : #[ ReadSaveTerm : */ /** * Reads a single term from the given buffer at @e bin and write the * translated term back to this buffer at @e bout. * * ReadSaveTerm32() is currently the only instantiation of a * ReadSaveTerm-function. It only deals with data that already has the correct * endianness and that is resized to 32bit words but without being renumbered * or translated in any other way. It uses the compress buffer * AR.CompressBuffer. * * The function is reentrant in order to cope with nested function arguments. * It is called by ReadSaveExpression() and itself. * * The @e return @e value indicates the position in the input buffer up to * which the data has already been successfully processed. The parameter * @e bout returns the corresponding position in the output buffer. * * @param bin start of the input buffer * @param binend end of the input buffer * @param bout as input points to the beginning of the output buffer, * as output points behind the already translated data in * the output buffer * @param boutend end of already decompressed data in output buffer * @param top end of output buffer * @param terminbuf flag whether decompressed data is already in the output * buffer. used in recursive calls * @return pointer to the next unprocessed data in the input buffer */ UBYTE * ReadSaveTerm32(UBYTE *bin, UBYTE *binend, UBYTE **bout, UBYTE *boutend, UBYTE *top, int terminbuf) { GETIDENTITY UBYTE *boutbuf; int32_t len, j, id; int32_t *r, *t, *coeff, *end, *newtermsize, *rend; int32_t *newsubtermp; int32_t *in = (int32_t *)bin; int32_t *out = (int32_t *)*bout; /* if called recursively the term is already decompressed in buffer. is this the case? */ if ( terminbuf ) { /* don't do any decompression, just adjust the pointers */ len = *out; end = out + len; r = in + 1; rend = (int32_t *)boutend; coeff = end - ABS(*(end-1)); newtermsize = (int32_t *)*bout; out = newtermsize + 1; } else { /* do decompression of necessary. always return if the space in the buffer is not sufficient */ int32_t rbuf; r = (int32_t *)AR.CompressBuffer; rbuf = *r; len = j = *in; /* first copy from AR.CompressBuffer if necessary */ if ( j < 0 ) { ++in; if ( (UBYTE *)in >= binend ) { return ( bin ); } *out = len = -j + 1 + *in; end = out + *out; if ( (UBYTE *)end >= top ) { return ( bin ); } ++out; *r++ = len; while ( ++j <= 0 ) { int32_t bb = *r++; *out++ = bb; } j = *in++; } else if ( j == 0 ) { /* care for padding words */ while ( (UBYTE *)in < binend ) { *out++ = 0; if ( (UBYTE *)out > top ) { return ( (UBYTE *)bin ); } *r++ = 0; ++in; } *bout = (UBYTE *)out; return ( (UBYTE *)in ); } else { end = out + len; if ( (UBYTE *)end >= top ) { return ( bin ); } } if ( (UBYTE *)(in + j) >= binend ) { *(AR.CompressBuffer) = rbuf; return ( bin ); } if ( (UBYTE *)out + j >= top ) { return ( bin ); } /* second copy from input buffer */ while ( --j >= 0 ) { int32_t bb = *in++; *r++ = *out++ = bb; } rend = r; r = (int32_t *)AR.CompressBuffer + 1; coeff = end - ABS(*(end-1)); newtermsize = (int32_t *)*bout; out = newtermsize + 1; } /* iterate over subterms */ while ( out < coeff ) { id = *out++; ++r; t = out + *out - 1; newsubtermp = out; ++out; ++r; if ( id == SYMBOL ) { while ( out < t ) { ++out; ++r; /* symbol number */ /* if exponent is too big, rewrite as exponent function */ if ( ABS(*out) >= MAXPOWER ) { int32_t *a, *b; int32_t n; int32_t num = *(out-1); int32_t exp = *out; coeff += 9; end += 9; t += 9; if ( (UBYTE *)end > top ) return ( bin ); out -= 3; *out++ = EXPONENT; /* id */ *out++ = 13; /* size */ *out++ = 1; /* dirtyflag */ *out++ = -SYMBOL; /* first short arg */ *out++ = num; *out++ = 8; /* second arg, size */ *out++ = 0; /* dirtyflag */ *out++ = 6; /* term size */ *out++ = ABS(exp) & 0x0000FFFF; *out++ = ABS(exp) >> 16; *out++ = 1; *out++ = 0; *out++ = ( exp < 0 ) ? -5 : 5; a = ++r; b = out; n = rend - r; NCOPYI32(b, a, n) } else { ++out; ++r; } } } else if ( id == DOTPRODUCT ) { while ( out < t ) { AO.RenumberVec((UBYTE *)out); /* vector 1 */ ++out; ++r; AO.RenumberVec((UBYTE *)out); /* vector 2 */ ++out; ++r; /* if exponent is too big, rewrite as exponent function */ if ( ABS(*out) >= MAXPOWER ) { int32_t *a, *b; int32_t n; int32_t num1 = *(out-2); int32_t num2 = *(out-1); int32_t exp = *out; coeff += 17; end += 17; t += 17; if ( (UBYTE *)end > top ) return ( bin ); out -= 4; *out++ = EXPONENT; /* id */ *out++ = 22; /* size */ *out++ = 1; /* dirtyflag */ *out++ = 11; /* first arg, size */ *out++ = 0; /* dirtyflag */ *out++ = 9; /* term size */ *out++ = DOTPRODUCT; /* p1.p2 */ *out++ = 5; /* subterm size */ *out++ = num1; /* p1 */ *out++ = num2; /* p2 */ *out++ = 1; /* exponent */ *out++ = 1; /* coeff */ *out++ = 1; *out++ = 3; *out++ = 8; /* second arg, size */ *out++ = 0; /* dirtyflag */ *out++ = 6; /* term size */ *out++ = ABS(exp) & 0x0000FFFF; *out++ = ABS(exp) >> 16; *out++ = 1; *out++ = 0; *out++ = ( exp < 0 ) ? -5 : 5; a = ++r; b = out; n = rend - r; NCOPYI32(b, a, n) } else { ++out; ++r; } } } else if ( id == VECTOR ) { while ( out < t ) { AO.RenumberVec((UBYTE *)out); /* vector number */ ++out; ++r; ++out; ++r; /* index, do nothing */ } } else if ( id == INDEX ) { /* int32_t vectoroffset = -2 * *((int32_t *)AO.SaveHeader.wildoffset); */ void *dummy = (void *)AO.SaveHeader.wildoffset; /* to remove a warning about strict-aliasing rules in gcc */ int32_t vectoroffset = -2 * *((int32_t *)dummy); while ( out < t ) { /* if there is a vector, renumber it */ if ( *out < vectoroffset ) { AO.RenumberVec((UBYTE *)out); } ++out; ++r; } } else if ( id == SUBEXPRESSION ) { /* nothing to translate */ while ( out < t ) { ++out; ++r; } } else if ( id == DELTA ) { /* nothing to translate */ r += t - out; out = t; } else if ( id == HAAKJE ) { /* nothing to translate */ r += t - out; out = t; } else if ( id == GAMMA || id == LEVICIVITA || (id >= FUNCTION && AO.tensorList[id]) ) { /* int32_t vectoroffset = -2 * *((int32_t *)AO.SaveHeader.wildoffset); */ void *dummy = (void *)AO.SaveHeader.wildoffset; /* to remove a warning about strict-aliasing rules in gcc */ int32_t vectoroffset = -2 * *((int32_t *)dummy); while ( out < t ) { /* if there is a vector as an argument, renumber it */ if ( *out < vectoroffset ) { AO.RenumberVec((UBYTE *)out); } ++out; ++r; } } else if ( id >= FUNCTION ) { int32_t *argEnd; UBYTE *newbin; ++out; ++r; /* dirty flags */ /* loop over arguments */ while ( out < t ) { if ( *out < 0 ) { /* short notation arguments */ switch ( -*out ) { case SYMBOL: ++out; ++r; ++out; ++r; break; case SNUMBER: argEnd = out+2; ++out; ++r; if ( sizeof(WORD) == 2 ) { /* resize if needed */ if ( *out > (1<<15)-1 || *out < -(1<<15)+1 ) { int32_t *a, *b; int32_t n; int32_t num = *out; coeff += 6; end += 6; argEnd += 6; t += 6; if ( (UBYTE *)end > top ) return ( bin ); --out; *out++ = 8; /* argument size */ *out++ = 0; /* dirtyflag */ *out++ = 6; /* term size */ *out++ = ABS(num) & 0x0000FFFF; *out++ = ABS(num) >> 16; *out++ = 1; *out++ = 0; *out++ = ( num < 0 ) ? -5 : 5; a = ++r; b = out; n = rend - r; NCOPYI32(b, a, n) } else { ++out; ++r; } } else { ++out; ++r; } break; case VECTOR: ++out; ++r; AO.RenumberVec((UBYTE *)out); ++out; ++r; break; case INDEX: ++out; ++r; ++out; ++r; break; case MINVECTOR: ++out; ++r; AO.RenumberVec((UBYTE *)out); ++out; ++r; break; default: if ( -*out >= FUNCTION ) { ++out; ++r; break; } else { MesPrint("short function code %d not implemented.", *out); return ( (UBYTE *)in ); } } } else { /* long arguments */ int32_t *newargsize = out; argEnd = out + *out; ++out; ++r; ++out; ++r; /* dirty flags */ while ( out < argEnd ) { int32_t *keepsizep = out + *out; int32_t lenbuf = *out; int32_t **ppp = &out; /* to avoid a compiler warning */ /* recursion */ newbin = ReadSaveTerm32((UBYTE *)r, binend, (UBYTE **)ppp, (UBYTE *)rend, top, 1); r += lenbuf; if ( newbin == (UBYTE *)r ) { return ( (UBYTE *)in ); } /* if the term done by recursion has changed in size, we need to move the rest of the data accordingly */ if ( out > keepsizep ) { int32_t *a, *b; int32_t n; int32_t extention = out - keepsizep; a = r; b = out; n = rend - r; NCOPYI32(b, a, n) coeff += extention; end += extention; argEnd += extention; t += extention; } else if ( out < keepsizep ) { int32_t *a, *b; int32_t n; int32_t extention = keepsizep - out; a = keepsizep; b = out; n = rend - r; NCOPYI32(b, a, n) coeff -= extention; end -= extention; argEnd -= extention; t -= extention; } } *newargsize = out - newargsize; } } } else { MesPrint("ID %d not recognized.", id); return ( (UBYTE *)in ); } *newsubtermp = out - newsubtermp + 1; } if ( (UBYTE *)end >= top ) { return ( bin ); } /* do coefficient and adjust term size */ boutbuf = *bout; *bout = (UBYTE *)out; ResizeCoeff32(bout, (UBYTE *)end, top); if ( *bout >= top ) { *bout = boutbuf; return ( bin ); } *newtermsize = (int32_t *)*bout - newtermsize; return ( (UBYTE *)in ); } /* #] ReadSaveTerm : #[ ReadSaveExpression : */ /** * Reads an expression from the open file specified by AO.SaveData.Handle. * The endianness flip and a resizing without renumbering is done in this * function. Thereafter the buffer consists of chunks with a uniform maximal * word size (32bit at the moment). The actual renumbering is then done by * calling the function ReadSaveTerm32(). The result is returned in @e buffer. * * If the translation at some point doesn't fit into the buffer anymore, the * function returns and must be called again. In any case @e size returns the * number of successfully read bytes, @e outsize returns the number of * successfully written bytes, and the file will be positioned at the next * byte after the successfully read data. * * It is called by PutInStore(). * * @param buffer output buffer, holds the (translated) expression * @param top end of buffer * @param size number of read bytes * @param outsize number of written bytes * @return = 0 everything okay, != 0 an error occurred */ LONG ReadSaveExpression(UBYTE *buffer, UBYTE *top, LONG *size, LONG *outsize) { if ( AO.transFlag ) { UBYTE *in, *end, *out, *outend, *p; POSITION pos; LONG half; WORD lenW = AO.SaveHeader.lenWORD; /* remember the last file position in case an expression cannot be fully processed */ TELLFILE(AO.SaveData.Handle,&pos); /* adjust 'size' depending on whether the translated data is bigger or smaller */ half = (top-buffer)/2; if ( *size > half ) *size = half; if ( lenW < (WORD)sizeof(WORD) ) { if ( *size * (LONG)sizeof(WORD)/lenW > half ) *size = half*lenW/(LONG)sizeof(WORD); } else { if ( *size > half ) *size = half; } /* depending on the necessary resizing we position the input pointer either at the start of the buffer or in the middle. if the data will roughly remain the same size, we need only one processing step, so we put the 'in' at the middle and 'out' and the beginning. in the other cases we need two processing steps, so first we put 'in' at the beginning and write at the middle. the second step can then read from the middle and put its results at the beginning. */ in = out = buffer; if ( lenW == sizeof(WORD) ) in += half; else out += half; end = in + *size; outend = out + *size; if ( ReadFile(AO.SaveData.Handle, in, *size) != *size ) { return ( MesPrint("Error(3) reading stored expression.") ); } if ( AO.transFlag & 1 ) { p = in; end -= lenW; while ( p <= end ) { AO.FlipWORD(p); p += lenW; } end += lenW; } if ( lenW > (WORD)sizeof(WORD) ) { /* renumber first */ do { outend = out+*size; if ( outend > top ) outend = top; p = ReadSaveTerm32(in, end, &out, outend, top, 0); if ( p == in ) break; in = p; } while ( in <= end - lenW ); /* then resize */ *size = in - buffer; in = buffer + half; end = out; out = buffer; while ( in < end ) { /* resize without checking */ AO.ResizeNCWORD(in, out); in += lenW; out += sizeof(WORD); } } else { if ( lenW < (WORD)sizeof(WORD) ) { /* resize first */ while ( in < end ) { AO.ResizeWORD(in, out); in += lenW; out += sizeof(WORD); } in = buffer + half; end = out; out = buffer; } /* then renumber */ do { p = ReadSaveTerm32(in, end, &out, buffer+half, buffer+half, 0); if ( p == in ) break; in = p; } while ( in <= end - sizeof(WORD) ); *size = (in - buffer - half) * lenW / (ULONG)sizeof(WORD); } *outsize = out - buffer; ADDPOS(pos, *size); SeekFile(AO.SaveData.Handle, &pos, SEEK_SET); return ( 0 ); } else { return ( ReadFile(AO.SaveData.Handle, buffer, *size) != *size ); } } /* #] ReadSaveExpression : #] System Independent Saved Expressions : */ form-5.0.1/sources/threads.c0000644000175100017510000044214315217035721011437 /** @file threads.c * * Routines for the interface of FORM with the pthreads library * * This is the main part of the parallelization of TFORM. * It is important to also look in the files structs.h and variable.h * because the treatment of the A and B structs is essential (these * structs are used by means of the macros AM, AP, AC, AS, AR, AT, AN, * AO and AX). Also the definitions and use of the macros BHEAD and PHEAD * should be looked up. * * The sources are set up in such a way that if WITHPTHREADS isn't defined * there is no trace of pthread parallelization. * The reason is that TFORM is far more memory hungry than sequential FORM. * * Special attention should also go to the locks. The proper use of the * locks is essential and determines whether TFORM can work at all. * We use the LOCK/UNLOCK macros which are empty in the case of sequential FORM * These locks are at many places in the source files when workers can * interfere with each others data or with the data of the master. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #ifdef WITHPTHREADS #define WHOLEBRACKETS /* #[ Variables : The sortbot additions are from 17-may-2007 and after. They constitute an attempt to make the final merge sorting faster for the master. This way the master has only one compare per term. It does add some complexity, but the final merge routine (MasterMerge) is much simpler for the sortbots. On the other hand the original merging is for a large part a copy of the MergePatches routine in sort.c and hence even though complex the bad part has been thoroughly debugged. */ #include "form3.h" #ifdef WITH_ALARM // This is only required if we are blocking SIG_ALRM in the worker threads. #include #endif #ifdef WITHFLOAT #include int PackFloat(WORD *,mpf_t); int UnpackFloat(mpf_t, WORD *); void RatToFloat(mpf_t result, UWORD *formrat, int ratsize); #endif static int numberofthreads; static int numberofworkers; static int identityofthreads = 0; static int *listofavailables; static int topofavailables = 0; static pthread_key_t identitykey; static INILOCK(numberofthreadslock) static INILOCK(availabilitylock) static pthread_t *threadpointers = 0; static pthread_mutex_t *wakeuplocks; static pthread_mutex_t *wakeupmasterthreadlocks; static pthread_cond_t *wakeupconditions; static pthread_condattr_t *wakeupconditionattributes; static int *wakeup; static int *wakeupmasterthread; static INILOCK(wakeupmasterlock) static pthread_cond_t wakeupmasterconditions = PTHREAD_COND_INITIALIZER; static pthread_cond_t *wakeupmasterthreadconditions; static int wakeupmaster = 0; static int identityretval; /* static INILOCK(clearclocklock) */ static LONG *timerinfo; static LONG *sumtimerinfo; static int numberclaimed; static THREADBUCKET **threadbuckets, **freebuckets; static int numthreadbuckets; static int numberoffullbuckets; /* static int numberbusy = 0; */ INILOCK(dummylock) INIRWLOCK(dummyrwlock) static pthread_cond_t dummywakeupcondition = PTHREAD_COND_INITIALIZER; #ifdef WITHSORTBOTS static POSITION SortBotPosition; static int numberofsortbots; static INILOCK(wakeupsortbotlock) static pthread_cond_t wakeupsortbotconditions = PTHREAD_COND_INITIALIZER; static int topsortbotavailables = 0; static LONG numberofterms; #endif /* #] Variables : #[ Identity : #[ StartIdentity : */ /** * To be called once when we start up the threads. * Starts our identity administration. */ void StartIdentity(void) { pthread_key_create(&identitykey,FinishIdentity); } /* #] StartIdentity : #[ FinishIdentity : */ /** * The library needs a finishing routine */ void FinishIdentity(void *keyp) { DUMMYUSE(keyp); /* free(keyp); */ } /* #] FinishIdentity : #[ SetIdentity : */ /** * Assigns an integer value to a thread, starting at zero. */ int SetIdentity(int *identityretval) { /* #ifdef _MSC_VER printf("addr %d\n",&numberofthreadslock); printf("size %d\n",sizeof(numberofthreadslock)); #endif */ LOCK(numberofthreadslock); *identityretval = identityofthreads++; UNLOCK(numberofthreadslock); pthread_setspecific(identitykey,(void *)identityretval); return(*identityretval); } /* #] SetIdentity : #[ WhoAmI : */ /** * Returns the number of the current thread in our administration * * This routine is to be called in routines that need access to the thread * specific data and that don't get their B-struct passed as an argument. * Routines that get called frequently need their B-struct passed. * This is done with BHEAD and the argumentfield gets declared with * one of the BARG macros rather than the ARG macros. */ int WhoAmI(void) { int *identity; /* First a fast exit for when there is at most one thread */ if ( identityofthreads <= 1 ) return(0); /* Now the reading of the key. According to the book the statement should read: pthread_getspecific(identitykey,(void **)(&identity)); but according to the information in pthread.h it is: */ identity = (int *)pthread_getspecific(identitykey); return(*identity); } /* #] WhoAmI : #[ BeginIdentities : */ /** * Starts up the identity registration. This is the routine to be called * at the startup of TFORM. */ void BeginIdentities(void) { StartIdentity(); SetIdentity(&identityretval); } /* #] BeginIdentities : #] Identity : #[ StartHandleLock : */ /** * Routine to be called at the startup of TFORM. * We have this routine because we would like to keep all access to TFORM * specific data in this file. */ void StartHandleLock(void) { AM.handlelock = dummyrwlock; } /* #] StartHandleLock : #[ StartAllThreads : */ /** * In this routine we start 'number' threads. * The routine that runs the show for each worker is called RunThread. * It will call the allocations and all the worker specific action. * Then the master has to wait till all workers are asleep before continuing. * If we use SortBots (special threads to help the master during the * final stages of a big sort) they are started and their routine is * called RunSortBot. * The master then waits till all sortbots are asleep before continuing. * Finally the sort buffers of the master are parcelled up for the final * merge in big sorts in which the workers have to feed the master. * * @param number The number of main threads (including the master) * The number of workers is number-1. * @return Standard return conventions (OK -> 0) */ int StartAllThreads(int number) { int identity, j, dummy, mul; ALLPRIVATES *B; pthread_t thethread; identity = WhoAmI(); #ifdef WITHSORTBOTS timerinfo = (LONG *)Malloc1(sizeof(LONG)*number*2,"timerinfo"); sumtimerinfo = (LONG *)Malloc1(sizeof(LONG)*number*2,"sumtimerinfo"); for ( j = 0; j < number*2; j++ ) { timerinfo[j] = 0; sumtimerinfo[j] = 0; } mul = 2; #else timerinfo = (LONG *)Malloc1(sizeof(LONG)*number,"timerinfo"); sumtimerinfo = (LONG *)Malloc1(sizeof(LONG)*number,"sumtimerinfo"); for ( j = 0; j < number; j++ ) { timerinfo[j] = 0; sumtimerinfo[j] = 0; } mul = 1; #endif listofavailables = (int *)Malloc1(sizeof(int)*(number+1),"listofavailables"); threadpointers = (pthread_t *)Malloc1(sizeof(pthread_t)*number*mul,"threadpointers"); AB = (ALLPRIVATES **)Malloc1(sizeof(ALLPRIVATES *)*number*mul,"Private structs"); wakeup = (int *)Malloc1(sizeof(int)*number*mul,"wakeup"); wakeuplocks = (pthread_mutex_t *)Malloc1(sizeof(pthread_mutex_t)*number*mul,"wakeuplocks"); wakeupconditions = (pthread_cond_t *)Malloc1(sizeof(pthread_cond_t)*number*mul,"wakeupconditions"); wakeupconditionattributes = (pthread_condattr_t *) Malloc1(sizeof(pthread_condattr_t)*number*mul,"wakeupconditionattributes"); wakeupmasterthread = (int *)Malloc1(sizeof(int)*number*mul,"wakeupmasterthread"); wakeupmasterthreadlocks = (pthread_mutex_t *)Malloc1(sizeof(pthread_mutex_t)*number*mul,"wakeupmasterthreadlocks"); wakeupmasterthreadconditions = (pthread_cond_t *)Malloc1(sizeof(pthread_cond_t)*number*mul,"wakeupmasterthread"); numberofthreads = number; numberofworkers = number - 1; threadpointers[identity] = pthread_self(); topofavailables = 0; #ifdef WITH_ALARM /* During thread creation, we block SIGALRM on the main thread. The created threads will inherit this. This is required for #timeout to work properly in TFORM: only the main thread should recieve SIGALRM. */ sigset_t sig_set; sigemptyset(&sig_set); sigaddset(&sig_set, SIGALRM); pthread_sigmask(SIG_BLOCK, &sig_set, NULL); #endif for ( j = 1; j < number; j++ ) { if ( pthread_create(&thethread,NULL,RunThread,(void *)(&dummy)) ) goto failure; } /* Now we initialize the master at the same time that the workers are doing so. */ B = InitializeOneThread(identity); AR.infile = &(AR.Fscr[0]); AR.outfile = &(AR.Fscr[1]); AR.hidefile = &(AR.Fscr[2]); AM.sbuflock = dummylock; AS.inputslock = dummylock; AS.outputslock = dummylock; AS.MaxExprSizeLock = dummylock; AP.PreVarLock = dummylock; AC.halfmodlock = dummylock; MakeThreadBuckets(number,0); /* Now we wait for the workers to finish their startup. We don't want to initialize the sortbots yet and run the risk that some of them may end up with a lower number than one of the workers. */ MasterWaitAll(); #ifdef WITHSORTBOTS if ( numberofworkers > 2 ) { numberofsortbots = numberofworkers-2; for ( j = numberofworkers+1; j < 2*numberofworkers-1; j++ ) { if ( pthread_create(&thethread,NULL,RunSortBot,(void *)(&dummy)) ) goto failure; } } else { numberofsortbots = 0; } MasterWaitAllSortBots(); DefineSortBotTree(); #endif IniSortBlocks(number-1); AS.MasterSort = 0; AM.storefilelock = dummylock; #ifdef WITH_ALARM /* Now we allow the main thread to recieve SIGALRM again. */ pthread_sigmask(SIG_UNBLOCK, &sig_set, NULL); #endif /* MesPrint("AB = %x %x %x %d",AB[0],AB[1],AB[2], identityofthreads); */ return(0); failure: MesPrint("Cannot start %d threads",number); Terminate(-1); return(-1); } /* #] StartAllThreads : #[ InitializeOneThread : */ /** * Array for putting a label on memory allocations and error messages. */ UBYTE *scratchname[] = { (UBYTE *)"scratchsize", (UBYTE *)"scratchsize", (UBYTE *)"hidesize" }; /** * Initializes one thread. This includes the allocation of its private * space and all its buffers. Also the initialization of variables. * * @param identity The (TFORM defined) integer identifier of the thread. * @return A pointer to the struct with all private data of the thread. * We call this struct B and we have a system of macros * (defined in variable.h) that allows us to access its substructs in * the same way as the corresponding substructs in sequential FORM are * accessed. Example: * In TFORM AR is defined as B->R * In FORM AR is defined as A.R (here it is part of the A struct) * * One complication: * AM.ScratSize can be rather big. We don't want all the workers * to have an allocation of that size. Some computers may run out * of allocations. * We need on the workers: * AR.Fscr[0] : input for keep brackets and expressions in rhs * AR.Fscr[1] : output of the sorting to be fed to the master * AR.Fscr[2] : input for keep brackets and expressions in rhs * Hence the 0 and 2 channels can use a rather small buffer like * 10*AM.MaxTer. * The 1 channel needs a buffer roughly AM.ScratSize/#ofworkers. */ ALLPRIVATES *InitializeOneThread(int identity) { WORD *t, *ScratchBuf; int i, j, bsize, *bp; LONG ScratchSize[3], IOsize; ALLPRIVATES *B; UBYTE *s; wakeup[identity] = 0; wakeuplocks[identity] = dummylock; pthread_condattr_init(&(wakeupconditionattributes[identity])); pthread_condattr_setpshared(&(wakeupconditionattributes[identity]),PTHREAD_PROCESS_PRIVATE); wakeupconditions[identity] = dummywakeupcondition; pthread_cond_init(&(wakeupconditions[identity]),&(wakeupconditionattributes[identity])); wakeupmasterthread[identity] = 0; wakeupmasterthreadlocks[identity] = dummylock; wakeupmasterthreadconditions[identity] = dummywakeupcondition; bsize = sizeof(ALLPRIVATES); bsize = (bsize+sizeof(int)-1)/sizeof(int); B = (ALLPRIVATES *)Malloc1(sizeof(int)*bsize,"B struct"); for ( bp = (int *)B, j = 0; j < bsize; j++ ) *bp++ = 0; AB[identity] = B; /* 12-jun-2007 JV: For the timing one has to know a few things: The POSIX standard is that there is only a single process ID and that getrusage returns the time of all the threads together. Under Linux there are two methods though: The older LinuxThreads and NPTL. LinuxThreads gives each thread its own process id. This makes that we can time the threads with getrusage, and hence this was done. Under NPTL this has been 'corrected' and suddenly getruage doesn't work anymore the way it used to. Now we need clock_gettime(CLOCK_THREAD_CPUTIME_ID,&timing) which is declared in and we need -lrt extra in the link statement. (this is at least the case on blade02 at DESY-Zeuthen). See also the code in tools.c at the routine Timer. We may still have to include more stuff there. */ if ( identity > 0 ) TimeCPU(0); #ifdef WITHSORTBOTS if ( identity > numberofworkers ) { /* Some workspace is needed when we have a PolyFun and we have to add two terms and the new result is going to be longer than the old result. */ LONG length = AM.WorkSize*sizeof(WORD)/8+AM.MaxTer*2; AT.WorkSpace = (WORD *)Malloc1(length,"WorkSpace"); AT.WorkTop = AT.WorkSpace + length/sizeof(WORD); AT.WorkPointer = AT.WorkSpace; AT.identity = identity; /* The SB struct gets treated in IniSortBlocks. The SortBotIn variables will be defined DefineSortBotTree. */ if ( AN.SoScratC == 0 ) { AN.SoScratC = (UWORD *)Malloc1(2*(AM.MaxTal+2)*sizeof(UWORD),"Scratch in SortBot"); } AT.SS = (SORTING *)Malloc1(sizeof(SORTING),"dummy sort buffer"); AT.SS->PolyFlag = 0; AT.comsym[0] = 8; AT.comsym[1] = SYMBOL; AT.comsym[2] = 4; AT.comsym[3] = 0; AT.comsym[4] = 1; AT.comsym[5] = 1; AT.comsym[6] = 1; AT.comsym[7] = 3; AT.comnum[0] = 4; AT.comnum[1] = 1; AT.comnum[2] = 1; AT.comnum[3] = 3; AT.comfun[0] = FUNHEAD+4; AT.comfun[1] = FUNCTION; AT.comfun[2] = FUNHEAD; AT.comfun[3] = 0; #if FUNHEAD > 3 for ( i = 4; i <= FUNHEAD; i++ ) AT.comfun[i] = 0; #endif AT.comfun[FUNHEAD+1] = 1; AT.comfun[FUNHEAD+2] = 1; AT.comfun[FUNHEAD+3] = 3; AT.comind[0] = 7; AT.comind[1] = INDEX; AT.comind[2] = 3; AT.comind[3] = 0; AT.comind[4] = 1; AT.comind[5] = 1; AT.comind[6] = 3; AT.inprimelist = -1; AT.sizeprimelist = 0; AT.primelist = 0; AT.bracketinfo = 0; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); AR.sLevel = 0; AR.wranfia = 0; AR.wranfcall = 0; AR.wranfnpair1 = NPAIR1; AR.wranfnpair2 = NPAIR2; AN.NumFunSorts = 5; AN.MaxFunSorts = 5; AN.SplitScratch = 0; AN.SplitScratchSize = AN.InScratch = 0; AN.SplitScratch1 = 0; AN.SplitScratchSize1 = AN.InScratch1 = 0; AN.FunSorts = (SORTING **)Malloc1((AN.NumFunSorts+1)*sizeof(SORTING *),"FunSort pointers"); for ( i = 0; i <= AN.NumFunSorts; i++ ) AN.FunSorts[i] = 0; AN.FunSorts[0] = AT.S0 = AT.SS; AN.idfunctionflag = 0; AN.tryterm = 0; return(B); } if ( identity == 0 && AN.SoScratC == 0 ) { AN.SoScratC = (UWORD *)Malloc1(2*(AM.MaxTal+2)*sizeof(UWORD),"Scratch in SortBot"); } #endif AR.CurDum = AM.IndDum; for ( j = 0; j < 3; j++ ) { if ( identity == 0 ) { if ( j == 2 ) { ScratchSize[j] = AM.HideSize; } else { ScratchSize[j] = AM.ScratSize; } if ( ScratchSize[j] < 10*AM.MaxTer ) ScratchSize[j] = 10 * AM.MaxTer; } else { /* ScratchSize[j] = AM.ScratSize / (numberofthreads-1); ScratchSize[j] = ScratchSize[j] / 20; if ( ScratchSize[j] < 10*AM.MaxTer ) ScratchSize[j] = 10 * AM.MaxTer; */ if ( j == 1 ) ScratchSize[j] = AM.ThreadScratOutSize; else ScratchSize[j] = AM.ThreadScratSize; if ( ScratchSize[j] < 4*AM.MaxTer ) ScratchSize[j] = 4 * AM.MaxTer; AR.Fscr[j].name = 0; } ScratchSize[j] = ( ScratchSize[j] + 255 ) / 256; ScratchSize[j] = ScratchSize[j] * 256; ScratchBuf = (WORD *)Malloc1(ScratchSize[j]*sizeof(WORD),(char *)(scratchname[j])); AR.Fscr[j].POsize = ScratchSize[j] * sizeof(WORD); AR.Fscr[j].POfull = AR.Fscr[j].POfill = AR.Fscr[j].PObuffer = ScratchBuf; AR.Fscr[j].POstop = AR.Fscr[j].PObuffer + ScratchSize[j]; PUTZERO(AR.Fscr[j].POposition); AR.Fscr[j].pthreadslock = dummylock; AR.Fscr[j].wPOsize = AR.Fscr[j].POsize; AR.Fscr[j].wPObuffer = AR.Fscr[j].PObuffer; AR.Fscr[j].wPOfill = AR.Fscr[j].POfill; AR.Fscr[j].wPOfull = AR.Fscr[j].POfull; AR.Fscr[j].wPOstop = AR.Fscr[j].POstop; } AR.InInBuf = 0; AR.InHiBuf = 0; AR.Fscr[0].handle = -1; AR.Fscr[1].handle = -1; AR.Fscr[2].handle = -1; AR.FoStage4[0].handle = -1; AR.FoStage4[1].handle = -1; IOsize = AM.S0->file.POsize; #ifdef WITHZLIB AR.FoStage4[0].ziosize = IOsize; AR.FoStage4[1].ziosize = IOsize; AR.FoStage4[0].ziobuffer = 0; AR.FoStage4[1].ziobuffer = 0; #endif AR.FoStage4[0].POsize = ((IOsize+sizeof(WORD)-1)/sizeof(WORD))*sizeof(WORD); AR.FoStage4[1].POsize = ((IOsize+sizeof(WORD)-1)/sizeof(WORD))*sizeof(WORD); AR.hidefile = &(AR.Fscr[2]); AR.StoreData.Handle = -1; AR.SortType = AC.SortType; AN.IndDum = AM.IndDum; if ( identity > 0 ) { s = (UBYTE *)(FG.fname); i = 0; while ( *s ) { s++; i++; } s = (UBYTE *)Malloc1(sizeof(char)*(i+12),"name for Fscr[0] file"); snprintf((char *)s,i+12,"%s.%d",FG.fname,identity); s[i-3] = 's'; s[i-2] = 'c'; s[i-1] = '0'; AR.Fscr[0].name = (char *)s; s = (UBYTE *)(FG.fname); i = 0; while ( *s ) { s++; i++; } s = (UBYTE *)Malloc1(sizeof(char)*(i+12),"name for Fscr[1] file"); snprintf((char *)s,i+12,"%s.%d",FG.fname,identity); s[i-3] = 's'; s[i-2] = 'c'; s[i-1] = '1'; AR.Fscr[1].name = (char *)s; } AR.CompressBuffer = (WORD *)Malloc1((AM.CompressSize+10)*sizeof(WORD),"compresssize"); AR.ComprTop = AR.CompressBuffer + AM.CompressSize; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); /* Here we make all allocations for the struct AT (which is AB[identity].T or B->T with B = AB+identity). */ AT.WorkSpace = (WORD *)Malloc1(AM.WorkSize*sizeof(WORD),"WorkSpace"); AT.WorkTop = AT.WorkSpace + AM.WorkSize; AT.WorkPointer = AT.WorkSpace; AT.Nest = (NESTING)Malloc1((LONG)sizeof(struct NeStInG)*AM.maxFlevels,"functionlevels"); AT.NestStop = AT.Nest + AM.maxFlevels; AT.NestPoin = AT.Nest; AT.WildMask = (WORD *)Malloc1((LONG)AM.MaxWildcards*sizeof(WORD),"maxwildcards"); LOCK(availabilitylock); AT.ebufnum = inicbufs(); /* Buffer for extras during execution */ AT.fbufnum = inicbufs(); /* Buffer for caching in factorization */ AT.allbufnum = inicbufs(); /* Buffer for id,all */ AT.aebufnum = inicbufs(); /* Buffer for id,all */ UNLOCK(availabilitylock); AT.RepCount = (int *)Malloc1((LONG)((AM.RepMax+3)*sizeof(int)),"repeat buffers"); AN.RepPoint = AT.RepCount; AN.polysortflag = 0; AN.subsubveto = 0; AN.tryterm = 0; AT.RepTop = AT.RepCount + AM.RepMax; AT.WildArgTaken = (WORD *)Malloc1((LONG)AC.WildcardBufferSize*sizeof(WORD)/2 ,"argument list names"); AT.WildcardBufferSize = AC.WildcardBufferSize; AT.previousEfactor = 0; AT.identity = identity; AT.LoadBalancing = 0; /* Still to do: the SS stuff. the Fscr[3] the FoStage4[2] */ if ( AT.WorkSpace == 0 || AT.Nest == 0 || AT.WildMask == 0 || AT.RepCount == 0 || AT.WildArgTaken == 0 ) goto OnError; /* And initializations */ AT.comsym[0] = 8; AT.comsym[1] = SYMBOL; AT.comsym[2] = 4; AT.comsym[3] = 0; AT.comsym[4] = 1; AT.comsym[5] = 1; AT.comsym[6] = 1; AT.comsym[7] = 3; AT.comnum[0] = 4; AT.comnum[1] = 1; AT.comnum[2] = 1; AT.comnum[3] = 3; AT.comfun[0] = FUNHEAD+4; AT.comfun[1] = FUNCTION; AT.comfun[2] = FUNHEAD; AT.comfun[3] = 0; #if FUNHEAD > 3 for ( i = 4; i <= FUNHEAD; i++ ) AT.comfun[i] = 0; #endif AT.comfun[FUNHEAD+1] = 1; AT.comfun[FUNHEAD+2] = 1; AT.comfun[FUNHEAD+3] = 3; AT.comind[0] = 7; AT.comind[1] = INDEX; AT.comind[2] = 3; AT.comind[3] = 0; AT.comind[4] = 1; AT.comind[5] = 1; AT.comind[6] = 3; AT.locwildvalue[0] = SUBEXPRESSION; AT.locwildvalue[1] = SUBEXPSIZE; for ( i = 2; i < SUBEXPSIZE; i++ ) AT.locwildvalue[i] = 0; AT.mulpat[0] = TYPEMULT; AT.mulpat[1] = SUBEXPSIZE+3; AT.mulpat[2] = 0; AT.mulpat[3] = SUBEXPRESSION; AT.mulpat[4] = SUBEXPSIZE; AT.mulpat[5] = 0; AT.mulpat[6] = 1; for ( i = 7; i < SUBEXPSIZE+5; i++ ) AT.mulpat[i] = 0; AT.proexp[0] = SUBEXPSIZE+4; AT.proexp[1] = EXPRESSION; AT.proexp[2] = SUBEXPSIZE; AT.proexp[3] = -1; AT.proexp[4] = 1; for ( i = 5; i < SUBEXPSIZE+1; i++ ) AT.proexp[i] = 0; AT.proexp[SUBEXPSIZE+1] = 1; AT.proexp[SUBEXPSIZE+2] = 1; AT.proexp[SUBEXPSIZE+3] = 3; AT.proexp[SUBEXPSIZE+4] = 0; AT.dummysubexp[0] = SUBEXPRESSION; AT.dummysubexp[1] = SUBEXPSIZE+4; for ( i = 2; i < SUBEXPSIZE; i++ ) AT.dummysubexp[i] = 0; AT.dummysubexp[SUBEXPSIZE] = WILDDUMMY; AT.dummysubexp[SUBEXPSIZE+1] = 4; AT.dummysubexp[SUBEXPSIZE+2] = 0; AT.dummysubexp[SUBEXPSIZE+3] = 0; AT.MinVecArg[0] = 7+ARGHEAD; AT.MinVecArg[ARGHEAD] = 7; AT.MinVecArg[1+ARGHEAD] = INDEX; AT.MinVecArg[2+ARGHEAD] = 3; AT.MinVecArg[3+ARGHEAD] = 0; AT.MinVecArg[4+ARGHEAD] = 1; AT.MinVecArg[5+ARGHEAD] = 1; AT.MinVecArg[6+ARGHEAD] = -3; t = AT.FunArg; *t++ = 4+ARGHEAD+FUNHEAD; for ( i = 1; i < ARGHEAD; i++ ) *t++ = 0; *t++ = 4+FUNHEAD; *t++ = 0; *t++ = FUNHEAD; for ( i = 2; i < FUNHEAD; i++ ) *t++ = 0; *t++ = 1; *t++ = 1; *t++ = 3; AT.inprimelist = -1; AT.sizeprimelist = 0; AT.primelist = 0; AT.nfac = AT.nBer = 0; AT.factorials = 0; AT.bernoullis = 0; AR.wranfia = 0; AR.wranfcall = 0; AR.wranfnpair1 = NPAIR1; AR.wranfnpair2 = NPAIR2; AR.wranfseed = 0; AT.NormData = Malloc1(sizeof(*(AT.NormData)), "NormData thread pointers"); AT.NormDataSize = 1; AT.NormData[0] = AllocNormData(); AT.NormDepth = 0; AN.SplitScratch = 0; AN.SplitScratchSize = AN.InScratch = 0; AN.SplitScratch1 = 0; AN.SplitScratchSize1 = AN.InScratch1 = 0; /* Now the sort buffers. They depend on which thread. The master inherits the sortbuffer from AM.S0 */ if ( identity == 0 ) { AT.S0 = AM.S0; } else { /* For the moment we don't have special settings. They may become costly in virtual memory. */ AT.S0 = AllocSort(AM.S0->LargeSize*sizeof(WORD)/numberofworkers ,AM.S0->SmallSize*sizeof(WORD)/numberofworkers ,AM.S0->SmallEsize*sizeof(WORD)/numberofworkers ,AM.S0->TermsInSmall ,AM.S0->MaxPatches /* ,AM.S0->MaxPatches/numberofworkers */ ,AM.S0->MaxFpatches/numberofworkers ,AM.S0->file.POsize ,0); } AR.CompressPointer = AR.CompressBuffer; /* Install the store caches (15-aug-2006 JV) */ AT.StoreCache = AT.StoreCacheAlloc = 0; if ( AM.NumStoreCaches > 0 ) { STORECACHE sa, sb; LONG size; size = sizeof(struct StOrEcAcHe)+AM.SizeStoreCache; size = ((size-1)/sizeof(size_t)+1)*sizeof(size_t); AT.StoreCacheAlloc = (STORECACHE)Malloc1(size*AM.NumStoreCaches,"StoreCaches"); sa = AT.StoreCache = AT.StoreCacheAlloc; for ( i = 0; i < AM.NumStoreCaches; i++ ) { sb = (STORECACHE)(void *)((UBYTE *)sa+size); if ( i == AM.NumStoreCaches-1 ) { sa->next = 0; } else { sa->next = sb; } SETBASEPOSITION(sa->position,-1); SETBASEPOSITION(sa->toppos,-1); sa = sb; } } ReserveTempFiles(2); return(B); OnError:; MLOCK(ErrorMessageLock); MesPrint("Error initializing thread %d",identity); MUNLOCK(ErrorMessageLock); Terminate(-1); return(B); } /* #] InitializeOneThread : #[ FinalizeOneThread : */ /** * To be called at the end of the run to give the final time statistics for * this thread. * * @param identity The TFORM defined integer identity of the thread. * In principle we could find it out from here with a call * to WhoAmI but because this is to be called at a very * late stage during clean up, we don't want to run any risks. */ void FinalizeOneThread(int identity) { timerinfo[identity] = TimeCPU(1); } /* #] FinalizeOneThread : #[ ClearAllThreads : */ /** * To be called at the end of running TFORM. * Theoretically the system can clean up after up, but it may be better * to do it ourselves. */ void ClearAllThreads(void) { int i; MasterWaitAll(); for ( i = 1; i <= numberofworkers; i++ ) { WakeupThread(i,CLEARCLOCK); } #ifdef WITHSORTBOTS for ( i = numberofworkers+1; i <= numberofworkers+numberofsortbots; i++ ) { WakeupThread(i,CLEARCLOCK); } #endif } /* #] ClearAllThreads : #[ TerminateAllThreads : */ /** * To be called at the end of running TFORM. * Theoretically the system can clean up after up, but it may be better * to do it ourselves. */ void TerminateAllThreads(void) { int i; for ( i = 1; i <= numberofworkers; i++ ) { GetThread(i); WakeupThread(i,TERMINATETHREAD); } #ifdef WITHSORTBOTS for ( i = numberofworkers+1; i <= numberofworkers+numberofsortbots; i++ ) { WakeupThread(i,TERMINATETHREAD); } #endif for ( i = 1; i <= numberofworkers; i++ ) { pthread_join(threadpointers[i],NULL); } #ifdef WITHSORTBOTS for ( i = numberofworkers+1; i <= numberofworkers+numberofsortbots; i++ ) { pthread_join(threadpointers[i],NULL); } #endif } /* #] TerminateAllThreads : #[ MakeThreadBuckets : */ /** * Creates 2*number thread buckets. We want double the number because * we want to prepare number of them while another number are occupied. * * Each bucket should have about AC.ThreadBucketSize*AM.MaxTerm words. * * When loading a thread we only have to pass the address of a full bucket. * This gives more overlap between the master and the workers and hence * less waiting. * * The buckets are used because sending terms one by one to the workers * costs too much overhead. Hence we put a number of terms in each bucket * and then pass the whole bucket. In the ideal case the master loads the * buckets while the workers are processing the contents of the buckets * they have been assigned. In practise often the processing can go faster * than that the master can fill the buckets for all workers. * It should be possible to improve this bucket system, but the trivial * idea * * @param number The number of workers * @param par par = 0: First allocation * par = 1: Reallocation when we change the bucket size with the * threadbucketsize statement. */ int MakeThreadBuckets(int number, int par) { int i; LONG sizethreadbuckets; THREADBUCKET *thr; /* First we need a decent estimate. Not all terms should be maximal. Note that AM.MaxTer is in bytes!!! Maybe we should try to limit the size here a bit more effectively. This is a great consumer of memory. */ sizethreadbuckets = ( AC.ThreadBucketSize + 1 ) * AM.MaxTer + 2*sizeof(WORD); if ( AC.ThreadBucketSize >= 250 ) sizethreadbuckets /= 4; else if ( AC.ThreadBucketSize >= 90 ) sizethreadbuckets /= 3; else if ( AC.ThreadBucketSize >= 40 ) sizethreadbuckets /= 2; sizethreadbuckets /= sizeof(WORD); if ( par == 0 ) { numthreadbuckets = 2*(number-1); threadbuckets = (THREADBUCKET **)Malloc1(numthreadbuckets*sizeof(THREADBUCKET *),"threadbuckets"); freebuckets = (THREADBUCKET **)Malloc1(numthreadbuckets*sizeof(THREADBUCKET *),"threadbuckets"); } if ( par > 0 ) { if ( sizethreadbuckets <= threadbuckets[0]->threadbuffersize ) return(0); for ( i = 0; i < numthreadbuckets; i++ ) { thr = threadbuckets[i]; M_free(thr->deferbuffer,"deferbuffer"); } } else { for ( i = 0; i < numthreadbuckets; i++ ) { threadbuckets[i] = (THREADBUCKET *)Malloc1(sizeof(THREADBUCKET),"threadbuckets"); threadbuckets[i]->lock = dummylock; } } for ( i = 0; i < numthreadbuckets; i++ ) { thr = threadbuckets[i]; thr->threadbuffersize = sizethreadbuckets; thr->free = BUCKETFREE; thr->deferbuffer = (POSITION *)Malloc1(2*sizethreadbuckets*sizeof(WORD) +(AC.ThreadBucketSize+1)*sizeof(POSITION),"deferbuffer"); thr->threadbuffer = (WORD *)(thr->deferbuffer+AC.ThreadBucketSize+1); thr->compressbuffer = (WORD *)(thr->threadbuffer+sizethreadbuckets); thr->busy = BUCKETPREPARINGTERM; thr->usenum = thr->totnum = 0; thr->type = BUCKETDOINGTERMS; } return(0); } /* #] MakeThreadBuckets : #[ GetTimerInfo : */ /** * Returns a pointer to the static timerinfo together with information about * its size. This is used by the checkpoint code to save this information in * the recovery file. */ int GetTimerInfo(LONG** ti,LONG** sti) { *ti = timerinfo; *sti = sumtimerinfo; #ifdef WITHSORTBOTS return AM.totalnumberofthreads*2; #else return AM.totalnumberofthreads; #endif } /* #] GetTimerInfo : #[ WriteTimerInfo : */ /** * Writes data into the static timerinfo variable. This is used by the * checkpoint code to restore the correct timings for the individual threads. */ void WriteTimerInfo(LONG* ti,LONG* sti) { int i; #ifdef WITHSORTBOTS int max = AM.totalnumberofthreads*2; #else int max = AM.totalnumberofthreads; #endif for ( i=0; i 0) */ int LoadOneThread(int from, int identity, THREADBUCKET *thr, int par) { WORD *t1, *t2; ALLPRIVATES *B = AB[identity], *B0 = AB[from]; AR.DefPosition = AR0.DefPosition; AR.NoCompress = AR0.NoCompress; AR.gzipCompress = AR0.gzipCompress; AR.BracketOn = AR0.BracketOn; AR.CurDum = AR0.CurDum; AR.DeferFlag = AR0.DeferFlag; AR.TePos = 0; AR.sLevel = AR0.sLevel; AR.Stage4Name = AR0.Stage4Name; AR.GetOneFile = AR0.GetOneFile; AR.PolyFun = AR0.PolyFun; AR.PolyFunInv = AR0.PolyFunInv; AR.PolyFunType = AR0.PolyFunType; AR.PolyFunExp = AR0.PolyFunExp; AR.PolyFunVar = AR0.PolyFunVar; AR.PolyFunPow = AR0.PolyFunPow; AR.Eside = AR0.Eside; AR.Cnumlhs = AR0.Cnumlhs; /* AR.MaxBracket = AR0.MaxBracket; The compressbuffer contents are mainly relevant for keep brackets We should do this only if there is a keep brackets statement We may however still need the compressbuffer for expressions in the rhs. */ if ( par >= 1 ) { /* We may not need this %%%%% 7-apr-2006 */ t1 = AR.CompressBuffer; t2 = AR0.CompressBuffer; while ( t2 < AR0.CompressPointer ) *t1++ = *t2++; AR.CompressPointer = t1; } else { AR.CompressPointer = AR.CompressBuffer; } if ( AR.DeferFlag ) { if ( AR.infile->handle < 0 ) { AR.infile->POfill = AR0.infile->POfill; } else { /* We have to set the value of POposition to something that will force a read in the first try. */ AR.infile->POfull = AR.infile->POfill = AR.infile->PObuffer; } } if ( par == 0 ) { AN.threadbuck = thr; AN.ninterms = thr->firstterm; } else if ( par == 1 ) { WORD *tstop; t1 = thr->threadbuffer; tstop = t1 + *t1; t2 = AT.WorkPointer; while ( t1 < tstop ) *t2++ = *t1++; AN.ninterms = thr->firstterm; } AN.TeInFun = 0; AN.ncmod = AC.ncmod; AT.BrackBuf = AT0.BrackBuf; AT.bracketindexflag = AT0.bracketindexflag; AN.PolyFunTodo = 0; /* The relevant variables and the term are in their place. There is nothing more to do. */ return(0); } /* #] LoadOneThread : #[ BalanceRunThread : */ /** * To start a thread from the Generator routine we need to pass a number * of variables. * This is part of the second stage load balancing. The second stage is * when we interfere with the expansion tree in Generator and let branches * of the tree be treated by other workers. * Early experiments show disappointing results and hence the system is * currently disabled. * * @param identity The identity of the thread that will receive the term. * @param term The term to be passed to thread 'identity' * @param level The level at which we are in the tree. Defines the statement. * @return Standard return convention (OK -> 0) */ int BalanceRunThread(PHEAD int identity, WORD *term, WORD level) { GETBIDENTITY ALLPRIVATES *BB; WORD *t, *tt; int i, *ti, *tti; LoadOneThread(AT.identity,identity,0,2); /* Extra loading if needed. Quantities changed in Generator. Like the level that has to be passed. */ BB = AB[identity]; BB->R.level = level; BB->T.TMbuff = AT.TMbuff; ti = AT.RepCount; tti = BB->T.RepCount; i = AN.RepPoint - AT.RepCount; BB->N.RepPoint = BB->T.RepCount + i; for ( ; i >= 0; i-- ) tti[i] = ti[i]; t = term; i = *term; tt = BB->T.WorkSpace; NCOPY(tt,t,i); BB->T.WorkPointer = tt; WakeupThread(identity,HIGHERLEVELGENERATION); return(0); } /* #] BalanceRunThread : #[ SetWorkerFiles : */ /** * Initializes the scratch files at the start of the execution of a module. */ void SetWorkerFiles(void) { int id; ALLPRIVATES *B, *B0 = AB[0]; for ( id = 1; id < AM.totalnumberofthreads; id++ ) { B = AB[id]; AR.infile = &(AR.Fscr[0]); AR.outfile = &(AR.Fscr[1]); AR.hidefile = &(AR.Fscr[2]); AR.infile->handle = AR0.infile->handle; AR.hidefile->handle = AR0.hidefile->handle; if ( AR.infile->handle < 0 ) { AR.infile->PObuffer = AR0.infile->PObuffer; AR.infile->POstop = AR0.infile->POstop; AR.infile->POfill = AR0.infile->POfill; AR.infile->POfull = AR0.infile->POfull; AR.infile->POsize = AR0.infile->POsize; AR.InInBuf = AR0.InInBuf; AR.infile->POposition = AR0.infile->POposition; AR.infile->filesize = AR0.infile->filesize; } else { AR.infile->PObuffer = AR.infile->wPObuffer; AR.infile->POstop = AR.infile->wPOstop; AR.infile->POfill = AR.infile->wPOfill; AR.infile->POfull = AR.infile->wPOfull; AR.infile->POsize = AR.infile->wPOsize; AR.InInBuf = 0; PUTZERO(AR.infile->POposition); } /* If there is some writing, it betters happens to ones own outfile. Currently this is to be done only for InParallel. Merging of the outputs is then done by the CopyExpression routine. */ { AR.outfile->PObuffer = AR.outfile->wPObuffer; AR.outfile->POstop = AR.outfile->wPOstop; AR.outfile->POfill = AR.outfile->wPOfill; AR.outfile->POfull = AR.outfile->wPOfull; AR.outfile->POsize = AR.outfile->wPOsize; PUTZERO(AR.outfile->POposition); } if ( AR.hidefile->handle < 0 ) { AR.hidefile->PObuffer = AR0.hidefile->PObuffer; AR.hidefile->POstop = AR0.hidefile->POstop; AR.hidefile->POfill = AR0.hidefile->POfill; AR.hidefile->POfull = AR0.hidefile->POfull; AR.hidefile->POsize = AR0.hidefile->POsize; AR.InHiBuf = AR0.InHiBuf; AR.hidefile->POposition = AR0.hidefile->POposition; AR.hidefile->filesize = AR0.hidefile->filesize; } else { AR.hidefile->PObuffer = AR.hidefile->wPObuffer; AR.hidefile->POstop = AR.hidefile->wPOstop; AR.hidefile->POfill = AR.hidefile->wPOfill; AR.hidefile->POfull = AR.hidefile->wPOfull; AR.hidefile->POsize = AR.hidefile->wPOsize; AR.InHiBuf = 0; PUTZERO(AR.hidefile->POposition); } } if ( AR0.StoreData.dirtyflag ) { for ( id = 1; id < AM.totalnumberofthreads; id++ ) { B = AB[id]; AR.StoreData = AR0.StoreData; } } } /* #] SetWorkerFiles : #[ RunThread : */ /** * This is the routine that represents each worker. * The model is that the worker waits for a 'signal'. * If there is a signal it wakes up, looks at what signal and then takes * the corresponding action. After this it goes back to sleep. */ void *RunThread(void *dummy) { WORD *term, *ttin, *tt, *ttco, *oldwork; int identity, wakeupsignal, identityretv, i, tobereleased, errorcode; ALLPRIVATES *B; THREADBUCKET *thr; POSITION *ppdef; EXPRESSIONS e; DUMMYUSE(dummy); identity = SetIdentity(&identityretv); threadpointers[identity] = pthread_self(); B = InitializeOneThread(identity); while ( ( wakeupsignal = ThreadWait(identity) ) > 0 ) { switch ( wakeupsignal ) { /* #[ STARTNEWEXPRESSION : */ case STARTNEWEXPRESSION: /* Set up the sort routines etc. Start with getting some buffers synchronized with the compiler */ if ( UpdateOneThread(identity) ) { MLOCK(ErrorMessageLock); MesPrint("Update error in starting expression in thread %d in module %d",identity,AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } AR.DeferFlag = AC.ComDefer; AR.sLevel = AS.sLevel; AR.MaxDum = AM.IndDum; AR.expchanged = AB[0]->R.expchanged; AR.expflags = AB[0]->R.expflags; AR.PolyFun = AB[0]->R.PolyFun; AR.PolyFunInv = AB[0]->R.PolyFunInv; AR.PolyFunType = AB[0]->R.PolyFunType; AR.PolyFunExp = AB[0]->R.PolyFunExp; AR.PolyFunVar = AB[0]->R.PolyFunVar; AR.PolyFunPow = AB[0]->R.PolyFunPow; /* Now fire up the sort buffer. */ NewSort(BHEAD0); break; /* #] STARTNEWEXPRESSION : #[ LOWESTLEVELGENERATION : */ case LOWESTLEVELGENERATION: #ifdef INNERTEST if ( AC.InnerTest ) { if ( StrCmp(AC.TestValue,(UBYTE *)INNERTEST) == 0 ) { MesPrint("Testing(Worker%d): value = %s",AT.identity,AC.TestValue); } } #endif e = Expressions + AR.CurExpr; thr = AN.threadbuck; ppdef = thr->deferbuffer; ttin = thr->threadbuffer; ttco = thr->compressbuffer; term = AT.WorkPointer; thr->usenum = 0; tobereleased = 0; AN.inputnumber = thr->firstterm; AN.ninterms = thr->firstterm; do { thr->usenum++; /* For if the master wants to steal the bucket */ tt = term; i = *ttin; NCOPY(tt,ttin,i); AT.WorkPointer = tt; if ( AR.DeferFlag ) { tt = AR.CompressBuffer; i = *ttco; NCOPY(tt,ttco,i); AR.CompressPointer = tt; AR.DefPosition = ppdef[0]; ppdef++; } if ( thr->free == BUCKETTERMINATED ) { /* The next statement allows the master to steal the bucket for load balancing purposes. We do still execute the current term, but afterwards we drop out. Once we have written the release code, we cannot use this bucket anymore. Hence the exit to the label bucketstolen. */ if ( thr->usenum == thr->totnum ) { thr->free = BUCKETCOMINGFREE; } else { thr->free = BUCKETRELEASED; tobereleased = 1; } } /* What if we want to steal and we set thr->free while the thread is inside the next code for a long time? if ( AT.LoadBalancing ) { */ LOCK(thr->lock); thr->busy = BUCKETDOINGTERM; UNLOCK(thr->lock); /* } else { thr->busy = BUCKETDOINGTERM; } */ AN.RepPoint = AT.RepCount + 1; if ( ( e->vflags & ISFACTORIZED ) != 0 && term[1] == HAAKJE ) { StoreTerm(BHEAD term); } else { if ( AR.DeferFlag ) { AR.CurDum = AN.IndDum = Expressions[AR.CurExpr].numdummies + AM.IndDum; } else { AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); } if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( ( AP.PreDebug & THREADSDEBUG ) != 0 ) { MLOCK(ErrorMessageLock); MesPrint("Thread %w executing term:"); PrintTerm(term,"LLG"); MUNLOCK(ErrorMessageLock); } if ( ( AR.PolyFunType == 2 ) && ( AC.PolyRatFunChanged == 0 ) && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION ) ) { PolyFunClean(BHEAD term); } if ( Generator(BHEAD term,0) ) { LowerSortLevel(); MLOCK(ErrorMessageLock); MesPrint("Error in processing one term in thread %d in module %d",identity,AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } AN.ninterms++; } /* if ( AT.LoadBalancing ) { */ LOCK(thr->lock); thr->busy = BUCKETPREPARINGTERM; UNLOCK(thr->lock); /* } else { thr->busy = BUCKETPREPARINGTERM; } */ if ( thr->free == BUCKETTERMINATED ) { if ( thr->usenum == thr->totnum ) { thr->free = BUCKETCOMINGFREE; } else { thr->free = BUCKETRELEASED; tobereleased = 1; } } if ( tobereleased ) goto bucketstolen; } while ( *ttin ); thr->free = BUCKETCOMINGFREE; bucketstolen:; /* if ( AT.LoadBalancing ) { */ LOCK(thr->lock); thr->busy = BUCKETTOBERELEASED; UNLOCK(thr->lock); /* } else { thr->busy = BUCKETTOBERELEASED; } */ AT.WorkPointer = term; break; /* #] LOWESTLEVELGENERATION : #[ FINISHEXPRESSION : */ #ifdef WITHSORTBOTS case CLAIMOUTPUT: LOCK(AT.SB.MasterBlockLock[1]); break; #endif case FINISHEXPRESSION: /* Finish the sort Start with claiming the first block Once we have claimed it we can let the master know that everything is all right. */ LOCK(AT.SB.MasterBlockLock[1]); ThreadClaimedBlock(identity); /* Entry for when we work with sortbots */ #ifdef WITHSORTBOTS /* fall through */ case FINISHEXPRESSION2: #endif /* Now we may need here an fsync on the sort file */ if ( AC.ThreadSortFileSynch ) { if ( AT.S0->file.handle >= 0 ) { SynchFile(AT.S0->file.handle); } } AT.SB.FillBlock = 1; AT.SB.MasterFill[1] = AT.SB.MasterStart[1]; errorcode = EndSort(BHEAD AT.S0->sBuffer,0); UNLOCK(AT.SB.MasterBlockLock[AT.SB.FillBlock]); UpdateMaxSize(); if ( errorcode ) { MLOCK(ErrorMessageLock); MesPrint("Error terminating sort in thread %d in module %d",identity,AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } break; /* #] FINISHEXPRESSION : #[ CLEANUPEXPRESSION : */ case CLEANUPEXPRESSION: /* Cleanup everything and wait for the next expression */ if ( AR.outfile->handle >= 0 ) { CloseFile(AR.outfile->handle); AR.outfile->handle = -1; remove(AR.outfile->name); AR.outfile->POfill = AR.outfile->POfull = AR.outfile->PObuffer; PUTZERO(AR.outfile->POposition); PUTZERO(AR.outfile->filesize); } else { AR.outfile->POfill = AR.outfile->POfull = AR.outfile->PObuffer; PUTZERO(AR.outfile->POposition); PUTZERO(AR.outfile->filesize); } { CBUF *C = cbuf+AT.ebufnum; WORD **w, ii; if ( C->numrhs > 0 || C->numlhs > 0 ) { if ( C->rhs ) { w = C->rhs; ii = C->numrhs; do { *w++ = 0; } while ( --ii > 0 ); } if ( C->lhs ) { w = C->lhs; ii = C->numlhs; do { *w++ = 0; } while ( --ii > 0 ); } C->numlhs = C->numrhs = 0; ClearTree(AT.ebufnum); C->Pointer = C->Buffer; } } break; /* #] CLEANUPEXPRESSION : #[ HIGHERLEVELGENERATION : */ case HIGHERLEVELGENERATION: /* When foliating halfway the tree. This should only be needed in a second level load balancing */ term = AT.WorkSpace; AT.WorkPointer = term + *term; if ( Generator(BHEAD term,AR.level) ) { LowerSortLevel(); MLOCK(ErrorMessageLock); MesPrint("Error in load balancing one term at level %d in thread %d in module %d",AR.level,AT.identity,AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } AT.WorkPointer = term; break; /* #] HIGHERLEVELGENERATION : #[ STARTNEWMODULE : */ case STARTNEWMODULE: /* For resetting variables. */ SpecialCleanup(B); break; /* #] STARTNEWMODULE : #[ TERMINATETHREAD : */ case TERMINATETHREAD: goto EndOfThread; /* #] TERMINATETHREAD : #[ DOONEEXPRESSION : When a thread has to do a complete (not too big) expression. The number of the expression to be done is in AR.exprtodo. The code is mostly taken from Processor. The only difference is with what to do with the output. The output should go to the scratch buffer of the worker (which is free at the right moment). If this buffer is too small we have a problem. We could write to file or give the master what we have and from now on the master has to collect pieces until things are complete. Note: this assumes that the expressions don't keep their order. If they have to keep their order, don't use this feature. */ case DOONEEXPRESSION: { POSITION position, outposition; FILEHANDLE *fi, *fout, *oldoutfile; LONG dd = 0; WORD oldBracketOn = AR.BracketOn; WORD *oldBrackBuf = AT.BrackBuf; WORD oldbracketindexflag = AT.bracketindexflag; WORD fromspectator = 0; e = Expressions + AR.exprtodo; i = AR.exprtodo; AR.CurExpr = i; AR.SortType = AC.SortType; AR.expchanged = 0; if ( ( e->vflags & ISFACTORIZED ) != 0 ) { AR.BracketOn = 1; AT.BrackBuf = AM.BracketFactors; AT.bracketindexflag = 1; } position = AS.OldOnFile[i]; if ( e->status == HIDDENLEXPRESSION || e->status == HIDDENGEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) { AR.GetFile = 2; fi = AR.hidefile; } else { AR.GetFile = 0; fi = AR.infile; } /* PUTZERO(fi->POposition); if ( fi->handle >= 0 ) { fi->POfill = fi->POfull = fi->PObuffer; } */ SetScratch(fi,&position); term = oldwork = AT.WorkPointer; AR.CompressPointer = AR.CompressBuffer; AR.CompressPointer[0] = 0; AR.KeptInHold = 0; if ( GetTerm(BHEAD term) <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Expression %d has problems in scratchfile (t)",i); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( AT.bracketindexflag > 0 ) OpenBracketIndex(i); term[3] = i; if ( term[5] < 0 ) { fromspectator = -term[5]; PUTZERO(AM.SpectatorFiles[fromspectator-1].readpos); term[5] = AC.cbufnum; } PUTZERO(outposition); fout = AR.outfile; fout->POfill = fout->POfull = fout->PObuffer; fout->POposition = outposition; if ( fout->handle >= 0 ) { fout->POposition = outposition; } /* The next statement is needed because we need the system to believe that the expression is at position zero for the moment. In this worker, with no memory of other expressions, it is. This is needed for when a bracket index is made because there e->onfile is an offset. Afterwards, when the expression is written to its final location in the masters output e->onfile will get its real value. */ PUTZERO(e->onfile); if ( PutOut(BHEAD term,&outposition,fout,0) < 0 ) goto ProcErr; AR.DeferFlag = AC.ComDefer; AR.sLevel = AB[0]->R.sLevel; term = AT.WorkPointer; NewSort(BHEAD0); AR.MaxDum = AM.IndDum; AN.ninterms = 0; if ( fromspectator ) { while ( GetFromSpectator(term,fromspectator-1) ) { AT.WorkPointer = term + *term; AN.RepPoint = AT.RepCount + 1; AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( ( AR.PolyFunType == 2 ) && ( AC.PolyRatFunChanged == 0 ) && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION ) ) { PolyFunClean(BHEAD term); } if ( Generator(BHEAD term,0) ) { LowerSortLevel(); goto ProcErr; } } } else { while ( GetTerm(BHEAD term) ) { SeekScratch(fi,&position); AN.ninterms++; dd = AN.deferskipped; if ( ( e->vflags & ISFACTORIZED ) != 0 && term[1] == HAAKJE ) { StoreTerm(BHEAD term); } else { if ( AC.CollectFun && *term <= (AM.MaxTer/(2*(LONG)sizeof(WORD))) ) { if ( GetMoreTerms(term) < 0 ) { LowerSortLevel(); goto ProcErr; } SeekScratch(fi,&position); } AT.WorkPointer = term + *term; AN.RepPoint = AT.RepCount + 1; if ( AR.DeferFlag ) { AR.CurDum = AN.IndDum = Expressions[AR.exprtodo].numdummies; } else { AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); } if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( ( AR.PolyFunType == 2 ) && ( AC.PolyRatFunChanged == 0 ) && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION ) ) { PolyFunClean(BHEAD term); } if ( Generator(BHEAD term,0) ) { LowerSortLevel(); goto ProcErr; } AN.ninterms += dd; } SetScratch(fi,&position); if ( fi == AR.hidefile ) { AR.InHiBuf = (fi->POfull-fi->PObuffer) -DIFBASE(position,fi->POposition)/sizeof(WORD); } else { AR.InInBuf = (fi->POfull-fi->PObuffer) -DIFBASE(position,fi->POposition)/sizeof(WORD); } } } AN.ninterms += dd; if ( EndSort(BHEAD AT.S0->sBuffer,0) < 0 ) goto ProcErr; e->numdummies = AR.MaxDum - AM.IndDum; AR.BracketOn = oldBracketOn; AT.BrackBuf = oldBrackBuf; if ( ( e->vflags & TOBEFACTORED ) != 0 ) poly_factorize_expression(e); else if ( ( ( e->vflags & TOBEUNFACTORED ) != 0 ) && ( ( e->vflags & ISFACTORIZED ) != 0 ) ) poly_unfactorize_expression(e); if ( AT.S0->TermsLeft ) e->vflags &= ~ISZERO; else e->vflags |= ISZERO; if ( AR.expchanged == 0 ) e->vflags |= ISUNMODIFIED; if ( AT.S0->TermsLeft ) AR.expflags |= ISZERO; if ( AR.expchanged ) AR.expflags |= ISUNMODIFIED; AR.GetFile = 0; AT.bracketindexflag = oldbracketindexflag; /* Now copy the whole thing from fout to AR0.outfile Do this in one go to keep the lock occupied as short as possible */ SeekScratch(fout,&outposition); LOCK(AS.outputslock); oldoutfile = AB[0]->R.outfile; if ( e->status == INTOHIDELEXPRESSION || e->status == INTOHIDEGEXPRESSION ) { AB[0]->R.outfile = AB[0]->R.hidefile; } SeekScratch(AB[0]->R.outfile,&position); e->onfile = position; if ( CopyExpression(fout,AB[0]->R.outfile) < 0 ) { AB[0]->R.outfile = oldoutfile; UNLOCK(AS.outputslock); MLOCK(ErrorMessageLock); MesPrint("Error copying output of 'InParallel' expression to master. Thread: %d",identity); MUNLOCK(ErrorMessageLock); goto ProcErr; } AB[0]->R.outfile = oldoutfile; AB[0]->R.hidefile->POfull = AB[0]->R.hidefile->POfill; AB[0]->R.expflags = AR.expflags; UNLOCK(AS.outputslock); if ( fout->handle >= 0 ) { /* Now get rid of the file */ CloseFile(fout->handle); fout->handle = -1; remove(fout->name); PUTZERO(fout->POposition); PUTZERO(fout->filesize); fout->POfill = fout->POfull = fout->PObuffer; } UpdateMaxSize(); AT.WorkPointer = oldwork; } break; /* #] DOONEEXPRESSION : #[ DOBRACKETS : In case we have a bracket index we can have the worker treat one or more of the entries in the bracket index. The advantage is that identical terms will meet each other sooner in the sorting and hence fewer compares will be needed. Also this way the master doesn't need to fill the buckets. The main problem is the load balancing which can become very bad when there is a long tail without things outside the bracket. We get sent: 1: The number of the first bracket to be done 2: The number of the last bracket to be done */ case DOBRACKETS: { BRACKETINFO *binfo; BRACKETINDEX *bi; FILEHANDLE *fi; POSITION stoppos,where; e = Expressions + AR.CurExpr; binfo = e->bracketinfo; thr = AN.threadbuck; bi = &(binfo->indexbuffer[thr->firstbracket]); if ( AR.GetFile == 2 ) fi = AR.hidefile; else fi = AR.infile; where = bi->start; ADD2POS(where,AS.OldOnFile[AR.CurExpr]); SetScratch(fi,&(where)); stoppos = binfo->indexbuffer[thr->lastbracket].next; ADD2POS(stoppos,AS.OldOnFile[AR.CurExpr]); AN.ninterms = thr->firstterm; /* Now we have to put the 'value' of the bracket in the Compress buffer. */ ttco = AR.CompressBuffer; tt = binfo->bracketbuffer + bi->bracket; i = *tt; NCOPY(ttco,tt,i) AR.CompressPointer = ttco; term = AT.WorkPointer; while ( GetTerm(BHEAD term) ) { SeekScratch(fi,&where); AT.WorkPointer = term + *term; AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( ( AR.PolyFunType == 2 ) && ( AC.PolyRatFunChanged == 0 ) && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION ) ) { PolyFunClean(BHEAD term); } if ( ( AP.PreDebug & THREADSDEBUG ) != 0 ) { MLOCK(ErrorMessageLock); MesPrint("Thread %w executing term:"); PrintTerm(term,"DoBrackets"); MUNLOCK(ErrorMessageLock); } AT.WorkPointer = term + *term; if ( Generator(BHEAD term,0) ) { LowerSortLevel(); MLOCK(ErrorMessageLock); MesPrint("Error in processing one term in thread %d in module %d",identity,AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } AN.ninterms++; SetScratch(fi,&(where)); if ( ISGEPOS(where,stoppos) ) break; } AT.WorkPointer = term; thr->free = BUCKETCOMINGFREE; break; } /* #] DOBRACKETS : #[ CLEARCLOCK : The program only comes here after a .clear */ case CLEARCLOCK: /* LOCK(clearclocklock); */ sumtimerinfo[identity] += TimeCPU(1); timerinfo[identity] = TimeCPU(0); /* UNLOCK(clearclocklock); */ break; /* #] CLEARCLOCK : #[ MCTSEXPANDTREE : */ case MCTSEXPANDTREE: AT.optimtimes = AB[0]->T.optimtimes; find_Horner_MCTS_expand_tree(); break; /* #] MCTSEXPANDTREE : #[ OPTIMIZEEXPRESSION : */ case OPTIMIZEEXPRESSION: optimize_expression_given_Horner(); break; /* #] OPTIMIZEEXPRESSION : */ default: MLOCK(ErrorMessageLock); MesPrint("Illegal wakeup signal %d for thread %d",wakeupsignal,identity); MUNLOCK(ErrorMessageLock); Terminate(-1); break; } /* we need the following update in case we are using checkpoints. then we need to readjust the clocks when recovering using this information */ timerinfo[identity] = TimeCPU(1); } EndOfThread:; /* This is the end of the thread. We cleanup and exit. If we are using flint, call the per-thread cleanup function. This keep valgrind happy. */ #ifdef WITHFLINT flint_final_cleanup_thread(); #endif FinalizeOneThread(identity); return(0); ProcErr: Terminate(-1); return(0); } /* #] RunThread : #[ RunSortBot : */ /** * This is the routine that represents each sortbot. * The model is that the sortbot waits for a 'signal'. * If there is a signal it wakes up, looks at what signal and then takes * the corresponding action. After this it goes back to sleep. */ #ifdef WITHSORTBOTS void *RunSortBot(void *dummy) { int identity, wakeupsignal, identityretv; ALLPRIVATES *B, *BB; DUMMYUSE(dummy); identity = SetIdentity(&identityretv); threadpointers[identity] = pthread_self(); B = InitializeOneThread(identity); while ( ( wakeupsignal = SortBotWait(identity) ) > 0 ) { switch ( wakeupsignal ) { /* #[ INISORTBOT : */ case INISORTBOT: AR.CompressBuffer = AB[0]->R.CompressBuffer; AR.ComprTop = AB[0]->R.ComprTop; AR.CompressPointer = AB[0]->R.CompressPointer; AR.CurExpr = AB[0]->R.CurExpr; AR.PolyFun = AB[0]->R.PolyFun; AR.PolyFunInv = AB[0]->R.PolyFunInv; AR.PolyFunType = AB[0]->R.PolyFunType; AR.PolyFunExp = AB[0]->R.PolyFunExp; AR.PolyFunVar = AB[0]->R.PolyFunVar; AR.PolyFunPow = AB[0]->R.PolyFunPow; AR.SortType = AC.SortType; if ( AR.PolyFun == 0 ) { AT.SS->PolyFlag = 0; } else if ( AR.PolyFunType == 1 ) { AT.SS->PolyFlag = 1; } else if ( AR.PolyFunType == 2 ) { if ( AR.PolyFunExp == 2 || AR.PolyFunExp == 3 ) AT.SS->PolyFlag = 1; else AT.SS->PolyFlag = 2; } AT.SS->PolyWise = 0; AN.ncmod = AC.ncmod; LOCK(AT.SB.MasterBlockLock[1]); BB = AB[AT.SortBotIn1]; LOCK(BB->T.SB.MasterBlockLock[BB->T.SB.MasterNumBlocks]); BB = AB[AT.SortBotIn2]; LOCK(BB->T.SB.MasterBlockLock[BB->T.SB.MasterNumBlocks]); AT.SB.FillBlock = 1; AT.SB.MasterFill[1] = AT.SB.MasterStart[1]; SETBASEPOSITION(AN.theposition,0); // Reset the sortbot comparison count AT.SS->verbComparisons = 0; break; /* #] INISORTBOT : #[ RUNSORTBOT : */ case RUNSORTBOT: SortBotMerge(B); break; /* #] RUNSORTBOT : #[ TERMINATETHREAD : */ case TERMINATETHREAD: goto EndOfThread; /* #] TERMINATETHREAD : #[ CLEARCLOCK : The program only comes here after a .clear */ case CLEARCLOCK: /* LOCK(clearclocklock); */ sumtimerinfo[identity] += TimeCPU(1); timerinfo[identity] = TimeCPU(0); /* UNLOCK(clearclocklock); */ break; /* #] CLEARCLOCK : */ default: MLOCK(ErrorMessageLock); MesPrint("Illegal wakeup signal %d for thread %d",wakeupsignal,identity); MUNLOCK(ErrorMessageLock); Terminate(-1); break; } } EndOfThread:; /* This is the end of the thread. We cleanup and exit. If we are using flint, call the per-thread cleanup function. This keep valgrind happy. */ #ifdef WITHFLINT flint_final_cleanup_thread(); #endif FinalizeOneThread(identity); return(0); } #endif /* #] RunSortBot : #[ IAmAvailable : */ /** * To be called by a thread when it becomes available. * Puts it on a stack. * We use a stack model. It is also possible to define a circular queue. * This will be tried out at a later stage. * One advantage of a stack could be that if we cannot feed all threads * more sorting is done at the threads and the master has to do less. * * @param identity The identity thread that signals its availability. */ void IAmAvailable(int identity) { int top; LOCK(availabilitylock); top = topofavailables; listofavailables[topofavailables++] = identity; if ( top == 0 ) { UNLOCK(availabilitylock); LOCK(wakeupmasterlock); wakeupmaster = identity; pthread_cond_signal(&wakeupmasterconditions); UNLOCK(wakeupmasterlock); } else { UNLOCK(availabilitylock); } } /* #] IAmAvailable : #[ GetAvailableThread : */ /** * Gets an available thread from the top of the stack. * Maybe a circular buffer model would work better. This would mean that * we take the lowest available worker, rather than the highest. * We then have to work with high water marks and low water marks. * (writing point and reading point). Still to be investigated. */ int GetAvailableThread(void) { int retval = -1; LOCK(availabilitylock); if ( topofavailables > 0 ) retval = listofavailables[--topofavailables]; UNLOCK(availabilitylock); if ( retval >= 0 ) { /* Make sure the thread is indeed waiting and not between saying that it is available and starting to wait. */ LOCK(wakeuplocks[retval]); UNLOCK(wakeuplocks[retval]); } return(retval); } /* #] GetAvailableThread : #[ ConditionalGetAvailableThread : */ /** * Looks whether a thread is available. * If a thread is available it is taken from the stack of available threads. * * @return the identity of an available thread or -1 if none is available. */ int ConditionalGetAvailableThread(void) { int retval = -1; if ( topofavailables > 0 ) { LOCK(availabilitylock); if ( topofavailables > 0 ) { retval = listofavailables[--topofavailables]; } UNLOCK(availabilitylock); if ( retval >= 0 ) { /* Make sure the thread is indeed waiting and not between saying that it is available and starting to wait. */ LOCK(wakeuplocks[retval]); UNLOCK(wakeuplocks[retval]); } } return(retval); } /* #] ConditionalGetAvailableThread : #[ GetThread : */ /** * Gets a given thread from the list of available threads, even if * it isn't on the top of the stack. * * @param identity The number of the thread that we want to remove from the * list of available threads. * @return The number of the thread if it was available. -1 otherwise. */ int GetThread(int identity) { int retval = -1, j; LOCK(availabilitylock); for ( j = 0; j < topofavailables; j++ ) { if ( identity == listofavailables[j] ) break; } if ( j < topofavailables ) { --topofavailables; for ( ; j < topofavailables; j++ ) { listofavailables[j] = listofavailables[j+1]; } retval = identity; } UNLOCK(availabilitylock); return(retval); } /* #] GetThread : #[ ThreadWait : */ /** * To be called by a thread when it has nothing to do. * It goes to sleep and waits for a wakeup call. * The return value is the number of the wakeup signal. * * @param identity The number of the thread. * @return The number of the wake-up signal. */ int ThreadWait(int identity) { int retval, top, j; LOCK(wakeuplocks[identity]); LOCK(availabilitylock); top = topofavailables; for ( j = topofavailables; j > 0; j-- ) listofavailables[j] = listofavailables[j-1]; listofavailables[0] = identity; topofavailables++; if ( top == 0 || topofavailables == numberofworkers ) { UNLOCK(availabilitylock); LOCK(wakeupmasterlock); wakeupmaster = identity; pthread_cond_signal(&wakeupmasterconditions); UNLOCK(wakeupmasterlock); } else { UNLOCK(availabilitylock); } while ( wakeup[identity] == 0 ) { pthread_cond_wait(&(wakeupconditions[identity]),&(wakeuplocks[identity])); } retval = wakeup[identity]; wakeup[identity] = 0; UNLOCK(wakeuplocks[identity]); return(retval); } /* #] ThreadWait : #[ SortBotWait : */ #ifdef WITHSORTBOTS /** * To be called by a sortbot thread when it has nothing to do. * It goes to sleep and waits for a wakeup call. * The return value is the number of the wakeup signal. * * @param identity The number of the sortbot thread. * @return The number of the wake-up signal. */ int SortBotWait(int identity) { int retval; LOCK(wakeuplocks[identity]); LOCK(availabilitylock); topsortbotavailables++; if ( topsortbotavailables >= numberofsortbots ) { UNLOCK(availabilitylock); LOCK(wakeupsortbotlock); wakeupmaster = identity; pthread_cond_signal(&wakeupsortbotconditions); UNLOCK(wakeupsortbotlock); } else { UNLOCK(availabilitylock); } while ( wakeup[identity] == 0 ) { pthread_cond_wait(&(wakeupconditions[identity]),&(wakeuplocks[identity])); } retval = wakeup[identity]; wakeup[identity] = 0; UNLOCK(wakeuplocks[identity]); return(retval); } #endif /* #] SortBotWait : #[ ThreadClaimedBlock : */ /** * When the final sort of an expression starts the workers have to claim * the first block in the buffers of the master for their output. * The master may only continue after all workers have claimed their block * because otherwise it is possible that the master may claim this block for * reading before it has been written in. * Hence the master must wait till all blocks have been claimed. Then the * master will get signalled that it can continue. */ int ThreadClaimedBlock(int identity) { LOCK(availabilitylock); numberclaimed++; if ( numberclaimed >= numberofworkers ) { UNLOCK(availabilitylock); LOCK(wakeupmasterlock); wakeupmaster = identity; pthread_cond_signal(&wakeupmasterconditions); UNLOCK(wakeupmasterlock); } else { UNLOCK(availabilitylock); } return(0); } /* #] ThreadClaimedBlock : #[ MasterWait : */ /** * To be called by the master when it has to wait for one of the * workers to become available. * It goes to sleep and waits for a wakeupmaster call. * The return value is the identity of the process that wakes up the master. */ int MasterWait(void) { int retval; LOCK(wakeupmasterlock); while ( wakeupmaster == 0 ) { pthread_cond_wait(&wakeupmasterconditions,&wakeupmasterlock); } retval = wakeupmaster; wakeupmaster = 0; UNLOCK(wakeupmasterlock); return(retval); } /* #] MasterWait : #[ MasterWaitThread : */ /** * To be called by the master when it has to wait for a specific one of the * workers to become available. * The return value is the value of the signal. */ int MasterWaitThread(int identity) { int retval; LOCK(wakeupmasterthreadlocks[identity]); while ( wakeupmasterthread[identity] == 0 ) { pthread_cond_wait(&(wakeupmasterthreadconditions[identity]) ,&(wakeupmasterthreadlocks[identity])); } retval = wakeupmasterthread[identity]; wakeupmasterthread[identity] = 0; UNLOCK(wakeupmasterthreadlocks[identity]); return(retval); } /* #] MasterWaitThread : #[ MasterWaitAll : */ /** * To be called by the master when it has to wait for all of the * workers to finish a given task. * It goes to sleep and waits for a wakeup call in ThreadWait */ void MasterWaitAll(void) { LOCK(wakeupmasterlock); while ( topofavailables < numberofworkers ) { pthread_cond_wait(&wakeupmasterconditions,&wakeupmasterlock); } UNLOCK(wakeupmasterlock); return; } /* #] MasterWaitAll : #[ MasterWaitAllSortBots : */ #ifdef WITHSORTBOTS /** * To be called by the master when it has to wait for all of the * sortbots to start their task. */ void MasterWaitAllSortBots(void) { LOCK(wakeupsortbotlock); while ( topsortbotavailables < numberofsortbots ) { pthread_cond_wait(&wakeupsortbotconditions,&wakeupsortbotlock); } UNLOCK(wakeupsortbotlock); return; } #endif /* #] MasterWaitAllSortBots : #[ MasterWaitAllBlocks : */ /** * To be called by the master when it has to wait for all of the * workers to claim their first block in the sort buffers of the master. * It goes to sleep and waits for a wakeup call. */ void MasterWaitAllBlocks(void) { LOCK(wakeupmasterlock); while ( numberclaimed < numberofworkers ) { pthread_cond_wait(&wakeupmasterconditions,&wakeupmasterlock); } UNLOCK(wakeupmasterlock); return; } /* #] MasterWaitAllBlocks : #[ WakeupThread : */ /** * To be called when the indicated thread needs waking up. * The signal number should be nonzero! * * @param identity The number of the worker to be woken up * @param signalnumber The signal with which it should be woken up. */ void WakeupThread(int identity, int signalnumber) { if ( signalnumber == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal wakeup signal for thread %d",identity); MUNLOCK(ErrorMessageLock); Terminate(-1); } LOCK(wakeuplocks[identity]); wakeup[identity] = signalnumber; pthread_cond_signal(&(wakeupconditions[identity])); UNLOCK(wakeuplocks[identity]); } /* #] WakeupThread : #[ WakeupMasterFromThread : */ /** * To be called when the indicated thread needs to wake up the master. * The signal number should be nonzero! * * @param identity The number of the worker who wakes up the master. * @param signalnumber The signal with which the master should be woken up. */ void WakeupMasterFromThread(int identity, int signalnumber) { if ( signalnumber == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal wakeup signal for master %d",identity); MUNLOCK(ErrorMessageLock); Terminate(-1); } LOCK(wakeupmasterthreadlocks[identity]); wakeupmasterthread[identity] = signalnumber; pthread_cond_signal(&(wakeupmasterthreadconditions[identity])); UNLOCK(wakeupmasterthreadlocks[identity]); } /* #] WakeupMasterFromThread : #[ SendOneBucket : */ /** * To be called when there is a full bucket and an available thread * It prepares the thread and then wakes it up. */ int SendOneBucket(int type) { ALLPRIVATES *B0 = AB[0]; THREADBUCKET *thr = 0; int j, k, id; for ( j = 0; j < numthreadbuckets; j++ ) { if ( threadbuckets[j]->free == BUCKETFILLED ) { thr = threadbuckets[j]; for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; break; } } AN0.ninterms++; while ( ( id = GetAvailableThread() ) < 0 ) { MasterWait(); } /* Prepare the thread. Give it the term and variables. */ LoadOneThread(0,id,thr,0); thr->busy = BUCKETASSIGNED; thr->free = BUCKETINUSE; numberoffullbuckets--; /* And signal the thread to run. Form now on we may only interfere with this bucket 1: after it has been marked BUCKETCOMINGFREE 2: when thr->busy == BUCKETDOINGTERM and then only when protected by thr->lock. This would be for load balancing. */ WakeupThread(id,type); /* AN0.ninterms += thr->ddterms; */ return(0); } /* #] SendOneBucket : #[ InParallelProcessor : */ /** * We divide the expressions marked by partodo over the workers. * The workers are responsible for writing their results into the buffers * of the master (output). This is to be controlled by locks. * The order of the expressions may get changed this way. * * The InParallel statement allows the execution of complete expressions * in a single worker simultaneously. This is useful for when there are * many short expressions. This way we don't need the bottleneck of the * merging by the master. The complete sort for each expression is done * inside its own single worker. The bottleneck here is the writing of the * result into the scratch system. This is now done by the workers themselves. * Because each expression must be contiguous, the writing should be done * as quickly as possible and be protected by locks. * * The implementation of this statement gave a significant increase in * efficiency in the running of the Multiple Zeta Values program. */ int InParallelProcessor(void) { GETIDENTITY int i, id, retval = 0, num = 0; EXPRESSIONS e; if ( numberofworkers >= 2 ) { SetWorkerFiles(); for ( i = 0; i < NumExpressions; i++ ) { e = Expressions+i; if ( e->partodo <= 0 ) continue; if ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION || e->status == INTOHIDELEXPRESSION || e->status == INTOHIDEGEXPRESSION ) { } else { e->partodo = 0; continue; } if ( e->counter == 0 ) { /* Expression with zero terms */ e->partodo = 0; continue; } /* This expression should go to an idle worker */ while ( ( id = GetAvailableThread() ) < 0 ) { MasterWait(); } LoadOneThread(0,id,0,-1); AB[id]->R.exprtodo = i; WakeupThread(id,DOONEEXPRESSION); num++; } /* Now we have to wait for all workers to finish */ if ( num > 0 ) MasterWaitAll(); if ( AC.CollectFun ) AR.DeferFlag = 0; } else { for ( i = 0; i < NumExpressions; i++ ) { Expressions[i].partodo = 0; } } return(retval); } /* #] InParallelProcessor : #[ ThreadsProcessor : */ /** * This routine takes the role of the central part of the Processor routine * in the file proces.c when multiple threads are available. * It deals with the expressions that are not marked in the InParallel * statement. These are usually the large expressions. It will divide * the terms of these expressions over the workers, using a bucket system * to reduce overhead (buckets are collections of a number of terms that * are transferred together). * At the end of the expression when all terms have been assigned and * workers become available again, there is a load balancing system to * take terms from the buckets of workers that still have to do many terms * and give them to idle workers. This is called first level load balancing. * * A new feature is that for expressions with a bracket index the terms * can be distributed in collections of complete brackets (12-nov-2009). * * The routine is called for each expression separately by Processor. * * @param e The expression to be executed * @param LastExpression Indicates whether it is the last expression in which case * in the end the input scratch file can be deleted before * the output is written. This saves diskspace. */ int ThreadsProcessor(EXPRESSIONS e, WORD LastExpression, WORD fromspectator) { ALLPRIVATES *B0 = AB[0], *B = B0; int id, oldgzipCompress, endofinput = 0, j, still, k, defcount = 0, bra = 0, first = 1; LONG dd = 0, ddd, thrbufsiz, thrbufsiz0, thrbufsiz2, numbucket = 0, numpasses; LONG num, i; WORD *oldworkpointer = AT0.WorkPointer, *tt, *ttco = 0, *t1 = 0, ter, *tstop = 0, *t2; THREADBUCKET *thr = 0; FILEHANDLE *oldoutfile = AR0.outfile; GETTERM GetTermP = &GetTerm; POSITION eonfile = AS.OldOnFile[e-Expressions]; numberoffullbuckets = 0; /* Start up all threads. The lock needs to be around the whole loop to keep processes from terminating quickly and putting themselves in the list of available threads again. */ AM.tracebackflag = 1; AS.sLevel = AR0.sLevel; LOCK(availabilitylock); topofavailables = 0; for ( id = 1; id <= numberofworkers; id++ ) { WakeupThread(id,STARTNEWEXPRESSION); } UNLOCK(availabilitylock); NewSort(BHEAD0); AN0.ninterms = 1; /* Now for redefine */ if ( AC.numpfirstnum > 0 ) { for ( j = 0; j < AC.numpfirstnum; j++ ) { AC.inputnumbers[j] = -1; } } MasterWaitAll(); /* Determine a reasonable bucketsize. This is based on the value of AC.ThreadBucketSize and the number of terms. We want at least 5 buckets per worker at the moment. Some research should show whether this is reasonable. The number of terms in the expression is in e->counter */ thrbufsiz2 = thrbufsiz = AC.ThreadBucketSize-1; if ( ( e->counter / ( numberofworkers * 5 ) ) < thrbufsiz ) { thrbufsiz = e->counter / ( numberofworkers * 5 ) - 1; if ( thrbufsiz < 0 ) thrbufsiz = 0; } thrbufsiz0 = thrbufsiz; numpasses = 5; /* this is just for trying */ thrbufsiz = thrbufsiz0 / (2 << numpasses); /* Mark all buckets as free and take the first. */ for ( j = 0; j < numthreadbuckets; j++ ) threadbuckets[j]->free = BUCKETFREE; thr = threadbuckets[0]; /* #[ Whole brackets : First we look whether we have to work with entire brackets This is the case when there is a non-NULL address in e->bracketinfo. Of course we shouldn't have interference from a collect or keep statement. */ #ifdef WHOLEBRACKETS if ( e->bracketinfo && AC.CollectFun == 0 && AR0.DeferFlag == 0 ) { FILEHANDLE *curfile; int didone = 0; LONG num, n; AN0.expr = e; for ( n = 0; n < e->bracketinfo->indexfill; n++ ) { num = TreatIndexEntry(B0,n); if ( num > 0 ) { didone = 1; /* This bracket can be sent off. 1: Look for an empty bucket */ ReTry:; for ( j = 0; j < numthreadbuckets; j++ ) { switch ( threadbuckets[j]->free ) { case BUCKETFREE: thr = threadbuckets[j]; goto Found1; case BUCKETCOMINGFREE: thr = threadbuckets[j]; thr->free = BUCKETFREE; for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; j--; break; default: break; } } Found1:; if ( j < numthreadbuckets ) { /* Found an empty bucket. Fill it. */ thr->firstbracket = n; thr->lastbracket = n + num - 1; thr->type = BUCKETDOINGBRACKET; thr->free = BUCKETFILLED; thr->firstterm = AN0.ninterms; for ( j = n; j < n+num; j++ ) { AN0.ninterms += e->bracketinfo->indexbuffer[j].termsinbracket; } n += num-1; numberoffullbuckets++; if ( topofavailables > 0 ) { SendOneBucket(DOBRACKETS); } } /* All buckets are in use. Look/wait for an idle worker. Give it a bucket. After that, retry for a bucket */ else { while ( topofavailables <= 0 ) { MasterWait(); } SendOneBucket(DOBRACKETS); goto ReTry; } } } if ( didone ) { /* And now put the input back in the original position. */ switch ( e->status ) { case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: curfile = AR0.hidefile; break; default: curfile = AR0.infile; break; } SetScratch(curfile,&eonfile); GetTerm(B0,AT0.WorkPointer); /* Now we point the GetTerm that is used to the one that is selective */ GetTermP = &GetTerm2; /* Next wait till there is a bucket available and initialize thr to it. */ for(;;) { for ( j = 0; j < numthreadbuckets; j++ ) { switch ( threadbuckets[j]->free ) { case BUCKETFREE: thr = threadbuckets[j]; goto Found2; case BUCKETCOMINGFREE: thr = threadbuckets[j]; thr->free = BUCKETFREE; for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; j--; break; default: break; } } while ( topofavailables <= 0 ) { MasterWait(); } while ( topofavailables > 0 && numberoffullbuckets > 0 ) { SendOneBucket(DOBRACKETS); } } Found2:; while ( numberoffullbuckets > 0 ) { while ( topofavailables <= 0 ) { MasterWait(); } while ( topofavailables > 0 && numberoffullbuckets > 0 ) { SendOneBucket(DOBRACKETS); } } /* Disable the 'warming up' with smaller buckets. numpasses = 0; thrbufsiz = thrbufsiz0; */ AN0.lastinindex = -1; } MasterWaitAll(); } #endif /* #] Whole brackets : Now the loop to start a bucket */ for(;;) { if ( fromspectator ) { ter = GetFromSpectator(thr->threadbuffer,fromspectator-1); if ( ter == 0 ) fromspectator = 0; } else { ter = GetTermP(B0,thr->threadbuffer); /* At this point we could check whether the input term is just an expression that resides in a scratch file. If this is the case we should store the current input info (file and buffer content) and redirect the input. At the end we can go back to where we were. There are two possibilities: we are in the same scratchfile as the main input and the other expression is still in the input buffer, or we have to do some reading. The reading is of course done in GetTerm. How to set this up can also be studied in TestSub (in file proces.c) where it checks for EXPRESSION. */ } if ( ter < 0 ) break; if ( ter == 0 ) { endofinput = 1; goto Finalize; } dd = AN0.deferskipped; if ( AR0.DeferFlag ) { defcount = 0; thr->deferbuffer[defcount++] = AR0.DefPosition; ttco = thr->compressbuffer; t1 = AR0.CompressBuffer; j = *t1; NCOPY(ttco,t1,j); } else if ( first && ( AC.CollectFun == 0 ) ) { /* Brackets ? */ first = 0; t1 = tstop = thr->threadbuffer; tstop += *tstop; tstop -= ABS(tstop[-1]); t1++; while ( t1 < tstop ) { if ( t1[0] == HAAKJE ) { bra = 1; break; } t1 += t1[1]; } t1 = thr->threadbuffer; } /* Check whether we have a collect,function going. If so execute it. */ if ( AC.CollectFun && *(thr->threadbuffer) < (AM.MaxTer/((LONG)sizeof(WORD))-10) ) { if ( ( dd = GetMoreTerms(thr->threadbuffer) ) < 0 ) { LowerSortLevel(); goto ProcErr; } } /* Check whether we have a priority task: */ if ( topofavailables > 0 && numberoffullbuckets > 0 ) SendOneBucket(LOWESTLEVELGENERATION); /* Now put more terms in the bucket. Position tt after the first term */ tt = thr->threadbuffer; tt += *tt; thr->totnum = 1; thr->usenum = 0; /* Next we worry about the 'slow startup' in which we make the initial buckets smaller, so that we get all threads busy as soon as possible. */ if ( numpasses > 0 ) { numbucket++; if ( numbucket >= numberofworkers ) { numbucket = 0; numpasses--; if ( numpasses == 0 ) thrbufsiz = thrbufsiz0; else thrbufsiz = thrbufsiz0 / (2 << numpasses); } thrbufsiz2 = thrbufsiz + thrbufsiz/5; /* for completing brackets */ } /* we have already 1+dd terms */ while ( ( dd < thrbufsiz ) && ( tt - thr->threadbuffer ) < ( thr->threadbuffersize - AM.MaxTer/((LONG)sizeof(WORD)) - 2 ) ) { /* First check: */ if ( topofavailables > 0 && numberoffullbuckets > 0 ) SendOneBucket(LOWESTLEVELGENERATION); /* There is room in the bucket. Fill yet another term. */ if ( GetTermP(B0,tt) == 0 ) { endofinput = 1; break; } dd++; thr->totnum++; dd += AN0.deferskipped; if ( AR0.DeferFlag ) { thr->deferbuffer[defcount++] = AR0.DefPosition; t1 = AR0.CompressBuffer; j = *t1; NCOPY(ttco,t1,j); } if ( AC.CollectFun && *tt < (AM.MaxTer/((LONG)sizeof(WORD))-10) ) { if ( ( ddd = GetMoreTerms(tt) ) < 0 ) { LowerSortLevel(); goto ProcErr; } dd += ddd; } t1 = tt; tt += *tt; } /* Check whether there are regular brackets and if we have no DeferFlag and no collect, we try to add more terms till we finish the current bracket. We should however not overdo it. Let us say: up to 20% more terms are allowed. */ if ( bra ) { tstop = t1 + *t1; tstop -= ABS(tstop[-1]); t2 = t1+1; while ( t2 < tstop ) { if ( t2[0] == HAAKJE ) { break; } t2 += t2[1]; } if ( t2[0] == HAAKJE ) { t2 += t2[1]; num = t2 - t1; while ( ( dd < thrbufsiz2 ) && ( tt - thr->threadbuffer ) < ( thr->threadbuffersize - AM.MaxTer - 2 ) ) { /* First check: */ if ( topofavailables > 0 && numberoffullbuckets > 0 ) SendOneBucket(LOWESTLEVELGENERATION); /* There is room in the bucket. Fill yet another term. */ if ( GetTermP(B0,tt) == 0 ) { endofinput = 1; break; } /* Same bracket? */ tstop = tt + *tt; tstop -= ABS(tstop[-1]); if ( tstop-tt < num ) { /* Different: abort */ AR0.KeptInHold = 1; break; } for ( i = 1; i < num; i++ ) { if ( t1[i] != tt[i] ) break; } if ( i < num ) { /* Different: abort */ AR0.KeptInHold = 1; break; } /* Same bracket. We need this term. */ dd++; thr->totnum++; tt += *tt; } } } thr->ddterms = dd; /* total number of terms including keep brackets */ thr->firstterm = AN0.ninterms; AN0.ninterms += dd; *tt = 0; /* mark end of bucket */ thr->free = BUCKETFILLED; thr->type = BUCKETDOINGTERMS; numberoffullbuckets++; if ( topofavailables <= 0 && endofinput == 0 ) { /* Problem: topofavailables may already be > 0, but the thread has not yet gone into waiting. Can the signal get lost? How can we tell that a thread is waiting for a signal? All threads are busy. Try to load up another bucket. In the future we could be more sophisticated. At the moment we load a complete bucket which could be 1000 terms or even more. In principle it is better to keep a full bucket ready and check after each term we put in the next bucket. That way we don't waste time of the workers. */ for ( j = 0; j < numthreadbuckets; j++ ) { switch ( threadbuckets[j]->free ) { case BUCKETFREE: thr = threadbuckets[j]; if ( !endofinput ) goto NextBucket; /* If we are at the end of the input we mark the free buckets in a special way. That way we don't keep running into them. */ thr->free = BUCKETATEND; break; case BUCKETCOMINGFREE: thr = threadbuckets[j]; thr->free = BUCKETFREE; /* Bucket has just been finished. Put at the end of the list. We don't want an early bucket to wait to be treated last. */ for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; j--; /* we have to redo the same number j. */ break; default: break; } } /* We have no free bucket or we are at the end. The only thing we can do now is wait for a worker to come free, provided there are still buckets to send. */ } /* Look for the next bucket to send. There is at least one full bucket! */ for ( j = 0; j < numthreadbuckets; j++ ) { if ( threadbuckets[j]->free == BUCKETFILLED ) { thr = threadbuckets[j]; for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; break; } } /* Wait for a thread to become available The bucket we are going to use is in thr. */ DoBucket:; AN0.ninterms++; while ( ( id = GetAvailableThread() ) < 0 ) { MasterWait(); } /* Prepare the thread. Give it the term and variables. */ LoadOneThread(0,id,thr,0); LOCK(thr->lock); thr->busy = BUCKETASSIGNED; UNLOCK(thr->lock); thr->free = BUCKETINUSE; numberoffullbuckets--; /* And signal the thread to run. Form now on we may only interfere with this bucket 1: after it has been marked BUCKETCOMINGFREE 2: when thr->busy == BUCKETDOINGTERM and then only when protected by thr->lock. This would be for load balancing. */ WakeupThread(id,LOWESTLEVELGENERATION); /* AN0.ninterms += thr->ddterms; */ /* Now look whether there is another bucket filled and a worker available */ if ( topofavailables > 0 ) { /* there is a worker */ for ( j = 0; j < numthreadbuckets; j++ ) { if ( threadbuckets[j]->free == BUCKETFILLED ) { thr = threadbuckets[j]; for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; goto DoBucket; /* and we found a bucket */ } } /* no bucket is loaded but there is a thread available find a bucket to load. If there is none (all are USED or ATEND) we jump out of the loop. */ for ( j = 0; j < numthreadbuckets; j++ ) { switch ( threadbuckets[j]->free ) { case BUCKETFREE: thr = threadbuckets[j]; if ( !endofinput ) goto NextBucket; thr->free = BUCKETATEND; break; case BUCKETCOMINGFREE: thr = threadbuckets[j]; if ( endofinput ) { thr->free = BUCKETATEND; } else { thr->free = BUCKETFREE; for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; j--; } break; default: break; } } if ( j >= numthreadbuckets ) break; } else { /* No worker available. Look for a bucket to load. Its number will be in "still" */ Finalize:; still = -1; for ( j = 0; j < numthreadbuckets; j++ ) { switch ( threadbuckets[j]->free ) { case BUCKETFREE: thr = threadbuckets[j]; if ( !endofinput ) goto NextBucket; thr->free = BUCKETATEND; break; case BUCKETCOMINGFREE: thr = threadbuckets[j]; if ( endofinput ) thr->free = BUCKETATEND; else { thr->free = BUCKETFREE; for ( k = j+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; j--; } break; case BUCKETFILLED: if ( still < 0 ) still = j; break; default: break; } } if ( still < 0 ) { /* No buckets to be executed and no buckets FREE. We must be at the end. Break out of the loop. */ break; } thr = threadbuckets[still]; for ( k = still+1; k < numthreadbuckets; k++ ) threadbuckets[k-1] = threadbuckets[k]; threadbuckets[numthreadbuckets-1] = thr; goto DoBucket; } NextBucket:; } /* Now the stage one load balancing. If the load has been readjusted we have again filled buckets. In that case we jump back in the loop. Tricky point: when do the workers see the new value of AT.LoadBalancing? It should activate the locks on thr->busy */ if ( AC.ThreadBalancing ) { for ( id = 1; id <= numberofworkers; id++ ) { AB[id]->T.LoadBalancing = 1; } if ( LoadReadjusted() ) goto Finalize; for ( id = 1; id <= numberofworkers; id++ ) { AB[id]->T.LoadBalancing = 0; } } if ( AC.ThreadBalancing ) { /* The AS.Balancing flag should have Generator look for free workers and apply the "buro" method. There is still a serious problem. When for instance a sum_, there may be space created in a local compiler buffer for a wildcard substitution or whatever. Compiler buffer execution scribble space..... This isn't copied along? Look up ebufnum. There are 12 places with AddRHS! Problem: one process allocates in ebuf. Then term is given to other process. It would like to use from this ebuf, but the sender finishes first and removes the ebuf (and/or overwrites it). Other problem: local $ variables aren't copied along. */ AS.Balancing = 0; } MasterWaitAll(); AS.Balancing = 0; /* When we deal with the last expression we can now remove the input scratch file. This saves potentially much disk space (up to 1/3) */ if ( LastExpression ) { UpdateMaxSize(); if ( AR0.infile->handle >= 0 ) { CloseFile(AR0.infile->handle); AR0.infile->handle = -1; remove(AR0.infile->name); PUTZERO(AR0.infile->POposition); AR0.infile->POfill = AR0.infile->POfull = AR0.infile->PObuffer; } } /* We order the threads to finish in the MasterMerge routine It will start with waiting for all threads to finish. One could make an administration in which threads that have finished can start already with the final sort but 1: The load balancing should not make this super urgent 2: It would definitely not be very compatible with the second stage load balancing. */ oldgzipCompress = AR0.gzipCompress; AR0.gzipCompress = 0; if ( AR0.outtohide ) AR0.outfile = AR0.hidefile; if ( MasterMerge() < 0 ) { if ( AR0.outtohide ) AR0.outfile = oldoutfile; AR0.gzipCompress = oldgzipCompress; goto ProcErr; } if ( AR0.outtohide ) AR0.outfile = oldoutfile; AR0.gzipCompress = oldgzipCompress; /* Now wait for all threads to be ready to give them the cleaning up signal. With the new MasterMerge routine we can do the cleanup already automatically avoiding having to send these signals. */ MasterWaitAll(); AR0.sLevel--; for ( id = 1; id < AM.totalnumberofthreads; id++ ) { if ( GetThread(id) > 0 ) WakeupThread(id,CLEANUPEXPRESSION); } e->numdummies = 0; for ( id = 1; id < AM.totalnumberofthreads; id++ ) { if ( AB[id]->R.MaxDum - AM.IndDum > e->numdummies ) e->numdummies = AB[id]->R.MaxDum - AM.IndDum; AR0.expchanged |= AB[id]->R.expchanged; } /* And wait for all to be clean. */ MasterWaitAll(); AT0.WorkPointer = oldworkpointer; return(0); ProcErr:; return(-1); } /* #] ThreadsProcessor : #[ LoadReadjusted : */ /** * This routine does the load readjustment at the end of a module. * It may be that there are still some threads that have a bucket full of * difficult terms. In that case we steal the bucket from such a thread * and redistribute the terms over the available buckets to be sent to * the free threads. As we steal all remaining terms from the bucket * it can happen that eventually the same worker gets some of the terms * back at a later stage. * * The only tricky point is the stealing process. We have to do this * without having to send signals or testing locks for each term processed. * The lock is set around thr->busy when AT.LoadBalancing == 1 but * when does the worker see this? (caching?) * * Remark: the thr->busy == BUCKETASSIGNED flag is to prevent stealing * from a thread that has not done anything yet. */ int LoadReadjusted(void) { ALLPRIVATES *B0 = AB[0]; THREADBUCKET *thr = 0, *thrtogo = 0; int numtogo, numfree, numbusy, n, nperbucket, extra, i, j, u, bus; LONG numinput; WORD *t1, *c1, *t2, *c2, *t3; /* Start with waiting for at least one free processor. We don't want the master competing for time when all are busy. */ while ( topofavailables <= 0 ) MasterWait(); /* Now look for the fullest bucket and make a list of free buckets The bad part is that most numbers can change at any moment. */ restart:; numtogo = 0; numfree = 0; numbusy = 0; for ( j = 0; j < numthreadbuckets; j++ ) { thr = threadbuckets[j]; if ( thr->free == BUCKETFREE || thr->free == BUCKETATEND || thr->free == BUCKETCOMINGFREE ) { freebuckets[numfree++] = thr; } else if ( thr->type != BUCKETDOINGTERMS ) {} else if ( thr->totnum > 1 ) { /* never steal from a bucket with one term */ LOCK(thr->lock); bus = thr->busy; UNLOCK(thr->lock); if ( thr->free == BUCKETINUSE ) { n = thr->totnum-thr->usenum; if ( bus == BUCKETASSIGNED ) numbusy++; else if ( ( bus != BUCKETASSIGNED ) && ( n > numtogo ) ) { numtogo = n; thrtogo = thr; } } else if ( bus == BUCKETTOBERELEASED && thr->free == BUCKETRELEASED ) { freebuckets[numfree++] = thr; thr->free = BUCKETATEND; LOCK(thr->lock); thr->busy = BUCKETPREPARINGTERM; UNLOCK(thr->lock); } } } if ( numfree == 0 ) return(0); /* serious problem */ if ( numtogo > 0 ) { /* provisionally there is something to be stolen */ thr = thrtogo; /* If the number has changed there is good progress. Maybe there is another thread that needs assistance. We start all over. */ if ( thr->totnum-thr->usenum < numtogo ) goto restart; /* If the thread is in the term loading phase (thr->busy == BUCKETPREPARINGTERM) we better stay away from it. We wait now for the thread to be busy, and don't allow it now to drop out of this state till we are done here. This all depends on whether AT.LoadBalancing == 1 is seen by the thread. */ LOCK(thr->lock); if ( thr->busy != BUCKETDOINGTERM ) { UNLOCK(thr->lock); goto restart; } if ( thr->totnum-thr->usenum < numtogo ) { UNLOCK(thr->lock); goto restart; } thr->free = BUCKETTERMINATED; /* The above will signal the thread we want to terminate. Next all effort goes into making sure the landing is soft. Unfortunately we don't want to wait for a signal, because the thread may be working for a long time on a single term. */ if ( thr->usenum == thr->totnum ) { /* Terminated in the mean time or by now working on the last term. Try again. */ thr->free = BUCKETATEND; UNLOCK(thr->lock); goto restart; } goto intercepted; } /* This has always been commented. Indeed no lock is held here. */ /* UNLOCK(thr->lock); */ if ( numbusy > 0 ) { /* JD: this avoids large runtimes for tform tests under valgrind. What seems to happen is we return from here, goto Finalize, and end up in LoadReadjusted again without the threads having a chance to update their busy status. Then we end up here again. Sleep the thread for, say, 1us to allow threads to aquire the lock. */ struct timespec sleeptime; sleeptime.tv_sec = 0; sleeptime.tv_nsec = 1000L; nanosleep(&sleeptime, NULL); return(1); /* Wait a bit.... */ } return(0); intercepted:; /* We intercepted one successfully. Now it becomes interesting. Action: 1: determine how many terms per free bucket. 2: find the first untreated term. 3: put the terms in the free buckets. Remember: we still have the lock to avoid interference from the thread that is being robbed. We were holding it and then jumped here with goto intercepted. */ numinput = thr->firstterm + thr->usenum; nperbucket = numtogo / numfree; extra = numtogo - nperbucket*numfree; if ( AR0.DeferFlag ) { t1 = thr->threadbuffer; c1 = thr->compressbuffer; u = thr->usenum; for ( n = 0; n < thr->usenum; n++ ) { t1 += *t1; c1 += *c1; } t3 = t1; if ( extra > 0 ) { for ( i = 0; i < extra; i++ ) { thrtogo = freebuckets[i]; t2 = thrtogo->threadbuffer; c2 = thrtogo->compressbuffer; thrtogo->free = BUCKETFILLED; thrtogo->type = BUCKETDOINGTERMS; thrtogo->totnum = nperbucket+1; thrtogo->ddterms = 0; thrtogo->usenum = 0; thrtogo->busy = BUCKETASSIGNED; thrtogo->firstterm = numinput; numinput += nperbucket+1; for ( n = 0; n <= nperbucket; n++ ) { j = *t1; NCOPY(t2,t1,j); j = *c1; NCOPY(c2,c1,j); thrtogo->deferbuffer[n] = thr->deferbuffer[u++]; } *t2 = *c2 = 0; } } if ( nperbucket > 0 ) { for ( i = extra; i < numfree; i++ ) { thrtogo = freebuckets[i]; t2 = thrtogo->threadbuffer; c2 = thrtogo->compressbuffer; thrtogo->free = BUCKETFILLED; thrtogo->type = BUCKETDOINGTERMS; thrtogo->totnum = nperbucket; thrtogo->ddterms = 0; thrtogo->usenum = 0; thrtogo->busy = BUCKETASSIGNED; thrtogo->firstterm = numinput; numinput += nperbucket; for ( n = 0; n < nperbucket; n++ ) { j = *t1; NCOPY(t2,t1,j); j = *c1; NCOPY(c2,c1,j); thrtogo->deferbuffer[n] = thr->deferbuffer[u++]; } *t2 = *c2 = 0; } } } else { t1 = thr->threadbuffer; for ( n = 0; n < thr->usenum; n++ ) { t1 += *t1; } t3 = t1; if ( extra > 0 ) { for ( i = 0; i < extra; i++ ) { thrtogo = freebuckets[i]; t2 = thrtogo->threadbuffer; thrtogo->free = BUCKETFILLED; thrtogo->type = BUCKETDOINGTERMS; thrtogo->totnum = nperbucket+1; thrtogo->ddterms = 0; thrtogo->usenum = 0; thrtogo->busy = BUCKETASSIGNED; thrtogo->firstterm = numinput; numinput += nperbucket+1; for ( n = 0; n <= nperbucket; n++ ) { j = *t1; NCOPY(t2,t1,j); } *t2 = 0; } } if ( nperbucket > 0 ) { for ( i = extra; i < numfree; i++ ) { thrtogo = freebuckets[i]; t2 = thrtogo->threadbuffer; thrtogo->free = BUCKETFILLED; thrtogo->type = BUCKETDOINGTERMS; thrtogo->totnum = nperbucket; thrtogo->ddterms = 0; thrtogo->usenum = 0; thrtogo->busy = BUCKETASSIGNED; thrtogo->firstterm = numinput; numinput += nperbucket; for ( n = 0; n < nperbucket; n++ ) { j = *t1; NCOPY(t2,t1,j); } *t2 = 0; } } } *t3 = 0; /* This is some form of extra insurance */ if ( thr->free == BUCKETRELEASED && thr->busy == BUCKETTOBERELEASED ) { thr->free = BUCKETATEND; thr->busy = BUCKETPREPARINGTERM; } UNLOCK(thr->lock); return(1); } /* #] LoadReadjusted : #[ SortStrategy : */ /** * When the final sort to the scratch file should take place * in a thread we should redirect to a different PutOut say PutToMaster. * The buffer in the Master should be an integer number times the size * of the buffer for PutToMaster (the PObuffersize in the 'scratchfile'). * The action should be (assume the multiple is 3): * Once the worker has its buffer full it fills block 1. Next 2. etc. * After filling block 3 the next fill will be at 1 when it is available * again. Becarefull to have a locked variable that indicates whether the * Master has started to claim all blocks 1. * The Master starts working once all blocks 1 are full. * Each Worker has an array for the blocks that tells their status. ??? * (Maybe better the lock on the whole block). * There should be a lock on them. The locks will make the threads * wait properly. When the Master finished a block, it marks it as * empty. When the master reaches the end of the last block it moves * the remainder to the piece before block 1. Etc. * Once terminated the worker can do the same as currently after * the call to EndSort (leave control to the master). * The master starts after there is a signal that all blocks 1 have * been filled. The tricky point is this signal without having * threads spend time in a waiting loop. * Don't compress the terms. It costs more time and serves here no real * purpose. It only makes things slower for the master. * * At the moment the scratch buffer of the workers is 1/N times the scratch * buffer of the master which is usually about the size of the Large buffer * of the master. This way we can save a factor on the scratch buffer size * of the workers. Alternative: let PutToMaster write directly into the * buffer/block of the master and leave out the scratch of the worker * completely. */ /* #] SortStrategy : #[ PutToMaster : */ /** * Writes the term (uncompressed) to the masters buffers. * We put it inside a block. The blocks have locks. This makes * that we have to wait automatically when all blocks are full. * This routine takes the place of PutOut when making the final * sort in a thread. * It takes the place of FlushOut when the argument is NULL. * * We need an initialization first in which the first MasterBlockLock * is set and MasterBlock is set to 1. * At the end we need to unlock the last block. Both actions can * be done in the routine that calls EndSort for the thread. * * The initialization of the variables in SB is done in * IniSortBlocks. This is done only once but it has to wait till * all threads exist and the masters sort buffers have been allocated. * * Note: the zero block is reserved for leftovers at the end of the * last block that get moved back to the front to keep the terms * contiguous (done in MasterMerge). */ int PutToMaster(PHEAD WORD *term) { int i,j,nexti,ret = 0; int urgent = 0; WORD *t, *fill, *top, zero = 0; if ( term == 0 ) { /* Mark the end of the expression */ t = &zero; j = 1; } else { t = term; ret = j = *term; if ( j == 0 ) { j = 1; } /* Just in case there is a spurious end */ } i = AT.SB.FillBlock; /* The block we are working at */ fill = AT.SB.MasterFill[i]; /* Where we are filling */ top = AT.SB.MasterStop[i]; /* End of the block */ // If there is space in the block, and we have already written MINWRITENUMBEROFTERMS, // determine if the reading thread is waiting for us by trying to lock the previous // block. If we manage to lock it, then we still have time to continue filling this // block. If we can't lock it, the reading thread is waiting for us and we should // move to the next block ASAP. if ( j < top - fill && AT.SB.BlockTerms[i] > MINWRITENUMBEROFTERMS ) { const int prev = ( i == 1 ? AT.SB.MasterNumBlocks : i-1 ); if ( ! pthread_mutex_trylock(&(AT.SB.MasterBlockLock[prev])) ) { UNLOCK(AT.SB.MasterBlockLock[prev]); } else { urgent = 1; } } // If the term doesn't fit in the current block, or a thread is waiting for us // (and we've already written at least MINWRITENUMBEROFTERMS), move to the next: if ( ( j >= top - fill ) || urgent ) { nexti = i+1; if ( nexti > AT.SB.MasterNumBlocks ) { nexti = 1; } LOCK(AT.SB.MasterBlockLock[nexti]); UNLOCK(AT.SB.MasterBlockLock[i]); AT.SB.MasterFill[i] = AT.SB.MasterStart[i]; AT.SB.FillBlock = i = nexti; fill = AT.SB.MasterStart[i]; top = AT.SB.MasterStop[i]; if ( AT.SB.BlockTerms[i] != 0 ) { // In this case, there has been an accounting error in a previous use // of this block. Blocks that have been read from and unlocked, should // have BlockTerms == 0. MLOCK(ErrorMessageLock); MesPrint("Error in PutToMaster, starting a block with BlockTerms != 0"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } NCOPY(fill, t, j); AT.SB.BlockTerms[i]++; AT.SB.MasterFill[i] = fill; return(ret); } /* #] PutToMaster : #[ SortBotOut : */ #ifdef WITHSORTBOTS /** * This is the output routine of the SortBots. * It can run PutToMaster, except for the final merge. * In that case we need to do special things like calling PutOut. * Hence the first thing we have to do is to figure out where our * output should be going. */ int SortBotOut(PHEAD WORD *term) { WORD im; if ( AT.identity != 0 ) return(PutToMaster(BHEAD term)); if ( term == 0 ) { if ( FlushOut(&SortBotPosition,AR.outfile,1) ) return(-1); ADDPOS(AT.SS->SizeInFile[0],1); return(0); } else { numberofterms++; if ( ( im = PutOut(BHEAD term,&SortBotPosition,AR.outfile,1) ) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from MasterMerge/SortBotOut"); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(AT.SS->SizeInFile[0],im); return(im); } } #endif /* #] SortBotOut : #[ MasterMerge : */ /** * This is the routine in which the master merges the sorted output that * comes from the workers. It is similar to MergePatches in sort.c from which * it takes much code. * The important concept here is that we want the master to be working as * little as possible because it constitutes the bottleneck. * The workers fill the buffers of the master. These buffers are divided * into parts for each worker as is done with the file patches in MergePatches * but now also each worker part is divided into blocks. This allows the * worker to fill blocks while the master is already working on blocks that * were filled before. The blocks are arranged in a circular fashion. * The whole is controlled by locks which seems faster than setting it up * with signals. * * This routine is run by the master when we don't use the sortbots. */ int MasterMerge(void) { ALLPRIVATES *B0 = AB[0], *B = 0; SORTING *S = AT0.SS; WORD **poin, **poin2, ul, k, i, im, *m1, j; WORD lpat, mpat, level, l1, l2, r1, r2, r3, c; WORD *m2, *m3, r31, r33, ki, *rr; UWORD *coef; POSITION position; FILEHANDLE *fin, *fout; #ifdef WITHSORTBOTS if ( numberofworkers > 2 ) return(SortBotMasterMerge()); #endif fin = &S->file; if ( AR0.PolyFun == 0 ) { S->PolyFlag = 0; } else if ( AR0.PolyFunType == 1 ) { S->PolyFlag = 1; } else if ( AR0.PolyFunType == 2 ) { if ( AR0.PolyFunExp == 2 || AR0.PolyFunExp == 3 ) S->PolyFlag = 1; else S->PolyFlag = 2; } S->TermsLeft = 0; coef = AN0.SoScratC; poin = S->poina; poin2 = S->poin2a; rr = AR0.CompressPointer; *rr = 0; /* #[ Setup : */ S->inNum = numberofthreads; fout = AR0.outfile; /* Load the patches. The threads have to finish their sort first. */ S->lPatch = S->inNum - 1; /* Claim all zero blocks. We need them anyway. In principle the workers should never get into these. We also claim all last blocks. This is a safety procedure that should prevent the workers from working their way around the clock before the master gets started again. */ AS.MasterSort = 1; numberclaimed = 0; for ( i = 1; i <= S->lPatch; i++ ) { B = AB[i]; LOCK(AT.SB.MasterBlockLock[0]); LOCK(AT.SB.MasterBlockLock[AT.SB.MasterNumBlocks]); } /* Now wake up the threads and have them start their final sorting. They should start with claiming their block and the master is not allowed to continue until that has been done. This waiting of the master will be done below in MasterWaitAllBlocks */ for ( i = 0; i < S->lPatch; i++ ) { GetThread(i+1); WakeupThread(i+1,FINISHEXPRESSION); } /* Prepare the output file. */ if ( fout->handle >= 0 ) { PUTZERO(position); SeekFile(fout->handle,&position,SEEK_END); ADDPOS(position,((fout->POfill-fout->PObuffer)*sizeof(WORD))); } else { SETBASEPOSITION(position,(fout->POfill-fout->PObuffer)*sizeof(WORD)); } /* Wait for all threads to finish loading their first block. */ MasterWaitAllBlocks(); /* Claim all first blocks. We don't release the last blocks. The strategy is that we always keep the previous block. In principle it looks like it isn't needed for the last block but actually it is to keep the front from overrunning the tail when writing. */ for ( i = 1; i <= S->lPatch; i++ ) { B = AB[i]; LOCK(AT.SB.MasterBlockLock[1]); AT.SB.MasterBlock = 1; } /* #] Setup : Now construct the tree: */ lpat = 1; do { lpat <<= 1; } while ( lpat < S->lPatch ); mpat = ( lpat >> 1 ) - 1; k = lpat - S->lPatch; /* k is the number of empty places in the tree. they will be at the even positions from 2 to 2*k */ for ( i = 1; i < lpat; i++ ) { S->tree[i] = -1; } for ( i = 1; i <= k; i++ ) { im = ( i * 2 ) - 1; poin[im] = AB[i]->T.SB.MasterStart[AB[i]->T.SB.MasterBlock]; poin2[im] = poin[im] + *(poin[im]); S->used[i] = im; S->ktoi[im] = i-1; S->tree[mpat+i] = 0; poin[im-1] = poin2[im-1] = 0; } for ( i = (k*2)+1; i <= lpat; i++ ) { S->used[i-k] = i; S->ktoi[i] = i-k-1; poin[i] = AB[i-k]->T.SB.MasterStart[AB[i-k]->T.SB.MasterBlock]; poin2[i] = poin[i] + *(poin[i]); } /* the array poin tells the position of the i-th element of the S->tree 'S->used' is a stack with the S->tree elements that need to be entered into the S->tree. at the beginning this is S->lPatch. during the sort there will be only very few elements. poin2 is the next value of poin. it has to be determined before the comparisons as the position or the size of the term indicated by poin may change. S->ktoi translates a S->tree element back to its stream number. start the sort */ level = S->lPatch; /* introduce one term */ OneTerm: k = S->used[level]; i = k + lpat - 1; if ( !*(poin[k]) ) { // Stream k has hit the end-of-stream "0". We still need to decrement // BlockTerms, which includes the marker in the count. ki = S->ktoi[k]; AB[ki+1]->T.SB.BlockTerms[AB[ki+1]->T.SB.MasterBlock]--; do { if ( !( i >>= 1 ) ) { goto EndOfMerge; } } while ( !S->tree[i] ); if ( S->tree[i] == -1 ) { S->tree[i] = 0; level--; goto OneTerm; } k = S->tree[i]; S->used[level] = k; S->tree[i] = 0; } /* move terms down the tree */ while ( i >>= 1 ) { if ( S->tree[i] > 0 ) { if ( ( c = CompareTerms(B0, poin[S->tree[i]],poin[k],(WORD)0) ) > 0 ) { /* S->tree[i] is the smaller. Exchange and go on. */ S->used[level] = S->tree[i]; S->tree[i] = k; k = S->used[level]; } else if ( !c ) { /* Terms are equal */ /* S->TermsLeft--; Here the terms are equal and their coefficients have to be added. */ l1 = *( m1 = poin[S->tree[i]] ); l2 = *( m2 = poin[k] ); if ( S->PolyWise ) { /* Here we work with PolyFun */ WORD *tt1, *w; tt1 = m1; m1 += S->PolyWise; m2 += S->PolyWise; if ( S->PolyFlag == 2 ) { w = poly_ratfun_add(B0,m1,m2); if ( *tt1 + w[1] - m1[1] > AM.MaxTer/((LONG)sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex in PolyRatFun addition. MaxTermSize of %10l is too small",AM.MaxTer); MUNLOCK(ErrorMessageLock); Terminate(-1); } AT0.WorkPointer = w; if ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 && w[1] > FUNHEAD ) { goto cancelled; } } else { w = AT0.WorkPointer; if ( w + m1[1] + m2[1] > AT0.WorkTop ) { MLOCK(ErrorMessageLock); MesPrint("MasterMerge: A WorkSpace of %10l is too small",AM.WorkSize); MUNLOCK(ErrorMessageLock); Terminate(-1); } AddArgs(B0,m1,m2,w); } r1 = w[1]; if ( r1 <= FUNHEAD || ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 ) ) { goto cancelled; } if ( r1 == m1[1] ) { NCOPY(m1,w,r1); } else if ( r1 < m1[1] ) { r2 = m1[1] - r1; m2 = w + r1; m1 += m1[1]; while ( --r1 >= 0 ) *--m1 = *--m2; m2 = m1 - r2; r1 = S->PolyWise; while ( --r1 >= 0 ) *--m1 = *--m2; *m1 -= r2; poin[S->tree[i]] = m1; } else { // Here we are writing the new merged term *before* the original start of term1. // We can always do this, since before term1 there is previous term data of this // block, or the previous block, for which we are holding a lock. This requires // the existence of "block 0", if term1 is the first term of block 1! // It also requires the blocks to be contiguous in memory; we can't allocate // separate memory regions for each block without larger-scale changes. r2 = r1 - m1[1]; m2 = tt1 - r2; r1 = S->PolyWise; m1 = tt1; *m1 += r2; poin[S->tree[i]] = m2; NCOPY(m2,m1,r1); r1 = w[1]; NCOPY(m2,w,r1); } } #ifdef WITHFLOAT else if ( AT.SortFloatMode ) { WORD *term1, *term2; term1 = poin[S->tree[i]]; term2 = poin[k]; if ( MergeWithFloat(B0, &term1,&term2) == 0 ) goto cancelled; poin[S->tree[i]] = term1; } #endif else { r1 = *( m1 += l1 - 1 ); m1 -= ABS(r1) - 1; r1 = ( ( r1 > 0 ) ? (r1-1) : (r1+1) ) >> 1; r2 = *( m2 += l2 - 1 ); m2 -= ABS(r2) - 1; r2 = ( ( r2 > 0 ) ? (r2-1) : (r2+1) ) >> 1; if ( AddRat(B0,(UWORD *)m1,r1,(UWORD *)m2,r2,coef,&r3) ) { MLOCK(ErrorMessageLock); MesCall("MasterMerge"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( AN.ncmod != 0 ) { if ( ( AC.modmode & POSNEG ) != 0 ) { NormalModulus(coef,&r3); } else if ( BigLong(coef,r3,(UWORD *)AC.cmod,ABS(AN.ncmod)) >= 0 ) { WORD ii; SubPLon(coef,r3,(UWORD *)AC.cmod,ABS(AN.ncmod),coef,&r3); coef[r3] = 1; for ( ii = 1; ii < r3; ii++ ) coef[r3+ii] = 0; } } r3 *= 2; r33 = ( r3 > 0 ) ? ( r3 + 1 ) : ( r3 - 1 ); if ( r3 < 0 ) r3 = -r3; if ( r1 < 0 ) r1 = -r1; r1 *= 2; r31 = r3 - r1; if ( !r3 ) { /* Terms cancel */ cancelled: ul = S->used[level] = S->tree[i]; S->tree[i] = -1; /* We skip to the next term in stream ul */ im = *poin2[ul]; poin[ul] = poin2[ul]; ki = S->ktoi[ul]; AB[ki+1]->T.SB.BlockTerms[AB[ki+1]->T.SB.MasterBlock]--; if ( AB[ki+1]->T.SB.BlockTerms[AB[ki+1]->T.SB.MasterBlock] == 0 ) { /* We made it to the end of the block. We have to release the previous block and claim the next. */ B = AB[ki+1]; i = AT.SB.MasterBlock; if ( i == 1 ) { UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterNumBlocks]); } else { UNLOCK(AT.SB.MasterBlockLock[i-1]); } if ( i == AT.SB.MasterNumBlocks ) { i = 1; } else { i++; } LOCK(AT.SB.MasterBlockLock[i]); AT.SB.MasterBlock = i; poin[ul] = AT.SB.MasterStart[i]; im = *poin[ul]; poin2[ul] = poin[ul] + im; } else { poin2[ul] += im; } S->used[++level] = k; } else if ( !r31 ) { /* copy coef into term1 */ goto CopCof2; } else if ( r31 < 0 ) { /* copy coef into term1 and adjust the length of term1 */ goto CopCoef; } else { /* this is the dreaded calamity. is there enough space? */ if( (poin[S->tree[i]]+l1+r31) >= poin2[S->tree[i]] ) { /* no space! now the special trick for which we left 2*maxlng spaces open at the beginning of each patch. */ if ( (l1 + r31)*((LONG)sizeof(WORD)) >= AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("MasterMerge: Coefficient overflow during sort"); MUNLOCK(ErrorMessageLock); goto ReturnError; } m2 = poin[S->tree[i]]; m3 = ( poin[S->tree[i]] -= r31 ); do { *m3++ = *m2++; } while ( m2 < m1 ); m1 = m3; } CopCoef: *(poin[S->tree[i]]) += r31; CopCof2: m2 = (WORD *)coef; im = r3; NCOPY(m1,m2,im); *m1 = r33; } } /* Now skip to the next term in stream k. */ NextTerm: im = poin2[k][0]; poin[k] = poin2[k]; ki = S->ktoi[k]; AB[ki+1]->T.SB.BlockTerms[AB[ki+1]->T.SB.MasterBlock]--; if ( AB[ki+1]->T.SB.BlockTerms[AB[ki+1]->T.SB.MasterBlock] == 0 ) { /* We made it to the end of the block. We have to release the previous block and claim the next. */ B = AB[ki+1]; i = AT.SB.MasterBlock; if ( i == 1 ) { UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterNumBlocks]); } else { UNLOCK(AT.SB.MasterBlockLock[i-1]); } if ( i == AT.SB.MasterNumBlocks ) { i = 1; } else { i++; } LOCK(AT.SB.MasterBlockLock[i]); AT.SB.MasterBlock = i; poin[k] = AT.SB.MasterStart[i]; im = *poin[k]; poin2[k] = poin[k] + im; } else { poin2[k] += im; } goto OneTerm; } } else if ( S->tree[i] < 0 ) { S->tree[i] = k; level--; goto OneTerm; } } /* found the smallest in the set. indicated by k. write to its destination. */ S->TermsLeft++; if ( ( im = PutOut(B0,poin[k],&position,fout,1) ) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from MasterMerge with k = %d (stream %d)",k,S->ktoi[k]); MUNLOCK(ErrorMessageLock); goto ReturnError; } ADDPOS(S->SizeInFile[0],im); goto NextTerm; EndOfMerge: if ( FlushOut(&position,fout,1) ) goto ReturnError; ADDPOS(S->SizeInFile[0],1); CloseFile(fin->handle); remove(fin->name); fin->handle = -1; position = S->SizeInFile[0]; MULPOS(position,sizeof(WORD)); // Collect global sort statistics information from the threads. // The total GenTerms is the sum of the thread GenTerms. // The total small/large buffer sort info is the sum of the thread info. // The total comparison count is the sum of the thread counts. // The total unsorted size is the sum of the total generated terms sizes S->GenTerms = 0; for ( j = 1; j <= numberofworkers; j++ ) { S->GenTerms += AB[j]->T.SS->GenTerms; S->verbComparisons += AB[j]->T.SS->verbComparisons; S->verbSBsortTerms += AB[j]->T.SS->verbSBsortTerms; S->verbSBsortCap += AB[j]->T.SS->verbSBsortCap; S->verbLBsortPatches += AB[j]->T.SS->verbLBsortPatches; S->verbLBsortCap += AB[j]->T.SS->verbLBsortCap; S->verbUnsortedSize += AB[j]->T.SS->verbUnsortedSize; } WriteStats(&position,STATSPOSTSORT,NOCHECKLOGTYPE); Expressions[AR0.CurExpr].counter = S->TermsLeft; Expressions[AR0.CurExpr].size = position; /* Release all locks */ for ( i = 1; i <= S->lPatch; i++ ) { B = AB[i]; UNLOCK(AT.SB.MasterBlockLock[0]); if ( AT.SB.MasterBlock == 1 ) { UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterNumBlocks]); } else { UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterBlock-1]); } UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterBlock]); } AS.MasterSort = 0; return(0); ReturnError: for ( i = 1; i <= S->lPatch; i++ ) { B = AB[i]; UNLOCK(AT.SB.MasterBlockLock[0]); if ( AT.SB.MasterBlock == 1 ) { UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterNumBlocks]); } else { UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterBlock-1]); } UNLOCK(AT.SB.MasterBlockLock[AT.SB.MasterBlock]); } AS.MasterSort = 0; return(-1); } /* #] MasterMerge : #[ SortBotMasterMerge : */ #ifdef WITHSORTBOTS /** * This is the master routine for the final stage in a sortbot merge. * A sortbot merge is a merge in which the output of two workers is * merged into a single output which then can be given as one of two * streams to another sortbot. The idea is that each sortbot is responsible * for one one compare per term. In the end the master does the last * merge of only two streams and writes the result to the output. * There doesn't seem to be an advantage to splitting this last task. * * The use of the sortbots gives a measurable improvement but it isn't * optimal yet. * * This routine is run as master. Hence B = B0. Etc. */ int SortBotMasterMerge(void) { FILEHANDLE *fin, *fout; ALLPRIVATES *B = AB[0], *BB; POSITION position; SORTING *S = AT.SS; int i, j; /* Get the sortbots get to claim their writing blocks. We have to wait till all have been claimed because they also have to claim the last writing blocks of the workers to prevent the head of the circular buffer to overrun the tail. Before waiting we can do some needed initializations. Also the master has to claim the last writing blocks of its input. */ topsortbotavailables = 0; for ( i = numberofworkers+1; i <= numberofworkers+numberofsortbots; i++ ) { WakeupThread(i,INISORTBOT); } AS.MasterSort = 1; fout = AR.outfile; numberofterms = 0; AR.CompressPointer[0] = 0; numberclaimed = 0; BB = AB[AT.SortBotIn1]; LOCK(BB->T.SB.MasterBlockLock[BB->T.SB.MasterNumBlocks]); BB = AB[AT.SortBotIn2]; LOCK(BB->T.SB.MasterBlockLock[BB->T.SB.MasterNumBlocks]); MasterWaitAllSortBots(); /* Now we can start up the workers. They will claim their writing blocks. Here the master will wait till all writing blocks have been claimed. */ for ( i = 1; i <= numberofworkers; i++ ) { j = GetThread(i); WakeupThread(i,FINISHEXPRESSION); } /* Prepare the output file in the mean time. */ if ( fout->handle >= 0 ) { PUTZERO(SortBotPosition); SeekFile(fout->handle,&SortBotPosition,SEEK_END); ADDPOS(SortBotPosition,((fout->POfill-fout->PObuffer)*sizeof(WORD))); } else { SETBASEPOSITION(SortBotPosition,(fout->POfill-fout->PObuffer)*sizeof(WORD)); } MasterWaitAllBlocks(); /* Now we can start the sortbots after which the master goes in sortbot mode to do its part of the job (the very final merge and the writing to output file). */ topsortbotavailables = 0; for ( i = numberofworkers+1; i <= numberofworkers+numberofsortbots; i++ ) { WakeupThread(i,RUNSORTBOT); } if ( SortBotMerge(BHEAD0) ) { MLOCK(ErrorMessageLock); MesPrint("Called from SortBotMasterMerge"); MUNLOCK(ErrorMessageLock); AS.MasterSort = 0; return(-1); } /* And next the cleanup */ if ( S->file.handle >= 0 ) { fin = &S->file; CloseFile(fin->handle); remove(fin->name); fin->handle = -1; } position = S->SizeInFile[0]; MULPOS(position,sizeof(WORD)); // Collect global sort statistics information from the threads. // The total GenTerms is the sum of the thread GenTerms. // The total small/large buffer sort info is the sum of the thread info. // The total comparison count is the sum of the thread and sortbot counts. // The total unsorted size is the sum of the total generated terms sizes S->GenTerms = 0; for ( j = 1; j <= numberofworkers; j++ ) { S->GenTerms += AB[j]->T.SS->GenTerms; S->verbComparisons += AB[j]->T.SS->verbComparisons; S->verbSBsortTerms += AB[j]->T.SS->verbSBsortTerms; S->verbSBsortCap += AB[j]->T.SS->verbSBsortCap; S->verbLBsortPatches += AB[j]->T.SS->verbLBsortPatches; S->verbLBsortCap += AB[j]->T.SS->verbLBsortCap; S->verbUnsortedSize += AB[j]->T.SS->verbUnsortedSize; } for ( j = numberofworkers+1; j <= numberofworkers+numberofsortbots; j++ ) { S->verbComparisons += AB[j]->T.SS->verbComparisons; } S->TermsLeft = numberofterms; WriteStats(&position,STATSPOSTSORT,NOCHECKLOGTYPE); Expressions[AR.CurExpr].counter = S->TermsLeft; Expressions[AR.CurExpr].size = position; AS.MasterSort = 0; /* The next statement is to prevent one of the sortbots not having completely cleaned up before the next module starts. If this statement is omitted every once in a while one of the sortbots is still running when the next expression starts and misses its initialization. The result is usually disastrous. */ MasterWaitAllSortBots(); return(0); } #endif /* #] SortBotMasterMerge : #[ SortBotMerge : */ #ifdef WITHSORTBOTS /** * This routine is run by a sortbot and merges two sorted output streams into * a single sorted stream. */ int SortBotMerge(PHEAD0) { GETBIDENTITY ALLPRIVATES *Bin1 = AB[AT.SortBotIn1],*Bin2 = AB[AT.SortBotIn2]; WORD *term1, *term2, *wp; int blin1, blin2; /* Current block numbers */ int error = 0; WORD l1, l2, *m1, *m2, *w, r1, r2, r3, r33, r31, *tt1, ii; WORD *to, *from, im, c; UWORD *coef; SORTING *S = AT.SS; #ifdef WITHFLOAT WORD *fun1, *fun2, *fun3, *tstop1, *tstop2, size1, size2, size3, l3, jj, *m3; #endif /* Set the pointers to the input terms and the output space */ coef = AN.SoScratC; blin1 = 1; blin2 = 1; if ( AT.identity == 0 ) { wp = AT.WorkPointer; } else { wp = AT.WorkPointer = AT.WorkSpace; } /* Get the locks for reading the input This means that we can start once these locks have been cleared which means that there will be input. */ LOCK(Bin1->T.SB.MasterBlockLock[blin1]); LOCK(Bin2->T.SB.MasterBlockLock[blin2]); term1 = Bin1->T.SB.MasterStart[blin1]; term2 = Bin2->T.SB.MasterStart[blin2]; AT.SB.FillBlock = 1; /* Now the main loop. Keep going until one of the two hits the end. */ while ( *term1 && *term2 ) { if ( ( c = CompareTerms(BHEAD term1,term2,(WORD)0) ) > 0 ) { /* #[ One is smallest : */ Bin1->T.SB.BlockTerms[blin1]--; if ( SortBotOut(BHEAD term1) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from SortBotMerge with thread = %d",AT.identity); MUNLOCK(ErrorMessageLock); error = -1; goto ReturnError; } term1 += *term1; if ( Bin1->T.SB.BlockTerms[blin1] == 0 ) { if ( blin1 == 1 ) { UNLOCK(Bin1->T.SB.MasterBlockLock[Bin1->T.SB.MasterNumBlocks]); } else { UNLOCK(Bin1->T.SB.MasterBlockLock[blin1-1]); } if ( blin1 == Bin1->T.SB.MasterNumBlocks ) { blin1 = 1; } else { blin1++; } LOCK(Bin1->T.SB.MasterBlockLock[blin1]); Bin1->T.SB.MasterBlock = blin1; term1 = Bin1->T.SB.MasterStart[blin1]; } /* #] One is smallest : */ } else if ( c < 0 ) { /* #[ Two is smallest : */ Bin2->T.SB.BlockTerms[blin2]--; if ( SortBotOut(BHEAD term2) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from SortBotMerge with thread = %d",AT.identity); MUNLOCK(ErrorMessageLock); error = -1; goto ReturnError; } next2: term2 += *term2; if ( Bin2->T.SB.BlockTerms[blin2] == 0 ) { if ( blin2 == 1 ) { UNLOCK(Bin2->T.SB.MasterBlockLock[Bin2->T.SB.MasterNumBlocks]); } else { UNLOCK(Bin2->T.SB.MasterBlockLock[blin2-1]); } if ( blin2 == Bin2->T.SB.MasterNumBlocks ) { blin2 = 1; } else { blin2++; } LOCK(Bin2->T.SB.MasterBlockLock[blin2]); Bin2->T.SB.MasterBlock = blin2; term2 = Bin2->T.SB.MasterStart[blin2]; } /* #] Two is smallest : */ } else { /* #[ Equal : */ Bin1->T.SB.BlockTerms[blin1]--; Bin2->T.SB.BlockTerms[blin2]--; l1 = *( m1 = term1 ); l2 = *( m2 = term2 ); if ( S->PolyWise ) { /* Here we work with PolyFun */ tt1 = m1; m1 += S->PolyWise; m2 += S->PolyWise; if ( S->PolyFlag == 2 ) { AT.WorkPointer = wp; w = poly_ratfun_add(BHEAD m1,m2); if ( *tt1 + w[1] - m1[1] > AM.MaxTer/((LONG)sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex in PolyRatFun addition. MaxTermSize of %10l is too small",AM.MaxTer); MUNLOCK(ErrorMessageLock); Terminate(-1); } AT.WorkPointer = wp; if ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 && w[1] > FUNHEAD ) { goto cancelled; } } else { w = wp; if ( w + m1[1] + m2[1] > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesPrint("SortBotMerge(%d): A Maxtermsize of %10l is too small", AT.identity,AM.MaxTer/sizeof(WORD)); MesPrint("m1[1] = %d, m2[1] = %d, Space = %l",m1[1],m2[1],(LONG)(AT.WorkTop-wp)); PrintTerm(term1,"term1"); PrintTerm(term2,"term2"); MesPrint("PolyWise = %d",S->PolyWise); MUNLOCK(ErrorMessageLock); Terminate(-1); } AddArgs(BHEAD m1,m2,w); } r1 = w[1]; if ( r1 <= FUNHEAD || ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 ) ) { goto cancelled; } if ( r1 == m1[1] ) { NCOPY(m1,w,r1); } else if ( r1 < m1[1] ) { r2 = m1[1] - r1; m2 = w + r1; m1 += m1[1]; while ( --r1 >= 0 ) *--m1 = *--m2; m2 = m1 - r2; r1 = S->PolyWise; while ( --r1 >= 0 ) *--m1 = *--m2; *m1 -= r2; term1 = m1; } else { // Here we are writing the new merged term *before* the original start of term1. // We can always do this, since before term1 there is previous term data of this // block, or the previous block, for which we are holding a lock. This requires // the existence of "block 0", if term1 is the first term of block 1! // It also requires the blocks to be contiguous in memory; we can't allocate // separate memory regions for each block without larger-scale changes. r2 = r1 - m1[1]; m2 = tt1 - r2; r1 = S->PolyWise; m1 = tt1; *m1 += r2; term1 = m2; NCOPY(m2,m1,r1); r1 = w[1]; NCOPY(m2,w,r1); } } #ifdef WITHFLOAT else if ( AT.SortFloatMode ) { /* The terms are in m1/term1 and m2/term2 and their length in l1 and l2. We have to locate the floats which have already been verified in the compare routine. Once we have the new term we can jump to the code that writes away the result after adding the rationals. */ tstop1 = m1+l1; size1 = tstop1[-1]; tstop1 -= ABS(size1); tstop2 = m2+l2; size2 = tstop2[-1]; tstop2 -= ABS(size2); if ( AT.SortFloatMode == 3 ) { fun1 = m1+1; while ( fun1[0] != FLOATFUN && fun1+fun1[1] < tstop1 ) { fun1 += fun1[1]; } if ( size1 < 0 ) fun1[FUNHEAD+3] = -fun1[FUNHEAD+3]; UnpackFloat(aux1,fun1); fun2 = m2+1; while ( fun2[0] != FLOATFUN && fun2+fun2[1] < tstop2 ) { fun2 += fun2[1]; } if ( size2 < 0 ) fun2[FUNHEAD+3] = -fun2[FUNHEAD+3]; UnpackFloat(aux2,fun2); } else if ( AT.SortFloatMode == 1 ) { fun1 = m1+1; while ( fun1[0] != FLOATFUN && fun1+fun1[1] < tstop1 ) { fun1 += fun1[1]; } if ( size1 < 0 ) fun1[FUNHEAD+3] = -fun1[FUNHEAD+3]; UnpackFloat(aux1,fun1); fun2 = tstop2; RatToFloat(aux2,(UWORD *)fun2,size2); } else if ( AT.SortFloatMode == 2 ) { fun1 = tstop1; RatToFloat(aux1,(UWORD *)fun1,size1); fun2 = m2+1; while ( fun2[0] != FLOATFUN && fun2+fun2[1] < tstop2 ) { fun2 += fun2[1]; } if ( size2 < 0 ) fun2[FUNHEAD+3] = -fun2[FUNHEAD+3]; UnpackFloat(aux2,fun2); } else { MLOCK(ErrorMessageLock); MesPrint("Illegal value %d for AT.SortFloatMode in SortBotMerge.",AT.SortFloatMode); MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } mpf_add(aux3,aux1,aux2); size3 = mpf_sgn(aux3); if ( size3 == 0 ) { /* Cancelling! Rare! */ goto cancelled; } else if ( size3 < 0 ) mpf_neg(aux3,aux3); fun3 = TermMalloc("MasterMerge"); PackFloat(fun3,aux3); l3 = fun3[1]+(fun1-m1)+3; /* new size */ if ( l3 != l1 ) { /* Copy it all to wp */ if ( (l3)*((LONG)sizeof(WORD)) >= AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("MasterMerge: Coefficient overflow during sort"); MUNLOCK(ErrorMessageLock); goto ReturnError; } m3 = wp; m2 = term1; while ( m2 < fun1 ) *m3++ = *m2++; for ( jj = 0; jj < fun3[1]; jj++ ) *m3++ = fun3[jj]; *m3++ = 1; *m3++ = 1; *m3++ = size3 < 0 ? -3: 3; *wp = m3-wp; TermFree(fun3,"MasterMerge"); goto PutOutwp; } for ( jj = 0; jj < fun3[1]; jj++ ) fun1[jj] = fun3[jj]; fun1 += fun3[1]; *fun1++ = 1; *fun1++ = 1; *fun1++ = size3 < 0 ? -3: 3; *term1 = fun1-term1; TermFree(fun3,"MasterMerge"); } #endif else { r1 = *( m1 += l1 - 1 ); m1 -= ABS(r1) - 1; r1 = ( ( r1 > 0 ) ? (r1-1) : (r1+1) ) >> 1; r2 = *( m2 += l2 - 1 ); m2 -= ABS(r2) - 1; r2 = ( ( r2 > 0 ) ? (r2-1) : (r2+1) ) >> 1; if ( AddRat(BHEAD (UWORD *)m1,r1,(UWORD *)m2,r2,coef,&r3) ) { MLOCK(ErrorMessageLock); MesCall("SortBotMerge"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( AN.ncmod != 0 ) { if ( ( AC.modmode & POSNEG ) != 0 ) { NormalModulus(coef,&r3); } else if ( BigLong(coef,r3,(UWORD *)AC.cmod,ABS(AN.ncmod)) >= 0 ) { SubPLon(coef,r3,(UWORD *)AC.cmod,ABS(AN.ncmod),coef,&r3); coef[r3] = 1; for ( ii = 1; ii < r3; ii++ ) coef[r3+ii] = 0; } } if ( !r3 ) { goto cancelled; } r3 *= 2; r33 = ( r3 > 0 ) ? ( r3 + 1 ) : ( r3 - 1 ); if ( r3 < 0 ) r3 = -r3; if ( r1 < 0 ) r1 = -r1; r1 *= 2; r31 = r3 - r1; if ( !r31 ) { /* copy coef into term1 */ m2 = (WORD *)coef; im = r3; NCOPY(m1,m2,im); *m1 = r33; } else { to = wp; from = term1; while ( from < m1 ) *to++ = *from++; from = (WORD *)coef; im = r3; NCOPY(to,from,im); *to++ = r33; wp[0] = to - wp; PutOutwp: if ( SortBotOut(BHEAD wp) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from SortBotMerge with thread = %d",AT.identity); MUNLOCK(ErrorMessageLock); error = -1; goto ReturnError; } goto cancelled; } } if ( SortBotOut(BHEAD term1) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from SortBotMerge with thread = %d",AT.identity); MUNLOCK(ErrorMessageLock); error = -1; goto ReturnError; } cancelled:; /* Now we need two new terms */ term1 += *term1; if ( Bin1->T.SB.BlockTerms[blin1] == 0 ) { if ( blin1 == 1 ) { UNLOCK(Bin1->T.SB.MasterBlockLock[Bin1->T.SB.MasterNumBlocks]); } else { UNLOCK(Bin1->T.SB.MasterBlockLock[blin1-1]); } if ( blin1 == Bin1->T.SB.MasterNumBlocks ) { blin1 = 1; } else { blin1++; } LOCK(Bin1->T.SB.MasterBlockLock[blin1]); Bin1->T.SB.MasterBlock = blin1; term1 = Bin1->T.SB.MasterStart[blin1]; } goto next2; /* #] Equal : */ } } /* Copy the tail */ if ( *term1 ) { /* #[ Tail in one : */ while ( *term1 ) { Bin1->T.SB.BlockTerms[blin1]--; if ( SortBotOut(BHEAD term1) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from SortBotMerge with thread = %d",AT.identity); MUNLOCK(ErrorMessageLock); error = -1; goto ReturnError; } if ( Bin1->T.SB.BlockTerms[blin1] == 0 ) { if ( blin1 == 1 ) { UNLOCK(Bin1->T.SB.MasterBlockLock[Bin1->T.SB.MasterNumBlocks]); } else { UNLOCK(Bin1->T.SB.MasterBlockLock[blin1-1]); } if ( blin1 == Bin1->T.SB.MasterNumBlocks ) { blin1 = 1; } else { blin1++; } LOCK(Bin1->T.SB.MasterBlockLock[blin1]); Bin1->T.SB.MasterBlock = blin1; term1 = Bin1->T.SB.MasterStart[blin1]; } else { term1 += *term1; } } /* #] Tail in one : */ } else if ( *term2 ) { /* #[ Tail in two : */ while ( *term2 ) { Bin2->T.SB.BlockTerms[blin2]--; if ( SortBotOut(BHEAD term2) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from SortBotMerge with thread = %d",AT.identity); MUNLOCK(ErrorMessageLock); error = -1; goto ReturnError; } if ( Bin2->T.SB.BlockTerms[blin2] == 0 ) { if ( blin2 == 1 ) { UNLOCK(Bin2->T.SB.MasterBlockLock[Bin2->T.SB.MasterNumBlocks]); } else { UNLOCK(Bin2->T.SB.MasterBlockLock[blin2-1]); } if ( blin2 == Bin2->T.SB.MasterNumBlocks ) { blin2 = 1; } else { blin2++; } LOCK(Bin2->T.SB.MasterBlockLock[blin2]); Bin2->T.SB.MasterBlock = blin2; term2 = Bin2->T.SB.MasterStart[blin2]; } else { term2 += *term2; } } /* #] Tail in two : */ } // Both streams have hit the end-of-stream marker "0". We still need to // decrement the BlockTerms counters a final time, the marker is included // in the count. Bin1->T.SB.BlockTerms[blin1]--; Bin2->T.SB.BlockTerms[blin2]--; SortBotOut(BHEAD 0); ReturnError:; /* Release all locks. */ UNLOCK(Bin1->T.SB.MasterBlockLock[blin1]); if ( blin1 > 1 ) { UNLOCK(Bin1->T.SB.MasterBlockLock[blin1-1]); } else { UNLOCK(Bin1->T.SB.MasterBlockLock[Bin1->T.SB.MasterNumBlocks]); } UNLOCK(Bin2->T.SB.MasterBlockLock[blin2]); if ( blin2 > 1 ) { UNLOCK(Bin2->T.SB.MasterBlockLock[blin2-1]); } else { UNLOCK(Bin2->T.SB.MasterBlockLock[Bin2->T.SB.MasterNumBlocks]); } if ( AT.identity > 0 ) { UNLOCK(AT.SB.MasterBlockLock[AT.SB.FillBlock]); } /* And that was all folks */ return(error); } #endif /* #] SortBotMerge : #[ IniSortBlocks : */ static int SortBlocksInitialized = 0; /** * Initializes the blocks in the sort buffers of the master. * These blocks are needed to keep both the workers and the master working * simultaneously. See also the commentary at the routine MasterMerge. */ int IniSortBlocks(int numworkers) { ALLPRIVATES *B; SORTING *S; LONG totalsize, workersize, blocksize, numberofterms; int maxter, id, j; int numberofblocks = NUMBEROFBLOCKSINSORT, numparts; WORD *w; if ( SortBlocksInitialized ) return(0); SortBlocksInitialized = 1; if ( numworkers == 0 ) return(0); #ifdef WITHSORTBOTS if ( numworkers > 2 ) { numparts = 2*numworkers - 2; numberofblocks = numberofblocks/2; } else { numparts = numworkers; } #else numparts = numworkers; #endif S = AM.S0; totalsize = S->LargeSize + S->SmallEsize; workersize = totalsize / numparts; maxter = AM.MaxTer/sizeof(WORD); blocksize = ( workersize - maxter )/numberofblocks; numberofterms = blocksize / maxter; if ( numberofterms < MINIMUMNUMBEROFTERMS ) { /* This should have been taken care of in RecalcSetups. */ MesPrint("We have a problem with the size of the blocks in IniSortBlocks"); Terminate(-1); } /* Layout: For each worker block 0: size is maxter WORDS numberofblocks blocks of size blocksize WORDS */ w = S->lBuffer; if ( w == 0 ) w = S->sBuffer; for ( id = 1; id <= numparts; id++ ) { B = AB[id]; AT.SB.MasterBlockLock = (pthread_mutex_t *)Malloc1( sizeof(pthread_mutex_t)*(numberofblocks+1),"MasterBlockLock"); AT.SB.MasterStart = (WORD **)Malloc1(sizeof(WORD *)*(numberofblocks+1)*3,"MasterBlock"); AT.SB.MasterFill = AT.SB.MasterStart + (numberofblocks+1); AT.SB.MasterStop = AT.SB.MasterFill + (numberofblocks+1); AT.SB.MasterNumBlocks = numberofblocks; AT.SB.BlockTerms = (LONG*)Malloc1(sizeof(LONG)*(numberofblocks+1),"BlockTerms"); AT.SB.MasterBlock = 0; AT.SB.FillBlock = 0; AT.SB.MasterFill[0] = AT.SB.MasterStart[0] = w; AT.SB.BlockTerms[0] = 0; w += maxter; AT.SB.MasterStop[0] = w; AT.SB.MasterBlockLock[0] = dummylock; for ( j = 1; j <= numberofblocks; j++ ) { AT.SB.MasterFill[j] = AT.SB.MasterStart[j] = w; AT.SB.BlockTerms[j] = 0; w += blocksize; AT.SB.MasterStop[j] = w; AT.SB.MasterBlockLock[j] = dummylock; } } if ( w > S->sTop2 ) { MesPrint("Counting problem in IniSortBlocks"); Terminate(-1); } return(0); } /* #] IniSortBlocks : #[ UpdateSortBlocks : */ /** * A version of IniSortBlocks which only updates the pointers in the master's * buffer, to be used after reallocation of that buffer. */ int UpdateSortBlocks(int numworkers) { ALLPRIVATES *B; SORTING *S; LONG totalsize, workersize, blocksize, numberofterms; int maxter, id, j; int numberofblocks = NUMBEROFBLOCKSINSORT, numparts; WORD *w; if ( numworkers == 0 ) return(0); #ifdef WITHSORTBOTS if ( numworkers > 2 ) { numparts = 2*numworkers - 2; numberofblocks = numberofblocks/2; } else { numparts = numworkers; } #else numparts = numworkers; #endif S = AM.S0; totalsize = S->LargeSize + S->SmallEsize; workersize = totalsize / numparts; maxter = AM.MaxTer/sizeof(WORD); blocksize = ( workersize - maxter )/numberofblocks; numberofterms = blocksize / maxter; if ( numberofterms < MINIMUMNUMBEROFTERMS ) { /* This should have been taken care of in RecalcSetups. */ MesPrint("We have a problem with the size of the blocks in UpdateSortBlocks"); Terminate(-1); } /* Layout: For each worker block 0: size is maxter WORDS numberofblocks blocks of size blocksize WORDS */ w = S->lBuffer; if ( w == 0 ) w = S->sBuffer; for ( id = 1; id <= numparts; id++ ) { B = AB[id]; AT.SB.MasterFill[0] = AT.SB.MasterStart[0] = w; w += maxter; AT.SB.MasterStop[0] = w; for ( j = 1; j <= numberofblocks; j++ ) { AT.SB.MasterFill[j] = AT.SB.MasterStart[j] = w; w += blocksize; AT.SB.MasterStop[j] = w; } } if ( w > S->sTop2 ) { MesPrint("Counting problem in UpdateSortBlocks"); Terminate(-1); } return(0); } /* #] UpdateSortBlocks : #[ DefineSortBotTree : */ #ifdef WITHSORTBOTS /** * To be used in a sortbot merge. It initializes the whole sortbot * system by telling the sortbot which threads provide their input. */ void DefineSortBotTree(void) { ALLPRIVATES *B; int n, i, from; if ( numberofworkers <= 2 ) return; n = numberofworkers*2-2; for ( i = numberofworkers+1, from = 1; i <= n; i++ ) { B = AB[i]; AT.SortBotIn1 = from++; AT.SortBotIn2 = from++; } B = AB[0]; AT.SortBotIn1 = from++; AT.SortBotIn2 = from++; } #endif /* #] DefineSortBotTree : #[ GetTerm2 : Routine does a GetTerm but only when a bracket index is involved and only from brackets that have been judged not suitable for treatment as complete brackets by a single worker. Whether or not a bracket should be treated by a single worker is decided by TreatIndexEntry */ WORD GetTerm2(PHEAD WORD *term) { WORD *ttco, *tt, retval; LONG n,i; FILEHANDLE *fi; EXPRESSIONS e = AN.expr; BRACKETINFO *b = e->bracketinfo; BRACKETINDEX *bi = b->indexbuffer; POSITION where, eonfile = AS.OldOnFile[e-Expressions], bstart, bnext; /* 1: Get the current position. */ switch ( e->status ) { case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: fi = AR.hidefile; break; default: fi = AR.infile; break; } if ( AR.KeptInHold ) { retval = GetTerm(BHEAD term); return(retval); } SeekScratch(fi,&where); if ( AN.lastinindex < 0 ) { /* We have to test whether we have to do the first bracket */ if ( ( n = TreatIndexEntry(BHEAD 0) ) <= 0 ) { AN.lastinindex = n; where = bi[n].start; ADD2POS(where,eonfile); SetScratch(fi,&where); /* Put the bracket in the Compress buffer. */ ttco = AR.CompressBuffer; tt = b->bracketbuffer + bi[0].bracket; i = *tt; NCOPY(ttco,tt,i) AR.CompressPointer = ttco; retval = GetTerm(BHEAD term); return(retval); } else AN.lastinindex = n-1; } /* 2: Find the corresponding index number a: test whether it is in the current bracket */ n = AN.lastinindex; bstart = bi[n].start; ADD2POS(bstart,eonfile); bnext = bi[n].next; ADD2POS(bnext,eonfile); if ( ISLESSPOS(bstart,where) && ISLESSPOS(where,bnext) ) { retval = GetTerm(BHEAD term); return(retval); } for ( n++ ; n < b->indexfill; n++ ) { i = TreatIndexEntry(BHEAD n); if ( i <= 0 ) { /* Put the bracket in the Compress buffer. */ ttco = AR.CompressBuffer; tt = b->bracketbuffer + bi[n].bracket; i = *tt; NCOPY(ttco,tt,i) AR.CompressPointer = ttco; AN.lastinindex = n; where = bi[n].start; ADD2POS(where,eonfile); SetScratch(fi,&(where)); retval = GetTerm(BHEAD term); return(retval); } else n += i - 1; } return(0); } /* #] GetTerm2 : #[ TreatIndexEntry : */ /** * Routine has to decide whether a bracket has to be sent as a complete * bracket to a worker or whether it has to be treated by the bucket system. * Return value is positive when we should send it as a complete bracket and * 0 when it should be done via the buckets. * The positive return value indicates how many brackets should be treated. */ int TreatIndexEntry(PHEAD LONG n) { BRACKETINFO *b = AN.expr->bracketinfo; LONG numbra = b->indexfill - 1, i; LONG totterms; BRACKETINDEX *bi; POSITION pos1, average; /* 1: number of the bracket should be such that there is one bucket for each worker remaining. */ if ( ( numbra - n ) <= numberofworkers ) return(0); /* 2: size of the bracket contents should be less than what remains in the expression divided by the number of workers. */ bi = b->indexbuffer; DIFPOS(pos1,bi[numbra].next,bi[n].next); /* Size of what remains */ BASEPOSITION(average) = DIVPOS(pos1,(3*numberofworkers)); DIFPOS(pos1,bi[n].next,bi[n].start); /* Size of the current bracket */ if ( ISLESSPOS(average,pos1) ) return(0); /* It passes. Now check whether we can do more brackets */ totterms = bi->termsinbracket; if ( totterms > 2*AC.ThreadBucketSize ) return(1); for ( i = 1; i < numbra-n; i++ ) { DIFPOS(pos1,bi[n+i].next,bi[n].start); /* Size of the combined brackets */ if ( ISLESSPOS(average,pos1) ) return(i); totterms += bi->termsinbracket; if ( totterms > 2*AC.ThreadBucketSize ) return(i+1); } /* We have a problem at the end of the system. Just do one. */ return(1); } /* #] TreatIndexEntry : #[ SetHideFiles : */ void SetHideFiles(void) { int i; ALLPRIVATES *B, *B0 = AB[0]; for ( i = 1; i <= numberofworkers; i++ ) { B = AB[i]; AR.hidefile->handle = AR0.hidefile->handle; if ( AR.hidefile->handle < 0 ) { AR.hidefile->PObuffer = AR0.hidefile->PObuffer; AR.hidefile->POstop = AR0.hidefile->POstop; AR.hidefile->POfill = AR0.hidefile->POfill; AR.hidefile->POfull = AR0.hidefile->POfull; AR.hidefile->POsize = AR0.hidefile->POsize; AR.hidefile->POposition = AR0.hidefile->POposition; AR.hidefile->filesize = AR0.hidefile->filesize; } else { AR.hidefile->PObuffer = AR.hidefile->wPObuffer; AR.hidefile->POstop = AR.hidefile->wPOstop; AR.hidefile->POfill = AR.hidefile->wPOfill; AR.hidefile->POfull = AR.hidefile->wPOfull; AR.hidefile->POsize = AR.hidefile->wPOsize; PUTZERO(AR.hidefile->POposition); } } } /* #] SetHideFiles : #[ IniFbufs : */ void IniFbufs(void) { int i; for ( i = 0; i < AM.totalnumberofthreads; i++ ) { IniFbuffer(AB[i]->T.fbufnum); } } /* #] IniFbufs : #[ SetMods : */ void SetMods(void) { ALLPRIVATES *B; int i, n, j; for ( j = 0; j < AM.totalnumberofthreads; j++ ) { B = AB[j]; AN.ncmod = AC.ncmod; if ( AN.cmod != 0 ) M_free(AN.cmod,"AN.cmod"); n = ABS(AN.ncmod); AN.cmod = (UWORD *)Malloc1(sizeof(WORD)*n,"AN.cmod"); for ( i = 0; i < n; i++ ) AN.cmod[i] = AC.cmod[i]; } } /* #] SetMods : #[ UnSetMods : */ void UnSetMods(void) { ALLPRIVATES *B; int j; for ( j = 0; j < AM.totalnumberofthreads; j++ ) { B = AB[j]; if ( AN.cmod != 0 ) M_free(AN.cmod,"AN.cmod"); AN.cmod = 0; } } /* #] UnSetMods : #[ find_Horner_MCTS_expand_tree_threaded : */ void find_Horner_MCTS_expand_tree_threaded(void) { int id; while (( id = GetAvailableThread() ) < 0) MasterWait(); WakeupThread(id,MCTSEXPANDTREE); } /* #] find_Horner_MCTS_expand_tree_threaded : #[ optimize_expression_given_Horner_threaded : */ extern void optimize_expression_given_Horner_threaded(void) { int id; while (( id = GetAvailableThread() ) < 0) MasterWait(); WakeupThread(id,OPTIMIZEEXPRESSION); } /* #] optimize_expression_given_Horner_threaded : */ #endif form-5.0.1/sources/function.c0000644000175100017510000014765015217035721011637 /** @file function.c * * The file with the central routines for the pattern matching of * functions and their arguments. * The file also contains the routines for the execution of the * Symmetrize statement and its variations (like antisymmetrize etc). */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : function.c */ #include "form3.h" /* #] Includes : #[ Utilities : #[ MakeDirty : Routine finds the function with the address x in it and mark all arguments that contain x as dirty. if par == 0 term is a full term, else term is the start of a function */ int MakeDirty(WORD *term, WORD *x, WORD par) { WORD *next, *n; if ( !par ) { next = term; next += *term; next -= ABS(next[-1]); term++; if ( x < term ) return(0); if ( x >= next ) return(0); while ( term < next ) { n = term + term[1]; if ( x < n ) break; term = n; } /* next = n; */ } else { next = term + term[1]; if ( x < term || x >= next ) return(0); } if ( *term < FUNCTION ) return(0); if ( functions[*term-FUNCTION].spec >= TENSORFUNCTION ) return(0); term += FUNHEAD; if ( x < term ) return(0); next = term; NEXTARG(next) while ( x >= next ) { term = next; NEXTARG(next) } if ( *term < 0 ) return(0); term[1] = 1; term += ARGHEAD; if ( x < term ) return(1); next = term + *term; while ( x >= next ) { term = next; next += *next; } MakeDirty(term,x,0); return(1); } /* #] MakeDirty : #[ MarkDirty : Routine marks all functions dirty with the given flags. Is to be used when there is a possibility that symmetrization properties of functions may have changed. In that case we play it safe. */ void MarkDirty(WORD *term, WORD flags) { WORD *t, *r, *m, *tstop; GETSTOP(term,tstop); t = term+1; while ( t < tstop ) { if ( *t < FUNCTION ) { t += t[1]; continue; } t[2] |= flags; if ( *t < FUNCTION+WILDOFFSET && functions[*t-FUNCTION].spec > 0 ) { t += t[1]; continue; } if ( *t >= FUNCTION+WILDOFFSET && functions[*t-FUNCTION-WILDOFFSET].spec > 0 ) { t += t[1]; continue; } r = t + FUNHEAD; t += t[1]; while ( r < t ) { if ( *r <= 0 ) { if ( *r <= -FUNCTION ) r++; else r += 2; continue; } r[1] |= DIRTYFLAG; m = r + ARGHEAD; r += *r; while ( m < r ) { MarkDirty(m,flags); m += *m; } } } } /* #] MarkDirty : #[ PolyFunDirty : Routine marks the PolyFun or the PolyRatFun dirty. This is used when there is modular calculus and the modulus has changed for the current module. */ void PolyFunDirty(PHEAD WORD *term) { GETBIDENTITY WORD *t, *tstop, *endarg; tstop = term + *term; tstop -= ABS(tstop[-1]); t = term+1; while ( t < tstop ) { if ( *t == AR.PolyFun ) { if ( AR.PolyFunType == 2 ) t[2] |= MUSTCLEANPRF; endarg = t + t[1]; t[2] |= DIRTYFLAG; t += FUNHEAD; while ( t < endarg ) { if ( *t > 0 ) { t[1] |= DIRTYFLAG; } NEXTARG(t); } } else { t += t[1]; } } } /* #] PolyFunDirty : #[ PolyFunClean : Routine marks the PolyFun or the PolyRatFun clean. This is used when there is modular calculus and the modulus has changed for the current module. */ void PolyFunClean(PHEAD WORD *term) { GETBIDENTITY WORD *t, *tstop; tstop = term + *term; tstop -= ABS(tstop[-1]); t = term+1; while ( t < tstop ) { if ( *t == AR.PolyFun ) { t[2] &= ~MUSTCLEANPRF; } t += t[1]; } } /* #] PolyFunClean : #[ Symmetrize : (Anti)Symmetrizes the arguments of a function. Nlist tells of how many arguments are involved. Nlist == 0 All arguments must be sorted. Nlist > 0 Arguments mentioned are to be sorted, rest skipped. type = SYMMETRIC Full symmetrization type = ANTISYMMETRIC: Full symmetrization type = CYCLESYMMETRIC: Cyclic type = RCYCLESYMMETRIC:Cyclic or reverse Return value: OR of: 0 even, 1 odd 2 equal groups 4 there was a permutation. The information in Lijst tells what grouping is to be applied. The information is: ngroups number of groups gsize size of groups Lijst[0].... The groups. */ WORD Symmetrize(PHEAD WORD *func, WORD *Lijst, WORD ngroups, WORD gsize, WORD type) { GETBIDENTITY WORD **args,**arg,nargs; WORD *to, *r, *fstop; WORD i, j, k, ff, exch, nexch, neq; WORD *a1, *a2, *a3; WORD reverseorder; if ( ( type & REVERSEORDER ) != 0 ) reverseorder = -1; else reverseorder = 1; type &= ~REVERSEORDER; ff = ( *func > FUNCTION ) ? functions[*func-FUNCTION].spec: 0; if ( 2*func[1] > AN.arglistsize ) { if ( AN.arglist ) M_free(AN.arglist,"Symmetrize"); AN.arglistsize = 2*func[1] + 8; AN.arglist = (WORD **)Malloc1(AN.arglistsize*sizeof(WORD *),"Symmetrize"); } arg = args = AN.arglist; to = AT.WorkPointer; r = func; fstop = r + r[1]; r += FUNHEAD; nargs = 0; while ( r < fstop ) { /* Make list of arguments */ *arg++ = r; nargs++; if ( ff ) { if ( *r == FUNNYWILD ) r++; r++; } else { NEXTARG(r); } } exch = 0; nexch = 0; neq = 0; a1 = Lijst; if ( type == SYMMETRIC || type == ANTISYMMETRIC ) { for ( i = 1; i < ngroups; i++ ) { a3 = a2 = a1 + gsize; k = reverseorder*CompGroup(BHEAD ff,args,a1,a2,gsize); if ( k < 0 ) { j = i-1; for(;;) { for ( k = 0; k < gsize; k++ ) { r = args[a1[k]]; args[a1[k]] = args[a2[k]]; args[a2[k]] = r; } exch ^= 1; nexch = 4; if ( j <= 0 ) break; a1 -= gsize; a2 -= gsize; k = reverseorder*CompGroup(BHEAD ff,args,a1,a2,gsize); if ( k == 0 ) neq = 2; if ( k >= 0 ) break; j--; } } else if ( k == 0 ) neq = 2; a1 = a3; } } else if ( type == CYCLESYMMETRIC || type == RCYCLESYMMETRIC ) { WORD rev = 0, jmin = 0, ii, iimin; recycle: for ( j = 1; j < ngroups; j++ ) { for ( i = 0; i < ngroups; i++ ) { iimin = jmin + i; if ( iimin >= ngroups ) iimin -= ngroups; ii = j + i; if ( ii >= ngroups ) ii -= ngroups; k = reverseorder*CompGroup(BHEAD ff,args,Lijst+gsize*iimin,Lijst+gsize*ii,gsize); if ( k > 0 ) break; if ( k < 0 ) { jmin = j; nexch = 4; break; } } } if ( type == RCYCLESYMMETRIC && rev == 0 && ngroups > 1 ) { for ( j = 0; j < ngroups; j++ ) { for ( i = 0; i < ngroups; i++ ) { iimin = jmin + i; if ( iimin >= ngroups ) iimin -= ngroups; ii = j - i; if ( ii < 0 ) ii += ngroups; k = reverseorder*CompGroup(BHEAD ff,args,Lijst+gsize*iimin,Lijst+gsize*ii,gsize); if ( k > 0 ) break; if ( k < 0 ) { nexch = 4; jmin = 0; a1 = Lijst; a2 = Lijst + gsize * (ngroups-1); while ( a2 > a1 ) { for ( k = 0; k < gsize; k++ ) { r = args[a1[k]]; args[a1[k]] = args[a2[k]]; args[a2[k]] = r; } a1 += gsize; a2 -= gsize; } rev = 1; goto recycle; } } } } if ( jmin != 0 ) { arg = AN.arglist + func[1]; a1 = Lijst + gsize * jmin; k = gsize * ngroups; a2 = Lijst + k; for ( i = 0; i < k; i++ ) { if ( a1 >= a2 ) a1 = Lijst; *arg++ = args[*a1++]; } arg = AN.arglist + func[1]; a1 = Lijst; for ( i = 0; i < k; i++ ) args[*a1++] = *arg++; } } r = func; i = FUNHEAD; NCOPY(to,r,i); for ( i = 0; i < nargs; i++ ) { if ( ff ) { if ( *(args[i]) == FUNNYWILD ) { *to++ = *(args[i]); *to++ = args[i][1]; } else *to++ = *(args[i]); } else if ( ( j = *args[i] ) < 0 ) { *to++ = j; if ( j > -FUNCTION ) *to++ = args[i][1]; } else { r = args[i]; NCOPY(to,r,j); } } i = func[1]; to = func; r = AT.WorkPointer; NCOPY(to,r,i); return ( exch | nexch | neq ); } /* #] Symmetrize : #[ CompGroup : Routine compares two groups of arguments The arguments are in args[a1[i]] and args[a2[i]] for i = 0 to num type indicates the type of function. return value: -1 if there should be an exchange 0 if they are equal 1 if they are OK. */ int CompGroup(PHEAD WORD type, WORD **args, WORD *a1, WORD *a2, WORD num) { GETBIDENTITY WORD *t1, *t2, i1, i2, n, k; for ( n = 0; n < num; n++ ) { t1 = args[a1[n]]; t2 = args[a2[n]]; if ( type >= TENSORFUNCTION ) { if ( AR.Eside == LHSIDE || AR.Eside == LHSIDEX ) { if ( *t1 == FUNNYWILD ) { if ( *t2 == FUNNYWILD ) { if ( t1[1] < t2[1] ) return(1); if ( t1[1] > t2[1] ) return(-1); } return(-1); } else if ( *t2 == FUNNYWILD ) { return(1); } else { if ( *t1 < *t2 ) return(1); if ( *t1 > *t2 ) return(-1); } } else { if ( *t1 < *t2 ) return(1); if ( *t1 > *t2 ) return(-1); } } else if ( type == 0 ) { if ( AC.properorderflag ) { k = CompArg(t1,t2); if ( k < 0 ) return(1); if ( k > 0 ) return(-1); NEXTARG(t1) NEXTARG(t2) } else { if ( *t1 > 0 ) { i1 = *t1 - ARGHEAD - 1; t1 += ARGHEAD + 1; if ( *t2 > 0 ) { i2 = *t2 - ARGHEAD - 1; t2 += ARGHEAD + 1; while ( i1 > 0 && i2 > 0 ) { if ( *t1 > *t2 ) return(-1); else if ( *t1 < *t2 ) return(1); i1--; i2--; t1++; t2++; } if ( i1 > 0 ) return(-1); else if ( i2 > 0 ) return(1); } /* This seems to be a bug. Reported by Aneesh Monahar, 28-sep-2005 else return(1); */ else return(-1); } else if ( *t2 > 0 ) return(1); else { if ( *t1 != *t2 ) { if ( *t1 <= -FUNCTION && *t2 <= -FUNCTION ) { if ( *t1 < *t2 ) return(-1); return(1); } else { if ( *t1 < *t2 ) return(1); return(-1); } } if ( *t1 > -FUNCTION ) { if ( t1[1] != t2[1] ) { if ( t1[1] < t2[1] ) return(1); return(-1); } } } } } } return(0); } /* #] CompGroup : #[ FullSymmetrize : Relay function for Normalize to execute a full symmetrization of a function fun. It hooks into Symmetrize according to the calling conventions for it. type = 0: Symmetrize type = 1: AntiSymmetrize type = 2: CycleSymmetrize type = 3: RCycleSymmetrize Return values: bit 0: odd permutation bit 1: identical arguments bit 2: there was a permutation. */ int FullSymmetrize(PHEAD WORD *fun, int type) { GETBIDENTITY WORD *Lijst, count = 0; WORD *t, *funstop, i; int retval; if ( functions[*fun-FUNCTION].spec > 0 ) { count = fun[1] - FUNHEAD; for ( i = fun[1]-1; i >= FUNHEAD; i-- ) { if ( fun[i] == FUNNYWILD ) count--; } } else { funstop = fun + fun[1]; t = fun + FUNHEAD; while ( t < funstop ) { count++; NEXTARG(t) } } if ( count < 2 ) { fun[2] &= ~DIRTYSYMFLAG; return(0); } Lijst = AT.WorkPointer; for ( i = 0; i < count; i++ ) Lijst[i] = i; AT.WorkPointer += count; retval = Symmetrize(BHEAD fun,Lijst,count,1,type); fun[2] &= ~DIRTYSYMFLAG; AT.WorkPointer = Lijst; return(retval); } /* #] FullSymmetrize : #[ SymGen : Routine does the outer work in the symmetrization. It locates the function(s) and loads up the parameters. It also studies the result. if params[4] = -1 and no extra -> all extra -> strip groups with elements too large 0 -> if group with element too large: nofun >0 -> must have right number of arguments */ int SymGen(PHEAD WORD *term, WORD *params, WORD num, WORD level) { GETBIDENTITY WORD *t, *r, *m; WORD i, j, k, c1, c2, ngroup; WORD *rstop, Nlist, *inLijst, *Lijst, sign = 1, sumch = 0, count; DUMMYUSE(num); c1 = params[3]; /* function number */ c2 = FUNCTION + WILDOFFSET; Nlist = params[4]; if ( Nlist < 0 ) Nlist = 0; else Nlist = params[0] - 7; t = term; m = t + *t; m -= ABS(m[-1]); t++; while ( t < m ) { if ( *t == c1 || c1 > c2 ) { /* Candidate function */ if ( *t >= FUNCTION && functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { count = t[1] - FUNHEAD; } else { count = 0; r = t; rstop = t + t[1]; r += FUNHEAD; while ( r < rstop ) { count++; NEXTARG(r) } } if ( ( j = params[4] ) > 0 && j != count ) goto NextFun; if ( j == 0 ) { inLijst = params+7; for ( i = 0; i < Nlist; i++ ) if ( inLijst[i] > count-1 ) goto NextFun; } if ( Nlist > (params[0] - 7) ) Nlist = params[0] - 7; Lijst = AT.WorkPointer; inLijst = params + 7; ngroup = params[5]; if ( Nlist > 0 && j < 0 ) { k = 0; for ( i = 0; i < ngroup; i++ ) { for ( j = 0; j < params[6]; j++ ) { if ( inLijst[j] > count+1 ) { inLijst += params[6]; goto NextGroup; } } j = params[6]; NCOPY(Lijst,inLijst,j); k++; NextGroup:; } if ( k <= 1 ) goto NextFun; ngroup = k; inLijst = AT.WorkPointer; AT.WorkPointer = Lijst; Lijst = inLijst; } else if ( Nlist == 0 ) { for ( i = 0; i < count; i++ ) Lijst[i] = i; AT.WorkPointer += count; ngroup = count; } else { for ( i = 0; i < Nlist; i++ ) Lijst[i] = inLijst[i]; AT.WorkPointer += Nlist; } j = Symmetrize(BHEAD t,Lijst,ngroup,params[6],params[2]); AT.WorkPointer = Lijst; if ( params[2] == 4 ) { /* antisymmetric */ if ( ( j & 1 ) != 0 ) sign = -sign; if ( ( j & 2 ) != 0 ) return(0); /* equal arguments */ } if ( ( j & 4 ) != 0 ) sumch++; t[2] &= ~DIRTYSYMFLAG; } NextFun: t += t[1]; } if ( sign < 0 ) { t = term; t += *t - 1; *t = -*t; } if ( sumch ) { if ( Normalize(BHEAD term) ) { MLOCK(ErrorMessageLock); MesCall("SymGen"); MUNLOCK(ErrorMessageLock); return(-1); } if ( !*term ) return(0); *AN.RepPoint = 1; AR.expchanged = 1; if ( AR.CurDum > AM.IndDum && AR.sLevel <= 0 ) ReNumber(BHEAD term); } return(Generator(BHEAD term,level)); } /* #] SymGen : #[ SymFind : There is a certain amount of double work here, as this routine finds the function to be treated, while the SymGen routine has to find it again. Note however that this way things remain uniform and simple. Moreover this avoids problems with actions on more than one function simultaneously. Output in AT.TMout: Number,sym/anti,fun,lenpar,ngroups,gsize,fields */ int SymFind(PHEAD WORD *term, WORD *params) { GETBIDENTITY WORD *t, *r, *m; WORD j, c1, c2, count; WORD *rstop; c1 = params[4]; /* function number */ c2 = FUNCTION + WILDOFFSET; t = term; m = t + *t; m -= ABS(m[-1]); t++; while ( t < m ) { if ( *t == c1 || c1 > c2 ) { /* Candidate function */ if ( *t >= FUNCTION && functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { count = t[1] - FUNHEAD; } else { count = 0; r = t; rstop = t + t[1]; r += FUNHEAD; while ( r < rstop ) { count++; NEXTARG(r) } } if ( ( j = params[5] ) > 0 && j != count ) goto NextFun; if ( j == 0 ) { r = params + 8; rstop = params + params[1]; while ( r < rstop ) { if ( *r > count + 1 ) goto NextFun; r++; } } t = AT.TMout; r = params; j = r[1] - 1; *t++ = j; *t++ = SYMMETRIZE; r += 3; j--; NCOPY(t,r,j); return(1); } NextFun: t += t[1]; } return(0); } /* #] SymFind : #[ ChainIn : Equivalent to repeat id f(?a)*f(?b) = f(?a,?b); This one always takes less space. */ int ChainIn(PHEAD WORD *term, WORD funnum) { GETBIDENTITY WORD *t, *tend, *m, *tt, *ts; int action, normFlag = 0; if ( funnum < 0 ) { /* Dollar to be expanded */ funnum = DolToFunction(BHEAD -funnum); if ( AN.ErrorInDollar || funnum <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Dollar variable does not evaluate to function in ChainIn statement"); MUNLOCK(ErrorMessageLock); return(-1); } } do { action = 0; tend = term+*term; tend -= ABS(tend[-1]); t = term+1; while ( t < tend ) { if ( *t != funnum ) { t += t[1]; continue; } m = t; t += t[1]; tt = t; if ( t >= tend || *t != funnum ) continue; action = 1; normFlag = 1; while ( t < tend && *t == funnum ) { ts = t + t[1]; t += FUNHEAD; while ( t < ts ) *tt++ = *t++; } m[1] = tt - m; ts = term + *term; while ( t < ts ) *tt++ = *t++; *term = tt - term; break; } } while ( action ); if ( normFlag ) { /* We need to check the newly-constructed arguments w.r.t symmetry properties */ MarkDirty(term, DIRTYSYMFLAG); AT.WorkPointer = term + *term; Normalize(BHEAD term); } return(0); } /* #] ChainIn : #[ ChainOut : Equivalent to repeat id f(x1?,x2?,?a) = f(x1)*f(x2,?a); */ int ChainOut(PHEAD WORD *term, WORD funnum) { GETBIDENTITY WORD *t, *tend, *tt, *ts, *w, *ws; int flag = 0, i; if ( funnum < 0 ) { /* Dollar to be expanded */ funnum = DolToFunction(BHEAD -funnum); if ( AN.ErrorInDollar || funnum <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Dollar variable does not evaluate to function in ChainOut statement"); MUNLOCK(ErrorMessageLock); return(-1); } } tend = term+*term; if ( AT.WorkPointer < tend ) AT.WorkPointer = tend; tend -= ABS(tend[-1]); t = term+1; tt = term; w = AT.WorkPointer; while ( t < tend ) { if ( *t != funnum || t[1] == FUNHEAD ) { t += t[1]; continue; } flag = 1; while ( tt < t ) *w++ = *tt++; ts = t + t[1]; t += FUNHEAD; while ( t < ts ) { ws = w; for ( i = 0; i < FUNHEAD; i++ ) *w++ = tt[i]; if ( functions[*tt-FUNCTION].spec >= TENSORFUNCTION ) { *w++ = *t++; } else if ( *t < 0 ) { if ( *t <= -FUNCTION ) *w++ = *t++; else { *w++ = *t++; *w++ = *t++; } } else { i = *t; NCOPY(w,t,i); } ws[1] = w - ws; } tt = t; } if ( flag == 1 ) { ts = term + *term; while ( tt < ts ) *w++ = *tt++; *AT.WorkPointer = w - AT.WorkPointer; t = term; w = AT.WorkPointer; i = *w; NCOPY(t,w,i) AT.WorkPointer = term + *term; Normalize(BHEAD term); } return(0); } /* #] ChainOut : #] Utilities : #[ Patterns : #[ MatchFunction : WORD MatchFunction(pattern,interm,wilds) The routine assumes that the function numbers are the same. The contents are compared and a possible wildcard assignment is made. Note that it may be necessary to use a wildcard assignment stack to do things right. The routine can become arbitrarily complicated as there is no end to the possible wildcarding. Examples: - a: No wildcarding -> straight match - b: Individual arguments (object -> object) - c: whole arguments (object to subexpression) - d: any argumentlist e: part of an argument (object inside subexpression) The ones with a minus sign in front have been implemented. Note: the argument wilds allows backtracking when multiple ?a,?b give a match that later turns out to be useless. */ int MatchFunction(PHEAD WORD *pattern, WORD *interm, WORD *wilds) { GETBIDENTITY WORD *m, *t, *r, i; WORD *mstop = 0, *tstop = 0; WORD *argmstop, *argtstop; WORD *mtrmstop, *ttrmstop; WORD *msubstop, *mnextsub; WORD msizcoef, mcount, tcount, newvalue, j; WORD *oldm, *oldt; WORD *OldWork, numofwildarg; WORD nwstore, tobeeaten, reservevalue = 0, resernum = 0, withwild; WORD *wildargtaken; CBUF *C = cbuf+AT.ebufnum; int ntwa = AN.NumTotWildArgs; LONG oldcpointer = C->Pointer - C->Buffer; #ifdef WITHFLOAT // Pattern matching against float_ functions is currently disabled. // To relax this in the future, move this early return down to where gamma // functions and tensors are handled specially. if ( *interm == FLOATFUN ) return(0); #endif /* Test first for a straight match */ AN.RepFunList[AN.RepFunNum+1] = 0; if ( *wilds == 0 ) { m = pattern; t = interm; if ( *m != *t ) { if ( *m < (FUNCTION + WILDOFFSET) ) return(0); if ( *t < FUNCTION ) return(0); if ( functions[*t-FUNCTION].spec != functions[*m-FUNCTION-WILDOFFSET].spec ) return(0); } i = m[1]; if ( *m >= (FUNCTION + WILDOFFSET) ) { i--; m++; t++; } do { if ( *m++ != *t++ ) break; } while ( --i > 0 ); if ( i <= 0 ) { /* Arguments match */ if ( AN.SignCheck && AN.ExpectedSign ) return(0); i = *pattern - WILDOFFSET; if ( i >= FUNCTION ) { if ( *interm != GAMMA && !CheckWild(BHEAD i,FUNTOFUN,*interm,&newvalue) ) { AddWild(BHEAD i,FUNTOFUN,newvalue); return(1); } return(0); } else return(1); } } /* Store the current Wildcard assignments */ t = wildargtaken = OldWork = AT.WorkPointer; t += ntwa; m = AN.WildValue; nwstore = i = (m[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; if ( i > 0 ) { r = AT.WildMask; do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); *t++ = C->numrhs; } if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); Terminate(-1); } AT.WorkPointer = t; if ( *wilds ) { if ( *wilds == 1 ) goto endoloop; else goto enloop; /* tensors = 2 */ } m = pattern; t = interm; /* Single out the specials */ if ( *t == GAMMA ) { /* #[ GAMMA : For the gamma's we need to do two things: a: Find that there is a match b: Find where the match occurs in the string This last thing cannot be stored in the current conventions, but once the wildcard assignments have been made it is much easier to find it back. Alternative: replace the function number in the term temporarily by the offset inside the string. This makes things maybe easier. */ if ( *m != GAMMA ) goto NoCaseB; i = t[1] - m[1]; if ( m[1] == FUNHEAD+1 ) { if ( i ) goto NoCaseB; if ( m[FUNHEAD] < (AM.OffsetIndex+WILDOFFSET) || t[FUNHEAD] >= (AM.OffsetIndex+WILDOFFSET) ) goto NoCaseB; if ( CheckWild(BHEAD m[FUNHEAD]-WILDOFFSET,INDTOIND,t[FUNHEAD],&newvalue) ) goto NoCaseB; AddWild(BHEAD m[FUNHEAD]-WILDOFFSET,INDTOIND,newvalue); AT.WorkPointer = OldWork; if ( AN.SignCheck && AN.ExpectedSign ) return(0); return(1); /* m was eaten. we have a match! */ } if ( i < 0 ) goto NoCaseB; /* Pattern longer than target */ mstop = m + m[1]; tstop = t + t[1]; m += FUNHEAD; t += FUNHEAD; if ( *m >= (AM.OffsetIndex+WILDOFFSET) && *t < (AM.OffsetIndex+WILDOFFSET) ) { if ( CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,*t,&newvalue) ) goto NoCaseB; reservevalue = newvalue; withwild = 1; resernum = *m-WILDOFFSET; AddWild(BHEAD *m-WILDOFFSET,INDTOIND,newvalue); } else if ( *m != *t ) goto NoCaseB; else withwild = 0; m++; t++; oldm = m; argtstop = oldt = t; j = 0; /* No wildcard assignments yet */ while ( i >= 0 ) { if ( *m == *t ) { WithGamma: m++; t++; if ( m >= mstop ) { if ( t < tstop && mstop < AN.patstop ) { WORD k; mnextsub = pattern + pattern[1]; k = *mnextsub; while ( k == GAMMA && mnextsub[FUNHEAD] != pattern[FUNHEAD] ) { mnextsub += mnextsub[1]; if ( mnextsub >= AN.patstop ) goto FullOK; k = *mnextsub; } if ( k >= FUNCTION ) { if ( k > (FUNCTION + WILDOFFSET) ) k -= WILDOFFSET; if ( functions[k-FUNCTION].commute ) goto NoGamma; } } FullOK: if ( AN.SignCheck && AN.ExpectedSign ) goto NoGamma; AN.RepFunList[AN.RepFunNum+1] = WORDDIF(oldt,argtstop); return(1); } if ( t >= tstop ) goto NoCaseB; } else if ( *m >= (AM.OffsetIndex+WILDOFFSET) && *m < (AM.OffsetIndex + (WILDOFFSET<<1)) && ( *t >= 0 || *t < MINSPEC ) ) { /* Wildcard index */ if ( !CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,*t,&newvalue) ) { AddWild(BHEAD *m-WILDOFFSET,INDTOIND,newvalue); j = 1; goto WithGamma; } else goto NoGamma; } else if ( *m < MINSPEC && *m >= (AM.OffsetVector+WILDOFFSET) && *t < MINSPEC ) { /* Wildcard vector */ if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*t,&newvalue) ) { AddWild(BHEAD *m-WILDOFFSET,VECTOVEC,newvalue); j = 1; goto WithGamma; } else goto NoGamma; } else { NoGamma: if ( j ) { /* Undo wildcards */ m = AN.WildValue; t = OldWork + AN.NumTotWildArgs; r = AT.WildMask; j = nwstore; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } j = 0; } m = oldm; t = ++oldt; i--; if ( withwild ) { AddWild(BHEAD resernum,INDTOIND,reservevalue); } } } goto NoCaseB; /* #] GAMMA : #[ Tensors : */ } else if ( *t >= FUNCTION && functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { mstop = m + m[1]; tstop = t + t[1]; mcount = 0; m += FUNHEAD; t += FUNHEAD; AN.WildArgs = 0; tcount = WORDDIF(tstop,t); while ( m < mstop ) { if ( *m == FUNNYWILD ) { m++; AN.WildArgs++; } m++; mcount++; } tobeeaten = tcount - mcount + AN.WildArgs; if ( tobeeaten ) { if ( tobeeaten < 0 || AN.WildArgs == 0 ) { AT.WorkPointer = OldWork; return(0); /* Cannot match */ } } AT.WildArgTaken[0] = AN.WildEat = tobeeaten; for ( i = 1; i < AN.WildArgs; i++ ) AT.WildArgTaken[i] = 0; toploop: numofwildarg = 0; m = pattern; t = interm; mstop = m + m[1]; if ( *m != *t ) { i = *m - WILDOFFSET; if ( CheckWild(BHEAD i,FUNTOFUN,*t,&newvalue) ) goto NoCaseB; AddWild(BHEAD i,FUNTOFUN,newvalue); } m += FUNHEAD; t += FUNHEAD; while ( m < mstop ) { /* First test for an exact match */ if ( *m == *t ) { m++; t++; continue; } /* No exact match. Try ARGWILD */ AN.argaddress = t; if ( *m == FUNNYWILD ) { tobeeaten = AT.WildArgTaken[numofwildarg++]; if ( CheckWild(BHEAD m[1],ARGTOARG|EATTENSOR,tobeeaten,t) ) goto endloop; AddWild(BHEAD m[1],ARGTOARG|EATTENSOR,tobeeaten); m += 2; t += tobeeaten; continue; } /* Now the various cases: */ i = *m; if ( i < MINSPEC ) { if ( *t != i ) { if ( *t >= MINSPEC ) goto endloop; i -= WILDOFFSET; if ( i < AM.OffsetVector ) goto endloop; if ( CheckWild(BHEAD i,VECTOVEC,*t,&newvalue) ) goto endloop; AddWild(BHEAD i,VECTOVEC,newvalue); } } else if ( i >= AM.OffsetIndex ) { /* Index */ if ( i < ( AM.OffsetIndex + WILDOFFSET ) ) goto endloop; if ( i >= ( AM.OffsetIndex + (WILDOFFSET<<1) ) ) { /* Summed over index */ goto endloop; /* For the moment */ } i -= WILDOFFSET; if ( CheckWild(BHEAD i,INDTOIND,*t,&newvalue) ) goto endloop; /* Assignment not allowed */ AddWild(BHEAD i,INDTOIND,newvalue); } else goto endloop; m++; t++; } if ( AN.SignCheck && AN.ExpectedSign ) goto endloop; AT.WorkPointer = OldWork; if ( AN.WildArgs > 1 ) *wilds = 2; return(1); /* m was eaten. we have a match! */ endloop:; /* restore the current Wildcard assignments */ i = nwstore; if ( i > 0 ) { m = AN.WildValue; t = OldWork + ntwa; r = AT.WildMask; do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --i > 0 ); C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } enloop:; i = AN.WildArgs - 1; if ( i <= 0 ) { AT.WorkPointer = OldWork; return(0); } while ( --i >= 0 ) { if ( AT.WildArgTaken[i] == 0 ) { if ( i == 0 ) { AT.WorkPointer = OldWork; *wilds = 0; return(0); } } else { (AT.WildArgTaken[i])--; numofwildarg = 0; for ( j = 0; j <= i; j++ ) { numofwildarg += AT.WildArgTaken[j]; } AT.WildArgTaken[j] = AN.WildEat-numofwildarg; for ( j++; j < AN.WildArgs; j++ ) AT.WildArgTaken[j] = 0; break; } } goto toploop; /* #] Tensors : */ } /* Count the number of arguments. Either equal or an argument wildcard. */ mstop = m + m[1]; tstop = t + t[1]; mcount = 0; tcount = 0; m += FUNHEAD; t += FUNHEAD; while ( t < tstop ) { tcount++; NEXTARG(t) } AN.WildArgs = 0; while ( m < mstop ) { mcount++; if ( *m == -ARGWILD ) AN.WildArgs++; NEXTARG(m) } tobeeaten = tcount - mcount + AN.WildArgs; if ( tobeeaten ) { if ( tobeeaten < 0 || AN.WildArgs == 0 ) { AT.WorkPointer = OldWork; return(0); /* Cannot match */ } } /* Set up the array AT.WildArgTaken for the number of arguments that each wildarg eats. */ AT.WildArgTaken[0] = AN.WildEat = tobeeaten; for ( i = 1; i < AN.WildArgs; i++ ) AT.WildArgTaken[i] = 0; topofloop: numofwildarg = 0; /* Test for single wildcard object/argument */ m = pattern; t = interm; if ( *m != *t ) { i = *m - WILDOFFSET; if ( CheckWild(BHEAD i,FUNTOFUN,*t,&newvalue) ) goto NoCaseB; AddWild(BHEAD i,FUNTOFUN,newvalue); } mstop = m + m[1]; /* tstop = t + t[1]; */ m += FUNHEAD; t += FUNHEAD; while ( m < mstop ) { argmstop = oldm = m; argtstop = oldt = t; NEXTARG(argmstop) NEXTARG(argtstop) if ( t == tstop ) { /* This concerns a very rare bug */ if ( *m == -ARGWILD ) goto ArgAll; goto endofloop; } if ( *m < 0 && *t < 0 ) { if ( *t <= -FUNCTION ) { if ( *t == *m ) {} else if ( *m <= -FUNCTION-WILDOFFSET && functions[-*t-FUNCTION].spec == functions[-*m-FUNCTION-WILDOFFSET].spec ) { i = -*m - WILDOFFSET; if ( CheckWild(BHEAD i,FUNTOFUN,-*t,&newvalue) ) goto endofloop; AddWild(BHEAD i,FUNTOFUN,newvalue); } else if ( *m == -SYMBOL && m[1] >= 2*MAXPOWER ) { i = m[1] - 2*MAXPOWER; AN.argaddress = AT.FunArg; AT.FunArg[ARGHEAD+1] = -*t; if ( CheckWild(BHEAD i,SYMTOSUB,1,AN.argaddress) ) goto endofloop; AddWild(BHEAD i,SYMTOSUB,0); } else if ( *m == -ARGWILD ) { ArgAll: i = AT.WildArgTaken[numofwildarg++]; AN.argaddress = t; if ( CheckWild(BHEAD m[1],ARGTOARG,i,t) ) goto endofloop; AddWild(BHEAD m[1],ARGTOARG,i); /* m += 2; */ while ( --i >= 0 ) { NEXTARG(t) } argtstop = t; } else goto endofloop; } else if ( *t == *m ) { if ( t[1] == m[1] ) {} else if ( *t == -SYMBOL ) { j = SYMTOSYM; SymAll: if ( ( i = m[1] - 2*MAXPOWER ) < 0 ) goto endofloop; if ( CheckWild(BHEAD i,j,t[1],&newvalue) ) goto endofloop; AddWild(BHEAD i,j,newvalue); } else if ( *t == -INDEX ) { IndAll: i = m[1] - WILDOFFSET; if ( i < AM.OffsetIndex || i >= WILDOFFSET+AM.OffsetIndex ) goto endofloop; /* We kill the summed over indices here */ if ( CheckWild(BHEAD i,INDTOIND,t[1],&newvalue) ) goto endofloop; AddWild(BHEAD i,INDTOIND,newvalue); } else if ( *t == -VECTOR || *t == -MINVECTOR ) { i = m[1] - WILDOFFSET; if ( i < AM.OffsetVector ) goto endofloop; if ( CheckWild(BHEAD i,VECTOVEC,t[1],&newvalue) ) goto endofloop; AddWild(BHEAD i,VECTOVEC,newvalue); } else goto endofloop; } else if ( *m == -ARGWILD ) goto ArgAll; else if ( *m == -INDEX && m[1] >= AM.OffsetIndex+WILDOFFSET && m[1] < AM.OffsetIndex+(WILDOFFSET<<1) ) { if ( *t == -VECTOR ) goto IndAll; if ( *t == -SNUMBER && t[1] >= 0 && t[1] < AM.OffsetIndex ) goto IndAll; if ( *t == -MINVECTOR ) { i = m[1] - WILDOFFSET; AN.argaddress = AT.MinVecArg; AT.MinVecArg[ARGHEAD+3] = t[1]; if ( CheckWild(BHEAD i,INDTOSUB,1,AN.argaddress) ) goto endofloop; AddWild(BHEAD i,INDTOSUB,(WORD)0); } else goto endofloop; } else if ( *m == -SYMBOL && m[1] >= 2*MAXPOWER && *t == -SNUMBER ) { j = SYMTONUM; goto SymAll; } else if ( *m == -VECTOR && *t == -MINVECTOR && ( i = m[1] - WILDOFFSET ) >= AM.OffsetVector ) { /* ================================ AN.argaddress = AT.MinVecArg; AT.MinVecArg[ARGHEAD+3] = t[1]; if ( CheckWild(BHEAD i,VECTOSUB,1,AN.argaddress) ) goto endofloop; AddWild(BHEAD i,VECTOSUB,(WORD)0); ================================ */ if ( CheckWild(BHEAD i,VECTOMIN,t[1],&newvalue) ) goto endofloop; AddWild(BHEAD i,VECTOMIN,newvalue); } else if ( *m == -MINVECTOR && *t == -VECTOR && ( i = m[1] - WILDOFFSET ) >= AM.OffsetVector ) { /* ================================ AN.argaddress = AT.MinVecArg; AT.MinVecArg[ARGHEAD+3] = t[1]; if ( CheckWild(BHEAD i,VECTOSUB,1,AN.argaddress) ) goto endofloop; AddWild(BHEAD i,VECTOSUB,(WORD)0); ================================ */ if ( CheckWild(BHEAD i,VECTOMIN,t[1],&newvalue) ) goto endofloop; AddWild(BHEAD i,VECTOMIN,newvalue); } else goto endofloop; } else if ( *t <= -FUNCTION && *m > 0 ) { if ( ( m[ARGHEAD]+ARGHEAD == *m ) && m[*m-1] == 3 && m[*m-2] == 1 && m[*m-3] == 1 && m[ARGHEAD+1] >= FUNCTION && m[ARGHEAD+2] == *m-ARGHEAD-4 ) { /* Check for f(?a) etc */ WORD *mmmst, *mmm; if ( m[ARGHEAD+1] >= FUNCTION+WILDOFFSET ) { /* i = *m - WILDOFFSET; */ i = m[ARGHEAD+1] - WILDOFFSET; if ( CheckWild(BHEAD i,FUNTOFUN,-*t,&newvalue) ) goto endofloop; AddWild(BHEAD i,FUNTOFUN,newvalue); } else if ( m[ARGHEAD+1] != -*t ) goto endofloop; /* Only arguments allowed are ?a etc. */ mmmst = m+*m-3; mmm = m + ARGHEAD + FUNHEAD + 1; while ( mmm < mmmst ) { if ( *mmm != -ARGWILD ) goto endofloop; i = 0; AN.argaddress = t; if ( CheckWild(BHEAD mmm[1],ARGTOARG,i,t) ) goto endofloop; AddWild(BHEAD mmm[1],ARGTOARG,i); mmm += 2; } } else goto endofloop; } else if ( *m < 0 && *t > 0 ) { if ( *m == -SYMBOL ) { /* SYMTOSUB */ if ( m[1] < 2*MAXPOWER ) goto endofloop; i = m[1] - 2*MAXPOWER; AN.argaddress = t; if ( CheckWild(BHEAD i,SYMTOSUB,1,AN.argaddress) ) goto endofloop; AddWild(BHEAD i,SYMTOSUB,0); } else if ( *m == -VECTOR ) { if ( ( i = m[1] - WILDOFFSET ) < AM.OffsetVector ) goto endofloop; AN.argaddress = t; if ( CheckWild(BHEAD i,VECTOSUB,1,t) ) goto endofloop; AddWild(BHEAD i,VECTOSUB,(WORD)0); } else if ( *m == -INDEX ) { if ( ( i = m[1] - WILDOFFSET ) < AM.OffsetIndex ) goto endofloop; if ( i >= AM.OffsetIndex + WILDOFFSET ) goto endofloop; AN.argaddress = t; if ( CheckWild(BHEAD i,INDTOSUB,1,AN.argaddress) ) goto endofloop; AddWild(BHEAD i,INDTOSUB,(WORD)0); } else if ( *m == -ARGWILD ) goto ArgAll; else goto endofloop; } else if ( *m > 0 && *t > 0 ) { WORD ii = *t-*m; i = *m; do { if ( *m++ != *t++ ) break; } while ( --i > 0 ); if ( i == 1 && ii == 0 ) { /* sign difference */ goto endofloop; } else if ( i > 0 ) { WORD *cto, *cfrom, *csav, ci; WORD oRepFunNum; WORD *oRepFunList; WORD *oterstart,*oterstop,*opatstop; WORD oExpectedSign; WORD wildargs, wildeat; /* Not an exact match here. We have to hope that the pattern contains a composite wildcard. */ m = oldm; t = oldt; m += ARGHEAD; t += ARGHEAD; /* Point at (first?) term */ mtrmstop = m + *m; ttrmstop = t + *t; if ( mtrmstop < argmstop ) goto endofloop;/* More than one term */ msizcoef = mtrmstop[-1]; if ( msizcoef < 0 ) msizcoef = -msizcoef; msubstop = mtrmstop - msizcoef; m++; if ( m >= msubstop ) goto endofloop; /* Only coefficient */ /* Here we have a composite term. It can match provided it matches the entire argument. This argument must be a single term also and the coefficients should match (more or less). The matching takes: 1: Match the functions etc. Nothing can be left. 2: Match dotproducts and symbols. ONLY must match and nothing may be left. For safety it is best to take the term out and put it in workspace. */ if ( argtstop > ttrmstop ) goto endofloop; m--; oterstart = AN.terstart; oterstop = AN.terstop; opatstop = AN.patstop; oRepFunList = AN.RepFunList; oRepFunNum = AN.RepFunNum; AN.RepFunNum = 0; AN.RepFunList = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); if ( AT.WorkPointer+*t+5 > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } csav = cto = AT.WorkPointer; cfrom = t; ci = *t; while ( --ci >= 0 ) *cto++ = *cfrom++; AT.WorkPointer = cto; ci = msizcoef; cfrom = mtrmstop; --ci; if ( abs(*--cfrom) != abs(*--cto) ) { AT.WorkPointer = csav; AN.RepFunList = oRepFunList; AN.RepFunNum = oRepFunNum; AN.terstart = oterstart; AN.terstop = oterstop; AN.patstop = opatstop; goto endofloop; } i = (*cfrom != *cto) ? 1 : 0; /* buffer AN.ExpectedSign until we are beyond the goto */ while ( --ci >= 0 ) { if ( *--cfrom != *--cto ) { AT.WorkPointer = csav; AN.RepFunList = oRepFunList; AN.RepFunNum = oRepFunNum; AN.terstart = oterstart; AN.terstop = oterstop; AN.patstop = opatstop; goto endofloop; } } oExpectedSign = AN.ExpectedSign; /* buffer AN.ExpectedSign until we are beyond FindRest/FindOnly */ AN.ExpectedSign = i; *m -= msizcoef; wildargs = AN.WildArgs; wildeat = AN.WildEat; for ( i = 0; i < wildargs; i++ ) wildargtaken[i] = AT.WildArgTaken[i]; AN.ForFindOnly = 0; AN.UseFindOnly = 1; AN.nogroundlevel++; if ( FindRest(BHEAD csav,m) && ( AN.UsedOtherFind || FindOnly(BHEAD csav,m) ) ) {} else { nomatch: *m += msizcoef; AT.WorkPointer = csav; AN.RepFunList = oRepFunList; AN.RepFunNum = oRepFunNum; AN.terstart = oterstart; AN.terstop = oterstop; AN.patstop = opatstop; AN.WildArgs = wildargs; AN.WildEat = wildeat; AN.ExpectedSign = oExpectedSign; AN.nogroundlevel--; for ( i = 0; i < wildargs; i++ ) AT.WildArgTaken[i] = wildargtaken[i]; goto endofloop; } /* if ( *m == 1 || m[1] < FUNCTION || functions[m[1]-FUNCTION].spec >= TENSORFUNCTION ) { */ if ( *m == 1 || m[1] < FUNCTION ) { if ( AN.ExpectedSign ) goto nomatch; } else { if ( m[1] > FUNCTION + WILDOFFSET ) { if ( functions[m[1]-FUNCTION-WILDOFFSET].spec >= TENSORFUNCTION ) { if ( AN.ExpectedSign != AN.RepFunList[AN.RepFunNum-1] ) goto nomatch; } } else { if ( AN.ExpectedSign != AN.RepFunList[AN.RepFunNum-1] ) goto nomatch; /* if ( functions[m[1]-FUNCTION].spec >= TENSORFUNCTION ) { if ( AN.ExpectedSign != AN.RepFunList[AN.RepFunNum-1] ) goto nomatch; } */ } } AN.nogroundlevel--; AN.ExpectedSign = oExpectedSign; AN.WildArgs = wildargs; AN.WildEat = wildeat; for ( i = 0; i < wildargs; i++ ) AT.WildArgTaken[i] = wildargtaken[i]; Substitute(BHEAD csav,m,1); cto = csav; cfrom = cto + *cto - msizcoef; cto++; *m += msizcoef; AT.WorkPointer = csav; AN.RepFunList = oRepFunList; AN.RepFunNum = oRepFunNum; AN.terstart = oterstart; AN.terstop = oterstop; AN.patstop = opatstop; if ( *cto != SUBEXPRESSION ) goto endofloop; cto += cto[1]; if ( cto < cfrom ) goto endofloop; } } else goto endofloop; t = argtstop; /* Next argument */ m = argmstop; } if ( AN.SignCheck && AN.ExpectedSign ) goto endofloop; AT.WorkPointer = OldWork; if ( AN.WildArgs > 1 ) *wilds = 1; if ( AN.SignCheck && AN.ExpectedSign ) return(0); return(1); /* m was eaten. we have a match! */ endofloop:; /* restore the current Wildcard assignments */ i = nwstore; if ( i > 0 ) { m = AN.WildValue; t = OldWork + ntwa; r = AT.WildMask; do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --i > 0 ); C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } endoloop:; i = AN.WildArgs-1; if ( i <= 0 ) { AT.WorkPointer = OldWork; return(0); } while ( --i >= 0 ) { if ( AT.WildArgTaken[i] == 0 ) { if ( i == 0 ) { AT.WorkPointer = OldWork; return(0); } } else { (AT.WildArgTaken[i])--; numofwildarg = 0; for ( j = 0; j <= i; j++ ) { numofwildarg += AT.WildArgTaken[j]; } AT.WildArgTaken[j] = AN.WildEat-numofwildarg; /* ----> bug to be replaced in other source code */ for ( j++; j < AN.WildArgs; j++ ) AT.WildArgTaken[j] = 0; break; } } goto topofloop; NoCaseB: /* Restore the old Wildcard assignments */ i = nwstore; if ( i > 0 ) { m = AN.WildValue; t = OldWork + ntwa; r = AT.WildMask; do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --i > 0 ); C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } AT.WorkPointer = OldWork; return(0); /* no match */ } /* #] MatchFunction : #[ ScanFunctions : WORD ScanFunctions(inpat,inter,par) Finds in which functions to look for a match. inpat is the start of the pattern still to be matched. inter is the start of the term still to be matched. par gives information about commutativity. par = 0: nothing special par = 1: regular noncommuting function par = 2: GAMMA function AN.patstop: end of the functions field in the search pattern AN.terstop: end of the functions field in the target pattern AN.terstart: address of entire term; The actual matching of the functions and their arguments is done in a number of different routines. Mainly MatchFunction when there are no symmetry properties. Also: MatchE MatchCy FunMatchSy FunMatchCy The main problem here is backtracking, ie continuing with wildcard possibilities when a first assignment doesn't work. Important note: this was completely forgotten in the symmetric functions till 6-jan-2009. As of the moment this still has to be fixed. ??????21-mar-2023????? Is this still unfixed????? Functions inside functions can cause problems when antisymmetric functions are involved. The sign of the term may be at stake. At the lowest level this is no problem but in f(-fas(n2,n1)) this plays a role. Next is when we have a product of functions inside an argument. The strategy must be that we test the sign only at the last function. Hence, when inpat+inpat[1] >= AN.patstop. We might relax that to the last antisymmetric function at a later stage. New scheme to be implemented for non-commuting objects: When we are matching a second (or higher) function, any match can only be directly after the last matched non-commuting function or a commuting function. This will take care of whatever happens in MatchE etc. */ int ScanFunctions(PHEAD WORD *inpat, WORD *inter, WORD par) { GETBIDENTITY WORD i, *m, *t, *r, sym, psym; WORD *newpat, *newter, *instart, *oinpat = 0, *ointer = 0; WORD nwstore, offset, *OldWork, SetStop = 0, oRepFunNum = AN.RepFunNum; WORD wilds, wildargs = 0, wildeat = 0, *wildargtaken; WORD *Oterfirstcomm = AN.terfirstcomm; CBUF *C = cbuf+AT.ebufnum; int ntwa = AN.NumTotWildArgs; LONG oldcpointer = C->Pointer - C->Buffer; WORD oldSignCheck = AN.SignCheck; instart = inter; /* Only active for the last function in the pattern. The actual test on the sign is in MatchFunction or the symmetric functions */ if ( AN.nogroundlevel ) { AN.SignCheck = ( inpat + inpat[1] >= AN.patstop ) ? 1 : 0; } else { AN.SignCheck = 0; } /* Store the current Wildcard assignments */ t = wildargtaken = OldWork = AT.WorkPointer; t += ntwa; m = AN.WildValue; nwstore = i = (m[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; if ( i > 0 ) { r = AT.WildMask; do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); *t++ = C->numrhs; } if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); Terminate(-1); } AT.WorkPointer = t; do { #ifndef NEWCOMMUTE /* Find an eligible unsubstituted function */ if ( AN.RepFunNum > 0 ) { /* First try a non-commuting function, just after the last substituted non-commuting function. */ if ( *inter >= FUNCTION && functions[*inter-FUNCTION].commute ) { do { offset = WORDDIF(inter,AN.terstart); for ( i = 0; i < AN.RepFunNum; i += 2 ) { if ( AN.RepFunList[i] >= offset ) break; } if ( i >= AN.RepFunNum ) break; inter += inter[1]; } while ( inter < AN.terfirstcomm ); if ( inter < AN.terfirstcomm ) { /* Check that it is directly after */ for ( i = 0; i < AN.RepFunNum; i += 2 ) { if ( functions[AN.terstart[AN.RepFunList[i]]-FUNCTION].commute && AN.RepFunList[i]+AN.terstart[AN.RepFunList[i]+1] == offset ) break; } if ( i < AN.RepFunNum ) goto trythis; } inter = AN.terfirstcomm; } /* Now try one of the commuting functions */ while ( inter < AN.terstop ) { offset = WORDDIF(inter,AN.terstart); for ( i = 0; i < AN.RepFunNum; i += 2 ) { if ( AN.RepFunList[i] == offset ) break; } if ( i >= AN.RepFunNum ) break; inter += inter[1]; } if ( inter >= AN.terstop ) goto Failure; trythis:; } else { /* The first function can be anywhere. We have no problems. */ offset = WORDDIF(inter,AN.terstart); } #else /* first find an unsubstituted function */ do { offset = WORDDIF(inter,AN.terstart); for ( i = 0; i < AN.RepFunNum; i += 2 ) { if ( AN.RepFunList[i] == offset ) break; } if ( i >= AN.RepFunNum ) break; inter += inter[1]; } while ( inter < AN.terstop ); if ( inter >= AN.terstop ) goto Failure; #endif wilds = 0; /* We found one */ if ( *inter >= FUNCTION && *inpat >= FUNCTION ) { if ( *inpat == *inter || *inpat >= FUNCTION + WILDOFFSET ) { /* if ( inter[1] == FUNHEAD ) goto rewild; */ if ( functions[*inter-FUNCTION].spec >= TENSORFUNCTION && ( *inter == *inpat || functions[*inpat-FUNCTION-WILDOFFSET].spec >= TENSORFUNCTION ) ) { sym = functions[*inter-FUNCTION].symmetric & ~REVERSEORDER; if ( *inpat == *inter ) psym = sym; else psym = functions[*inpat-FUNCTION-WILDOFFSET].symmetric & ~REVERSEORDER; if ( sym == ANTISYMMETRIC || sym == SYMMETRIC || psym == SYMMETRIC || psym == ANTISYMMETRIC ) { if ( sym == ANTISYMMETRIC && psym == SYMMETRIC ) goto rewild; if ( sym == SYMMETRIC && psym == ANTISYMMETRIC ) goto rewild; /* Special function call for (anti)symmetric tensors */ if ( MatchE(BHEAD inpat,inter,instart,par) ) goto OnSuccess; } else if ( sym == CYCLESYMMETRIC || sym == RCYCLESYMMETRIC || psym == CYCLESYMMETRIC || psym == RCYCLESYMMETRIC ) { /* Special function call for (r)cyclic tensors */ if ( MatchCy(BHEAD inpat,inter,instart,par) ) goto OnSuccess; } else goto rewild; } else if ( functions[*inter-FUNCTION].spec <= 0 && ( *inter == *inpat || functions[*inpat-FUNCTION-WILDOFFSET].spec <= 0 ) ) { sym = functions[*inter-FUNCTION].symmetric & ~REVERSEORDER; if ( *inpat == *inter ) psym = sym; else psym = functions[*inpat-FUNCTION-WILDOFFSET].symmetric & ~REVERSEORDER; if ( psym == SYMMETRIC || sym == SYMMETRIC /* The next statement was commented out. Why???? Werkt nog niet. Teken wordt nog niet bijgehouden. 5-nov-2001 */ || psym == ANTISYMMETRIC || sym == ANTISYMMETRIC ) { if ( sym == ANTISYMMETRIC && psym == SYMMETRIC ) goto rewild; if ( sym == SYMMETRIC && psym == ANTISYMMETRIC ) goto rewild; if ( FunMatchSy(BHEAD inpat,inter,instart,par) ) goto OnSuccess; } else if ( sym == CYCLESYMMETRIC || sym == RCYCLESYMMETRIC || psym == CYCLESYMMETRIC || psym == RCYCLESYMMETRIC ) { if ( FunMatchCy(BHEAD inpat,inter,instart,par) ) goto OnSuccess; } else goto rewild; } else goto rewild; AN.terfirstcomm = Oterfirstcomm; } else if ( par > 0 ) { SetStop = 1; goto maybenext; } } else { rewild: AN.terfirstcomm = Oterfirstcomm; if ( *inter != SUBEXPRESSION && MatchFunction(BHEAD inpat,inter,&wilds) ) { AN.terfirstcomm = Oterfirstcomm; if ( wilds ) { /* Store wildcards to continue in MatchFunction if the current wildcards do not work out. */ wildargs = AN.WildArgs; wildeat = AN.WildEat; for ( i = 0; i < wildargs; i++ ) wildargtaken[i] = AT.WildArgTaken[i]; oinpat = inpat; ointer = inter; } if ( par && *inter == GAMMA && AN.RepFunList[AN.RepFunNum+1] ) { SetStop = 1; goto NoMat; } if ( par == 2 ) { if ( *inter < FUNCTION || functions[*inter-FUNCTION].commute ) { goto NoMat; } par = 1; } AN.RepFunList[AN.RepFunNum] = offset; AN.RepFunNum += 2; newpat = inpat + inpat[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AN.UsedOtherFind = 1; goto OnSuccess; } AN.RepFunNum -= 2; goto NoMat; } goto OnSuccess; } if ( *inter < FUNCTION || functions[*inter-FUNCTION].commute ) { newter = inter + inter[1]; if ( newter >= AN.terstop ) goto Failure; if ( *inter == GAMMA && inpat[1] < inter[1] - AN.RepFunList[AN.RepFunNum-1] ) { if ( ScanFunctions(BHEAD newpat,newter,2) ) goto OnSuccess; AN.terfirstcomm = Oterfirstcomm; } else if ( *newter == SUBEXPRESSION ) {} else if ( functions[*inter-FUNCTION].commute ) { if ( ScanFunctions(BHEAD newpat,newter,1) ) goto OnSuccess; AN.terfirstcomm = Oterfirstcomm; if ( ( *newpat < (FUNCTION+WILDOFFSET) && ( functions[*newpat-FUNCTION].commute == 0 ) ) || ( *newpat >= (FUNCTION+WILDOFFSET) && ( functions[*newpat-FUNCTION-WILDOFFSET].commute == 0 ) ) ) { newter = AN.terfirstcomm; if ( newter < AN.terstop && ScanFunctions(BHEAD newpat,newter,1) ) goto OnSuccess; } } else { if ( ScanFunctions(BHEAD newpat,instart,1) ) goto OnSuccess; AN.terfirstcomm = Oterfirstcomm; } SetStop = par; } else { /* Shouldn't this be newpat instead of inpat????? */ if ( par && inter > instart && ( ( *newpat < (FUNCTION+WILDOFFSET) && functions[*newpat-FUNCTION].commute ) || ( *newpat >= (FUNCTION+WILDOFFSET) && functions[*newpat-FUNCTION-WILDOFFSET].commute ) ) ) { SetStop = 1; } else { newter = instart; if ( ScanFunctions(BHEAD newpat,newter,par) ) goto OnSuccess; AN.terfirstcomm = Oterfirstcomm; } } /* Restore the old Wildcard assignments */ NoMat: i = nwstore; if ( i > 0 ) { m = AN.WildValue; t = OldWork + ntwa; r = AT.WildMask; do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --i > 0 ); C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } /* AN.RepFunNum -= 2; */ AN.RepFunNum = oRepFunNum; if ( wilds ) { inter = ointer; inpat = oinpat; AN.WildArgs = wildargs; AN.WildEat = wildeat; for ( i = 0; i < wildargs; i++ ) AT.WildArgTaken[i] = wildargtaken[i]; goto rewild; } if ( SetStop ) break; } else if ( par ) { maybenext: if ( *inpat < (FUNCTION+WILDOFFSET) ) { if ( *inpat < FUNCTION || functions[*inpat-FUNCTION].commute ) break; } else { if ( functions[*inpat-FUNCTION-WILDOFFSET].commute ) break; } }} inter += inter[1]; } while ( inter < AN.terstop ); Failure: AN.SignCheck = oldSignCheck; AT.WorkPointer = OldWork; return(0); OnSuccess: if ( AT.idallflag && AN.nogroundlevel <= 0 ) { if ( AT.idallmaxnum > 0 && AT.idallnum >= AT.idallmaxnum ) { AN.terfirstcomm = Oterfirstcomm; AN.SignCheck = oldSignCheck; AT.WorkPointer = OldWork; return(0); } SubsInAll(BHEAD0); AT.idallnum++; if ( AT.idallmaxnum == 0 || AT.idallnum < AT.idallmaxnum ) goto NoMat; } AN.terfirstcomm = Oterfirstcomm; AN.SignCheck = oldSignCheck; /* Now the disorder test */ if ( AN.DisOrderFlag && AN.RepFunNum >= 4 ) { WORD k, kk; for ( i = 2; i < AN.RepFunNum; i += 2 ) { /* ------------> We still have to copy the code from Normalize wrt properorderflag */ m = AN.terstart + AN.RepFunList[i-2]; t = AN.terstart + AN.RepFunList[i]; if ( *m != *t ) { if ( *m > *t ) continue; goto doesmatch; } if ( *m >= FUNCTION && functions[*m-FUNCTION].spec >= TENSORFUNCTION ) { k = m[1] - FUNHEAD; kk = t[1] - FUNHEAD; m += FUNHEAD; t += FUNHEAD; } else { k = m[1] - FUNHEAD; kk = t[1] - FUNHEAD; m += FUNHEAD; t += FUNHEAD; } while ( k > 0 && kk > 0 ) { if ( *m < *t ) goto NextFor; else if ( *m++ > *t++ ) goto doesmatch; k--; kk--; } if ( k > 0 ) goto doesmatch; NextFor:; } SetStop = 1; goto NoMat; } doesmatch: AT.WorkPointer = OldWork; return(1); } /* #] ScanFunctions : #] Patterns : */ form-5.0.1/sources/polywrap.cc0000644000175100017510000014631615217035721012030 /** @file polywrap.cc * * Contains methods to call the polynomial methods (written in C++) * from the rest of Form (written in C). These include polynomial * gcd computation, factorization and polyratfuns. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #include "poly.h" #include "polygcd.h" #include "polyfact.h" #include #include #include #include #include //#define DEBUG #ifdef DEBUG #include "mytime.h" #endif // denompower is increased by this factor when divmod_heap fails const int POLYWRAP_DENOMPOWER_INCREASE_FACTOR = 2; using namespace std; /* #[ poly_determine_modulus : */ /** Modulus for polynomial algebra * * Description * =========== * This method determines whether polynomial algebra is done with a * modulus or not. This depends on AC.ncmod. If only_funargs is set * it also depends on (AC.modmode & ALSOFUNARGS). * * The program terminates if the feature is not * implemented. Polynomial algebra modulo M > WORDSIZE in not * implemented. If multi_error is set, multivariate algebra mod M is * not implemented. * Notes * ===== * - If AC.ncmod>0 and only_funargs=true and * AC.modmode&ALSOFUNARGS=false, AN.ncmod is set to zero, for * otherwise RaisPow calculates mod M. */ WORD poly_determine_modulus (PHEAD bool multi_error, bool is_fun_arg, string message) { if (AC.ncmod==0) return 0; if (!is_fun_arg || (AC.modmode & ALSOFUNARGS)) { if (ABS(AC.ncmod)>1) { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: %s with modulus > WORDSIZE not implemented",message.c_str()); MUNLOCK(ErrorMessageLock); Terminate(-1); } if (multi_error && AN.poly_num_vars>1) { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: multivariate %s with modulus not implemented",message.c_str()); MUNLOCK(ErrorMessageLock); Terminate(-1); } return *AC.cmod; } AN.ncmod = 0; return 0; } /* #] poly_determine_modulus : #[ poly_gcd : */ /** Polynomial gcd * * Description * =========== * This method calculates the greatest common divisor of two * polynomials, given by two zero-terminated Form-style term lists. * * Notes * ===== * - The result is written at newly allocated memory * - Called from ratio.c * - Calls polygcd::gcd */ WORD *poly_gcd(PHEAD WORD *a, WORD *b, WORD fit) { #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { WORD *ret = flint_gcd(BHEAD a, b, fit); return ret; } #endif #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_gcd" << endl; #endif // //MesPrint("Calling poly_gcd with:"); //{ // WORD *at = a; // MesPrint(" a:"); // while ( *at ) { // MesPrint(" %a",*at,at); // at += *at; // } // MesPrint(" b:"); // at = b; // while ( *at ) { // MesPrint(" %a",*at,at); // at += *at; // } //} // Extract variables vector e; e.reserve(2); e.push_back(a); e.push_back(b); poly::get_variables(BHEAD e, false, true); // Check for modulus calculus WORD modp=poly_determine_modulus(BHEAD true, true, "polynomial GCD"); // Convert to polynomials poly pa(poly::argument_to_poly(BHEAD a, false, true), modp, 1); poly pb(poly::argument_to_poly(BHEAD b, false, true), modp, 1); // Calculate gcd poly gcd(polygcd::gcd(pa,pb)); // Allocate new memory and convert to Form notation int newsize = (gcd.size_of_form_notation()+1); WORD *res; if ( fit ) { if ( newsize*sizeof(WORD) >= (size_t)(AM.MaxTer) ) { MLOCK(ErrorMessageLock); MesPrint("poly_gcd: Term too complex (%d words). Maybe increasing MaxTermSize (%d words) can help", newsize, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } res = TermMalloc("poly_gcd"); } else { res = (WORD *)Malloc1(newsize*sizeof(WORD), "poly_gcd"); } poly::poly_to_argument(gcd, res, false); poly_free_poly_vars(BHEAD "AN.poly_vars_qcd"); // reset modulo calculation AN.ncmod = AC.ncmod; return res; } /* #] poly_gcd : #[ poly_divmod : if fit == 1 the answer must fit inside a term. */ WORD *poly_divmod(PHEAD WORD *a, WORD *b, int divmod, WORD fit) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_divmod" << endl; #endif // check for modulus calculus WORD modp=poly_determine_modulus(BHEAD false, true, "polynomial division"); // get variables vector e; e.reserve(2); e.push_back(a); e.push_back(b); poly::get_variables(BHEAD e, false, false); // add extra variables to keep track of denominators const int DENOMSYMBOL = MAXPOSITIVE; // WORD *new_poly_vars = (WORD *)Malloc1((AN.poly_num_vars+1)*sizeof(WORD), "AN.poly_vars"); // WCOPY(new_poly_vars, AN.poly_vars, AN.poly_num_vars); // new_poly_vars[AN.poly_num_vars] = DENOMSYMBOL; // if (AN.poly_num_vars > 0) // M_free(AN.poly_vars, "AN.poly_vars"); // AN.poly_num_vars++; // AN.poly_vars = new_poly_vars; AN.poly_vars[AN.poly_num_vars++] = DENOMSYMBOL; // convert to polynomials poly dena(BHEAD 0); poly denb(BHEAD 0); poly pa(poly::argument_to_poly(BHEAD a, false, true, &dena), modp, 1); poly pb(poly::argument_to_poly(BHEAD b, false, true, &denb), modp, 1); // remove contents poly numres(polygcd::integer_content(pa)); poly denres(polygcd::integer_content(pb)); pa /= numres; pb /= denres; if (divmod==0) { numres *= denb; denres *= dena; } else { denres = dena; } poly gcdres(polygcd::integer_gcd(numres,denres)); numres /= gcdres; denres /= gcdres; // determine lcoeff(b) poly lcoeffb(pb.integer_lcoeff()); poly pres(BHEAD 0); if (!lcoeffb.is_one()) { if (AN.poly_num_vars > 2) { // the original polynomial is multivariate (one dummy variable has // been added), so it is not trivial to determine which power of // lcoeff(b) can be in the answer int denompower = 0, prevdenompower = 0; poly pq(BHEAD 0); poly pr(BHEAD 0); // try denompower = 0, if this fails increase denompower until division succeeds bool div_fail = true; do { if(denompower < prevdenompower) { // denompower increased beyond INT_MAX MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: pseudo-division failed in poly_divmod (denompower > INT_MAX)"); MUNLOCK(ErrorMessageLock); Terminate(1); } if(denompower != 0) { // multiply a by lcoeffb^(denompower-prevdenompower) WORD n = lcoeffb[lcoeffb[1]]; RaisPow(BHEAD (UWORD *)&lcoeffb[2+AN.poly_num_vars], &n, denompower-prevdenompower); lcoeffb[1] = 2 + AN.poly_num_vars + ABS(n); lcoeffb[0] = 1 + lcoeffb[1]; lcoeffb[lcoeffb[1]] = n; pa *= lcoeffb; denres *= lcoeffb; } // try division poly ppow(BHEAD 0); poly::divmod_heap(pa,pb,pq,pr,false,true,div_fail); // sets div_fail // increase denompower for next iteration prevdenompower = denompower; denompower = (denompower==0 ? 1 : denompower*POLYWRAP_DENOMPOWER_INCREASE_FACTOR+1 ); // generates 2^n-1 when POLYWRAP_DENOMPOWER_INCREASE_FACTOR = 2 } while(div_fail); pres = (divmod==0 ? pq : pr); } else { // one variable, so the power is the difference of the degrees int denompower = MaX(0, pa.degree(0) - pb.degree(0) + 1); // multiply a by that power WORD n = lcoeffb[lcoeffb[1]]; RaisPow(BHEAD (UWORD *)&lcoeffb[2+AN.poly_num_vars], &n, denompower); lcoeffb[1] = 2 + AN.poly_num_vars + ABS(n); lcoeffb[0] = 1 + lcoeffb[1]; lcoeffb[lcoeffb[1]] = n; pa *= lcoeffb; denres *= lcoeffb; pres = (divmod==0 ? pa/pb : pa%pb); } } else { pres = (divmod==0 ? pa/pb : pa%pb); } // convert to Form notation // NOTE: this part can be rewritten with poly::size_of_form_notation_with_den() // and poly::poly_to_argument_with_den(). WORD *res; // special case: a=0 if (pres[0]==1) { if ( fit ) { res = TermMalloc("poly_divmod"); } else { res = (WORD *)Malloc1(sizeof(WORD), "poly_divmod"); } res[0] = 0; } else { pres *= numres; WORD nden; UWORD *den = (UWORD *)NumberMalloc("poly_divmod"); // allocate the memory; note that this overestimates the size, // since the estimated denominators are too large int ressize = pres.size_of_form_notation() + pres.number_of_terms()*2*ABS(denres[denres[1]]) + 1; if ( fit ) { if ( ressize*sizeof(WORD) > (size_t)(AM.MaxTer) ) { MLOCK(ErrorMessageLock); MesPrint("poly_divmod: Term too complex (%d words). Maybe increasing MaxTermSize (%d words) can help", ressize, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } res = TermMalloc("poly_divmod"); } else { res = (WORD *)Malloc1(ressize*sizeof(WORD), "poly_divmod"); } int L=0; for (int i=1; i!=pres[0]; i+=pres[i]) { res[L]=1; // length bool first = true; for (int j=0; j 0) { if (first) { first = false; res[L+1] = 1; // symbols res[L+2] = 2; // length } res[L+1+res[L+2]++] = AN.poly_vars[j]; // symbol res[L+1+res[L+2]++] = pres[i+1+j]; // power } if (!first) res[L] += res[L+2]; // fix length // numerator WORD nnum = pres[i+pres[i]-1]; WCOPY(&res[L+res[L]], &pres[i+pres[i]-1-ABS(nnum)], ABS(nnum)); // calculate denominator nden = denres[denres[1]]; WCOPY(den, &denres[2+AN.poly_num_vars], ABS(nden)); if (nden!=1 || den[0]!=1) Simplify(BHEAD (UWORD *)&res[L+res[L]], &nnum, den, &nden); // gcd(num,den) Pack((UWORD *)&res[L+res[L]], &nnum, den, nden); // format res[L] += 2*ABS(nnum)+1; // fix length res[L+res[L]-1] = SGN(nnum)*(2*ABS(nnum)+1); // length of coefficient L += res[L]; // fix length } res[L] = 0; NumberFree(den,"poly_divmod"); } // clean up poly_free_poly_vars(BHEAD "AN.poly_vars_divmod"); // reset modulo calculation AN.ncmod = AC.ncmod; return res; } /* #] poly_divmod : #[ poly_div : Routine divides the expression in arg1 by the expression in arg2. We did not take out special cases. The arguments are zero terminated sequences of term(s). The action is to divide arg1 by arg2: [arg1/arg2]. The answer should be a buffer (allocated by Malloc1) with a zero terminated sequence of terms (or just zero). */ WORD *poly_div(PHEAD WORD *a, WORD *b, WORD fit) { #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { WORD *ret = flint_div(BHEAD a, b, fit); return ret; } #endif #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_div" << endl; #endif return poly_divmod(BHEAD a, b, 0, fit); } /* #] poly_div : #[ poly_rem : Routine divides the expression in arg1 by the expression in arg2 and takes the remainder. We did not take out special cases. The arguments are zero terminated sequences of term(s). The action is to divide arg1 by arg2 and take the remainder: [arg1%arg2]. The answer should be a buffer (allocated by Malloc1) with a zero terminated sequence of terms (or just zero). */ WORD *poly_rem(PHEAD WORD *a, WORD *b, WORD fit) { #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { WORD *ret = flint_rem(BHEAD a, b, fit); return ret; } #endif #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_rem" << endl; #endif return poly_divmod(BHEAD a, b, 1, fit); } /* #] poly_rem : #[ poly_ratfun_read : */ /** Read a PolyRatFun * * Description * =========== * This method reads a polyratfun starting at the pointer a. The * resulting numerator and denominator are written in num and * den. If MUSTCLEANPRF, the result is normalized. * * Notes * ===== * - Calls polygcd::gcd */ void poly_ratfun_read (WORD *a, poly &num, poly &den) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_ratfun_read" << endl; #endif POLY_GETIDENTITY(num); int modp = num.modp; WORD *astop = a+a[1]; bool clean = (a[2] & MUSTCLEANPRF) == 0; a += FUNHEAD; if (a >= astop) { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: PolyRatFun cannot have zero arguments"); MUNLOCK(ErrorMessageLock); Terminate(-1); } poly den_num(BHEAD 1),den_den(BHEAD 1); num = poly::argument_to_poly(BHEAD a, true, !clean, &den_num); num.setmod(modp,1); NEXTARG(a); if (a < astop) { den = poly::argument_to_poly(BHEAD a, true, !clean, &den_den); den.setmod(modp,1); NEXTARG(a); } else { den = poly(BHEAD 1, modp, 1); } if (a < astop) { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: PolyRatFun cannot have more than two arguments"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // JD: At this point, num and den are certainly sorted into the correct order by // poly::argument_to_poly, but we can't rely on the clean flag to know if there // are any negative powers. Check for them, and set clean = false if there are any. vector minpower(AN.poly_num_vars, MAXPOSITIVE); for (int i=1; i e; e.reserve(4); for (WORD *t=t1+FUNHEAD; t AM.MaxTer/(int)sizeof(WORD)) { MLOCK(ErrorMessageLock); MesPrint ("ERROR: PolyRatFun doesn't fit in a term"); MesPrint ("(1) num size = %d, den size = %d, rest = %d, MaxTermSize = %d words", num.size_of_form_notation()+ARGHEAD, den.size_of_form_notation()+ARGHEAD, FUNHEAD + 3 + 1, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Format result in Form notation WORD *t = oldworkpointer; *t++ = AR.PolyFun; // function *t++ = 0; // length (to be determined) // *t++ &= ~MUSTCLEANPRF; // clean polyratfun *t++ = 0; FILLFUN3(t); // header poly::poly_to_argument(num,t, true); // argument 1 (numerator) if (*t>0 && t[1]==DIRTYFLAG) // to Form order poly_sort(BHEAD t); t += (*t>0 ? *t : 2); poly::poly_to_argument(den,t, true); // argument 2 (denominator) if (*t>0 && t[1]==DIRTYFLAG) // to Form order poly_sort(BHEAD t); t += (*t>0 ? *t : 2); oldworkpointer[1] = t - oldworkpointer; // length AT.WorkPointer = t; poly_free_poly_vars(BHEAD "AN.poly_vars_ratfun_add"); // reset modulo calculation AN.ncmod = AC.ncmod; return oldworkpointer; } /* #] poly_ratfun_add : #[ poly_ratfun_normalize : */ /** Multiplication/normalization of PolyRatFuns * * Description * =========== * This method searches a term for multiple polyratfuns and * multiplies their contents. The result is properly * normalized. Normalization also works for terms with a single * polyratfun. * * Notes * ===== * - The result overwrites the original term * - Called from proces.c * - Calls poly::operators and polygcd::gcd */ int poly_ratfun_normalize (PHEAD WORD *term) { #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { flint_ratfun_normalize(BHEAD term); return 0; } #endif #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_ratfun_normalize" << endl; #endif // Strip coefficient WORD *tstop = term + *term; int ncoeff = tstop[-1]; tstop -= ABS(ncoeff); // if only one clean polyratfun, return immediately int num_polyratfun = 0; for (WORD *t=term+1; t 1) break; } if (num_polyratfun <= 1) return 0; WORD oldsorttype = AR.SortType; AR.SortType = SORTHIGHFIRST; /* When there are polyratfun's with only one variable: rename them temporarily to TMPPOLYFUN. */ for (WORD *t=term+1; t e; for (WORD *t=term+1; t AM.MaxTer/(int)sizeof(WORD)) { MLOCK(ErrorMessageLock); MesPrint ("ERROR: PolyRatFun doesn't fit in a term"); MesPrint ("(2) num size = %d, den size = %d, rest = %d, MaxTermSize = %d words", num1.size_of_form_notation()+ARGHEAD, den1.size_of_form_notation()+ARGHEAD, FUNHEAD + s-term + 3, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Format result in Form notation WORD *t = s; *t++ = AR.PolyFun; // function *t++ = 0; // size (to be determined) *t++ &= ~MUSTCLEANPRF; // clean polyratfun FILLFUN3(t); // header poly::poly_to_argument(num1,t,true); // argument 1 (numerator) if (*t>0 && t[1]==DIRTYFLAG) // to Form order poly_sort(BHEAD t); t += (*t>0 ? *t : 2); poly::poly_to_argument(den1,t,true); // argument 2 (denominator) if (*t>0 && t[1]==DIRTYFLAG) // to Form order poly_sort(BHEAD t); t += (*t>0 ? *t : 2); s[1] = t - s; // function length *t++ = 1; // term coefficient *t++ = 1; *t++ = 3; term[0] = t-term; // term length poly_free_poly_vars(BHEAD "AN.poly_vars_ratfun_normalize"); // reset modulo calculation AN.ncmod = AC.ncmod; tstop = term + *term; tstop -= ABS(tstop[-1]); for (WORD *t=term+1; t0 && (var>maxvar || (var==maxvar && pow>maxpow))) { maxvar = var; maxpow = pow; sign = SGN(*(t+*t-1)); } } // if negative coefficient, multiply by -1 if (sign==-1) { a.factor[i] *= poly(BHEAD sign); if (a.power[i] % 2 == 1) overall_sign*=-1; } } // if overall minus sign if (overall_sign == -1) { // look at constant factor and multiply by -1 for (int i=0; i<(int)a.factor.size(); i++) if (a.factor[i].is_integer()) { a.factor[i] *= poly(BHEAD -1); return; } // otherwise, add a factor of -1 a.add_factor(poly(BHEAD -1), 1); } } /* #] poly_fix_minus_signs : #[ poly_factorize : */ /** Factorization of function arguments / dollars * * Description * =========== * This method factorizes a Form style argument or zero-terminated * term list. * * Notes * ===== * - Called from poly_factorize_{argument,dollar} * - Calls polyfact::factorize */ WORD *poly_factorize (PHEAD WORD *argin, WORD *argout, bool with_arghead, bool is_fun_arg) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_factorize" << endl; #endif poly::get_variables(BHEAD vector(1,argin), with_arghead, true); poly den(BHEAD 0); poly a(poly::argument_to_poly(BHEAD argin, with_arghead, true, &den)); // check for modulus calculus WORD modp=poly_determine_modulus(BHEAD true, is_fun_arg, "polynomial factorization"); a.setmod(modp,1); // factorize factorized_poly f(polyfact::factorize(a)); poly_fix_minus_signs(f); poly num(BHEAD 1); for (int i=0; i<(int)f.factor.size(); i++) if (f.factor[i].is_integer()) num = f.factor[i]; // determine size int len = with_arghead ? ARGHEAD : 0; if (!num.is_one() || !den.is_one()) { len++; len += MaX(ABS(num[num[1]]), den[den[1]])*2+1; len += with_arghead ? ARGHEAD : 1; } for (int i=0; i<(int)f.factor.size(); i++) { if (!f.factor[i].is_integer()) { len += f.power[i] * f.factor[i].size_of_form_notation(); len += f.power[i] * (with_arghead ? ARGHEAD : 1); } } len++; if (argout != NULL) { // check size if (len >= AM.MaxTer) { MLOCK(ErrorMessageLock); MesPrint ("ERROR: factorization doesn't fit in a term (len = %d, MaxTermSize = %d words)", len/sizeof(WORD), AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } } else { // allocate size argout = (WORD*) Malloc1(len*sizeof(WORD), "poly_factorize"); } WORD *old_argout = argout; // constant factor if (!num.is_one() || !den.is_one()) { int n = max(ABS(num[num[1]]), ABS(den[den[1]])); if (with_arghead) { *argout++ = ARGHEAD + 2 + 2*n; for (int i=1; i 0 ? *argout : 2; else { while (*argout!=0) argout+=*argout; argout++; } } *argout=0; poly_free_poly_vars(BHEAD "AN.poly_vars_factorize"); // reset modulo calculation AN.ncmod = AC.ncmod; return old_argout; } /* #] poly_factorize : #[ poly_factorize_argument : */ /** Factorization of function arguments * * Description * =========== * This method factorizes the Form-style argument argin. * * Notes * ===== * - The result is written at argout * - Called from argument.c * - Calls poly_factorize */ int poly_factorize_argument(PHEAD WORD *argin, WORD *argout) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_factorize_argument" << endl; #endif #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { flint_factorize_argument(BHEAD argin, argout); return 0; } #endif poly_factorize(BHEAD argin,argout,true,true); return 0; } /* #] poly_factorize_argument : #[ poly_factorize_dollar : */ /** Factorization of dollar variables * * Description * =========== * This method factorizes a dollar variable. * * Notes * ===== * - The result is written at newly allocated memory. * - Called from dollar.c * - Calls poly_factorize */ WORD *poly_factorize_dollar (PHEAD WORD *argin) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_factorize_dollar" << endl; #endif #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { return flint_factorize_dollar(BHEAD argin); } #endif return poly_factorize(BHEAD argin,NULL,false,false); } /* #] poly_factorize_dollar : #[ poly_factorize_expression : */ /** Factorization of expressions * * Description * =========== * This method factorizes an expression. * * Notes * ===== * - The result overwrites the input expression * - Called from proces.c * - Calls polyfact::factorize */ int poly_factorize_expression(EXPRESSIONS expr) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_factorize_expression" << endl; #endif GETIDENTITY; if (AT.WorkPointer + AM.MaxTer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); Terminate(-1); } WORD *term = AT.WorkPointer; WORD startebuf = cbuf[AT.ebufnum].numrhs; FILEHANDLE *file; POSITION pos; FILEHANDLE *oldinfile = AR.infile; FILEHANDLE *oldoutfile = AR.outfile; WORD oldBracketOn = AR.BracketOn; WORD *oldBrackBuf = AT.BrackBuf; WORD oldbracketindexflag = AT.bracketindexflag; char oldCommercial[COMMERCIALSIZE+2]; strcpy(oldCommercial, (char*)AC.Commercial); strcpy((char*)AC.Commercial, "factorize"); // locate is the input if (expr->status == HIDDENGEXPRESSION || expr->status == HIDDENLEXPRESSION || expr->status == INTOHIDEGEXPRESSION || expr->status == INTOHIDELEXPRESSION) { AR.InHiBuf = 0; file = AR.hidefile; AR.GetFile = 2; } else { AR.InInBuf = 0; file = AR.outfile; AR.GetFile = 0; } // read and write to expression file AR.infile = AR.outfile = file; // dummy indices are not allowed if (expr->numdummies > 0) { MesPrint("ERROR: factorization with dummy indices not implemented"); Terminate(-1); } // determine whether the expression in on file or in memory if (file->handle >= 0) { pos = expr->onfile; SeekFile(file->handle,&pos,SEEK_SET); if (ISNOTEQUALPOS(pos,expr->onfile)) { MesPrint("ERROR: something wrong in scratch file [poly_factorize_expression]"); Terminate(-1); } file->POposition = expr->onfile; file->POfull = file->PObuffer; if (expr->status == HIDDENGEXPRESSION) AR.InHiBuf = 0; else AR.InInBuf = 0; } else { file->POfill = (WORD *)((UBYTE *)(file->PObuffer)+BASEPOSITION(expr->onfile)); } SetScratch(AR.infile, &(expr->onfile)); // read the first header term WORD size = GetTerm(BHEAD term); if (size <= 0) { MesPrint ("ERROR: something wrong with expression [poly_factorize_expression]"); Terminate(-1); } // store position: this is where the output will go pos = expr->onfile; ADDPOS(pos, size*sizeof(WORD)); // use polynomial as buffer, because it is easy to extend poly buffer(BHEAD 0); int bufpos = 0; int sumcommu = 0; // read all terms while (GetTerm(BHEAD term)) { // substitute non-symbols by extra symbols sumcommu += DoesCommu(term); if ( sumcommu > 1 ) { MesPrint("ERROR: Cannot factorize an expression with more than one noncommuting object"); Terminate(-1); } buffer.check_memory(bufpos); if (LocalConvertToPoly(BHEAD term, buffer.terms + bufpos, startebuf,0) < 0) { MesPrint("ERROR: in LocalConvertToPoly [factorize_expression]"); Terminate(-1); } bufpos += *(buffer.terms + bufpos); } buffer[bufpos] = 0; // parse the polynomial AN.poly_num_vars = 0; poly::get_variables(BHEAD vector(1,buffer.terms), false, true); poly den(BHEAD 0); poly a(poly::argument_to_poly(BHEAD buffer.terms, false, true, &den)); // check for modulus calculus WORD modp=poly_determine_modulus(BHEAD true, false, "polynomial factorization"); a.setmod(modp,1); // create output SetScratch(file, &pos); NewSort(BHEAD0); CBUF *C = cbuf+AC.cbufnum; CBUF *CC = cbuf+AT.ebufnum; // turn brackets on. We force the existence of a bracket index. WORD nexpr = expr - Expressions; AR.BracketOn = 1; AT.BrackBuf = AM.BracketFactors; AT.bracketindexflag = 1; ClearBracketIndex(-nexpr-2); // Clears the index made during primary generation OpenBracketIndex(nexpr); // Set up a new index if (a.is_zero()) { expr->numfactors = 1; } else if (a.is_one() && den.is_one()) { expr->numfactors = 1; term[0] = 8; term[1] = SYMBOL; term[2] = 4; term[3] = FACTORSYMBOL; term[4] = 1; term[5] = 1; term[6] = 1; term[7] = 3; AT.WorkPointer += *term; Generator(BHEAD term, C->numlhs); AT.WorkPointer = term; } else { factorized_poly fac; bool iszero = false; if (!(expr->vflags & ISFACTORIZED)) { // factorize the polynomial fac = polyfact::factorize(a); poly_fix_minus_signs(fac); } else { int factorsymbol=-1; for (int i=0; inumfactors; i++) { poly origfac(a.coefficient(factorsymbol, i)); factorized_poly fac2; if (origfac.is_zero()) iszero=true; else { fac2 = polyfact::factorize(origfac); poly_fix_minus_signs(fac2); denpow *= den; } for (int j=0; j<(int)fac2.power.size(); j++) fac.add_factor(fac2.factor[j], fac2.power[j]); } // update denominator, since each factor was scaled den=denpow; } expr->numfactors = 0; // coefficient poly num(BHEAD 1); for (int i=0; i<(int)fac.factor.size(); i++) if (fac.factor[i].is_integer()) num *= fac.factor[i]; poly gcd(polygcd::integer_gcd(num,den)); den/=gcd; num/=gcd; if (iszero) expr->numfactors++; if (!iszero || (expr->vflags & KEEPZERO)) { if (!num.is_one() || !den.is_one()) { expr->numfactors++; int n = max(ABS(num[num[1]]), ABS(den[den[1]])); term[0] = 6 + 2*n; term[1] = SYMBOL; term[2] = 4; term[3] = FACTORSYMBOL; term[4] = expr->numfactors; for (int i=0; inumlhs); AT.WorkPointer = term; } vector fac_arg(fac.factor.size(), poly(BHEAD 0)); // convert the non-constant factors to Form-style arguments for (int i=0; i<(int)fac.factor.size(); i++) if (!fac.factor[i].is_integer()) { buffer.check_memory(fac.factor[i].size_of_form_notation()+1); poly::poly_to_argument(fac.factor[i], buffer.terms, false); NewSort(BHEAD0); for (WORD *t=buffer.terms; *t!=0; t+=*t) { // substitute extra symbols if (ConvertFromPoly(BHEAD t, term, numxsymbol, CC->numrhs-startebuf+numxsymbol, startebuf-numxsymbol, 1) <= 0 ) { MesPrint("ERROR: in ConvertFromPoly [factorize_expression]"); Terminate(-1); return(-1); } // store term AT.WorkPointer += *term; Generator(BHEAD term, C->numlhs); AT.WorkPointer = term; } // sort and store in buffer WORD *buffer; if (EndSort(BHEAD (WORD *)((void *)(&buffer)),2) < 0) return -1; LONG bufsize=0; for (WORD *t=buffer; *t!=0; t+=*t) bufsize+=*t; fac_arg[i].check_memory(bufsize+ARGHEAD+1); for (int j=0; j order; vector > comp(fac.factor.size(), vector(fac.factor.size(), 0)); for (int i=0; i<(int)fac.factor.size(); i++) if (!fac.factor[i].is_integer()) { order.push_back(i); for (int j=i+1; j<(int)fac.factor.size(); j++) if (!fac.factor[j].is_integer()) { comp[i][j] = CompArg(fac_arg[j].terms, fac_arg[i].terms); comp[j][i] = -comp[i][j]; } } for (int i=0; i<(int)order.size(); i++) for (int j=0; j+1<(int)order.size(); j++) if (comp[order[i]][order[j]] == 1) swap(order[i],order[j]); // create the final expression for (int i=0; i<(int)order.size(); i++) for (int j=0; jnumfactors++; WORD *tstop = fac_arg[order[i]].terms + *fac_arg[order[i]].terms; for (WORD *t=fac_arg[order[i]].terms+ARGHEAD; tnumfactors; // store term AT.WorkPointer += *term; Generator(BHEAD term, C->numlhs); AT.WorkPointer = term; } } } } // final sorting if (EndSort(BHEAD NULL,0) < 0) { LowerSortLevel(); Terminate(-1); } // set factorized flag if (expr->numfactors > 0) expr->vflags |= ISFACTORIZED; // clean up AR.infile = oldinfile; AR.outfile = oldoutfile; AR.BracketOn = oldBracketOn; AT.BrackBuf = oldBrackBuf; AT.bracketindexflag = oldbracketindexflag; strcpy((char*)AC.Commercial, oldCommercial); poly_free_poly_vars(BHEAD "AN.poly_vars_factorize_expression"); return 0; } /* #] poly_factorize_expression : #[ poly_unfactorize_expression : */ /** Unfactorization of expressions * * Description * =========== * This method expands a factorized expression. * * Notes * ===== * - The result overwrites the input expression * - Called from proces.c */ #if ( SUBEXPSIZE == 5 ) static WORD genericterm[] = {38,1,4,FACTORSYMBOL,0 ,EXPRESSION,15,0,1,0,13,10,8,1,4,FACTORSYMBOL,0,1,1,3 ,EXPRESSION,15,0,1,0,13,10,8,1,4,FACTORSYMBOL,0,1,1,3 ,1,1,3,0}; static WORD genericterm2[] = {23,1,4,FACTORSYMBOL,0 ,EXPRESSION,15,0,1,0,13,10,8,1,4,FACTORSYMBOL,0,1,1,3 ,1,1,3,0}; #endif int poly_unfactorize_expression(EXPRESSIONS expr) { GETIDENTITY; int i, j, nfac = expr->numfactors, nfacp, nexpr = expr - Expressions; int expriszero = 0; FILEHANDLE *oldinfile = AR.infile; FILEHANDLE *oldoutfile = AR.outfile; char oldCommercial[COMMERCIALSIZE+2]; WORD *oldworkpointer = AT.WorkPointer; WORD *term = AT.WorkPointer, *t, *w, size; FILEHANDLE *file; POSITION pos, oldpos; WORD oldBracketOn = AR.BracketOn; WORD *oldBrackBuf = AT.BrackBuf; CBUF *C = cbuf+AC.cbufnum; if ( ( expr->vflags & ISFACTORIZED ) == 0 ) return(0); if ( AT.WorkPointer + AM.MaxTer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); Terminate(-1); } oldpos = AS.OldOnFile[nexpr]; AS.OldOnFile[nexpr] = expr->onfile; strcpy(oldCommercial, (char*)AC.Commercial); strcpy((char*)AC.Commercial, "unfactorize"); /* locate the input */ if ( expr->status == HIDDENGEXPRESSION || expr->status == HIDDENLEXPRESSION || expr->status == INTOHIDEGEXPRESSION || expr->status == INTOHIDELEXPRESSION ) { AR.InHiBuf = 0; file = AR.hidefile; AR.GetFile = 2; } else { AR.InInBuf = 0; file = AR.outfile; AR.GetFile = 0; } /* read and write to expression file */ AR.infile = AR.outfile = file; /* set the input file to the correct position */ if ( file->handle >= 0 ) { pos = expr->onfile; SeekFile(file->handle,&pos,SEEK_SET); if (ISNOTEQUALPOS(pos,expr->onfile)) { MesPrint("ERROR: something wrong in scratch file unfactorize_expression"); Terminate(-1); } file->POposition = expr->onfile; file->POfull = file->PObuffer; if ( expr->status == HIDDENGEXPRESSION ) AR.InHiBuf = 0; else AR.InInBuf = 0; } else { file->POfill = (WORD *)((UBYTE *)(file->PObuffer)+BASEPOSITION(expr->onfile)); } SetScratch(AR.infile, &(expr->onfile)); /* Test for whether the first factor is zero. */ if ( GetFirstBracket(term,nexpr) < 0 ) Terminate(-1); if ( term[4] != 1 || *term != 8 || term[1] != SYMBOL || term[3] != FACTORSYMBOL || term[4] != 1 ) { expriszero = 1; } SetScratch(AR.infile, &(expr->onfile)); /* Read the prototype. After this we have the file ready for the output at pos. */ size = GetTerm(BHEAD term); if ( size <= 0 ) { MesPrint ("ERROR: something wrong with expression unfactorize_expression"); Terminate(-1); } pos = expr->onfile; ADDPOS(pos, size*sizeof(WORD)); /* Set the brackets straight */ AR.BracketOn = 1; AT.BrackBuf = AM.BracketFactors; AT.bracketinfo = 0; while ( nfac > 2 ) { nfacp = nfac - nfac%2; /* Prepare the bracket index. We have: e->bracketinfo: the old input bracket index e->newbracketinfo: the bracket index made for our current input We need to keep e->bracketinfo in case other workers need it (InParallel) Hence we work with AT.bracketinfo which takes priority. Note that in Processor we forced a newbracketinfo to be made. */ if ( AT.bracketinfo != 0 ) ClearBracketIndex(-1); AT.bracketinfo = expr->newbracketinfo; OpenBracketIndex(nexpr); /* Now emulate the terms: sum_(i,0,nfacp,2,factor_^(i/2+1)*F[factor_^(i+1)]*F[factor_^(i+2)]) +factor_^(nfacp/2+1)*F[factor_^nfac] */ NewSort(BHEAD0); if ( expriszero == 0 ) { for ( i = 0; i < nfacp; i += 2 ) { t = genericterm; w = term = oldworkpointer; j = *t; NCOPY(w,t,j); term[4] = i/2+1; term[7] = nexpr; term[16] = i+1; term[22] = nexpr; term[31] = i+2; AT.WorkPointer = term + *term; Generator(BHEAD term, C->numlhs); } if ( nfac > nfacp ) { t = genericterm2; w = term = oldworkpointer; j = *t; NCOPY(w,t,j); term[4] = i/2+1; term[7] = nexpr; term[16] = nfac; AT.WorkPointer = term + *term; Generator(BHEAD term, C->numlhs); } } if ( EndSort(BHEAD AM.S0->sBuffer,0) < 0 ) { LowerSortLevel(); Terminate(-1); } /* Set the file back into reading position */ SetScratch(file, &pos); nfac = (nfac+1)/2; if ( expriszero ) { nfac = 1; } } if ( AT.bracketinfo != 0 ) ClearBracketIndex(-1); AT.bracketinfo = expr->newbracketinfo; expr->newbracketinfo = 0; /* Reset the brackets to make them ready for the final pass */ AR.BracketOn = oldBracketOn; AT.BrackBuf = oldBrackBuf; if ( AR.BracketOn ) OpenBracketIndex(nexpr); /* We distinguish two cases: nfac == 2 and nfac == 1 After preparing the term we skip the factor_ part. */ NewSort(BHEAD0); if ( expriszero == 0 ) { if ( nfac == 1 ) { t = genericterm2; w = term = oldworkpointer; j = *t; NCOPY(w,t,j); term[7] = nexpr; term[16] = nfac; } else if ( nfac == 2 ) { t = genericterm; w = term = oldworkpointer; j = *t; NCOPY(w,t,j); term[7] = nexpr; term[16] = 1; term[22] = nexpr; term[31] = 2; } else { AS.OldOnFile[nexpr] = oldpos; return(-1); } term[4] = term[0]-4; term += 4; AT.WorkPointer = term + *term; Generator(BHEAD term, C->numlhs); } if ( EndSort(BHEAD AM.S0->sBuffer,0) < 0 ) { LowerSortLevel(); Terminate(-1); } /* Final Cleanup */ expr->numfactors = 0; expr->vflags &= ~ISFACTORIZED; if ( AT.bracketinfo != 0 ) ClearBracketIndex(-1); AR.infile = oldinfile; AR.outfile = oldoutfile; strcpy((char*)AC.Commercial, oldCommercial); AT.WorkPointer = oldworkpointer; AS.OldOnFile[nexpr] = oldpos; return(0); } /* #] poly_unfactorize_expression : #[ poly_inverse : */ WORD *poly_inverse(PHEAD WORD *arga, WORD *argb) { #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { return flint_inverse(BHEAD arga, argb); } #endif #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_inverse" << endl; #endif // Extract variables vector e; e.reserve(2); e.push_back(arga); e.push_back(argb); poly::get_variables(BHEAD e, false, true); if (AN.poly_num_vars > 1) { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: multivariate polynomial inverse is generally impossible"); MUNLOCK(ErrorMessageLock); Terminate(-1); } poly finalden(BHEAD 1), finalres(BHEAD 1); int ressize = 0; WORD *res = NULL; // Convert to polynomials poly dena(BHEAD 0); // We need to keep the overall denominator of arga, to multiply the result poly a(poly::argument_to_poly(BHEAD arga, false, true, &dena)); poly b(poly::argument_to_poly(BHEAD argb, false, true)); // Divide out the integer content, FORM has not already done this. poly content_a(BHEAD 0), content_b(BHEAD 0); content_a = polygcd::integer_content(a); content_b = polygcd::integer_content(b); a /= content_a; b /= content_b; poly invamodp(BHEAD 0), invbmodp(BHEAD 0); WORD modp = 0; // Special cases: // Possibly strange that we give 1 for inverse_(x1,1) but here we take MMA's convention. if ((a.is_one() && b.is_one()) || a.is_one()) { finalres = poly(BHEAD 1); } else if (b.is_one()) { finalres = poly(BHEAD 0); } else { // Check for modulus calculus modp=poly_determine_modulus(BHEAD true, true, "polynomial inverse"); const bool mod_calc = modp==0 ? false : true; a.setmod(modp,1); b.setmod(modp,1); // Check the gcd of a,b: if it is != 1, the inverse does not exist. poly gcd(polygcd::gcd(a,b)); if (!gcd.is_one()) { MLOCK(ErrorMessageLock); if (mod_calc) { MesPrint ((char*)"ERROR: polynomial inverse does not exist (mod %d)", modp); } else { MesPrint ((char*)"ERROR: polynomial inverse does not exist"); } MUNLOCK(ErrorMessageLock); Terminate(-1); } bool inv_exists = true; do { // If we are not using modulus calculus, find a suitable prime for xgcd: if (!mod_calc) { vector x(1,0); modp = polyfact::choose_prime(a.integer_lcoeff()*b.integer_lcoeff(), x, modp); } poly amodp(a,modp,1); poly bmodp(b,modp,1); // Calculate gcd vector xgcd(polyfact::extended_gcd_Euclidean_lifted(amodp,bmodp)); invamodp = poly(xgcd[0]); invbmodp = poly(xgcd[1]); inv_exists = ((invamodp * amodp) % bmodp).is_one(); if (!inv_exists && mod_calc) { // Control should not reach here! MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: polynomial inverse does not exist (mod %d) B", modp); MUNLOCK(ErrorMessageLock); Terminate(-1); } // If the inverse does not exist and we are not working in modulus calculus, // choose a new prime and try again. This loop should always terminate, as // we have already checked that gcd(a,b) == 1. } while (!inv_exists); // estimate of the size of the Form notation; might be extended later ressize = invamodp.size_of_form_notation()+1; res = (WORD *)Malloc1(ressize*sizeof(WORD), "poly_inverse"); // initialize polynomials to store the result poly primepower(BHEAD modp); poly inva(invamodp,modp,1); poly invb(invbmodp,modp,1); while (true) { // convert to Form notation int j=0; WORD n=0; for (int i=1; i0?4:0) + 3) { int newressize = 2*ressize; WORD *newres = (WORD *)Malloc1(newressize*sizeof(WORD), "poly_inverse"); WCOPY(newres, res, ressize); M_free(res, "poly_inverse"); res = newres; ressize = newressize; } res[j] = 1; if (inva[i+1]>0) { res[j+res[j]++] = SYMBOL; res[j+res[j]++] = 4; res[j+res[j]++] = AN.poly_vars[0]; res[j+res[j]++] = inva[i+1]; } MakeLongRational(BHEAD (UWORD *)&inva[i+2], inva[i+inva[i]-1], (UWORD*)&primepower.terms[3], primepower.terms[primepower.terms[1]], (UWORD *)&res[j+res[j]], &n); res[j] += 2*ABS(n); res[j+res[j]++] = SGN(n)*(2*ABS(n)+1); j += res[j]; } res[j]=0; // if modulus calculus is set, this is the answer if (a.modp != 0) break; // otherwise check over integers poly den(BHEAD 0); poly check(poly::argument_to_poly(BHEAD res, false, true, &den)); // Shortcut: if b's lcoeff doesn't divide the lcoeff of check*a, // b certainly doesn't divide check*a: if (poly::divides(b.integer_lcoeff(), check.integer_lcoeff()*a.integer_lcoeff())) { check = check*a - den; if (poly::divides(b, check)) break; } // if incorrect, lift with quadratic p-adic Newton's iteration. poly error((poly(BHEAD 1) - a*inva - b*invb) / primepower); poly errormodpp(error, modp, inva.modn); inva.modn *= 2; invb.modn *= 2; poly dinva((inva * errormodpp) % b); poly dinvb((invb * errormodpp) % a); inva += dinva * primepower; invb += dinvb * primepower; primepower *= primepower; } // One more round trip from form -> poly -> form, to multiply by dena in an easy way finalres = poly(poly::argument_to_poly(BHEAD res, false, true, &finalden)); } finalres *= dena; // The overall denominator additionally needs to be multiplied by content_a: finalden *= content_a; const WORD finalden_size = finalden.terms[finalden.terms[1]]; const int finalsize = finalres.size_of_form_notation_with_den(finalden_size)+1; if (ressize < finalsize) { if (res != NULL) { M_free(res, "poly_inverse"); } res = (WORD *)Malloc1(finalsize*sizeof(WORD), "poly_inverse"); } poly::poly_to_argument_with_den(finalres, finalden_size, (UWORD*)&(finalden.terms[finalden.terms[1] - ABS(finalden_size)]), res, false); // clean up and reset modulo calculation poly_free_poly_vars(BHEAD "AN.poly_vars_inverse"); AN.ncmod = AC.ncmod; return res; } /* #] poly_inverse : #[ poly_mul : */ WORD *poly_mul(PHEAD WORD *a, WORD *b) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL : poly_mul" << endl; #endif #ifdef WITHFLINT if ( AC.FlintPolyFlag && AC.ncmod==0 ) { return flint_mul(BHEAD a, b); } #endif // Extract variables vector e; e.reserve(2); e.push_back(a); e.push_back(b); poly::get_variables(BHEAD e, false, false); // TODO: any performance effect by sort_vars=true? // Convert to polynomials poly dena(BHEAD 0); poly denb(BHEAD 0); poly pa(poly::argument_to_poly(BHEAD a, false, true, &dena)); poly pb(poly::argument_to_poly(BHEAD b, false, true, &denb)); // Check for modulus calculus WORD modp = poly_determine_modulus(BHEAD true, true, "polynomial multiplication"); pa.setmod(modp, 1); // NOTE: mul_ is currently implemented by translating negative powers of // symbols to extra symbols. For future improvement, it may be better to // compute // (content(a) * content(b)) * (a/content(a)) * (b/content(b)) // to avoid introducing extra symbols for "mixed" cases, e.g., // (1+x) * (1/x) -> (1+x) * (1+Z1_). assert(dena.is_integer()); assert(denb.is_integer()); assert(modp == 0 || dena.is_one()); assert(modp == 0 || denb.is_one()); // multiplication pa *= pb; // convert to Form notation WORD *res; if (dena.is_one() && denb.is_one()) { res = (WORD *)Malloc1((pa.size_of_form_notation() + 1) * sizeof(WORD), "poly_mul"); poly::poly_to_argument(pa, res, false); } else { dena *= denb; res = (WORD *)Malloc1((pa.size_of_form_notation_with_den(dena[dena[1]]) + 1) * sizeof(WORD), "poly_mul"); poly::poly_to_argument_with_den(pa, dena[dena[1]], (const UWORD *)&dena[2+AN.poly_num_vars], res, false); } // clean up and reset modulo calculation poly_free_poly_vars(BHEAD "AN.poly_vars_mul"); AN.ncmod = AC.ncmod; return res; } /* #] poly_mul : #[ poly_free_poly_vars : */ void poly_free_poly_vars(PHEAD const char *text) { if ( AN.poly_vars_type == 0 ) { TermFree(AN.poly_vars, text); } else { M_free(AN.poly_vars, text); } AN.poly_num_vars = 0; AN.poly_vars = 0; } /* #] poly_free_poly_vars : */ form-5.0.1/sources/mytime.cc0000644000175100017510000000417715217035721011455 /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #ifdef HAVE_CONFIG_H #include #endif // A timing routine for debugging. Only on Unix (where sys/time.h is available). #ifdef UNIX #include #include #include #include #ifndef timersub /* timersub is not in POSIX, but presents on most BSD derivatives. This implementation is borrowed from glibc. (TU 23 Oct 2011) */ #define timersub(a, b, result) \ do { \ (result)->tv_sec = (a)->tv_sec - (b)->tv_sec; \ (result)->tv_usec = (a)->tv_usec - (b)->tv_usec; \ if ((result)->tv_usec < 0) { \ --(result)->tv_sec; \ (result)->tv_usec += 1000000; \ } \ } while (0) #endif bool starttime_set = false; timeval starttime; double thetime () { if (!starttime_set) { gettimeofday(&starttime,NULL); starttime_set=true; } timeval now,diff; gettimeofday(&now,NULL); timersub(&now,&starttime,&diff); return diff.tv_sec+diff.tv_usec/1000000.0; } std::string thetime_str() { char res[10]; snprintf (res,10,"%.4lf", thetime()); return res; } #endif // UNIX form-5.0.1/sources/pre.c0000644000175100017510000061621215217035721010573 /** @file pre.c * * This is the preprocessor and all its routines. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include "form3.h" #include "comtool.h" #ifdef WITHFLOAT #include "math.h" #endif static UBYTE pushbackchar = 0; static int oldmode = 0; static int stopdelay = 0; static STREAM *oldstream = 0; static UBYTE underscore[2] = {'_',0}; static PREVAR *ThePreVar = 0; static int ExitDoLoops(int, const char *); static KEYWORD precommands[] = { {"add" , DoPreAdd , 0, 0} ,{"addseparator" , DoPreAddSeparator,0,0} ,{"append" , DoPreAppend , 0, 0} ,{"appendpath" , DoPreAppendPath, 0, 0} ,{"assign" , DoPreAssign , 0, 0} ,{"break" , DoPreBreak , 0, 0} ,{"breakdo" , DoBreakDo , 0, 0} ,{"call" , DoCall , 0, 0} ,{"case" , DoPreCase , 0, 0} ,{"clearflag" , DoClearUserFlag, 0, 0} ,{"clearoptimize", DoClearOptimize, 0, 0} ,{"close" , DoPreClose , 0, 0} ,{"closedictionary", DoPreCloseDictionary,0,0} ,{"commentchar" , DoCommentChar , 0, 0} ,{"continuedo" , DoContinueDo , 0, 0} ,{"create" , DoPreCreate , 0, 0} ,{"debug" , DoDebug , 0, 0} ,{"default" , DoPreDefault , 0, 0} ,{"define" , DoDefine , 0, 0} ,{"do" , DoDo , 0, 0} ,{"else" , DoElse , 0, 0} ,{"elseif" , DoElseif , 0, 0} ,{"enddo" , DoEnddo , 0, 0} #ifdef WITHFLOAT ,{"endfloat" , DoEndFloat , 0, 0} #endif ,{"endif" , DoEndif , 0, 0} ,{"endinside" , DoEndInside , 0, 0} ,{"endnamespace" , DoEndNamespace , 0, 0} ,{"endprocedure" , DoEndprocedure , 0, 0} ,{"endswitch" , DoPreEndSwitch , 0, 0} ,{"exchange" , DoPreExchange , 0, 0} ,{"external" , DoExternal , 0, 0} ,{"factdollar" , DoFactDollar , 0, 0} ,{"fromexternal" , DoFromExternal , 0, 0} ,{"if" , DoIf , 0, 0} ,{"ifdef" , DoIfydef , 0, 0} ,{"ifndef" , DoIfndef , 0, 0} ,{"include" , DoInclude , 0, 0} ,{"inside" , DoInside , 0, 0} ,{"message" , DoMessage , 0, 0} ,{"namespace" , DoNamespace , 0, 0} ,{"opendictionary", DoPreOpenDictionary,0,0} ,{"optimize" , DoOptimize , 0, 0} ,{"pipe" , DoPipe , 0, 0} ,{"preout" , DoPreOut , 0, 0} ,{"prependpath" , DoPrePrependPath,0, 0} ,{"printtimes" , DoPrePrintTimes, 0, 0} ,{"procedure" , DoProcedure , 0, 0} ,{"procedureextension" , DoPrcExtension , 0, 0} ,{"prompt" , DoPrompt , 0, 0} ,{"redefine" , DoRedefine , 0, 0} ,{"remove" , DoPreRemove , 0, 0} ,{"reset" , DoPreReset , 0, 0} ,{"reverseinclude" , DoReverseInclude , 0, 0} ,{"rmexternal" , DoRmExternal , 0, 0} ,{"rmseparator" , DoPreRmSeparator,0, 0} ,{"setexternal" , DoSetExternal , 0, 0} ,{"setexternalattr" , DoSetExternalAttr , 0, 0} ,{"setflag" , DoSetUserFlag , 0, 0} ,{"setrandom" , DoSetRandom , 0, 0} ,{"show" , DoPreShow , 0, 0} ,{"skipextrasymbols" , DoSkipExtraSymbols , 0, 0} ,{"sortreallocate", DoPreSortReallocate , 0, 0} #ifdef WITHFLOAT ,{"startfloat" , DoStartFloat , 0, 0} #endif ,{"switch" , DoPreSwitch , 0, 0} ,{"system" , DoSystem , 0, 0} ,{"terminate" , DoTerminate , 0, 0} ,{"timeoutafter" , DoTimeOutAfter , 0, 0} ,{"toexternal" , DoToExternal , 0, 0} ,{"undefine" , DoUndefine , 0, 0} ,{"use" , DoUse , 0, 0} ,{"usedictionary", DoPreUseDictionary,0,0} ,{"write" , DoPreWrite , 0, 0} }; /* #] Includes : # [ PreProcessor : #[ GetInput : Gets one input character. If we reach the end of a stream we pop to the previous stream and try again. If there are no more streams we let this be known. */ UBYTE GetInput(void) { UBYTE c; while ( AC.CurrentStream ) { c = GetFromStream(AC.CurrentStream); if ( c != ENDOFSTREAM ) { #ifdef WITHMPI if ( PF.me == MASTER && AC.NoShowInput <= 0 && AC.CurrentStream->type != PREVARSTREAM ) #else if ( AC.NoShowInput <= 0 && AC.CurrentStream->type != PREVARSTREAM ) #endif CharOut(c); return(c); } AC.CurrentStream = CloseStream(AC.CurrentStream); if ( stopdelay && AC.CurrentStream == oldstream ) { stopdelay = 0; AP.AllowDelay = 1; } } return(ENDOFINPUT); } /* #] GetInput : #[ ClearPushback : */ void ClearPushback(void) { pushbackchar = 0; } /* #] ClearPushback : #[ GetChar : Reads one character. If it encounters a quote it immediately takes the whole preprocessor variable and opens a stream for it and starts reading the stream. Note that we have to take special precautions for escaped quotes. That is why we remember the previous character. We allow the (dubious?) construction of ending a stream with a backslash and then using it to escape an object in the parent stream. */ UBYTE GetChar(int level) { UBYTE namebuf[MAXPRENAMESIZE+2], c, *s, *t; static UBYTE lastchar, charinbuf = 0; int i, j, raiselow, olddelay; STREAM *stream; if ( level > 0 ) { lastchar = '`'; goto higherlevel; } if ( pushbackchar ) { c = pushbackchar; pushbackchar = 0; return(c); } if ( charinbuf ) { c = charinbuf; charinbuf = 0; return(c); } c = GetInput(); for(;;) { if ( c == '\\' ) { charinbuf = GetInput(); if ( charinbuf != LINEFEED ) { pushbackchar = charinbuf; charinbuf = 0; break; } charinbuf = 0; /* Escaped linefeed -> skip leading blanks */ while ( ( c = GetInput() ) == ' ' || c == '\t' ) {} } else if ( c == '\'' || c == '`' ) { if ( AP.DelayPrevar == 1 && c == '\'' ) { AP.DelayPrevar = 0; break; } lastchar = c; higherlevel: c = GetInput(); if ( c == '!' && lastchar == '`' ) { if ( stopdelay == 0 ) oldstream = AC.CurrentStream; AP.AllowDelay = 0; stopdelay = 1; c = GetInput(); } if ( c == '~' && lastchar == '`' ) { if ( AP.AllowDelay ) { pushbackchar = c; c = lastchar; AP.DelayPrevar = 1; break; } } else { pushbackchar = c; } olddelay = AP.DelayPrevar; AP.DelayPrevar = 0; i = 0; lastchar = 0; for (;;) { if ( pushbackchar ) { c = pushbackchar; pushbackchar = 0; } else { c = GetInput(); } if ( c == ENDOFINPUT || ( ( c == '\'' || c == LINEFEED ) && lastchar != '\\' ) ) { break; } if ( c == '{' ) { /* Try the preprocessor calculator */ if ( PreCalc() == 0 ) Terminate(-1); c = GetInput(); /* This is either a { or a number */ if ( c == '{' ) { MesPrint("@Illegal set inside preprocessor variable name"); Terminate(-1); } } if ( c == '`' && lastchar != '\\' ) { c = GetChar(1); if ( c == ENDOFINPUT || ( ( c == '\'' || c == LINEFEED ) && lastchar != '\\' ) ) { break; } } if ( lastchar == '\\' ) { i--; lastchar = 0; } else lastchar = c; namebuf[i++] = c; if ( i > MAXPRENAMESIZE ) { namebuf[i] = 0; Error1("Preprocessor variable name too long: ",namebuf); } } namebuf[i++] = 0; if ( c != '\'' ) { Error1("Unmatched quotes for preprocessor variable",namebuf); } AP.DelayPrevar = olddelay; if ( namebuf[0] == '$' ) { raiselow = PRENOACTION; if ( AP.PreproFlag && *AP.preStart) { s = EndOfToken(AP.preStart); c = *s; *s = 0; if ( ( StrICmp(AP.preStart,(UBYTE *)"ifdef") == 0 || StrICmp(AP.preStart,(UBYTE *)"ifndef") == 0 ) && GetDollar(namebuf+1) < 0 ) { *s = c; c = ' '; break; } *s = c; } else { s = EndOfToken(namebuf+1); if ( *s == '[' ) { while ( *s ) s++; } } if ( *s == '-' && s[1] == '-' && s[2] == 0 ) raiselow = PRELOWERAFTER; else if ( *s == '+' && s[1] == '+' && s[2] == 0 ) raiselow = PRERAISEAFTER; c = *s; *s = 0; if ( OpenStream(namebuf+1,DOLLARSTREAM,0,raiselow) == 0 ) { *s = c; MesPrint("@Undefined variable %s used as preprocessor variable", namebuf); Terminate(-1); } *s = c; } else { raiselow = PRENOACTION; if ( AP.PreproFlag && *AP.preStart) { s = EndOfToken(AP.preStart); c = *s; *s = 0; if ( ( StrICmp(AP.preStart,(UBYTE *)"ifdef") == 0 || StrICmp(AP.preStart,(UBYTE *)"ifndef") == 0 ) && GetPreVar(namebuf,WITHOUTERROR) == 0 ) { *s = c; c = ' '; break; } *s = c; } s = EndOfToken(namebuf); if ( *s == '_' ) s++; if ( *s == '-' && s[1] == '-' && s[2] == 0 ) raiselow = PRELOWERAFTER; else if ( *s == '+' && s[1] == '+' && s[2] == 0 ) raiselow = PRERAISEAFTER; else if ( *s == '(' && namebuf[i-2] == ')' ) { /* Now count the arguments and separate them by zeroes Check on the ?var construction and if present, reset some comma's. Make the assignments of the variables Run the macro. Undefine the variables */ int nargs = 1; PREVAR *p; size_t p_offset; *s++ = 0; namebuf[i-2] = 0; if ( StrICmp(namebuf,(UBYTE *)"random_") == 0 ) { UBYTE *ranvalue; ranvalue = PreRandom(s); PutPreVar(namebuf,ranvalue,0,1); M_free(ranvalue,"PreRandom"); goto dostream; } else if ( StrICmp(namebuf,(UBYTE *)"tolower_") == 0 ) { UBYTE *ss = s; while ( *ss ) { *ss = (UBYTE)(tolower(*ss)); ss++; } PutPreVar(namebuf,s,0,1); goto dostream; } else if ( StrICmp(namebuf,(UBYTE *)"toupper_") == 0 ) { UBYTE *ss = s; while ( *ss ) { *ss = (UBYTE)(toupper(*ss)); ss++; } PutPreVar(namebuf,s,0,1); goto dostream; } else if ( StrICmp(namebuf,(UBYTE *)"takeleft_") == 0 ) { UBYTE *ss = s; int x = 0, nsize; while ( *ss != ',' && *ss ) ss++; nsize = ss-s; if ( *ss ) { *ss++ = 0; while ( FG.cTable[*ss] == 1 ) x = 10*x + (*ss++ - '0'); if ( x > nsize ) x = nsize; } else x = 0; PutPreVar(namebuf,s+x,0,1); goto dostream; } else if ( StrICmp(namebuf,(UBYTE *)"takeright_") == 0 ) { UBYTE *ss = s; int x = 0, nsize; while ( *ss != ',' && *ss ) ss++; nsize = ss-s; if ( *ss ) { *ss++ = 0; while ( FG.cTable[*ss] == 1 ) x = 10*x + (*ss++ - '0'); if ( x > nsize ) x = nsize; } else x = 0; x = nsize - x; s[x] = 0; PutPreVar(namebuf,s,0,1); goto dostream; } else if ( StrICmp(namebuf,(UBYTE *)"keepleft_") == 0 ) { UBYTE *ss = s; int x = 0, nsize; while ( *ss != ',' && *ss ) ss++; nsize = ss-s; if ( *ss ) { *ss++ = 0; while ( FG.cTable[*ss] == 1 ) x = 10*x + (*ss++ - '0'); if ( x > nsize ) x = nsize; } else x = nsize; s[x] = 0; PutPreVar(namebuf,s,0,1); goto dostream; } else if ( StrICmp(namebuf,(UBYTE *)"keepright_") == 0 ) { UBYTE *ss = s; int x = 0, nsize; while ( *ss != ',' && *ss ) ss++; nsize = ss-s; if ( *ss ) { *ss++ = 0; while ( FG.cTable[*ss] == 1 ) x = 10*x + (*ss++ - '0'); if ( x > nsize ) x = nsize; } else x = nsize; x = nsize-x; PutPreVar(namebuf,s+x,0,1); goto dostream; } while ( *s ) { if ( *s == '\\' ) s++; if ( *s == ',' ) { *s = 0; nargs++; } s++; } GetPreVar(namebuf,WITHERROR); p = ThePreVar; if ( p == 0 ) { MesPrint("@Illegal use of arguments in preprocessor variable %s",namebuf); Terminate(-1); } if ( p->nargs <= 0 || ( p->wildarg == 0 && nargs != p->nargs ) || ( p->wildarg > 0 && nargs < p->nargs-1 ) ) { MesPrint("@Arguments of macro %s do not match",namebuf); Terminate(-1); } if ( p->wildarg > 0 ) { /* Change some zeroes into commas */ s = namebuf; for ( j = 0; j < p->wildarg; j++ ) { while ( *s ) s++; s++; } for ( j = 0; j < nargs-p->nargs; j++ ) { while ( *s ) s++; *s++ = ','; } } /* Now we can make the assignments */ s = namebuf; while ( *s ) s++; s++; t = p->argnames; p_offset = p - PreVar; for ( j = 0; j < p->nargs; j++ ) { if ( ( nargs == p->nargs-1 ) && ( *t == '?' ) ) { PutPreVar(t,0,0,0); } else { PutPreVar(t,s,0,0); while ( *s ) s++; s++; } p = PreVar + p_offset; while ( *t ) t++; t++; } } dostream:; if ( ( stream = OpenStream(namebuf,PREVARSTREAM,0,raiselow) ) == 0 ) { /* Eat comma before or after. This is `no value' */ } else if ( stream->inbuffer == 0 ) { c = GetInput(); if ( level > 0 && c == '\'' ) return(c); goto endofloop; } } c = GetInput(); } else if ( c == '{' ) { /* Try the preprocessor calculator */ if ( PreCalc() == 0 ) Terminate(-1); c = GetInput(); /* This is either a { or a number */ break; } else break; endofloop:; } return(c); } /* #] GetChar : #[ CharOut : */ void CharOut(UBYTE c) { if ( c == LINEFEED ) { AM.OutBuffer[AP.InOutBuf++] = c; WriteString(INPUTOUT,AM.OutBuffer,AP.InOutBuf); AP.InOutBuf = 0; } else { if ( AP.InOutBuf >= AM.OutBufSize || c == LINEFEED ) { WriteString(INPUTOUT,AM.OutBuffer,AP.InOutBuf); AP.InOutBuf = 0; } AM.OutBuffer[AP.InOutBuf++] = c; } } /* #] CharOut : #[ UnsetAllowDelay : */ void UnsetAllowDelay(void) { if ( ThePreVar != 0 ) { if ( ThePreVar->nargs > 0 ) AP.AllowDelay = 0; } } /* #] UnsetAllowDelay : #[ GetPreVar : We use the model of a heap. If the same name has been used more than once the last definition is used. This gives the impression of local variables. There are two types: The regular ones and the expression variables. The last ones are like UNCHANGED_exprname and ZERO_exprname or UNCHANGED_ and ZERO_. */ static UBYTE *yes = (UBYTE *)"1"; static UBYTE *no = (UBYTE *)"0"; static UBYTE numintopolynomial[12]; #include "vector.h" static Vector(UBYTE, exprstr); /* Used for numactiveexprs_ and activeexprnames_. */ UBYTE *GetPreVar(UBYTE *name, int flag) { GETIDENTITY int i, mode; WORD number; UBYTE *t, c = 0, *tt = 0; t = name; while ( *t ) t++; if ( t[-1] == '-' && t[-2] == '-' && t-2 > name && t[-3] != '_' ) { t -= 2; c = *t; *t = 0; tt = t; } else if ( t[-1] == '+' && t[-2] == '+' && t-2 > name && t[-3] != '_' ) { t -= 2; c = *t; *t = 0; tt = t; } else if ( StrICmp(name,(UBYTE *)"time_") == 0 ) { UBYTE millibuf[24]; LONG millitime, timepart; int timepart1, timepart2; static char timestring[40]; /* millitime = TimeCPU(1); */ millitime = GetRunningTime(); timepart = millitime%1000; millitime /= 1000; timepart /= 10; timepart1 = timepart / 10; timepart2 = timepart % 10; NumToStr(millibuf,millitime); snprintf(timestring,40,"%s.%1d%1d",millibuf,timepart1,timepart2); return((UBYTE *)timestring); } else if ( ( StrICmp(name,(UBYTE *)"timer_") == 0 ) || ( StrICmp(name,(UBYTE *)"stopwatch_") == 0 ) ) { static char timestring[40]; snprintf(timestring,40,"%ld",(long int)(GetRunningTime() - AP.StopWatchZero)); return((UBYTE *)timestring); } else if ( StrICmp(name, (UBYTE *)"numactiveexprs_") == 0 ) { /* the number of active expressions */ int n = 0; for ( i = 0; i < NumExpressions; i++ ) { EXPRESSIONS e = Expressions + i; switch ( e->status ) { case LOCALEXPRESSION: case GLOBALEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: n++; break; } } VectorReserve(exprstr, 41); /* up to 128-bit */ LongCopy(n, (char *)VectorPtr(exprstr)); return VectorPtr(exprstr); } else if ( StrICmp(name, (UBYTE *)"activeexprnames_") == 0 ) { /* the list of active expressions separated by commas */ int j = 0; VectorReserve(exprstr, 16); /* at least 1 character for '\0' */ for ( i = 0; i < NumExpressions; i++ ) { UBYTE *p, *s; int len, k; EXPRESSIONS e = Expressions + i; switch ( e->status ) { case LOCALEXPRESSION: case GLOBALEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: s = AC.exprnames->namebuffer + e->name; len = StrLen(s); VectorSize(exprstr) = j; /* j bytes must be copied in extending the buffer. */ VectorReserve(exprstr, j + len * 2 + 1); p = VectorPtr(exprstr); if ( j > 0 ) p[j++] = ','; for ( k = 0; k < len; k++ ) { if ( s[k] == ',' || s[k] == '|' ) p[j++] = '\\'; p[j++] = s[k]; } break; } } VectorPtr(exprstr)[j] = '\0'; return VectorPtr(exprstr); } else if ( StrICmp(name, (UBYTE *)"path_") == 0 ) { /* the current FORM path (for debugging both in .c and .frm) */ if ( AM.Path ) { return(AM.Path); } else { return((UBYTE *)""); } } t = name; while ( *t && *t != '_' ) t++; for ( i = NumPre-1; i >= 0; i-- ) { if ( *t == '_' && ( StrICmp(name,PreVar[i].name) == 0 ) ) { if ( c ) *tt = c; ThePreVar = PreVar+i; return(PreVar[i].value); } else if ( StrCmp(name,PreVar[i].name) == 0 ) { if ( c ) *tt = c; ThePreVar = PreVar+i; return(PreVar[i].value); } } if ( *t == '_' ) { if ( StrICmp(name,(UBYTE *)"EXTRASYMBOLS_") == 0 ) goto extrashort; *t = 0; if ( StrICmp(name,(UBYTE *)"UNCHANGED") == 0 ) mode = 1; else if ( StrICmp(name,(UBYTE *)"ZERO") == 0 ) mode = 0; else if ( StrICmp(name,(UBYTE *)"SHOWINPUT") == 0 ) { *t++ = '_'; if ( c ) *tt = c; if ( AC.NoShowInput > 0 ) return(no); else return(yes); } else if ( StrICmp(name,(UBYTE *)"EXTRASYMBOLS") == 0 ) { *t++ = '_'; extrashort:; number = cbuf[AM.sbufnum].numrhs; t = numintopolynomial; NumCopy(number,t); return(numintopolynomial); } else mode = -1; *t++ = '_'; if ( mode >= 0 ) { ThePreVar = 0; if ( *t ) { if ( GetName(AC.exprnames,t,&number,NOAUTO) == CEXPRESSION ) { if ( c ) *tt = c; if ( ( Expressions[number].vflags & ( 1 << mode ) ) != 0 ) return(yes); else return(no); } } else { /* Here we have to test all active results. These are in `negative' so the flags have to be zero. */ if ( c ) *tt = c; if ( ( AR.expflags & ( 1 << mode ) ) == 0 ) return(yes); else return(no); } } } if ( ( t = (UBYTE *)(getenv((char *)(name))) ) != 0 ) { if ( c ) *tt = c; ThePreVar = 0; return(t); } if ( c ) *tt = c; if ( flag == WITHERROR ) { Error1("Undefined preprocessor variable",name); } return(0); } /* #] GetPreVar : #[ PutPreVar : */ /** * Inserts/Updates a preprocessor variable in the name administration. * * @param name Character string with the variable name. * @param value Character string with a possible value. * Special case: if this argument is zero, then we have no * value. Note: This is different from having an empty * argument! This should only occur when the name starts * with a ? * @param args Character string with possible arguments. * @param mode =0: always create a new name entry, =1: try to do a * redefinition if possible. * @return Index of used entry in name list. */ int PutPreVar(UBYTE *name, UBYTE *value, UBYTE *args, int mode) { int i, ii, num = 2, nnum = 2, numargs = 0; UBYTE *s, *t, *u = 0; PREVAR *p; if ( value == 0 && name[0] != '?' ) { MesPrint("@Illegal empty value for preprocessor variable %s",name); Terminate(-1); } if ( args ) { s = args; num++; while ( *s ) { if ( *s != ' ' && *s != '\t' ) num++; s++; } } if ( mode == 1 ) { i = NumPre; while ( --i >= 0 ) { if ( StrCmp(name,PreVar[i].name) == 0 ) { u = PreVar[i].name; break; } } } else i = -1; if ( i < 0 ) { p = (PREVAR *)FromList(&AP.PreVarList); ii = p - PreVar; } else { p = &(PreVar[i]); ii = i; } if ( value ) { s = value; while ( *s ) { s++; num++; } } else num = 1; if ( i >= 0 ) { if ( p->value ) { s = p->value; while ( *s ) { s++; nnum++; } } else nnum = 1; if ( nnum >= num ) { /* We can keep this in place */ if ( value && p->value ) { s = value; t = p->value; while ( *s ) *t++ = *s++; *t = 0; } else p->value = 0; return(i); } } s = name; while ( *s ) { s++; num++; } t = (UBYTE *)Malloc1(num,"PreVariable"); p->name = t; s = name; while ( *s ) *t++ = *s++; *t++ = 0; if ( value ) { p->value = t; s = value; while ( *s ) *t++ = *s++; *t = 0; if ( AM.atstartup && t[-1] == '\n' ) t[-1] = 0; } else p->value = 0; p->wildarg = 0; if ( args ) { int first = 1; t++; p->argnames = t; s = args; while ( *s ) { if ( *s == ' ' || *s == '\t' ) { s++; continue; } if ( *s == ',' ) { s++; *t++ = 0; numargs++; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '?' ) { if ( p->wildarg > 0 ) { Error0("More than one ?var in #define"); } p->wildarg = numargs; } } else if ( *s == '?' && first ) { p->wildarg = 1; *t++ = *s++; } else { *t++ = *s++; } first = 0; } *t = 0; numargs++; p->nargs = numargs; } else { p->nargs = 0; p->argnames = 0; } if ( u ) M_free(u,"replace PreVar value"); return(ii); } /* #] PutPreVar : #[ PopPreVars : */ void PopPreVars(int tonumber) { PREVAR *p = &(PreVar[NumPre]); while ( NumPre > tonumber ) { NumPre--; p--; M_free(p->name,"popping PreVar"); p->name = p->value = 0; } } /* #] PopPreVars : #[ IniModule : */ void IniModule(int type) { GETIDENTITY WORD **w, i; CBUF *C = cbuf+AC.cbufnum; /*[05nov2003 mt]:*/ #ifdef WITHMPI /* To prevent * (1) FlushOut() and PutOut() on the slaves to send a mess to the master * compiling a module, * (2) EndSort() called from poly_factorize_expression() on the master * waits for the slaves. */ PF.parallel=0; /*BTW, this was the bug preventing usage of more than 1 expression!*/ #endif AR.BracketOn = 0; AR.StoreData.dirtyflag = 0; AC.bracketindexflag = 0; AT.bracketindexflag = 0; /*[06nov2003 mt]:*/ #ifdef WITHMPI /* This flag may be set in the procedure tokenize(). */ AC.RhsExprInModuleFlag = 0; /*[20oct2009 mt]:*/ PF.mkSlaveInfile=0; PF.slavebuf.PObuffer=NULL; for(i=0; irhs ) { w = C->rhs; i = C->maxrhs; do { *w++ = 0; } while ( --i > 0 ); } if ( C->lhs ) { w = C->lhs; i = C->maxlhs; do { *w++ = 0; } while ( --i > 0 ); } } C->numlhs = C->numrhs = 0; ClearTree(AC.cbufnum); while ( AC.NumLabels > 0 ) { AC.NumLabels--; if ( AC.LabelNames[AC.NumLabels] ) M_free(AC.LabelNames[AC.NumLabels],"LabelName"); } C->Pointer = C->Buffer; AC.Commercial[0] = 0; AC.IfStack = AC.IfHeap; AC.arglevel = 0; AC.termlevel = 0; AC.IfLevel = 0; AC.WhileLevel = 0; AC.RepLevel = 0; AC.insidelevel = 0; AC.dolooplevel = 0; AC.MustTestTable = 0; AO.PrintType = 0; /* Otherwise statistics can get spoiled */ AC.ComDefer = 0; AC.CollectFun = 0; AM.S0->PolyWise = 0; AC.SymChangeFlag = 0; AP.lhdollarerror = 0; AR.PolyFun = AC.lPolyFun; AR.PolyFunInv = AC.lPolyFunInv; AR.PolyFunType = AC.lPolyFunType; AR.PolyFunExp = AC.lPolyFunExp; AR.PolyFunVar = AC.lPolyFunVar; AR.PolyFunPow = AC.lPolyFunPow; AC.mparallelflag = AC.parallelflag | AM.hparallelflag; AC.inparallelflag = 0; AC.mProcessBucketSize = AC.ProcessBucketSize; NumPotModdollars = 0; AC.topolynomialflag = 0; #ifdef WITHPTHREADS if ( AM.totalnumberofthreads > 1 ) AS.MultiThreaded = 1; else AS.MultiThreaded = 0; for ( i = 1; i < AM.totalnumberofthreads; i++ ) { AB[i]->T.S0->PolyWise = 0; } #endif OpenTemp(); } /* #] IniModule : #[ IniSpecialModule : */ void IniSpecialModule(int type) { DUMMYUSE(type); } /* #] IniSpecialModule : #[ PreProcessor : */ void PreProcessor(void) { int moduletype = FIRSTMODULE; int specialtype = 0; int error1 = 0, error2 = 0, retcode, retval; UBYTE c, *t, *s; AP.StopWatchZero = GetRunningTime(); AC.compiletype = 0; AP.PreContinuation = 0; AP.PreAssignLevel = 0; AP.gNumPre = NumPre; AC.iPointer = AC.iBuffer; AC.iPointer[0] = 0; if ( AC.CheckpointFlag == -1 ) DoRecovery(&moduletype); AC.CheckpointStamp = Timer(0); for(;;) { /* if ( A.StatisticsFlag ) CharOut(LINEFEED); */ IniModule(moduletype); /*Re-define preprocessor variable CMODULE_ as a current module number, starting from 1*/ /*The module counter is AC.CModule, it is incremented in IniModule*/ { UBYTE buf[24];/*64/Log_2[10] = 19.3, this is enough for any integer*/ NumToStr(buf,AC.CModule); PutPreVar((UBYTE *)"CMODULE_",buf,0,1); } if ( specialtype ) IniSpecialModule(specialtype); for(;;) { /* Read a single line/statement */ c = GetChar(0); if ( c == AP.ComChar ) { /* This line is commentary */ LoadInstruction(5); if ( AC.CurrentStream->FoldName ) { t = AP.preStart; if ( *t && t[1] && t[2] == '#' && t[3] == ']' ) { t += 4; while ( *t == ' ' || *t == '\t' ) t++; s = AC.CurrentStream->FoldName; while ( *s == *t ) { s++; t++; } if ( *s == 0 && ( *t == ' ' || *t == '\t' || *t == ':' ) ) { while ( *t == ' ' || *t == '\t' ) t++; if ( *t == ':' ) { AC.CurrentStream = CloseStream(AC.CurrentStream); } } } } *AP.preStart = 0; continue; } while ( c == ' ' || c == '\t' ) c = GetChar(0); if ( c == LINEFEED ) continue; if ( c == ENDOFINPUT ) { /* CharOut(LINEFEED); */ Warning(".end instruction generated"); moduletype = ENDMODULE; specialtype = 0; goto endmodule; /* Fake one */ } if ( c == '#' ) { if ( PreProInstruction() ) { error1++; error2++; AP.preError++; } *AP.preStart = 0; } else if ( c == '.' ) { if ( ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) || ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) ) { LoadInstruction(1); continue; } if ( ModuleInstruction(&moduletype,&specialtype) ) { error2++; AP.preError++; } if ( specialtype ) SetSpecialMode(moduletype,specialtype); if ( AP.PreInsideLevel != 0 ) { MesPrint("@end of module instructions may not be used inside"); MesPrint("@the scope of a %#inside %#endinside construction."); Terminate(-1); } if ( AC.RepLevel > 0 ) { MesPrint("&EndRepeat statement(s) missing"); error2++; AP.preError++; } if ( AC.tablecheck == 0 ) { AC.tablecheck = 1; if ( TestTables() ) { error2++; AP.preError++; } } if ( AP.PreContinuation ) { error1++; error2++; MesPrint("&Unfinished statement. Missing ;?"); } if ( moduletype == GLOBALMODULE ) MakeGlobal(); else { endmodule: if ( error2 == 0 && AM.qError == 0 ) { retcode = ExecModule(moduletype); #ifdef WITHMPI if(PF.slavebuf.PObuffer!=NULL){ M_free(PF.slavebuf.PObuffer,"PF inbuf"); PF.slavebuf.PObuffer=NULL; } #endif UpdatePositions(); if ( retcode < 0 ) error1++; if ( retcode ) { error2++; AP.preError++; } } else { EXPRESSIONS e; WORD j; for ( j = 0, e = Expressions; j < NumExpressions; j++, e++ ) { if ( e->replace == NEWLYDEFINEDEXPRESSION ) e->replace = REGULAREXPRESSION; } } switch ( moduletype ) { case STOREMODULE: if ( ExecStore() ) error1++; break; case CLEARMODULE: FullCleanUp(); error1 = error2 = AP.preError = 0; AM.atstartup = 1; PutPreVar((UBYTE *)"DATE_",(UBYTE *)MakeDate(),0,1); AM.atstartup = 0; if ( AM.resetTimeOnClear ) { #ifdef WITHPTHREADS ClearAllThreads(); #endif AM.SumTime += TimeCPU(1); TimeCPU(0); } AP.StopWatchZero = GetRunningTime(); break; case ENDMODULE: Terminate( -( error1 | error2 ) ); } } AC.tablecheck = 0; AC.compiletype = 0; if ( AC.exprfillwarning > 0 ) { AC.exprfillwarning = 0; } if ( AC.CheckpointFlag && error1 == 0 && error2 == 0 ) DoCheckpoint(moduletype); break; /* start a new module */ } else { if ( ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) || ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) ) { pushbackchar = c; LoadInstruction(5); continue; } UngetChar(c); if ( AP.PreContinuation ) { retval = LoadStatement(OLDSTATEMENT); } else { AC.CurrentStream->prevline = AC.CurrentStream->linenumber; retval = LoadStatement(NEWSTATEMENT); } if ( retval < 0 ) { error1++; if ( retval == -1 ) AP.PreContinuation = 0; else AP.PreContinuation = 1; TryRecover(0); } else if ( retval > 0 ) AP.PreContinuation = 0; else AP.PreContinuation = 1; if ( error1 == 0 && !AP.PreContinuation ) { if ( ( AP.PreDebug & PREPROONLY ) == 0 ) { int onpmd = NumPotModdollars; #ifdef WITHMPI WORD oldRhsExprInModuleFlag = AC.RhsExprInModuleFlag; if ( AP.PreAssignFlag ) AC.RhsExprInModuleFlag = 0; #endif if ( AP.PreOut || ( AP.PreDebug & DUMPTOCOMPILER ) == DUMPTOCOMPILER ) MesPrint(" %s",AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel]); retcode = CompileStatement(AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel]); if ( retcode < 0 ) error1++; if ( retcode ) { error2++; AP.preError++; } if ( AP.PreAssignFlag ) { if ( retcode == 0 ) { if ( ( retcode = CatchDollar(0) ) < 0 ) error1++; else if ( retcode > 0 ) { error2++; AP.preError++; } } else CatchDollar(-1); POPPREASSIGNLEVEL; if ( AP.PreAssignLevel <=0 ) AP.PreAssignFlag = 0; NumPotModdollars = onpmd; #ifdef WITHMPI AC.RhsExprInModuleFlag = oldRhsExprInModuleFlag; #endif } } else { MesPrint(" %s",AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel]); } } else if ( !AP.PreContinuation ) { if ( AP.PreAssignLevel > 0 ) { POPPREASSIGNLEVEL; if ( AP.PreAssignLevel <=0 ) AP.PreAssignFlag = 0; } } /* if ( !AP.PreContinuation ) AP.PreAssignFlag = 0; */ } } } } /* #] PreProcessor : #[ PreProInstruction : */ int PreProInstruction(void) { UBYTE *s, *t; KEYWORD *key; AP.PreproFlag = 1; AP.preFill = 0; AP.AllowDelay = 0; AP.DelayPrevar = 0; oldmode = 0; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) { LoadInstruction(3); if ( ( StrICmp(AP.preStart,(UBYTE *)"case") == 0 || StrICmp(AP.preStart,(UBYTE *)"default") == 0 ) && AP.PreSwitchModes[AP.PreSwitchLevel] == SEARCHINGPRECASE ) { LoadInstruction(0); } else if ( StrICmp(AP.preStart,(UBYTE *)"assign ") == 0 ) {} else { LoadInstruction(1); } } else if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) { LoadInstruction(3); if ( ( StrICmp(AP.preStart,(UBYTE *)"else") == 0 || StrICmp(AP.preStart,(UBYTE *)"elseif") == 0 ) && AP.PreIfStack[AP.PreIfLevel] == LOOKINGFORELSE ) { LoadInstruction(0); } else if ( StrICmp(AP.preStart,(UBYTE *)"assign ") == 0 ) {} else { LoadInstruction(1); } } else { LoadInstruction(0); } AP.PreproFlag = 0; t = AP.preStart; if ( *t == '-' ) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] == EXECUTINGPRESWITCH && AP.PreIfStack[AP.PreIfLevel] == EXECUTINGIF ) AC.NoShowInput = 1; } else if ( *t == '+' ) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] == EXECUTINGPRESWITCH && AP.PreIfStack[AP.PreIfLevel] == EXECUTINGIF ) AC.NoShowInput = 0; } else if ( *t == ':' ) {} else { retry:; key = FindKeyWord(t,precommands,sizeof(precommands)/sizeof(KEYWORD)); s = EndOfToken(t); if ( key == 0 ) { if ( *s == ';' ) { *s = 0; goto retry; } else { *s = 0; MesPrint("@Unrecognized preprocessor instruction: %s",t); return(-1); } } while ( *s == ' ' || *s == '\t' || *s == ',' ) s++; t = s; while ( *t ) t++; while ( ( t[-1] == ';' ) && ( t[-2] != '\\' ) ) { t--; *t = 0; } return((key->func)(s)); } return(0); } /* #] PreProInstruction : #[ LoadInstruction : 0: preprocessor instruction that may involve matching of brackets 1: runs straight to end-of-line 2: runs to ; 3: only gets one word without `' interpretation. 5: with pushbackchar, but inside commentary. -> 1 To be added: In define, redefine, call and listed do we may have delayed substitution of preprocessor variables. */ int LoadInstruction(int mode) { UBYTE *s, *sstart, *t, c, cp; LONG position, fillpos = 0; int bralevel = 0, parlevel = 0, first = 1; int quotelevel = 0; if ( AP.preFill ) { s = AP.preFill; AP.preFill = 0; if ( s[1] != LINEFEED && s[1] != ENDOFINPUT ) { s[0] = s[1]; s++; } else { oldmode = mode; return(0); } } else { s = AP.preStart; } sstart = s; *s = 0; for(;;) { if ( ( mode & 1 ) == 1 ) { if ( pushbackchar && ( mode == 3 || mode == 5 ) ) { c = pushbackchar; pushbackchar = 0; } else c = GetInput(); } else { c = GetChar(0); } if ( mode == 2 && c == ';' ) break; if ( ( mode == 1 || mode == 5 ) && c == LINEFEED ) break; if ( mode == 3 && FG.cTable[c] != 0 ) { if ( c == '$' ) { pushbackchar = '$'; *s++ = 'a'; *s++ = 's'; *s++ = 's'; *s++ = 'i'; *s++ = 'g'; *s++ = 'n'; *s++ = ' '; *s = 0; } if ( c == '\'' || c == '`' ) { /* we do not expand preprocessor variables */ mode = 1; } else { AP.preFill = s; *s++ = 0; *s = c; oldmode = mode; return(0); } } if ( mode == 0 && first ) { if ( c == '$' ) { dodollar: s = sstart; *s++ = 'a'; *s++ = 's'; *s++ = 's'; *s++ = 'i'; *s++ = 'g'; *s++ = 'n'; *s = 0; pushbackchar = c; oldmode = mode; return(0); } if ( c == ' ' || c == '\t' || c == ',' ) {} else first = 0; } else if ( mode == 1 && first && c == '$' && oldmode == 3 ) goto dodollar; if ( c == ENDOFINPUT || ( c == LINEFEED /* && bralevel == 0 */ && quotelevel == 0 ) ) { if ( mode == 2 && c == ENDOFINPUT ) { MesPrint("@Unexpected end of instruction"); oldmode = mode; return(-1); } /* if ( mode == 0 && bralevel ) { MesPrint("@Unmatched brackets"); oldmode = mode; return(-1); } */ if ( mode != 2 ) break; } if ( quotelevel ) { if ( c == '\\' ) { if ( ( mode == 1 ) || ( mode == 5 ) ) c = GetInput(); else { c = GetChar(0); } if ( c == ENDOFINPUT ) { MesPrint("@Unmatched \""); if ( mode == 2 && c == ENDOFINPUT ) { MesPrint("@Unexpected end of instruction"); } /* if ( mode == 0 && bralevel ) { MesPrint("@Unmatched brackets"); } */ oldmode = mode; return(-1); } else if ( c == LINEFEED ) {} else if ( c == '"' ) { *s++ = '\\'; } else { *s++ = '\\'; } } else if ( c == '"' ) { quotelevel = 0; AP.AllowDelay = 0; } } else if ( c == '\\' ) { if ( ( mode == 1 ) || ( mode == 5 ) ) cp = GetInput(); else { cp = GetChar(0); } if ( cp == LINEFEED ) continue; if ( mode != 2 || cp != ';' ) *s++ = c; c = cp; } else if ( c == '"' ) { /* Now look back in the buffer and determine what the keyword is. If it is define or redefine, put AllowDelay to 1. */ t = AP.preStart; while ( FG.cTable[*t] <= 1 ) t++; cp = *t; *t = 0; if ( ( StrICmp(AP.preStart,(UBYTE *)"define") == 0 ) || ( StrICmp(AP.preStart,(UBYTE *)"redefine") == 0 ) ) { AP.AllowDelay = 1; oldstream = AC.CurrentStream; } *t = cp; quotelevel = 1; } else if ( quotelevel == 0 && bralevel == 0 && c == '(' ) { t = AP.preStart; while ( FG.cTable[*t] <= 1 ) t++; cp = *t; *t = 0; if ( ( parlevel == 0 ) && ( StrICmp(AP.preStart,(UBYTE *)"call") == 0 ) ) { AP.AllowDelay = 1; oldstream = AC.CurrentStream; } *t = cp; parlevel++; } else if ( quotelevel == 0 && bralevel == 0 && c == ')' ) { parlevel--; } else if ( quotelevel == 0 && parlevel == 0 && c == '{' ) { t = AP.preStart; while ( FG.cTable[*t] <= 1 ) t++; cp = *t; *t = 0; if ( ( bralevel == 0 ) && ( ( StrICmp(AP.preStart,(UBYTE *)"call") == 0 ) || ( StrICmp(AP.preStart,(UBYTE *)"do") == 0 ) ) ) { AP.AllowDelay = 1; oldstream = AC.CurrentStream; } *t = cp; bralevel++; } else if ( quotelevel == 0 && parlevel == 0 && c == '}' ) { bralevel--; if ( bralevel < 0 ) { if ( mode != 5 ) { MesPrint("@Unmatched brackets"); oldmode = mode; return(-1); } bralevel = 0; } } if ( s >= (AP.preStop-1) ) { UBYTE **ppp; position = s - AP.preStart; if ( AP.preFill ) fillpos = AP.preFill - AP.preStart; ppp = &(AP.preStart); /* to avoid a compiler warning */ if ( DoubleLList((void ***)ppp,&AP.pSize,sizeof(UBYTE), "instruction buffer") ) { *s = 0; oldmode = mode; return(-1); } AP.preStop = AP.preStart + AP.pSize-3; s = AP.preStart + position; if ( AP.preFill ) AP.preFill = fillpos + AP.preStart; } *s++ = c; } *s = 0; oldmode = mode; if ( mode == 0 ) { if ( ExpandTripleDots(1) < 0 ) return(-1); } return(0); } /* #] LoadInstruction : #[ LoadStatement : Puts the current string together in the input buffer. Does things like placing comma's where needed and expand ... We force a comma after the keyword. Before 8-sep-2009 the program might not put a comma if a + or - followed. And then the compiler ate the + or - and we needed repair code in the routines that used the + or - (Print, modulus, multiply and (a)bracket). This worked but the problem was with statements like Dimension -4; which then would be processed as Dimension 4; (JV) */ int LoadStatement(int type) { UBYTE *s, c, cp; int retval = 0, stringlevel = 0, newstatement = 0; if ( type == NEWSTATEMENT ) { AP.eat = 1; newstatement = 1; s = AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel]; } else { s = AC.iPointer; *s = 0; c = ' '; goto blank; } *s = 0; for(;;) { c = GetChar(0); if ( c == ENDOFINPUT ) { retval = -1; break; } if ( stringlevel == 0 ) { if ( c == LINEFEED ) { if ( AP.eat < 0 ) { s--; AP.eat = 0; } retval = 0; break; } if ( c == ';' ) { if ( AP.eat < 0 ) { s--; AP.eat = 0; } while ( ( c = GetChar(0) ) == ' ' || c == '\t' ) {} if ( c != LINEFEED ) UngetChar(c); retval = 1; break; } } if ( c == '\\' ) { cp = GetChar(0); if ( cp == LINEFEED ) continue; *s++ = c; c = cp; } if ( c == '"' ) { if ( stringlevel == 0 ) stringlevel = 1; else stringlevel = 0; AP.eat = 0; } else if ( stringlevel == 0 ) { if ( c == '\t' ) c = ' '; if ( c == ' ' ) { blank: if ( newstatement < 0 ) newstatement = 0; if ( AP.eat && ( newstatement == 0 ) ) continue; c = ','; AP.eat = -2; if ( newstatement > 0 ) newstatement = -1; } else if ( chartype[c] <= 3 ) { AP.eat = 0; if ( newstatement < 0 ) newstatement = 0; } else if ( c == ',' ) { if ( newstatement > 0 ) { newstatement = -1; AP.eat = -2; } /* else if ( AP.eat == -2 ) { s--; } */ else if ( AP.eat == -2 ) { AP.eat = 1; continue; } else { goto doall; } } else { doall:; if ( AP.eat < 0 ) { if ( newstatement == 0 ) s--; else { newstatement = 0; } } else if ( newstatement == 1 ) newstatement = 0; AP.eat = 1; if ( c == '*' && s > AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel] && s[-1] == '*' ) { s[-1] = '^'; continue; } } } if ( s >= AC.iStop ) { if ( !AP.iBufError ) { LONG position = s - AC.iBuffer; LONG position2 = AC.iPointer - AC.iBuffer; UBYTE **ppp = &(AC.iBuffer); /* to avoid a compiler warning */ if ( DoubleLList((void ***)ppp,&AC.iBufferSize ,sizeof(UBYTE),"statement buffer") ) { *s = 0; retval = -1; AP.iBufError = 1; } AC.iPointer = AC.iBuffer + position2; AC.iStop = AC.iBuffer + AC.iBufferSize-2; s = AC.iBuffer + position; } if ( AP.iBufError ) { for(;;){ c = GetChar(0); if ( c == ENDOFINPUT ) { retval = -1; break; } if ( c == '"' ) { if ( stringlevel > 0 ) stringlevel = 0; else stringlevel = 1; } else if ( c == LINEFEED && !stringlevel ) { retval = -2; break; } else if ( c == ';' && !stringlevel ) { while ( ( c = GetChar(0) ) == ' ' || c == '\t' ) {} if ( c != LINEFEED ) UngetChar(c); retval = -1; break; } else if ( c == '\\' ) c = GetChar(0); } break; } } *s++ = c; } AC.iPointer = s; *s = 0; if ( stringlevel > 0 ) { MesPrint("@Unbalanced \". Runaway string"); retval = -1; } if ( retval == 1 ) { if ( ExpandTripleDots(0) < 0 ) retval = -1; } return(retval); } /* #] LoadStatement : #[ ExpandTripleDots : */ static inline int IsSignChar(UBYTE c) { return c == '+' || c == '-'; } static inline int IsAlphanumericChar(UBYTE c) { return FG.cTable[c] == 0 || FG.cTable[c] == 1; } static inline int CanParseSignedNumber(const UBYTE *s) { while ( IsSignChar(*s) ) s++; return FG.cTable[*s] == 1; } int ExpandTripleDots(int par) { UBYTE *s, *s1, *s2, *n1, *n2, *t1, *t2, *startp, operator1, operator2, c, cc; UBYTE *nBuffer, *strngs, *Buffer, *Stop; LONG withquestion, x1, x2, y1, y2, number, inc, newsize, pow, fullsize; int i, error = 0, i1 ,i2, ii, *nums = 0; if ( par == 0 ) { Buffer = AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel]; Stop = AC.iStop; } else { Buffer = AP.preStart; Stop = AP.preStop; } s = Buffer; while ( *s ) s++; fullsize = s - Buffer; if ( fullsize < 7 ) return(error); s = Buffer+2; while ( *s ) { if ( *s != '.' || ( s[-1] != ',' && FG.cTable[s[-1]] != 5 ) ) { s++; continue; } if ( s[-1] == '%' || s[-1] == '^' || s[1] != '.' || s[2] != '.' ) { s++; continue; } s1 = s - 2; s += 3; if ( *s != s[-4] && ( *s != '+' || s[-4] != '-' ) && ( *s != '-' || s[-4] != '+' ) ) { MesPrint("&Improper operators for ..."); error = -1; } operator1 = s[-4]; operator2 = *s++; if ( operator1 == ':' ) operator1 = '.'; if ( operator2 == ':' ) operator2 = '.'; /* We have now O1...O2 (O stands for operator) Full syntax is [str]#1[?]O1...O2[str]#2[?] (Special case) in which both strings are identical and if one ? then also the other. O1...O2 (General case) in which the difference in the patterns is just numerical. */ s2 = s; /* the beginning of the second string */ if ( *s2 != '<' || *s1 != '>' ) { /* Special case */ startp = s1+1; withquestion = ( *s1 == '?' ); s1--; while ( FG.cTable[*s1] == 1 && s1 >= Buffer ) s1--; n1 = s1+1; /* Beginning of first number */ if ( FG.cTable[*n1] != 1 ) { MesPrint("&No first number in ... operator"); error = -1; } while ( FG.cTable[*s1] <= 1 && s1 >= Buffer ) s1--; s1++; /* We have now the first string from s1 to n1, number from n1 */ t1 = s1; t2 = s2; while ( t1 < n1 && *t1 == *t2 ) { t1++; t2++; } n2 = t2; if ( FG.cTable[*t2] != 1 ) { MesPrint("&No second number in ... operator"); error = -1; } x2 = 0; while ( FG.cTable[*t2] == 1 ) x2 = 10*x2 + *t2++ - '0'; x1 = 0; while ( FG.cTable[*t1] == 1 ) x1 = 10*x1 + *t1++ - '0'; if ( withquestion != ( *t2 == '?' ) ) { MesPrint("&Improper use of ? in ... operator"); if ( *t2 == '?' ) t2++; error = -1; } else if ( withquestion ) t2++; if ( FG.cTable[*t2] <= 2 ) { MesPrint("&Illegal object after ... construction"); error = -1; } c = *n1; *n1 = 0; s = t2; if ( error ) continue; /* At this point the syntax has been fulfilled. We have str in s1. x1,x2 are #1,#2 operator1,operator2 are the two operators. s points at whatever comes after. Expansion will have to be computed. */ if ( x2 < x1 ) { number = x1-x2; inc = -1; y1 = x2; y2 = x1; } else { number = x2-x1; inc = 1; y1 = x1; y2 = x2; } newsize = (number+1)*(n1-s1) /* the strings */ + number /* the operators */ +(number+1)*(withquestion?1:0) /* questionmarks */ +(number+1); /* last digits */ pow = 10; for ( i = 1; i < 10; i++, pow *= 10 ) { if ( y1 >= pow ) newsize += number+1; else if ( y2 >= pow ) newsize += y2-pow+1; else break; } while ( Buffer+(fullsize+newsize-(s-s1)) >= Stop ) { LONG strpos = s1-Buffer; LONG endstr = n1-Buffer; LONG startq = startp - Buffer; LONG position = s - Buffer; UBYTE **ppp; if ( par == 0 ) { LONG position2 = AC.iPointer - AC.iBuffer; ppp = &(AC.iBuffer); /* to avoid a compiler warning */ if ( DoubleLList((void ***)ppp,&AC.iBufferSize ,sizeof(UBYTE),"statement buffer") ) { Terminate(-1); } AC.iPointer = AC.iBuffer + position2; AC.iStop = AC.iBuffer + AC.iBufferSize-2; Buffer = AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel]; Stop = AC.iStop; } else { LONG fillpos = 0; if ( AP.preFill ) fillpos = AP.preFill - AP.preStart; ppp = &(AP.preStart); /* to avoid a compiler warning */ if ( DoubleLList((void ***)ppp,&AP.pSize,sizeof(UBYTE), "instruction buffer") ) { Terminate(-1); } AP.preStop = AP.preStart + AP.pSize-3; if ( AP.preFill ) AP.preFill = fillpos + AP.preStart; Buffer = AP.preStart; Stop = AP.preStop; } s = Buffer + position; n1 = Buffer + endstr; s1 = Buffer + strpos; startp = Buffer + startq; } /* We have space for the expansion in the buffer. There are two cases: new size > old size old size >= new size Note that whereever we move things, it will be at least startp. */ if ( newsize > (s-s1) ) { t2 = Buffer + fullsize; t1 = t2 + (newsize - (s-s1)); *t1 = 0; while ( t2 > s ) { *--t1 = *--t2; } } else if ( newsize < (s-s1) ) { t1 = s1 + newsize; t2 = s; s = t1; while ( *t2 ) *t1++ = *t2++; *t1 = 0; } for ( x1 += inc, t1 = startp; number > 0; number--, x1 += inc ) { *t1++ = operator1; cc = operator1; operator1 = operator2; operator2 = cc; t2 = s1; while ( *t2 ) *t1++ = *t2++; x2 = x1; n2 = t1; do { *t1++ = '0' + x2 % 10; x2 /= 10; } while ( x2 ); s2 = t1 - 1; while ( s2 > n2 ) { cc = *s2; *s2 = *n2; *n2++ = cc; s2--; } if ( withquestion ) *t1++ = '?'; } fullsize += newsize - ( s - s1 ); *n1 = c; } else { /* General case. Find the patterns first */ t1 = s1; s1--; while ( s1 > Buffer ) { if ( *s1 == '<' ) break; s1--; } t2 = s2; while ( *t2 ) { if ( *t2 == '>' ) break; t2++; } if ( *s1 != '<' || *t2 != '>' ) { MesPrint("&Illegal attempt to use ... operator"); return(-1); } s1++; s2++; /* Pointers to the patterns */ nums = (int *)Malloc1((t1-s1)*2*(sizeof(int)+sizeof(UBYTE)) ,"Expand ..."); strngs = (UBYTE *)(nums + 2*(t1-s1)); n1 = s1; n2 = s2; ii = -1; i = 0; s = strngs; while ( n1 < t1 || n2 < t2 ) { /* Check the next characters can be parsed as numbers including signs. */ if ( CanParseSignedNumber(n1) && CanParseSignedNumber(n2) ) { /* * Don't allow the cases that one has the sign and the other doesn't, * and the meaning changes without the sign. For example, * +...+ Allowed * +...+ Allowed * +...+ Allowed * +...+ Not allowed */ int sign1 = IsSignChar(*n1); int sign2 = IsSignChar(*n2); int inword1 = s1 < n1 && IsAlphanumericChar(n1[-1]); int inword2 = s2 < n2 && IsAlphanumericChar(n2[-1]); if ( ( sign1 ^ sign2 ) && ( inword1 || inword2 ) ) break; /* Not allowed. */ if ( sign1 || sign2 ) { *s++ = '+'; /* Marker indicating we need the sign. */ } } else { /* If they are not numbers, they should be same. */ if ( *n1 == *n2 ) { *s++ = *n1++; n2++; continue; } else break; } ParseSignedNumber(x1,n1) ParseSignedNumber(x2,n2) if ( x1 == x2 ) { if ( s != strngs && ( s[-1] == '+' || s[-1] == '-' ) ) { /* We need the sign. */ s--; if ( x1 >= 0 ) { *s++ = '+'; } } s = NumCopy(x1, s); } else { nums[2*i] = x1; nums[2*i+1] = x2; i++; *s++ = 0; } } if ( n1 < t1 || n2 < t2 ) { MesPrint("&Improper use of ... operator."); theend: M_free(nums,"Expand ..."); return(-1); } *s = 0; if ( i == 0 ) ii = 0; else { ii = nums[0] - nums[1]; if ( ii < 0 ) ii = -ii; for ( x1 = 1; x1 < i; x1++ ) { x2 = nums[2*x1]-nums[2*x1+1]; if ( x2 < 0 ) x2 = -x2; if ( x2 != ii ) { MesPrint("&Improper synchronization of numbers in ... operator"); goto theend; } } } ii++; /* We have now proper syntax. There are i+1 strings in strngs and i pairs of numbers in nums. Each time a start value and a finish value. We have ii steps. If ii <= 2, it will fit in the existing allocation. But this is hardly useful. We make a new allocation and copy from the old. Compute space. */ x2 = s - strngs - i; /* -1 for end-of-string and +1 for the operator*/ for ( i1 = 0; i1 < i; i1++ ) { i2 = nums[2*i1]; x1 = nums[2*i1+1]; if ( i2 < 0 ) i2 = -i2; if ( x1 < 0 ) x1 = -x1; if ( x1 > i2 ) i2 = x1; x1 = 2; while ( i2 > 0 ) { i2 /= 10; x1++; } x2 += x1; } x2 *= ii; /* Space for the expanded string (a bit more) */ x2 += fullsize; x2 += 5; /* This will definitely hold everything */ x2 += sizeof(UBYTE *); x2 = x2 - (x2 & (sizeof(UBYTE *)-1)); nBuffer = (UBYTE *)Malloc1(x2,"input buffer"); n1 = nBuffer; s = Buffer; s1--; while ( s < s1 ) *n1++ = *s++; /* Solution of the special case that no comma was generated due to the presence of < to start the pattern. We get a comma when the word before ends in an alphanumeric character, a _ or a ] and the word inside starts with an alphanumeric character, a [ (or an _ (for future considerations)) */ if ( ( ( n1 > nBuffer ) && ( ( FG.cTable[n1[-1]] <= 1 ) || ( n1[-1] == '_' ) || ( n1[-1] == ']' ) ) ) && ( ( FG.cTable[strngs[0]] <= 1 ) || ( strngs[0] == '[' ) || ( strngs[0] == '_' ) ) ) *n1++ = ','; for ( i1 = 0; i1 < ii; i1++ ) { s = strngs; while ( *s ) *n1++ = *s++; for ( i2 = 0; i2 < i; i2++ ) { if ( n1 > nBuffer && IsSignChar(n1[-1]) ) { /* We need the sign of counters. */ n1--; if ( nums[2*i2] >= 0 ) { *n1++ = '+'; } } n1 = NumCopy((WORD)(nums[2*i2]),n1); if ( nums[2*i2] > nums[2*i2+1] ) nums[2*i2]--; else nums[2*i2]++; s++; while ( *s ) *n1++ = *s++; } if ( ( i1 & 1 ) == 0 ) *n1++ = operator1; else *n1++ = operator2; } n1--; /* drop the trailing operator */ s = t2 + 1; n2 = n1; /* Similar extra comma */ if ( ( ( ( FG.cTable[n1[-1]] <= 1 ) || ( n1[-1] == '_' ) || ( n1[-1] == ']' ) ) ) && ( ( FG.cTable[s[0]] <= 1 ) || ( s[0] == '[' ) || ( s[0] == '_' ) ) ) *n1++ = ','; while ( *s ) *n1++ = *s++; *n1 = 0; if ( par == 0 ) { LONG nnn1 = n1-nBuffer; LONG nnn2 = n2-nBuffer; LONG nnn3; while ( AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel] + x2 >= AC.iStop ) { LONG position = s-Buffer; LONG position2 = AC.iPointer - AC.iBuffer; UBYTE **ppp; ppp = &(AC.iBuffer); /* to avoid a compiler warning */ if ( DoubleLList((void ***)ppp,&AC.iBufferSize ,sizeof(UBYTE),"statement buffer") ) { Terminate(-1); } AC.iPointer = AC.iBuffer + position2; AC.iStop = AC.iBuffer + AC.iBufferSize-2; Buffer = AC.iBuffer+AP.PreAssignStack[AP.PreAssignLevel]; Stop = AC.iStop; s = Buffer + position; } /* This can be improved. We only have to start from the first term. */ for ( nnn3 = 0; nnn3 < nnn1; nnn3++ ) Buffer[nnn3] = nBuffer[nnn3]; Buffer[nnn3] = 0; n1 = Buffer + nnn1; n2 = Buffer + nnn2; M_free(nBuffer,"input buffer"); M_free(nums,"Expand ..."); } else { /* Comes here only inside a real preprocessor instruction */ AP.preStop = nBuffer + x2 - 2; AP.pSize = x2; M_free(AP.preStart,"input buffer"); M_free(nums,"Expand ..."); AP.preStart = nBuffer; Buffer = AP.preStart; Stop = AP.preStop; } fullsize = n1 - Buffer; s = n2; } } return(error); } /* #] ExpandTripleDots : #[ FindKeyWord : */ KEYWORD *FindKeyWord(UBYTE *theword, KEYWORD *table, int size) { int low,med,hi; UBYTE *s1, *s2; low = 0; hi = size-1; while ( hi >= low ) { med = (hi+low)/2; s1 = (UBYTE *)(table[med].name); s2 = theword; while ( *s1 && tolower(*s1) == tolower(*s2) ) { s1++; s2++; } if ( *s1 == 0 && /*[30apr2004 mt]:*/ /* The bug!: FG.cTable[*s2] != 1 && FG.cTable[*s2] != 2 */ FG.cTable[*s2] != 0 && FG.cTable[*s2] != 1 /* ( *s2 == ' ' || *s2 == '\t' || *s2 == 0 || *s2 == ',' || *s2 == '(' ) */ ) return(table+med); if ( tolower(*s2) > tolower(*s1) ) low = med+1; else hi = med - 1; } return(0); } /* #] FindKeyWord : #[ FindInKeyWord : */ KEYWORD *FindInKeyWord(UBYTE *theword, KEYWORD *table, int size) { int i; UBYTE *s1, *s2; for ( i = 0; i < size; i++ ) { s1 = (UBYTE *)(table[i].name); s2 = theword; while ( *s1 && tolower(*s1) == tolower(*s2) ) { s1++; s2++; } if ( *s2 == 0 || *s2 == ' ' || *s2 == ',' || *s2 == '\t' ) return(table+i); } return(0); } /* #] FindInKeyWord : #[ TheDefine : */ /** * Preprocessor assignment. Possible arguments and values are treated and the * new preprocessor variable is put into the name administration. * * @param s Pointer to the character string following the preprocessor * command. * @param mode Bitmask. 0-bit clear: always create a new name entry, 0-bit * set: try to redefine an existing name, 1-bit set: ignore * preprocessor if/switch status. * @return zero: no errors, negative number: errors. */ int TheDefine(UBYTE *s, int mode) { UBYTE *name, *value, *valpoin, *args = 0, c; if ( ( mode & 2 ) == 0 ) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); } else { mode &= ~2; } name = s; if ( chartype[*s] != 0 ) goto illname; s++; while ( chartype[*s] <= 1 ) s++; value = s; while ( *s == ' ' || *s == '\t' ) s++; c = *s; *value = 0; if ( c == 0 ) { if ( PutPreVar(name,(UBYTE *)"1",0,mode) < 0 ) return(-1); return(0); } if ( c == '(' ) { /* arguments. scan for correctness */ s++; args = s; for (;;) { if ( chartype[*s] != 0 ) goto illarg; s++; while ( chartype[*s] <= 1 ) s++; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == ')' ) break; if ( *s != ',' ) goto illargs; s++; while ( *s == ' ' || *s == '\t' ) s++; } *s++ = 0; while ( *s == ' ' || *s == '\t' ) s++; c = *s; } if ( c == '"' ) { s++; valpoin = value = s; while ( *s != '"' ) { if ( *s == '\\' ) { if ( s[1] == 'n' ) { *valpoin++ = LINEFEED; s += 2; } else if ( s[1] == '"' ) { *valpoin++ = '"'; s += 2; } else if ( s[1] == 0 ) goto illval; else { *valpoin++ = *s++; *valpoin++ = *s++; } } else *valpoin++ = *s++; } *valpoin = 0; if ( PutPreVar(name,value,args,mode) < 0 ) return(-1); } else { MesPrint("@Illegal string for preprocessor variable %s. Forgotten double quotes (\") ?",name); return(-1); } return(0); illname:; MesPrint("@Illegally formed name of preprocessor variable"); return(-1); illarg:; MesPrint("@Illegally formed name of argument of preprocessor definition"); return(-1); illargs:; MesPrint("@Illegally formed arguments of preprocessor definition"); return(-1); illval:; MesPrint("@Illegal valpoin for preprocessor variable %s",name); return(-1); } /* #] TheDefine : #[ DoCommentChar : */ int DoCommentChar(UBYTE *s) { UBYTE c; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == '\t' ) s++; if ( *s == 0 || *s == '\n' ) { MesPrint("@No valid comment character specified"); return(-1); } c = *s++; while ( *s == ' ' || *s == '\t' ) s++; if ( *s != 0 && *s != '\n' ) { MesPrint("@Comment character should be a single valid character"); return(-1); } AP.ComChar = c; return(0); } /* #] DoCommentChar : #[ DoPreAssign : Routine assigns a 'value' to a $variable. Syntax: #assign next line(s) a statement of the type $name = expression; Note: at the moment of the assign there cannot be an 'open' statement. */ int DoPreAssign(UBYTE *s) { int error = 0; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) { return(0); } if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) { return(0); } if ( *s ) { MesPrint("@Illegal characters in %#assign instruction"); error = 1; } PUSHPREASSIGNLEVEL; AP.PreAssignFlag = 1; /* if ( AP.PreContinuation ) { MesPrint("@Assign instructions cannot occur inside statements"); MesPrint("@Missing ; ?"); AP.PreContinuation = 0; error = 1; } */ return(error); } /* #] DoPreAssign : #[ DoDefine : */ int DoDefine(UBYTE *s) { return(TheDefine(s,0)); } /* #] DoDefine : #[ DoRedefine : */ int DoRedefine(UBYTE *s) { return(TheDefine(s,1)); } /* #] DoRedefine : #[ ClearMacro : Undefines the arguments of a macro after its use. */ int ClearMacro(UBYTE *name) { int i; PREVAR *p; UBYTE *s; for ( i = NumPre-1, p = &(PreVar[NumPre-1]); i >= 0; i--, p-- ) { if ( StrCmp(name,p->name) == 0 ) break; } if ( i < 0 ) return(-1); if ( p->nargs <= 0 ) return(0); s = p->argnames; for ( i = 0; i < p->nargs; i++ ) { TheUndefine(s); while ( *s ) s++; s++; } return(0); } /* #] ClearMacro : #[ TheUndefine : There is a complication here. If there are redefine statements they will be pointing at the wrong variable if their number is greater than the number of the variable we pop. */ int TheUndefine(UBYTE *name) { int i, inum, error = 0; PREVAR *p; for ( i = NumPre-1, p = &(PreVar[NumPre-1]); i >= 0; i--, p-- ) { if ( StrCmp(name,p->name) == 0 ) { M_free(p->name,"undefining PreVar"); NumPre--; inum = i; while ( i < NumPre ) { p->name = p[1].name; p->value = p[1].value; p++; i++; } p->name = 0; p->value = 0; { CBUF *CC = cbuf + AC.cbufnum; int j, k; for ( j = 1; j <= CC->numlhs; j++ ) { if ( CC->lhs[j][0] == TYPEREDEFPRE ) { if ( CC->lhs[j][2] > inum ) CC->lhs[j][2]--; else if ( CC->lhs[j][2] == inum ) { for ( k = inum - 1; k >= 0; k-- ) if ( StrCmp(name, PreVar[k].name) == 0 ) break; if ( k >= 0 ) CC->lhs[j][2] = k; else { MesPrint("@Conflict between undefining a preprocessor variable and a redefine statement"); error = 1; } } } } #ifdef PARALLELCODE for ( j = 0; j < AC.numpfirstnum; j++ ) { if ( AC.pfirstnum[j] > inum ) AC.pfirstnum[j]--; else if ( AC.pfirstnum[j] == inum ) { for ( k = inum - 1; k >= 0; k-- ) if ( StrCmp(name, PreVar[k].name) == 0 ) break; if ( k >= 0 ) AC.pfirstnum[j] = k; } } #endif } break; } } return(error); } /* #] TheUndefine : #[ DoUndefine : */ int DoUndefine(UBYTE *s) { UBYTE *name, *t; int error = 0, retval; /* int i; PREVAR *p; */ if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); name = s; if ( chartype[*s] != 0 ) goto illname; s++; while ( chartype[*s] <= 1 ) s++; t = s; if ( *s && *s != ' ' && *s != '\t' ) goto illname; while ( *s == ' ' || *s == '\t' ) s++; if ( *s ) { MesPrint("@Undefine should just have a variable name"); error = -1; } *t = 0; if ( ( retval = TheUndefine(name) ) != 0 ) { if ( error == 0 ) return(retval); if ( error > 0 ) error = retval; } /* for ( i = NumPre-1, p = &(PreVar[NumPre-1]); i >= 0; i--, p-- ) { if ( StrCmp(name,p->name) == 0 ) { M_free(p->name,"undefining PreVar"); NumPre--; while ( i < NumPre ) { p->name = p[1].name; p->value = p[1].value; p++; i++; } p->name = 0; p->value = 0; break; } } */ return(error); illname:; MesPrint("@Illegally formed name of preprocessor variable"); return(-1); } /* #] DoUndefine : #[ DoInclude : */ int DoInclude(UBYTE *s) { return(Include(s,FILESTREAM)); } /* #] DoInclude : #[ DoReverseInclude : */ int DoReverseInclude(UBYTE *s) { return(Include(s,REVERSEFILESTREAM)); } /* #] DoReverseInclude : #[ Include : */ int Include(UBYTE *s, int type) { UBYTE *name = s, *fold, *t, c, c1 = 0, c2 = 0, c3 = 0; int str1offset, withnolist = AC.NoShowInput; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( *s == '-' || *s == '+' ) { if ( *s == '-' ) withnolist = 1; else withnolist = 0; s++; while ( *s == ' ' || *s == '\t' ) s++; name = s; } if ( *s == '"' ) { while ( *s && *s != '"' ) { if ( *s == '\\' ) s++; s++; } t = s++; } else { while ( *s && *s != ' ' && *s != '\t' ) { if ( *s == '\\' ) s++; s++; } t = s; } while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '#' ) { *t = 0; s++; while ( *s == ' ' || *s == '\t' ) s++; fold = s; if ( *s == 0 ) { MesPrint("@Empty fold name"); return(-1); } continue_fold: while ( *s && *s != ' ' && *s != '\t' ) { if ( *s == '\\' ) s++; s++; } t = s; while ( *s == ' ' || *s == '\t' ) s++; if ( *s ) { /* * A non-whitespace character is found. Continue parsing the fold. */ goto continue_fold; } } else if ( *s == 0 ) { fold = 0; } else { MesPrint("@Improper syntax for file name"); return(-1); } *t = 0; if ( fold ) { fold = strDup1(fold,"foldname"); } /* We have the name of the file in 'name' and the fold in 'fold' (or NULL) */ if ( OpenStream(name,type,0,PRENOACTION) == 0 ) { if ( fold ) { M_free(fold,"foldname"); fold = 0; } return(-1); } if ( fold ) { LONG position = -1; int foldopen = 0; LONG linenum = 0, prevline = 0; name = strDup1(name,"name of include file"); AC.CurrentStream->FoldName = strDup1(fold,"name of fold"); AC.NoShowInput++; for(;;) { c = GetFromStream(AC.CurrentStream); if ( c == ENDOFSTREAM ) { AC.CurrentStream = CloseStream(AC.CurrentStream); goto nofold; } if ( c == AP.ComChar ) { str1offset = AC.CurrentStream-AC.Streams; LoadInstruction(1); if ( AC.CurrentStream != str1offset+AC.Streams ) { c = ENDOFSTREAM; } else { t = AP.preStart; if ( t[2] == '#' && ( ( t[3] == '[' && !foldopen ) || ( t[3] == ']' && foldopen ) ) ) { t += 4; while ( *t == ' ' || *t == '\t' ) t++; s = AC.CurrentStream->FoldName; while ( *s == *t ) { s++; t++; } if ( *s == 0 && ( *t == ' ' || *t == '\t' || *t == ':' ) ) { while ( *t == ' ' || *t == '\t' ) t++; if ( *t == ':' ) { if ( foldopen == 0 ) { foldopen = 1; position = GetStreamPosition(AC.CurrentStream); linenum = AC.CurrentStream->linenumber; prevline = AC.CurrentStream->prevline; c3 = AC.CurrentStream->isnextchar; c1 = AC.CurrentStream->nextchar[0]; c2 = AC.CurrentStream->nextchar[1]; } else { foldopen = 0; PositionStream(AC.CurrentStream,position); AC.CurrentStream->linenumber = linenum; AC.CurrentStream->prevline = prevline; AC.CurrentStream->eqnum = 1; AC.NoShowInput--; AC.CurrentStream->isnextchar = c3; AC.CurrentStream->nextchar[0] = c1; AC.CurrentStream->nextchar[1] = c2; break; } } } } } } else { while ( c != LINEFEED && c != ENDOFSTREAM ) { c = GetFromStream(AC.CurrentStream); if ( c == ENDOFSTREAM ) { AC.CurrentStream = CloseStream(AC.CurrentStream); break; } } } if ( c == ENDOFSTREAM ) { nofold: MesPrint("@Cannot find fold %s in file %s",fold,name); UngetChar(c); AC.NoShowInput--; M_free(name,"name of include file"); Terminate(-1); } } M_free(name,"name of include file"); } AC.NoShowInput = withnolist; if ( fold ) { M_free(fold,"foldname"); fold = 0; } return(0); } /* #] Include : #[ DoPreExchange : Exchanges the names of expressions or the contents of dollars Syntax: #exchange expr1,expr2 #exchange $var1,$var2 */ int DoPreExchange(UBYTE *s) { int error = 0; UBYTE *s1, *s2; WORD num1, num2; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == '$' ) { s++; s1 = s; while ( FG.cTable[*s] <= 1 ) s++; if ( *s != ',' && *s != ' ' && *s != '\t' ) goto syntax; *s++ = 0; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s != '$' ) goto syntax; s++; s2 = s; while ( FG.cTable[*s] <= 1 ) s++; if ( *s != 0 && *s != ';' ) goto syntax; *s = 0; if ( ( num1 = GetDollar(s1) ) <= 0 ) { MesPrint("@$%s has not been defined (yet)",s1); error = 1; } if ( ( num2 = GetDollar(s2) ) <= 0 ) { MesPrint("@$%s has not been defined (yet)",s2); error = 1; } if ( error == 0 ) { ExchangeDollars((int)num1,(int)num2); } } else { s1 = s; s = SkipAName(s); if ( *s != ',' && *s != ' ' && *s != '\t' ) goto syntax; *s++ = 0; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( FG.cTable[*s] != 0 && *s != '[' ) goto syntax; s2 = s; s = SkipAName(s); if ( *s != 0 && *s != ';' ) goto syntax; *s = 0; if ( GetName(AC.exprnames,s1,&num1,NOAUTO) != CEXPRESSION ) { MesPrint("@%s is not an expression",s1); error = 1; } if ( GetName(AC.exprnames,s2,&num2,NOAUTO) != CEXPRESSION ) { MesPrint("@%s is not an expression",s2); error = 1; } if ( error == 0 ) { ExchangeExpressions((int)num1,(int)num2); } } return(error); syntax: MesPrint("@Proper syntax: %#exchange expr1,expr2 or %#exchange $var1,$var2"); return(1); } /* #] DoPreExchange : #[ DoCall : */ int DoCall(UBYTE *s) { UBYTE *t, *u, *v, *name, c, cp, *args1, *args2, *t1, *t2, *wild = 0; int bratype = 0, wildargs = 0, inwildargs = 0, nwildargs = 0; PROCEDURE *p; int streamoffset; int i, namesize, narg1, narg2, bralevel, numpre; LONG i1, i2; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); /* 1: Get the name of the procedure. 2: Locate the procedure. */ name = s; s = EndOfToken(s); c = *s; *s = 0; for ( i = NumProcedures-1; i >= 0; i-- ) { if ( StrCmp(Procedures[i].name,name) == 0 ) break; } // AP.ProcList.num = NumProcedures is incremented inside FromList p = (PROCEDURE *)FromList(&AP.ProcList); if ( i < 0 ) { /* Try to find a file */ namesize = 0; t = name; while ( *t ) { t++; namesize++; } t = AP.procedureExtension; while ( *t ) { t++; namesize++; } t = p->name = (UBYTE *)Malloc1(namesize+2,"procedure"); u = name; while ( *u ) *t++ = *u++; *t++ = '.'; v = AP.procedureExtension; while ( *v ) *t++ = *v++; *t = 0; p->loadmode = 0; /* buffer should be freed at end */ p->mustfree = 1; p->p.buffer = LoadInputFile(p->name,PROCEDUREFILE); if ( p->p.buffer == 0 ) return(-1); t[-4] = 0; } else { p->p.buffer = Procedures[i].p.buffer; p->name = Procedures[i].name; p->loadmode = 1; p->mustfree = 0; // this is just a copy of pointers to a permanently stored procedure } t = p->p.buffer; SKIPBLANKS(t) if ( *t++ != '#' ) goto wrongfile; SKIPBLANKS(t) t += 9; SKIPBLANKS(t) u = EndOfToken(t); cp = *u; *u = 0; if ( StrCmp(t,name) != 0 ) goto wrongfile; *u = cp; *s = c; /* The pointer p points to the contents of the procedure (in memory) Now we have to match the arguments. u points to after the name in the 'file', s to after the name in the call statement. */ bralevel = narg1 = narg2 = 0; args2 = u; SKIPBLANKS(u) if ( *u == '(' ) { u++; SKIPBLANKS(u) args2 = u; while ( *u != ')' ) { if ( *u == '?' ) { wildargs++; u++; nwildargs = narg2+1; } narg2++; u = EndOfToken(u); SKIPBLANKS(u) if ( *u == ',' ) { u++; SKIPBLANKS(u) } else if ( *u != ')' || ( wildargs > 1 ) ) { MesPrint("@Illegal argument field in procedure %s",p->name); return(-1); } } } while ( *u != LINEFEED ) u++; SKIPBLANKS(s) args1 = s+1; if ( *s == '(' ) bratype = 1; do { if ( *s == '{' && bratype == 0 ) bralevel++; else if ( *s == '(' && bratype == 1 ) bralevel++; else if ( *s == '}' && bratype == 0 ) { bralevel--; if ( bralevel == 0 ) { *s = 0; narg1++; if ( wildargs && narg1 == nwildargs ) wild = s; } } else if ( *s == ')' && bratype == 1 ) { bralevel--; if ( bralevel == 0 ) { *s = 0; narg1++; if ( wildargs && narg1 == nwildargs ) wild = s; } } /*[12dec2003 mt]:*/ /*else if ( *s == ',' || *s == '|' ) {*/ else if (set_in(*s,AC.separators)) {/*Function set_in see in file tools.c*/ /*:[12dec2003 mt]*/ *s = 0; narg1++; if ( wildargs && narg1 == nwildargs ) wild = s; } else if ( *s == '\\' ) s++; s++; } while ( bralevel > 0 ); if ( wildargs && narg1 >= narg2-1 ) { inwildargs = narg1-narg2+1; if ( inwildargs == 0 ) nwildargs = 0; else { while ( inwildargs > 1 ) { *wild = ','; while ( *wild ) wild++; inwildargs--; } } } else if ( narg1 != narg2 && ( narg2 != 0 || narg1 != 1 || *args1 != 0 ) ) { MesPrint("@Arguments of procedure %s are not matching",p->name); return(-1); } numpre = -NumPre-1; /* For the stream */ for ( i = 0; i < narg2; i++ ) { t = args2; if ( *t == '?' ) { args2++; } if ( *t == '?' && inwildargs == 0 ) { args2 = EndOfToken(args2); c = *args2; *args2 = 0; if ( PutPreVar(t,(UBYTE *)"",0,0) < 0 ) return(-1); } else { args2 = EndOfToken(args2); c = *args2; *args2 = 0; t1 = t2 = args1; while ( *t1 ) { if ( *t1 == '\\' ) t1++; if ( t1 != t2 ) *t2 = *t1; t2++; t1++; } *t2 = 0; if ( PutPreVar(t,args1,0,0) < 0 ) return(-1); args1 = t1+1; /* Next argument */ } *args2 = c; SKIPBLANKS(args2) /* skip to next name */ args2++; SKIPBLANKS(args2) } streamoffset = AC.CurrentStream - AC.Streams; args1 = AC.CurrentStream->name; AC.CurrentStream->name = p->name; i1 = AC.CurrentStream->linenumber; i2 = AC.CurrentStream->prevline; AC.CurrentStream->prevline = AC.CurrentStream->linenumber = 2; OpenStream(u+1,PREREADSTREAM3,numpre,PRENOACTION); AC.Streams[streamoffset].name = args1; AC.Streams[streamoffset].linenumber = i1; AC.Streams[streamoffset].prevline = i2; AddToPreTypes(PRETYPEPROCEDURE); return(0); wrongfile:; if ( i < 0 ) MesPrint("@File %s is not a proper procedure",p->name); else MesPrint("!!!Internal error with procedure names: %s",name); return(-1); } /* #] DoCall : #[ DoDebug : */ int DoDebug(UBYTE *s) { int x; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); NeedNumber(x,s,nonumber) if ( x < 0 || x >(PREPROONLY | DUMPTOCOMPILER | DUMPOUTTERMS | DUMPINTERMS | DUMPTOSORT | DUMPTOPARALLEL #ifdef WITHPTHREADS | THREADSDEBUG #endif ) ) goto nonumber; AP.PreDebug = 0; if ( ( x & PREPROONLY ) != 0 ) AP.PreDebug |= PREPROONLY; /* 1 */ if ( ( x & DUMPTOCOMPILER ) != 0 ) AP.PreDebug |= DUMPTOCOMPILER; /* 2 */ if ( ( x & DUMPOUTTERMS ) != 0 ) AP.PreDebug |= DUMPOUTTERMS; /* 4 */ if ( ( x & DUMPINTERMS ) != 0 ) AP.PreDebug |= DUMPINTERMS; /* 8 */ if ( ( x & DUMPTOSORT ) != 0 ) AP.PreDebug |= DUMPTOSORT; /* 16 */ if ( ( x & DUMPTOPARALLEL ) != 0 ) AP.PreDebug |= DUMPTOPARALLEL; /* 32 */ #ifdef WITHPTHREADS if ( ( x & THREADSDEBUG ) != 0 ) AP.PreDebug |= THREADSDEBUG; /* 64 */ #endif return(0); nonumber: MesPrint("@Illegal argument for debug instruction"); return(1); } /* #] DoDebug : #[ DoTerminate : */ int DoTerminate(UBYTE *s) { int x; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( *s ) { NeedNumber(x,s,nonumber) Terminate(x); } else { Terminate(-1); } return(0); nonumber: MesPrint("@Illegal argument for terminate instruction"); return(1); } /* #] DoTerminate : #[ DoContinueDo : */ /** * Jumps forward to the corresponding `#enddo` of the specified number of outer `#do` loops. * * @par Syntax: * @code * #continuedo [=1] * @endcode * * If `number` is omitted, it defaults to 1. * If `number` is zero then the instruction has no effect. */ int DoContinueDo(UBYTE *s) { DOLOOP *loop; WORD levels; int result; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( NumDoLoops <= 0 ) { MesPrint("@%#continuedo without %#do"); return(1); } SkipSpaces(&s); if ( *s == 0 ) { levels = 1; } else if ( FG.cTable[*s] == 1 ) { ParseNumber(levels,s); SkipSpaces(&s); if ( *s != 0 ) goto improper; } else { improper: MesPrint("@Improper syntax of %#continuedo instruction"); return(1); } if ( levels > NumDoLoops ) { MesPrint("@Too many loop levels requested in %#continuedo instruction"); return(1); } result = ExitDoLoops(levels-1,"continuedo"); if ( result != 0 ) return(result); if ( levels <= 0 ) return(0); if ( AC.CurrentStream->type == PREREADSTREAM3 || AP.PreTypes[AP.NumPreTypes] == PRETYPEPROCEDURE ) { MesPrint("@Trying to jump out of a procedure with a %#continuedo instruction"); return(1); } loop = &(DoLoops[NumDoLoops-1]); AP.NumPreTypes = loop->NumPreTypes+1; AP.PreIfLevel = loop->PreIfLevel; AP.PreSwitchLevel = loop->PreSwitchLevel; return(DoEnddo(s)); } /* #] DoContinueDo : #[ DoDo : The do loop has three varieties: #do i = num1,num2 [,num3] #do i = {string1,string2,....,stringn} The | as separator is also allowed for backwards compatibility #do i = expression One by one all terms of the expression */ int DoDo(UBYTE *s) { GETIDENTITY UBYTE *t, c, *u, *uu; DOLOOP *loop; WORD expnum; LONG linenum = AC.CurrentStream->linenumber; int oldNoShowInput = AC.NoShowInput, i, oldpreassignflag; if ( ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) || ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) ) { if ( PreSkip((UBYTE *)"do",(UBYTE *)"enddo",1) ) return(-1); return(0); } /* if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); */ AddToPreTypes(PRETYPEDO); loop = (DOLOOP *)FromList(&AP.LoopList); loop->firstdollar = loop->lastdollar = loop->incdollar = -1; loop->NumPreTypes = AP.NumPreTypes-1; loop->PreIfLevel = AP.PreIfLevel; loop->PreSwitchLevel = AP.PreSwitchLevel; AC.NoShowInput = 1; if ( PreLoad(&(loop->p),(UBYTE *)"do",(UBYTE *)"enddo",1,"doloop") ) return(-1); AC.NoShowInput = oldNoShowInput; loop->NoShowInput = AC.NoShowInput; /* Get now the name. We have to take great care when the name is terminated! */ s = loop->p.buffer + (s - AP.preStart); SKIPBLANKS(s) loop->name = s; if ( chartype[*s] != 0 ) goto illname; s++; while ( chartype[*s] <= 1 ) s++; t = s; while ( *s == ' ' || *s == '\t' ) s++; if ( *s != '=' ) goto illdo; s++; while ( *s == ' ' || *s == '\t' ) s++; *t = 0; if ( *s == '{' ) { loop->type = LISTEDLOOP; s++; loop->vars = s; loop->lastnum = 0; while ( *s != '}' && *s != 0 ) { if ( set_in(*s,AC.separators) ) { *s = 0; loop->lastnum++; } else if ( *s == '\\' ) s++; s++; } if ( *s == 0 ) goto illdo; *s++ = 0; loop->lastnum++; loop->firstnum = 0; loop->contents = s; } else if ( *s == '-' || *s == '+' || chartype[*s] == 1 || *s == '$' ) { loop->type = NUMERICALLOOP; t = s; while ( *s && *s != ',' ) s++; if ( *s == 0 ) goto illdo; if ( *t == '$' ) { c = *s; *s = 0; if ( GetName(AC.dollarnames,t+1,&loop->firstdollar,NOAUTO) != CDOLLAR ) { MesPrint("@%s is undefined in first parameter in %#do instruction",t); return(-1); } loop->firstnum = DolToLong(BHEAD loop->firstdollar); if ( AN.ErrorInDollar ) { MesPrint("@%s does not evaluate into a valid loop parameter",t); return(-1); } *s++ = c; } else { *s = '}'; if ( PreEval(t,&loop->firstnum) == 0 ) goto illdo; *s++ = ','; } t = s; while ( *s && *s != ',' && *s != ';' && *s != LINEFEED ) s++; c = *s; if ( *t == '$' ) { *s = 0; if ( GetName(AC.dollarnames,t+1,&loop->lastdollar,NOAUTO) != CDOLLAR ) { MesPrint("@%s is undefined in second parameter in %#do instruction",t); return(-1); } loop->lastnum = DolToLong(BHEAD loop->lastdollar); if ( AN.ErrorInDollar ) { MesPrint("@%s does not evaluate into a valid loop parameter",t); return(-1); } *s++ = c; } else { *s = '}'; if ( PreEval(t,&loop->lastnum) == 0 ) goto illdo; *s++ = c; } if ( c == ',' ) { t = s; while ( *s && *s != ';' && *s != LINEFEED ) s++; if ( *t == '$' ) { c = *s; *s = 0; if ( GetName(AC.dollarnames,t+1,&loop->incdollar,NOAUTO) != CDOLLAR ) { MesPrint("@%s is undefined in third parameter in %#do instruction",t); return(-1); } loop->incnum = DolToLong(BHEAD loop->incdollar); if ( AN.ErrorInDollar ) { MesPrint("@%s does not evaluate into a valid loop parameter",t); return(-1); } *s++ = c; } else { c = *s; *s = '}'; if ( PreEval(t,&loop->incnum) == 0 ) goto illdo; *s++ = c; } } else loop->incnum = 1; loop->contents = s; } else if ( ( chartype[*s] == 0 ) || ( *s == '[' ) ) { int oldNumPotModdollars = NumPotModdollars; #ifdef WITHMPI WORD oldRhsExprInModuleFlag = AC.RhsExprInModuleFlag; AC.RhsExprInModuleFlag = 0; #endif t = s; if ( ( s = SkipAName(s) ) == 0 ) goto illdo; c = *s; *s = 0; if ( GetName(AC.exprnames,t,&expnum,NOAUTO) == CEXPRESSION ) { loop->type = ONEEXPRESSION; /* We should remember the expression by name for when it gets renumbered!!! If it gets deleted there will be a crash or at least the loop terminates. */ loop->vars = t; } else goto illdo; if ( c == ',' || c == '\t' || c == ';' ) { s++; } else if ( c != 0 && c != '\n' ) goto illdo; while ( *s == ',' || *s == '\t' || *s == ';' ) s++; if ( *s != 0 && *s != '\n' ) goto illdo; loop->firstnum = 0; s++; loop->contents = s; loop->incnum = 0; /* Next determine size of statement and allocate space */ while ( *t ) t++; i = t - loop->vars; t = loop->name; while ( *t ) { t++; i++; } i += 4; loop->dollarname = Malloc1((LONG)i,"do-loop instruction"); /* Construct the statement */ u = loop->dollarname; *u++ = '$'; t = loop->name; while ( *t ) *u++ = *t++; *u++ = '_'; uu = u; *u++ = '='; t = loop->vars; while ( *t ) *u++ = *t++; *t = 0; *u = 0; /* Compile and put in dollar variable. Note that we remember the dollar by name and that this name ends in _ */ oldpreassignflag = AP.PreAssignFlag; AP.PreAssignFlag = 2; CompileStatement(loop->dollarname); if ( CatchDollar(0) ) { MesPrint("@Cannot load expression in do loop"); return(-1); } AP.PreAssignFlag = oldpreassignflag; NumPotModdollars = oldNumPotModdollars; #ifdef WITHMPI AC.RhsExprInModuleFlag = oldRhsExprInModuleFlag; #endif *uu = 0; } else goto illdo; /* Syntax problems */ loop->errorsinloop = 0; /* loop->startlinenumber = linenum+1; 5-oct-2000 One too much? */ loop->startlinenumber = linenum; PutPreVar(loop->name,(UBYTE *)"0",0,0); loop->firstloopcall = 1; return(DoEnddo(s)); illname:; MesPrint("@Improper name for do loop variable"); return(-1); illdo:; MesPrint("@Improper syntax in do loop instruction"); return(-1); } /* #] DoDo : #[ DoBreakDo : #breakdo [num] jumps out of num #do-loops (if there are that many) (default is 1) */ int DoBreakDo(UBYTE *s) { WORD levels; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( NumDoLoops <= 0 ) { MesPrint("@%#breakdo without %#do"); return(1); } /* if ( AP.PreTypes[AP.NumPreTypes] != PRETYPEDO ) { MessPreNesting(4); return(-1); } */ while ( *s && ( *s == ',' || *s == ' ' || *s == '\t' ) ) s++; if ( *s == 0 ) { levels = 1; } else if ( FG.cTable[*s] == 1 ) { levels = 0; while ( *s >= '0' && *s <= '9' ) { levels = 10*levels + *s++ - '0'; } if ( *s != 0 ) goto improper; } else { improper: MesPrint("@Improper syntax of %#breakdo instruction"); return(1); } if ( levels > NumDoLoops ) { MesPrint("@Too many loop levels requested in %#breakdo instruction"); Terminate(-1); } return(ExitDoLoops(levels,"breakdo")); } /** * Exits the specified number of nested `#do` loops. * * @param levels The number of loops to exit. * @param instruction The instruction name used for error reporting. * @return 0 on success, nonzero on error. */ static int ExitDoLoops(int levels, const char *instruction) { DOLOOP *loop; while ( levels > 0 ) { while ( AC.CurrentStream->type != PREREADSTREAM && AC.CurrentStream->type != PREREADSTREAM2 && AC.CurrentStream->type != PREREADSTREAM3 ) { AC.CurrentStream = CloseStream(AC.CurrentStream); } while ( AP.PreTypes[AP.NumPreTypes] != PRETYPEDO && AP.PreTypes[AP.NumPreTypes] != PRETYPEPROCEDURE ) AP.NumPreTypes--; if ( AC.CurrentStream->type == PREREADSTREAM3 || AP.PreTypes[AP.NumPreTypes] == PRETYPEPROCEDURE ) { MesPrint("@Trying to jump out of a procedure with a %#%s instruction",instruction); return(1); } loop = &(DoLoops[NumDoLoops-1]); AP.NumPreTypes = loop->NumPreTypes; AP.PreIfLevel = loop->PreIfLevel; AP.PreSwitchLevel = loop->PreSwitchLevel; NumDoLoops--; DoUndefine(loop->name); M_free(loop->p.buffer,"loop->p.buffer"); loop->firstloopcall = 0; AC.CurrentStream = CloseStream(AC.CurrentStream); levels--; } return(0); } /* #] DoBreakDo : #[ DoElse : */ int DoElse(UBYTE *s) { if ( AP.PreTypes[AP.NumPreTypes] != PRETYPEIF ) { if ( AP.PreIfLevel <= 0 ) MesPrint("@%#else without corresponding %#if"); else MessPreNesting(1); return(-1); } if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); while ( *s == ' ' ) s++; if ( tolower(*s) == 'i' && tolower(s[1]) == 'f' && s[2] && FG.cTable[s[2]] > 1 && s[2] != '_' ) { s += 2; while ( *s == ' ' ) s++; return(DoElseif(s)); } if ( AP.PreIfLevel <= 0 ) { MesPrint("@%#else without corresponding %#if"); return(-1); } switch ( AP.PreIfStack[AP.PreIfLevel] ) { case EXECUTINGIF: AP.PreIfStack[AP.PreIfLevel] = LOOKINGFORENDIF; break; case LOOKINGFORELSE: AP.PreIfStack[AP.PreIfLevel] = EXECUTINGIF; break; case LOOKINGFORENDIF: break; } return(0); } /* #] DoElse : #[ DoElseif : */ int DoElseif(UBYTE *s) { int condition; if ( AP.PreTypes[AP.NumPreTypes] != PRETYPEIF ) { if ( AP.PreIfLevel <= 0 ) MesPrint("@%#elseif without corresponding %#if"); else MessPreNesting(2); return(-1); } if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfLevel <= 0 ) { MesPrint("@%#elseif without corresponding %#if"); return(-1); } switch ( AP.PreIfStack[AP.PreIfLevel] ) { case EXECUTINGIF: AP.PreIfStack[AP.PreIfLevel] = LOOKINGFORENDIF; break; case LOOKINGFORELSE: if ( ( condition = EvalPreIf(s) ) < 0 ) return(-1); AP.PreIfStack[AP.PreIfLevel] = condition; break; case LOOKINGFORENDIF: break; } return(0); } /* #] DoElseif : #[ DoEnddo : At the first call there is no stream yet. After that we have to close the stream and start a new one. */ int DoEnddo(UBYTE *s) { GETIDENTITY DOLOOP *loop; UBYTE *t, *tt, *value, numstr[16]; LONG xval; int xsign, retval; DUMMYUSE(s); if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); /* if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH || AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) { if ( AP.PreTypes[AP.NumPreTypes] == PRETYPEDO ) AP.NumPreTypes--; else { MessPreNesting(3); return(-1); } return(0); } */ if ( NumDoLoops <= 0 ) { MesPrint("@%#enddo without %#do"); return(1); } if ( AP.PreTypes[AP.NumPreTypes] != PRETYPEDO ) { MessPreNesting(4); return(-1); } loop = &(DoLoops[NumDoLoops-1]); if ( !loop->firstloopcall ) AC.CurrentStream = CloseStream(AC.CurrentStream); if ( loop->errorsinloop ) { MesPrint("++++Errors in Loop"); goto finish; } if ( loop->type == LISTEDLOOP ) { if ( loop->firstnum >= loop->lastnum ) goto finish; loop->firstnum++; t = value = loop->vars; while ( *value ) value++; value++; loop->vars = value; value = tt = t; while ( *value ) { if ( *value == '\\' ) value++; *tt++ = *value++; } *tt = 0; PutPreVar(loop->name,t,0,1); /* We overwrite the definition */ } else if ( loop->type == NUMERICALLOOP ) { if ( !loop->firstloopcall ) { /* Test whether the variable was changed inside the loop into a different numerical value. If so, adjust. */ t = GetPreVar(loop->name,WITHOUTERROR); if ( t ) { value = t; xsign = 1; while ( *value && ( *value == ' ' || *value == '-' || *value == '+' ) ) { if ( *value == '-' ) xsign = -xsign; value++; } t = value; xval = 0; while ( *value >= '0' && *value <= '9' ) xval = 10*xval + *value++ - '0'; while ( *value && *value == ' ' ) value++; if ( *value == 0 ) { /* Now we may substitute the loopvalue. */ if ( xsign < 0 ) xval = -xval; if ( loop->incdollar >= 0 ) { loop->incnum = DolToLong(BHEAD loop->incdollar); if ( AN.ErrorInDollar ) { MesPrint("@%s does not evaluate into a valid third loop parameter",DOLLARNAME(Dollars,loop->incdollar)); return(-1); } } loop->firstnum = xval + loop->incnum; } } if ( loop->lastdollar >= 0 ) { loop->lastnum = DolToLong(BHEAD loop->lastdollar); if ( AN.ErrorInDollar ) { MesPrint("@%s does not evaluate into a valid second loop parameter",DOLLARNAME(Dollars,loop->lastdollar)); return(-1); } } } if ( ( loop->incnum > 0 && loop->firstnum > loop->lastnum ) || ( loop->incnum < 0 && loop->firstnum < loop->lastnum ) ) goto finish; NumToStr(numstr,loop->firstnum); t = numstr; loop->firstnum += loop->incnum; PutPreVar(loop->name,t,0,1); /* We overwrite the definition */ } else if ( loop->type == ONEEXPRESSION ) { /* Find the dollar expression */ WORD numdollar = GetDollar(loop->dollarname+1); DOLLARS d = Dollars + numdollar; WORD *w, *dw, v, *ww; if ( (d->where) == 0 ) { d->type = DOLUNDEFINED; M_free(loop->dollarname,"do-loop instruction"); goto finish; } w = d->where + loop->incnum; if ( *w == 0 ) { M_free(d->where,"dollar"); d->where = 0; d->type = DOLUNDEFINED; M_free(loop->dollarname,"do-loop instruction"); goto finish; } loop->incnum += *w; /* Now the term has to be converted to text. */ ww = w + *w; v = *ww; *ww = 0; dw = d->where; d->where = w; t = WriteDollarToBuffer(numdollar,1); d->where = dw; *ww = v; PutPreVar(loop->name,t,0,1); /* We overwrite the definition */ M_free(t,"dollar"); } if ( loop->firstloopcall ) OpenStream(loop->contents,PREREADSTREAM2,0,PRENOACTION); else OpenStream(loop->contents,PREREADSTREAM,0,PRENOACTION); AC.CurrentStream->prevline = AC.CurrentStream->linenumber = loop->startlinenumber; AC.CurrentStream->eqnum = 0; loop->firstloopcall = 0; return(0); finish:; NumDoLoops--; retval = DoUndefine(loop->name); M_free(loop->p.buffer,"loop->p.buffer"); loop->firstloopcall = 0; AP.NumPreTypes--; return(retval); } /* #] DoEnddo : #[ DoEndif : */ int DoEndif(UBYTE *s) { DUMMYUSE(s); if ( AP.PreTypes[AP.NumPreTypes] != PRETYPEIF ) { if ( AP.PreIfLevel <= 0 ) MesPrint("@%#endif without corresponding %#if"); else MessPreNesting(5); return(-1); } AP.NumPreTypes--; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfLevel <= 0 ) { MesPrint("@%#endif without corresponding %#if"); return(-1); } AP.PreIfLevel--; return(0); } /* #] DoEndif : #[ DoEndprocedure : Action is simple: close the current stream if it is still the stream from which the statement came. Then pop the current procedure and all its local derivatives. if loadmode > 1 the procedure was defined locally. */ int DoEndprocedure(UBYTE *s) { DUMMYUSE(s); if ( AP.PreTypes[AP.NumPreTypes] != PRETYPEPROCEDURE ) { MessPreNesting(6); return(-1); } AP.NumPreTypes--; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); AC.CurrentStream = CloseStream(AC.CurrentStream); do { NumProcedures--; if ( Procedures[NumProcedures].mustfree == 1 ) { M_free(Procedures[NumProcedures].p.buffer,"procedures buffer"); M_free(Procedures[NumProcedures].name,"procedures name"); } } while ( Procedures[NumProcedures].loadmode > 1 ); return(0); } /* #] DoEndprocedure : #[ DoIf : */ int DoIf(UBYTE *s) { int condition; AddToPreTypes(PRETYPEIF); if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] == EXECUTINGIF ) { condition = EvalPreIf(s); if ( condition < 0 ) return(-1); } else condition = LOOKINGFORENDIF; if ( AP.PreIfLevel+1 >= AP.MaxPreIfLevel ) { int **ppp = &AP.PreIfStack; /* To avoid a compiler warning */ if ( DoubleList((void ***)ppp,&AP.MaxPreIfLevel,sizeof(int), "PreIfLevels") ) return(-1); } AP.PreIfStack[++AP.PreIfLevel] = condition; return(0); } /* #] DoIf : #[ DoIfdef : */ int DoIfdef(UBYTE *s, int par) { int condition; AddToPreTypes(PRETYPEIF); if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] == EXECUTINGIF ) { while ( *s == ' ' || *s == '\t' ) s++; if ( ( *s == 0 ) == ( par == 1 ) ) condition = LOOKINGFORELSE; else condition = EXECUTINGIF; } else condition = LOOKINGFORENDIF; if ( AP.PreIfLevel+1 >= AP.MaxPreIfLevel ) { int **ppp = &AP.PreIfStack; /* to avoid a compiler warning */ if ( DoubleList((void ***)ppp,&AP.MaxPreIfLevel,sizeof(int), "PreIfLevels") ) return(-1); } AP.PreIfStack[++AP.PreIfLevel] = condition; return(0); } /* #] DoIfdef : #[ DoIfydef : */ int DoIfydef(UBYTE *s) { return DoIfdef(s,1); } /* #] DoIfydef : #[ DoIfndef : */ int DoIfndef(UBYTE *s) { return DoIfdef(s,2); } /* #] DoIfndef : #[ DoInside : #inside $var1,...,$varn statements without .sort #endinside executes the statements on the contents of the $ variables as if they are a module. The results are put back in the dollar variables. To do this right we need a struct with old compiler buffer list of numbers of dollars length of the list length of the array containing the list Because we need to compose statements, the statement buffer must be empty. This means that we have to test for that. Same at the end. We must have a completed statement. */ int DoInside(UBYTE *s) { GETIDENTITY int numdol, error = 0; WORD *nb, newsize, i; UBYTE *name, c; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.PreInsideLevel != 0 ) { MesPrint("@Illegal nesting of %#inside/%#endinside instructions"); return(-1); } /* if ( AP.PreContinuation ) { error = -1; MesPrint("@%#inside cannot be inside a regular statement"); } */ PUSHPREASSIGNLEVEL /* Now the dollars to do */ AP.inside.numdollars = 0; for(;;) { while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) break; if ( *s != '$' ) { MesPrint("@%#inside instruction can have only $ variables for parameters"); return(-1); } s++; name = s; while (chartype[*s] <= 1 ) s++; c = *s; *s = 0; if ( ( numdol = GetDollar(name) ) < 0 ) { MesPrint("@%#inside: $%s has not (yet) been defined",name); *s = c; error = -1; } else { *s = c; if ( AP.inside.numdollars >= AP.inside.size ) { if ( AP.inside.buffer == 0 ) newsize = 20; else newsize = 2*AP.inside.size; nb = (WORD *)Malloc1(newsize*sizeof(WORD),"insidebuffer"); if ( AP.inside.buffer ) { for ( i = 0; i < AP.inside.size; i++ ) nb[i] = AP.inside.buffer[i]; M_free(AP.inside.buffer,"insidebuffer"); } AP.inside.buffer = nb; AP.inside.size = newsize; } AP.inside.buffer[AP.inside.numdollars++] = numdol; } } /* We have to store the configuration of the compiler buffer, so that we know where to start executing and how to reset the buffer. */ AP.inside.oldcompiletype = AC.compiletype; AP.inside.oldparallelflag = AC.mparallelflag; AP.inside.oldnumpotmoddollars = NumPotModdollars; AP.inside.oldcbuf = AC.cbufnum; AP.inside.oldrbuf = AM.rbufnum; AP.inside.oldcnumlhs = AR.Cnumlhs, AddToPreTypes(PRETYPEINSIDE); AP.PreInsideLevel = 1; AC.cbufnum = AP.inside.inscbuf; AM.rbufnum = AP.inside.inscbuf; clearcbuf(AC.cbufnum); AC.compiletype = 0; AC.mparallelflag = PARALLELFLAG; #ifdef WITHMPI /* * We use AC.RhsExprInModuleFlag, PotModdollars, and AC.pfirstnum * in order to check (1) whether there are expression names in RHS, * (2) which dollar variables can be modified, and (3) which * preprocessor variables can be redefined, in #inside. * We store the current values of them, and then reset them. */ PF_StoreInsideInfo(); AC.RhsExprInModuleFlag = 0; NumPotModdollars = 0; AC.numpfirstnum = 0; #endif return(error); } /* #] DoInside : #[ DoEndInside : */ int DoEndInside(UBYTE *s) { GETIDENTITY WORD numdol, *oldworkpointer = AT.WorkPointer, *term, *t, j, i; DOLLARS d, nd; WORD oldbracketon = AR.BracketOn; WORD *oldcompresspointer = AR.CompressPointer; int oldmultithreaded = AS.MultiThreaded; /* int oldmparallelflag = AC.mparallelflag; */ FILEHANDLE *f; #ifdef WITHMPI int error = 0; #endif DUMMYUSE(s); if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.PreTypes[AP.NumPreTypes] != PRETYPEINSIDE ) { if ( AP.PreInsideLevel != 1 ) MesPrint("@%#endinside without corresponding %#inside"); else MessPreNesting(11); return(-1); } AP.NumPreTypes--; if ( AP.PreInsideLevel != 1 ) { MesPrint("@%#endinside without corresponding %#inside"); return(-1); } if ( AP.PreContinuation ) { MesPrint("@%#endinside: previous statement not terminated."); Terminate(-1); } AC.compiletype = AP.inside.oldcompiletype; AR.Cnumlhs = cbuf[AM.rbufnum].numlhs; #ifdef WITHMPI /* * If the #inside...#endinside contains expressions in RHS, only the master executes it * and then broadcasts the result to the all slaves. If not, the all processes execute * it and in this case no MPI interactions are needed. */ if ( PF.me == MASTER || !AC.RhsExprInModuleFlag ) { #endif AR.BracketOn = 0; AS.MultiThreaded = 0; /* AC.mparallelflag = PARALLELFLAG; */ if ( AR.CompressPointer == 0 ) AR.CompressPointer = AR.CompressBuffer; f = AR.infile; AR.infile = AR.outfile; AR.outfile = f; /* Now we have to execute the statements on the proper dollars. */ for ( i = 0; i < AP.inside.numdollars; i++ ) { numdol = AP.inside.buffer[i]; nd = d = Dollars + numdol; if ( d->type != DOLZERO ) { if ( d->type != DOLTERMS ) nd = DolToTerms(BHEAD numdol); term = nd->where; NewSort(BHEAD0); NewSort(BHEAD0); AR.MaxDum = AM.IndDum; while ( *term ) { t = oldworkpointer; j = *term; NCOPY(t,term,j); AT.WorkPointer = t; AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); if ( Generator(BHEAD oldworkpointer,0) ) { MesPrint("@Called from %#endinside"); MesPrint("@Evaluating variable $%s",DOLLARNAME(Dollars,numdol)); Terminate(-1); } } AT.WorkPointer = oldworkpointer; CleanDollarFactors(d); if ( d->where ) { M_free(d->where,"dollar contents"); d->where = 0; } EndSort(BHEAD (WORD *)((void *)(&(d->where))),2); LowerSortLevel(); term = d->where; while ( *term ) term += *term; d->size = term - d->where; if ( nd != d ) M_free(nd,"Copy of dollar variable"); if ( d->where[0] == 0 ) { M_free(d->where,"dollar contents"); d->where = 0; d->type = DOLZERO; } } } #ifdef WITHMPI } if ( AC.RhsExprInModuleFlag ) { /* * The only master executed the statements in #inside. * We need to broadcast the result to the all slaves. */ for ( i = 0; i < AP.inside.numdollars; i++ ) { /* * Mark $-variables specified in the #inside instruction as modified * such that they will be broadcast. */ AddPotModdollar(AP.inside.buffer[i]); } /* Now actual broadcast of modified variables. */ if ( NumPotModdollars > 0 ) { error = PF_BroadcastModifiedDollars(); if ( error ) goto cleanup; } if ( AC.numpfirstnum > 0 ) { error = PF_BroadcastRedefinedPreVars(); if ( error ) goto cleanup; } } cleanup: #endif f = AR.infile; AR.infile = AR.outfile; AR.outfile = f; AC.cbufnum = AP.inside.oldcbuf; AM.rbufnum = AP.inside.oldrbuf; AR.Cnumlhs = AP.inside.oldcnumlhs; AR.BracketOn = oldbracketon; AP.PreInsideLevel = 0; AR.CompressPointer = oldcompresspointer; AS.MultiThreaded = oldmultithreaded; AC.mparallelflag = AP.inside.oldparallelflag; NumPotModdollars = AP.inside.oldnumpotmoddollars; POPPREASSIGNLEVEL #ifdef WITHMPI PF_RestoreInsideInfo(); if ( error ) return error; #endif return(0); } /* #] DoEndInside : #[ DoMessage : */ int DoMessage(UBYTE *s) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == '\t' ) s++; MesPrint("~~~%s",s); return(0); } /* #] DoMessage : #[ DoPipe : */ int DoPipe(UBYTE *s) { #ifndef WITHPIPE DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); #ifdef WITHPIPE FLUSHCONSOLE; while ( *s == ' ' || *s == '\t' ) s++; if ( OpenStream(s,PIPESTREAM,0,PRENOACTION) == 0 ) return(-1); return(0); #else Error0("Pipes not implemented on this computer/system"); return(-1); #endif } /* #] DoPipe : #[ DoPrcExtension : */ int DoPrcExtension(UBYTE *s) { UBYTE *t, *u, c; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == '\t' ) s++; if ( *s == 0 || *s == '\n' ) { MesPrint("@No valid procedure extension specified"); return(-1); } if ( FG.cTable[*s] != 0 ) { MesPrint("@Procedure extension should be a string starting with an alphabetic character. No whitespace."); return(-1); } t = s; while ( *s && *s != '\n' && *s != ' ' && *s != '\t' ) s++; u = s; while ( *s == ' ' || *s == '\t' ) s++; if ( *s != 0 && *s != '\n' ) { MesPrint("@Too many parameters in ProcedureExtension instruction"); return(-1); } c = *u; *u = 0; if ( AP.procedureExtension ) M_free(AP.procedureExtension,"ProcedureExtension"); AP.procedureExtension = strDup1(t,"ProcedureExtension"); *u = c; return(0); } /* #] DoPrcExtension : #[ DoPreOut : */ int DoPreOut(UBYTE *s) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( tolower(*s) == 'o' ) { if ( tolower(s[1]) == 'n' && s[2] == 0 ) { AP.PreOut = 1; return(0); } if ( tolower(s[1]) == 'f' && tolower(s[2]) == 'f' && s[3] == 0 ) { AP.PreOut = 0; return(0); } } MesPrint("@Illegal option in PreOut instruction"); return(-1); } /* #] DoPreOut : #[ DoPrePrintTimes : */ int DoPrePrintTimes(UBYTE *s) { DUMMYUSE(s); if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); PrintRunningTime(); return(0); } /* #] DoPrePrintTimes : #[ DoPreSortReallocate : */ int DoPreSortReallocate(UBYTE *s) { DUMMYUSE(s); if ( AC.SortReallocateFlag == 0 ) { /* Currently off, so set to 2. Then the reallocation code knows the flag was set here, since "On sortreallocate;" sets it to 1. */ AC.SortReallocateFlag = 2; } /* If the flag is already on, do nothing. */ return(0); } /* #] DoPreSortReallocate : #[ DoPreAppend : Syntax: #append */ int DoPreAppend(UBYTE *s) { UBYTE *name, *to; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); while ( *s == ' ' || *s == '\t' ) s++; /* Determine where to write */ if ( *s == '<' ) { s++; name = to = s; while ( *s && *s != '>' ) { if ( *s == '\\' ) s++; *to++ = *s++; } if ( *s == 0 ) { MesPrint("@Improper termination of filename"); return(-1); } s++; *to = 0; if ( *name ) { GetAppendChannel((char *)name); } else goto improper; } else { improper: MesPrint("@Proper syntax is: %#append "); return(-1); } return(0); } /* #] DoPreAppend : #[ DoPreCreate : Syntax: #create */ int DoPreCreate(UBYTE *s) { UBYTE *name, *to; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); while ( *s == ' ' || *s == '\t' ) s++; /* Determine where to write */ if ( *s == '<' ) { s++; name = to = s; while ( *s && *s != '>' ) { if ( *s == '\\' ) s++; *to++ = *s++; } if ( *s == 0 ) { MesPrint("@Improper termination of filename"); return(-1); } s++; *to = 0; if ( *name ) { GetChannel((char *)name,0); } else goto improper; } else { improper: MesPrint("@Proper syntax is: %#create "); return(-1); } return(0); } /* #] DoPreCreate : #[ DoPreRemove : */ int DoPreRemove(UBYTE *s) { UBYTE *name, *to; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '<' ) { s++; } else { MesPrint("@Proper syntax is: %#remove "); return(-1); } name = to = s; while ( *s && *s != '>' ) { if ( *s == '\\' ) s++; *to++ = *s++; } if ( *s == 0 ) { MesPrint("@Improper filename"); return(-1); } s++; *to = 0; CloseChannel((char *)name); remove((char *)name); return(0); } /* #] DoPreRemove : #[ DoPreClose : */ int DoPreClose(UBYTE *s) { UBYTE *name, *to; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '<' ) { s++; } else { MesPrint("@Proper syntax is: %#close "); return(-1); } name = to = s; while ( *s && *s != '>' ) { if ( *s == '\\' ) s++; *to++ = *s++; } if ( *s == 0 ) { MesPrint("@Improper filename"); return(-1); } s++; *to = 0; return(CloseChannel((char *)name)); } /* #] DoPreClose : #[ DoPreWrite : Syntax: #write [] "formatstring" [,objects] The format string can contain the following special objects/codes \n newline \t tab \! if last entry in string: no linefeed at end \b put \ in output %$ $-variable (to be found among the objects) %e expression (name to be found among the objects) %E expression without ; (name to be found among the objects) %s string (to be found among the objects) (with or without "") %S subterms (see PrintSubtermList) */ int DoPreWrite(UBYTE *s) { HANDLERS h; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHMPI if ( PF.me != MASTER ) return 0; #endif h.oldsilent = AM.silent; h.newlogonly = h.oldlogonly = AM.FileOnlyFlag; h.newhandle = h.oldhandle = AC.LogHandle; h.oldprinttype = AO.PrintType; while ( *s == ' ' || *s == '\t' ) s++; /* Determine where to write */ if( (s=defineChannel(s,&h))==0 ) return(-1); return(writeToChannel(WRITEOUT,s,&h)); } /* #] DoPreWrite : #[ DoProcedure : We have to read this procedure into a buffer. The only complications are: 1: we have to seek through the file to do this efficiently the file operations under VMS cannot do this properly (unless we use the proper ANSI structs?) This is the reason why we read whole input files under VMS. 2: what to do when the same name is used twice. Note that we have to do the reading without substitution of preprocessor variables. */ int DoProcedure(UBYTE *s) { UBYTE c; PROCEDURE *p; LONG i; if ( ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) || ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) ) { if ( PreSkip((UBYTE *)"procedure",(UBYTE *)"endprocedure",1) ) return(-1); return(0); } // AP.ProcList.num = NumProcedures is incremented inside FromList p = (PROCEDURE *)FromList(&AP.ProcList); if ( PreLoad(&(p->p),(UBYTE *)"procedure",(UBYTE *)"endprocedure" ,1,(char *)"procedure") ) return(-1); // If the procedure below is not local (loadmode 0) or has been called (loadmode 1), this is a // nested procedure definition. We must free its allocations when we hit its DoEndprocedure. // If it seems local (loadmode 2) but is tagged as "mustfree", it is multiply nested and we // similarly must free its allocations. if ( NumProcedures >= 2 && ( Procedures[NumProcedures-2].loadmode != 2 || Procedures[NumProcedures-2].mustfree ) ) { p->mustfree = 1; } // Otherwise, we are defining a local procedure at "ground level", and we keep the definition // on the procedure stack until FORM terminates. else { p->mustfree = 0; } p->loadmode = 2; s = p->p.buffer + 10; while ( *s == ' ' || *s == LINEFEED ) s++; if ( chartype[*s] ) { MesPrint("@Illegal name for procedure"); return(-1); } p->name = s++; while ( chartype[*s] == 0 || chartype[*s] == 1 ) s++; c = *s; *s = 0; p->name = strDup1(p->name,"procedure"); *s = c; /* Check for double names */ for ( i = NumProcedures-2; i >= 0; i-- ) { if ( StrCmp(Procedures[i].name,p->name) == 0 ) { Error1("Multiple occurrence of procedure name ",p->name); } } return(0); } /* #] DoProcedure : #[ DoPreBreak : */ int DoPreBreak(UBYTE *s) { DUMMYUSE(s); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.PreTypes[AP.NumPreTypes] != PRETYPESWITCH ) { if ( AP.PreSwitchLevel <= 0 ) MesPrint("@Break without corresponding Switch"); else MessPreNesting(7); return(-1); } if ( AP.PreSwitchLevel <= 0 ) { MesPrint("@Break without corresponding Switch"); return(-1); } if ( AP.PreSwitchModes[AP.PreSwitchLevel] == EXECUTINGPRESWITCH ) AP.PreSwitchModes[AP.PreSwitchLevel] = SEARCHINGPREENDSWITCH; return(0); } /* #] DoPreBreak : #[ DoPreCase : */ int DoPreCase(UBYTE *s) { UBYTE *t; if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.PreTypes[AP.NumPreTypes] != PRETYPESWITCH ) { if ( AP.PreSwitchLevel <= 0 ) MesPrint("@Case without corresponding Switch"); else MessPreNesting(8); return(-1); } if ( AP.PreSwitchLevel <= 0 ) { MesPrint("@Case without corresponding Switch"); return(-1); } if ( AP.PreSwitchModes[AP.PreSwitchLevel] != SEARCHINGPRECASE ) return(0); SKIPBLANKS(s) t = s; while ( *s ) { if ( *s == '\\' ) s++; s++; } while ( s > t && ( s[-1] == ' ' || s[-1] == '\t' ) && s[-2] != '\\' ) { if ( s[-2] == '\\' ) s--; s--; } if ( *t == '"' && s > t+1 && s[-1] == '"' && s[-2] != '\\' ) { t++; s--; *s = 0; } else *s = 0; s = AP.PreSwitchStrings[AP.PreSwitchLevel]; while ( *t == *s && *t ) { s++; t++; } if ( *t || *s ) return(0); /* case did not match */ AP.PreSwitchModes[AP.PreSwitchLevel] = EXECUTINGPRESWITCH; return(0); } /* #] DoPreCase : #[ DoPreDefault : */ int DoPreDefault(UBYTE *s) { DUMMYUSE(s); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.PreTypes[AP.NumPreTypes] != PRETYPESWITCH ) { if ( AP.PreSwitchLevel <= 0 ) MesPrint("@Default without corresponding Switch"); else MessPreNesting(9); return(-1); } if ( AP.PreSwitchLevel <= 0 ) { MesPrint("@Default without corresponding Switch"); return(-1); } if ( AP.PreSwitchModes[AP.PreSwitchLevel] != SEARCHINGPRECASE ) return(0); AP.PreSwitchModes[AP.PreSwitchLevel] = EXECUTINGPRESWITCH; return(0); } /* #] DoPreDefault : #[ DoPreEndSwitch : */ int DoPreEndSwitch(UBYTE *s) { DUMMYUSE(s); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.PreTypes[AP.NumPreTypes] != PRETYPESWITCH ) { if ( AP.PreSwitchLevel <= 0 ) MesPrint("@EndSwitch without corresponding Switch"); else MessPreNesting(10); return(-1); } AP.NumPreTypes--; if ( AP.PreSwitchLevel <= 0 ) { MesPrint("@EndSwitch without corresponding Switch"); return(-1); } M_free(AP.PreSwitchStrings[AP.PreSwitchLevel--],"pre switch string"); return(0); } /* #] DoPreEndSwitch : #[ DoPreSwitch : There should be a string after this. We have to store it somewhere. */ int DoPreSwitch(UBYTE *s) { UBYTE *t, *switchstring, **newstrings; int newnum, i, *newmodes; if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); SKIPBLANKS(s) t = s; while ( *s ) { if ( *s == '\\' ) s++; s++; } while ( s > t && ( s[-1] == ' ' || s[-1] == '\t' ) && s[-2] != '\\' ) { if ( s[-2] == '\\' ) s--; s--; } if ( *t == '"' && s > t+1 && s[-1] == '"' && s[-2] != '\\' ) { t++; s--; *s = 0; } else *s = 0; switchstring = (UBYTE *)Malloc1((s-t)+1,"case string"); s = switchstring; while ( *t ) { if ( *t == '\\' ) t++; *s++ = *t++; } *s = 0; if ( AP.PreSwitchLevel >= AP.NumPreSwitchStrings ) { newnum = 2*AP.NumPreSwitchStrings; newstrings = (UBYTE **)Malloc1(sizeof(UBYTE *)*(newnum+1),"case strings"); newmodes = (int *)Malloc1(sizeof(int)*(newnum+1),"case strings"); for ( i = 0; i < AP.NumPreSwitchStrings; i++ ) newstrings[i] = AP.PreSwitchStrings[i]; M_free(AP.PreSwitchStrings,"AP.PreSwitchStrings"); for ( i = 0; i <= AP.NumPreSwitchStrings; i++ ) newmodes[i] = AP.PreSwitchModes[i]; M_free(AP.PreSwitchModes,"AP.PreSwitchModes"); AP.PreSwitchStrings = newstrings; AP.PreSwitchModes = newmodes; AP.NumPreSwitchStrings = newnum; } AP.PreSwitchStrings[++AP.PreSwitchLevel] = switchstring; if ( ( AP.PreSwitchLevel > 1 ) && ( AP.PreSwitchModes[AP.PreSwitchLevel-1] != EXECUTINGPRESWITCH ) ) AP.PreSwitchModes[AP.PreSwitchLevel] = SEARCHINGPREENDSWITCH; else AP.PreSwitchModes[AP.PreSwitchLevel] = SEARCHINGPRECASE; AddToPreTypes(PRETYPESWITCH); return(0); } /* #] DoPreSwitch : #[ DoPreShow : Print the contents of the preprocessor variables */ int DoPreShow(UBYTE *s) { int i; UBYTE *name, c; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) { MesPrint("%#The preprocessor variables:"); for ( i = 0; i < NumPre; i++ ) { MesPrint("%d: %s = \"%s\"",i,PreVar[i].name,PreVar[i].value); } } else { while ( *s ) { name = s; while ( *s && *s != ' ' && *s != '\t' && *s != ',' ) s++; c = *s; *s = 0; for ( i = 0; i < NumPre; i++ ) { if ( StrCmp(PreVar[i].name,name) == 0 ) MesPrint("%d: %s = \"%s\"",i,PreVar[i].name,PreVar[i].value); } *s = c; while ( *s == ' ' || *s == '\t' ) s++; } } return(0); } /* #] DoPreShow : #[ DoSystem : */ /* * A macro for translating the contents of `x' into a string after expanding. */ #define STRINGIFY(x) STRINGIFY__(x) #define STRINGIFY__(x) #x int DoSystem(UBYTE *s) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHSYSTEM FLUSHCONSOLE; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '-' && s[1] == 'e' ) { LONG err; UBYTE str[24]; s += 2; if ( *s != ' ' ) { MesPrint("@Syntax error in #system command."); return(-1); } while ( *s == ' ' || *s == '\t' ) s++; err = system((char *)s); NumToStr(str,err); PutPreVar((UBYTE *)"SYSTEMERROR_",str,0,1); } else if ( system((char *)s) ) { MesPrint("@System call returned with error condition"); Terminate(-1); } return(0); #else Error0("External programs not implemented on this computer/system"); return(-1); #endif } /* #] DoSystem : #[ PreLoad : Loads a loop or procedure into a special buffer. Note: The current instruction is already in the preStart buffer */ int PreLoad(PRELOAD *p, UBYTE *start, UBYTE *stop, int mode, char *message) { UBYTE *s, *t, *top, *newbuffer, c; LONG i, ppsize, linenum = AC.CurrentStream->linenumber; int size1, size2, level, com=0, last=1, strng = 0; p->size = AP.pSize; p->buffer = (UBYTE *)Malloc1(p->size+1,message); top = p->buffer + p->size - 2; t = p->buffer; *t++ = '#'; s = start; size1 = size2 = 0; while ( *s ) { s++; size1++; } s = stop; while ( *s ) { s++; size2++; } s = AP.preStart; while ( *s ) *t++ = *s++; *t++ = LINEFEED; level = 1; i = 100; for (;;) { c = GetInput(); if ( c == ENDOFINPUT ) { MesPrint("@Missing %#%s, Should match line %l",stop,linenum); return(-1); } if ( c == AP.ComChar && last == 1 ) com = 1; if ( c == LINEFEED ) { last = 1; com = 0; } else last = 0; if ( ( c == '"' ) && ( com == 0 ) ) { strng ^= 1; } if ( ( c == '#' ) && ( com == 0 ) ) i = 0; else i++; if ( t >= top ) { ppsize = t - p->buffer; p->size *= 2; newbuffer = (UBYTE *)Malloc1(p->size,message); t = newbuffer; s = p->buffer; while ( --ppsize >= 0 ) *t++ = *s++; M_free(p->buffer,"loading do loop"); p->buffer = newbuffer; top = p->buffer + p->size - 2; } *t++ = c; if ( strng == 0 ) { if ( ( i == size2 ) && ( com == 0 ) ) { *t = 0; if ( StrICmp(t-size2,(UBYTE *)(stop)) == 0 ) { while ( ( c = GetInput() ) != LINEFEED && c != ENDOFINPUT ) {} level--; if ( level <= 0 ) break; if ( c == ENDOFINPUT ) Error1("Missing #",stop); *t++ = LINEFEED; *t = 0; last = 1; } } if ( ( i == size1 ) && mode && ( com == 0 ) ) { *t = 0; if ( StrICmp(t-size1,(UBYTE *)(start)) == 0 ) { /* while ( ( c = GetInput() ) != LINEFEED && c != ENDOFINPUT ) {} if ( c == ENDOFINPUT ) Error1("Missing #",stop); */ level++; } } if ( i == 1 && t[-2] == LINEFEED ) { if ( c == '-' ) AC.NoShowInput = 1; else if ( c == '+' ) AC.NoShowInput = 0; } } } *t++ = LINEFEED; *t = 0; return(0); } /* #] PreLoad : #[ PreSkip : Skips a loop or procedure. Note: The current instruction is already in the preStart buffer */ #define SKIPBUFSIZE 20 int PreSkip(UBYTE *start, UBYTE *stop, int mode) { UBYTE *s, *t, buffer[SKIPBUFSIZE+2], c; LONG i, linenum = AC.CurrentStream->linenumber; int size1, size2, level, com=0, last=1; t = buffer; *t++ = '#'; s = start; size1 = size2 = 0; while ( *s ) { s++; size1++; } s = stop; while ( *s ) { s++; size2++; } level = 1; i = 0; for (;;) { c = GetInput(); if ( c == ENDOFINPUT ) { MesPrint("@Missing %#%s, Should match line %l",stop,linenum); return(-1); } if ( c == AP.ComChar && last == 1 ) com = 1; if ( c == LINEFEED ) { last = 1; com = 0; i = 0; t = buffer; } else last = 0; if ( ( c == '#' ) && ( com == 0 ) ) { i = 0; t = buffer; } else i++; if ( i < SKIPBUFSIZE ) *t++ = c; if ( ( i == size2 ) && ( com == 0 ) ) { *t = 0; if ( StrICmp(t-size2,(UBYTE *)(stop)) == 0 ) { while ( ( c = GetInput() ) != LINEFEED && c != ENDOFINPUT ) {} level--; if ( level <= 0 ) { pushbackchar = LINEFEED; break; } if ( c == ENDOFINPUT ) Error1("Missing #",stop); i = 0; t = buffer; } } if ( ( i == size1 ) && mode && ( com == 0 ) ) { *t = 0; if ( StrICmp(t-size1,(UBYTE *)(start)) == 0 ) { while ( ( c = GetInput() ) != LINEFEED && c != ENDOFINPUT ) {} level++; i = 0; t = buffer; } } } return(0); } /* #] PreSkip : #[ StartPrepro : */ void StartPrepro(void) { int **ppp; AP.MaxPreIfLevel = 2; ppp = &AP.PreIfStack; if ( DoubleList((void ***)ppp,&AP.MaxPreIfLevel,sizeof(int), "PreIfLevels") ) Terminate(-1); AP.PreIfLevel = 0; AP.PreIfStack[0] = EXECUTINGIF; AP.NumPreSwitchStrings = 10; AP.PreSwitchStrings = (UBYTE **)Malloc1(sizeof(UBYTE *)* (AP.NumPreSwitchStrings+1),"case strings"); AP.PreSwitchModes = (int *)Malloc1(sizeof(int)* (AP.NumPreSwitchStrings+1),"case strings"); AP.PreSwitchModes[0] = EXECUTINGPRESWITCH; AP.PreSwitchLevel = 0; } /* #] StartPrepro : #[ EvalPreIf : Evaluates the condition in an if instruction. The return value is EXECUTINGIF if the condition is true. If it is false the returnvalue is LOOKINGFORELSE. An error gives a return value of -1 */ int EvalPreIf(UBYTE *s) { UBYTE *t, *u; int val; t = s; while ( *t ) t++; *t++ = ')'; *t = 0; if ( ( u = PreIfEval(s,&val) ) == 0 ) return(-1); if ( u < t ) { MesPrint("@Unmatched parentheses in condition"); return(-1); } if ( val ) return(EXECUTINGIF); else return(LOOKINGFORELSE); } /* #] EvalPreIf : #[ PreIfEval : Used for recursions in the evaluation of a preprocessor if-condition. It determines whether the contents of () is true or false (or in error). The return value is the address of the first character after the closing parenthesis or null if there is an error. In value we find true(1) or false(0) We enter after the opening parenthesis. There are levels: 0: orlevel: a || b 1: andlevel: a && b 2: eqlevel: a == b or a != b or a = b 3: cmplevel: a > b or a >= b or a < b or a <= b or a >~ b etc */ UBYTE *PreIfEval(UBYTE *s, int *value) { int orlevel = 0, andlevel = 0, eqlevel = 0, cmplevel = 0; int type, val; LONG val2; int ortype, orval, cmptype, cmpval, eqtype, eqval, andtype, andval; UBYTE *t, *eqt, *cmpt, c; int eqop, cmpop; ortype = orval = cmptype = cmpval = eqtype = eqval = andtype = andval = 0; eqop = cmpop = 0; eqt = cmpt = 0; *value = 0; while ( *s != ')' ) { while ( *s == ' ' || *s == '\t' || *s == '\n' || *s == '\r' ) s++; t = s; s = pParseObject(s,&type,&val2); if ( s == 0 ) return(0); val = val2; c = *s; *s++ = 0; /* in case the object is a string without " */ while ( c == ' ' || c == '\t' || c == '\n' || c == '\r' ) { c = *s; *s++ = 0; } if ( *t == '"' ) t++; switch(c) { case '|': if ( *s != '|' ) goto illoper; s++; /* fall through */ case ')': if ( cmplevel ) { if ( type == 0 || cmptype == 0 ) goto illobject; val = PreCmp(type,val,t,cmptype,cmpval,cmpt,cmpop); type = 0; cmplevel = 0; } if ( eqlevel ) { val = PreEq(type,val,t,eqtype,eqval,eqt,eqop); type = 0; eqlevel = 0; } if ( andlevel ) { if ( andtype != 0 || type != 0 ) goto illobject; val &= andval; andlevel = 0; } if ( orlevel ) { if ( ortype != 0 || type != 0 ) goto illobject; val |= orval; } if ( c == ')' ) { *value = val; return(s); } orlevel = 1; orval = val; ortype = type; break; case '&': if ( *s != '&' ) goto illoper; s++; if ( cmplevel ) { if ( type == 0 || cmptype == 0 ) goto illobject; val = PreCmp(type,val,t,cmptype,cmpval,cmpt,cmpop); type = 0; cmplevel = 0; } if ( eqlevel ) { val = PreEq(type,val,t,eqtype,eqval,eqt,eqop); type = 0; eqlevel = 0; } if ( andlevel ) { if ( andtype != 0 || type != 0 ) goto illobject; val &= andval; } andlevel = 1; andval = val; andtype = type; break; case '!': case '=': if ( eqlevel ) goto illorder; if ( cmplevel ) { if ( type == 0 || cmptype == 0 ) goto illobject; val = PreCmp(type,val,t,cmptype,cmpval,cmpt,cmpop); type = 0; cmplevel = 0; } if ( c == '!' && *s != '=' ) goto illoper; if ( *s == '=' ) s++; if ( c == '!' ) eqop = 1; else eqop = 0; eqlevel = 1; eqt = t; eqval = val; eqtype = type; break; case '>': case '<': if ( cmplevel ) goto illorder; if ( c == '<' ) cmpop = -1; else cmpop = 1; cmplevel = 1; cmpt = t; cmpval = val; cmptype = type; if ( *s == '=' ) { s++; if ( *s == '~' ) { s++; cmpop *= 4; } else cmpop *= 2; } else if ( *s == '~' ) { s++; cmpop *= 3; } break; default: goto illoper; } } return(s); illorder: MesPrint("@illegal order of operators"); return(0); illobject: MesPrint("@illegal object for this operator"); return(0); illoper: MesPrint("@illegal operator"); return(0); } /* #] PreIfEval : #[ PreCmp : */ int PreCmp(int type, int val, UBYTE *t, int type2, int val2, UBYTE *t2, int cmpop) { if ( type == 2 || type2 == 2 || cmpop < -2 || cmpop > 2 ) { if ( cmpop < 0 && cmpop > -3 ) cmpop -= 2; if ( cmpop > 0 && cmpop < 3 ) cmpop += 2; if ( cmpop == 3 ) val = StrCmp(t2,t) > 0; else if ( cmpop == 4 ) val = StrCmp(t2,t) >= 0; else if ( cmpop == -3 ) val = StrCmp(t2,t) < 0; else if ( cmpop == -4 ) val = StrCmp(t2,t) <= 0; } else { if ( cmpop == 1 ) val = ( val2 > val ); else if ( cmpop == 2 ) val = ( val2 >= val ); else if ( cmpop == -1 ) val = ( val2 < val ); else if ( cmpop == -2 ) val = ( val2 <= val ); } return(val); } /* #] PreCmp : #[ PreEq : */ int PreEq(int type, int val, UBYTE *t, int type2, int val2, UBYTE *t2, int eqop) { UBYTE str[20]; if ( type == 2 || type2 == 2 ) { if ( type != 2 ) { NumToStr(str,val ); t = str; } if ( type2 != 2 ) { NumToStr(str,val2); t2 = str; } if ( eqop == 1 ) val = StrCmp(t,t2) != 0; else val = StrCmp(t,t2) == 0; } else { if ( eqop ) val = val != val2; else val = val == val2; } return(val); } /* #] PreEq : #[ pParseObject : Parses a preprocessor object. We can have: 1: a number (type = 1) 2: a string (type = 2) 3: an expression between parentheses (type = 0) 4: a special function (type = 3) If the object is not a number, an expression or a special operator we try to interpret it as a string. */ UBYTE *pParseObject(UBYTE *s, int *type, LONG *val2) { UBYTE *t, c; int sign, val = 0; LONG x; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '(' ) { s++; while ( *s == ' ' || *s == '\t' || *s == '\n' || *s == '\r' ) s++; s = PreIfEval(s,&val); *type = 0; *val2 = val; return(s); } else if ( *s == '$' && s[1] == '(' ) { s += 2; while ( *s == ' ' || *s == '\t' || *s == '\n' || *s == '\r' ) s++; s = PreIfDollarEval(s,&val); *type = 0; *val2 = val; return(s); } if ( *s == 0 ) { illend: MesPrint("@illegal end of condition"); return(0); } if ( *s == '"' ) { s++; while ( *s && *s != '"' ) { if ( *s == '\\' ) s++; s++; } if ( *s == 0 ) goto illend; else *s = 0; *type = 2; s++; while ( *s == ' ' || *s == '\t' || *s == '\n' || *s == '\r' ) s++; return(s); } t = s; sign = 1; x = 0; if ( chartype[*t] == 0 ) { /* Special operators and strings without "" */ do { t++; } while ( chartype[*t] <= 1 ); if ( *t == '(' ) { WORD ttype; c = *t; *t = 0; if ( StrICmp(s,(UBYTE *)"termsin") == 0 ) { UBYTE *tt; WORD numdol, numexp; ttype = 0; together: *t++ = c; while ( *t == ' ' || *t == '\t' || *t == '\n' || *t == '\r' ) t++; if ( *t == '$' ) { t++; tt = t; while (chartype[*tt] <= 1 ) tt++; c = *tt; *tt = 0; if ( ( numdol = GetDollar(t) ) > 0 ) { *tt = c; if ( ttype == 1 ) { x = SizeOfDollar(numdol); } else { x = TermsInDollar(numdol); } } else { MesPrint("@$%s has not (yet) been defined",t); *tt = c; Terminate(-1); } } else { tt = SkipAName(t); c = *tt; *tt = 0; if ( GetName(AC.exprnames,t,&numexp,NOAUTO) == NAMENOTFOUND ) { MesPrint("@%s has not (yet) been defined",t); *tt = c; Terminate(-1); } else { *tt = c; if ( ttype == 1 ) { x = SizeOfExpression(numexp); } else { x = TermsInExpression(numexp); } } } while ( *tt == ' ' || *tt == '\t' || *tt == '\n' || *tt == '\r' ) tt++; if ( *tt != ')' ) { MesPrint("@Improper use of terms($var) or terms(expr)"); Terminate(-1); } *type = 3; s = tt+1; *val2 = x; return(s); } else if ( StrICmp(s,(UBYTE *)"sizeof") == 0 ) { ttype = 1; goto together; } else if ( StrICmp(s,(UBYTE *)"exists") == 0 ) { UBYTE *tt; WORD numdol, numexp; *t++ = c; while ( *t == ' ' || *t == '\t' || *t == '\n' || *t == '\r' ) t++; if ( *t == '$' ) { t++; tt = t; while (chartype[*tt] <= 1 ) tt++; c = *tt; *tt = 0; if ( ( numdol = GetDollar(t) ) >= 0 ) { x = 1; } else { x = 0; } *tt = c; } else if ( *t == '"' ) { /* see whether a file exists */ /* UBYTE *name, *oldname; */ t++; tt = t; for (;;) { if ( *tt == '\\' ) tt++; else if ( *tt == '"' ) break; tt++; } c = *tt; *tt = 0; /* Try to open the file. If possible, return 1. Afterwards close it. We do have to run through the FORMPATH. Hence we use LocateFile. This routine may change the name to the full name. oldname = name = strDup1(t,"name in exists"); x = LocateFile(&name,-1); */ x = OpenFile((char *)t); if ( x >= 0 ) { CloseFile(x); x = 1; /* if ( name != oldname ) M_free(name,"name from LocateFile"); */ } else x = 0; /* M_free(oldname,"name in exists"); */ *tt++ = c; } else { tt = SkipAName(t); c = *tt; *tt = 0; if ( GetName(AC.exprnames,t,&numexp,NOAUTO) == NAMENOTFOUND ) { x = 0; } else { x = 1; } *tt = c; } while ( *tt == ' ' || *tt == '\t' || *tt == '\n' || *tt == '\r' ) tt++; if ( *tt != ')' ) { MesPrint("@Improper use of exists($var) or exists(expr)"); Terminate(-1); } *type = 3; s = tt+1; *val2 = x; return(s); } else if ( StrICmp(s,(UBYTE *)"isnumerical") == 0 ) { GETIDENTITY UBYTE *tt; WORD numdol, numexp; *t++ = c; while ( *t == ' ' || *t == '\t' || *t == '\n' || *t == '\r' ) t++; if ( *t == '$' ) { t++; tt = t; while (chartype[*tt] <= 1 ) tt++; c = *tt; *tt = 0; if ( ( numdol = GetDollar(t) ) < 0 ) { MesPrint("@$ variable in isnumerical(%s) does not exist",t); Terminate(-1); } x = DolToLong(BHEAD numdol); if ( AN.ErrorInDollar ) { DOLLARS d = Dollars + numdol; x = 0; if ( d->type == DOLNUMBER || d->type == DOLTERMS ) { if ( d->where[0] == 0 ) x = 1; else if ( d->where[d->where[0]] == 0 ) { if ( ABS(d->where[d->where[0]-1]) == d->where[0]-1 ) x = 1; } } } else x = 1; *tt = c; } else { tt = SkipAName(t); c = *tt; *tt = 0; if ( GetName(AC.exprnames,t,&numexp,NOAUTO) == NAMENOTFOUND ) { MesPrint("@expression in isnumerical(%s) does not exist",t); Terminate(-1); } x = TermsInExpression(numexp); if ( x != 1 ) x = 0; else { WORD *term = AT.WorkPointer; if ( GetFirstTerm(term,numexp,1) < 0 ) { MesPrint("@error reading expression in isnumerical(%s)",t); Terminate(-1); } if ( *term == ABS(term[*term-1])+1 ) x = 1; else x = 0; } *tt = c; } while ( *tt == ' ' || *tt == '\t' || *tt == '\n' || *tt == '\r' ) tt++; if ( *tt != ')' ) { MesPrint("@Improper use of isnumerical($var) or numerical(expr)"); Terminate(-1); } *type = 3; s = tt+1; *val2 = x; return(s); } else if ( StrICmp(s,(UBYTE *)("maxpowerof")) == 0 ) { UBYTE *tt; WORD numsym; int stype; *t++ = c; while ( *t == ' ' || *t == '\t' || *t == '\n' || *t == '\r' ) t++; tt = SkipAName(t); c = *tt; *tt = 0; if ( ( stype = GetName(AC.varnames,t,&numsym,NOAUTO) ) == NAMENOTFOUND ) { MesPrint("@%s has not (yet) been defined",t); *tt = c; Terminate(-1); } else if ( stype != CSYMBOL ) { MesPrint("@%s should be a symbol",t); *tt = c; Terminate(-1); } else { *tt = c; x = symbols[numsym].maxpower; } while ( *tt == ' ' || *tt == '\t' || *tt == '\n' || *tt == '\r' ) tt++; if ( *tt != ')' ) { MesPrint("@Improper use of maxpowerof(symbol)"); Terminate(-1); } *type = 3; s = tt+1; *val2 = x; return(s); } else if ( StrICmp(s,(UBYTE *)("minpowerof")) == 0 ) { UBYTE *tt; WORD numsym; int stype; *t++ = c; while ( *t == ' ' || *t == '\t' || *t == '\n' || *t == '\r' ) t++; tt = SkipAName(t); c = *tt; *tt = 0; if ( ( stype = GetName(AC.varnames,t,&numsym,NOAUTO) ) == NAMENOTFOUND ) { MesPrint("@%s has not (yet) been defined",t); *tt = c; Terminate(-1); } else if ( stype != CSYMBOL ) { MesPrint("@%s should be a symbol",t); *tt = c; Terminate(-1); } else { *tt = c; x = symbols[numsym].minpower; } while ( *tt == ' ' || *tt == '\t' || *tt == '\n' || *tt == '\r' ) tt++; if ( *tt != ')' ) { MesPrint("@Improper use of minpowerof(symbol)"); Terminate(-1); } *type = 3; s = tt+1; *val2 = x; return(s); } else if ( StrICmp(s,(UBYTE *)"isfactorized") == 0 ) { UBYTE *tt; WORD numdol, numexp; *t++ = c; while ( *t == ' ' || *t == '\t' || *t == '\n' || *t == '\r' ) t++; if ( *t == '$' ) { t++; tt = t; while (chartype[*tt] <= 1 ) tt++; c = *tt; *tt = 0; if ( ( numdol = GetDollar(t) ) > 0 ) { if ( Dollars[numdol].factors != 0 ) x = 1; else x = 0; } else { MesPrint("@ %s should be the name of an expression or a $ variable",t-1); Terminate(-1); } *tt = c; } else { tt = SkipAName(t); c = *tt; *tt = 0; if ( GetName(AC.exprnames,t,&numexp,NOAUTO) == NAMENOTFOUND ) { MesPrint("@ %s should be the name of an expression or a $ variable",t); Terminate(-1); } else { if ( ( Expressions[numexp].vflags & ISFACTORIZED ) != 0 ) x = 1; else x = 0; } *tt = c; } while ( *tt == ' ' || *tt == '\t' || *tt == '\n' || *tt == '\r' ) tt++; if ( *tt != ')' ) { MesPrint("@Improper use of isfactorized($var) or isfactorized(expr)"); Terminate(-1); } *type = 3; s = tt+1; *val2 = x; return(s); } else if ( StrICmp(s,(UBYTE *)"isdefined") == 0 ) { UBYTE *tt; *t++ = c; while ( *t == ' ' || *t == '\t' || *t == '\n' || *t == '\r' ) t++; tt = SkipAName(t); c = *tt; *tt = 0; if ( GetPreVar(t,WITHOUTERROR) != 0 ) x = 1; else x = 0; *tt = c; while ( *tt == ' ' || *tt == '\t' || *tt == '\n' || *tt == '\r' ) tt++; if ( *tt != ')' ) { MesPrint("@Improper use of isdefined(var)"); Terminate(-1); } *type = 3; s = tt+1; *val2 = x; return(s); } else if ( StrICmp(s,(UBYTE *)"flag") == 0 ) { UBYTE *tt; WORD x = 0, numexp; { *t++ = c; while ( *t == ' ' || *t == '\t' ) t++; if ( FG.cTable[*t] != 1 ) goto flagerror; while ( FG.cTable[*t] == 1 ) x = 10*x + (*t++ - '0'); if ( x < 1 || x > BITSINWORD ) { MesPrint("@Illegal number %d for flag in flag condition",x); goto flagerror; } while ( *t == ' ' || *t == '\t' ) t++; if ( *t != ',' ) goto flagerror; t++; while ( *t == ' ' || *t == '\t' ) t++; tt = SkipAName(t); c = *tt; *tt = 0; if ( GetName(AC.exprnames,t,&numexp,NOAUTO) == NAMENOTFOUND ) { MesPrint("@ %s should be the name of an expression",t); goto flagerror; } *tt = c; while ( *t == ' ' || *t == '\t' ) t++; if ( *tt != ')' ) { flagerror: MesPrint("@Improper use of flag(num,expr)"); Terminate(-1); return(0); } if ( ( Expressions[numexp].uflags & ( 1 << (x-1) ) ) != 0 ) *val2 = 1; else *val2 = 0; *type = 3; s = tt+1; return(s); } } else *t = c; } else if ( *t == '=' || *t == '<' || *t == '>' || *t == '!' || *t == ')' || *t == ' ' || *t == '\t' || *t == 0 || *t == '\n' ) { *val2 = 0; *type = 2; return(t); } else { MesPrint("@Illegal use of string in preprocessor condition: %s",s); Terminate(-1); } } while ( *t == '-' || *t == '+' || *t == ' ' || *t == '\t' ) { if ( *t == '-' ) sign = -sign; t++; } while ( chartype[*t] == 1 ) { x = 10*x + *t++ - '0'; } while ( *t == ' ' || *t == '\t' ) t++; if ( chartype[*t] == 8 || *t == ')' || *t == '=' || *t == 0 ) { *val2 = sign > 0 ? x: -x; *type = 1; return(t); } while ( chartype[*t] != 8 && *t != ')' && *t != '=' && *t ) t++; while ( ( t > s ) && ( t[-1] == ' ' || t[-1] == '\t' ) ) t--; *type = 2; *val2 = val; return(t); } /* #] pParseObject : #[ PreCalc : To be called when a { is encountered. Action: read first till matching }. This is to be stored. Next we look whether this is a set or whether it can be evaluated. If it is a set we consider it as a new stream. The stream will have to be deallocated when read completely. If it is to be evaluated we do that and put the result in a stream. */ UBYTE *PreCalc(void) { UBYTE *buff, *s = 0, *t, *newb, c; int size, i, n, parlevel = 0, bralevel = 0; LONG answer; ULONG uanswer; size = n = 0; buff = 0; c = '{'; for (;;) { if ( n >= size ) { if ( size == 0 ) size = 72; else size *= 2; if ( ( newb = (UBYTE *)Malloc1(size+2,"{}") ) == 0 ) return(0); s = newb; if ( buff ) { i = n; t = buff; NCOPYB(s,t,i); M_free(buff,"pre calc buffer"); } else s = newb; buff = newb; } *s++ = c; n++; c = GetChar(0); if ( c == 0 ) { Error0("Unmatched {}"); M_free(buff,"precalc buffer"); return(0); } else if ( c == '{' ) { bralevel++; } else if ( c == '}' ) { if ( --bralevel < 0 ) { *s++ = c; *s = 0; break; } } else if ( c == '(' ) { parlevel++; } else if ( c == ')' ) { if ( --parlevel < 0 ) { *s++ = c; *s = 0; goto setstring; } } else if ( chartype[c] != 1 && chartype[c] != 5 && chartype[c] != 6 && c != '!' && c != '&' && c != '|' && c != '\\' ) { *s++ = c; *s = 0; goto setstring; } } if ( parlevel > 0 ) goto setstring; /* Try now to evaluate the string. If it works, copy the resulting value back into buff as a string. */ answer = 0; if ( PreEval(buff+1,&answer) == 0 ) goto setstring; t = buff + size; s = buff; if ( answer < 0 ) { *s++ = '-'; } uanswer = LongAbs(answer); n = 0; do { *--t = ( uanswer % 10 ) + '0'; uanswer /= 10; n++; } while ( uanswer > 0 ); NCOPYB(s,t,n); *s = 0; setstring:; /* Open a stream that contains the current string. Mark it to be removed after termination. */ if ( OpenStream(buff,PRECALCSTREAM,0,PRENOACTION) == 0 ) return(0); return(buff); } /* #] PreCalc : #[ PreEval : Operations are: +, -, *, /, %, &, |, ^, !, ^% (postfix 2log), ^/ (postfix sqrt) */ UBYTE *PreEval(UBYTE *s, LONG *x) { LONG y, z, a; int tobemultiplied, tobeadded = 1, expsign, i; UBYTE *t; *x = 0; a = 1; while ( *s == ' ' || *s == '\t' ) s++; for(;;){ if ( *s == '+' || *s == '-' ) { if ( *s == '-' ) tobeadded = -1; else tobeadded = 1; s++; while ( *s == '-' || *s == '+' || *s == ' ' || *s == '\t' ) { if ( *s == '-' ) tobeadded = -tobeadded; s++; } } tobemultiplied = 0; for(;;){ while ( *s == ' ' || *s == '\t' ) s++; if ( *s <= '9' && *s >= '0' ) { ULONG uy; ParseNumber(uy,s) y = uy; /* may cause an implementation-defined behaviour */ } else if ( *s == '(' || *s == '{' ) { if ( ( t = PreEval(s+1,&y) ) == 0 ) return(0); s = t; } else return(0); while ( *s == ' ' || *s == '\t' ) s++; expsign = 1; while ( *s == '^' || *s == '!' ) { s++; if ( s[-1] == '!' ) { /* factorial of course */ while ( *s == ' ' || *s == '\t' ) s++; if ( y < 0 ) { MesPrint("@Negative value in preprocessor factorial: %l",y); return(0); } else if ( y == 0 ) y = 1; else if ( y > 1 ) { z = y-1; while ( z > 0 ) { y = y*z; z--; } } continue; } else if ( *s == '%' ) { /* ^% is postfix 2log */ s++; while ( *s == ' ' || *s == '\t' ) s++; z = y; if ( z <= 0 ) { MesPrint("@Illegal value in preprocessor logarithm: %l",z); return(0); } y = 0; z >>= 1; while ( z ) { y++; z >>= 1; } continue; } else if ( *s == '/' ) { /* ^/ is postfix sqrt */ LONG yy, zz; s++; while ( *s == ' ' || *s == '\t' ) s++; z = y; if ( z <= 0 ) { MesPrint("@Illegal value in preprocessor square root: %l",z); return(0); } if ( z > 8 ) { /* Very crude integer square root */ zz = z; yy = 0; zz >>= 1; while ( zz ) { yy++; zz >>= 1; } zz = z >> (yy/2); i = 10; y = 0; do { yy = zz/2 + z/(2*zz); i--; if ( y == yy ) break; y = zz; zz = yy; } while ( y != yy && i > 0 ); while ( y*y < z ) y++; while ( y*y > z ) y--; } else if ( z >= 4 ) y = 2; else if ( z == 0 ) y = 0; else y = 1; continue; } while ( *s == ' ' || *s == '\t' ) s++; while ( *s == '-' || *s == '+' || *s == ' ' || *s == '\t' ) { if ( *s == '-' ) expsign = -expsign; } if ( *s <= '9' && *s >= '0' ) { ParseNumber(z,s) } else if ( *s == '(' || *s == '{' ) { if ( ( t = PreEval(s+1,&z) ) == 0 ) return(0); s = t; } else return(0); while ( *s == ' ' || *s == '\t' ) s++; y = iexp(y,(int)z); } if ( tobemultiplied == 0 ) { if ( expsign < 0 ) a = 1/y; else a = y; } else { if ( tobemultiplied > 2 && expsign != 1 ) { MesPrint("&Incorrect use of ^ with & or |. Use brackets!"); Terminate(-1); } tobemultiplied *= expsign; if ( tobemultiplied == 1 ) a *= y; else if ( tobemultiplied == 3 ) a &= y; else if ( tobemultiplied == 4 ) a |= y; else { if ( y == 0 || tobemultiplied == -2 ) { MesPrint("@Division by zero in preprocessor calculator"); Terminate(-1); } if ( tobemultiplied == 2 ) a %= y; else a /= y; } } if ( *s == '%' ) tobemultiplied = 2; else if ( *s == '*' ) tobemultiplied = 1; else if ( *s == '/' ) tobemultiplied = -1; else if ( *s == '&' ) tobemultiplied = 3; else if ( *s == '|' ) tobemultiplied = 4; else { ULONG ux, ua; ux = *x; ua = a; if ( tobeadded >= 0 ) ux += ua; else ux -= ua; *x = ULongToLong(ux); if ( *s == ')' || *s == '}' ) return(s+1); else if ( *s == '-' || *s == '+' ) { tobeadded = 1; break; } else return(0); } s++; } } /* return(0); */ } /* #] PreEval : #[ AddToPreTypes : */ void AddToPreTypes(int type) { if ( AP.NumPreTypes >= AP.MaxPreTypes ) { int i, *newlist = (int *)Malloc1(sizeof(int)*(2*AP.MaxPreTypes+1) ,"preprocessor type lists"); for ( i = 0; i <= AP.MaxPreTypes; i++ ) newlist[i] = AP.PreTypes[i]; M_free(AP.PreTypes,"preprocessor type lists"); AP.PreTypes = newlist; AP.MaxPreTypes = 2*AP.MaxPreTypes; } AP.PreTypes[++AP.NumPreTypes] = type; } /* #] AddToPreTypes : #[ MessPreNesting : */ void MessPreNesting(int par) { MesPrint("@(%d)Illegal nesting of %#if, %#do, %#procedure and/or %#switch",par); } /* #] MessPreNesting : #[ DoPreAddSeparator : Preprocessor directives "addseparator" and "rmseparator" add/remove separator characters used to separate function arguments. Example: #define QQ "a|g|a" #addseparator % *Comma must be quoted!: #rmseparator "," #rmseparator | #call H(a,a%`QQ') Characters ' ', '\t' and '"' are ignored! */ int DoPreAddSeparator(UBYTE *s) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); for(;*s != '\0';s++){ while ( *s == ' ' || *s == '\t' || *s == '"') s++; /* Todo: if ( set_in(*s,invalidseparators) ) { MesPrint("@Invalid separator specified"); return(-1); } */ set_set(*s,AC.separators); } return(0); } /* #] DoPreAddSeparator : #[ DoPreRmSeparator : See commentary with DoPreAddSeparator Characters ' ', '\t' and '"' are ignored! */ int DoPreRmSeparator(UBYTE *s) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); for(;*s != '\0';s++){ while ( *s == ' ' || *s == '\t' || *s == '"') s++; set_del(*s,AC.separators); } return(0); } /* #] DoPreRmSeparator : #[ DoExternal: #external ["prevar"] command */ int DoExternal(UBYTE *s) { #ifdef WITHEXTERNALCHANNEL UBYTE *prevar=0; int externalD= 0; #else DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHEXTERNALCHANNEL while ( *s == ' ' || *s == '\t' ) s++; if(*s == '"'){/*prevar to store the descriptor is defined*/ prevar=++s; if ( chartype[*s] == 0 )for(;*s != '"'; s++)switch(chartype[*s]){ case 10:/*'\0' fits here*/ MesPrint("@Can't finde closing \""); Terminate(-1); case 0:case 1: continue; default: break; } if(*s != '"'){ MesPrint("@Illegal name of preprocessor variable to store external channel"); return(-1); } *s='\0'; for(s++; *s == ' ' || *s == '\t'; s++); } if(*s == '\0'){ MesPrint("@Illegal external command"); return(-1); } /*here s is a command*/ /*See the file extcmd.c*/ /*[08may2006 mt]:*/ externalD=openExternalChannel( s, AX.daemonize, AX.shellname, AX.stderrname); /*:[08may2006 mt]*/ if(externalD<1){/*error?*/ /*Not quite correct - terminate the program on error:*/ Error1("Can't start external program",s); return(-1); } /*Now external command runs.*/ if(prevar){/*Store the external channel descriptor in the provided variable:*/ UBYTE buf[21];/* 64/Log_2[10] = 19.3, so this is enough forever...*/ NumToStr(buf,externalD); if ( PutPreVar(prevar,buf,0,1) < 0 ) return(-1); } AX.currentExternalChannel=externalD; /*[08may2006 mt]:*/ if(AX.currentPrompt!=0){/*Change default terminator*/ if(setTerminatorForExternalChannel( (char *)AX.currentPrompt)){ MesPrint("@Prompt is too long"); return(-1); } } setKillModeForExternalChannel(AX.killSignal,AX.killWholeGroup); /*:[08may2006 mt]*/ return(0); #else /*ifdef WITHEXTERNALCHANNEL*/ Error0("External channel: not implemented on this computer/system"); return(-1); #endif /*ifdef WITHEXTERNALCHANNEL ... else*/ } /* #] DoExternal: #[ DoPrompt: #prompt string */ int DoPrompt(UBYTE *s) { #ifndef WITHEXTERNALCHANNEL DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); #ifdef WITHEXTERNALCHANNEL while ( *s == ' ' || *s == '\t' ) s++; if ( AX.currentPrompt ) M_free(AX.currentPrompt,"external channel prompt"); if ( *s == '\0' ) AX.currentPrompt = (UBYTE *)strDup1((UBYTE *)"","external channel prompt"); else AX.currentPrompt = strDup1(s,"external channel prompt"); if( setTerminatorForExternalChannel( (char *)AX.currentPrompt) > 0 ){ MesPrint("@Prompt is too long"); return(-1); } /*else: if 0, ok; if -1, there is no current channel-ok, just prompt is stored.*/ return(0); #else /*ifdef WITHEXTERNALCHANNEL*/ Error0("External channel: not implemented on this computer/system"); return(-1); #endif /*ifdef WITHEXTERNALCHANNEL ... else*/ } /* #] DoPrompt: #[ DoSetExternal: #setexternal n */ int DoSetExternal(UBYTE *s) { #ifdef WITHEXTERNALCHANNEL int n=0; #else DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHEXTERNALCHANNEL while ( *s == ' ' || *s == '\t' ) s++; while ( chartype[*s] == 1 ) { n = 10*n + *s++ - '0'; } while ( *s == ' ' || *s == '\t' ) s++; if(*s!='\0'){ MesPrint("@setexternal: number expected"); return(-1); } if(selectExternalChannel(n)<0){ MesPrint("@setexternal: invalid number"); return(-1); } AX.currentExternalChannel=n; return(0); #else /*ifdef WITHEXTERNALCHANNEL*/ Error0("External channel: not implemented on this computer/system"); return(-1); #endif /*ifdef WITHEXTERNALCHANNEL ... else*/ } /* #] DoSetExternal: #[ DoSetExternalAttr: */ static FORM_INLINE UBYTE *pickupword(UBYTE *s) { for(;*s>' ';s++)switch(*s){ case '=': case ',': case ';': return(s); }/*for(;*s>' ';s++)switch(*s)*/ return(s); } /*Returns 0 if the first string (case insensitively) equal to the beginning of the second string (of length n): */ static inline int strINCmp(UBYTE *a, UBYTE *b, int n) { for(;n>0;n--)if(tolower(*a++)!=tolower(*b++)) return(1); return(*a != '\0'); } #define KILL "kill" #define KILLALL "killall" #define DAEMON "daemon" #define SHELL "shell" #define STDERR "stderr" #define TRUE_EXPR "true" #define FALSE_EXPR "false" #define NOSHELL "noshell" #define TERMINAL "terminal" /* Expects comma-separated list of pairs name=value */ int DoSetExternalAttr(UBYTE *s) { #ifdef WITHEXTERNALCHANNEL int lnam,lval; UBYTE *nam,*val; #else DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHEXTERNALCHANNEL do{ /*Read the name:*/ while ( *s == ' ' || *s == '\t' ) s++; s=pickupword(nam=s); lnam=s-nam; while ( *s == ' ' || *s == '\t' ) s++; if(*s++!='='){ MesPrint("@External channel:'=' expected instead of %s",s-1); return(-1); } /*Read the value:*/ while ( *s == ' ' || *s == '\t' ) s++; val=s; for(;;){ UBYTE *m; s=pickupword(s); m=s; while ( *s == ' ' || *s == '\t' ) s++; if( (*s == ',')||(*s == '\n')||(*s == ';')||(*s == '\0') ){ s=m; break; } }/*for(;;)*/ lval=s-val; while ( *s == ' ' || *s == '\t' ) s++; if(strINCmp((UBYTE *)SHELL,nam,lnam)==0){ if(AX.shellname!=NULL) M_free(AX.shellname,"external channel shellname"); if(strINCmp((UBYTE *)NOSHELL,val,lval)==0) AX.shellname=NULL; else{ UBYTE *ch,*b; b=ch=AX.shellname=Malloc1(lval+1,"external channel shellname"); while(ch-b='0' && *val<= '9' ) n = 10*n + *val++ - '0'; else{ MesPrint("@External channel: number expected for %s",KILL); return(-1); } } AX.killSignal=n; }else if(strINCmp((UBYTE *)STDERR,nam,lnam)==0){ if( AX.stderrname != NULL ) { M_free(AX.stderrname,"external channel stderrname"); } if(strINCmp((UBYTE *)TERMINAL,val,lval)==0) AX.stderrname = NULL; else{ UBYTE *ch,*b; b=ch=AX.stderrname=Malloc1(lval+1,"external channel stderrname"); while(ch-b' ')&&(*(s-1)!=';') ){ MesPrint("@External channel: syntax error: %s",s-1); return(-1); } return(0); #else /*ifdef WITHEXTERNALCHANNEL*/ Error0("External channel: not implemented on this computer/system"); return(-1); #endif /*ifdef WITHEXTERNALCHANNEL ... else*/ } /* #] DoSetExternalAttr: #[ DoRmExternal: #rmexternal [n] (if 0, close all) */ int DoRmExternal(UBYTE *s) { #ifdef WITHEXTERNALCHANNEL int n = -1; #else DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHEXTERNALCHANNEL while ( *s == ' ' || *s == '\t' ) s++; if( chartype[*s] == 1 ){ for(n=0; chartype[*s] == 1 ; s++) { n = 10*n + *s - '0'; } while ( *s == ' ' || *s == '\t' ) s++; } if(*s!='\0'){ MesPrint("@rmexternal: invalid number"); return(-1); } switch(n){ case 0:/*Close all opened channels*/ closeAllExternalChannels(); AX.currentExternalChannel=0; /*Do not clean AX.currentPrompt!*/ return(0); case -1:/*number is not specified - try current*/ n=AX.currentExternalChannel; /* fall through */ default: closeExternalChannel(n);/*No reaction for possible error*/ } if (n == AX.currentExternalChannel)/*cleaned up by closeExternalChannel()*/ AX.currentExternalChannel=0; return(0); #else /*ifdef WITHEXTERNALCHANNEL*/ Error0("External channel: not implemented on this computer/system"); return(-1); #endif /*ifdef WITHEXTERNALCHANNEL ... else*/ } /* #] DoRmExternal: #[ DoFromExternal : #fromexternal is used to read the text from the running external program, the syntax is similar to the #include directive. #fromexternal "varname" is used to read the text from the running external program into the preprocessor variable varname. directive. #fromexternal "varname" maxlength is used to read the text from the running external program into the preprocessor variable varname. directive. Only first maxlength characters are stored. FORM continues to read the running external program output until the external program outputs a prompt. */ int DoFromExternal(UBYTE *s) { #ifdef WITHEXTERNALCHANNEL UBYTE *prevar=0; int lbuf=-1; int withNoList=AC.NoShowInput; int oldpreassignflag; #else DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHEXTERNALCHANNEL FLUSHCONSOLE; while ( *s == ' ' || *s == '\t' ) s++; /*[17may2006 mt]:*/ if ( *s == '-' || *s == '+' ) { if ( *s == '-' ) withNoList = 1; else withNoList = 0; s++; while ( *s == ' ' || *s == '\t' ) s++; }/*if ( *s == '-' || *s == '+' )*/ /*:[17may2006 mt]*/ /*[02feb2006 mt]:*/ if(*s == '"'){/*prevar to store the output is defined*/ prevar=++s; if ( *s=='$' || chartype[*s] == 0 )for(;*s != '"'; s++)switch(chartype[*s]){ case 10:/*'\0' fits here*/ MesPrint("@Can't finde closing \""); Terminate(-1); case 0:case 1: continue; default: break; } if(*s != '"'){ MesPrint("@Illegal name to store output of external channel"); return(-1); } *s='\0'; for(s++; *s == ' ' || *s == '\t'; s++); }/*if(*s == '"')*/ if(*s != '\0'){ if( chartype[*s] == 1 ){ for(lbuf=0; chartype[*s] == 1 ; s++) { lbuf = 10*lbuf + *s - '0'; } while ( *s == ' ' || *s == '\t' ) s++; } if( (*s!='\0')||(lbuf<0) ){ MesPrint("@Illegal buffer length in fromexternal"); return(-1); } }/*if(*s != '\0')*/ /*:[02feb20006 mt]*/ if(getCurrentExternalChannel()!=AX.currentExternalChannel) /*[08may20006 mt]:*/ /*selectExternalChannel(AX.currentExternalChannel);*/ if(selectExternalChannel(AX.currentExternalChannel)){ MesPrint("@No current external channel"); return(-1); } /*:[08may20006 mt]*/ /*[02feb2006 mt]:*/ if(prevar!=0){/*The result must be stored into preprovar*/ UBYTE *buf; int cc = 0; if(lbuf == -1){/*Unlimited buffer, everything must be stored*/ int i; buf=Malloc1( (lbuf=255)+1,"Fromexternal"); /*[18may20006 mt]:*/ /*for(i=0;(cc=getcFromExtChannel())!=EOF;i++){*/ /* May 2006: now getcFromExtChannelOk returns EOF while getcFromExtChannelFailure returns -2 (see comments in exctcmd.c):*/ for(i=0;(cc=getcFromExtChannel())>0;i++){ /*:[18may20006 mt]*/ if(i==lbuf){ int j; UBYTE *tmp=Malloc1( (lbuf*=2)+1,"Fromexternal"); for(j=0;j0;i++)*/ /*[18may20006 mt]:*/ if(cc == -2){ MesPrint("@No current external channel"); return(-1); } lbuf=i; /*:[18may20006 mt]*/ buf[i]='\0'; }else{/*Fixed buffer, only lbuf chars must be stored*/ int i; buf=Malloc1(lbuf+1,"Fromexternal"); for(i=0; i0) while(getcFromExtChannel()>0);/*Eat the rest*/ else if(cc == -2){ MesPrint("@No current external channel"); return(-1); } /*:[18may20006 mt]*/ } /*[18may20006 mt]:*/ if(*prevar == '$'){/*Put the answer to the dollar variable*/ int oldNumPotModdollars = NumPotModdollars; #ifdef WITHMPI WORD oldRhsExprInModuleFlag = AC.RhsExprInModuleFlag; AC.RhsExprInModuleFlag = 0; #endif /*Here lbuf is the actual length of buf!*/ /*"prevar=buf'\0'":*/ UBYTE *pbuf=Malloc1(StrLen(prevar)+1+lbuf+1,"Fromexternal to dollar"); UBYTE *c=pbuf; UBYTE *b=prevar; while(*b!='\0'){*c++ = *b++;} *c++='='; b=buf; while( (*c++=*b++)!='\0' ); oldpreassignflag = AP.PreAssignFlag; AP.PreAssignFlag = 1; if ( ( cc = CompileStatement(pbuf) ) || ( cc = CatchDollar(0) ) ) { Error1("External channel: can't asign output to dollar variable ",prevar); } AP.PreAssignFlag = oldpreassignflag; NumPotModdollars = oldNumPotModdollars; #ifdef WITHMPI AC.RhsExprInModuleFlag = oldRhsExprInModuleFlag; #endif M_free(pbuf,"Fromexternal to dollar"); }else{ cc = PutPreVar(prevar, buf, 0, 1) < 0; } /*:[18may20006 mt]*/ M_free(buf,"Fromexternal"); if ( cc ) return(-1); return(0); } /*:[02feb2006 mt]*/ if ( OpenStream(s,EXTERNALCHANNELSTREAM,0,PRENOACTION) == 0 ) return(-1); /*[17may2006 mt]:*/ AC.NoShowInput = withNoList; /*:[17may2006 mt]*/ return(0); #else Error0("External channel: not implemented on this computer/system"); return(-1); #endif } /* #] DoFromExternal : #[ DoToExternal : #toexetrnal */ #ifdef WITHEXTERNALCHANNEL /*A wrapper to writeBufToExtChannel, see the file extcmd.c:*/ LONG WriteToExternalChannel(int handle, UBYTE *buffer, LONG size) { /*ATT! handle is not used! Actual output is performed to the current external channel, see extcmd.c!*/ DUMMYUSE(handle); if(writeBufToExtChannel((char*)buffer,size)) return(-1); return(size); } #endif /*ifdef WITHEXTERNALCHANNEL*/ int DoToExternal(UBYTE *s) { #ifdef WITHEXTERNALCHANNEL HANDLERS h; LONG (*OldWrite)(int handle, UBYTE *buffer, LONG size) = WriteFile; int ret=-1; #else DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.preError ) return(0); #ifdef WITHEXTERNALCHANNEL h.oldsilent=AM.silent; h.newlogonly = h.oldlogonly = AM.FileOnlyFlag; h.newhandle = h.oldhandle = AC.LogHandle; h.oldprinttype = AO.PrintType; WriteFile=&WriteToExternalChannel; while ( *s == ' ' || *s == '\t' ) s++; if(AX.currentExternalChannel==0){ MesPrint("@No current external channel"); goto DoToExternalReady; } if(getCurrentExternalChannel()!=AX.currentExternalChannel) selectExternalChannel(AX.currentExternalChannel); ret=writeToChannel(EXTERNALCHANNELOUT,s,&h); DoToExternalReady: WriteFile=OldWrite; return(ret); #else /*ifdef WITHEXTERNALCHANNEL*/ Error0("External channel: not implemented on this computer/system"); return(-1); #endif /*ifdef WITHEXTERNALCHANNEL ... else*/ } /* #] DoToExternal : #[ defineChannel : */ UBYTE *defineChannel(UBYTE *s, HANDLERS *h) { UBYTE *name,*to; if ( *s != '<' ) return(s); s++; name = to = s; while ( *s && *s != '>' ) { if ( *s == '\\' ) s++; *to++ = *s++; } if ( *s == 0 ) { MesPrint("@Improper termination of filename"); return(0); } s++; *to = 0; if ( *name ) { h->newhandle = GetChannel((char *)name,0); h->newlogonly = 1; } else if ( AC.LogHandle >= 0 ) { h->newhandle = AC.LogHandle; h->newlogonly = 1; } return(s); } /* #] defineChannel : #[ writeToChannel : */ int writeToChannel(int wtype, UBYTE *s, HANDLERS *h) { UBYTE *to, *fstring, *ss, *sss, *s1, c, c1; WORD num, number, nfac; WORD oldOptimizationLevel; UBYTE Out[MAXLINELENGTH+14], *stopper; int nosemi, i; int plus = 0; /* Now determine the format string */ while ( *s == ',' || *s == ' ' ) s++; if ( *s != '"' ) { MesPrint("@No format string present"); return(-1); } s++; fstring = to = s; while ( *s ) { if ( *s == '\\' ) { s++; if ( *s == '\\' ) { *to++ = *s++; if ( *s == '\\' ) *to++ = *s++; } else if ( *s == '"' ) *to++ = *s++; else { *to++ = '\\'; *to++ = *s++; } } else if ( *s == '"' ) break; else *to++ = *s++; } if ( *s != '"' ) { MesPrint("@No closing \" in format string"); return(-1); } *to = 0; s++; if ( AC.LineLength > 20 && AC.LineLength <= MAXLINELENGTH ) stopper = Out + AC.LineLength; else stopper = Out + MAXLINELENGTH; to = Out; /* s points now at the list of objects (if any) we can start executing the format string. */ AM.silent = 0; AC.LogHandle = h->newhandle; AM.FileOnlyFlag = h->newlogonly; if ( h->newhandle >= 0 ) { AO.PrintType |= PRINTLFILE; } while ( *fstring ) { if ( to >= stopper ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { *to++ = '&'; } num = to - Out; WriteString(wtype,Out,num); to = Out; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { number = 7; for ( i = 0; i < number; i++ ) *to++ = ' '; to[-2] = '&'; } } if ( *fstring == '\\' ) { fstring++; if ( *fstring == 'n' ) { num = to - Out; WriteString(wtype,Out,num); to = Out; fstring++; } else if ( *fstring == 't' ) { *to++ = '\t'; fstring++; } else if ( *fstring == 'b' ) { *to++ = '\\'; fstring++; } else *to++ = *fstring++; } else if ( *fstring == '%' ) { plus = 0; retry: fstring++; if ( *fstring == 'd' ) { int sign,dig; number = -1; donumber: while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; sign = 1; while ( *s == '+' || *s == '-' ) { if ( *s == '-' ) sign = -sign; s++; } dig = 0; ss = s; if ( sign < 0 ) { ss--; *ss = '-'; dig++; } while ( *s >= '0' && *s <= '9' ) { s++; dig++; } if ( number < 0 ) { while ( ss < s ) { if ( to >= stopper ) { num = to - Out; WriteString(wtype,Out,num); to = Out; } if ( *ss == '\\' ) ss++; *to++ = *ss++; } } else { if ( number < dig ) { dig = number; ss = s - dig; } while ( number > dig ) { if ( to >= stopper ) { num = to - Out; WriteString(wtype,Out,num); to = Out; } *to++ = ' '; number--; } while ( ss < s ) { if ( to >= stopper ) { num = to - Out; WriteString(wtype,Out,num); to = Out; } if ( *ss == '\\' ) ss++; *to++ = *ss++; } } fstring++; } else if ( *fstring == '$' ) { UBYTE *dolalloc; number = AO.OutSkip; dodollar: while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { number = 7; } if ( *s != '$' ) { nodollar: MesPrint("@$-variable expected in #write instruction"); AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } s++; ss = s; while ( chartype[*s] <= 1 ) s++; if ( s == ss ) goto nodollar; c = *s; *s = 0; num = GetDollar(ss); if ( num < 0 ) { MesPrint("@#write instruction: $%s has not been defined",ss); AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } *s = c; if ( *s == '[' ) { if ( Dollars[num].nfactors <= 0 ) { *s = 0; MesPrint("@#write instruction: $%s has not been factorized",ss); AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } /* Now get the number between the [] */ nfac = GetDollarNumber(&s,Dollars+num); if ( Dollars[num].nfactors == 1 && nfac == 1 ) goto writewhole; if ( ( dolalloc = WriteDollarFactorToBuffer(num,nfac,0) ) == 0 ) { AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } goto writealloc; } else if ( *s && *s != ' ' && *s != ',' && *s != '\t' ) { MesPrint("@#write instruction: illegal characters after $-variable"); AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } else { writewhole: if ( ( dolalloc = WriteDollarToBuffer(num,0) ) == 0 ) { AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } else { writealloc: ss = dolalloc; while ( *ss ) { if ( to >= stopper ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { *to++ = '&'; } num = to - Out; WriteString(wtype,Out,num); to = Out; for ( i = 0; i < number; i++ ) *to++ = ' '; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) to[-2] = '&'; } if ( chartype[*ss] > 3 ) { *to++ = *ss++; } else { sss = ss; while ( chartype[*ss] <= 3 ) ss++; if ( ( to + (ss-sss) ) >= stopper ) { if ( (ss-sss) >= (stopper-Out) ) { if ( ( to - stopper ) < 10 ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { *to++ = '&'; } num = to - Out; WriteString(wtype,Out,num); to = Out; for ( i = 0; i < number; i++ ) *to++ = ' '; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) to[-2] = '&'; } while ( (ss-sss) >= (stopper-Out) ) { while ( to < stopper-1 ) { *to++ = *sss++; } if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { *to++ = '&'; } else { *to++ = '\\'; } num = to - Out; WriteString(wtype,Out,num); to = Out; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { for ( i = 0; i < number; i++ ) *to++ = ' '; to[-2] = '&'; } } } else { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { *to++ = '&'; } num = to - Out; WriteString(wtype,Out,num); to = Out; for ( i = 0; i < number; i++ ) *to++ = ' '; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) to[-2] = '&'; } } while ( sss < ss ) *to++ = *sss++; } } } M_free(dolalloc,"written dollar"); fstring++; } } else if ( *fstring == 's' ) { fstring++; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s == '"' ) { s++; ss = s; while ( *s ) { if ( *s == '\\' ) s++; else if ( *s == '"' ) break; s++; } if ( *s == 0 ) { MesPrint("@#write instruction: Missing \" in string"); AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } while ( ss < s ) { if ( to >= stopper ) { num = to - Out; WriteString(wtype,Out,num); to = Out; } if ( *ss == '\\' ) ss++; *to++ = *ss++; } s++; } else { sss = ss = s; while ( *s && *s != ',' ) { if ( *s == '\\' ) { s++; sss = s+1; } s++; } while ( s > sss+1 && ( s[-1] == ' ' || s[-1] == '\t' ) ) s--; while ( ss < s ) { if ( to >= stopper ) { num = to - Out; WriteString(wtype,Out,num); to = Out; } if ( *ss == '\\' ) ss++; *to++ = *ss++; } } } else if ( *fstring == 'X' ) { fstring++; if ( cbuf[AM.sbufnum].numrhs > 0 ) { /* This should be only to the value of AM.oldnumextrasymbols */ UBYTE *s = GetPreVar(AM.oldnumextrasymbols,0); WORD x = 0; while ( *s >= '0' && *s <= '9' ) x = 10*x + *s++ - '0'; if ( x > 0 ) PrintSubtermList(1,x); else PrintSubtermList(1,cbuf[AM.sbufnum].numrhs); } } else if ( *fstring == 'O' ) { number = AO.OutSkip; dooptim: fstring++; /* First test whether there is an optimization buffer */ if ( AO.OptimizeResult.code == NULL && AO.OptimizationLevel != 0 ) { MesPrint("@In #write instruction: no optimization results available!"); return(-1); } num = to - Out; WriteString(wtype,Out,num); to = Out; if ( AO.OptimizationLevel != 0 ) { WORD oldoutskip = AO.OutSkip; AO.OutSkip = number; optimize_print_code(0); AO.OutSkip = oldoutskip; } } else if ( *fstring == 'e' || *fstring == 'E' ) { if ( *fstring == 'E' || AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) nosemi = 1; else nosemi = 0; fstring++; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( chartype[*s] != 0 && *s != '[' ) { noexpr: MesPrint("@expression name expected in #write instruction"); AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } ss = s; if ( ( s = SkipAName(ss) ) == 0 || s[-1] == '_' ) goto noexpr; s1 = s; c = c1 = *s1; if ( c1 == '(' ) { SKIPBRA3(s) if ( *s == ')' ) { AO.CurBufWrt = s1+1; c = *s; *s = 0; } else { MesPrint("@Illegal () specifier in expression name in #write"); AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } } else AO.CurBufWrt = (UBYTE *)underscore; *s1 = 0; num = to - Out; if ( num > 0 ) WriteUnfinString(wtype,Out,num); to = Out; oldOptimizationLevel = AO.OptimizationLevel; AO.OptimizationLevel = 0; if ( WriteOne(ss,(int)num,nosemi,plus) < 0 ) { AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } AO.OptimizationLevel = oldOptimizationLevel; *s1 = c1; if ( s > s1 ) *s++ = c; } /* File content */ else if ( ( *fstring == 'f' ) || ( *fstring == 'F' ) ) { LONG n; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; ss = s; while ( *s && *s != ',' ) { if ( *s == '\\' ) s++; s++; } c = *s; *s = 0; s1 = LoadInputFile(ss,HEADERFILE); *s = c; /* There should have been a way to pass the file size. Also there should be conversions for \r\n etc. */ if ( s1 ) { ss = s1; while ( *ss ) ss++; n = ss-s1; WriteString(wtype,s1,n); M_free(s1,"copy file"); } else if ( *fstring == 'F' ) { *s = 0; MesPrint("@Error in #write: could not open file %s",ss); *s = c; goto ReturnWithError; } fstring++; } else if ( *fstring == '%' ) { *to++ = *fstring++; } else if ( FG.cTable[*fstring] == 1 ) { /* %#S */ number = 0; while ( FG.cTable[*fstring] == 1 ) { number = 10*number + *fstring++ - '0'; } if ( *fstring == 'O' ) goto dooptim; else if ( *fstring == 'd' ) goto donumber; else if ( *fstring == '$' ) goto dodollar; else if ( *fstring == 't' ) { /* `tab' position */ if ( number < (WORD)(stopper-Out) ) { while ( (WORD)(to-Out) < number ) *to++ = ' '; } fstring++; } else if ( *fstring == 'X' || *fstring == 'x' ) { if ( number > 0 && number <= cbuf[AM.sbufnum].numrhs ) { UBYTE buffer[80], *out, *old1, *old2, *old3; WORD *term, first; if ( *fstring == 'X' ) { out = StrCopy((UBYTE *)AC.extrasym,buffer); if ( AC.extrasymbols == 0 ) { out = NumCopy(number,out); out = StrCopy((UBYTE *)"_",out); } else if ( AC.extrasymbols == 1 ) { if ( AC.OutputMode == CMODE ) { out = StrCopy((UBYTE *)"[",out); out = NumCopy(number,out); out = StrCopy((UBYTE *)"]",out); } else { out = StrCopy((UBYTE *)"(",out); out = NumCopy(number,out); out = StrCopy((UBYTE *)")",out); } } out = StrCopy((UBYTE *)"=",out); ss = buffer; while ( ss < out ) { if ( to >= stopper ) { num = to - Out; WriteString(wtype,Out,num); to = Out; } *to++ = *ss++; } } term = cbuf[AM.sbufnum].rhs[number]; first = 1; if ( *term == 0 ) { *to++ = '0'; } else { old1 = AO.OutFill; old2 = AO.OutputLine; old3 = AO.OutStop; AO.OutFill = to; AO.OutputLine = Out; AO.OutStop = Out + AC.LineLength; while ( *term ) { if ( WriteInnerTerm(term,first) ) Terminate(-1); term += *term; first = 0; } to = Out + (AO.OutFill-AO.OutputLine); AO.OutFill = old1; AO.OutputLine = old2; AO.OutStop = old3; } } fstring++; } else { goto IllegControlSequence; } } else if ( *fstring == '+' ) { plus = 1; goto retry; } else if ( *fstring == 0 ) { *to++ = 0; } else { IllegControlSequence: MesPrint("@Illegal control sequence in format string in #write instruction"); ReturnWithError: AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(-1); } } else { *to++ = *fstring++; } } /* Now flush the output */ num = to - Out; /*[15apr2004 mt]:*/ if(wtype==EXTERNALCHANNELOUT){ if(num!=0) WriteUnfinString(wtype,Out,num); }else /*:[15apr2004 mt]*/ WriteString(wtype,Out,num); /* and restore original parameters */ AM.FileOnlyFlag = h->oldlogonly; AC.LogHandle = h->oldhandle; AO.PrintType = h->oldprinttype; AM.silent = h->oldsilent; return(0); } /* #] writeToChannel : #[ DoFactDollar : Executes the #factdollar $var instruction */ int DoFactDollar(UBYTE *s) { GETIDENTITY WORD numdollar, *oldworkpointer; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == '\t' ) s++; if ( *s == '$' ) { if ( GetName(AC.dollarnames,s+1,&numdollar,NOAUTO) != CDOLLAR ) { MesPrint("@%s is undefined",s); return(-1); } s = SkipAName(s+1); if ( *s != 0 ) { MesPrint("@#FactDollar should have a single $variable for its argument"); return(-1); } NewSort(BHEAD0); oldworkpointer = AT.WorkPointer; if ( DollarFactorize(BHEAD numdollar) ) return(-1); AT.WorkPointer = oldworkpointer; LowerSortLevel(); return(0); } else if ( ParenthesesTest(s) ) return(-1); else { MesPrint("@#FactDollar should have a single $variable for its argument"); return -1; } } /* #] DoFactDollar : #[ GetDollarNumber : */ WORD GetDollarNumber(UBYTE **inp, DOLLARS d) { UBYTE *s = *inp, c, *name; WORD number, nfac, *w; DOLLARS dd; s++; if ( *s == '$' ) { s++; name = s; while ( FG.cTable[*s] < 2 ) s++; c = *s; *s = 0; if ( GetName(AC.dollarnames,name,&number,NOAUTO) == NAMENOTFOUND ) { MesPrint("@dollar in #write should have been defined previously"); Terminate(-1); } *s = c; dd = Dollars + number; if ( c == '[' ) { *inp = s; nfac = GetDollarNumber(inp,dd); s = *inp; if ( *s != ']' ) { MesPrint("@Illegal factor for dollar variable"); Terminate(-1); } *inp = s+1; if ( nfac == 0 ) { if ( dd->nfactors > d->nfactors ) { TooBig: MesPrint("@Factor number for dollar variable too large"); Terminate(-1); } return(dd->nfactors); } w = dd->factors[nfac-1].where; if ( w == 0 ) { if ( dd->factors[nfac-1].value > d->nfactors || dd->factors[nfac-1].value < 0 ) goto TooBig; return(dd->factors[nfac-1].value); } if ( *w == 4 && w[4] == 0 && w[3] == 3 && w[2] == 1 && w[1] <= d->nfactors ) return(w[1]); if ( w[*w] == 0 && w[*w-1] == *w-1 ) goto TooBig; IllNum: MesPrint("@Illegal factor number for dollar variable"); Terminate(-1); } else { /* The dollar should be a number */ if ( dd->type == DOLZERO ) { return(0); } else if ( dd->type == DOLTERMS || dd->type == DOLNUMBER ) { w = dd->where; if ( *w == 4 && w[4] == 0 && w[3] == 3 && w[2] == 1 && w[1] <= d->nfactors ) return(w[1]); if ( w[*w] == 0 && w[*w-1] == *w-1 ) goto TooBig; goto IllNum; } else goto IllNum; } } else if ( FG.cTable[*s] == 1 ) { WORD x = *s++ - '0'; while ( FG.cTable[*s] == 1 ) { x = 10*x + *s++ - '0'; if ( x > d->nfactors ) { MesPrint("@Factor number %d for dollar variable too large",x); Terminate(-1); } } if ( *s != ']' ) { MesPrint("@Illegal factor number for dollar variable"); Terminate(-1); } s++; *inp = s; return(x); } else { MesPrint("@Illegal factor indicator for dollar variable"); Terminate(-1); } return(-1); } /* #] GetDollarNumber : #[ DoSetRandom : Executes the #SetRandom number */ int DoSetRandom(UBYTE *s) { ULONG x; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == '\t' ) s++; x = 0; while ( FG.cTable[*s] == 1 ) { x = 10*x + (*s++-'0'); } while ( *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) { #ifdef WITHPTHREADS #ifdef WITHSORTBOTS int id, totnum = MaX(2*AM.totalnumberofthreads-3,AM.totalnumberofthreads); #else int id, totnum = AM.totalnumberofthreads; #endif for ( id = 0; id < totnum; id++ ) { AB[id]->R.wranfseed = x; if ( AB[id]->R.wranfia ) M_free(AB[id]->R.wranfia,"wranf"); AB[id]->R.wranfia = 0; } #else AR.wranfseed = x; if ( AR.wranfia ) M_free(AR.wranfia,"wranf"); AR.wranfia = 0; #endif return(0); } else { MesPrint("@proper syntax is #SetRandom number"); return(-1); } } /* #] DoSetRandom : #[ DoOptimize : Executes the #Optimize(expr) instruction. */ int DoOptimize(UBYTE *s) { GETIDENTITY UBYTE *exprname; WORD numexpr; int error = 0, i; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); DUMMYUSE(*s) exprname = s; s = SkipAName(s); if ( *s != 0 && *s != ';' ) { MesPrint("@proper syntax is #Optimize,expression"); return(-1); } *s = 0; if ( GetName(AC.exprnames,exprname,&numexpr,NOAUTO) != CEXPRESSION ) { MesPrint("@%s is not an expression",exprname); error = 1; } else if ( AP.preError == 0 ) { EXPRESSIONS e = Expressions + numexpr; POSITION position; int firstterm; WORD *term = AT.WorkPointer; ClearOptimize(); if ( AO.OptimizationLevel == 0 ) return(0); switch ( e->status ) { case LOCALEXPRESSION: case GLOBALEXPRESSION: break; default: MesPrint("@Expression %s is not an active unhidden local or global expression.",exprname); Terminate(-1); break; } #ifdef WITHMPI if ( PF.me == MASTER ) #endif RevertScratch(); for ( i = NumExpressions-1; i >= 0; i-- ) { AS.OldOnFile[i] = Expressions[i].onfile; AS.OldNumFactors[i] = Expressions[i].numfactors; AS.Oldvflags[i] = Expressions[i].vflags; Expressions[i].vflags &= ~(ISUNMODIFIED|ISZERO); } for ( i = 0; i < NumExpressions; i++ ) { if ( i == numexpr ) { PutPreVar(AM.oldnumextrasymbols, GetPreVar((UBYTE *)"EXTRASYMBOLS_",0),0,1); Optimize(numexpr, 0); AO.OptimizeResult.nameofexpr = strDup1(exprname,"optimize expression name"); continue; } #ifdef WITHMPI if ( PF.me == MASTER ) { #endif e = Expressions + i; switch ( e->status ) { case LOCALEXPRESSION: case SKIPLEXPRESSION: case DROPLEXPRESSION: case DROPPEDEXPRESSION: case GLOBALEXPRESSION: case SKIPGEXPRESSION: case DROPGEXPRESSION: case HIDELEXPRESSION: case HIDEGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: break; default: continue; } AR.GetFile = 0; SetScratch(AR.infile,&(e->onfile)); if ( GetTerm(BHEAD term) <= 0 ) { MesPrint("@Expression %d has problems reading from scratchfile",i); Terminate(-1); } term[3] = i; AR.DeferFlag = 0; SeekScratch(AR.outfile,&position); e->onfile = position; *AM.S0->sBuffer = 0; firstterm = -1; do { WORD *oldipointer = AR.CompressPointer; WORD *comprtop = AR.ComprTop; AR.ComprTop = AM.S0->sTop; AR.CompressPointer = AM.S0->sBuffer; if ( firstterm > 0 ) { if ( PutOut(BHEAD term,&position,AR.outfile,1) < 0 ) goto DoSerr; } else if ( firstterm < 0 ) { if ( PutOut(BHEAD term,&position,AR.outfile,0) < 0 ) goto DoSerr; firstterm++; } else { if ( PutOut(BHEAD term,&position,AR.outfile,-1) < 0 ) goto DoSerr; firstterm++; } AR.CompressPointer = oldipointer; AR.ComprTop = comprtop; } while ( GetTerm(BHEAD term) ); if ( FlushOut(&position,AR.outfile,1) ) { DoSerr: MesPrint("@Expression %d has problems writing to scratchfile",i); Terminate(-1); } #ifdef WITHMPI } #endif } /* Now some administration and we are done */ UpdateMaxSize(); } else { ClearOptimize(); } return(error); } /* #] DoOptimize : #[ DoClearOptimize : Clears all relevant buffers of the output optimization */ int DoClearOptimize(UBYTE *s) { if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); DUMMYUSE(*s); return(ClearOptimize()); } /* #] DoClearOptimize : #[ DoSkipExtraSymbols : Adds the intermediate variables of the previous optimization to the list of extra symbols, provided it has not yet been erased by a #clearoptimize To remove them again one needs to use the 'delete extrasymbols;' or the 'delete extrasymbols>num;' statement in which num is the old number of extra symbols. */ int DoSkipExtraSymbols(UBYTE *s) { CBUF *C = cbuf + AM.sbufnum; WORD tt = 0, j = 0, oldval = AO.OptimizeResult.minvar; if ( AO.OptimizeResult.code == NULL ) return(0); if ( AO.OptimizationLevel == 0 ) return(0); while ( *s == ',' ) s++; if ( *s == 0 ) { AO.OptimizeResult.minvar = AO.OptimizeResult.maxvar+1; } else { while ( *s <= '9' && *s >= '0' ) j = 10*j + *s++ - '0'; if ( *s ) { MesPrint("@Illegal use of #SkipExtraSymbols instruction"); Terminate(-1); } AO.OptimizeResult.minvar += j; if ( AO.OptimizeResult.minvar > AO.OptimizeResult.maxvar ) AO.OptimizeResult.minvar = AO.OptimizeResult.maxvar+1; } j = AO.OptimizeResult.minvar - oldval; while ( j > 0 ) { AddRHS(AM.sbufnum,1); AddNtoC(AM.sbufnum,1,&tt,16); AddToCB(C,0) InsTree(AM.sbufnum,C->numrhs); j--; } return(0); } /* #] DoSkipExtraSymbols : #[ DoPreReset : Does a reset of variables. Currently only the timer (stopwatch) of `timer_' */ int DoPreReset(UBYTE *s) { UBYTE *ss, c; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) { MesPrint("@proper syntax is #Reset variable"); return(-1); } ss = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( ( StrICmp(ss,(UBYTE *)"timer") == 0 ) || ( StrICmp(ss,(UBYTE *)"stopwatch") == 0 ) ) { *s = c; AP.StopWatchZero = GetRunningTime(); return(0); } else { *s = c; MesPrint("@proper syntax is #Reset variable"); return(-1); } } /* #] DoPreReset : #[ DoPreAppendPath : */ static int DoAddPath(UBYTE *s, int bPrepend) { /* NOTE: this doesn't support some file systems, e.g., 0x5c with CP932. */ UBYTE *path, *path_end, *current_dir, *current_dir_end, *NewPath, *t; int bRelative, n; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); /* Parse the path in the input. */ while ( *s == ' ' || *s == '\t' ) s++; /* skip spaces */ if ( *s == '"' ) { /* the path is given by "..." */ path = ++s; while ( *s && *s != '"' ) { if ( SEPARATOR != '\\' && *s == '\\' ) { /* escape character, e.g., "\\\"" */ if ( !s[1] ) goto ImproperPath; s++; } s++; } if ( *s != '"' ) goto ImproperPath; path_end = s++; } else { path = s; while ( *s && *s != ' ' && *s != '\t' ) { if ( SEPARATOR != '\\' && *s == '\\' ) { /* escape character, e.g., "\\ " */ if ( !s[1] ) goto ImproperPath; s++; } s++; } path_end = s; } if ( path == path_end ) goto ImproperPath; /* empty path */ while ( *s == ' ' || *s == '\t' ) s++; /* skip spaces */ if ( *s ) goto ImproperPath; /* extra tokens found */ /* Check if the path is an absolute path. */ bRelative = 1; if ( path[0] == SEPARATOR ) { /* starts with the directory separator */ bRelative = 0; } #ifdef WINDOWS else if ( chartype[path[0]] == 0 && path[1] == ':' ) { /* starts with (drive letter): */ bRelative = 0; } #endif /* Get the current file directory when a relative path is given. */ if ( bRelative ) { if ( !AC.CurrentStream ) goto FileNameUnavailable; if ( AC.CurrentStream->type != FILESTREAM && AC.CurrentStream->type != REVERSEFILESTREAM ) goto FileNameUnavailable; if ( !AC.CurrentStream->name ) goto FileNameUnavailable; s = current_dir = current_dir_end = AC.CurrentStream->name; while ( *s ) { if ( SEPARATOR != '\\' && *s == '\\' && s[1] ) { /* escape character, e.g., "\\\"" */ s += 2; continue; } if ( *s == SEPARATOR ) { current_dir_end = s; } s++; } } else { current_dir = current_dir_end = NULL; } /* Allocate a buffer for new AM.Path. */ n = path_end - path; if ( AM.Path ) n += StrLen(AM.Path) + 1; if ( current_dir != current_dir_end ) n+= current_dir_end - current_dir + 1; s = NewPath = (UBYTE *)Malloc1(n + 1,"add path"); /* Construct new FORM path. */ if ( bPrepend ) { if ( current_dir != current_dir_end ) { t = current_dir; while ( t != current_dir_end ) *s++ = *t++; *s++ = SEPARATOR; } t = path; while ( t != path_end ) *s++ = *t++; if ( AM.Path ) *s++ = PATHSEPARATOR; } if ( AM.Path ) { t = AM.Path; while ( *t ) *s++ = *t++; } if ( !bPrepend ) { if ( AM.Path ) *s++ = PATHSEPARATOR; if ( current_dir != current_dir_end ) { t = current_dir; while ( t != current_dir_end ) *s++ = *t++; *s++ = SEPARATOR; } t = path; while ( t != path_end ) *s++ = *t++; } *s = '\0'; /* Update AM.Path. */ if ( AM.Path ) M_free(AM.Path,"add path"); AM.Path = NewPath; return(0); ImproperPath: MesPrint("@Improper syntax for %#%sPath", bPrepend ? "Prepend" : "Append"); return(-1); FileNameUnavailable: /* This may be improved in future. */ MesPrint("@Sorry, %#%sPath can't resolve the current file name from here", bPrepend ? "Prepend" : "Append"); return(-1); } /** * Appends the given path (absolute or relative to the current file directory) * to the FORM path. * * Syntax: * #appendpath */ int DoPreAppendPath(UBYTE *s) { return DoAddPath(s, 0); } /* #] DoPreAppendPath : #[ DoPrePrependPath : */ /** * Prepends the given path (absolute or relative to the current file directory) * to the FORM path. * * Syntax: * #prependpath */ int DoPrePrependPath(UBYTE *s) { return DoAddPath(s, 1); } /* #] DoPrePrependPath : #[ DoTimeOutAfter : Executes the #timeoutafter number */ int DoTimeOutAfter(UBYTE *s) { #ifdef WITH_ALARM ULONG x; #else DUMMYUSE(s); #endif if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); #ifdef WITH_ALARM while ( *s == ' ' || *s == '\t' ) s++; x = 0; while ( FG.cTable[*s] == 1 ) { x = 10*x + (*s++-'0'); } while ( *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) { alarm(x); return(0); } else { MesPrint("@proper syntax is #TimeoutAfter number"); return(-1); } #else Error0("#timeoutafter not implemented on this computer/system"); return(-1); #endif } /* #] DoTimeOutAfter : #[ DoNamespace : Syntax: #Namespace name ..... #use variables ..... #EndNamespace Effect: All variables/expressions defined inside the range of the namespace get name_ prepended. This holds also for $-variables, names of procedures and names of files. Namespaces can be used in a nested way. cf this_is_deep_x A leading _ takes the role of what is super:: in some other languages. Remarks: Names of preprocessor variables are excluded! Names of built in objects are excluded! (like sum_, d_ etc.) */ int DoNamespace(UBYTE *s) { UBYTE *s1, *s2, c; NAMESPACE *namespace; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( FG.cTable[*s] != 0 ) { MesPrint("@Illegal name in #namespace instruction: %s",s); return(-1); } s1 = s; while ( FG.cTable[*s1] <= 1 ) s1++; s2 = s1; while ( *s2 == ' ' || *s2 == ',' || *s2 == '\t' ) s2++; if ( *s2 != 0 ) { MesPrint("@A #namespace instruction can only have one name with only alphanumeric characters."); return(-1); } c = *s1; *s1 = 0; /* Now we have the name and the statement is legal. We can proceed creating the namespace and its use tree. */ namespace = (NAMESPACE *)Malloc1(sizeof(NAMESPACE),"namespace"); namespace->name = strDup1(s,"namespace_name"); namespace->usenames = MakeNameTree(); if ( AP.firstnamespace == 0 ) { namespace->previous = 0; namespace->next = 0; AP.firstnamespace = namespace; AP.lastnamespace = namespace; } else { AP.lastnamespace->next = namespace; namespace->next = 0; namespace->previous = AP.lastnamespace; AP.lastnamespace = namespace; } *s1 = c; return(0); } /* #] DoNamespace : #[ DoEndNamespace : */ int DoEndNamespace(UBYTE *s) { NAMESPACE *namespace; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s != 0 ) { MesPrint("@Illegal #endnamespace instruction"); return(-1); } namespace = AP.lastnamespace; AP.lastnamespace = namespace->previous; M_free(namespace->name,"namespace_name"); FreeNameTree(namespace->usenames); M_free(namespace,"namespace"); return(0); } /* #] DoEndNamespace : #[ SkipName : */ UBYTE *SkipName(UBYTE *s) { UBYTE *t = s, *s1, c; int num = 0, block = 0; if ( *s == '[' ) { straight: SKIPBRA1(s) if ( *s == 0 ) { MesPrint("&Illegal name: '%s'",t); return(0); } s++; s1 = s; while ( FG.cTable[*s] <= 1 || *s == '_' ) s++; if ( s1 != s ) goto witherror; } else if ( *s == '$' ) { s++; while ( *s == '_' ) { s++; num++; } block = 1; while ( FG.cTable[*s] <= 1 || *s == '_' ) { if ( FG.cTable[*s] != 0 && block == 1 ) { blocked: MesPrint("&Illegally formed name: %s",t); return(0); } if ( *s == '_' ) { num++; block = 1; } else block = 0; s++; } if ( s[-1] == '_' && num > 1 ) goto built; } else if ( FG.cTable[*s] == 0 ) { regular: while ( FG.cTable[*s] <= 1 || *s == '_' ) { if ( FG.cTable[*s] != 0 && block == 1 ) goto blocked; if ( *s == '_' ) { block = 1; num++; } else block = 0; s++; } if ( *s == '[' ) goto straight; if ( s[-1] == '_' && num > 1 ) { built: c = *s; *s = 0; MesPrint("&Built in objects cannot be part of namespaces: %s",t); *s = c; return(0); } } else if ( *s == '_' ) { while ( *s == '_' ) { s++; num++; } if ( FG.cTable[*s] == 0 ) { block = 0; goto regular; } goto witherror; } else if ( *s == '@' ) { s++; block = 1; if ( *s == '_' || FG.cTable[*s] == 1 ) { MesPrint("@Illegally formed name: %s",s-1); } goto regular; } else if ( *s == '#' ) { /* name of a procedure */ s++; while ( *s == '_' ) { s++; num++; } block = 1; while ( FG.cTable[*s] <= 1 || *s == '_' ) { if ( FG.cTable[*s] != 0 && block == 1 ) goto blocked; if ( *s == '_' ) { num++; block = 1; } else block = 0; s++; } if ( s[-1] == '_' ) { witherror: c = *s; *s = 0; MesPrint("&Illegally formed name: %s",t); *s = c; return(0); } } else if ( *s == '<' ) { /* name of a file. Can be anything (more or less) */ s++; while ( *s && *s != '>' ) s++; if ( *s != '>' ) goto witherror; s++; } return(s); } /* #] SkipName : #[ ConstructName : Routine gets a 'raw' name and modifies it if the namespace settings ask for it. It puts the new name in a buffer that may be expanded if the names become rather long. Note that eventually that name needs to be copied, because we do not allocate new buffers for each name. type tells what kind of name we look for */ UBYTE *ConstructName(UBYTE *s,UBYTE type) { int len; UBYTE *t, *u; WORD number; NAMESPACE *namespace; if ( AP.lastnamespace == 0 ) return(s); if ( *s == '@' ) return(s+1); if ( GetName(AP.lastnamespace->usenames,s,&number,NOAUTO) != NAMENOTFOUND ) return(s); /* Now the real stuff First we have to compute the size of the new name. */ len = StrLen(s) + 1; namespace = AP.firstnamespace; while ( namespace ) { len += StrLen(namespace->name)+1; namespace = namespace->previous; } if ( len > AP.fullnamesize ) { while ( len > AP.fullnamesize ) AP.fullnamesize *= 2; M_free(AP.fullname,"AP.fullname"); AP.fullname = (UBYTE *)Malloc1(AP.fullnamesize*sizeof(UBYTE *),"AP.fullname"); } namespace = AP.firstnamespace; t = AP.fullname; switch ( type ) { case ' ': case 0: while ( namespace ) { u = namespace->name; while ( *u ) *t++ = *u++; *t++ = '_'; namespace = namespace->previous; } while ( *s ) *t++ = *s++; *t = 0; break; case '$': case '#': *t++ = type; while ( namespace ) { u = namespace->name; while ( *u ) *t++ = *u++; *t++ = '_'; namespace = namespace->previous; } if ( type == '$' ) s++; while ( *s ) *t++ = *s++; *t = 0; break; case '<': while ( namespace ) { u = namespace->name; while ( *u ) *t++ = *u++; *t++ = '_'; namespace = namespace->previous; } s++; while ( *s ) *t++ = *s++; t--; /* strip the '>' */ *t = 0; break; default: MesPrint("&Unrecognized datatype in ConstructName"); *t = 0; break; } return(AP.fullname); } /* #] ConstructName : #[ DoUse : Routine makes (inside the confines of the current namespace) a list of variables that are excluded from the namespace. Once the namespace is ended, the list is removed. The list can include names of variables, dollars and procedures. Preprocessor variables are excluded from the namespace. Their inclusion would be too complicated for the input streams. Note that the preprocessor variables that are arguments in a #do or in a procedure are on a stack and should not cause problems. Names of variables can be just that. Names of $-variables are also straightforward. Names of procedures should be preceeded by a # character. Names of files (like in #include) should be enclosed by <>. The names are stored in a balanced tree. Each namespace may have its own tree. The toplevel (no namespace) does not allow a #use. */ int DoUse(UBYTE *s) { NAMESPACE *namespace; UBYTE *t, c; int number; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AP.lastnamespace == 0 ) { MesPrint("@It is not allowed to use #use outside the scope of a namespace."); return(-1); } namespace = AP.lastnamespace; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; while ( *s ) { t = s; if ( ( s = SkipName(t) ) == 0 ) return(-1); if ( s == t ) { MesPrint("@Unrecognized object in #use instruction: %s",t); return(-1); } c = *s; *s = 0; /* In usenames we only need the names to know whether they are 'protected'. We need to keep the $, # and <> to avoid potential double names. */ AddName(namespace->usenames,t,0,0,&number); *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; } return(0); } /* #] DoUse : #[ UserFlags : Syntax: #ClearFlag number(s),expression(s) #ClearFlag number(s) #ClearFlag expression(s) #ClearFlag #SetFlag number(s),expression(s) #SetFlag number(s) #SetFlag expression(s) #SetFlag par == 0: Clear, par == 1: Set. */ int UserFlags(UBYTE *s,int par) { int mask = 0, error = 0, i; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) { /* Treat all flags in all active expressions */ allexpr: for ( i = 0; i < NumExpressions; i++ ) { switch ( Expressions[i].status ) { case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: case LOCALEXPRESSION: case GLOBALEXPRESSION: case SKIPLEXPRESSION: case SKIPGEXPRESSION: case HIDELEXPRESSION: case HIDEGEXPRESSION: if ( par == 1 ) Expressions[i].uflags |= ~mask; else Expressions[i].uflags &= mask; break; case DROPPEDEXPRESSION: case DROPLEXPRESSION: case DROPGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case STOREDEXPRESSION: case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: case SPECTATOREXPRESSION: default: break; } } } else if ( FG.cTable[*s] == 1 ) { mask = (int)WORDMASK; while ( FG.cTable[*s] == 1 ) { int x = 0; while ( FG.cTable[*s] == 1 ) { x = 10*x + (*s++-'0'); } if ( x < 1 || x > BITSINWORD ) { MesPrint("@Illegal number %d for flag in #...Flag instruction",x); return(1); } mask ^= (1<<(x-1)); while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } if ( *s == 0 ) goto allexpr; } else { /* Clear all flags in all expressions that are specified */ mask = (int)WORDMASK; } while ( *s ) { /* now read the expressions */ UBYTE *s1, c; WORD num1; if ( FG.cTable[*s] != 0 && *s != '[' ) goto syntax; s1 = s; s = SkipAName(s); c = *s; *s = 0; if ( GetName(AC.exprnames,s1,&num1,NOAUTO) != CEXPRESSION ) { MesPrint("@%s is not an active expression",s1); error = 1; return(error); } switch ( Expressions[num1].status ) { case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: case LOCALEXPRESSION: case GLOBALEXPRESSION: case SKIPLEXPRESSION: case SKIPGEXPRESSION: case HIDELEXPRESSION: case HIDEGEXPRESSION: if ( par == 1 ) Expressions[num1].uflags |= ~mask; else Expressions[num1].uflags &= mask; break; case DROPPEDEXPRESSION: case DROPLEXPRESSION: case DROPGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case STOREDEXPRESSION: case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: case SPECTATOREXPRESSION: default: MesPrint("@%s is not an active expression",s1); error = 1; break; } *s = c; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } return(error); syntax: MesPrint("@Illegal name in #...Flag instruction."); return(1); } /* #] UserFlags : #[ DoClearUserFlag : */ int DoClearUserFlag(UBYTE *s) { return(UserFlags(s,0)); } /* #] DoClearUserFlag : #[ DoSetUserFlag : */ int DoSetUserFlag(UBYTE *s) { return(UserFlags(s,1)); } /* #] DoSetUserFlag : #[ DoStartFloat : If there is a number follwing, it will be the new default precision. If float has been started before, the old one will be removed first. If there are two numbers, the second one is the maximum weight for MZV's. */ #ifdef WITHFLOAT int DoStartFloat(UBYTE *s) { GETIDENTITY int error = 0; LONG x; UBYTE *ss; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); if ( AR.PolyFun != 0 ) { MesPrint("@Simultaneous use of Poly(Rat)Fun and float_ is not allowed."); error = 1; } if ( AC.ncmod != 0 ) { MesPrint("@Simultaneous use of floating point and modulus arithmetic makes no sense."); error = 1; } if ( AT.aux_ ) { // First, we clean up any previous floating point system. ClearfFloat(); ClearMZVTables(); } while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; /* The first parameter is the float precision */ ss = s; if ( *s >= '0' && *s <= '9' ) { x = 0; do { x = 10*x + (*s++-'0'); } while ( *s >= '0' && *s <= '9' ); /* The precision can either be in digits or bits. AC.DefaultPrecision is always in bits. */ if ( tolower(*s) == 'd' ) { AC.tDefaultPrecision = (LONG)ceil(x*log2(10.0)); s++; } else if ( tolower(*s) == 'b' ) { AC.tDefaultPrecision = x; s++; } else goto IllPar; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; /* The second parameter is either absent, which implies zero MZV weight, or of the form MZV = */ if ( tolower(*s) == 'm' && tolower(s[1]) == 'z' && tolower(s[2]) == 'v') { s+=3; while ( *s == ' ' || *s == '\t' ) s++; if ( *s != '=') goto IllPar; s++; while ( *s == ' ' || *s == '\t' ) s++; if ( *s >= '0' && *s <= '9' ) { x = 0; do { x = 10*x + (*s++ - '0'); } while ( *s >= '0' && *s <= '9' ); AC.tMaxWeight = x; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } else goto IllPar; } else { AC.tMaxWeight = 0; } if ( *s ) goto IllPar; } else if ( *s != 0 ) { IllPar: MesPrint("@Illegal parameter in %#StartFloat: %s ",ss); error = 1; } if ( error == 0 ) { if ( AC.tDefaultPrecision && ( AC.tDefaultPrecision != AC.DefaultPrecision || AT.aux_ == 0 ) ) { AC.DefaultPrecision = AC.tDefaultPrecision; AC.tDefaultPrecision = 0; } if ( AC.tMaxWeight && ( AC.tMaxWeight != AC.MaxWeight || AT.aux_ == 0 ) ) { AC.MaxWeight = AC.tMaxWeight; AC.tMaxWeight = 0; } SetFloatPrecision(AC.DefaultPrecision+AC.MaxWeight+1); SetupMPFTables(); if ( AC.MaxWeight > 0 ) SetupMZVTables(); SetfFloatPrecision(AC.DefaultPrecision); } else { AC.tDefaultPrecision = 0; AC.tMaxWeight = 0; } return(error); } #endif /* #] DoStartFloat : #[ DoEndFloat : */ #ifdef WITHFLOAT int DoEndFloat(UBYTE *s) { int error = 0; if ( AP.PreSwitchModes[AP.PreSwitchLevel] != EXECUTINGPRESWITCH ) return(0); if ( AP.PreIfStack[AP.PreIfLevel] != EXECUTINGIF ) return(0); while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( *s != 0 ) { MesPrint("@Illegal parameter in %#EndFloat instruction: %s ",s); error = 1; } if ( error == 0 ) { ClearfFloat(); ClearMZVTables(); } return(error); } #endif /* #] DoEndFloat : # ] PreProcessor : */ form-5.0.1/sources/mallocprotect.h0000644000175100017510000002570315217035721012661 #ifndef MALLOCPROTECT_H #define MALLOCPROTECT_H /** @file mall.h * * Malloc debugger extension, inline functions * this file is the include file for the file tools.c */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Documentation : The enhanced malloc debugger. It intercepts access (both write AND read) to the memory outside the allocated chunk in the following manner: it prints out (to the stderr) the information about the event and goes to the spilock. The user is able to attach the debugger to the running process, investigate the problem and continue evaluation. In case of error, the debugger will print to the stderr the following information: "***** PID: ###, Addr: ###, signal ### (code ###)" "Attach gdb -p ### and set var loopForever=0 in a corresponding frame to continue" or for TFORM: "Attach gdb -p ### and set var loopForever=0 in a corresponding frame of a thread with LPW id ### to continue" and go to the spilock. The user may attach gdb by the command gdb -p ### and type "where" (in case of TFORM, the user should first switch to the proper thread). Then investigation of the corresponding frames should clarify the situation. In order to continue the program, the user might set (in the corresponding frame of the corresponding thread) the variable loopForever to 0. The debugger will try to remove local problem lead to the exception. To activate the debugger, the macro MALLOCPROTECT should be defined. There are three possible values: #define MALLOCPROTECT -1 (any integer <0) #define MALLOCPROTECT 0 #define MALLOCPROTECT 1 (any integer>0) If MALLOCPROTECT < 0, the debugger will intercept any access to the memory before the allocated chunk, even one byte. If MALLOCPROTECT == 0, the debugger will intercept any access to the memory before the allocated chunk, even one byte, and access to the memory page next to the allocated one. If MALLOCPROTECT > 0, the debugger will intercept any access to the memory after the allocated chunk, even one byte, and access to the memory page before the allocated one. The original FORM malloc debugger is able to catch errors when the allocated memory is freed improper, or if some small portion OUT of the allocated chunk is written. This debugger is a complementary one. It permits to catch situation when some small portion of memory before or after the allocated chunk is written or even just read. The idea is to protect the beginning or the end of the allocated chunk for any kind of access and install the SIGSEGV handler in order to intercept the access to this memory. Moreover, the allocated memory is always immediately returned to the system so if the user tries to access the memory after it is freed then the handler is triggered, also. The problem here is that we are able to allocate / protect only the whole page. So the user has to run the debugger twice: one time with the left alignment (#define MALLOCPROTECT <0), and then with the right alignment (#define MALLOCPROTECT >0). During the first run the possible errors like x[-1] will be caught, and the second run will manifest reading over the allocated ares. The leftmost extra page is always allocated and protected. The size of the allocated chunk is stored in the beginning of this page. #] Documentation : #[ Includes : */ #include #include #include #include #include #ifdef WITHPTHREADS #ifdef LINUX #include #endif #endif /* #] Includes : */ static int pageSize=4096;/*the default value*/ /* #[ segv_handler : */ /*The handler will be invoked on some signal (usually SIGSEGV). It will print some diagnostics to stderr and hands up in infinite loop waiting the user for debugging:*/ static void segv_handler(int sig, siginfo_t *sip, void *xxx) { char *vadr; char *errStr; int actionBeforeExit=0;/* < 0 - unprotect, > 0 - map */ switch(sip->si_signo){/* All POSIX signals for which the field siginfo_t.si_addr is defined:*/ case SIGILL: switch(sip->si_code){ case ILL_ILLOPC: errStr="SIGILL: Illegal opcode"; break; case ILL_ILLOPN: errStr="SIGILL: Illegal operand"; break; case ILL_ILLADR: errStr="SIGILL: Illegal addressing mode"; break; case ILL_ILLTRP: errStr="SIGILL: Illegal trap"; break; case ILL_PRVOPC: errStr="SIGILL: Privileged opcode"; break; case ILL_PRVREG: errStr="SIGILL: Privileged register"; break; case ILL_COPROC: errStr="SIGILL: Coprocessor error"; break; case ILL_BADSTK: errStr="SIGILL: Internal stack error"; break; default: errStr="SIGILL: Unknown signal code"; }/*case SIGILL:*/ break; case SIGFPE: switch(sip->si_code){ case FPE_INTDIV: errStr="SIGFPE: Integer divide-by-zero"; break; case FPE_INTOVF: errStr="SIGFPE: Integer overflow"; break; case FPE_FLTDIV: errStr="SIGFPE: Floating point divide-by-zero"; break; case FPE_FLTOVF: errStr="SIGFPE: Floating point overflow"; break; case FPE_FLTUND: errStr="SIGFPE: Floating point underflow"; break; case FPE_FLTRES: errStr="SIGFPE: Floating point inexact result"; break; case FPE_FLTINV: errStr="SIGFPE: Invalid floating point operation"; break; case FPE_FLTSUB: errStr="SIGFPE: Subscript out of range"; break; default: errStr="SIGFPE: Unknown signal code"; }/*switch(sip->si_code)*/ break; case SIGSEGV: switch(sip->si_code){ case SEGV_MAPERR: errStr="SIGSEGV: Address not mapped"; actionBeforeExit = 1; break; case SEGV_ACCERR: errStr="SIGSEGV: Invalid permissions"; actionBeforeExit = -1; break; default: errStr="SIGSEGV: Unknown signal code"; }/*switch(sip->si_code)*/ break; case SIGBUS: switch(sip->si_code){ case BUS_ADRALN: errStr="SIGBUS: Invalid address alignment"; break; case BUS_ADRERR: errStr="SIGBUS: Non-existent physical address"; break; case BUS_OBJERR: errStr="SIGBUS: Object-specific hardware error"; break; default: errStr="SIGBUS: Unknown signal code"; }/*switch(sip->si_code)*/ break; default: errStr="Unknown signal"; }/*switch(sip->si_signo)*/ vadr = (caddr_t)sip->si_addr; fprintf(stderr, "\n***** PID: %ld, Addr: %p, signal %s (code %d)\n", (long)getpid(), vadr, errStr,sip->si_code); {/*Block*/ /*The process hangs up at this block. Attach gdb to investigate and continue: */ volatile int loopForever=1; size_t alignedAdr=((size_t)vadr) & (~(pageSize-1)); fprintf(stderr, " Attach gdb -p %ld and set var loopForever=0 in a corresponding frame", (long)getpid()); #ifdef CORRECTCODE #ifdef WITHPTHREADS #ifdef LINUX fprintf(stderr, "\n of a thread with LPW id %ld",(long)syscall(SYS_gettid)); #else /*If the compiler fails here, just remove the next line:*/ fprintf(stderr, "\n of thread with LPW id %ld",(long)gettid()); #endif #endif #endif fprintf(stderr, " to continue\n"); while(loopForever) sleep(1); if(actionBeforeExit<0)/*After changing loopForever=0, unprotect the page to continue:*/ mprotect((char*)alignedAdr, pageSize, PROT_READ | PROT_WRITE); if(actionBeforeExit>0)/*After changing loopForever=0, map the page to continue:*/ /* mmap((void*)alignedAdr,pageSize,PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_ANONYMOUS, 0, 0); */ mmap((void*)alignedAdr,pageSize,PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_ANON, 0, 0); }/*Block*/ }/*segv_handler*/ /* #] segv_handler : */ /* #[ mprotectInit : */ static FORM_INLINE int mprotectInit(void) { struct sigaction sa; pageSize = getpagesize(); sa.sa_sigaction = &segv_handler; sigemptyset(&sa.sa_mask); sigaddset(&sa.sa_mask, SIGIO); sigaddset(&sa.sa_mask, SIGALRM); sa.sa_flags = SA_SIGINFO; if (sigaction(SIGILL, &sa, NULL)) { fprintf(stderr,"Error on assigning %s.\n","SIGILL"); return SIGILL; } if (sigaction(SIGFPE, &sa, NULL)) { fprintf(stderr,"Error on assigning %s.\n","SIGFPE"); return SIGFPE; } if (sigaction(SIGSEGV, &sa, NULL)) { fprintf(stderr,"Error on assigning %s.\n","SIGSEGV"); return SIGSEGV; } if (sigaction(SIGBUS, &sa, NULL)) { fprintf(stderr,"Error on assigning %s.\n","SIGBUS"); return SIGBUS; } return 0; }/*mprotectInit*/ /* #] mprotectInit : */ /* #[ mprotectMalloc : */ static void *mprotectMalloc(size_t theSize) { #if MALLOCPROTECT < 0 /*Only one side is protected*/ size_t nPages=1; #else /*Both sides are protected*/ size_t nPages=2; #if MALLOCPROTECT > 0 /*will need the original theSize*/ size_t requestedSize=theSize; #endif #endif char *ret=NULL; size_t *ptr; /*Align required size to the pagesize:*/ if(theSize % pageSize) nPages++; theSize= (theSize/pageSize+nPages)*pageSize; /* ret=(char*)mmap(0,theSize,PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_ANONYMOUS, 0, 0); */ ret=(char*)mmap(0,theSize,PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_ANON, 0, 0); if(ret == MAP_FAILED) return NULL; ptr=(size_t *)ret; *ptr=theSize; if(mprotect(ret, pageSize, PROT_NONE))return NULL; #if MALLOCPROTECT < 0 return ret+pageSize; #else if(mprotect(ret+(theSize-pageSize), pageSize, PROT_NONE))return NULL; #if MALLOCPROTECT ==0 return ret+pageSize; #endif #endif /*MALLOCPROTECT > 0, but we need conditional compilation since the variable requestedSize:*/ #if MALLOCPROTECT > 0 /*Potential problems with alignment if the requested size is not a multiple of items. But no problems on x86-64:*/ return ret+ (theSize-pageSize-requestedSize); #endif }/*mprotectMalloc*/ /* #] mprotectMalloc : */ /* #[ mprotectFree : */ static void mprotectFree(char *ptr) { size_t theSize; if(ptr==NULL) return; #if MALLOCPROTECT > 0 /*The memory block was moved to the right, find the left page boundary:*/ {/*Block*/ size_t alignedPtr=((size_t)ptr) & (~(pageSize-1)); ptr=(char*)alignedPtr; }/*Block*/ #endif ptr-=pageSize; mprotect(ptr, pageSize, PROT_READ); theSize=*((size_t*)ptr); munmap(ptr,theSize); }/*mprotectFree*/ /* #] mprotectFree : */ #endif form-5.0.1/sources/compcomm.c0000644000175100017510000057321415217035721011623 /** @file compcomm.c * * Compiler routines for most statements that don't involve algebraic * expressions. Exceptions: all routines involving declarations are in * the file names.c * When making new statements one can add the compiler routines here and * have a look whether there is already a routine that is similar. In that * case one can make a copy and modify it. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ includes : */ #include "form3.h" #include "comtool.h" #ifdef WITHFLOAT #include #include #endif static KEYWORD formatoptions[] = { {"allfloat", (TFUN)0, ALLINTEGERDOUBLE, 0} ,{"c", (TFUN)0, CMODE, 0} ,{"doublefortran", (TFUN)0, DOUBLEFORTRANMODE, 0} ,{"float", (TFUN)0, 0, 2} #ifdef WITHFLOAT ,{"floatprecision", (TFUN)0, 0, 5} #endif ,{"fortran", (TFUN)0, FORTRANMODE, 0} ,{"fortran90", (TFUN)0, FORTRANMODE, 4} ,{"maple", (TFUN)0, MAPLEMODE, 0} ,{"mathematica", (TFUN)0, MATHEMATICAMODE, 0} ,{"normal", (TFUN)0, NORMALFORMAT, 1} ,{"nospaces", (TFUN)0, NOSPACEFORMAT, 3} ,{"pfortran", (TFUN)0, PFORTRANMODE, 0} ,{"quadfortran", (TFUN)0, QUADRUPLEFORTRANMODE, 0} ,{"quadruplefortran", (TFUN)0, QUADRUPLEFORTRANMODE, 0} ,{"rational", (TFUN)0, RATIONALMODE, 1} ,{"reduce", (TFUN)0, REDUCEMODE, 0} ,{"spaces", (TFUN)0, NORMALFORMAT, 3} ,{"vortran", (TFUN)0, VORTRANMODE, 0} }; static KEYWORD trace4options[] = { {"contract", (TFUN)0, CHISHOLM, 0 } ,{"nocontract", (TFUN)0, 0, CHISHOLM } ,{"nosymmetrize",(TFUN)0, 0, ALSOREVERSE} ,{"notrick", (TFUN)0, NOTRICK, 0 } ,{"symmetrize", (TFUN)0, ALSOREVERSE, 0 } ,{"trick", (TFUN)0, 0, NOTRICK } }; static KEYWORD chisoptions[] = { {"nosymmetrize",(TFUN)0, 0, ALSOREVERSE} ,{"symmetrize", (TFUN)0, ALSOREVERSE, 0 } }; static KEYWORDV writeoptions[] = { {"stats", &(AC.StatsFlag), 1, 0} ,{"statistics", &(AC.StatsFlag), 1, 0} ,{"shortstats", &(AC.ShortStats), 1, 0} ,{"shortstatistics",&(AC.ShortStats), 1, 0} ,{"warnings", &(AC.WarnFlag), 1, 0} ,{"allwarnings", &(AC.WarnFlag), 2, 0} ,{"setup", &(AC.SetupFlag), 1, 0} ,{"names", &(AC.NamesFlag), 1, 0} ,{"allnames", &(AC.NamesFlag), 2, 0} ,{"codes", &(AC.CodesFlag), 1, 0} ,{"highfirst", &(AC.SortType), SORTHIGHFIRST, SORTLOWFIRST} ,{"lowfirst", &(AC.SortType), SORTLOWFIRST, SORTHIGHFIRST} ,{"powerfirst", &(AC.SortType), SORTPOWERFIRST, SORTHIGHFIRST} ,{"tokens", &(AC.TokensWriteFlag),1, 0} }; static KEYWORDV onoffoptions[] = { {"compress", &(AC.NoCompress), 0, 1} ,{"checkpoint", &(AC.CheckpointFlag), 1, 0} ,{"insidefirst", &(AC.insidefirst), 1, 0} ,{"propercount", &(AC.BottomLevel), 1, 0} ,{"stats", &(AC.StatsFlag), 1, 0} ,{"statistics", &(AC.StatsFlag), 1, 0} ,{"shortstats", &(AC.ShortStats), 1, 0} ,{"shortstatistics",&(AC.ShortStats), 1, 0} ,{"names", &(AC.NamesFlag), 1, 0} ,{"allnames", &(AC.NamesFlag), 2, 0} ,{"warnings", &(AC.WarnFlag), 1, 0} ,{"allwarnings", &(AC.WarnFlag), 2, 0} ,{"highfirst", &(AC.SortType), SORTHIGHFIRST, SORTLOWFIRST} ,{"lowfirst", &(AC.SortType), SORTLOWFIRST, SORTHIGHFIRST} ,{"powerfirst", &(AC.SortType), SORTPOWERFIRST, SORTHIGHFIRST} ,{"setup", &(AC.SetupFlag), 1, 0} ,{"codes", &(AC.CodesFlag), 1, 0} ,{"tokens", &(AC.TokensWriteFlag),1,0} ,{"properorder", &(AC.properorderflag),1,0} ,{"threadloadbalancing",&(AC.ThreadBalancing),1, 0} ,{"threads", &(AC.ThreadsFlag),1, 0} ,{"threadsortfilesynch",&(AC.ThreadSortFileSynch),1, 0} ,{"threadstats", &(AC.ThreadStats),1, 0} ,{"finalstats", &(AC.FinalStats),1, 0} ,{"fewerstats", &(AC.ShortStatsMax), 10, 0} ,{"fewerstatistics",&(AC.ShortStatsMax), 10, 0} ,{"processstats", &(AC.ProcessStats),1, 0} ,{"oldparallelstats",&(AC.OldParallelStats),1,0} ,{"parallel", &(AC.parallelflag),PARALLELFLAG,NOPARALLEL_USER} ,{"nospacesinnumbers",&(AO.NoSpacesInNumbers),1,0} ,{"indentspace", &(AO.IndentSpace),INDENTSPACE,0} ,{"totalsize", &(AM.PrintTotalSize), 1, 0} ,{"flag", (int *)&(AC.debugFlags), 1, 0} ,{"oldfactarg", &(AC.OldFactArgFlag), 1, 0} ,{"memdebugflag", &(AC.MemDebugFlag), 1, 0} ,{"oldgcd", &(AC.OldGCDflag), 1, 0} ,{"oldprfsign", &(AC.OldPRFSignFlag), 1, 0} ,{"innertest", &(AC.InnerTest), 1, 0} ,{"wtimestats", &(AC.WTimeStatsFlag), 1, 0} ,{"sortreallocate", &(AC.SortReallocateFlag), 1, 0} ,{"backtrace", &(AC.PrintBacktraceFlag), 1, 0} ,{"flint", &(AC.FlintPolyFlag), 1, 0} ,{"humanstats", &(AC.HumanStatsFlag), 1, 0} ,{"humanstatistics", &(AC.HumanStatsFlag), 1, 0} ,{"grccverbose", &(AC.GrccVerbose), 1, 0} ,{"sortverbose", &(AC.SortVerbose), 1, 0} }; static WORD one = 1; /* #] includes : #[ CoFormat : */ int CoFormat(UBYTE *s) { int error = 0, x; KEYWORD *key; UBYTE *ss; while ( *s == ' ' || *s == ',' ) s++; if ( *s == 0 ) { AC.OutputMode = 72; AC.OutputSpaces = NORMALFORMAT; return(error); } /* First the optimization level */ if ( *s == 'O' || *s == 'o' ) { if ( ( FG.cTable[s[1]] == 1 ) || ( s[1] == '=' && FG.cTable[s[2]] == 1 ) ) { s++; if ( *s == '=' ) s++; x = 0; while ( *s >= '0' && *s <= '9' ) x = 10*x + *s++ - '0'; while ( *s == ',' ) s++; AO.OptimizationLevel = x; AO.Optimize.greedytimelimit = 0; AO.Optimize.mctstimelimit = 0; AO.Optimize.printstats = 0; AO.Optimize.debugflags = 0; AO.Optimize.schemeflags = 0; AO.Optimize.mctsdecaymode = 1; /* default is decreasing C_p with iteration number */ if ( AO.inscheme ) { M_free(AO.inscheme,"Horner input scheme"); AO.inscheme = 0; AO.schemenum = 0; } switch ( x ) { case 0: break; case 1: AO.Optimize.mctsconstant.fval = -1.0; AO.Optimize.horner = O_OCCURRENCE; AO.Optimize.hornerdirection = O_FORWARDORBACKWARD; AO.Optimize.method = O_CSE; break; case 2: AO.Optimize.horner = O_OCCURRENCE; AO.Optimize.hornerdirection = O_FORWARDORBACKWARD; AO.Optimize.method = O_GREEDY; AO.Optimize.greedyminnum = 10; AO.Optimize.greedymaxperc = 5; break; case 3: AO.Optimize.mctsconstant.fval = 1.0; AO.Optimize.horner = O_MCTS; AO.Optimize.hornerdirection = O_FORWARDORBACKWARD; AO.Optimize.method = O_GREEDY; AO.Optimize.mctsnumexpand = 1000; AO.Optimize.mctsnumkeep = 10; AO.Optimize.mctsnumrepeat = 1; AO.Optimize.greedyminnum = 10; AO.Optimize.greedymaxperc = 5; break; case 4: AO.Optimize.horner = O_SIMULATED_ANNEALING; AO.Optimize.saIter = 1000; AO.Optimize.saMaxT.fval = 2000; AO.Optimize.saMinT.fval = 1; break; default: error = 1; MesPrint("&Illegal optimization specification in format statement"); break; } if ( error == 0 && *s != 0 && x > 0 ) return(CoOptimizeOption(s)); return(error); } #ifdef EXPOPT { UBYTE c; ss = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICont(ss,(UBYTE *)"optimize") == 0 ) { *s = c; while ( *s == ',' ) s++; if ( *s == '=' ) s++; AO.OptimizationLevel = 3; AO.Optimize.mctsconstant.fval = 1.0; AO.Optimize.horner = O_MCTS; AO.Optimize.hornerdirection = O_FORWARDORBACKWARD; AO.Optimize.method = O_GREEDY; AO.Optimize.mctstimelimit = 0; AO.Optimize.mctsnumexpand = 1000; AO.Optimize.mctsnumkeep = 10; AO.Optimize.mctsnumrepeat = 1; AO.Optimize.greedytimelimit = 0; AO.Optimize.greedyminnum = 10; AO.Optimize.greedymaxperc = 5; AO.Optimize.printstats = 0; AO.Optimize.debugflags = 0; AO.Optimize.schemeflags = 0; AO.Optimize.mctsdecaymode = 1; if ( AO.inscheme ) { M_free(AO.inscheme,"Horner input scheme"); AO.inscheme = 0; AO.schemenum = 0; } return(CoOptimizeOption(s)); } else { error = 1; MesPrint("&Illegal optimization specification in format statement"); return(error); } } #endif } else if ( FG.cTable[*s] == 1 ) { x = 0; while ( FG.cTable[*s] == 1 ) x = 10*x + *s++ - '0'; if ( x <= 0 || x >= MAXLINELENGTH ) { error = 1; MesPrint("&Illegal value for linesize: %d",x); x = 72; } if ( x < 39 ) { MesPrint(" ... Too small value for linesize corrected to 39"); x = 39; } AO.DoubleFlag = 0; /* The next line resets the mode to normal. Because the special modes reset the line length we have a little problem with the special modes and customized line length. We try to improve by removing the next line */ /* AC.OutputMode = 0; */ AC.LineLength = x; if ( *s != 0 ) { error = 1; MesPrint("&Illegal linesize field in format statement"); } } else { key = FindKeyWord(s,formatoptions, sizeof(formatoptions)/sizeof(KEYWORD)); if ( key ) { if ( key->type == FORTRANMODE || key->type == PFORTRANMODE || key->type == DOUBLEFORTRANMODE || key->type == QUADRUPLEFORTRANMODE || key->type == VORTRANMODE ) { if (AC.LineLength > 72) AC.LineLength = 72; } if ( key->flags == 0 ) { if ( key->type == FORTRANMODE || key->type == PFORTRANMODE || key->type == DOUBLEFORTRANMODE || key->type == ALLINTEGERDOUBLE || key->type == QUADRUPLEFORTRANMODE || key->type == VORTRANMODE ) { AC.IsFortran90 = ISNOTFORTRAN90; if ( AC.Fortran90Kind ) { M_free(AC.Fortran90Kind,"Fortran90 Kind"); AC.Fortran90Kind = 0; } } if ( ( key->type == ALLINTEGERDOUBLE ) && AO.DoubleFlag != 0 ) { AO.DoubleFlag |= 4; } else { AO.DoubleFlag = 0; AC.OutputMode = key->type & NODOUBLEMASK; if ( ( key->type & DOUBLEPRECISIONFLAG ) != 0 ) { AO.DoubleFlag = 1; } else if ( ( key->type & QUADRUPLEPRECISIONFLAG ) != 0 ) { AO.DoubleFlag = 2; } } } else if ( key->flags == 1 ) { AC.OutputMode = AC.OutNumberType = key->type; } else if ( key->flags == 2 ) { while ( FG.cTable[*s] == 0 ) s++; if ( *s == 0 ) AC.OutNumberType = 10; else if ( *s == ',' ) { s++; x = 0; while ( FG.cTable[*s] == 1 ) x = 10*x + *s++ - '0'; if ( *s != 0 ) { error = 1; MesPrint("&Illegal float format specifier"); } else { if ( x < 3 ) { x = 3; MesPrint("& ... float format value corrected to 3"); } if ( x > 100 ) { x = 100; MesPrint("& ... float format value corrected to 100"); } AC.OutNumberType = x; } } } else if ( key->flags == 3 ) { AC.OutputSpaces = key->type; } else if ( key->flags == 4 ) { AC.IsFortran90 = ISFORTRAN90; if ( AC.Fortran90Kind ) { M_free(AC.Fortran90Kind,"Fortran90 Kind"); AC.Fortran90Kind = 0; } while ( FG.cTable[*s] <= 1 ) s++; if ( *s == ',' ) { s++; ss = s; while ( *ss && *ss != ',' ) ss++; if ( *ss == ',' ) { MesPrint("&No white space or comma's allowed in Fortran90 option: %s",s); error = 1; } else { AC.Fortran90Kind = strDup1(s,"Fortran90 Kind"); } } AO.DoubleFlag = 0; AC.OutputMode = key->type & NODOUBLEMASK; } #ifdef WITHFLOAT else if ( key->flags == 5 ) { /* Syntax: Format FloatPrecision [precision]; Format FloatPrecision off; */ while ( FG.cTable[*s] == 0 ) s++; while ( *s == ' ' || *s == '\t' || *s == ',' ) s++; if ( *s == 0 ) { AO.FloatPrec = 0; } else if ( tolower(*s) == 'o' && tolower(s[1]) == 'f' && tolower(s[2]) == 'f' ) { ss = s; s += 3; while ( *s == ' ' || *s == '\t' || *s == ',' ) s++; if ( *s ) { s = ss; goto WrongOption; } AO.FloatPrec = -1; } else if ( FG.cTable[*s] == 1 ) { ss = s; ParseNumber(AO.FloatPrec,s) /* The precision can either be in digits or bits. AO.FloatPrec is in digits. */ if ( tolower(*s) == 'd' ) { s++; } else if ( tolower(*s) == 'b' ) { AO.FloatPrec = AO.FloatPrec*log10(2.0); s++; } else { s = ss; goto WrongOption; } while ( *s == ' ' || *s == '\t' || *s == ',' ) s++; if ( *s ) { s = ss; goto WrongOption; } } else { WrongOption: MesPrint("&Illegal option in Format FloatPrecision: %s",s); error = 1; } } #endif } else if ( ( *s == 'c' || *s == 'C' ) && ( FG.cTable[s[1]] == 1 ) ) { UBYTE *ss = s+1; WORD x = 0; while ( *ss >= '0' && *ss <= '9' ) x = 10*x + *ss++ - '0'; if ( *ss != 0 ) goto Unknown; AC.OutputMode = CMODE; AC.Cnumpows = x; } else { Unknown: MesPrint("&Unknown option: %s",s); error = 1; } } return(error); } /* #] CoFormat : #[ CoCollect : Collect,functionname */ int CoCollect(UBYTE *s) { /* --------------change 17-feb-2003 Added percentage */ WORD numfun; int type,x = 0; UBYTE *t = SkipAName(s), *t1, *t2; AC.AltCollectFun = 0; if ( t == 0 ) goto syntaxerror; t1 = t; while ( *t1 == ',' || *t1 == ' ' || *t1 == '\t' ) t1++; *t = 0; t = t1; if ( *t1 && ( FG.cTable[*t1] == 0 || *t1 == '[' ) ) { t2 = SkipAName(t1); if ( t2 == 0 ) goto syntaxerror; t = t2; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; *t2 = 0; } else t1 = 0; if ( *t && FG.cTable[*t] == 1 ) { while ( *t >= '0' && *t <= '9' ) x = 10*x + *t++ - '0'; if ( x > 100 ) x = 100; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t ) goto syntaxerror; } else { if ( *t ) goto syntaxerror; x = 100; } if ( ( ( type = GetName(AC.varnames,s,&numfun,WITHAUTO) ) != CFUNCTION ) || ( functions[numfun].spec != 0 ) ) { MesPrint("&%s should be a regular function",s); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&numfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } AC.CollectFun = numfun+FUNCTION; AC.CollectPercentage = (WORD)x; if ( t1 ) { if ( ( ( type = GetName(AC.varnames,t1,&numfun,WITHAUTO) ) != CFUNCTION ) || ( functions[numfun].spec != 0 ) ) { MesPrint("&%s should be a regular function",t1); if ( type < 0 ) { if ( GetName(AC.exprnames,t1,&numfun,NOAUTO) == NAMENOTFOUND ) AddFunction(t1,0,0,0,0,0,-1,-1); } return(1); } AC.AltCollectFun = numfun+FUNCTION; } return(0); syntaxerror: MesPrint("&Collect statement needs one or two functions (and a percentage) for its argument(s)"); return(1); } /* #] CoCollect : #[ setonoff : */ int setonoff(UBYTE *s, int *flag, int onvalue, int offvalue) { if ( StrICmp(s,(UBYTE *)"on") == 0 ) *flag = onvalue; else if ( StrICmp(s,(UBYTE *)"off") == 0 ) *flag = offvalue; else { MesPrint("&Unknown option: %s, on or off expected",s); return(1); } return(0); } /* #] setonoff : #[ CoCompress : */ int CoCompress(UBYTE *s) { GETIDENTITY UBYTE *t, c; if ( StrICmp(s,(UBYTE *)"on") == 0 ) { AC.NoCompress = 0; AR.gzipCompress = 0; } else if ( StrICmp(s,(UBYTE *)"off") == 0 ) { AC.NoCompress = 1; AR.gzipCompress = 0; } else { t = s; while ( FG.cTable[*t] <= 1 ) t++; c = *t; *t = 0; if ( StrICmp(s,(UBYTE *)"gzip") == 0 ) { #ifndef WITHZLIB Warning("gzip compression not supported on this platform"); #endif s = t; *s = c; if ( *s == 0 ) { AR.gzipCompress = GZIPDEFAULT; /* Normally should be 6 */ return(0); } while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; t = s; if ( FG.cTable[*s] == 1 ) { AR.gzipCompress = *s - '0'; s++; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == 0 ) return(0); } MesPrint("&Unknown gzip option: %s, a digit was expected",t); return(1); } else { MesPrint("&Unknown option: %s, on, off or gzip expected",s); return(1); } } return(0); } /* #] CoCompress : #[ CoFlags : */ int CoFlags(UBYTE *s,int value) { int i, error = 0; if ( *s != ',' ) { MesPrint("&Proper syntax is: On/Off Flag,number[s];"); error = 1; } while ( *s == ',' ) { do { s++; } while ( *s == ',' ); i = 0; if ( FG.cTable[*s] != 1 ) { MesPrint("&Proper syntax is: On/Off Flag,number[s];"); error = 1; break; } while ( FG.cTable[*s] == 1 ) { i = 10*i + *s++ - '0'; } if ( i <= 0 || i > MAXFLAGS ) { MesPrint("&The number of a flag in On/Off Flag should be in the range 0-%d",(int)MAXFLAGS); error = 1; break; } AC.debugFlags[i] = value; } if ( *s ) { MesPrint("&Proper syntax is: On/Off Flag,number[s];"); error = 1; } return(error); } /* #] CoFlags : #[ CoOff : */ int CoOff(UBYTE *s) { GETIDENTITY UBYTE *t, c; int i, num = sizeof(onoffoptions)/sizeof(KEYWORD); for (;;) { while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == 0 ) return(0); if ( chartype[*s] != 0 ) { MesPrint("&Illegal character or option encountered in OFF statement"); return(-1); } t = s; while ( chartype[*s] == 0 ) s++; c = *s; *s = 0; for ( i = 0; i < num; i++ ) { if ( StrICont(t,(UBYTE *)(onoffoptions[i].name)) == 0 ) break; } if ( i >= num ) { MesPrint("&Unrecognized option in OFF statement: %s",t); *s = c; return(-1); } else if ( StrICont(t,(UBYTE *)"compress") == 0 ) { AR.gzipCompress = 0; } else if ( StrICont(t,(UBYTE *)"checkpoint") == 0 ) { PrintDeprecation("the checkpoint mechanism", "issues/626"); AC.CheckpointInterval = 0; if ( AC.CheckpointRunBefore ) { free(AC.CheckpointRunBefore); AC.CheckpointRunBefore = NULL; } if ( AC.CheckpointRunAfter ) { free(AC.CheckpointRunAfter); AC.CheckpointRunAfter = NULL; } if ( AC.NoShowInput == 0 ) MesPrint("Checkpoints deactivated."); } else if ( StrICont(t,(UBYTE *)"threads") == 0 ) { AS.MultiThreaded = 0; } else if ( StrICont(t,(UBYTE *)"flag") == 0 ) { *s = c; return(CoFlags(s,0)); } else if ( StrICont(t,(UBYTE *)"innertest") == 0 ) { *s = c; AC.InnerTest = 0; if ( AC.TestValue ) { M_free(AC.TestValue,"InnerTest"); AC.TestValue = 0; } } else if ( StrICont(t,(UBYTE *)"sortreallocate") == 0 ) { if ( AC.SortReallocateFlag == 2 ) { /* The flag has been set by #sortreallocate, and it was off before. Leave it as 2, so that the reallocation still happens in the current module. It will be turned off after the reallocation is done. */ return(0); } } *s = c; *onoffoptions[i].var = onoffoptions[i].flags; AR.SortType = AC.SortType; AC.mparallelflag = AC.parallelflag | AM.hparallelflag; } } /* #] CoOff : #[ CoOn : */ int CoOn(UBYTE *s) { GETIDENTITY UBYTE *t, c; int i, num = sizeof(onoffoptions)/sizeof(KEYWORD); LONG interval; for (;;) { while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == 0 ) return(0); if ( chartype[*s] != 0 ) { MesPrint("&Illegal character or option encountered in ON statement"); return(-1); } t = s; while ( chartype[*s] == 0 ) s++; c = *s; *s = 0; for ( i = 0; i < num; i++ ) { if ( StrICont(t,(UBYTE *)(onoffoptions[i].name)) == 0 ) break; } if ( i >= num ) { MesPrint("&Unrecognized option in ON statement: %s",t); *s = c; return(-1); } if ( StrICont(t,(UBYTE *)"backtrace") == 0 ) { #ifndef ENABLE_BACKTRACE Warning("backtrace not supported on this platform"); #endif } else if ( StrICont(t,(UBYTE *)"compress") == 0 ) { AR.gzipCompress = 0; *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s ) { t = s; while ( FG.cTable[*s] <= 1 ) s++; c = *s; *s = 0; if ( StrICmp(t,(UBYTE *)"gzip") == 0 ) { #ifndef WITHZLIB Warning("gzip compression not supported on this platform"); #endif #ifdef WITHZSTD /* If gzip is specified, turn off zstd compression. zlib still goes via the wrapper. */ ZWRAP_useZSTDcompression(0); #endif } else if ( StrICmp(t,(UBYTE *)"zstd") == 0 ) { #ifdef WITHZSTD ZWRAP_useZSTDcompression(1); #else Warning("zstd compression not supported on this platform"); #endif } else { MesPrint("&Unrecognized option in ON compress statement: %s",t); return(-1); } /* Whether we are using zlib or zstd, accept and use a compression level. */ *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( FG.cTable[*s] == 1 ) { AR.gzipCompress = *s++ - '0'; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s ) { MesPrint("&Unrecognized option in ON compress gzip/zstd statement: %s",t); return(-1); } } else if ( *s == 0 ) { AR.gzipCompress = GZIPDEFAULT; } else { MesPrint("&Unrecognized option in ON compress gzip/zstd statement: %s, single digit expected",t); return(-1); } } } else if ( StrICont(t,(UBYTE *)"checkpoint") == 0 ) { PrintDeprecation("the checkpoint mechanism", "issues/626"); AC.CheckpointInterval = 0; if ( AC.CheckpointRunBefore ) { free(AC.CheckpointRunBefore); AC.CheckpointRunBefore = NULL; } if ( AC.CheckpointRunAfter ) { free(AC.CheckpointRunAfter); AC.CheckpointRunAfter = NULL; } *s = c; while ( *s ) { while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( FG.cTable[*s] == 1 ) { interval = 0; t = s; do { interval = 10*interval + *s++ - '0'; } while ( FG.cTable[*s] == 1 ); if ( *s == 's' || *s == 'S' ) { s++; } else if ( *s == 'm' || *s == 'M' ) { interval *= 60; s++; } else if ( *s == 'h' || *s == 'H' ) { interval *= 3600; s++; } else if ( *s == 'd' || *s == 'D' ) { interval *= 86400; s++; } if ( *s != ',' && FG.cTable[*s] != 6 && FG.cTable[*s] != 10 ) { MesPrint("&Unrecognized time interval in ON Checkpoint statement: %s", t); return(-1); } AC.CheckpointInterval = interval * 100; /* in 1/100 of seconds */ } else if ( FG.cTable[*s] == 0 ) { int type; t = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(t,(UBYTE *)"run") == 0 ) { type = 3; } else if ( StrICmp(t,(UBYTE *)"runafter") == 0 ) { type = 2; } else if ( StrICmp(t,(UBYTE *)"runbefore") == 0 ) { type = 1; } else { MesPrint("&Unrecognized option in ON Checkpoint statement: %s", t); *s = c; return(-1); } *s = c; if ( *s != '=' && FG.cTable[*(s+1)] != 9 ) { MesPrint("&Unrecognized option in ON Checkpoint statement: %s", t); return(-1); } ++s; t = ++s; while ( *s ) { if ( FG.cTable[*s] == 9 ) { c = *s; *s = 0; if ( type & 1 ) { if ( AC.CheckpointRunBefore ) { free(AC.CheckpointRunBefore); AC.CheckpointRunBefore = NULL; } if ( s-t > 0 ) { AC.CheckpointRunBefore = Malloc1(s-t+1, "AC.CheckpointRunBefore"); StrCopy(t, (UBYTE*)AC.CheckpointRunBefore); } } if ( type & 2 ) { if ( AC.CheckpointRunAfter ) { free(AC.CheckpointRunAfter); AC.CheckpointRunAfter = NULL; } if ( s-t > 0 ) { AC.CheckpointRunAfter = Malloc1(s-t+1, "AC.CheckpointRunAfter"); StrCopy(t, (UBYTE*)AC.CheckpointRunAfter); } } *s = c; break; } ++s; } if ( FG.cTable[*s] != 9 ) { MesPrint("&Unrecognized option in ON Checkpoint statement: %s", t); return(-1); } ++s; } } /* if ( AC.NoShowInput == 0 ) { MesPrint("Checkpoints activated."); if ( AC.CheckpointInterval ) { MesPrint("-> Minimum saving interval: %l seconds.", AC.CheckpointInterval/100); } else { MesPrint("-> No minimum saving interval given. Saving after EVERY module."); } if ( AC.CheckpointRunBefore ) { MesPrint("-> Calling script \"%s\" before saving.", AC.CheckpointRunBefore); } if ( AC.CheckpointRunAfter ) { MesPrint("-> Calling script \"%s\" after saving.", AC.CheckpointRunAfter); } } */ } else if ( StrICont(t,(UBYTE *)"indentspace") == 0 ) { *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s ) { i = 0; while ( FG.cTable[*s] == 1 ) { i = 10*i + *s++ - '0'; } if ( *s ) { MesPrint("&Unrecognized option in ON IndentSpace statement: %s",t); return(-1); } if ( i > 40 ) { Warning("IndentSpace parameter adjusted to 40"); i = 40; } AO.IndentSpace = i; } else { AO.IndentSpace = AM.ggIndentSpace; } return(0); } else if ( ( StrICont(t,(UBYTE *)"fewerstats") == 0 ) || ( StrICont(t,(UBYTE *)"fewerstatistics") == 0 ) ) { *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s ) { i = 0; while ( FG.cTable[*s] == 1 ) { i = 10*i + *s++ - '0'; } if ( *s ) { MesPrint("&Unrecognized option in ON FewerStatistics statement: %s",t); return(-1); } if ( i > AM.S0->MaxPatches ) { if ( AC.WarnFlag ) MesPrint("&Warning: FewerStatistics parameter greater than MaxPatches(=%d). Adjusted to %d" ,AM.S0->MaxPatches,(AM.S0->MaxPatches+1)/2); i = (AM.S0->MaxPatches+1)/2; } AC.ShortStatsMax = i; } else { AC.ShortStatsMax = 10; /* default value */ } return(0); } else if ( StrICont(t,(UBYTE *)"threads") == 0 ) { if ( AM.totalnumberofthreads > 1 ) AS.MultiThreaded = 1; } else if ( StrICont(t,(UBYTE *)"flag") == 0 ) { *s = c; return(CoFlags(s,1)); } else if ( StrICont(t,(UBYTE *)"innertest") == 0 ) { UBYTE *t; *s = c; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s ) { t = s; while ( *t ) t++; while ( t[-1] == ' ' || t[-1] == '\t' ) t--; c = *t; *t = 0; if ( AC.TestValue ) M_free(AC.TestValue,"InnerTest"); AC.TestValue = strDup1(s,"InnerTest"); *t = c; s = t; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; } else { if ( AC.TestValue ) { M_free(AC.TestValue,"InnerTest"); AC.TestValue = 0; } } } else if ( StrICont(t,(UBYTE *)"flint") == 0 ) { #ifndef WITHFLINT MesPrint("&Warning: FORM was not built with FLINT support."); MesPrint("Statement has no effect."); #endif } else { *s = c; } *onoffoptions[i].var = onoffoptions[i].type; AR.SortType = AC.SortType; AC.mparallelflag = AC.parallelflag | AM.hparallelflag; } } /* #] CoOn : #[ CoInsideFirst : */ int CoInsideFirst(UBYTE *s) { return(setonoff(s,&AC.insidefirst,1,0)); } /* #] CoInsideFirst : #[ CoProperCount : */ int CoProperCount(UBYTE *s) { return(setonoff(s,&AC.BottomLevel,1,0)); } /* #] CoProperCount : #[ CoDelete : */ int CoDelete(UBYTE *s) { int error = 0; if ( StrICmp(s,(UBYTE *)"storage") == 0 ) { if ( DeleteStore(1) < 0 ) { MesPrint("&Cannot restart storage file"); error = 1; } } else { UBYTE *t = s, c; while ( *t && *t != ',' && *t != '>' ) t++; c = *t; *t = 0; if ( ( StrICmp(s,(UBYTE *)"extrasymbols") == 0 ) || ( StrICmp(s,(UBYTE *)"extrasymbol") == 0 ) ) { WORD x = 0; /* Either deletes all extra symbols or deletes above a given number */ *t = c; s = t; if ( *s == '>' ) { s++; if ( FG.cTable[*s] != 1 ) goto unknown; while ( *s <= '9' && *s >= '0' ) x = 10*x + *s++ - '0'; if ( *s ) goto unknown; } else if ( *s ) goto unknown; if ( x < AM.gnumextrasym ) x = AM.gnumextrasym; PruneExtraSymbols(x); } else { *t = c; unknown: MesPrint("&Unknown option: %s",s); error = 1; } } return(error); } /* #] CoDelete : #[ CoKeep : */ int CoKeep(UBYTE *s) { if ( StrICmp(s,(UBYTE *)"brackets") == 0 ) AC.ComDefer = 1; else { MesPrint("&Unknown option: '%s'",s); return(1); } return(0); } /* #] CoKeep : #[ CoFixIndex : */ int CoFixIndex(UBYTE *s) { int x, y, error = 0; while ( *s ) { if ( FG.cTable[*s] != 1 ) { proper: MesPrint("&Proper syntax is: FixIndex,number:value[,number,value];"); return(1); } ParseNumber(x,s) if ( *s != ':' ) goto proper; s++; if ( *s != '-' && *s != '+' && FG.cTable[*s] != 1 ) goto proper; ParseSignedNumber(y,s) if ( *s && *s != ',' ) goto proper; while ( *s == ',' ) s++; if ( x >= AM.OffsetIndex ) { MesPrint("&Fixed index out of allowed range. Change ConstIndex in setup file?"); MesPrint("&Current value of ConstIndex = %d",AM.OffsetIndex-1); error = 1; } if ( y != (int)((WORD)y) ) { MesPrint("&Value of d_(%d,%d) outside range for this computer",x,x); error = 1; } if ( error == 0 ) AC.FixIndices[x] = y; } return(error); } /* #] CoFixIndex : #[ CoMetric : */ int CoMetric(UBYTE *s) { DUMMYUSE(s); MesPrint("&The metric statement does not do anything yet"); return(1); } /* #] CoMetric : #[ DoPrint : */ int DoPrint(UBYTE *s, int par) { int i, error = 0, numdol = 0, type; WORD handle = -1; UBYTE *name, c, *t; EXPRESSIONS e; WORD numexpr, tofile = 0, *w, par2 = 0; CBUF *C = cbuf + AC.cbufnum; while ( *s == ',' ) s++; if ( ( *s == '+' || *s == '-' ) && ( s[1] == 'f' || s[1] == 'F' ) ) { t = s + 2; while ( *t == ' ' || *t == ',' ) t++; if ( *t == '"' ) { if ( *s == '+' ) { tofile = 1; handle = AC.LogHandle; } s = t; } } else if ( *s == '<' ) { UBYTE *filename; s++; filename = s; while ( *s && *s != '>' ) s++; if ( *s == 0 ) { MesPrint("&Improper filename in print statement"); return(1); } *s++ = 0; tofile = 1; if ( ( handle = GetChannel((char *)filename,1) ) < 0 ) return(1); SKIPBLANKS(s) if ( *s == ',' ) s++; SKIPBLANKS(s) if ( *s == '+' && ( s[1] == 's' || s[1] == 'S' ) ) { s += 2; par2 |= PRINTONETERM; if ( *s == 's' || *s == 'S' ) { s++; par2 |= PRINTONEFUNCTION; if ( *s == 's' || *s == 'S' ) { s++; par2 |= PRINTALL; } } SKIPBLANKS(s) if ( *s == ',' ) s++; SKIPBLANKS(s) } } if ( par == PRINTON && *s == '"' ) { WORD code[3]; if ( tofile == 1 ) code[0] = TYPEFPRINT; else code[0] = TYPEPRINT; code[1] = handle; code[2] = par2; s++; name = s; while ( *s && *s != '"' ) { if ( *s == '\\' ) s++; if ( *s == '%' && s[1] == '$' ) numdol++; s++; } if ( *s != '"' ) { MesPrint("&String in print statement should be enclosed in \""); return(1); } *s = 0; AddComString(3,code,name,1); *s++ = '"'; while ( *s == ',' ) { s++; if ( *s == '$' ) { s++; name = s; while ( FG.cTable[*s] <= 1 ) s++; c = *s; *s = 0; type = GetName(AC.dollarnames,name,&numexpr,NOAUTO); if ( type == NAMENOTFOUND ) { MesPrint("&$ variable %s not (yet) defined",name); error = 1; } else { C->lhs[C->numlhs][1] += 2; *(C->Pointer)++ = DOLLAREXPRESSION; *(C->Pointer)++ = numexpr; numdol--; } } else { MesPrint("&Illegal object in print statement"); error = 1; return(error); } *s = c; if ( c == '[' ) { w = C->Pointer; s++; s = GetDoParam(s,&(C->Pointer),-1); if ( s == 0 ) return(1); if ( *s != ']' ) { MesPrint("&unmatched [] in $ factor"); return(1); } C->lhs[C->numlhs][1] += C->Pointer - w; s++; } } if ( *s != 0 ) { MesPrint("&Illegal object in print statement"); error = 1; } if ( numdol > 0 ) { MesPrint("&More $ variables asked for than provided"); error = 1; } *(C->Pointer)++ = 0; return(error); } if ( *s == 0 ) { /* All active expressions */ AllExpr: for ( e = Expressions, i = NumExpressions; i > 0; i--, e++ ) { if ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) e->printflag = par; } return(error); } while ( *s ) { if ( *s == '+' ) { s++; if ( tolower(*s) == 'f' ) par |= PRINTLFILE; else if ( tolower(*s) == 's' ) { if ( tolower(s[1]) == 's' ) { if ( tolower(s[2]) == 's' ) { par |= PRINTONEFUNCTION | PRINTONETERM | PRINTALL; s++; } else if ( ( par & 3 ) < 2 ) par |= PRINTONEFUNCTION | PRINTONETERM; s++; } else { if ( ( par & 3 ) < 2 ) par |= PRINTONETERM; } } else { illeg: MesPrint("&Illegal option in (n)print statement"); error = 1; } s++; if ( *s == 0 ) goto AllExpr; } else if ( *s == '-' ) { s++; if ( tolower(*s) == 'f' ) par &= ~PRINTLFILE; else if ( tolower(*s) == 's' ) { if ( tolower(s[1]) == 's' ) { if ( tolower(s[2]) == 's' ) { par &= ~PRINTALL; s++; } else if ( ( par & 3 ) < 2 ) { par &= ~PRINTONEFUNCTION; par &= ~PRINTALL; } s++; } else { if ( ( par & 3 ) < 2 ) { par &= ~PRINTONETERM; par &= ~PRINTONEFUNCTION; par &= ~PRINTALL; } } } else goto illeg; s++; if ( *s == 0 ) goto AllExpr; } else if ( FG.cTable[*s] == 0 || *s == '[' ) { name = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Improper name in (n)print statement"); return(1); } c = *s; *s = 0; if ( ( GetName(AC.exprnames,name,&numexpr,NOAUTO) == CEXPRESSION ) && ( Expressions[numexpr].status == LOCALEXPRESSION || Expressions[numexpr].status == GLOBALEXPRESSION ) ) { FoundExpr:; if ( c == '[' && s[1] == ']' ) { Expressions[numexpr].printflag = par | PRINTCONTENTS; *s++ = c; c = *++s; } else Expressions[numexpr].printflag = par; } else if ( GetLastExprName(name,&numexpr) && ( Expressions[numexpr].status == LOCALEXPRESSION || Expressions[numexpr].status == GLOBALEXPRESSION || Expressions[numexpr].status == UNHIDELEXPRESSION || Expressions[numexpr].status == UNHIDEGEXPRESSION ) ) { goto FoundExpr; } else { MesPrint("&%s is not the name of an active expression",name); error = 1; } *s++ = c; if ( c == 0 ) return(0); if ( c == '-' || c == '+' ) s--; } else if ( *s == ',' ) s++; else { MesPrint("&Illegal object in (n)print statement"); return(1); } } return(0); } /* #] DoPrint : #[ CoPrint : */ int CoPrint(UBYTE *s) { return(DoPrint(s,PRINTON)); } /* #] CoPrint : #[ CoPrintB : */ int CoPrintB(UBYTE *s) { return(DoPrint(s,PRINTCONTENT)); } /* #] CoPrintB : #[ CoNPrint : */ int CoNPrint(UBYTE *s) { return(DoPrint(s,PRINTOFF)); } /* #] CoNPrint : #[ CoPushHide : */ int CoPushHide(UBYTE *s) { GETIDENTITY WORD *ScratchBuf; int i; if ( AR.Fscr[2].PObuffer == 0 ) { ScratchBuf = (WORD *)Malloc1(AM.HideSize*sizeof(WORD),"hidesize"); AR.Fscr[2].POsize = AM.HideSize * sizeof(WORD); AR.Fscr[2].POfull = AR.Fscr[2].POfill = AR.Fscr[2].PObuffer = ScratchBuf; AR.Fscr[2].POstop = AR.Fscr[2].PObuffer + AM.HideSize; PUTZERO(AR.Fscr[2].POposition); } while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; AC.HideLevel += 2; if ( *s ) { MesPrint("&PushHide statement should have no arguments"); return(-1); } for ( i = 0; i < NumExpressions; i++ ) { switch ( Expressions[i].status ) { case DROPLEXPRESSION: case SKIPLEXPRESSION: case LOCALEXPRESSION: Expressions[i].status = HIDELEXPRESSION; Expressions[i].hidelevel = AC.HideLevel-1; break; case DROPGEXPRESSION: case SKIPGEXPRESSION: case GLOBALEXPRESSION: Expressions[i].status = HIDEGEXPRESSION; Expressions[i].hidelevel = AC.HideLevel-1; break; default: break; } } return(0); } /* #] CoPushHide : #[ CoPopHide : */ int CoPopHide(UBYTE *s) { int i; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( AC.HideLevel <= 0 ) { MesPrint("&PopHide statement without corresponding PushHide statement"); return(-1); } AC.HideLevel -= 2; if ( *s ) { MesPrint("&PopHide statement should have no arguments"); return(-1); } for ( i = 0; i < NumExpressions; i++ ) { switch ( Expressions[i].status ) { case HIDDENLEXPRESSION: if ( Expressions[i].hidelevel > AC.HideLevel ) Expressions[i].status = UNHIDELEXPRESSION; break; case HIDDENGEXPRESSION: if ( Expressions[i].hidelevel > AC.HideLevel ) Expressions[i].status = UNHIDEGEXPRESSION; break; default: break; } } return(0); } /* #] CoPopHide : #[ SetExprCases : */ int SetExprCases(int par, int setunset, int val) { switch ( par ) { case SKIP: switch ( val ) { case SKIPLEXPRESSION: if ( !setunset ) val = LOCALEXPRESSION; break; case SKIPGEXPRESSION: if ( !setunset ) val = GLOBALEXPRESSION; break; case LOCALEXPRESSION: if ( setunset ) val = SKIPLEXPRESSION; break; case GLOBALEXPRESSION: if ( setunset ) val = SKIPGEXPRESSION; break; case INTOHIDEGEXPRESSION: case INTOHIDELEXPRESSION: default: break; } break; case DROP: switch ( val ) { case SKIPLEXPRESSION: case LOCALEXPRESSION: case HIDELEXPRESSION: if ( setunset ) val = DROPLEXPRESSION; break; case DROPLEXPRESSION: if ( !setunset ) val = LOCALEXPRESSION; break; case SKIPGEXPRESSION: case GLOBALEXPRESSION: case HIDEGEXPRESSION: if ( setunset ) val = DROPGEXPRESSION; break; case DROPGEXPRESSION: if ( !setunset ) val = GLOBALEXPRESSION; break; case HIDDENLEXPRESSION: case UNHIDELEXPRESSION: if ( setunset ) val = DROPHLEXPRESSION; break; case HIDDENGEXPRESSION: case UNHIDEGEXPRESSION: if ( setunset ) val = DROPHGEXPRESSION; break; case DROPHLEXPRESSION: if ( !setunset ) val = HIDDENLEXPRESSION; break; case DROPHGEXPRESSION: if ( !setunset ) val = HIDDENGEXPRESSION; break; case INTOHIDEGEXPRESSION: case INTOHIDELEXPRESSION: default: break; } break; case HIDE: switch ( val ) { case DROPLEXPRESSION: case SKIPLEXPRESSION: case LOCALEXPRESSION: if ( setunset ) val = HIDELEXPRESSION; break; case HIDELEXPRESSION: if ( !setunset ) val = LOCALEXPRESSION; break; case DROPGEXPRESSION: case SKIPGEXPRESSION: case GLOBALEXPRESSION: if ( setunset ) val = HIDEGEXPRESSION; break; case HIDEGEXPRESSION: if ( !setunset ) val = GLOBALEXPRESSION; break; case INTOHIDEGEXPRESSION: case INTOHIDELEXPRESSION: default: break; } break; case UNHIDE: switch ( val ) { case HIDDENLEXPRESSION: case DROPHLEXPRESSION: if ( setunset ) val = UNHIDELEXPRESSION; break; case UNHIDELEXPRESSION: if ( !setunset ) val = HIDDENLEXPRESSION; break; case HIDDENGEXPRESSION: case DROPHGEXPRESSION: if ( setunset ) val = UNHIDEGEXPRESSION; break; case UNHIDEGEXPRESSION: if ( !setunset ) val = HIDDENGEXPRESSION; break; case INTOHIDEGEXPRESSION: case INTOHIDELEXPRESSION: default: break; } break; case INTOHIDE: switch ( val ) { case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: MesPrint("&Expression is already hidden"); return(-1); case DROPHLEXPRESSION: case DROPHGEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: if ( setunset ) { MesPrint("&Cannot unhide/drop and put intohide expression in the same module"); return(-1); } break; case LOCALEXPRESSION: case DROPLEXPRESSION: case SKIPLEXPRESSION: case HIDELEXPRESSION: if ( setunset ) val = INTOHIDELEXPRESSION; break; case GLOBALEXPRESSION: case DROPGEXPRESSION: case SKIPGEXPRESSION: case HIDEGEXPRESSION: if ( setunset ) val = INTOHIDEGEXPRESSION; break; case INTOHIDELEXPRESSION: if ( !setunset ) val = LOCALEXPRESSION; break; case INTOHIDEGEXPRESSION: if ( !setunset ) val = GLOBALEXPRESSION; break; default: break; } break; default: break; } return(val); } /* #] SetExprCases : #[ SetExpr : */ int SetExpr(UBYTE *s, int setunset, int par) { WORD *w, numexpr; int error = 0, i; UBYTE *name, c; if ( *s == 0 ) { for ( i = 0; i < NumExpressions; i++ ) { w = &(Expressions[i].status); *w = SetExprCases(par,setunset,*w); if ( *w < 0 ) error = 1; if ( ( par == HIDE || par == INTOHIDE ) && setunset == 1 ) Expressions[i].hidelevel = AC.HideLevel; } return(0); } while ( *s ) { if ( *s == ',' ) { s++; continue; } if ( *s == '0' ) { s++; continue; } name = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Improper name for an expression: '%s'",name); return(1); } c = *s; *s = 0; if ( GetName(AC.exprnames,name,&numexpr,NOAUTO) == CEXPRESSION ) { w = &(Expressions[numexpr].status); *w = SetExprCases(par,setunset,*w); if ( *w < 0 ) error = 1; if ( ( par == HIDE || par == INTOHIDE ) && setunset == 1 ) Expressions[numexpr].hidelevel = AC.HideLevel; } else if ( GetName(AC.varnames,name,&numexpr,NOAUTO) != NAMENOTFOUND ) { MesPrint("&%s is not an expression",name); error = 1; } *s = c; } return(error); } /* #] SetExpr : #[ CoDrop : */ int CoDrop(UBYTE *s) { return(SetExpr(s,1,DROP)); } /* #] CoDrop : #[ CoNoDrop : */ int CoNoDrop(UBYTE *s) { return(SetExpr(s,0,DROP)); } /* #] CoNoDrop : #[ CoSkip : */ int CoSkip(UBYTE *s) { return(SetExpr(s,1,SKIP)); } /* #] CoSkip : #[ CoNoSkip : */ int CoNoSkip(UBYTE *s) { return(SetExpr(s,0,SKIP)); } /* #] CoNoSkip : #[ CoHide : */ int CoHide(UBYTE *inp) { GETIDENTITY WORD *ScratchBuf; if ( AR.Fscr[2].PObuffer == 0 ) { ScratchBuf = (WORD *)Malloc1(AM.HideSize*sizeof(WORD),"hidesize"); AR.Fscr[2].POsize = AM.HideSize * sizeof(WORD); AR.Fscr[2].POfull = AR.Fscr[2].POfill = AR.Fscr[2].PObuffer = ScratchBuf; AR.Fscr[2].POstop = AR.Fscr[2].PObuffer + AM.HideSize; PUTZERO(AR.Fscr[2].POposition); } return(SetExpr(inp,1,HIDE)); } /* #] CoHide : #[ CoIntoHide : */ int CoIntoHide(UBYTE *inp) { GETIDENTITY WORD *ScratchBuf; if ( AR.Fscr[2].PObuffer == 0 ) { ScratchBuf = (WORD *)Malloc1(AM.HideSize*sizeof(WORD),"hidesize"); AR.Fscr[2].POsize = AM.HideSize * sizeof(WORD); AR.Fscr[2].POfull = AR.Fscr[2].POfill = AR.Fscr[2].PObuffer = ScratchBuf; AR.Fscr[2].POstop = AR.Fscr[2].PObuffer + AM.HideSize; PUTZERO(AR.Fscr[2].POposition); } return(SetExpr(inp,1,INTOHIDE)); } /* #] CoIntoHide : #[ CoNoIntoHide : */ int CoNoIntoHide(UBYTE *inp) { return(SetExpr(inp,0,INTOHIDE)); } /* #] CoNoIntoHide : #[ CoNoHide : */ int CoNoHide(UBYTE *inp) { return(SetExpr(inp,0,HIDE)); } /* #] CoNoHide : #[ CoUnHide : */ int CoUnHide(UBYTE *inp) { return(SetExpr(inp,1,UNHIDE)); } /* #] CoUnHide : #[ CoNoUnHide : */ int CoNoUnHide(UBYTE *inp) { return(SetExpr(inp,0,UNHIDE)); } /* #] CoNoUnHide : #[ AddToCom : */ void AddToCom(int n, WORD *array) { CBUF *C = cbuf+AC.cbufnum; #ifdef COMPBUFDEBUG MesPrint(" %a",n,array); #endif while ( C->Pointer+n >= C->Top ) DoubleCbuffer(AC.cbufnum,C->Pointer,18); while ( --n >= 0 ) *(C->Pointer)++ = *array++; } /* #] AddToCom : #[ AddComString : */ int AddComString(int n, WORD *array, UBYTE *thestring, int par) { CBUF *C = cbuf+AC.cbufnum; UBYTE *s = thestring, *w; #ifdef COMPBUFDEBUG WORD *cc; UBYTE *ww; #endif int i, numchars = 0, size, zeroes; while ( *s ) { if ( *s == '\\' ) s++; else if ( par == 1 && ( ( *s == '%' && s[1] != 't' && s[1] != 'T' && s[1] != '$' && s[1] != 'w' && s[1] != 'W' && s[1] != 'r' && s[1] != 0 ) || *s == '#' || *s == '@' || *s == '&' ) ) { numchars++; } s++; numchars++; } AddLHS(AC.cbufnum); size = numchars/sizeof(WORD)+1; while ( C->Pointer+size+n+2 >= C->Top ) DoubleCbuffer(AC.cbufnum,C->Pointer,19); #ifdef COMPBUFDEBUG cc = C->Pointer; #endif *(C->Pointer)++ = array[0]; *(C->Pointer)++ = size+n+2; for ( i = 1; i < n; i++ ) *(C->Pointer)++ = array[i]; *(C->Pointer)++ = size; #ifdef COMPBUFDEBUG ww = #endif w = (UBYTE *)(C->Pointer); zeroes = size*sizeof(WORD)-numchars; s = thestring; while ( *s ) { if ( *s == '\\' ) s++; else if ( par == 1 && ( ( *s == '%' && s[1] != 't' && s[1] != 'T' && s[1] != '$' && s[1] != 'w' && s[1] != 'W' && s[1] != 'r' && s[1] != 0 ) || *s == '#' || *s == '@' || *s == '&' ) ) { *w++ = '%'; } *w++ = *s++; } while ( --zeroes >= 0 ) *w++ = 0; C->Pointer += size; #ifdef COMPBUFDEBUG MesPrint("LH: %a",size+1+n,cc); MesPrint(" %s",thestring); #endif return(0); } /* #] AddComString : #[ Add2ComStrings : */ int Add2ComStrings(int n, WORD *array, UBYTE *string1, UBYTE *string2) { CBUF *C = cbuf+AC.cbufnum; UBYTE *s1 = string1, *s2 = string2, *w; int i, num1chars = 0, num2chars = 0, size1, size2, zeroes1, zeroes2; AddLHS(AC.cbufnum); while ( *s1 ) { s1++; num1chars++; } size1 = num1chars/sizeof(WORD)+1; if ( s2 ) { while ( *s2 ) { s2++; num2chars++; } size2 = num2chars/sizeof(WORD)+1; } else size2 = 0; while ( C->Pointer+size1+size2+n+3 >= C->Top ) DoubleCbuffer(AC.cbufnum,C->Pointer,20); *(C->Pointer)++ = array[0]; *(C->Pointer)++ = size1+size2+n+3; for ( i = 1; i < n; i++ ) *(C->Pointer)++ = array[i]; *(C->Pointer)++ = size1; w = (UBYTE *)(C->Pointer); zeroes1 = size1*sizeof(WORD)-num1chars; s1 = string1; while ( *s1 ) { *w++ = *s1++; } while ( --zeroes1 >= 0 ) *w++ = 0; C->Pointer += size1; *(C->Pointer)++ = size2; if ( size2 ) { w = (UBYTE *)(C->Pointer); zeroes2 = size2*sizeof(WORD)-num2chars; s2 = string2; while ( *s2 ) { *w++ = *s2++; } while ( --zeroes2 >= 0 ) *w++ = 0; C->Pointer += size2; } return(0); } /* #] Add2ComStrings : #[ CoDiscard : */ int CoDiscard(UBYTE *s) { if ( *s == 0 ) { Add2Com(TYPEDISCARD) return(0); } MesPrint("&Illegal argument in discard statement: '%s'",s); return(1); } /* #] CoDiscard : #[ CoContract : Syntax: Contract Contract:# Contract # Contract:#,# */ static WORD ccarray[5] = { TYPEOPERATION,5,CONTRACT,0,0 }; int CoContract(UBYTE *s) { int x; if ( *s == ':' ) { s++; ParseNumber(x,s) if ( *s != ',' && *s ) { proper: MesPrint("&Illegal number in contract statement"); return(1); } if ( *s ) s++; ccarray[4] = x; } else ccarray[4] = 0; if ( FG.cTable[*s] == 1 ) { ParseNumber(x,s) if ( *s ) goto proper; ccarray[3] = x; } else if ( *s ) goto proper; else ccarray[3] = -1; return(AddNtoL(5,ccarray)); } /* #] CoContract : #[ CoGoTo : */ int CoGoTo(UBYTE *inp) { UBYTE *s = inp; int x; while ( FG.cTable[*s] <= 1 ) s++; if ( *s ) { MesPrint("&Label should be an alpha-numeric string"); return(1); } x = GetLabel(inp); Add3Com(TYPEGOTO,x); return(0); } /* #] CoGoTo : #[ CoLabel : */ int CoLabel(UBYTE *inp) { UBYTE *s = inp; int x; while ( FG.cTable[*s] <= 1 ) s++; if ( *s ) { MesPrint("&Label should be an alpha-numeric string"); return(1); } x = GetLabel(inp); if ( AC.Labels[x] >= 0 ) { MesPrint("&Label %s defined more than once",AC.LabelNames[x]); return(1); } AC.Labels[x] = cbuf[AC.cbufnum].numlhs; return(0); } /* #] CoLabel : #[ DoArgument : Layout: par,full size,numlhs(+1),par,scale scale is for normalize */ int DoArgument(UBYTE *s, int par) { GETIDENTITY UBYTE *name, *t, *v, c; WORD *oldworkpointer = AT.WorkPointer, *w, *ww, number, *scale; int error = 0, zeroflag, type, x; AC.lhdollarflag = 0; while ( *s == ',' ) s++; w = AT.WorkPointer; *w++ = par; w++; switch ( par ) { case TYPEARG: if ( AC.arglevel >= MAXNEST ) { MesPrint("@Nesting of argument statements more than %d levels" ,(WORD)MAXNEST); return(-1); } AC.argsumcheck[AC.arglevel] = NestingChecksum(); AC.argstack[AC.arglevel] = cbuf[AC.cbufnum].Pointer - cbuf[AC.cbufnum].Buffer + 2; AC.arglevel++; *w++ = cbuf[AC.cbufnum].numlhs; break; case TYPENORM: case TYPENORM4: case TYPESPLITARG: case TYPESPLITFIRSTARG: case TYPESPLITLASTARG: case TYPEFACTARG: case TYPEARGTOEXTRASYMBOL: *w++ = cbuf[AC.cbufnum].numlhs+1; break; } *w++ = par; scale = w; *w++ = 1; *w++ = 0; if ( *s == '^' ) { s++; ParseSignedNumber(x,s) while ( *s == ',' ) s++; *scale = x; } if ( *s == '(' ) { t = s+1; SKIPBRA3(s) /* We did check the brackets already */ if ( par == TYPEARG ) { MesPrint("&Illegal () entry in argument statement"); error = 1; s++; goto skipbracks; } else if ( par == TYPESPLITFIRSTARG ) { MesPrint("&Illegal () entry in splitfirstarg statement"); error = 1; s++; goto skipbracks; } else if ( par == TYPESPLITLASTARG ) { MesPrint("&Illegal () entry in splitlastarg statement"); error = 1; s++; goto skipbracks; } v = t; while ( v < s ) { if ( *v == '?' ) { MesPrint("&Wildcarding not allowed in this type of statement"); error = 1; break; } v++; } v = s++; if ( *t == '(' && v[-1] == ')' ) { t++; v--; if ( par == TYPESPLITARG ) oldworkpointer[0] = TYPESPLITARG2; else if ( par == TYPEFACTARG ) oldworkpointer[0] = TYPEFACTARG2; else if ( par == TYPENORM4 ) oldworkpointer[0] = TYPENORM4; else if ( par == TYPENORM ) { if ( *t == '-' ) { oldworkpointer[0] = TYPENORM3; t++; } else { oldworkpointer[0] = TYPENORM2; *scale = 0; } } } if ( error == 0 ) { CBUF *C = cbuf+AC.cbufnum; WORD oldnumrhs = C->numrhs, oldnumlhs = C->numlhs; WORD prototype[SUBEXPSIZE+40]; /* Up to 10 nested sums! */ WORD *m, *mm; int i, retcode; LONG oldpointer = C->Pointer - C->Buffer; *v = 0; prototype[0] = SUBEXPRESSION; prototype[1] = SUBEXPSIZE; prototype[2] = C->numrhs+1; prototype[3] = 1; prototype[4] = AC.cbufnum; AT.WorkPointer += TYPEARGHEADSIZE+1; AddLHS(AC.cbufnum); if ( ( retcode = CompileAlgebra(t,LHSIDE,prototype) ) < 0 ) error = 1; else { prototype[2] = retcode; ww = C->lhs[retcode]; AC.lhdollarflag = 0; if ( *ww == 0 ) { *w++ = -2; *w++ = 0; } else if ( ww[ww[0]] != 0 ) { MesPrint("&There should be only one term between ()"); error = 1; } else if ( NewSort(BHEAD0) ) { if ( !error ) error = 1; } else if ( NewSort(BHEAD0) ) { LowerSortLevel(); if ( !error ) error = 1; } else { AN.RepPoint = AT.RepCount + 1; m = AT.WorkPointer; mm = ww; i = *mm; while ( --i >= 0 ) *m++ = *mm++; mm = AT.WorkPointer; AT.WorkPointer = m; AR.Cnumlhs = C->numlhs; if ( Generator(BHEAD mm,C->numlhs) ) { LowerSortLevel(); error = 1; } else if ( EndSort(BHEAD mm,0) < 0 ) { error = 1; AT.WorkPointer = mm; } else if ( *mm == 0 ) { *w++ = -2; *w++ = 0; AT.WorkPointer = mm; } else if ( mm[mm[0]] != 0 ) { error = 1; AT.WorkPointer = mm; } else { AT.WorkPointer = mm; m = mm+*mm; if ( par == TYPEFACTARG ) { if ( *mm != ABS(m[-1])+1 ) { *mm -= ABS(m[-1]); /* Strip coefficient */ } mm[-1] = -*mm-1; w += *mm+1; } else { *mm -= ABS(m[-1]); /* Strip coefficient */ /* if ( *mm == 1 ) { *w++ = -2; *w++ = 0; } else */ { mm[-1] = -*mm-1; w += *mm+1; } } oldworkpointer[1] = w - oldworkpointer; } LowerSortLevel(); } oldworkpointer[5] = AC.lhdollarflag; } *v = ')'; C->numrhs = oldnumrhs; C->numlhs = oldnumlhs; C->Pointer = C->Buffer + oldpointer; } } skipbracks: if ( *s == 0 ) { *w++ = 0; *w++ = 2; *w++ = 1; } else { do { if ( *s == ',' ) { s++; continue; } ww = w; *w++ = 0; w++; if ( FG.cTable[*s] > 1 && *s != '[' && *s != '{' ) { MesPrint("&Illegal parameters in statement"); error = 1; break; } while ( FG.cTable[*s] == 0 || *s == '[' || *s == '{' ) { if ( *s == '{' ) { name = s+1; SKIPBRA2(s) c = *s; *s = 0; number = DoTempSet(name,s); name--; *s++ = c; c = *s; *s = 0; goto doset; } else { name = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Illegal name '%s'",name); return(1); } c = *s; *s = 0; if ( ( type = GetName(AC.varnames,name,&number,WITHAUTO) ) == CSET ) { doset: if ( Sets[number].type != CFUNCTION ) goto nofun; #ifdef WITHFLOAT WORD *r1, *r2; r1 = SetElements + Sets[number].first; r2 = SetElements + Sets[number].last; while ( r1 < r2 ) { if ( *r1++ == FLOATFUN ) { MesPrint("&Illegal use of argument environment and float_."); error = 1; } } #endif *w++ = CSET; *w++ = number; } else if ( type == CFUNCTION ) { #ifdef WITHFLOAT if ( (number + FUNCTION) == FLOATFUN ) { MesPrint("&Illegal use of argument environment and float_."); error = 1; } #endif *w++ = CFUNCTION; *w++ = number + FUNCTION; } else { nofun: MesPrint("&%s is not a function or a set of functions" ,name); error = 1; } } *s = c; while ( *s == ',' ) s++; } ww[1] = w - ww; ww = w; w++; zeroflag = 0; while ( FG.cTable[*s] == 1 ) { ParseNumber(x,s) if ( *s && *s != ',' ) { MesPrint("&Illegal separator after number"); error = 1; while ( *s && *s != ',' ) s++; } while ( *s == ',' ) s++; if ( x == 0 ) zeroflag = 1; if ( !zeroflag ) *w++ = (WORD)x; } *ww = w - ww; } while ( *s ); } oldworkpointer[1] = w - oldworkpointer; if ( par == TYPEARG ) { /* To make sure. The Pointer might move in the future */ AC.argstack[AC.arglevel-1] = cbuf[AC.cbufnum].Pointer - cbuf[AC.cbufnum].Buffer + 2; } AddNtoL(oldworkpointer[1],oldworkpointer); AT.WorkPointer = oldworkpointer; return(error); } /* #] DoArgument : #[ CoArgument : */ int CoArgument(UBYTE *s) { return(DoArgument(s,TYPEARG)); } /* #] CoArgument : #[ CoEndArgument : */ int CoEndArgument(UBYTE *s) { CBUF *C = cbuf+AC.cbufnum; while ( *s == ',' ) s++; if ( *s ) { MesPrint("&Illegal syntax for EndArgument statement"); return(1); } if ( AC.arglevel <= 0 ) { MesPrint("&EndArgument without corresponding Argument statement"); return(1); } AC.arglevel--; cbuf[AC.cbufnum].Buffer[AC.argstack[AC.arglevel]] = C->numlhs; if ( AC.argsumcheck[AC.arglevel] != NestingChecksum() ) { MesNesting(); return(1); } return(0); } /* #] CoEndArgument : #[ CoInside : */ int CoInside(UBYTE *s) { return(ExecInside(s)); } /* #] CoInside : #[ CoEndInside : */ int CoEndInside(UBYTE *s) { CBUF *C = cbuf+AC.cbufnum; while ( *s == ',' ) s++; if ( *s ) { MesPrint("&Illegal syntax for EndInside statement"); return(1); } if ( AC.insidelevel <= 0 ) { MesPrint("&EndInside without corresponding Inside statement"); return(1); } AC.insidelevel--; cbuf[AC.cbufnum].Buffer[AC.insidestack[AC.insidelevel]] = C->numlhs; if ( AC.insidesumcheck[AC.insidelevel] != NestingChecksum() ) { MesNesting(); return(1); } return(0); } /* #] CoEndInside : #[ CoNormalize : */ int CoNormalize(UBYTE *s) { return(DoArgument(s,TYPENORM)); } /* #] CoNormalize : #[ CoMakeInteger : */ int CoMakeInteger(UBYTE *s) { return(DoArgument(s,TYPENORM4)); } /* #] CoMakeInteger : #[ CoSplitArg : */ int CoSplitArg(UBYTE *s) { return(DoArgument(s,TYPESPLITARG)); } /* #] CoSplitArg : #[ CoSplitFirstArg : */ int CoSplitFirstArg(UBYTE *s) { return(DoArgument(s,TYPESPLITFIRSTARG)); } /* #] CoSplitFirstArg : #[ CoSplitLastArg : */ int CoSplitLastArg(UBYTE *s) { return(DoArgument(s,TYPESPLITLASTARG)); } /* #] CoSplitLastArg : #[ CoFactArg : */ int CoFactArg(UBYTE *s) { if ( ( AC.topolynomialflag & TOPOLYNOMIALFLAG ) != 0 ) { MesPrint("&ToPolynomial statement and FactArg statement are not allowed in the same module"); return(1); } AC.topolynomialflag |= FACTARGFLAG; return(DoArgument(s,TYPEFACTARG)); } /* #] CoFactArg : #[ DoSymmetrize : Syntax: Symmetrize Fun[:[number]] [Fields] -> par = 0; AntiSymmetrize Fun[:[number]] [Fields] -> par = 1; CycleSymmetrize Fun[:[number]] [Fields] -> par = 2; RCycleSymmetrize Fun[:[number]] [Fields]-> par = 3; */ int DoSymmetrize(UBYTE *s, int par) { GETIDENTITY int extra = 0, error = 0, err, fix, x, groupsize, num, i; UBYTE *name, c; WORD funnum, *w, *ww, type; for(;;) { name = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Improper function name"); return(1); } c = *s; *s = 0; if ( c != ',' || ( FG.cTable[s[1]] != 0 && s[1] != '[' ) ) break; if ( par <= 0 && StrICmp(name,(UBYTE *)"cyclic") == 0 ) extra = 2; else if ( par <= 0 && StrICmp(name,(UBYTE *)"rcyclic") == 0 ) extra = 6; else { MesPrint("&Illegal option: '%s'",name); error = 1; } *s++ = c; } if ( ( err = GetVar(name,&type,&funnum,CFUNCTION,WITHAUTO) ) == NAMENOTFOUND ) { MesPrint("&Undefined function: %s",name); AddFunction(name,0,0,0,0,0,-1,-1); *s++ = c; return(1); } funnum += FUNCTION; if ( err == -1 ) error = 1; *s = c; if ( *s == ':' ) { s++; if ( *s == ',' || *s == '(' || *s == 0 ) fix = -1; else if ( FG.cTable[*s] == 1 ) { ParseNumber(fix,s) if ( fix == 0 ) Warning("Restriction to zero arguments removed"); } else { MesPrint("&Illegal character after :"); return(1); } } else fix = 0; w = AT.WorkPointer; *w++ = TYPEOPERATION; w++; *w++ = SYMMETRIZE; *w++ = par | extra; *w++ = funnum; *w++ = fix; /* And now the argument lists. We have either ,#,#,... or (#,#,..,#),(#,... */ w += 2; ww = w; groupsize = -1; while ( *s == ',' ) s++; while ( *s ) { if ( *s == '(' ) { s++; num = 0; while ( *s && *s != ')' ) { if ( *s == ',' ) { s++; continue; } if ( FG.cTable[*s] != 1 ) goto illarg; ParseNumber(x,s) if ( x <= 0 || ( fix > 0 && x > fix ) ) goto illnum; num++; *w++ = x-1; } if ( *s == 0 ) { MesPrint("&Improper termination of statement"); return(1); } if ( groupsize < 0 ) groupsize = num; else if ( groupsize != num ) goto group; s++; } else if ( FG.cTable[*s] == 1 ) { if ( groupsize < 0 ) groupsize = 1; else if ( groupsize != 1 ) { group: MesPrint("&All groups should have the same number of arguments"); return(1); } ParseNumber(x,s) if ( x <= 0 || ( fix > 0 && x > fix ) ) { illnum: MesPrint("&Illegal argument number: %d",x); return(1); } *w++ = x-1; } else { illarg: MesPrint("&Illegal argument"); return(1); } while ( *s == ',' ) s++; } /* Now the completion */ if ( w == ww ) { ww[-1] = 1; ww[-2] = 0; if ( fix > 0 ) { for ( i = 0; i < fix; i++ ) *w++ = i; ww[-2] = fix; /* Bugfix 31-oct-2001. Reported by York Schroeder */ } } else { ww[-1] = groupsize; ww[-2] = (w-ww)/groupsize; } AT.WorkPointer[1] = w - AT.WorkPointer; AddNtoL(AT.WorkPointer[1],AT.WorkPointer); return(error); } /* #] DoSymmetrize : #[ CoSymmetrize : */ int CoSymmetrize(UBYTE *s) { return(DoSymmetrize(s,SYMMETRIC)); } /* #] CoSymmetrize : #[ CoAntiSymmetrize : */ int CoAntiSymmetrize(UBYTE *s) { return(DoSymmetrize(s,ANTISYMMETRIC)); } /* #] CoAntiSymmetrize : #[ CoCycleSymmetrize : */ int CoCycleSymmetrize(UBYTE *s) { return(DoSymmetrize(s,CYCLESYMMETRIC)); } /* #] CoCycleSymmetrize : #[ CoRCycleSymmetrize : */ int CoRCycleSymmetrize(UBYTE *s) { return(DoSymmetrize(s,RCYCLESYMMETRIC)); } /* #] CoRCycleSymmetrize : #[ CoWrite : */ int CoWrite(UBYTE *s) { GETIDENTITY UBYTE *option; KEYWORDV *key; option = s; if ( ( ( s = SkipAName(s) ) == 0 ) || *s != 0 ) { MesPrint("&Proper use of write statement is: write option"); return(1); } key = (KEYWORDV *)FindInKeyWord(option,(KEYWORD *)writeoptions,sizeof(writeoptions)/sizeof(KEYWORD)); if ( key == 0 ) { MesPrint("&Unrecognized option in write statement"); return(1); } *key->var = key->type; AR.SortType = AC.SortType; return(0); } /* #] CoWrite : #[ CoNWrite : */ int CoNWrite(UBYTE *s) { GETIDENTITY UBYTE *option; KEYWORDV *key; option = s; if ( ( ( s = SkipAName(s) ) == 0 ) || *s != 0 ) { MesPrint("&Proper use of nwrite statement is: nwrite option"); return(1); } key = (KEYWORDV *)FindInKeyWord(option,(KEYWORD *)writeoptions,sizeof(writeoptions)/sizeof(KEYWORD)); if ( key == 0 ) { MesPrint("&Unrecognized option in nwrite statement"); return(1); } *key->var = key->flags; AR.SortType = AC.SortType; return(0); } /* #] CoNWrite : #[ CoRatio : */ static WORD ratstring[6] = { TYPEOPERATION, 6, RATIO, 0, 0, 0 }; int CoRatio(UBYTE *s) { UBYTE c, *t; int i, type, error = 0; WORD numsym, *rs; rs = ratstring+3; for ( i = 0; i < 3; i++ ) { if ( *s ) { t = s; s = SkipAName(s); c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,t,&numsym,WITHAUTO) ) != CSYMBOL ) && type != CDUBIOUS ) { MesPrint("&%s is not a symbol",t); error = 4; if ( type < 0 ) numsym = AddSymbol(t,-MAXPOWER,MAXPOWER,0,0); } *s = c; if ( *s == ',' ) s++; } else { if ( error == 0 ) MesPrint("&The ratio statement needs three symbols for its arguments"); error++; numsym = 0; } *rs++ = numsym; } AddNtoL(6,ratstring); return(error); } /* #] CoRatio : #[ CoRedefine : We have a preprocessor variable and a (new) value for it. This value is inside a string that must be stored. */ int CoRedefine(UBYTE *s) { UBYTE *name, c, *args = 0; int numprevar; WORD code[2]; name = s; if ( FG.cTable[*s] || ( s = SkipAName(s) ) == 0 || s[-1] == '_' ) { MesPrint("&Illegal name for preprocessor variable in redefine statement"); return(1); } c = *s; *s = 0; for ( numprevar = NumPre-1; numprevar >= 0; numprevar-- ) { if ( StrCmp(name,PreVar[numprevar].name) == 0 ) break; } if ( numprevar < 0 ) { MesPrint("&There is no preprocessor variable with the name `%s'",name); *s = c; return(1); } *s = c; /* The next code worries about arguments. It is a direct copy of the code in TheDefine in the preprocessor. */ if ( *s == '(' ) { /* arguments. scan for correctness */ s++; args = s; for (;;) { if ( chartype[*s] != 0 ) goto illarg; s++; while ( chartype[*s] <= 1 ) s++; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == ')' ) break; if ( *s != ',' ) goto illargs; s++; while ( *s == ' ' || *s == '\t' ) s++; } *s++ = 0; while ( *s == ' ' || *s == '\t' ) s++; } while ( *s == ',' ) s++; if ( *s != '"' ) { encl: MesPrint("&Value for %s should be enclosed in double quotes" ,PreVar[numprevar].name); return(1); } s++; name = s; /* actually name points to the new string */ while ( *s && *s != '"' ) { if ( *s == '\\' ) s++; s++; } if ( *s != '"' ) goto encl; *s = 0; code[0] = TYPEREDEFPRE; code[1] = numprevar; /* AddComString(2,code,name,0); */ Add2ComStrings(2,code,name,args); *s = '"'; #ifdef PARALLELCODE /* Now we prepare the input numbering system for pthreads. We need a list of preprocessor variables that are redefined in this module. */ { int j; WORD *newpf; LONG *newin; for ( j = 0; j < AC.numpfirstnum; j++ ) { if ( numprevar == AC.pfirstnum[j] ) break; } if ( j >= AC.numpfirstnum ) { /* add to list */ if ( j >= AC.sizepfirstnum ) { if ( AC.sizepfirstnum <= 0 ) { AC.sizepfirstnum = 10; } else { AC.sizepfirstnum = 2 * AC.sizepfirstnum; } newin = (LONG *)Malloc1(AC.sizepfirstnum*(sizeof(WORD)+sizeof(LONG)),"AC.pfirstnum"); newpf = (WORD *)(newin+AC.sizepfirstnum); for ( j = 0; j < AC.numpfirstnum; j++ ) { newpf[j] = AC.pfirstnum[j]; newin[j] = AC.inputnumbers[j]; } if ( AC.inputnumbers ) M_free(AC.inputnumbers,"AC.pfirstnum"); AC.inputnumbers = newin; AC.pfirstnum = newpf; } AC.pfirstnum[AC.numpfirstnum] = numprevar; AC.inputnumbers[AC.numpfirstnum] = -1; AC.numpfirstnum++; } } #endif return(0); illarg:; MesPrint("&Illegally formed name in argument of redefine statement"); return(1); illargs:; MesPrint("&Illegally formed arguments in redefine statement"); return(1); } /* #] CoRedefine : #[ CoRenumber : renumber or renumber,0 Only exchanges (n^2 until no improvement) renumber,1 All permutations (could be slow) */ int CoRenumber(UBYTE *s) { int x; UBYTE *inp; while ( *s == ',' ) s++; inp = s; if ( *s == 0 ) { x = 0; } else ParseNumber(x,s) if ( *s == 0 && x >= 0 && x <= 1 ) { Add3Com(TYPERENUMBER,x); return(0); } MesPrint("&Illegal argument in Renumber statement: '%s'",inp); return(1); } /* #] CoRenumber : #[ CoSum : */ int CoSum(UBYTE *s) { CBUF *C = cbuf+AC.cbufnum; UBYTE *ss = 0, c, *t; int error = 0, i = 0, type, x; WORD numindex,number; while ( *s ) { t = s; if ( *s == '$' ) { t++; s++; while ( FG.cTable[*s] < 2 ) s++; c = *s; *s = 0; if ( ( number = GetDollar(t) ) < 0 ) { MesPrint("&Undefined variable $%s",t); if ( !error ) error = 1; number = AddDollar(t,0,0,0); } numindex = -number; } else { if ( ( s = SkipAName(s) ) == 0 ) return(1); c = *s; *s = 0; if ( ( ( type = GetOName(AC.exprnames,t,&numindex,NOAUTO) ) != NAMENOTFOUND ) || ( ( type = GetOName(AC.varnames,t,&numindex,WITHAUTO) ) != CINDEX ) ) { if ( type != NAMENOTFOUND ) error = NameConflict(type,t); else { MesPrint("&%s should have been declared as an index",t); error = 1; numindex = AddIndex(s,AC.lDefDim,AC.lDefDim4) + AM.OffsetIndex; } } } Add3Com(TYPESUM,numindex); i = 3; *s = c; if ( *s == 0 ) break; if ( *s != ',' ) { MesPrint("&Illegal separator between objects in sum statement."); return(1); } s++; if ( FG.cTable[*s] == 0 || *s == '[' || *s == '$' ) { while ( FG.cTable[*s] == 0 || *s == '[' || *s == '$' ) { if ( *s == '$' ) { s++; ss = t = s; while ( FG.cTable[*s] < 2 ) s++; c = *s; *s = 0; if ( ( number = GetDollar(t) ) < 0 ) { MesPrint("&Undefined variable $%s",t); if ( !error ) error = 1; number = AddDollar(t,0,0,0); } numindex = -number; } else { ss = t = s; if ( ( s = SkipAName(s) ) == 0 ) return(1); c = *s; *s = 0; if ( ( ( type = GetOName(AC.exprnames,t,&numindex,NOAUTO) ) != NAMENOTFOUND ) || ( ( type = GetOName(AC.varnames,t,&numindex,WITHAUTO) ) != CINDEX ) ) { if ( type != NAMENOTFOUND ) error = NameConflict(type,t); else { MesPrint("&%s should have been declared as an index",t); error = 1; numindex = AddIndex(s,AC.lDefDim,AC.lDefDim4) + AM.OffsetIndex; } } } AddToCB(C,numindex) i++; C->Pointer[-i+1] = i; *s = c; if ( *s == 0 ) return(error); if ( *s != ',' ) { MesPrint("&Illegal separator between objects in sum statement."); return(1); } s++; } if ( FG.cTable[*s] == 1 ) { C->Pointer[-i+1]--; C->Pointer--; s = ss; } } else if ( FG.cTable[*s] == 1 ) { while ( FG.cTable[*s] == 1 ) { t = s; x = *s++ - '0'; while( FG.cTable[*s] == 1 ) x = 10*x + *s++ - '0'; if ( *s && *s != ',' ) { MesPrint("&%s is not a legal fixed index",t); return(1); } else if ( x >= AM.OffsetIndex ) { MesPrint("&%d is too large to be a fixed index",x); error = 1; } else { AddToCB(C,x) i++; C->Pointer[-i] = TYPESUMFIX; C->Pointer[-i+1] = i; } if ( *s == 0 ) break; s++; } } else { MesPrint("&Illegal object in sum statement"); error = 1; } } return(error); } /* #] CoSum : #[ CoToTensor : */ static WORD cttarray[7] = { TYPEOPERATION,7,TENVEC,0,0,1,0 }; int CoToTensor(UBYTE *s) { UBYTE c, *t; int type, j, nargs, error = 0; WORD number, dol[2] = { 0, 0 }; cttarray[1] = 6; /* length */ cttarray[3] = 0; /* tensor */ cttarray[4] = 0; /* vector */ cttarray[5] = 1; /* option flags */ /* cttarray[6] = 0; set veto */ /* Count the number of the arguments. The validity of them is not checked here. */ nargs = 0; t = s; for (;;) { while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == 0 ) break; if ( *s == '!' ) { s++; if ( *s == '{' ) { SKIPBRA2(s) s++; } else { if ( ( s = SkipAName(s) ) == 0 ) goto syntax_error; } } else { if ( ( s = SkipAName(s) ) == 0 ) goto syntax_error; } nargs++; } if ( nargs < 2 ) goto not_enough_arguments; s = t; /* Parse options, which are given as the arguments except the last two. */ for ( j = 2; j < nargs; j++ ) { while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( *s == '!' ) { /* Handle !set or !{vector,...}. Note: If two or more sets are specified, then only the last one is used. */ s++; cttarray[1] = 7; cttarray[5] |= 8; if ( FG.cTable[*s] == 0 || *s == '[' || *s == '_' ) { t = s; if ( ( s = SkipAName(s) ) == 0 ) goto syntax_error; c = *s; *s = 0; type = GetName(AC.varnames,t,&number,WITHAUTO); if ( type == CVECTOR ) { /* As written in the manual, "!p" (without "{}") should work. */ cttarray[6] = DoTempSet(t,s); *s = c; goto check_tempset; } else if ( type != CSET ) { MesPrint("&%s is not the name of a set or a vector",t); error = 1; } *s = c; cttarray[6] = number; } else if ( *s == '{' ) { t = ++s; SKIPBRA2(s) *s = 0; cttarray[6] = DoTempSet(t,s); *s++ = '}'; check_tempset: if ( cttarray[6] < 0 ) { error = 1; } if ( AC.wildflag ) { MesPrint("&Improper use of wildcard(s) in set specification"); error = 1; } } } else { /* Other options. */ t = s; if ( ( s = SkipAName(s) ) == 0 ) goto syntax_error; c = *s; *s = 0; if ( StrICmp(t,(UBYTE *)"nosquare") == 0 ) cttarray[5] |= 2; else if ( StrICmp(t,(UBYTE *)"functions") == 0 ) cttarray[5] |= 4; else { MesPrint("&Unrecognized option in ToTensor statement: '%s'",t); *s = c; return(1); } *s = c; } } /* Now parse a vector and a tensor. The ordering doesn't matter. */ for ( j = 0; j < 2; j++ ) { while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; t = s; if ( ( s = SkipAName(s) ) == 0 ) goto syntax_error; c = *s; *s = 0; if ( t[0] == '$' ) { dol[j] = GetDollar(t+1); if ( dol[j] < 0 ) dol[j] = AddDollar(t+1,DOLUNDEFINED,0,0); } else { type = GetName(AC.varnames,t,&number,WITHAUTO); if ( type == CVECTOR ) { cttarray[4] = number + AM.OffsetVector; } else if ( type == CFUNCTION && ( functions[number].spec > 0 ) ) { cttarray[3] = number + FUNCTION; } else { MesPrint("&%s is not a vector or a tensor",t); error = 1; } } *s = c; } if ( cttarray[3] == 0 || cttarray[4] == 0 ) { if ( dol[0] == 0 && dol[1] == 0 ) { goto not_enough_arguments; } else if ( cttarray[3] ) { if ( dol[1] ) cttarray[4] = dol[1]; else if ( dol[0] ) { cttarray[4] = dol[0]; } else { goto not_enough_arguments; } } else if ( cttarray[4] ) { if ( dol[1] ) { cttarray[3] = -dol[1]; } else if ( dol[0] ) cttarray[3] = -dol[0]; else { goto not_enough_arguments; } } else { if ( dol[0] == 0 || dol[1] == 0 ) { goto not_enough_arguments; } else { cttarray[3] = -dol[0]; cttarray[4] = dol[1]; } } } AddNtoL(cttarray[1],cttarray); return(error); syntax_error: MesPrint("&Syntax error in ToTensor statement"); return(1); not_enough_arguments: MesPrint("&ToTensor statement needs a vector and a tensor"); return(1); } /* #] CoToTensor : #[ CoToVector : */ static WORD ctvarray[6] = { TYPEOPERATION,6,TENVEC,0,0,0 }; int CoToVector(UBYTE *s) { UBYTE *t, c; int j, type, error = 0; WORD number, dol[2]; dol[0] = dol[1] = 0; ctvarray[3] = ctvarray[4] = ctvarray[5] = 0; for ( j = 0; j < 2; j++ ) { t = s; if ( ( s = SkipAName(s) ) == 0 ) { proper: MesPrint("&Arguments of ToVector statement should be a vector and a tensor"); return(1); } c = *s; *s = 0; if ( *t == '$' ) { dol[j] = GetDollar(t+1); if ( dol[j] < 0 ) dol[j] = AddDollar(t+1,DOLUNDEFINED,0,0); } else if ( ( type = GetName(AC.varnames,t,&number,WITHAUTO) ) == CVECTOR ) ctvarray[4] = number + AM.OffsetVector; else if ( type == CFUNCTION && ( functions[number].spec > 0 ) ) ctvarray[3] = number+FUNCTION; else { MesPrint("&%s is not a vector or a tensor",t); error = 1; } *s = c; if ( *s && *s != ',' ) goto proper; if ( *s ) s++; } if ( *s != 0 ) goto proper; if ( ctvarray[3] == 0 || ctvarray[4] == 0 ) { if ( dol[0] == 0 && dol[1] == 0 ) { MesPrint("&ToVector statement needs a vector and a tensor"); error = 1; } else if ( ctvarray[3] ) { if ( dol[1] ) ctvarray[4] = dol[1]; else if ( dol[0] ) ctvarray[4] = dol[0]; else { MesPrint("&ToVector statement needs a vector and a tensor"); error = 1; } } else if ( ctvarray[4] ) { if ( dol[1] ) ctvarray[3] = -dol[1]; else if ( dol[0] ) ctvarray[3] = -dol[0]; else { MesPrint("&ToVector statement needs a vector and a tensor"); error = 1; } } else { if ( dol[0] == 0 || dol[1] == 0 ) { MesPrint("&ToVector statement needs a vector and a tensor"); error = 1; } else { ctvarray[3] = -dol[0]; ctvarray[4] = dol[1]; } } } AddNtoL(6,ctvarray); return(error); } /* #] CoToVector : #[ CoTrace4 : */ int CoTrace4(UBYTE *s) { int error = 0, type, option = CHISHOLM; UBYTE *t, c; WORD numindex, one = 1; KEYWORD *key; for (;;) { t = s; if ( FG.cTable[*s] == 1 ) break; if ( ( s = SkipAName(s) ) == 0 ) { proper: MesPrint("&Proper syntax for Trace4 is 'Trace4[,options],index;'"); return(1); } if ( *s == 0 ) break; c = *s; *s = 0; if ( ( key = FindKeyWord(t,trace4options, sizeof(trace4options)/sizeof(KEYWORD)) ) == 0 ) break; else { option |= key->type; option &= ~key->flags; } if ( ( *s++ = c ) != ',' ) { MesPrint("&Illegal separator in Trace4 statement"); return(1); } if ( *s == 0 ) goto proper; } s = t; if ( FG.cTable[*s] == 1 ) { retry: ParseNumber(numindex,s) if ( *s != 0 ) { MesPrint("&Last argument of Trace4 should be an index"); return(1); } if ( numindex >= AM.OffsetIndex ) { MesPrint("&fixed index >= %d. Change value of OffsetIndex in setup file" ,AM.OffsetIndex); return(1); } } else if ( *s == '$' ) { if ( ( type = GetName(AC.dollarnames,s+1,&numindex,NOAUTO) ) == CDOLLAR ) numindex = -numindex; else { MesPrint("&%s is undefined",s); numindex = AddDollar(s+1,DOLINDEX,&one,1); return(1); } tests: s = SkipAName(s); if ( *s != 0 ) { MesPrint("&Trace4 should have a single index or $variable for its argument"); return(1); } } else if ( ( type = GetName(AC.varnames,s,&numindex,WITHAUTO) ) == CINDEX ) { numindex += AM.OffsetIndex; goto tests; } else if ( type != -1 ) { if ( type != CDUBIOUS ) { if ( ( FG.cTable[*s] != 0 ) && ( *s != '[' ) ) { if ( *s == '+' && FG.cTable[s[1]] == 1 ) { s++; goto retry; } goto proper; } NameConflict(type,s); type = MakeDubious(AC.varnames,s,&numindex); } return(1); } else { MesPrint("&%s is not an index",s); numindex = AddIndex(s,AC.lDefDim,AC.lDefDim4) + AM.OffsetIndex; return(1); } if ( error ) return(error); if ( ( option & CHISHOLM ) != 0 ) Add4Com(TYPECHISHOLM,numindex,(option & ALSOREVERSE)); Add5Com(TYPEOPERATION,TAKETRACE,4 + (option & NOTRICK),numindex); return(0); } /* #] CoTrace4 : #[ CoTraceN : */ int CoTraceN(UBYTE *s) { WORD numindex, one = 1; int type; if ( FG.cTable[*s] == 1 ) { retry: ParseNumber(numindex,s) if ( *s != 0 ) { proper: MesPrint("&TraceN should have a single index for its argument"); return(1); } if ( numindex >= AM.OffsetIndex ) { MesPrint("&fixed index >= %d. Change value of OffsetIndex in setup file" ,AM.OffsetIndex); return(1); } } else if ( *s == '$' ) { if ( ( type = GetName(AC.dollarnames,s+1,&numindex,NOAUTO) ) == CDOLLAR ) numindex = -numindex; else { MesPrint("&%s is undefined",s); numindex = AddDollar(s+1,DOLINDEX,&one,1); return(1); } tests: s = SkipAName(s); if ( *s != 0 ) { MesPrint("&TraceN should have a single index or $variable for its argument"); return(1); } } else if ( ( type = GetName(AC.varnames,s,&numindex,WITHAUTO) ) == CINDEX ) { numindex += AM.OffsetIndex; goto tests; } else if ( type != -1 ) { if ( type != CDUBIOUS ) { if ( ( FG.cTable[*s] != 0 ) && ( *s != '[' ) ) { if ( *s == '+' && FG.cTable[s[1]] == 1 ) { s++; goto retry; } goto proper; } NameConflict(type,s); type = MakeDubious(AC.varnames,s,&numindex); } return(1); } else { MesPrint("&%s is not an index",s); numindex = AddIndex(s,AC.lDefDim,AC.lDefDim4) + AM.OffsetIndex; return(1); } Add5Com(TYPEOPERATION,TAKETRACE,0,numindex); return(0); } /* #] CoTraceN : #[ CoChisholm : */ int CoChisholm(UBYTE *s) { int error = 0, type, option = CHISHOLM; UBYTE *t, c; WORD numindex, one = 1; KEYWORD *key; for (;;) { t = s; if ( FG.cTable[*s] == 1 ) break; if ( ( s = SkipAName(s) ) == 0 ) { proper: MesPrint("&Proper syntax for Chisholm is 'Chisholm[,options],index;'"); return(1); } if ( *s == 0 ) break; c = *s; *s = 0; if ( ( key = FindKeyWord(t,chisoptions, sizeof(chisoptions)/sizeof(KEYWORD)) ) == 0 ) break; else { option |= key->type; option &= ~key->flags; } if ( ( *s++ = c ) != ',' ) { MesPrint("&Illegal separator in Chisholm statement"); return(1); } if ( *s == 0 ) goto proper; } s = t; if ( FG.cTable[*s] == 1 ) { ParseNumber(numindex,s) if ( *s != 0 ) { MesPrint("&Last argument of Chisholm should be an index"); return(1); } if ( numindex >= AM.OffsetIndex ) { MesPrint("&fixed index >= %d. Change value of OffsetIndex in setup file" ,AM.OffsetIndex); return(1); } } else if ( *s == '$' ) { if ( ( type = GetName(AC.dollarnames,s+1,&numindex,NOAUTO) ) == CDOLLAR ) numindex = -numindex; else { MesPrint("&%s is undefined",s); numindex = AddDollar(s+1,DOLINDEX,&one,1); return(1); } tests: s = SkipAName(s); if ( *s != 0 ) { MesPrint("&Chisholm should have a single index or $variable for its argument"); return(1); } } else if ( ( type = GetName(AC.varnames,s,&numindex,WITHAUTO) ) == CINDEX ) { numindex += AM.OffsetIndex; goto tests; } else if ( type != -1 ) { if ( type != CDUBIOUS ) { NameConflict(type,s); type = MakeDubious(AC.varnames,s,&numindex); } return(1); } else { MesPrint("&%s is not an index",s); numindex = AddIndex(s,AC.lDefDim,AC.lDefDim4) + AM.OffsetIndex; return(1); } if ( error ) return(error); Add4Com(TYPECHISHOLM,numindex,(option & ALSOREVERSE)); return(0); } /* #] CoChisholm : #[ DoChain : Syntax: Chainxx functionname; */ int DoChain(UBYTE *s, int option) { WORD numfunc,type; if ( *s == '$' ) { if ( ( type = GetName(AC.dollarnames,s+1,&numfunc,NOAUTO) ) == CDOLLAR ) numfunc = -numfunc; else { MesPrint("&%s is undefined",s); numfunc = AddDollar(s+1,DOLINDEX,&one,1); return(1); } tests: s = SkipAName(s); if ( *s != 0 ) { MesPrint("&ChainIn/ChainOut should have a single function or $variable for its argument"); return(1); } } else if ( ( type = GetName(AC.varnames,s,&numfunc,WITHAUTO) ) == CFUNCTION ) { numfunc += FUNCTION; goto tests; } else if ( type != -1 ) { if ( type != CDUBIOUS ) { NameConflict(type,s); type = MakeDubious(AC.varnames,s,&numfunc); } return(1); } else { MesPrint("&%s is not a function",s); numfunc = AddFunction(s,0,0,0,0,0,-1,-1) + FUNCTION; return(1); } Add3Com(option,numfunc); return(0); } /* #] DoChain : #[ CoChainin : Syntax: Chainin functionname; */ int CoChainin(UBYTE *s) { return(DoChain(s,TYPECHAININ)); } /* #] CoChainin : #[ CoChainout : Syntax: Chainout functionname; */ int CoChainout(UBYTE *s) { return(DoChain(s,TYPECHAINOUT)); } /* #] CoChainout : #[ CoExit : */ int CoExit(UBYTE *s) { UBYTE *name; WORD code = TYPEEXIT; while ( *s == ',' ) s++; if ( *s == 0 ) { Add3Com(TYPEEXIT,0); return(0); } name = s+1; s++; while ( *s ) { if ( *s == '\\' ) s++; s++; } if ( name[-1] != '"' || s[-1] != '"' ) { MesPrint("&Illegal syntax for exit statement"); return(1); } s[-1] = 0; AddComString(1,&code,name,0); s[-1] = '"'; return(0); } /* #] CoExit : #[ CoInParallel : */ int CoInParallel(UBYTE *s) { return(DoInParallel(s,1)); } /* #] CoInParallel : #[ CoNotInParallel : */ int CoNotInParallel(UBYTE *s) { return(DoInParallel(s,0)); } /* #] CoNotInParallel : #[ DoInParallel : InParallel; InParallel,names; NotInParallel; NotInParallel,names; */ int DoInParallel(UBYTE *s, int par) { #ifdef PARALLELCODE EXPRESSIONS e; WORD i; #endif WORD number; UBYTE *t, c; int error = 0; #ifndef WITHPTHREADS DUMMYUSE(par); #endif if ( *s == 0 ) { AC.inparallelflag = par; #ifdef PARALLELCODE for ( i = NumExpressions-1; i >= 0; i-- ) { e = Expressions+i; if ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) { e->partodo = par; } } #endif } else { for(;;) { /* Look for a (comma separated) list of variables */ while ( *s == ',' ) s++; if ( *s == 0 ) break; if ( *s == '[' || FG.cTable[*s] == 0 ) { t = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Improper name for an expression: '%s'",t); return(1); } c = *s; *s = 0; if ( GetName(AC.exprnames,t,&number,NOAUTO) == CEXPRESSION ) { #ifdef PARALLELCODE e = Expressions+number; if ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) { e->partodo = par; } #endif } else if ( GetName(AC.varnames,t,&number,NOAUTO) != NAMENOTFOUND ) { MesPrint("&%s is not an expression",t); error = 1; } *s = c; } else { MesPrint("&Illegal object in InParallel statement"); error = 1; while ( *s && *s != ',' ) s++; if ( *s == 0 ) break; } } } return(error); } /* #] DoInParallel : #[ CoInExpression : */ int CoInExpression(UBYTE *s) { GETIDENTITY UBYTE *t, c; WORD *w, number; int error = 0; w = AT.WorkPointer; if ( AC.inexprlevel >= MAXNEST ) { MesPrint("@Nesting of inexpression statements more than %d levels",(WORD)MAXNEST); return(-1); } AC.inexprsumcheck[AC.inexprlevel] = NestingChecksum(); AC.inexprstack[AC.inexprlevel] = cbuf[AC.cbufnum].Pointer - cbuf[AC.cbufnum].Buffer + 2; AC.inexprlevel++; *w++ = TYPEINEXPRESSION; w++; w++; for(;;) { /* Look for a (comma separated) list of variables */ while ( *s == ',' ) s++; if ( *s == 0 ) break; if ( *s == '[' || FG.cTable[*s] == 0 ) { t = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Improper name for an expression: '%s'",t); return(1); } c = *s; *s = 0; if ( GetName(AC.exprnames,t,&number,NOAUTO) == CEXPRESSION ) { *w++ = number; } else if ( GetName(AC.varnames,t,&number,NOAUTO) != NAMENOTFOUND ) { MesPrint("&%s is not an expression",t); error = 1; } *s = c; } else { MesPrint("&Illegal object in InExpression statement"); error = 1; while ( *s && *s != ',' ) s++; if ( *s == 0 ) break; } } AT.WorkPointer[1] = w - AT.WorkPointer; AddNtoL(AT.WorkPointer[1],AT.WorkPointer); return(error); } /* #] CoInExpression : #[ CoEndInExpression : */ int CoEndInExpression(UBYTE *s) { CBUF *C = cbuf+AC.cbufnum; while ( *s == ',' ) s++; if ( *s ) { MesPrint("&Illegal syntax for EndInExpression statement"); return(1); } if ( AC.inexprlevel <= 0 ) { MesPrint("&EndInExpression without corresponding InExpression statement"); return(1); } AC.inexprlevel--; cbuf[AC.cbufnum].Buffer[AC.inexprstack[AC.inexprlevel]] = C->numlhs; if ( AC.inexprsumcheck[AC.inexprlevel] != NestingChecksum() ) { MesNesting(); return(1); } return(0); } /* #] CoEndInExpression : #[ CoSetExitFlag : */ int CoSetExitFlag(UBYTE *s) { if ( *s ) { MesPrint("&Illegal syntax for the SetExitFlag statement"); return(1); } Add2Com(TYPESETEXIT); return(0); } /* #] CoSetExitFlag : #[ CoTryReplace : */ int CoTryReplace(UBYTE *p) { GETIDENTITY UBYTE *name, c; WORD *w, error = 0, i, which = -1, c1, minvec = 0; w = AT.WorkPointer; *w++ = TYPETRY; *w++ = 3; *w++ = 0; *w++ = REPLACEMENT; *w++ = FUNHEAD; FILLFUN(w) /* Now we have to read a function argument for the replace_ function. Current arguments that we allow involve only single arguments that do not expand further. No brackets! */ while ( *p ) { /* No numbers yet */ if ( *p == '-' && minvec == 0 && which == (CVECTOR+1) ) { minvec = 1; p++; } if ( *p == '[' || FG.cTable[*p] == 0 ) { name = p; if ( ( p = SkipAName(p) ) == 0 ) return(1); c = *p; *p = 0; i = GetName(AC.varnames,name,&c1,WITHAUTO); if ( which >= 0 && i >= 0 && i != CDUBIOUS && which != (i+1) ) { MesPrint("&Illegal combination of objects in TryReplace"); error = 1; } else if ( minvec && i != CVECTOR && i != CDUBIOUS ) { MesPrint("&Currently a - sign can be used only with a vector in TryReplace"); error = 1; } else switch ( i ) { case CSYMBOL: *w++ = -SYMBOL; *w++ = c1; break; case CVECTOR: if ( minvec ) *w++ = -MINVECTOR; else *w++ = -VECTOR; *w++ = c1 + AM.OffsetVector; minvec = 0; break; case CINDEX: *w++ = -INDEX; *w++ = c1 + AM.OffsetIndex; if ( c1 >= AM.WilInd && c == '?' ) { *p++ = c; c = *p; } break; case CFUNCTION: *w++ = -c1-FUNCTION; break; case CDUBIOUS: minvec = 0; error = 1; break; default: MesPrint("&Illegal object type in TryReplace: %s",name); error = 1; i = 0; break; } if ( which < 0 ) which = i+1; else which = -1; *p = c; if ( *p == ',' ) p++; continue; } else { MesPrint("&Illegal object in TryReplace"); error = 1; while ( *p && *p != ',' ) { if ( *p == '(' ) SKIPBRA3(p) else if ( *p == '{' ) SKIPBRA2(p) else if ( *p == '[' ) SKIPBRA1(p) else p++; } } if ( *p == ',' ) p++; if ( which < 0 ) which = 0; else which = -1; } if ( which >= 0 ) { MesPrint("&Odd number of arguments in TryReplace"); error = 1; } i = w - AT.WorkPointer; AT.WorkPointer[1] = i; AT.WorkPointer[2] = i - 3; AT.WorkPointer[4] = i - 3; AddNtoL((int)i,AT.WorkPointer); return(error); } /* #] CoTryReplace : #[ CoModulus : Old syntax: Modulus [-] number [:number] New syntax: Modulus [option(s)] number Options are: NoFunctions/CoefficientsOnly/AlsoFunctions PlusMin/Positive InverseTable PrintPowersOf(number) AlsoPowers/NoPowers AlsoDollars/NoDollars Notice: We change the defaults. This may cause problems to some. */ int CoModulus(UBYTE *inp) { GETIDENTITY int Retval = 0, sign = 1; UBYTE *p, c; while ( *inp == ',' || *inp == ' ' || *inp == '\t' ) inp++; if ( *inp == 0 ) { SwitchOff: if ( AC.modpowers ) M_free(AC.modpowers,"AC.modpowers"); AC.modpowers = 0; AN.ncmod = AC.ncmod = 0; if ( AC.halfmod ) M_free(AC.halfmod,"halfmod"); AC.halfmod = 0; AC.nhalfmod = 0; if ( AC.modinverses ) M_free(AC.modinverses,"modinverses"); AC.modinverses = 0; AC.modmode = 0; return(0); } #ifdef WITHFLOAT if ( AT.aux_ != 0 ) { MesPrint("&Simultaneous use of floating point and modulus arithmetic makes no sense."); Retval = 1; } #endif AC.modmode = 0; if ( *inp == '-' ) { sign = -1; inp++; } else { while ( FG.cTable[*inp] == 0 ) { p = inp; while ( FG.cTable[*inp] == 0 ) inp++; c = *inp; *inp = 0; if ( StrICmp(p,(UBYTE *)"nofunctions") == 0 ) { AC.modmode &= ~ALSOFUNARGS; } else if ( StrICmp(p,(UBYTE *)"alsofunctions") == 0 ) { AC.modmode |= ALSOFUNARGS; } else if ( StrICmp(p,(UBYTE *)"coefficientsonly") == 0 ) { AC.modmode &= ~ALSOFUNARGS; AC.modmode &= ~ALSOPOWERS; sign = -1; } else if ( StrICmp(p,(UBYTE *)"plusmin") == 0 ) { AC.modmode |= POSNEG; } else if ( StrICmp(p,(UBYTE *)"positive") == 0 ) { AC.modmode &= ~POSNEG; } else if ( StrICmp(p,(UBYTE *)"inversetable") == 0 ) { AC.modmode |= INVERSETABLE; } else if ( StrICmp(p,(UBYTE *)"noinversetable") == 0 ) { AC.modmode &= ~INVERSETABLE; } else if ( StrICmp(p,(UBYTE *)"nodollars") == 0 ) { AC.modmode &= ~ALSODOLLARS; } else if ( StrICmp(p,(UBYTE *)"alsodollars") == 0 ) { AC.modmode |= ALSODOLLARS; } else if ( StrICmp(p,(UBYTE *)"printpowersof") == 0 ) { *inp = c; if ( *inp != '(' ) { badsyntax: MesPrint("&Bad syntax in argument of PrintPowersOf(number) in Modulus statement"); return(1); } while ( *inp == ',' || *inp == ' ' || *inp == '\t' ) inp++; inp++; p = inp; if ( FG.cTable[*inp] != 1 ) goto badsyntax; do { inp++; } while ( FG.cTable[*inp] == 1 ); c = *inp; *inp = 0; if ( GetLong(p,(UWORD *)AC.powmod,&AC.npowmod) ) Retval = -1; if ( TakeModulus((UWORD *)AC.powmod,&AC.npowmod,AC.cmod,AC.ncmod,NOUNPACK) ) Retval = -1; if ( AC.npowmod == 0 ) { MesPrint("&Improper value for generator"); Retval = -1; } if ( MakeModTable() ) Retval = -1; AC.DirtPow = 1; *inp = c; while ( *inp == ',' || *inp == ' ' || *inp == '\t' ) inp++; if ( *inp != ')' ) goto badsyntax; inp++; c = *inp; } else if ( StrICmp(p,(UBYTE *)"alsopowers") == 0 ) { AC.modmode |= ALSOPOWERS; sign = 1; } else if ( StrICmp(p,(UBYTE *)"nopowers") == 0 ) { AC.modmode &= ~ALSOPOWERS; sign = -1; } else { MesPrint("&Unrecognized option %s in Modulus statement",inp); return(1); } *inp = c; while ( *inp == ',' || *inp == ' ' || *inp == '\t' ) inp++; if ( *inp == 0 ) { MesPrint("&Modulus statement with no value!!!"); return(1); } } } p = inp; if ( FG.cTable[*inp] != 1 ) { MesPrint("&Invalid value for modulus:%s",inp); if ( AC.modpowers ) M_free(AC.modpowers,"AC.modpowers"); AC.modpowers = 0; AN.ncmod = AC.ncmod = 0; if ( AC.halfmod ) M_free(AC.halfmod,"halfmod"); AC.halfmod = 0; AC.nhalfmod = 0; if ( AC.modinverses ) M_free(AC.modinverses,"modinverses"); AC.modinverses = 0; return(1); } do { inp++; } while ( FG.cTable[*inp] == 1 ); c = *inp; *inp = 0; Retval = GetLong(p,(UWORD *)AC.cmod,&AC.ncmod); if ( Retval == 0 && AC.ncmod == 0 ) goto SwitchOff; if ( sign < 0 ) AC.ncmod = -AC.ncmod; AN.ncmod = AC.ncmod; if ( ( AC.modmode & INVERSETABLE ) != 0 ) MakeInverses(); if ( AC.halfmod ) M_free(AC.halfmod,"halfmod"); AC.halfmod = 0; AC.nhalfmod = 0; return(Retval); } /* #] CoModulus : #[ CoRepeat : */ int CoRepeat(UBYTE *inp) { int error = 0; AC.RepSumCheck[AC.RepLevel] = NestingChecksum(); AC.RepLevel++; if ( AC.RepLevel > AM.RepMax ) { MesPrint("&Too many repeat levels. Maximum is %d",AM.RepMax); return(1); } Add3Com(TYPEREPEAT,-1) /* Means indefinite */ while ( *inp == ' ' || *inp == ',' || *inp == '\t' ) inp++; if ( *inp ) { error = CompileStatement(inp); if ( CoEndRepeat(inp) ) error = 1; } return(error); } /* #] CoRepeat : #[ CoEndRepeat : */ int CoEndRepeat(UBYTE *inp) { CBUF *C = cbuf+AC.cbufnum; int level, error = 0, repeatlevel = 0; DUMMYUSE(inp); AC.RepLevel--; if ( AC.RepLevel < 0 ) { MesPrint("&EndRepeat without Repeat"); AC.RepLevel = 0; return(1); } else if ( AC.RepSumCheck[AC.RepLevel] != NestingChecksum() ) { MesNesting(); error = 1; } level = C->numlhs+1; while ( level > 0 ) { if ( C->lhs[--level][0] == TYPEREPEAT ) { if ( repeatlevel == 0 ) { Add3Com(TYPEENDREPEAT,level) return(error); } repeatlevel--; } else if ( C->lhs[level][0] == TYPEENDREPEAT ) repeatlevel++; } return(1); } /* #] CoEndRepeat : #[ DoBrackets : Reads in the bracket information. Storage is in the form of a regular term. No subterms and arguments are allowed. */ int DoBrackets(UBYTE *inp, int par) { GETIDENTITY UBYTE *p, *pp, c; WORD *to, i, type, *w, error = 0; WORD c1,c2, *WorkSave; int biflag; p = inp; WorkSave = to = AT.WorkPointer; to++; if ( AT.BrackBuf == 0 ) { AR.MaxBracket = 100; AT.BrackBuf = (WORD *)Malloc1(sizeof(WORD)*(AR.MaxBracket+1),"bracket buffer"); } *AT.BrackBuf = 0; AR.BracketOn = 0; AC.bracketindexflag = 0; AT.bracketindexflag = 0; if ( *p == '+' || *p == '-' ) p++; if ( p[-1] == ',' && *p ) p--; if ( p[-1] == '+' && *p ) { biflag = 1; if ( *p != ',' ) { *--p = ','; } } else if ( p[-1] == '-' && *p ) { biflag = -1; if ( *p != ',' ) { *--p = ','; } } else biflag = 0; while ( *p == ',' ) { redo: AR.BracketOn++; while ( *p == ',' ) p++; if ( *p == 0 ) break; if ( *p == '0' ) { p++; while ( *p == '0' ) p++; continue; } inp = pp = p; p = SkipAName(p); if ( p == 0 ) return(1); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c1,WITHAUTO); if ( c == '.' ) { if ( type == CVECTOR || type == CDUBIOUS ) { *p++ = c; inp = p; p = SkipAName(p); if ( p == 0 ) return(1); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c2,WITHAUTO); if ( type != CVECTOR && type != CDUBIOUS ) { MesPrint("&Not a vector in dotproduct in bracket statement: %s",inp); error = 1; } else type = CDOTPRODUCT; } else { MesPrint("&Illegal use of . after %s in bracket statement",inp); error = 1; *p++ = c; goto redo; } } switch ( type ) { case CSYMBOL : *to++ = SYMBOL; *to++ = 4; *to++ = c1; *to++ = 1; break; case CVECTOR : *to++ = INDEX; *to++ = 3; *to++ = AM.OffsetVector + c1; break; case CFUNCTION : *to++ = c1+FUNCTION; *to++ = FUNHEAD; *to++ = 0; FILLFUN3(to) break; case CDOTPRODUCT : *to++ = DOTPRODUCT; *to++ = 5; *to++ = c1 + AM.OffsetVector; *to++ = c2 + AM.OffsetVector; *to++ = 1; break; case CDELTA : *to++ = DELTA; *to++ = 4; *to++ = EMPTYINDEX; *to++ = EMPTYINDEX; break; case CSET : *to++ = SETSET; *to++ = 4; *to++ = c1; *to++ = Sets[c1].type; break; default : MesPrint("&Illegal bracket request for %s",pp); error = 1; break; } *p = c; } if ( *p ) { MesCerr("separator",p); AC.BracketNormalize = 0; AT.WorkPointer = WorkSave; error = 1; return(error); } *to++ = 1; *to++ = 1; *to++ = 3; *AT.WorkPointer = to - AT.WorkPointer; AT.WorkPointer = to; AC.BracketNormalize = 1; if ( BracketNormalize(BHEAD WorkSave) ) { error = 1; AR.BracketOn = 0; } else { w = WorkSave; if ( *w == 4 || !*w ) { AR.BracketOn = 0; } else { i = *(w+*w-1); if ( i < 0 ) i = -i; *w -= i; i = *w; if ( i > AR.MaxBracket ) { WORD *newbuf; newbuf = (WORD *)Malloc1(sizeof(WORD)*(i+1),"bracket buffer"); AR.MaxBracket = i; if ( AT.BrackBuf != 0 ) M_free(AT.BrackBuf,"bracket buffer"); AT.BrackBuf = newbuf; } to = AT.BrackBuf; NCOPY(to,w,i); } } AC.BracketNormalize = 0; if ( par == 1 ) AR.BracketOn = -AR.BracketOn; if ( error == 0 ) { AC.bracketindexflag = biflag; AT.bracketindexflag = biflag; } AT.WorkPointer = WorkSave; return(error); } /* #] DoBrackets : #[ CoBracket : */ int CoBracket(UBYTE *inp) { return(DoBrackets(inp,0)); } /* #] CoBracket : #[ CoAntiBracket : */ int CoAntiBracket(UBYTE *inp) { return(DoBrackets(inp,1)); } /* #] CoAntiBracket : #[ CoMultiBracket : Syntax: MultiBracket:{A|B} bracketinfo:...:{A|B} bracketinfo; */ int CoMultiBracket(UBYTE *inp) { GETIDENTITY int i, error = 0, error1, type, num; UBYTE *s, c; WORD *to, *from; if ( *inp != ':' ) { MesPrint("&Illegal Multiple Bracket separator: %s",inp); return(1); } inp++; if ( AC.MultiBracketBuf == 0 ) { AC.MultiBracketBuf = (WORD **)Malloc1(sizeof(WORD *)*MAXMULTIBRACKETLEVELS,"multi bracket buffer"); for ( i = 0; i < MAXMULTIBRACKETLEVELS; i++ ) { AC.MultiBracketBuf[i] = 0; } } else { for ( i = 0; i < MAXMULTIBRACKETLEVELS; i++ ) { if ( AC.MultiBracketBuf[i] ) { M_free(AC.MultiBracketBuf[i],"bracket buffer i"); AC.MultiBracketBuf[i] = 0; } } AC.MultiBracketLevels = 0; } AC.MultiBracketLevels = 0; /* Start with disabling the regular brackets. */ if ( AT.BrackBuf == 0 ) { AR.MaxBracket = 100; AT.BrackBuf = (WORD *)Malloc1(sizeof(WORD)*(AR.MaxBracket+1),"bracket buffer"); } *AT.BrackBuf = 0; AR.BracketOn = 0; AC.bracketindexflag = 0; AT.bracketindexflag = 0; /* Now loop through the various levels, separated by the colons. */ for ( i = 0; i < MAXMULTIBRACKETLEVELS; i++ ) { if ( *inp == 0 ) goto RegEnd; /* 1: skip to ':', determine bracket or antibracket */ s = inp; while ( *s && *s != ':' ) { if ( *s == '[' ) { SKIPBRA1(s) s++; } else if ( *s == '{' ) { SKIPBRA2(s) s++; } else s++; } c = *s; *s = 0; if ( StrICont(inp,(UBYTE *)"antibrackets") == 0 ) { type = 1; } else if ( StrICont(inp,(UBYTE *)"brackets") == 0 ) { type = 0; } else { MesPrint("&Illegal (anti)bracket specification in MultiBracket statement"); if ( error == 0 ) error = 1; goto NextLevel; } while ( FG.cTable[*inp] == 0 ) inp++; if ( *inp != ',' ) { MesPrint("&Illegal separator after (anti)bracket specification in MultiBracket statement"); if ( error == 0 ) error = 1; goto NextLevel; } inp++; /* 2: call DoBrackets. */ error1 = DoBrackets(inp, type); if ( error < 0 ) return(error1); if ( error1 > error ) error = error1; /* 3: copy bracket information to the multi bracket arrays */ if ( AR.BracketOn ) { num = AT.BrackBuf[0]; to = AC.MultiBracketBuf[i] = (WORD *)Malloc1((num+2)*sizeof(WORD),"bracket buffer i"); from = AT.BrackBuf; *to++ = AR.BracketOn; NCOPY(to,from,num); *to = 0; } /* 4: set ready for the next level */ NextLevel: *s = c; if ( c == ':' ) s++; inp = s; *AT.BrackBuf = 0; AR.BracketOn = 0; } if ( *inp != 0 ) { MesPrint("&More than %d levels in MultiBracket statement",(WORD)MAXMULTIBRACKETLEVELS); if ( error == 0 ) error = 1; } RegEnd: AC.MultiBracketLevels = i; *AT.BrackBuf = 0; AR.BracketOn = 0; AC.bracketindexflag = 0; AT.bracketindexflag = 0; return(error); } /* #] CoMultiBracket : #[ CountComp : This routine reads the count statement. The syntax is: count minimum,object,size[,object,size] Objects can be: symbol dotproduct vector function Vectors can have the auxiliary flags: +v +f +d +?setname Output for the compiler: TYPECOUNT,size,minimum,objects with the objects: SYMBOL,4,number,size DOTPRODUCT,5,v1,v2,size FUNCTION,4,number,size VECTOR,5,number,bits,size or VECTOR,6,number,bits,setnumber,size Currently only used in the if statement */ WORD *CountComp(UBYTE *inp, WORD *to) { GETIDENTITY UBYTE *p, c; WORD *w, mini = 0, type, c1, c2; int error = 0; p = inp; w = to; AR.Eside = 2; *w++ = TYPECOUNT; *w++ = 0; *w++ = 0; while ( *p == ',' ) { p++; inp = p; if ( *p == '[' || FG.cTable[*p] == 0 ) { if ( ( p = SkipAName(inp) ) == 0 ) return(0); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c1,WITHAUTO); if ( c == '.' ) { if ( type == CVECTOR || type == CDUBIOUS ) { *p++ = c; inp = p; p = SkipAName(p); if ( p == 0 ) return(0); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c2,WITHAUTO); if ( type != CVECTOR && type != CDUBIOUS ) { MesPrint("&Not a vector in dotproduct in if statement: %s",inp); error = 1; } else type = CDOTPRODUCT; } else { MesPrint("&Illegal use of . after %s in if statement",inp); if ( type == NAMENOTFOUND ) MesPrint("&%s is not a properly declared variable",inp); error = 1; *p++ = c; while ( *p && *p != ')' && *p != ',' ) p++; if ( *p == ',' && FG.cTable[p[1]] == 1 ) { p++; while ( *p && *p != ')' && *p != ',' ) p++; } continue; } } *p = c; switch ( type ) { case CSYMBOL: *w++ = SYMBOL; *w++ = 4; *w++ = c1; Sgetnum: if ( *p != ',' ) { MesCerr("sequence",p); while ( *p && *p != ')' && *p != ',' ) p++; error = 1; } p++; inp = p; ParseSignedNumber(mini,p) if ( FG.cTable[p[-1]] != 1 || ( *p && *p != ')' && *p != ',' ) ) { while ( *p && *p != ')' && *p != ',' ) p++; error = 1; c = *p; *p = 0; MesPrint("&Improper value in count: %s",inp); *p = c; while ( *p && *p != ')' && *p != ',' ) p++; } *w++ = mini; break; case CFUNCTION: *w++ = FUNCTION; *w++ = 4; *w++ = c1+FUNCTION; goto Sgetnum; case CDOTPRODUCT: *w++ = DOTPRODUCT; *w++ = 5; *w++ = c2 + AM.OffsetVector; *w++ = c1 + AM.OffsetVector; goto Sgetnum; case CVECTOR: *w++ = VECTOR; *w++ = 5; *w++ = c1 + AM.OffsetVector; if ( *p == ',' ) { *w++ = VECTBIT | DOTPBIT | FUNBIT; goto Sgetnum; } else if ( *p == '+' ) { p++; *w = 0; while ( *p && *p != ',' ) { if ( *p == 'v' || *p == 'V' ) { *w |= VECTBIT; p++; } else if ( *p == 'd' || *p == 'D' ) { *w |= DOTPBIT; p++; } else if ( *p == 'f' || *p == 'F' || *p == 't' || *p == 'T' ) { *w |= FUNBIT; p++; } else if ( *p == '?' ) { p++; inp = p; if ( *p == '{' ) { /* } */ SKIPBRA2(p) if ( p == 0 ) return(0); if ( ( c1 = DoTempSet(inp+1,p) ) < 0 ) return(0); if ( Sets[c1].type != CFUNCTION ) { MesPrint("&set type conflict: Function expected"); return(0); } type = CSET; c = *++p; } else { p = SkipAName(p); if ( p == 0 ) return(0); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c1,WITHAUTO); } if ( type != CSET && type != CDUBIOUS ) { MesPrint("&%s is not a set",inp); error = 1; } w[-2] = 6; *w++ |= SETBIT; *w++ = c1; *p = c; goto Sgetnum; } else { MesCerr("specifier for vector",p); error = 1; } } w++; goto Sgetnum; } else { MesCerr("specifier for vector",p); while ( *p && *p != ')' && *p != ',' ) p++; error = 1; *w++ = VECTBIT | DOTPBIT | FUNBIT; goto Sgetnum; } case CDUBIOUS: goto skipfield; default: *p = 0; MesPrint("&%s is not a symbol, function, vector or dotproduct",inp); error = 1; skipfield: while ( *p && *p != ')' && *p != ',' ) p++; if ( *p && FG.cTable[p[1]] == 1 ) { p++; while ( *p && *p != ')' && *p != ',' ) p++; } break; } } else { MesCerr("name",p); while ( *p && *p != ',' ) p++; error = 1; } } to[1] = w-to; if ( *p == ')' ) p++; if ( *p ) { MesCerr("end of statement",p); return(0); } if ( error ) return(0); return(w); } /* #] CountComp : #[ CoIf : Reads the if statement: There must be a pair of parentheses. Much work is delegated to the routines in compi2 and CountComp. The goto is kept hanging as it is forward. The address in which the label must be written is pushed on the AC.IfStack. Here we allow statements of the type if ( condition ) single statement; compile the if statement. test character at end if not ; or ) copy the statement after the proper parenthesis to the beginning of the AC.iBuffer. Have it compiled. generate an endif statement. */ static UWORD *CIscratC = 0; int CoIf(UBYTE *inp) { GETIDENTITY int error = 0, level; WORD *w, *ww, *u, *s, *OldWork, *OldSpace = AT.WorkSpace; WORD gotexp = 0; /* Indicates whether there can be a condition */ WORD lenpp, lenlev, ncoef, i, number; UBYTE *p, *pp, *ppp, c; CBUF *C = cbuf+AC.cbufnum; LONG x; #ifdef WITHFLOAT int spec; #endif if ( *inp == '(' && inp[1] == ',' ) inp += 2; else if ( *inp == '(' ) inp++; /* Usually we enter at the bracket */ if ( CIscratC == 0 ) CIscratC = (UWORD *)Malloc1((AM.MaxTal+2)*sizeof(UWORD),"CoIf"); lenpp = 0; lenlev = 1; if ( AC.IfLevel >= AC.MaxIf ) DoubleIfBuffers(); AC.IfCount[lenpp++] = 0; /* IfStack is used for organizing the 'go to' for the various if levels */ *AC.IfStack++ = C->Pointer-C->Buffer+2; /* IfSumCheck is used to test for illegal nesting of if, argument or repeat. */ AC.IfSumCheck[AC.IfLevel] = NestingChecksum(); AC.IfLevel++; w = OldWork = AT.WorkPointer; *w++ = TYPEIF; w += 2; p = inp; for(;;) { inp = p; level = 0; ReDo: if ( FG.cTable[*p] == 1 ) { /* Number */ if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } #ifdef WITHFLOAT pp = CheckFloat(p,&spec); if ( pp > p ) { /* Got one */ HaveFloat: if ( spec == -1 ) { MesPrint("&The floating point system has not been started: %s",p); if ( !error ) error = 1; } else { WORD *ow = AT.WorkPointer; AT.WorkPointer = w; c = *pp; *pp = 0; ReadFloat((SBYTE *)p); /* Is now at AT.WorkPointer */ *pp = c; p = pp; AT.WorkPointer[0] = IFFLOATNUMBER; w = AT.WorkPointer + AT.WorkPointer[1]; AT.WorkPointer = ow; if ( level ) w[FUNHEAD+3] = -w[FUNHEAD+3]; } goto DoneWithNumber; } /* Notation: Same as FLOATFUN but FLOATFUN replaced by IFFLOATNUMBER. */ #endif u = w; *w++ = LONGNUMBER; /* Notation: LONGNUMBER,size,reducedsize*sign,numerator,denominator with the length of denominator and numerator equal to reducedsize */ w += 2; if ( GetLong(p,(UWORD *)w,&ncoef) ) { ncoef = 1; error = 1; } w[-1] = ncoef; while ( FG.cTable[*++p] == 1 ); if ( *p == '/' ) { p++; if ( FG.cTable[*p] != 1 ) { MesCerr("sequence",p); error = 1; goto OnlyNum; } if ( GetLong(p,CIscratC,&ncoef) ) { ncoef = 1; error = 1; } while ( FG.cTable[*++p] == 1 ); if ( ncoef == 0 ) { MesPrint("&Division by zero!"); error = 1; } else { if ( w[-1] != 0 ) { if ( Simplify(BHEAD (UWORD *)w,(WORD *)(w-1), CIscratC,&ncoef) ) error = 1; else { i = w[-1]; if ( i >= ncoef ) { i = w[-1]; w += i; i -= ncoef; s = (WORD *)CIscratC; NCOPY(w,s,ncoef); while ( --i >= 0 ) *w++ = 0; } else { w += i; i = ncoef - i; while ( --i >= 0 ) *w++ = 0; s = (WORD *)CIscratC; NCOPY(w,s,ncoef); } } } } } else { OnlyNum: w += ncoef; if ( ncoef > 0 ) { ncoef--; *w++ = 1; while ( --ncoef >= 0 ) *w++ = 0; } } u[1] = WORDDIF(w,u); u[2] = (u[1] - 3)/2; if ( level ) u[2] = -u[2]; #ifdef WITHFLOAT DoneWithNumber: #endif gotexp = 1; } else if ( *p == '+' ) { p++; goto ReDo; } else if ( *p == '-' ) { level ^= 1; p++; goto ReDo; } else if ( *p == 'c' || *p == 'C' ) { /* Count or Coefficient */ if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } while ( FG.cTable[*++p] == 0 ); c = *p; *p = 0; if ( !StrICmp(inp,(UBYTE *)"count") ) { *p = c; if ( c != '(' ) { MesPrint("&no ( after count"); error = 1; goto endofif; } inp = p; SKIPBRA4(p); c = *++p; *p = 0; *inp = ','; w = CountComp(inp,w); *p = c; *inp = '('; if ( w == 0 ) { error = 1; goto endofif; } gotexp = 1; } else if ( ConWord(inp,(UBYTE *)"coefficient") && ( p - inp ) > 3 ) { *w++ = COEFFI; *w++ = 2; *p = c; gotexp = 1; } else goto NoGood; inp = p; } else if ( *p == 'm' || *p == 'M' ) { /* match */ if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } while ( !FG.cTable[*++p] ); c = *p; *p = 0; if ( !StrICmp(inp,(UBYTE *)"match") ) { *p = c; if ( c != '(' ) { MesPrint("&no ( after match"); error = 1; goto endofif; } p++; inp = p; SKIPBRA4(p); *p = '='; /* Now we can call the reading of the lhs of an id statement. This has to be modified in the future. */ AT.WorkSpace = AT.WorkPointer = w; ppp = inp; while ( FG.cTable[*ppp] == 0 && ppp < p ) ppp++; if ( *ppp == ',' ) AC.idoption = 0; else AC.idoption = SUBMULTI; level = CoIdExpression(inp,TYPEIF); AT.WorkSpace = OldSpace; AT.WorkPointer = OldWork; if ( level != 0 ) { if ( level < 0 ) { error = -1; goto endofif; } error = 1; } /* If we pop numlhs we are in good shape */ s = u = C->lhs[C->numlhs]; while ( u < C->Pointer ) *w++ = *u++; C->numlhs--; C->Pointer = s; *p++ = ')'; inp = p; gotexp = 1; } else if ( !StrICmp(inp,(UBYTE *)"multipleof") ) { if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } *p = c; if ( c != '(' ) { MesPrint("&no ( after multipleof"); error = 1; goto endofif; } p++; if ( FG.cTable[*p] != 1 ) { Nomulof: MesPrint("&multipleof needs a short positive integer argument"); error = 1; goto endofif; } ParseNumber(x,p) if ( *p != ')' || x <= 0 || x > MAXPOSITIVE ) goto Nomulof; p++; *w++ = MULTIPLEOF; *w++ = 3; *w++ = (WORD)x; inp = p; gotexp = 1; } else { NoGood: MesPrint("&Unrecognized word: %s",inp); *p = c; error = 1; level = 0; if ( c == '(' ) SKIPBRA4(p) inp = ++p; gotexp = 1; } } else if ( *p == 'f' || *p == 'F' ) { /* FindLoop */ if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } while ( FG.cTable[*++p] == 0 ); c = *p; *p = 0; if ( !StrICmp(inp,(UBYTE *)"findloop") ) { *p = c; if ( c != '(' ) { MesPrint("&no ( after findloop"); error = 1; goto endofif; } inp = p; SKIPBRA4(p); c = *++p; *p = 0; *inp = ','; if ( CoFindLoop(inp) ) { error = 1; goto endofif; } s = u = C->lhs[C->numlhs]; while ( u < C->Pointer ) *w++ = *u++; C->numlhs--; C->Pointer = s; *p = c; *inp = '('; if ( w == 0 ) { error = 1; goto endofif; } gotexp = 1; } else if ( !StrICmp(inp,(UBYTE *)"flag") ) { UBYTE cc = c, *pppp; *p = cc; if ( cc != '(' ) { MesPrint("&no ( after flag"); error = 1; goto endofif; } inp = p; SKIPBRA4(p); cc = *++p; *p = 0; *inp = ','; pppp = p; ww = w; *w++ = IFUSERFLAG; *w++ = 0; while ( *inp ) { int x = 0; while ( *inp == ',' ) inp++; if ( *inp == 0 || *inp == ')' ) break; while ( *inp >= '0' && *inp <= '9' ) x = 10*x+(*inp++-'0'); if ( x < 1 || x > BITSINWORD ) { MesPrint("&Flag number %d outside the permitted range 1-%d.",BITSINWORD); error = 1; } *w++ = x-1; } ww[1] = w-ww; p = pppp; *p = cc; *inp = '('; gotexp = 1; if ( ww[1] <= 2 ) { MesPrint("&The userflag condition in the if statement needs arguments."); error = 1; } inp = p; gotexp = 1; } else goto NoGood; } else if ( *p == 'e' || *p == 'E' ) { /* Expression */ if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } while ( FG.cTable[*++p] == 0 ); c = *p; *p = 0; if ( !StrICmp(inp,(UBYTE *)"expression") ) { *p = c; if ( c != '(' ) { MesPrint("&no ( after expression"); error = 1; goto endofif; } p++; ww = w; *w++ = IFEXPRESSION; w++; while ( *p != ')' ) { if ( *p == ',' ) { p++; continue; } if ( *p == '[' || FG.cTable[*p] == 0 ) { pp = p; if ( ( p = SkipAName(p) ) == 0 ) { MesPrint("&Improper name for an expression: '%s'",pp); error = 1; goto endofif; } c = *p; *p = 0; if ( GetName(AC.exprnames,pp,&number,NOAUTO) == CEXPRESSION ) { *w++ = number; } else if ( GetName(AC.varnames,pp,&number,NOAUTO) != NAMENOTFOUND ) { MesPrint("&%s is not an expression",pp); error = 1; *w++ = number; } *p = c; } else { MesPrint("&Illegal object in Expression in if-statement"); error = 1; while ( *p && *p != ',' && *p != ')' ) p++; if ( *p == 0 || *p == ')' ) break; } } ww[1] = w - ww; p++; gotexp = 1; } else goto NoGood; inp = p; } else if ( *p == 'i' || *p == 'I' ) { /* IsFactorized */ if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } while ( FG.cTable[*++p] == 0 ); c = *p; *p = 0; if ( !StrICmp(inp,(UBYTE *)"isfactorized") ) { *p = c; if ( c != '(' ) { /* No expression means current expression */ ww = w; *w++ = IFISFACTORIZED; w++; } else { p++; ww = w; *w++ = IFISFACTORIZED; w++; while ( *p != ')' ) { if ( *p == ',' ) { p++; continue; } if ( *p == '[' || FG.cTable[*p] == 0 ) { pp = p; if ( ( p = SkipAName(p) ) == 0 ) { MesPrint("&Improper name for an expression: '%s'",pp); error = 1; goto endofif; } c = *p; *p = 0; if ( GetName(AC.exprnames,pp,&number,NOAUTO) == CEXPRESSION ) { *w++ = number; } else if ( GetName(AC.varnames,pp,&number,NOAUTO) != NAMENOTFOUND ) { MesPrint("&%s is not an expression",pp); error = 1; *w++ = number; } *p = c; } else { MesPrint("&Illegal object in IsFactorized in if-statement"); error = 1; while ( *p && *p != ',' && *p != ')' ) p++; if ( *p == 0 || *p == ')' ) break; } } p++; } ww[1] = w - ww; gotexp = 1; } else goto NoGood; inp = p; } else if ( *p == 'o' || *p == 'O' ) { /* Occurs */ /* Tests whether variables occur inside a term. At the moment this is done one by one. If we want to do them in groups we should do the reading a bit different: each as a variable in a term, and then use Normalize to get the variables grouped and in order. That way FindVar (in if.c) can work more efficiently. Still to be done!!! TASK: Nice little task for someone to learn. */ UBYTE cc; if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } while ( FG.cTable[*++p] == 0 ); c = cc = *p; *p = 0; if ( !StrICmp(inp,(UBYTE *)"occurs") ) { WORD c1, c2, type; *p = cc; if ( cc != '(' ) { MesPrint("&no ( after occurs"); error = 1; goto endofif; } inp = p; SKIPBRA4(p); cc = *++p; *p = 0; *inp = ','; pp = p; ww = w; *w++ = IFOCCURS; *w++ = 0; while ( *inp ) { while ( *inp == ',' ) inp++; if ( *inp == 0 || *inp == ')' ) break; /* Now read a list of names We can have symbols, vectors, dotproducts, indices, functions. There could also be dummy indices and/or extra symbols. */ if ( *inp == '[' || FG.cTable[*inp] == 0 ) { if ( ( p = SkipAName(inp) ) == 0 ) return(0); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c1,WITHAUTO); if ( c == '.' ) { if ( type == CVECTOR || type == CDUBIOUS ) { *p++ = c; inp = p; p = SkipAName(p); if ( p == 0 ) return(0); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c2,WITHAUTO); if ( type != CVECTOR && type != CDUBIOUS ) { MesPrint("&Not a vector in dotproduct in if statement: %s",inp); error = 1; } else type = CDOTPRODUCT; } else { MesPrint("&Illegal use of . after %s in if statement",inp); if ( type == NAMENOTFOUND ) MesPrint("&%s is not a properly declared variable",inp); error = 1; *p++ = c; while ( *p && *p != ')' && *p != ',' ) p++; if ( *p == ',' && FG.cTable[p[1]] == 1 ) { p++; while ( *p && *p != ')' && *p != ',' ) p++; } continue; } } *p = c; switch ( type ) { case CSYMBOL: /* To worry about extra symbols */ *w++ = SYMBOL; *w++ = c1; break; case CINDEX: *w++ = INDEX; *w++ = c1 + AM.OffsetIndex; break; case CVECTOR: *w++ = VECTOR; *w++ = c1 + AM.OffsetVector; break; case CDOTPRODUCT: *w++ = DOTPRODUCT; *w++ = c1 + AM.OffsetVector; *w++ = c2 + AM.OffsetVector; break; case CFUNCTION: *w++ = FUNCTION; *w++ = c1+FUNCTION; break; default: MesPrint("&Illegal variable %s in occurs condition in if statement",inp); error = 1; break; } inp = p; } else { MesPrint("&Illegal object %s in occurs condition in if statement",inp); error = 1; break; } } ww[1] = w-ww; p = pp; *p = cc; *inp = '('; gotexp = 1; if ( ww[1] <= 2 ) { MesPrint("&The occurs condition in the if statement needs arguments."); error = 1; } } else goto NoGood; inp = p; } else if ( *p == '$' ) { if ( gotexp == 1 ) { MesCerr("position for )",p); error = 1; } p++; inp = p; while ( FG.cTable[*p] == 0 || FG.cTable[*p] == 1 ) p++; c = *p; *p = 0; if ( ( i = GetDollar(inp) ) < 0 ) { MesPrint("&undefined dollar expression %s",inp); error = 1; i = AddDollar(inp,DOLUNDEFINED,0,0); } *p = c; *w++ = IFDOLLAR; *w++ = 3; *w++ = i; /* And then the IFDOLLAREXTRA pieces for [1] [$y] etc */ if ( *p == '[' ) { p++; if ( ( w = GetIfDollarFactor(&p,w) ) == 0 ) { error = 1; goto endofif; } else if ( *p != ']' ) { error = 1; goto endofif; } p++; } inp = p; gotexp = 1; } #ifdef WITHFLOAT else if ( *p == '.' ) { pp = CheckFloat(p,&spec); if ( pp > p ) goto HaveFloat; } #endif else if ( *p == '(' ) { if ( gotexp ) { MesCerr("parenthesis",p); error = 1; goto endofif; } gotexp = 0; if ( ++lenlev >= AC.MaxIf ) DoubleIfBuffers(); AC.IfCount[lenpp++] = w-OldWork; *w++ = SUBEXPR; w += 2; p++; } else if ( *p == ')' ) { if ( gotexp == 0 ) { MesCerr("position for )",p); error = 1; } gotexp = 1; u = AC.IfCount[--lenpp]+OldWork; lenlev--; u[1] = w - u; if ( lenlev <= 0 ) { /* End if condition */ AT.WorkSpace = OldSpace; AT.WorkPointer = OldWork; AddNtoL(OldWork[1],OldWork); p++; if ( *p == ')' ) { MesPrint("&unmatched parenthesis in if/while ()"); error = 1; while ( *++p == ')' ); } if ( *p ) { level = CompileStatement(p); if ( level ) error = level; while ( *p ) p++; if ( CoEndIf(p) && error == 0 ) error = 1; } return(error); } p++; } else if ( *p == '>' ) { if ( gotexp == 0 ) goto NoExp; if ( p[1] == '=' ) { *w++ = GREATEREQUAL; *w++ = 2; p += 2; } else { *w++ = GREATER; *w++ = 2; p++; } gotexp = 0; } else if ( *p == '<' ) { if ( gotexp == 0 ) goto NoExp; if ( p[1] == '=' ) { *w++ = LESSEQUAL; *w++ = 2; p += 2; } else { *w++ = LESS; *w++ = 2; p++; } gotexp = 0; } else if ( *p == '=' ) { if ( gotexp == 0 ) goto NoExp; if ( p[1] == '=' ) p++; *w++ = EQUAL; *w++ = 2; p++; gotexp = 0; } else if ( *p == '!' && p[1] == '=' ) { if ( gotexp == 0 ) { p++; goto NoExp; } *w++ = NOTEQUAL; *w++ = 2; p += 2; gotexp = 0; } else if ( *p == '|' && p[1] == '|' ) { if ( gotexp == 0 ) { p++; goto NoExp; } *w++ = ORCOND; *w++ = 2; p += 2; gotexp = 0; } else if ( *p == '&' && p[1] == '&' ) { if ( gotexp == 0 ) { p++; NoExp: p++; MesCerr("sequence",p); error = 1; } else { *w++ = ANDCOND; *w++ = 2; p += 2; gotexp = 0; } } else if ( *p == 0 ) { MesPrint("&Unmatched parentheses"); error = 1; goto endofif; } else { if ( FG.cTable[*p] == 0 ) { WORD ij; inp = p; while ( ( ij = FG.cTable[*++p] ) == 0 || ij == 1 ); c = *p; *p = 0; goto NoGood; } MesCerr("sequence",p); error = 1; p++; } } endofif:; return(error); } /* #] CoIf : #[ CoElse : */ int CoElse(UBYTE *p) { int error = 0; CBUF *C = cbuf+AC.cbufnum; if ( *p != 0 ) { while ( *p == ',' ) p++; if ( tolower(*p) == 'i' && tolower(p[1]) == 'f' && p[2] == '(' ) return(CoElseIf(p+2)); MesPrint("&No extra text allowed as part of an else statement"); error = 1; } if ( AC.IfLevel <= 0 ) { MesPrint("&else statement without if"); return(1); } if ( AC.IfSumCheck[AC.IfLevel-1] != NestingChecksum() - 1 ) { MesNesting(); error = 1; } Add3Com(TYPEELSE,AC.IfLevel) C->Buffer[AC.IfStack[-1]] = C->numlhs; AC.IfStack[-1] = C->Pointer - C->Buffer - 1; return(error); } /* #] CoElse : #[ CoElseIf : */ int CoElseIf(UBYTE *inp) { CBUF *C = cbuf+AC.cbufnum; if ( AC.IfLevel <= 0 ) { MesPrint("&elseif statement without if"); return(1); } Add3Com(TYPEELSE,-AC.IfLevel) AC.IfLevel--; C->Buffer[*--AC.IfStack] = C->numlhs; return(CoIf(inp)); } /* #] CoElseIf : #[ CoEndIf : It puts a RHS-level at the position indicated in the AC.IfStack. This corresponds to the label belonging to a forward goto. It is the goto that belongs either to the failing condition of the if (no else statement), or the completion of the success path (with else statement) The code is a jump to the next statement. It is there to prevent problems with if ( .. ) if ( .. ) endif; elseif ( .. ) */ int CoEndIf(UBYTE *inp) { CBUF *C = cbuf+AC.cbufnum; WORD i = C->numlhs, to, k = -AC.IfLevel; int error = 0; while ( *inp == ',' ) inp++; if ( *inp != 0 ) { error = 1; MesPrint("&No extra text allowed as part of an endif/elseif statement"); } if ( AC.IfLevel <= 0 ) { MesPrint("&Endif statement without corresponding if"); return(1); } AC.IfLevel--; C->Buffer[*--AC.IfStack] = i+1; if ( AC.IfSumCheck[AC.IfLevel] != NestingChecksum() ) { MesNesting(); error = 1; } Add3Com(TYPEENDIF,i+1) /* Now the search for the TYPEELSE in front of the elseif statements */ to = C->numlhs; while ( i > 0 ) { if ( C->lhs[i][0] == TYPEELSE && C->lhs[i][2] == to ) to = i; if ( C->lhs[i][0] == TYPEIF ) { if ( C->lhs[i][2] == to ) { i--; if ( i <= 0 || C->lhs[i][0] != TYPEELSE || C->lhs[i][2] != k ) break; C->lhs[i][2] = C->numlhs; to = i; } } i--; } return(error); } /* #] CoEndIf : #[ CoWhile : */ int CoWhile(UBYTE *inp) { CBUF *C = cbuf+AC.cbufnum; WORD startnum = C->numlhs + 1; int error; AC.WhileLevel++; error = CoIf(inp); if ( C->numlhs > startnum && C->lhs[startnum][2] == C->numlhs && C->lhs[C->numlhs][0] == TYPEENDIF ) { C->lhs[C->numlhs][2] = startnum-1; AC.WhileLevel--; } else C->lhs[startnum][2] = startnum; return(error); } /* #] CoWhile : #[ CoEndWhile : */ int CoEndWhile(UBYTE *inp) { int error = 0; WORD i; CBUF *C = cbuf+AC.cbufnum; if ( AC.WhileLevel <= 0 ) { MesPrint("&EndWhile statement without corresponding While"); return(1); } AC.WhileLevel--; i = C->Buffer[AC.IfStack[-1]]; error = CoEndIf(inp); C->lhs[C->numlhs][2] = i - 1; return(error); } /* #] CoEndWhile : #[ DoFindLoop : Function,arguments=number,loopsize=number,outfun=function,include=index; */ static char *messfind[] = { "Findloop(function,arguments=#,loopsize(=#|<#)[,include=index])" ,"Replaceloop,function,arguments=#,loopsize(=#|<#),outfun=function[,include=index]" }; static WORD comfindloop[7] = { TYPEFINDLOOP,7,0,0,0,0,0 }; int DoFindLoop(UBYTE *inp, int mode) { UBYTE *s, c; WORD funnum, nargs = 0, nloop = 0, indexnum = 0, outfun = 0; int type, aflag, lflag, indflag, outflag, error = 0, sym; while ( *inp == ',' ) inp++; if ( ( s = SkipAName(inp) ) == 0 ) { syntax: MesPrint("&Proper syntax is:"); MesPrint("%s",messfind[mode]); return(1); } c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,inp,&funnum,WITHAUTO) ) == NAMENOTFOUND ) || type != CFUNCTION || ( ( sym = (functions[funnum].symmetric) & ~REVERSEORDER ) != SYMMETRIC && sym != ANTISYMMETRIC ) ) { MesPrint("&%s should be a (anti)symmetric function or tensor",inp); error = 1; } funnum += FUNCTION; *s = c; inp = s; aflag = lflag = indflag = outflag = 0; while ( *inp == ',' ) { while ( *inp == ',' ) inp++; s = inp; if ( ( s = SkipAName(inp) ) == 0 ) goto syntax; c = *s; *s = 0; if ( StrICont(inp,(UBYTE *)"arguments") == 0 ) { if ( c != '=' ) goto syntax; *s++ = c; NeedNumber(nargs,s,syntax) aflag++; inp = s; } else if ( StrICont(inp,(UBYTE *)"loopsize") == 0 ) { if ( c != '=' && c != '<' ) goto syntax; *s++ = c; if ( FG.cTable[*s] == 1 ) { NeedNumber(nloop,s,syntax) if ( nloop < 2 ) { MesPrint("&loopsize should be at least 2"); error = 1; } if ( c == '<' ) nloop = -nloop; } else if ( tolower(*s) == 'a' && tolower(s[1]) == 'l' && tolower(s[2]) == 'l' && FG.cTable[s[3]] > 1 ) { nloop = -1; s += 3; if ( c != '=' ) goto syntax; } inp = s; lflag++; } else if ( StrICont(inp,(UBYTE *)"include") == 0 ) { if ( c != '=' ) goto syntax; *s++ = c; if ( ( inp = SkipAName(s) ) == 0 ) goto syntax; c = *inp; *inp = 0; if ( ( type = GetName(AC.varnames,s,&indexnum,WITHAUTO) ) != CINDEX ) { MesPrint("&%s is not a proper index",s); error = 1; } else if ( indexnum < WILDOFFSET && indices[indexnum].dimension == 0 ) { MesPrint("&%s should be a summable index",s); error = 1; } indexnum += AM.OffsetIndex; *inp = c; indflag++; } else if ( StrICont(inp,(UBYTE *)"outfun") == 0 ) { if ( c != '=' ) goto syntax; *s++ = c; if ( ( inp = SkipAName(s) ) == 0 ) goto syntax; c = *inp; *inp = 0; if ( ( type = GetName(AC.varnames,s,&outfun,WITHAUTO) ) != CFUNCTION ) { MesPrint("&%s is not a proper function or tensor",s); error = 1; } outfun += FUNCTION; outflag++; *inp = c; } else { MesPrint("&Unrecognized option in FindLoop or ReplaceLoop: %s",inp); error = 1; *s = c; inp = s; while ( *inp && *inp != ',' ) inp++; } } if ( *inp != 0 && mode == REPLACELOOP ) goto syntax; if ( mode == FINDLOOP && outflag > 0 ) { MesPrint("&outflag option is illegal in FindLoop"); error = 1; } if ( mode == REPLACELOOP && outflag == 0 ) goto syntax; if ( aflag == 0 || lflag == 0 ) goto syntax; comfindloop[3] = funnum; comfindloop[4] = nloop; comfindloop[5] = nargs; comfindloop[6] = outfun; comfindloop[1] = 7; if ( indflag ) { if ( mode == 0 ) comfindloop[2] = indexnum + 5; else comfindloop[2] = -indexnum - 5; } else comfindloop[2] = mode; AddNtoL(comfindloop[1],comfindloop); return(error); } /* #] DoFindLoop : #[ CoFindLoop : */ int CoFindLoop(UBYTE *inp) { return(DoFindLoop(inp,FINDLOOP)); } /* #] CoFindLoop : #[ CoReplaceLoop : */ int CoReplaceLoop(UBYTE *inp) { int error = DoFindLoop(inp,REPLACELOOP); if ( error ) { Terminate(-1); } return(error); } /* #] CoReplaceLoop : #[ CoFunPowers : */ static UBYTE *FunPowOptions[] = { (UBYTE *)"nofunpowers" ,(UBYTE *)"commutingonly" ,(UBYTE *)"allfunpowers" }; int CoFunPowers(UBYTE *inp) { UBYTE *option, c; int i, maxoptions = sizeof(FunPowOptions)/sizeof(UBYTE *); while ( *inp == ',' ) inp++; option = inp; inp = SkipAName(inp); c = *inp; *inp = 0; for ( i = 0; i < maxoptions; i++ ) { if ( StrICont(option,FunPowOptions[i]) == 0 ) { if ( c ) { *inp = c; MesPrint("&Illegal FunPowers statement"); return(1); } AC.funpowers = i; return(0); } } MesPrint("&Illegal option in FunPowers statement: %s",option); return(1); } /* #] CoFunPowers : #[ CoUnitTrace : */ int CoUnitTrace(UBYTE *s) { WORD num; if ( FG.cTable[*s] == 1 ) { ParseNumber(num,s) if ( *s != 0 ) { nogood: MesPrint("&Value of UnitTrace should be a (positive) number or a symbol"); return(1); } AC.lUniTrace[0] = SNUMBER; AC.lUniTrace[2] = num; } else { if ( GetName(AC.varnames,s,&num,WITHAUTO) == CSYMBOL ) { AC.lUniTrace[0] = SYMBOL; AC.lUniTrace[2] = num; num = -num; } else goto nogood; s = SkipAName(s); if ( *s ) goto nogood; } AC.lUnitTrace = num; return(0); } /* #] CoUnitTrace : #[ CoTerm : Note: termstack holds the offset of the term statement in the compiler buffer. termsortstack holds the offset of the last sort statement (or the corresponding term statement) */ int CoTerm(UBYTE *s) { GETIDENTITY WORD *w = AT.WorkPointer; int error = 0; while ( *s == ',' ) s++; if ( *s ) { MesPrint("&Illegal syntax for Term statement"); return(1); } if ( AC.termlevel+1 >= AC.maxtermlevel ) { if ( AC.maxtermlevel <= 0 ) { AC.maxtermlevel = 20; AC.termstack = (LONG *)Malloc1(AC.maxtermlevel*sizeof(LONG),"termstack"); AC.termsortstack = (LONG *)Malloc1(AC.maxtermlevel*sizeof(LONG),"termsortstack"); AC.termsumcheck = (WORD *)Malloc1(AC.maxtermlevel*sizeof(WORD),"termsumcheck"); } else { DoubleBuffer((void **)AC.termstack,(void **)AC.termstack+AC.maxtermlevel, sizeof(LONG),"doubling termstack"); DoubleBuffer((void **)AC.termsortstack, (void **)AC.termsortstack+AC.maxtermlevel, sizeof(LONG),"doubling termsortstack"); DoubleBuffer((void **)AC.termsumcheck, (void **)AC.termsumcheck+AC.maxtermlevel, sizeof(LONG),"doubling termsumcheck"); AC.maxtermlevel *= 2; } } AC.termsumcheck[AC.termlevel] = NestingChecksum(); AC.termstack[AC.termlevel] = cbuf[AC.cbufnum].Pointer - cbuf[AC.cbufnum].Buffer + 2; AC.termsortstack[AC.termlevel] = AC.termstack[AC.termlevel] + 1; AC.termlevel++; *w++ = TYPETERM; w++; *w++ = cbuf[AC.cbufnum].numlhs; *w++ = cbuf[AC.cbufnum].numlhs; AT.WorkPointer[1] = w - AT.WorkPointer; AddNtoL(AT.WorkPointer[1],AT.WorkPointer); return(error); } /* #] CoTerm : #[ CoEndTerm : */ int CoEndTerm(UBYTE *s) { CBUF *C = cbuf+AC.cbufnum; while ( *s == ',' ) s++; if ( *s ) { MesPrint("&Illegal syntax for EndTerm statement"); return(1); } if ( AC.termlevel <= 0 ) { MesPrint("&EndTerm without corresponding Argument statement"); return(1); } AC.termlevel--; cbuf[AC.cbufnum].Buffer[AC.termstack[AC.termlevel]] = C->numlhs; cbuf[AC.cbufnum].Buffer[AC.termsortstack[AC.termlevel]] = C->numlhs; if ( AC.termsumcheck[AC.termlevel] != NestingChecksum() ) { MesNesting(); return(1); } return(0); } /* #] CoEndTerm : #[ CoSort : */ int CoSort(UBYTE *s) { GETIDENTITY WORD *w = AT.WorkPointer; int error = 0; while ( *s == ',' ) s++; if ( *s ) { MesPrint("&Illegal syntax for Sort statement"); error = 1; } if ( AC.termlevel <= 0 ) { MesPrint("&The Sort statement can only be used inside a term environment"); error = 1; } if ( error ) return(error); *w++ = TYPESORT; w++; w++; cbuf[AC.cbufnum].Buffer[AC.termsortstack[AC.termlevel-1]] = *w = cbuf[AC.cbufnum].numlhs+1; w++; AC.termsortstack[AC.termlevel-1] = cbuf[AC.cbufnum].Pointer - cbuf[AC.cbufnum].Buffer + 3; if ( AC.termsumcheck[AC.termlevel-1] != NestingChecksum() - 1 ) { MesNesting(); return(1); } AT.WorkPointer[1] = w - AT.WorkPointer; AddNtoL(AT.WorkPointer[1],AT.WorkPointer); return(error); } /* #] CoSort : #[ CoPolyFun : Collect,functionname */ int CoPolyFun(UBYTE *s) { GETIDENTITY WORD numfun; int type, error = 0; UBYTE *t; AR.PolyFun = AC.lPolyFun = 0; AR.PolyFunInv = AC.lPolyFunInv = 0; AR.PolyFunType = AC.lPolyFunType = 0; AR.PolyFunExp = AC.lPolyFunExp = 0; AR.PolyFunVar = AC.lPolyFunVar = 0; AR.PolyFunPow = AC.lPolyFunPow = 0; if ( *s == 0 ) { return(0); } t = SkipAName(s); if ( t == 0 || *t != 0 ) { MesPrint("&PolyFun statement needs a single commuting function for its argument"); return(1); } if ( ( ( type = GetName(AC.varnames,s,&numfun,WITHAUTO) ) != CFUNCTION ) || ( functions[numfun].spec != 0 ) || ( functions[numfun].commute != 0 ) ) { MesPrint("&%s should be a regular commuting function",s); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&numfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } error = 1; } else { AR.PolyFun = AC.lPolyFun = numfun+FUNCTION; AR.PolyFunType = AC.lPolyFunType = 1; } #ifdef WITHFLOAT if ( mpfaux_ != 0 ) { MesPrint("&Simultaneous use of PolyFun and float_ is not allowed."); error = 1; } #endif return(error); } /* #] CoPolyFun : #[ CoPolyRatFun : PolyRatFun [,functionname[,functionname](option)] */ int CoPolyRatFun(UBYTE *s) { GETIDENTITY WORD numfun; int type, error = 0; UBYTE *t, c; AR.PolyFun = AC.lPolyFun = 0; AR.PolyFunInv = AC.lPolyFunInv = 0; AR.PolyFunType = AC.lPolyFunType = 0; AR.PolyFunExp = AC.lPolyFunExp = 0; AR.PolyFunVar = AC.lPolyFunVar = 0; AR.PolyFunPow = AC.lPolyFunPow = 0; if ( *s == 0 ) return(error); t = SkipAName(s); if ( t == 0 ) goto NumErr; c = *t; *t = 0; #ifdef WITHFLOAT if ( mpfaux_ != 0 ) { MesPrint("&Simultaneous use of PolyFun and float_ is not allowed."); error = 1; } #endif if ( ( ( type = GetName(AC.varnames,s,&numfun,WITHAUTO) ) != CFUNCTION ) || ( functions[numfun].spec != 0 ) || ( functions[numfun].commute != 0 ) ) { MesPrint("&%s should be a regular commuting function",s); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&numfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } AR.PolyFun = AC.lPolyFun = numfun+FUNCTION; AR.PolyFunInv = AC.lPolyFunInv = 0; AR.PolyFunType = AC.lPolyFunType = 2; AC.PolyRatFunChanged = 1; if ( c == 0 ) return(error); *t = c; if ( *t == '-' ) { AC.PolyRatFunChanged = 0; t++; } while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t == 0 ) return(error); if ( *t != '(' ) { s = t; t = SkipAName(s); if ( t == 0 ) goto NumErr; c = *t; *t = 0; if ( ( ( type = GetName(AC.varnames,s,&numfun,WITHAUTO) ) != CFUNCTION ) || ( functions[numfun].spec != 0 ) || ( functions[numfun].commute != 0 ) ) { MesPrint("&%s should be a regular commuting function",s); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&numfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } AR.PolyFunInv = AC.lPolyFunInv = numfun+FUNCTION; if ( c == 0 ) return(error); *t = c; if ( *t == '-' ) { AC.PolyRatFunChanged = 0; t++; } while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t == 0 ) return(error); } if ( *t == '(' ) { t++; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; /* Next we need a keyword like (divergence,ep) (expand,ep,maxpow) */ s = t; t = SkipAName(s); if ( t == 0 ) goto NumErr; c = *t; *t = 0; if ( ( StrICmp(s,(UBYTE *)"divergence") == 0 ) || ( StrICmp(s,(UBYTE *)"finddivergence") == 0 ) ) { if ( c != ',' ) { MesPrint("&Illegal option field in PolyRatFun statement."); return(1); } *t = c; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; s = t; t = SkipAName(s); if ( t == 0 ) goto NumErr; c = *t; *t = 0; if ( ( type = GetName(AC.varnames,s,&AC.lPolyFunVar,WITHAUTO) ) != CSYMBOL ) { MesPrint("&Illegal symbol %s in option field in PolyRatFun statement.",s); return(1); } *t = c; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t != ')' ) { MesPrint("&Illegal termination of option in PolyRatFun statement."); return(1); } AR.PolyFunExp = AC.lPolyFunExp = 1; AR.PolyFunVar = AC.lPolyFunVar; symbols[AC.lPolyFunVar].minpower = -MAXPOWER; symbols[AC.lPolyFunVar].maxpower = MAXPOWER; } else if ( StrICmp(s,(UBYTE *)"expand") == 0 ) { WORD x = 0, etype = 2; if ( c != ',' ) { MesPrint("&Illegal option field in PolyRatFun statement."); return(1); } *t = c; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; s = t; t = SkipAName(s); if ( t == 0 ) goto NumErr; c = *t; *t = 0; if ( ( type = GetName(AC.varnames,s,&AC.lPolyFunVar,WITHAUTO) ) != CSYMBOL ) { MesPrint("&Illegal symbol %s in option field in PolyRatFun statement.",s); return(1); } *t = c; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t > '9' || *t < '0' ) { MesPrint("&Illegal option field in PolyRatFun statement."); return(1); } while ( *t <= '9' && *t >= '0' ) x = 10*x + *t++ - '0'; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t != ')' ) { s = t; t = SkipAName(s); if ( t == 0 ) goto ParErr; c = *t; *t = 0; if ( StrICmp(s,(UBYTE *)"fixed") == 0 ) { etype = 3; } else if ( StrICmp(s,(UBYTE *)"relative") == 0 ) { etype = 2; } else { MesPrint("&Illegal termination of option in PolyRatFun statement."); return(1); } *t = c; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t != ')' ) { MesPrint("&Illegal termination of option in PolyRatFun statement."); return(1); } } AR.PolyFunExp = AC.lPolyFunExp = etype; AR.PolyFunVar = AC.lPolyFunVar; AR.PolyFunPow = AC.lPolyFunPow = x; symbols[AC.lPolyFunVar].minpower = -MAXPOWER; symbols[AC.lPolyFunVar].maxpower = MAXPOWER; } else { ParErr: MesPrint("&Illegal option %s in PolyRatFun statement.",s); return(1); } t++; while ( *t == ',' || *t == ' ' || *t == '\t' ) t++; if ( *t == 0 ) return(error); } NumErr:; MesPrint("&PolyRatFun statement needs one or two commuting function(s) for its argument(s)"); return(1); } /* #] CoPolyRatFun : #[ CoMerge : */ int CoMerge(UBYTE *inp) { UBYTE *s = inp; int type; WORD numfunc, option = 0; if ( tolower(s[0]) == 'o' && tolower(s[1]) == 'n' && tolower(s[2]) == 'c' && tolower(s[3]) == 'e' && tolower(s[4]) == ',' ) { option = 1; s += 5; } else if ( tolower(s[0]) == 'a' && tolower(s[1]) == 'l' && tolower(s[2]) == 'l' && tolower(s[3]) == ',' ) { option = 0; s += 4; } if ( *s == '$' ) { if ( ( type = GetName(AC.dollarnames,s+1,&numfunc,NOAUTO) ) == CDOLLAR ) numfunc = -numfunc; else { MesPrint("&%s is undefined",s); numfunc = AddDollar(s+1,DOLINDEX,&one,1); return(1); } tests: s = SkipAName(s); if ( *s != 0 ) { MesPrint("&Merge/shuffle should have a single function or $variable for its argument"); return(1); } } else if ( ( type = GetName(AC.varnames,s,&numfunc,WITHAUTO) ) == CFUNCTION ) { numfunc += FUNCTION; goto tests; } else if ( type != -1 ) { if ( type != CDUBIOUS ) { NameConflict(type,s); type = MakeDubious(AC.varnames,s,&numfunc); } return(1); } else { MesPrint("&%s is not a function",s); numfunc = AddFunction(s,0,0,0,0,0,-1,-1) + FUNCTION; return(1); } Add4Com(TYPEMERGE,numfunc,option); return(0); } /* #] CoMerge : #[ CoStuffle : Important for future options: The bit, given by 256 (bit 8) is reserved internally for keeping track of the sign in the number of Stuffle additions. */ int CoStuffle(UBYTE *inp) { UBYTE *s = inp, *ss, c; int type; WORD numfunc, option = 0; if ( tolower(s[0]) == 'o' && tolower(s[1]) == 'n' && tolower(s[2]) == 'c' && tolower(s[3]) == 'e' && tolower(s[4]) == ',' ) { option = 1; s += 5; } else if ( tolower(s[0]) == 'a' && tolower(s[1]) == 'l' && tolower(s[2]) == 'l' && tolower(s[3]) == ',' ) { option = 0; s += 4; } ss = SkipAName(s); c = *ss; *ss = 0; if ( *s == '$' ) { if ( ( type = GetName(AC.dollarnames,s+1,&numfunc,NOAUTO) ) == CDOLLAR ) numfunc = -numfunc; else { MesPrint("&%s is undefined",s); numfunc = AddDollar(s+1,DOLINDEX,&one,1); return(1); } tests: *ss = c; if ( *ss != '+' && *ss != '-' && ss[1] != 0 ) { MesPrint("&Stuffle should have a single function or $variable for its argument, followed by either + or -"); return(1); } if ( *ss == '-' ) option += 2; } else if ( ( type = GetName(AC.varnames,s,&numfunc,WITHAUTO) ) == CFUNCTION ) { numfunc += FUNCTION; goto tests; } else if ( type != -1 ) { if ( type != CDUBIOUS ) { NameConflict(type,s); type = MakeDubious(AC.varnames,s,&numfunc); } return(1); } else { MesPrint("&%s is not a function",s); numfunc = AddFunction(s,0,0,0,0,0,-1,-1) + FUNCTION; return(1); } Add4Com(TYPESTUFFLE,numfunc,option); return(0); } /* #] CoStuffle : #[ CoProcessBucket : */ int CoProcessBucket(UBYTE *s) { LONG x; while ( *s == ',' || *s == '=' ) s++; ParseNumber(x,s) if ( *s && *s != ' ' && *s != '\t' ) { MesPrint("&Numerical value expected for ProcessBucketSize"); return(1); } AC.ProcessBucketSize = x; return(0); } /* #] CoProcessBucket : #[ CoThreadBucket : */ int CoThreadBucket(UBYTE *s) { LONG x; while ( *s == ',' || *s == '=' ) s++; ParseNumber(x,s) if ( *s && *s != ' ' && *s != '\t' ) { MesPrint("&Numerical value expected for ThreadBucketSize"); return(1); } if ( x <= 0 ) { Warning("Negative of zero value not allowed for ThreadBucketSize. Adjusted to 1."); x = 1; } AC.ThreadBucketSize = x; #ifdef WITHPTHREADS if ( AS.MultiThreaded ) MakeThreadBuckets(-1,1); #endif return(0); } /* #] CoThreadBucket : #[ DoArgPlode : Syntax: a list of functions. If the functions have an argument it must be a function. In the case f(g) we treat f(g(...)) with g any argument. (not yet implemented) */ int DoArgPlode(UBYTE *s, int par) { GETIDENTITY WORD numfunc, type, error = 0, *w, n; UBYTE *t,c; int i; w = AT.WorkPointer; *w++ = par; w++; while ( *s == ',' ) s++; while ( *s ) { if ( *s == '$' ) { MesPrint("&We don't do dollar variables yet in ArgImplode/ArgExplode"); return(1); } t = s; if ( ( s = SkipAName(s) ) == 0 ) return(1); c = *s; *s = 0; if ( ( type = GetName(AC.varnames,t,&numfunc,WITHAUTO) ) == CFUNCTION ) { numfunc += FUNCTION; } else if ( type != -1 ) { if ( type != CDUBIOUS ) { NameConflict(type,t); type = MakeDubious(AC.varnames,t,&numfunc); } error = 1; } else { MesPrint("&%s is not a function",t); numfunc = AddFunction(s,0,0,0,0,0,-1,-1) + FUNCTION; return(1); } *s = c; *w++ = numfunc; *w++ = FUNHEAD; #if FUNHEAD > 2 for ( i = 2; i < FUNHEAD; i++ ) *w++ = 0; #endif if ( *s && *s != ',' ) { MesPrint("&Illegal character in ArgImplode/ArgExplode statement: %s",s); return(1); } while ( *s == ',' ) s++; } n = w - AT.WorkPointer; AT.WorkPointer[1] = n; AddNtoL(n,AT.WorkPointer); return(error); } /* #] DoArgPlode : #[ CoArgExplode : */ int CoArgExplode(UBYTE *s) { return(DoArgPlode(s,TYPEARGEXPLODE)); } /* #] CoArgExplode : #[ CoArgImplode : */ int CoArgImplode(UBYTE *s) { return(DoArgPlode(s,TYPEARGIMPLODE)); } /* #] CoArgImplode : #[ CoClearTable : */ int CoClearTable(UBYTE *s) { UBYTE c, *t; int j, type, error = 0; WORD numfun; TABLES T, TT; if ( *s == 0 ) { MesPrint("&The ClearTable statement needs at least one (table) argument."); return(1); } while ( *s ) { t = s; s = SkipAName(s); c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,t,&numfun,WITHAUTO) ) != CFUNCTION ) && type != CDUBIOUS ) { nofunc: MesPrint("&%s is not a table",t); error = 4; if ( type < 0 ) numfun = AddFunction(t,0,0,0,0,0,-1,-1); *s = c; if ( *s == ',' ) s++; continue; } /* else if ( ( ( T = functions[numfun].tabl ) == 0 ) || ( T->sparse == 0 ) ) goto nofunc; */ else if ( ( T = functions[numfun].tabl ) == 0 ) goto nofunc; numfun += FUNCTION; *s = c; if ( *s == ',' ) s++; /* Now we clear the table. */ if ( T->sparse ) { if ( T->boomlijst ) M_free(T->boomlijst,"TableTree"); for (j = 0; j < T->buffersfill; j++ ) { /* was <= */ finishcbuf(T->buffers[j]); } if ( T->buffers ) M_free(T->buffers,"Table buffers"); finishcbuf(T->bufnum); T->boomlijst = 0; T->numtree = 0; T->rootnum = 0; T->MaxTreeSize = 0; T->boomlijst = 0; T->bufnum = inicbufs(); T->bufferssize = 8; T->buffers = (WORD *)Malloc1(sizeof(WORD)*T->bufferssize,"Table buffers"); T->buffersfill = 0; T->buffers[T->buffersfill++] = T->bufnum; T->totind = 0; /* At the moment there are this many */ T->reserved = 0; ClearTableTree(T); if ( T->spare ) { if ( T->tablepointers ) M_free(T->tablepointers,"tablepointers"); T->tablepointers = 0; TT = T->spare; if ( TT->tablepointers ) M_free(TT->tablepointers,"tablepointers"); for (j = 0; j < TT->buffersfill; j++ ) { finishcbuf(TT->buffers[j]); } if ( TT->boomlijst ) M_free(TT->boomlijst,"TableTree"); if ( TT->buffers )M_free(TT->buffers,"Table buffers"); if ( TT->mm ) M_free(TT->mm,"tableminmax"); if ( TT->flags ) M_free(TT->flags,"tableflags"); M_free(TT,"table"); SpareTable(T); } } else EmptyTable(T); } return(error); } /* #] CoClearTable : #[ CoDenominators : */ int CoDenominators(UBYTE *s) { WORD numfun; int type; UBYTE *t = SkipAName(s), *t1; if ( t == 0 ) goto syntaxerror; t1 = t; while ( *t1 == ',' || *t1 == ' ' || *t1 == '\t' ) t1++; if ( *t1 ) goto syntaxerror; *t = 0; if ( ( ( type = GetName(AC.varnames,s,&numfun,WITHAUTO) ) != CFUNCTION ) || ( functions[numfun].spec != 0 ) ) { if ( type < 0 ) { if ( GetName(AC.exprnames,s,&numfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } goto syntaxerror; } Add3Com(TYPEDENOMINATORS,numfun+FUNCTION); return(0); syntaxerror: MesPrint("&Denominators statement needs one regular function for its argument"); return(1); } /* #] CoDenominators : #[ CoDropCoefficient : */ int CoDropCoefficient(UBYTE *s) { if ( *s == 0 ) { Add2Com(TYPEDROPCOEFFICIENT) return(0); } MesPrint("&Illegal argument in DropCoefficient statement: '%s'",s); return(1); } /* #] CoDropCoefficient : #[ CoDropSymbols : */ int CoDropSymbols(UBYTE *s) { if ( *s == 0 ) { Add2Com(TYPEDROPSYMBOLS) return(0); } MesPrint("&Illegal argument in DropSymbols statement: '%s'",s); return(1); } /* #] CoDropSymbols : #[ CoToPolynomial : Converts the current term as much as possible to symbols. Keeps a list of all objects converted to symbols in AM.sbufnum. Note that this cannot be executed in parallel because we have only a single compiler buffer for this. Hence we switch on the noparallel module option. Option(s): OnlyFunctions [,name1][,name2][,...,namem]; */ int CoToPolynomial(UBYTE *inp) { int error = 0; while ( *inp == ' ' || *inp == ',' || *inp == '\t' ) inp++; if ( ( AC.topolynomialflag & ~TOPOLYNOMIALFLAG ) != 0 ) { MesPrint("&ToPolynomial statement and FactArg statement are not allowed in the same module"); return(1); } if ( AO.OptimizeResult.code != NULL ) { MesPrint("&Using ToPolynomial statement when there are still optimization results active."); MesPrint("&Please use #ClearOptimize instruction first."); MesPrint("&This will loose the optimized expression."); return(1); } if ( *inp == 0 ) { Add3Com(TYPETOPOLYNOMIAL,DOALL) } else { int numargs = 0; WORD *funnums = 0, type, num; UBYTE *s, c; s = SkipAName(inp); if ( s == 0 ) return(1); c = *s; *s = 0; if ( StrICmp(inp,(UBYTE *)"onlyfunctions") ) { MesPrint("&Illegal option %s in ToPolynomial statement",inp); *s = c; return(1); } *s = c; inp = s; while ( *inp == ' ' || *inp == ',' || *inp == '\t' ) inp++; s = inp; while ( *s ) s++; /* Get definitely enough space for the numbers of the functions */ funnums = (WORD *)Malloc1(((LONG)(s-inp)+3)*sizeof(WORD),"ToPlynomial"); while ( *inp ) { s = SkipAName(inp); if ( s == 0 ) return(1); c = *s; *s = 0; type = GetName(AC.varnames,inp,&num,WITHAUTO); if ( type != CFUNCTION ) { MesPrint("&%s is not a function in ToPolynomial statement",inp); error = 1; } funnums[3+numargs++] = num+FUNCTION; *s = c; inp = s; while ( *inp == ' ' || *inp == ',' || *inp == '\t' ) inp++; } funnums[0] = TYPETOPOLYNOMIAL; funnums[1] = numargs+3; funnums[2] = ONLYFUNCTIONS; AddNtoL(numargs+3,funnums); if ( funnums ) M_free(funnums,"ToPolynomial"); } AC.topolynomialflag |= TOPOLYNOMIALFLAG; #ifdef WITHMPI /* In ParFORM, ToPolynomial has to be executed on the master. */ AC.mparallelflag |= NOPARALLEL_CONVPOLY; #endif return(error); } /* #] CoToPolynomial : #[ CoFromPolynomial : Converts the current term as much as possible back from extra symbols to their original values. Does not look inside functions. */ int CoFromPolynomial(UBYTE *inp) { while ( *inp == ' ' || *inp == ',' || *inp == '\t' ) inp++; if ( *inp == 0 ) { if ( AO.OptimizeResult.code != NULL ) { MesPrint("&Using FromPolynomial statement when there are still optimization results active."); MesPrint("&Please use #ClearOptimize instruction first."); MesPrint("&This will loose the optimized expression."); return(1); } Add2Com(TYPEFROMPOLYNOMIAL) return(0); } MesPrint("&Illegal argument in FromPolynomial statement: '%s'",inp); return(1); } /* #] CoFromPolynomial : #[ CoArgToExtraSymbol : Converts the specified function arguments into extra symbols. Syntax: ArgToExtraSymbol [ToNumber] [] */ int CoArgToExtraSymbol(UBYTE *s) { CBUF *C = cbuf + AC.cbufnum; WORD *lhs; /* TODO: resolve interference with rational arithmetic. (#138) */ if ( ( AC.topolynomialflag & ~TOPOLYNOMIALFLAG ) != 0 ) { MesPrint("&ArgToExtraSymbol statement and FactArg statement are not allowed in the same module"); return(1); } if ( AO.OptimizeResult.code != NULL ) { MesPrint("&Using ArgToExtraSymbol statement when there are still optimization results active."); MesPrint("&Please use #ClearOptimize instruction first."); MesPrint("&This will loose the optimized expression."); return(1); } SkipSpaces(&s); int tonumber = ConsumeOption(&s, "tonumber"); int ret = DoArgument(s,TYPEARGTOEXTRASYMBOL); if ( ret ) return(ret); /* * The "scale" parameter is unused. Instead, we put the "tonumber" * parameter. */ lhs = C->lhs[C->numlhs]; if ( lhs[4] != 1 ) { Warning("scale parameter (^n) is ignored in ArgToExtraSymbol"); } lhs[4] = tonumber; AC.topolynomialflag |= TOPOLYNOMIALFLAG; /* This flag is also used in ParFORM. */ #ifdef WITHMPI /* * In ParFORM, the conversion to extra symbols has to be performed on * the master. */ AC.mparallelflag |= NOPARALLEL_CONVPOLY; #endif return(0); } /* #] CoArgToExtraSymbol : #[ CoExtraSymbols : */ int CoExtraSymbols(UBYTE *inp) { UBYTE *arg1, *arg2, c, *s; WORD i, j, type, number; while ( *inp == ' ' || *inp == ',' || *inp == '\t' ) inp++; if ( FG.cTable[*inp] != 0 ) { MesPrint("&Illegal argument in ExtraSymbols statement: '%s'",inp); return(1); } arg1 = inp; while ( FG.cTable[*inp] == 0 ) inp++; c = *inp; *inp = 0; if ( ( StrICmp(arg1,(UBYTE *)"array") == 0 ) || ( StrICmp(arg1,(UBYTE *)"vector") == 0 ) ) { AC.extrasymbols = 1; } else if ( StrICmp(arg1,(UBYTE *)"underscore") == 0 ) { AC.extrasymbols = 0; } /* else if ( StrICmp(arg1,(UBYTE *)"nothing") == 0 ) { AC.extrasymbols = 2; } */ else { MesPrint("&Illegal keyword in ExtraSymbols statement: '%s'",arg1); return(1); } *inp = c; while ( *inp == ' ' || *inp == ',' || *inp == '\t' ) inp++; if ( FG.cTable[*inp] != 0 ) { MesPrint("&Illegal argument in ExtraSymbols statement: '%s'",inp); return(1); } arg2 = inp; while ( FG.cTable[*inp] <= 1 ) inp++; if ( *inp != 0 ) { MesPrint("&Illegal end of ExtraSymbols statement: '%s'",inp); return(1); } /* Now check whether this object has been declared already. That would not be allowed. */ if ( AC.extrasymbols == 1 ) { type = GetName(AC.varnames,arg2,&number,NOAUTO); if ( type != NAMENOTFOUND ) { MesPrint("&ExtraSymbols statement: '%s' has already been declared before",arg2); return(1); } } else if ( AC.extrasymbols == 0 ) { if ( *arg2 == 'N' ) { s = arg2+1; while ( FG.cTable[*s] == 1 ) s++; if ( *s == 0 ) { MesPrint("&ExtraSymbols statement: '%s' creates conflicts with summed indices",arg2); return(1); } } } if ( AC.extrasym ) { M_free(AC.extrasym,"extrasym"); AC.extrasym = 0; } i = inp - arg2 + 1; AC.extrasym = (UBYTE *)Malloc1(i*sizeof(UBYTE),"extrasym"); for ( j = 0; j < i; j++ ) AC.extrasym[j] = arg2[j]; return(0); } /* #] CoExtraSymbols : #[ GetIfDollarFactor : */ WORD *GetIfDollarFactor(UBYTE **inp, WORD *w) { LONG x; WORD number; UBYTE *name, c, *s; s = *inp; if ( FG.cTable[*s] == 1 ) { x = 0; while ( FG.cTable[*s] == 1 ) { x = 10*x + *s++ - '0'; if ( x >= MAXPOSITIVE ) { MesPrint("&Value in dollar factor too large"); while ( FG.cTable[*s] == 1 ) s++; *inp = s; return(0); } } *w++ = IFDOLLAREXTRA; *w++ = 3; *w++ = -x-1; *inp = s; return(w); } if ( *s != '$' ) { MesPrint("&Factor indicator for $-variable should be a number or a $-variable."); return(0); } s++; name = s; while ( FG.cTable[*s] < 2 ) s++; c = *s; *s = 0; if ( GetName(AC.dollarnames,name,&number,NOAUTO) == NAMENOTFOUND ) { MesPrint("&dollar in if statement should have been defined previously"); return(0); } *s = c; *w++ = IFDOLLAREXTRA; *w++ = 3; *w++ = number; if ( c == '[' ) { s++; *inp = s; if ( ( w = GetIfDollarFactor(inp,w) ) == 0 ) return(0); s = *inp; if ( *s != ']' ) { MesPrint("&unmatched [] in $ in if statement"); return(0); } s++; *inp = s; } return(w); } /* #] GetIfDollarFactor : #[ GetDoParam : */ UBYTE *GetDoParam(UBYTE *inp, WORD **wp, int par) { LONG x; WORD number; UBYTE *name, c; if ( FG.cTable[*inp] == 1 ) { x = 0; while ( *inp >= '0' && *inp <= '9' ) { x = 10*x + *inp++ - '0'; if ( x > MAXPOSITIVE ) { if ( par == -1 ) { MesPrint("&Value in dollar factor too large"); } else { MesPrint("&Value in do loop boundaries too large"); } while ( FG.cTable[*inp] == 1 ) inp++; return(0); } } if ( par > 0 ) { *(*wp)++ = SNUMBER; *(*wp)++ = (WORD)x; } else { *(*wp)++ = DOLLAREXPR2; *(*wp)++ = -((WORD)x)-1; } return(inp); } if ( *inp != '$' ) { return(0); } inp++; name = inp; while ( FG.cTable[*inp] < 2 ) inp++; c = *inp; *inp = 0; if ( GetName(AC.dollarnames,name,&number,NOAUTO) == NAMENOTFOUND ) { if ( par == -1 ) { MesPrint("&dollar in print statement should have been defined previously"); } else { MesPrint("&dollar in do loop boundaries should have been defined previously"); } return(0); } *inp = c; if ( par > 0 ) { *(*wp)++ = DOLLAREXPRESSION; *(*wp)++ = number; } else { *(*wp)++ = DOLLAREXPR2; *(*wp)++ = number; } if ( c == '[' ) { inp++; inp = GetDoParam(inp,wp,0); if ( inp == 0 ) return(0); if ( *inp != ']' ) { if ( par == -1 ) { MesPrint("&unmatched [] in $ in print statement"); } else { MesPrint("&unmatched [] in do loop boundaries"); } return(0); } inp++; } return(inp); } /* #] GetDoParam : #[ CoDo : */ int CoDo(UBYTE *inp) { GETIDENTITY CBUF *C = cbuf+AC.cbufnum; WORD *w, numparam; int error = 0, i; UBYTE *name, c; if ( AC.doloopstack == 0 ) { AC.doloopstacksize = 20; AC.doloopstack = (WORD *)Malloc1(AC.doloopstacksize*2*sizeof(WORD),"doloop stack"); AC.doloopnest = AC.doloopstack + AC.doloopstacksize; } if ( AC.dolooplevel >= AC.doloopstacksize ) { WORD *newstack, *newnest, newsize; newsize = AC.doloopstacksize * 2; newstack = (WORD *)Malloc1(newsize*2*sizeof(WORD),"doloop stack"); newnest = newstack + newsize; for ( i = 0; i < newsize; i++ ) { newstack[i] = AC.doloopstack[i]; newnest[i] = AC.doloopnest[i]; } M_free(AC.doloopstack,"doloop stack"); AC.doloopstack = newstack; AC.doloopnest = newnest; AC.doloopstacksize = newsize; } AC.doloopnest[AC.dolooplevel] = NestingChecksum(); w = AT.WorkPointer; *w++ = TYPEDOLOOP; w++; /* Space for the length of the statement */ /* Now the $loopvariable */ while ( *inp == ',' ) inp++; if ( *inp != '$' ) { error = 1; MesPrint("&do loop parameter should be a dollar variable"); } else { inp++; name = inp; if ( FG.cTable[*inp] != 0 ) { error = 1; MesPrint("&illegal name for do loop parameter"); } while ( FG.cTable[*inp] < 2 ) inp++; c = *inp; *inp = 0; if ( GetName(AC.dollarnames,name,&numparam,NOAUTO) == NAMENOTFOUND ) { numparam = AddDollar(name,DOLUNDEFINED,0,0); } *w++ = numparam; *inp = c; AddPotModdollar(numparam); } w++; /* space for the level of the enddo statement */ while ( *inp == ',' ) inp++; if ( *inp != '=' ) goto IllSyntax; inp++; while ( *inp == ',' ) inp++; /* The start value */ inp = GetDoParam(inp,&w,1); if ( inp == 0 || *inp != ',' ) goto IllSyntax; while ( *inp == ',' ) inp++; /* The end value */ inp = GetDoParam(inp,&w,1); if ( inp == 0 || ( *inp != 0 && *inp != ',' ) ) goto IllSyntax; /* The increment value */ if ( *inp != ',' ) { if ( *inp == 0 ) { *w++ = SNUMBER; *w++ = 1; } else goto IllSyntax; } else { while ( *inp == ',' ) inp++; inp = GetDoParam(inp,&w,1); } if ( inp == 0 || *inp != 0 ) goto IllSyntax; *w = 0; AT.WorkPointer[1] = w - AT.WorkPointer; /* Put away and set information for placing enddo information. */ AddNtoL(AT.WorkPointer[1],AT.WorkPointer); AC.doloopstack[AC.dolooplevel++] = C->numlhs; return(error); IllSyntax: MesPrint("&Illegal syntax for do statement"); return(1); } /* #] CoDo : #[ CoEndDo : */ int CoEndDo(UBYTE *inp) { CBUF *C = cbuf+AC.cbufnum; WORD scratch[3]; while ( *inp == ',' ) inp++; if ( *inp ) { MesPrint("&Illegal syntax for EndDo statement"); return(1); } if ( AC.dolooplevel <= 0 ) { MesPrint("&EndDo without corresponding Do statement"); return(1); } AC.dolooplevel--; scratch[0] = TYPEENDDOLOOP; scratch[1] = 3; scratch[2] = AC.doloopstack[AC.dolooplevel]; AddNtoL(3,scratch); cbuf[AC.cbufnum].lhs[AC.doloopstack[AC.dolooplevel]][3] = C->numlhs; if ( AC.doloopnest[AC.dolooplevel] != NestingChecksum() ) { MesNesting(); return(1); } return(0); } /* #] CoEndDo : #[ CoFactDollar : */ int CoFactDollar(UBYTE *inp) { WORD numdollar; if ( *inp == '$' ) { if ( GetName(AC.dollarnames,inp+1,&numdollar,NOAUTO) != CDOLLAR ) { MesPrint("&%s is undefined",inp); numdollar = AddDollar(inp+1,DOLINDEX,&one,1); return(1); } inp = SkipAName(inp+1); if ( *inp != 0 ) { MesPrint("&FactDollar should have a single $variable for its argument"); return(1); } AddPotModdollar(numdollar); } else { MesPrint("&%s is not a $-variable",inp); return(1); } Add3Com(TYPEFACTOR,numdollar); return(0); } /* #] CoFactDollar : #[ CoFactorize : */ int CoFactorize(UBYTE *s) { return(DoFactorize(s,1)); } /* #] CoFactorize : #[ CoNFactorize : */ int CoNFactorize(UBYTE *s) { return(DoFactorize(s,0)); } /* #] CoNFactorize : #[ CoUnFactorize : */ int CoUnFactorize(UBYTE *s) { return(DoFactorize(s,3)); } /* #] CoUnFactorize : #[ CoNUnFactorize : */ int CoNUnFactorize(UBYTE *s) { return(DoFactorize(s,2)); } /* #] CoNUnFactorize : #[ DoFactorize : */ int DoFactorize(UBYTE *s,int par) { EXPRESSIONS e; WORD i; WORD number; UBYTE *t, c; int error = 0, keepzeroflag = 0; if ( *s == '(' ) { s++; while ( *s != ')' && *s ) { if ( FG.cTable[*s] == 0 ) { t = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp((UBYTE *)"keepzero",t) == 0 ) { keepzeroflag = 1; } else { MesPrint("&Illegal option in [N][Un]Factorize statement: %s",t); error = 1; } *s = c; } while ( *s == ',' ) s++; if ( *s && *s != ')' && FG.cTable[*s] != 0 ) { MesPrint("&Illegal character in option field of [N][Un]Factorize statement"); error = 1; return(error); } } if ( *s ) s++; while ( *s == ',' || *s == ' ' ) s++; } if ( *s == 0 ) { for ( i = NumExpressions-1; i >= 0; i-- ) { e = Expressions+i; if ( e->replace >= 0 ) { e = Expressions + e->replace; } if ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION || e->status == INTOHIDELEXPRESSION || e->status == INTOHIDEGEXPRESSION ) { switch ( par ) { case 0: e->vflags &= ~TOBEFACTORED; break; case 1: e->vflags |= TOBEFACTORED; e->vflags &= ~TOBEUNFACTORED; break; case 2: e->vflags &= ~TOBEUNFACTORED; break; case 3: e->vflags |= TOBEUNFACTORED; e->vflags &= ~TOBEFACTORED; break; } } if ( ( e->vflags & TOBEFACTORED ) != 0 ) { if ( keepzeroflag ) e->vflags |= KEEPZERO; else e->vflags &= ~KEEPZERO; } else e->vflags &= ~KEEPZERO; } } else { for(;;) { /* Look for a (comma separated) list of variables */ while ( *s == ',' ) s++; if ( *s == 0 ) break; if ( *s == '[' || FG.cTable[*s] == 0 ) { t = s; if ( ( s = SkipAName(s) ) == 0 ) { MesPrint("&Improper name for an expression: '%s'",t); return(1); } c = *s; *s = 0; if ( GetName(AC.exprnames,t,&number,NOAUTO) == CEXPRESSION ) { e = Expressions+number; if ( e->replace >= 0 ) { e = Expressions + e->replace; } if ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION || e->status == INTOHIDELEXPRESSION || e->status == INTOHIDEGEXPRESSION ) { switch ( par ) { case 0: e->vflags &= ~TOBEFACTORED; break; case 1: e->vflags |= TOBEFACTORED; e->vflags &= ~TOBEUNFACTORED; break; case 2: e->vflags &= ~TOBEUNFACTORED; break; case 3: e->vflags |= TOBEUNFACTORED; e->vflags &= ~TOBEFACTORED; break; } } if ( ( e->vflags & TOBEFACTORED ) != 0 ) { if ( keepzeroflag ) e->vflags |= KEEPZERO; else e->vflags &= ~KEEPZERO; } else e->vflags &= ~KEEPZERO; } else if ( GetName(AC.varnames,t,&number,NOAUTO) != NAMENOTFOUND ) { MesPrint("&%s is not an expression",t); error = 1; } *s = c; } else { MesPrint("&Illegal object in (N)Factorize statement"); error = 1; while ( *s && *s != ',' ) s++; if ( *s == 0 ) break; } } } return(error); } /* #] DoFactorize : #[ CoOptimizeOption : */ int CoOptimizeOption(UBYTE *s) { UBYTE *name, *t1, *t2, c1, c2, *value, *u; int error = 0, x; double d; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; while ( *s ) { name = s; while ( FG.cTable[*s] == 0 ) s++; t1 = s; c1 = *t1; while ( *s == ' ' || *s == '\t' ) s++; if ( *s != '=' ) { correctuse: MesPrint("&Correct use in Format,Optimize statement is Optionname=value"); error = 1; while ( *s == ' ' || *s == ',' || *s == '\t' || *s == '=' ) s++; *t1 = c1; continue; } *t1 = 0; s++; while ( *s == ' ' || *s == '\t' ) s++; if ( *s == 0 ) goto correctuse; value = s; while ( FG.cTable[*s] <= 1 || *s=='.' || *s=='*' || *s == '(' || *s == ')' ) { if ( *s == '(' ) { SKIPBRA4(s) } s++; } t2 = s; c2 = *t2; while ( *s == ' ' || *s == '\t' ) s++; if ( *s && *s != ',' ) goto correctuse; if ( *s ) { s++; while ( *s == ' ' || *s == '\t' ) s++; } *t2 = 0; /* Now we have name=value with name and value zero terminated strings. */ if ( StrICmp(name,(UBYTE *)"horner") == 0 ) { if ( StrICmp(value,(UBYTE *)"occurrence") == 0 ) { AO.Optimize.horner = O_OCCURRENCE; } else if ( StrICmp(value,(UBYTE *)"mcts") == 0 ) { AO.Optimize.horner = O_MCTS; } else if ( StrICmp(value,(UBYTE *)"sa") == 0 ) { AO.Optimize.horner = O_SIMULATED_ANNEALING; } else { AO.Optimize.horner = -1; MesPrint("&Unrecognized option value in Format,Optimize statement: %s=%s",name,value); error = 1; } } else if ( StrICmp(name,(UBYTE *)"hornerdirection") == 0 ) { if ( StrICmp(value,(UBYTE *)"forward") == 0 ) { AO.Optimize.hornerdirection = O_FORWARD; } else if ( StrICmp(value,(UBYTE *)"backward") == 0 ) { AO.Optimize.hornerdirection = O_BACKWARD; } else if ( StrICmp(value,(UBYTE *)"forwardorbackward") == 0 ) { AO.Optimize.hornerdirection = O_FORWARDORBACKWARD; } else if ( StrICmp(value,(UBYTE *)"forwardandbackward") == 0 ) { AO.Optimize.hornerdirection = O_FORWARDANDBACKWARD; } else { AO.Optimize.method = -1; MesPrint("&Unrecognized option value in Format,Optimize statement: %s=%s",name,value); error = 1; } } else if ( StrICmp(name,(UBYTE *)"method") == 0 ) { if ( StrICmp(value,(UBYTE *)"none") == 0 ) { AO.Optimize.method = O_NONE; } else if ( StrICmp(value,(UBYTE *)"cse") == 0 ) { AO.Optimize.method = O_CSE; } else if ( StrICmp(value,(UBYTE *)"csegreedy") == 0 ) { AO.Optimize.method = O_CSEGREEDY; } else if ( StrICmp(value,(UBYTE *)"greedy") == 0 ) { AO.Optimize.method = O_GREEDY; } else { AO.Optimize.method = -1; MesPrint("&Unrecognized option value in Format,Optimize statement: %s=%s",name,value); error = 1; } } else if ( StrICmp(name,(UBYTE *)"timelimit") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option TimeLimit in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.mctstimelimit = 0; AO.Optimize.greedytimelimit = 0; error = 1; } else { AO.Optimize.mctstimelimit = x/2; AO.Optimize.greedytimelimit = x/2; } } else if ( StrICmp(name,(UBYTE *)"mctstimelimit") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option MCTSTimeLimit in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.mctstimelimit = 0; error = 1; } else { AO.Optimize.mctstimelimit = x; } } else if ( StrICmp(name,(UBYTE *)"mctsnumexpand") == 0 ) { int y; x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u == '*' || *u == 'x' || *u == 'X' ) { u++; y = x; x = 0; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; } else { y = 1; } if ( *u != 0 ) { MesPrint("&Option MCTSNumExpand in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.mctsnumexpand= 0; AO.Optimize.mctsnumrepeat= 1; error = 1; } else { AO.Optimize.mctsnumexpand= x; AO.Optimize.mctsnumrepeat= y; } } else if ( StrICmp(name,(UBYTE *)"mctsnumrepeat") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option MCTSNumExpand in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.mctsnumrepeat= 1; error = 1; } else { AO.Optimize.mctsnumrepeat= x; } } else if ( StrICmp(name,(UBYTE *)"mctsnumkeep") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option MCTSNumKeep in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.mctsnumkeep= 0; error = 1; } else { AO.Optimize.mctsnumkeep= x; } } else if ( StrICmp(name,(UBYTE *)"mctsconstant") == 0 ) { d = 0; if ( sscanf ((char*)value, "%lf", &d) != 1 ) { MesPrint("&Option MCTSConstant in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.mctsconstant.fval = 0; error = 1; } else { AO.Optimize.mctsconstant.fval = d; } } else if ( StrICmp(name,(UBYTE *)"greedytimelimit") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option GreedyTimeLimit in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.greedytimelimit = 0; error = 1; } else { AO.Optimize.greedytimelimit = x; } } else if ( StrICmp(name,(UBYTE *)"greedyminnum") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option GreedyMinNum in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.greedyminnum= 0; error = 1; } else { AO.Optimize.greedyminnum= x; } } else if ( StrICmp(name,(UBYTE *)"greedymaxperc") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option GreedyMaxPerc in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.greedymaxperc= 0; error = 1; } else { AO.Optimize.greedymaxperc= x; } } else if ( StrICmp(name,(UBYTE *)"stats") == 0 ) { if ( StrICmp(value,(UBYTE *)"on") == 0 ) { AO.Optimize.printstats = 1; } else if ( StrICmp(value,(UBYTE *)"off") == 0 ) { AO.Optimize.printstats = 0; } else { AO.Optimize.printstats = 0; MesPrint("&Unrecognized option value in Format,Optimize statement: %s=%s",name,value); error = 1; } } else if ( StrICmp(name,(UBYTE *)"printscheme") == 0 ) { if ( StrICmp(value,(UBYTE *)"on") == 0 ) { AO.Optimize.schemeflags |= 1; } else if ( StrICmp(value,(UBYTE *)"off") == 0 ) { AO.Optimize.schemeflags &= ~1; } else { AO.Optimize.schemeflags &= ~1; MesPrint("&Unrecognized option value in Format,Optimize statement: %s=%s",name,value); error = 1; } } else if ( StrICmp(name,(UBYTE *)"debugflag") == 0 ) { /* This option is for debugging purposes only. Not in the manual! 0x1: Print statements in reverse order. 0x2: Print the scheme of the variables. */ x = 0; u = value; if ( FG.cTable[*u] == 1 ) { while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Numerical value for DebugFlag in Format,Optimize statement should be a nonnegative number: %s",value); AO.Optimize.debugflags = 0; error = 1; } else { AO.Optimize.debugflags = x; } } else if ( StrICmp(value,(UBYTE *)"on") == 0 ) { AO.Optimize.debugflags = 1; } else if ( StrICmp(value,(UBYTE *)"off") == 0 ) { AO.Optimize.debugflags = 0; } else { AO.Optimize.debugflags = 0; MesPrint("&Unrecognized option value in Format,Optimize statement: %s=%s",name,value); error = 1; } } else if ( StrICmp(name,(UBYTE *)"scheme") == 0 ) { UBYTE *ss, *s1, c; WORD type, numsym; AO.schemenum = 0; u = value; if ( *u != '(' ) { noscheme: MesPrint("&Option Scheme in Format,Optimize statement should be an array of names or integers between (): %s",value); error = 1; break; } u++; ss = u; while ( *ss == ' ' || *ss == '\t' || *ss == ',' ) ss++; if ( FG.cTable[*ss] == 0 || *ss == '$' || *ss == '[' ) { /* Name */ s1 = u; SKIPBRA3(s1) if ( *s1 != ')' ) goto noscheme; while ( ss < s1 ) { if ( *ss++ == ',' ) AO.schemenum++; } *ss++ = 0; while ( *ss == ' ' ) ss++; if ( *ss != 0 ) goto noscheme; ss = u; if ( AO.schemenum < 1 ) { MesPrint("&Option Scheme in Format,Optimize statement should have at least one name or number between ()"); error = 1; break; } if ( AO.inscheme ) M_free(AO.inscheme,"Horner input scheme"); AO.inscheme = (WORD *)Malloc1((AO.schemenum+1)*sizeof(WORD),"Horner input scheme"); while ( *ss == ' ' || *ss == '\t' || *ss == ',' ) ss++; AO.schemenum = 0; for(;;) { if ( *ss == 0 ) break; s1 = ss; ss = SkipAName(s1); c = *ss; *ss = 0; if ( ss[-1] == '_' ) { /* Now AC.extrasym followed by a number and _ */ UBYTE *u1, *u2; u1 = s1; u2 = AC.extrasym; while ( *u1 == *u2 ) { u1++; u2++; } if ( *u2 == 0 ) { /* Good start */ numsym = 0; while ( *u1 >= '0' && *u1 <= '9' ) numsym = 10*numsym + *u1++ - '0'; if ( u1 != ss-1 || numsym == 0 || AC.extrasymbols != 0 ) { MesPrint("&Improper use of extra symbol in scheme format option"); goto noscheme; } numsym = MAXVARIABLES-numsym; ss++; goto GotTheNumber; } } else if ( *s1 == '$' ) { GETIDENTITY int numdollar; if ( ( numdollar = GetDollar(s1+1) ) < 0 ) { MesPrint("&Undefined variable %s",s1); error = 5; } else if ( ( numsym = DolToSymbol(BHEAD numdollar) ) < 0 ) { MesPrint("&$%s does not evaluate to a symbol",s1); error = 5; } *ss = c; goto GotTheNumber; } else if ( c == '(' ) { if ( StrCmp(s1,AC.extrasym) == 0 ) { if ( (AC.extrasymbols&1) != 1 ) { MesPrint("&Improper use of extra symbol in scheme format option"); goto noscheme; } *ss++ = c; numsym = 0; while ( *ss >= '0' && *ss <= '9' ) numsym = 10*numsym + *ss++ - '0'; if ( *ss != ')' ) { MesPrint("&Extra symbol should have a number for its argument."); goto noscheme; } numsym = MAXVARIABLES-numsym; ss++; goto GotTheNumber; } } type = GetName(AC.varnames,s1,&numsym,WITHAUTO); if ( ( type != CSYMBOL ) && type != CDUBIOUS ) { MesPrint("&%s is not a symbol",s1); error = 4; if ( type < 0 ) numsym = AddSymbol(s1,-MAXPOWER,MAXPOWER,0,0); } *ss = c; GotTheNumber: AO.inscheme[AO.schemenum++] = numsym; while ( *ss == ' ' || *ss == '\t' || *ss == ',' ) ss++; } } } else if ( StrICmp(name,(UBYTE *)"mctsdecaymode") == 0 ) { x = 0; u = value; if ( FG.cTable[*u] == 1 ) { while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option MCTSDecayMode in Format,Optimize statement should be a nonnegative integer: %s",value); AO.Optimize.mctsdecaymode = 0; error = 1; } else { AO.Optimize.mctsdecaymode = x; } } else { AO.Optimize.mctsdecaymode = 0; MesPrint("&Unrecognized option value in Format,Optimize statement: %s=%s",name,value); error = 1; } } else if ( StrICmp(name,(UBYTE *)"saiter") == 0 ) { x = 0; u = value; while ( *u >= '0' && *u <= '9' ) x = 10*x + *u++ - '0'; if ( *u != 0 ) { MesPrint("&Option SAIter in Format,Optimize statement should be a positive integer: %s",value); AO.Optimize.saIter = 0; error = 1; } else { AO.Optimize.saIter= x; } } else if ( StrICmp(name,(UBYTE *)"samaxt") == 0 ) { d = 0; if ( sscanf ((char*)value, "%lf", &d) != 1 ) { MesPrint("&Option SAMaxT in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.saMaxT.fval = 0; error = 1; } else { AO.Optimize.saMaxT.fval = d; } } else if ( StrICmp(name,(UBYTE *)"samint") == 0 ) { d = 0; if ( sscanf ((char*)value, "%lf", &d) != 1 ) { MesPrint("&Option SAMinT in Format,Optimize statement should be a positive number: %s",value); AO.Optimize.saMinT.fval = 0; error = 1; } else { AO.Optimize.saMinT.fval = d; } } else { MesPrint("&Unrecognized option name in Format,Optimize statement: %s",name); error = 1; } *t1 = c1; *t2 = c2; } return(error); } /* #] CoOptimizeOption : #[ DoPutInside : Syntax: PutIn[side],functionname[,brackets] -> par = 1 AntiPutIn[side],functionname,antibrackets -> par = -1 */ int CoPutInside(UBYTE *inp) { return(DoPutInside(inp,1)); } int CoAntiPutInside(UBYTE *inp) { return(DoPutInside(inp,-1)); } int DoPutInside(UBYTE *inp, int par) { GETIDENTITY UBYTE *p, c; WORD *to, type, c1,c2,funnum, *WorkSave; int error = 0; while ( *inp == ' ' || *inp == '\t' || *inp == ',' ) inp++; /* First we need the name of a function. (Not a tensor or table!) */ p = SkipAName(inp); if ( p == 0 ) return(1); c = *p; *p = 0; type = GetName(AC.varnames,inp,&funnum,WITHAUTO); if ( type != CFUNCTION || functions[funnum].tabl != 0 || functions[funnum].spec ) { MesPrint("&PutInside/AntiPutInside expects a regular function for its first argument"); MesPrint("&Argument is %s",inp); error = 1; } funnum += FUNCTION; *p = c; inp = p; while ( *inp == ' ' || *inp == '\t' || *inp == ',' ) inp++; if ( *inp == 0 ) { if ( par == 1 ) { WORD tocompiler[4]; tocompiler[0] = TYPEPUTINSIDE; tocompiler[1] = 4; tocompiler[2] = 0; tocompiler[3] = funnum; AddNtoL(4,tocompiler); } else { MesPrint("&AntiPutInside needs inside information."); error = 1; } return(error); } WorkSave = to = AT.WorkPointer; *to++ = TYPEPUTINSIDE; *to++ = 4; *to++ = par; *to++ = funnum; to++; while ( *inp ) { while ( *inp == ' ' || *inp == '\t' || *inp == ',' ) inp++; if ( *inp == 0 ) break; p = SkipAName(inp); if ( p == 0 ) { error = 1; break; } c = *p; *p = 0; type = GetName(AC.varnames,inp,&c1,WITHAUTO); if ( c == '.' ) { if ( type == CVECTOR || type == CDUBIOUS ) { *p++ = c; inp = p; p = SkipAName(inp); if ( p == 0 ) return(1); c = *p; *p = 0; type = GetName(AC.varnames,inp,&c2,WITHAUTO); if ( type != CVECTOR && type != CDUBIOUS ) { MesPrint("&Not a vector in dotproduct in PutInside/AntiPutInside statement: %s",inp); error = 1; } else type = CDOTPRODUCT; } else { MesPrint("&Illegal use of . after %s in PutInside/AntiPutInside statement",inp); error = 1; *p = c; inp = p; continue; } } switch ( type ) { case CSYMBOL : *to++ = SYMBOL; *to++ = 4; *to++ = c1; *to++ = 1; break; case CVECTOR : *to++ = INDEX; *to++ = 3; *to++ = AM.OffsetVector + c1; break; case CFUNCTION : *to++ = c1+FUNCTION; *to++ = FUNHEAD; *to++ = 0; FILLFUN3(to) break; case CDOTPRODUCT : *to++ = DOTPRODUCT; *to++ = 5; *to++ = c1 + AM.OffsetVector; *to++ = c2 + AM.OffsetVector; *to++ = 1; break; case CDELTA : *to++ = DELTA; *to++ = 4; *to++ = EMPTYINDEX; *to++ = EMPTYINDEX; break; default : MesPrint("&Illegal variable request for %s in PutInside/AntiPutInside statement",inp); error = 1; break; } *p = c; inp = p; } *to++ = 1; *to++ = 1; *to++ = 3; AT.WorkPointer[1] = to - AT.WorkPointer; AT.WorkPointer[4] = AT.WorkPointer[1]-4; AT.WorkPointer = to; AC.BracketNormalize = 1; if ( Normalize(BHEAD WorkSave+4) ) { error = 1; } else { WorkSave[1] = WorkSave[4]+4; to = WorkSave + WorkSave[1] - 1; c1 = ABS(*to); WorkSave[1] -= c1; WorkSave[4] -= c1; AddNtoL(WorkSave[1],WorkSave); } AC.BracketNormalize = 0; AT.WorkPointer = WorkSave; return(error); } /* #] DoPutInside : #[ CoSwitch : Syntax: Switch $var; Be careful with illegal nestings with repeat, if, while. */ int CoSwitch(UBYTE *s) { WORD numdollar; SWITCH *sw; if ( *s == '$' ) { if ( GetName(AC.dollarnames,s+1,&numdollar,NOAUTO) != CDOLLAR ) { MesPrint("&%s is undefined in switch statement",s); numdollar = AddDollar(s+1,DOLINDEX,&one,1); return(1); } s = SkipAName(s+1); if ( *s != 0 ) { MesPrint("&Switch should have a single $variable for its argument"); return(1); } /* AddPotModdollar(numdollar); */ } else { MesPrint("&%s is not a $-variable in switch statement",s); return(1); } /* Now create the switch table. We will add to it each time we run into a new case. It will all be sorted out the moment we run into the endswitch statement. */ AC.SwitchLevel++; if ( AC.SwitchInArray >= AC.MaxSwitch ) DoubleSwitchBuffers(); AC.SwitchHeap[AC.SwitchLevel] = AC.SwitchInArray; sw = AC.SwitchArray + AC.SwitchInArray; sw->iflevel = AC.IfLevel; sw->whilelevel = AC.WhileLevel; sw->nestingsum = NestingChecksum(); Add4Com(TYPESWITCH,numdollar,AC.SwitchInArray); AC.SwitchInArray++; return(0); } /* #] CoSwitch : #[ CoCase : */ int CoCase(UBYTE *s) { SWITCH *sw = AC.SwitchArray + AC.SwitchHeap[AC.SwitchLevel]; WORD x = 0, sign = 1; while ( *s == ',' ) s++; SKIPBLANKS(s); while ( *s == '-' || *s == '+' ) { if ( *s == '-' ) sign = -sign; s++; } while ( FG.cTable[*s] == 1 ) { x = 10*x + *s++ - '0'; } x = sign*x; if ( sw->iflevel != AC.IfLevel || sw->whilelevel != AC.WhileLevel || sw->nestingsum != NestingChecksum() ) { MesPrint("&Illegal nesting of switch/case/default with if/while/repeat/loop/argument/term/..."); return(-1); } /* Now add a case to the table with the current 'address'. */ if ( sw->numcases >= sw->tablesize ) { int i; SWITCHTABLE *newtable; WORD newsize; if ( sw->tablesize == 0 ) newsize = 10; else newsize = 2*sw->tablesize; newtable = (SWITCHTABLE *)Malloc1(newsize*sizeof(SWITCHTABLE),"Switch table"); if ( sw->table ) { for ( i = 0; i < sw->tablesize; i++ ) newtable[i] = sw->table[i]; M_free(sw->table,"Switch table"); } sw->table = newtable; sw->tablesize = newsize; } if ( sw->numcases == 0 ) { sw->mincase = sw->maxcase = x; } else if ( x > sw->maxcase ) sw->maxcase = x; else if ( x < sw->mincase ) sw->mincase = x; sw->table[sw->numcases].ncase = x; sw->table[sw->numcases].value = cbuf[AC.cbufnum].numlhs; sw->table[sw->numcases].compbuffer = AC.cbufnum; sw->numcases++; return(0); } /* #] CoCase : #[ CoBreak : */ int CoBreak(UBYTE *s) { /* This involves a 'postponed' jump to the end. This can be done in a special routine during execution. That routine should also pop the switch level. */ SWITCH *sw = AC.SwitchArray + AC.SwitchHeap[AC.SwitchLevel]; if ( sw->iflevel != AC.IfLevel || sw->whilelevel != AC.WhileLevel || sw->nestingsum != NestingChecksum() ) { MesPrint("&Illegal nesting of switch/case/default with if/while/repeat/loop/argument/term/..."); return(-1); } if ( *s ) { MesPrint("&No parameters allowed in Break statement"); return(-1); } Add3Com(TYPEENDSWITCH,AC.SwitchHeap[AC.SwitchLevel]); return(0); } /* #] CoBreak : #[ CoDefault : */ int CoDefault(UBYTE *s) { /* A bit like case, except that the address gets stored directly in the SWITCH struct. */ SWITCH *sw = AC.SwitchArray + AC.SwitchHeap[AC.SwitchLevel]; if ( sw->iflevel != AC.IfLevel || sw->whilelevel != AC.WhileLevel || sw->nestingsum != NestingChecksum() ) { MesPrint("&Illegal nesting of switch/case/default with if/while/repeat/loop/argument/term/..."); return(-1); } if ( *s ) { MesPrint("&No parameters allowed in Default statement"); return(-1); } sw->defaultcase.ncase = 0; sw->defaultcase.value = cbuf[AC.cbufnum].numlhs; sw->defaultcase.compbuffer = AC.cbufnum; return(0); } /* #] CoDefault : #[ CoEndSwitch : */ int CoEndSwitch(UBYTE *s) { /* We store this address in the SWITCH struct. Next we sort the table by ncase. Then we decide whether the table is DENSE or SPARSE. If it is dense we change the allocation and spread the cases is necessary. Finally we pop levels. */ SWITCH *sw = AC.SwitchArray + AC.SwitchHeap[AC.SwitchLevel]; WORD i; WORD totcases = sw->maxcase-sw->mincase+1; while ( *s == ',' ) s++; SKIPBLANKS(s) if ( *s ) { MesPrint("&No parameters allowed in EndSwitch statement"); return(-1); } if ( sw->iflevel != AC.IfLevel || sw->whilelevel != AC.WhileLevel || sw->nestingsum != NestingChecksum() ) { MesPrint("&Illegal nesting of switch/case/default with if/while/repeat/loop/argument/term/..."); return(-1); } if ( sw->defaultcase.value == 0 ) CoDefault(s); if ( totcases > sw->numcases*AM.jumpratio ) { /* The factor is experimental */ sw->caseoffset = 0; sw->typetable = SPARSETABLE; /* Now we need to sort sw->table */ SwitchSplitMerge(sw->table,sw->numcases); } else { /* DENSE */ SWITCHTABLE *ntable; sw->caseoffset = sw->mincase; sw->typetable = DENSETABLE; ntable = (SWITCHTABLE *)Malloc1(totcases*sizeof(SWITCHTABLE),"Switch table"); for ( i = 0; i < totcases; i++ ) { ntable[i].ncase = i+sw->caseoffset; ntable[i].value = sw->defaultcase.value; ntable[i].compbuffer = sw->defaultcase.compbuffer; } for ( i = 0; i < sw->numcases; i++ ) { ntable[sw->table[i].ncase-sw->caseoffset] = sw->table[i]; } M_free(sw->table,"Switch table"); sw->table = ntable; sw->numcases = totcases; } sw->endswitch.ncase = 0; sw->endswitch.value = cbuf[AC.cbufnum].numlhs; sw->endswitch.compbuffer = AC.cbufnum; if ( sw->defaultcase.value == 0 ) { sw->defaultcase = sw->endswitch; } Add3Com(TYPEENDSWITCH,AC.SwitchHeap[AC.SwitchLevel]); /* Now we need to pop. */ AC.SwitchLevel--; return(0); } /* #] CoEndSwitch : #[ CoSetUserFlag : */ int CoSetUserFlag(UBYTE *s) { int error = 0; while ( *s && ( *s == ',' || *s == ' ' || *s == '\t' ) ) s++; while ( *s && ( FG.cTable[*s] == 1 ) ) { int x = 0; while ( *s && ( FG.cTable[*s] == 1 ) ) x = 10*x+(*s++ - '0'); if ( x < 1 || x > BITSINWORD ) { MesPrint("&Flag number %d outside the permitted range 1-%d.",BITSINWORD); error = 1; } else { Add3Com(TYPESETUSERFLAG,x-1); } while ( *s && ( *s == ',' || *s == ' ' || *s == '\t' ) ) s++; } if ( *s ) { MesPrint("&Illegal character in SetUserFlag statement: %s",s); error = 1; } return(error); } /* #] CoSetUserFlag : #[ CoClearUserFlag : */ int CoClearUserFlag(UBYTE *s) { int error = 0; while ( *s && ( *s == ',' || *s == ' ' || *s == '\t' ) ) s++; while ( *s && ( FG.cTable[*s] == 1 ) ) { int x = 0; while ( *s && ( FG.cTable[*s] == 1 ) ) x = 10*x+(*s++ - '0'); if ( x < 1 || x > BITSINWORD ) { MesPrint("&Flag number %d outside the permitted range 1-%d.",BITSINWORD); error = 1; } else { Add3Com(TYPECLEARUSERFLAG,x); } while ( *s && ( *s == ',' || *s == ' ' || *s == '\t' ) ) s++; } if ( *s ) { MesPrint("&Illegal character in SetUserFlag statement: %s",s); error = 1; } return(error); } /* #] CoClearUserFlag : #[ CoCreateAllLoops : Syntax: CoCreateAllLoops,in-function,out-function,type-argument,ifnoloop; Types allowed: vector, index, symbol, snumber ifnoloop: ifnoloop=0 or ifnoloop=1 in-function can be a tensor. In that case type can be only vector or index. out-function can be a tensor. In that case type can be only vector or index. */ int CoCreateAllLoops(UBYTE *s) { GETIDENTITY UBYTE *inname, *outname, *stype, c; WORD infun, outfun, x, type, tensorflag, typenum; WORD *WorkSave, *to; while ( *s == ',' || *s == ' ' ) s++; inname = s; s = SkipAName(s); c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,inname,&infun,WITHAUTO) ) != CFUNCTION ) || ( ( functions[infun].spec != 0 ) && ( functions[infun].spec != TENSORFUNCTION ) ) ) { MesPrint("&%s should be a regular function or a tensor.",inname); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&infun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } infun += FUNCTION; *s++ = c; while ( *s == ',' || *s == ' ' ) s++; outname = s; s = SkipAName(s); c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,outname,&outfun,WITHAUTO) ) != CFUNCTION ) || ( ( functions[outfun].spec != 0 ) && ( functions[outfun].spec != TENSORFUNCTION ) ) ) { MesPrint("&%s should be a regular function or a tensor.",outname); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&outfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } outfun += FUNCTION; *s++ = c; if ( functions[infun].spec == TENSORFUNCTION || functions[outfun].spec == TENSORFUNCTION ) tensorflag = 1; else tensorflag = 0; /* Now the type: type=.... */ while ( *s == ',' || *s == ' ' ) s++; stype = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(stype,(UBYTE *)"type") != 0 || c != '=' ) { MesPrint("&In CreateAllLoops statement: expected type=vartype."); return(1); } *s++ = c; stype = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(stype,(UBYTE *)"vector") == 0 ) { typenum = -VECTOR; } else if ( StrICmp(stype,(UBYTE *)"index") == 0 ) { typenum = -INDEX; } else if ( StrICmp(stype,(UBYTE *)"symbol") == 0 ) { if ( tensorflag ) goto notintensor; typenum = -SYMBOL; } else if ( StrICmp(stype,(UBYTE *)"snumber") == 0 ) { if ( tensorflag ) goto notintensor; typenum = -SNUMBER; } else { MesPrint("&Unknown/not allowed variable type in CreateAllLoops: %s",stype); return(1); } *s = c; while ( *s == ',' || *s == ' ' ) s++; stype = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(stype,(UBYTE *)"ifnoloop") != 0 || c != '=' ) { MesPrint("&Unrecognised option in CreateAllLoops statement: %s",stype); return(1); } *s++ = c; x = -1; if ( FG.cTable[*s] == 1 ) { x = 0; do { x = 10*x + (*s++-'0'); } while (FG.cTable[*s] == 1); } if ( x != 0 && x != 1 ) { MesPrint("&Only options allowed for ifnoloop are 0 or 1."); return(1); } WorkSave = to = AT.WorkPointer; *to++ = TYPEALLLOOPS; *to++ = 6; *to++ = infun; *to++ = outfun; *to++ = typenum; *to++ = x; AddNtoL(WorkSave[1],WorkSave); return(0); notintensor: MesPrint("&Variable type not allowed in tensors: %s",stype); return(1); } /* #] CoCreateAllLoops : #[ CoCreateAllPaths : Syntax: CreateAllPaths,end-function,intermediate-function,out-function,type-argument,ifnopath; Types allowed: vector, index, symbol, snumber ifnoloop: ifnoloop=0 or ifnoloop=1 in-function can be a tensor. In that case type can be only vector or index. out-function can be a tensor. In that case type can be only vector or index. */ int CoCreateAllPaths(UBYTE *s) { GETIDENTITY UBYTE *endname,*inname, *outname, *stype, c; WORD endfun, infun, outfun, x, type, tensorflag, typenum; WORD *WorkSave, *to; while ( *s == ',' || *s == ' ' ) s++; endname = s; s = SkipAName(s); c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,endname,&endfun,WITHAUTO) ) != CFUNCTION ) || ( ( functions[endfun].spec != 0 ) && ( functions[endfun].spec != TENSORFUNCTION ) ) ) { MesPrint("&%s should be a regular function or a tensor.",endname); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&endfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } endfun += FUNCTION; *s++ = c; while ( *s == ',' || *s == ' ' ) s++; inname = s; s = SkipAName(s); c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,inname,&infun,WITHAUTO) ) != CFUNCTION ) || ( ( functions[infun].spec != 0 ) && ( functions[infun].spec != TENSORFUNCTION ) ) ) { MesPrint("&%s should be a regular function or a tensor.",inname); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&infun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } infun += FUNCTION; *s++ = c; while ( *s == ',' || *s == ' ' ) s++; outname = s; s = SkipAName(s); c = *s; *s = 0; if ( ( ( type = GetName(AC.varnames,outname,&outfun,WITHAUTO) ) != CFUNCTION ) || ( ( functions[outfun].spec != 0 ) && ( functions[outfun].spec != TENSORFUNCTION ) ) ) { MesPrint("&%s should be a regular function or a tensor.",outname); if ( type < 0 ) { if ( GetName(AC.exprnames,s,&outfun,NOAUTO) == NAMENOTFOUND ) AddFunction(s,0,0,0,0,0,-1,-1); } return(1); } outfun += FUNCTION; *s++ = c; if ( functions[infun].spec == TENSORFUNCTION || functions[outfun].spec == TENSORFUNCTION ) tensorflag = 1; else tensorflag = 0; /* Now the type: type=.... */ while ( *s == ',' || *s == ' ' ) s++; stype = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(stype,(UBYTE *)"type") != 0 || c != '=' ) { MesPrint("&In CreateAllPaths statement: expected type=vartype."); return(1); } *s++ = c; stype = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(stype,(UBYTE *)"vector") == 0 ) { typenum = -VECTOR; } else if ( StrICmp(stype,(UBYTE *)"index") == 0 ) { typenum = -INDEX; } else if ( StrICmp(stype,(UBYTE *)"symbol") == 0 ) { if ( tensorflag ) goto notintensor; typenum = -SYMBOL; } else if ( StrICmp(stype,(UBYTE *)"snumber") == 0 ) { if ( tensorflag ) goto notintensor; typenum = -SNUMBER; } else { MesPrint("&Unknown/not allowed variable type in CreateAllPaths: %s",stype); return(1); } *s = c; while ( *s == ',' || *s == ' ' ) s++; stype = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(stype,(UBYTE *)"ifnopath") != 0 || c != '=' ) { MesPrint("&Unrecognised option in CreateAllPaths statement: %s",stype); return(1); } *s++ = c; x = -1; if ( FG.cTable[*s] == 1 ) { x = 0; do { x = 10*x + (*s++-'0'); } while (FG.cTable[*s] == 1); } if ( x != 0 && x != 1 ) { MesPrint("&Only options allowed for ifnopath are 0 or 1."); return(1); } WorkSave = to = AT.WorkPointer; *to++ = TYPEALLPATHS; *to++ = 7; *to++ = endfun; *to++ = infun; *to++ = outfun; *to++ = typenum; *to++ = x; AddNtoL(WorkSave[1],WorkSave); return(0); notintensor: MesPrint("&CreateAllPaths: Variable type not allowed in tensors: %s",stype); return(1); } /* #] CoCreateAllPaths : #[ CoCreateAll : Syntax: subkey, two or three functions, type, ifnone */ int CoCreateAll(UBYTE *s) { UBYTE *subkey; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; subkey = s; while ( FG.cTable[*s] == 0 ) s++; if ( *s != ' ' && *s != ',' && *s != '\t' ) { MesPrint("&Illegal subkey in CoCreate statement."); return(1); } /* c = *s; */ *s++ = 0; while ( *s == ' ' || *s == ',' || *s == '\t' ) s++; if ( StrICmp(subkey,(UBYTE *)"loops") == 0 ) { return(CoCreateAllLoops(s)); } else if ( StrICmp(subkey,(UBYTE *)"paths") == 0 ) { return(CoCreateAllPaths(s)); } /* else if ( StrICmp(subkey,(UBYTE *)"motics") == 0 ) { } else if ( StrICmp(subkey,(UBYTE *)"onepi") == 0 ) { } else if ( StrICmp(subkey,(UBYTE *)"cuts") == 0 ) { } */ else { MesPrint("&Illegal subkey in CoCreate statement: %s.",subkey); return(1); } } /* #] CoCreateAll : */ form-5.0.1/sources/module.c0000644000175100017510000004652015217035721011271 /** @file module.c * * A number of routines that deal with the moduleoption statement and the * execution of modules. * Additionally there are the execution of the exec and pipe instructions. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include "form3.h" /* #] Includes : #[ Modules : #[ ModuleInstruction : Enters after the . of .sort etc We have word[[(options)][:commentary];] Word is one of 'clear end global sort store' Options are 'polyfun, endloopifunchanged, endloopifzero' Additions for solving equations can be added to 'word' The flag in the moduleoptions is for telling whether the current option can be followed by others. If it is > 0 it cannot. */ static KEYWORD ModuleWords[] = { {"clear", (TFUN)0, CLEARMODULE, 0} ,{"end", (TFUN)0, ENDMODULE, 0} ,{"global", (TFUN)0, GLOBALMODULE, 0} ,{"sort", (TFUN)0, SORTMODULE, 0} ,{"store", (TFUN)0, STOREMODULE, 0} }; static KEYWORD ModuleOptions[] = { {"inparallel", DoinParallel, 1, 1} ,{"local", DoModLocal, MODLOCAL, 0} ,{"maximum", DoModMax, MODMAX, 0} ,{"minimum", DoModMin, MODMIN, 0} ,{"noparallel", DoNoParallel, NOPARALLEL_USER,0} ,{"notinparallel", DonotinParallel,0, 1} ,{"parallel", DoParallel, PARALLELFLAG, 0} ,{"polyfun", DoPolyfun, POLYFUN, 0} ,{"polyratfun", DoPolyratfun, POLYFUN, 0} ,{"processbucketsize", DoProcessBucket,0, 0} ,{"sum", DoModSum, MODSUM, 0} }; int ModuleInstruction(int *moduletype, int *specialtype) { UBYTE *t, *s, *u, c; KEYWORD *key; int addit = 0, error = 0, i, j; DUMMYUSE(specialtype); LoadInstruction(0); AC.firstctypemessage = 0; s = AP.preStart; SKIPBLANKS(s) t = EndOfToken(s); c = *t; *t = 0; AC.origin = FROMPOINTINSTRUCTION; key = FindKeyWord(AP.preStart,ModuleWords,sizeof(ModuleWords)/sizeof(KEYWORD)); if ( key == 0 ) { MesPrint("@Unrecognized module terminator: %s",s); error = 1; key = ModuleWords; while ( StrCmp((UBYTE *)key->name,(UBYTE *)"end") ) key++; } *t = c; *moduletype = key->type; SKIPBLANKS(t); while ( *t == '(' ) { /* There are options */ s = t+1; SKIPBRA3(t) if ( *t == 0 ) { MesPrint("@Improper options field in . instruction"); error = 1; } else { *t = 0; if ( CoModOption(s) ) error = 1; *t++ = ')'; } } if ( *t == ':' ) { /* There is an 'advertisement' */ t++; SKIPBLANKS(t) s = t; i = 0; while ( *t && *t != ';' ) { if ( *t == '\\' ) t++; t++; i++; } u = t; while ( u > s && u[-1] == ' ' ) { u--; i--; } if ( *u == '\\' ) { u++; i++; } for ( j = COMMERCIALSIZE-1; j >= 0; j-- ) { if ( i <= 0 ) break; AC.Commercial[j] = *--u; i--; if ( u > s && u[-1] == '\\' ) u--; } for ( ; j >= 0; j-- ) AC.Commercial[j] = ' '; AC.Commercial[COMMERCIALSIZE] = 0; addit += 2; } if ( addit && *t != ';' ) { MesPrint("@Improper ending of . instruction"); error = -1; } return(error); } /* #] ModuleInstruction : #[ CoModuleOption : ModuleOption, options; */ int CoModuleOption(UBYTE *s) { UBYTE *t,*tt,c; KEYWORD *option; int error = 0, polyflag = 0; AC.origin = FROMMODULEOPTION; if ( *s ) do { s = ToToken(s); t = EndOfToken(s); c = *t; *t = 0; option = FindKeyWord(s,ModuleOptions, sizeof(ModuleOptions)/sizeof(KEYWORD)); if ( option == 0 ) { if ( polyflag ) { *t = c; t++; s = SkipAName(t); polyflag = 0; continue; } else { MesPrint("@Unrecognized module option: %s",s); error = 1; polyflag = 0; *t = c; } } else { *t = c; SKIPBLANKS(t) if ( (option->func)(t) ) error = 1; } if ( error ) return(error); if ( StrCmp((UBYTE *)(option->name),(UBYTE *)("polyfun")) == 0 || StrCmp((UBYTE *)(option->name),(UBYTE *)("polyratfun")) == 0 ) { polyflag = 1; t++; t = SkipAName(t); } else polyflag = 0; if ( option->flags > 0 ) return(error); while ( *t ) { if ( *t == ',' ) { tt = t+1; while ( *tt == ',' ) tt++; if ( *tt != '$' ) break; t = tt+1; } if ( *t == ')' ) break; if ( *t == '(' ) SKIPBRA3(t) else if ( *t == '{' ) SKIPBRA2(t) else if ( *t == '[' ) SKIPBRA1(t) t++; } s = t; } while ( *s == ',' ); if ( *s ) { MesPrint("@Unrecognized module option: %s",s); error = 1; } return(error); } /* #] CoModuleOption : #[ CoModOption : To be called from a .instruction. Only recognizes polyfun. The newer ones should be via the ModuleOption statement. */ int CoModOption(UBYTE *s) { UBYTE *t,c; int error = 0; AC.origin = FROMPOINTINSTRUCTION; if ( *s ) do { s = ToToken(s); t = EndOfToken(s); c = *t; *t = 0; if ( StrICmp(s,(UBYTE *)"polyfun") == 0 ) { *t = c; SKIPBLANKS(t) if ( DoPolyfun(t) ) error = 1; } else if ( StrICmp(s,(UBYTE *)"polyratfun") == 0 ) { *t = c; SKIPBLANKS(t) if ( DoPolyratfun(t) ) error = 1; } else { MesPrint("@Unrecognized module option in .instruction: %s",s); error = 1; *t = c; } while ( *t ) { if ( *t == ',' || *t == ')' ) break; if ( *t == '(' ) SKIPBRA3(t) else if ( *t == '{' ) SKIPBRA2(t) else if ( *t == '[' ) SKIPBRA1(t) t++; } s = t; } while ( *s == ',' ); if ( *s ) { MesPrint("@Unrecognized module option in .instruction: %s",s); error = 1; } return(error); } /* #] CoModOption : #[ SetSpecialMode : */ void SetSpecialMode(int moduletype, int specialtype) { DUMMYUSE(moduletype); DUMMYUSE(specialtype); } /* #] SetSpecialMode : #[ MakeGlobal : void MakeGlobal() { } #] MakeGlobal : #[ ExecModule : */ int ExecModule(int moduletype) { /* Here we check module options and other things that should be done at the start of a module. */ #ifdef WITHFLOAT if ( ( AC.tMaxWeight != 0 && AC.tMaxWeight != AC.MaxWeight ) || ( AC.tDefaultPrecision != 0 && AC.tDefaultPrecision != AC.DefaultPrecision ) ) { AC.DefaultPrecision = AC.tDefaultPrecision; AC.tDefaultPrecision = 0; AC.MaxWeight = AC.tMaxWeight; AC.tMaxWeight = 0; ClearMZVTables(); SetupMZVTables(); } #endif return(DoExecute(moduletype,0)); } /* #] ExecModule : #[ ExecStore : */ int ExecStore(void) { return(0); } /* #] ExecStore : #[ FullCleanUp : Remark 27-oct-2005 by JV This routine (and CleanUp in startup.c) may still need some work: What to do with preprocessor variables What to do with files we write to */ void FullCleanUp(void) { int j; while ( AC.CurrentStream->previous >= 0 ) AC.CurrentStream = CloseStream(AC.CurrentStream); AP.PreSwitchLevel = AP.PreIfLevel = 0; for ( j = NumProcedures-1; j >= 0; j-- ) { if ( Procedures[j].name ) M_free(Procedures[j].name,"name of procedure"); if ( Procedures[j].p.buffer ) M_free(Procedures[j].p.buffer,"buffer of procedure"); } NumProcedures = 0; while ( NumPre > AP.gNumPre ) { NumPre--; M_free(PreVar[NumPre].name,"PreVar[NumPre].name"); PreVar[NumPre].name = PreVar[NumPre].value = 0; } AC.DidClean = 0; for ( j = 0; j < NumExpressions; j++ ) { AC.exprnames->namenode[Expressions[j].node].type = CDELETE; AC.DidClean = 1; } CompactifyTree(AC.exprnames,EXPRNAMES); for ( j = AO.NumDictionaries-1; j >= 0; j-- ) { RemoveDictionary(AO.Dictionaries[j]); M_free(AO.Dictionaries[j],"Dictionary"); } AO.NumDictionaries = AO.gNumDictionaries = 0; M_free(AO.Dictionaries,"Dictionaries"); AO.Dictionaries = 0; AO.SizeDictionaries = 0; AP.OpenDictionary = 0; AO.CurrentDictionary = 0; AP.ComChar = AP.cComChar; if ( AP.procedureExtension ) M_free(AP.procedureExtension,"procedureextension"); AP.procedureExtension = strDup1(AP.cprocedureExtension,"procedureextension"); AC.StatsFlag = AM.gStatsFlag = AM.ggStatsFlag; AC.extrasymbols = AM.gextrasymbols = AM.ggextrasymbols; AC.extrasym[0] = AM.gextrasym[0] = AM.ggextrasym[0] = 'Z'; AC.extrasym[1] = AM.gextrasym[1] = AM.ggextrasym[1] = 0; AO.NoSpacesInNumbers = AM.gNoSpacesInNumbers = AM.ggNoSpacesInNumbers; AO.IndentSpace = AM.gIndentSpace = AM.ggIndentSpace; AC.ThreadStats = AM.gThreadStats = AM.ggThreadStats; AC.OldFactArgFlag = AM.gOldFactArgFlag = AM.ggOldFactArgFlag; AC.FinalStats = AM.gFinalStats = AM.ggFinalStats; AC.OldGCDflag = AM.gOldGCDflag = AM.ggOldGCDflag; AC.ThreadsFlag = AM.gThreadsFlag = AM.ggThreadsFlag; if ( AC.ThreadsFlag && AM.totalnumberofthreads > 1 ) AS.MultiThreaded = 1; AC.ThreadBucketSize = AM.gThreadBucketSize = AM.ggThreadBucketSize; AC.ThreadBalancing = AM.gThreadBalancing = AM.ggThreadBalancing; AC.ThreadSortFileSynch = AM.gThreadSortFileSynch = AM.ggThreadSortFileSynch; AC.ShortStatsMax = AM.gShortStatsMax = AM.ggShortStatsMax; AC.SizeCommuteInSet = AM.gSizeCommuteInSet = 0; #ifdef WITHFLOAT AC.MaxWeight = AM.gMaxWeight = AM.ggMaxWeight; AC.DefaultPrecision = AM.gDefaultPrecision = AM.ggDefaultPrecision; #endif NumExpressions = 0; if ( DeleteStore(0) < 0 ) { MesPrint("@Cannot restart the storage file"); Terminate(-1); } RemoveDollars(); CleanUp(1); ResetVariables(2); IniVars(); } /* #] FullCleanUp : #[ DoPolyfun : */ int DoPolyfun(UBYTE *s) { GETIDENTITY UBYTE *t, c; WORD funnum, eqsign = 0; if ( AC.origin == FROMPOINTINSTRUCTION ) { if ( *s == 0 || *s == ',' || *s == ')' ) { AR.PolyFun = 0; AR.PolyFunType = 0; return(0); } if ( *s != '=' ) { MesPrint("@Proper use in point instructions is: PolyFun[=functionname]"); return(-1); } eqsign = 1; } else { if ( *s == 0 ) { AR.PolyFun = 0; AR.PolyFunType = 0; return(0); } if ( *s != '=' && *s != ',' ) { MesPrint("@Proper use is: PolyFun[{ ,=}functionname]"); return(-1); } if ( *s == '=' ) eqsign = 1; } s++; SKIPBLANKS(s) t = EndOfToken(s); c = *t; *t = 0; if ( GetName(AC.varnames,s,&funnum,WITHAUTO) != CFUNCTION ) { if ( AC.origin != FROMPOINTINSTRUCTION && eqsign == 0 ) { AR.PolyFun = 0; AR.PolyFunType = 0; return(0); } MesPrint("@ %s is not a properly declared function",s); *t = c; return(-1); } if ( functions[funnum].spec > 0 || functions[funnum].commute != 0 ) { MesPrint("@The PolyFun must be a regular commuting function!"); *t = c; return(-1); } AR.PolyFun = funnum+FUNCTION; AR.PolyFunType = 1; *t = c; SKIPBLANKS(t) if ( *t && *t != ',' && *t != ')' ) { t++; c = *t; *t = 0; MesPrint("@Improper ending of end-of-module instruction: %s",s); *t = c; return(-1); } return(0); } /* #] DoPolyfun : #[ DoPolyratfun : */ int DoPolyratfun(UBYTE *s) { GETIDENTITY UBYTE *t, c; WORD funnum; if ( AC.origin == FROMPOINTINSTRUCTION ) { if ( *s == 0 || *s == ',' || *s == ')' ) { AR.PolyFun = 0; AR.PolyFunType = 0; AR.PolyFunInv = 0; AR.PolyFunExp = 0; return(0); } if ( *s != '=' ) { MesPrint("@Proper use in point instructions is: PolyRatFun[=functionname[+functionname]]"); return(-1); } } else { if ( *s == 0 ) { AR.PolyFun = 0; AR.PolyFunType = 0; AR.PolyFunInv = 0; AR.PolyFunExp = 0; return(0); } if ( *s != '=' && *s != ',' ) { MesPrint("@Proper use is: PolyRatFun[{ ,=}functionname[+functionname]]"); return(-1); } } s++; SKIPBLANKS(s) t = EndOfToken(s); c = *t; *t = 0; if ( GetName(AC.varnames,s,&funnum,WITHAUTO) != CFUNCTION ) { Error1:; MesPrint("@ %s is not a properly declared function",s); *t = c; return(-1); } if ( functions[funnum].spec > 0 || functions[funnum].commute != 0 ) { Error2:; MesPrint("@The PolyRatFun must be a regular commuting function!"); *t = c; return(-1); } AR.PolyFun = funnum+FUNCTION; AR.PolyFunType = 2; AR.PolyFunInv = 0; AR.PolyFunExp = 0; AC.PolyRatFunChanged = 1; *t = c; if ( *t == '+' ) { t++; s = t; t = EndOfToken(s); c = *t; *t = 0; if ( GetName(AC.varnames,s,&funnum,WITHAUTO) != CFUNCTION ) goto Error1; if ( functions[funnum].spec > 0 || functions[funnum].commute != 0 ) goto Error2; AR.PolyFunInv = funnum+FUNCTION; *t = c; } SKIPBLANKS(t) if ( *t && *t != ',' && *t != ')' ) { t++; c = *t; *t = 0; MesPrint("@Improper ending of end-of-module instruction: %s",s); *t = c; return(-1); } return(0); } /* #] DoPolyratfun : #[ DoNoParallel : */ int DoNoParallel(UBYTE *s) { if ( *s == 0 || *s == ',' || *s == ')' ) { AC.mparallelflag |= NOPARALLEL_USER; return(0); } MesPrint("@NoParallel should not have extra parameters"); return(-1); } /* #] DoNoParallel : #[ DoParallel : */ int DoParallel(UBYTE *s) { if ( *s == 0 || *s == ',' || *s == ')' ) { AC.mparallelflag &= ~NOPARALLEL_USER; return(0); } MesPrint("@Parallel should not have extra parameters"); return(-1); } /* #] DoParallel : #[ DoModSum : */ int DoModSum(UBYTE *s) { while ( *s == ',' ) s++; if ( *s != '$' ) { MesPrint("@Module Sum should mention which $-variables"); return(-1); } s = DoModDollar(s,MODSUM); if ( s && *s != 0 && *s != ')' ) { MesPrint("@Irregular end of Sum option of Module statement"); return(-1); } return(0); } /* #] DoModSum : #[ DoModMax : */ int DoModMax(UBYTE *s) { while ( *s == ',' ) s++; if ( *s != '$' ) { MesPrint("@Module Maximum should mention which $-variables"); return(-1); } s = DoModDollar(s,MODMAX); if ( s && *s != 0 ) { MesPrint("@Irregular end of Maximum option of Module statement"); return(-1); } return(0); } /* #] DoModMax : #[ DoModMin : */ int DoModMin(UBYTE *s) { while ( *s == ',' ) s++; if ( *s != '$' ) { MesPrint("@Module Minimum should mention which $-variables"); return(-1); } s = DoModDollar(s,MODMIN); if ( s && *s != 0 ) { MesPrint("@Irregular end of Minimum option of Module statement"); return(-1); } return(0); } /* #] DoModMin : #[ DoModLocal : */ int DoModLocal(UBYTE *s) { while ( *s == ',' ) s++; if ( *s != '$' ) { MesPrint("@ModuleOption Local should mention which $-variables"); return(-1); } s = DoModDollar(s,MODLOCAL); if ( s && *s != 0 ) { MesPrint("@Irregular end of Local option of ModuleOption statement"); return(-1); } return(0); } /* #] DoModLocal : #[ DoProcessBucket : */ int DoProcessBucket(UBYTE *s) { LONG x; while ( *s == ',' || *s == '=' ) s++; ParseNumber(x,s) if ( *s && *s != ' ' && *s != '\t' ) { MesPrint("&Numerical value expected for ProcessBucketSize"); return(1); } AC.mProcessBucketSize = x; return(0); } /* #] DoProcessBucket : #[ DoModDollar : */ UBYTE * DoModDollar(UBYTE *s, int type) { UBYTE *name, c; WORD number; MODOPTDOLLAR *md; int nummodopt; while ( *s == '$' ) { /* Read the name of the dollar Mark the type */ s++; name = s; if ( FG.cTable[*s] == 0 ) { while ( FG.cTable[*s] == 0 || FG.cTable[*s] == 1 ) s++; c = *s; *s = 0; number = GetDollar(name); if ( number < 0 ) { UBYTE *s1; number = AddDollar(s,0,0,0); s1 = strDup1((UBYTE *)"Undefined $-variable in module option; option ignored: $","Undefined $-variable in ModuleOption"); s1 = AddToString(s1,name,0); Warning((char *)s1); M_free(s1,"Undefined $-variable in ModuleOption"); } for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( number == ModOptdollars[nummodopt].number && type != ModOptdollars[nummodopt].type ) { UBYTE *s1; s1 = strDup1((UBYTE *)"Conflicting module options for $-variable; later option ignored: $","Conflicting $-variable in ModuleOption"); s1 = AddToString(s1,name,0); Warning((char *)s1); M_free(s1,"Conflicting $-variable in ModuleOption"); break; } } md = (MODOPTDOLLAR *)FromList(&AC.ModOptDolList); md->number = number; md->type = type; #ifdef WITHPTHREADS if ( DollarLocalCopy(type) ) { int j, i; DOLLARS dglobal, dlocal; md->dstruct = (DOLLARS)Malloc1( sizeof(struct DoLlArS)*AM.totalnumberofthreads,"Local DOLLARS"); /* Now copy the global dollar into the local copies. This can be nontrivial if the value needs an allocation. We don't really need the locks. */ dglobal = Dollars + number; for ( j = 0; j < AM.totalnumberofthreads; j++ ) { dlocal = md->dstruct + j; dlocal->index = dglobal->index; dlocal->node = dglobal->node; dlocal->type = dglobal->type; dlocal->name = dglobal->name; dlocal->size = dglobal->size; dlocal->where = dglobal->where; if ( dlocal->size > 0 ) { dlocal->where = (WORD *)Malloc1((dlocal->size+1)*sizeof(WORD),"Local dollar value"); for ( i = 0; i < dlocal->size; i++ ) dlocal->where[i] = dglobal->where[i]; dlocal->where[dlocal->size] = 0; } INIRECLOCK(dlocal->pthreadslock); dlocal->nfactors = dglobal->nfactors; if ( dglobal->nfactors > 1 ) { int nsize; WORD *t, *m; dlocal->factors = (FACDOLLAR *)Malloc1(dglobal->nfactors*sizeof(FACDOLLAR),"Dollar factors"); for ( i = 0; i < dglobal->nfactors; i++ ) { nsize = dglobal->factors[i].size; dlocal->factors[i].type = DOLUNDEFINED; dlocal->factors[i].value = dglobal->factors[i].value; if ( ( dlocal->factors[i].size = nsize ) > 0 ) { dlocal->factors[i].where = t = (WORD *)Malloc1(sizeof(WORD)*(nsize+1),"DollarCopyFactor"); m = dglobal->factors[i].where; NCOPY(t,m,nsize); *t = 0; } else { dlocal->factors[i].where = 0; } } } else { dlocal->factors = 0; } } } else { md->dstruct = 0; } #endif *s = c; } else { MesPrint("&Illegal name for $-variable in module option"); while ( *s != ',' && *s != 0 && *s != ')' ) s++; } while ( *s == ',' ) s++; } return(s); } /* #] DoModDollar : #[ DoinParallel : The idea is that we should have the commands ModuleOption,InParallel; ModuleOption,InParallel,name1,name2,...,namen; ModuleOption,NotInParallel,name1,name2,...,namen; The advantage over the InParallel statement is that this statement comes after the definition of the expressions. */ int DoinParallel(UBYTE *s) { return(DoInParallel(s,1)); } /* #] DoinParallel : #[ DonotinParallel : */ int DonotinParallel(UBYTE *s) { return(DoInParallel(s,0)); } /* #] DonotinParallel : #] Modules : #[ External : #[ DoExecStatement : */ int DoExecStatement(void) { #ifdef WITHSYSTEM FLUSHCONSOLE; if ( system((char *)(AP.preStart)) ) return(-1); return(0); #else Error0("External programs not implemented on this computer/system"); return(-1); #endif } /* #] DoExecStatement : #[ DoPipeStatement : */ int DoPipeStatement(void) { #ifdef WITHPIPE FLUSHCONSOLE; if ( OpenStream(AP.preStart,PIPESTREAM,0,PRENOACTION) == 0 ) return(-1); return(0); #else Error0("Pipes not implemented on this computer/system"); return(-1); #endif } /* #] DoPipeStatement : #] External : */ form-5.0.1/sources/Makefile.am0000644000175100017510000001111615217035721011665 SRCBASE = \ argument.c \ checkpoint.c \ comexpr.c \ compcomm.c \ compiler.c \ compress.c \ comtool.c \ comtool.h \ declare.h \ diagrams.c \ diawrap.cc \ dict.c \ dollar.c \ execute.c \ extcmd.c \ factor.c \ features.cc \ findpat.c \ form3.h \ fsizes.h \ ftypes.h \ function.c \ grcc.cc \ grcc.h \ grccparam.h \ if.c \ index.c \ inivar.h \ lus.c \ mallocprotect.h \ message.c \ minos.c \ minos.h \ model.c \ module.c \ mytime.cc \ mytime.h \ names.c \ normal.c \ notation.c \ opera.c \ optimize.cc \ pattern.c \ poly.cc \ poly.h \ polyfact.cc \ polyfact.h \ polygcd.cc \ polygcd.h \ polywrap.cc \ portsignals.h \ pre.c \ proces.c \ ratio.c \ reken.c \ reshuf.c \ sch.c \ setfile.c \ smart.c \ sort.c \ spectator.c \ startup.c \ store.c \ structs.h \ symmetr.c \ tables.c \ token.c \ tools.c \ transform.c \ variable.h \ vector.h \ wildcard.c INCBASE = if ONUNIX SRCBASE += \ unixfile.c \ unix.h endif if ONWINDOWS SRCBASE += \ fwin.h endif if WITHFLINT SRCBASE += \ flintinterface.cc \ flintinterface.h \ flintwrap.cc endif if WITHFLOAT SRCBASE += \ evaluate.c \ float.c endif if WITHZSTD SRCBASE += \ ../extern/zstd/zlibWrapper/gzclose.c \ ../extern/zstd/zlibWrapper/gzcompatibility.h \ ../extern/zstd/zlibWrapper/gzguts.h \ ../extern/zstd/zlibWrapper/gzlib.c \ ../extern/zstd/zlibWrapper/gzread.c \ ../extern/zstd/zlibWrapper/gzwrite.c \ ../extern/zstd/zlibWrapper/zstd_zlibwrapper.c \ ../extern/zstd/zlibWrapper/zstd_zlibwrapper.h # Slight abuse of INCBASE, in case zconf.h does not define STDC (e.g. on Fedora >= 40) INCBASE += -I$(top_srcdir)/extern/zstd/zlibWrapper -DSTDC endif SRCPTHREAD = \ threads.c SRCPARALLEL = \ mpi.c \ parallel.c \ parallel.h \ mpidbg.h # Automatic versioning. CLEANFILES = version.h *.gcno *.gcda *.gcov gmon.out form-startup.$(OBJEXT): version.h tform-startup.$(OBJEXT): version.h parform-startup.$(OBJEXT): version.h vorm-startup.$(OBJEXT): version.h tvorm-startup.$(OBJEXT): version.h parvorm-startup.$(OBJEXT): version.h .PHONY: update_version_h version.h: update_version_h $(UPDATE_VERSION_H) dist-hook: $(DISTHOOK_VERSION_H) if FIXED_VERSION UPDATE_VERSION_H = \ [ -f version.h ] || $(LN_S) "$(srcdir)/version.h.in" version.h DISTHOOK_VERSION_H = \ cp "$(srcdir)/version.h.in" "$(distdir)/version.h.in" else UPDATE_VERSION_H = \ $(SHELL) "$(top_srcdir)/scripts/git-version-gen.sh" -C "$(srcdir)" -c -o version.h DISTHOOK_VERSION_H = \ $(SHELL) "$(top_srcdir)/scripts/git-version-gen.sh" -C "$(srcdir)" -c -o "$(distdir)/version.h.in" endif bin_PROGRAMS = if BUILD_FORM bin_PROGRAMS += form form_SOURCES = $(SRCBASE) form_CPPFLAGS = $(INCBASE) form_CFLAGS = $(COMPILEFLAGS) form_CXXFLAGS = $(COMPILEFLAGS) form_LDFLAGS = $(LINKFLAGS) $(STATIC_LDFLAGS) form_LDADD = $(TOOL_LIBS) endif if BUILD_VORM bin_PROGRAMS += vorm vorm_SOURCES = $(SRCBASE) vorm_CPPFLAGS = -DDEBUGGING $(INCBASE) vorm_CFLAGS = $(DEBUGCOMPILEFLAGS) vorm_CXXFLAGS = $(DEBUGCOMPILEFLAGS) vorm_LDFLAGS = $(DEBUGLINKFLAGS) vorm_LDADD = $(DEBUGTOOL_LIBS) endif if BUILD_TFORM bin_PROGRAMS += tform tform_SOURCES = $(SRCBASE) $(SRCPTHREAD) tform_CPPFLAGS = -DWITHPTHREADS $(PTHREAD_CPPFLAGS) $(INCBASE) tform_CFLAGS = $(COMPILEFLAGS) $(PTHREAD_CFLAGS) tform_CXXFLAGS = $(COMPILEFLAGS) $(PTHREAD_CFLAGS) tform_LDFLAGS = $(LINKFLAGS) $(STATIC_LDFLAGS) tform_LDADD = $(PTHREAD_LIBS) $(TOOL_LIBS) endif if BUILD_TVORM bin_PROGRAMS += tvorm tvorm_SOURCES = $(SRCBASE) $(SRCPTHREAD) tvorm_CPPFLAGS = -DWITHPTHREADS -DDEBUGGING $(PTHREAD_CPPFLAGS) $(INCBASE) tvorm_CFLAGS = $(DEBUGCOMPILEFLAGS) $(PTHREAD_CFLAGS) tvorm_CXXFLAGS = $(DEBUGCOMPILEFLAGS) $(PTHREAD_CFLAGS) tvorm_LDFLAGS = $(DEBUGLINKFLAGS) tvorm_LDADD = $(PTHREAD_LIBS) $(DEBUGTOOL_LIBS) endif if BUILD_PARFORM bin_PROGRAMS += parform parform_SOURCES = $(SRCBASE) $(SRCPARALLEL) parform_CPPFLAGS = -DWITHMPI -DPF_WITHGETENV -DPF_WITHLOG $(MPI_CPPFLAGS) $(INCBASE) parform_CFLAGS = $(COMPILEFLAGS) $(MPI_CFLAGS) parform_CXXFLAGS = $(COMPILEFLAGS) $(MPI_CXXFLAGS) parform_LDFLAGS = $(LINKFLAGS) $(MPI_STATIC_LDFLAGS) parform_LDADD = $(TOOL_LIBS) parform_LINK = $(MPICXX) $(parform_CXXFLAGS) $(CXXFLAGS) $(parform_LDFLAGS) $(LDFLAGS) -o $@ endif if BUILD_PARVORM bin_PROGRAMS += parvorm parvorm_SOURCES = $(SRCBASE) $(SRCPARALLEL) parvorm_CPPFLAGS = -DWITHMPI -DPF_WITHGETENV -DPF_WITHLOG -DDEBUGGING $(MPI_CPPFLAGS) $(INCBASE) parvorm_CFLAGS = $(DEBUGCOMPILEFLAGS) $(MPI_CFLAGS) parvorm_CXXFLAGS = $(DEBUGCOMPILEFLAGS) $(MPI_CXXFLAGS) parvorm_LDFLAGS = $(DEBUGLINKFLAGS) parvorm_LDADD = $(DEBUGTOOL_LIBS) parvorm_LINK = $(MPICXX) $(parvorm_CXXFLAGS) $(CXXFLAGS) $(parvorm_LDFLAGS) $(LDFLAGS) -o $@ endif form-5.0.1/sources/reken.c0000644000175100017510000030505115217035721011105 /** @file reken.c * * This file contains the numerical routines. * The arithmetic in FORM is normally over the rational numbers. * Hence there are routines for dealing with integers and with rational * of 'arbitrary precision' (within limits) * There are also routines for that calculus modulus an integer. * In addition there are the routines for factorials and Bernoulli numbers. * The random number function is currently only for internal purposes. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : reken.c */ #include "form3.h" #include #ifdef WITHGMP #include #define GMPSPREAD (GMP_LIMB_BITS/BITSINWORD) #endif #define GCDMAX 3 #define NEWTRICK 1 /* #] Includes : #[ RekenRational : #[ Pack : void Pack(a,na,b,nb) Packs the contents of the numerator a and the denominator b into one normalized fraction a. */ void Pack(UWORD *a, WORD *na, UWORD *b, WORD nb) { WORD c, sgn = 1, i; UWORD *to,*from; if ( (c = *na) == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Caught a zero in Pack"); MUNLOCK(ErrorMessageLock); return; } if ( nb == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Division by zero in Pack"); MUNLOCK(ErrorMessageLock); return; } if ( *na < 0 ) { sgn = -sgn; c = -c; } if ( nb < 0 ) { sgn = -sgn; nb = -nb; } *na = MaX(c,nb); to = a + c; i = *na - c; while ( --i >= 0 ) *to++ = 0; i = *na - nb; from = b; NCOPY(to,from,nb); while ( --i >= 0 ) *to++ = 0; if ( sgn < 0 ) *na = -*na; } /* #] Pack : #[ UnPack : void UnPack(a,na,denom,numer) Determines the sizes of the numerator and the denominator in the normalized fraction a with length na. */ void UnPack(UWORD *a, WORD na, WORD *denom, WORD *numer) { UWORD *pos; WORD i, sgn = na; if ( na < 0 ) { na = -na; } i = na; if ( i > 1 ) { /* Find the respective leading words */ a += i; a--; pos = a + i; while ( !(*a) ) { i--; a--; } while ( !(*pos) ) { na--; pos--; } } *denom = na; if ( sgn < 0 ) i = -i; *numer = i; } /* #] UnPack : #[ Mully : WORD Mully(a,na,b,nb) Multiplies the rational a by the Long b. */ int Mully(PHEAD UWORD *a, WORD *na, UWORD *b, WORD nb) { GETBIDENTITY UWORD *d, *e; WORD i, sgn = 1; WORD nd, ne, adenom, anumer; if ( !nb ) { *na = 0; return(0); } else if ( *b == 1 ) { if ( nb == 1 ) return(0); else if ( nb == -1 ) { *na = -*na; return(0); } } if ( *na < 0 ) { sgn = -sgn; *na = -*na; } if ( nb < 0 ) { sgn = -sgn; nb = -nb; } UnPack(a,*na,&adenom,&anumer); d = NumberMalloc("Mully"); e = NumberMalloc("Mully"); for ( i = 0; i < nb; i++ ) { e[i] = *b++; } ne = nb; if ( Simplify(BHEAD a+*na,&adenom,e,&ne) ) goto MullyEr; if ( MulLong(a,anumer,e,ne,d,&nd) ) goto MullyEr; b = a+*na; for ( i = 0; i < *na; i++ ) { e[i] = *b++; } ne = adenom; *na = nd; b = d; *na = nd; for ( i = 0; i < *na; i++ ) { a[i] = *b++; } Pack(a,na,e,ne); if ( sgn < 0 ) *na = -*na; NumberFree(d,"Mully"); NumberFree(e,"Mully"); return(0); MullyEr: MLOCK(ErrorMessageLock); MesCall("Mully"); MUNLOCK(ErrorMessageLock); NumberFree(d,"Mully"); NumberFree(e,"Mully"); SETERROR(-1) } /* #] Mully : #[ Divvy : WORD Divvy(a,na,b,nb) Divides the rational a by the Long b. */ int Divvy(PHEAD UWORD *a, WORD *na, UWORD *b, WORD nb) { GETBIDENTITY UWORD *d,*e; WORD i, sgn = 1; WORD nd, ne, adenom, anumer; if ( !nb ) { MLOCK(ErrorMessageLock); MesPrint("Division by zero in Divvy"); MUNLOCK(ErrorMessageLock); return(-1); } d = NumberMalloc("Divvy"); e = NumberMalloc("Divvy"); if ( nb < 0 ) { sgn = -sgn; nb = -nb; } if ( *na < 0 ) { sgn = -sgn; *na = -*na; } UnPack(a,*na,&adenom,&anumer); for ( i = 0; i < nb; i++ ) { e[i] = *b++; } ne = nb; if ( Simplify(BHEAD a,&anumer,e,&ne) ) goto DivvyEr; if ( MulLong(a+*na,adenom,e,ne,d,&nd) ) goto DivvyEr; *na = anumer; Pack(a,na,d,nd); if ( sgn < 0 ) *na = -*na; NumberFree(d,"Divvy"); NumberFree(e,"Divvy"); return(0); DivvyEr: MLOCK(ErrorMessageLock); MesCall("Divvy"); MUNLOCK(ErrorMessageLock); NumberFree(d,"Divvy"); NumberFree(e,"Divvy"); SETERROR(-1) } /* #] Divvy : #[ AddRat : WORD AddRat(a,na,b,nb,c,nc) */ int AddRat(PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { GETBIDENTITY UWORD *d, *e, *f, *g; WORD nd, ne, nf, ng, adenom, anumer, bdenom, bnumer; if ( !na ) { WORD i; *nc = nb; if ( nb < 0 ) nb = -nb; nb *= 2; for ( i = 0; i < nb; i++ ) *c++ = *b++; return(0); } else if ( !nb ) { WORD i; *nc = na; if ( na < 0 ) na = -na; na *= 2; for ( i = 0; i < na; i++ ) *c++ = *a++; return(0); } else if ( b[1] == 1 && a[1] == 1 ) { if ( na == 1 ) { if ( nb == 1 ) { *c = *a + *b; c[1] = 1; if ( *c < *a ) { c[2] = 1; c[3] = 0; *nc = 2; } else { *nc = 1; } return(0); } else if ( nb == -1 ) { if ( *b > *a ) { *c = *b - *a; *nc = -1; } else if ( *b < *a ) { *c = *a - *b; *nc = 1; } else *nc = 0; c[1] = 1; return(0); } } else if ( na == -1 ){ if ( nb == -1 ) { c[1] = 1; *c = *a + *b; if ( *c < *a ) { c[2] = 1; c[3] = 0; *nc = -2; } else { *nc = -1; } return(0); } else if ( nb == 1 ) { if ( *b > *a ) { *c = *b - *a; *nc = 1; } else if ( *b < *a ) { *c = *a - *b; *nc = -1; } else *nc = 0; c[1] = 1; return(0); } } } UnPack(a,na,&adenom,&anumer); UnPack(b,nb,&bdenom,&bnumer); if ( na < 0 ) na = -na; if ( nb < 0 ) nb = -nb; if ( na == 1 && nb == 1 ) { RLONG t1, t2, t3; t3 = ((RLONG)a[1])*((RLONG)b[1]); t1 = ((RLONG)a[0])*((RLONG)b[1]); t2 = ((RLONG)a[1])*((RLONG)b[0]); if ( ( anumer > 0 && bnumer > 0 ) || ( anumer < 0 && bnumer < 0 ) ) { if ( ( t1 = t1 + t2 ) < t2 ) { c[2] = 1; c[0] = (UWORD)t1; c[1] = (UWORD)(t1 >> BITSINWORD); *nc = 3; } else { c[0] = (UWORD)t1; if ( ( c[1] = (UWORD)(t1 >> BITSINWORD) ) != 0 ) *nc = 2; else *nc = 1; } } else { if ( t1 == t2 ) { *nc = 0; return(0); } if ( t1 > t2 ) { t1 -= t2; } else { t1 = t2 - t1; anumer = -anumer; } c[0] = (UWORD)t1; if ( ( c[1] = (UWORD)(t1 >> BITSINWORD) ) != 0 ) *nc = 2; else *nc = 1; } if ( anumer < 0 ) *nc = -*nc; d = NumberMalloc("AddRat"); d[0] = (UWORD)t3; if ( ( d[1] = (UWORD)(t3 >> BITSINWORD) ) != 0 ) nd = 2; else nd = 1; if ( Simplify(BHEAD c,nc,d,&nd) ) goto AddRer1; } /* else if ( a[na] == 1 && b[nb] == 1 && adenom == 1 && bdenom == 1 ) { if ( AddLong(a,na,b,nb,c,&nc) ) goto AddRer2; i = ABS(nc); d = c + i; *d++ = 1; while ( --i > 0 ) *d++ = 0 ; return(0); } */ else { d = NumberMalloc("AddRat"); e = NumberMalloc("AddRat"); f = NumberMalloc("AddRat"); g = NumberMalloc("AddRat"); if ( GcdLong(BHEAD a+na,adenom,b+nb,bdenom,d,&nd) ) goto AddRer; if ( *d == 1 && nd == 1 ) nd = 0; if ( nd ) { if ( DivLong(a+na,adenom,d,nd,e,&ne,c,nc) ) goto AddRer; if ( DivLong(b+nb,bdenom,d,nd,f,&nf,c,nc) ) goto AddRer; if ( MulLong(a,anumer,f,nf,c,nc) ) goto AddRer; if ( MulLong(b,bnumer,e,ne,g,&ng) ) goto AddRer; } else { if ( MulLong(a+na,adenom,b,bnumer,c,nc) ) goto AddRer; if ( MulLong(b+nb,bdenom,a,anumer,g,&ng) ) goto AddRer; } if ( AddLong(c,*nc,g,ng,c,nc) ) goto AddRer; if ( !*nc ) { NumberFree(g,"AddRat"); NumberFree(f,"AddRat"); NumberFree(e,"AddRat"); NumberFree(d,"AddRat"); return(0); } if ( nd ) { if ( Simplify(BHEAD c,nc,d,&nd) ) goto AddRer; if ( MulLong(e,ne,d,nd,g,&ng) ) goto AddRer; if ( MulLong(g,ng,f,nf,d,&nd) ) goto AddRer; } else { if ( MulLong(a+na,adenom,b+nb,bdenom,d,&nd) ) goto AddRer; } NumberFree(g,"AddRat"); NumberFree(f,"AddRat"); NumberFree(e,"AddRat"); } Pack(c,nc,d,nd); NumberFree(d,"AddRat"); return(0); AddRer: NumberFree(g,"AddRat"); NumberFree(f,"AddRat"); NumberFree(e,"AddRat"); AddRer1: NumberFree(d,"AddRat"); /* AddRer2: */ MLOCK(ErrorMessageLock); MesCall("AddRat"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] AddRat : #[ MulRat : WORD MulRat(a,na,b,nb,c,nc) Multiplies the rationals a and b. The Gcd of the individual pieces is divided out first to minimize the chances of spurious overflows. */ int MulRat(PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { WORD i; WORD sgn = 1; if ( *b == 1 && b[1] == 1 ) { if ( nb == 1 ) { *nc = na; i = ABS(na); i *= 2; while ( --i >= 0 ) *c++ = *a++; return(0); } else if ( nb == -1 ) { *nc = - na; i = ABS(na); i *= 2; while ( --i >= 0 ) *c++ = *a++; return(0); } } if ( *a == 1 && a[1] == 1 ) { if ( na == 1 ) { *nc = nb; i = ABS(nb); i *= 2; while ( --i >= 0 ) *c++ = *b++; return(0); } else if ( na == -1 ) { *nc = - nb; i = ABS(nb); i *= 2; while ( --i >= 0 ) *c++ = *b++; return(0); } } if ( na < 0 ) { na = -na; sgn = -sgn; } if ( nb < 0 ) { nb = -nb; sgn = -sgn; } if ( !na || !nb ) { *nc = 0; return(0); } if ( na != 1 || nb != 1 ) { GETBIDENTITY UWORD *xd,*xe, *xf,*xg; WORD dden, dnumr, eden, enumr; UnPack(a,na,&dden,&dnumr); UnPack(b,nb,&eden,&enumr); xd = NumberMalloc("MulRat"); xf = NumberMalloc("MulRat"); for ( i = 0; i < dnumr; i++ ) xd[i] = a[i]; a += na; for ( i = 0; i < dden; i++ ) xf[i] = a[i]; xe = NumberMalloc("MulRat"); xg = NumberMalloc("MulRat"); for ( i = 0; i < enumr; i++ ) xe[i] = b[i]; b += nb; for ( i = 0; i < eden; i++ ) xg[i] = b[i]; if ( Simplify(BHEAD xd,&dnumr,xg,&eden) || Simplify(BHEAD xe,&enumr,xf,&dden) || MulLong(xd,dnumr,xe,enumr,c,nc) || MulLong(xf,dden,xg,eden,xd,&dnumr) ) { MLOCK(ErrorMessageLock); MesCall("MulRat"); MUNLOCK(ErrorMessageLock); NumberFree(xd,"MulRat"); NumberFree(xe,"MulRat"); NumberFree(xf,"MulRat"); NumberFree(xg,"MulRat"); SETERROR(-1) } Pack(c,nc,xd,dnumr); NumberFree(xd,"MulRat"); NumberFree(xe,"MulRat"); NumberFree(xf,"MulRat"); NumberFree(xg,"MulRat"); } else { UWORD y; UWORD a0,a1,b0,b1; RLONG xx; y = a[0]; b1=b[1]; do { a0 = y % b1; y = b1; } while ( ( b1 = a0 ) != 0 ); if ( y != 1 ) { a0 = a[0] / y; b1 = b[1] / y; } else { a0 = a[0]; b1 = b[1]; } y=b[0]; a1=a[1]; do { b0 = y % a1; y = a1; } while ( ( a1 = b0 ) != 0 ); if ( y != 1 ) { a1 = a[1] / y; b0 = b[0] / y; } else { a1 = a[1]; b0 = b[0]; } xx = ((RLONG)a0)*b0; if ( xx & AWORDMASK ) { *nc = 2; c[0] = (UWORD)xx; c[1] = (UWORD)(xx >> BITSINWORD); xx = ((RLONG)a1)*b1; c[2] = (UWORD)xx; c[3] = (UWORD)(xx >> BITSINWORD); } else { c[0] = (UWORD)xx; xx = ((RLONG)a1)*b1; if ( xx & AWORDMASK ) { c[1] = 0; c[2] = (UWORD)xx; c[3] = (UWORD)(xx >> BITSINWORD); *nc = 2; } else { c[1] = (UWORD)xx; *nc = 1; } } } if ( sgn < 0 ) *nc = -*nc; return(0); } /* #] MulRat : #[ DivRat : WORD DivRat(a,na,b,nb,c,nc) Divides the rational a by the rational b. */ int DivRat(PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { GETBIDENTITY WORD i, j; int ret; UWORD *xd,*xe,xx; if ( !nb ) { MLOCK(ErrorMessageLock); MesPrint("Rational division by zero"); MUNLOCK(ErrorMessageLock); return(-1); } j = i = (nb >= 0)? nb: -nb; xd = b; xe = b + i; do { xx = *xd; *xd++ = *xe; *xe++ = xx; } while ( --j > 0 ); ret = MulRat(BHEAD a,na,b,nb,c,nc); xd = b; xe = b + i; do { xx = *xd; *xd++ = *xe; *xe++ = xx; } while ( --i > 0 ); return(ret); } /* #] DivRat : #[ Simplify : WORD Simplify(a,na,b,nb) Determines the greatest common denominator of a and b and divides both by it. A possible sign is put in a. This is the simplification of the fraction a/b. */ int Simplify(PHEAD UWORD *a, WORD *na, UWORD *b, WORD *nb) { GETBIDENTITY UWORD *x1,*x2,*x3; UWORD *x4; WORD n1,n2,n3,n4,sgn = 1; WORD i; UWORD *Siscrat5, *Siscrat6, *Siscrat7, *Siscrat8; if ( *na < 0 ) { *na = -*na; sgn = -sgn; } if ( *nb < 0 ) { *nb = -*nb; sgn = -sgn; } Siscrat5 = NumberMalloc("Simplify"); Siscrat6 = NumberMalloc("Simplify"); Siscrat7 = NumberMalloc("Simplify"); Siscrat8 = NumberMalloc("Simplify"); x1 = Siscrat8; x2 = Siscrat7; if ( *nb == 1 ) { x3 = Siscrat6; if ( DivLong(a,*na,b,*nb,x1,&n1,x2,&n2) ) goto SimpErr; if ( !n2 ) { for ( i = 0; i < n1; i++ ) *a++ = *x1++; *na = n1; *b = 1; } else { UWORD y1, y2, y3; y2 = *b; y3 = *x2; do { y1 = y2 % y3; y2 = y3; } while ( ( y3 = y1 ) != 0 ); if ( ( *x2 = y2 ) != 1 ) { *b /= y2; if ( DivLong(a,*na,x2,(WORD)1,x1,&n1,x3,&n3) ) goto SimpErr; for ( i = 0; i < n1; i++ ) *a++ = *x1++; *na = n1; } } } #ifdef NEWTRICK else if ( *na >= GCDMAX && *nb >= GCDMAX ) { n1 = i = *na; x3 = a; NCOPY(x1,x3,i); x3 = b; n2 = i = *nb; NCOPY(x2,x3,i); x4 = Siscrat5; x2 = Siscrat6; x3 = Siscrat7; if ( GcdLong(BHEAD Siscrat8,n1,Siscrat7,n2,x2,&n3) ) goto SimpErr; n2 = n3; if ( *x2 != 1 || n2 != 1 ) { DivLong(a,*na,x2,n2,x1,&n1,x4,&n4); *na = i = n1; NCOPY(a,x1,i); DivLong(b,*nb,x2,n2,x3,&n3,x4,&n4); *nb = i = n3; NCOPY(b,x3,i); } } #endif else { x4 = Siscrat5; n1 = i = *na; x3 = a; NCOPY(x1,x3,i); x3 = b; n2 = i = *nb; NCOPY(x2,x3,i); x1 = Siscrat8; x2 = Siscrat7; x3 = Siscrat6; for(;;){ if ( DivLong(x1,n1,x2,n2,x4,&n4,x3,&n3) ) goto SimpErr; if ( !n3 ) break; if ( n2 == 1 ) { while ( ( *x1 = (*x2) % (*x3) ) != 0 ) { *x2 = *x3; *x3 = *x1; } *x2 = *x3; break; } if ( DivLong(x2,n2,x3,n3,x4,&n4,x1,&n1) ) goto SimpErr; if ( !n1 ) { x2 = x3; n2 = n3; x3 = Siscrat7; break; } if ( n3 == 1 ) { while ( ( *x2 = (*x3) % (*x1) ) != 0 ) { *x3 = *x1; *x1 = *x2; } *x2 = *x1; n2 = 1; break; } if ( DivLong(x3,n3,x1,n1,x4,&n4,x2,&n2) ) goto SimpErr; if ( !n2 ) { x2 = x1; n2 = n1; x1 = Siscrat7; break; } if ( n1 == 1 ) { while ( ( *x3 = (*x1) % (*x2) ) != 0 ) { *x1 = *x2; *x2 = *x3; } break; } } if ( *x2 != 1 || n2 != 1 ) { DivLong(a,*na,x2,n2,x1,&n1,x4,&n4); *na = i = n1; NCOPY(a,x1,i); DivLong(b,*nb,x2,n2,x3,&n3,x4,&n4); *nb = i = n3; NCOPY(b,x3,i); } } if ( sgn < 0 ) *na = -*na; NumberFree(Siscrat5,"Simplify"); NumberFree(Siscrat6,"Simplify"); NumberFree(Siscrat7,"Simplify"); NumberFree(Siscrat8,"Simplify"); return(0); SimpErr: MLOCK(ErrorMessageLock); MesCall("Simplify"); MUNLOCK(ErrorMessageLock); NumberFree(Siscrat5,"Simplify"); NumberFree(Siscrat6,"Simplify"); NumberFree(Siscrat7,"Simplify"); NumberFree(Siscrat8,"Simplify"); SETERROR(-1) } /* #] Simplify : #[ AccumGCD : WORD AccumGCD(PHEAD a,na,b,nb) Routine takes the rational GCD of the fractions in a and b and replaces a by the GCD of the two. The rational GCD is defined as the rational that consists of the GCD of the numerators divided by the GCD of the denominators */ int AccumGCD(PHEAD UWORD *a, WORD *na, UWORD *b, WORD nb) { GETBIDENTITY WORD nna,nnb,numa,numb,dena,denb,numc,denc; UWORD *GCDbuffer = NumberMalloc("AccumGCD"); int i; nna = *na; if ( nna < 0 ) nna = -nna; nna = (nna-1)/2; nnb = nb; if ( nnb < 0 ) nnb = -nnb; nnb = (nnb-1)/2; UnPack(a,nna,&dena,&numa); UnPack(b,nnb,&denb,&numb); if ( GcdLong(BHEAD a,numa,b,numb,GCDbuffer,&numc) ) goto AccErr; numa = numc; for ( i = 0; i < numa; i++ ) a[i] = GCDbuffer[i]; if ( GcdLong(BHEAD a+nna,dena,b+nnb,denb,GCDbuffer,&denc) ) goto AccErr; dena = denc; for ( i = 0; i < dena; i++ ) a[i+nna] = GCDbuffer[i]; Pack(a,&numa,a+nna,dena); *na = INCLENG(numa); NumberFree(GCDbuffer,"AccumGCD"); return(0); AccErr: MLOCK(ErrorMessageLock); MesCall("AccumGCD"); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"AccumGCD"); SETERROR(-1) } /* #] AccumGCD : #[ TakeRatRoot: */ int TakeRatRoot(UWORD *a, WORD *n, WORD power) { WORD numer,denom, nn; if ( ( power & 1 ) == 0 && *n < 0 ) return(1); if ( ABS(*n) == 1 && a[0] == 1 && a[1] == 1 ) return(0); nn = ABS(*n); UnPack(a,nn,&denom,&numer); if ( TakeLongRoot(a+nn,&denom,power) ) return(1); if ( TakeLongRoot(a,&numer,power) ) return(1); Pack(a,&numer,a+nn,denom); if ( *n < 0 ) *n = -numer; else *n = numer; return(0); } /* #] TakeRatRoot: #] RekenRational : #[ RekenLong : #[ AddLong : WORD AddLong(a,na,b,nb,c,nc) Long addition. Uses addition and subtraction of positive numbers. */ int AddLong(UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { WORD sgn, res; if ( na < 0 ) { if ( nb < 0 ) { if ( AddPLon(a,-na,b,-nb,c,nc) ) return(-1); *nc = -*nc; return(0); } else { na = -na; sgn = -1; } } else { if ( nb < 0 ) { nb = -nb; sgn = 1; } else { return( AddPLon(a,na,b,nb,c,nc) ); } } if ( ( res = BigLong(a,na,b,nb) ) > 0 ) { SubPLon(a,na,b,nb,c,nc); if ( sgn < 0 ) *nc = -*nc; } else if ( res < 0 ) { SubPLon(b,nb,a,na,c,nc); if ( sgn > 0 ) *nc = -*nc; } else { *nc = 0; *c = 0; } return(0); } /* #] AddLong : #[ AddPLon : WORD AddPLon(a,na,b,nb,c,nc) Adds two long integers a and b and puts the result in c. The length of a and b are na and nb. The length of c is returned in nc. c can be a or b. */ int AddPLon(UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { UWORD carry = 0, e, nd = 0; while ( na && nb ) { e = *a; *c = e + *b + carry; if ( carry ) { if ( e < *c ) carry = 0; } else { if ( e > *c ) carry = 1; } a++; b++; c++; nd++; na--; nb--; } while ( na ) { if ( carry ) { *c = *a++ + carry; if ( *c++ ) carry = 0; } else *c++ = *a++; nd++; na--; } while ( nb ) { if ( carry ) { *c = *b++ + carry; if ( *c++ ) carry = 0; } else *c++ = *b++; nd++; nb--; } if ( carry ) { nd++; if ( nd > (UWORD)AM.MaxTal ) { MLOCK(ErrorMessageLock); MesPrint("Overflow in addition"); MUNLOCK(ErrorMessageLock); return(-1); } *c++ = carry; } *nc = nd; return(0); } /* #] AddPLon : #[ SubPLon : void SubPLon(a,na,b,nb,c,nc) Subtracts b from a. Assumes that a > b. Result in c. c can be a or b. */ void SubPLon(UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { UWORD borrow = 0, e, nd = 0; while ( nb ) { e = *a; if ( borrow ) { *c = e - *b - borrow; if ( *c < e ) borrow = 0; } else { *c = e - *b; if ( *c > e ) borrow = 1; } a++; b++; c++; na--; nb--; nd++; } while ( na ) { if ( borrow ) { if ( *a ) { *c++ = *a++ - 1; borrow = 0; } else { *c++ = (UWORD)(-1); a++; } } else *c++ = *a++; na--; nd++; } while ( nd && !*--c ) { nd--; } *nc = (WORD)nd; } /* #] SubPLon : #[ MulLong : WORD MulLong(a,na,b,nb,c,nc) Does a Long multiplication. Assumes that WORD is half the size of a LONG to work out the scheme! The number of operations is the canonical na*nm multiplications. c should not overlap with a or b. */ int MulLong(UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { WORD sgn = 1; UWORD i, *ic, *ia; RLONG t, bb; if ( !na || !nb ) { *nc = 0; return(0); } if ( na < 0 ) { na = -na; sgn = -sgn; } if ( nb < 0 ) { nb = -nb; sgn = -sgn; } *nc = i = na + nb; if ( i > (UWORD)(AM.MaxTal+1) ) goto MulLov; ic = c; /* #[ GMP stuff : */ #ifdef WITHGMP if (na > 3 && nb > 3) { /* mp_limb_t res; */ UWORD *to, *from; int j; GETIDENTITY UWORD *DLscrat9 = NumberMalloc("MulLong"), *DLscratA = NumberMalloc("MulLong"), *DLscratB = NumberMalloc("MulLong"); #if ( GMPSPREAD != 1 ) if ( na & 1 ) { from = a; a = to = DLscrat9; j = na; NCOPY(to, from, j); a[na++] = 0; ++*nc; } else #endif if ( (LONG)a & (sizeof(mp_limb_t)-1) ) { from = a; a = to = DLscrat9; j = na; NCOPY(to, from, j); } #if ( GMPSPREAD != 1 ) if ( nb & 1 ) { from = b; b = to = DLscratA; j = nb; NCOPY(to, from, j); b[nb++] = 0; ++*nc; } else #endif if ( (LONG)b & (sizeof(mp_limb_t)-1) ) { from = b; b = to = DLscratA; j = nb; NCOPY(to, from, j); } if ( ( *nc > (WORD)i ) || ( (LONG)c & (LONG)(sizeof(mp_limb_t)-1) ) ) { ic = DLscratB; } if ( na < nb ) { /* res = */ mpn_mul((mp_ptr)ic, (mp_srcptr)b, nb/GMPSPREAD, (mp_srcptr)a, na/GMPSPREAD); } else { /* res = */ mpn_mul((mp_ptr)ic, (mp_srcptr)a, na/GMPSPREAD, (mp_srcptr)b, nb/GMPSPREAD); } while ( ic[i-1] == 0 ) i--; *nc = i; /* if ( res == 0 ) *nc -= GMPSPREAD; else if ( res <= WORDMASK ) --*nc; */ if ( ic != c ) { j = *nc; NCOPY(c, ic, j); } if ( sgn < 0 ) *nc = -(*nc); NumberFree(DLscrat9,"MulLong"); NumberFree(DLscratA,"MulLong"); NumberFree(DLscratB,"MulLong"); return(0); } #endif /* #] GMP stuff : */ do { *ic++ = 0; } while ( --i > 0 ); do { ia = a; ic = c++; t = 0; i = na; bb = (RLONG)(*b++); do { t = (*ia++) * bb + t + *ic; *ic++ = (WORD)t; t >>= BITSINWORD; /* should actually be a swap */ } while ( --i > 0 ); if ( t ) *ic = (UWORD)t; } while ( --nb > 0 ); if ( !*ic ) (*nc)--; if ( *nc > AM.MaxTal ) goto MulLov; if ( sgn < 0 ) *nc = -(*nc); return(0); MulLov: MLOCK(ErrorMessageLock); MesPrint("Overflow in Multiplication"); MUNLOCK(ErrorMessageLock); return(-1); } /* #] MulLong : #[ BigLong : WORD BigLong(a,na,b,nb) Returns > 0 if a > b, < 0 if b > a and 0 if a == b */ int BigLong(UWORD *a, WORD na, UWORD *b, WORD nb) { a += na; b += nb; while ( na && !*--a ) na--; while ( nb && !*--b ) nb--; if ( nb < na ) return(1); if ( nb > na ) return(-1); while ( --na >= 0 ) { if ( *a > *b ) return(1); else if ( *b > *a ) return(-1); a--; b--; } return(0); } /* #] BigLong : #[ DivLong : WORD DivLong(a,na,b,nb,c,nc,d,nd) This is the long division which knows a couple of exceptions. It uses therefore a recursive call for the renormalization. The quotient comes in c and the remainder in d. d may be overlapping with b. It may also be identical to a. c should not overlap with a, but it can overlap with b. */ int DivLong(UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc, UWORD *d, WORD *nd) { WORD sgna = 1, sgnb = 1, ne, nf, ng, nh; WORD i, ni; UWORD *w1, *w2; RLONG t, v; UWORD *e, *f, *ff, *g, norm, estim; #ifdef WITHGMP UWORD *DLscrat9, *DLscratA, *DLscratB, *DLscratC; #endif RLONG esthelp; if ( !nb ) { MLOCK(ErrorMessageLock); MesPrint("Division by zero"); MUNLOCK(ErrorMessageLock); return(-1); } if ( !na ) { *nc = *nd = 0; return(0); } if ( na < 0 ) { sgna = -sgna; na = -na; } if ( nb < 0 ) { sgnb = -sgnb; nb = -nb; } if ( na < nb ) { for ( i = 0; i < na; i++ ) *d++ = *a++; *nd = na; *nc = 0; } else if ( nb == na && ( i = BigLong(b,nb,a,na) ) >= 0 ) { if ( i > 0 ) { for ( i = 0; i < na; i++ ) *d++ = *a++; *nd = na; *nc = 0; } else { *c = 1; *nc = 1; *nd = 0; } } else if ( nb == 1 ) { if ( *b == 1 ) { for ( i = 0; i < na; i++ ) *c++ = *a++; *nc = na; *nd = 0; } else { w1 = a+na; *nc = ni = na; *nd = 1; w2 = c+ni; v = (RLONG)(*b); t = (RLONG)(*--w1); while ( --ni >= 0 ) { *--w2 = t / v; t -= v * (*w2); if ( ni ) { t <<= BITSINWORD; t += *--w1; } } if ( ( *d = (UWORD)t ) == 0 ) *nd = 0; if ( !*(c+na-1) ) (*nc)--; } } else { GETIDENTITY /* #[ GMP stuff : We start with copying a and b. Then we make space for c and d. Next we call mpn_tdiv_qr We adjust sizes and copy to c and d if needed. Finally the signs are settled. */ #ifdef WITHGMP if ( na > 4 && nb > 3 ) { UWORD *ic, *id, *to, *from; int j = na - nb; DLscrat9 = NumberMalloc("DivLong"); DLscratA = NumberMalloc("DivLong"); DLscratB = NumberMalloc("DivLong"); DLscratC = NumberMalloc("DivLong"); #if ( GMPSPREAD != 1 ) if ( na & 1 ) { from = a; a = to = DLscrat9; i = na; NCOPY(to, from, i); a[na++] = 0; } else #endif if ( (LONG)a & (sizeof(mp_limb_t)-1) ) { from = a; a = to = DLscrat9; i = na; NCOPY(to, from, i); } #if ( GMPSPREAD != 1 ) if ( nb & 1 ) { from = b; b = to = DLscratA; i = nb; NCOPY(to, from, i); b[nb++] = 0; } else #endif if ( ( (LONG)b & (sizeof(mp_limb_t)-1) ) != 0 ) { from = b; b = to = DLscratA; i = nb; NCOPY(to, from, i); } #if ( GMPSPREAD != 1 ) /* Not recognizing this case was a nasty and extremely rare bug. In the case that c == a and na is odd and nc == na and b still needs to be used, the least significant UWORD of b got overwritten by zero. (22-mar-2023) */ ic = DLscratB; id = DLscratC; #else if ( ( (LONG)c & (sizeof(mp_limb_t)-1) ) != 0 ) ic = DLscratB; else ic = c; if ( ( (LONG)d & (sizeof(mp_limb_t)-1) ) != 0 ) id = DLscratC; else id = d; #endif mpn_tdiv_qr((mp_limb_t *)ic,(mp_limb_t *)id,(mp_size_t)0, (const mp_limb_t *)a,(mp_size_t)(na/GMPSPREAD), (const mp_limb_t *)b,(mp_size_t)(nb/GMPSPREAD)); while ( j >= 0 && ic[j] == 0 ) j--; j++; *nc = j; if ( c != ic ) { NCOPY(c,ic,j); } j = nb-1; while ( j >= 0 && id[j] == 0 ) j--; j++; *nd = j; if ( d != id ) { NCOPY(d,id,j); } if ( sgna < 0 ) { *nc = -(*nc); *nd = -(*nd); } if ( sgnb < 0 ) { *nc = -(*nc); } NumberFree(DLscrat9,"DivLong"); NumberFree(DLscratA,"DivLong"); NumberFree(DLscratB,"DivLong"); NumberFree(DLscratC,"DivLong"); return(0); } #endif /* #] GMP stuff : */ /* Start with normalization operation */ e = NumberMalloc("DivLong"); f = NumberMalloc("DivLong"); g = NumberMalloc("DivLong"); if ( b[nb-1] == (FULLMAX-1) ) norm = 1; else { norm = (UWORD)(((ULONG)FULLMAX) / (ULONG)((b[nb-1]+1L))); } f[na] = 0; if ( MulLong(b,nb,&norm,1,e,&ne) || MulLong(a,na,&norm,1,f,&nf) ) { NumberFree(e,"DivLong"); NumberFree(f,"DivLong"); NumberFree(g,"DivLong"); return(-1); } if ( BigLong(f+nf-ne,ne,e,ne) >= 0 ) { SubPLon(f+nf-ne,ne,e,ne,f+nf-ne,&nh); w1 = c + (nf-ne); *nc = nf-ne+1; } else { nh = ne; *nc = nf-ne; w1 = 0; } w2 = c; i = *nc; do { *w2++ = 0; } while ( --i > 0 ); nf = na; ni = nf-ne; esthelp = (RLONG)(e[ne-1]) + 1L; while ( nf >= ne ) { if ( (WORD)esthelp == 0 ) { estim = (WORD)(((((RLONG)(f[nf]))<>BITSINWORD); } else { estim = (WORD)(((((RLONG)(f[nf]))< 0 ) && !*w2 ) { nh--; w2--; } } if ( BigLong(f+ni,nh,e,ne) >= 0 ) { estim++; SubPLon(f+ni,nh,e,ne,f+ni,&nh); if ( BigLong(f+ni,nh,e,ne) >= 0 ) { estim++; SubPLon(f+ni,nh,e,ne,f+ni,&nh); if ( BigLong(f+ni,nh,e,ne) >= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Problems in DivLong"); AO.OutSkip = 3; FiniLine(); i = na; while ( --i >= 0 ) { TalToLine((UWORD)(*a++)); TokenToLine((UBYTE *)" "); } FiniLine(); i = nb; while ( --i >= 0 ) { TalToLine((UWORD)(*b++)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); MUNLOCK(ErrorMessageLock); NumberFree(e,"DivLong"); NumberFree(f,"DivLong"); NumberFree(g,"DivLong"); return(-1); } } } c[ni] = estim; nf--; ni--; } if ( w1 ) *w1 = 1; /* Finish with the renormalization operation */ if ( nh > 0 ) { if ( norm == 1 ) { *nd = i = nh; ff = f; NCOPY(d,ff,i); } else { w1 = f+nh; *nd = ni = nh; w2 = d+ni; v = norm; t = (RLONG)(*--w1); while ( --ni >= 0 ) { *--w2 = t / v; t -= v * (*w2); if ( ni ) { t <<= BITSINWORD; t += *--w1; } } if ( t ) { MLOCK(ErrorMessageLock); MesPrint("Error in DivLong"); MUNLOCK(ErrorMessageLock); NumberFree(e,"DivLong"); NumberFree(f,"DivLong"); NumberFree(g,"DivLong"); return(-1); } if ( !*(d+nh-1) ) (*nd)--; } } else { *nd = 0; } NumberFree(e,"DivLong"); NumberFree(f,"DivLong"); NumberFree(g,"DivLong"); } if ( sgna < 0 ) { *nc = -(*nc); *nd = -(*nd); } if ( sgnb < 0 ) { *nc = -(*nc); } return(0); } /* #] DivLong : #[ RaisPow : WORD RaisPow(a,na,b) Raises a to the power b. a is a Long integer and b >= 0. The method that is used works with a bitdecomposition of b. */ int RaisPow(PHEAD UWORD *a, WORD *na, UWORD b) { GETBIDENTITY WORD i, nu; UWORD *it, *iu, c; UWORD *is, *iss; WORD ns, nt, nmod; nmod = ABS(AN.ncmod); if ( !*na || ( ( *na == 1 ) && ( *a == 1 ) ) ) return(0); if ( !b ) { *na=1; *a=1; return(0); } is = NumberMalloc("RaisPow"); it = NumberMalloc("RaisPow"); for ( i = 0; i < ABS(*na); i++ ) is[i] = a[i]; ns = *na; c = b; for ( i = 0; i < BITSINWORD; i++ ) { if ( !c ) break; c /= 2; } i--; c = 1 << i; while ( --i >= 0 ) { c /= 2; if(MulLong(is,ns,is,ns,it,&nt)) goto RaisOvl; if ( b & c ) { if ( MulLong(it,nt,a,*na,is,&ns) ) goto RaisOvl; } else { iu = is; is = it; it = iu; nu = ns; ns = nt; nt = nu; } if ( nmod != 0 ) { if ( DivLong(is,ns,(UWORD *)AC.cmod,nmod,it,&nt,is,&ns) ) goto RaisOvl; } } if ( ( nmod != 0 ) && ( ( AC.modmode & POSNEG ) != 0 ) ) { NormalModulus(is,&ns); } if ( ( *na = i = ns ) != 0 ) { iss = is; i=ABS(i); NCOPY(a,iss,i); } NumberFree(is,"RaisPow"); NumberFree(it,"RaisPow"); return(0); RaisOvl: MLOCK(ErrorMessageLock); MesCall("RaisPow"); MUNLOCK(ErrorMessageLock); NumberFree(is,"RaisPow"); NumberFree(it,"RaisPow"); SETERROR(-1) } /* #] RaisPow : #[ RaisPowCached : */ /** Computes power x^n and caches the value * * Description * =========== * Calculates the power x^n and stores the results for caching * purposes. The pointer c (i.e., the pointer, and not what it * points to) is overwritten. What it points to should not be * overwritten in the calling function. * * Notes * ===== * - Caching is done in AT.small_power[]. This array is extended * if necessary. */ void RaisPowCached (PHEAD WORD x, WORD n, UWORD **c, WORD *nc) { int i,j; WORD new_small_power_maxx, new_small_power_maxn, ID; WORD *new_small_power_n; UWORD **new_small_power; /* check whether to extend the array */ if (x>=AT.small_power_maxx || n>=AT.small_power_maxn) { new_small_power_maxx = AT.small_power_maxx; if (x>=AT.small_power_maxx) new_small_power_maxx = MaX(2*AT.small_power_maxx, x+1); new_small_power_maxn = AT.small_power_maxn; if (n>=AT.small_power_maxn) new_small_power_maxn = MaX(2*AT.small_power_maxn, n+1); new_small_power_n = (WORD*) Malloc1(new_small_power_maxx*new_small_power_maxn*sizeof(WORD),"RaisPowCached"); new_small_power = (UWORD **) Malloc1(new_small_power_maxx*new_small_power_maxn*sizeof(UWORD *),"RaisPowCached"); for (i=0; i 0 ) { SubPLon((UWORD *)AC.cmod,(ABS(AC.ncmod)),a,n,a,&n); if ( *na > 0 ) { *na = -n; } else { *na = n; } return(1); } return(0); } /* #] NormalModulus : #[ MakeInverses : */ /** * Makes a table of inverses in modular calculus * The modulus is in AC.cmod and AC.ncmod * One should notice that the table of inverses can only be made if * the modulus fits inside a single FORM word. Otherwise the table lookup * becomes too difficult and the table too long. */ int MakeInverses(void) { WORD n = AC.cmod[0], i, inv2; if ( AC.ncmod != 1 ) return(1); if ( AC.modinverses == 0 ) { LOCK(AC.halfmodlock); if ( AC.modinverses == 0 ) { AC.modinverses = (UWORD *)Malloc1(n*sizeof(UWORD),"modinverses"); AC.modinverses[0] = 0; AC.modinverses[1] = 1; for ( i = 2; i < n; i++ ) { if ( GetModInverses(i,n, (WORD *)(&(AC.modinverses[i])),&inv2) ) { SETERROR(-1) } } } UNLOCK(AC.halfmodlock); } return(0); } /* #] MakeInverses : #[ GetModInverses : */ /** * Input m1 and m2, which are relative prime. * determines a*m1+b*m2 = 1 (and 1 is the gcd of m1 and m2) * then a*m1 = 1 mod m2 and hence im1 = a. * and b*m2 = 1 mod m1 and hence im2 = b. * Set m1 = 0*m1+1*m2 = a1*m1+b1*m2 * m2 = 1*m1+0*m2 = a2*m1+b2*m2 * If everything is OK, the return value is zero */ int GetModInverses(WORD m1, WORD m2, WORD *im1, WORD *im2) { WORD a1, a2, a3; WORD b1, b2, b3; WORD x = m1, y, c, d = m2; if ( x < 1 || d <= 1 ) goto somethingwrong; a1 = 0; a2 = 1; b1 = 1; b2 = 0; for(;;) { c = d/x; y = d%x; /* a good compiler makes this faster than y=d-c*x */ if ( y == 0 ) break; a3 = a1-c*a2; a1 = a2; a2 = a3; b3 = b1-c*b2; b1 = b2; b2 = b3; d = x; x = y; } if ( x != 1 ) goto somethingwrong; if ( a2 < 0 ) a2 += m2; if ( b2 < 0 ) b2 += m1; if (im1!=NULL) *im1 = a2; if (im2!=NULL) *im2 = b2; return(0); somethingwrong: MLOCK(ErrorMessageLock); MesPrint("Error trying to determine inverses in GetModInverses"); MUNLOCK(ErrorMessageLock); return(-1); } /* #] GetModInverses : #[ GetLongModInverses : */ int GetLongModInverses(PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *ia, WORD *nia, UWORD *ib, WORD *nib) { UWORD *s, *t, *sa, *sb, *ta, *tb, *x, *y, *swap1; WORD ns, nt, nsa, nsb, nta, ntb, nx, ny, swap2; s = NumberMalloc("GetLongModInverses"); ns = na; WCOPY(s, a, ABS(ns)); t = NumberMalloc("GetLongModInverses"); nt = nb; WCOPY(t, b, ABS(nt)); sa = NumberMalloc("GetLongModInverses"); nsa = 1; sa[0] = 1; sb = NumberMalloc("GetLongModInverses"); nsb = 0; ta = NumberMalloc("GetLongModInverses"); nta = 0; tb = NumberMalloc("GetLongModInverses"); ntb = 1; tb[0] = 1; x = NumberMalloc("GetLongModInverses"); y = NumberMalloc("GetLongModInverses"); while (nt != 0) { DivLong(s,ns,t,nt,x,&nx,y,&ny); swap1=s; s=y; y=swap1; ns=ny; MulLong(x,nx,ta,nta,y,&ny); AddLong(sa,nsa,y,-ny,sa,&nsa); MulLong(x,nx,tb,ntb,y,&ny); AddLong(sb,nsb,y,-ny,sb,&nsb); swap1=s; s=t; t=swap1; swap2=ns; ns=nt; nt=swap2; swap1=sa; sa=ta; ta=swap1; swap2=nsa; nsa=nta; nta=swap2; swap1=sb; sb=tb; tb=swap1; swap2=nsb; nsb=ntb; ntb=swap2; } if (ia!=NULL) { *nia = nsa*ns; WCOPY(ia,sa,ABS(*nia)); } if (ib!=NULL) { *nib = nsb*ns; WCOPY(ib,sb,ABS(*nib)); } NumberFree(s,"GetLongModInverses"); NumberFree(t,"GetLongModInverses"); NumberFree(sa,"GetLongModInverses"); NumberFree(sb,"GetLongModInverses"); NumberFree(ta,"GetLongModInverses"); NumberFree(tb,"GetLongModInverses"); NumberFree(x,"GetLongModInverses"); NumberFree(y,"GetLongModInverses"); return 0; } /* #] GetLongModInverses : #[ Product : WORD Product(a,na,b) Multiplies the Long number in a with the WORD b. */ int Product(UWORD *a, WORD *na, WORD b) { WORD i, sgn = 1; RLONG t, u; if ( *na < 0 ) { *na = -(*na); sgn = -sgn; } if ( b < 0 ) { b = -b; sgn = -sgn; } t = 0; u = (RLONG)b; for ( i = 0; i < *na; i++ ) { t += *a * u; *a++ = (UWORD)t; t >>= BITSINWORD; } if ( t > 0 ) { if ( ++(*na) > AM.MaxTal ) { MLOCK(ErrorMessageLock); MesPrint("Overflow in Product"); MUNLOCK(ErrorMessageLock); return(-1); } *a = (UWORD)t; } if ( sgn < 0 ) *na = -(*na); return(0); } /* #] Product : #[ Quotient : UWORD Quotient(a,na,b) Routine divides the long number a by b with the assumption that there is no remainder (like while computing binomials). */ UWORD Quotient(UWORD *a, WORD *na, WORD b) { RLONG v, t; WORD i, j, sgn = 1; if ( ( i = *na ) < 0 ) { sgn = -1; i = -i; } if ( b < 0 ) { b = -b; sgn = -sgn; } if ( i == 1 ) { if ( ( *a /= (UWORD)b ) == 0 ) *na = 0; if ( sgn < 0 ) *na = -*na; return(0); } a += i; j = i; v = (RLONG)b; t = (RLONG)(*--a); while ( --i >= 0 ) { *a = t / v; t -= v * (*a); if ( i ) { t <<= BITSINWORD; t += *--a; } } a += j - 1; if ( !*a ) j--; if ( sgn < 0 ) j = -j; *na = j; return(0); } /* #] Quotient : #[ Remain10 : WORD Remain10(a,na) Routine divides a by 10 and gives the remainder as return value. The value of a will be the quotient! a must be positive. */ WORD Remain10(UWORD *a, WORD *na) { WORD i; RLONG t, u; UWORD *b; i = *na; t = 0; b = a + i - 1; while ( --i >= 0 ) { t += *b; *b-- = u = t / 10; t -= u * 10; if ( i > 0 ) t <<= BITSINWORD; } if ( ( *na > 0 ) && !a[*na-1] ) (*na)--; return((WORD)t); } /* #] Remain10 : #[ Remain4 : WORD Remain4(a,na) Routine divides a by 10000 and gives the remainder as return value. The value of a will be the quotient! a must be positive. */ WORD Remain4(UWORD *a, WORD *na) { WORD i; RLONG t, u; UWORD *b; i = *na; t = 0; b = a + i - 1; while ( --i >= 0 ) { t += *b; *b-- = u = t / 10000; t -= u * 10000; if ( i > 0 ) t <<= BITSINWORD; } if ( ( *na > 0 ) && !a[*na-1] ) (*na)--; return((WORD)t); } /* #] Remain4 : #[ PrtLong : void PrtLong(a,na,s) Puts the long number a in string s. */ void PrtLong(UWORD *a, WORD na, UBYTE *s) { GETIDENTITY WORD q, i; UBYTE *sa, *sb; UBYTE c; UWORD *bb, *b; if ( na < 0 ) { *s++ = '-'; na = -na; } b = NumberMalloc("PrtLong"); bb = b; i = na; while ( --i >= 0 ) *bb++ = *a++; a = b; if ( na > 2 ) { sa = s; do { q = Remain4(a,&na); *sa++ = (UBYTE)('0' + (q%10)); q /= 10; *sa++ = (UBYTE)('0' + (q%10)); q /= 10; *sa++ = (UBYTE)('0' + (q%10)); q /= 10; *sa++ = (UBYTE)('0' + (q%10)); } while ( na ); while ( sa[-1] == '0' ) sa--; sb = s; s = sa; sa--; while ( sa > sb ) { c = *sa; *sa = *sb; *sb = c; sa--; sb++; } } else if ( na ) { sa = s; do { q = Remain10(a,&na); *sa++ = (UBYTE)('0' + q); } while ( na ); sb = s; s = sa; sa--; while ( sa > sb ) { c = *sa; *sa = *sb; *sb = c; sa--; sb++; } } else *s++ = '0'; *s = '\0'; NumberFree(b,"PrtLong"); } /* #] PrtLong : #[ GetLong : WORD GetLong(s,a,na) Reads a long number from a string. The string is zero terminated and contains only digits! New algorithm: try to read 4 digits together before the result is accumulated. */ int GetLong(UBYTE *s, UWORD *a, WORD *na) { /* UWORD digit; *a = 0; *na = 0; while ( FG.cTable[*s] == 1 ) { digit = *s++ - '0'; if ( *na && Product(a,na,(WORD)10) ) return(-1); if ( digit && AddLong(a,*na,&digit,(WORD)1,a,na) ) return(-1); } return(0); */ UWORD digit, x = 0, y = 0; *a = 0; *na = 0; while ( FG.cTable[*s] == 1 ) { x = *s++ - '0'; if ( FG.cTable[*s] != 1 ) { y = 10; break; } x = 10*x + *s++ - '0'; if ( FG.cTable[*s] != 1 ) { y = 100; break; } x = 10*x + *s++ - '0'; if ( FG.cTable[*s] != 1 ) { y = 1000; break; } x = 10*x + *s++ - '0'; if ( *na && Product(a,na,(WORD)10000) ) return(-1); if ( ( digit = x ) != 0 && AddLong(a,*na,&digit,(WORD)1,a,na) ) return(-1); y = 0; } if ( y ) { if ( *na && Product(a,na,(WORD)y) ) return(-1); if ( ( digit = x ) != 0 && AddLong(a,*na,&digit,(WORD)1,a,na) ) return(-1); } return(0); } /* #] GetLong : #[ GCD : WORD GCD(a,na,b,nb,c,nc) Algorithm to compute the GCD of two long numbers. See Knuth, sec 4.5.2 algorithm L. We assume that both numbers are positive NOTE!!!!!. NumberMalloc gets called and it may not be freed */ #ifdef EXTRAGCD #define Convert(ia,aa,naa) \ if ( (LONG)ia < 0 ) { \ ia = (ULONG)(-(LONG)ia); \ aa[0] = ia; \ if ( ( aa[1] = ia >> BITSINWORD ) != 0 ) naa = -2; \ else naa = -1; \ } \ else if ( ia == 0 ) { aa[0] = 0; naa = 0; } \ else { \ aa[0] = ia; \ if ( ( aa[1] = ia >> BITSINWORD ) != 0 ) naa = 2; \ else naa = 1; \ } void GCD(UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { int ja = 0, jb = 0, j; UWORD *r,*t; UWORD *x1, *x2, *x3; WORD nd,naa,nbb; ULONG ia,ib,ic,id,u,v,w,q,T; UWORD aa[2], bb[2]; /* First eliminate easy powers of 2^... */ while ( a[0] == 0 ) { na--; ja++; a++; } while ( b[0] == 0 ) { nb--; jb++; b++; } if ( ja > jb ) ja = jb; if ( ja > 0 ) { j = ja; do { *c++ = 0; } while ( --j > 0 ); } /* Now arrange things such that a >= b */ if ( na < nb ) { jb = na; na = nb; nb = jb; exch: r = a; a = b; b = r; } else if ( na == nb ) { r = a+na; t = b+nb; j = na; while ( --j >= 0 ) { if ( *--r > *--t ) break; if ( *r < *t ) goto exch; } if ( j < 0 ) { out: j = nb; NCOPY(c,b,j); *nc = nb+ja; return; } } /* { MLOCK(ErrorMessageLock); MesPrint("Ordered input, ja = %d",(WORD)ja); AO.OutSkip = 3; FiniLine(); j = na; r = a; while ( --j >= 0 ) { TalToLine((UWORD)(*r++)); TokenToLine((UBYTE *)" "); } FiniLine(); j = nb; r = b; while ( --j >= 0 ) { TalToLine((UWORD)(*r++)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); MUNLOCK(ErrorMessageLock); } */ /* We have now that A > B The loop recognizes the case that na-nb >= 1 In that case we just have to divide! */ r = x1 = NumberMalloc("GCD"); t = x2 = NumberMalloc("GCD"); x3 = NumberMalloc("GCD"); j = na; NCOPY(r,a,j); j = nb; NCOPY(t,b,j); for(;;) { while ( na > nb ) { toobad: DivLong(x1,na,x2,nb,c,nc,x3,&nd); if ( nd == 0 ) { b = x2; goto out; } t = x1; x1 = x2; x2 = x3; x3 = t; na = nb; nb = nd; if ( na == 2 ) break; } /* Here we can use the shortcut. */ if ( na == 2 ) { v = x1[0] + ( ((ULONG)x1[1]) << BITSINWORD ); w = x2[0]; if ( nb == 2 ) w += ((ULONG)x2[1]) << BITSINWORD; #ifdef EXTRAGCD2 v = GCD2(v,w); #else do { u = v%w; v = w; w = u; } while ( w ); #endif c[0] = (UWORD)v; if ( ( c[1] = (UWORD)(v >> BITSINWORD) ) != 0 ) *nc = 2+ja; else *nc = 1+ja; NumberFree(x1,"GCD"); NumberFree(x2,"GCD"); NumberFree(x3,"GCD"); return; } if ( na == 1 ) { UWORD ui, uj; ui = x1[0]; uj = x2[0]; #ifdef EXTRAGCD2 ui = (UWORD)GCD2((ULONG)ui,(ULONG)uj); #else do { nd = ui%uj; ui = uj; uj = nd; } while ( nd ); #endif c[0] = ui; *nc = 1 + ja; NumberFree(x1,"GCD"); NumberFree(x2,"GCD"); NumberFree(x3,"GCD"); return; } ia = 1; ib = 0; ic = 0; id = 1; u = ( ((ULONG)x1[na-1]) << BITSINWORD ) + x1[na-2]; v = ( ((ULONG)x2[nb-1]) << BITSINWORD ) + x2[nb-2]; while ( v+ic != 0 && v+id != 0 && ( q = (u+ia)/(v+ic) ) == (u+ib)/(v+id) ) { T = ia-q*ic; ia = ic; ic = T; T = ib-q*id; ib = id; id = T; T = u - q*v; u = v; v = T; } if ( ib == 0 ) goto toobad; Convert(ia,aa,naa); Convert(ib,bb,nbb); MulLong(x1,na,aa,naa,x3,&nd); MulLong(x2,nb,bb,nbb,c,nc); AddLong(x3,nd,c,*nc,c,nc); Convert(ic,aa,naa); Convert(id,bb,nbb); MulLong(x1,na,aa,naa,x3,&nd); t = c; na = j = *nc; r = x1; NCOPY(r,t,j); MulLong(x2,nb,bb,nbb,c,nc); AddLong(x3,nd,c,*nc,x2,&nb); } } #endif /* #] GCD : #[ GcdLong : WORD GcdLong(a,na,b,nb,c,nc) Returns the Greatest Common Divider of a and b in c. If a and or b are zero an error message will be returned. The answer is always positive. In principle a and c can be the same. */ #ifndef NEWTRICK /* #[ Old Routine : */ int GcdLong(PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { GETBIDENTITY if ( !na || !nb ) { if ( !na && !nb ) { MLOCK(ErrorMessageLock); MesPrint("Cannot take gcd"); MUNLOCK(ErrorMessageLock); return(-1); } if ( !na ) { *nc = abs(nb); NCOPY(c,b,*nc); *nc = abs(nb); return(0); } *nc = abs(na); NCOPY(c,a,*nc); *nc = abs(na); return(0); } if ( na < 0 ) na = -na; if ( nb < 0 ) nb = -nb; if ( na == 1 && nb == 1 ) { #ifdef EXTRAGCD2 *c = (UWORD)GCD2((ULONG)*a,(ULONG)*b); #else UWORD x,y,z; x = *a; y = *b; do { z = x % y; x = y; } while ( ( y = z ) != 0 ); *c = x; #endif *nc = 1; } else if ( na <= 2 && nb <= 2 ) { RLONG lx,ly,lz; if ( na == 2 ) { lx = (((RLONG)(a[1]))<> BITSINWORD) ) != 0 ) *nc = 2; else *nc = 1; } } else { #ifdef EXTRAGCD GCD(a,na,b,nb,c,nc); #else #ifdef NEWGCD UWORD *x3,*x1,*x2, *GLscrat7, *GLscrat8; WORD n1,n2,n3,n4; WORD i, j; x1 = c; x3 = a; n1 = i = na; NCOPY(x1,x3,i); GLscrat7 = NumberMalloc("GcdLong"); GLscrat8 = NumberMalloc("GcdLong"); x2 = GLscrat8; x3 = b; n2 = i = nb; NCOPY(x2,x3,i); x1 = c; i = 0; while ( x1[0] == 0 ) { i += BITSINWORD; x1++; n1--; } while ( ( x1[0] & 1 ) == 0 ) { i++; SCHUIF(x1,n1) } x2 = GLscrat8; j = 0; while ( x2[0] == 0 ) { j += BITSINWORD; x2++; n2--; } while ( ( x2[0] & 1 ) == 0 ) { j++; SCHUIF(x2,n2) } if ( j > i ) j = i; /* powers of two in GCD */ for(;;){ if ( n1 > n2 ) { firstbig: SubPLon(x1,n1,x2,n2,x1,&n3); n1 = n3; if ( n1 == 0 ) { x1 = c; n1 = i = n2; NCOPY(x1,x2,i); break; } while ( ( x1[0] & 1 ) == 0 ) SCHUIF(x1,n1) if ( n1 == 1 ) { if ( DivLong(x2,n2,x1,n1,GLscrat7,&n3,x2,&n4) ) goto GcdErr; n2 = n4; if ( n2 == 0 ) { i = n1; x2 = c; NCOPY(x2,x1,i); break; } #ifdef EXTRAGCD2 *c = (UWORD)GCD2((ULONG)x1[0],(ULONG)x2[0]); #else { UWORD x,y,z; x = x1[0]; y = x2[0]; do { z = x % y; x = y; } while ( ( y = z ) != 0 ); *c = x; } #endif n1 = 1; break; } } else if ( n1 < n2 ) { lastbig: SubPLon(x2,n2,x1,n1,x2,&n3); n2 = n3; if ( n2 == 0 ) { i = n1; x2 = c; NCOPY(x2,x1,i); break; } while ( ( x2[0] & 1 ) == 0 ) SCHUIF(x2,n2) if ( n2 == 1 ) { if ( DivLong(x1,n1,x2,n2,GLscrat7,&n3,x1,&n4) ) goto GcdErr; n1 = n4; if ( n1 == 0 ) { x1 = c; n1 = i = n2; NCOPY(x1,x2,i); break; } #ifdef EXTRAGCD2 *c = (UWORD)GCD2((ULONG)x2[0],(ULONG)x1[0]); #else { UWORD x,y,z; x = x2[0]; y = x1[0]; do { z = x % y; x = y; } while ( ( y = z ) != 0 ); *c = x; } #endif n1 = 1; break; } } else { for ( i = n1-1; i >= 0; i-- ) { if ( x1[i] > x2[i] ) goto firstbig; else if ( x1[i] < x2[i] ) goto lastbig; } i = n1; x2 = c; NCOPY(x2,x1,i); break; } } /* Now the GCD is in c but still needs j powers of 2. */ x1 = c; while ( j >= BITSINWORD ) { for ( i = n1; i > 0; i-- ) x1[i] = x1[i-1]; x1[0] = 0; n1++; j -= BITSINWORD; } if ( j > 0 ) { ULONG a1,a2 = 0; for ( i = 0; i < n1; i++ ) { a1 = x1[i]; a1 <<= j; a2 += a1; x1[i] = a2; a2 >>= BITSINWORD; } if ( a2 != 0 ) { x1[n1++] = a2; } } *nc = n1; NumberFree(GLscrat7,"GcdLong"); NumberFree(GLscrat8,"GcdLong"); #else UWORD *x1,*x2,*x3,*x4,*c1,*c2; WORD n1,n2,n3,n4,i; x1 = c; x3 = a; n1 = i = na; NCOPY(x1,x3,i); x1 = c; c1 = x2 = NumberMalloc("GcdLong"); x3 = NumberMalloc("GcdLong"); x4 = NumberMalloc("GcdLong"); c2 = b; n2 = i = nb; NCOPY(c1,c2,i); for(;;){ if ( DivLong(x1,n1,x2,n2,x4,&n4,x3,&n3) ) goto GcdErr; if ( !n3 ) { x1 = x2; n1 = n2; break; } if ( DivLong(x2,n2,x3,n3,x4,&n4,x1,&n1) ) goto GcdErr; if ( !n1 ) { x1 = x3; n1 = n3; break; } if ( DivLong(x3,n3,x1,n1,x4,&n4,x2,&n2) ) goto GcdErr; if ( !n2 ) { *nc = n1; NumberFree(x2,"GcdLong"); NumberFree(x3,"GcdLong"); NumberFree(x4,"GcdLong"); return(0); } } *nc = i = n1; NCOPY(c,x1,i); NumberFree(x2,"GcdLong"); NumberFree(x3,"GcdLong"); NumberFree(x4,"GcdLong"); #endif #endif } return(0); GcdErr: MLOCK(ErrorMessageLock); MesCall("GcdLong"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] Old Routine : */ #else /* New routine for GcdLong that uses smart shortcuts. Algorithm by J. Vermaseren 15-nov-2006. It runs faster for very big numbers but only by a fixed factor. There is no improvement in the power behaviour. Improvement on the whole of hf9 (multiple zeta values at weight 9): Better than a factor 2 on a 32 bits architecture and 2.76 on a 64 bits architecture. On hf10 (MZV's at weight 10), 64 bits architecture: factor 7. If we have two long numbers (na,nb > GCDMAX) we will work in a truncated way. At the moment of writing (15-nov-2006) it isn't clear whether this algorithm is an invention or a reinvention. A short search on the web didn't show anything. 31-jul-2007: A better search shows that this is an adaptation of the Lehmer-Euclid algorithm, already described in Knuth. Here we can work without upper and lower limit because we are only interested in the GCD, not the extra numbers. Also it takes already some features of the double digit Lehmer-Euclid algorithm of Jebelean it seems. Maybe this can be programmed slightly better and we can get another few percent speed increase. Further improvements for the asymptotic case come from splitting the calculation as in Karatsuba and working with FFT divisions and multiplications etc. But this is when hundreds of words are involved at the least. Algorithm 1: while ( na > nb || nb < GCDMAX ) { if ( nb == 0 ) { result in a } c = a % b; a = b; b = c; } 2: Make the truncated values in which a and b are the combinations of the top two words of a and b. The whole numbers are aa and bb now. 3: ma1 = 1; ma2 = 0; mb1 = 0; mb2 = 1; 4: A = a; B = b; m = a/b; c = a - m*b; c = ma1*a+ma2*b-m*(mb1*a+mb2*b) = (ma1-m*mb1)*a+(ma2-m*mb2)*b mc1 = ma1-m*mb1; mc2 = ma2-m*mb2; 5: a = b; ma1 = mb1; ma2 = mb2; b = c; mb1 = mc1; mb2 = mc2; 6: if ( b != 0 && nb >= FULLMAX ) goto 4; 7: Now construct the new quantities ma1*aa+ma2*bb and mb1*aa+mb2*bb 8: goto 1; The essence of the above algorithm is that we do the divisions only on relatively short numbers. Also usually there are many steps 4&5 for each step 7. This eliminates many operations. The termination at FULLMAX is that we make errors by not considering the tail of the number. If we run b down all the way, the errors combine in such a way that the new numbers may be of the same order as the old numbers. By stopping halfway we don't get the error beyond halfway either. Unfortunately this means that a >= FULLMAX and hence na > nb which means that next we will have a complete division. But just once. Running the steps 4-6 till a < FULLMAX runs already into problems. It may be necessary to experiment a bit to obtain the optimum value of GCDMAX. */ int GcdLong(PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { GETBIDENTITY UWORD x,y,z; UWORD *x1,*x2,*x3,*x4,*x5,*d; UWORD *GLscrat6, *GLscrat7, *GLscrat8, *GLscrat9, *GLscrat10; WORD n1,n2,n3,n4,n5,i; RLONG lx,ly,lz; LONG ma1, ma2, mb1, mb2, mc1, mc2, m; if ( !na || !nb ) { if ( !na && !nb ) { MLOCK(ErrorMessageLock); MesPrint("Cannot take gcd"); MUNLOCK(ErrorMessageLock); return(-1); } if ( !na ) { *nc = abs(nb); NCOPY(c,b,*nc); *nc = abs(nb); return(0); } *nc = abs(na); NCOPY(c,a,*nc); *nc = abs(na); return(0); } if ( na < 0 ) na = -na; if ( nb < 0 ) nb = -nb; /* #[ GMP stuff : */ #ifdef WITHGMP if ( na > 3 && nb > 3 ) { int ii; mp_limb_t *upa, *upb, *upc, xx; UWORD *uw, *u1, *u2; unsigned int tcounta, tcountb, tcounta1, tcountb1; mp_size_t ana, anb, anc; u1 = uw = NumberMalloc("GcdLong"); upa = (mp_limb_t *)u1; ana = na; tcounta1 = 0; while ( a[0] == 0 ) { a++; ana--; tcounta1++; } for ( ii = 0; ii < ana; ii++ ) { *uw++ = *a++; } if ( ( ana & 1 ) != 0 ) { *uw = 0; ana++; } ana /= 2; u2 = uw = NumberMalloc("GcdLong"); upb = (mp_limb_t *)u2; anb = nb; tcountb1 = 0; while ( b[0] == 0 ) { b++; anb--; tcountb1++; } for ( ii = 0; ii < anb; ii++ ) { *uw++ = *b++; } if ( ( anb & 1 ) != 0 ) { *uw = 0; anb++; } anb /= 2; xx = upa[0]; tcounta = 0; while ( ( xx & 15 ) == 0 ) { tcounta += 4; xx >>= 4; } while ( ( xx & 1 ) == 0 ) { tcounta += 1; xx >>= 1; } xx = upb[0]; tcountb = 0; while ( ( xx & 15 ) == 0 ) { tcountb += 4; xx >>= 4; } while ( ( xx & 1 ) == 0 ) { tcountb += 1; xx >>= 1; } if ( tcounta ) { mpn_rshift(upa,upa,ana,tcounta); if ( upa[ana-1] == 0 ) ana--; } if ( tcountb ) { mpn_rshift(upb,upb,anb,tcountb); if ( upb[anb-1] == 0 ) anb--; } upc = (mp_limb_t *)(NumberMalloc("GcdLong")); if ( ( ana > anb ) || ( ( ana == anb ) && ( upa[ana-1] >= upb[ana-1] ) ) ) { anc = mpn_gcd(upc,upa,ana,upb,anb); } else { anc = mpn_gcd(upc,upb,anb,upa,ana); } tcounta = tcounta1*BITSINWORD + tcounta; tcountb = tcountb1*BITSINWORD + tcountb; if ( tcountb > tcounta ) tcountb = tcounta; tcounta = tcountb/BITSINWORD; tcountb = tcountb%BITSINWORD; if ( tcountb ) { xx = mpn_lshift(upc,upc,anc,tcountb); if ( xx ) { upc[anc] = xx; anc++; } } uw = (UWORD *)upc; anc *= 2; while ( uw[anc-1] == 0 ) anc--; for ( ii = 0; ii < (int)tcounta; ii++ ) *c++ = 0; for ( ii = 0; ii < anc; ii++ ) *c++ = *uw++; *nc = anc + tcounta; NumberFree(u1,"GcdLong"); NumberFree(u2,"GcdLong"); NumberFree((UWORD *)(upc),"GcdLong"); return(0); } #endif /* #] GMP stuff : */ /* #[ Easy cases : */ if ( na == 1 && nb == 1 ) { x = *a; y = *b; do { z = x % y; x = y; } while ( ( y = z ) != 0 ); *c = x; *nc = 1; return(0); } else if ( na <= 2 && nb <= 2 ) { if ( na == 2 ) { lx = (((RLONG)(a[1]))<> BITSINWORD) ) != 0 ) *nc = 2; else *nc = 1; } return(0); } /* #] Easy cases : */ GLscrat6 = NumberMalloc("GcdLong"); GLscrat7 = NumberMalloc("GcdLong"); GLscrat8 = NumberMalloc("GcdLong"); GLscrat9 = NumberMalloc("GcdLong"); GLscrat10 = NumberMalloc("GcdLong"); restart:; /* #[ Easy cases : */ if ( na == 1 && nb == 1 ) { x = *a; y = *b; do { z = x % y; x = y; } while ( ( y = z ) != 0 ); *c = x; *nc = 1; } else if ( na <= 2 && nb <= 2 ) { if ( na == 2 ) { lx = (((RLONG)(a[1]))<> BITSINWORD) ) != 0 ) *nc = 2; else *nc = 1; } } /* #] Easy cases : #[ Original code : */ else if ( na < GCDMAX || nb < GCDMAX || na != nb ) { if ( na < nb ) { x2 = GLscrat8; x3 = a; n2 = i = na; NCOPY(x2,x3,i); x1 = c; x3 = b; n1 = i = nb; NCOPY(x1,x3,i); } else { x1 = c; x3 = a; n1 = i = na; NCOPY(x1,x3,i); x2 = GLscrat8; x3 = b; n2 = i = nb; NCOPY(x2,x3,i); } x1 = c; x2 = GLscrat8; x3 = GLscrat7; x4 = GLscrat6; for(;;){ if ( DivLong(x1,n1,x2,n2,x4,&n4,x3,&n3) ) goto GcdErr; if ( !n3 ) { x1 = x2; n1 = n2; break; } if ( n2 <= 2 ) { a = x2; b = x3; na = n2; nb = n3; goto restart; } if ( n3 >= GCDMAX && n2 == n3 ) { a = GLscrat9; b = GLscrat10; na = n2; nb = n3; for ( i = 0; i < na; i++ ) a[i] = x2[i]; for ( i = 0; i < nb; i++ ) b[i] = x3[i]; goto newtrick; } if ( DivLong(x2,n2,x3,n3,x4,&n4,x1,&n1) ) goto GcdErr; if ( !n1 ) { x1 = x3; n1 = n3; break; } if ( n3 <= 2 ) { a = x3; b = x1; na = n3; nb = n1; goto restart; } if ( n1 >= GCDMAX && n1 == n3 ) { a = GLscrat9; b = GLscrat10; na = n3; nb = n1; for ( i = 0; i < na; i++ ) a[i] = x3[i]; for ( i = 0; i < nb; i++ ) b[i] = x1[i]; goto newtrick; } if ( DivLong(x3,n3,x1,n1,x4,&n4,x2,&n2) ) goto GcdErr; if ( !n2 ) { *nc = n1; goto normalend; } if ( n1 <= 2 ) { a = x1; b = x2; na = n1; nb = n2; goto restart; } if ( n2 >= GCDMAX && n2 == n1 ) { a = GLscrat9; b = GLscrat10; na = n1; nb = n2; for ( i = 0; i < na; i++ ) a[i] = x1[i]; for ( i = 0; i < nb; i++ ) b[i] = x2[i]; goto newtrick; } } *nc = i = n1; NCOPY(c,x1,i); } /* #] Original code : #[ New code : */ else { /* This is the new algorithm starting at step 3. 3: ma1 = 1; ma2 = 0; mb1 = 0; mb2 = 1; 4: A = a; B = b; m = a/b; c = a - m*b; c = ma1*a+ma2*b-m*(mb1*a+mb2*b) = (ma1-m*mb1)*a+(ma2-m*mb2)*b mc1 = ma1-m*mb1; mc2 = ma2-m*mb2; 5: a = b; ma1 = mb1; ma2 = mb2; b = c; mb1 = mc1; mb2 = mc2; 6: if ( b != 0 ) goto 4; */ newtrick:; ma1 = 1; ma2 = 0; mb1 = 0; mb2 = 1; lx = (((RLONG)(a[na-1]))< lx ) { lz = lx; lx = ly; ly = lz; d = a; a = b; b = d; } do { m = lx/ly; mc1 = ma1-m*mb1; mc2 = ma2-m*mb2; ma1 = mb1; ma2 = mb2; mb1 = mc1; mb2 = mc2; lz = lx - m*ly; lx = ly; ly = lz; } while ( ly >= FULLMAX ); /* Next the construction of the two new numbers 7: Now construct the new quantities a = ma1*aa+ma2*bb and b = mb1*aa+mb2*bb */ x1 = GLscrat6; x2 = GLscrat7; x3 = GLscrat8; x5 = GLscrat10; if ( ma1 < 0 ) { ma1 = -ma1; x1[0] = (UWORD)ma1; x1[1] = (UWORD)(ma1 >> BITSINWORD); if ( x1[1] ) n1 = -2; else n1 = -1; } else { x1[0] = (UWORD)ma1; x1[1] = (UWORD)(ma1 >> BITSINWORD); if ( x1[1] ) n1 = 2; else n1 = 1; } if ( MulLong(a,na,x1,n1,x2,&n2) ) goto GcdErr; if ( ma2 < 0 ) { ma2 = -ma2; x1[0] = (UWORD)ma2; x1[1] = (UWORD)(ma2 >> BITSINWORD); if ( x1[1] ) n1 = -2; else n1 = -1; } else { x1[0] = (UWORD)ma2; x1[1] = (UWORD)(ma2 >> BITSINWORD); if ( x1[1] ) n1 = 2; else n1 = 1; } if ( MulLong(b,nb,x1,n1,x3,&n3) ) goto GcdErr; if ( AddLong(x2,n2,x3,n3,c,&n4) ) goto GcdErr; if ( mb1 < 0 ) { mb1 = -mb1; x1[0] = (UWORD)mb1; x1[1] = (UWORD)(mb1 >> BITSINWORD); if ( x1[1] ) n1 = -2; else n1 = -1; } else { x1[0] = (UWORD)mb1; x1[1] = (UWORD)(mb1 >> BITSINWORD); if ( x1[1] ) n1 = 2; else n1 = 1; } if ( MulLong(a,na,x1,n1,x2,&n2) ) goto GcdErr; if ( mb2 < 0 ) { mb2 = -mb2; x1[0] = (UWORD)mb2; x1[1] = (UWORD)(mb2 >> BITSINWORD); if ( x1[1] ) n1 = -2; else n1 = -1; } else { x1[0] = (UWORD)mb2; x1[1] = (UWORD)(mb2 >> BITSINWORD); if ( x1[1] ) n1 = 2; else n1 = 1; } if ( MulLong(b,nb,x1,n1,x3,&n3) ) goto GcdErr; if ( AddLong(x2,n2,x3,n3,x5,&n5) ) goto GcdErr; a = c; na = n4; b = x5; nb = n5; if ( nb == 0 ) { *nc = n4; goto normalend; } x4 = GLscrat9; for ( i = 0; i < na; i++ ) x4[i] = a[i]; a = x4; if ( na < 0 ) na = -na; if ( nb < 0 ) nb = -nb; /* The typical case now is that in a we have the last step to go to loose the leading word, while in b we have lost the leading word. We could go to DivLong now but we can also add an extra step that is less wasteful. In the case that the new leading word of b is extrememly short (like 1) we make a rather large error of course. In the worst case the whole will be intercepted by DivLong after all, but that is so rare that it shouldn't influence any timing in a measurable way. */ if ( nb >= GCDMAX && na == nb+1 && b[nb-1] >= HALFMAX && b[nb-1] > a[na-1] ) { lx = (((RLONG)(a[na-1]))< i1 ) { *a = 0; *na = 0; return(0); } *a = i1; *na = 1; GBscrat3 = NumberMalloc("GetBinom"); GBscrat4 = NumberMalloc("GetBinom"); for ( j = 2; j <= i2; j++ ) { GBscrat3[0] = i1+1-j; if ( MulLong(a,*na,GBscrat3,(WORD)1,GBscrat4,&k) ) goto CalledFrom; GBscrat3[0] = j; if ( DivLong(GBscrat4,k,GBscrat3,(WORD)1,a,na,GBscrat3,&l) ) goto CalledFrom; } NumberFree(GBscrat3,"GetBinom"); NumberFree(GBscrat4,"GetBinom"); return(0); CalledFrom: MLOCK(ErrorMessageLock); MesCall("GetBinom"); MUNLOCK(ErrorMessageLock); NumberFree(GBscrat3,"GetBinom"); NumberFree(GBscrat4,"GetBinom"); SETERROR(-1) } /* #] GetBinom : #[ LcmLong : WORD LcmLong(a,na,b,nb) Computes the LCM of the long numbers a and b and puts the result in c. c is allowed to be equal to a. */ int LcmLong(PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc) { int error = 0; UWORD *d = NumberMalloc("LcmLong"); UWORD *e = NumberMalloc("LcmLong"); UWORD *f = NumberMalloc("LcmLong"); WORD nd, ne, nf; GcdLong(BHEAD a, na, b, nb, d, &nd); DivLong(a,na,d,nd,e,&ne,f,&nf); if ( MulLong(b,nb,e,ne,c,nc) ) { MLOCK(ErrorMessageLock); MesCall("LcmLong"); MUNLOCK(ErrorMessageLock); error = -1; } NumberFree(f,"LcmLong"); NumberFree(e,"LcmLong"); NumberFree(d,"LcmLong"); return(error); } /* #] LcmLong : #[ TakeLongRoot: int TakeLongRoot(a,n,power) Takes the 'power'-root of the long number in a. If the root could be taken the return value is zero. If the root could not be taken, the return value is 1. The root will be in a if it could be taken, otherwise there will be garbage Algorithm: (assume b is guess of root, b' better guess) b' = (a-(power-1)*b^power)/(n*b^(power-1)) Note: power should be positive! */ int TakeLongRoot(UWORD *a, WORD *n, WORD power) { GETIDENTITY int numbits, guessbits, i, retval = 0; UWORD x, *b, *c, *d, *e; WORD na, nb, nc, nd, ne; if ( *n < 0 && ( power & 1 ) == 0 ) return(1); if ( power == 1 ) return(0); if ( *n < 0 ) { na = -*n; } else { na = *n; } if ( na == 1 ) { /* Special cases that are the most frequent */ if ( a[0] == 1 ) return(0); if ( power < BITSINWORD && na == 1 && a[0] == (UWORD)(1<> 8 ) != 0 ) { numbits += 8; x >>= 8; } if ( ( x >> 4 ) != 0 ) { numbits += 4; x >>= 4; } if ( ( x >> 2 ) != 0 ) { numbits += 2; x >>= 2; } if ( ( x >> 1 ) != 0 ) numbits++; guessbits = numbits / power; if ( guessbits <= 0 ) return(1); /* root < 2 and 1 we did already */ nb = guessbits/BITSINWORD; /* The recursion is: (b'-b) = (a/b^(power-1)-b)/n = (a/c-b)/n = (d-b)/n (remainder of a/c is e) = c/n (we reuse the scratch array c) Termination can be tricky. When a/c has no remainder and = b we have a root. When d = b but the remainder of a/c != 0, there is definitely no root. */ b = NumberMalloc("TakeLongRoot"); c = NumberMalloc("TakeLongRoot"); d = NumberMalloc("TakeLongRoot"); e = NumberMalloc("TakeLongRoot"); for ( i = 0; i < nb; i++ ) { b[i] = 0; } b[nb] = 1 << (guessbits%BITSINWORD); nb++; for(;;) { nc = nb; for ( i = 0; i < nb; i++ ) c[i] = b[i]; if ( RaisPow(BHEAD c,&nc,power-1) ) goto TLcall; if ( DivLong(a,na,c,nc,d,&nd,e,&ne) ) goto TLcall; nb = -nb; if ( AddLong(d,nd,b,nb,c,&nc) ) goto TLcall; nb = -nb; if ( nc == 0 ) { if ( ne == 0 ) break; retval = 1; break; /* else { NumberFree(b,"TakeLongRoot"); NumberFree(c,"TakeLongRoot"); NumberFree(d,"TakeLongRoot"); NumberFree(e,"TakeLongRoot"); return(1); } */ } DivLong(c,nc,(UWORD *)(&power),1,d,&nd,e,&ne); if ( nd == 0 ) { retval = 1; break; /* NumberFree(b,"TakeLongRoot"); NumberFree(c,"TakeLongRoot"); NumberFree(d,"TakeLongRoot"); NumberFree(e,"TakeLongRoot"); return(1); */ /* This code tries b+1 as a final possibility. We believe this is not needed UWORD one = 1; if ( AddLong(b,nb,&one,1,c,&nc) ) goto TLcall; if ( RaisPow(BHEAD c,&nc,power-1) ) goto TLcall; if ( DivLong(a,na,c,nc,d,&nd,e,&ne) ) goto TLcall; if ( ne != 0 ) return(1); nb = -nb; if ( SubLong(d,nd,b,nb,c,&nc) ) goto TLcall; nb = -nb; if ( nc != 0 ) { NumberFree(b,"TakeLongRoot"); NumberFree(c,"TakeLongRoot"); NumberFree(d,"TakeLongRoot"); NumberFree(e,"TakeLongRoot"); return(1); } break; */ } if ( AddLong(b,nb,d,nd,b,&nb) ) goto TLcall; } for ( i = 0; i < nb; i++ ) a[i] = b[i]; if ( *n < 0 ) *n = -nb; else *n = nb; NumberFree(b,"TakeLongRoot"); NumberFree(c,"TakeLongRoot"); NumberFree(d,"TakeLongRoot"); NumberFree(e,"TakeLongRoot"); return(retval); TLcall: MLOCK(ErrorMessageLock); MesCall("TakeLongRoot"); MUNLOCK(ErrorMessageLock); NumberFree(b,"TakeLongRoot"); NumberFree(c,"TakeLongRoot"); NumberFree(d,"TakeLongRoot"); NumberFree(e,"TakeLongRoot"); Terminate(-1); return(-1); } /* #] TakeLongRoot: #[ MakeRational: Makes the integer a mod m into a traction b/c with |b|,|c| < sqrt(m) For the algorithm, see MakeLongRational. */ int MakeRational(WORD a,WORD m, WORD *b, WORD *c) { LONG x1,x2,x3,x4,y1,y2; if ( a < 0 ) { a = a+m; } if ( a <= 1 ) { if ( a > m/2 ) a = a-m; *b = a; *c = 1; return(0); } x1 = m; x2 = a; if ( x2*x2 >= m ) { y1 = x1/x2; y2 = x1%x2; x3 = 1; x4 = -y1; x1 = x2; x2 = y2; while ( x2*x2 >= m ) { y1 = x1/x2; y2 = x1%x2; x1 = x2; x2 = y2; y2 = x3-y1*x4; x3 = x4; x4 = y2; } } else x4 = 1; if ( x2 == 0 ) { return(1); } if ( x2 > m/2 ) *b = x2-m; else *b = x2; if ( x4 > m/2 ) { *c = x4-m; *c = -*c; *b = -*b; } else if ( x4 <= -m/2 ) { x4 += m; *c = x4; } else if ( x4 < 0 ) { x4 = -x4; *c = x4; *b = -*b; } else *c = x4; return(0); } /* #] MakeRational: #[ MakeLongRational: Converts the long number a mod m into the fraction b One of the properties of b is that num,den < sqrt(m) The algorithm: Start with: m 0 a 1 Make now c=m%a, c1=m/a c c2=0-c1*1 Make now d=a%c d1=a/c d d2=1-d1*c2 Make now e=c%d e1=c/d e e2=1-e1*d2 etc till in the first column we get a number < sqrt(m) We have then f,f2 and the fraction is f/f2. If at any moment we get a zero, m contained an unlucky prime. Note that this can be made a lot faster when we make the same improvements as in the GCD routine. That is something for later. #ifdef WITHMAKERATIONAL */ #define COPYLONG(x1,nx1,x2,nx2) { int i; for(i=0;i 0 ) { DivLong(x1,nx1,x2,nx2,y1,&ny1,y2,&ny2); if ( ny2 == 0 ) { retval = 1; goto cleanup; } COPYLONG(x1,nx1,x2,nx2) COPYLONG(x2,nx2,y2,ny2) MulLong(y1,ny1,x4,nx4,y2,&ny2); ny2 = -ny2; AddLong(x3,nx3,y2,ny2,y1,&ny1); COPYLONG(x3,nx3,x4,nx4) COPYLONG(x4,nx4,y1,ny1) } /* Now we have the answer. It is x2/x4. It has to be packed into b. */ gottheanswer: if ( nx4 < 0 ) { sign = -sign; nx4 = -nx4; } COPYLONG(b,*nb,x2,nx2) Pack(b,nb,x4,nx4); if ( sign < 0 ) *nb = -*nb; cleanup: NumberFree(y2,"MakeRational"); NumberFree(y1,"MakeRational"); NumberFree(x4,"MakeRational"); NumberFree(x3,"MakeRational"); NumberFree(x2,"MakeRational"); NumberFree(x1,"MakeRational"); NumberFree(root,"MakeRational"); return(retval); } /* #endif #] MakeLongRational: #[ ChineseRemainder: */ /** * Routine takes a1 mod m1 and a2 mod m2 and returns a mod m1*m2 with * a mod m1 = a1 and a mod m2 = a2 * Chinese remainder: * a%(m1*m2) = q1*m1+a1 * a%(m1*m2) = q2*m2+a2 * Compute n1 such that (n1*m1)%m2 is one * Compute n2 such that (n2*m2)%m1 is one * Then (a1*n2*m2+a2*n1*m1)%(m1*m2) is a%(m1*m2) * */ #ifdef WITHCHINESEREMAINDER int ChineseRemainder(PHEAD MODNUM *a1, MODNUM *a2, MODNUM *a) { UWORD *inv1 = NumberMalloc("ChineseRemainder"); UWORD *inv2 = NumberMalloc("ChineseRemainder"); UWORD *fac1 = NumberMalloc("ChineseRemainder"); UWORD *fac2 = NumberMalloc("ChineseRemainder"); UWORD two[1]; WORD ninv1, ninv2, nfac1, nfac2; if ( a1->na < 0 ) { AddLong(a1->a,a1->na,a1->m,a1->nm,a1->a,&(a1->na)); } if ( a2->na < 0 ) { AddLong(a2->a,a2->na,a2->m,a2->nm,a2->a,&(a2->na)); } MulLong(a1->m,a1->nm,a2->m,a2->nm,a->m,&(a->nm)); GetLongModInverses(BHEAD a1->m,a1->nm,a2->m,a2->nm,inv1,&ninv1,inv2,&ninv2); MulLong(inv1,ninv1,a1->m,a1->nm,fac1,&nfac1); MulLong(inv2,ninv2,a2->m,a2->nm,fac2,&nfac2); MulLong(fac1,nfac1,a2->a,a2->na,inv1,&ninv1); MulLong(fac2,nfac2,a1->a,a1->na,inv2,&ninv2); AddLong(inv1,ninv1,inv2,ninv2,a->a,&(a->na)); two[0] = 2; MulLong(a->a,a->na,two,1,fac1,&nfac1); if ( BigLong(fac1,nfac1,a->m,a->nm) > 0 ) { a->nm = -a->nm; AddLong(a->a,a->na,a->m,a->nm,a->a,&(a->na)); a->nm = -a->nm; } NumberFree(fac2,"ChineseRemainder"); NumberFree(fac1,"ChineseRemainder"); NumberFree(inv2,"ChineseRemainder"); NumberFree(inv1,"ChineseRemainder"); return(0); } #endif /* #] ChineseRemainder: #] RekenLong : #[ RekenTerms : #[ CompCoef : WORD CompCoef(term1,term2) Compares the coefficients of term1 and term2 by subtracting them. This does more work than needed but this routine is only called when sorting functions and function arguments. (and comparing values */ /* #define 64SAVE */ WORD CompCoef(WORD *term1, WORD *term2) { GETIDENTITY UWORD *c; WORD n1,n2,n3,*a; GETCOEF(term1,n1); GETCOEF(term2,n2); if ( term1[1] == 0 && n1 == 1 ) { if ( term2[1] == 0 && n2 == 1 ) return(0); if ( n2 < 0 ) return(1); return(-1); } else if ( term2[1] == 0 && n2 == 1 ) { if ( n1 < 0 ) return(-1); return(1); } if ( n1 > 0 ) { if ( n2 < 0 ) return(1); } else { if ( n2 > 0 ) return(-1); a = term1; term1 = term2; term2 = a; n3 = -n1; n1 = -n2; n2 = n3; } if ( term1[1] == 1 && term2[1] == 1 && n1 == 1 && n2 == 1 ) { if ( (UWORD)*term1 > (UWORD)*term2 ) return(1); else if ( (UWORD)*term1 < (UWORD)*term2 ) return(-1); else return(0); } /* The next call should get dedicated code, as AddRat does more than strictly needed. Also more attention should be given to overflow. */ c = NumberMalloc("CompCoef"); if ( AddRat(BHEAD (UWORD *)term1,n1,(UWORD *)term2,-n2,c,&n3) ) { MLOCK(ErrorMessageLock); MesCall("CompCoef"); MUNLOCK(ErrorMessageLock); NumberFree(c,"CompCoef"); SETERROR(-1) } NumberFree(c,"CompCoef"); return(n3); } /* #] CompCoef : #[ Modulus : WORD Modulus(term) Routine takes the coefficient of term modulus b. The answer is in term again and the length of term is adjusted. */ int Modulus(WORD *term) { WORD *t; WORD n1; t = term; GETCOEF(t,n1); if ( TakeModulus((UWORD *)t,&n1,AC.cmod,AC.ncmod,UNPACK) ) { MLOCK(ErrorMessageLock); MesCall("Modulus"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( !n1 ) { *term = 0; return(0); } else if ( n1 > 0 ) { n1 *= 2; t += n1; /* Note that n1 >= 0 */ n1++; } else if ( n1 < 0 ) { n1 *= 2; t += -n1; n1--; } *t++ = n1; *term = WORDDIF(t,term); return(0); } /* #] Modulus : #[ TakeModulus : WORD TakeModulus(a,na,cmodvec,ncmod,par) Routine gets the rational number in a with reduced length na. It is called when AC.ncmod != 0 and the number in AC.cmod is the number wrt which we need the modulus. The result is returned in a and na again. If par == NOUNPACK we only do a single number, not a fraction. In addition we don't do fancy. We want a positive number and the input was supposed to be positive. We don't pack the result. The calling routine is responsible for that. This may not be a good idea. To be checked. */ int TakeModulus(UWORD *a, WORD *na, UWORD *cmodvec, WORD ncmod, WORD par) { GETIDENTITY UWORD *c, *d, *e, *f, *g, *h; UWORD *x4,*x2; UWORD *x3,*x1,*x5,*x6,*x7,*x8; WORD y3,y1,y5,y6; WORD n1, i, y2, y4; WORD nh, tdenom, tnumer, nmod; LONG x; if ( ncmod == 0 ) return(0); /* No modulus operation */ nmod = ABS(ncmod); n1 = *na; if ( ( par & UNPACK ) != 0 ) UnPack(a,n1,&tdenom,&tnumer); else { tnumer = n1; } /* We fish out the special case that the coefficient is short as well. There is no need to make lots of calls etc */ if ( ( ( par & UNPACK ) == 0 ) && nmod == 1 && ( n1 == 1 || n1 == -1 ) ) { goto simplecase; } else if ( nmod == 1 && ( n1 == 1 || n1 == -1 ) ) { if ( a[1] != 1 ) { a[1] = a[1] % cmodvec[0]; if ( a[1] == 0 ) { MesPrint("Division by zero in short modulus arithmetic"); return(-1); } y1 = 0; if ( ( AC.modinverses != 0 ) && ( ( par & NOINVERSES ) == 0 ) ) { y1 = AC.modinverses[a[1]]; } else { GetModInverses(a[1],cmodvec[0],&y1,&y2); } x = a[0]; a[0] = (x*y1) % cmodvec[0]; a[1] = 1; } else { simplecase: a[0] = a[0] % cmodvec[0]; } if ( a[0] == 0 ) { *na = 0; return(0); } if ( ( AC.modmode & POSNEG ) != 0 ) { if ( a[0] > (UWORD)(cmodvec[0]/2) ) { a[0] = cmodvec[0] - a[0]; *na = -*na; } } else if ( *na < 0 ) { *na = 1; a[0] = cmodvec[0] - a[0]; } return(0); } c = NumberMalloc("TakeModulus"); d = NumberMalloc("TakeModulus"); e = NumberMalloc("TakeModulus"); f = NumberMalloc("TakeModulus"); g = NumberMalloc("TakeModulus"); h = NumberMalloc("TakeModulus"); n1 = ABS(n1); if ( DivLong(a,tnumer,(UWORD *)cmodvec,nmod, c,&nh,a,&tnumer) ) goto ModErr; if ( tnumer == 0 ) { *na = 0; goto normalreturn; } if ( ( par & UNPACK ) == 0 ) { if ( ( AC.modmode & POSNEG ) != 0 ) { NormalModulus(a,&tnumer); } else if ( tnumer < 0 ) { SubPLon((UWORD *)cmodvec,nmod,a,-tnumer,a,&tnumer); } *na = tnumer; goto normalreturn; } if ( tdenom == 1 && a[n1] == 1 ) { if ( ( AC.modmode & POSNEG ) != 0 ) { NormalModulus(a,&tnumer); } else if ( tnumer < 0 ) { SubPLon((UWORD *)cmodvec,nmod,a,-tnumer,a,&tnumer); } *na = tnumer; i = ABS(tnumer); a += i; *a++ = 1; while ( --i > 0 ) *a++ = 0; goto normalreturn; } if ( DivLong(a+n1,tdenom,(UWORD *)cmodvec,nmod,c,&nh,a+n1,&tdenom) ) goto ModErr; if ( !tdenom ) { MLOCK(ErrorMessageLock); MesPrint("Division by zero in modulus arithmetic"); if ( AP.DebugFlag ) { AO.OutSkip = 3; FiniLine(); i = *na; if ( i < 0 ) i = -i; while ( --i >= 0 ) { TalToLine((UWORD)(*a++)); TokenToLine((UBYTE *)" "); } i = *na; if ( i < 0 ) i = -i; while ( --i >= 0 ) { TalToLine((UWORD)(*a++)); TokenToLine((UBYTE *)" "); } TalToLine((UWORD)(*na)); AO.OutSkip = 0; FiniLine(); } MUNLOCK(ErrorMessageLock); NumberFree(c,"TakeModulus"); NumberFree(d,"TakeModulus"); NumberFree(e,"TakeModulus"); NumberFree(f,"TakeModulus"); NumberFree(g,"TakeModulus"); NumberFree(h,"TakeModulus"); return(-1); } if ( ( AC.modinverses != 0 ) && ( ( par & NOINVERSES ) == 0 ) && ( tdenom == 1 || tdenom == -1 ) ) { *d = AC.modinverses[a[n1]]; y1 = 1; y2 = tdenom; if ( MulLong(a,tnumer,d,y1,c,&y3) ) goto ModErr; if ( DivLong(c,y3,(UWORD *)cmodvec,nmod,d,&y5,a,&tdenom) ) goto ModErr; if ( y2 < 0 ) tdenom = -tdenom; } else { x2 = (UWORD *)cmodvec; x1 = c; i = nmod; while ( --i >= 0 ) *x1++ = *x2++; x1 = c; x2 = a+n1; x3 = d; x4 = e; x5 = f; x6 = g; y1 = nmod; y2 = tdenom; y4 = 0; y5 = 1; *x5 = 1; for(;;) { if ( DivLong(x1,y1,x2,y2,h,&nh,x3,&y3) ) goto ModErr; if ( MulLong(x5,y5,h,nh,x6,&y6) ) goto ModErr; if ( AddLong(x4,y4,x6,-y6,x6,&y6) ) goto ModErr; if ( !y3 ) { if ( y2 != 1 || *x2 != 1 ) { MLOCK(ErrorMessageLock); MesPrint("Inverse in modulus arithmetic doesn't exist"); MesPrint("Denominator and modulus are not relative prime"); MUNLOCK(ErrorMessageLock); goto ModErr; } break; } x7 = x1; x1 = x2; y1 = y2; x2 = x3; y2 = y3; x3 = x7; x8 = x4; x4 = x5; y4 = y5; x5 = x6; y5 = y6; x6 = x8; } if ( y5 < 0 && AddLong((UWORD *)cmodvec,nmod,x5,y5,x5,&y5) ) goto ModErr; if ( MulLong(a,tnumer,x5,y5,c,&y3) ) goto ModErr; if ( DivLong(c,y3,(UWORD *)cmodvec,nmod,d,&y5,a,&tdenom) ) goto ModErr; } if ( !tdenom ) { *na = 0; goto normalreturn; } if ( ( ( AC.modmode & POSNEG ) != 0 ) && ( ( par & FROMFUNCTION ) == 0 ) ) { NormalModulus(a,&tdenom); } else if ( tdenom < 0 ) { SubPLon((UWORD *)cmodvec,nmod,a,-tdenom,a,&tdenom); } *na = tdenom; i = ABS(tdenom); a += i; *a++ = 1; while ( --i > 0 ) *a++ = 0; normalreturn: NumberFree(c,"TakeModulus"); NumberFree(d,"TakeModulus"); NumberFree(e,"TakeModulus"); NumberFree(f,"TakeModulus"); NumberFree(g,"TakeModulus"); NumberFree(h,"TakeModulus"); return(0); ModErr: MLOCK(ErrorMessageLock); MesCall("TakeModulus"); MUNLOCK(ErrorMessageLock); NumberFree(c,"TakeModulus"); NumberFree(d,"TakeModulus"); NumberFree(e,"TakeModulus"); NumberFree(f,"TakeModulus"); NumberFree(g,"TakeModulus"); NumberFree(h,"TakeModulus"); SETERROR(-1) } /* #] TakeModulus : #[ TakeNormalModulus : WORD TakeNormalModulus(a,na,par) added by Jan [01-09-2010] */ int TakeNormalModulus (UWORD *a, WORD *na, UWORD *c, WORD nc, WORD par) { WORD n; WORD nhalfc; UWORD *halfc; GETIDENTITY; /* determine c/2 by right shifting */ halfc = NumberMalloc("TakeNormalModulus"); nhalfc=nc; WCOPY(halfc,c,nc); for (n=0; n 99 -> -1 */ if (BigLong(a,ABS(*na),halfc,nhalfc) > 0) { TakeModulus(a,na,c,nc,par); n = ABS(*na); if (BigLong(a,n,halfc,nhalfc) > 0) { SubPLon(c,nc,a,n,a,&n); *na = (*na > 0 ? -n : n); } } NumberFree(halfc,"TakeNormalModulus"); return(0); } /* #] TakeNormalModulus : #[ MakeModTable : WORD MakeModTable() */ int MakeModTable(void) { LONG size, i, j, n; n = ABS(AC.ncmod); if ( AC.modpowers ) { M_free(AC.modpowers,"AC.modpowers"); AC.modpowers = NULL; } if ( n > 2 ) { MLOCK(ErrorMessageLock); MesPrint("&No memory for modulus generator power table"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( n == 0 ) return(0); size = (LONG)(*AC.cmod); if ( n == 2 ) size += (((LONG)AC.cmod[1])<> BITSINWORD); MulLong((UWORD *)MMscratC,nScrat,(UWORD *)AC.powmod, AC.npowmod,(UWORD *)MMscrat7,&n2); TakeModulus(MMscrat7,&n2,AC.cmod,AC.ncmod,NOUNPACK); *MMscratC = *MMscrat7; MMscratC[1] = MMscrat7[1]; nScrat = n2; } NumberFree(MMscrat7,"MakeModTable"); NumberFree(MMscratC,"MakeModTable"); j = size * 2; for ( i = 4; i < j; i+=2 ) { if ( AC.modpowers[i] == 0 && AC.modpowers[i+1] == 0 ) { MLOCK(ErrorMessageLock); MesPrint("&improper generator for this modulus"); MUNLOCK(ErrorMessageLock); M_free(AC.modpowers,"AC.modpowers"); return(-1); } } AC.modpowers[2] = AC.modpowers[3] = 0; } return(0); } /* #] MakeModTable : #] RekenTerms : #[ Functions : #[ Factorial : WORD Factorial(n,a,na) Starts with only the value of fac_(0). Builds up what is needed and remembers it for the next time. We have: AT.nfac: the number of the highest stored factorial AT.pfac: the array of locations in the array of stored factorials AT.factorials: the array with stored factorials */ int Factorial(PHEAD WORD n, UWORD *a, WORD *na) { GETBIDENTITY UWORD *b, *c; WORD nc; int i, j; LONG ii; if ( n > AT.nfac ) { if ( AT.factorials == 0 ) { AT.nfac = 0; AT.mfac = 50; AT.sfact = 400; AT.pfac = (LONG *)Malloc1((AT.mfac+2)*sizeof(LONG),"factorials"); AT.factorials = (UWORD *)Malloc1(AT.sfact*sizeof(UWORD),"factorials"); AT.factorials[0] = 1; AT.pfac[0] = 0; AT.pfac[1] = 1; } b = a; c = AT.factorials+AT.pfac[AT.nfac]; nc = i = AT.pfac[AT.nfac+1] - AT.pfac[AT.nfac]; while ( --i >= 0 ) *b++ = *c++; for ( j = AT.nfac+1; j <= n; j++ ) { Product(a,&nc,j); if ( nc > AM.MaxTal ) { MLOCK(ErrorMessageLock); MesPrint("Overflow in factorial. MaxTal = %d",AM.MaxTal); MesPrint("Increase MaxTerm in %s",setupfilename); MUNLOCK(ErrorMessageLock); return(-1); } if ( j > AT.mfac ) { /* double the pfac buffer */ LONG *p; p = (LONG *)Malloc1((AT.mfac*2+2)*sizeof(LONG),"factorials"); i = AT.mfac; for ( i = AT.mfac+1; i >= 0; i-- ) p[i] = AT.pfac[i]; M_free(AT.pfac,"factorial offsets"); AT.pfac = p; AT.mfac *= 2; } if ( AT.pfac[j] + nc >= AT.sfact ) { /* double the factorials buffer */ UWORD *f; f = (UWORD *)Malloc1(AT.sfact*2*sizeof(UWORD),"factorials"); ii = AT.sfact; c = AT.factorials; b = f; while ( --ii >= 0 ) *b++ = *c++; M_free(AT.factorials,"factorials"); AT.factorials = f; AT.sfact *= 2; } b = a; c = AT.factorials + AT.pfac[j]; i = nc; while ( --i >= 0 ) *c++ = *b++; AT.pfac[j+1] = AT.pfac[j] + nc; } *na = nc; AT.nfac = n; } else if ( n == 0 ) { *a = 1; *na = 1; } else { *na = i = AT.pfac[n+1] - AT.pfac[n]; b = AT.factorials + AT.pfac[n]; while ( --i >= 0 ) *a++ = *b++; } return(0); } /* #] Factorial : #[ Bernoulli : WORD Bernoulli(n,a,na) Starts with only the value of bernoulli_(0). Builds up what is needed and remembers it for the next time. b_0 = 1 (n+1)*b_n = -b_{n-1}-sum_(i,1,n-1,b_i*b_{n-i}) The n-1 plays only a role for b_2. We have hard coded b_0,b_1,b_2 and b_odd. After that: (2n+1)*b_2n = -sum_(i,1,n-1,b_2i*b_{2n-2i}) We have: AT.nBer: the number of the highest stored Bernoulli number AT.pBer: the array of locations in the array of stored Bernoulli numbers AT.bernoullis: the array with stored Bernoulli numbers */ int Bernoulli(WORD n, UWORD *a, WORD *na) { GETIDENTITY UWORD *b, *c, *scrib, *ntop, *ntop1; WORD i, i1, i2, nhalf, nqua, nscrib, nntop, nntop1, *oldworkpointer; UWORD twee = 2, twonplus1; int j; LONG ii; if ( n <= 1 ) { if ( n == 0 ) { a[0] = a[1] = 1; *na = 3; } else if ( n == 1 ) { a[0] = 1; a[1] = 2; *na = 3; } return(0); } if ( ( n & 1 ) != 0 ) { a[0] = a[1] = 0; *na = 0; return(0); } nhalf = n/2; if ( nhalf > AT.nBer ) { oldworkpointer = AT.WorkPointer; if ( AT.bernoullis == 0 ) { AT.nBer = 1; AT.mBer = 50; AT.sBer = 400; AT.pBer = (LONG *)Malloc1((AT.mBer+2)*sizeof(LONG),"bernoullis"); AT.bernoullis = (UWORD *)Malloc1(AT.sBer*sizeof(UWORD),"bernoullis"); AT.pBer[1] = 0; AT.pBer[2] = 3; AT.bernoullis[0] = 3; AT.bernoullis[1] = 1; AT.bernoullis[2] = 12; if ( nhalf == 1 ) { a[0] = 1; a[1] = 12; *na = 3; return(0); } } while ( nhalf > AT.mBer ) { LONG *p; p = (LONG *)Malloc1((AT.mBer*2+1)*sizeof(LONG),"bernoullis"); i = AT.mBer; for ( i = AT.mBer; i >= 0; i-- ) p[i] = AT.pBer[i]; M_free(AT.pBer,"factorial pointers"); AT.pBer = p; AT.mBer *= 2; } for ( n = AT.nBer+1; n <= nhalf; n++ ) { scrib = (UWORD *)(AT.WorkPointer); nqua = n/2; if ( ( n & 1 ) == 1 ) { nscrib = 0; ntop = scrib; } else { b = AT.bernoullis + AT.pBer[nqua]; nscrib = *b++; i = (WORD)(REDLENG(nscrib)); MulRat(BHEAD b,i,b,i,scrib,&nscrib); ntop = scrib + 2*nscrib; nqua--; } for ( j = 1; j <= nqua; j++ ) { b = AT.bernoullis + AT.pBer[j]; c = AT.bernoullis + AT.pBer[n-j]; i1 = (WORD)(*b); i2 = (WORD)(*c); i1 = REDLENG(i1); i2 = REDLENG(i2); MulRat(BHEAD b+1,i1,c+1,i2,ntop,&nntop); Mully(BHEAD ntop,&nntop,&twee,1); if ( nscrib ) { i = (WORD)nntop; if ( i < 0 ) i = -i; ntop1 = ntop + 2*i; AddRat(BHEAD ntop,nntop,scrib,nscrib,ntop1,&nntop1); } else { ntop1 = ntop; nntop1 = nntop; } nscrib = i1 = (WORD)nntop1; if ( i1 < 0 ) i1 = - i1; i1 = 2*i1; for ( i = 0; i < i1; i++ ) scrib[i] = ntop1[i]; ntop = scrib + i1; } twonplus1 = 2*n+1; Divvy(BHEAD scrib,&nscrib,&twonplus1,-1); i1 = INCLENG(nscrib); i2 = i1; if ( i2 < 0 ) i2 = -i2; i = (WORD)(AT.bernoullis[AT.pBer[n-1]]); if ( i < 0 ) i = -i; AT.pBer[n] = AT.pBer[n-1]+i; if ( AT.pBer[n] + i2 >= AT.sBer ) { UWORD *f; f = (UWORD *)Malloc1(AT.sBer*2*sizeof(UWORD),"bernoullis"); ii = AT.sBer; c = AT.bernoullis; b = f; while ( --ii >= 0 ) *b++ = *c++; M_free(AT.bernoullis,"bernoullis"); AT.bernoullis = f; AT.sBer *= 2; } c = AT.bernoullis + AT.pBer[n]; b = scrib; *c++ = i1; for ( i = 1; i < i2; i++ ) *c++ = *b++; } AT.nBer = nhalf; AT.WorkPointer = oldworkpointer; } b = AT.bernoullis + AT.pBer[nhalf]; *na = i = (WORD)(*b++); if ( i < 0 ) i = -i; i--; while ( --i >= 0 ) *a++ = *b++; return(0); } /* #] Bernoulli : #[ NextPrime : */ /** * Gives the next prime number in the list of prime numbers. * * If the list isn't long enough we expand it. * For ease in ParForm and because these lists shouldn't be very big * we let each worker keep its own list. * * The list is cut off at MAXPOWER, because we don't want to get into * trouble that the power of a variable gets larger than the prime number. */ #if ( BITSINWORD == 32 ) void StartPrimeList(PHEAD0) { int i, j; AR.PrimeList[AR.numinprimelist++] = 3; for ( i = 5; i < 46340; i += 2 ) { for ( j = 0; j < AR.numinprimelist && AR.PrimeList[j]*AR.PrimeList[j] <= i; j++ ) { if ( i % AR.PrimeList[j] == 0 ) goto nexti; } AR.PrimeList[AR.numinprimelist++] = i; nexti:; } AR.notfirstprime = 1; } #endif WORD NextPrime(PHEAD WORD num) { int i, j; WORD *newpl; LONG newsize, x; #if ( BITSINWORD == 32 ) if ( AR.notfirstprime == 0 ) StartPrimeList(BHEAD0); #endif if ( num > AT.inprimelist ) { while ( AT.inprimelist < num ) { if ( num >= AT.sizeprimelist ) { if ( AT.sizeprimelist == 0 ) newsize = 32; else newsize = 2*AT.sizeprimelist; while ( num >= newsize ) newsize = newsize*2; newpl = (WORD *)Malloc1(newsize*sizeof(WORD),"NextPrime"); for ( i = 0; i < AT.sizeprimelist; i++ ) { newpl[i] = AT.primelist[i]; } if ( AT.sizeprimelist > 0 ) { M_free(AT.primelist,"NextPrime"); } AT.sizeprimelist = newsize; AT.primelist = newpl; } if ( AT.inprimelist < 0 ) { i = MAXPOSITIVE; } else { i = AT.primelist[AT.inprimelist]; } while ( i > MAXPOWER ) { i -= 2; x = i; #if ( BITSINWORD == 32 ) for ( j = 0; j < AR.numinprimelist && AR.PrimeList[j]*(LONG)(AR.PrimeList[j]) <= x; j++ ) { if ( x % AR.PrimeList[j] == 0 ) goto nexti; } #else for ( j = 3; j*((LONG)j) <= x; j += 2 ) { if ( x % j == 0 ) goto nexti; } #endif AT.inprimelist++; AT.primelist[AT.inprimelist] = i; break; nexti:; } if ( i < MAXPOWER ) { MLOCK(ErrorMessageLock); MesPrint("There are not enough short prime numbers for this calculation"); MesPrint("Try to use a computer with a %d-bits architecture", (int)(BITSINWORD*4)); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } return(AT.primelist[num]); } /* #] NextPrime : #[ Moebius : Returns the value of the Moebius function if n fits inside a WORD. The method we use is a bit like the sieve of Erathostenes. */ WORD Moebius(PHEAD WORD nn) { WORD i,n = nn, x; LONG newsize; SBYTE *newtable, mu; #if ( BITSINWORD == 32 ) if ( AR.notfirstprime == 0 ) StartPrimeList(BHEAD0); #endif /* First we make sure that: a: the table is big enough. b: the number is not already in the table. */ if ( nn >= AR.moebiustablesize ) { if ( AR.moebiustablesize <= 0 ) { newsize = (LONG)nn + 20; } else { newsize = (LONG)nn*2; } if ( newsize > MAXPOSITIVE ) newsize = MAXPOSITIVE; newtable = (SBYTE *)Malloc1(newsize*sizeof(SBYTE),"Moebius"); for ( i = 0; i < AR.moebiustablesize; i++ ) newtable[i] = AR.moebiustable[i]; for ( ; i < newsize; i++ ) newtable[i] = 2; if ( AR.moebiustablesize > 0 ) M_free(AR.moebiustable,"Moebius"); AR.moebiustable = newtable; AR.moebiustablesize = newsize; } /* NOTE: nn == MAXPOSITIVE never fits in moebiustable. */ if ( nn != MAXPOSITIVE && AR.moebiustable[nn] != 2 ) return((WORD)AR.moebiustable[nn]); mu = 1; if ( n == 1 ) goto putvalue; if ( n % 2 == 0 ) { n /= 2; if ( n % 2 == 0 ) { mu = 0; goto putvalue; } if ( AR.moebiustable[n] != 2 ) { mu = -AR.moebiustable[n]; goto putvalue; } mu = -mu; if ( n == 1 ) goto putvalue; } #if ( BITSINWORD == 32 ) for ( i = 0; i < AR.numinprimelist; i++ ) { x = AR.PrimeList[i]; #else for ( x = 3; x < MAXPOSITIVE; x += 2 ) { #endif if ( n % x == 0 ) { n /= x; if ( n % x == 0 ) { mu = 0; goto putvalue; } if ( AR.moebiustable[n] != 2 ) { mu = -AR.moebiustable[n]; goto putvalue; } mu = -mu; if ( n == 1 ) goto putvalue; } if ( n < x*x ) break; /* notice that x*x always fits inside a WORD */ } mu = -mu; putvalue: if ( nn != MAXPOSITIVE ) AR.moebiustable[nn] = mu; return((WORD)mu); } /* #] Moebius : #[ wranf : A random number generator that generates random WORDs with a very long sequence. It is based on the Knuth generator. We take some care that each thread can run its own, but each uses its own startup. Hence the seed includes the identity of the thread. For NPAIR1, NPAIR2 we can use any pair from the table on page 28. Candidates are 24,55 (the example on the pages 171,172) or (33,97) or (38,89) These values are defined in fsizes.h and used in startup.c and threads.c */ #define WARMUP 6 static void wranfnew(PHEAD0) { int i; LONG j; for ( i = 0; i < AR.wranfnpair1; i++ ) { j = AR.wranfia[i] - AR.wranfia[i+(AR.wranfnpair2-AR.wranfnpair1)]; if ( j < 0 ) j += (LONG)1 << (2*BITSINWORD-2); AR.wranfia[i] = j; } for ( i = AR.wranfnpair1; i < AR.wranfnpair2; i++ ) { j = AR.wranfia[i] - AR.wranfia[i-AR.wranfnpair1]; if ( j < 0 ) j += (LONG)1 << (2*BITSINWORD-2); AR.wranfia[i] = j; } } void iniwranf(PHEAD0) { int imax = AR.wranfnpair2-1; ULONG i, ii, seed = AR.wranfseed; LONG j, k; ULONG offset = 12345; #ifdef PARALLELCODE int id; #if defined(WITHPTHREADS) id = AT.identity; #elif defined(WITHMPI) id = PF.me; #endif seed += id; i = id + 1; if ( i > 1 ) { ULONG pow, accu; pow = offset; accu = 1; while ( i ) { if ( ( i & 1 ) != 0 ) accu *= pow; i /= 2; pow = pow*pow; } offset = accu; } #endif if ( seed < ((LONG)1<<(BITSINWORD-1)) ) { j = ( (seed+31459L) << (BITSINWORD-2))+offset; } else if ( seed < ((LONG)1<<(BITSINWORD+10-1)) ) { j = ( (seed+31459L) << (BITSINWORD-10-2))+offset; } else { j = ( (seed+31459L) << 1)+offset; } if ( ( seed & 1 ) == 1 ) seed++; j += seed; AR.wranfia[imax] = j; k = 1; for ( i = 0; i <= (ULONG)(imax); i++ ) { ii = (AR.wranfnpair1*i)%AR.wranfnpair2; AR.wranfia[ii] = k; k = ULongToLong((ULONG)j - (ULONG)k); if ( k < 0 ) k += (LONG)1 << (2*BITSINWORD-2); j = AR.wranfia[ii]; } for ( i = 0; i < WARMUP; i++ ) wranfnew(BHEAD0); AR.wranfcall = 0; } UWORD wranf(PHEAD0) { UWORD wval; if ( AR.wranfia == 0 ) { AR.wranfia = (ULONG *)Malloc1(AR.wranfnpair2*sizeof(ULONG),"wranf"); iniwranf(BHEAD0); } if ( AR.wranfcall >= AR.wranfnpair2) { wranfnew(BHEAD0); AR.wranfcall = 0; } wval = (UWORD)(AR.wranfia[AR.wranfcall++]>>(BITSINWORD-1)); return(wval); } /* Returns a random UWORD in the range (0,...,imax-1) */ UWORD iranf(PHEAD UWORD imax) { UWORD i; ULONG x, xmax; if (imax < 2) return 0; x = (LONG)1 << BITSINWORD; xmax = x - x%imax; while ( ( i = wranf(BHEAD0) ) >= xmax ) {} return(i%imax); } /* #] wranf : #[ PreRandom : The random number generator of the preprocessor. This one is completely different from the execution time generator random_(number). In the preprocessor we generate a floating point number in a string according to a distribution. Currently allowed are: RANDOM_(log,min,max) RANDOM_(lin,min,max) The return value is a string with the floating point number. */ UBYTE *PreRandom(UBYTE *s) { GETIDENTITY UBYTE *mode,*mins = 0,*maxs = 0, *outval; float num; double minval, maxval, value = 0; int linlog = -1; mode = s; while ( FG.cTable[*s] <= 1 ) s++; if ( *s == ',' ) { *s = 0; s++; } mins = s; while ( *s && *s != ',' ) s++; if ( *s == ',' ) { *s = 0; s++; } maxs = s; while ( *s && *s != ',' ) s++; if ( *s || *maxs == 0 || *mins == 0 ) { MesPrint("@Illegal arguments in macro RANDOM_"); Terminate(-1); } if ( StrICmp(mode,(UBYTE *)"lin") == 0 ) { linlog = 0; } else if ( StrICmp(mode,(UBYTE *)"log") == 0 ) { linlog = 1; } else { MesPrint("@Illegal mode argument in macro RANDOM_"); Terminate(-1); } sscanf((char *)mins,"%f",&num); minval = num; sscanf((char *)maxs,"%f",&num); maxval = num; /* * Note on ParFORM: we should use the same random number on all the * processes in the complication phase. The random number is generated * on the master and broadcast to the other processes. */ { UWORD x; double xx; #ifdef WITHMPI x = 0; if ( PF.me == MASTER ) { x = wranf(BHEAD0); } x = (UWORD)PF_BroadcastNumber((LONG)x); #else x = wranf(BHEAD0); #endif xx = x/pow(2.0,(double)(BITSINWORD-1)); if ( linlog == 0 ) { value = minval + (maxval-minval)*xx; } else if ( linlog == 1 ) { value = minval * pow(maxval/minval,xx); } } outval = (UBYTE *)Malloc1(64,"PreRandom"); if ( ABS(value) < 0.00001 || ABS(value) > 1000000. ) { snprintf((char *)outval,64,"%e",value); } else if ( ABS(value) < 0.0001 ) { snprintf((char *)outval,64,"%10f",value); } else if ( ABS(value) < 0.001 ) { snprintf((char *)outval,64,"%9f",value); } else if ( ABS(value) < 0.01 ) { snprintf((char *)outval,64,"%8f",value); } else if ( ABS(value) < 0.1 ) { snprintf((char *)outval,64,"%7f",value); } else if ( ABS(value) < 1. ) { snprintf((char *)outval,64,"%6f",value); } else if ( ABS(value) < 10. ) { snprintf((char *)outval,64,"%5f",value); } else if ( ABS(value) < 100. ) { snprintf((char *)outval,64,"%4f",value); } else if ( ABS(value) < 1000. ) { snprintf((char *)outval,64,"%3f",value); } else if ( ABS(value) < 10000. ) { snprintf((char *)outval,64,"%2f",value); } else { snprintf((char *)outval,64,"%1f",value); } return(outval); } /* #] PreRandom : #] Functions : */ form-5.0.1/sources/findpat.c0000644000175100017510000010766415217035721011440 /** @file findpat.c * * Pattern matching of symbols and dotproducts. * There are various routines because of the options in the id-statements * like once, only, multi and many. * These are among the oldest routines in FORM and that can be noticed, * because the interplay with the function matching is not complete. * When we match functions and halfway we fail we can backtrack properly. * With the symbols, the dotproducts and the vectors (in pattern.c) there * is no proper backtracking. Hence the routines here need still quite * some work or may even have to be rewritten. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : findpat.c */ #include "form3.h" /* #] Includes : #[ Patterns : #[ FindOnly : WORD FindOnly(term,pattern) The current version doesn't scan function arguments yet. 10-Apr-1988 This routine searches for an exact match. This means in particular: 1: x^# must match exactly. 2: x^n? must have a single value for n that cannot be adapted. When setp != 0 it points to a collection of sets A match can occur only if no object will be left that belongs to any of these sets. */ int FindOnly(PHEAD WORD *term, WORD *pattern) { GETBIDENTITY WORD *t, *m; WORD *tstop, *mstop; WORD *xstop, *ystop, *setp = AN.ForFindOnly; WORD n, nt, *p, nq; WORD older[NORMSIZE], *q, newval1, newval2, newval3; AN.UsedOtherFind = 0; m = pattern; mstop = m + *m; m++; t = term; t += *term - 1; tstop = t - ABS(*t) + 1; t = term; t++; while ( t < tstop && *t > DOTPRODUCT ) t += t[1]; while ( m < mstop && *m > DOTPRODUCT ) m += m[1]; if ( m < mstop ) { do { /* #[ SYMBOLS : */ if ( *m == SYMBOL ) { ystop = m + m[1]; m += 2; n = 0; p = older; if ( t < tstop ) while ( *t != SYMBOL ) { t += t[1]; if ( t >= tstop ) { OnlyZer1: do { if ( *m >= 2*MAXPOWER ) return(0); if ( m[1] >= 2*MAXPOWER ) nt = m[1]; else if ( m[1] <= -2*MAXPOWER ) nt = -m[1]; else return(0); nt -= 2*MAXPOWER; if ( CheckWild(BHEAD nt,SYMTONUM,0,&newval3) ) return(0); AddWild(BHEAD nt,SYMTONUM,0); m += 2; } while ( m < ystop ); goto EndLoop; } } else goto OnlyZer1; xstop = t + t[1]; t += 2; do { if ( *m == *t && t < xstop ) { if ( m[1] == t[1] ) { m += 2; t += 2; } else if ( m[1] >= 2*MAXPOWER ) { nt = t[1]; nq = m[1]; goto OnlyL2; } else if ( m[1] <= -2*MAXPOWER ) { nt = -t[1]; nq = -m[1]; OnlyL2: nq -= 2*MAXPOWER; if ( CheckWild(BHEAD nq,SYMTONUM,nt,&newval3) ) return(0); AddWild(BHEAD nq,SYMTONUM,nt); m += 2; t += 2; } else { *p++ = *t++; *p++ = *t++; n += 2; } } else if ( *m >= 2*MAXPOWER ) { while ( t < xstop ) { *p++ = *t++; *p++ = *t++; n += 2; } nq = n; p = older; while ( nq > 0 ) { if ( !CheckWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,*p,&newval1) ) { if ( m[1] == p[1] ) { AddWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,newval1); break; } else if ( m[1] >= 2*MAXPOWER && m[1] != *m ) { if ( !CheckWild(BHEAD m[1]-2*MAXPOWER,SYMTONUM,p[1],&newval3) ) { AddWild(BHEAD m[1]-2*MAXPOWER,SYMTONUM,p[1]); AddWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,newval1); break; } } else if ( m[1] <= -2*MAXPOWER && m[1] != -(*m) ) { if ( !CheckWild(BHEAD -m[1]-2*MAXPOWER,SYMTONUM,-p[1],&newval3) ) { AddWild(BHEAD -m[1]-2*MAXPOWER,SYMTONUM,-p[1]); AddWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,newval1); break; } } } nq -= 2; p += 2; } if ( nq <= 0 ) return(0); nq -= 2; n -= 2; q = p + 2; while ( --nq >= 0 ) *p++ = *q++; m += 2; } else { if ( t >= xstop || *m < *t ) { if ( m[1] >= 2*MAXPOWER ) nt = m[1]; else if ( m[1] <= -2*MAXPOWER ) nt = -m[1]; else return(0); nt -= 2*MAXPOWER; if ( CheckWild(BHEAD nt,SYMTONUM,0,&newval3) ) return(0); AddWild(BHEAD nt,SYMTONUM,0); m += 2; } else { *p++ = *t++; *p++ = *t++; n += 2; } } } while ( m < ystop ); if ( setp ) { while ( t < xstop ) { *p++ = *t++; *p++ = *t++; n+= 2; } p = older; while ( n > 0 ) { nq = setp[1] - 2; m = setp + 2; while ( --nq >= 0 ) { if ( Sets[*m].type != CSYMBOL ) { m++; continue; } t = SetElements + Sets[*m].first; tstop = SetElements + Sets[*m].last; while ( t < tstop ) { if ( *t++ == *p ) return(0); } m++; } n -= 2; p += 2; } } return(1); } /* #] SYMBOLS : #[ DOTPRODUCTS : */ else if ( *m == DOTPRODUCT ) { ystop = m + m[1]; m += 2; n = 0; p = older; if ( t < tstop ) { if ( *t < DOTPRODUCT ) goto OnlyZer2; while ( *t > DOTPRODUCT ) { t += t[1]; if ( t >= tstop || *t < DOTPRODUCT ) { OnlyZer2: do { if ( *m >= (AM.OffsetVector+WILDOFFSET) || m[1] >= (AM.OffsetVector+WILDOFFSET) ) return(0); if ( m[2] >= 2*MAXPOWER ) nq = m[2]; else if ( m[2] <= -2*MAXPOWER ) nq = -m[2]; else return(0); nq -= 2*MAXPOWER; if ( CheckWild(BHEAD nq,SYMTONUM,0,&newval3) ) return(0); AddWild(BHEAD nq,SYMTONUM,0); m += 3; } while ( m < ystop ); goto EndLoop; } } } else goto OnlyZer2; xstop = t + t[1]; t += 2; do { if ( *m == *t && m[1] == t[1] && t < xstop ) { if ( t[2] != m[2] ) { if ( m[2] >= 2*MAXPOWER ) { nq = m[2]; nt = t[2]; } else if ( m[2] <= -2*MAXPOWER ) { nq = -m[2]; nt = -t[2]; } else return(0); nq -= 2*MAXPOWER; if ( CheckWild(BHEAD nq,SYMTONUM,nt,&newval3) ) return(0); AddWild(BHEAD nq,SYMTONUM,nt); } t += 3; m += 3; } else if ( *m >= (AM.OffsetVector+WILDOFFSET) ) { while ( t < xstop ) { *p++ = *t++; *p++ = *t++; *p++ = *t++; n += 3; } nq = n; p = older; while ( nq > 0 ) { if ( *m == m[1] ) { if ( *p != p[1] ) goto NextInDot; } if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*p,&newval1) && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,p[1],&newval2) ) { if ( p[2] == m[2] ) { OnlyL9: AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval2); AddWild(BHEAD *m-WILDOFFSET,VECTOVEC,newval1); break; } if ( m[2] >= 2*MAXPOWER ) { if ( !CheckWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,p[2],&newval3) ) { AddWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,newval3); goto OnlyL9; } } else if ( m[2] <= -2*MAXPOWER ) { if ( !CheckWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2],&newval3) ) { AddWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2]); goto OnlyL9; } } } if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,p[1],&newval1) && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,*p,&newval2) ) { if ( p[2] == m[2] ) { OnlyL10: AddWild(BHEAD *m-WILDOFFSET,VECTOVEC,newval1); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval2); break; } if ( m[2] >= 2*MAXPOWER ) { if ( !CheckWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,p[2],&newval3) ) { AddWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,p[2]); goto OnlyL10; } } else if ( m[2] <= -2*MAXPOWER ) { if ( !CheckWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2],&newval3) ) { AddWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2]); goto OnlyL10; } } } NextInDot: p += 3; nq -= 3; } if ( nq <= 0 ) return(0); q = p+3; nq -= 3; n -= 3; while ( --nq >= 0 ) *p++ = *q++; m += 3; } else if ( m[1] >= (AM.OffsetVector+WILDOFFSET) ) { while ( *m >= *t && t < xstop ) { *p++ = *t++; *p++ = *t++; *p++ = *t++; n += 3; } nq = n; p = older; while ( nq > 0 ) { if ( *m == *p && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,p[1],&newval1) ) { if ( p[2] == m[2] ) { AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } else if ( m[2] >= 2*MAXPOWER ) { if ( !CheckWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,p[2],&newval3) ) { AddWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,p[2]); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } else if ( m[2] <= -2*MAXPOWER ) { if ( !CheckWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2],&newval3) ) { AddWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2]); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } } if ( *m == p[1] && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,*p,&newval1) ) { if ( p[2] == m[2] ) { AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } if ( m[2] >= 2*MAXPOWER ) { if ( !CheckWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,p[2],&newval3) ) { AddWild(BHEAD m[2]-2*MAXPOWER,SYMTONUM,p[2]); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } else if ( m[2] <= -2*MAXPOWER ) { if ( !CheckWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2],&newval3) ) { AddWild(BHEAD -m[2]-2*MAXPOWER,SYMTONUM,-p[2]); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } } p += 3; nq -= 3; } if ( nq <= 0 ) return(0); q = p+3; nq -= 3; n -= 3; while ( --nq >= 0 ) *p++ = *q++; m += 3; } else { if ( t >= xstop || *m < *t || ( *m == *t && m[1] < t[1] ) ) { if ( m[2] > 2*MAXPOWER ) nt = m[2]; else if ( m[2] <= -2*MAXPOWER ) nt = -m[2]; else return(0); nt -= 2*MAXPOWER; if ( CheckWild(BHEAD nt,SYMTONUM,0,&newval3) ) return(0); AddWild(BHEAD nt,SYMTONUM,0); m += 3; } else { *p++ = *t++; *p++ = *t++; *p++ = *t++; n += 3; } } } while ( m < ystop ); t = xstop; } /* #] DOTPRODUCTS : */ else { MLOCK(ErrorMessageLock); MesPrint("Error in pattern(1)"); MUNLOCK(ErrorMessageLock); Terminate(-1); } EndLoop:; } while ( m < mstop ); } if ( setp ) { /* while ( t < tstop && *t > SYMBOL ) t += t[1]; if ( t < tstop && setp[1] > 2 ) return(0); */ /* There were nonempty sets */ /* Empty sets are rejected by the compiler */ } return(1); } /* #] FindOnly : #[ FindOnce : WORD FindOnce(term,pattern) Searches for a single match in term. The difference with multi lies mainly in the fact that here functions may occur. The functions have not been implemented yet. (10-Apr-1988) Wildcard powers are adjustable. The value closer to zero is taken. Positive and negative gives (o surprise) zero. */ int FindOnce(PHEAD WORD *term, WORD *pattern) { GETBIDENTITY WORD *t, *m; WORD *tstop, *mstop; WORD *xstop, *ystop; WORD n, nt, *p, nq, mt, ch; WORD older[2*NORMSIZE], *q, newval1, newval2, newval3; AN.UsedOtherFind = 0; m = pattern; mstop = m + *m; m++; t = term; t += *term - 1; tstop = t - ABS(*t) + 1; t = term; t++; while ( t < tstop && *t > DOTPRODUCT ) t += t[1]; while ( m < mstop && *m > DOTPRODUCT ) m += m[1]; if ( m < mstop ) { do { /* #[ SYMBOLS : */ if ( *m == SYMBOL ) { ystop = m + m[1]; m += 2; n = 0; p = older; if ( t < tstop ) while ( *t != SYMBOL ) { t += t[1]; if ( t >= tstop ) { TryZero: do { if ( *m >= 2*MAXPOWER ) return(0); if ( m[1] >= 2*MAXPOWER ) nt = m[1]; else if ( m[1] <= -2*MAXPOWER ) nt = -m[1]; else return(0); nt -= 2*MAXPOWER; if ( ( ch = CheckWild(BHEAD nt,SYMTONUM,0,&newval3) ) != 0 ) { if ( ch > 1 ) return(0); if ( AN.oldtype != SYMTONUM ) return(0); if ( *AN.MaskPointer == 2 ) return(0); } AddWild(BHEAD nt,SYMTONUM,0); m += 2; } while ( m < ystop ); goto EndLoop; } } else goto TryZero; xstop = t + t[1]; t += 2; do { if ( *m == *t && t < xstop ) { nt = t[1]; mt = m[1]; if ( ( mt > 0 && mt <= nt ) || ( mt < 0 && mt >= nt ) ) { m += 2; t += 2; } else if ( mt >= 2*MAXPOWER ) goto OnceL2; else if ( mt <= -2*MAXPOWER ) { nt = -nt; mt = -mt; OnceL2: mt -= 2*MAXPOWER; if ( ( ch = CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) != 0 ) { if ( ch > 1 ) return(0); if ( AN.oldtype != SYMTONUM ) return(0); if ( AN.oldvalue <= 0 ) { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } } AddWild(BHEAD mt,SYMTONUM,nt); m += 2; t += 2; } else { *p++ = *t++; *p++ = *t++; n += 2; } } else if ( *m >= 2*MAXPOWER ) { while ( t < xstop ) { *p++ = *t++; *p++ = *t++; n += 2; } nq = n; p = older; while ( nq > 0 ) { nt = p[1]; if ( !CheckWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,*p,&newval1) ) { mt = m[1]; if ( ( mt > 0 && mt <= nt ) || ( mt < 0 && mt >= nt ) ) { AddWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,newval1); break; } else if ( mt >= 2*MAXPOWER && mt != *m ) { OnceL4a: mt -= 2*MAXPOWER; if ( ( ch = CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) != 0 ) { if ( ch > 1 ) return(0); if ( AN.oldtype == SYMTONUM ) { if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } else { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } AddWild(BHEAD mt,SYMTONUM,nt); AddWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,newval1); break; } } else { AddWild(BHEAD mt,SYMTONUM,nt); AddWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,newval1); break; } } else if ( mt <= -2*MAXPOWER && mt != -(*m) ) { nt = -nt; mt = -mt; goto OnceL4a; } } nq -= 2; p += 2; } if ( nq <= 0 ) return(0); nq -= 2; n -= 2; q = p + 2; while ( --nq >= 0 ) *p++ = *q++; m += 2; } else { if ( t >= xstop || *m < *t ) { if ( m[1] >= 2*MAXPOWER ) nt = m[1]; else if ( m[1] <= -2*MAXPOWER ) nt = -m[1]; else return(0); nt -= 2*MAXPOWER; if ( ( ch = CheckWild(BHEAD nt,SYMTONUM,0,&newval3) ) != 0 ) { if ( ch > 1 ) return(0); if ( AN.oldtype != SYMTONUM ) return(0); if ( *AN.MaskPointer == 2 ) return(0); } AddWild(BHEAD nt,SYMTONUM,0); m += 2; } else { *p++ = *t++; *p++ = *t++; n += 2; } } } while ( m < ystop ); } /* #] SYMBOLS : #[ DOTPRODUCTS : */ else if ( *m == DOTPRODUCT ) { ystop = m + m[1]; m += 2; n = 0; p = older; if ( t < tstop ) { if ( *t < DOTPRODUCT ) goto OnceOp; while ( *t > DOTPRODUCT ) { t += t[1]; if ( t >= tstop || *t < DOTPRODUCT ) { OnceOp: do { if ( *m >= (AM.OffsetVector+WILDOFFSET) || m[1] >= (AM.OffsetVector+WILDOFFSET) ) return(0); if ( m[2] >= 2*MAXPOWER ) { nq = m[2] - 2*MAXPOWER; } else if ( m[2] <= -2*MAXPOWER ) { nq = -m[2] - 2*MAXPOWER; } else return(0); if ( CheckWild(BHEAD nq,SYMTONUM,(WORD)0,&newval3) ) { if ( AN.oldtype != SYMTONUM ) return(0); if ( *AN.MaskPointer == 2 ) return(0); } AddWild(BHEAD nq,SYMTONUM,(WORD)0); m += 3; } while ( m < ystop ); goto EndLoop; } } } else goto OnceOp; xstop = t + t[1]; t += 2; do { if ( *m == *t && m[1] == t[1] && t < xstop ) { nt = t[2]; mt = m[2]; /* if ( ( nt > 0 && nt < mt ) || ( nt < 0 && nt > mt ) ) { if ( mt <= -2*MAXPOWER ) { mt = -mt; nt = -nt; } else if ( mt < 2*MAXPOWER ) return(0); mt -= 2*MAXPOWER; if ( CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) { if ( AN.oldtype != SYMTONUM ) return(0); if ( AN.oldvalue <= 0 ) { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } } AddWild(BHEAD mt,SYMTONUM,nt); m += 3; t += 3; } else if ( ( nt > 0 && nt >= mt && mt > -2*MAXPOWER ) || ( nt < 0 && nt <= mt && mt < 2*MAXPOWER ) ) { m += 3; t += 3; } */ if ( ( mt > 0 && mt <= nt ) || ( mt < 0 && mt >= nt ) ) { m += 3; t += 3; } else if ( mt >= 2*MAXPOWER ) goto OnceL7; else if ( mt <= -2*MAXPOWER ) { nt = -nt; mt = -mt; OnceL7: mt -= 2*MAXPOWER; if ( CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) { if ( AN.oldtype != SYMTONUM ) return(0); if ( AN.oldvalue <= 0 ) { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } } AddWild(BHEAD mt,SYMTONUM,nt); m += 3; t += 3; } else { *p++ = *t++; *p++ = *t++; *p++ = *t++; n += 3; } } else if ( *m >= (AM.OffsetVector+WILDOFFSET) ) { while ( t < xstop ) { *p++ = *t++; *p++ = *t++; *p++ = *t++; n += 3; } nq = n; p = older; while ( nq > 0 ) { if ( *m == m[1] ) { if ( *p != p[1] ) goto NextInDot; } if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*p,&newval1) && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,p[1],&newval2) ) { nt = p[2]; mt = m[2]; if ( ( mt > 0 && nt >= mt ) || ( mt < 0 && nt <= mt ) ) { OnceL9: AddWild(BHEAD *m-WILDOFFSET,VECTOVEC,newval1); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval2); break; } if ( mt >= 2*MAXPOWER ) { OnceL9a: mt -= 2*MAXPOWER; if ( CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) { if ( AN.oldtype == SYMTONUM ) { if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } else { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } AddWild(BHEAD mt,SYMTONUM,nt); goto OnceL9; } } else { AddWild(BHEAD mt,SYMTONUM,nt); goto OnceL9; } } else if ( mt <= -2*MAXPOWER ) { mt = -mt; nt = -nt; goto OnceL9a; } } if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,p[1],&newval1) && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,*p,&newval2) ) { nt = p[2]; mt = m[2]; if ( ( mt > 0 && nt >= mt ) || ( mt < 0 && nt <= mt ) ) { OnceL10: AddWild(BHEAD *m-WILDOFFSET,VECTOVEC,newval1); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval2); break; } if ( mt >= 2*MAXPOWER ) { OnceL10a: mt -= 2*MAXPOWER; if ( CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) { if ( AN.oldtype == SYMTONUM ) { if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } else { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } AddWild(BHEAD mt,SYMTONUM,nt); goto OnceL10; } } else { AddWild(BHEAD mt,SYMTONUM,nt); goto OnceL10; } } else if ( mt <= -2*MAXPOWER ) { mt = -mt; nt = -nt; goto OnceL10a; } } NextInDot: p += 3; nq -= 3; } if ( nq <= 0 ) return(0); else { q = p+3; nq -= 3; n -= 3; while ( --nq >= 0 ) *p++ = *q++; } m += 3; } else if ( m[1] >= (AM.OffsetVector+WILDOFFSET) ) { while ( *m >= *t && t < xstop ) { *p++ = *t++; *p++ = *t++; *p++ = *t++; n += 3; } nq = n; p = older; while ( nq > 0 ) { if ( *m == *p && !CheckWild(BHEAD m[1]-WILDOFFSET, VECTOVEC,p[1],&newval1) ) { nt = p[2]; mt = m[2]; if ( ( mt > 0 && nt >= mt ) || ( mt < 0 && nt <= mt ) ) { AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } else if ( mt >= 2*MAXPOWER ) { OnceL7a: mt -= 2*MAXPOWER; if ( CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) { if ( AN.oldtype == SYMTONUM ) { if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } else { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } AddWild(BHEAD mt,SYMTONUM,nt); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } else { AddWild(BHEAD mt,SYMTONUM,nt); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } else if ( mt <= -2*MAXPOWER ) { mt = -mt; nt = -nt; goto OnceL7a; } } if ( *m == p[1] && !CheckWild(BHEAD m[1]-WILDOFFSET, VECTOVEC,*p,&newval1) ) { nt = p[2]; mt = m[2]; if ( ( mt > 0 && nt >= mt ) || ( mt < 0 && nt <= mt ) ) { AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } if ( mt >= 2*MAXPOWER ) { OnceL8a: mt -= 2*MAXPOWER; if ( CheckWild(BHEAD mt,SYMTONUM,nt,&newval3) ) { if ( AN.oldtype == SYMTONUM ) { if ( AN.oldvalue >= 0 ) { if ( nt > AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt < 0 ) nt = 0; } } else { if ( nt < AN.oldvalue ) nt = AN.oldvalue; else { if ( *AN.MaskPointer == 2 ) return(0); if ( nt > 0 ) nt = 0; } } AddWild(BHEAD mt,SYMTONUM,nt); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } else { AddWild(BHEAD mt,SYMTONUM,nt); AddWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,newval1); break; } } else if ( mt < -2*MAXPOWER ) { mt = -mt; nt = -nt; goto OnceL8a; } } p += 3; nq -= 3; } if ( nq <= 0 ) return(0); q = p+3; nq -= 3; n -= 3; while ( --nq >= 0 ) *p++ = *q++; m += 3; } else { if ( t >= xstop || *m < *t || ( *m == *t && m[1] < t[1] ) ) { if ( m[2] >= 2*MAXPOWER ) nt = m[2]; else if ( m[2] <= -2*MAXPOWER ) nt = -m[2]; else return(0); nt -= 2*MAXPOWER; if ( CheckWild(BHEAD nt,SYMTONUM,0,&newval3) ) { if ( AN.oldtype != SYMTONUM ) return(0); if ( *AN.MaskPointer == 2 ) return(0); } AddWild(BHEAD nt,SYMTONUM,0); m += 3; } else { *p++ = *t++; *p++ = *t++; *p++ = *t++; n += 3; } } } while ( m < ystop ); t = xstop; } /* #] DOTPRODUCTS : */ else { MLOCK(ErrorMessageLock); MesPrint("Error in pattern(2)"); MUNLOCK(ErrorMessageLock); Terminate(-1); } EndLoop:; } while ( m < mstop ); } else { return(-1); } return(1); } /* #] FindOnce : #[ FindMulti : WORD FindMulti(term,pattern) Note that multi cannot deal with wildcards. Those patterns revert to many which gives subsequent calls to once. */ WORD FindMulti(PHEAD WORD *term, WORD *pattern) { GETBIDENTITY WORD *t, *m, *p; WORD *tstop, *mstop; WORD *xstop, *ystop; WORD mt, power, n, nq; WORD older[2*NORMSIZE], *q, newval1; AN.UsedOtherFind = 0; m = pattern; mstop = m + *m; m++; t = term; t += *term - 1; tstop = t - ABS(*t) + 1; t = term; t++; while ( t < tstop && *t > DOTPRODUCT ) t += t[1]; while ( m < mstop && *m > DOTPRODUCT ) m += m[1]; power = -1; /* No power yet */ if ( m < mstop ) { do { /* #[ SYMBOLS : */ if ( *m == SYMBOL ) { ystop = m + m[1]; m += 2; if ( t >= tstop ) return(0); while ( *t != SYMBOL ) { t += t[1]; if ( t >= tstop ) return(0); } xstop = t + t[1]; t += 2; p = older; n = 0; do { if ( *m >= 2*MAXPOWER ) { while ( t < xstop ) { *p++ = *t++; *p++ = *t++; n += 2; } nq = n; p = older; while ( nq > 0 ) { if ( !CheckWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,*p,&newval1) ) { mt = p[1]/m[1]; if ( mt > 0 ) { if ( power < 0 || mt < power ) power = mt; AddWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,newval1); break; } } nq -= 2; p += 2; } if ( nq <= 0 ) return(0); nq -= 2; n -= 2; q = p + 2; while ( --nq >= 0 ) *p++ = *q++; m += 2; } else if ( t >= xstop ) return(0); else if ( *m == *t ) { if ( ( mt = t[1]/m[1] ) <= 0 ) return(0); if ( power < 0 || mt < power ) power = mt; m += 2; t += 2; } else if ( *m < *t ) return(0); else { *p++ = *t++; *p++ = *t++; n += 2; } } while ( m < ystop ); } /* #] SYMBOLS : #[ DOTPRODUCTS : */ else if ( *m == DOTPRODUCT ) { ystop = m + m[1]; m += 2; if ( t >= tstop ) return(0); while ( *t != DOTPRODUCT ) { t += t[1]; if ( t >= tstop ) return(0); } xstop = t + t[1]; t += 2; do { if ( t >= xstop ) return(0); if ( *t == *m ) { if ( t[1] == m[1] ) { if ( ( mt = t[2]/m[2] ) <= 0 ) return(0); if ( power < 0 || mt < power ) power = mt; m += 3; } else if ( t[1] > m[1] ) return(0); } else if ( *t > *m ) return(0); t += 3; } while ( m < ystop ); t = xstop; } /* #] DOTPRODUCTS : */ else { MLOCK(ErrorMessageLock); MesPrint("Error in pattern(3)"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } while ( m < mstop ); } if ( power < 0 ) power = 0; return(power); } /* #] FindMulti : #[ FindRest : WORD FindRest(term,pattern) This routine scans for anything but dotproducts and symbols. */ int FindRest(PHEAD WORD *term, WORD *pattern) { GETBIDENTITY WORD *t, *m, *tt, wild, regular; WORD *tstop, *mstop; WORD *xstop, *ystop; WORD n, *p, nq; WORD older[NORMSIZE], *q, newval1, newval2; int i, ntwa; AN.UsedOtherFind = 0; AN.findTerm = term; AN.findPattern = pattern; m = AN.WildValue; i = (m[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; ntwa = 0; while ( i > 0 ) { if ( m[0] == ARGTOARG ) ntwa++; m += m[1]; i--; } t = term; t += *term - 1; tstop = t - ABS(*t) + 1; t = term; t++; p = t; while ( t < tstop && *t > DOTPRODUCT ) t += t[1]; tstop = t; t = p; m = pattern; mstop = m + *m; m++; p = m; while ( m < mstop && *m > DOTPRODUCT ) m += m[1]; mstop = m; m = p; if ( m < mstop ) { do { /* #[ FUNCTIONS : */ if ( *m >= FUNCTION ) { if ( *mstop > 5 && !MatchIsPossible(pattern,term) ) return(0); ystop = m; n = 0; do { m += m[1]; n++; } while ( m < mstop && *m >= FUNCTION ); AT.WorkPointer += n; while ( t < tstop && *t == SUBEXPRESSION ) t += t[1]; tt = xstop = t; nq = 0; while ( t < tstop && ( *t >= FUNCTION || *t == SUBEXPRESSION ) ) { if ( *t != SUBEXPRESSION ) { nq++; if ( functions[*t-FUNCTION].commute ) tt = t + t[1]; } t += t[1]; } if ( nq < n ) return(0); AN.terstart = term; AN.terstop = t; AN.terfirstcomm = tt; AN.patstop = m; AN.NumTotWildArgs = ntwa; if ( !ScanFunctions(BHEAD ystop,xstop,0) ) return(0); } /* #] FUNCTIONS : #[ VECTORS : */ else if ( *m == VECTOR ) { while ( t < tstop && *t != VECTOR ) t += t[1]; if ( t >= tstop ) return(0); xstop = t + t[1]; ystop = m + m[1]; t += 2; m += 2; n = 0; p = older; do { if ( *m == *t && m[1] == t[1] && t < xstop ) { m += 2; t += 2; } else if ( *m >= (AM.OffsetVector+WILDOFFSET) ) { if ( t < xstop ) { p = older + n; do { *p++ = *t++; n++; } while ( t < xstop ); } p = older; nq = n; if ( ( m[1] < (AM.OffsetIndex+WILDOFFSET) ) || ( m[1] >= (AM.OffsetIndex+2*WILDOFFSET) ) ) { while ( nq > 0 ) { if ( m[1] == p[1] ) { if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*p,&newval1) ) { RestL11: AddWild(BHEAD *m-WILDOFFSET,VECTOVEC,newval1); break; } } p += 2; nq -= 2; } } else { /* Double wildcard */ while ( nq > 0 ) { if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*p,&newval1) && !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,p[1],&newval2) ) { AddWild(BHEAD m[1]-WILDOFFSET,INDTOIND,newval2); goto RestL11; } p += 2; nq -= 2; } } if ( nq > 0 ) { nq -= 2; q = p + 2; n -= 2; while ( --nq >= 0 ) *p++ = *q++; } else return(0); m += 2; } else if ( ( *m <= *t ) && ( m[1] >= (AM.OffsetIndex + WILDOFFSET) ) && ( m[1] < (AM.OffsetIndex + 2*WILDOFFSET) ) ) { if ( *m == *t && t < xstop ) { p = older; p += n; *p++ = *t++; *p++ = *t++; n += 2; } p = older; nq = n; while ( nq > 0 ) { if ( *m == *p ) { if ( !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,p[1],&newval1) ) { AddWild(BHEAD m[1]-WILDOFFSET,INDTOIND,newval1); break; } } p += 2; nq -= 2; } if ( nq > 0 ) { nq -= 2; q = p + 2; n -= 2; while ( --nq >= 0 ) *p++ = *q++; } else return(0); m += 2; } else { if ( t >= xstop ) return(0); *p++ = *t++; *p++ = *t++; n += 2; } } while ( m < ystop ); } /* #] VECTORS : #[ INDICES : */ else if ( *m == INDEX ) { /* This needs only to say that there is a match, after matching a 'wildcard'. This has to be prepared in TestMatch. The C->rhs should provide the replacement inside the prototype! Next question: id,p=q/2+r/2 */ while ( *t != INDEX ) { t += t[1]; if ( t >= tstop ) return(0); } xstop = t + t[1]; ystop = m + m[1]; t += 2; m += 2; n = 0; p = older; do { if ( *m == *t && t < xstop && m < ystop ) { t++; m++; } else if ( ( *m >= (AM.OffsetIndex+WILDOFFSET) ) && ( *m < (AM.OffsetIndex+2*WILDOFFSET) ) ) { while ( t < xstop ) { *p++ = *t++; n++; } if ( !n ) return(0); nq = n; q = older; do { if ( !CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,*q,&newval1) ) { AddWild(BHEAD *m-WILDOFFSET,INDTOIND,newval1); break; } q++; nq--; } while ( nq > 0 ); if ( nq <= 0 ) return (0); n--; nq--; p = q + 1; while ( nq > 0 ) { *q++ = *p++; nq--; } p--; m++; } else if ( ( *m >= (AM.OffsetVector+WILDOFFSET) ) && ( *m < (AM.OffsetVector+2*WILDOFFSET) ) ) { while ( t < xstop ) { *p++ = *t++; n++; } if ( !n ) return(0); nq = n; q = older; do { if ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*q,&newval1) ) { AddWild(BHEAD *m-WILDOFFSET,VECTOVEC,newval1); break; } q++; nq--; } while ( nq > 0 ); if ( nq <= 0 ) return (0); n--; nq--; p = q + 1; while ( nq > 0 ) { *q++ = *p++; nq--; } p--; m++; } else { if ( t >= xstop ) return(0); *p++ = *t++; n++; } } while ( m < ystop ); /* return(0); */ } /* #] INDICES : #[ DELTAS : */ else if ( *m == DELTA ) { while ( *t != DELTA ) { t += t[1]; if ( t >= tstop ) return(0); } xstop = t + t[1]; ystop = m + m[1]; t += 2; m += 2; n = 0; p = older; do { if ( *t == *m && t[1] == m[1] && t < xstop ) { m += 2; t += 2; } else if ( ( *m >= (AM.OffsetIndex+WILDOFFSET) ) && ( *m < (AM.OffsetIndex+2*WILDOFFSET) ) && ( m[1] >= (AM.OffsetIndex+WILDOFFSET) ) && ( m[1] < (AM.OffsetIndex+2*WILDOFFSET) ) ) { /* Two dummies */ while ( t < xstop ) { *p++ = *t++; *p++ = *t++; n += 2; } if ( !n ) return(0); nq = n; q = older; do { if ( !CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,*q,&newval1) && !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,q[1],&newval2) ) { AddWild(BHEAD *m-WILDOFFSET,INDTOIND,newval1); AddWild(BHEAD m[1]-WILDOFFSET,INDTOIND,newval2); break; } if ( !CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,q[1],&newval1) && !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,*q,&newval2) ) { AddWild(BHEAD *m-WILDOFFSET,INDTOIND,newval1); AddWild(BHEAD m[1]-WILDOFFSET,INDTOIND,newval2); break; } q += 2; nq -= 2; } while ( nq > 0 ); if ( nq <= 0 ) return(0); n -= 2; nq -= 2; p = q + 2; while ( nq > 0 ) { *q++ = *p++; nq--; } p -= 2; m += 2; } else if ( ( m[1] >= (AM.OffsetIndex+WILDOFFSET) ) && ( m[1] < (AM.OffsetIndex+2*WILDOFFSET) ) ) { wild = m[1]; regular = *m; OneWild: while ( ( regular == *t || regular == t[1] ) && t < xstop ) { *p++ = *t++; *p++ = *t++; n += 2; } if ( !n ) return(0); nq = n; q = older; do { if ( regular == *q && !CheckWild(BHEAD wild-WILDOFFSET,INDTOIND,q[1],&newval1) ) { AddWild(BHEAD wild-WILDOFFSET,INDTOIND,newval1); break; } if ( regular == q[1] && !CheckWild(BHEAD wild-WILDOFFSET,INDTOIND,*q,&newval1) ) { AddWild(BHEAD wild-WILDOFFSET,INDTOIND,newval1); break; } q += 2; nq -= 2; } while ( nq > 0 ); if ( nq <= 0 ) return(0); n -= 2; nq -= 2; p = q + 2; while ( nq > 0 ) { *q++ = *p++; nq--; } p -= 2; m += 2; } else if ( ( *m >= (AM.OffsetIndex+WILDOFFSET) ) && ( *m < (AM.OffsetIndex+2*WILDOFFSET) ) ) { wild = *m; regular = m[1]; goto OneWild; } else { if ( t >= tstop || *m < *t || ( *m == *t && m[1] < t[1] ) ) return(0); *p++ = *t++; *p++ = *t++; n += 2; } } while ( m < ystop ); } /* #] DELTAS : */ else { MLOCK(ErrorMessageLock); MesPrint("Pattern not yet implemented"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } while ( m < mstop ); return(1); } else return(-1); } /* #] FindRest : #] Patterns : */ form-5.0.1/sources/polyfact.cc0000644000175100017510000012612215217035721011765 /** @file polyfact.cc * * Contains the routines for factorizing multivariate polynomials */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ include : */ #include "poly.h" #include "polygcd.h" #include "polyfact.h" #include #include #include #include #include //#define DEBUG #ifdef DEBUG #include "mytime.h" #endif using namespace std; /* #] include : #[ tostring : */ // Turns a factorized_poly into a readable string const string factorized_poly::tostring () const { // empty if (factor.size()==0) return "no_factors"; string res; // polynomial for (int i=0; i<(int)factor.size(); i++) { if (i>0) res += "*"; res += "("; res += poly(factor[i],0,1).to_string(); res += ")"; if (power[i]>1) { res += "^"; char tmp[100]; snprintf (tmp,100,"%i",power[i]); res += tmp; } } // modulo p^n if (factor[0].modp>0) { res += " (mod "; char tmp[12]; snprintf (tmp,12,"%i",factor[0].modp); res += tmp; if (factor[0].modn > 1) { snprintf (tmp,12,"%i",factor[0].modn); res += "^"; res += tmp; } res += ")"; } return res; } /* #] tostring : #[ ostream operator : */ // ostream operator for outputting a factorized_poly ostream& operator<< (ostream &out, const factorized_poly &a) { return out << a.tostring(); } // ostream operator for outputting a vector template ostream& operator<< (ostream &out, const vector &v) { out<<"{"; for (int i=0; i<(int)v.size(); i++) { if (i>0) out<<","; out< polyfact::extended_gcd_Euclidean_lifted (const poly &a, const poly &b) { #ifdef DEBUGALL cout << "*** [" << thetime() << "] CALL: extended_Euclidean_lifted("< res; res.push_back(sa); res.push_back(sb); #ifdef DEBUGALL cout << "*** [" << thetime() << "] RES : extended_Euclidean_lifted("< polyfact::solve_Diophantine_univariate (const vector &a, const poly &b) { #ifdef DEBUGALL cout << "*** [" << thetime() << "] CALL: solve_Diophantine_univariate(" < s(1,b); for (int i=0; i+1<(int)a.size(); i++) { poly A(BHEAD 1,b.modp,b.modn); for (int j=i+1; j<(int)a.size(); j++) A *= a[j]; vector t(extended_gcd_Euclidean_lifted(a[i],A)); poly prev(s.back()); s.back() = t[1] * prev % a[i]; s.push_back(t[0] * prev % A); } #ifdef DEBUGALL cout << "*** [" << thetime() << "] RES : solve_Diophantine_univariate(" <, with the ideal I=. The * input a1,...,ak and b consists of multivariate polynomials and * Ai = product(aj|j!=i). The solution si consists therefore of * multivariate polynomials as well. * * When deg(c,x1) < sum(deg(ai,x1)), the result is the unique result * with deg(si,x1) < deg(ai,x1) for all i. This is necessary for the * Hensel construction. * * The equation is solved in the following way: * - reduce with the homomorphism * - solve the equation in one less variable * - use ideal-adic Newton's iteration to add the xm-terms. * * Notes * ===== * - The ai must be pairwise relatively prime modulo . * - The method returns an empty vector() iff the * Diophantine equation has no solution (typically happens in * gcd calculations with unlucky reductions). * * [for details, see "Algorithms for Computer Algebra", pp. 264-273] */ const vector polyfact::solve_Diophantine_multivariate (const vector &a, const poly &b, const vector &x, const vector &c, int d) { #ifdef DEBUGALL cout << "*** [" << thetime() << "] CALL: solve_Diophantine_multivariate(" <(a.size(),poly(BHEAD 0)); if (x.size() == 1) return solve_Diophantine_univariate(a,b); // Reduce the polynomial with the homomorphism poly simple(poly::simple_poly(BHEAD x.back(),c.back())); vector ared (a); for (int i=0; i<(int)ared.size(); i++) ared[i] %= simple; poly bred(b % simple); vector xred(x.begin(),x.end()-1); vector cred(c.begin(),c.end()-1); // Solve the equation in one less variable vector s(solve_Diophantine_multivariate(ared,bred,xred,cred,d)); if (s == vector()) return vector(); // Cache the Ai = product(aj | j!=i). vector A(a.size(), poly(BHEAD 1,b.modp,b.modn)); for (int i=0; i<(int)a.size(); i++) for (int j=0; j<(int)a.size(); j++) if (i!=j) A[i] *= a[j]; // Add the powers (xm-c{m-1})^k with ideal-adic Newton iteration. poly term(BHEAD 1,b.modp,b.modn); poly error(b); for (int i=0; i<(int)A.size(); i++) error -= s[i] * A[i]; for (int deg=1; deg<=d; deg++) { if (error.is_zero()) break; error /= simple; term *= simple; vector ds(solve_Diophantine_multivariate(ared, error%simple, xred, cred, d)); if (ds == vector()) return vector(); for (int i=0; i<(int)s.size(); i++) { s[i] += ds[i] * term; error -= ds[i] * A[i]; } } if (!error.is_zero()) return vector(); #ifdef DEBUGALL cout << "*** [" << thetime() << "] RES : solve_Diophantine_multivariate(" < polyfact::lift_coefficients (const poly &_A, const vector &_a) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: lift_coefficients("<<_A<<","<<_a<<")"< a(_a); poly term(BHEAD 1); int x = A.first_variable(); // Replace the leading term of all factors with lterm(A) mod p poly lead(A.integer_lcoeff()); for (int i=0; i<(int)a.size(); i++) { a[i] *= lead / a[i].integer_lcoeff(); if (i>0) A*=lead; } // Solve Diophantine equation vector s(solve_Diophantine_univariate(a,poly(BHEAD 1,A.modp,1))); // Replace the leading term of all factors with lterm(A) mod p^n for (int i=0; i<(int)a.size(); i++) { a[i].setmod(A.modp,A.modn); a[i] += (lead - a[i].integer_lcoeff()) * poly::simple_poly(BHEAD x,0,a[i].degree(x)); } // Calculate the error, express it in terms of ai and add corrections. for (int k=2; k<=A.modn; k++) { term *= poly(BHEAD A.modp); poly error(BHEAD -1); for (int i=0; i<(int)a.size(); i++) error *= a[i]; error += A; if (error.is_zero()) break; error /= term; error.setmod(A.modp,1); for (int i=0; i<(int)a.size(); i++) a[i] += term * (error * s[i] % a[i]); } // Fix leading coefficients by dividing out integer contents. for (int i=0; i<(int)a.size(); i++) a[i] /= polygcd::integer_content(poly(a[i],0,1)); #ifdef DEBUG cout << "*** [" << thetime() << "] RES : lift_coefficients("<<_A<<","<<_a<<") = "< > &state, vector > > &terms, vector &term, int sumdeg) { // store the term if (dep == (int)state.size()) { terms[sumdeg].push_back(term); return; } // recursively create new terms term.push_back(0); for (int deg=0; sumdeg+deg<(int)state[dep].size(); deg++) if (state[dep][deg] > 0) { term.back() = deg; predetermine(dep+1, state, terms, term, sumdeg+deg); } term.pop_back(); } /* #] predetermine : #[ lift_variables : */ /** Multivariate Hensel lifting of variables * * Description * =========== * Given a multivariate polynomial A modulo a prime power p^n and * a list of univariate polynomials a1(x1),...,am(x1), such that * * - A(x1,...,xm) = a1(x1)*...*ak(x1) mod , * - gcd(ai,aj) = 1 (for i!=j), * * with the ideal I=, the method returns a * list of multivariate polynomials A1(x1,...xm),...,Ak(x1,...,xm), * such that * * A(x1,...,xm) = A1(x1,...,xm)*...*Ak(x1,...,xm) mod p^n * * with * * Ai(x1,...,xm) = ai(x1) mod . * * The correct multivariate leading coefficients should be given in * the parameter lc. * * [for details, see "Algorithms for Computer Algebra", pp. 250-273] * * Before Hensel lifting, predetermination of coefficients is used * for efficiency. * [for details, see Wang, "An Improved Polynomial Factoring * Algorithm", Math. Comput. 32 (1978) pp. 1215-1231] * * Notes * ===== * - The polynomial A must be primitive. * - Returns empty vector() if lifting is impossible. */ const vector polyfact::lift_variables (const poly &A, const vector &_a, const vector &x, const vector &c, const vector &lc) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: lift_variables("< a(_a); // First method: predetermine coefficients // check feasibility, otherwise it tries too many possibilities int cnt = POLYFACT_MAX_PREDETERMINATION; for (int i=0; i<(int)a.size(); i++) { if (a[i].number_of_terms() == 0) return vector(); cnt /= a[i].number_of_terms(); } if (cnt>0) { // state[n][d]: coefficient of x^d in a[n] is // 0: non-existent, 1: undetermined, 2: determined int D = A.degree(x[0]); vector > state(a.size(), vector(D+1, 0)); for (int i=0; i<(int)a.size(); i++) for (int j=1; j > > terms(D+1); vector term; predetermine(0,state,terms,term); // count the number of undetermined coefficients vector num_undet(terms.size(),0); for (int i=0; i<(int)terms.size(); i++) for (int j=0; j<(int)terms[i].size(); j++) for (int k=0; k<(int)terms[i][j].size(); k++) if (state[k][terms[i][j][k]] == 1) num_undet[i]++; // replace the current leading coefficients by the correct ones for (int i=0; i<(int)a.size(); i++) a[i] += (lc[i] - a[i].lcoeff_univar(x[0])) * poly::simple_poly(BHEAD x[0],0,a[i].degree(x[0])); bool changed; do { changed = false; for (int i=0; i<(int)terms.size(); i++) { // is only one coefficient in a equation is undetermined, solve // the equation to determine this coefficient if (num_undet[i] == 1) { // generate equation poly lhs(BHEAD 0), rhs(A.coefficient(x[0],i), A.modp, A.modn); int which_idx=-1, which_deg=-1; for (int j=0; j<(int)terms[i].size(); j++) { poly coeff(BHEAD 1, A.modp, A.modn); bool undet=false; for (int k=0; k<(int)terms[i][j].size(); k++) { if (state[k][terms[i][j][k]] == 1) { undet = true; which_idx=k; which_deg=terms[i][j][k]; } else coeff *= a[k].coefficient(x[0], terms[i][j][k]); } if (undet) lhs = coeff; else rhs -= coeff; } // solve equation if (A.modn > 1) rhs.setmod(0,1); if (lhs.is_zero() || !(rhs%lhs).is_zero()) return vector(); a[which_idx] += (rhs / lhs - a[which_idx].coefficient(x[0],which_deg)) * poly::simple_poly(BHEAD x[0],0,which_deg); state[which_idx][which_deg] = 2; // update number of undetermined coefficients for (int j=0; j<(int)terms.size(); j++) for (int k=0; k<(int)terms[j].size(); k++) if (terms[j][k][which_idx] == which_deg) num_undet[j]--; changed = true; } } } while (changed); // if this is the complete result, skip lifting poly check(BHEAD 1, A.modn>1?0:A.modp, 1); for (int i=0; i<(int)a.size(); i++) check *= a[i]; if (check == A) return a; } // Second method: Hensel lifting // Calculate A and lc's modulo Ii = (for i=2,...,m) vector simple(x.size(), poly(BHEAD 0)); for (int i=(int)x.size()-2; i>=0; i--) simple[i] = poly::simple_poly(BHEAD x[i+1],c[i],1); // Calculate the maximum degree of A in x2,...,xm int maxdegA=0; for (int i=1; i<(int)x.size(); i++) maxdegA = MaX(maxdegA, A.degree(x[i])); // Iteratively add the variables x2,...,xm for (int xi=1; xi<(int)x.size(); xi++) { // replace the current leading coefficients by the correct ones for (int i=0; i<(int)a.size(); i++) a[i] += (lc[i] - a[i].lcoeff_univar(x[0])) * poly::simple_poly(BHEAD x[0],0,a[i].degree(x[0])); vector anew(a); for (int i=0; i<(int)anew.size(); i++) for (int j=xi-1; j<(int)c.size(); j++) anew[i] %= simple[j]; vector xnew(x.begin(), x.begin()+xi); vector cnew(c.begin(), c.begin()+xi-1); poly term(BHEAD 1,A.modp,A.modn); // Iteratively add the powers xi^k for (int deg=1, maxdeg=A.degree(x[xi]); deg<=maxdeg; deg++) { term *= simple[xi-1]; // Calculate the error, express it in terms of ai and add corrections. poly error(BHEAD -1,A.modp,A.modn); for (int i=0; i<(int)a.size(); i++) error *= a[i]; error += A; for (int i=xi; i<(int)c.size(); i++) error %= simple[i]; if (error.is_zero()) break; error /= term; error %= simple[xi-1]; vector s(solve_Diophantine_multivariate(anew,error,xnew,cnew,maxdegA)); if (s == vector()) return vector(); for (int i=0; i<(int)a.size(); i++) a[i] += s[i] * term; } // check whether PRODUCT(a[i]) = A mod over the integers or ZZ/p poly check(BHEAD -1, A.modn>1?0:A.modp, 1); for (int i=0; i<(int)a.size(); i++) check *= a[i]; check += A; for (int i=xi; i<(int)c.size(); i++) check %= simple[i]; if (!check.is_zero()) return vector(); } #ifdef DEBUG cout << "*** [" << thetime() << "] RES : lift_variables("< &x, WORD p) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: choose_prime("< is returned. This is * necessary, e.g., in the case of a non-squarefree input * polynomial * * [for details, see: * - "Algorithms for Computer Algebra", pp. 337-343, * - Wang, "An Improved Polynomial Factoring Algorithm", * Math. Comput. 32 (1978) pp. 1215-1231] */ const vector polyfact::choose_ideal (const poly &a, int p, const factorized_poly &lc, const vector &x) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: polyfact::choose_ideal(" <(); POLY_GETIDENTITY(a); vector c(x.size()-1); int dega = a.degree(x[0]); poly amodI(a); // choose random c for (int i=0; i<(int)c.size(); i++) { c[i] = 1 + wranf(BHEAD0) % ((p-1) / POLYFACT_IDEAL_FRACTION); amodI %= poly::simple_poly(BHEAD x[i+1],c[i],1); } poly amodIp(amodI); amodIp.setmod(p,1); // check if leading coefficient is non-zero [equivalent to degree=old_degree] if (amodIp.degree(x[0]) != dega) return c = vector(); // check if leading coefficient is squarefree [equivalent to gcd(a,a')==const] if (!polygcd::gcd_Euclidean(amodIp, amodIp.derivative(x[0])).is_integer()) return c = vector(); if (a.modp>0 && a.modn==1) return c; // check for unique prime factors in each factor lc[i] of the leading coefficient vector d(1, polygcd::integer_content(amodI)); for (int i=0; i<(int)lc.factor.size(); i++) { // constant factor if (i==0 && lc.factor[i].is_integer()) { d[0] *= lc.factor[i]; continue; } // factor modulo I poly q(lc.factor[i]); for (int j=0; j<(int)c.size(); j++) q %= poly::simple_poly(BHEAD x[j+1],c[j]); if (q.sign() == -1) q *= poly(BHEAD -1); // divide out common factors for (int j=(int)d.size()-1; j>=0; j--) { poly r(d[j]); while (!r.is_one()) { r = polygcd::integer_gcd(r,q); q /= r; } } // check whether there is some factor left if (q.is_one()) return vector(); d.push_back(q); } #ifdef DEBUG cout << "*** [" << thetime() << "] RES : polyfact::choose_ideal(" < > polyfact::Berlekamp_Qmatrix (const poly &_a) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: Berlekamp_Qmatrix("<<_a<<")\n"; #endif if (_a.all_variables() == vector()) return vector >(0); POLY_GETIDENTITY(_a); poly a(_a); int x = a.first_variable(); int n = a.degree(x); int p = a.modp; poly lc(a.integer_lcoeff()); a /= lc; vector > Q(n, vector(n)); // c is the vector of coefficients of the polynomial a vector c(n+1,0); for (int j=1; j d(n,0); d[0]=1; for (int i=0; i<=(n-1)*p; i++) { // store the coefficients of x^(i*p) mod a if (i%p==0) Q[i/p] = d; // transform d=x^i mod a into d=x^(i+1) mod a vector e(n); for (int j=0; j0?d[j-1]:0)) % p; if (e[j]<0) e[j]+=p; } d=e; } // Q = Q - I for (int i=0; i idx; for (int k=0; k is suitable * for returning the factors. * * [for details, see "Algorithms for Computer Algebra", pp. 346-359] */ const vector polyfact::Berlekamp_find_factors (const poly &_a, const vector > &_q) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: Berlekamp_find_factors("<<_a<<","<<_q<<")\n"; #endif if (_a.all_variables() == vector()) return vector(1,_a); POLY_GETIDENTITY(_a); vector > q=_q; int rank=0; for (int i=0; i<(int)q.size(); i++) if (q[i]!=vector(q[i].size(),0)) rank++; poly a(_a); int x = a.first_variable(); int n = a.degree(x); int p = a.modp; a /= a.integer_lcoeff(); // Vector of factors, represented as dense polynomials mod p vector > fac(1, vector(n+1,0)); fac[0] = poly::to_coefficient_list(a); bool finished=false; // Loop over the columns of q + constant, i.e., an exhaustive list of possible factors for (int i=1; i(n,0)) continue; for (int s=0; s

c = polygcd::coefficient_list_gcd(fac[j], q[i], p); // If a non-trivial factor is found, add it to the list if (c.size()!=1 && c.size()!=fac[j].size()) { fac.push_back(c); fac[j] = poly::coefficient_list_divmod(fac[j], c, p, 0); if ((int)fac.size() == rank) finished=true; } } // Increase the constant term by one q[i][0] = (q[i][0]+1) % p; } } // Convert the densely represented polynomials to sparse ones vector res(fac.size(),poly(BHEAD 0, p)); for (int i=0; i<(int)fac.size(); i++) res[i] = poly::from_coefficient_list(BHEAD fac[i],x,p); #ifdef DEBUG cout << "*** [" << thetime() << "] RES : Berlekamp_find_factors("<<_a<<","<<_q<<") = "<) than is possible over the integers. This might be caused * by a unlucky choice of p or I, but might also happen for choices. * * When this happens, the coefficients of the factors are large * after Hensel lifting, and therefore the factor does not divide * the polynomial viewed as polynomial over the integers. * * This method combines those incorrect factors into correct ones. * * Notes * ===== * Theoretically, this method takes exponential time (for ugly, * constructed cases), but in practice it is fast. This can be fixed * by implementing Van Hoeij's knapsack method (see: "Factoring * polynomials and the knapsack problem" by M. van Hoeij). [TODO] */ const vector polyfact::combine_factors (const poly &a, const vector &f) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: combine_factors("< res; int num_used = 0; vector used(f.size(), false); // Loop over all bitmasks with num=1,2,...,size(factors)/2 bits // set, that contain only unused factors for (int num=1; num<=(int)(f.size() - num_used)/2; num++) { vector next(f.size() - num_used, 0); for (int i=0; i * - Use Hensel lifting and factor combination to find the correct * factors over the integers * * Notes * ===== * The polynomial must be primitive and squarefree */ const vector polyfact::factorize_squarefree (const poly &a, const vector &x) { #ifdef DEBUG cout << "*** [" << thetime() << "] CALL: factorize_squarefree("< c,d,bestc,bestd; vector > q,bestq; // Factorize leading coefficient factorized_poly lc(factorize(a.lcoeff_univar(x[0]))); // Try a number of primes int prime_tries = 0; while (prime_tries1) { if (a.modp == 0) { p = choose_prime(a,x,p); n = 0; if (a.degree(x[0]) % p == 0) continue; // Univariate case: check whether the polynomial mod p is squarefree // Multivariate case: this check is done after choosing I (for efficiency) if (x.size()==1) { poly amodp(a,p,1); if (polygcd::gcd_Euclidean(amodp, amodp.derivative(x[0])).degree(x[0]) != 0) continue; } } // Try a number of ideals if (x.size()>1) for (int ideal_tries=0; ideal_tries0) break; } if (x.size()==1 || c.size()>0) { amodI = a; for (int i=0; i<(int)c.size(); i++) amodI %= poly::simple_poly(BHEAD x[i+1],c[i]); // Determine Q-matrix and its rank. Smaller rank is better. q = Berlekamp_Qmatrix(poly(amodI,p,1)); int rank=0; for (int i=0; i<(int)q.size(); i++) if (q[i]!=vector(q[i].size(),0)) rank++; if (rank(1, a); if (x.size() > 1 && f.size() > 1) { // The correct leading coefficients of the factors can be // reconstructed from prime number factors of the leading // coefficients modulo I. This is possible since all factors of // the leading coefficient have unique prime factors for the ideal // I is chosen as such. poly amodI(a); for (int i=0; i<(int)c.size(); i++) amodI %= poly::simple_poly(BHEAD x[i+1],c[i]); poly delta(polygcd::integer_content(amodI)); vector lcmodI(lc.factor.size(), poly(BHEAD 0)); for (int i=0; i<(int)lc.factor.size(); i++) { lcmodI[i] = lc.factor[i]; for (int j=0; j<(int)c.size(); j++) lcmodI[i] %= poly::simple_poly(BHEAD x[j+1],c[j]); } vector correct_lc(f.size(), poly(BHEAD 1,p,n)); for (int j=0; j<(int)f.size(); j++) { poly lc_f(f[j].integer_lcoeff() * delta); WORD nlc_f = lc_f[lc_f[1]]; poly quo(BHEAD 0),rem(BHEAD 0); WORD nquo,nrem; for (int i=(int)lcmodI.size()-1; i>=0; i--) { if (i==0 && lc.factor[i].is_integer()) continue; do { DivLong((UWORD *)&lc_f[2+AN.poly_num_vars], nlc_f, (UWORD *)&lcmodI[i][2+AN.poly_num_vars], lcmodI[i][lcmodI[i][1]], (UWORD *)&quo[0], &nquo, (UWORD *)&rem[0], &nrem); if (nrem == 0) { correct_lc[j] *= lc.factor[i]; lc_f.termscopy(&quo[0], 2+AN.poly_num_vars, ABS(nquo)); nlc_f = nquo; } } while (nrem == 0); } } for (int i=0; i<(int)correct_lc.size(); i++) { poly correct_modI(correct_lc[i]); for (int j=0; j<(int)c.size(); j++) correct_modI %= poly::simple_poly(BHEAD x[j+1],c[j]); poly d(polygcd::integer_gcd(correct_modI, f[i].integer_lcoeff())); correct_lc[i] *= f[i].integer_lcoeff() / d; delta /= correct_modI / d; f[i] *= correct_modI / d; } // increase n, because of multiplying with delta if (!delta.is_one()) { poly deltapow(BHEAD 1); for (int i=1; i<(int)correct_lc.size(); i++) deltapow *= delta; while (!deltapow.is_zero()) { deltapow /= poly(BHEAD p); n++; } for (int i=0; i<(int)f.size(); i++) { f[i].modn = n; correct_lc[i].modn = n; } } poly aa(a,p,n); for (int i=0; i<(int)correct_lc.size(); i++) { correct_lc[i] *= delta; f[i] *= delta; if (i>0) aa *= delta; } f = lift_variables(aa,f,x,c,correct_lc); for (int i=0; i<(int)f.size(); i++) if (a.modp == 0) f[i] /= polygcd::integer_content(poly(f[i],0,1)); else f[i] /= polygcd::content_univar(f[i], x[0]); if (f==vector()) { #ifdef DEBUG cout << "factor_squarefree failed (lift_var step)" << endl; #endif goto try_again; } } // set modulus of the factors correctly if (a.modp==0) for (int i=0; i<(int)f.size(); i++) f[i].setmod(0,1); // Final check (not sure if this is necessary, but it doesn't hurt) poly check(BHEAD 1,a.modp,a.modn); for (int i=0; i<(int)f.size(); i++) check *= f[i]; if (check != a) { #ifdef DEBUG cout << "factor_squarefree failed (final check) : " << f << endl; #endif goto try_again; } #ifdef DEBUG cout << "*** [" << thetime() << "] RES : factorize_squarefree("< x = a.all_variables(); // No variables, so just one factor if (x.size() == 0) { factorized_poly res; if (a.is_one()) return res; res.add_factor(a,1); return res; } // Remove content poly conta(polygcd::content_univar(a,x[0])); factorized_poly faca(factorize(conta)); poly ppa(a / conta); // Find a squarefree factorization factorized_poly b(squarefree_factors(ppa)); #ifdef DEBUG cout << "*** [" << thetime() << "] ... : factorize("< c(factorize_squarefree(b.factor[i], x)); for (int j=0; j<(int)c.size(); j++) { faca.factor.push_back(c[j]); faca.power.push_back(b.power[i]); } } #ifdef DEBUG cout << "*** [" << thetime() << "] RES : factorize("<. */ /* #] License : */ /* #define HIDEDEBUG #[ Includes : proces.c */ #include "form3.h" WORD printscratch[2]; /* #] Includes : #[ Processor : #[ Processor : WORD Processor() */ /** * This is the central processor. * It accepts a stream of Expressions which is accessed by calls to GetTerm. * The expressions reside either in AR.infile or AR.hidefile * The definitions of an expression are seen as an id-statement, so the * primary Expressions should be written to the system of scratch files * as single terms with an expression pointer. Each expression is terminated * with a zero and the whole is terminated by two zeroes. * * The routine DoExecute should determine whether results are to be * printed, should revert the scratch I/O directions etc. * In principle it is DoExecute that calls Processor. * * @return if everything OK: 0. Otherwise error. The preprocessor * may continue with compilation though. Really fatal errors should * return on the spot by calling Terminate. */ int Processor(void) { GETIDENTITY WORD *term, *t, i, size; int retval = 0; EXPRESSIONS e; POSITION position; WORD last, LastExpression, fromspectator; LONG dd = 0; CBUF *C = cbuf+AC.cbufnum; int firstterm; CBUF *CC = cbuf+AT.ebufnum; WORD **w, *cpo, *cbo; FILEHANDLE *curfile, *oldoutfile = AR.outfile; WORD oldBracketOn = AR.BracketOn; WORD *oldBrackBuf = AT.BrackBuf; WORD oldbracketindexflag = AT.bracketindexflag; #ifdef WITHPTHREADS int OldMultiThreaded = AS.MultiThreaded, Oldmparallelflag = AC.mparallelflag; #endif if ( CC->numrhs > 0 || CC->numlhs > 0 ) { if ( CC->rhs ) { w = CC->rhs; i = CC->numrhs; do { *w++ = 0; } while ( --i > 0 ); } if ( CC->lhs ) { w = CC->lhs; i = CC->numlhs; do { *w++ = 0; } while ( --i > 0 ); } CC->numlhs = CC->numrhs = 0; ClearTree(AT.ebufnum); CC->Pointer = CC->Buffer; } if ( NumExpressions == 0 ) return(0); AR.expflags = 0; AR.CompressPointer = AR.CompressBuffer; AR.NoCompress = AC.NoCompress; term = AT.WorkPointer; if ( ( (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer) ) > AT.WorkTop ) { MesWork(); } UpdatePositions(); C->rhs[C->numrhs+1] = C->Pointer; AR.KeptInHold = 0; if ( AC.CollectFun ) AR.DeferFlag = 0; AR.outtohide = 0; AN.PolyFunTodo = 0; #ifdef HIDEDEBUG MesPrint("Status at the start of Processor (HideLevel = %d)",AC.HideLevel); for ( i = 0; i < NumExpressions; i++ ) { e = Expressions+i; ExprStatus(e); } #endif /* Next determine the last expression. This is used for removing the input file when the final stage of the sort of this expression is reached. That can save up to 1/3 in disk space. */ for ( i = NumExpressions-1; i >= 0; i-- ) { e = Expressions+i; if ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == HIDELEXPRESSION || e->status == HIDEGEXPRESSION || e->status == SKIPLEXPRESSION || e->status == SKIPGEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION || e->status == INTOHIDELEXPRESSION || e->status == INTOHIDEGEXPRESSION ) break; } last = i; for ( i = NumExpressions-1; i >= 0; i-- ) { AS.OldOnFile[i] = Expressions[i].onfile; AS.OldNumFactors[i] = Expressions[i].numfactors; /* AS.Oldvflags[i] = e[i].vflags; */ AS.Oldvflags[i] = Expressions[i].vflags; AS.Olduflags[i] = Expressions[i].uflags; Expressions[i].vflags &= ~(ISUNMODIFIED|ISZERO); } #ifdef WITHPTHREADS /* When we run with threads we have to make sure that all local input buffers are pointed correctly. Of course this isn't needed if we run on a single thread only. */ if ( AC.partodoflag && AM.totalnumberofthreads > 1 ) { AS.MultiThreaded = 1; AC.mparallelflag = PARALLELFLAG; } if ( AS.MultiThreaded && AC.mparallelflag == PARALLELFLAG ) { SetWorkerFiles(); } /* We start with running the expressions with expr->partodo in parallel. The current model is: give each worker an expression. Wait for workers to finish and tell them where to write. Then give them a new expression. Workers may have to wait for each other. This is also the case with the last one. */ if ( AS.MultiThreaded && AC.mparallelflag == PARALLELFLAG ) { if ( InParallelProcessor() ) { retval = 1; } AS.MultiThreaded = OldMultiThreaded; AC.mparallelflag = Oldmparallelflag; } #endif #ifdef WITHMPI if ( AC.RhsExprInModuleFlag && PF.rhsInParallel && (AC.mparallelflag == PARALLELFLAG || AC.partodoflag) ) { if ( PF_BroadcastRHS() ) { retval = -1; } } PF.exprtodo = -1; /* This means, the slave does not perform inparallel */ if ( AC.partodoflag > 0 ) { if ( PF_InParallelProcessor() ) { retval = -1; } } #endif for ( i = 0; i < NumExpressions; i++ ) { #ifdef INNERTEST if ( AC.InnerTest ) { if ( StrCmp(AC.TestValue,(UBYTE *)INNERTEST) == 0 ) { MesPrint("Testing(Processor): value = %s",AC.TestValue); } } #endif e = Expressions+i; #ifdef WITHPTHREADS if ( AC.partodoflag > 0 && e->partodo > 0 && AM.totalnumberofthreads > 2 ) { e->partodo = 0; continue; } #endif #ifdef WITHMPI if ( AC.partodoflag > 0 && e->partodo > 0 && PF.numtasks > 2 ) { e->partodo = 0; continue; } #endif AS.CollectOverFlag = 0; AR.expchanged = 0; if ( i == last ) LastExpression = 1; else LastExpression = 0; if ( e->inmem ) { /* #[ in memory : Memory allocated by poly.c only thusfar. Here GetTerm cannot work. For the moment we ignore this for parallelization. */ WORD j; AR.GetFile = 0; SetScratch(AR.infile,&(e->onfile)); if ( GetTerm(BHEAD term) <= 0 ) { MesPrint("(1) Expression %d has problems in scratchfile",i); retval = -1; break; } term[3] = i; AR.CurExpr = i; SeekScratch(AR.outfile,&position); e->onfile = position; if ( PutOut(BHEAD term,&position,AR.outfile,0) < 0 ) goto ProcErr; AR.DeferFlag = AC.ComDefer; NewSort(BHEAD0); AN.ninterms = 0; t = e->inmem; while ( *t ) { for ( j = 0; j < *t; j++ ) term[j] = t[j]; t += *t; AN.ninterms++; dd = AN.deferskipped; if ( AC.CollectFun && *term <= (AM.MaxTer/(2*(LONG)(sizeof(WORD)))) ) { if ( GetMoreFromMem(term,&t) ) { LowerSortLevel(); goto ProcErr; } } AT.WorkPointer = term + *term; AN.RepPoint = AT.RepCount + 1; AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( Generator(BHEAD term,0) ) { LowerSortLevel(); goto ProcErr; } AN.ninterms += dd; } AN.ninterms += dd; if ( EndSort(BHEAD AM.S0->sBuffer,0) < 0 ) goto ProcErr; if ( AM.S0->TermsLeft ) e->vflags &= ~ISZERO; else e->vflags |= ISZERO; if ( AR.expchanged == 0 ) e->vflags |= ISUNMODIFIED; if ( AM.S0->TermsLeft ) AR.expflags |= ISZERO; if ( AR.expchanged ) AR.expflags |= ISUNMODIFIED; AR.GetFile = 0; /* #] in memory : */ } else { AR.CurExpr = i; switch ( e->status ) { case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: AR.GetFile = 2; #ifdef WITHMPI if ( PF.me == MASTER ) SetScratch(AR.hidefile,&(e->onfile)); #else SetScratch(AR.hidefile,&(e->onfile)); AR.InHiBuf = AR.hidefile->POfull-AR.hidefile->POfill; #ifdef HIDEDEBUG MesPrint("Hidefile: onfile: %15p, POposition: %15p, filesize: %15p",&(e->onfile) ,&(AR.hidefile->POposition),&(AR.hidefile->filesize)); MesPrint("Set hidefile to buffer position %l/%l; AR.InHiBuf = %l" ,(AR.hidefile->POfill-AR.hidefile->PObuffer)*sizeof(WORD) ,(AR.hidefile->POfull-AR.hidefile->PObuffer)*sizeof(WORD) ,AR.InHiBuf ); #endif #endif curfile = AR.hidefile; goto commonread; case INTOHIDELEXPRESSION: case INTOHIDEGEXPRESSION: AR.outtohide = 1; /* BugFix 12-feb-2016 This may not work when the file is open and we move around. AR.hidefile->POfill = AR.hidefile->POfull; */ SetEndHScratch(AR.hidefile,&position); /* fall through */ case LOCALEXPRESSION: case GLOBALEXPRESSION: AR.GetFile = 0; /*[20oct2009 mt]:*/ #ifdef WITHMPI if( ( PF.me == MASTER ) || (PF.mkSlaveInfile) ) #endif SetScratch(AR.infile,&(e->onfile)); /*:[20oct2009 mt]*/ curfile = AR.infile; commonread:; #ifdef WITHMPI if ( PF_Processor(e,i,LastExpression) ) { MesPrint("Error in PF_Processor"); goto ProcErr; } /*[20oct2009 mt]:*/ if ( AC.mparallelflag != PARALLELFLAG ){ if(PF.me != MASTER) break; #endif /*:[20oct2009 mt]*/ if ( GetTerm(BHEAD term) <= 0 ) { #ifdef HIDEDEBUG MesPrint("Error condition 1a"); ExprStatus(e); #endif MesPrint("(2) Expression %d has problems in scratchfile(process)",i); retval = -1; break; } term[3] = i; if ( term[5] < 0 ) { /* Fill with spectator */ fromspectator = -term[5]; PUTZERO(AM.SpectatorFiles[fromspectator-1].readpos); term[5] = AC.cbufnum; } else fromspectator = 0; if ( AR.outtohide ) { SeekScratch(AR.hidefile,&position); e->onfile = position; if ( PutOut(BHEAD term,&position,AR.hidefile,0) < 0 ) goto ProcErr; } else { SeekScratch(AR.outfile,&position); e->onfile = position; if ( PutOut(BHEAD term,&position,AR.outfile,0) < 0 ) goto ProcErr; } AR.DeferFlag = AC.ComDefer; AR.Eside = RHSIDE; if ( ( e->vflags & ISFACTORIZED ) != 0 ) { AR.BracketOn = 1; AT.BrackBuf = AM.BracketFactors; AT.bracketindexflag = 1; } if ( AT.bracketindexflag > 0 ) OpenBracketIndex(i); #ifdef WITHPTHREADS if ( AS.MultiThreaded && AC.mparallelflag == PARALLELFLAG ) { if ( ThreadsProcessor(e,LastExpression,fromspectator) ) { MesPrint("Error in ThreadsProcessor"); goto ProcErr; } if ( AR.outtohide ) { AR.outfile = oldoutfile; AR.hidefile->POfull = AR.hidefile->POfill; } } else #endif { NewSort(BHEAD0); AR.MaxDum = AM.IndDum; AN.ninterms = 0; for(;;) { if ( fromspectator ) size = GetFromSpectator(term,fromspectator-1); else size = GetTerm(BHEAD term); if ( size <= 0 ) break; SeekScratch(curfile,&position); if ( ( e->vflags & ISFACTORIZED ) != 0 && term[1] == HAAKJE ) { StoreTerm(BHEAD term); } else { AN.ninterms++; dd = AN.deferskipped; if ( AC.CollectFun && *term <= (AM.MaxTer/(2*(LONG)(sizeof(WORD)))) ) { if ( GetMoreTerms(term) < 0 ) { LowerSortLevel(); goto ProcErr; } SeekScratch(curfile,&position); } AT.WorkPointer = term + *term; AN.RepPoint = AT.RepCount + 1; if ( AR.DeferFlag ) { AN.IndDum = Expressions[AR.CurExpr].numdummies + AM.IndDum; AR.CurDum = AN.IndDum; } else { AN.IndDum = AM.IndDum; AR.CurDum = ReNumber(BHEAD term); } if ( AC.SymChangeFlag ) MarkDirty(term,DIRTYSYMFLAG); if ( AN.ncmod ) { if ( ( AC.modmode & ALSOFUNARGS ) != 0 ) MarkDirty(term,DIRTYFLAG); else if ( AR.PolyFun ) PolyFunDirty(BHEAD term); } else if ( AC.PolyRatFunChanged ) PolyFunDirty(BHEAD term); if ( ( AR.PolyFunType == 2 ) && ( AC.PolyRatFunChanged == 0 ) && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION ) ) { PolyFunClean(BHEAD term); } if ( Generator(BHEAD term,0) ) { LowerSortLevel(); goto ProcErr; } AN.ninterms += dd; } SetScratch(curfile,&position); if ( AR.GetFile == 2 ) { AR.InHiBuf = (curfile->POfull-curfile->PObuffer) -DIFBASE(position,curfile->POposition)/sizeof(WORD); } else { AR.InInBuf = (curfile->POfull-curfile->PObuffer) -DIFBASE(position,curfile->POposition)/sizeof(WORD); } } AN.ninterms += dd; if ( LastExpression ) { UpdateMaxSize(); if ( AR.infile->handle >= 0 ) { CloseFile(AR.infile->handle); AR.infile->handle = -1; remove(AR.infile->name); PUTZERO(AR.infile->POposition); } AR.infile->POfill = AR.infile->POfull = AR.infile->PObuffer; } if ( AR.outtohide ) AR.outfile = AR.hidefile; if ( EndSort(BHEAD AM.S0->sBuffer,0) < 0 ) goto ProcErr; if ( AR.outtohide ) { AR.outfile = oldoutfile; AR.hidefile->POfull = AR.hidefile->POfill; } e->numdummies = AR.MaxDum - AM.IndDum; UpdateMaxSize(); } AR.BracketOn = oldBracketOn; AT.BrackBuf = oldBrackBuf; if ( ( e->vflags & TOBEFACTORED ) != 0 ) { poly_factorize_expression(e); } else if ( ( ( e->vflags & TOBEUNFACTORED ) != 0 ) && ( ( e->vflags & ISFACTORIZED ) != 0 ) ) { poly_unfactorize_expression(e); } AT.bracketindexflag = oldbracketindexflag; if ( AM.S0->TermsLeft ) e->vflags &= ~ISZERO; else e->vflags |= ISZERO; if ( AR.expchanged == 0 ) e->vflags |= ISUNMODIFIED; if ( AM.S0->TermsLeft ) AR.expflags |= ISZERO; if ( AR.expchanged ) AR.expflags |= ISUNMODIFIED; AR.GetFile = 0; AR.outtohide = 0; /*[20oct2009 mt]:*/ #ifdef WITHMPI } #endif #ifdef WITHPTHREADS if ( e->status == INTOHIDELEXPRESSION || e->status == INTOHIDEGEXPRESSION ) { SetHideFiles(); } #endif break; case SKIPLEXPRESSION: case SKIPGEXPRESSION: /* This can be greatly improved of course by file-to-file copy. */ #ifdef WITHMPI if ( PF.me != MASTER ) break; #endif AR.GetFile = 0; SetScratch(AR.infile,&(e->onfile)); if ( GetTerm(BHEAD term) <= 0 ) { #ifdef HIDEDEBUG MesPrint("Error condition 1b"); ExprStatus(e); #endif MesPrint("(3) Expression %d has problems in scratchfile",i); retval = -1; break; } term[3] = i; AR.DeferFlag = 0; SeekScratch(AR.outfile,&position); e->onfile = position; *AM.S0->sBuffer = 0; firstterm = -1; do { WORD *oldipointer = AR.CompressPointer; WORD *comprtop = AR.ComprTop; AR.ComprTop = AM.S0->sTop; AR.CompressPointer = AM.S0->sBuffer; if ( firstterm > 0 ) { if ( PutOut(BHEAD term,&position,AR.outfile,1) < 0 ) goto ProcErr; } else if ( firstterm < 0 ) { if ( PutOut(BHEAD term,&position,AR.outfile,0) < 0 ) goto ProcErr; firstterm++; } else { if ( PutOut(BHEAD term,&position,AR.outfile,-1) < 0 ) goto ProcErr; firstterm++; } AR.CompressPointer = oldipointer; AR.ComprTop = comprtop; } while ( GetTerm(BHEAD term) ); if ( FlushOut(&position,AR.outfile,1) ) goto ProcErr; UpdateMaxSize(); break; case HIDELEXPRESSION: case HIDEGEXPRESSION: #ifdef WITHMPI if ( PF.me != MASTER ) break; #endif AR.GetFile = 0; SetScratch(AR.infile,&(e->onfile)); if ( GetTerm(BHEAD term) <= 0 ) { #ifdef HIDEDEBUG MesPrint("Error condition 1c"); ExprStatus(e); #endif MesPrint("(4) Expression %d has problems in scratchfile",i); retval = -1; break; } term[3] = i; AR.DeferFlag = 0; SetEndHScratch(AR.hidefile,&position); e->onfile = position; #ifdef HIDEDEBUG if ( AR.hidefile->handle >= 0 ) { POSITION possize,pos; PUTZERO(possize); PUTZERO(pos); SeekFile(AR.hidefile->handle,&pos,SEEK_CUR); SeekFile(AR.hidefile->handle,&possize,SEEK_END); SeekFile(AR.hidefile->handle,&pos,SEEK_SET); MesPrint("Processor Hide1: filesize(th) = %12p, filesize(ex) = %12p",&(position), &(possize)); MesPrint(" in buffer: %l",(AR.hidefile->POfill-AR.hidefile->PObuffer)*sizeof(WORD)); } #endif *AM.S0->sBuffer = 0; firstterm = -1; cbo = cpo = AM.S0->sBuffer; do { WORD *oldipointer = AR.CompressPointer; WORD *oldibuffer = AR.CompressBuffer; WORD *comprtop = AR.ComprTop; AR.ComprTop = AM.S0->sTop; AR.CompressPointer = cpo; AR.CompressBuffer = cbo; if ( firstterm > 0 ) { if ( PutOut(BHEAD term,&position,AR.hidefile,1) < 0 ) goto ProcErr; } else if ( firstterm < 0 ) { if ( PutOut(BHEAD term,&position,AR.hidefile,0) < 0 ) goto ProcErr; firstterm++; } else { if ( PutOut(BHEAD term,&position,AR.hidefile,-1) < 0 ) goto ProcErr; firstterm++; } cpo = AR.CompressPointer; cbo = AR.CompressBuffer; AR.CompressPointer = oldipointer; AR.CompressBuffer = oldibuffer; AR.ComprTop = comprtop; } while ( GetTerm(BHEAD term) ); #ifdef HIDEDEBUG if ( AR.hidefile->handle >= 0 ) { POSITION possize,pos; PUTZERO(possize); PUTZERO(pos); SeekFile(AR.hidefile->handle,&pos,SEEK_CUR); SeekFile(AR.hidefile->handle,&possize,SEEK_END); SeekFile(AR.hidefile->handle,&pos,SEEK_SET); MesPrint("Processor Hide2: filesize(th) = %12p, filesize(ex) = %12p",&(position), &(possize)); MesPrint(" in buffer: %l",(AR.hidefile->POfill-AR.hidefile->PObuffer)*sizeof(WORD)); } #endif if ( FlushOut(&position,AR.hidefile,1) ) goto ProcErr; AR.hidefile->POfull = AR.hidefile->POfill; #ifdef HIDEDEBUG if ( AR.hidefile->handle >= 0 ) { POSITION possize,pos; PUTZERO(possize); PUTZERO(pos); SeekFile(AR.hidefile->handle,&pos,SEEK_CUR); SeekFile(AR.hidefile->handle,&possize,SEEK_END); SeekFile(AR.hidefile->handle,&pos,SEEK_SET); MesPrint("Processor Hide3: filesize(th) = %12p, filesize(ex) = %12p",&(position), &(possize)); MesPrint(" in buffer: %l",(AR.hidefile->POfill-AR.hidefile->PObuffer)*sizeof(WORD)); } #endif /* Because we direct the e->onfile already to the hide file, we need to change the status of the expression. Otherwise the use of parts (or the whole) of the expression looks in the infile while the position is that of the hide file. We choose to get everything from the hide file. On average that should give least file activity. */ if ( e->status == HIDELEXPRESSION ) { e->status = HIDDENLEXPRESSION; AS.OldOnFile[i] = e->onfile; AS.OldNumFactors[i] = Expressions[i].numfactors; } if ( e->status == HIDEGEXPRESSION ) { e->status = HIDDENGEXPRESSION; AS.OldOnFile[i] = e->onfile; AS.OldNumFactors[i] = Expressions[i].numfactors; } #ifdef WITHPTHREADS SetHideFiles(); #endif UpdateMaxSize(); break; case DROPPEDEXPRESSION: case DROPLEXPRESSION: case DROPGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case STOREDEXPRESSION: case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: case SPECTATOREXPRESSION: default: break; } } AR.KeptInHold = 0; } AR.DeferFlag = 0; AT.WorkPointer = term; #ifdef HIDEDEBUG MesPrint("Status at the end of Processor (HideLevel = %d)",AC.HideLevel); for ( i = 0; i < NumExpressions; i++ ) { e = Expressions+i; ExprStatus(e); } #endif return(retval); ProcErr: AT.WorkPointer = term; if ( AM.tracebackflag ) MesCall("Processor"); return(-1); } /* #] Processor : #[ TestSub : WORD TestSub(term,level) */ /** * TestSub hunts for subexpression pointers. * If one is found its power is given in AN.TeSuOut. * and the returnvalue is 'expressionnumber'. * If the expression number is negative it is an expression on disk. * * In addition this routine tries to locate subexpression pointers * in functions. It also notices that action must be taken with any * of the special functions. * * @param term The term in which TestSub hunts for potential action * @param level The number of the 'level' in the compiler buffer. * @return The number of the (sub)expression that was encountered. * * Other values that are returned are in AN.TeSuOut, AR.TePos, AT.TMbuff, * AN.TeInFun, AN.Frozen, AT.TMaddr * * The level in the compiler buffer is more or less the number of the * statement in the module. Hence it refers to the element in the lhs array. * * This routine is one of the most important routines in FORM. */ #define DONE(x) { retvalue = x; goto Done; } WORD TestSub(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD *m, *t, *r, retvalue = 0, funflag, j, oldncmod, nexpr, *Tpattern = 0; WORD *stop, *t1, *t2, funnum, wilds, tbufnum, stilldirty = 0; NESTING n; CBUF *C = cbuf+AT.ebufnum; LONG isp, i; TABLES T; COMPARE oldcompareroutine = (COMPARE)(AR.CompareRoutine); WORD oldsorttype = AR.SortType; ReStart: tbufnum = 0; i = 0; retvalue = 0; AT.TMbuff = AM.rbufnum; funflag = 0; t = term; r = t + *t - 1; m = r - ABS(*r) + 1; t++; if ( t < m ) do { if ( *t == SUBEXPRESSION ) { /* Subexpression encountered There may be more than one. The old strategy was to take the last. A newer strategy was to take the lowest power first. The current strategy is that we compute the number of terms generated by this subexpression and take the minimum of that. */ #ifdef WHICHSUBEXPRESSION WORD *tmin = t, AN.nbino; /* LONG minval = MAXLONG; */ LONG minval = -1; LONG mm, mnum1 = 1; if ( AN.BinoScrat == 0 ) { AN.BinoScrat = (UWORD *)Malloc1((AM.MaxTal+2)*sizeof(UWORD),"GetBinoScrat"); } #endif if ( t[3] ) { r = t + t[1]; while ( AN.subsubveto == 0 && *r == SUBEXPRESSION && r < m && r[3] ) { #ifdef WHICHSUBEXPRESSION mnum1++; #endif if ( r[1] == t[1] && r[2] == t[2] && r[4] == t[4] ) { j = t[1] - SUBEXPSIZE; t1 = t + SUBEXPSIZE; t2 = r + SUBEXPSIZE; while ( j > 0 && *t1++ == *t2++ ) j--; if ( j <= 0 ) { t[3] += r[3]; if ( t[3] == 0 ) { t1 = r + r[1]; t2 = term + *term; *term -= r[1]+t[1]; r = t; while ( t1 < t2 ) *r++ = *t1++; goto ReStart; } else { t1 = r + r[1]; t2 = term + *term; *term -= r[1]; m -= r[1]; while ( t1 < t2 ) *r++ = *t1++; r = t; } } } #ifdef WHICHSUBEXPRESSION else if ( t[2] >= 0 ) { /* Compute Binom(numterms+power-1,power-1) We need potentially long arithmetic. That is why we had to allocate AN.BinoScrat */ if ( AN.last1 == t[3] && AN.last2 == cbuf[t[4]].NumTerms[t[2]] + t[3] - 1 ) { if ( AN.last3 > minval ) { minval = AN.last3; tmin = t; } } else { AN.last1 = t[3]; mm = AN.last2 = cbuf[t[4]].NumTerms[t[2]] + t[3] - 1; if ( t[3] == 1 ) { if ( mm > minval ) { minval = mm; tmin = t; } } else if ( t[3] > 0 ) { if ( mm > MAXPOSITIVE ) goto TooMuch; GetBinom(AN.BinoScrat,&AN.nbino,(WORD)mm,t[3]); if ( AN.nbino > 2 ) goto TooMuch; if ( AN.nbino == 2 ) { mm = AN.BinoScrat[1]; mm = ( mm << BITSINWORD ) + AN.BinoScrat[0]; } else if ( AN.nbino == 1 ) mm = AN.BinoScrat[0]; else mm = 0; if ( mm > minval ) { minval = mm; tmin = t; } } AN.last3 = mm; } } #endif t = r; r += r[1]; } #ifdef WHICHSUBEXPRESSION if ( mnum1 > 1 && t[2] >= 0 ) { /* To keep the flowcontrol simple we duplicate some code here */ if ( AN.last1 == t[3] && AN.last2 == cbuf[t[4]].NumTerms[t[2]] + t[3] - 1 ) { if ( AN.last3 > minval ) { minval = AN.last3; tmin = t; } } else { AN.last1 = t[3]; mm = AN.last2 = cbuf[t[4]].NumTerms[t[2]] + t[3] - 1; if ( t[3] == 1 ) { if ( mm > minval ) { minval = mm; tmin = t; } } else if ( t[3] > 0 ) { if ( mm > MAXPOSITIVE ) { /* We will generate more terms than we can count */ TooMuch:; MLOCK(ErrorMessageLock); MesPrint("Attempt to generate more terms than FORM can count"); MUNLOCK(ErrorMessageLock); Terminate(-1); } GetBinom(AN.BinoScrat,&AN.nbino,(WORD)mm,t[3]); if ( AN.nbino > 2 ) goto TooMuch; if ( AN.nbino == 2 ) { mm = AN.BinoScrat[1]; mm = ( mm << BITSINWORD ) + AN.BinoScrat[0]; } else if ( AN.nbino == 1 ) mm = AN.BinoScrat[0]; else mm = 0; if ( mm > minval ) { minval = mm; tmin = t; } } AN.last3 = mm; } } t = tmin; #endif /* AR.TePos = 0; */ AR.TePos = WORDDIF(t,term); AT.TMbuff = t[4]; if ( t[4] == AM.dbufnum && (t+t[1]) < m && t[t[1]] == DOLLAREXPR2 ) { if ( t[t[1]+2] < 0 ) AT.TMdolfac = -t[t[1]+2]; else { /* resolve the element number */ AT.TMdolfac = GetDolNum(BHEAD t+t[1],m)+1; } } else AT.TMdolfac = 0; if ( t[3] < 0 ) { AN.TeInFun = 1; AR.TePos = WORDDIF(t,term); DONE(t[2]) } else { AN.TeInFun = 0; AN.TeSuOut = t[3]; } if ( t[2] < 0 ) { AN.TeSuOut = -t[3]; DONE(-t[2]) } DONE(t[2]) } } else if ( *t == EXPRESSION ) { WORD *toTMaddr; i = -t[2] - 1; if ( t[3] < 0 ) { AN.TeInFun = 1; AR.TePos = WORDDIF(t,term); DONE(i) } nexpr = t[3]; toTMaddr = m = AT.WorkPointer; AN.Frozen = 0; /* We have to be very careful with respect to setting variables like AN.TeInFun, because we may still call Generator and that may change those variables. That is why we set them at the last moment only. */ j = t[1]; AT.WorkPointer += j; r = t; NCOPY(m,r,j); r = t + t[1]; t += SUBEXPSIZE; while ( t < r ) { if ( *t == FROMBRAC ) { WORD *ttstop,*tttstop; /* Note: Convention is that wildcards are done after the expression has been picked up. So no wildcard substitutions are needed here. */ t += 2; AN.Frozen = m = AT.WorkPointer; /* We should check now for subexpressions and if necessary we substitute them. Keep in mind: only one term allowed! In retrospect (26-jan-2010): take also functions that have a dirty flag on */ j = *t; tttstop = t + j; GETSTOP(t,ttstop); *m++ = j; t++; while ( t < ttstop ) { if ( *t == SUBEXPRESSION ) break; if ( *t >= FUNCTION && ( ( t[2] & DIRTYFLAG ) == DIRTYFLAG ) ) break; j = t[1]; NCOPY(m,t,j); } if ( t < ttstop ) { /* We ran into a subexpression or a function with a 'dirty' argument. It could also be a $ or just e[(a^2)*b]. In all cases we should evaluate */ while ( t < tttstop ) *m++ = *t++; *AT.WorkPointer = m-AT.WorkPointer; m = AT.WorkPointer; AT.WorkPointer = m + *m; NewSort(BHEAD0); if ( Generator(BHEAD m,AR.Cnumlhs) ) { LowerSortLevel(); goto EndTest; } if ( EndSort(BHEAD m,0) < 0 ) goto EndTest; AN.Frozen = m; if ( *m == 0 ) { *m++ = 4; *m++ = 1; *m++ = 1; *m++ = 3; } else if ( m[*m] != 0 ) { MLOCK(ErrorMessageLock); MesPrint("Bracket specification in expression should be one single term"); MUNLOCK(ErrorMessageLock); Terminate(-1); } else { m += *m; m -= ABS(m[-1]); *m++ = 1; *m++ = 1; *m++ = 3; *AN.Frozen = m - AN.Frozen; } } else { while ( t < tttstop ) *m++ = *t++; *AT.WorkPointer = m-AT.WorkPointer; m = AT.WorkPointer; AT.WorkPointer = m + *m; if ( Normalize(BHEAD m) ) { MLOCK(ErrorMessageLock); MesPrint("Error while picking up contents of bracket"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( !*m ) { *m++ = 4; *m++ = 1; *m++ = 1; *m++ = 3; } else m += *m; } AT.WorkPointer = m; break; } t += t[1]; } AN.TeInFun = 0; AR.TePos = 0; AN.TeSuOut = nexpr; AT.TMaddr = toTMaddr; DONE(i) } else if ( *t >= FUNCTION ) { if ( t[0] == EXPONENT ) { if ( t[1] == FUNHEAD+4 && t[FUNHEAD] == -SYMBOL && t[FUNHEAD+2] == -SNUMBER && t[FUNHEAD+3] < MAXPOWER && t[FUNHEAD+3] > -MAXPOWER ) { t[0] = SYMBOL; t[1] = 4; t[2] = t[FUNHEAD+1]; t[3] = t[FUNHEAD+3]; r = term + *term; m = t + FUNHEAD+4; t += 4; while ( m < r ) *t++ = *m++; *term = WORDDIF(t,term); goto ReStart; } else if ( t[1] == FUNHEAD+ARGHEAD+11 && t[FUNHEAD] == ARGHEAD+9 && t[FUNHEAD+ARGHEAD] == 9 && t[FUNHEAD+ARGHEAD+1] == DOTPRODUCT && t[FUNHEAD+ARGHEAD+8] == 3 && t[FUNHEAD+ARGHEAD+7] == 1 && t[FUNHEAD+ARGHEAD+6] == 1 && t[FUNHEAD+ARGHEAD+5] == 1 && t[FUNHEAD+ARGHEAD+9] == -SNUMBER && t[FUNHEAD+ARGHEAD+10] < MAXPOWER && t[FUNHEAD+ARGHEAD+10] > -MAXPOWER ) { t[0] = DOTPRODUCT; t[1] = 5; t[2] = t[FUNHEAD+ARGHEAD+3]; t[3] = t[FUNHEAD+ARGHEAD+4]; t[4] = t[FUNHEAD+ARGHEAD+10]; r = term + *term; m = t + FUNHEAD+ARGHEAD+11; t += 5; while ( m < r ) *t++ = *m++; *term = WORDDIF(t,term); goto ReStart; } } funnum = *t; if ( *t >= FUNCTION + WILDOFFSET ) funnum -= WILDOFFSET; if ( *t == EXPONENT ) { /* Test whether the second argument is an integer */ r = t+FUNHEAD; NEXTARG(r) if ( *r == -SNUMBER && r[1] < MAXPOWER && r+2 == t+t[1] && t[FUNHEAD] > -FUNCTION && ( t[FUNHEAD] != -SNUMBER || t[FUNHEAD+1] != 0 ) && t[FUNHEAD] != ARGHEAD ) { if ( r[1] == 0 ) { if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Encountered 0^0. Fatal error."); MUNLOCK(ErrorMessageLock); SETERROR(-1); } *t = DUMMYFUN; /* Now mark it clean to avoid further interference. Normalize will remove this object. */ t[2] = 0; } else { /* Note that the case 0^ is treated in Normalize */ t1 = AddRHS(AT.ebufnum,1); m = t + FUNHEAD; if ( *m > 0 ) { m += ARGHEAD; i = t[FUNHEAD] - ARGHEAD; while ( (t1 + i + 10) > C->Top ) t1 = DoubleCbuffer(AT.ebufnum,t1,9); while ( --i >= 0 ) *t1++ = *m++; } else { if ( (t1 + 20) > C->Top ) t1 = DoubleCbuffer(AT.ebufnum,t1,10); ToGeneral(m,t1,1); t1 += *t1; } *t1++ = 0; C->rhs[C->numrhs+1] = t1; C->Pointer = t1; /* No provisions yet for commuting objects */ C->CanCommu[C->numrhs] = 1; *t++ = SUBEXPRESSION; *t++ = SUBEXPSIZE; *t++ = C->numrhs; *t++ = r[1]; *t++ = AT.ebufnum; #if SUBEXPSIZE > 5 Important: we may not have enough spots here #endif FILLSUB(t) /* Important: We have maybe only 5 spots! */ r += 2; m = term + *term; do { *t++ = *r++; } while ( r < m ); *term -= WORDDIF(r,t); goto ReStart; } } } else if ( *t == SUMF1 || *t == SUMF2 ) { /* What we are looking for is: 1-st argument: Single symbol or index. 2-nd argument: Number. 3-rd argument: Number. (4-th argument):Number. One more argument. This would activate the summation procedure. Note that the initiated recursion here can be done without upsetting the regular procedures. */ WORD *tstop, lcounter, lcmin, lcmax, lcinc; tstop = t + t[1]; r = t+FUNHEAD; if ( r+6 < tstop && r[2] == -SNUMBER && r[4] == -SNUMBER && ( ( r[0] == -SYMBOL ) || ( r[0] == -INDEX && r[1] >= AM.OffsetIndex && r[3] >= 0 && r[3] < AM.OffsetIndex && r[5] >= 0 && r[5] < AM.OffsetIndex ) ) ) { lcounter = r[0] == -INDEX ? -r[1]: r[1]; /* The loop counter */ lcmin = r[3]; lcmax = r[5]; r += 6; if ( *r == -SNUMBER && r+2 < tstop ) { lcinc = r[1]; r += 2; } else lcinc = 1; if ( r < tstop && ( ( *r > 0 && (r+*r) == tstop ) || ( *r <= -FUNCTION && r+1 == tstop ) || ( *r > -FUNCTION && *r < 0 && r+2 == tstop ) ) ) { m = AddRHS(AT.ebufnum,1); if ( *r > 0 ) { i = *r - ARGHEAD; r += ARGHEAD; while ( (m + i + 10) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,11); while ( --i >= 0 ) *m++ = *r++; } else { while ( (m + 20) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,12); ToGeneral(r,m,1); m += *m; } *m++ = 0; C->rhs[C->numrhs+1] = m; C->Pointer = m; m = AT.TMout; *m++ = 6; if ( *t == SUMF1 ) *m++ = SUMNUM1; else *m++ = SUMNUM2; *m++ = lcounter; *m++ = lcmin; *m++ = lcmax; *m++ = lcinc; m = t + t[1]; r = C->rhs[C->numrhs]; /* Test now if the argument was already evaluated. In that case it needs a new subexpression prototype. In either case we replace the function now by a subexpression prototype. */ if ( *r >= (SUBEXPSIZE+4) && ABS(*(r+*r-1)) < (*r - 1) && r[1] == SUBEXPRESSION ) { r++; i = r[1] - 5; *t++ = *r++; *t++ = *r++; *t++ = C->numrhs; r++; *t++ = *r++; *t++ = AT.ebufnum; r++; while ( --i >= 0 ) *t++ = *r++; } else { *t++ = SUBEXPRESSION; *t++ = 4+SUBEXPSIZE; *t++ = C->numrhs; *t++ = 1; *t++ = AT.ebufnum; FILLSUB(t) if ( lcounter < 0 ) { *t++ = INDTOIND; *t++ = 4; *t++ = -lcounter; } else { *t++ = SYMTONUM; *t++ = 4; *t++ = lcounter; } *t++ = lcmin; } t2 = term + *term; while ( m < t2 ) *t++ = *m++; *term = WORDDIF(t,term); AN.TeInFun = -C->numrhs; AR.TePos = 0; AN.TeSuOut = 0; AT.TMbuff = AT.ebufnum; DONE(C->numrhs) } } } else if ( *t == TOPOLOGIES ) { MesPrint("&The topologies_ function was removed in FORM 5.0."); MesPrint("&See the TopologiesOnly_ option of diagrams_."); Terminate(-1); } else if ( *t == DIAGRAMS ) { /* Syntax: diagrams_(model,setinparticles,setoutparticles, setextmomenta,setintmomenta,couplings or loops) */ if ( AC.nummodels > 0 ) { /* No model, no diagrams */ t1 = t+FUNHEAD; t2 = t+t[1]; if ( t1[0] == -SETSET && Sets[t1[1]].type == CMODEL && t1[2] == -SETSET && ( Sets[t1[3]].type == CFUNCTION || ( Sets[t1[3]].type == ANYTYPE && ( Sets[t1[3]].first == Sets[t1[3]].last ) ) ) && t1[4] == -SETSET && ( Sets[t1[5]].type == CFUNCTION || ( Sets[t1[5]].type == ANYTYPE && ( Sets[t1[5]].first == Sets[t1[5]].last ) ) ) && t1[6] == -SETSET && ( Sets[t1[7]].type == CVECTOR || ( Sets[t1[7]].type == ANYTYPE && ( Sets[t1[7]].first == Sets[t1[7]].last ) ) ) && t1[8] == -SETSET && ( Sets[t1[9]].type == CVECTOR || ( Sets[t1[9]].type == ANYTYPE && ( Sets[t1[9]].first == Sets[t1[9]].last ) ) ) && t1+12 <= t2 ) { /* Test that the sets of particles correspond to particles of the set model. */ MODEL *m = AC.models[SetElements[Sets[t1[1]].first]]; int nn0,nn1,nn2; for ( nn0 = 3; nn0 <= 5; nn0 += 2 ) { for ( nn1 = Sets[t1[nn0]].first; nn1 < Sets[t1[nn0]].last; nn1++ ) { for ( nn2 = 0; nn2 < m->nparticles; nn2++ ) { if ( m->vertices[nn2]->particles[0].number == SetElements[nn1] || m->vertices[nn2]->particles[1].number == SetElements[nn1] ) break; } if ( nn2 >= m->nparticles ) goto doesnotwork; } } /* Now test for a single argument indicating the order in perturbation theory. */ if ( ( t1[10] == -SNUMBER && t1[11] >= 0 && t1+12 == t2 ) || ( t1[10] == -SYMBOL && t1+12 == t2 ) || ( t1+10+t1[10] == t2 && t1+10+ARGHEAD+t1[10+ARGHEAD] == t2 && t1[11+ARGHEAD] == SYMBOL ) ) { /* Now test that all symbols are valid coupling constants. */ if ( t1+12 > t2 ) { WORD *tt1 = t1+13+ARGHEAD, im; t2 -= ABS(t2[-1]); while ( tt1 < t2 ) { for ( im = 0; im < m->ncouplings; im++ ) { if ( *tt1 == m->couplings[im] ) break; } if ( im >= m->ncouplings ) goto doesnotwork; tt1 += 2; } } AN.TeInFun = -15; AN.TeSuOut = 0; AR.TePos = -1; AR.funoffset = t - term; DONE(1) } else if ( ( ( t1[10] == -SNUMBER && t1[11] >= 0 && t1+12 == t2-2 ) || ( t1[10] == -SYMBOL && t1+12 == t2-2 ) || ( t1+10+t1[10] == t2-2 && t1+10+ARGHEAD+t1[10+ARGHEAD] == t2-2 && t1[11+ARGHEAD] == SYMBOL ) ) && t2[-2] == -SNUMBER ) { /* With options at t2[-2],t2[-1] Now test that all symbols are valid coupling constants. */ t2 -= 2; if ( t1+12 > t2 ) { WORD *tt1 = t1+13+ARGHEAD, im; t2 -= ABS(t2[-1]); while ( tt1 < t2 ) { for ( im = 0; im < m->ncouplings; im++ ) { if ( *tt1 == m->couplings[im] ) break; } if ( im >= m->ncouplings ) goto doesnotwork; tt1 += 2; } } AN.TeInFun = -15; AN.TeSuOut = 0; AR.TePos = -1; AR.funoffset = t - term; DONE(1) } doesnotwork:; } } } if ( functions[funnum-FUNCTION].spec <= 0 || ( t[2] & (DIRTYFLAG|MUSTCLEANPRF) ) != 0 ) { funflag = 1; } if ( *t <= MAXBUILTINFUNCTION ) { if ( *t <= DELTAP && *t >= THETA ) { /* Speeds up by 2 or 3 compares */ if ( *t == THETA || *t == THETA2 ) { WORD *tstop, *tt2, kk; tstop = t + t[1]; tt2 = t + FUNHEAD; while ( tt2 < tstop ) { if ( *tt2 > 0 && tt2[1] != 0 ) goto DoSpec; NEXTARG(tt2) } if ( !AT.RecFlag ) { if ( ( kk = DoTheta(BHEAD t) ) == 0 ) { *term = 0; DONE(0) } else if ( kk > 0 ) { m = t + t[1]; r = term + *term; while ( m < r ) *t++ = *m++; *term = WORDDIF(t,term); goto ReStart; } } } else if ( *t == DELTA2 || *t == DELTAP ) { WORD *tstop, *tt2, kk; tstop = t + t[1]; tt2 = t + FUNHEAD; while ( tt2 < tstop ) { if ( *tt2 > 0 && tt2[1] != 0 ) goto DoSpec; NEXTARG(tt2) } if ( !AT.RecFlag ) { if ( ( kk = DoDelta(t) ) == 0 ) { *term = 0; DONE(0) } else if ( kk > 0 ) { m = t + t[1]; r = term + *term; while ( m < r ) *t++ = *m++; *term = WORDDIF(t,term); goto ReStart; } } } } else if ( *t == DISTRIBUTION && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] >= -2 && t[FUNHEAD+1] <= 2 && t[FUNHEAD+2] == -SNUMBER && t[FUNHEAD+4] <= -FUNCTION && t[FUNHEAD+5] <= -FUNCTION ) { WORD *ttt = t+FUNHEAD+6, *tttstop = t+t[1]; while ( ttt < tttstop ) { if ( *ttt == -DOLLAREXPRESSION ) break; NEXTARG(ttt); } if ( ttt >= tttstop ) { AN.TeInFun = -1; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } } else if ( *t == DELTA3 && ((t[1]-FUNHEAD) & 1 ) == 0 ) { AN.TeInFun = -2; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } else if ( ( *t == TABLEFUNCTION ) && ( t[FUNHEAD] <= -FUNCTION ) && ( T = functions[-t[FUNHEAD]-FUNCTION].tabl ) != 0 && ( t[1] >= FUNHEAD+1+2*ABS(T->numind) ) && ( t[FUNHEAD+1] == -SYMBOL ) ) { /* The case of table_(tab,sym1,...,symn) */ for ( isp = 0; isp < ABS(T->numind); isp++ ) { if ( t[FUNHEAD+1+2*isp] != -SYMBOL ) break; } if ( isp >= ABS(T->numind) ) { AN.TeInFun = -3; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } } else if ( *t == TABLEFUNCTION && t[FUNHEAD] <= -FUNCTION && ( T = functions[-t[FUNHEAD]-FUNCTION].tabl ) != 0 && ( t[1] == FUNHEAD+2 ) && ( t[FUNHEAD+1] <= -FUNCTION ) ) { /* The case of table_(tab,fun) */ AN.TeInFun = -3; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } else if ( *t == FACTORIN ) { if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -DOLLAREXPRESSION ) { AN.TeInFun = -4; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } else if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -EXPRESSION ) { AN.TeInFun = -5; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } } else if ( *t == TERMSINBRACKET ) { if ( t[1] == FUNHEAD || ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] == 0 ) ) { AN.TeInFun = -6; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } /* The other cases have not yet been implemented We still have to add the case of short arguments First the different bracket in same expression else if ( t[1] > FUNHEAD+ARGHEAD && t[FUNHEAD] == t[1]-FUNHEAD && t[FUNHEAD+ARGHEAD] == t[1]-FUNHEAD-ARGHEAD && t[t[1]-1] == 3 && t[t[1]-2] == 1 && t[t[1]-3] == 1 ) { AN.TeInFun = -6; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } Next the bracket in an other expression else if ( t[1] > FUNHEAD+ARGHEAD+2 && t[FUNHEAD] == -EXPRESSION && t[FUNHEAD+2] == t[1]-FUNHEAD-2 && t[FUNHEAD+ARGHEAD+2] == t[1]-FUNHEAD-ARGHEAD-2 && t[t[1]-1] == 3 && t[t[1]-2] == 1 && t[t[1]-3] == 1 ) { AN.TeInFun = -6; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } */ } else if ( *t == EXTRASYMFUN ) { if ( t[1] == FUNHEAD+2 && ( ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] <= cbuf[AM.sbufnum].numrhs && t[FUNHEAD+1] > 0 ) || ( t[FUNHEAD] == -SYMBOL && t[FUNHEAD+1] < MAXVARIABLES && t[FUNHEAD+1] >= MAXVARIABLES-cbuf[AM.sbufnum].numrhs ) ) ) { AN.TeInFun = -7; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } else if ( t[1] == FUNHEAD ) { AN.TeInFun = -7; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } } else if ( *t == DIVFUNCTION || *t == REMFUNCTION || *t == INVERSEFUNCTION || *t == MULFUNCTION || *t == GCDFUNCTION ) { WORD *tf; int todo = 1, numargs = 0; tf = t + FUNHEAD; while ( tf < t + t[1] ) { DOLLARS d; if ( *tf == -DOLLAREXPRESSION ) { d = Dollars + tf[1]; if ( d->type == DOLWILDARGS ) { WORD *tterm = AT.WorkPointer, *tw; WORD *ta = term, *tb = tterm, *tc, *td = term + *term; while ( ta < t ) *tb++ = *ta++; tc = tb; while ( ta < tf ) *tb++ = *ta++; tw = d->where+1; while ( *tw ) { if ( *tw < 0 ) { if ( *tw > -FUNCTION ) *tb++ = *tw++; *tb++ = *tw++; } else { int ia; for ( ia = 0; ia < *tw; ia++ ) *tb++ = *tw++; } } NEXTARG(ta) while ( ta < t+t[1] ) *tb++ = *ta++; tc[1] = tb-tc; while ( ta < td ) *tb++ = *ta++; *tterm = tb - tterm; { int ia, na = *tterm; ta = tterm; tb = term; for ( ia = 0; ia < na; ia++ ) *tb++ = *ta++; } if ( tb > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); goto EndTest2; } AT.WorkPointer = tb; goto ReStart; } } NEXTARG(tf); } tf = t + FUNHEAD; while ( tf < t + t[1] ) { numargs++; if ( *tf > 0 && tf[1] != 0 ) todo = 0; NEXTARG(tf); } if ( todo && numargs == 2 ) { if ( *t == DIVFUNCTION ) AN.TeInFun = -9; else if ( *t == REMFUNCTION ) AN.TeInFun = -10; else if ( *t == INVERSEFUNCTION ) AN.TeInFun = -11; else if ( *t == MULFUNCTION ) AN.TeInFun = -14; else if ( *t == GCDFUNCTION ) AN.TeInFun = -8; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } else if ( todo && numargs == 3 ) { if ( *t == DIVFUNCTION ) AN.TeInFun = -9; else if ( *t == REMFUNCTION ) AN.TeInFun = -10; else if ( *t == GCDFUNCTION ) AN.TeInFun = -8; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } else if ( todo && *t == GCDFUNCTION ) { AN.TeInFun = -8; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } } else if ( *t == PERMUTATIONS && ( ( t[1] >= FUNHEAD+1 && t[FUNHEAD] <= -FUNCTION ) || ( t[1] >= FUNHEAD+3 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+2] <= -FUNCTION ) ) ) { AN.TeInFun = -12; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } else if ( *t == PARTITIONS ) { if ( TestPartitions(t,&(AT.partitions)) ) { AT.partitions.where = t-term; AN.TeInFun = -13; AN.TeSuOut = 0; AR.TePos = -1; DONE(1) } } } } t += t[1]; } while ( t < m ); if ( funflag ) { /* Search in functions */ DoSpec: t = term; AT.NestPoin->termsize = t; if ( AT.NestPoin == AT.Nest ) AN.EndNest = t + *t; t++; oldncmod = AN.ncmod; if ( t < m ) do { if ( *t < FUNCTION ) { t += t[1]; continue; } if ( AN.ncmod && ( ( AC.modmode & ALSOFUNARGS ) == 0 ) ) { if ( *t != AR.PolyFun ) AN.ncmod = 0; else AN.ncmod = oldncmod; } r = t + t[1]; funnum = *t; if ( *t >= FUNCTION + WILDOFFSET ) funnum -= WILDOFFSET; if ( ( *t == NUMFACTORS || *t == FIRSTTERM || *t == CONTENTTERM ) && t[1] == FUNHEAD+2 && ( t[FUNHEAD] == -EXPRESSION || t[FUNHEAD] == -DOLLAREXPRESSION ) ) { /* if ( *t == NUMFACTORS ) { This we leave for Normalize } */ } else if ( functions[funnum-FUNCTION].spec <= 0 ) { AT.NestPoin->funsize = t + 1; t1 = t; t += FUNHEAD; while ( t < r ) { /* Sum over arguments */ if ( *t > 0 && t[1] ) { /* Argument is dirty */ AT.NestPoin->argsize = t; AT.NestPoin++; /* stop = t + *t; */ t2 = t; t += ARGHEAD; while ( t < AT.NestPoin[-1].argsize+*(AT.NestPoin[-1].argsize) ) { /* Sum over terms */ AT.RecFlag++; i = *t; AN.subsubveto = 1; /* AN.subsubveto repairs a bug that became apparent in an example by York Schroeder: f(k1.k1)*replace_(k1,2*k2) Is it possible to repair the counting of the various length indicators? (JV 1-jun-2010) */ if ( ( retvalue = TestSub(BHEAD t,level) ) != 0 ) { /* Possible size changes: Note defs at 471,467,460,400,425,328 */ redosize: if ( i > *t ) { /* i -= *t; *t2 -= i; t1[1] -= i; t += *t; r = t + i; m = term + *term; while ( r < m ) *t++ = *r++; *term -= i; */ i -= *t; t += *t; r = t + i; m = AN.EndNest; while ( r < m ) *t++ = *r++; t = AT.NestPoin[-1].argsize + ARGHEAD; n = AT.Nest; while ( n < AT.NestPoin ) { *(n->argsize) -= i; *(n->funsize) -= i; *(n->termsize) -= i; n++; } AN.EndNest -= i; } AN.subsubveto = 0; t1[2] = 1; if ( *t1 == AR.PolyFun && AR.PolyFunType == 2 ) t1[2] |= MUSTCLEANPRF; AT.RecFlag--; AT.NestPoin--; AN.TeInFun++; AR.TePos = 0; AN.ncmod = oldncmod; DONE(retvalue) } else { /* * Somehow the next line fixes Issue #106. */ i = *t; Normalize(BHEAD t); /* if ( i > *t ) { retvalue = 1; goto redosize; } */ /* * Experimentally, the next line fixes Issue #105. */ if ( *t == 0 ) { retvalue = 1; goto redosize; } { WORD *tend = t + *t, *tt = t+1; stilldirty = 0; tend -= ABS(tend[-1]); while ( tt < tend ) { if ( *tt == SUBEXPRESSION || *tt == EXPRESSION ) { stilldirty = 1; break; } tt += tt[1]; } } if ( i > *t ) { /* We should not forget to correct the Nest stack. That caused trouble in the past. */ retvalue = 1; i -= *t; t += *t; r = t + i; m = AN.EndNest; while ( r < m ) *t++ = *r++; t = AT.NestPoin[-1].argsize + ARGHEAD; n = AT.Nest; while ( n < AT.NestPoin ) { *(n->argsize) -= i; *(n->funsize) -= i; *(n->termsize) -= i; n++; } AN.EndNest -= i; } } AN.subsubveto = 0; AT.RecFlag--; t += *t; } AT.NestPoin--; /* Argument contains no subexpressions. It should be normalized and sorted. The main problem is the storage. */ t = AT.NestPoin->argsize; j = *t; t += ARGHEAD; NewSort(BHEAD0); if ( *t1 == AR.PolyFun && AR.PolyFunType == 2 ) { AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); AR.SortType = SORTHIGHFIRST; } if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; while ( t < AT.NestPoin->argsize+*(AT.NestPoin->argsize) ) { m = AT.WorkPointer; r = t + *t; do { *m++ = *t++; } while ( t < r ); r = AT.WorkPointer; AT.WorkPointer = r + *r; if ( Normalize(BHEAD r) ) { if ( *t1 == AR.PolyFun && AR.PolyFunType == 2 ) { AR.SortType = oldsorttype; AR.CompareRoutine = (COMPAREDUMMY)oldcompareroutine; t1[2] |= MUSTCLEANPRF; } LowerSortLevel(); goto EndTest; } if ( AN.ncmod != 0 ) { if ( *r ) { if ( Modulus(r) ) { LowerSortLevel(); AT.WorkPointer = r; if ( *t1 == AR.PolyFun && AR.PolyFunType == 2 ) { AR.SortType = oldsorttype; AR.CompareRoutine = (COMPAREDUMMY)oldcompareroutine; t1[2] |= MUSTCLEANPRF; } goto EndTest; } } } if ( AR.PolyFun > 0 ) { if ( PrepPoly(BHEAD r,1) != 0 ) goto EndTest; } if ( *r ) StoreTerm(BHEAD r); AT.WorkPointer = r; } if ( EndSort(BHEAD AT.WorkPointer+ARGHEAD,1) < 0 ) goto EndTest; m = AT.WorkPointer+ARGHEAD; if ( *t1 == AR.PolyFun && AR.PolyFunType == 2 ) { AR.SortType = oldsorttype; AR.CompareRoutine = (COMPAREDUMMY)oldcompareroutine; t1[2] |= MUSTCLEANPRF; } while ( *m ) m += *m; i = WORDDIF(m,AT.WorkPointer); *AT.WorkPointer = i; AT.WorkPointer[1] = stilldirty; if ( ToFast(AT.WorkPointer,AT.WorkPointer) ) { m = AT.WorkPointer; if ( *m <= -FUNCTION ) { m++; i = 1; } else { m += 2; i = 2; } } j = i - j; if ( j > 0 ) { r = m + j; if ( r > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); goto EndTest2; } do { *--r = *--m; } while ( m > AT.WorkPointer ); AT.WorkPointer = r; m = AN.EndNest; r = m + j; stop = AT.NestPoin->argsize+*(AT.NestPoin->argsize); do { *--r = *--m; } while ( m >= stop ); } else if ( j < 0 ) { m = AT.NestPoin->argsize+*(AT.NestPoin->argsize); r = m + j; do { *r++ = *m++; } while ( m < AN.EndNest ); } m = AT.NestPoin->argsize; r = AT.WorkPointer; while ( --i >= 0 ) *m++ = *r++; n = AT.Nest; while ( n <= AT.NestPoin ) { if ( *(n->argsize) > 0 && n != AT.NestPoin ) *(n->argsize) += j; *(n->funsize) += j; *(n->termsize) += j; n++; } AN.EndNest += j; /* (AT.NestPoin->argsize)[1] = 0; */ if ( funnum == DENOMINATOR || funnum == EXPONENT ) { if ( Normalize(BHEAD term) ) { /* In this case something has been substituted Either a $ or a replace_????? Originally we had here: goto EndTest; It seems better to restart. */ AN.ncmod = oldncmod; goto ReStart; } /* And size changes here????? */ } AN.ncmod = oldncmod; goto ReStart; } else if ( *t == -DOLLAREXPRESSION ) { if ( ( *t1 == TERMSINEXPR || *t1 == SIZEOFFUNCTION ) && t1[1] == FUNHEAD+2 ) {} else { if ( AR.Eside != LHSIDE ) { AN.TeInFun = 1; AR.TePos = 0; AT.TMbuff = AM.dbufnum; t1[2] |= DIRTYFLAG; AN.ncmod = oldncmod; DONE(1) } AC.lhdollarflag = 1; } } else if ( *t == -TERMSINBRACKET ) { if ( AR.Eside != LHSIDE ) { AN.TeInFun = 1; AR.TePos = 0; t1[2] |= DIRTYFLAG; AN.ncmod = oldncmod; DONE(1) } } else if ( AN.ncmod != 0 && *t == -SNUMBER ) { if ( AN.ncmod == 1 || AN.ncmod == -1 ) { isp = (UWORD)(AC.cmod[0]); isp = t[1] % isp; if ( ( AC.modmode & POSNEG ) != 0 ) { if ( isp > (UWORD)(AC.cmod[0])/2 ) isp = isp - (UWORD)(AC.cmod[0]); else if ( -isp > (UWORD)(AC.cmod[0])/2 ) isp = isp + (UWORD)(AC.cmod[0]); } else { if ( isp < 0 ) isp += (UWORD)(AC.cmod[0]); } if ( isp <= MAXPOSITIVE && isp >= -MAXPOSITIVE ) { t[1] = isp; } } } NEXTARG(t) } if ( funnum >= FUNCTION && functions[funnum-FUNCTION].tabl ) { /* Test whether the table catches Test 1: index arguments and range. i will be the number of the element in the table. */ WORD rhsnumber, *oldwork = AT.WorkPointer; WORD ii, *p, *pp, *ppstop; MINMAX *mm; T = functions[funnum-FUNCTION].tabl; /* Because of tables with a variable number of indices we need to make a copy of the pattern. If we do this in the WorkSpace we get problems with EndNest. This is why we use TermMalloc. Now Tpattern is a copy that can be modified. */ #ifdef WITHPTHREADS pp = T->pattern[AT.identity]; #else pp = T->pattern; #endif if ( Tpattern == 0 ) Tpattern = TermMalloc("Tpattern"); p = Tpattern; ii = pp[1]; for ( i = 0; i < ii; i++ ) *p++ = *pp++; p = Tpattern + FUNHEAD+1; mm = T->mm; if ( T->sparse ) { WORD xx; t = t1+FUNHEAD; if ( T->numind == 0 ) { isp = 0; xx = 0; } else { if ( T->numind < 0 ) { if ( *t != -SNUMBER && t[2] != -SNUMBER ) { xx = ABS(T->numind); goto teststrict; } xx = t[1]+1; if ( xx < 2 || xx > -T->numind ) goto teststrict; } else xx = T->numind; for ( i = 0; i < xx; i++, t += 2 ) { if ( *t != -SNUMBER ) break; } if ( i < xx ) goto teststrict; isp = FindTableTree(T,t1+FUNHEAD,2); } if ( isp < 0 ) { teststrict: if ( T->strict == -2 ) { rhsnumber = AM.zerorhs; tbufnum = AM.zbufnum; } else if ( T->strict == -3 ) { rhsnumber = AM.onerhs; tbufnum = AM.zbufnum; } else if ( T->strict < 0 ) goto NextFun; else { MLOCK(ErrorMessageLock); MesPrint("Element in table is undefined"); if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } goto showtable; } /* Copy the indices; */ t = t1+FUNHEAD+1; for ( i = 0; i < xx; i++ ) { *p = *t; p+=2; t+=2; } } else { rhsnumber = T->tablepointers[isp+ABS(T->numind)]; #if ( TABLEEXTENSION == 2 ) tbufnum = T->bufnum; #else tbufnum = T->tablepointers[isp+ABS(T->numind)+1]; #endif t = t1+FUNHEAD+1; ii = xx; while ( --ii >= 0 ) { *p = *t; t += 2; p += 2; } } if ( xx < ABS(T->numind) ) { p--; ppstop = Tpattern+Tpattern[1]; pp = p+2*(-T->numind-xx); while ( pp < ppstop ) *p++ = *pp++; Tpattern[1] = p - Tpattern; } goto caughttable; } else { i = 0; t = t1 + FUNHEAD; j = T->numind; while ( --j >= 0 ) { if ( *t != -SNUMBER ) goto NextFun; t++; if ( *t < mm->mini || *t > mm->maxi ) { if ( T->bounds ) { MLOCK(ErrorMessageLock); MesPrint("Table boundary check. Argument %d", T->numind-j); showtable: AO.OutFill = AO.OutputLine = (UBYTE *)m; AO.OutSkip = 8; IniLine(0); WriteSubTerm(t1,1); FiniLine(); MUNLOCK(ErrorMessageLock); if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } SETERROR(-1) } if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } goto NextFun; } i += ( *t - mm->mini ) * (LONG)(mm->size); *p = *t++; p += 2; mm++; } /* Test now whether the entry exists. */ i *= TABLEEXTENSION; if ( T->tablepointers[i] == -1 ) { if ( T->strict == -2 ) { rhsnumber = AM.zerorhs; tbufnum = AM.zbufnum; } else if ( T->strict == -3 ) { rhsnumber = AM.onerhs; tbufnum = AM.zbufnum; } else if ( T->strict < 0 ) { if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } goto NextFun; } else { MLOCK(ErrorMessageLock); MesPrint("Element in table is undefined"); if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } goto showtable; } } else { rhsnumber = T->tablepointers[i]; #if ( TABLEEXTENSION == 2 ) tbufnum = T->bufnum; #else tbufnum = T->tablepointers[i+1]; #endif } } /* If there are more arguments we have to do some pattern matching. This should be easy. We adapted the pattern, so that the array indices match already. Note that if there is no match the program will become very slow. */ caughttable: #ifdef WITHPTHREADS AN.FullProto = T->prototype[AT.identity]; #else AN.FullProto = T->prototype; #endif AN.WildValue = AN.FullProto + SUBEXPSIZE; AN.WildStop = AN.FullProto+AN.FullProto[1]; ClearWild(BHEAD0); AN.RepFunNum = 0; AN.RepFunList = AN.EndNest; AT.WorkPointer = (WORD *)(((UBYTE *)(AN.EndNest)) + AM.MaxTer/2); if ( AT.WorkPointer >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); } wilds = 0; if ( MatchFunction(BHEAD Tpattern,t1,&wilds) > 0 ) { AT.WorkPointer = oldwork; if ( AT.NestPoin != AT.Nest ) { AN.ncmod = oldncmod; if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } DONE(1) } m = AN.FullProto; retvalue = m[2] = rhsnumber; m[4] = tbufnum; t = t1; j = t[1]; i = m[1]; if ( j > i ) { j = i - j; NCOPY(t,m,i); m = term + *term; while ( r < m ) *t++ = *r++; *term += j; } else if ( j < i ) { j = i-j; t = term + *term; while ( t >= r ) { t[j] = *t; t--; } t = t1; NCOPY(t,m,i); *term += j; } else { NCOPY(t,m,j); } AN.TeInFun = 0; AR.TePos = 0; AN.TeSuOut = -1; if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; AT.TMbuff = tbufnum; AN.ncmod = oldncmod; DONE(retvalue); } AT.WorkPointer = oldwork; if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } } NextFun:; } else if ( ( t[2] & DIRTYFLAG ) != 0 ) { t += FUNHEAD; while ( t < r ) { if ( *t == FUNNYDOLLAR ) { if ( AR.Eside != LHSIDE ) { AN.TeInFun = 1; AR.TePos = 0; AT.TMbuff = AM.dbufnum; AN.ncmod = oldncmod; DONE(1) } AC.lhdollarflag = 1; } t++; } } t = r; AN.ncmod = oldncmod; } while ( t < m ); } Done: if ( Tpattern ) { TermFree(Tpattern,"Tpattern"); Tpattern = 0; } return(retvalue); EndTest:; MLOCK(ErrorMessageLock); EndTest2:; MesCall("TestSub"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] TestSub : #[ InFunction : WORD InFunction(term,termout) */ /** * Makes the replacement of the subexpression with the number 'replac' * in a function argument. Additional information is passed in some * of the AR, AN, AT variables. * * @param term The input term * @param termout The output term * @return 0: everything is fine, Negative: fatal, Positive: error. * * Special attention should be given to nested functions! */ int InFunction(PHEAD WORD *term, WORD *termout) { GETBIDENTITY WORD *m, *t, *r, *rr, sign = 1, oldncmod; WORD *u, *v, *w, *from, *to, ipp, olddefer = AR.DeferFlag, oldPolyFun = AR.PolyFun, i, j; LONG numterms; from = t = term; r = t + *t - 1; m = r - ABS(*r) + 1; t++; while ( t < m ) { if ( *t >= FUNCTION+WILDOFFSET ) ipp = *t - WILDOFFSET; else ipp = *t; if ( AR.TePos ) { if ( ( term + AR.TePos ) == t ) { m = termout; while ( from < t ) *m++ = *from++; *m++ = DENOMINATOR; *m++ = t[1] + 4 + FUNHEAD + ARGHEAD; *m++ = DIRTYFLAG; FILLFUN3(m) *m++ = t[1] + 4 + ARGHEAD; *m++ = 1; FILLARG(m) *m++ = t[1] + 4; t[3] = -t[3]; v = t + t[1]; while ( t < v ) *m++ = *t++; from[3] = -from[3]; *m++ = 1; *m++ = 1; *m++ = 3; r = term + *term; while ( t < r ) *m++ = *t++; if ( (m-termout) > (LONG)(AM.MaxTer/sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Output term too large (%d words) (MaxTermSize: %d words)", m-termout, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); goto TooLarge; } *termout = WORDDIF(m,termout); return(0); } } else if ( ( *t >= FUNCTION && functions[ipp-FUNCTION].spec <= 0 ) && ( t[2] & DIRTYFLAG ) == DIRTYFLAG ) { m = termout; r = t + t[1]; u = t; t += FUNHEAD; oldncmod = AN.ncmod; while ( t < r ) { /* t points at an argument */ if ( *t > 0 && t[1] ) { /* Argument has been modified */ WORD oldsorttype = AR.SortType; /* This whole argument must be redone */ if ( ( AN.ncmod != 0 ) && ( ( AC.modmode & ALSOFUNARGS ) == 0 ) && ( *u != AR.PolyFun ) ) { AN.ncmod = 0; } AR.DeferFlag = 0; v = t + *t; t += ARGHEAD; /* First term */ LONG copy = t - from; const LONG size = t - u; NCOPY(m, from, copy); w = m - size; to = m; NewSort(BHEAD0); if ( *u == AR.PolyFun && AR.PolyFunType == 2 ) { AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); AR.SortType = SORTHIGHFIRST; } /* AR.PolyFun = 0; */ while ( t < v ) { i = *t; NCOPY(m,t,i); m = to; if ( AT.WorkPointer < m+*m ) AT.WorkPointer = m + *m; if ( Generator(BHEAD m,AR.Cnumlhs) ) { AN.ncmod = oldncmod; LowerSortLevel(); goto InFunc; } } /* w = the function */ /* v = the next argument */ /* u = the function */ /* to is new argument */ to -= ARGHEAD; if ( EndSort(BHEAD m,1) < 0 ) { AN.ncmod = oldncmod; goto InFunc; } AR.PolyFun = oldPolyFun; if ( *u == AR.PolyFun && AR.PolyFunType == 2 ) { AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); AR.SortType = oldsorttype; } while ( *m ) m += *m; *to = WORDDIF(m,to); to[1] = 1; /* ??????? or rather 0?. 24-mar-2006 JV */ if ( ToFast(to,to) ) { if ( *to <= -FUNCTION ) m = to+1; else m = to+2; } w[1] = WORDDIF(m,w) + WORDDIF(r,v); r = term + *term; t = v; while ( t < r ) *m++ = *t++; if ( (m-termout) > (LONG)(AM.MaxTer/sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Output term too large (%d words) (MaxTermSize: %d words)", m-termout, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); goto TooLarge; } *termout = WORDDIF(m,termout); AR.DeferFlag = olddefer; AN.ncmod = oldncmod; return(0); } else if ( *t == -DOLLAREXPRESSION ) { if ( AR.Eside == LHSIDE ) { NEXTARG(t) AC.lhdollarflag = 1; } else { /* This whole argument must be redone */ DOLLARS d = Dollars + t[1]; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[1] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif oldncmod = AN.ncmod; if ( ( AN.ncmod != 0 ) && ( ( AC.modmode & ALSOFUNARGS ) == 0 ) && ( *u != AR.PolyFun ) ) { AN.ncmod = 0; } AR.DeferFlag = 0; v = t + 2; LONG copy = t - from; const LONG size = t - u; NCOPY(m, from, copy); w = m - size; to = m; switch ( d->type ) { case DOLINDEX: if ( d->index >= 0 && d->index < AM.OffsetIndex ) { *m++ = -SNUMBER; *m++ = d->index; } else { *m++ = -INDEX; *m++ = d->index; } break; case DOLZERO: *m++ = -SNUMBER; *m++ = 0; break; case DOLNUMBER: if ( d->where[0] == 4 && ( d->where[1] & MAXPOSITIVE ) == d->where[1] ) { *m++ = -SNUMBER; if ( d->where[3] >= 0 ) *m++ = d->where[1]; else *m++ = -d->where[1]; break; } /* fall through */ case DOLTERMS: /* Here we have the special case of the PolyRatFun That function may have a different sort of the terms in the argument. */ to = m; r = d->where; *m++ = 0; *m++ = 1; FILLARG(m) while ( *r ) { i = *r; NCOPY(m,r,i) } *to = m-to; if ( ToFast(to,to) ) { if ( *to <= -FUNCTION ) m = to+1; else m = to+2; } else if ( *u == AR.PolyFun && AR.PolyFunType == 2 ) { AR.PolyFun = 0; NewSort(BHEAD0); AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); r = to + ARGHEAD; while ( r < m ) { rr = r; r += *r; if ( SymbolNormalize(rr) ) goto InFunc; if ( StoreTerm(BHEAD rr) ) { AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); LowerSortLevel(); Terminate(-1); } } if ( EndSort(BHEAD to+ARGHEAD,1) < 0 ) goto InFunc; AR.PolyFun = oldPolyFun; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); m = to+ARGHEAD; if ( *m == 0 ) { *to = -SNUMBER; to[1] = 0; m = to + 2; } else { while ( *m ) m += *m; *t = m - to; if ( ToFast(to,to) ) { if ( *to <= -FUNCTION ) m = to+1; else m = to+2; } } } w[1] = w[1] - 2 + (m-to); break; case DOLSUBTERM: to = m; r = d->where; i = r[1]; *m++ = i+4+ARGHEAD; *m++ = 1; FILLARG(m) *m++ = i+4; while ( --i >= 0 ) *m++ = *r++; *m++ = 1; *m++ = 1; *m++ = 3; if ( ToFast(to,to) ) { if ( *to <= -FUNCTION ) m = to+1; else m = to+2; } w[1] = w[1] - 2 + (m-to); break; case DOLARGUMENT: to = m; r = d->where; if ( *r > 0 ) { i = *r - 2; *m++ = *r++; *m++ = 1; r++; while ( --i >= 0 ) *m++ = *r++; } else if ( *r <= -FUNCTION ) *m++ = *r++; else { *m++ = *r++; *m++ = *r++; } w[1] = w[1] - 2 + (m-to); break; case DOLWILDARGS: to = m; r = d->where; if ( *r > 0 ) { /* Tensor arguments */ i = *r++; while ( --i >= 0 ) { if ( *r < 0 ) { *m++ = -VECTOR; *m++ = *r++; } else if ( *r >= AM.OffsetIndex ) { *m++ = -INDEX; *m++ = *r++; } else { *m++ = -SNUMBER; *m++ = *r++; } } } else { /* Regular arguments */ r++; while ( *r ) { if ( *r > 0 ) { i = *r - 2; *m++ = *r++; *m++ = 1; r++; while ( --i >= 0 ) *m++ = *r++; } else if ( *r <= -FUNCTION ) *m++ = *r++; else { *m++ = *r++; *m++ = *r++; } } } w[1] = w[1] - 2 + (m-to); break; case DOLUNDEFINED: default: MLOCK(ErrorMessageLock); MesPrint("!!!Undefined $-variable: $%s!!!", AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif Terminate(-1); } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif r = term + *term; t = v; while ( t < r ) *m++ = *t++; if ( (m-termout) > (LONG)(AM.MaxTer/sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Output term too large (%d words) (MaxTermSize: %d words)", m-termout, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); goto TooLarge; } *termout = WORDDIF(m,termout); AR.DeferFlag = olddefer; AN.ncmod = oldncmod; return(0); } } else if ( *t == -TERMSINBRACKET ) { if ( AC.ComDefer ) numterms = CountTerms1(BHEAD0); else numterms = 1; /* Compose the output term First copy the part till this function argument m points at the output term space u points at the start of the function t points at the start of the argument */ LONG copy = t - from; const LONG size = t - u; NCOPY(m, from, copy); w = m - size; if ( ( numterms & MAXPOSITIVE ) == numterms ) { *m++ = -SNUMBER; *m++ = numterms & MAXPOSITIVE; w[1] += 1; } else if ( ( i = numterms >> BITSINWORD ) == 0 ) { *m++ = ARGHEAD+4; for ( j = 1; j < ARGHEAD; j++ ) *m++ = 0; *m++ = 4; *m++ = numterms & WORDMASK; *m++ = 1; *m++ = 3; w[1] += ARGHEAD+3; } else { *m++ = ARGHEAD+6; for ( j = 1; j < ARGHEAD; j++ ) *m++ = 0; *m++ = 6; *m++ = numterms & WORDMASK; *m++ = i; *m++ = 1; *m++ = 0; *m++ = 5; w[1] += ARGHEAD+5; } from++; /* Skip our function */ r = term + *term; while ( from < r ) *m++ = *from++; if ( (m-termout) > (LONG)(AM.MaxTer/sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Output term too large (%d words) (MaxTermSize: %d words)", m-termout, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); goto TooLarge; } *termout = WORDDIF(m,termout); return(0); } else { NEXTARG(t) } } t = u; } else if ( ( *t >= FUNCTION && functions[ipp-FUNCTION].spec > 0 ) && ( t[2] & DIRTYFLAG ) == DIRTYFLAG ) { /* Could be FUNNYDOLLAR */ u = t; v = t + t[1]; t += FUNHEAD; while ( t < v ) { if ( *t == FUNNYDOLLAR ) { if ( AR.Eside != LHSIDE ) { DOLLARS d = Dollars + t[1]; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[1] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif oldncmod = AN.ncmod; if ( ( AN.ncmod != 0 ) && ( ( AC.modmode & ALSOFUNARGS ) == 0 ) && ( *u != AR.PolyFun ) ) { AN.ncmod = 0; } m = termout; LONG copy = t - from; const LONG size = t - u; NCOPY(m, from, copy); w = m - size; to = m; switch ( d->type ) { case DOLINDEX: *m++ = d->index; break; case DOLZERO: *m++ = 0; break; case DOLNUMBER: case DOLTERMS: if ( d->where[0] == 4 && d->where[4] == 0 && d->where[3] == 3 && d->where[2] == 1 && d->where[1] < AM.OffsetIndex ) { *m++ = d->where[1]; } else { wrongtype:; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s has wrong type for tensor substitution", AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); AN.ncmod = oldncmod; return(-1); } break; case DOLARGUMENT: if ( d->where[0] == -INDEX ) { *m++ = d->where[1]; break; } else if ( d->where[0] == -VECTOR ) { *m++ = d->where[1]; break; } else if ( d->where[0] == -MINVECTOR ) { *m++ = d->where[1]; sign = -sign; break; } else if ( d->where[0] == -SNUMBER ) { if ( d->where[1] >= 0 && d->where[1] < AM.OffsetIndex ) { *m++ = d->where[1]; break; } } goto wrongtype; case DOLWILDARGS: if ( d->where[0] > 0 ) { r = d->where; i = *r++; while ( --i >= 0 ) *m++ = *r++; } else { r = d->where + 1; while ( *r ) { if ( *r == -INDEX ) { *m++ = r[1]; r += 2; continue; } else if ( *r == -VECTOR ) { *m++ = r[1]; r += 2; continue; } else if ( *r == -MINVECTOR ) { *m++ = r[1]; r += 2; sign = -sign; continue; } else if ( *r == -SNUMBER ) { if ( r[1] >= 0 && r[1] < AM.OffsetIndex ) { *m++ = r[1]; r += 2; continue; } } goto wrongtype; } } break; case DOLSUBTERM: r = d->where; if ( *r == INDEX && r[1] == 3 ) { *m++ = r[2]; } else goto wrongtype; break; case DOLUNDEFINED: #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s is undefined in tensor substitution", AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); AN.ncmod = oldncmod; return(-1); } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif w[1] = w[1] - 2 + (m-to); from += 2; term += *term; while ( from < term ) *m++ = *from++; if ( sign < 0 ) m[-1] = -m[-1]; if ( (m-termout) > (LONG)(AM.MaxTer/sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Output term too large (%d words) (MaxTermSize: %d words)", m-termout, AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); goto TooLarge; } *termout = m - termout; AN.ncmod = oldncmod; return(0); } else { AC.lhdollarflag = 1; } } t++; } t = u; } t += t[1]; } MLOCK(ErrorMessageLock); MesPrint("Internal error in InFunction: Function not encountered."); if ( AM.tracebackflag ) { MesPrint("%w: AR.TePos = %d",AR.TePos); MesPrint("%w: AN.TeInFun = %d",AN.TeInFun); termout = term; AO.OutFill = AO.OutputLine = (UBYTE *)AT.WorkPointer + AM.MaxTer; AO.OutSkip = 3; FiniLine(); i = *termout; while ( --i >= 0 ) { TalToLine((UWORD)(*termout++)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); MesCall("InFunction"); } MUNLOCK(ErrorMessageLock); return(1); InFunc: MLOCK(ErrorMessageLock); MesCall("InFunction"); MUNLOCK(ErrorMessageLock); SETERROR(-1) TooLarge: MLOCK(ErrorMessageLock); MesCall("InFunction"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] InFunction : #[ InsertTerm : WORD InsertTerm(term,replac,extractbuff,position,termout) */ /** * Puts the terms 'term' and 'position' together into a single * legal term in termout. replac is the number of the subexpression * that should be replaced. It must be a positive term. * When action is needed in the argument of a function all terms * in that argument are dealt with recursively. The subexpression * is sorted. Only one subexpression is done at a time this way. * * @param term the input term * @param replac number of the subexpression pointer to replace * @param extractbuff number of the compiler buffer replac refers to * @param position position from where to take the term in the compiler buffer * @param termout the output term * @param tepos offset in term where the subexpression is. * @return Normal conventions (OK = 0). */ int InsertTerm(PHEAD WORD *term, WORD replac, WORD extractbuff, WORD *position, WORD *termout, WORD tepos) { GETBIDENTITY WORD *m, *t, *r, i, l2, j; WORD *u, *v, l1, *coef; coef = AT.WorkPointer; if ( ( AT.WorkPointer = coef + 2*AM.MaxTal ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } t = term; r = t + *t; l1 = l2 = r[-1]; m = r - ABS(l2); if ( tepos > 0 ) { t = term + tepos; goto foundit; } t++; while ( t < m ) { if ( *t == SUBEXPRESSION && t[2] == replac && t[3] && t[4] == extractbuff ) { r = t + t[1]; while ( *r == SUBEXPRESSION && r[2] == replac && r[3] && r < m && r[4] == extractbuff ) { t = r; r += r[1]; } foundit:; u = m; r = term; m = termout; do { *m++ = *r++; } while ( r < t ); if ( t[1] > SUBEXPSIZE ) { /* if this is a dollar expression there are no wildcards */ i = *--m; if ( ( l2 = WildFill(BHEAD m,position,t) ) < 0 ) goto InsCall; *m = i; m += l2-1; l2 = *m; i = ( j = ABS(l2) ) - 1; r = coef + i; do { *--r = *--m; } while ( --i > 0 ); } else { v = t; t = position; r = t + *t; l2 = r[-1]; r -= ( j = ABS(l2) ); t++; if ( t < r ) do { *m++ = *t++; } while ( t < r ); t = v; } t += t[1]; while ( t < u && *t == DOLLAREXPR2 ) t += t[1]; ComAct: if ( t < u ) do { *m++ = *t++; } while ( t < u ); if ( *r == 1 && r[1] == 1 && j == 3 ) { if ( l2 < 0 ) l1 = -l1; i = ABS(l1)-1; NCOPY(m,t,i); *m++ = l1; } else { if ( MulRat(BHEAD (UWORD *)u,REDLENG(l1),(UWORD *)r,REDLENG(l2), (UWORD *)m,&l1) ) goto InsCall; l2 = l1; l2 *= 2; if ( l2 < 0 ) { m -= l2; *m++ = l2-1; } else { m += l2; *m++ = l2+1; } } *termout = WORDDIF(m,termout); if ( (*termout)*((LONG)sizeof(WORD)) > AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex during substitution (%d words). MaxTermSize (%l words) is too small.", *termout, AM.MaxTer/(LONG)sizeof(WORD) ); goto InsCall2; } AT.WorkPointer = coef; return(0); } t += t[1]; } /* The next action is for when there is no subexpression pointer. We append the extra term. Effectively the routine becomes now a merge routine for two terms. */ v = t; u = m; r = term; m = termout; do { *m++ = *r++; } while ( r < t ); t = position; r = t + *t; l2 = r[-1]; r -= ( j = ABS(l2) ); t++; if ( t < r ) do { *m++ = *t++; } while ( t < r ); t = v; goto ComAct; InsCall: MLOCK(ErrorMessageLock); InsCall2: MesCall("InsertTerm"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] InsertTerm : #[ PasteFile : WORD PasteFile(num,acc,pos,accf,renum,freeze,nexpr) */ /** * Gets a term from stored expression expr and puts it in * the accumulator at position number. It returns the length of the * term that came from file. * * @param number number of partial terms to skip in accum * @param accum the accumulator * @param position file position from where to get the stored term * @param accfill returns tail position in accum * @param renumber the renumber struct for the variables in the stored expression * @param freeze information about if we need only the contents of a bracket * @param nexpr the number of the stored expression * @return Normal conventions (OK = 0). */ LONG PasteFile(PHEAD WORD number, WORD *accum, POSITION *position, WORD **accfill, RENUMBER renumber, WORD *freeze, WORD nexpr) { GETBIDENTITY WORD *r, l, *m, i; WORD *stop, *s1, *s2; /* POSITION AccPos; bug 12-apr-2008 JV */ WORD InCompState; WORD *oldipointer; LONG retlength; stop = (WORD *)(((UBYTE *)(accum)) + 2*AM.MaxTer); *accum++ = number; while ( --number >= 0 ) accum += *accum; if ( freeze ) { /* AccPos = *position; bug 12-apr-2008 JV */ oldipointer = AR.CompressPointer; do { AR.CompressPointer = oldipointer; /* if ( ( l = GetFromStore(accum,&AccPos,renumber,&InCompState,nexpr) ) < 0 ) bug 12-apr-2008 JV */ if ( ( l = GetFromStore(accum,position,renumber,&InCompState,nexpr) ) < 0 ) goto PasErr; if ( !l ) { *accum = 0; return(0); } r = accum; m = r + *r; m -= ABS(m[-1]); r++; while ( r < m && *r != HAAKJE ) r += r[1]; if ( r >= m ) { if ( *freeze != 4 ) l = -1; } else { /* The algorithm for accepting terms with a given (freeze) representation outside brackets is rather crude. A refinement would be to store the part outside the bracket and skip the term when this part doesn't alter (and is unacceptable). Once accepting one can keep accepting till the bracket alters and then one may stop the generation. It is necessary to set up a struct to remember the bracket and the progress status. */ m = AT.WorkPointer; s2 = r; r = accum; *m++ = WORDDIF(s2,r) + 3; r++; while ( r < s2 ) *m++ = *r++; *m++ = 1; *m++ = 1; *m++ = 3; m = AT.WorkPointer; if ( Normalize(BHEAD AT.WorkPointer) ) goto PasErr; r = freeze; i = *m; while ( --i >= 0 && *m++ == *r++ ) {} if ( i > 0 ) { l = -1; } else { /* Term to be accepted */ r = accum; s1 = r + *r; r++; m = s2; m += m[1]; do { *r++ = *m++; } while ( m < s1 ); *accum = l = WORDDIF(r,accum); } } } while ( l < 0 ); retlength = InCompState; /* retlength = DIFBASE(AccPos,*position) / sizeof(WORD); bug 12-apr-2008 JV */ } else { if ( ( l = GetFromStore(accum,position,renumber,&InCompState,nexpr) ) < 0 ) { MLOCK(ErrorMessageLock); MesCall("PasteFile"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( l == 0 ) { *accum = 0; return(0); } retlength = InCompState; } accum += l; if ( accum > stop ) { MLOCK(ErrorMessageLock); MesPrint("Buffer too small in PasteFile"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } *accum = 0; *accfill = accum; return(retlength); PasErr: MLOCK(ErrorMessageLock); MesCall("PasteFile"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] PasteFile : #[ PasteTerm : WORD PasteTerm(number,accum,position,times,divby) */ /** * Puts the term at position in the accumulator accum at position * 'number+1'. if times > 0 the coefficient of this term is * multiplied by times/divby. * * @param number The number of term fragments in accum that should be skipped * @param accum The accumulator of term fragments * @param position A position in (typically) a compiler buffer from where * a (piece of a) term comes. * @param times Multiply the result by this * @param divby Divide the result by this. * * This routine is typically used when we have to replace a (sub)expression * pointer by a power of a (sub)expression. This uses mostly a binomial * expansion and the new term is the old term multiplied one by one * by terms of the new expression. The factors times and divby keep track * of the binomial coefficient. * Once this is complete, the routine FiniTerm will make the contents * of the accumulator into a proper term that still needs to be normalized. */ WORD *PasteTerm(PHEAD WORD number, WORD *accum, WORD *position, WORD times, WORD divby) { GETBIDENTITY WORD *t, *r, x, y, z; WORD *m, *u, l1, a[2]; m = (WORD *)(((UBYTE *)(accum)) + AM.MaxTer); /* m = (WORD *)(((UBYTE *)(accum)) + 2*AM.MaxTer); */ *accum++ = number; while ( --number >= 0 ) accum += *accum; if ( times == divby ) { t = position; r = t + *t; if ( t < r ) do { *accum++ = *t++; } while ( t < r ); } else { u = accum; t = position; r = t + *t - 1; l1 = *r; r -= ABS(*r) - 1; if ( t < r ) do { *accum++ = *t++; } while ( t < r ); if ( divby > times ) { x = divby; y = times; } else { x = times; y = divby; } z = x%y; while ( z ) { x = y; y = z; z = x%y; } if ( y != 1 ) { divby /= y; times /= y; } a[1] = divby; a[0] = times; if ( MulRat(BHEAD (UWORD *)t,REDLENG(l1),(UWORD *)a,1,(UWORD *)accum,&l1) ) { MLOCK(ErrorMessageLock); MesCall("PasteTerm"); MUNLOCK(ErrorMessageLock); return(0); } x = l1; x *= 2; if ( x < 0 ) { accum -= x; *accum++ = x - 1; } else { accum += x; *accum++ = x + 1; } *u = WORDDIF(accum,u); } if ( accum >= m ) { MLOCK(ErrorMessageLock); MesPrint("Buffer too small in PasteTerm"); MUNLOCK(ErrorMessageLock); return(0); } *accum = 0; return(accum); } /* #] PasteTerm : #[ FiniTerm : WORD FiniTerm(term,accum,termout,number) */ /** * Concatenates the contents of the accumulator into a single * legal term, which replaces the subexpression pointer * * @param term the input term with the (sub)expression subterm * @param accum the accumulator with the term fragments * @param termout the location where the output should be written * @param number the number of term fragments in the accumulator * @param tepos the position of the subterm in term to be replaced */ int FiniTerm(PHEAD WORD *term, WORD *accum, WORD *termout, WORD number, WORD tepos) { GETBIDENTITY WORD *m, *t, *r, i, numacc, l2, ipp; WORD *u, *v, l1, *coef = AT.WorkPointer, *oldaccum; if ( ( AT.WorkPointer = coef + 2*AM.MaxTal ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } oldaccum = accum; t = term; m = t + *t - 1; l1 = REDLENG(*m); i = ABS(*m) - 1; r = coef + i; do { *--r = *--m; } while ( --i > 0 ); /* Copies coefficient */ if ( tepos > 0 ) { t = term + tepos; goto foundit; } t++; if ( t < m ) do { if ( ( ( *t == SUBEXPRESSION && ( *(r=t+t[1]) != SUBEXPRESSION || r >= m || !r[3] ) ) || *t == EXPRESSION ) && t[2] == number && t[3] ) { foundit:; u = m; r = term; m = termout; if ( r < t ) do { *m++ = *r++; } while ( r < t ); numacc = *accum++; if ( numacc >= 0 ) do { if ( *t == EXPRESSION ) { v = t + t[1]; r = t + SUBEXPSIZE; while ( r < v ) { if ( *r == WILDCARDS ) { r += 2; i = *--m; if ( ( l2 = WildFill(BHEAD m,accum,r) ) < 0 ) goto FiniCall; goto AllWild; } r += r[1]; } goto NoWild; } else if ( t[1] > SUBEXPSIZE && t[SUBEXPSIZE] != FROMBRAC ) { i = *--m; if ( ( l2 = WildFill(BHEAD m,accum,t) ) < 0 ) goto FiniCall; AllWild: *m = i; m += l2-1; l2 = *m; m -= ABS(l2) - 1; r = m; } else { NoWild: r = accum; v = r + *r - 1; l2 = *v; v -= ABS(l2) - 1; r++; if ( r < v ) do { *m++ = *r++; } while ( r < v ); } if ( *r == 1 && r[1] == 1 && ABS(l2) == 3 ) { if ( l2 < 0 ) l1 = -l1; } else { l2 = REDLENG(l2); if ( l2 == 0 ) { t = oldaccum; numacc = *t++; AO.OutSkip = 3; FiniLine(); while ( --numacc >= 0 ) { i = *t; while ( --i >= 0 ) { TalToLine((UWORD)(*t++)); TokenToLine((UBYTE *)" "); } } AO.OutSkip = 0; FiniLine(); goto FiniCall; } if ( MulRat(BHEAD (UWORD *)coef,l1,(UWORD *)r,l2,(UWORD *)coef,&l1) ) goto FiniCall; if ( AN.ncmod != 0 && TakeModulus((UWORD *)coef,&l1,AC.cmod,AN.ncmod,UNPACK|AC.modmode) ) goto FiniCall; } accum += *accum; } while ( --numacc >= 0 ); if ( *t == SUBEXPRESSION ) { while ( t+t[1] < u && t[t[1]] == DOLLAREXPR2 ) t += t[1]; } t += t[1]; if ( t < u ) do { *m++ = *t++; } while ( t < u ); l2 = l1; /* Code to economize when taking x = (a+b)/2 */ r = termout+1; while ( r < m ) { if ( *r == SUBEXPRESSION ) { t = r + r[1]; l1 = (WORD)(cbuf[r[4]].CanCommu[r[2]]); while ( t < m ) { if ( *t == SUBEXPRESSION && t[1] == r[1] && t[2] == r[2] && t[4] == r[4] ) { i = t[1] - SUBEXPSIZE; u = r + SUBEXPSIZE; v = t + SUBEXPSIZE; while ( i > 0 ) { if ( *v++ != *u++ ) break; i--; } if ( i <= 0 ) { u = r; r[3] += t[3]; r = t + t[1]; while ( r < m ) *t++ = *r++; m = t; r = u; goto Nextr; } if ( l1 && cbuf[t[4]].CanCommu[t[2]] ) break; while ( t+t[1] < m && t[t[1]] == DOLLAREXPR2 ) t += t[1]; } else if ( l1 ) { if ( *t == SUBEXPRESSION && cbuf[t[4]].CanCommu[t[2]] ) break; if ( *t >= FUNCTION+WILDOFFSET ) ipp = *t - WILDOFFSET; else ipp = *t; if ( *t >= FUNCTION && functions[ipp-FUNCTION].commute && l1 ) break; if ( *t == EXPRESSION ) break; } t += t[1]; } r += r[1]; } else r += r[1]; Nextr:; } i = ABS(l2); i *= 2; i++; l2 = ( l2 >= 0 ) ? i: -i; r = coef; while ( --i > 0 ) *m++ = *r++; *m++ = l2; *termout = WORDDIF(m,termout); AT.WorkPointer = coef; return(0); } t += t[1]; } while ( t < m ); AT.WorkPointer = coef; return(1); FiniCall: MLOCK(ErrorMessageLock); MesCall("FiniTerm"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] FiniTerm : #[ Generator : WORD Generator(BHEAD term,level) */ static WORD zeroDollar[] = { 0, 0 }; /* static LONG debugcounter = 0; */ /** * The heart of the program. * Here the expansion tree is set up in one giant recursion * * @param term the input term. may be overwritten * @param level the level in the compiler buffer (number of statement) * @return Normal conventions (OK = 0). * * The routine looks first whether there are unsubstituted (sub)expressions. * If so, one of them gets inserted term by term and the new term is * used in a renewed call to Generator. * If there are no (sub)expressions, the term is normalized, the * compiler level is raised (next statement) and the program looks * what type of statement this is. If this is a special statement it * is either treated on the spot or the appropriate routine is called. * If it is a substitution, the pattern matcher is called (TestMatch) * which tells whether there was a match. If so we need to call * TestSub again to test for (sub)expressions. * If we run out of levels, the term receives a final treatment for * modulus calculus and/or brackets and is then sent off to the * sorting routines. */ int Generator(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD replac, *accum, *termout, *t, i, j, tepos, applyflag = 0, *StartBuf; WORD *a, power, power1, DumNow = AR.CurDum, oldtoprhs, oldatoprhs, extractbuff; int ret; int *RepSto = AN.RepPoint, iscopy = 0; CBUF *C = cbuf+AM.rbufnum, *CC = cbuf + AT.ebufnum, *CCC = cbuf + AT.aebufnum; LONG posisub, oldcpointer, oldacpointer; DOLLARS d = 0; WORD numfac[5], idfunctionflag; #ifdef WITHPTHREADS int nummodopt, dtype = -1, id; #endif oldtoprhs = CC->numrhs; oldcpointer = CC->Pointer - CC->Buffer; oldatoprhs = CCC->numrhs; oldacpointer = CCC->Pointer - CCC->Buffer; ReStart: if ( ( replac = TestSub(BHEAD term,level) ) == 0 ) { if ( applyflag ) { TableReset(); applyflag = 0; } /* if ( AN.PolyNormFlag > 1 ) { if ( PolyFunMul(BHEAD term) < 0 ) goto GenCall; AN.PolyNormFlag = 0; if ( !*term ) goto Return0; } */ Renormalize: AN.PolyNormFlag = 0; AN.idfunctionflag = 0; if ( ( ret = Normalize(BHEAD term) ) != 0 ) { if ( ret > 0 ) { if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; goto ReStart; } goto GenCall; } idfunctionflag = AN.idfunctionflag; if ( !*term ) { AN.PolyNormFlag = 0; goto Return0; } if ( AN.PolyNormFlag ) { if ( AN.PolyFunTodo == 0 ) { if ( PolyFunMul(BHEAD term) < 0 ) goto GenCall; if ( !*term ) { AN.PolyNormFlag = 0; goto Return0; } } else { WORD oldPolyFunExp = AR.PolyFunExp; AR.PolyFunExp = 0; if ( PolyFunMul(BHEAD term) < 0 ) goto GenCall; AT.WorkPointer = term+*term; AR.PolyFunExp = oldPolyFunExp; if ( !*term ) { AN.PolyNormFlag = 0; goto Return0; } if ( Normalize(BHEAD term) < 0 ) goto GenCall; if ( !*term ) { AN.PolyNormFlag = 0; goto Return0; } AT.WorkPointer = term+*term; if ( AN.PolyNormFlag ) { if ( PolyFunMul(BHEAD term) < 0 ) goto GenCall; if ( !*term ) { AN.PolyNormFlag = 0; goto Return0; } AT.WorkPointer = term+*term; } AN.PolyFunTodo = 0; } } if ( idfunctionflag > 0 ) { if ( TakeIDfunction(BHEAD term) ) { AT.WorkPointer = term + *term; goto ReStart; } } if ( AT.WorkPointer < (WORD *)(((UBYTE *)(term)) + AM.MaxTer) ) AT.WorkPointer = (WORD *)(((UBYTE *)(term)) + AM.MaxTer); do { SkipCount: level++; if ( level > AR.Cnumlhs ) { if ( AR.DeferFlag && AR.sLevel <= 0 ) { #ifdef WITHMPI if ( PF.me != MASTER && AC.mparallelflag == PARALLELFLAG && PF.exprtodo < 0 ) { if ( PF_Deferred(term,level) ) goto GenCall; } else #endif { if ( Deferred(BHEAD term,level) ) goto GenCall; } goto Return0; } if ( AN.ncmod != 0 ) { if ( Modulus(term) ) goto GenCall; if ( !*term ) goto Return0; } if ( AR.CurDum > AM.IndDum && AR.sLevel <= 0 ) { WORD olddummies = AN.IndDum; AN.IndDum = AM.IndDum; ReNumber(BHEAD term); Normalize(BHEAD term); AN.IndDum = olddummies; if ( !*term ) goto Return0; olddummies = DetCurDum(BHEAD term); if ( olddummies > AR.MaxDum ) AR.MaxDum = olddummies; } if ( AR.PolyFun > 0 && ( AR.sLevel <= 0 || AN.FunSorts[AR.sLevel]->PolyFlag > 0 ) ) { if ( PrepPoly(BHEAD term,0) != 0 ) goto Return0; } else if ( AR.PolyFun > 0 ) { if ( PrepPoly(BHEAD term,1) != 0 ) goto Return0; } if ( AR.sLevel <= 0 && AR.BracketOn ) { if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; termout = AT.WorkPointer; if ( AT.WorkPointer + *term + 3 > AT.WorkTop ) goto OverWork; if ( PutBracket(BHEAD term) ) return(-1); AN.RepPoint = RepSto; *AT.WorkPointer = 0; ret = StoreTerm(BHEAD termout); AT.WorkPointer = termout; CC->numrhs = oldtoprhs; CC->Pointer = CC->Buffer + oldcpointer; CCC->numrhs = oldatoprhs; CCC->Pointer = CCC->Buffer + oldacpointer; return(ret); } else { if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; if ( AT.WorkPointer >= AT.WorkTop ) goto OverWork; *AT.WorkPointer = 0; AN.RepPoint = RepSto; ret = StoreTerm(BHEAD term); CC->numrhs = oldtoprhs; CC->Pointer = CC->Buffer + oldcpointer; CCC->numrhs = oldatoprhs; CCC->Pointer = CCC->Buffer + oldacpointer; return(ret); } } i = C->lhs[level][0]; if ( i >= TYPECOUNT ) { /* #[ Special action : */ switch ( i ) { case TYPECOUNT: if ( CountDo(term,C->lhs[level]) < C->lhs[level][2] ) { AT.WorkPointer = term + *term; goto Return0; } break; case TYPEMULT: if ( MultDo(BHEAD term,C->lhs[level]) ) goto GenCall; goto ReStart; case TYPEGOTO: level = AC.Labels[C->lhs[level][2]]; break; case TYPEDISCARD: AT.WorkPointer = term + *term; goto Return0; case TYPEIF: #ifdef WITHPTHREADS { /* We may be writing in the space here when wildcards are involved in a match(). Hence we have to make a private copy here!!!! */ WORD ic, jc, *ifcode, *jfcode; jfcode = C->lhs[level]; jc = jfcode[1]; ifcode = AT.WorkPointer; AT.WorkPointer += jc; for ( ic = 0; ic < jc; ic++ ) ifcode[ic] = jfcode[ic]; while ( !DoIfStatement(BHEAD ifcode,term) ) { level = C->lhs[level][2]; if ( C->lhs[level][0] != TYPEELIF ) break; } AT.WorkPointer = ifcode; } #else while ( !DoIfStatement(BHEAD C->lhs[level],term) ) { level = C->lhs[level][2]; if ( C->lhs[level][0] != TYPEELIF ) break; } #endif break; case TYPEELIF: do { level = C->lhs[level][2]; } while ( C->lhs[level][0] == TYPEELIF ); break; case TYPEELSE: case TYPEENDIF: level = C->lhs[level][2]; break; case TYPESUMFIX: { WORD *cp = AR.CompressPointer, *op = AR.CompressPointer; WORD *tlhs = C->lhs[level] + 3, *m, jlhs; WORD theindex = C->lhs[level][2]; if ( theindex < 0 ) { /* $-variable */ #ifdef WITHPTHREADS int ddtype = -1; theindex = -theindex; d = Dollars + theindex; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( theindex == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { ddtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(ddtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #else theindex = -theindex; d = Dollars + theindex; #endif if ( d->type != DOLINDEX || d->index < AM.OffsetIndex || d->index >= AM.OffsetIndex + WILDOFFSET ) { MLOCK(ErrorMessageLock); MesPrint("$%s should have been an index" ,AC.dollarnames->namebuffer+d->name); AN.currentTerm = term; MesPrint("Current term: %t"); AN.listinprint = printscratch; printscratch[0] = DOLLAREXPRESSION; printscratch[1] = theindex; MesPrint("$%s = %$" ,AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); #ifdef WITHPTHREADS if ( ddtype > 0 && ! DollarLocalCopy(ddtype) ) { UNLOCK(d->pthreadslock); } #endif goto GenCall; } theindex = d->index; #ifdef WITHPTHREADS if ( ddtype > 0 && ! DollarLocalCopy(ddtype) ) { UNLOCK(d->pthreadslock); } #endif } cp[1] = SUBEXPSIZE+4; cp += SUBEXPSIZE; *cp++ = INDTOIND; *cp++ = 4; *cp++ = theindex; i = C->lhs[level][1] - 3; cp++; AR.CompressPointer = cp; while ( --i >= 0 ) { cp[-1] = *tlhs++; termout = AT.WorkPointer; if ( ( jlhs = WildFill(BHEAD termout,term,op)) < 0 ) goto GenCall; m = term; jlhs = *m; while ( --jlhs >= 0 ) { if ( *m++ != *termout++ ) break; } if ( jlhs >= 0 ) { termout = AT.WorkPointer; AT.WorkPointer = termout + *termout; if ( Generator(BHEAD termout,level) ) goto GenCall; AT.WorkPointer = termout; } else { AR.CompressPointer = op; goto SkipCount; } } AR.CompressPointer = op; goto CommonEnd; } case TYPESUM: { WORD *wp, *cp = AR.CompressPointer, *op = AR.CompressPointer; WORD theindex; WORD *ow; /* At this point it is safest to determine CurDum */ AR.CurDum = DetCurDum(BHEAD term); i = C->lhs[level][1]-2; wp = C->lhs[level] + 2; cp[1] = SUBEXPSIZE+4*i; cp += SUBEXPSIZE; while ( --i >= 0 ) { theindex = *wp++; if ( theindex < 0 ) { /* $-variable */ #ifdef WITHPTHREADS int ddtype = -1; theindex = -theindex; d = Dollars + theindex; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( theindex == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { ddtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(ddtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #else theindex = -theindex; d = Dollars + theindex; #endif if ( d->type != DOLINDEX || d->index < AM.OffsetIndex || d->index >= AM.OffsetIndex + WILDOFFSET ) { MLOCK(ErrorMessageLock); MesPrint("$%s should have been an index" ,AC.dollarnames->namebuffer+d->name); AN.currentTerm = term; MesPrint("Current term: %t"); AN.listinprint = printscratch; printscratch[0] = DOLLAREXPRESSION; printscratch[1] = theindex; MesPrint("$%s = %$" ,AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); #ifdef WITHPTHREADS if ( ddtype > 0 && ! DollarLocalCopy(ddtype) ) { UNLOCK(d->pthreadslock); } #endif goto GenCall; } theindex = d->index; #ifdef WITHPTHREADS if ( ddtype > 0 && ! DollarLocalCopy(ddtype) ) { UNLOCK(d->pthreadslock); } #endif } *cp++ = INDTOIND; *cp++ = 4; *cp++ = theindex; *cp++ = ++AR.CurDum; } ow = AT.WorkPointer; AR.CompressPointer = cp; if ( WildFill(BHEAD ow,term,op) < 0 ) goto GenCall; AR.CompressPointer = op; i = ow[0]; WORD term_changed = 0; for ( j = 0; j < i; j++ ) { if ( term[j] != ow[j] ) term_changed = 1; term[j] = ow[j]; } // If the term was modified by WildFill, set RepCount. if ( term_changed ) *AN.RepPoint = 1; AT.WorkPointer = ow; // Most other calls to ReNumber reset AN.IndDum to AM.IndDum first. Here it is // not done, but doing it is one way to fix Issue #710. The fix that is actually // implemented is to change a comparison in FunLevel and then a reset of // AN.IndDum appears unnecessary here. But maybe one day this comment is useful. ReNumber(BHEAD term); goto Renormalize; } case TYPECHISHOLM: if ( Chisholm(BHEAD term,level) ) goto GenCall; CommonEnd: AT.WorkPointer = term + *term; goto Return0; case TYPEARG: if ( ( i = execarg(BHEAD term,level) ) < 0 ) goto GenCall; level = C->lhs[level][2]; if ( i > 0 ) goto ReStart; break; case TYPENORM: case TYPENORM2: case TYPENORM3: case TYPENORM4: case TYPESPLITARG: case TYPESPLITARG2: case TYPESPLITFIRSTARG: case TYPESPLITLASTARG: case TYPEARGTOEXTRASYMBOL: if ( execarg(BHEAD term,level) < 0 ) goto GenCall; level = C->lhs[level][2]; break; case TYPEFACTARG: case TYPEFACTARG2: { WORD jjj; if ( ( jjj = execarg(BHEAD term,level) ) < 0 ) goto GenCall; if ( jjj > 0 ) goto ReStart; level = C->lhs[level][2]; break; } case TYPEEXIT: if ( C->lhs[level][2] > 0 ) { MLOCK(ErrorMessageLock); MesPrint("%s",C->lhs[level]+3); MUNLOCK(ErrorMessageLock); } Terminate(-1); goto GenCall; case TYPESETEXIT: AM.exitflag = 1; /* no danger of race conditions */ break; case TYPEPRINT: AN.currentTerm = term; AN.numlistinprint = (C->lhs[level][1] - C->lhs[level][4] - 5)/2; AN.listinprint = C->lhs[level]+5+C->lhs[level][4]; MLOCK(ErrorMessageLock); AO.ErrorBlock = 1; MesPrint((char *)(C->lhs[level]+5)); AO.ErrorBlock = 0; MUNLOCK(ErrorMessageLock); break; case TYPEFPRINT: { int oldFOflag; WORD oldPrintType, oldLogHandle = AC.LogHandle; AC.LogHandle = C->lhs[level][2]; MLOCK(ErrorMessageLock); oldFOflag = AM.FileOnlyFlag; oldPrintType = AO.PrintType; if ( AC.LogHandle >= 0 ) { AM.FileOnlyFlag = 1; AO.PrintType |= PRINTLFILE; } AO.PrintType |= C->lhs[level][3]; AN.currentTerm = term; AN.numlistinprint = (C->lhs[level][1] - C->lhs[level][4] - 5)/2; AN.listinprint = C->lhs[level]+5+C->lhs[level][4]; MesPrint((char *)(C->lhs[level]+5)); AO.PrintType = oldPrintType; AM.FileOnlyFlag = oldFOflag; MUNLOCK(ErrorMessageLock); AC.LogHandle = oldLogHandle; } break; case TYPEREDEFPRE: j = C->lhs[level][2]; #ifdef WITHMPI { /* * Regardless of parallel/nonparallel switch, we need to set * AC.inputnumbers[ii], which indicates that the corresponding * preprocessor variable is redefined and so we need to * send/broadcast it. */ int ii; for ( ii = 0; ii < AC.numpfirstnum; ii++ ) { if ( AC.pfirstnum[ii] == j ) break; } AC.inputnumbers[ii] = AN.ninterms; } #endif #ifdef WITHPTHREADS if ( AS.MultiThreaded ) { int ii; for ( ii = 0; ii < AC.numpfirstnum; ii++ ) { if ( AC.pfirstnum[ii] == j ) break; } if ( AN.inputnumber < AC.inputnumbers[ii] ) break; LOCK(AP.PreVarLock); if ( AN.inputnumber >= AC.inputnumbers[ii] ) { a = C->lhs[level]+4; if ( a[a[-1]] == 0 ) PutPreVar(PreVar[j].name,(UBYTE *)(a),0,1); else PutPreVar(PreVar[j].name,(UBYTE *)(a) ,(UBYTE *)(a+a[-1]+1),1); /* PutPreVar(PreVar[j].name,(UBYTE *)(C->lhs[level]+4),0,1); */ AC.inputnumbers[ii] = AN.inputnumber; } UNLOCK(AP.PreVarLock); } else #endif { a = C->lhs[level]+4; LOCK(AP.PreVarLock); if ( a[a[-1]] == 0 ) PutPreVar(PreVar[j].name,(UBYTE *)(a),0,1); else PutPreVar(PreVar[j].name,(UBYTE *)(a) ,(UBYTE *)(a+a[-1]+1),1); UNLOCK(AP.PreVarLock); } break; case TYPERENUMBER: AT.WorkPointer = term + *term; if ( FullRenumber(BHEAD term,C->lhs[level][2]) ) goto GenCall; AT.WorkPointer = term + *term; if ( *term == 0 ) goto Return0; break; case TYPETRY: if ( TryDo(BHEAD term,C->lhs[level],level) ) goto GenCall; AT.WorkPointer = term + *term; goto Return0; case TYPEASSIGN: { WORD onc = AR.NoCompress, oldEside = AR.Eside; WORD oldrepeat = *AN.RepPoint; /* Here we have to assign an expression to a $ variable. */ AR.Eside = RHSIDE; AR.NoCompress = 1; AN.cTerm = AN.currentTerm = term; AT.WorkPointer = term + *term; *AT.WorkPointer++ = 0; if ( AssignDollar(BHEAD term,level) ) goto GenCall; AT.WorkPointer = term + *term; AN.cTerm = 0; *AN.RepPoint = oldrepeat; AR.NoCompress = onc; AR.Eside = oldEside; break; } case TYPEFINDLOOP: if ( Lus(term,C->lhs[level][3],C->lhs[level][4], C->lhs[level][5],C->lhs[level][6],C->lhs[level][2]) ) { AT.WorkPointer = term + *term; goto Renormalize; } break; case TYPEINSIDE: if ( InsideDollar(BHEAD C->lhs[level],level) < 0 ) goto GenCall; level = C->lhs[level][2]; break; case TYPETERM: ret = execterm(BHEAD term,level); AN.RepPoint = RepSto; AR.CurDum = DumNow; CC->numrhs = oldtoprhs; CC->Pointer = CC->Buffer + oldcpointer; CCC->numrhs = oldatoprhs; CCC->Pointer = CCC->Buffer + oldacpointer; return(ret); case TYPEDETCURDUM: AT.WorkPointer = term + *term; AR.CurDum = DetCurDum(BHEAD term); break; case TYPEINEXPRESSION: {WORD *ll = C->lhs[level]; int numexprs = (int)(ll[1]-3); ll += 3; while ( numexprs-- >= 0 ) { if ( *ll == AR.CurExpr ) break; ll++; } if ( numexprs < 0 ) level = C->lhs[level][2]; } break; case TYPEMERGE: AT.WorkPointer = term + *term; if ( DoShuffle(term,level,C->lhs[level][2],C->lhs[level][3]) ) goto GenCall; AT.WorkPointer = term + *term; goto Return0; case TYPESTUFFLE: AT.WorkPointer = term + *term; if ( DoStuffle(term,level,C->lhs[level][2],C->lhs[level][3]) ) goto GenCall; AT.WorkPointer = term + *term; goto Return0; case TYPETESTUSE: AT.WorkPointer = term + *term; if ( TestUse(term,level) ) goto GenCall; AT.WorkPointer = term + *term; break; case TYPEAPPLY: AT.WorkPointer = term + *term; if ( ApplyExec(term,C->lhs[level][2],level) < C->lhs[level][2] ) { AT.WorkPointer = term + *term; *AN.RepPoint = 1; goto ReStart; } AT.WorkPointer = term + *term; break; /* case TYPEAPPLYRESET: AT.WorkPointer = term + *term; if ( ApplyReset(level) ) goto GenCall; AT.WorkPointer = term + *term; break; */ case TYPECHAININ: { int lter = *term; AT.WorkPointer = term + *term; if ( ChainIn(BHEAD term,C->lhs[level][2]) ) goto GenCall; AT.WorkPointer = term + *term; /* Symmetry properties might mean the term has vanished */ if ( *term == 0 ) goto Return0; if ( *term != lter ) *AN.RepPoint = 1; } break; case TYPECHAINOUT: { int lter = *term; AT.WorkPointer = term + *term; if ( ChainOut(BHEAD term,C->lhs[level][2]) ) goto GenCall; AT.WorkPointer = term + *term; if ( *term != lter ) *AN.RepPoint = 1; } break; case TYPEFACTOR: AT.WorkPointer = term + *term; if ( DollarFactorize(BHEAD C->lhs[level][2]) ) goto GenCall; AT.WorkPointer = term + *term; break; case TYPEARGIMPLODE: AT.WorkPointer = term + *term; if ( ArgumentImplode(BHEAD term,C->lhs[level]) ) goto GenCall; AT.WorkPointer = term + *term; break; case TYPEARGEXPLODE: AT.WorkPointer = term + *term; if ( ArgumentExplode(BHEAD term,C->lhs[level]) ) goto GenCall; AT.WorkPointer = term + *term; break; case TYPEDENOMINATORS: if ( DenToFunction(term,C->lhs[level][2]) ) goto ReStart; break; case TYPEDROPCOEFFICIENT: DropCoefficient(BHEAD term); break; case TYPETRANSFORM: AT.WorkPointer = term + *term; if ( RunTransform(BHEAD term,C->lhs[level]+2) ) goto GenCall; AT.WorkPointer = term + *term; if ( *term == 0 ) goto Return0; goto ReStart; case TYPETOPOLYNOMIAL: AT.WorkPointer = term + *term; termout = AT.WorkPointer; if ( ConvertToPoly(BHEAD term,termout,C->lhs[level],0) < 0 ) goto GenCall; if ( *termout == 0 ) goto Return0; i = termout[0]; t = term; NCOPY(t,termout,i); AT.WorkPointer = term + *term; break; case TYPEFROMPOLYNOMIAL: AT.WorkPointer = term + *term; termout = AT.WorkPointer; if ( ConvertFromPoly(BHEAD term,termout,0,numxsymbol,0,0) < 0 ) goto GenCall; if ( *term == 0 ) goto Return0; i = termout[0]; t = term; NCOPY(t,termout,i); AT.WorkPointer = term + *term; goto ReStart; case TYPEDOLOOP: level = TestDoLoop(BHEAD C->lhs[level],level); if ( level < 0 ) goto GenCall; break; case TYPEENDDOLOOP: level = TestEndDoLoop(BHEAD C->lhs[C->lhs[level][2]],C->lhs[level][2]); if ( level < 0 ) goto GenCall; break; case TYPEDROPSYMBOLS: DropSymbols(BHEAD term); break; case TYPEPUTINSIDE: AT.WorkPointer = term + *term; if ( PutInside(BHEAD term,C->lhs[level]) < 0 ) goto GenCall; AT.WorkPointer = term + *term; /* * We need to call Generator() to convert slow notation to * fast notation, which fixes Issue #30. */ if ( Generator(BHEAD term,level) < 0 ) goto GenCall; goto Return0; case TYPETOSPECTATOR: if ( PutInSpectator(term,C->lhs[level][2]) < 0 ) goto GenCall; goto Return0; case TYPECANONICALIZE: AT.WorkPointer = term + *term; if ( DoCanonicalize(BHEAD term,C->lhs[level]) ) goto GenCall; AT.WorkPointer = term + *term; if ( *term == 0 ) goto Return0; break; case TYPESWITCH: AT.WorkPointer = term + *term; if ( DoSwitch(BHEAD term,C->lhs[level]) ) goto GenCall; goto Return0; case TYPEENDSWITCH: AT.WorkPointer = term + *term; if ( DoEndSwitch(BHEAD term,C->lhs[level]) ) goto GenCall; goto Return0; case TYPESETUSERFLAG: Expressions[AR.CurExpr].uflags |= 1 << (C->lhs[level][2]); break; case TYPECLEARUSERFLAG: Expressions[AR.CurExpr].uflags &= ~(1 << (C->lhs[level][2])); break; case TYPEALLLOOPS: AT.WorkPointer = term + *term; if ( AllLoops(BHEAD term,level) ) goto GenCall; goto Return0; case TYPEALLPATHS: AT.WorkPointer = term + *term; if ( AllPaths(BHEAD term,level) ) goto GenCall; goto Return0; #ifdef WITHFLOAT case TYPEEVALUATE: AT.WorkPointer = term + *term; if ( C->lhs[level][2] == MZV || C->lhs[level][2] == EULER || C->lhs[level][2] == MZVHALF || C->lhs[level][2] == ALLMZVFUNCTIONS ) { if ( EvaluateEuler(BHEAD term,level,C->lhs[level][2]) ) goto GenCall; } else { if ( EvaluateFun(BHEAD term,level,C->lhs[level]) ) goto GenCall; } /* else if ( C->lhs[level][2] == SQRTFUNCTION ) { if ( EvaluateSqrt(BHEAD term,level,C->lhs[level][2]) ) goto GenCall; } else { MLOCK(ErrorMessageLock); MesPrint("Illegal function %d in evaluate statement.",C->lhs[level][2]); MUNLOCK(ErrorMessageLock); goto GenCall; } */ goto Return0; case TYPETOFLOAT: AT.WorkPointer = term + *term; if ( ToFloat(BHEAD term,level) ) goto GenCall; goto Return0; case TYPETORAT: AT.WorkPointer = term + *term; if ( ToRat(BHEAD term,level) ) goto GenCall; goto Return0; case TYPESTRICTROUNDING: AT.WorkPointer = term + *term; if ( StrictRounding(BHEAD term,level,C->lhs[level][2],C->lhs[level][3]) ) goto GenCall; goto Return0; case TYPECHOP: AT.WorkPointer = term + *term; if ( Chop(BHEAD term,level) ) goto GenCall; goto Return0; #endif } goto SkipCount; /* #] Special action : */ } } while ( ( i = TestMatch(BHEAD term,&level) ) == 0 ); if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; if ( i > 0 ) replac = TestSub(BHEAD term,level); else replac = i; if ( replac >= 0 || AT.TMout[1] != SYMMETRIZE ) { *AN.RepPoint = 1; AR.expchanged = 1; } if ( replac < 0 ) { /* Terms come from automatic generation */ AutoGen: i = *AT.TMout; t = termout = AT.WorkPointer; if ( ( AT.WorkPointer += i ) > AT.WorkTop ) goto OverWork; accum = AT.TMout; while ( --i >= 0 ) *t++ = *accum++; if ( (*(FG.Operation[termout[1]]))(BHEAD term,termout,replac,level) ) goto GenCall; AT.WorkPointer = termout; goto Return0; } } if ( applyflag ) { TableReset(); applyflag = 0; } if ( AN.TeInFun ) { /* Match in function argument */ if ( AN.TeInFun < 0 && !AN.TeSuOut ) { if ( AR.TePos >= 0 ) goto AutoGen; switch ( AN.TeInFun ) { case -1: if ( DoDistrib(BHEAD term,level) ) goto GenCall; break; case -2: if ( DoDelta3(BHEAD term,level) ) goto GenCall; break; case -3: if ( DoTableExpansion(term,level) ) goto GenCall; break; case -4: if ( FactorIn(BHEAD term,level) ) goto GenCall; break; case -5: if ( FactorInExpr(BHEAD term,level) ) goto GenCall; break; case -6: if ( TermsInBracket(BHEAD term,level) < 0 ) goto GenCall; break; case -7: if ( ExtraSymFun(BHEAD term,level) < 0 ) goto GenCall; break; case -8: if ( GCDfunction(BHEAD term,level) < 0 ) goto GenCall; break; case -9: if ( DIVfunction(BHEAD term,level,0) < 0 ) goto GenCall; break; case -10: if ( DIVfunction(BHEAD term,level,1) < 0 ) goto GenCall; break; case -11: if ( DIVfunction(BHEAD term,level,2) < 0 ) goto GenCall; break; case -12: if ( DoPermutations(BHEAD term,level) ) goto GenCall; break; case -13: if ( DoPartitions(BHEAD term,level) ) goto GenCall; break; case -14: if ( DIVfunction(BHEAD term,level,3) < 0 ) goto GenCall; break; case -15: if ( GenDiagrams(BHEAD term,level) < 0 ) goto GenCall; break; } } else { termout = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; if ( InFunction(BHEAD term,termout) ) goto GenCall; AT.WorkPointer = termout + *termout; *AN.RepPoint = 1; AR.expchanged = 1; if ( *termout && Generator(BHEAD termout,level) < 0 ) goto GenCall; AT.WorkPointer = termout; } } else if ( replac > 0 ) { power = AN.TeSuOut; tepos = AR.TePos; if ( power < 0 ) { /* Table expansion */ power = -power; tepos = 0; } extractbuff = AT.TMbuff; if ( extractbuff == AM.dbufnum ) { d = DolToTerms(BHEAD replac); if ( d && d->where != 0 ) { iscopy = 1; if ( AT.TMdolfac > 0 ) { /* We need a factor */ if ( AT.TMdolfac == 1 ) { if ( d->nfactors ) { numfac[0] = 4; numfac[1] = d->nfactors; numfac[2] = 1; numfac[3] = 3; numfac[4] = 0; } else { numfac[0] = 0; } StartBuf = numfac; } else { if ( (AT.TMdolfac-1) > d->nfactors && d->nfactors > 0 ) { MLOCK(ErrorMessageLock); MesPrint("Attempt to use an nonexisting factor %d of a $-variable",(WORD)(AT.TMdolfac-1)); if ( d->nfactors == 1 ) MesPrint("There is only one factor"); else MesPrint("There are only %d factors",(WORD)(d->nfactors)); MUNLOCK(ErrorMessageLock); goto GenCall; } if ( d->nfactors > 1 ) { DOLLARS dd; LONG dsize; WORD *td1, *td2; dd = Dollars + replac; #ifdef WITHPTHREADS { int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( replac == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { dd = ModOptdollars[nummodopt].dstruct+AT.identity; } } } } #endif dsize = dd->factors[AT.TMdolfac-2].size; /* We copy only the factor we need */ if ( dsize == 0 ) { numfac[0] = 4; numfac[1] = d->factors[AT.TMdolfac-2].value; numfac[2] = 1; numfac[3] = 3; numfac[4] = 0; StartBuf = numfac; if ( numfac[1] < 0 ) { numfac[1] = -numfac[1]; numfac[3] = -numfac[3]; } } else { d->factors[AT.TMdolfac-2].where = td2 = (WORD *)Malloc1( (dsize+1)*sizeof(WORD),"Copy of factor"); td1 = dd->factors[AT.TMdolfac-2].where; StartBuf = td2; d->size = dsize; d->type = DOLTERMS; NCOPY(td2,td1,dsize); *td2 = 0; } } else if ( d->nfactors == 1 ) { StartBuf = d->where; } else { MLOCK(ErrorMessageLock); if ( d->nfactors == 0 ) { MesPrint("Attempt to use factor %d of an unfactored $-variable",(WORD)(AT.TMdolfac-1)); } else { MesPrint("Internal error. Illegal number of factors for $-variable"); } MUNLOCK(ErrorMessageLock); goto GenCall; } } } else StartBuf = d->where; } else { d = Dollars + replac; StartBuf = zeroDollar; } posisub = 0; i = DetCommu(d->where); #ifdef WITHPTHREADS if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( replac == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( dtype == MODMAX || dtype == MODMIN ) { if ( StartBuf[0] && StartBuf[StartBuf[0]] ) { MLOCK(ErrorMessageLock); MesPrint("A dollar variable with modoption max or min can have only one term"); MUNLOCK(ErrorMessageLock); goto GenCall; } } if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { LOCK(d->pthreadslock); } } } #endif } else { StartBuf = cbuf[extractbuff].Buffer; posisub = cbuf[extractbuff].rhs[replac] - StartBuf; i = (WORD)cbuf[extractbuff].CanCommu[replac]; } if ( power == 1 ) { /* Just a single power */ termout = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; while ( StartBuf[posisub] ) { if ( extractbuff == AT.allbufnum ) WildDollars(BHEAD &(StartBuf[posisub])); AT.WorkPointer = (WORD *)(((UBYTE *)(termout)) + AM.MaxTer); if ( InsertTerm(BHEAD term,replac,extractbuff, &(StartBuf[posisub]),termout,tepos) < 0 ) goto GenCall; AT.WorkPointer = termout + *termout; *AN.RepPoint = 1; AR.expchanged = 1; posisub += StartBuf[posisub]; /* For multiple table substitutions it may be better to do modulus arithmetic right here Turns out to be not very effective. if ( AN.ncmod != 0 ) { if ( Modulus(termout) ) goto GenCall; if ( !*termout ) goto Return0; } */ #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } if ( ( AS.Balancing && CC->numrhs == 0 ) && StartBuf[posisub] ) { if ( ( id = ConditionalGetAvailableThread() ) >= 0 ) { if ( BalanceRunThread(BHEAD id,termout,level) < 0 ) goto GenCall; } } else #endif if ( Generator(BHEAD termout,level) < 0 ) goto GenCall; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { dtype = 0; break; } #endif if ( iscopy == 0 && ( extractbuff != AM.dbufnum ) ) { /* There are cases in which a bigger buffer is created on the fly, like with wildcard buffers. We play it safe here. Maybe we can be more selective in some distant future? */ StartBuf = cbuf[extractbuff].Buffer; } } if ( extractbuff == AT.allbufnum ) { CBUF *Ce = cbuf + extractbuff; Ce->Pointer = Ce->rhs[Ce->numrhs--]; } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); dtype = 0; } #endif if ( iscopy ) { if ( d->nfactors > 1 ) { int j; for ( j = 0; j < d->nfactors; j++ ) { if ( d->factors[j].where ) M_free(d->factors[j].where,"Copy of factor"); } M_free(d->factors,"Dollar factors"); } M_free(d,"Copy of dollar variable"); d = 0; iscopy = 0; } AT.WorkPointer = termout; } else if ( i <= 1 ) { /* Use binomials */ LONG posit, olw; WORD *same, *ow = AT.WorkPointer; LONG olpw = AT.posWorkPointer; power1 = power+1; WantAddLongs(power1); olw = posit = AT.lWorkPointer; AT.lWorkPointer += power1; same = ++AT.WorkPointer; a = accum = ( AT.WorkPointer += power1+1 ); AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + 2*AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; AT.lWorkSpace[posit] = posisub; same[-1] = 0; *same = 1; *accum = 0; tepos = AR.TePos; i = 1; do { if ( StartBuf[AT.lWorkSpace[posit]] ) { if ( ( a = PasteTerm(BHEAD i-1,accum, &(StartBuf[AT.lWorkSpace[posit]]),i,*same) ) == 0 ) goto GenCall; AT.lWorkSpace[posit+1] = AT.lWorkSpace[posit]; same[1] = *same + 1; if ( i > 1 && AT.lWorkSpace[posit] < AT.lWorkSpace[posit-1] ) *same = 1; AT.lWorkSpace[posit] += StartBuf[AT.lWorkSpace[posit]]; i++; posit++; same++; } else { i--; posit--; same--; } if ( i > power ) { termout = AT.WorkPointer = a; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + 2*AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; if ( FiniTerm(BHEAD term,accum,termout,replac,tepos) ) goto GenCall; AT.WorkPointer = termout + *termout; *AN.RepPoint = 1; AR.expchanged = 1; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } if ( ( AS.Balancing && CC->numrhs == 0 ) && ( i > 0 ) && ( id = ConditionalGetAvailableThread() ) >= 0 ) { if ( BalanceRunThread(BHEAD id,termout,level) < 0 ) goto GenCall; } else #endif if ( Generator(BHEAD termout,level) ) goto GenCall; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { dtype = 0; break; } #endif if ( iscopy == 0 && ( extractbuff != AM.dbufnum ) ) StartBuf = cbuf[extractbuff].Buffer; i--; posit--; same--; } } while ( i > 0 ); #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); dtype = 0; } #endif if ( iscopy ) { if ( d->nfactors > 1 ) { int j; for ( j = 0; j < d->nfactors; j++ ) { if ( d->factors[j].where ) M_free(d->factors[j].where,"Copy of factor"); } M_free(d->factors,"Dollar factors"); } M_free(d,"Copy of dollar variable"); d = 0; iscopy = 0; } AT.WorkPointer = ow; AT.lWorkPointer = olw; AT.posWorkPointer = olpw; } else { /* No binomials */ LONG posit, olw, olpw = AT.posWorkPointer; WantAddLongs(power); posit = olw = AT.lWorkPointer; AT.lWorkPointer += power; a = accum = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + 2*AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; for ( i = 0; i < power; i++ ) AT.lWorkSpace[posit++] = posisub; posit = olw; *accum = 0; tepos = AR.TePos; i = 0; while ( i >= 0 ) { if ( StartBuf[AT.lWorkSpace[posit]] ) { if ( ( a = PasteTerm(BHEAD i,accum, &(StartBuf[AT.lWorkSpace[posit]]),1,1) ) == 0 ) goto GenCall; AT.lWorkSpace[posit] += StartBuf[AT.lWorkSpace[posit]]; i++; posit++; } else { AT.lWorkSpace[posit--] = posisub; i--; } if ( i >= power ) { termout = AT.WorkPointer = a; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + 2*AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; if ( FiniTerm(BHEAD term,accum,termout,replac,tepos) ) goto GenCall; AT.WorkPointer = termout + *termout; *AN.RepPoint = 1; AR.expchanged = 1; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } if ( ( AS.Balancing && CC->numrhs == 0 ) && ( i > 0 ) && ( id = ConditionalGetAvailableThread() ) >= 0 ) { if ( BalanceRunThread(BHEAD id,termout,level) < 0 ) goto GenCall; } else #endif if ( Generator(BHEAD termout,level) ) goto GenCall; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { dtype = 0; break; } #endif if ( iscopy == 0 && ( extractbuff != AM.dbufnum ) ) StartBuf = cbuf[extractbuff].Buffer; i--; posit--; } } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); dtype = 0; } #endif if ( iscopy ) { if ( d->nfactors > 1 ) { int j; for ( j = 0; j < d->nfactors; j++ ) { if ( d->factors[j].where ) M_free(d->factors[j].where,"Copy of factor"); } M_free(d->factors,"Dollar factors"); } M_free(d,"Copy of dollar variable"); d = 0; iscopy = 0; } AT.WorkPointer = accum; AT.lWorkPointer = olw; AT.posWorkPointer = olpw; } } else { /* Expression from disk */ POSITION StartPos; LONG position, olpw, opw, comprev, extra; RENUMBER renumber; WORD *Freeze, *aa, *dummies; replac = -replac-1; power = AN.TeSuOut; Freeze = AN.Frozen; if ( Expressions[replac].status == STOREDEXPRESSION ) { POSITION firstpos; SETSTARTPOS(firstpos); /* Note that AT.TMaddr is needed for GetTable just once! */ /* We need space for the previous term in the compression This is made available in AR.CompressBuffer, although we may get problems with this sooner or later. Hence we need to keep a set of pointers in AR.CompressBuffer Note that after the last call there has been no use made of AR.CompressPointer, so it points automatically at its original position! */ WantAddPointers(power+1); comprev = opw = AT.pWorkPointer; AT.pWorkPointer += power+1; WantAddPositions(power+1); position = olpw = AT.posWorkPointer; AT.posWorkPointer += power + 1; AT.pWorkSpace[comprev++] = AR.CompressPointer; for ( i = 0; i < power; i++ ) { PUTZERO(AT.posWorkSpace[position]); position++; } position = olpw; if ( ( renumber = GetTable(replac,&(AT.posWorkSpace[position]),1) ) == 0 ) goto GenCall; dummies = AT.WorkPointer; *dummies++ = AR.CurDum; AT.WorkPointer += power+2; accum = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + 2*AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; aa = AT.WorkPointer; *accum = 0; i = 0; StartPos = AT.posWorkSpace[position]; dummies[i] = AR.CurDum; while ( i >= 0 ) { skippedfirst: AR.CompressPointer = AT.pWorkSpace[comprev-1]; if ( ( extra = PasteFile(BHEAD i,accum,&(AT.posWorkSpace[position]) ,&a,renumber,Freeze,replac) ) < 0 ) goto GenCall; if ( Expressions[replac].numdummies > 0 ) { AR.CurDum = dummies[i] + Expressions[replac].numdummies; } if ( NOTSTARTPOS(firstpos) ) { if ( ISMINPOS(firstpos) || ISEQUALPOS(firstpos,AT.posWorkSpace[position]) ) { firstpos = AT.posWorkSpace[position]; /* ADDPOS(AT.posWorkSpace[position],extra * sizeof(WORD)); */ goto skippedfirst; } } if ( extra ) { /* ADDPOS(AT.posWorkSpace[position],extra * sizeof(WORD)); */ i++; AT.posWorkSpace[++position] = StartPos; AT.pWorkSpace[comprev++] = AR.CompressPointer; dummies[i] = AR.CurDum; } else { PUTZERO(AT.posWorkSpace[position]); position--; i--; AR.CurDum = dummies[i]; comprev--; } if ( i >= power ) { termout = AT.WorkPointer = a; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + 2*AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) goto OverWork; if ( FiniTerm(BHEAD term,accum,termout,replac,0) ) goto GenCall; if ( *termout ) { AT.WorkPointer = termout + *termout; *AN.RepPoint = 1; AR.expchanged = 1; #ifdef WITHPTHREADS if ( ( AS.Balancing && CC->numrhs == 0 ) && ( i > 0 ) && ( id = ConditionalGetAvailableThread() ) >= 0 ) { if ( BalanceRunThread(BHEAD id,termout,level) < 0 ) goto GenCall; } else #endif if ( Generator(BHEAD termout,level) ) goto GenCall; } i--; position--; AR.CurDum = dummies[i]; comprev--; } AT.WorkPointer = aa; } AT.WorkPointer = accum; AT.posWorkPointer = olpw; AT.pWorkPointer = opw; /* Bug fix. See also GetTable #ifdef WITHPTHREADS M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); #endif */ if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); } else { /* Active expression */ aa = accum = AT.WorkPointer; if ( ( (WORD *)(((UBYTE *)(AT.WorkPointer)) + 2 * AM.MaxTer + sizeof(WORD)) ) > AT.WorkTop ) goto OverWork; *accum++ = -1; AT.WorkPointer++; if ( DoOnePow(BHEAD term,power,replac,accum,aa,level,Freeze) ) goto GenCall; AT.WorkPointer = aa; } } Return0: AR.CurDum = DumNow; AN.RepPoint = RepSto; CC->numrhs = oldtoprhs; CC->Pointer = CC->Buffer + oldcpointer; CCC->numrhs = oldatoprhs; CCC->Pointer = CCC->Buffer + oldacpointer; return(0); GenCall: if ( AM.tracebackflag ) { termout = term; MLOCK(ErrorMessageLock); AO.OutFill = AO.OutputLine = (UBYTE *)AT.WorkPointer; AO.OutSkip = 3; FiniLine(); i = *termout; while ( --i >= 0 ) { TalToLine((UWORD)(*termout++)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); MesCall("Generator"); MUNLOCK(ErrorMessageLock); } CC->numrhs = oldtoprhs; CC->Pointer = CC->Buffer + oldcpointer; CCC->numrhs = oldatoprhs; CCC->Pointer = CCC->Buffer + oldacpointer; return(-1); OverWork: CC->numrhs = oldtoprhs; CC->Pointer = CC->Buffer + oldcpointer; CCC->numrhs = oldatoprhs; CCC->Pointer = CCC->Buffer + oldacpointer; MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* #] Generator : #[ DoOnePow : WORD DoOnePow(term,power,nexp,accum,aa,level,freeze) */ /** * Routine gets one power of an expression in the scratch system. * If there are more powers needed there will be a recursion. * * No attempt is made to use binomials because we have no * information about commuting properties. * * There is a searching for the contents of brackets if needed. * This searching may be rather slow because of the single links. * * @param term is the term we are adding to. * @param power is the power of the expression that we need. * @param nexp is the number of the expression. * @param accum is the accumulator of terms. It accepts the termfragments * that are made into a proper term in FiniTerm * @param aa points to the start of the entire accumulator. In *aa * we store the number of term fragments that are in the * accumulator. * @param level is the current depth in the tree of statements. It is * needed to continue to the next operation/substitution * with each generated term * @param freeze is the pointer to the bracket information that should * be matched. */ #ifdef WITHPTHREADS char freezestring[] = "freeze<-xxxx"; #endif int DoOnePow(PHEAD WORD *term, WORD power, WORD nexp, WORD * accum, WORD *aa, WORD level, WORD *freeze) { GETBIDENTITY POSITION oldposition, startposition; WORD *acc, *termout, fromfreeze = 0; WORD *oldipointer = AR.CompressPointer; FILEHANDLE *fi; WORD type, retval; WORD oldGetOneFile = AR.GetOneFile; WORD olddummies = AR.CurDum; WORD extradummies = Expressions[nexp].numdummies; /* The next code is for some tricky debugging. (5-jan-2010 JV) Normally it should be disabled. */ /* #ifdef WITHPTHREADS if ( freeze ) { MLOCK(ErrorMessageLock); if ( AT.identity < 10 ) { freezestring[8] = '0'+AT.identity; freezestring[9] = '>'; freezestring[10] = 0; } else if ( AT.identity < 100 ) { freezestring[8] = '0'+AT.identity/10; freezestring[9] = '0'+AT.identity%10; freezestring[10] = '>'; freezestring[11] = 0; } else { freezestring[8] = 0; } PrintTerm(freeze,freezestring); MUNLOCK(ErrorMessageLock); } #else if ( freeze ) PrintTerm(freeze,"freeze"); #endif */ type = Expressions[nexp].status; if ( type == HIDDENLEXPRESSION || type == HIDDENGEXPRESSION || type == DROPHLEXPRESSION || type == DROPHGEXPRESSION || type == UNHIDELEXPRESSION || type == UNHIDEGEXPRESSION ) { AR.GetOneFile = 2; fi = AR.hidefile; } else { AR.GetOneFile = 0; fi = AR.infile; } if ( fi->handle >= 0 ) { PUTZERO(oldposition); #ifdef WITHSEEK LOCK(AS.inputslock); SeekFile(fi->handle,&oldposition,SEEK_CUR); UNLOCK(AS.inputslock); #endif } else { SETBASEPOSITION(oldposition,fi->POfill-fi->PObuffer); } if ( freeze && ( Expressions[nexp].bracketinfo != 0 ) ) { POSITION *brapos; /* There is a bracket index AR.CompressPointer = oldipointer; */ (*aa)++; power--; if ( ( brapos = FindBracket(nexp,freeze) ) == 0 ) goto EndExpr; startposition = *brapos; goto doterms; } startposition = AS.OldOnFile[nexp]; retval = GetOneTerm(BHEAD accum,fi,&startposition,0); if ( retval > 0 ) { /* Skip prototype */ (*aa)++; power--; doterms: AR.CompressPointer = oldipointer; for (;;) { retval = GetOneTerm(BHEAD accum,fi,&startposition,0); if ( retval <= 0 ) break; /* Here should come the code to test for []. */ if ( freeze ) { WORD *t, *m, *r, *mstop; WORD *tset; t = accum; m = freeze; m += *m; m -= ABS(m[-1]); mstop = m; m = freeze + 1; r = t; r += *t; r -= ABS(r[-1]); t++; tset = t; while ( t < r && *t != HAAKJE ) t += t[1]; if ( t >= r ) { if ( m < mstop ) { if ( fromfreeze ) goto EndExpr; goto NextTerm; } t = tset; } else { r = tset; while ( r < t && m < mstop ) { if ( *r == *m ) { m++; r++; } else { if ( fromfreeze ) goto EndExpr; goto NextTerm; } } if ( r < t || m < mstop ) { if ( fromfreeze ) goto EndExpr; goto NextTerm; } } fromfreeze = 1; r = tset; m = accum; m += *m; while ( t < m ) *r++ = *t++; *accum = WORDDIF(r,accum); } if ( extradummies > 0 ) { if ( olddummies > AM.IndDum ) { MoveDummies(BHEAD accum,olddummies-AM.IndDum); } AR.CurDum = olddummies+extradummies; } acc = accum; acc += *acc; if ( power <= 0 ) { termout = acc; AT.WorkPointer = (WORD *)(((UBYTE *)(acc)) + 2*AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } if ( FiniTerm(BHEAD term,aa,termout,nexp,0) ) goto PowCall; if ( *termout ) { MarkPolyRatFunDirty(termout) /* PolyFunDirty(BHEAD termout); */ AT.WorkPointer = termout + *termout; *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,level) ) goto PowCall; } } else { if ( acc > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } if ( DoOnePow(BHEAD term,power,nexp,acc,aa,level,freeze) ) goto PowCall; } NextTerm:; AR.CompressPointer = oldipointer; } EndExpr: (*aa)--; } AR.CompressPointer = oldipointer; if ( fi->handle >= 0 ) { #ifdef WITHSEEK LOCK(AS.inputslock); SeekFile(fi->handle,&oldposition,SEEK_SET); UNLOCK(AS.inputslock); if ( ISNEGPOS(oldposition) ) { MLOCK(ErrorMessageLock); MesPrint("File error"); goto PowCall2; } #endif } else { fi->POfill = fi->PObuffer + BASEPOSITION(oldposition); } AR.GetOneFile = oldGetOneFile; AR.CurDum = olddummies; return(0); PowCall:; MLOCK(ErrorMessageLock); #ifdef WITHSEEK PowCall2:; #endif MesCall("DoOnePow"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] DoOnePow : #[ Deferred : WORD Deferred(term,level) */ /** * Picks up the deferred brackets. * These are the bracket contents of which we postpone the reading * when we use the 'Keep Brackets' statement. These contents are * multiplying the terms just before they are sent to the sorting * system. * Special attention goes to having it thread-safe * We have to lock positioning the file and reading it in * a thread specific buffer. * * @param term The term that must be multiplied by the contents of the * current bracket * @param level The compiler level. This is needed because after * multiplying term by term we call Generator again. */ int Deferred(PHEAD WORD *term, WORD level) { GETBIDENTITY POSITION startposition; WORD *t, *m, *mstop, *tstart, decr, oldb, *termout, i, *oldwork, retval; WORD *oldipointer = AR.CompressPointer, *oldPOfill = AR.infile->POfill; WORD oldGetOneFile = AR.GetOneFile; AR.GetOneFile = 1; oldwork = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); termout = AT.WorkPointer; AR.DeferFlag = 0; startposition = AR.DefPosition; /* Store old position */ if ( AR.infile->handle >= 0 ) { /* PUTZERO(oldposition); SeekFile(AR.infile->handle,&oldposition,SEEK_CUR); */ } else { /* SETBASEPOSITION(oldposition,AR.infile->POfill-AR.infile->PObuffer); */ AR.infile->POfill = (WORD *)((UBYTE *)(AR.infile->PObuffer) +BASEPOSITION(startposition)); } /* Look in the CompressBuffer where the bracket contents start */ t = m = AR.CompressBuffer; t += *t; mstop = t - ABS(t[-1]); m++; while ( *m != HAAKJE && m < mstop ) m += m[1]; if ( m >= mstop ) { /* No deferred action! */ AT.WorkPointer = term + *term; if ( Generator(BHEAD term,level) ) goto DefCall; AR.DeferFlag = 1; AT.WorkPointer = oldwork; AR.GetOneFile = oldGetOneFile; return(0); } mstop = m + m[1]; decr = WORDDIF(mstop,AR.CompressBuffer)-1; tstart = AR.CompressPointer + decr; m = AR.CompressBuffer; t = AR.CompressPointer; i = *m; NCOPY(t,m,i); oldb = *tstart; AR.TePos = 0; AN.TeSuOut = 0; /* Status: First bracket content starts at mstop. Next term starts at startposition. Decompression information is in AR.CompressPointer. The outside of the bracket runs from AR.CompressBuffer+1 to mstop. */ for(;;) { *tstart = *(AR.CompressPointer)-decr; AR.CompressPointer = AR.CompressPointer+AR.CompressPointer[0]; if ( InsertTerm(BHEAD term,0,AM.rbufnum,tstart,termout,0) < 0 ) { goto DefCall; } *tstart = oldb; AT.WorkPointer = termout + *termout; if ( Generator(BHEAD termout,level) ) goto DefCall; AR.CompressPointer = oldipointer; AT.WorkPointer = termout; retval = GetOneTerm(BHEAD AT.WorkPointer,AR.infile,&startposition,0); if ( retval >= 0 ) AR.CompressPointer = oldipointer; if ( retval <= 0 ) break; t = AR.CompressPointer; if ( *t < (1 + decr + ABS(*(t+*t-1))) ) break; t++; m = AR.CompressBuffer+1; while ( m < mstop ) { if ( *m != *t ) goto Thatsit; m++; t++; } } Thatsit:; /* Finished. Reposition the file, restore information and return. */ if ( AR.infile->handle < 0 ) AR.infile->POfill = oldPOfill; AR.DeferFlag = 1; AR.GetOneFile = oldGetOneFile; AT.WorkPointer = oldwork; return(0); DefCall:; MLOCK(ErrorMessageLock); MesCall("Deferred"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] Deferred : #[ PrepPoly : WORD PrepPoly(term,par) */ /** * Routine checks whether the count of function AR.PolyFun is zero * or one. If it is one and it has one scalarlike argument the * coefficient of the term is pulled inside the argument. * If the count is zero a new function is made with the coefficient * as its only argument. The function should be placed at its * proper position. * * When this function is active it places the PolyFun as last * object before the coefficient. This is needed because otherwise * the compress algorithm has problems in MergePatches. * * The bracket routine should also place the PolyFun at a * comparable spot. * The compression should then stop at the PolyFun. It doesn't * really have to stop when writing the final result but this may * be too complicated. * * The parameter par tells whether we are at groundlevel or * inside a function or dollar variable. */ int PrepPoly(PHEAD WORD *term,WORD par) { GETBIDENTITY WORD count = 0, i, jcoef, ncoef; WORD *t, *m, *r, *tstop, *poly = 0, *v, *w, *vv, *ww; WORD *oldworkpointer = AT.WorkPointer; /* The problem here is that the function will be forced into 'long' notation. After this -SNUMBER,1 becomes 6,0,4,1,1,3 and the pattern matcher cannot match a short 1 with a long 1. But because this is an undocumented feature for very special purposes, we don't do anything about it. (30-aug-2011) */ if ( AR.PolyFunType == 2 && AR.PolyFunExp != 2 ) { WORD oldtype = AR.SortType; AR.SortType = SORTHIGHFIRST; if ( poly_ratfun_normalize(BHEAD term) != 0 ) Terminate(-1); /* if ( ReadPolyRatFun(BHEAD term) != 0 ) Terminate(-1); */ oldworkpointer = AT.WorkPointer; AR.SortType = oldtype; } AT.PolyAct = 0; t = term; GETSTOP(t,tstop); t++; while ( t < tstop ) { if ( *t == AR.PolyFun ) { if ( count > 0 ) return(0); poly = t; count++; } t += t[1]; } r = m = term + *term; i = ABS(m[-1]); if ( par > 0 ) { if ( count == 0 ) return(0); else if ( AR.PolyFunType == 1 || (AR.PolyFunType == 2 && AR.PolyFunExp == 2) ) goto DoOne; else if ( AR.PolyFunType == 2 ) goto DoTwo; else goto DoError; } else if ( count == 0 ) { /* #[ Create a PolyFun : */ poly = t = tstop; if ( i == 3 && m[-2] == 1 && (m[-3]&MAXPOSITIVE) == m[-3] ) { *m++ = AR.PolyFun; if ( AR.PolyFunType == 1 || (AR.PolyFunType == 2 && AR.PolyFunExp == 2) ) { *m++ = FUNHEAD+2; FILLFUN(m) *m++ = -SNUMBER; *m = m[-2-FUNHEAD] < 0 ? -m[-4-FUNHEAD]: m[-4-FUNHEAD]; m++; } else if ( AR.PolyFunType == 2 ) { *m++ = FUNHEAD+4; FILLFUN(m) *m++ = -SNUMBER; *m = m[-2-FUNHEAD] < 0 ? -m[-4-FUNHEAD]: m[-4-FUNHEAD]; m++; *m++ = -SNUMBER; *m++ = 1; } } else { WORD *vm; r = tstop; if ( AR.PolyFunType == 1 || (AR.PolyFunType == 2 && AR.PolyFunExp == 2) ) { *m++ = AR.PolyFun; *m++ = FUNHEAD+ARGHEAD+i+1; FILLFUN(m) *m++ = ARGHEAD+i+1; *m++ = 0; FILLARG(m) *m++ = i+1; NCOPY(m,r,i); } else if ( AR.PolyFunType == 2 ) { WORD *num, *den, size, sign, sizenum, sizeden; if ( m[-1] < 0 ) { sign = -1; size = -m[-1]; } else { sign = 1; size = m[-1]; } num = m - size; size = (size-1)/2; den = num + size; sizenum = size; while ( num[sizenum-1] == 0 ) sizenum--; sizeden = size; while ( den[sizeden-1] == 0 ) sizeden--; v = m; AT.PolyAct = WORDDIF(v,term); *v++ = AR.PolyFun; v++; FILLFUN(v); vm = v; *v++ = ARGHEAD+2*sizenum+2; *v++ = 0; FILLARG(v); *v++ = 2*sizenum+2; for ( i = 0; i < sizenum; i++ ) *v++ = num[i]; *v++ = 1; for ( i = 1; i < sizenum; i++ ) *v++ = 0; *v++ = sign*(2*sizenum+1); if ( ToFast(vm,vm) ) v = vm+2; vm = v; *v++ = ARGHEAD+2*sizeden+2; *v++ = 0; FILLARG(v); *v++ = 2*sizeden+2; for ( i = 0; i < sizeden; i++ ) *v++ = den[i]; *v++ = 1; for ( i = 1; i < sizeden; i++ ) *v++ = 0; *v++ = 2*sizeden+1; if ( ToFast(vm,vm) ) v = vm+2; i = v-m; m[1] = i; w = num; NCOPY(w,m,i); *w++ = 1; *w++ = 1; *w++ = 3; *term = w - term; return(0); } } /* #] Create a PolyFun : */ } else if ( AR.PolyFunType == 1 || (AR.PolyFunType == 2 && AR.PolyFunExp == 2) ) { DoOne:; /* #[ One argument : */ m = term + *term; r = poly + poly[1]; if ( ( poly[1] == FUNHEAD+2 && poly[FUNHEAD+1] == 0 && poly[FUNHEAD] == -SNUMBER ) || poly[1] == FUNHEAD ) return(1); t = poly + FUNHEAD; if ( t >= r ) return(0); if ( m[-1] == 3 && *tstop == 1 && tstop[1] == 1 ) { i = poly[1]; t = poly; NCOPY(m,t,i); } else if ( *t <= -FUNCTION ) { if ( t+1 < r ) return(0); /* More than one argument */ r = tstop; *m++ = AR.PolyFun; *m++ = FUNHEAD*2+ARGHEAD+i+1; FILLFUN(m) *m++ = FUNHEAD+ARGHEAD+i+1; *m++ = 0; FILLARG(m) *m++ = FUNHEAD+i+1; *m++ = -*t++; *m++ = FUNHEAD; FILLFUN(m) NCOPY(m,r,i); } else if ( *t < 0 ) { if ( t+2 < r ) return(0); /* More than one argument */ r = tstop; if ( *t == -SNUMBER ) { if ( t[1] == 0 ) return(1); /* Term should be zero now */ *m = AR.PolyFun; w = m+1; m += FUNHEAD+ARGHEAD; v = m; *m++ = 5+i; *m++ = SNUMBER; *m++ = 4; *m++ = t[1]; *m++ = 1; NCOPY(m,r,i); if ( m >= AT.WorkSpace && m < AT.WorkTop ) AT.WorkPointer = m; if ( Normalize(BHEAD v) ) Terminate(-1); AT.WorkPointer = oldworkpointer; m = w; if ( *v == 4 && v[2] == 1 && (v[1]&MAXPOSITIVE) == v[1] ) { *m++ = FUNHEAD+2; FILLFUN(m) *m++ = -SNUMBER; *m++ = v[3] < 0 ? -v[1] : v[1]; } else if ( *v == 0 ) return(1); else { *m++ = FUNHEAD+ARGHEAD+*v; FILLFUN(m) *m++ = ARGHEAD+*v; *m++ = 0; FILLARG(m) m = v + *v; } } else if ( *t == -SYMBOL ) { *m++ = AR.PolyFun; *m++ = FUNHEAD+ARGHEAD+5+i; FILLFUN(m) *m++ = ARGHEAD+5+i; *m++ = 0; FILLARG(m) *m++ = 5+i; *m++ = SYMBOL; *m++ = 4; *m++ = t[1]; *m++ = 1; NCOPY(m,r,i); } else return(0); /* Not symbol-like */ } else { if ( t + *t < r ) return(0); /* More than one argument */ i = m[-1]; *m++ = AR.PolyFun; w = m; m += ARGHEAD+FUNHEAD-1; t += ARGHEAD; jcoef = i < 0 ? (i+1)>>1:(i-1)>>1; v = t; /* Test now the scalar nature of the argument. No indices allowed. */ while ( t < r ) { WORD *vstop; vv = t + *t; vstop = vv - ABS(vv[-1]); t++; while( t < vstop ) { if ( *t == INDEX ) return(0); t += t[1]; } t = vv; } /* Now multiply each term by the coefficient. */ t = v; while ( t < r ) { ww = m; v = t + *t; ncoef = v[-1]; vv = v - ABS(ncoef); if ( ncoef < 0 ) ncoef++; else ncoef--; ncoef >>= 1; while ( t < vv ) *m++ = *t++; if ( MulRat(BHEAD (UWORD *)vv,ncoef,(UWORD *)tstop,jcoef, (UWORD *)m,&ncoef) ) Terminate(-1); ncoef *= 2; m += ABS(ncoef); if ( ncoef < 0 ) ncoef--; else ncoef++; *m++ = ncoef; *ww = WORDDIF(m,ww); if ( AN.ncmod != 0 ) { if ( Modulus(ww) ) Terminate(-1); if ( *ww == 0 ) return(1); m = ww + *ww; } t = v; } *w = (WORDDIF(m,w))+1; w[FUNHEAD-1] = w[0] - FUNHEAD; w[FUNHEAD] = 0; w[1] = 0; /* omission survived for years. 23-mar-2006 JV */ w += FUNHEAD-1; if ( ToFast(w,w) ) { if ( *w <= -FUNCTION ) { w[-FUNHEAD+1] = FUNHEAD+1; m = w+1; } else { w[-FUNHEAD+1] = FUNHEAD+2; m = w+2; } } } t = poly + poly[1]; while ( t < tstop ) *poly++ = *t++; /* #] One argument : */ } else if ( AR.PolyFunType == 2 ) { DoTwo:; /* #[ Two arguments : */ WORD *num, *den, size, sign, sizenum, sizeden; /* First make sure that the PolyFun is last */ m = term + *term; if ( poly + poly[1] < tstop ) { for ( i = 0; i < poly[1]; i++ ) m[i] = poly[i]; t = poly; v = poly + poly[1]; while ( v < tstop ) *t++ = *v++; poly = t; for ( i = 0; i < m[1]; i++ ) t[i] = m[i]; t += m[1]; } AT.PolyAct = WORDDIF(poly,term); /* If needed we convert the coefficient into a PolyRatFun and then we call poly_ratfun_normalize */ if ( m[-1] == 3 && m[-2] == 1 && m[-3] == 1 ) return(0); if ( AR.PolyFunExp != 1 ) { if ( m[-1] < 0 ) { sign = -1; size = -m[-1]; } else { sign = 1; size = m[-1]; } num = m - size; size = (size-1)/2; den = num + size; sizenum = size; while ( num[sizenum-1] == 0 ) sizenum--; sizeden = size; while ( den[sizeden-1] == 0 ) sizeden--; v = m; *v++ = AR.PolyFun; *v++ = FUNHEAD + 2*(ARGHEAD+sizenum+sizeden+2); /* *v++ = MUSTCLEANPRF; */ *v++ = 0; FILLFUN3(v); *v++ = ARGHEAD+2*sizenum+2; *v++ = 0; FILLARG(v); *v++ = 2*sizenum+2; for ( i = 0; i < sizenum; i++ ) *v++ = num[i]; *v++ = 1; for ( i = 1; i < sizenum; i++ ) *v++ = 0; *v++ = sign*(2*sizenum+1); *v++ = ARGHEAD+2*sizeden+2; *v++ = 0; FILLARG(v); *v++ = 2*sizeden+2; for ( i = 0; i < sizeden; i++ ) *v++ = den[i]; *v++ = 1; for ( i = 1; i < sizeden; i++ ) *v++ = 0; *v++ = 2*sizeden+1; w = num; i = v - m; NCOPY(w,m,i); } else { w = m-ABS(m[-1]); } *w++ = 1; *w++ = 1; *w++ = 3; *term = w - term; { WORD oldtype = AR.SortType; AR.SortType = SORTHIGHFIRST; /* if ( count > 0 ) poly_ratfun_normalize(BHEAD term); else ReadPolyRatFun(BHEAD term); */ poly_ratfun_normalize(BHEAD term); /* oldworkpointer = AT.WorkPointer; */ AR.SortType = oldtype; } goto endofit; /* #] Two arguments : */ } else { DoError:; MLOCK(ErrorMessageLock); MesPrint("Illegal value for PolyFunType in PrepPoly"); MUNLOCK(ErrorMessageLock); Terminate(-1); } r = term + *term; AT.PolyAct = WORDDIF(poly,term); while ( r < m ) *poly++ = *r++; *poly++ = 1; *poly++ = 1; *poly++ = 3; *term = WORDDIF(poly,term); endofit:; return(0); } /* #] PrepPoly : #[ PolyFunMul : WORD PolyFunMul(term) */ /** * Multiplies the arguments of multiple occurrences of the polyfun. * In this routine we do the original PolyFun with one argument only. * The PolyRatFun (PolyFunType = 2) is done in a dedicated routine * in the file polywrap.cc * The new result is written over the old result. * * @param term It contains the input term and later the output. * @return Normal conventions (OK = 0). */ int PolyFunMul(PHEAD WORD *term) { GETBIDENTITY WORD *t, *fun1, *fun2, *t1, *t2, *m, *w, *ww, *tt1, *tt2, *tt4, *arg1, *arg2; WORD *tstop, i, dirty = 0, OldPolyFunPow = AR.PolyFunPow, minp1, minp2; WORD n1, n2, i1, i2, l1, l2, l3, l4, action = 0, noac = 0; int retval = 0; if ( AR.PolyFunType == 2 && AR.PolyFunExp == 1 ) { WORD pow = 0, pow1; t = term + 1; t1 = term + *term; t1 -= ABS(t1[-1]); w = t; while ( t < t1 ) { if ( *t != AR.PolyFun ) { SkipFun: if ( t == w ) { t += t[1]; w = t; } else { i = t[1]; NCOPY(w,t,i) } continue; } pow1 = 0; t2 = t + t[1]; t += FUNHEAD; if ( *t < 0 ) { if ( *t == -SYMBOL && t[1] == AR.PolyFunVar ) pow1++; else if ( *t != -SNUMBER ) goto NoLegal; t += 2; } else if ( t[0] == ARGHEAD+8 && t[ARGHEAD] == 8 && t[ARGHEAD+1] == SYMBOL && t[ARGHEAD+3] == AR.PolyFunVar && t[ARGHEAD+5] == 1 && t[ARGHEAD+6] == 1 && t[ARGHEAD+7] == 3 ) { pow1 += t[ARGHEAD+4]; t += *t; } else { NoLegal: MLOCK(ErrorMessageLock); MesPrint("Illegal term with divergence in PolyRatFun"); MesCall("PolyFunMul"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( *t < 0 ) { if ( *t == -SYMBOL && t[1] == AR.PolyFunVar ) pow1--; else if ( *t != -SNUMBER ) goto NoLegal; t += 2; } else if ( t[0] == ARGHEAD+8 && t[ARGHEAD] == 8 && t[ARGHEAD+1] == SYMBOL && t[ARGHEAD+3] == AR.PolyFunVar && t[ARGHEAD+5] == 1 && t[ARGHEAD+6] == 1 && t[ARGHEAD+7] == 3 ) { pow1 -= t[ARGHEAD+4]; t += *t; } else goto NoLegal; if ( t == t2 ) pow += pow1; else goto SkipFun; } m = w; *w++ = AR.PolyFun; *w++ = 0; FILLFUN(w); if ( pow > 1 ) { *w++ = 8+ARGHEAD; *w++ = 0; FILLARG(w); *w++ = 8; *w++ = SYMBOL; *w++ = 4; *w++ = AR.PolyFunVar; *w++ = pow; *w++ = 1; *w++ = 1; *w++ = 3; *w++ = -SNUMBER; *w++ = 1; } else if ( pow == 1 ) { *w++ = -SYMBOL; *w++ = AR.PolyFunVar; *w++ = -SNUMBER; *w++ = 1; } else if ( pow < -1 ) { *w++ = -SNUMBER; *w++ = 1; *w++ = 8+ARGHEAD; *w++ = 0; FILLARG(w); *w++ = 8; *w++ = SYMBOL; *w++ = 4; *w++ = AR.PolyFunVar; *w++ = -pow; *w++ = 1; *w++ = 1; *w++ = 3; } else if ( pow == -1 ) { *w++ = -SNUMBER; *w++ = 1; *w++ = -SYMBOL; *w++ = AR.PolyFunVar; } else { *w++ = -SNUMBER; *w++ = 1; *w++ = -SNUMBER; *w++ = 1; } m[1] = w - m; *w++ = 1; *w++ = 1; *w++ = 3; *term = w - term; if ( w > AT.WorkSpace && w < AT.WorkTop ) AT.WorkPointer = w; return(0); } ReStart: if ( AR.PolyFunType == 2 && ( ( AR.PolyFunExp != 2 ) || ( AR.PolyFunExp == 2 && AN.PolyNormFlag > 1 ) ) ) { WORD count1 = 0, count2 = 0, count3; WORD oldtype = AR.SortType; t = term + 1; t1 = term + *term; t1 -= ABS(t1[-1]); while ( t < t1 ) { if ( *t == AR.PolyFun ) { if ( t[2] && dirty == 0 ) { /* Any dirty flag on? */ dirty = 1; /* ReadPolyRatFun(BHEAD term); */ /* ToPolyFunGeneral(BHEAD term); */ poly_ratfun_normalize(BHEAD term); if ( term[0] == 0 ) return(0); count1 = 0; action++; goto ReStart; } t2 = t + t[1]; tt2 = t+FUNHEAD; count3 = 0; while ( tt2 < t2 ) { count3++; NEXTARG(tt2); } if ( count3 == 2 ) { count1++; if ( ( t[2] & MUSTCLEANPRF ) != 0 ) { /* Better civilize this guy */ action++; w = AT.WorkPointer; AR.SortType = SORTHIGHFIRST; t2 = t + t[1]; tt2 = t+FUNHEAD; while ( tt2 < t2 ) { if ( *tt2 > 0 ) { tt4 = tt2; tt1 = tt2 + ARGHEAD; tt2 += *tt2; NewSort(BHEAD0); while ( tt1 < tt2 ) { i = *tt1; ww = w; NCOPY(ww,tt1,i); AT.WorkPointer = ww; Normalize(BHEAD w); StoreTerm(BHEAD w); } EndSort(BHEAD w,1); ww = w; while ( *ww ) ww += *ww; if ( ww-w != *tt4-ARGHEAD ) { /* Little problem */ /* Solution: brute force copy Maybe it will never come here???? */ WORD *r1 = TermMalloc("PolyFunMul"); WORD ii = (ww-w)-(*tt4-ARGHEAD); /* increment */ WORD *r2 = tt4+ARGHEAD, *r3, *r4 = r1; i = r2 - term; r3 = term; NCOPY(r4,r3,i); i = ww-w; ww = w; NCOPY(r4,ww,i); r3 = tt2; i = term+*term-tt2; NCOPY(r4,r3,i); *r1 = i = r4-r1; r4 = term; r3 = r1; NCOPY(r4,r3,i); t[1] += ii; t1 += ii; *tt4 += ii; tt2 = tt4 + *tt4; TermFree(r1,"PolyFunMul"); } else { i = ww-w; ww = w; tt1 = tt4+ARGHEAD; NCOPY(tt1,ww,i); AT.WorkPointer = w; } } else if ( *tt2 <= -FUNCTION ) tt2++; else tt2 += 2; } AR.SortType = oldtype; } } } t += t[1]; } if ( count1 <= 1 ) { goto checkaction; } if ( AR.PolyFunExp == 1 ) { t = term + *term; t -= ABS(t[-1]); *t++ = 1; *t++ = 1; *t++ = 3; *term = t - term; } { AR.SortType = SORTHIGHFIRST; /* retval = ReadPolyRatFun(BHEAD term); */ /* ToPolyFunGeneral(BHEAD term); */ retval = poly_ratfun_normalize(BHEAD term); if ( *term == 0 ) return(retval); AR.SortType = oldtype; } t = term + 1; t1 = term + *term; t1 -= ABS(t1[-1]); while ( t < t1 ) { if ( *t == AR.PolyFun ) { t2 = t + t[1]; tt2 = t+FUNHEAD; count3 = 0; while ( tt2 < t2 ) { count3++; NEXTARG(tt2); } if ( count3 == 2 ) { count2++; } } t += t[1]; } if ( count1 >= count2 ) { t = term + 1; while ( t < t1 ) { if ( *t == AR.PolyFun ) { t2 = t; t = t + t[1]; t2[2] |= (DIRTYFLAG|MUSTCLEANPRF); t2 += FUNHEAD; while ( t2 < t ) { if ( *t2 > 0 ) t2[1] = DIRTYFLAG; NEXTARG(t2); } } else t += t[1]; } } w = term + *term; if ( w > AT.WorkSpace && w < AT.WorkTop ) AT.WorkPointer = w; checkaction: if ( action ) retval = action; return(retval); } retry: if ( term >= AT.WorkSpace && term+*term < AT.WorkTop ) AT.WorkPointer = term + *term; GETSTOP(term,tstop); t = term+1; while ( *t != AR.PolyFun && t < tstop ) t += t[1]; while ( t < tstop && *t == AR.PolyFun ) { if ( t[1] > FUNHEAD ) { if ( t[FUNHEAD] < 0 ) { if ( t[FUNHEAD] <= -FUNCTION && t[1] == FUNHEAD+1 ) break; if ( t[FUNHEAD] > -FUNCTION && t[1] == FUNHEAD+2 ) { if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] == 0 ) { *term = 0; return(0); } break; } } else if ( t[FUNHEAD] == t[1] - FUNHEAD ) break; } noac = 1; t += t[1]; } if ( *t != AR.PolyFun || t >= tstop ) goto done; fun1 = t; t += t[1]; while ( t < tstop && *t == AR.PolyFun ) { if ( t[1] > FUNHEAD ) { if ( t[FUNHEAD] < 0 ) { if ( t[FUNHEAD] <= -FUNCTION && t[1] == FUNHEAD+1 ) break; if ( t[FUNHEAD] > -FUNCTION && t[1] == FUNHEAD+2 ) { if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] == 0 ) { *term = 0; return(0); } break; } } else if ( t[FUNHEAD] == t[1] - FUNHEAD ) break; } noac = 1; t += t[1]; } if ( *t != AR.PolyFun || t >= tstop ) goto done; fun2 = t; /* We have two functions of the proper type. Count terms (needed for the specials) */ t = fun1 + FUNHEAD; if ( *t < 0 ) { n1 = 1; arg1 = AT.WorkPointer; ToGeneral(t,arg1,1); AT.WorkPointer = arg1 + *arg1; } else { t += ARGHEAD; n1 = 0; t1 = fun1 + fun1[1]; arg1 = t; while ( t < t1 ) { n1++; t += *t; } } t = fun2 + FUNHEAD; if ( *t < 0 ) { n2 = 1; arg2 = AT.WorkPointer; ToGeneral(t,arg2,1); AT.WorkPointer = arg2 + *arg2; } else { t += ARGHEAD; n2 = 0; t2 = fun2 + fun2[1]; arg2 = t; while ( t < t2 ) { n2++; t += *t; } } /* Now we can start the multiplications. We first multiply the terms without coefficients, then normalize, and finally put the coefficients in place. This is because one has often truncated series and the high powers may get killed, while their coefficients are the most expensive ones. Note: We may run into fun(-SNUMBER,value) */ w = AT.WorkPointer; NewSort(BHEAD0); if ( AR.PolyFunType == 2 && AR.PolyFunExp == 2 ) { AT.TrimPower = 1; /* We have to find the lowest power in both polynomials. This will be needed to temporarily correct the AR.PolyFunPow */ minp1 = MAXPOWER; for ( t1 = arg1, i1 = 0; i1 < n1; i1++, t1 += *t1 ) { if ( *t1 == 4 ) { if ( minp1 > 0 ) minp1 = 0; } else if ( ABS(t1[*t1-1]) == (*t1-1) ) { if ( minp1 > 0 ) minp1 = 0; } else { if ( t1[1] == SYMBOL && t1[2] == 4 && t1[3] == AR.PolyFunVar ) { if ( t1[4] < minp1 ) minp1 = t1[4]; } else { MesPrint("Illegal term in expanded polyratfun."); goto PolyCall; } } } minp2 = MAXPOWER; for ( t2 = arg2, i2 = 0; i2 < n2; i2++, t2 += *t2 ) { if ( *t2 == 4 ) { if ( minp2 > 0 ) minp2 = 0; } else if ( ABS(t2[*t2-1]) == (*t2-1) ) { if ( minp2 > 0 ) minp2 = 0; } else { if ( t2[1] == SYMBOL && t2[2] == 4 && t2[3] == AR.PolyFunVar ) { if ( t2[4] < minp2 ) minp2 = t2[4]; } else { MesPrint("Illegal term in expanded polyratfun."); goto PolyCall; } } } AR.PolyFunPow += minp1+minp2; } for ( t1 = arg1, i1 = 0; i1 < n1; i1++, t1 += *t1 ) { for ( t2 = arg2, i2 = 0; i2 < n2; i2++, t2 += *t2 ) { m = w; m++; GETSTOP(t1,tt1); t = t1 + 1; while ( t < tt1 ) *m++ = *t++; GETSTOP(t2,tt2); t = t2+1; while ( t < tt2 ) *m++ = *t++; *m++ = 1; *m++ = 1; *m++ = 3; *w = WORDDIF(m,w); AT.WorkPointer = m; if ( Normalize(BHEAD w) ) { LowerSortLevel(); goto PolyCall; } if ( *w ) { m = w + *w; if ( m[-1] != 3 || m[-2] != 1 || m[-3] != 1 ) { l3 = REDLENG(m[-1]); m -= ABS(m[-1]); t = t1 + *t1 - 1; l1 = REDLENG(*t); if ( MulRat(BHEAD (UWORD *)m,l3,(UWORD *)tt1,l1,(UWORD *)m,&l4) ) { LowerSortLevel(); goto PolyCall; } if ( AN.ncmod != 0 && TakeModulus((UWORD *)m,&l4,AC.cmod,AN.ncmod,UNPACK|AC.modmode) ) { LowerSortLevel(); goto PolyCall; } if ( l4 == 0 ) continue; t = t2 + *t2 - 1; l2 = REDLENG(*t); if ( MulRat(BHEAD (UWORD *)m,l4,(UWORD *)tt2,l2,(UWORD *)m,&l3) ) { LowerSortLevel(); goto PolyCall; } if ( AN.ncmod != 0 && TakeModulus((UWORD *)m,&l3,AC.cmod,AN.ncmod,UNPACK|AC.modmode) ) { LowerSortLevel(); goto PolyCall; } } else { m -= 3; t = t1 + *t1 - 1; l1 = REDLENG(*t); t = t2 + *t2 - 1; l2 = REDLENG(*t); if ( MulRat(BHEAD (UWORD *)tt1,l1,(UWORD *)tt2,l2,(UWORD *)m,&l3) ) { LowerSortLevel(); goto PolyCall; } if ( AN.ncmod != 0 && TakeModulus((UWORD *)m,&l3,AC.cmod,AN.ncmod,UNPACK|AC.modmode) ) { LowerSortLevel(); goto PolyCall; } } if ( l3 == 0 ) continue; l3 = INCLENG(l3); m += ABS(l3); m[-1] = l3; *w = WORDDIF(m,w); AT.WorkPointer = m; if ( StoreTerm(BHEAD w) ) { LowerSortLevel(); goto PolyCall; } } } } if ( EndSort(BHEAD w,0) < 0 ) goto PolyCall; AR.PolyFunPow = OldPolyFunPow; AT.TrimPower = 0; if ( *w == 0 ) { *term = 0; return(0); } t = w; while ( *t ) t += *t; AT.WorkPointer = t; n1 = WORDDIF(t,w); t1 = term; while ( t1 < fun1 ) *t++ = *t1++; t2 = t; *t++ = AR.PolyFun; *t++ = FUNHEAD+ARGHEAD+n1; *t++ = 0; FILLFUN3(t) *t++ = ARGHEAD+n1; *t++ = 0; FILLARG(t) NCOPY(t,w,n1); if ( ToFast(t2+FUNHEAD,t2+FUNHEAD) ) { if ( t2[FUNHEAD] > -FUNCTION ) t2[1] = FUNHEAD+2; else t2[FUNHEAD] = FUNHEAD+1; t = t2 + t2[1]; } t1 = fun1 + fun1[1]; while ( t1 < fun2 ) *t++ = *t1++; t1 = fun2 + fun2[1]; t2 = term + *term; while ( t1 < t2 ) *t++ = *t1++; *AT.WorkPointer = n1 = WORDDIF(t,AT.WorkPointer); if ( n1*((LONG)sizeof(WORD)) > AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex (%d words). MaxTermSize (%l words) is too small.", n1, AM.MaxTer/(LONG)sizeof(WORD) ); goto PolyCall2; } m = term; t = AT.WorkPointer; NCOPY(m,t,n1); action++; goto retry; done: AT.WorkPointer = term + *term; if ( action && noac ) { if ( Normalize(BHEAD term) ) goto PolyCall; AT.WorkPointer = term + *term; } return(0); PolyCall:; MLOCK(ErrorMessageLock); PolyCall2:; AR.PolyFunPow = OldPolyFunPow; MesCall("PolyFunMul"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] PolyFunMul : #] Processor : */ form-5.0.1/sources/grcc.cc0000644000175100017510000113675715217035721011102 // { ( [ //************************************************************** // grcc.cc /* #[ License : */ /* * Copyright (C) 2023-2026 T. Kaneko * When using this file you are requested to refer to the publication * Comput.Phys.Commun. 92 (1995) 127-152 * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #ifndef NOFORM extern "C" { #include "form3.h" } #endif #include #include #include #include #include #include #include //============================================================== // new default values of options // #define OLDDEFAULT // new function for the output in python format // #define NEWOUTPY //============================================================== // For debugging // // #define MONITOR // in graph elimination // #define CHECK // check consistency //============================================================== // optimization : best combination depends on process by process #define SIMPSEL // optimization : lower and upper bound of deg of target node of connection. #define MINMAXLEG // optimization : optimization with respect to 'extonly' particles #define OPTEXTONLY // check unique interaction by name or by code #define UNIQINTR // possible extensions of the program // #define ORBITS // reverse direction of an edge of agraph when anti-particle flows on it. // In this case the direction of edges will be diffrent // from ones of original mgraph. // #define EDGEPORDER //-------------------------------------------------------------- #include "grcc.h" #ifdef GRCC_NAMESPACE using namespace Grcc; #endif #define MAXSTR 1024 //-------------------------------------------------------------- // Macro functions #define CLWIGHTD(x) (5*(x)) #define CLWIGHTO(x) (3*(x)-2) #define MAXSTRLEN 81 #define MASK(n) ((1ul) << (n)) #define BOOLSTR(x) ((x) ? "True" : "False") //-------------------------------------------------------------- // Static variables static OptDef optDef0[] = { {"Step", "Generate particle assigned graphs", GRCC_AGraph, 0}, {"Outgrf", "Output to file (out.grf)", False, 0}, {"Outgrp", "Output to file (out.grp)", False, 0}, {"OPI", "Only 1PI graphs", True , 0}, {"NoSelfLoop", "Exclude graphs with loops consist of 1 edge", True , 0}, {"NoTadpole", "Exclude graphs with tadpoles (2 edge connected)", True , 0}, {"No1PtBlock", "Exclude graphs with tadpole blocks (2 node connected)", False, 0}, {"No2PtL1PI", "Exclude graphs with 2-point subgraphs", False, 0}, {"NoExtSelf", "Exclude graphs with 2-pt subgraphs at ext. particles", False, 0}, {"NoAdj2PtV", "Exclude graphs with an edge connecting 2-pt vertices", False, 0}, {"Block", "Exclude graphs with more than one block", False, 0}, {"NoMultiEdge","Exclude graphs with multi-edges", False, 0}, {"SymmInitial","Symmetrize initial particles", False, 0}, {"SymmFinal", "Symmetrize final particles", False, 0}, }; static OptDef optDef1[] = { {"Step", "Generate particle assigned graphs", GRCC_AGraph, 0}, {"Outgrf", "Ouput to file (out.grf)", False, 0}, {"Outgrp", "Ouput to file (out.grp)", False, 0}, {"OPI", "Only 1PI graphs", False, 0}, {"NoSelfLoop", "Exclude graphs with loops consist of 1 edge", False, 0}, {"NoTadpole", "Exclude graphs with tadpoles (2 edge connected)", False, 0}, {"No1PtBlock", "Exclude graphs with tadpole blocks (2 node connected)", False, 0}, {"No2PtL1PI", "Exclude graphs with 2-point subgraphs", False, 0}, {"NoExtSelf", "Exclude graphs with 2-pt subgraphs at ext. particles", False, 0}, {"NoAdj2PtV", "Exclude graphs with an edge connecting 2-pt vertices", False, 0}, {"Block", "Exclude graphs with more than one block", False, 0}, {"NoMultiEdge","Exclude graphs with multi-edges", False, 0}, {"SymmInitial","Symmetrize initial particles", False, 0}, {"SymmFinal", "Symmetrize final particles", False, 0}, }; #ifdef OLDDEFAULT static OptDef *optDef = &(optDef0[0]); static int nOptDef = sizeof(optDef0)/sizeof(OptDef); #else static OptDef *optDef = &(optDef1[0]); static int nOptDef = sizeof(optDef1)/sizeof(OptDef); #endif static OptQGDef optQGDef[] = { {"onepi", "onepr", "one-particle illreducible"}, {"onshell", "offshell", "without self-energy part at external particles"}, {"nosigma", "sigma", "no 2-point functions"}, {"nosnail", "snail", "without snail"}, {"notadpole", "tadpole", "without tadpole"}, {"simple", "notsimple", "without self-loop nor multi-edge"}, {"bipart", "nonbipart", "only bipartite graph"}, {"cycli", "cyclr", "???"}, {"floop", "", "without fermion loops of odd length"}, #ifdef GRCC_QGRAF_OPT_TOPOL {"topol", "?", "topology"}, #endif }; static int nOptQGDef = sizeof(optQGDef)/sizeof(OptQGDef); static int prlevel = 2; static ErExit *erExit = NULL; static void *erExitArg = NULL; //************************************************************** // Utility functions //============================================================== static void grcc_fprintf(FILE* out, const char* fmt, ...); static void erEnd(const char *msg); static Bool nextPart(int nelem, int nclist, int *clist, int *nl, int *r); static void prilist(int n, const int *a, const char *msg); static int *newArray(int size, int val); static int *deleteArray(int *a); static int **newMat(int n0, int n1, int val); static int **deleteMat(int **m, int n0); static void prIntArray(int n, int *p, const char *msg); static void prIntArrayErr(int n, int *p, const char *msg); static int *intdup(int n, int *v); static int *delintdup(int *v); static void bsort(int n, int *ord, int *a); static void sorti(int n, int *a); static int sortb(int n, int *a); static int toSList(int n, int *a); static int intSetAdd(int n, int *a, int v, const int size); static int intSListAdd(int n, int *a, int v, const int size); static int cmpArray(int na, int *a, int nb, int *b); static Bool leqArray(int n, int *a, int *b); static void prMomStr(int mom, const char *ms, int mn); static void listDiff(int na, int *a, int nb, int *b, int *np, int *p, int *nq, int *q, int *nr, int *r); static Bool isSubSList(int na, int *a, int nb, int *b); static int subtrSet(int na, int *a, int nb, int *b, int *c, int size); static int nextPerm(int nelem, int nclass, int *cl, int *r, int *q, int *p, int count); static BigInt ipow(int n, int p); static BigInt factorial(int n); // for debugging #ifdef CHECK static Bool isIn(int n, int *a, int v); #endif //============================================================== // class Options //-------------------------------------------------------------- Options::Options(void) { if (nOptDef != GRCC_OPT_Size) { grcc_fprintf(GRCC_Stderr, "*** Options: inconsistent default values\n"); grcc_fprintf(GRCC_Stderr, "nOptDef=%d, GRCC_OPT_Size=%d\n", nOptDef, GRCC_OPT_Size); GRCC_ABORT(); } model = NULL; proc = NULL; sproc = NULL; outmg = NULL; endmg = NULL; outag = NULL; argmg = NULL; argemg = NULL; argag = NULL; setDefaultValues(); // QGraf options if (nOptQGDef != GRCC_QGRAF_OPT_Size) { grcc_fprintf(GRCC_Stderr, "*** Options: inconsistent default values\n"); grcc_fprintf(GRCC_Stderr, "nOptQGDef=%d, GRCC_QGRAF_OPT_Size=%d\n", nOptQGDef, GRCC_QGRAF_OPT_Size); GRCC_ABORT(); } nqgopt = 0; for (int j = 0; j < nOptQGDef; j++) { qgref[nqgopt].name = optQGDef[j].name; qgref[nqgopt].index = j; qgref[nqgopt].sign = +1; nqgopt++; if (strlen(optQGDef[j].cname) > 0) { qgref[nqgopt].name = optQGDef[j].cname; qgref[nqgopt].index = j; qgref[nqgopt].sign = -1; nqgopt++; } } // default values for (int j = 0; j < GRCC_QGRAF_OPT_Size; j++) { qgopt[j] = 0; } // for output out = new Output(this); // subrpocess sproc = NULL; // measuring time time0 = 0.0; time1 = 0.0; } //-------------------------------------------------------------- Options::~Options(void) { outmg = NULL; outag = NULL; argmg = NULL; argag = NULL; delete out; } //-------------------------------------------------------------- void Options::setDefaultValues(void) { int j; // default values for (j = 0; j < GRCC_OPT_Size; j++) { values[j] = optDef[j].defaultv; } values[GRCC_OPT_Step] = GRCC_AGraph; // print level prlevel = 1; } //-------------------------------------------------------------- void Options::setOldDefaultValues(void) { int j; // default values for (j = 0; j < GRCC_OPT_Size; j++) { values[j] = optDef0[j].defaultv; } values[GRCC_OPT_Step] = GRCC_AGraph; // print level prlevel = 1; } //-------------------------------------------------------------- void Options::setOutMG(OutEGB *omg, void *pt) { outmg = omg; argmg = pt; } //-------------------------------------------------------------- void Options::setEndMG(OutEGB *emg, void *pt) { endmg = emg; argemg = pt; } //-------------------------------------------------------------- void Options::setOutAG(OutEG *oag, void *pt) { outag = oag; argag = pt; } //-------------------------------------------------------------- void Options::setErExit(ErExit *ere, void *erearg) { erExit = ere; erExitArg = erearg; } //-------------------------------------------------------------- void Options::printLevel(int l) { prlevel = l; } //-------------------------------------------------------------- void Options::setValue(int ind, int val) { if (0 <= ind && ind < GRCC_OPT_Size) { values[ind] = val; } else { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** Options::setValue : invalid index=%d ", ind); grcc_fprintf(GRCC_Stderr, "(val=%d)\n", val); } erEnd("Options::setValue : invalid index"); } } //-------------------------------------------------------------- int Options::getValue(int ind) { if (0 <= ind && ind < GRCC_OPT_Size) { return values[ind]; } else { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** Options::getValue : invalid index=%d\n", ind); } erEnd("Options::getValue : invalid index"); } return -1; } //-------------------------------------------------------------- void Options::setQGrafOpt(int *qg) { // reset options : default is to generate all connected graphs #ifdef OLDDEFAULT values[GRCC_OPT_1PI] = False; values[GRCC_OPT_NoSelfLoop] = False; values[GRCC_OPT_NoTadpole] = False; values[GRCC_OPT_No1PtBlock] = False; values[GRCC_OPT_No2PtL1PI] = False; values[GRCC_OPT_NoExtSelf] = False; values[GRCC_OPT_NoAdj2PtV] = False; values[GRCC_OPT_Block] = False; values[GRCC_OPT_SymmInitial] = False; values[GRCC_OPT_SymmFinal] = False; #endif for (int j = 0; j < GRCC_QGRAF_OPT_Size; j++) { qgopt[j] = qg[j]; } // {"onepi", "onepr"}, if (qgopt[GRCC_QGRAF_OPT_ONEPI] > 0) { values[GRCC_OPT_1PI] = True; } else if (qgopt[GRCC_QGRAF_OPT_ONEPI] < 0) { values[GRCC_OPT_1PI] = False; } // {"onshell", "offshell"} if (qgopt[GRCC_QGRAF_OPT_ONSHELL] > 0) { values[GRCC_OPT_NoExtSelf] = 1; } else if (qgopt[GRCC_QGRAF_OPT_ONSHELL] < 0) { values[GRCC_OPT_NoExtSelf] = 0; } // {"nosigma", "sigma"} // {"nosnail", "snail"}, if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] > 0) { values[GRCC_OPT_NoTadpole] = True; values[GRCC_OPT_No1PtBlock] = True; } else if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] < 0) { values[GRCC_OPT_NoTadpole] = False; values[GRCC_OPT_No1PtBlock] = False; } // {"notadpole", "tadpole"} if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] > 0) { values[GRCC_OPT_NoTadpole] = True; } else if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] < 0) { values[GRCC_OPT_NoTadpole] = False; } // {"simple", "notsimple"}, if (qgopt[GRCC_QGRAF_OPT_SIMPLE] > 0) { values[GRCC_OPT_NoSelfLoop] = True; values[GRCC_OPT_NoMultiEdge] = True; } else if (qgopt[GRCC_QGRAF_OPT_SIMPLE] < 0) { values[GRCC_OPT_NoSelfLoop] = False; values[GRCC_OPT_NoMultiEdge] = False; } // {"bipart", "nonbipart"}, // {"cycli", "cyclr"}, #ifdef GRCC_QGRAF_OPT_TOPOL // {"topol", ""}, if (qgopt[GRCC_QGRAF_OPT_TOPOL] > 0) { values[GRCC_OPT_SymmInitial] = True; values[GRCC_OPT_SymmFinal] = True; } #endif } //-------------------------------------------------------------- void Options::print(void) { int j; grcc_fprintf(GRCC_Stdout, "Options\n"); grcc_fprintf(GRCC_Stdout, "+++ GRCC_OPT_Size=%d, print level=%d: ", GRCC_OPT_Size, prlevel); grcc_fprintf(GRCC_Stdout, "symbol = value (default)\n"); for (j=0; j < GRCC_OPT_Size; j++) { grcc_fprintf(GRCC_Stdout, " %4d GRCC_OPT_%-15s = %2d (%2d)\n", j, optDef[j].name, values[j], optDef[j].defaultv); } grcc_fprintf(GRCC_Stdout, " outgrf=%s, outgrp=%s\n", out->outgrf, out->outgrp); grcc_fprintf(GRCC_Stdout, " GRCC_QGRAF_OPT_Size=%d:\n", GRCC_QGRAF_OPT_Size); for (j=0; j < GRCC_QGRAF_OPT_Size; j++) { grcc_fprintf(GRCC_Stdout, " %4d %-10s = %2d\n", j, optQGDef[j].name, qgopt[j]); } } //-------------------------------------------------------------- const OptDef *Options::getDef(void) { return optDef; } //-------------------------------------------------------------- const OptDef *Options::getOldDef(void) { return optDef0; } //-------------------------------------------------------------- const OptQGDef *Options::getQGDef(void) { return optQGDef; } //-------------------------------------------------------------- void Options::setOutputF(Bool outf, const char *fname) { values[GRCC_OPT_Outgrf] = outf; out->setOutgrf(fname); } //-------------------------------------------------------------- void Options::setOutputP(Bool outp, const char *fname) { values[GRCC_OPT_Outgrp] = outp; out->setOutgrp(fname); } //-------------------------------------------------------------- void Options::printModel(void) { if (prlevel > 0) { if (model != NULL) { model->prModel(); } else { grcc_fprintf(GRCC_Stdout, "*** model is not defined\n"); } } } //-------------------------------------------------------------- void Options::outModel(void) { if (out != NULL && model != NULL) { out->outModelF(); out->outModelP(); } } //-------------------------------------------------------------- void Options::begin(Model *mdl) { model = mdl; if (out != NULL) { if (values[GRCC_OPT_Outgrf]) { out->outBeginF(model, values[GRCC_OPT_Outgrf]); if (model != NULL) { out->outModelF(); } } if (values[GRCC_OPT_Outgrp]) { out->outBeginP(model, values[GRCC_OPT_Outgrp]); if (model != NULL) { out->outModelP(); } } } } //-------------------------------------------------------------- void Options::end(void) { if (prlevel > 1) { grcc_fprintf(GRCC_Stdout, "Optimization: "); #ifdef SIMPSEL grcc_fprintf(GRCC_Stdout, "SIMPSEL=1 "); #else grcc_fprintf(GRCC_Stdout, "SIMPSEL=0 "); #endif #ifdef MINMAXLEG grcc_fprintf(GRCC_Stdout, "MINMAXLEG=1 "); #else grcc_fprintf(GRCC_Stdout, "MINMAXLEG=0 "); #endif #ifdef OPTEXTONLY grcc_fprintf(GRCC_Stdout, "OPTEXTONLY=1 "); #else grcc_fprintf(GRCC_Stdout, "OPTEXTONLY=0 "); #endif grcc_fprintf(GRCC_Stdout, "\n"); } if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outEndF(); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outEndP(); } model = NULL; } // //-------------------------------------------------------------- void Options::beginProc(Process *prc) { proc = prc; if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outProcBeginF(prc); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outProcBeginP(prc); } if (proc != NULL) { proc->mgrcount = 0; proc->agrcount = 0; } } //-------------------------------------------------------------- void Options::endProc(void) { int k; if (proc == NULL) { if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outProcEndF(); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outProcEndP(); } return; } if (prlevel > 0) { grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, "+++ Proc %d: ext=%d, loop=%d, ", proc->id, proc->nExtern, proc->loop); if (model != NULL) { grcc_fprintf(GRCC_Stdout, "order="); prIntArray(model->ncouple, proc->clist, ": "); model->prParticleArray(proc->ninitl, proc->initlPart, "-->"); model->prParticleArray(proc->nfinal, proc->finalPart, ""); } grcc_fprintf(GRCC_Stdout, " (%8.2f sec)\n", proc->sec); grcc_fprintf(GRCC_Stdout, " Proc %d: Total M-Graphs=%ld, M-Graphs=", proc->id, proc->nMGraphs); proc->wMGraphs.print(" (Conn)\n"); grcc_fprintf(GRCC_Stdout, " Proc %d: Total M-Graphs=%ld, M-Graphs=", proc->id, proc->nMOPI); proc->wMOPI.print(" (1PI)\n"); grcc_fprintf(GRCC_Stdout, " Proc %d: Total A-Graphs=%ld, A-Graphs=", proc->id, proc->nAGraphs); proc->wAGraphs.print(" (Conn)\n"); grcc_fprintf(GRCC_Stdout, " Proc %d: Total A-Graphs=%ld, A-Graphs=", proc->id, proc->nAOPI); proc->wAOPI.print(" (1PI)\n"); grcc_fprintf(GRCC_Stdout, "# { %d,{", proc->ninitl); for (k = 0; k < proc->ninitl; k++) { if (k != 0) { grcc_fprintf(GRCC_Stdout, ", "); } if (proc->model != NULL) { grcc_fprintf(GRCC_Stdout, "\"%s\"", proc->model->particleName(proc->initlPart[k])); } else { grcc_fprintf(GRCC_Stdout, "%d", proc->initlPart[k]); } } grcc_fprintf(GRCC_Stdout, "}, %d,{", proc->nfinal); for (k = 0; k < proc->nfinal; k++) { if (k != 0) { grcc_fprintf(GRCC_Stdout, ", "); } if (proc->model != NULL) { grcc_fprintf(GRCC_Stdout, "\"%s\"", proc->model->particleName(proc->finalPart[k])); } else { grcc_fprintf(GRCC_Stdout, "%d", proc->initlPart[k]); } } grcc_fprintf(GRCC_Stdout, "}, "); if (model != NULL) { grcc_fprintf(GRCC_Stdout, "{"); for (k = 0; k < model->ncouple; k++) { if (k != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "%d", proc->clist[k]); } grcc_fprintf(GRCC_Stdout, "},"); } grcc_fprintf(GRCC_Stdout, "},%6ldL,%6ldL,%3ldL, -1.0, %4.2f},\n", proc->nAOPI, proc->wAOPI.num, proc->wAOPI.den, proc->sec); } if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outProcEndF(); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outProcEndP(); } proc = NULL; } //-------------------------------------------------------------- void Options::beginSubProc(SProcess *sprc) { sproc = sprc; // 'beginProc' is called before if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outSProcBeginF(sprc); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outSProcBeginP(sprc); } if (proc != NULL) { return; } if (sprc != NULL) { sproc->mgrcount = 0; sproc->agrcount = 0; } } //-------------------------------------------------------------- void Options::endSubProc(void) { MGraph *mgraph; if (sproc == NULL) { if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outProcEndF(); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outProcEndP(); } return; } mgraph = sproc->mgraph; if (sproc != NULL) { sproc->resultMGraph(mgraph->cDiag, mgraph->wscon, mgraph->c1PI, mgraph->wsopi); } if (prlevel > 1) { grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, "+++ Subproc %d: ext=%d, loop=%d, nodes=%d, edges=%d\n", sproc->id, sproc->nExtern, sproc->loop, sproc->nNodes, sproc->nEdges); grcc_fprintf(GRCC_Stdout, " Subproc %d: Total M-Graphs=%ld, M-Wsum=", sproc->id, sproc->nMGraphs); sproc->wMGraphs.print(" (Conn)\n"); grcc_fprintf(GRCC_Stdout, " Subproc %d: Total M-Graphs=%ld, M-Wsum=", sproc->id, sproc->nMOPI); sproc->wMOPI.print(" (1PI)\n"); grcc_fprintf(GRCC_Stdout, " Subproc %d: Total A-Graphs=%ld, A-Wsum=", sproc->id, sproc->nAGraphs); sproc->wAGraphs.print(" (Conn)\n"); grcc_fprintf(GRCC_Stdout, " Subproc %d: Total A-Graphs=%ld, A-Wsum=", sproc->id, sproc->nAOPI); sproc->wAOPI.print(" (1PI)\n"); } if (prlevel > 0) { grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, "* Total %ld MGraphs; %ld 1PI", mgraph->cDiag, mgraph->c1PI); grcc_fprintf(GRCC_Stdout, " wscon = "); mgraph->wscon.print(" ( "); mgraph->wsopi.print(" 1PI)\n"); #ifdef MONITOR grcc_fprintf(GRCC_Stdout, "* refine: %ld\n", mgraph->nCallRefine); grcc_fprintf(GRCC_Stdout, "* discarded for refinement: %ld\n", mgraph->discardRefine); grcc_fprintf(GRCC_Stdout, "* discarded for disconnected: %ld\n", mgraph->discardDisc); grcc_fprintf(GRCC_Stdout, "* discarded for duplication: %ld\n", mgraph->discardIso); #endif } if (proc != NULL) { return; } if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outProcEndF(); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outProcEndP(); } } //-------------------------------------------------------------- void Options::newMGraph(MGraph *mgr) { MGraph *mgraph = mgr; if (proc != NULL) { proc->mgrcount++; mgr->egraph->mId = proc->mgrcount; } else if (sproc != NULL) { sproc->mgrcount++; mgr->egraph->mId = sproc->mgrcount; } if (out != NULL && values[GRCC_OPT_Step] == GRCC_MGraph) { if (values[GRCC_OPT_Outgrf]) { out->outEGraphF(mgraph->egraph); } if (values[GRCC_OPT_Outgrp]) { out->outEGraphP(mgraph->egraph); } } if (sproc != NULL) { sproc->endMGraph(mgr); } if (endmg != NULL) { (*endmg)(mgr->egraph, argemg); } } //-------------------------------------------------------------- void Options::newAGraph(EGraph *egraph) { Fraction sf, zr; if (proc != NULL) { proc->agrcount++; egraph->sId = proc->agrcount; } else if (sproc != NULL) { sproc->agrcount++; egraph->sId = sproc->agrcount; } if (sproc != NULL) { zr = Fraction(0, 1); if ((egraph->nsym)*(egraph->esym) != 0) { sf = Fraction(egraph->extperm, egraph->nsym*egraph->esym); } else { sf = zr; } if (egraph->mgraph->opi) { sproc->resultAGraph(1, sf, 1, sf); } else { sproc->resultAGraph(1, sf, 0, zr); } } if (out != NULL && values[GRCC_OPT_Outgrf]) { out->outEGraphF(egraph); } if (out != NULL && values[GRCC_OPT_Outgrp]) { out->outEGraphP(egraph); } if (outag != NULL) { (*outag)(egraph, argag); } sproc->endAGraph(egraph); } //============================================================== Output::Output(Options *optn) { opt = optn; model = NULL; proc = NULL; sproc = NULL; outgrfp = NULL; outgrpp = NULL; procId = -1; outgrf = NULL; outgrp = NULL; outproc = False; } //-------------------------------------------------------------- Output::~Output(void) { if (outgrfp != NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** file has not been closed : \"%s\"\n", outgrf); } fclose(outgrfp); outgrfp = NULL; erEnd("file has not been closed"); } if (outgrf != NULL) { free(outgrf); outgrf = NULL; } if (outgrpp != NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** file has not been closed : \"%s\"\n", outgrp); } fclose(outgrpp); outgrpp = NULL; erEnd("file has not been closed"); } if (outgrp != NULL) { free(outgrp); outgrp = NULL; } } //-------------------------------------------------------------- void Output::setOutgrf(const char *fname) { if (outgrf != NULL && strcmp(outgrf, fname) == 0) { return; } if (outgrf != NULL) { // delete outgrf; free(outgrf); } if (fname == NULL || strlen(fname) < 1) { outgrf = NULL; } else { outgrf = strdup(fname); } } //-------------------------------------------------------------- void Output::setOutgrp(const char *fname) { if (outgrp != NULL && strcmp(outgrp, fname) == 0) { return; } if (outgrp != NULL) { free(outgrp); } if (fname == NULL || strlen(fname) < 1) { outgrp = NULL; } else { outgrp = strdup(fname); } } //-------------------------------------------------------------- Bool Output::outBeginF(Model *mdl, Bool pr) { time_t tp; struct tm *tm; char sdate[MAXSTRLEN]; model = mdl; if (outgrf == NULL || strlen(outgrf) < 1) { outgrfp = NULL; return True; } else if (outgrfp != NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** outBegin: \"%s\" is already opened\n", outgrf); } erEnd("outBegin: file is already opened\n"); } if (!pr) { return True; } if ((outgrfp = fopen(outgrf, "w")) == NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** outBegin: cannot open %s\n", outgrf); } return False; } tp = time(NULL); tm = localtime(&tp); strftime(sdate, MAXSTRLEN, "%Y/%m/%d %H:%M:%S", tm); fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"); fprintf(outgrfp, "%% Generated by grcc at \"%s\"\n", sdate); fprintf(outgrfp, "Version={2,2,0,0};\n"); if (model != NULL) { fprintf(outgrfp, "Model=\"./%s.mdl\";\n", model->name); } else { fprintf(outgrfp, "Model=\"./Phi34.mdl\";\n"); } return True; } //-------------------------------------------------------------- Bool Output::outBeginP(Model *mdl, Bool pr) { time_t tp; struct tm *tm; char sdate[MAXSTRLEN]; model = mdl; if (outgrp == NULL || strlen(outgrp) < 1) { outgrpp = NULL; return True; } else if (outgrpp != NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** outBegin: \"%s\" is already opened\n", outgrp); } erEnd("outBegin: file is already opened\n"); } if (!pr) { return True; } if ((outgrpp = fopen(outgrp, "w")) == NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** outBegin: cannot open %s\n", outgrp); } return False; } tp = time(NULL); tm = localtime(&tp); strftime(sdate, MAXSTRLEN, "%Y/%m/%d %H:%M:%S", tm); fprintf(outgrpp, "################################\n"); fprintf(outgrpp, "# Generated by 'grcc' at \"%s\"\n", sdate); return True; } //-------------------------------------------------------------- void Output::outEndF(void) { if (outgrfp == NULL) { return; } fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"); fprintf(outgrfp, "End=1;\n"); fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"); fclose(outgrfp); outgrfp = NULL; free(outgrf); outgrf = NULL; } //-------------------------------------------------------------- void Output::outEndP(void) { if (outgrpp == NULL) { return; } fprintf(outgrpp, "################################\n"); fprintf(outgrpp, "# End\n"); fprintf(outgrpp, "################################\n"); fclose(outgrpp); outgrpp = NULL; free(outgrp); outgrp = NULL; } //-------------------------------------------------------------- void Output::outProcBeginF(Process *prc) { int k, ex; if (prc == NULL) { return; } proc = prc; sproc = NULL; procId = proc->id; if (outgrfp == NULL) { return; } if (outproc) { return; } outproc = True; fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"); fprintf(outgrfp, "Process=%d;\n", proc->id); fprintf(outgrfp, "External=%d;\n", proc->ninitl+proc->nfinal); for (k = 0, ex = 0; k < proc->ninitl; k++, ex++) { fprintf(outgrfp, "%4d= initial %s;\n", ex, proc->model->particleName(proc->initlPart[k])); } for (k = 0; k < proc->nfinal; k++, ex++) { fprintf(outgrfp, "%4d= final %s;\n", ex, proc->model->particleName(proc->finalPart[k])); } fprintf(outgrfp, "Eend;\n"); for (k = 0; k < proc->model->ncouple; k++) { fprintf(outgrfp, "%s=%d; ", proc->model->cnlist[k], proc->clist[k]); } fprintf(outgrfp, "Loop=%d;\n", proc->loop); fprintf(outgrfp, "OPI=%s;\n", (opt->values[GRCC_OPT_1PI] > 0? "Yes" : "No")); fprintf(outgrfp, "Assign=%s;\n", (opt->values[GRCC_OPT_Step]==GRCC_AGraph ? "Yes" : "No")); fprintf(outgrfp, "%% Options : dummy values\n"); fprintf(outgrfp, "Expand=Yes; ExpMin=0; ExpMax=-1;\n"); fprintf(outgrfp, "Block=No; Tadpole=Yes; Extself=Yes;\n"); fprintf(outgrfp, "Selfe=Yes; Countert=No; AnyCT=No;Undefp=No;\n"); } //-------------------------------------------------------------- void Output::outProcBeginP(Process *prc) { if (prc == NULL) { return; } proc = prc; sproc = NULL; procId = proc->id; if (outgrpp == NULL) { return; } if (outproc) { return; } outproc = True; fprintf(outgrpp, "# Process=%d;\n", proc->id); } //-------------------------------------------------------------- void Output::outProcBegin0(int next, int couple, int loop) { int k, ex; procId = 0; if (outgrfp == NULL) { return; } if (outproc) { return; } outproc = True; fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"); fprintf(outgrfp, "Process=%d;\n", procId); fprintf(outgrfp, "External=%d;\n", next); int ninit = (next + 1) / 2; for (k = 0, ex = 0; k < ninit; k++, ex++) { fprintf(outgrfp, "%4d= initial undef;\n", ex); } for (k = 0; k < next - ninit; k++, ex++) { fprintf(outgrfp, "%4d= final undef;\n", ex); } fprintf(outgrfp, "Eend;\n"); fprintf(outgrfp, "GRCC_PHI=%d; ", couple); // fprintf(outgrfp, "PHI=%d; ", couple); fprintf(outgrfp, "Loop=%d;\n", loop); fprintf(outgrfp, "OPI=%s;\n", (opt->values[GRCC_OPT_1PI] > 0? "Yes" : "No")); fprintf(outgrfp, "Assign=No;\n"); fprintf(outgrfp, "%% Options : dummy values\n"); fprintf(outgrfp, "Expand=Yes; ExpMin=0; ExpMax=-1;\n"); fprintf(outgrfp, "Block=No; Tadpole=Yes; Extself=Yes;\n"); fprintf(outgrfp, "Selfe=Yes; Countert=No; AnyCT=No;Undefp=No;\n"); } //-------------------------------------------------------------- void Output::outSProcBeginF(SProcess *sprc) { int j, k, ex; PNodeClass *pnc; if (sprc == NULL) { return; } sproc = sprc; procId = sproc->id; pnc = sproc->pnclass; if (outgrfp == NULL) { return; } if (outproc) { return; } outproc = True; fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"); fprintf(outgrfp, "Process=%d;\n", sproc->id); fprintf(outgrfp, "External=%d;\n", sproc->nExtern); ex = 0; for (j = 0; j < pnc->nclass; j++) { if (pnc->type[j] == GRCC_AT_Initial) { for (k = 0; k < pnc->count[j]; k++) { fprintf(outgrfp, "%4d= initial %s;\n", ex, model->particleName(pnc->particle[j])); ex++; } } else if (pnc->type[j] == GRCC_AT_Final) { for (k = 0; k < pnc->count[j]; k++) { fprintf(outgrfp, "%4d= final %s;\n", ex, model->particleName(-pnc->particle[j])); ex++; } } } fprintf(outgrfp, "Eend;\n"); for (k = 0; k < sproc->model->ncouple; k++) { fprintf(outgrfp, "%s=%d; ", sproc->model->cnlist[k], sproc->clist[k]); } fprintf(outgrfp, "Loop=%d;\n", sproc->loop); fprintf(outgrfp, "OPI=%s;\n", (opt->values[GRCC_OPT_1PI] > 0? "Yes" : "No")); fprintf(outgrfp, "Assign=%s;\n", (opt->values[GRCC_OPT_Step]==GRCC_AGraph ? "Yes" : "No")); fprintf(outgrfp, "%% Options : dummy values\n"); fprintf(outgrfp, "Expand=Yes; ExpMin=0; ExpMax=-1;\n"); fprintf(outgrfp, "Block=No; Tadpole=Yes; Extself=Yes;\n"); fprintf(outgrfp, "Selfe=Yes; Countert=No; AnyCT=No;Undefp=No;\n"); } //-------------------------------------------------------------- void Output::outSProcBeginP(SProcess *sprc) { if (sprc == NULL) { return; } sproc = sprc; procId = sproc->id; if (outgrpp == NULL) { return; } if (outproc) { return; } outproc = True; fprintf(outgrpp, "# SProcess=%d;\n", sproc->id); } //-------------------------------------------------------------- void Output::outProcEndF(void) { if (outgrfp == NULL) { return; } if (proc != NULL) { fprintf(outgrfp, "%%------------------------------\n"); fprintf(outgrfp, "Pend=%d;\n", proc->id); } else if (sproc != NULL) { fprintf(outgrfp, "%%------------------------------\n"); fprintf(outgrfp, "Pend=%d;\n", sproc->id); } else { fprintf(outgrfp, "%%------------------------------\n"); fprintf(outgrfp, "Pend=1;\n"); } fflush(outgrfp); } //-------------------------------------------------------------- void Output::outProcEndP(void) { if (outgrpp == NULL) { return; } fflush(outgrpp); } //-------------------------------------------------------------- void Output::outEGraphF(EGraph *egraph) { int nd, lg, ptcl, ed, intr, j, k, loop; Model *mdl = egraph->model; Bool popt; EFLine *fl; if (outgrfp == NULL) { return; } fprintf(outgrfp, "%%------------------------------\n"); if (egraph->assigned) { fprintf(outgrfp, "Graph=%ld;\n", egraph->sId); fprintf(outgrfp, "%% AGraph=%ld;\n", egraph->aId); } else { fprintf(outgrfp, "Graph=%ld;\n", egraph->mId); } fprintf(outgrfp, "Gtype=%ld;\n", egraph->mId); if (egraph->assigned) { fprintf(outgrfp, "Sfactor=%ld;\n", egraph->nsym * egraph->esym * egraph->fsign); } else { fprintf(outgrfp, "Sfactor=%ld;\n", egraph->nsym * egraph->esym); } fprintf(outgrfp, "%% ExtPerm=%ld; NSym=%ld; ESym=%ld; NSym1=%ld;" " Multp=%ld;\n", egraph->extperm, egraph->nsym, egraph->esym, egraph->nsym1, egraph->multp); fprintf(outgrfp, "Vertex=%d;\n", egraph->nNodes - egraph->nExtern); for (nd = 0; nd < egraph->nNodes; nd++) { fprintf(outgrfp, "%4d", nd); if (mdl != NULL && egraph->assigned && !egraph->isExternal(nd)) { intr = egraph->nodes[nd]->intrct; loop = mdl->interacts[intr]->loop; popt = False; // not tree vertex if (loop > 0) { fprintf(outgrfp, "[loop=%d", loop); popt = True; } // multiple coupling constants if (mdl->ncouple > 1) { if (popt) { fprintf(outgrfp, ";order={"); } else { fprintf(outgrfp, "[order={"); popt = True; } for (j = 0; j < mdl->interacts[intr]->nclist; j++) { if (j != 0) { fprintf(outgrfp, ","); } fprintf(outgrfp, "%d", mdl->interacts[intr]->clist[j]); } fprintf(outgrfp, "}"); } if (popt) { fprintf(outgrfp, "]"); } } else if (!egraph->isExternal(nd)) { loop = egraph->nodes[nd]->extloop; // not tree vertex if (loop > 0) { fprintf(outgrfp, "[loop=%d]", loop); } } fprintf(outgrfp, "={"); // list of legs for (lg = 0; lg < egraph->nodes[nd]->deg; lg++) { if (lg != 0) { fprintf(outgrfp, ", "); } ed = V2Iedge(egraph->nodes[nd]->edges[lg]); // fprintf(outgrfp, "%4d", egraph->nodes[nd]->edges[lg]); fprintf(outgrfp, "%4d", abs(egraph->nodes[nd]->edges[lg])); ptcl = egraph->edges[ed]->ptcl; if (mdl != NULL && ptcl != 0 && egraph->assigned) { if (egraph->nodes[nd]->edges[lg] < 0) { ptcl = mdl->normalParticle(-ptcl); } else { ptcl = mdl->normalParticle(ptcl); } fprintf(outgrfp, "[%s]", mdl->particleName(ptcl)); } else { fprintf(outgrfp, "[undef]"); } } fprintf(outgrfp, "};\n"); } // print Fermion line as comment line if (egraph->nFlines >= 0) { fprintf(outgrfp, "%% FLines=%d; FSign=%d; sId=%ld;\n", egraph->nFlines, egraph->fsign, egraph->sId); } for (j = 0; j < egraph->nFlines; j++) { fl = egraph->flines[j]; fprintf(outgrfp, "%% %4d", j); if (fl->ftype == FL_Open) { fprintf(outgrfp, "[FOpen]=["); } else if (fl->ftype == FL_Closed) { fprintf(outgrfp, "[FLoop]=["); } else { fprintf(outgrfp, " ?%d", fl->ftype); } for (k = 0; k < fl->nlist; k++) { if (k != 0) { fprintf(outgrfp, ", "); } fprintf(outgrfp, "%d", fl->elist[k]); } fprintf(outgrfp, "];\n"); } fprintf(outgrfp, "Vend;\n"); fprintf(outgrfp, "Gend;\n"); } //-------------------------------------------------------------- #ifdef NEWOUTPY void Output::outEGraphP(EGraph *eg) { if (outgrpp == NULL) { return; } if (eg->assigned) { grcc_fprintf(GRCC_Stdout, "outEGraphP:egraph:egraph[%ld]\n", eg->mId-1); eg->printPy(outgrpp, eg->mId); return; } else { grcc_fprintf(GRCC_Stdout, "outEGraphP:mgraph:egraph[%ld]\n", eg->mId-1); eg->mgraph->printPy(outgrpp, eg->mId); return; } } #else void Output::outEGraphP(EGraph *eg) { int j, nd, lg, ed, k; ENode *node; static char undef[] = "Undef"; char *s; EFLine *fl; if (outgrpp == NULL) { return; } if (eg->assigned) { fprintf(outgrpp, "egraph[%ld] = {\n", eg->sId-1); } else { fprintf(outgrpp, "egraph[%ld] = {\n", eg->mId-1); } // process if (proc != NULL) { fprintf(outgrpp, " \"Process\": {\n"); proc->outProcP(outgrpp); fprintf(outgrpp, " },\n"); } // graph fprintf(outgrpp, " \"GId\": [%ld, %ld, %ld],\n", eg->mId, eg->aId, eg->sId); fprintf(outgrpp, " \"GParam\": {\"Assigned\":%d, " "\"NNodes\":%d, \"NEdges\":%d, \"NFLines\":%d},\n", eg->assigned, eg->nNodes, eg->nEdges, eg->nFlines); fprintf(outgrpp, " \"Sym\": {\"FSign\":%d, \"NSym\":%ld, " "\"ESym\":%ld, \"NSym1\":%ld, \"Multp\":%ld},\n", eg->fsign, eg->nsym, eg->esym, eg->nsym1, eg->multp); // nodes fprintf(outgrpp, " \"Nodes\": [\n"); for (nd = 0; nd < eg->nNodes; nd++) { node = eg->nodes[nd]; if (model==NULL) { s = undef; } else if(!eg->assigned) { if (eg->isExternal(nd)) { ed = Abs(eg->nodes[nd]->edges[0])-1; s = model->particleName(eg->edges[ed]->ptcl); } else { s = undef; } } else if (eg->isExternal(nd)) { s = model->particleName(node->intrct); } else { s = model->interacts[node->intrct]->name; } fprintf(outgrpp, " [%d, \"%s\", %d, [", nd, s, node->extloop); for (lg = 0; lg < eg->nodes[nd]->deg; lg++) { if (lg != 0) { fprintf(outgrpp, ", "); } fprintf(outgrpp, "%d", eg->nodes[nd]->edges[lg]); } fprintf(outgrpp, "]],\n"); } fprintf(outgrpp, " ],\n"); // edges fprintf(outgrpp, " \"Edges\": [\n"); for (ed = 0; ed < eg->nEdges; ed++) { if (model != NULL) { s = model->particleName(eg->edges[ed]->ptcl); fprintf(outgrpp, " [%d, \"%s\", [%d, %d]],\n", ed+1, s, eg->edges[ed]->nodes[0], eg->edges[ed]->nodes[1]); } else { fprintf(outgrpp, " [%d, \"Undef\", [%d, %d]],\n", ed+1, eg->edges[ed]->nodes[0], eg->edges[ed]->nodes[1]); } } fprintf(outgrpp, " ],\n"); if (eg->nFlines >= 0) { // print Fermion line as comment line fprintf(outgrpp, " \"FLines\": [\n"); for (j = 0; j < eg->nFlines; j++) { fl = eg->flines[j]; fprintf(outgrpp, " [%d, ", j); if (fl->ftype == FL_Open) { fprintf(outgrpp, "\"FOpen\", "); } else if (fl->ftype == FL_Closed) { fprintf(outgrpp, "\"FLoop\", "); } else { fprintf(outgrpp, "\"Undef%d\", ", fl->ftype); } fprintf(outgrpp, "["); for (k = 0; k < fl->nlist; k++) { if (k != 0) { fprintf(outgrpp, ", "); } fprintf(outgrpp, "%d", fl->elist[k]); } fprintf(outgrpp, "]],\n"); } fprintf(outgrpp, " ]\n"); } // end of a graph fprintf(outgrpp, "};\n"); } #endif //-------------------------------------------------------------- void Output::outModelF(void) { char *mdlfn; FILE *mdlfp; Particle *pt; Interaction *vt; int j, k, l, ln; const char *ptn; if (model == NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** Output::outModel : model is not defined\n"); } return; } ln = strlen(model->name)+5; mdlfn = new char[ln]; snprintf(mdlfn, ln, "%s.mdl", model->name); if ((mdlfp = fopen(mdlfn, "w")) == NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** Output::outModel : cannot open \"%s\"\n", mdlfn); } return; } for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp); fprintf(mdlfp, "%% File \"%s\"\n", mdlfn); fprintf(mdlfp, "%% Generated by graph generater\n"); fprintf(mdlfp, " Version={2,2,0};\n"); // copupling constants fprintf(mdlfp, " Order={"); for (j = 0; j < model->ncouple; j++) { if (j != 0) { fprintf(mdlfp, ", "); } fprintf(mdlfp, "%s", model->cnlist[j]); } fprintf(mdlfp, "};\n"); for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp); fprintf(mdlfp, "%% particles\n"); for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp); for (j = 1; j < model->nParticles; j++) { pt = model->particles[j]; fprintf(mdlfp, " Particle=%s; Antiparticle=%s;\n", pt->name, pt->aname); ptn = pt->typeGName(); fprintf(mdlfp, " PType=%s; Charge=0; Color=1; Mass=0; Width=0;\n", ptn); fprintf(mdlfp, " PCode=%d; Massless; \n", pt->pcode); fprintf(mdlfp, " Pend;\n"); fprintf(mdlfp, "%%\n"); } for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp); fprintf(mdlfp, "%% interactions\n"); for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp); for (j = 0; j < model->nInteracts; j++) { vt = model->interacts[j]; fprintf(mdlfp, " Vertex={"); for (k = 0; k < vt->nplist; k++) { if (k != 0) { fprintf(mdlfp, ", "); } fprintf(mdlfp, "%s", model->particleName(vt->plist[k])); } fprintf(mdlfp, "}; "); for (k = 0; k < model->ncouple; k++) { fprintf(mdlfp, "%s=%d; ", model->cnlist[k], vt->clist[k]); } fprintf(mdlfp, "FName=%s; Vend;\n", vt->name); } for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp); fprintf(mdlfp, " Mend;\n"); for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp); fclose(mdlfp); delete[] mdlfn; } //-------------------------------------------------------------- void Output::outModelP(void) { char *mdlfn; FILE *mdlfp; Particle *pt; Interaction *vt; int j, k, l, ln; const char *ptn; if (model == NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** Output::outModel : "); grcc_fprintf(GRCC_Stderr, "model is not defined\n"); } return; } ln = strlen(model->name)+5; mdlfn = new char[ln]; snprintf(mdlfn, ln, "%s.mdp", model->name); if ((mdlfp = fopen(mdlfn, "w")) == NULL) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** Output::outModel : cannot open \"%s\"\n", mdlfn); } return; } for (l = 0; l < 60; l++) { putc('#', mdlfp); } putc('\n', mdlfp); fprintf(mdlfp, "# File \"%s\"\n", mdlfn); fprintf(mdlfp, "# Generated by graph generater grcc\n"); // copupling constants fprintf(mdlfp, "Model={\n"); fprintf(mdlfp, " \"Model\": ["); fprintf(mdlfp, "\"%s\", %d, [", model->name, model->ncouple); for (j = 0; j < model->ncouple; j++) { if (j != 0) { fprintf(mdlfp, ", "); } fprintf(mdlfp, "\"%s\"", model->cnlist[j]); } fprintf(mdlfp, "], "); if (model->defpart == GRCC_DEFBYCODE) { fprintf(mdlfp, "\"ByCode\""); } else { fprintf(mdlfp, "\"ByName\""); } fprintf(mdlfp, "],\n"); fprintf(mdlfp, " \"Particles\": [\n"); for (j = 1; j < model->nParticles; j++) { pt = model->particles[j]; ptn = pt->typeName(); fprintf(mdlfp, " [\"%s\", %d, \"%s\", %d, \"%s\", %d],\n", pt->name, pt->pcode, pt->aname, pt->acode, ptn, pt->extonly); } fprintf(mdlfp, " ],\n"); fprintf(mdlfp, " \"Interactions\": [\n"); for (j = 0; j < model->nInteracts; j++) { vt = model->interacts[j]; fprintf(mdlfp, " [\"%s\", %d, %d, [", vt->name, vt->id, vt->nplist); for (k = 0; k < vt->nplist; k++) { if (k != 0) { fprintf(mdlfp, ", "); } if (model->defpart == GRCC_DEFBYCODE) { fprintf(mdlfp, "%d", vt->plist[k]); } else { fprintf(mdlfp, "\"%s\"", model->particleName(vt->plist[k])); } } fprintf(mdlfp, "], ["); for (k = 0; k < model->ncouple; k++) { if (k != 0) { fprintf(mdlfp, ","); } fprintf(mdlfp, "%d", vt->clist[k]); } fprintf(mdlfp, "]],\n"); } fprintf(mdlfp, " ],\n"); fprintf(mdlfp, "};\n"); fclose(mdlfp); delete[] mdlfn; } //************************************************************** // model.cc //============================================================== static const char *ptypenames[] = GRCC_PT_Table; static const char *pgtypenames[] = GRCC_PT_GTable; //============================================================== // class Particle //-------------------------------------------------------------- Particle::Particle(Model *modl, int pid, PInput *pinp) { static char buff[100]; static int nbuff=100; int j; mdl = modl; // the model id = pid; // id of this particle if (pinp->name == NULL || strlen(pinp->name) < 1) { if (pinp->pcode != 0) { snprintf(buff, nbuff, "pa%d", pinp->pcode); name = strdup(buff); } else { snprintf(buff, nbuff, "pi%d", pid); name = strdup(buff); } } else { name = strdup(pinp->name); // the name of the particle } if (pinp->aname == NULL) { if (pinp->acode != 0) { snprintf(buff, nbuff, "ap%d", Abs(pinp->acode)); aname = strdup(buff); } else { snprintf(buff, nbuff, "ai%d", pid); aname = strdup(buff); } } else { aname = strdup(pinp->aname); // the name of the anti-particle } pcode = pinp->pcode; acode = pinp->acode; if (Abs(mdl->defpart) == GRCC_DEFBYCODE) { neutral = (pcode == acode); } else if (Abs(mdl->defpart) == GRCC_DEFBYNAME) { neutral = ((strcmp(name, aname)==0) ? True : False); } // convert ptype string to its code. if (Abs(mdl->defpart) == GRCC_DEFBYCODE) { if (pinp->ptypec < GRCC_PT_Undef || pinp->ptypec > GRCC_PT_Size) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** particle type is not defined: %d\n", pinp->ptypec); } erEnd("particle type is not defined (illegal code)"); } ptype = pinp->ptypec; } else if (Abs(mdl->defpart) == GRCC_DEFBYNAME) { if (pinp->ptypen == NULL) { erEnd("particle type is not defined (NULL)"); } ptype = -1; for (j = 0; j < GRCC_PT_Size; j++) { if (strcmp(pinp->ptypen, ptypenames[j]) == 0) { ptype = j; break; } } if (ptype < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** particle type \"%s\" is not defined\n", pinp->ptypen); } erEnd("particle type is not defined (name)"); } } if (ptype == GRCC_PT_Undef && ptype != 0) { erEnd("illegal ptype"); } extonly = pinp->extonly; cmindeg = 0; cmaxdeg = 0; } //-------------------------------------------------------------- Particle::~Particle(void) { free(aname); free(name); } //-------------------------------------------------------------- char *Particle::particleName(int p) { if (p < 0) { return aname; } else { return name; } } //-------------------------------------------------------------- int Particle::particleCode(int p) { if (p < 0) { return acode; } else { return pcode; } } //-------------------------------------------------------------- int Particle::isNeutral(void) { return neutral; } //-------------------------------------------------------------- const char *Particle::typeName(void) { return ptypenames[ptype]; } //-------------------------------------------------------------- const char *Particle::typeGName(void) { return pgtypenames[ptype]; } //-------------------------------------------------------------- char *Particle::aparticle(void) { static char prtcl[] = "Particle"; if (isNeutral()) { return prtcl; } else { return aname; } } //-------------------------------------------------------------- void Particle::prParticle(void) { if (isNeutral()) { grcc_fprintf(GRCC_Stdout, "pid=%d, name=\"%s\", real_field, ", id, name); } else { grcc_fprintf(GRCC_Stdout, "pid=%d, name=\"%s\", aname=\"%s\", ", id, name, aname); } grcc_fprintf(GRCC_Stdout, "ptype=%s, pcode=%d, acode=%d, extonly=%d, cdeg=(%d,%d)\n", ptypenames[ptype], pcode, acode, extonly, cmindeg, cmaxdeg); } //============================================================== // class Interaction //-------------------------------------------------------------- Interaction::Interaction(Model *modl, int iid, const char *nam, int icd, int *cpl, int nlgs, int *plst, int csm, int lp) { static char buff[100]; static int nbuff=100; static Bool prmsg = True; Particle *p; int j, ndir, sdir, jdir, nmaj, jmaj, ngho, sgho, jgho, ptcl; Bool ok; mdl = modl; // the model id = iid; // id of this interaction icode = icd; // id of this interaction csum = csm; // the total orders of coupling constants nlegs = nlgs; // the size of plist[] loop = lp; // the number of loops if (nam == NULL || strlen(nam) < 1) { snprintf(buff, nbuff, "vt%d", icd); name = strdup(buff); } else { name = strdup(nam); // the name of the interaction } nclist = mdl->ncouple; clist = new int[nclist]; icode = icd; for (j = 0; j < mdl->ncouple; j++) { clist[j] = cpl[j]; } plist = new int[nlegs]; nplist = nlegs; for (j = 0; j < nlegs; j++) { plist[j] = plst[j]; } nslist = 0; slist = NULL; // check fermion number conservation ndir = 0; sdir = 0; jdir = 0; nmaj = 0; jmaj = 0; ngho = 0; sgho = 0; jgho = 0; ok = True; for (j = 0; j < nplist; j++) { if (plist[j] > 0) { p = mdl->particles[plist[j]]; ptcl = 1; } else { p = mdl->particles[-plist[j]]; ptcl = -1; } if (p->ptype == GRCC_PT_Dirac) { ndir++; if (ptcl > 0) { sdir++; } else { sdir--; } if (Abs(sdir) == 1) { jdir = j; } else if ((Abs(sdir) == 0 && j != jdir + 1) || Abs(sdir) > 1) { grcc_fprintf(GRCC_Stderr, "*** Interaction: Dirac and anti-Dirac should " "arranged in pairs in an interaction.\n"); ok = False; } } else if (p->ptype == GRCC_PT_Ghost) { ngho++; if (ptcl > 0) { sgho++; } else { sgho--; } if (Abs(sgho) == 1) { jgho = j; } else if ((Abs(sgho) == 0 && j != jgho + 1) || Abs(sgho) > 1) { grcc_fprintf(GRCC_Stderr, "*** Interaction: Ghost and anti-Ghost should " "arranged in pairs in an interaction.\n"); ok = False; } } else if (p->ptype == GRCC_PT_Majorana) { nmaj++; if (nmaj % 2 == 1) { jmaj = j; } else if (j != jmaj + 1) { grcc_fprintf(GRCC_Stderr, "*** Interaction: two Majoranas should " "arranged in pairs in an interaction.\n"); ok = False; } } } if (sdir != 0) { grcc_fprintf(GRCC_Stderr, "*** Interaction: Dirac number is not conserved\n"); ok = False; } if (sgho != 0) { grcc_fprintf(GRCC_Stderr, "*** Interaction: Ghost number is not conserved\n"); ok = False; } if (nmaj % 2 != 0) { grcc_fprintf(GRCC_Stderr, "*** Interaction: odd number of Majorana particles\n"); ok = False; } if (ndir + nmaj + ngho > 2 && prmsg) { grcc_fprintf(GRCC_Stderr, "+++ Interaction: more than 2 " "Dirac/Majorana/Ghost " "particles are interacting.\n"); grcc_fprintf(GRCC_Stderr, " Interaction has %d Dirac, %d Ghost " "and %d Majorana particles.\n", ndir, nmaj, ngho); grcc_fprintf(GRCC_Stderr, " Sign factors related to fermions may " "be inconsistent with your calculation method.\n"); prmsg = False; } if (!ok) { prInteraction(); erEnd("illegal Dirac/Majorana/Ghost interaction"); } } //-------------------------------------------------------------- Interaction::~Interaction(void) { if (slist != NULL) { delete[] slist; } if (plist != NULL) { delete[] plist; } if (clist != NULL) { delete[] clist; } free(name); } //-------------------------------------------------------------- void Interaction::prInteraction(void) { int j; grcc_fprintf(GRCC_Stdout, "vid=%d, icode=%d, name=\"%s\", loop=%d, csum=%d, cpl=", id, icode, name, loop, csum); prIntArray(mdl->ncouple, clist, ", legs=["); for (j = 0; j < nplist; j++) { if (j != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "%s", mdl->particleName(plist[j])); } grcc_fprintf(GRCC_Stdout, "];\n"); } //============================================================== // class Model //-------------------------------------------------------------- Model::Model(MInput *minp) { static PInput pundef = {"undef", "undef", 0, 0, "undef", 0, 0}; int j; if (minp->name == NULL || strlen(minp->name) < 1) { erEnd("model should have a name"); } name = strdup(minp->name); ncouple = minp->ncouple; if (ncouple >= GRCC_MAXNCPLG) { erEnd("too many coupling constants in the model (GRCC_MAXNCPLG)"); } // cnlist = minp->cnamlist; cnlist = new char*[ncouple]; for (j = 0; j < ncouple; j++) { cnlist[j] = strdup(minp->cnamlist[j]); } nParticles = 0; particles = new Particle*[GRCC_MAXMPARTICLES]; for (j = 0; j < GRCC_MAXMPARTICLES; j++) { particles[j] = NULL; } pdef = False; nInteracts = 0; interacts = new Interaction*[GRCC_MAXMINTERACT]; for (j = 0; j < GRCC_MAXMINTERACT; j++) { interacts[j] = NULL; } vdef = False; if (particles == NULL || interacts == NULL) { erEnd("memory allocation failed"); } #ifdef UNIQINTR if (minp->defpart != GRCC_DEFBYNAME && minp->defpart != GRCC_DEFBYCODE) { erEnd("illegal value of defpart"); } #else if (Abs(minp->defpart) != GRCC_DEFBYNAME && Abs(minp->defpart) != GRCC_DEFBYCODE) { erEnd("illegal value of defpart"); } #endif defpart = minp->defpart; maxnlegs = 0; maxcpl = 0; maxloop = 0; ncplgcp = 0; cplgvl = NULL; addParticle(&pundef); } //-------------------------------------------------------------- Model::~Model(void) { int j; if (ncplgcp > 0) { for (j = ncplgcp-1; j >= 0; j--) { cplgvl[j] = delintdup(cplgvl[j]); } delete[] cplgvl; cplgnvl = delintdup(cplgnvl); cplglg = delintdup(cplglg); cplgcp = delintdup(cplgcp); } for (j = GRCC_MAXMINTERACT-1; j >= 0; j--) { if (interacts[j] != NULL) { interacts[j]->slist = delintdup(interacts[j]->slist); delete interacts[j]; interacts[j] = NULL; } } delete[] interacts; interacts = NULL; for (j = GRCC_MAXMPARTICLES-1; j >= 0; j--) { if (particles[j] != NULL) { delete particles[j]; particles[j] = NULL; } } delete[] particles; particles = NULL; for (j=ncouple-1; j>=0; j--) { free(cnlist[j]); } delete[] cnlist; free(name); } //-------------------------------------------------------------- void Model::prModel(void) { static char hdr[] = "#=================================================\n"; static char hd1[] = "#-------------------------------------------------\n"; int j; grcc_fprintf(GRCC_Stdout, "%s", hdr); grcc_fprintf(GRCC_Stdout, "Model=\"%s\", ", name); grcc_fprintf(GRCC_Stdout, "coupling=["); for (j = 0; j < ncouple; j++) { if (j != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "\"%s\"", cnlist[j]); } grcc_fprintf(GRCC_Stdout, "];\n"); grcc_fprintf(GRCC_Stdout, "%s", hd1); grcc_fprintf(GRCC_Stdout, "Particles=%d;\n", nParticles); for (j = 1; j < nParticles; j++) { particles[j]->prParticle(); } grcc_fprintf(GRCC_Stdout, "EndParticle;\n"); grcc_fprintf(GRCC_Stdout, "allPart (%d) = [", nallPart); for (j = 0; j < nallPart; j++) { if (j != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "%d", allPart[j]); } grcc_fprintf(GRCC_Stdout, "]\n"); grcc_fprintf(GRCC_Stdout, "%s", hd1); grcc_fprintf(GRCC_Stdout, "Interactions=%d;\n", nInteracts); for (j = 0; j < nInteracts; j++) { interacts[j]->prInteraction(); } grcc_fprintf(GRCC_Stdout, "EndInteraction;\n"); grcc_fprintf(GRCC_Stdout, "%s", hd1); grcc_fprintf(GRCC_Stdout, "InteractionTable;\n"); grcc_fprintf(GRCC_Stdout, "# %d class in (total coupling, degree)\n", ncplgcp); for (j = 0; j < ncplgcp; j++) { grcc_fprintf(GRCC_Stdout, " class=%d: cp=%d, lg=%d, vl=", j, cplgcp[j], cplglg[j]); prIntArray(cplgnvl[j], cplgvl[j], "\n"); } grcc_fprintf(GRCC_Stdout, "EndInteractionTable;\n"); grcc_fprintf(GRCC_Stdout, "%s", hdr); } //-------------------------------------------------------------- void Model::addParticle(PInput *pinp) { int nid, aid, pid, pcd, acd; if (nParticles >= GRCC_MAXMPARTICLES) { erEnd("particle table overflow (GRCC_MAXMPARTICLES)"); } // uniqueness check if (Abs(defpart) == GRCC_DEFBYCODE) { pcd = findParticleCode(pinp->pcode); acd = findParticleCode(pinp->acode); if (pcd > 0 || acd > 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** particle code [%d, %d] ", pinp->pcode, pinp->acode); grcc_fprintf(GRCC_Stderr, "is already used.\n"); } erEnd("particle code is already defined"); } } else if (Abs(defpart) == GRCC_DEFBYNAME) { if (pinp->name == NULL || pinp->aname == NULL || strlen(pinp->name) < 1 || strlen(pinp->aname) < 1) { erEnd("no name of particle or anti-particle."); } nid = findParticleName(pinp->name); aid = findParticleName(pinp->aname); if (nid > 0 || aid > 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** particle name [%s, %s] ", pinp->name, pinp->aname); grcc_fprintf(GRCC_Stderr, "is already used.\n"); } erEnd("particle name is already defined."); } } pid = nParticles++; particles[pid] = new Particle(this, pid, pinp); } //-------------------------------------------------------------- void Model::addParticleEnd(void) { int p, ap; pdef = True; #ifdef OPTEXTONLY nallPart = 0; for (p = nParticles-1; p >= 1; p--) { if (!particles[p]->extonly) { ap = antiParticle(p); if (ap != p) { allPart[nallPart++] = ap; } } } for (p = 1; p < nParticles; p++) { if (!particles[p]->extonly) { allPart[nallPart++] = p; } } sorti(nallPart, allPart); #else nallPart = 0; for (p = nParticles-1; p >= 1; p--) { ap = antiParticle(p); if (ap != p) { allPart[nallPart++] = ap; } } for (p = 1; p < nParticles; p++) { allPart[nallPart++] = p; } sorti(nallPart, allPart); #endif } //-------------------------------------------------------------- void Model::addInteraction(IInput *iinp) { int vid, nlegs, j, k, c; int csum, lp2, lp; int plist[GRCC_MAXLEGS]; if (!pdef) { erEnd("call 'addParticleEnd' before 'addInteraction'"); } if (nInteracts >= GRCC_MAXMINTERACT) { erEnd("too many interactions in the model (GRCC_MAXMINTERACT)"); } nlegs = iinp->nplistn; if (nlegs >= GRCC_MAXLEGS) { erEnd("too many legs in an interaction (GRCC_MAXLEGS)"); } // check identifier if (defpart == GRCC_DEFBYCODE) { if (iinp->icode < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** vertex code %d should be positive\n", iinp->icode); } erEnd("vertex code should be positive"); } else { vid = findInteractionCode(iinp->icode); if (vid >= 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** vertex code %d is already used\n", iinp->icode); } erEnd("vertex code is already used"); } } } else if (defpart == GRCC_DEFBYNAME) { if (iinp->name == NULL || strlen(iinp->name) < 1) { erEnd("no name of vertex\n"); } vid = findInteractionName(iinp->name); if (vid >= 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** vertex name %s is already used\n", iinp->name); erEnd("vertex name is already used"); } } } else { #ifdef UNIQINTR // defpart =< 0 erEnd("illegal value of defpart"); #else // don't care about duplicated name/code of interaction ; #endif } vid = nInteracts++; for (j = 0; j < nlegs; j++) { if (Abs(defpart) == GRCC_DEFBYCODE) { plist[j] = findParticleCode(iinp->plistc[j]); if (plist[j] == 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** particle code %d ", iinp->plistc[j]); grcc_fprintf(GRCC_Stderr, "is not defined\n"); } erEnd("particle is not defined (code)"); } } else if (Abs(defpart) == GRCC_DEFBYNAME) { plist[j] = findParticleName(iinp->plistn[j]); if (plist[j] == 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** particle name %s ", iinp->plistn[j]); grcc_fprintf(GRCC_Stderr, "is not defined\n"); } erEnd("particle is not defined (name)"); } } } csum = 0; for (j = 0; j < ncouple; j++) { c = iinp->cvallist[j]; if (c < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** illegal value of c-constants \n"); for (k = 0; k < ncouple; k++) { grcc_fprintf(GRCC_Stderr, " %s = %d\n", cnlist[k], iinp->cvallist[k]); } } erEnd("illegal value of c-constants"); } csum += c; } if (csum < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** illegal total coupling-constants %d\n", csum); for (k = 0; k < ncouple; k++) { grcc_fprintf(GRCC_Stderr, " %s = %d\n", cnlist[k], iinp->cvallist[k]); } } erEnd("illegal value of c-constants"); } // assume : csum = nlegs - 2 + 2*loop lp2 = csum - nlegs + 2; if (lp2 % 2 != 0 || lp2 < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** illegal coupling const : "); grcc_fprintf(GRCC_Stderr, "nlegs - 2 + 2*loop: 2*loop = %d\n", lp2); } erEnd("illegal value of c-constants"); } lp = lp2/2; maxnlegs = Max(maxnlegs, nlegs); maxloop = Max(maxloop , lp); maxcpl = Max(maxcpl , csum); interacts[vid] = new Interaction(this, vid, iinp->name, iinp->icode, iinp->cvallist, nlegs, plist, csum, lp); } //-------------------------------------------------------------- void Model::addInteractionEnd(void) { int lst[GRCC_MAXMINTERACT]; int tcp[GRCC_MAXMINTERACT], tlg[GRCC_MAXMINTERACT]; int tnvl[GRCC_MAXMINTERACT], *tvl[GRCC_MAXMINTERACT]; Interaction *vt; int cp, lg, j, k, p; vdef = True; ncplgcp = 0; for (cp = 0; cp <= maxcpl; cp++) { for (lg = 0; lg <= maxnlegs; lg++) { k = 0; for (j = 0; j < nInteracts; j++) { vt = interacts[j]; if (vt->csum == cp && vt->nlegs == lg) { lst[k++] = j; } } if (k > 0) { tcp[ncplgcp] = cp; tlg[ncplgcp] = lg; tnvl[ncplgcp] = k; tvl[ncplgcp] = intdup(k, lst); ncplgcp++; } } } cplgcp = intdup(ncplgcp, tcp); cplglg = intdup(ncplgcp, tlg); cplgnvl = intdup(ncplgcp, tnvl); cplgvl = new int*[ncplgcp]; for (j = 0; j < ncplgcp; j++) { if (cplgnvl[j] > 0) { cplgvl[j] = tvl[j]; } else { cplgvl[j] = NULL; } } for (j = 0; j < nInteracts; j++) { vt = interacts[j]; if (vt->slist != NULL) { erEnd("addInteractionEnd: vt->nslist != NULL"); } vt->slist = intdup(vt->nplist, vt->plist); vt->nslist = toSList(vt->nplist, vt->slist); } for (p = 0; p < nParticles; p++) { particles[p]->cmindeg = 0; particles[p]->cmaxdeg = 0; } for (j = 0; j < nInteracts; j++) { vt = interacts[j]; for (k = 0; k < vt->nplist; k++) { p = abs(vt->plist[k]); if (particles[p]->cmindeg == 0) { particles[p]->cmindeg = vt->nlegs; particles[p]->cmaxdeg = vt->nlegs; } else { particles[p]->cmindeg = Min(particles[p]->cmindeg, vt->nlegs); particles[p]->cmaxdeg = Max(particles[p]->cmaxdeg, vt->nlegs); } } } } //-------------------------------------------------------------- int Model::findParticleName(const char *name) { int j; for (j = 0; j < nParticles; j++) { if (strcmp(name, particles[j]->name) == 0) { return j; } } for (j = 0; j < nParticles; j++) { if (strcmp(name, particles[j]->aname) == 0) { return -j; } } return 0; } //-------------------------------------------------------------- int Model::findParticleCode(int pcd) { int j; for (j = 0; j < nParticles; j++) { if (pcd == particles[j]->pcode) { return j; } else if (pcd == particles[j]->acode) { return -j; } } return 0; } //-------------------------------------------------------------- char *Model::particleName(int p) { int q; if (Abs(p) >= nParticles) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "\n*** Model::particleName: "); grcc_fprintf(GRCC_Stderr, "illegal particle id=%d\n", p); } erEnd("Model::particleName: illegal particle"); } if (p < 0) { q = - p; } else { q = p; } return particles[q]->particleName(p); } //-------------------------------------------------------------- int Model::particleCode(int p) { int q; if (Abs(p) >= nParticles) { grcc_fprintf(GRCC_Stderr, "\n*** Model::particleCode: illegal particle id=%d\n", p); erEnd("Model::particleCode: illegal particle"); } if (p < 0) { q = - p; } else { q = p; } return particles[q]->particleCode(p); } //-------------------------------------------------------------- void Model::prParticleArray(int n, int *a, const char *msg) { int j; grcc_fprintf(GRCC_Stdout, "["); for (j = 0; j < n; j++) { if (j != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "%s", particleName(a[j])); } grcc_fprintf(GRCC_Stdout, "]%s", msg); } //-------------------------------------------------------------- int Model::findMClass(const int cpl, const int dgr) { int j; for (j = 0; j < ncplgcp; j++) { if (cplgcp[j] == cpl && cplglg[j] == dgr) { return j; } } return -1; } //-------------------------------------------------------------- int Model::normalParticle(int pt) { int ptc = Abs(pt); Particle *p; if (ptc >= nParticles) { return 0; } p = particles[ptc]; if (p->isNeutral()) { return ptc; } else { return pt; } } //-------------------------------------------------------------- int Model::antiParticle(int pt) { int ptc = Abs(pt); Particle *p; p = particles[ptc]; if (p->isNeutral()) { return ptc; } else { return -pt; } } //-------------------------------------------------------------- int *Model::allParticles(int *len) { *len = nallPart; return allPart; } //-------------------------------------------------------------- int Model::findInteractionName(const char *name) { int j; for (j = 0; j < nInteracts; j++) { if (strcmp(name, interacts[j]->name) == 0) { return j; } } return -1; } //-------------------------------------------------------------- int Model::findInteractionCode(int icd) { int j; for (j = 0; j < nInteracts; j++) { if (icd == interacts[j]->icode) { return j; } } return -1; } //-------------------------------------------------------------- void Model::printMInput(MInput *min) { grcc_fprintf(GRCC_Stdout, " \"Model\": [\"%s\", %d, [", min->name, min->ncouple); for (int j = 0; j < min->ncouple; j++) { if (j != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "\"%s\"", min->cnamlist[j]); } grcc_fprintf(GRCC_Stdout, "], "); if (min->defpart == GRCC_DEFBYCODE) { grcc_fprintf(GRCC_Stdout, "\"ByCode\""); } else { grcc_fprintf(GRCC_Stdout, "\"ByName\""); } grcc_fprintf(GRCC_Stdout, "],\n"); } //-------------------------------------------------------------- void Model::printPInput(PInput *pin) { grcc_fprintf(GRCC_Stdout, " [\"%s\"(%d), \"%s\"(%d), \"%s\"(%d), %d],\n", pin->name, pin->pcode, pin->aname, pin->acode, pin->ptypen, pin->ptypec, pin->extonly); } //-------------------------------------------------------------- void Model::printIInput(IInput *iin) { int j; grcc_fprintf(GRCC_Stdout, " [\"%s\"(%d), %d, [", iin->name, iin->icode, iin->nplistn); for (j = 0; j < iin->nplistn; j++) { if (j != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "\"%s\"(%d)", iin->plistn[j], iin->plistc[j]); } grcc_fprintf(GRCC_Stdout, "], ["); for (j = 0; j < GRCC_MAXNCPLG; j++) { if (j != 0) { grcc_fprintf(GRCC_Stdout, ", "); } grcc_fprintf(GRCC_Stdout, "%d", iin->cvallist[j]); } grcc_fprintf(GRCC_Stdout, "],\n"); } //************************************************************** // proc.cc //============================================================== // class PNodeClass //-------------------------------------------------------------- PNodeClass::PNodeClass(SProcess *spc, int nnods, int nclss, NCInput *cls) { // Create a class of nodes // nnodes : # nodes // nclss : # classes // cls : table of class inputs // int j, k, nn, lp2; Bool ok = True; sproc = spc; nnodes = nnods; nclass = nclss; deg = new int[nclass]; type = new int[nclass]; particle = new int[nclass]; count = new int[nclass]; couple = new int[nclass]; cmindeg = new int[nclass]; cmaxdeg = new int[nclass]; for (j = 0; j < nclass; j++) { deg[j] = cls[j].cldeg; count[j] = cls[j].clnum; type[j] = cls[j].cltyp; cmindeg[j] = cls[j].cmind; cmaxdeg[j] = cls[j].cmaxd; particle[j] = cls[j].ptcl; couple[j] = cls[j].cple; lp2 = (couple[j]-deg[j]+2); if (!isATExternal(type[j]) && (lp2 % 2 != 0 || lp2 < 0)) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** PNodeClass: illegal loop: " ": 2*loop=cpl[%d](%d)-deg[%d](%d)+2 =2*loop = %d\n", j, couple[j], j, deg[j], lp2); for (k = 0; k < nclss; k++) { grcc_fprintf(GRCC_Stderr, "k=%d, deg=%d, typ=%d, ptcl=%d, ", k, deg[k], type[k], particle[k]); grcc_fprintf(GRCC_Stderr, "cpl=%d, cnt=%d\n", couple[k], count[k]); } } ok = False; } } if (!ok) { erEnd("PNodeClass: illegal loop"); } cl2nd = new int[nclass+1]; nd2cl = new int[nnodes]; cl2mcl = new int[nnodes]; nn = 0; for (j = 0; j < nclass; j++) { cl2nd[j] = nn; for (k = 0; k < count[j]; k++, nn++) { nd2cl[nn] = j; } if (isATExternal(type[j])) { cl2mcl[j] = -1; } else { cl2mcl[j] = spc->model->findMClass(couple[j], deg[j]); if (cl2mcl[j] < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** PNodeClass : no vertex : "); grcc_fprintf(GRCC_Stderr, "coupling=%d, degree=%d\n", couple[j], deg[j]); } erEnd("PNodeClass : no vertex"); } } } cl2nd[nclass] = nnodes; } //-------------------------------------------------------------- PNodeClass::PNodeClass(SProcess *spc, int nnods, int nclss, int *dgs, int *typ, int *ptcl, int *cpl, int *cnt, int *cmind, int *cmaxd) { // Create a class of nodes // nnodes : # nodes // nclss : # classes // dgs : degree of a node, which is common to the vertices in a class // typ : initial/final/vertex // ptcl : particle code or list of possible interactions // cpl : values of coupling constants. // cnt : the number of nodes in this class // int j, k, nn, lp2; Bool ok = True; sproc = spc; nnodes = nnods; nclass = nclss; deg = new int[nclass]; type = new int[nclass]; particle = new int[nclass]; count = new int[nclass]; couple = new int[nclass]; cmindeg = new int[nclass]; cmaxdeg = new int[nclass]; for (j = 0; j < nclass; j++) { deg[j] = dgs[j]; type[j] = typ[j]; particle[j] = ptcl[j]; count[j] = cnt[j]; couple[j] = cpl[j]; cmindeg[j] = cmind[j]; cmaxdeg[j] = cmaxd[j]; lp2 = (cpl[j]-dgs[j]+2); if (!isATExternal(type[j]) && (lp2 % 2 != 0 || lp2 < 0)) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** PNodeClass: illegal loop: " ": 2*loop=cpl[%d](%d)-deg[%d](%d)+2 =2*loop = %d\n", j, cpl[j], j, dgs[j], lp2); for (k = 0; k < nclss; k++) { grcc_fprintf(GRCC_Stderr, "k=%d, dgs=%d, typ=%d, ptcl=%d, ", k, dgs[k], typ[k], ptcl[k]); grcc_fprintf(GRCC_Stderr, "cpl=%d, cnt=%d\n", cpl[k], cnt[k]); } } ok = False; } } if (!ok) { erEnd("PNodeClass: illegal loop"); } cl2nd = new int[nclass+1]; nd2cl = new int[nnodes]; cl2mcl = new int[nnodes]; nn = 0; for (j = 0; j < nclass; j++) { cl2nd[j] = nn; for (k = 0; k < count[j]; k++, nn++) { nd2cl[nn] = j; } if (isATExternal(type[j])) { cl2mcl[j] = -1; } else { cl2mcl[j] = spc->model->findMClass(couple[j], deg[j]); if (cl2mcl[j] < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** PNodeClass : no vertex : "); grcc_fprintf(GRCC_Stderr, "coupling=%d, degree=%d\n", couple[j], deg[j]); } erEnd("PNodeClass : no vertex"); } } } cl2nd[nclass] = nnodes; } //-------------------------------------------------------------- PNodeClass::~PNodeClass(void) { delete[] cl2mcl; delete[] nd2cl; delete[] cl2nd; delete[] cmaxdeg; delete[] cmindeg; delete[] couple; delete[] count; delete[] particle; delete[] type; delete[] deg; } //-------------------------------------------------------------- void PNodeClass::prPNodeClass(void) { int j; grcc_fprintf(GRCC_Stdout, "+++ PNodeClass: nclass=%d, nnodes=%d\n", nclass, nnodes); for (j = 0; j < nclass; j++) { prElem(j); } grcc_fprintf(GRCC_Stdout, "\n"); } //-------------------------------------------------------------- void PNodeClass::prElem(int j) { int tp; grcc_fprintf(GRCC_Stdout, "%3d: %-7s(%2d), ", j, GRCC_AT_NdStr(type[j]), type[j]); grcc_fprintf(GRCC_Stdout, "deg=%d, count=%d, nodes[%d--%d], couple=%d, cmindeg=%d, cmaxdeg=%d", deg[j], count[j], cl2nd[j], cl2nd[j+1], couple[j], cmindeg[j], cmaxdeg[j]); tp = type[j]; if (isATExternal(tp)) { if (sproc->model != NULL) { grcc_fprintf(GRCC_Stdout, ", ptcl=%s ", sproc->model->particleName(particle[j])); } else { grcc_fprintf(GRCC_Stdout, ", ptcl=%d ", particle[j]); } } grcc_fprintf(GRCC_Stdout, "\n"); } //============================================================== // class SProcess //-------------------------------------------------------------- SProcess::SProcess(Model *mdl, Process *prc, Options *opts, int sid, int *clst, int ncls, int *cdeg, int *ctyp, int *ptcl, int *cpl, int *cnum, int *cmind, int *cmaxd) { // Construct a Subprocess object // mdl : model // prc : process (may be NULL) // opts : options // sid : id of the sprocess // ncls : the number of classes // cdeg[ncls] : the table of degrees of nodes. // ctyp[ncls] : the table of nodes in the classes // ptcl[ncls] : particle(External)/interaction code(Internal) // cpl[ncls] : the table of total order of coupling constants. // cnum[ncls] : the table of nodes in the classes // cmind[ncls] : the table of min(deg of connectable vertex) // cmaxd[ncls] : the table of max(deg of connectable vertex) int j, cp, lp2, ndeg, nvrt, tcpl0; bool ok; if (ncls < 1) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: no class %d\n", ncls); erEnd("SProcess::SProcess: no Class"); } id = sid; model = mdl; proc = prc; opt = opts; nclass = ncls; nNodes = 0; nEdges = 0; nExtern = 0; tCouple = 0; loop = 0; mgraph = NULL; egraph = NULL; astack = NULL; mgrcount = 0; agrcount = 0; extperm = 1; // the results of the graph generation nMGraphs = 0; // the number of generated M-graphs nMOPI = 0; // the number of 1PI M-graphs wMGraphs.setValue(0,1); // the weighted sum of M-graphs wMOPI.setValue(0,1); // the weighted sum of 1PI M-graphs nAGraphs = 0; // the number of generated A-graphs nAOPI = 0; // the number of 1PI A-graphs wAGraphs.setValue(0,1); // the weighted sum of A-graphs wAOPI.setValue(0,1); // the weighted sum of 1PI A-graphs // check input nNodes = 0; nExtern = 0; ndeg = 0; nvrt = 0; ok = True; tcpl0 = 0; for (j = 0; j < model->ncouple; j++) { clist[j] = clst[j]; tcpl0 += clist[j]; } for (j = 0; j < nclass; j++) { cp = cpl[j]; if (cp > 0) { lp2 = cpl[j] - cdeg[j] + 2; if (lp2 % 2 != 0 || lp2 < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop:" "class %d, cp=%d, deg=%d, lp2=%d\n", j, cp, cdeg[j], lp2); } ok = False; } } tCouple += cp*cnum[j]; ndeg += cdeg[j]*cnum[j]; if (!isATExternal(ctyp[j])) { nvrt += cnum[j]; } else if (isATExternal(ctyp[j])) { if (model->normalParticle(ptcl[j]) == 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "illegal particle code: "); grcc_fprintf(GRCC_Stderr, "code: class %d, ptcl=%d\n", j, ptcl[j]); } ok = False; } else { nExtern += cnum[j]; } extperm *= factorial(cnum[j]); } else { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal type: "); grcc_fprintf(GRCC_Stderr, "class %d, type=%d\n", j, ctyp[j]); } ok = False; } } if (tcpl0 != tCouple) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "illegal coupling constants:"); grcc_fprintf(GRCC_Stderr, " %d != %d\n", tcpl0, tCouple); } ok = False; } if (ndeg == nExtern) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "no vertices: "); grcc_fprintf(GRCC_Stderr, "nExtern=%d, ndeg=%d\n", nExtern, ndeg); } ok = False; } if (ndeg % 2 == 0) { nEdges = ndeg/2; } else { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "illegal total deg = %d (not even)\n", ndeg); } ok = False; } nNodes = nvrt + nExtern; if (nNodes >= GRCC_MAXNODES) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "too many nodes = %d\n", nNodes); grcc_fprintf(GRCC_Stderr, " nExtern=%d, nvert=%d (GRCC_MAXNODES)\n", nExtern, nvert); } ok = False; } if (!ok) { prSProcess(); erEnd("SProcess::SProcess: illegal input"); } if (proc == NULL) { opt->beginProc(NULL); } lp2 = tCouple - nExtern + 2; if (lp2 % 2 != 0 || lp2 < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop: " "tCouple=%d, nExtern=%d, 2*loop=%d\n", tCouple, nExtern, lp2); } ok = False; } loop = lp2/2; // stack for assignment if (opt->values[GRCC_OPT_Step] == GRCC_AGraph) { astack = new AStack(GRCC_MAXNSTACK, GRCC_MAXESTACK); } // save to PNodeClass object pnclass = new PNodeClass(this, nNodes, nclass, cdeg, ctyp, ptcl, cpl, cnum, cmind, cmaxd); } //-------------------------------------------------------------- SProcess::SProcess(Model *mdl, Process *prc, Options *opts, int sid, int *clst, int ncls, NCInput *cls) { // Construct a Subprocess object // mdl : model // prc : process (may be NULL) // opts : options // sid : id of the sprocess // ncls : the number of classes // cls : input data of classes int j, cp, lp2, ndeg, nvrt, tcpl0; bool ok; if (ncls < 1) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: no class %d\n", ncls); erEnd("SProcess::SProcess: no Class"); } id = sid; model = mdl; proc = prc; opt = opts; nclass = ncls; nNodes = 0; nEdges = 0; nExtern = 0; tCouple = 0; loop = 0; mgraph = NULL; egraph = NULL; astack = NULL; mgrcount = 0; agrcount = 0; extperm = 1; // the results of the graph generation nMGraphs = 0; // the number of generated M-graphs nMOPI = 0; // the number of 1PI M-graphs wMGraphs.setValue(0,1); // the weighted sum of M-graphs wMOPI.setValue(0,1); // the weighted sum of 1PI M-graphs nAGraphs = 0; // the number of generated A-graphs nAOPI = 0; // the number of 1PI A-graphs wAGraphs.setValue(0,1); // the weighted sum of A-graphs wAOPI.setValue(0,1); // the weighted sum of 1PI A-graphs // check input nNodes = 0; nExtern = 0; ndeg = 0; nvrt = 0; ok = True; tcpl0 = 0; for (j = 0; j < model->ncouple; j++) { clist[j] = clst[j]; tcpl0 += clist[j]; } for (j = 0; j < nclass; j++) { cp = cls[j].cple; if (cp > 0) { lp2 = cls[j].cple - cls[j].cldeg + 2; if (lp2 % 2 != 0 || lp2 < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop: " "class %d, cp=%d, deg=%d, lp2=%d\n", j, cp, cls[j].cldeg, lp2); } ok = False; } } tCouple += cp*cls[j].clnum; ndeg += cls[j].cldeg*cls[j].clnum; if (!isATExternal(cls[j].cltyp)) { nvrt += cls[j].clnum; } else if (isATExternal(cls[j].cltyp)) { if (model->normalParticle(cls[j].ptcl) == 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "illegal particle code: "); grcc_fprintf(GRCC_Stderr, "code: class %d, ptcl=%d\n", j, cls[j].ptcl); } ok = False; } else { nExtern += cls[j].clnum; } extperm *= factorial(cls[j].clnum); } else { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal type: "); grcc_fprintf(GRCC_Stderr, "class %d, type=%d\n", j, cls[j].cltyp); } ok = False; } } if (tcpl0 != tCouple) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "illegal coupling constants:"); grcc_fprintf(GRCC_Stderr, " %d != %d\n", tcpl0, tCouple); } ok = False; } if (ndeg == nExtern) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "no vertices: "); grcc_fprintf(GRCC_Stderr, "nExtern=%d, ndeg=%d\n", nExtern, ndeg); } ok = False; } if (ndeg % 2 == 0) { nEdges = ndeg/2; } else { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "illegal total deg = %d (not even)\n", ndeg); } ok = False; } nNodes = nvrt + nExtern; if (nNodes >= GRCC_MAXNODES) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: "); grcc_fprintf(GRCC_Stderr, "too many nodes = %d\n", nNodes); grcc_fprintf(GRCC_Stderr, " nExtern=%d, nvert=%d (GRCC_MAXNODES)\n", nExtern, nvert); } ok = False; } if (!ok) { erEnd("SProcess::SProcess: illegal input"); } if (proc == NULL) { opt->beginProc(NULL); } lp2 = tCouple - nExtern + 2; if (lp2 % 2 != 0 || lp2 < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop: " "tCouple=%d, nExtern=%d, 2*loop=%d\n", tCouple, nExtern, lp2); } ok = False; } loop = lp2/2; // stack for assignment if (opt->values[GRCC_OPT_Step] == GRCC_AGraph) { astack = new AStack(GRCC_MAXNSTACK, GRCC_MAXESTACK); } // save to PNodeClass object pnclass = new PNodeClass(this, nNodes, nclass, cls); } //-------------------------------------------------------------- SProcess::~SProcess(void) { delete pnclass; delete astack; delete mgraph; model = NULL; } //-------------------------------------------------------------- void SProcess::prSProcess(void) { grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, "+++ Subprocess %d, class=%d\n", id, nclass); if (pnclass != NULL) { pnclass->prPNodeClass(); } else { grcc_fprintf(GRCC_Stdout, " pnclass = NULL\n"); } } //-------------------------------------------------------------- BigInt SProcess::generate(void) { // Entry point of Feynman graph generation int cldeg[GRCC_MAXNODES], clnum[GRCC_MAXNODES], cltyp[GRCC_MAXNODES]; int cmind[GRCC_MAXNODES], cmaxd[GRCC_MAXNODES]; int ncl; BigInt ng; ncl = toMNodeClass(cltyp, cldeg, clnum, cmind, cmaxd); opt->beginSubProc(this); mgraph = new MGraph(id, ncl, cldeg, clnum, cltyp, cmind, cmaxd, opt); ng = mgraph->generate(); opt->endSubProc(); delete mgraph; mgraph = NULL; return ng; } //-------------------------------------------------------------- int SProcess::toMNodeClass(int *cltyp, int *cldeg, int *clnum, int *cmind, int *cmaxd) { int j; for (j = 0; j < nclass; j++) { if (isATExternal(pnclass->type[j])) { cltyp[j] = -1; } else { cltyp[j] = (pnclass->couple[j]-pnclass->deg[j]+2)/2; } cldeg[j] = pnclass->deg[j]; clnum[j] = pnclass->count[j]; cmind[j] = pnclass->cmindeg[j]; cmaxd[j] = pnclass->cmaxdeg[j]; } return nclass; } //-------------------------------------------------------------- void SProcess::assign(MGraph *mgr) { PNodeClass *pnc; pnc = match(mgr); agraph = new Assign(this, mgr, pnc); #ifdef CHECK agraph->checkAG("SProcess::assign"); #endif delete pnc; delete agraph; agraph = NULL; } //-------------------------------------------------------------- PNodeClass *SProcess::match(MGraph *mgr) { PNodeClass *pnc = NULL; int typ[GRCC_MAXNODES], dgs[GRCC_MAXNODES]; int cnt[GRCC_MAXNODES], ptcl[GRCC_MAXNODES]; int cpl[GRCC_MAXNODES]; int n2m[GRCC_MAXNODES]; int cmind[GRCC_MAXNODES], cmaxd[GRCC_MAXNODES]; int j, k, l, nd, mc, mcl, mclss; if (mgr->nNodes != nNodes) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::match: different nNodes=%d != %d\n", nNodes, mgr->nNodes); } erEnd("SProcess::match: different nNodes"); } mcl = toMNodeClass(typ, dgs, cnt, cmind, cmaxd); nd = 0; for (j = 0; j < mcl; j++) { for (k = 0; k < cnt[j]; k++, nd++) { n2m[nd] = j; } } nd = 0; mclss = mgr->curcl->nClasses; for (j = 0; j < mclss; j++) { for (k = 0; k < mgr->curcl->clist[j]; k++, nd++) { mc = mgr->nodes[nd]->clss; if (mc != n2m[nd]) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** SProcess::match: "); grcc_fprintf(GRCC_Stderr, "inconsistent class\n"); for (l = 0; l < nNodes; l++) { grcc_fprintf(GRCC_Stderr, " %d: %d, %d\n", j, mgr->nodes[l]->clss, n2m[l]); } } erEnd("SProcess::match: inconsistent class"); } } } for (j = 0; j < mcl; j++) { dgs[j] = pnclass->deg[j]; typ[j] = pnclass->type[j]; ptcl[j] = pnclass->particle[j]; cnt[j] = pnclass->count[j]; cpl[j] = pnclass->couple[j]; cmind[j] = pnclass->cmindeg[j]; cmaxd[j] = pnclass->cmaxdeg[j]; } pnc = new PNodeClass(this, nNodes, mcl, dgs, typ, ptcl, cpl, cnt, cmind, cmaxd); return pnc; } //-------------------------------------------------------------- void SProcess::resultMGraph(BigInt nmgraphs, Fraction mwsum, BigInt nmopi, Fraction mwopi) { nMGraphs += nmgraphs; nMOPI += nmopi; wMGraphs.add(mwsum); wMOPI.add(mwopi); } //-------------------------------------------------------------- void SProcess::resultAGraph(BigInt nmgraphs, Fraction mwsum, BigInt nmopi, Fraction mwopi) { nAGraphs += nmgraphs; nAOPI += nmopi; wAGraphs.add(mwsum); wAOPI.add(mwopi); } //-------------------------------------------------------------- void SProcess::endMGraph(MGraph *mgr) { egraph = mgr->egraph; if (opt->values[GRCC_OPT_Step] != GRCC_MGraph) { assign(mgr); } } //-------------------------------------------------------------- void SProcess::endAGraph(EGraph *egr) { egraph = egr; } //============================================================== // class Process //-------------------------------------------------------------- Process::Process(int pid, Model *modl, Options *optn, int nini, int *intlPrt, int nfin, int *finlPrt, int *coupling) { // Define a process and construct a set of sprocesses // model : Model object // optn : Option object // initlPart : list of particle-id of initlPart particles // finalPart : list of particle-id of final particles // coupling : list of coupling constants int j, lp2; Bool ok; char buff[MAXSTR]; id = pid; model = modl; opt = optn; ninitl = nini; nfinal = nfin; initlPart = intdup(ninitl, intlPrt); finalPart = intdup(nfinal, finlPrt); // count total number of coupling constants. ctotal = 0; for (j = 0; j < GRCC_MAXNCPLG; j++) { if (j < model->ncouple) { clist[j] = coupling[j]; ctotal += coupling[j]; } else { clist[j] = 0; } } if (ctotal < 1) { erEnd("Process: coupling constant = 0"); } nExtern = 0; loop = -1; maxnlegs = 0; mgrcount = 0; agrcount = 0; // table of sprocesses nSubproc = 0; sproc = NULL; // the results of the graph generation nMGraphs = 0; // the number of generated M-graphs nMOPI = 0; // the number of 1PI M-graphs wMGraphs.setValue(0,1); // the weighted sum of M-graphs wMOPI.setValue(0,1); // the weighted sum of 1PI M-graphs nAGraphs = 0; // the number of generated A-graphs nAOPI = 0; // the number of 1PI A-graphs wAGraphs.setValue(0,1); // the weighted sum of A-graphs wAOPI.setValue(0,1); // the weighted sum of 1PI A-graphs ok = True; // numbers nExtern = ninitl + nfinal; maxnlegs = Max(nExtern, model->maxnlegs); // count loops lp2 = ctotal - nExtern + 2; if (lp2 % 2 != 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** cannot generate : 2*loop is odd : " "2*loop = %d, ctotal=%d, nExtern=%d\n", lp2, ctotal, nExtern); } ok = False; } else if (lp2 < 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** cannot make a connected graph : " "2*loop=%d, ctotal=%d, nExtern=%d\n", lp2, ctotal, nExtern); } ok = False; } loop = lp2 / 2; if (!ok) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** Process: illegal input: lp2 = %d\n", lp2); } erEnd("Process: illegal input"); } if (opt->out->outgrp != NULL) { snprintf(buff, MAXSTR, "out%d.prp", pid); prProcessP(buff); } // construct sprocesses mkSProcess(); } //-------------------------------------------------------------- Process::~Process(void) { initlPart = delintdup(initlPart); finalPart = delintdup(finalPart); for (int j = 0; j < nSubproc; j++) { delete sptbl[j]; } // delete sproc; } //-------------------------------------------------------------- void Process::prProcess(void) { grcc_fprintf(GRCC_Stdout, "+++ process options : OPI = %d, (Step) = %d, coupling=%d: ", opt->values[GRCC_OPT_1PI], opt->values[GRCC_OPT_Step], ctotal); prIntArray(model->ncouple, clist, "\n"); } //-------------------------------------------------------------- void Process::prProcessP(const char *fname) { FILE *fp; if ((fp = fopen(fname, "w")) == NULL) { grcc_fprintf(GRCC_Stderr, "*** cannot open \"%s\"\n", fname); return; } fprintf(fp, "Process = {\n"); outProcP(fp); fprintf(fp, "};\n"); fclose(fp); } //-------------------------------------------------------------- void Process::outProcP(FILE *fp) { int j; if (model == NULL) { return; } fprintf(fp, " \"Model\": \"%s\",\n", model->name); fprintf(fp, " \"Initial\": ["); for (j = 0; j < ninitl; j++) { if (j != 0) { fprintf(fp, ", "); } fprintf(fp, "\"%s\"", model->particleName(initlPart[j])); } fprintf(fp, "],\n"); fprintf(fp, " \"Final\": ["); for (j = 0; j < nfinal; j++) { if (j != 0) { fprintf(fp, ", "); } fprintf(fp, "\"%s\"", model->particleName(finalPart[j])); } fprintf(fp, "],\n"); fprintf(fp, " \"Couple\": ["); for (j = 0; j < model->ncouple; j++) { if (j != 0) { fprintf(fp, ", "); } fprintf(fp, "%d", clist[j]); } fprintf(fp, "],\n"); fprintf(fp, " \"Options\": {\n"); for (j = 0; j < GRCC_OPT_Size; j++) { if (j == GRCC_OPT_Outgrf || j == GRCC_OPT_Outgrp) { continue; } fprintf(fp, " \"%s\":%d,\n", optDef[j].name, opt->values[j]); } fprintf(fp, " \"%s\":", optDef[GRCC_OPT_Outgrf].name); if (opt->out->outgrf != NULL) { fprintf(fp, "\"%s\",\n", opt->out->outgrf); } else { fprintf(fp, "0,\n"); } fprintf(fp, " \"%s\":", optDef[GRCC_OPT_Outgrp].name); if (opt->out->outgrp != NULL) { fprintf(fp, "\"%s\",\n", opt->out->outgrp); } else { fprintf(fp, "0,\n"); } fprintf(fp, " }\n"); } //-------------------------------------------------------------- void Process::mkSProcess(void) { // Construct sprocesses // Each sprocess is a set of nodes whose degree and order of // coupling constants are determined. // Only the total coupling constants are considered here even if // two or more coupling constants are defined in the model NCInput cls[GRCC_MAXMINTERACT]; int r, j, k, lin2, nvtx, nleg, nc, n0; int nl[GRCC_MAXMINTERACT]; double proct0 = 0, proct1 = 0; if (model->ncplgcp < 1) { erEnd("function 'addInteractionEnd' has not been called"); } // output file to start process opt->beginProc(this); // starting time Second(&proct0); // generate all possible number of (nl[i]), // \sum_i nl[i]*cplgcp[i] = (total number of coupling constants) r = -1; nSubproc = 0; ngraphs = 0; nopi = 0; wgraphs = 0; wopi = 0; // for partitions of (leg, order) while (nextPart(ctotal, model->ncplgcp, model->cplgcp, nl, &r)) { // count the total number of vertices and legs. nvtx = 0; nleg = 0; for (j = 0; j < model->ncplgcp; j++) { nvtx += nl[j]; nleg += nl[j]*model->cplglg[j]; } // count loops lin2 = nExtern + nleg; if (lin2 % 2 != 0) { continue; } loop = lin2/2 - nExtern - nvtx + 1; if (loop < 0) { continue; } nc = 0; if (opt->values[GRCC_OPT_SymmInitial]) { n0 = nc; for (j = 0; j < ninitl; j++) { for (k = n0; k < nc; k++) { if (cls[k].ptcl == initlPart[j]) { cls[k].clnum++; break; } } if (k >= nc) { cls[nc].ptcl = initlPart[j]; cls[nc].clnum = 1; cls[nc].cple = 0; cls[nc].clnum = 1; cls[nc].cldeg = 1; cls[nc].cltyp = GRCC_AT_Initial; cls[nc].ptcl = initlPart[j]; cls[nc].cmind = model->particles[Abs(cls[nc].ptcl)]->cmindeg; cls[nc].cmaxd = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg; if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) { cls[nc].cmind = Max(cls[nc].cmind, 3); } nc++; } } } else { for (j = 0; j < ninitl; j++) { cls[nc].ptcl = initlPart[j]; cls[nc].clnum = 1; cls[nc].cple = 0; cls[nc].cldeg = 1; cls[nc].cltyp = GRCC_AT_Initial; cls[nc].cmind = model->particles[Abs(cls[nc].ptcl)]->cmindeg; cls[nc].cmaxd = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg; if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) { cls[nc].cmind = Max(cls[nc].cmind, 3); } nc++; } } if (opt->values[GRCC_OPT_SymmFinal]) { n0 = nc; for (j = 0; j < nfinal; j++) { for (k = n0; k < nc; k++) { if (cls[k].ptcl == model->antiParticle(finalPart[j])) { cls[k].clnum++; break; } } if (k >= nc) { cls[nc].ptcl = model->antiParticle(finalPart[j]); cls[nc].clnum = 1; cls[nc].cple = 0; cls[nc].cldeg = 1; cls[nc].cltyp = GRCC_AT_Final; cls[nc].cmind = model->particles[Abs(cls[nc].ptcl)]->cmindeg; cls[nc].cmaxd = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg; if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) { cls[nc].cmind = Max(cls[nc].cmind, 3); } nc++; } } } else { for (j = 0; j < nfinal; j++) { cls[nc].ptcl = model->antiParticle(finalPart[j]); cls[nc].cldeg = 1; cls[nc].cple = 0; cls[nc].clnum = 1; cls[nc].cltyp = GRCC_AT_Final; cls[nc].cmind = model->particles[Abs(cls[nc].ptcl)]->cmindeg; cls[nc].cmaxd = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg; if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) { cls[nc].cmind = Max(cls[nc].cmind, 3); } nc++; } } for (j = 0; j < model->ncplgcp; j++) { if (nl[j] > 0) { cls[nc].ptcl = 0; cls[nc].cple = model->cplgcp[j]; cls[nc].cldeg = model->cplglg[j]; cls[nc].clnum = nl[j]; // number of loops cls[nc].cltyp = (model->cplgcp[j] - model->cplglg[j] + 2)/2; cls[nc].cmind = 0; cls[nc].cmaxd = 0; nc++; } } // create a sprocess ??? to be rewritten sproc = new SProcess(model, this, opt, nSubproc, clist, nc, cls); // list of sprocesses if (nSubproc >= GRCC_MAXSUBPROCS) { erEnd("Subclass: too many sprocesses (GRCC_MAXSUBPROCS)"); } sptbl[nSubproc++] = sproc; // generate M-graphs sproc->generate(); // summation of the numbers and weighted numbers of graphs nMGraphs += sproc->nMGraphs; nMOPI += sproc->nMOPI; wMGraphs.add(sproc->wMGraphs); wMOPI.add(sproc->wMOPI); nAGraphs += sproc->nAGraphs; nAOPI += sproc->nAOPI; wAGraphs.add(sproc->wAGraphs); wAOPI.add(sproc->wAOPI); if (nAGraphs > 0) { ngraphs = nAGraphs; } else { ngraphs = nAGraphs; } // delete sproc; // sproc = NULL; } // ending time Second(&proct1); sec = proct1-proct0; // output file to finish process opt->endProc(); } //************************************************************** // mgraph.cc //============================================================== //-------------------------------------------------------------- MNodeClass::MNodeClass(int nnodes, int nclasses) { // Input // nnodes : possible maximal number of nodes // nclasses : possible maximal number of classes int j, k; nNodes = nnodes; nClasses = nclasses; maxdeg = 0; for (j = 0; j < nNodes; j++) { for (k = 0; k < nNodes; k++) { clmat[j][k] = 0; } clist[j] = 0; ndcl[j] = 0; flist[j] = 0; clord[j] = 0; cmindeg[j] = 0; cmaxdeg[j] = 0; } flist[nNodes] = 0; flg0 = 0; flg1 = 0; flg2 = 0; } //-------------------------------------------------------------- MNodeClass::~MNodeClass(void) { } //============================================================== // class MNodeClass //-------------------------------------------------------------- void MNodeClass::init(int *cl, int mxdeg, int **adjmat) { // initialize the object // Argument // cl[j] : list of number of nodes in the j-th class // mxdeg : maximum degree to nodes // adjmat[j][k] : adjacency matrix int j; for (j = 0; j < nClasses; j++) { clist[j] = cl[j]; clord[j] = j; } maxdeg = mxdeg; mkNdCl(); mkClMat(adjmat); mkFlist(); flg0 = 0; flg1 = 0; flg2 = 0; } //-------------------------------------------------------------- void MNodeClass::copy(MNodeClass* mnc) { // copy MNodeClass 'mnc' to this object int j, k; nClasses = mnc->nClasses; for (k = 0; k < nClasses; k++) { clist[k] = mnc->clist[k]; } maxdeg = mnc->maxdeg; for (j = 0; j < nNodes; j++) { ndcl[j] = mnc->ndcl[j]; clord[j] = mnc->clord[j]; for (k = 0; k < nClasses; k++) { clmat[j][k] = mnc->clmat[j][k]; } } for (k = 0; k < nClasses+1; k++) { flist[k] = mnc->flist[k]; } } //-------------------------------------------------------------- void MNodeClass::mkFlist(void) { // Construct flist // The set of nodes in class 'c' is [flist[c],...,flist[c+1]-1] int j, f; f = 0; for (j = 0; j < nClasses; j++) { flist[j] = f; f += clist[j]; } flist[nClasses] = f; } //-------------------------------------------------------------- void MNodeClass::mkNdCl(void) { // Construct ndcl // ndcl[nd] = (the class id in which node 'nd' belongs) int c, k; int nd = 0; for (c = 0; c < nClasses; c++) { for (k = 0; k < clist[c]; k++) { ndcl[nd++] = c; } } } //-------------------------------------------------------------- int MNodeClass::clCmp(int nd0, int nd1, int cn) { // Comparison of two nodes 'nd0' and 'nd1' // in lexicographic ordering of [class, connection configuration] int cmp; // Wether two nodes are in a same class or not. cmp = ndcl[nd0] - ndcl[nd1]; if (cmp != 0) { return cmp; } // Sign '-' signifies the reverse ordering cmp = - cmpMNCArray(clmat[nd0], clmat[nd1], cn); if (cmp != 0) { return cmp; } return cmp; } //-------------------------------------------------------------- void MNodeClass::mkClMat(int **adjmat) { // Construct a matrix 'clmat[nd][tc]' which is the number // of edges connecting 'nd' and all nodes in class 'tc'. int nd, td, tc; for (nd = 0; nd < nNodes; nd++) { for (td = 0; td < nNodes; td++) { tc = ndcl[td]; // another node if (nd == td) { clmat[nd][tc] += CLWIGHTD(adjmat[nd][td]); } else { clmat[nd][tc] += CLWIGHTO(adjmat[nd][td]); } } } } //-------------------------------------------------------------- void MNodeClass::incMat(int nd, int td, int val) { // Increase the number of edges by 'val' between 'nd' and 'td'. int tdc = ndcl[td]; // class of 'td' clmat[nd][tdc] += val; // modify matrix 'clmat'. } //-------------------------------------------------------------- void MNodeClass::printMat(void) { // Print configuration matrix. int j1, j2; grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, "nClasses=%d", nClasses); grcc_fprintf(GRCC_Stdout, " clord="); prIntArray(nClasses, clord, ""); grcc_fprintf(GRCC_Stdout, " flist="); prIntArray(nClasses, flist, "\n"); grcc_fprintf(GRCC_Stdout, "flg = (%d, %d, %d)\n", flg0, flg1, flg2); // the first line grcc_fprintf(GRCC_Stdout, "nd: cl: "); for (j2 = 0; j2 < nClasses; j2++) { grcc_fprintf(GRCC_Stdout, "%2d ", j2); } grcc_fprintf(GRCC_Stdout, "\n"); // print raw for (j1 = 0; j1 < nNodes; j1++) { grcc_fprintf(GRCC_Stdout, "%2d; %2d: [", j1, ndcl[j1]); for (j2 = 0; j2 < nClasses; j2++) { grcc_fprintf(GRCC_Stdout, " %2d", clmat[j1][j2]); } grcc_fprintf(GRCC_Stdout, "]\n"); } } //-------------------------------------------------------------- int MNodeClass::cmpMNCArray(int *a0, int *a1, int ma) { int j, k; for (k = 0; k < ma; k++) { j = clord[k]; if (a0[j] < a1[j]) { return -1; } else if (a0[j] > a1[j]) { return 1; } } return 0; } //-------------------------------------------------------------- void MNodeClass::reorder(MGraph *mg) { int flg[GRCC_MAXNODES]; int co, cn; int f0, f1, f2; f0 = 0; f1 = 0; f2 = 0; for (co = 0; co < nClasses; co++) { cn = flist[co]; if (mg->nodes[cn]->freelg < 1) { flg[co] = 0; f0++; } else if (mg->nodes[cn]->freelg < mg->nodes[cn]->deg) { flg[co] = mg->nodes[cn]->deg + maxdeg*clist[co]; f1++; } else { flg[co] = maxdeg*(mg->nodes[cn]->deg + maxdeg*clist[co]); f2++; } } if (f0 < nClasses) { bsort(nClasses, clord, flg); } flg0 = f0; flg1 = f0 + f1; flg2 = f0 + f1 + f2; } //============================================================== // class MNode : nodes in MGraph //-------------------------------------------------------------- MNode::MNode(int vid, int vclss, NCInput *mgi) { // Arguments // vid : identifier of the vertex // vdeg : degree of the node // vextlp : external node (-1) or looped vertex // vclss : class of the node id = vid; // id of the node clss = vclss; // class to which the node belongs deg = mgi->cldeg; // degree of the node freelg = mgi->cldeg; // number of free legs extloop = mgi->cltyp; // external node or not cmindeg = mgi->cmind; // min(deg of connectable vertex) cmaxdeg = mgi->cmaxd; // max(deg of connectable vertex) } //-------------------------------------------------------------- MNode::MNode(int vid, int vdeg, int vextlp, int vclss, int cmin, int cmax) { // Arguments // vid : identifier of the vertex // vdeg : degree of the node // vextlp : external node (-1) or looped vertex // vclss : class of the node id = vid; // id of the node deg = vdeg; // degree of the node freelg = vdeg; // number of free legs clss = vclss; // class to which the node belongs extloop = vextlp; // external node or not cmindeg = cmin; // min(deg of connectable vertex) cmaxdeg = cmax; // max(deg of connectable vertex) } //=============================================================== // class MGraph : scalar graph expressed by matrix form //--------------------------------------------------------------- MGraph::MGraph(int pid, int ncl, int *cldeg, int *clnum, int *cltyp, int *cmind, int *cmaxd, Options *opts) { int nn, ne, j, k; // initial conditions nClasses = ncl; clist = new int[ncl]; opt = opts; mId = -1; mindeg = -1; maxdeg = -1; ne = 0; nn = 0; for (j = 0; j < nClasses; j++) { clist[j] = clnum[j]; nn += clnum[j]; ne += cldeg[j]*clnum[j]; if (mindeg < 0) { mindeg = cldeg[j]; } else { mindeg = Min(mindeg, cldeg[j]); } if (maxdeg < 0) { maxdeg = cldeg[j]; } else { maxdeg = Max(maxdeg, cldeg[j]); } } if (ne % 2 != 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "Sum of degrees are not even\n"); for (j = 0; j < nClasses; j++) { grcc_fprintf(GRCC_Stderr, "class %2d: %2d %2d %2d\n", j, cldeg[j], clnum[j], cltyp[j]); } } erEnd("illegal degrees of nodes"); } pId = pid; nNodes = nn; nodes = new MNode*[nNodes]; group = new SGroup(); #ifdef ORBITS orbits = new MOrbits(); #endif nEdges = ne / 2; nLoops = nEdges - nNodes + 1; egraph = new EGraph(nNodes, nEdges, maxdeg); nn = 0; nExtern = 0; for (j = 0; j < nClasses; j++) { for (k = 0; k < clist[j]; k++, nn++) { nodes[nn] = new MNode(nn, cldeg[j], cltyp[j], j, cmind[j], cmaxd[j]); egraph->setExtLoop(nn, cltyp[j]); if (cltyp[j] < 0) { nExtern++; } } } egraph->endSetExtLoop(); init(); } //--------------------------------------------------------------- MGraph::MGraph(int pid, int ncl, NCInput *mgi, Options *opts) { int nn, ne, j, k; // initial conditions nClasses = ncl; clist = new int[ncl]; opt = opts; mId = -1; mindeg = -1; maxdeg = -1; ne = 0; nn = 0; for (j = 0; j < nClasses; j++) { clist[j] = mgi[j].clnum; nn += mgi[j].clnum; ne += mgi[j].cldeg*mgi[j].clnum; if (mindeg < 0) { mindeg = mgi[j].cldeg; } else { mindeg = Min(mindeg, mgi[j].cldeg); } if (maxdeg < 0) { maxdeg = mgi[j].cldeg; } else { maxdeg = Max(maxdeg, mgi[j].cldeg); } } if (ne % 2 != 0) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "Sum of degrees are not even\n"); for (j = 0; j < nClasses; j++) { grcc_fprintf(GRCC_Stderr, "class %2d: %2d %2d %2d\n", j, mgi[j].cldeg, mgi[j].clnum, mgi[j].cltyp); } } erEnd("illegal degrees of nodes"); } pId = pid; nNodes = nn; if (nNodes < 0) { grcc_fprintf(GRCC_Stdout, "*** nNodes = %d\n", nNodes); erEnd("MGraph::MGrap : nNodes < 0"); } nodes = new MNode*[nNodes]; group = new SGroup(); #ifdef ORBITS orbits = new MOrbits(); #endif nEdges = ne / 2; nLoops = nEdges - nNodes + 1; egraph = new EGraph(nNodes, nEdges, maxdeg); nn = 0; nExtern = 0; for (j = 0; j < nClasses; j++) { for (k = 0; k < clist[j]; k++, nn++) { nodes[nn] = new MNode(nn, j, mgi+j); egraph->setExtLoop(nn, mgi[j].cltyp); if (mgi[j].cltyp < 0) { nExtern++; } } } egraph->endSetExtLoop(); init(); } //--------------------------------------------------------------- void MGraph::init(void) { // generated set of graphs cDiag = 0; c1PI = 0; cNoTadpole = 0; cNoTadBlock = 0; c1PINoTadBlock = 0; // the current graph adjMat = newMat(nNodes, nNodes, 0); nsym = ToBigInt(0); esym = ToBigInt(0); wscon = Fraction(0, 1); wsopi = Fraction(0, 1); // current node classification curcl = new MNodeClass(nNodes, nClasses); // table of n-edge connected components mconn = new MConn(nNodes, nEdges); // measures of efficiency ngen = 0; ngconn = 0; #ifdef MONITOR nCallRefine = 0; discardRefine = 0; discardDisc = 0; discardIso = 0; #endif // work space for isIsomorphic modmat = newMat(nNodes, nNodes, 0); // work space for bisearchME bidef = newArray(nNodes, 0); bilow = newArray(nNodes, 0); bicol = newArray(nNodes, 0); bicount = 0; } //--------------------------------------------------------------- MGraph::~MGraph(void) { int j; // group->delGroup(); bicol = deleteArray(bicol); bilow = deleteArray(bilow); bidef = deleteArray(bidef); modmat = deleteMat(modmat, nNodes); delete mconn; delete curcl; adjMat = deleteMat(adjMat, nNodes); #ifdef ORBITS delete orbits; #endif delete egraph; delete group; for (j = 0; j < nNodes; j++) { delete nodes[j]; nodes[j] = NULL; } delete[] nodes; delete[] clist; } //--------------------------------------------------------------- void MGraph::printAdjMat(MNodeClass *cl) { int j1, j2; grcc_fprintf(GRCC_Stdout, " "); for (j2 = 0; j2 < nNodes; j2++) { grcc_fprintf(GRCC_Stdout, " %2d", j2); } grcc_fprintf(GRCC_Stdout, "\n"); for (j1 = 0; j1 < nNodes; j1++) { grcc_fprintf(GRCC_Stdout, "%2d : [", j1); for (j2 = 0; j2 < nNodes; j2++) { grcc_fprintf(GRCC_Stdout, " %2d", adjMat[j1][j2]); } grcc_fprintf(GRCC_Stdout, "] %2d\n", cl->ndcl[j1]); } } //--------------------------------------------------------------- void MGraph::print(void) { int j; grcc_fprintf(GRCC_Stdout, "MGraph: pId=%d, cDiag=%ld, c1PI=%ld\n", pId, cDiag, c1PI); grcc_fprintf(GRCC_Stdout, " nNodes=%d, nEdges=%d, nExtern=%d, nLoops=%d " "mindeg=%d, maxdeg=%d, sym=(%ld, %ld)\n", nNodes, nEdges, nExtern, nLoops, mindeg, maxdeg, nsym, esym); grcc_fprintf(GRCC_Stdout, " Nodes=%d\n", nNodes); for (j = 0; j < nNodes; j++) { grcc_fprintf(GRCC_Stdout, " %2d: id=%d, deg=%d, clss=%d, extloop=%d, ", j, nodes[j]->id, nodes[j]->deg, nodes[j]->clss, nodes[j]->extloop); grcc_fprintf(GRCC_Stdout, "mind=%d, maxd=%d, freelg=%d\n", nodes[j]->cmindeg, nodes[j]->cmaxdeg, nodes[j]->freelg); } curcl->printMat(); grcc_fprintf(GRCC_Stdout, "\n"); printAdjMat(curcl); } //--------------------------------------------------------------- void MGraph::printPy(FILE *fp, long mId) { fprintf(fp, "#TGraph : (gseq, gid, nodes, amat)\n"); fprintf(fp, "(%ld, (%d, %d),\n", mId, pId, -1); fprintf(fp, " [ # nodes: (cid, deg0, loop, part)\n"); for (int j = 0; j < nNodes; j++) { fprintf(fp, " (%2d,%2d,%2d,%2d), # %2d\n", nodes[j]->clss, nodes[j]->deg, nodes[j]->extloop, 0, j); } fprintf(fp, " ],\n"); fprintf(fp, " [\n"); fprintf(fp, " #"); for (int j2 = 0; j2 < nNodes; j2++) { fprintf(fp, " %4d", j2); } fprintf(fp, "\n"); for (int j1 = 0; j1 < nNodes; j1++) { fprintf(fp, " ["); for (int j2 = 0; j2 < nNodes; j2++) { fprintf(fp, " %2d, ", adjMat[j1][j2]); } fprintf(fp, "], # %2d\n", j1); } fprintf(fp, " ], # nodes\n"); fprintf(fp, " [ # group of 2 elements\n"); fprintf(fp, " [],\n"); fprintf(fp, " ], # group\n"); fprintf(fp, ")\n"); } //--------------------------------------------------------------- Bool MGraph::isConnected(void) { // Check graph can be a connected one. // If a connected component without free leg is not the whole graph then // return False, otherwise return True. int j, n, nv; for (j = 0; j < nNodes; j++) { nodes[j]->visited = -1; } if (visit(0)) { return True; } nv = 0; for (n = 0; n < nNodes; n++) { if (nodes[n]->visited >= 0) { nv++; } } return (nv == nNodes); } //--------------------------------------------------------------- Bool MGraph::visit(int nd) { // Visiting connected node used for 'isConnected' // If child nodes has free legs, then this function returns True. // otherwise it returns False. int td; // This node has free legs. if (nodes[nd]->freelg > 0) { return True; } nodes[nd]->visited = 0; for (td = 0; td < nNodes; td++) { if ((adjMat[nd][td] > 0) && (nodes[td]->visited < 0)) { if (visit(td)) { return True; } } } // all the child nodes has no free legs. return False; } //--------------------------------------------------------------- Bool MGraph::isIsomorphic(MNodeClass *cl) { // Check whether the current graph is the Representative // of a isomorphic class. // nsym = symmetry factor by the permutation of nodes. // esym = symmetry factor by the permutation of edge. // If this graph is not a representative, then returns False. int j1, j2, cmp, nself; int *perm; nsym = ToBigInt(0); esym = ToBigInt(1); group->newGroup(nNodes, cl->nClasses, cl->clist); #ifdef ORBITS orbits->initPerm(nNodes); #endif while (True) { perm = group->genNext(); if (perm == NULL) { // calculate permutations of edges esym = ToBigInt(1); for (j1 = 0; j1 < nNodes; j1++) { if (adjMat[j1][j1] > 0) { nself = adjMat[j1][j1]/2; esym *= factorial(nself); esym *= ipow(2, nself); } for (j2 = j1+1; j2 < nNodes; j2++) { if (adjMat[j1][j2] > 0) { esym *= factorial(adjMat[j1][j2]); } } } return True; } permMat(nNodes, perm, adjMat, modmat); cmp = compMat(nNodes, adjMat, modmat); if (cmp < 0) { return False; } else if (cmp == 0) { // if ngroup < 0, symmetry group is $S_{-group}$. group->addGroup(perm); nsym = nsym + ToBigInt(1); #ifdef ORBITS orbits->fromPerm(perm); #endif } } } //--------------------------------------------------------------- void MGraph::permMat(int size, int *perm, int **mat0, int **mat1) { // apply permutation to matrix 'mat0' and obtain 'mat1' int j1, j2; for (j1 = 0; j1 < size; j1++) { for (j2 = 0; j2 < size; j2++) { mat1[j1][j2] = mat0[perm[j1]][perm[j2]]; } } } //--------------------------------------------------------------- int MGraph::compMat(int size, int **mat0, int **mat1) { // comparison of matrix int j1, j2, cmp; for (j1 = 0; j1 < size; j1++) { for (j2 = 0; j2 < size; j2++) { cmp = mat0[j1][j2] - mat1[j1][j2]; if (cmp != 0) { return cmp; } } } return 0; } //--------------------------------------------------------------- MNodeClass *MGraph::refineClass(MNodeClass *cl) { // Refine the classification // cl : the current 'MNodeClass' object // cn : the class number // Returns (the new class number corresponds to 'cn') if OK, or // 'None' if ordering condition is not satisfied MNodeClass *ccl = cl; MNodeClass *xcl = NULL; MNodeClass *ncl = NULL; int ucl[GRCC_MAXNODES]; int ccn = cl->nClasses; int nucl, nce; int td, cmp; int nccl; #ifdef MONITOR nCallRefine++; #endif nucl = 0; while (ccl->nClasses != nucl) { // repeat refinement. nce = 0; nucl = 0; for (td = 1; td < nNodes; td++) { // 'td' is the next node and the current node is 'td-1'. // Count up the number of the elements in the current class // corresponding to the current node nce++; cmp = ccl->clCmp(td-1, td, ccn); // the ordering condition is not satisfied. if (cmp > 0) { if (ccl != cl) { delete ccl; } return NULL; } else if (cmp < 0) { // 'td' is in the next class to the current node. ucl[nucl++] = nce; // close the current class // start new class nce = 0; } // nothing to do for the case of 'cmp == 0'. } // close array 'ucl'. ucl[nucl++] = nce + 1; #ifdef CHECK // inconsistent if (nucl < ccl->nClasses) { erEnd("refineClasses : smaller number of classes"); } #endif // preparation of the next repetition. xcl = new MNodeClass(nNodes, nucl); xcl->init(ucl, maxdeg, adjMat); ccn = xcl->nClasses; nccl = ccl->nClasses; if (ccl != cl) { delete ccl; } ccl = xcl; if (ccl->nClasses == nccl) { ccl->reorder(this); return ccl; } nucl = 0; } return ncl; } //--------------------------------------------------------------- void MGraph::biconnME(void) { // Count the number of 1PI components. int j, j1, root, vr, next, nart; MCOpi mopi; MCBlock mblk; ULong momset; // initialization bicount = 0; mconn->init(); mconn->initCEdges(this); for (j = 0; j < nNodes; j++) { bidef[j] = -1; bilow[j] = -1; bicol[j] = 0; } bipart = True; // find a root for the root of bisearch // root must be an external node // or an vertex when there are not external nodes. root = -1; vr = -1; for (j = 0; j < nNodes; j++) { if (bidef[j] < 0) { if (isExternal(j)) { root = j; break; } else if (vr < 0) { vr = j; } } } // case (2) if (root < 0) { root = vr; } if (root >= 0) { bisearchME(root, -1, 0, 1, &mopi, &mblk, &momset, &next, &nart); mconn->nlpopic = 0; mconn->nctopic = 0; for (j = 0; j < mconn->nopic; j++) { if (mconn->opics[j].loop > 0) { mconn->nlpopic++; } else if (mconn->opics[j].ctloop > 0) { mconn->nctopic++; } } mconn->ne0bridges = 0; mconn->ne1bridges = 0; for (j = 0; j < mconn->nbridges; j++) { if (mconn->bridges[j].next == 0) { mconn->ne0bridges++; } if (mconn->bridges[j].next == 1) { mconn->ne1bridges++; } } mconn->nselfloops = 0; for (j = 0; j < nNodes; j++) { mconn->nselfloops += adjMat[j][j]/2; } mconn->nmultiedges = 0; for (j = 0; j < nNodes; j++) { for (j1 = j+1; j1 < nNodes; j1++) { if (adjMat[j][j1] > 1) { mconn->nmultiedges++; } } } mconn->na1blocks = 0; for (j = 0; j < mconn->nblocks; j++) { if (mconn->blocks[j].nartps == 1) { mconn->na1blocks++; } } mconn->neblocks = mconn->nblocks + mconn->nctopic; #ifdef CHECK if (True) { if (isExternal(root)) { momset |= MASK(root); } ULong m = 0; for (j = 0; j < nExtern; j++) { m |= MASK(j); } bool ok = True; if (momset != m) { grcc_fprintf(GRCC_Stdout, "*** momset = %ld != %ld\n", momset, m); ok = False; } if (mconn->nbacked != nLoops) { grcc_fprintf(GRCC_Stdout, "*** nbacked = %d != %c\n", mconn->nbacked, nLoops); ok = False; } if (! ok) { print(); egraph->print(); mconn->print(); erEnd("biconnME: illegal connection"); } } #endif // no vertex. } else { // no vertices // Connected ==> only when ex=2, loop=0 mconn->nopic = 0; mconn->ne0bridges = 0; mconn->ne1bridges = 0; } } //--------------------------------------------------------------- void MGraph::bisearchME(int nd, int pd, int ned, int col, MCOpi *mopi, MCBlock *mblk, ULong *momset, int *next, int *nart) { // Search biconnected component // visit : pd --> nd --> td // ned : the number of edges between pd and nd. // Output // // | // x----+ // | | // ----x pd | // | | // x----x nd | n art. pints. // | /|\ | // | / | \ | // m art p. x-x | x-x // n1 x n3 // n2 // // output of bisearchME(n1, nd, ...) ==> npart = m // output of bisearchME(n2, nd, ...) ==> npart = 1 // output of bisearchME(n3, nd, ...) ==> npart = n // // output of bisearchME(nd, pd, ...) ==> npart = n+1 // n1 => block of (m+1) articulation points // n2 => block of 2 articulation points // n3 => no block // Bool newv; int td, td0, lp, conn, next1, nart1, nart2, nvisit, ndart; int opit, opit0, blkt, l; MCOpi mopi1; MCBlock mblk1; ULong momset1, momset2, momset3; mopi->init(); mblk->init(); *momset = 0; // # the set of momenta *next = 0; // # external below 'nd' inclusive *nart = 0; // # articulation points 'nd' inclusive nart1 = 0; // # articulation points below 'nd' nart2 = 0; // # 'nd' is articulation point then 1 ndart = 0; // # the number of blocks attached to 'nd' newv = (bidef[nd] < 0); if (! newv) { grcc_fprintf(GRCC_Stdout, "*** nd=%d, pd=%d, bidef[nd]=%d\n", nd, pd, bidef[nd]); erEnd("bisearchME: illegal connection"); } bidef[nd] = bicount; bilow[nd] = bicount; bicol[nd] = col; bicount++; opit0 = mconn->opistkptr; if (pd < 0) { mconn->pushNode(nd); } // external node and not the root if (isExternal(nd)) { if (pd >= 0) { // not the root *momset = MASK(nd); mopi->next = 1; mopi->nlegs = 1; mopi->mom0lg = 0; mblk->nartps = 1; *next = 1; *nart = 1; mconn->addCEdge(nd, pd, *momset); return; } } nvisit = 0; td0 = -1; for (td = 0; td < nNodes; td++) { conn = adjMat[nd][td]; // td is not adjacent to nd if (conn < 1) { continue; } nvisit++; td0 = td; momset1 = 0; // external node if (isExternal(td) && bidef[td] < 0) { bicol[td] = - col; (*next)++; ndart++; mconn->addArtic(nd, 1); mblk->nartps++; nart2 = 1; momset1 = MASK(td); mopi->nlegs++; mopi->next++; mconn->addCEdge(td, nd, momset1); *momset |= momset1; if (newv) { mconn->pushNode(td); } // self-loop : pd --> nd --> nd } else if (td == nd) { lp = conn/2; mopi->loop += lp; mopi->nedges += lp; ndart += lp; bipart = False; mconn->addArtic(nd, lp); mconn->addBlockSelf(nd, lp); mblk->nartps++; nart2 = 1; for (l = 0; l < lp; l++) { int m = nExtern + mconn->nbacked; mconn->nbacked++; momset1 = MASK(m); mconn->addCEdge(td, nd, momset1); } // back to the parent : pd --> nd --> pd, pd is a vertex } else if (td == pd) { if (ned > 1) { bilow[nd] = Min(bilow[nd], bidef[pd]); mopi->loop += ned - 1; mblk->loop += ned - 1; } else { // cancel this visit nvisit--; } // td is already visited } else if (bidef[td] >= 0) { bipart &= (bicol[td] == - col); bilow[nd] = Min(bilow[nd], bidef[td]); if (bidef[nd] >= bidef[td]) { // new back-edge is found mopi->loop += conn; mopi->nedges += conn; mblk->loop += conn; mconn->pushEdge(td, nd); for (l = 0; l < conn; l++) { int m = nExtern + mconn->nbacked; mconn->nbacked++; momset1 = MASK(m); *momset |= momset1; mconn->addCEdge(td, nd, momset1); } } else { // reverse direction of back-edge int cn = 0; for (int ed = 0; ed < mconn->sedges; ed++) { if (mconn->cedges[ed].nodes[0] == nd && mconn->cedges[ed].nodes[1] == td && mconn->cedges[ed].momdir > 0) { cn++; *momset &= ~ (mconn->cedges[ed].momset); } else if (mconn->cedges[ed].nodes[1] == nd && mconn->cedges[ed].nodes[0] == td && mconn->cedges[ed].momdir < 0) { cn++; *momset &= ~ (mconn->cedges[ed].momset); } } if (cn != conn) { grcc_fprintf(GRCC_Stdout, "*** revisit back-ed (%d --> %d) cn=%d != conn=%d\n", nd, td, cn, conn); grcc_fprintf(GRCC_Stdout, " sedges = %d\n", mconn->sedges); for (int ed = 0; ed < mconn->sedges; ed++) { grcc_fprintf(GRCC_Stdout, " %d : (%d --> %d) : [%2d*%2ld]\n", ed, mconn->cedges[ed].nodes[0], mconn->cedges[ed].nodes[1], mconn->cedges[ed].momdir, mconn->cedges[ed].momset); } print(); egraph->print(); mconn->print(); erEnd("bisearchME: illegal connection"); } } // new node } else if (bidef[td] < 0) { // stack pointer if (pd < 0 && isExternal(nd)) { opit = opit0; } else { opit = mconn->opistkptr; } blkt = mconn->blkstkptr; mblk1.init(); mconn->pushEdge(nd, td); // visit child bisearchME(td, nd, adjMat[td][nd], - col, &mopi1, &mblk1, &momset1, &next1, &nart1); // momset momset2 = 0; for (l = 0; l < conn - 1; l++) { int m = nExtern + mconn->nbacked; mconn->nbacked++; momset3 = MASK(m); mconn->addCEdge(nd, td, momset3); momset2 |= momset3; } mconn->addCEdge(td, nd, momset1 | momset2); *momset |= momset1; // articulation point of bridge if (bilow[td] > bidef[nd]) { // new OPI component (not including 'td') int mom0lg = (momset1 == 0) ? 1 : 0; mopi1.nlegs++; mopi1.mom0lg += mom0lg; mconn->addOPIc(&mopi1, opit); mopi1.init(); mopi1.nlegs = 1; mopi1.mom0lg = mom0lg; if (pd >= 0 || !isExternal(nd)) { // opi mconn->addBridge(nd, td, next1, nExtern); // block ndart++; mconn->addArtic(nd, 1); // discard nparts from nodes below td mblk1.nartps = 2; mconn->addBlock(&mblk1, blkt); mblk1.init(); mblk1.nartps = 1; nart1 = 0; nart2 = 1; // nd is an articulation point } } else if (bilow[td] == bidef[nd]) { // articulation point of a block mopi1.nedges += conn; if (pd >= 0 || !isExternal(nd)) { ndart++; mconn->addArtic(nd, 1); mblk1.nartps++; mconn->addBlock(&mblk1, blkt); mblk1.init(); mblk1.nartps = 1; nart1 = 0; nart2 = 1; // nd is an articulation point } } else { // inside a block mopi1.nedges += conn; } bilow[nd] = Min(bilow[nd], bilow[td]); mopi->nlegs += mopi1.nlegs; mopi->next += mopi1.next; mopi->loop += mopi1.loop; mopi->nedges += mopi1.nedges; mopi->ctloop += mopi1.ctloop; mopi->mom0lg += mopi1.mom0lg; mblk->nartps += mblk1.nartps; mblk->loop += mblk1.loop; *next += next1; *nart += nart1; } // of "if (bidef[td] < 0)" } // end of for // no connection except for 'pd'==>'nd'. Then 'nd' is an art. point if (nvisit == 0) { nart2 = 1; } *nart += nart2; // add # loop inside counter terms if (newv) { if (pd >= 0) { mconn->pushNode(nd); } mopi->ctloop += Max(0, nodes[nd]->extloop); } // 'nd' is the root node if (pd < 0) { if (isExternal(nd)) { if (td0 >= 0) { mconn->addArtic(td0, 1); } if (mconn->nopic > 0) { (mconn->opics[mconn->nopic-1].next)++; } } else { mconn->addOPIc(mopi, opit0); if (ndart == 1) { // 'nd' has only 1 child // the root is not really an art. point (*nart)--; mconn->addArtic(nd, -1); (mconn->blocks[mconn->nblocks-1].nartps)--; } } } } //--------------------------------------------------------------- BigInt MGraph::generate(void) { // Generate graphs // the generation process starts from 'connectClass'. MNodeClass *cl; // Initial classification of nodes. cl = new MNodeClass(nNodes, nClasses); cl->init(clist, maxdeg, adjMat); cl->reorder(this); connectClass(cl); delete cl; return cDiag; } //--------------------------------------------------------------- void MGraph::connectClass(MNodeClass *cl) { // Connect nodes in a class to others int sc, sn; MNodeClass *xcl; xcl = refineClass(cl); if (xcl == NULL) { #ifdef MONITOR discardRefine++; #endif } else { if (xcl->flg0 >= xcl->nClasses) { newGraph(xcl); } else { sc = xcl->clord[xcl->flg0]; sn = xcl->flist[sc]; connectNode(xcl->flg0, sn, xcl); } } if (xcl != cl && xcl != NULL) { delete xcl; } } //------------------------------------------------------------ void MGraph::connectNode(int so, int ss, MNodeClass *cl) { int sc, sn; sc = cl->clord[so]; if (ss >= cl->flist[sc+1]) { connectClass(cl); return; } for (sn = ss; sn < cl->flist[sc+1]; sn++) { connectLeg(so, sn, so, sn, cl); return; } } //------------------------------------------------------------ void MGraph::connectLeg(int so, int sn, int to, int ts, MNodeClass *cl) { // Add one connection between two legs. // 1. select another node to connect // 2. determine multiplicity of the connection int sc, tc, tn, maxself, nc2, nc, maxcon, ts1, ncm, to1; sc = cl->clord[so]; #ifdef CHECK if (sn >= cl->flist[sc+1]) { erEnd("connectLeg : illegal control"); return; } #endif // There remains no free legs in the node 'sn' : move to next node. if (nodes[sn]->freelg < 1) { if (!isConnected()) { #ifdef MONITOR discardDisc++; #endif } else { // next node in the current class. connectNode(so, sn+1, cl); } return; } // connect a free leg of the current node 'sn'. for (to1 = to; to1 < cl->nClasses; to1++) { tc = cl->clord[to1]; if (to1 == to) { ts1 = ts; } else { ts1 = cl->flist[tc]; } #ifdef MINMAXLEG if (ts1 >= nNodes) { continue; } if ((nodes[sn]->cmindeg > 0 && nodes[ts1]->deg < nodes[sn]->cmindeg) ||(nodes[sn]->cmaxdeg > 0 && nodes[ts1]->deg > nodes[sn]->cmaxdeg) | (nodes[ts1]->cmindeg > 0 && nodes[sn]->deg < nodes[ts1]->cmindeg) ||(nodes[ts1]->cmaxdeg > 0 && nodes[sn]->deg > nodes[ts1]->cmaxdeg)) { continue; } #endif for (tn = ts1; tn < cl->flist[tc+1]; tn++) { if (sc == tc && sn > tn) { continue; } else if (nodes[tn]->freelg < 1) { continue; // self-loop } else if (sn == tn) { if (opt->values[GRCC_OPT_NoSelfLoop] > 0) { continue; } if (nNodes > 1) { // there are two or more nodes in the graph : // avoid disconnected graph maxself = Min((nodes[sn]->freelg)/2, (nodes[sn]->deg-1)/2); } else { // there is only one node the graph. maxself = nodes[sn]->freelg/2; } if ((nExtern > 1) && (opt->values[GRCC_OPT_1PI] > 0 || opt->values[GRCC_OPT_NoTadpole] > 0) && nNodes > 1) { // there are two or more nodes in the graph : // avoid to generate tadpole maxself = Min((nodes[sn]->deg-2)/2, maxself); } // for the number of connection. for (nc2 = maxself; nc2 > 0; nc2--) { nc = 2*nc2; ncm = CLWIGHTD(nc); adjMat[sn][sn] = nc; nodes[sn]->freelg -= nc; cl->incMat(sn, tn, ncm); // next connection connectLeg(so, sn, to1, tn+1, cl); // restore the configuration cl->incMat(tn, sn, - ncm); adjMat[sn][sn] = 0; nodes[sn]->freelg += nc; } // connections between different nodes. } else { // maximum possible connection number maxcon = Min(nodes[sn]->freelg, nodes[tn]->freelg); // avoid disconnected graphs. if (nNodes > 2 && nodes[sn]->deg == nodes[tn]->deg) { maxcon = Min(maxcon, nodes[sn]->deg-1); } if (opt->values[GRCC_OPT_NoMultiEdge] > 0) { maxcon = Min(maxcon, 1); } #ifdef CHECK if ((adjMat[sn][tn] != 0) || (adjMat[sn][tn] != adjMat[tn][sn])) { grcc_fprintf(GRCC_Stdout, "*** inconsistent connection: sn=%d, tn=%d", sn, tn); printAdjMat(cl); erEnd("inconsistent connection "); } #endif // vary number of connections for (nc = maxcon; nc > 0; nc--) { ncm = CLWIGHTO(nc); adjMat[sn][tn] = nc; adjMat[tn][sn] = nc; nodes[sn]->freelg -= nc; nodes[tn]->freelg -= nc; cl->incMat(sn, tn, ncm); cl->incMat(tn, sn, ncm); // next connection connectLeg(so, sn, to1, tn+1, cl); // restore configuration cl->incMat(sn, tn, - ncm); cl->incMat(tn, sn, - ncm); adjMat[sn][tn] = 0; adjMat[tn][sn] = 0; nodes[sn]->freelg += nc; nodes[tn]->freelg += nc; } } } } } //------------------------------------------------------------ Bool MGraph::isOptM(void) { Bool ok = True; opi = (mconn->nopic == 1); opiloop = (mconn->nlpopic <= 1); tadpole = (mconn->ne0bridges >= ((nExtern == 1) ? 0 : 1)); selfloop = (mconn->nselfloops > 0); multiedge = (mconn->nmultiedges > 0); tadblock = (mconn->na1blocks > 0); block = (mconn->neblocks <= 1); extself = (mconn->ne1bridges > 0); if (opt->values[GRCC_OPT_1PI] > 0) { ok = ok && opi; } else if (opt->values[GRCC_OPT_1PI] < 0) { ok = ok && !opi; } if (opt->values[GRCC_OPT_NoExtSelf] > 0) { ok = ok && !extself; } else if (opt->values[GRCC_OPT_NoExtSelf] < 0) { ok = ok && extself; } if (opt->values[GRCC_OPT_NoTadpole] > 0) { #ifdef OLDOPT ok = ok && !tadpole; #else if (nExtern > 1) { ok = ok && !tadpole; } #endif } else if (opt->values[GRCC_OPT_NoTadpole] < 0) { #ifdef OLDOPT ok = ok && !tadpole; #else if (nExtern > 1) { ok = ok && tadpole; } #endif } if (opt->values[GRCC_OPT_NoSelfLoop] > 0) { } else if (opt->values[GRCC_OPT_NoSelfLoop] < 0) { ok = ok && selfloop; } if (opt->values[GRCC_OPT_NoMultiEdge] > 0) { } else if (opt->values[GRCC_OPT_NoMultiEdge] < 0) { ok = ok && multiedge; } if (opt->values[GRCC_OPT_No1PtBlock] > 0) { if (nExtern > 1) { ok = ok && !tadblock; } } else if (opt->values[GRCC_OPT_No1PtBlock] < 0) { if (nExtern > 1) { ok = ok && tadblock; } } if (opt->values[GRCC_OPT_Block] > 0) { ok = ok && block; } else if (opt->values[GRCC_OPT_Block] < 0) { ok = ok && !block; } return ok; } //------------------------------------------------------------ void MGraph::newGraph(MNodeClass *cl) { // A new candidate diagram is obtained. // It may be a disconnected graph // // Things to be done in the steps followed by this function. // 1. convert data format which treat the edges as objects. // 2. definition of loop momenta to the edges. // 3. analysis of loop structure in a graph. // 4. assignment of particles to edges and vertices to nodes // 5. recalculate symmetry factor int connected; MNodeClass *xcl; Bool ok; ngen++; // refine class and check ordering condition xcl = refineClass(cl); if (xcl == NULL) { #ifdef MONITOR discardRefine++; #endif // check whether this is a connected graph or not. } else { connected = isConnected(); if (!connected) { #ifdef MONITOR discardDisc++; #endif // connected graph : check isomorphism of the graph } else { ngconn++; if (!isIsomorphic(xcl)) { #ifdef MONITOR discardIso++; #endif // We got a new connected and a unique representation of a class. } else { biconnME(); if (isOptM()) { egraph->fromMGraph(this); if (egraph->isOptE()) { curcl->copy(xcl); #ifdef ORBITS orbits->toOrbits(); #endif ok = True; if (opt->outmg != NULL) { if (opt->proc != NULL) { egraph->mId = opt->proc->mgrcount + 1; egraph->sId = opt->proc->agrcount + 1; } else if (opt->sproc != NULL) { egraph->mId = opt->sproc->mgrcount + 1; egraph->sId = opt->sproc->agrcount + 1; } else { egraph->mId = cDiag; } ok = (*(opt->outmg))(egraph, opt->argmg); } if (ok) { // # generated graphs cDiag++; wscon.add(1, nsym*esym); // # generated 1PI graphs if (opi) { wsopi.add(1, nsym*esym); c1PI++; } // # no tadpoles if (!tadpole) { cNoTadpole++; } // # no tadblocks if (!tadblock) { cNoTadBlock++; if (opi) { c1PINoTadBlock++; } } #ifdef MONITOR grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, "Graph : %ld (%ld)", cDiag, ngen); grcc_fprintf(GRCC_Stdout, " sym. factor = (%ld*%ld)\n", nsym, esym); printAdjMat(cl); // cl->printMat(); # ifdef ORBITS orbits->print(); # endif #endif // go to next step opt->newMGraph(this); } else { } } else { } } else { ; } } } } if (xcl != cl && xcl != NULL) { delete xcl; } } //============================================================== // class MOrbits: orbits of nodes //-------------------------------------------------------------- MOrbits::MOrbits(void) { nOrbits = 0; nNodes = 0; } //-------------------------------------------------------------- MOrbits::~MOrbits(void) { } //-------------------------------------------------------------- void MOrbits::print(void) { int c; grcc_fprintf(GRCC_Stdout, "Orbits : nOrbits=%d: nd2or=", nOrbits); prIntArray(nNodes, nd2or, "\n"); for (c = 0; c < nOrbits; c++) { grcc_fprintf(GRCC_Stdout, " %2d: (%2d -- %2d) :", c, flist[c], flist[c+1]-1); prIntArray(flist[c+1]-flist[c], or2nd+flist[c], "\n"); } } //--------------------------------------------------------------- void MOrbits::initPerm(int nnodes) { int j; nNodes = nnodes; for (j = 0; j < nNodes; j++) { nd2or[j] = j; } } //--------------------------------------------------------------- void MOrbits::fromPerm(int *perm) { // update the orbits of nodes by the permutation int j, j1, k, l; for (j = 0; j < nNodes; j++) { if (nd2or[j] != j) { // not the first element of an old orbit continue; } // merge orbits to orbit 'j' k = j; for (j1 = 0; j1 < nNodes && (k = perm[k]) != j; j1++) { if (nd2or[k] == j) { // 'k' is already in 'j' ; } else { // old orbit 'k' had several elements: merge to orbit 'j' for (l = 0; l < nNodes; l++) { if (nd2or[l] == k) { nd2or[l] = j; } } } } #ifdef CHECK if (j1 >= nNodes) { grcc_fprintf(GRCC_Stdout, "*** fromPerm: illegal control: j=%d, k=%d\n", j, k); grcc_fprintf(GRCC_Stdout, "perm="); prIntArray(nNodes, perm, " nd2or="); prIntArray(nNodes, nd2or, "\n"); erEnd("fromPerm: illegal control"); } #endif } } //-------------------------------------------------------------- void MOrbits::toOrbits(void) { // fill elements from 'nd2or' int nd, nel, k, lor; lor = -1; nel = 0; nOrbits = 0; for (nd = 0; nd < nNodes; nd++) { if (nd2or[nd] > lor) { // lowest element of a new orbit lor = nd2or[nd]; flist[nOrbits++] = nel; for (k = nd; k < nNodes; k++) { if (nd2or[k] == lor) { or2nd[nel++] = k; } } } } flist[nOrbits] = nNodes; } //************************************************************** // n-edge connected components //============================================================ // class MCEdge //------------------------------------------------------------ MCEdge::MCEdge(void) { ; } //------------------------------------------------------------ MCEdge::~MCEdge(void) { ; } //============================================================ // class MCOpi: one n-edge connected component //------------------------------------------------------------ MCOpi::MCOpi(void) { init(); } //------------------------------------------------------------ MCOpi::~MCOpi(void) { nodes = NULL; } //------------------------------------------------------------ void MCOpi::init(void) { nodes = NULL; nnodes = 0; nlegs = 0; next = 0; nedges = 0; loop = 0; ctloop = 0; mom0lg = 0; } //============================================================ // class MCBridge //------------------------------------------------------------ MCBridge::MCBridge(void) { } //------------------------------------------------------------ MCBridge::~MCBridge(void) { } //============================================================ // class MCBlock //------------------------------------------------------------ MCBlock::MCBlock(void) { init(); } //------------------------------------------------------------ MCBlock::~MCBlock(void) { } //------------------------------------------------------------ void MCBlock::init(void) { edges = NULL; nmedges = 0; nartps = 0; loop = 0; } //============================================================ // class MConn: table of n-edge connected components //------------------------------------------------------------ MConn::MConn(int nnod, int nedg) { // nnod : the number of nodes // nedg : the number of edges snodes = nnod; sedges = nedg; cedges = new MCEdge[sedges]; opics = new MCOpi[snodes]; bridges = new MCBridge[sedges]; blocks = new MCBlock[sedges]; articuls = new int[snodes]; // workspace opisp = new int[snodes]; opistk = new int[snodes]; blksp = new Edge2n[sedges]; blkstk = new Edge2n[sedges]; init(); } //------------------------------------------------------------ MConn::~MConn(void) { delete[] blkstk; delete[] blksp; delete[] opistk; delete[] opisp; delete[] articuls; delete[] blocks; delete[] bridges; delete[] opics; delete[] cedges; } //------------------------------------------------------------ void MConn::init(void) { int j; nopic = 0; nlpopic = 0; nbacked = 0; nctopic = 0; nbridges = 0; ne0bridges = 0; ne1bridges = 0; nselfloops = 0; nmultiedges = 0; nbacked = 0; nblocks = 0; na1blocks = 0; narticuls = 0; neblocks = 0; opistkptr = 0; nopisp = 0; blkstkptr = 0; nblksp = 0; for (j = 0; j < snodes; j++) { articuls[j] = 0; } } //------------------------------------------------------------ void MConn::pushNode(int nd) { if (opistkptr >= snodes) { erEnd("MConn::pushNode: opistkptr >= snodes"); } opistk[opistkptr++] = nd; } //------------------------------------------------------------ void MConn::pushEdge(int n0, int n1) { if (blkstkptr >= sedges) { erEnd("MConn::pushEdge: blkstkptr >= sedges"); } if (n0 <= n1) { blkstk[blkstkptr][0] = n0; blkstk[blkstkptr][1] = n1; } else { blkstk[blkstkptr][0] = n1; blkstk[blkstkptr][1] = n0; } blkstkptr++; } //------------------------------------------------------------ void MConn::initCEdges(MGraph *mg) { int ed, n0, n1, e; ed = 0; for (n0 = 0; n0 < mg->nNodes; n0++) { for (e = 0; e < mg->adjMat[n0][n0]/2; e++, ed++) { cedges[ed].nodes[0] = n0; cedges[ed].nodes[1] = n0; cedges[ed].momdir = 0; } for (n1 = n0+1; n1 < mg->nNodes; n1++) { for (e = 0; e < mg->adjMat[n0][n1]; e++, ed++) { cedges[ed].nodes[0] = n0; cedges[ed].nodes[1] = n1; cedges[ed].momdir = 0; } } } if (ed != sedges) { grcc_fprintf(GRCC_Stdout, "*** ed=%d != sedges=%d\n", ed, sedges); erEnd("MConn::initCEdge: table overflow"); } } //------------------------------------------------------------ void MConn::addCEdge(int n0, int n1, ULong momset) { int m0, m1, dir, ed; if (n0 <= n1) { m0 = n0; m1 = n1; dir = 1; } else { m0 = n1; m1 = n0; dir = -1; } for (ed = 0; ed < sedges; ed++) { if (cedges[ed].nodes[0] == m0 && cedges[ed].nodes[1] == m1 && cedges[ed].momdir == 0) { cedges[ed].momdir = dir; cedges[ed].momset = momset; return; } } } //------------------------------------------------------------ void MConn::addOPIc(MCOpi *mopi, int stp) { int j, nn; if (nopic >= snodes) { erEnd("MConn::addOPIc: table overflow"); } nn = opistkptr - stp; for (j = 0; j < nn; j++) { opisp[nopisp+j] = opistk[stp+j]; } opics[nopic].nnodes = nn; opics[nopic].nlegs = mopi->nlegs; opics[nopic].nedges = mopi->nedges; opics[nopic].next = mopi->next; opics[nopic].loop = mopi->loop; opics[nopic].ctloop = mopi->ctloop; opics[nopic].mom0lg = mopi->mom0lg; opics[nopic].nodes = opisp + nopisp; nopisp += nn; opistkptr = stp; nopic++; } //------------------------------------------------------------ void MConn::addBridge(int n0, int n1, int nex, int nextot) { if (nbridges >= sedges) { erEnd("MConn::addBridge: table overflow"); } if (n0 <= n1) { bridges[nbridges].nodes[0] = n0; bridges[nbridges].nodes[1] = n1; } else { bridges[nbridges].nodes[0] = n1; bridges[nbridges].nodes[1] = n0; } bridges[nbridges].next = Min(nex, nextot-nex); nbridges++; } //------------------------------------------------------------ void MConn::addArtic(int nd, int mul) { articuls[nd] += mul; if (articuls[nd] == mul) { narticuls++; } else if (articuls[nd] == 0) { narticuls--; } } //------------------------------------------------------------ void MConn::addBlock(MCBlock *mblk, int stp) { int j, nn; if (nopic >= snodes) { erEnd("MConn::addOPIc: table overflow"); } nn = blkstkptr - stp; for (j = 0; j < nn; j++) { blksp[nblksp+j][0] = blkstk[stp+j][0]; blksp[nblksp+j][1] = blkstk[stp+j][1]; } blocks[nblocks].edges = blksp + nblksp; blocks[nblocks].nmedges = nn; blocks[nblocks].nartps = mblk->nartps; blocks[nblocks].loop = mblk->loop; nblksp += nn; blkstkptr = stp; nblocks++; } //------------------------------------------------------------ void MConn::addBlockSelf(int nd, int mult) { MCBlock mblk; int j, stp; mblk.edges = NULL; mblk.nmedges = 0; mblk.nartps = 1; mblk.loop = 1; for (j = 0; j < mult; j++) { stp = blkstkptr; pushEdge(nd, nd); addBlock(&mblk, stp); } } //------------------------------------------------------------ void MConn::print(void) { int j, k; grcc_fprintf(GRCC_Stdout, "+++ MConn object: snodes=%d, sedges=%d\n", snodes, sedges); grcc_fprintf(GRCC_Stdout, " nopic=%d, nlpopic=%d, nbacked=%d, nctopic=%d, " "nbridges=%d, ne0bridges=%d, ne1bridges=%d\n", nopic, nlpopic, nbacked, nctopic, nbridges, ne0bridges, ne1bridges); grcc_fprintf(GRCC_Stdout, " nblocks=%d, neblocks=%d, na1blocks=%d, narticuls=%d, nselfloop=%d\n", nblocks, neblocks, na1blocks, narticuls, nselfloops); grcc_fprintf(GRCC_Stdout, " nmultiedges=%d\n", nmultiedges); grcc_fprintf(GRCC_Stdout, " cEdges (%d)\n", sedges); if (sedges > 0) { for (j = 0; j < sedges; j++) { grcc_fprintf(GRCC_Stdout, " %2d: (%d,%d)[%2d*%2ld] \n", j, cedges[j].nodes[0], cedges[j].nodes[1], cedges[j].momdir, cedges[j].momset); } } grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, " 1PI components (%d)\n", nopic); for (j = 0; j < nopic; j++) { grcc_fprintf(GRCC_Stdout, " %d: nleg=%d, nnodes=%d, nedge=%d, ", j, opics[j].nlegs, opics[j].nnodes, opics[j].nedges); grcc_fprintf(GRCC_Stdout, "next=%d, loop=%d, ctlp=%d: m0lg=%d [", opics[j].next, opics[j].loop, opics[j].ctloop, opics[j].mom0lg); for (k = 0; k < opics[j].nnodes; k++) { grcc_fprintf(GRCC_Stdout, " %d", opics[j].nodes[k]); } grcc_fprintf(GRCC_Stdout, "]\n"); } grcc_fprintf(GRCC_Stdout, " bridges (%d)\n", nbridges); if (nbridges > 0) { grcc_fprintf(GRCC_Stdout, " "); for (j = 0; j < nbridges; j++) { grcc_fprintf(GRCC_Stdout, "(%d,%d)[mom=%d] ", bridges[j].nodes[0], bridges[j].nodes[1], bridges[j].next); } grcc_fprintf(GRCC_Stdout, "\n"); } grcc_fprintf(GRCC_Stdout, " blocks (%d)\n", nblocks); for (j = 0; j < nblocks; j++) { grcc_fprintf(GRCC_Stdout, " %d: nmedges=%d, nartps=%d, loop=%d: [", j, blocks[j].nmedges, blocks[j].nartps, blocks[j].loop); for (k = 0; k < blocks[j].nmedges; k++) { grcc_fprintf(GRCC_Stdout, " (%d,%d)", blocks[j].edges[k][0], blocks[j].edges[k][1]); } grcc_fprintf(GRCC_Stdout, "]\n"); } grcc_fprintf(GRCC_Stdout, " articulation points (%d)\n", narticuls); if (narticuls > 0) { grcc_fprintf(GRCC_Stdout, " "); for (j = 0; j < snodes; j++) { if (articuls[j] != 0) { #if 0 grcc_fprintf(GRCC_Stdout, "%d(%d) ", j, articuls[j]); #else grcc_fprintf(GRCC_Stdout, "%d ", j); #endif } } grcc_fprintf(GRCC_Stdout, "\n"); } } //------------------------------------------------------------ void MConn::prEdges(void) { int j; grcc_fprintf(GRCC_Stdout, " cEdges (%d)", sedges); if (sedges > 0) { for (j = 0; j < sedges; j++) { if (j % 5 == 0) { grcc_fprintf(GRCC_Stdout, "\n "); } grcc_fprintf(GRCC_Stdout, "(%d,%d)[%2d*%3ld] ", cedges[j].nodes[0], cedges[j].nodes[1], cedges[j].momdir, cedges[j].momset); } grcc_fprintf(GRCC_Stdout, "\n"); } } //************************************************************** // sgroup.cc //============================================================== // compile options //============================================================ // table of group elements //------------------------------------------------------------ SGroup::SGroup(void) { // should be called before graph generation nnodes = -1; nelem = 0; elem = NULL; } //------------------------------------------------------------ SGroup::~SGroup(void) { int j; if (elem != NULL) { for (j = GRCC_MAXGROUP-1; j >= 0; j--) { if (elem[j] != NULL) { delete[] elem[j]; elem[j] = NULL; } } delete[] elem; elem = NULL; } } //------------------------------------------------------------ void SGroup::print(void) { int j; grcc_fprintf(GRCC_Stdout, "SGroup : nnodes = %d, nelem=%ld, cgen=%d, csav=%d\n", nnodes, nelem, cgen, csav); grcc_fprintf(GRCC_Stdout, " eclass ="); prIntArray(neclass, eclass, "\n"); for (j = 0; j < nelem; j++) { grcc_fprintf(GRCC_Stdout, " %4d: ", j); prIntArray(nnodes, elem[j], "\n"); } } //------------------------------------------------------------ void SGroup::newGroup(int nnd, int nclss, int *clss) { int j; clearGroup(); nnodes = nnd; neclass = nclss; if (neclass > GRCC_MAXNODES) { erEnd("newGroup : too many classes (GRCC_MAXNODES)"); } for (j = 0; j < neclass; j++) { eclass[j] = clss[j]; } nelem = 0; if (elem == NULL) { elem = new int*[GRCC_MAXGROUP]; for (j = 0; j < GRCC_MAXGROUP; j++) { elem[j] = NULL; } } } //------------------------------------------------------------ void SGroup::clearGroup(void) { nelem = 0; csav = -1; cgen = -1; } //------------------------------------------------------------ void SGroup::delGroup(void) { int j; for (j = 0; j < GRCC_MAXGROUP; j++) { if (elem[j] != NULL) { delete[] elem[j]; elem[j] = NULL; } } delete[] elem; elem = NULL; clearGroup(); } //------------------------------------------------------------ int *SGroup::genNext(void) { cgen = nextPerm(nnodes, neclass, eclass, pgr, pgq, permg, cgen); if (cgen < 0) { return NULL; } return permg; } //------------------------------------------------------------ void SGroup::addGroup(int *p) { int j; if (nelem >= GRCC_MAXGROUP) { erEnd("addGroup : too many elements (GRCC_MAXGROUP)"); } if (elem[nelem] == NULL) { elem[nelem] = new int[GRCC_MAXNODES]; } for (j = 0; j < nnodes; j++) { elem[nelem][j] = p[j]; } nelem++; } //------------------------------------------------------------ BigInt SGroup::nElem(void) { return nelem; } //------------------------------------------------------------ int *SGroup::nextElem(void) { if (nelem < 0) { cgen = nextPerm(nelem, neclass, eclass, psr, psq, perms, cgen); return perms; } if (cgen < 0) { cgen = 0; } if (cgen >= nelem) { return NULL; } else { return elem[cgen++]; } } //************************************************************** // egraph.cc // Generate scalar connected Feynman graphs. //============================================================== static const char *GRCC_ND_names[] = GRCC_ND_NAMES; static const char *GRCC_ED_names[] = GRCC_ED_NAMES; //============================================================== // class ENode //-------------------------------------------------------------- ENode::ENode(void) { id = -1; egraph = NULL; edges = NULL; maxdeg = 0; deg = 0; klow = NULL; extloop = 0; ndtype = GRCC_ND_Undef; intrct = -1; } //-------------------------------------------------------------- ENode::ENode(EGraph *egrph, int loops, int sdeg) { id = -1; egraph = egrph; edges = NULL; maxdeg = sdeg; deg = 0; klow = NULL; extloop = 0; ndtype = GRCC_ND_Undef; intrct = -1; edges = new int[sdeg]; klow = new int[loops+1]; } //-------------------------------------------------------------- ENode::~ENode(void) { if (klow != NULL) { delete[] klow; delete[] edges; klow = NULL; edges = NULL;; } } //-------------------------------------------------------------- void ENode::copy(ENode *en) { int d; deg = en->deg; extloop = en->extloop; ndtype = en->ndtype; for (d = 0; d < deg; d++) { edges[d] = en->edges[d]; } } //-------------------------------------------------------------- void ENode::initAss(EGraph *egrph, int nid, int sdg) { id = nid; egraph = egrph; maxdeg = sdg; } //-------------------------------------------------------------- void ENode::setId(EGraph *egrph, const int nid) { id = nid; egraph = egrph; } //-------------------------------------------------------------- void ENode::setExtern(int typ, int pt) { intrct = pt; if (typ == GRCC_AT_Initial || typ == GRCC_AT_Final) { extloop = typ; } else { grcc_fprintf(GRCC_Stderr, "** ENode::setExternal:: illegal typ=%d\n", typ); erEnd("ENode::setExternal:: illegal typ"); } } //-------------------------------------------------------------- void ENode::setType(int typ) { #ifdef CHECK if (ndtype != GRCC_ND_Undef && ndtype != typ) { grcc_fprintf(GRCC_Stderr, "*** ndtype is already defined : old=%d, new = %d\n", ndtype, typ); erEnd("ndtype is already defined"); } #endif ndtype = typ; } //-------------------------------------------------------------- void ENode::print(void) { int j; grcc_fprintf(GRCC_Stdout, "Enode %d deg=%d, extl=%2d, intr=%d ", id, deg, extloop, intrct); if (egraph->bicount > 0) { grcc_fprintf(GRCC_Stdout, "(%-8s) ", GRCC_ND_names[ndtype]); } grcc_fprintf(GRCC_Stdout, "edge=["); for (j = 0; j < deg; j++) { grcc_fprintf(GRCC_Stdout, " %2d", edges[j]); } grcc_fprintf(GRCC_Stdout, "]\n"); } //============================================================== // class EEdge //-------------------------------------------------------------- EEdge::EEdge(void) { id = -1; egraph = NULL; nodes[0] = -1; nodes[1] = -1; // nlegs[0] = -1; // nlegs[1] = -1; ptcl = GRCC_PT_Undef; deleted = False; edtype = GRCC_ED_Undef; cut = False; emom = NULL; lmom = NULL; momset = 0; momdir = 0; } //-------------------------------------------------------------- EEdge::EEdge(EGraph *egrph, int nedges, int nloops) { id = -1; egraph = egrph; nodes[0] = -1; nodes[1] = -1; nlegs[0] = -1; nlegs[1] = -1; ptcl = GRCC_PT_Undef; deleted = False; edtype = GRCC_ED_Undef; cut = False; emom = new int[nedges]; lmom = new int[nloops]; } //-------------------------------------------------------------- EEdge::~EEdge(void) { if (lmom != NULL) { delete[] lmom; } if (emom != NULL) { delete[] emom; } } //-------------------------------------------------------------- void EEdge::copy(EEdge *ee) { nodes[0] = ee->nodes[0]; nodes[1] = ee->nodes[1]; id = ee->id; ext = ee->ext; dir = ee->dir; edtype = ee->edtype; cut = ee->cut; } //-------------------------------------------------------------- void EEdge::setId(EGraph *egrph, const int eid) { id = eid; egraph = egrph; } //-------------------------------------------------------------- void EEdge::setType(int typ) { #ifdef CHECK if (edtype != GRCC_ED_Undef) { erEnd("edtype is already defined"); } #endif edtype = typ; } //-------------------------------------------------------------- void EEdge::setEMom(int nedges, int *em, int dir) { int e; for (e = 0; e < nedges; e++) { if (em[e] != 0) { emom[e] = dir; } } } //-------------------------------------------------------------- void EEdge::setLMom(int k, int dir) { lmom[k] = dir; } //-------------------------------------------------------------- void EEdge::print(void) { int zero, n, k; grcc_fprintf(GRCC_Stdout, "Edge %2d ext=%d ptcl=%2d ", id, ext, ptcl); if (egraph == NULL || !egraph->assigned) { grcc_fprintf(GRCC_Stdout, "[%d, %d]", nodes[0], nodes[1]); } else { grcc_fprintf(GRCC_Stdout, "[(%d,%d), (%d,%d))", nodes[0], nlegs[0], nodes[1], nlegs[1]); } if (momdir != 0) { grcc_fprintf(GRCC_Stdout, "[%2d*%2lu]", momdir, momset); } if (egraph != NULL && egraph->bicount > 0) { if (cut) { grcc_fprintf(GRCC_Stdout, " %-9s ", "Cut"); } else { grcc_fprintf(GRCC_Stdout, " %-9s ", GRCC_ED_names[edtype]); } grcc_fprintf(GRCC_Stdout, "c%2d: ", opicomp); grcc_fprintf(GRCC_Stdout, "%s%d =", (ext)?"Q":"p", id); zero = True; for (n = 0; n < egraph->nEdges; n++) { if (emom[n] != 0) { prMomStr(emom[n], "Q", n); zero = False; } } for (k = 0; k < egraph->nLoops; k++) { if (lmom[k] != 0) { prMomStr(lmom[k], "k", k); zero = False; } } if (zero) { grcc_fprintf(GRCC_Stdout, " 0"); } } else { if (egraph == NULL) { grcc_fprintf(GRCC_Stdout, " egraph=NULL"); } else { grcc_fprintf(GRCC_Stdout, " egraph->bicount=%d", egraph->bicount); } } grcc_fprintf(GRCC_Stdout, "\n"); } //============================================================== // class EFLine //-------------------------------------------------------------- EFLine::EFLine(void) { ftype = FL_Open; fkind = 0; nlist = 0; } //-------------------------------------------------------------- void EFLine::print(const char *msg) { if (ftype == FL_Open) { grcc_fprintf(GRCC_Stdout, " Open"); } else if (ftype == FL_Closed) { grcc_fprintf(GRCC_Stdout, " Loop"); } else { grcc_fprintf(GRCC_Stdout, " ?%d", ftype); } if (fkind == GRCC_PT_Dirac) { grcc_fprintf(GRCC_Stdout, " Dirac"); } else if (fkind == GRCC_PT_Majorana) { grcc_fprintf(GRCC_Stdout, " Major"); } else if (fkind == GRCC_PT_Ghost) { grcc_fprintf(GRCC_Stdout, " Ghost"); } else { grcc_fprintf(GRCC_Stdout, " ?%d", fkind); } grcc_fprintf(GRCC_Stdout, " len=%d ", nlist); prIntArray(nlist, elist, msg); } //============================================================== // class EGraph //-------------------------------------------------------------- EGraph::EGraph(int nnodes, int nedges, int mxdeg) { // Arguments // nnodes : the number of nodes // nedges : the number of edges // mxdeg : the maximum number of degrees of nodes int j; opt = NULL; mgraph = NULL; econn = NULL; sNodes = nnodes; sEdges = nedges; sMaxdeg = mxdeg; sLoops = sEdges - sNodes + 1; // assume connected graph pId = -1; mId = -1; aId = -1; sId = 0; gSubId = -1; assigned = False; nNodes = sNodes; nEdges = sEdges; nLoops = 0; nExtern = 0; nsym = 1; esym = 1; extperm = 1; nsym1 = 1; multp = 1; totalc = 0; nodes = new ENode*[sNodes]; for (j = 0; j < sNodes; j++) { nodes[j] = new ENode(this, sNodes, sMaxdeg); } edges = new EEdge*[sEdges]; for (j = 0; j < sEdges; j++) { edges[j] = new EEdge(this, sEdges, sLoops); } bidef = new int[sNodes]; bilow = new int[sNodes]; bicount = -1; extMom = new int[sEdges+1]; fsign = 1; nFlines = -1; for (j = 0; j < GRCC_MAXFLINES; j++) { flines[j] = NULL; } } //-------------------------------------------------------------- EGraph::~EGraph(void) { int j; for (j = GRCC_MAXFLINES-1; j >= 0; j--) { if (flines[j] != NULL) { delete flines[j]; flines[j] = NULL; } } delete[] extMom; delete[] bilow; delete[] bidef; for (j = 0; j < sEdges; j++) { delete edges[j]; edges[j] = NULL; } delete[] edges; for (j = 0; j < sNodes; j++) { delete nodes[j]; nodes[j] = NULL; } delete[] nodes; } //-------------------------------------------------------------- void EGraph::copy(EGraph *eg) { int nd, ed; #ifdef CHECK if (sNodes < eg->nNodes || sEdges < eg->nEdges || sMaxdeg < eg->sMaxdeg || sLoops < eg->nLoops) { erEnd("EGraph::copy: sizes are too small"); } #endif model = eg->model; proc = eg->proc; sproc = eg->sproc; mgraph = eg->mgraph; opt = mgraph->opt; econn = mgraph->mconn; pId = eg->pId; mId = eg->mId; gSubId = eg->gSubId; nNodes = eg->nNodes; nEdges = eg->nEdges; nExtern = eg->nExtern; nLoops = eg->nLoops; for (nd = 0; nd < nNodes; nd++) { nodes[nd]->copy(eg->nodes[nd]); } for (ed = 0; ed < nEdges; ed++) { edges[ed]->copy(eg->edges[ed]); } nsym = eg->nsym; esym = eg->esym; extperm = eg->extperm; nsym1 = eg->nsym1; multp = eg->multp; bicount = -1; } //-------------------------------------------------------------- void EGraph::setExtLoop(int nd, int val) { // set the node 'nd' being an external node (-1) or a looped vertex nodes[nd]->extloop = val; } //-------------------------------------------------------------- void EGraph::endSetExtLoop(void) { // end of calling 'setExtLoop'. int n; nExtern = 0; for (n = 0; n < nNodes; n++) { if (isExternal(n)) { nExtern++; } } } //-------------------------------------------------------------- void EGraph::fromDGraph(DGraph *dg) { int deg[GRCC_MAXNODES]; int maxdeg, nextern, nconn, tc; int n0, n1, e; if (dg->nnodes > GRCC_MAXNODES) { grcc_fprintf(GRCC_Stderr, "*** too many nodes (GRCC_MAXNODES)\n"); GRCC_ABORT(); } if (dg->nedges > GRCC_MAXEDGES) { grcc_fprintf(GRCC_Stderr, "*** too many edges (GRCC_MAXEDGES)\n"); GRCC_ABORT(); } for (e = 0; e < dg->nedges; e++) { if (dg->edges[e][0] >= dg->nnodes || dg->edges[e][0] >= dg->nnodes) { grcc_fprintf(GRCC_Stderr, "*** undefined node:"); grcc_fprintf(GRCC_Stderr, "edge[%d] = {%d, %d}\n", e, dg->edges[e][0], dg->edges[e][0]); GRCC_ABORT(); } } for (n0 = 0; n0 < dg->nnodes; n0++) { deg[n0] = 0; } for (e = 0; e < dg->nedges; e++) { deg[dg->edges[e][0]]++; deg[dg->edges[e][1]]++; } maxdeg = 0; nextern = 0; for (n0 = 0; n0 < dg->nnodes; n0++) { maxdeg = Max(maxdeg, deg[n0]); if (deg[n0] == 1) { nextern++; } if (deg[n0] < 0) { grcc_fprintf(GRCC_Stderr, "+++ node %d is isolated\n", n0); } } mgraph = NULL; model = NULL; proc = NULL; sproc = NULL; opt = NULL; nNodes = dg->nnodes; nEdges = dg->nedges; nLoops = 0; nExtern = nextern; pId = 0; mId = 0; aId = 0; gSubId = 0; nsym = 1; nsym1 = 1; esym = 1; extperm = 1; multp = 1; maxdeg = maxdeg; for (n0 = 0; n0 < dg->nnodes; n0++) { nodes[n0]->deg = 0; nodes[n0]->extloop = dg->nodes[n0].extloop; } for (e = 0; e < dg->nedges; e++) { n0 = dg->edges[e][0]; n1 = dg->edges[e][1]; edges[e]->nodes[0] = n0; edges[e]->nodes[1] = n1; edges[e]->ext = (isExternal(n0) || isExternal(n1)); edges[e]->momdir = 0; nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(e, -1); nodes[n1]->edges[nodes[n1]->deg++] = I2Vedge(e, +1); } for (n0 = 0; n0 < dg->nnodes; n0++) { nodes[n0]->setId(this, n0); nodes[n0]->intrct = dg->nodes[n0].intrct; } for (e = 0; e < nEdges; e++) { edges[e]->setId(this, e); } tc = 0; for (n0 = 0; n0 < nNodes; n0++) { if (isExternal(n0)) { setExtern(n0, 1, GRCC_AT_Initial); } else { tc += 2*nodes[n0]->extloop + nodes[n0]->deg - 2; } } totalc = tc; // get the number of connected components nconn = connComp(); nLoops = nEdges - nNodes + nconn; bicount = -1; } //-------------------------------------------------------------- void EGraph::fromMGraph(MGraph *mg) { // construct EGraph from adjacency matrix. // This function should be called after // EGraph(), setExtLoop() and endSetExtLoop(). int n0, n1, m0, m1, ed, e; int j, ni, nf; PNodeClass *pnc; int k; #ifdef CHECK if (sNodes < mg->nNodes || sEdges < mg->nEdges || sMaxdeg < mg->maxdeg) { erEnd("EGraph::fromMGraph: sizes are too small"); } if (sLoops < mg->nLoops) { grcc_fprintf(GRCC_Stdout, "too small sLoops : %d < %d\n", sLoops, mg->nLoops); erEnd("too small sLoops"); } #endif mgraph = mg; opt = mgraph->opt; econn = mgraph->mconn; sproc = opt->sproc; if (sproc == NULL) { proc = NULL; model = NULL; } else { proc = sproc->proc; model = sproc->model; } nNodes = mg->nNodes; nEdges = mg->nEdges; nLoops = mg->nLoops; nExtern = mg->nExtern; pId = mg->pId; mId = mg->cDiag; aId = -1; if (opt->proc != NULL) { mId = mg->opt->proc->mgrcount; sId = mg->opt->proc->agrcount; } else if (mg->opt->sproc != NULL) { mId = mg->opt->sproc->mgrcount; sId = mg->opt->sproc->agrcount; } else { mId = mg->cDiag; sId = mg->cDiag; } gSubId = 0; nsym = mg->nsym; esym = mg->esym; extperm = 1; nsym1 = nsym; multp = 1; maxdeg = mg->maxdeg; totalc = 0; if (proc != NULL) { for (j = 0; j < proc->model->ncouple; j++) { totalc += proc->clist[j]; } } for (ed = 0; ed < nEdges; ed++) { edges[ed]->edtype = GRCC_ED_Undef; } ed = 0; for (n0 = 0; n0 < nNodes; n0++) { nodes[n0]->deg = 0; } for (n0 = 0; n0 < nNodes; n0++) { for (e = 0; e < mg->adjMat[n0][n0]/2; e++, ed++) { edges[ed]->nodes[0] = n0; edges[ed]->nodes[1] = n0; nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(ed, -1); nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(ed, +1); edges[ed]->ext = isExternal(n0); } for (n1 = n0+1; n1 < nNodes; n1++) { for (e = 0; e < mg->adjMat[n0][n1]; e++, ed++) { edges[ed]->nodes[0] = n0; edges[ed]->nodes[1] = n1; nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(ed, -1); nodes[n1]->edges[nodes[n1]->deg++] = I2Vedge(ed, +1); edges[ed]->ext = (isExternal(n0) || isExternal(n1)); } } } #ifdef CHECK if (ed != nEdges) { grcc_fprintf(GRCC_Stdout, "*** EGraph::init: ed=%d != nEdges=%d\n", ed, nEdges+1); erEnd("EGraph::init: illegal connection"); } #endif for (j = 0; j < nNodes; j++) { nodes[j]->setId(this, j); nodes[j]->intrct = mg->nodes[j]->extloop; } for (j = 0; j < nEdges; j++) { edges[j]->setId(this, j); } ni = 0; nf = 0; if (proc != NULL) { ni = proc->ninitl; for (j = 0; j < ni; j++) { setExtern(j, proc->initlPart[j], GRCC_AT_Initial); } nf = proc->nfinal; for (j = 0; j < nf; j++) { setExtern(j+ni, proc->finalPart[j], GRCC_AT_Final); } nExtern = ni + nf; } else if (sproc != NULL) { pnc = sproc->pnclass; for (j = 0; j < sproc->pnclass->nclass; j++) { if (pnc->type[j] == GRCC_AT_Initial || pnc->type[j] == GRCC_AT_External) { for (k = pnc->cl2nd[j]; k < pnc->cl2nd[j+1]; k++) { setExtern(j, k, GRCC_AT_Initial); ni++; } } else if (sproc->pnclass->type[j] == GRCC_AT_Final) { for (k = pnc->cl2nd[j]; k < pnc->cl2nd[j+1]; k++) { setExtern(j, k, GRCC_AT_Final); nf++; } } } nExtern = ni + nf; } totalc = 0; for (j = 0; j < nNodes; j++) { if (!isExternal(j)) { totalc += 2*nodes[j]->extloop + nodes[j]->deg - 2; } } for (ed = 0; ed < nEdges; ed++) { edges[ed]->momdir = 0; } for (e = 0; e < econn->sedges; e++) { m0 = econn->cedges[e].nodes[0]; m1 = econn->cedges[e].nodes[1]; bool found = False; for (ed = 0; ed < nEdges; ed++) { if (edges[ed]->momdir != 0) { continue; } n0 = edges[ed]->nodes[0]; n1 = edges[ed]->nodes[1]; if (m0 == n0 && m1 == n1) { edges[ed]->momdir = econn->cedges[e].momdir; edges[ed]->momset = econn->cedges[e].momset; found = True; break; } else if (m0 == n1 && m1 == n0) { edges[ed]->momdir = - econn->cedges[e].momdir; edges[ed]->momset = econn->cedges[e].momset; found = True; break; } } if (! found) { grcc_fprintf(GRCC_Stdout, "*** EGraph::fromMGraph:edge (%d->%d) is not found\n", m0, m1); } } bicount = -1; } //-------------------------------------------------------------- ENode *EGraph::setExtern(int n0, int pt, int ndtyp) { ENode *nd; int npt, ept, eg; nd = nodes[n0]; if (nd->deg != 1) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** illegal external particle %d, %d, %d\n", n0,pt,ndtyp); } erEnd("illegal external particle"); } // particle comes into the node if (ndtyp == GRCC_AT_Initial) { npt = pt; } else if (ndtyp == GRCC_AT_Final) { npt = -pt; } else { npt = 0; if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** illegal type of an external particle : " "node = %d, particle = %d, type = %d", n0, pt, ndtyp); } erEnd("illegal type of an external particle"); } // edge attached to the external node eg = n0; // particle flows on e from leg=0 to 1. if (model != NULL){ npt = model->normalParticle(npt); ept = model->normalParticle(npt); } else { npt = 0; ept = 0; } nd->setExtern(ndtyp, npt); edges[eg]->ptcl = ept; return nd; } //-------------------------------------------------------------- void EGraph::print(void) { // print the EGraph int nd, ed, nlp; nlp = nEdges - nNodes + 1; grcc_fprintf(GRCC_Stdout, "\nEGraph\n"); grcc_fprintf(GRCC_Stdout, " pId=%d, gSubId=%ld, mId=%ld, aId=%ld, sId=%ld\n", pId, gSubId, mId, aId, sId); grcc_fprintf(GRCC_Stdout, " sNodes=%d, sEdges=%d, sMaxdeg=%d, sLoops=%d\n", sNodes, sEdges, sMaxdeg, sLoops); grcc_fprintf(GRCC_Stdout, " nNodes=%d, nEdges=%d, nExtern=%d, nLoops=%d, totalc=%d\n", nNodes, nEdges, nExtern, nlp, totalc); grcc_fprintf(GRCC_Stdout, " "); if (model == NULL) { grcc_fprintf(GRCC_Stdout, "model=NULL,"); } else { grcc_fprintf(GRCC_Stdout, "model=\"%s\",", model->name); } if (proc == NULL) { grcc_fprintf(GRCC_Stdout, "proc=NULL,"); } else { grcc_fprintf(GRCC_Stdout, "proc=%d,", proc->id); } if (sproc == NULL) { grcc_fprintf(GRCC_Stdout, "sproc=NULL,"); } else { grcc_fprintf(GRCC_Stdout, "sproc=%d,", sproc->id); } grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, " assigned=%d, sym = (%ld * %ld) ", assigned, nsym, esym); grcc_fprintf(GRCC_Stdout, "extperm=%ld, nsym1=%ld, multp=%ld\n", extperm, nsym1, multp); grcc_fprintf(GRCC_Stdout, " Nodes\n"); for (nd = 0; nd < nNodes; nd++) { if (isExternal(nd)) { grcc_fprintf(GRCC_Stdout, " %2d Extern ", nd); } else { grcc_fprintf(GRCC_Stdout, " %2d Vertex ", nd); } nodes[nd]->print(); } grcc_fprintf(GRCC_Stdout, " Edges\n"); for (ed = 0; ed < nEdges; ed++) { if (edges[ed]->ext) { grcc_fprintf(GRCC_Stdout, " %2d Extern ", ed); } else { grcc_fprintf(GRCC_Stdout, " %2d Intern ", ed); } edges[ed]->print(); } if (bicount > 0) { grcc_fprintf(GRCC_Stdout, " Biconn: nopicomp=%d, nopi2p=%d, opi2plp=%d, nadj2ptv=%d\n", nopicomp, nopi2p, opi2plp, nadj2ptv); } grcc_fprintf(GRCC_Stdout, "\n"); if (nFlines > 0) { prFLines(); } } //-------------------------------------------------------------- void EGraph::printPy(FILE *fp, long mId) { if (!assigned) { mgraph->printPy(fp, mId); return; } fprintf(fp, "#AGraph : (gseq, {spid, gid, ...}, nodes, node-group)\n"); fprintf(fp, "(%ld,\n", mId); // {'proc':0, 'subproc':0, 'tgraph':1, ... } fprintf(fp, " {'proc':%d, 'subproc':%d, ", proc->id, sproc->id); fprintf(fp, "'tgraph':%ld, ", mId); fprintf(fp, "'OPI':%s, ", BOOLSTR(opt->values[GRCC_OPT_1PI])); fprintf(fp, "'agraph':%ld, \n", aId); fprintf(fp, " 'nnodes':%d, 'nnsym':%ld, 'nesym':%ld, },\n", nNodes, nsym, esym); // #nodes fprintf(fp, " [ #nodes\n"); for (int nd = 0; nd < nNodes; nd++) { ENode *end = nodes[nd]; // #node 0: external=phi // #node 4: phi3=0 fprintf(fp, " [ #node %d: ", nd); fprintf(fp, "\n"); // {'deg':1, 'cid':-3, ..., } fprintf(fp, " {'deg':%d, 'cid':%d, 'extern':%s, ", end->deg, 0, BOOLSTR(isExternal(nd))); fprintf(fp, "'intr':%d, 'loop':%d, },\n", end->intrct, end->extloop); // legs : (edge, leg, particle) // [ (0, 1, 0), ... ], fprintf(fp, " [ "); for (int lg = 0; lg < end->deg; lg++) { int ed = V2Iedge(end->edges[lg]); int ptcl = edges[ed]->ptcl; int edlg = (edges[ed]->nodes[0] == nd) ? 1 : 0; int nnd = edges[ed]->nodes[edlg]; int nlg = edges[ed]->nlegs[edlg]; fprintf(fp, "(%d, %d, %d), ", nnd, ptcl, nlg); } fprintf(fp, "],\n"); fprintf(fp, " ],\n"); // end #node } fprintf(fp, " ], #node\n"); fprintf(fp, " [ # group of 1 elements\n"); fprintf(fp, " [], #\n"); fprintf(fp, " ], # group\n"); fprintf(fp, ")\n"); } //-------------------------------------------------------------- void EGraph::prFLines(void) { int j; grcc_fprintf(GRCC_Stdout, " Fermion lines %d, sign=%d (mId=%ld, aId=%ld)\n", nFlines, fsign, mId, aId); for (j = 0; j < nFlines; j++) { grcc_fprintf(GRCC_Stdout, "%4d ", j); flines[j]->print("\n"); } } //-------------------------------------------------------------- int EGraph::dirEdge(int n, int e) { if (nodes[n]->edges[e] > 0) { return 1; } else { return -1; } } //-------------------------------------------------------------- int EGraph::cmpMom(int *lm0, int *em0, int *lm1, int *em1) { int lp, ed, cmp, sgn = 0; for (lp = 0; lp < nLoops; lp++) { if (lm0[lp] != 0) { if (lm1[lp] == 0) { return 1; } else if (sgn == 0) { sgn = lm0[lp]*lm1[lp]; // cancel first non-zero elements #ifdef CHECK if (Abs(sgn) != 1) { erEnd("cmpMom : illegal element of lmom"); } #endif } else { cmp = lm0[lp] - sgn*lm1[lp]; if (cmp != 0) { return cmp; } } } else if (lm1[lp] != 0) { // lm0[lp] == 0 return -1; } } for (ed = 0; ed < nEdges; ed++) { if (em0[ed] != 0) { if (em1[ed] == 0) { return 1; } else if (sgn == 0) { sgn = em0[ed]*em1[ed]; // cancel first non-zero elements #ifdef CHECK if (Abs(sgn) != 1) { erEnd("cmpMom : illegal element of emom"); } #endif } else { cmp = em0[ed] - sgn*em1[ed]; if (cmp != 0) { return cmp; } } } else if (em1[ed] != 0) { // em0[ed] == 0 return -1; } } return 0; } //-------------------------------------------------------------- int EGraph::groupLMom(int *grp, int *ed2gr) { // grp[g] : the number of elements in the group g (in [0,...,(ngrp-1)]) // ed2gr[ed] : group number of edge ed. int ed0, ed1, cmp, ngrp = -1; for (ed0 = 0; ed0 < nEdges; ed0++) { ed2gr[ed0] = -1; grp[ed0] = 0; } for (ed0 = 0; ed0 < nEdges; ed0++) { if (ed2gr[ed0] < 0) { ngrp++; ed2gr[ed0] = ngrp; grp[ngrp]++; for (ed1 = ed0+1; ed1 < nEdges; ed1++) { cmp = cmpMom(edges[ed0]->lmom, edges[ed0]->emom, edges[ed1]->lmom, edges[ed1]->emom); if (cmp == 0) { ed2gr[ed1] = ngrp; grp[ngrp]++; } } } } ngrp++; return ngrp; } //-------------------------------------------------------------- Bool EGraph::optQGrafM(Options *opt) { int *qgopt = opt->qgopt; int nopis[GRCC_MAXEDGES]; ULong mext = 0; mext = (~ mext) << nExtern; #ifdef PRINT grcc_fprintf(GRCC_Stdout, "optQGrafM:"); print(); #endif #ifdef PRINT grcc_fprintf(GRCC_Stdout, "optQGrafM: %8ld\n", mId); econn->print(); #endif // count the number of self-energy 1PI components. int maxlegs = 0; for (int j = 0; j < econn->nopic; j++) { maxlegs = Max(maxlegs, econn->opics[j].nlegs); } if (maxlegs >= GRCC_MAXEDGES) { grcc_fprintf(GRCC_Stdout, "*** table overflow\n"); GRCC_ABORT(); } for (int k = 0; k < GRCC_MAXEDGES; k++) { nopis[k] = 0; } for (int j = 0; j < econn->nopic; j++) { nopis[econn->opics[j].nlegs]++; } // if (qgopt[GRCC_QGRAF_OPT_ONEPI] > 0) { if (econn->nopic != 1) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_ONEPI] < 0) { if (econn->nopic < 2) { return False; } } if (qgopt[GRCC_QGRAF_OPT_ONSHELL] != 0) { if (nExtern == 1) { if (qgopt[GRCC_QGRAF_OPT_ONSHELL] > 0) { if (econn->nopic != 1) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_ONSHELL] < 0) { if (econn->nopic == 1) { return False; } } } else { if (qgopt[GRCC_QGRAF_OPT_ONSHELL] > 0) { if (econn->ne1bridges > 0) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_ONSHELL] < 0) { if (econn->ne1bridges <= 0) { return False; } } } } if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] != 0) { if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] > 0) { if (nExtern == 1) { if (econn->nblocks != 1) { return False; } } else { if (mgraph->mconn->ne0bridges >= 1 || mgraph->mconn->na1blocks >= 1) { return False; } } } else if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] < 0) { if (nExtern == 1) { if (econn->nblocks == 1) { return False; } } else { if (mgraph->mconn->ne0bridges < 1 && mgraph->mconn->na1blocks < 1) { return False; } } } } if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] != 0) { if (nExtern == 1) { if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] > 0) { if (econn->nopic != 1) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] < 0) { if (econn->nopic == 1) { return False; } } } else { if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] > 0) { if (mgraph->mconn->ne0bridges != 0) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] < 0) { if (mgraph->mconn->ne0bridges == 0) { return False; } } } } if (qgopt[GRCC_QGRAF_OPT_NOSIGMA] != 0) { bool ok = True; if (nExtern != 2) { if (nopis[2] > 1) { ok = False; } } for (int j = 0; j < econn->nopic; j++) { if (econn->opics[j].nlegs >= 2 && econn->opics[j].nlegs == econn->opics[j].mom0lg) { ok = False; } } // loop momenta for (int j = 0; j < econn->sedges - 1; j++) { ULong momj = econn->cedges[j].momset; if (momj == 0) { continue; } int extj = 0; if (econn->cedges[j].nodes[0] < nExtern) { extj = 1; } else if (econn->cedges[j].nodes[1] < nExtern) { extj = 1; } for (int k = j+1; k < econn->sedges; k++) { ULong momk = econn->cedges[k].momset; if (momk == 0) { continue; } int extk = 0; if (econn->cedges[k].nodes[0] < nExtern) { extk = 1; } else if (econn->cedges[k].nodes[1] < nExtern) { extk = 1; } if ( momj == momk) { if (nExtern == 2) { if (extj + extk != 2) { ok = False; } } else { ok = False; } } } } if (qgopt[GRCC_QGRAF_OPT_NOSIGMA] > 0) { if (! ok) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_NOSIGMA] < 0) { if (ok) { return False; } } } if (qgopt[GRCC_QGRAF_OPT_SIMPLE] > 0) { if (mgraph->selfloop || mgraph->multiedge) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_SIMPLE] < 0) { if (!mgraph->selfloop && !mgraph->multiedge) { return False; } } if (qgopt[GRCC_QGRAF_OPT_BIPART] > 0) { if (! mgraph->bipart) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_BIPART] < 0) { if (mgraph->bipart) { return False; } } // GRCC_QGRAF_OPT_CYCLI if (qgopt[GRCC_QGRAF_OPT_CYCLI] != 0) { int nb = 0; for (int k = 0; k < econn->nblocks; k++) { if (econn->blocks[k].loop > 0) { nb++; } } if (qgopt[GRCC_QGRAF_OPT_CYCLI] > 0) { if (nb > 1) { return False; } } else if (qgopt[GRCC_QGRAF_OPT_CYCLI] < 0) { if (nb <= 1) { return False; } } } return True; } //-------------------------------------------------------------- Bool EGraph::optQGrafA(Options *opt) { #ifdef PRINT grcc_fprintf(GRCC_Stdout, "optQGrafA: %8ld\n", mId); econn->print(); #endif Bool retval = True; if (opt->qgopt[GRCC_QGRAF_OPT_FLOOP] != 0) { for (int fl=0; fl < nFlines; fl++) { if (flines[fl]->ftype == FL_Closed) { if (flines[fl]->nlist % 2 != 0) { retval = False; break; } } } // `notfloop_' is the dual of `floop_', so flip the decision: if (opt->qgopt[GRCC_QGRAF_OPT_FLOOP] == -1) { retval = (retval == True ? False : True); } } return retval; } //-------------------------------------------------------------- Bool EGraph::isOptE(void) { EGraph edupv = EGraph(sNodes, sEdges, sMaxdeg); EGraph *edup = &edupv; int grp[GRCC_MAXEDGES], ed2gr[GRCC_MAXEDGES]; int g, ed, ngrp; Bool ok; int minopi2p; // if (opt->values[GRCC_OPT_No2PtL1PI] == 0 // && opt->values[GRCC_OPT_NoAdj2PtV] == 0) { // return True; // } for (ed = 0; ed < nEdges; ed++) { edges[ed]->cut = False; } biconnE(); // QGraf options if (! optQGrafM(opt)) { return False; } if (opt->values[GRCC_OPT_NoAdj2PtV] > 0) { if (nadj2ptv > 0) { return False; } } else if (opt->values[GRCC_OPT_NoAdj2PtV] < 0) { if (nadj2ptv < 1) { return False; } } if (opt->values[GRCC_OPT_No2PtL1PI] == 0) { return True; } if (nExtern == 2 && nopicomp == 1) { minopi2p = 2; } else { minopi2p = 1; } if (opi2plp > 0 && nopi2p >= minopi2p) { if (opt->values[GRCC_OPT_No2PtL1PI] > 0) { return False; } else if (opt->values[GRCC_OPT_No2PtL1PI] < 0) { return True; } } edup->copy(this); ngrp = groupLMom(grp, ed2gr); for (g = 0; g < ngrp; g++) { ok = True; if (grp[g] < 2) { continue; } for (ed = 0; ed < nEdges; ed++) { if (ed2gr[ed] == g) { if (edges[ed]->ext) { ok = False; break; } edup->edges[ed]->cut = True; } else { edup->edges[ed]->cut = False; } } if (ok) { edup->gSubId++; edup->biconnE(); if (edup->nExtern == 2 && edup->nopicomp == 1) { minopi2p = 2; } else { minopi2p = 1; } if (edup->opi2plp > 0 && edup->nopi2p >= minopi2p) { if (opt->values[GRCC_OPT_No2PtL1PI] > 0) { return False; } else if (opt->values[GRCC_OPT_No2PtL1PI] < 0) { return True; } } } } if (opt->values[GRCC_OPT_No2PtL1PI] > 0) { return True; } else if (opt->values[GRCC_OPT_No2PtL1PI] < 0) { return False; } else { erEnd("isOptE: illegal control"); return False; } } //-------------------------------------------------------------- int EGraph::findRoot(void) { int root, vr, er, e, nd0, nd1; root = -1; vr = -1; er = -1; for (e = 0; e < nEdges; e++) { if (edges[e]->cut || edges[e]->edtype == GRCC_ED_Deleted) { continue; } if (edges[e]->visited) { continue; } if (root < 0) { if (edges[e]->ext) { nd0 = edges[e]->nodes[0]; nd1 = edges[e]->nodes[1]; if (isExternal(nd0) && !isExternal(nd1)) { root = nd1; break; } else if (!isExternal(nd0) && isExternal(nd1)) { root = nd0; break; } } } if (er < 0) { er = edges[e]->nodes[0]; } if (vr < 0) { vr = edges[e]->nodes[0]; } } // if root >= 0 : vertex adjacent to an external node if (root < 0) { // if vr >= 0 : a vertex if (vr >= 0) { root = vr; // no vertex, only external nodes; } else { root = er; } } return root; } //--------------------------------------------------------------- int EGraph::connComp(void) { // Count the number of connected component // If a connected component without free leg is not the whole graph then // return False, otherwise return True. int j, ncc, nelem; for (j = 0; j < nNodes; j++) { nodes[j]->visited = -1; } ncc = 0; // # connected components nelem = 0; // # visited nodes while (nelem < nNodes) { for (j = 0; j < nNodes; j++) { if (nodes[j]->visited < 0) { break; } } if (j >= nNodes) { break; } nelem += connVisit(j, ncc); ncc++; } if (nelem != nNodes) { erEnd("EGraph::connComp: illegal control"); } return ncc; } //--------------------------------------------------------------- int EGraph::connVisit(int nd, int ncc) { // Visiting connected node used for 'connComp' int e, en, nn, j, nelem; nelem = 1; nodes[nd]->visited = ncc; for (e = 0; e < nodes[nd]->deg; e++) { en = V2Iedge(nodes[nd]->edges[e]); for (j = 0; j < 2; j++) { nn = edges[en]->nodes[j]; if (nodes[nn]->visited < 0) { nelem += connVisit(nn, ncc); } } } return nelem; } //-------------------------------------------------------------- void EGraph::biconnE(void) { int e, ie, root; int extlst[GRCC_MAXEDGES], intlst[GRCC_MAXEDGES]; int opiext, opiloop; nadj2ptv = 0; for (e = 0; e < nEdges; e++) { if (nodes[edges[e]->nodes[0]]->deg == 2 && nodes[edges[e]->nodes[1]]->deg == 2 && edges[e]->nodes[0] != edges[e]->nodes[1]) { nadj2ptv++; } } biinitE(); // initialization bconn = 0; // the number of connected components opiext = 0; opiloop = 0; for (e = 0; e < nEdges; e++) { // root of a spanning tree to be searched. root = findRoot(); if (root < 0) { // no root : end of search break; } // recursive search bisearchE(root, extlst, intlst, &opiext, &opiloop); // opi2plp = Max(opi2plp, opiloop); // ??? // adjust the #external for the root if (isExternal(root)) { opiext++; } // 2 point function if (opiext == 2) { opi2plp = Max(opi2plp, opiloop); nopi2p++; } for (ie = 0; ie < nEdges; ie++) { if (intlst[ie]) { edges[ie]->opicomp = nopicomp; } } nopicomp++; bconn++; // the number of connected component } // momentum conservation of external particles extMomConsv(); #ifdef CHECK chkMomConsv(); #endif return; } //-------------------------------------------------------------- void EGraph::biinitE(void) { int n, j, e; bicount = 0; // counter of visiting node loopm = 0; // # of independent loop momentum nopicomp = 0; opi2plp = 0; nopi2p = 0; for (n = 0; n < nNodes; n++) { bidef[n] = -1; bilow[n] = -1; nodes[n]->ndtype = GRCC_ND_Undef; for (j = 0; j < nLoops; j++) { nodes[n]->klow[j] = -1; } } for (e = 0; e < nEdges; e++) { // edges[e]->cut is defined before edges[e]->visited = False; edges[e]->conid = -1; // connected component edges[e]->edtype = GRCC_ED_Undef; edges[e]->opicomp = -1; for (j = 0; j < nEdges; j++) { edges[e]->emom[j] = 0; // coefficients of ext. mom. } for (j = 0; j < nLoops; j++) { edges[e]->lmom[j] = 0; // coefficients of loop mom. } } } //-------------------------------------------------------------- void EGraph::bisearchE(int nd, int *extlst, int *intlst, int *opiext, int *opiloop) { // Search in the spanning tree below 'nd'. // Arguments: // nd : input : node to be visited // extlst : output : set of external lines in the current 1PI comp. // intlst : output : set of internal lines in the current 1PI comp. // opiext : output : no. external lines of the current 1PI component // opiloop : output : no. loops of the current 1PI component // // EGraph variables // bicount : counter of visiting node // loopm : no. of independent loop momentum // nopicomp : no. of OPI components // opi2plp : maximum number loops among 2-point looped OPI components // nopi2p : no. of 2-point OPI components // edges[ie]->opicomp : OPI component no. of the edge // int k, e, ie, ed, td, dir, j; int opiext1, opiloop1; int extlst1[GRCC_MAXEDGES]; // set of external nodes below int intlst1[GRCC_MAXEDGES]; // set of vertices in the 1PI component (*opiext) = 0; (*opiloop) = 0; // visit node 'nd' bidef[nd] = bicount; bilow[nd] = bicount; for (k = 0; k < nLoops; k++) { nodes[nd]->klow[k] = bicount; } bicount++; for (j = 0; j < nEdges; j++) { extlst[j] = False; intlst[j] = False; } // go to children : nd --> ed --> td for (e = 0; e < nodes[nd]->deg; e++) { ed = V2Iedge(nodes[nd]->edges[e]); // check this edge is already visited if (edges[ed]->edtype == GRCC_ED_Deleted) { // permanently deleted edge continue; } else if (edges[ed]->visited) { // already visited (backword visit) continue; } else if (edges[ed]->cut) { // cut edge : treat as nd is an external (*opiext)++; nodes[nd]->setType(GRCC_ND_CPoint); continue; } else if (!isExternal(nd) && edges[ed]->ext) { // external edges[ed]->setType(GRCC_ED_Extern); edges[ed]->visited = True; edges[ed]->emom[ed] = 1; extlst[ed] = True; (*opiext)++; nodes[nd]->setType(GRCC_ND_CPoint); continue; } // mark visited edges[ed]->visited = True; // momentum is assigned on the backward move. (nd) 1 --> 0 (td) td = edges[ed]->nodes[0]; dir = 1; if (td == nd) { td = edges[ed]->nodes[1]; dir = -1; } // biconnected component if (bidef[td] >= 0) { // a back edge is found. Already visited. Don't go further bilow[nd] = Min(bilow[nd], bilow[td]); edges[ed]->setType(GRCC_ED_Back); intlst[ed] = True; (*opiloop)++; // create new loop momentum k = loopm++; nodes[nd]->klow[k] = Min(nodes[nd]->klow[k], nodes[td]->klow[k]); edges[ed]->setLMom(k, dir); // self-loop if (td == nd) { nodes[nd]->setType(GRCC_ND_CPoint); } } else { // not a back edge // go down further bisearchE(td, extlst1, intlst1, &opiext1, &opiloop1); // the set of external particles for (j = 0; j < nEdges; j++) { extlst[j] = extlst[j] || extlst1[j]; } // loop momenta for (k = 0; k < nLoops; k++) { if (nodes[td]->klow[k] <= nodes[nd]->klow[k]) { // inside loop 'k' edges[ed]->setLMom(k, dir); } nodes[nd]->klow[k] = Min(nodes[nd]->klow[k], nodes[td]->klow[k]); } // cut point ? if (bilow[td] >= bidef[nd]) { // a cut point is found if (nodes[nd]->ndtype == GRCC_ND_Undef) { nodes[nd]->setType(GRCC_ND_CPoint); #ifdef CHECK } else if (nodes[nd]->ndtype != GRCC_ND_CPoint) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "bisearch: node %d is a cut point ", nd); grcc_fprintf(GRCC_Stderr, "(not undef %d)\n", nodes[nd]->ndtype); } #endif } } // cut point // bridge ? if (bilow[td] > bidef[nd]) { // a bridge is found if (edges[ed]->edtype == GRCC_ED_Undef) { edges[ed]->setType(GRCC_ED_Bridge); nodes[td]->setType(GRCC_ND_CPoint); #ifdef CHECK } else if (edges[ed]->edtype != GRCC_ED_Bridge) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "bisearch: edges %d is a bridge ", ed); grcc_fprintf(GRCC_Stderr, "(not undef %d)\n", edges[ed]->edtype); } #endif } if (!edges[ed]->ext) { // internal bridge opiext1++; // from bridge for (ie = 0; ie < nEdges; ie++) { if (intlst1[ie]) { // OPI component No. edges[ie]->opicomp = nopicomp; intlst1[ie] = False; } } // 2pt OPI component if (opiext1 == 2) { opi2plp = Max(opi2plp, opiloop1); // the number of 2pt looped OPI components nopi2p++; } // the number of OPI components nopicomp++; } opiext1 = 1; // from bridge opiloop1 = 0; } else { // not a bridge bilow[nd] = Min(bilow[nd], bilow[td]); if (edges[ed]->edtype == GRCC_ED_Undef) { edges[ed]->setType(GRCC_ED_Inloop); #ifdef CHECK } else if (edges[ed]->edtype != GRCC_ED_Inloop) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "bisearch: "); grcc_fprintf(GRCC_Stderr, "edges %d is not undef (%d)\n", ed, edges[ed]->edtype); } #endif } intlst1[ed] = True; } // merge to the current variables for (ie = 0; ie < nEdges; ie++) { intlst[ie] = intlst[ie] || intlst1[ie]; } (*opiext) += opiext1; (*opiloop) += opiloop1; // linear combination of external momenta edges[ed]->setEMom(nEdges, extlst1, dir); } // end of a child } // for (ed) return; } //-------------------------------------------------------------- void EGraph::extMomConsv(void) { int e, ex, lex, rs; lex = -1; for (e = 0; e < nEdges; e++) { if (edges[e]->ext) { lex = e; extMom[e] = edges[e]->emom[e]; } else { extMom[e] = 0; } } // eliminate momentum of the last external particle if (lex < 0) { return; } for (e = 0; e < nEdges; e++) { rs = edges[e]->emom[lex]; if (rs != 0) { for (ex = 0; ex < nEdges; ex++) { edges[e]->emom[ex] -= rs*extMom[ex]; } } } } //-------------------------------------------------------------- void EGraph::chkMomConsv(void) { // check momentum conservation int esum[GRCC_MAXEDGES]; int lsum[GRCC_MAXNODES]; Bool ok, okn; int n, ex, lk, ej, e, dir; if (bicount < 1) { return; } ok = True; for (n = 0; n < nNodes; n++) { if (isExternal(n)) { continue; } for (ex = 0; ex < nEdges; ex++) { esum[ex] = 0; } for (lk = 0; lk < nLoops; lk++) { lsum[lk] = 0; } for (ej = 0; ej < nodes[n]->deg; ej++) { e = V2Iedge(nodes[n]->edges[ej]); if (edges[e]->nodes[0] == edges[e]->nodes[0]) { continue; } dir = dirEdge(n, ej); for (ex = 0; ex < nEdges; ex++) { if (edges[e]->ext) { esum[ex] += dir*edges[e]->emom[ex]; } } for (lk = 0; lk < nLoops; lk++) { lsum[lk] += dir*edges[e]->lmom[lk]; } } okn = True; for (ex = 0; ex < nEdges; ex++) { if (esum[ex] != 0) { okn = False; grcc_fprintf(GRCC_Stderr, "chkMomConsv:n=%d, esum[%d]=%d\n", n, ex, esum[ex]); } } for (lk = 0; lk < nLoops; lk++) { if (lsum[lk] != 0) { okn = False; grcc_fprintf(GRCC_Stderr, "chkMomConsv:n=%d, lsum[%d]=%d\n", n, lk, lsum[lk]); } } if (!okn) { ok = False; grcc_fprintf(GRCC_Stderr, "*** Violation of momentum conservation "); grcc_fprintf(GRCC_Stderr, "at node =%d\n",n); } } if (!ok) { print(); erEnd("inconsistent momentum"); } } //-------------------------------------------------------------- int EGraph::legParticle(int ed, int el) { // outgoing particle from (edge, leg) = (ed, el) return model->normalParticle((2*el-1)*edges[ed]->ptcl); } //-------------------------------------------------------------- int EGraph::isFermion(int ed) { // return if particle on the edge ed follows Fermi statistics or not. int ptcl, ptype; ptcl = edges[ed]->ptcl; ptype = model->particles[Abs(ptcl)]->ptype; return (ptype == GRCC_PT_Dirac || ptype == GRCC_PT_Majorana || ptype == GRCC_PT_Ghost); } //-------------------------------------------------------------- int EGraph::fltrace(int fk, int nd0, int *fl) { // fk : kind of fermion // = (GRCC_PT_Dirac, GRCC_PT_Majorana or GRCC_PT_Ghost) // nd0 : the last node visited // fl : list of signed edge on the fermion line. // fl[j] : // (V2Iedge(fl[j]), V2Ileg(fl[j])) is the next node // fl[0] should be already defined int nfl, k, i, nd, nl, e, ed, el, fgcnt, fkind, lk; nfl = 1; // maximal possible length of a fline is nEdges for (k = 0; k < nEdges; k++) { if (k >= nfl) { grcc_fprintf(GRCC_Stdout, "*** fltrace:illegal contorl: k=%d, nEdges=%d\n", k, nEdges); break; } // get next node : nd0 ---- nd (nl) e = fl[k]; ed = V2Iedge(e); el = V2Ileg(e); #ifdef CHECK if (ed > nEdges) { grcc_fprintf(GRCC_Stderr, "*** fltrace: ed=%d > nEdges=%d, fl=", ed, nEdges); prIntArray(nNodes, fl, "\n"); erEnd("fltrace: illegal fl"); } #endif nd = edges[ed]->nodes[el]; nl = edges[ed]->nlegs[el]; // end of the fline if (isExternal(nd) || nd == nd0) { fgcnt = 1; break; } // find leg of nd for going next fgcnt = 0; ed = 0; lk = 0; for (i = 0; i < nodes[nd]->deg; i++) { e = nodes[nd]->edges[i]; ed = V2Iedge(e); fkind = model->particles[Abs(edges[ed]->ptcl)]->ptype; // lk = 1 : (# of fkind particle) is even // lk = -1 : (# of fkind particle) is odd if (fkind == fk) { if (lk == 1) { lk = -1; } else { lk = 1; } } else { lk = 0; } if (!edges[ed]->visited) { if (!isFermion(ed)) { edges[ed]->visited = True; } else { if (fkind == fk) { // i should be the neighbor of nl // (nl, i) or (i, nl) should be a pair of fkind // (nl, i) : lk = -1 // (i, nl) : lk = 1 if ((lk == 1 && nl == i+1) || (lk == -1 && nl == i-1)) { edges[ed]->visited = True; fgcnt++; if (fgcnt == 1) { // -e = (signed edge points the next node) fl[nfl++] = - e; break; } } } } } // not visited } // end of for k if (fgcnt == 0) { grcc_fprintf(GRCC_Stdout, "*** fline: Fermion number is not conserved\n"); grcc_fprintf(GRCC_Stdout, " nd=%d, e=%d, ed=%d, fgcnt=%d\n", nd, e, ed, fgcnt); // erEnd("fline: Fermion number is not conserved"); } else if (fgcnt > 1) { grcc_fprintf(GRCC_Stdout, "+++ fline: more than two fermions: check fsign\n"); grcc_fprintf(GRCC_Stdout, " nd=%d, e=%d, ed=%d, fgcnt=%d\n", nd, e, ed, fgcnt); } } if (k >= nEdges || k >= nfl) { grcc_fprintf(GRCC_Stdout, "*** fline: illegal control\n"); grcc_fprintf(GRCC_Stdout, " nEdges=%d, nfl=%d, k=%d, ", nEdges, nfl, k); prIntArray(nfl, fl, "\n"); erEnd("fline: illegal control"); } return nfl; } //-------------------------------------------------------------- void EGraph::getFLines(void) { int fl[GRCC_MAXNODES]; int nextn, exto[GRCC_MAXNODES]; int e, ed, nd, floop, nswap, nfl, fkind, el, ptcl; nFlines = 0; for (ed = 0; ed < nEdges; ed++) { edges[ed]->visited = False; } nextn = 0; for (ed = 0; ed < nEdges; ed++) { if (edges[ed]->visited) { continue; } if (!edges[ed]->ext) { continue; } el = 0; nd = edges[ed]->nodes[el]; if (!isExternal(nd)) { el = 1; nd = edges[ed]->nodes[el]; if (!isExternal(nd)) { erEnd("*** illegal control"); } } if (!isFermion(ed)) { continue; } ptcl = legParticle(ed, 1-el); if (ptcl < 0) { continue; } // el ed el1 // x----<----x e = (signed edge of (ed, el1)) // nd ptcl(>= 0) // external fl[0] = - I2Vedge(ed, el); nfl = 1; fkind = model->particles[Abs(edges[ed]->ptcl)]->ptype; edges[ed]->visited = True; nfl = fltrace(fkind, nd, fl); addFLine(FL_Open, fkind, nfl, fl); e = fl[nfl-1]; exto[nextn++] = edges[V2Iedge(e)]->nodes[V2Ileg(e)]; } // closed Fermion line floop = 0; for (ed = 0; ed < nEdges; ed++) { if (edges[ed]->visited) { continue; } if (!isFermion(ed)) { continue; } el = 0; ptcl = legParticle(ed, 1-el); if (ptcl < 0) { el = 1; } nd = edges[ed]->nodes[el]; // el ed el1 // x----<----x e = (signed edge of (ed, el1)) // nd ptcl fl[0] = - I2Vedge(ed, el); nfl = 1; edges[ed]->visited = True; fkind = model->particles[Abs(edges[ed]->ptcl)]->ptype; nfl = fltrace(fkind, nd, fl); addFLine(FL_Closed, fkind, nfl, fl); floop++; } if (nextn > 0) { nswap = sortb(nextn, exto); } else { nswap = 0; } if ((floop+nswap) % 2 == 0) { fsign = 1; } else { fsign = -1; } } //-------------------------------------------------------------- void EGraph::addFLine(const FLType ft, int fk, int nfl, int *fl) { int j; if (nFlines >= GRCC_MAXFLINES) { erEnd("too many Fermion lines (GRCC_MAXEDGES)"); } if (flines[nFlines] == NULL) { flines[nFlines] = new EFLine(); } flines[nFlines]->ftype = ft; flines[nFlines]->fkind = fk; flines[nFlines]->nlist = nfl; for (j = 0; j < nfl; j++) { flines[nFlines]->elist[j] = fl[j]; } nFlines++; } //************************************************************** // assign.cc //============================================================== // Assign particles to the edges and interactions to nodes. // Completed graph data is saved in the form of EGraph. // method : selection of assignable node //=============================================================== // class NCand NCand::NCand(const NCandSt sta, const int dega, const int nilst, int *ilst) { // candidate list of interactions attached to a vertex. int j; deg = dega; st = sta; nilist = nilst; for (j = 0; j < nilist; j++) { ilist[j] = ilst[j]; } #ifdef CHECK if (st == AS_Assigned) { if (nilist != 1) { erEnd("illegal assignment"); } } else if (st == AS_AssExt) { if (nilist != 1) { erEnd("illegal assignment"); } } #endif } //--------------------------------------------------------------- NCand::~NCand(void) { } //--------------------------------------------------------------- void NCand::prNCand(const char* msg) { grcc_fprintf(GRCC_Stdout, "%d %d ", st, deg); prIntArray(nilist, ilist, msg); } //=============================================================== // class ECand ECand::ECand(int dt, int nplst, int *plst) { int j; det = dt; nplist = nplst; for (j = 0; j < nplist; j++) { plist[j] = plst[j]; } if (det && nplist != 1) { if (prlevel > 0) { grcc_fprintf(GRCC_Stderr, "*** ECand : len(plist) != 1 : det=%d ", det); prIntArrayErr(nplist, plist, "\n"); } erEnd("ECand : len(plist) != 1"); } } //--------------------------------------------------------------- ECand::~ECand(void) { } //--------------------------------------------------------------- void ECand::prECand(const char *msg) { prIntArray(nplist, plist, ""); grcc_fprintf(GRCC_Stdout, " (det=%d)%s", det, msg); } //=============================================================== // class ANode ANode::ANode(int dg) { int j; deg = dg; nlegs = 0; anodes = new int[deg]; aedges = new int[deg]; aelegs = new int[deg]; cand = NULL; for (j = 0; j < deg; j++) { anodes[j] = -1; aedges[j] = -1; aelegs[j] = -1; } } //--------------------------------------------------------------- ANode::~ANode(void) { if (cand != NULL) { delete cand; cand = NULL; } if (aelegs != NULL) { delete[] aelegs; delete[] aedges; delete[] anodes; aelegs = NULL; aedges = NULL; anodes = NULL; } } //--------------------------------------------------------------- int ANode::newleg(void) { // add a slot for a leg int lg = nlegs; nlegs++; #ifdef CHECK if (nlegs > deg) { grcc_fprintf(GRCC_Stderr, "*** ANode::newleg : nlegs = %d > deg = %d\n", nlegs, deg); erEnd("ANode::newleg : nlegs > deg"); } #endif return lg; } //=============================================================== // class AEdge AEdge::AEdge(int n0, int l0, int n1, int l1) { nodes[0] = n0; // node of 0 side of the edge nodes[1] = n1; // node of 1 side of the edge nlegs[0] = l0; // leg ot the node of 0 side of the edge nlegs[1] = l1; // leg ot the node of 1 side of the edge ptcl = GRCC_PT_Undef; // particle defined in the model cand = NULL; // candidate } //--------------------------------------------------------------- AEdge::~AEdge(void) { if (cand != NULL) { delete cand; } } //=============================================================== // class Assign Assign::Assign(SProcess *sprc, MGraph *mgr, PNodeClass *pnc) { Bool ok; int j; if (sprc == NULL) { erEnd("Assign: sproc == NULL"); } // pointers to related objects sproc = sprc; model = sproc->model; opt = sproc->opt; mgraph = mgr; pnclass = pnc; egraph = mgraph->egraph; if (egraph == NULL) { erEnd("Assign: egraph == NULL"); } astack = sproc->astack; if (astack == NULL) { erEnd("Assign: astack == NULL"); } nNodes = mgraph->nNodes; nEdges = mgraph->nEdges; nExtern = sproc->nExtern; nETotal = 0; // total number of edges // counters of graphs nAGraphs = 0; wAGraphs = Fraction(0,1); nAOPI = 0; wAOPI = Fraction(0,1); nodes = new ANode*[nNodes]; edges = new AEdge*[nEdges]; for (j = 0; j < nNodes; j++) { nodes[j] = NULL; } for (j = 0; j < nEdges; j++) { edges[j] = NULL; } for (j = 0; j < model->ncouple; j++) { cplleft[j] = sproc->clist[j]; } // initialize astack astack->setAGraph(this); astack->checkPoint(checkpoint0); // import from mgraph ok = fromMGraph(); #ifdef CHECK checkAG("Assign::Assign"); #endif if (ok) { // start assignment assignAllVertices(); } else { // cannot assign } // restore from the stack #ifdef CHECK astack->restoreMsg(checkpoint0, "Assign"); #else astack->restore(checkpoint0); #endif } //=============================================================== Assign::~Assign(void) { int j; for (j = 0; j < nEdges; j++) { delete edges[j]; edges[j] = NULL; } delete[] edges; edges = NULL; for (j = 0; j < nNodes; j++) { delete nodes[j]; nodes[j] = NULL; } delete[] nodes; nodes = NULL; } //--------------------------------------------------------------- void Assign::prCand(const char *msg) { // Print candidate table int n, e, ne; AEdge *ed; grcc_fprintf(GRCC_Stdout, "\n"); grcc_fprintf(GRCC_Stdout, "+++ Candidate list: %s\n", msg); grcc_fprintf(GRCC_Stdout, " Nodes %d\n", nNodes); for (n = 0; n < nNodes; n++) { grcc_fprintf(GRCC_Stdout, "%d: edges=", n); prIntArray(nodes[n]->deg, nodes[n]->aedges, ": cand="); if (nodes[n]->cand == NULL) { grcc_fprintf(GRCC_Stdout, "NULL\n"); } else { nodes[n]->cand->prNCand("\n"); } } ne = Min(nEdges, nETotal); grcc_fprintf(GRCC_Stdout, " Edges %d\n", ne); for (e = 0; e < ne; e++) { ed = edges[e]; if (ed == NULL) { grcc_fprintf(GRCC_Stdout, "NULL_Edge\n"); } else { grcc_fprintf(GRCC_Stdout, "%d: %d->%d: cand=", e, ed->nodes[0], ed->nodes[1]); if (edges[e]->cand == NULL) { grcc_fprintf(GRCC_Stdout, "NULL\n"); } else { edges[e]->cand->prECand("\n"); } } } } //=============================================================== void Assign::checkAG(const char *msg) { int n, lg; Bool ok = True; for (n = 0; n < nNodes; n++) { for (lg = 0; lg < nodes[n]->deg; lg++) { if (nodes[n]->aedges[lg] < 0) { grcc_fprintf(GRCC_Stdout, "*** checkAG:%s: n=%d, lg=%d, aedges=%d\n", msg, n, lg, nodes[n]->aedges[lg]); ok = False; } } } if (!ok) { prCand("checkAG"); erEnd("checkAG: failed"); } } //=============================================================== // control of the process of particle/interaction assignment //--------------------------------------------------------------- Bool Assign::assignAllVertices(void) { // Entry point of the assignment procedure Bool ok; #ifdef CHECK checkCand("assignAllVertices:1"); #endif // start main part #ifdef SIMPSEL ok = selectVertexSimp(-1); #else ok = selectVertex(); #endif #ifdef CHECK checkCand("assignAllVertices:2"); #endif return ok; } //--------------------------------------------------------------- Bool Assign::selectVertexSimp(int lastv) { // Select a vertex for assignment of particles to legs // // Argument // lastv : previously assigned vertex; Nothing when lastv<0. Bool ok; int v; #ifdef CHECK checkCand("selectVertexSimp"); #endif // find a vertex to which interaction is assigned v = selUnAssVertexSimp(lastv); // no more vertex if (v < 0) { ok = allAssigned(); if (ok) { if (!egraph->optQGrafA(opt)) { return False; } // egraph->biconnE(); // necessary ??? opt->newAGraph(egraph); } return ok; } // select a leg and assign a particle to it ok = selectLeg(v, -1); return ok; } //--------------------------------------------------------------- Bool Assign::selectVertex(void) { // Select a vertex for assignment of particles to legs // // Argument // lastv : previously assigned vertex; Nothing when lastv<0. Bool ok; int v; #ifdef CHECK checkCand("selectVertex"); #endif // find a vertex to which interaction is assigned v = selUnAssVertex(); // no more vertex if (v < 0) { ok = allAssigned(); if (ok) { if (!egraph->optQGrafA(opt)) { return False; } egraph->biconnE(); opt->newAGraph(egraph); } return ok; } // select a leg and assign a particle to it ok = selectLeg(v, -1); return ok; } //--------------------------------------------------------------- Bool Assign::selectLeg(int v, int lastlg) { // Select a leg of vertex 'v' for assignment of particle, // where the last assigned leg was 'lastlg'. int pt, ln, j; Bool ok; CheckPt sav, sav0; int nplist, plist[GRCC_MAXMPARTICLES2]; #ifdef CHECK checkNode(v, "selectLeg:0"); checkCand("selectLeg"); #endif // find a leg to be assigned ln = selUnAssLeg(v, lastlg); // no more assignable leg for the current node if (ln < 0) { // move to next vertex ok = assignVertex(v); return ok; } // make the list of possible particles, incoming to the vertex astack->checkPoint(sav0); nplist = candPart(v, ln, plist, GRCC_MAXMPARTICLES2); // no candidate if (nplist < 1) { return False; } // assign each of possible particle to the leg 'lg'. astack->checkPoint(sav); for (j = 0; j < nplist; j++) { pt = plist[j]; // try to assign 'pt' to (v, ln) if(assignPLeg(v, ln, pt)) { // move to next leg selectLeg(v, ln); } #ifdef CHECK astack->restoreMsg(sav, "selectLeg2"); #else astack->restore(sav); #endif } #ifdef CHECK astack->restoreMsg(sav0, "selectLeg2"); #else astack->restore(sav0); #endif return True; } //--------------------------------------------------------------- void Assign::saveCouple(int *sav) { int j; if (model->ncouple > 1) { for (j = 0; j < model->ncouple; j++) { sav[j] = cplleft[j]; } } } //--------------------------------------------------------------- void Assign::restoreCouple(int *sav) { int j; if (model->ncouple > 1) { for (j = 0; j < model->ncouple; j++) { cplleft[j] = sav[j]; } } } //--------------------------------------------------------------- Bool Assign::subCouple(int *cpl) { int j; if (model->ncouple > 1) { for (j = 0; j < model->ncouple; j++) { cplleft[j] -= cpl[j]; if (cplleft[j] < 0) { return False; } } } return True; } //--------------------------------------------------------------- Bool Assign::assignVertex(int v) { // Assign interactions to vertex 'v' Bool done, ok; CheckPt sav, sav1; NCand *nc; int ia, n, j, cl; NCandSt vst; Bool ok1; int savc0[GRCC_MAXNCPLG], savc1[GRCC_MAXNCPLG]; #ifdef CHECK checkCand("assignVertex"); #endif // save the configuration astack->checkPoint(sav); saveCouple(savc0); // assign to all vertices with only one candidate done = False; for (n = 0; n < nNodes; n++) { // check if vertex cl = pnclass->nd2cl[n]; if (!isATExternal(pnclass->type[cl])) { nc = nodes[n]->cand; if (nc->st == AS_UnAssLegs && nc->nilist == 1) { // bind interaction to the vertex ia = nc->ilist[0]; vst = assignIVertex(n, ia); if (vst == AS_Impossible) { // discard the current configuration #ifdef CHECK astack->restoreMsg(sav, "assignVertex"); #else astack->restore(sav); #endif restoreCouple(savc0); return False; } else if (vst == AS_Assigned) { if (!subCouple(model->interacts[ia]->clist)) { #ifdef CHECK astack->restoreMsg(sav, "assignVertex"); #else astack->restore(sav); #endif restoreCouple(savc0); return False; } } if (n == v) { done = (vst == AS_Assigned); } } } } // uniquely determined ok = True; if (done) { // move to the next vertex #ifdef SIMPSEL ok = selectVertexSimp(v); #else ok = selectVertex(); #endif #ifdef CHECK astack->restoreMsg(sav, "assignVertex"); #else astack->restore(sav); #endif restoreCouple(savc0); return ok; } // there are still several possibilities. astack->checkPoint(sav1); saveCouple(savc1); for (j = 0; j < nodes[v]->cand->nilist; j++) { ia = nodes[v]->cand->ilist[j]; // bind interaction to the vertex ok1 = True; vst = assignIVertex(v, ia); if (vst == AS_Assigned) { ok1 = subCouple(model->interacts[ia]->clist); } if (ok1 && (vst == AS_Assigned || vst == AS_Assigned0)) { // move to the next vertex #ifdef SIMPSEL ok = selectVertexSimp(v); #else ok = selectVertex(); #endif } #ifdef CHECK astack->restoreMsg(sav1, "assignVertex"); #else astack->restore(sav1); #endif restoreCouple(savc1); } #ifdef CHECK astack->restoreMsg(sav, "assignVertex"); #else astack->restore(sav); #endif restoreCouple(savc0); return ok; } //--------------------------------------------------------------- Bool Assign::allAssigned(void) { // Assignment of particles and interactions is finished. // Check isomorphism etc. and count symmetry factor // The sign from Fermi statistics is calculated inf fillEGraph BigInt nsym, esym, nsym1; MNodeClass *cl; Bool ok = True; #ifdef OPTEXTONLY #else Bool ext; int e, p; #endif #ifdef CHECK checkCand("allAssigned"); #endif // check order of coupling constants #ifdef CHECK if (!checkOrderCpl()) { erEnd("allAssigned: checkOrderCpl = False"); } #endif // check duplication by violating ordering condition if (!isOrdLegs()) { return False; } // classification of nodes cl = mgraph->curcl; // check isomorphism and calculate sfactor nsym = 0; esym = 0; ok = isIsomorphic(cl, &nsym, &esym, &nsym1); if (!ok || nsym < 1 || esym < 1) { return False; } //-------------------------- // Now we got a new agraph. // Update counters nAGraphs++; wAGraphs.add(1,nsym*esym); if (mgraph->opi) { nAOPI++; wAOPI.add(1,nsym*esym); } #ifdef CHECK checkAG("allAssigned"); #endif // fill information to resulting Egraph fillEGraph(nAGraphs, nsym, esym, nsym1); #ifdef OPTEXTONLY #else // check extonly particles for (e = 0; e < nEdges; e++) { p = Abs(egraph->edges[e]->ptcl); ext = egraph->edges[e]->ext; if (!ext) { if (model->particles[p]->extonly) { return False; } } } #endif return True; } //=============================================================== // Interface to MGraph and EGraph //--------------------------------------------------------------- Bool Assign::fromMGraph(void) { // Import from MGraph int npall, *pall; int np[1]; Bool ok; int j, k, n, nn, n1, deg, nc, ptcl, cl, typ, mcl, cl1, typ1; int lcn, ia; int nilist, ilist[GRCC_MAXMINTERACT]; NCandSt st; // create ANodes for (j = 0; j < nNodes; j++) { nodes[j] = new ANode(mgraph->nodes[j]->deg); } // initialization of edge table nETotal = 0; // List of all particles pall = model->allParticles(&npall); // add nodes for (n = 0; n < mgraph->nNodes; n++) { cl = pnclass->nd2cl[n]; typ = pnclass->type[cl]; // external particle if (isATExternal(typ)) { #ifdef CHECK if (mgraph->nodes[n]->deg != 1) { grcc_fprintf(GRCC_Stdout, "*** assign:fromMGraph : " "external but deg[%d] = %d != 1, type=%d\n", n, mgraph->nodes[n]->deg, typ); mgraph->print(); erEnd("assign:fromMGraph : illegal external particle"); } #endif np[0] = pnclass->particle[cl]; nodes[n]->cand = new NCand(AS_AssExt, 1, 1, np); for (n1 = 0; n1 < mgraph->nNodes; n1++) { nc = mgraph->adjMat[n][n1]; for (k = 0; k < nc; k++) { addEdge(n, n1, 1, np); } } // vertex } else { // candidates of vertices deg = mgraph->nodes[n]->deg; st = AS_UnAssLegs; cl = sproc->pnclass->nd2cl[n]; // class in the process mcl = sproc->pnclass->cl2mcl[cl]; // class in the model if (nodes[n]->cand != NULL) { delete nodes[n]->cand; } lcn = model->ncouple; // multiple coupling constants are defined in the model. if (lcn > 1) { nilist = 0; for (j = 0; j < model->cplgnvl[mcl]; j++) { ia = model->cplgvl[mcl][j]; // select by coupling constants if (leqArray(lcn, model->interacts[ia]->clist, cplleft)) { ilist[nilist++] = ia; } } nodes[n]->cand = new NCand(st, deg, nilist, ilist); // there is only one coupling constant } else { nodes[n]->cand = new NCand(st, deg, model->cplgnvl[mcl], model->cplgvl[mcl]); } // vertices for (n1 = n; n1 < mgraph->nNodes; n1++) { cl1 = pnclass->nd2cl[n1]; typ1 = pnclass->type[cl1]; if (!isATExternal(typ1)) { nc = mgraph->adjMat[n][n1]; if (n == n1) { nc = nc/2; } for (k = 0; k < nc; k++) { addEdge(n, n1, npall, pall); } } } } } #ifdef CHECK if (nETotal != nEdges) { grcc_fprintf(GRCC_Stdout, "*** Assign::fromMGraph nETotal=%d != nEdges=%d\n", nETotal, nEdges); erEnd("Assign::fromMGraph nETotal= != nEdges"); } #endif // assign particle of an edge next to an external particle for (n = 0; n < mgraph->nNodes; n++) { cl = pnclass->nd2cl[n]; typ = pnclass->type[cl]; if (isATExternal(typ)) { cl = pnclass->nd2cl[n]; ptcl = pnclass->particle[cl]; // particle ptcl flows in to the node and // particle (- ptcl) flows in from the edge. #ifdef CHECK if (ptcl == 0) { erEnd("fromMGraph: ptcl=0"); } #endif ok = assignPLeg(n, 0, -ptcl); if (!ok) { // impossible config return False; } nn = nodes[n]->anodes[0]; ok = updateCandNode(nn); if (!ok) { // impossible config return False; } } } #ifdef CHECK checkCand("fromMGraph"); checkAG("fromMGraph"); #endif return True; } //--------------------------------------------------------------- void Assign::addEdge(int n0, int n1, int nplist, int *plist) { // add an edge and set connection information // n0 -- (new edge) -- n1, with candidates 'plist' int lg0, lg1, eid; AEdge *aed; #ifdef CHECK if (n0 >= nNodes || n1 >= nNodes) { grcc_fprintf(GRCC_Stdout, "*** Assign::addEdge : undefined nodes %d: [%d, %d]", nETotal, n0, n1); erEnd("Assign::addEdge : undefined nodes"); } #endif // legs to be connected lg0 = nodes[n0]->newleg(); lg1 = nodes[n1]->newleg(); // create edge #ifdef CHECK if (nETotal >= nEdges) { erEnd("too many edges"); } #endif aed = new AEdge(n0, lg0, n1, lg1); aed->cand = new ECand(False, nplist, plist); #ifdef CHECK if (edges[nETotal] != NULL) { erEnd("edges[nETotal] != NULL"); } #endif // registor to the edge table eid = nETotal; edges[nETotal++] = aed; // connect edge and nodes connect(n0, lg0, eid, 0, n1, lg1); } //--------------------------------------------------------------- void Assign::connect(int n0, int l0, int eg, int el, int n1, int l1) { // Connect (n0, l0) -- (eg, el) -- (nl) ANode *nd0, *nd1; AEdge *ed; int eo; nd0 = nodes[n0]; nd1 = nodes[n1]; ed = edges[eg]; eo = 1 - el; nd0->anodes[l0] = n1; nd0->aedges[l0] = eg; nd0->aelegs[l0] = el; nd1->anodes[l1] = n0; nd1->aedges[l1] = eg; nd1->aelegs[l1] = eo; ed->nodes[el] = n0; ed->nlegs[el] = l0; ed->nodes[eo] = n1; ed->nlegs[eo] = l1; } //--------------------------------------------------------------- Bool Assign::fillEGraph(int aid, BigInt nsym, BigInt esym, BigInt nsym1) { // Set variables of egraph with the result of particle assignment // Adjust the ordering of legs of vertices in a consistent way // with the interaction defined in the model. ANode *an; ENode *en; int work[3][GRCC_MAXLEGS]; int n, lr, e; int *elist; int lg, ed, eg; #ifdef CHECK int cl, ok = True; #endif egraph->assigned = True; egraph->aId = aid; egraph->nsym = nsym; egraph->esym = esym; egraph->bicount = -1; if (sproc != NULL) { egraph->extperm = sproc->extperm; } else { egraph->extperm = 1; } egraph->nsym1 = nsym1; egraph->multp = (egraph->extperm * egraph->nsym1) / egraph->nsym; #ifdef CHECK checkAG("fillEGraph:0"); #endif // external node for (n = 0; n < nNodes; n++) { // vertices #ifdef CHECK cl = pnclass->nd2cl[n]; if (isATExternal(pnclass->type[cl])) { ; } else if (nodes[n]->cand->st != AS_Assigned) { grcc_fprintf(GRCC_Stdout, "*** fillEGraph : node %d is not assigned", n); prCand("fillEGraph: node"); erEnd("fillEGraph : node is not assigned"); } #endif an = nodes[n]; en = egraph->nodes[n]; en->initAss(egraph, n, an->deg); en->intrct = an->cand->ilist[0]; elist = reordLeg(n, work[0], work[1], work[2]); for (lr = 0; lr < nodes[n]->deg; lr++) { if (elist == NULL) { lg = lr; } else { lg = elist[lr]; } #ifdef CHECK if (lg < 0 || lg >= nodes[n]->deg) { grcc_fprintf(GRCC_Stdout, "*** fillEGraph: n=%d, lr=%d: 0 <= lg=%d < %d\n", n, lr, lg, nodes[n]->deg); erEnd("fillEGraph: illegal reordering"); } #endif ed = an->aedges[lg]; eg = an->aelegs[lg]; en->edges[lr] = I2Vedge(ed, 2*eg-1); egraph->edges[ed]->nodes[eg] = n; egraph->edges[ed]->nlegs[eg] = lr; } } // edges for (e = 0; e < nEdges; e++) { #ifdef CHECK if (edges[e]->cand->nplist != 1) { grcc_fprintf(GRCC_Stdout, "*** fillEGraph : edge %d is not assigned", e); prCand("fillEGraph: edge"); erEnd("fillEGraph : edge is not assigned"); } #endif egraph->edges[e]->ptcl = edges[e]->cand->plist[0]; } #ifdef EDGEPORDER for (e = 0; e < nEdges; e++) { if (egraph->edges[e]->ptcl < 0) { egraph->edges[e]->ptcl = - edges[e]->cand->plist[0]; n = egraph->edges[e]->nodes[0]; lr = egraph->edges[e]->nlegs[0]; egraph->edges[e]->nodes[0] = egraph->edges[e]->nodes[1]; egraph->edges[e]->nlegs[0] = egraph->edges[e]->nlegs[1]; egraph->edges[e]->nodes[1] = n; egraph->edges[e]->nlegs[1] = lr; egraph->nodes[n]->edges[lr] = - egraph->nodes[n]->edges[lr]; n = egraph->edges[e]->nodes[0]; lr = egraph->edges[e]->nlegs[0]; egraph->nodes[n]->edges[lr] = - egraph->nodes[n]->edges[lr]; } } #endif #ifdef CHECK for (ed = 0; ed < nEdges; ed++) { n = egraph->edges[ed]->nodes[0]; lr = egraph->edges[ed]->nlegs[0]; if (egraph->nodes[n]->edges[lr] != -ed-1) { grcc_fprintf(GRCC_Stderr, "+++ node[%d][%d]=%d != - (edge[%d][0] + 1) = %d\n", n, lr, egraph->nodes[n]->edges[lr], e, -ed-1); ok = False; } n = egraph->edges[ed]->nodes[1]; lr = egraph->edges[ed]->nlegs[1]; if (egraph->nodes[n]->edges[lr] != ed+1) { grcc_fprintf(GRCC_Stderr, "+++ node[%d][%d]=%d != + (edge[%d][0] + 1) = %d\n", n, lr, egraph->nodes[n]->edges[lr], e, ed+1); ok = False; } } if (!ok) { egraph->print(); erEnd("fillEGraph: illegal connection"); } #endif // analyse fermion line and determine Fermi statistical sign factor egraph->getFLines(); #ifdef CHECK checkAG("fillEGraph:0"); #endif return True; } //--------------------------------------------------------------- int *Assign::reordLeg(int n, int *reord, int *plist, int *used) { // Reorder legs of node 'n' in accordance with the definition // of the interaction in the model // // plist[record[j]] = model->interacts[ia]->plist[j] int lg, ia, lr, deg, pt, ed; int *ilegs; #ifdef CHECK Bool found; #endif // external node if (nodes[n]->cand->st == AS_AssExt) { reord[0] = 0; return 0; } // degree of the node deg = nodes[n]->deg; if (deg <= 1) { reord[0] = 0; return 0; } // list of particles at the legs of the node 'n' for (lg = 0; lg < deg; lg++) { ed = nodes[n]->aedges[lg]; pt = edges[ed]->cand->plist[0]; plist[lg] = legEdgeParticle(n, lg, pt); used[lg] = 0; } // list of legs in the interaction ia = nodes[n]->cand->ilist[0]; ilegs = model->interacts[ia]->plist; // reorder #ifdef CHECK found = False; #endif for (lr = 0; lr < deg; lr++) { for (lg = 0; lg < deg; lg++) { if (used[lg] == 0 && plist[lg] == ilegs[lr]) { reord[lr] = lg; used[lg] = 1; #ifdef CHECK found = True; #endif break; } } #ifdef CHECK if (!found) { grcc_fprintf(GRCC_Stdout, "*** reordLeg: illegal list of particles:" "interaction %d ", ia); prIntArray(deg, ilegs, "; "); grcc_fprintf(GRCC_Stdout, "vertex %d ", n); prIntArray(deg, plist, "\n"); prCand("reordLeg"); erEnd("reordLeg: illegal list of particles"); } #endif } return reord; } //============================================================== // Adjust the direction of a particle on an edge and on a leg of // node. //--------------------------------------------------------------- int Assign::getLegParticle(int n, int ln) { // Get particle code of (n, ln) when particle 'pt' runs // in the direction of the edge at (n, ln). // // Get particle code in the direction the edge at (n, ln) // when particle 'pt' is at leg (n, ln). // // These two cases are realized by the same function ANode *nd; int elg, ed, pt; nd = nodes[n]; elg = nd->aelegs[ln]; ed = nd->aedges[ln]; pt = edges[ed]->cand->plist[0]; // normalization of sign for neutral particle if (elg == 0) { return model->normalParticle(-pt); } else { return model->normalParticle(pt); } } //--------------------------------------------------------------- int Assign::legEdgeParticle(int n, int ln, int pt) { // Get particle code of (n, ln) when particle 'pt' runs // in the direction of the edge at (n, ln). // // Get particle code in the direction the edge at (n, nl) // when particle 'pt' is at leg (n, ln). // // These two cases are realized by the same function // normalization of sign for neutral particle if (nodes[n]->aelegs[ln] == 0) { return model->normalParticle(-pt); } else { return model->normalParticle(pt); } } //--------------------------------------------------------------- int Assign::legPart(int v, int lg, int nplist, int *plist, int *rlist, const int size) { // Convert list of candidate particles in 'plist' at (v, lg) ==> edge // or edge ==> (v, lg) int j, nrlist; nrlist = 0; for (j = 0; j < nplist; j++) { nrlist = intSetAdd(nrlist, rlist, legEdgeParticle(v, lg, plist[j]), size); } return nrlist; } //--------------------------------------------------------------- int Assign::candPart(int v, int ln, int *plist, const int size) { // update candidate particles incoming to (v, ln) int en; int ntplist; ECand *ec; en = nodes[v]->aedges[ln]; #ifdef CHECK if (edges[en]->cand->det) { grcc_fprintf(GRCC_Stdout, "*** candPart : particle of leg (%d, %d) " "is assigned to %d\n", v, ln, edges[en]->cand->plist[0]); checkCand("candPart"); mgraph->printAdjMat(mgraph->curcl); prCand("candPart"); erEnd("candPart : particle of leg is assigned"); } #endif ec = edges[en]->cand; ntplist = legPart(v, ln, ec->nplist, ec->plist, plist, size); return ntplist; } //============================================================== // tools for assignment //--------------------------------------------------------------- int Assign::selUnAssVertexSimp(int lastv) { // Select a vertex for assignment to its leg. // We take one with minimum number of candidates // // There may be better method. int v0, v; // select vertex one by one in the sequential order of node number v0 = Max(lastv+1, nExtern); for (v = v0; v < nNodes; v++) { if (nodes[v]->cand->st == AS_UnAssLegs) { return v; } } return -1; } //--------------------------------------------------------------- int Assign::selUnAssVertex(void) { // Select a vertex for assignment to its leg. // We take one with minimum number of candidates // // There may be better method. int v0, v, nl; // select vertex one by one in the sequential order of node number v0 = -1; nl = 0; for (v = 0; v < nNodes; v++) { if (nodes[v]->cand->st == AS_UnAssLegs) { if (nodes[v]->cand->nilist == 1) { return v; } else if (nodes[v]->cand->nilist > 1) { // select node with fewer candidates if (v0 < 0 || nodes[v]->cand->nilist < nl) { v0 = v; nl = nodes[v]->cand->nilist; } } } } return v0; } //--------------------------------------------------------------- int Assign::selUnAssLeg(int v, int lastlg) { // Select a leg of vertex 'v' for the assignment. // The lastly selected leg was 'lastlg'. int lg0, lg, e; #ifdef CHECK int n0, n1; #endif // lg0 = Max(lastlg, lastlg + 1); lg0 = lastlg + 1; for (lg = lg0; lg < nodes[v]->deg; lg++) { #ifdef CHECK if (lastlg >= 0) { n0 = nodes[v]->anodes[lastlg]; } else { n0 = -1; } n1 = nodes[v]->anodes[lg]; if (n0 > n1) { grcc_fprintf(GRCC_Stdout, "*** selUnAssLeg: n0=%d > n1=%d\n", n0, n1); grcc_fprintf(GRCC_Stdout, "*** illegal connection\n"); erEnd("selUnAssLeg: n0 > n1"); } #endif e = nodes[v]->aedges[lg]; if (!edges[e]->cand->det) { return lg; } } return -1; } //--------------------------------------------------------------- NCandSt Assign::assignIVertex(int v, int ia) { // Try to assign interaction 'ia' to 'v' int lplist[GRCC_MAXLEGS], iplist[GRCC_MAXLEGS]; int lg, e, pt, deg; if (nodes[v]->cand->st == AS_Assigned || nodes[v]->cand->st == AS_AssExt) { return AS_Assigned0; } deg = nodes[v]->deg; if (deg != model->interacts[ia]->nlegs) { return AS_Impossible; } // list of particles at the legs of the vertex for (lg = 0; lg < deg; lg++) { e = nodes[v]->aedges[lg]; if (edges[e]->cand->nplist != 1) { return AS_UnAssLegs; } else { pt = edges[e]->cand->plist[0]; lplist[lg] = legEdgeParticle(v, lg, pt); } iplist[lg] = model->interacts[ia]->plist[lg]; } sorti(deg, lplist); sorti(deg, iplist); // from interaction if (cmpArray(deg, lplist, deg, iplist) == 0) { // orders of coupling constants should be checked ??? astack->pushNode(v); nodes[v]->cand->st = AS_Assigned; nodes[v]->cand->nilist = 1; nodes[v]->cand->ilist[0] = ia; return AS_Assigned; } return AS_Impossible; } //--------------------------------------------------------------- Bool Assign::assignPLeg(int n, int ln, int pt) { // A particle 'pt' is assigned to leg 'ln' of node 'n' ANode *nd; int e, ept; Bool ok; #ifdef CHECK checkNode(n, "assignPLeg0"); checkCand("assignPLeg"); #endif // nodes and the edge nd = nodes[n]; e = nd->aedges[ln]; // already determined if (edges[e]->cand->det) { return True; } if (!isOrdPLeg(n, ln, pt)) { return False; } // particle on the edge ept = legEdgeParticle(n, ln, pt); #ifdef CHECK if (!isIn(edges[e]->cand->nplist, edges[e]->cand->plist, ept)) { grcc_fprintf(GRCC_Stdout, "*** assignPLeg: particle %d is not in the cand. of e=%d", ept, e); edges[e]->cand->prECand("\n"); prCand("assignPLeg"); erEnd("assignPLeg: particle is not in the cand."); } #endif // save the current configuration astack->pushEdge(e); // determine the particle on the edge edges[e]->cand->nplist = 1; edges[e]->cand->plist[0] = ept; ok = detEdge(e); return ok; } //--------------------------------------------------------------- Bool Assign::detEdge(int e) { Bool ok0, ok1; if (edges[e]->cand->nplist != 1) { return False; } edges[e]->cand->det = True; // update candidate list ok0 = updateCandNode(edges[e]->nodes[0]); if (ok0) { ok1 = updateCandNode(edges[e]->nodes[1]); } else { ok1 = False; } return (ok0 && ok1); } //--------------------------------------------------------------- Bool Assign::isOrdPLeg(int n, int ln, int pt) { int e0, el, ln0, ep0, pt0, nn, n0, n1, ln1, pt1, e1, ep1; if (nodes[n]->deg < 2) { return True; } nn = nodes[n]->anodes[ln]; if (n <= nn) { n0 = n; n1 = nn; ln0 = ln; pt0 = pt; } else { n0 = nn; n1 = n; e0 = nodes[n]->aedges[ln]; el = nodes[n]->aelegs[ln]; ln0 = edges[e0]->nlegs[1-el]; ep0 = legEdgeParticle(n, ln, pt); pt0 = legEdgeParticle(n0, ln0, ep0); } for (ln1 = 0; ln1 < nodes[n0]->deg; ln1++) { if (ln1 == ln0 || n1 != nodes[n0]->anodes[ln1]) { continue; } e1 = nodes[n0]->aedges[ln1]; if (!edges[e1]->cand->det) { continue; } ep1 = edges[e1]->cand->plist[0]; pt1 = legEdgeParticle(n0, ln1, ep1); if ((ln0 < ln1 && pt0 > pt1) || (ln0 > ln1 && pt0 < pt1)) { return False; } } return True; } //============================================================== // Operations of candidate //--------------------------------------------------------------- Bool Assign::candPartClassify(int v, int *npdass, int *pdass, int *npuass, int *puass, const int size) { // Construct the classified lists of particles possible to assign to // the legs of node v // // pdass = (duplicated set of particles where edges has a unique // candidate) // puass = (duplicated set of other candidate particles) int lg, e, npl, ass, jd, ju, j, pt, pts; jd = 0; ju = 0; for (lg = 0; lg < nodes[v]->deg; lg++) { e = nodes[v]->aedges[lg]; npl = edges[e]->cand->nplist; if (npl < 1) { return False; } ass = (npl == 1); for (j = 0; j < edges[e]->cand->nplist; j++) { pt = edges[e]->cand->plist[j]; pts = legEdgeParticle(v, lg, pt); if (ass) { jd = intSListAdd(jd, pdass, pts, size); } else { ju = intSListAdd(ju, puass, pts, size); } } } *npdass = jd; *npuass = ju; return True; } //--------------------------------------------------------------- Bool Assign::updateCandNode(int v) { // Update the configuration // - nodes[v]->cand->ilist // - edges[e]->cand->plist for the adjacent edge // - nodes[n]->cand->unass for the adjacent node 'n' of 'e' int npdass, pdass[GRCC_MAXPSLIST]; int npuass, puass[GRCC_MAXPSLIST]; int nsub0, sub0[GRCC_MAXPSLIST]; int niplist, iplist[GRCC_MAXPSLIST]; int nd0, d0[GRCC_MAXMPARTICLES2]; int nd1, d1[GRCC_MAXMPARTICLES2]; int ns0, s0[GRCC_MAXMPARTICLES2]; int neplist, eplist[GRCC_MAXMPARTICLES2]; int nitlist, itlist[GRCC_MAXMINTERACT]; int e, it, j, k, i, lg; // external node if (nodes[v]->cand->st == AS_AssExt) { #ifdef CHECK e = nodes[v]->aedges[0]; if (e < 0 || edges[e]->cand->nplist != 1) { grcc_fprintf(GRCC_Stdout, "*** illegal external node: v=%d e=%d :", v, e); prCand("updateCandNode"); erEnd("illegal external node"); } #endif return True; } // impossible configuration. if (nodes[v]->cand->nilist < 1) { return False; } // list of possible particles on the edges of the vertex. // pdass = (set of assigned particles) // puass = (list of particles of edges with two of more candidates) niplist = 0; nitlist = 0; if (!candPartClassify(v, &npdass, pdass, &npuass, puass, GRCC_MAXPSLIST)) { return False; } if (npdass < 1) { return False; } // from interaction : slist // Conditions : // 1. pdass \subset slist // 2. slist-pdass \subset puass // from interaction : slist // conditions : pdass \subset slist \subset (pdass + puass) // sub0 = slist - pdass, nitlist = 0; for (j = 0; j < nodes[v]->cand->nilist; j++) { it = nodes[v]->cand->ilist[j]; // conditions: // 1. pdass \subset slist <==> pdass-slist = \emptyset // 2. slist-pdass \subset puass <==> (slist-pdass)-puass = \emptyset if (isSubSList(npdass, pdass, model->interacts[it]->nslist, model->interacts[it]->slist) ) { nsub0 = subtrSet(model->interacts[it]->nslist, model->interacts[it]->slist, npdass, pdass, sub0, GRCC_MAXPSLIST); if (nsub0 < 1) { // slist == pdass : no additional candidate particle nitlist = intSetAdd(nitlist, itlist, it, GRCC_MAXMINTERACT); } else { if (isSubSList(nsub0, sub0, npuass, puass)) { nitlist = intSetAdd(nitlist, itlist, it, GRCC_MAXMINTERACT); for (k = 0; k < nsub0; k++) { niplist = intSetAdd(niplist,iplist,sub0[k],GRCC_MAXPSLIST); } } } } } if (nitlist < 1) { return False; } if (nitlist != nodes[v]->cand->nilist) { astack->pushNode(v); nodes[v]->cand->nilist = nitlist; for (i = 0; i < nitlist; i++) { nodes[v]->cand->ilist[i] = itlist[i]; } #ifdef CHECK } else if (nitlist > nodes[v]->cand->nilist) { erEnd("larger ncand"); #endif } // edge for (lg = 0; lg < nodes[v]->deg; lg++) { e = nodes[v]->aedges[lg]; if (edges[e]->cand->nplist > 1) { // elist = {candidate particles in the direction of the edge} // s0 = plist \cap elist neplist = legPart(v, lg, niplist, iplist, eplist, GRCC_MAXMPARTICLES2); listDiff(edges[e]->cand->nplist, edges[e]->cand->plist, neplist, eplist, &nd0, d0, &ns0, s0, &nd1, d1); if (ns0 < 1) { return False; } if (ns0 < edges[e]->cand->nplist) { astack->pushEdge(e); edges[e]->cand->nplist = ns0; for (i = 0; i < ns0; i++) { edges[e]->cand->plist[i] = s0[i]; } } } } for (lg = 0; lg < nodes[v]->deg; lg++) { e = nodes[v]->aedges[lg]; if (edges[e]->cand->nplist == 1 && !edges[e]->cand->det) { if(!detEdge(e)) { return False; } } } return True; } //============================================================== // Check order of coupling constants, duplication and isomorphism //-------------------------------------------------------------- Bool Assign::checkOrderCpl(void) { // Check order of coupling constants int ord[GRCC_MAXNCPLG]; int lcn, n, ia, j, cl; // list of coupling constants lcn = model->ncouple; if (lcn == 1) { return True; } // sum up for each coupling constants for (j = 0; j < GRCC_MAXNCPLG; j++) { ord[j] = 0; } for (n = 0; n < nNodes; n++) { cl = pnclass->nd2cl[n]; if (!isATExternal(pnclass->type[cl])) { ia = nodes[n]->cand->ilist[0]; for (j = 0; j < lcn; j++) { ord[j] += model->interacts[ia]->clist[j]; } } } // comparison for (j = 0; j < lcn; j++) { if (sproc->clist[j] != ord[j]) { return False; } } return True; } //-------------------------------------------------------------- Bool Assign::isOrdLegs(void) { // Whether graph is duplicated because of the violation // of ordering in the case of multiple connections // v0 <-- v --> v1 int v, l0, v0, l1, v1, e0, e1, q0, q1, p0, p1, cl; for (v = 0; v < nNodes; v++) { cl = pnclass->nd2cl[v]; if (!isATExternal(pnclass->type[cl])) { for (l0 = 0; l0 < nodes[v]->deg; l0++) { v0 = nodes[v]->anodes[l0]; for (l1 = l0+1; l1 < nodes[v]->deg; l1++) { v1 = nodes[v]->anodes[l1]; if (v0 == v1 && v <= v0) { // multiple connections (v, l0) and (v, l1) e0 = nodes[v]->aedges[l0]; e1 = nodes[v]->aedges[l1]; q0 = edges[e0]->cand->plist[0]; q1 = edges[e1]->cand->plist[0]; p0 = legEdgeParticle(v, l0, q0); p1 = legEdgeParticle(v, l1, q1); if (p0 > p1) { // violation of ordering return False; } } } } } } return True; } //-------------------------------------------------------------- Bool Assign::isIsomorphic(MNodeClass *cl, BigInt *nsym, BigInt *esym, BigInt *nsym1) { // Check whether the current graph is the representive of // a isomorphic class. // Returns (nsym, esym) // nsym = symmetry factor by the permutation of nodes. // esym = symmetry factor by the permutation of edge. // If this graph is not a representative, then returns (0,0). int j, cmp, n, cln; BigInt ngelem; int *p; Bool invext; ngelem = mgraph->group->nElem(); #ifdef CHECK if (mgraph->nsym > 1 && ngelem <= 1) { grcc_fprintf(GRCC_Stdout, "*** isIsomorphic: illegal group: " "ngelem=%ld, mgraph->sym=(%ld, %ld)\n", ngelem, mgraph->nsym, mgraph->esym); erEnd("Assign::isIsomorphic: illegal group"); } #endif if (ngelem == 0) { *nsym = 1; *nsym1 = 1; } else { *nsym = 0; *nsym1 = 0; for (j = 0; j < ngelem; j++) { // check the graph is the representative and count 'nsym'. //p = mgraph->group->nextElem(); p = mgraph->group->elem[j]; cmp = cmpPermGraph(p, cl); if (cmp < 0) { // duplicated graph return False; } else if(cmp == 0) { // not duplicated (*nsym)++; if (opt->values[GRCC_OPT_SymmInitial] || opt->values[GRCC_OPT_SymmFinal]) { invext = True; for (n = 0; n < nNodes; n++) { cln = pnclass->nd2cl[n]; if (!isATExternal(pnclass->type[cln])) { continue; } if (p[n] != n) { invext = False; } } if (invext) { (*nsym1)++; } } else { (*nsym1)++; } } } } if (*nsym1 == 0) { *nsym1 = *nsym; } // calculate permutations of edges *esym = edgeSym(); if (*esym < 1) { return False; } return True; } //-------------------------------------------------------------- int Assign::cmpPermGraph(int *p, MNodeClass *cl) { // compare the graph with one permutated by 'p'. int n, cmp, n1, n2, p1, p2, j; ANode *nd1, *np1; // ANode *nd2, *np2; int njn, jn[GRCC_MAXLEGS]; int njp, jp[GRCC_MAXLEGS]; #ifdef CHECK if (p == NULL) { erEnd("Assign::cmpPermGraph: p==NULL"); } #endif for (n = 0; n < nNodes; n++) { if (!isATExternal(pnclass->type[pnclass->nd2cl[n]])) { cmp = cmpNodes(n, p[n], cl); if (cmp != 0) { return cmp; } } } njn = 0; njp = 0; for (n1 = 0; n1 < nNodes; n1++) { p1 = p[n1]; nd1 = nodes[n1]; np1 = nodes[p1]; for (n2 = n1; n2 < nNodes; n2++) { if (mgraph->adjMat[n1][n2] == 0) { continue; } p2 = p[n2]; if (p1 == n1 && p2 == n2) { continue; } cmp = mgraph->adjMat[n1][n2] - mgraph->adjMat[p1][p2]; if (cmp != 0) { return cmp; } njn = 0; njp = 0; for (j = 0; j < nd1->deg; j++) { if (nd1->anodes[j] == n2) { jn[njn++] = getLegParticle(n1, j); } } for (j = 0; j < np1->deg; j++) { if (np1->anodes[j] == p2) { jp[njp++] = getLegParticle(p1, j); } } cmp = njn - njp; if (cmp != 0) { return cmp; } // ignore ordering for multiple connections if (mgraph->adjMat[n1][n2] >= 2) { sorti(njn, jn); sorti(njn, jp); } for (j = 0; j < njn; j++) { cmp = jn[j] - jp[j]; if (cmp != 0) { return cmp; } } } } return 0; } //-------------------------------------------------------------- int Assign::cmpNodes(int nd0, int nd1, MNodeClass *cn) { // Comparison of two nodes 'nd0' and 'nd1' // Ordering is lexicographical (class, connection configuration) // int cmp; // Wether two nodes are in a same class or not. cmp = cn->ndcl[nd0] - cn->ndcl[nd1]; if (cmp != 0) { return cmp; } // interaction cmp = nodes[nd0]->cand->ilist[0] - nodes[nd1]->cand->ilist[0]; return cmp; } //-------------------------------------------------------------- BigInt Assign::edgeSym(void) { // calculate permutations of edges int lg[GRCC_MAXLEGS], lt[GRCC_MAXLEGS], lc; ANode *nd1; int n1, n2, j, k, mult; BigInt esym; esym = 1; for (n1 = 0; n1 < nNodes; n1++) { nd1 = nodes[n1]; for (n2 = n1; n2 < nNodes; n2++) { if (mgraph->adjMat[n1][n2] > 1) { lc = 0; for (j = 0; j < nd1->deg; j++) { if (nd1->anodes[j] == n2) { lg[lc] = 1; lt[lc] = getLegParticle(n1, j); lc++; } } for (j = 0; j < lc-1; j++) { if (lg[j] > 0) { for (k = lc-1; k > j; k--) { if (lt[j] == lt[k]) { lg[j] += lg[k]; lg[k] = 0; } } } } // calculate symmetry factor for (j = 0; j < lc; j++) { if (lg[j] < 1) { continue; } mult = lg[j]; if (mult > 1) { if (n1 == n2) { // self-loop esym *= ipow(2,mult/2)*factorial(mult/2); } else { esym *= factorial(mult); } } } } } } return esym; } #ifdef CHECK //============================================================== // check //-------------------------------------------------------------- Bool Assign::checkCand(const char *msg) { // Check the consistency of Candidate data Bool ok; ANode *na; NCand *nc; ECand *ec; int n, lg, e; // check 'nodes->cand' ok = True; for (n = 0; n < nNodes; n++) { na = nodes[n]; nc = na->cand; // check unassigned vertex if (nc->st == AS_UnAssLegs) { // check assigned vertex } else if (nc->st == AS_Assigned) { if (nc->nilist < 1) { grcc_fprintf(GRCC_Stdout, "*** checkCand:7:%s:status (%d) of node %d says" " interaction is assigned to %d but ilist=", msg, nc->st, n, nc->st); prIntArray(nc->nilist, nc->ilist, "\n"); ok = False; } for (lg = 0; lg < nc->deg; lg++) { e = na->aedges[lg]; ec = edges[e]->cand; if (ec->nplist != 1) { grcc_fprintf(GRCC_Stdout, "*** checkCand:8:%s:status (%d) of node %d says" " interaction is assigned " " but unassigned edge %d is found\n", msg, nc->st, n, e); ok = False; } } // external particle } else if (nc->st == AS_AssExt) { // pt = nc->ilist[0]; // *** pte = legEdgeParticle(n, 0, - pt); } else { grcc_fprintf(GRCC_Stdout, "*** checkCand:10:%s:illegal status of node %d : %d", msg, n, nc->st); ok = False; } } // check edges for (e = 0; e < nEdges; e++) { ec = edges[e]->cand; if (ec != NULL && ec->nplist < 1) { grcc_fprintf(GRCC_Stdout, "*** checkCand:12:%s:illegal edge %d\n", msg, e); ok = False; } } if (!ok) { grcc_fprintf(GRCC_Stdout, "*** checkCand:15:%s:illegal configuration\n", msg); prCand("checkCand"); grcc_fprintf(GRCC_Stdout, "*** checkCand:16:illegal configuration\n"); erEnd("checkCand:16:illegal configuration"); } return ok; } //-------------------------------------------------------------- void Assign::checkNode(int n, const char *msg) { int j, it; for (j = 0; j < nodes[n]->cand->nilist; j++) { it = nodes[n]->cand->ilist[j]; if (Abs(it) >= GRCC_MAXMINTERACT) { grcc_fprintf(GRCC_Stdout, "*** %s: n=%d, j=%d, it=%d\n", msg, n, j, it); nodes[n]->cand->prNCand(msg); grcc_fprintf(GRCC_Stdout, "\n"); erEnd("checkNode:illegal it"); } } } #endif // CHECK //************************************************************** // astack.cc //============================================================== // Assign particles to the edges and interactions to nodes. // Completed graph data is saved in the form of EGraph. //============================================================= // stack operations //-------------------------------------------------------------- void NStack::print(const char *msg) { grcc_fprintf(GRCC_Stdout, " node=%d, deg=%d, st=%d, ilist=", noden, deg, st); prilist(nilist, ilist, msg); } //-------------------------------------------------------------- void EStack::print(const char *msg) { grcc_fprintf(GRCC_Stdout, " edge=%d, det=%d, plist=", edgen, det); prilist(nplist, plist, msg); } //-------------------------------------------------------------- AStack::AStack(int nsize, int esize) { int j; agraph = NULL; nSize = nsize; eSize = esize; if (nSize > 0) { nStack = new NStack*[nSize]; } else { nStack = NULL; } if (eSize > 0) { eStack = new EStack*[eSize]; } else { eStack = NULL; } nStackP = 0; eStackP = 0; for (j = 0; j < nSize; j++) { nStack[j] = new NStack(); } for (j = 0; j < eSize; j++) { eStack[j] = new EStack(); } } //-------------------------------------------------------------- AStack::~AStack(void) { int j; if (eStack != NULL) { for (j = eSize-1; j >= 0; j--) { if (eStack[j] != NULL) { delete eStack[j]; eStack[j] = NULL; } } delete[] eStack; eStack = NULL; } if (nStack != NULL) { for (j = nSize-1; j >= 0; j--) { if (nStack[j] != NULL) { delete nStack[j]; nStack[j] = NULL; } } delete[] nStack; nStack = NULL; } } //-------------------------------------------------------------- void AStack::setAGraph(Assign *ag) { agraph = ag; } //-------------------------------------------------------------- void AStack::pushNode(int n) { NCand *nc; NStack *ns; int j; #ifdef CHECK if (agraph == NULL) { erEnd("pushNode: agraph is not defined"); } #endif if (nStackP >= GRCC_MAXNSTACK) { erEnd("N-stack overflow (GRCC_MAXNSTACK)"); } nc = agraph->nodes[n]->cand; if (nc->nilist >= GRCC_MAXMINTERACT) { erEnd("N-stack: too long list (GRCC_MAXMINTERACT)"); } ns = nStack[nStackP]; ns->noden = n; ns->deg = nc->deg; ns->st = nc->st; ns->nilist = nc->nilist; for (j = 0; j < nc->nilist; j++) { ns->ilist[j] = nc->ilist[j]; } nStackP++; } //-------------------------------------------------------------- void AStack::pushEdge(int e) { ECand *ec; EStack *es; int j; #ifdef CHECK if (agraph == NULL) { erEnd("pushEdge: agraph is not defined"); } #endif if (eStackP >= GRCC_MAXESTACK) { erEnd("E-stack overflow (GRCC_MAXESTACK)"); } ec = agraph->edges[e]->cand; if (ec->nplist >= GRCC_MAXMPARTICLES2) { erEnd("E-stack: Too long list (GRCC_MAXMPARTICLES)"); } es = eStack[eStackP]; es->edgen = e; es->det = ec->det; es->nplist = ec->nplist; for (j = 0; j < ec->nplist; j++) { es->plist[j] = ec->plist[j]; } eStackP++; } //-------------------------------------------------------------- void AStack::checkPoint(CheckPt sav) { sav[0] = nStackP; sav[1] = eStackP; } //-------------------------------------------------------------- void AStack::restoreNode(int spr) { NStack *stc; int sp, n, j; for (sp = nStackP-1; sp >= spr; sp--) { stc = nStack[sp]; n = stc->noden; agraph->nodes[n]->cand->deg = stc->deg; agraph->nodes[n]->cand->st = stc->st; agraph->nodes[n]->cand->nilist = stc->nilist; for (j = 0; j < stc->nilist; j++) { agraph->nodes[stc->noden]->cand->ilist[j] = stc->ilist[j]; } } nStackP = spr; } //-------------------------------------------------------------- void AStack::restoreEdge(int spr) { EStack *stc; int sp, e, j; for (sp = eStackP-1; sp >= spr; sp--) { stc = eStack[sp]; e = eStack[sp]->edgen; agraph->edges[e]->cand->det = stc->det; agraph->edges[e]->cand->nplist = stc->nplist; for (j = 0; j < stc->nplist; j++) { agraph->edges[e]->cand->plist[j] = stc->plist[j]; } } eStackP = spr; } //-------------------------------------------------------------- void AStack::restore(CheckPt sav) { restoreNode(sav[0]); restoreEdge(sav[1]); } #ifdef CHECK //-------------------------------------------------------------- void AStack::restoreMsg(CheckPt sav, const char *msg) { if (agraph == NULL) { erEnd("restore: agraph is not defined"); } restore(sav); if (!agraph->checkCand("restore")) { grcc_fprintf(GRCC_Stdout, "restore is called from %s\n", msg); } } #endif //-------------------------------------------------------------- void AStack::prStack(void) { int j; grcc_fprintf(GRCC_Stdout, "+++ prStack : (%d, %d)", nStackP, eStackP); for (j = 0; j < nStackP; j++) { grcc_fprintf(GRCC_Stdout, "N:%4d ", j); nStack[j]->print("\n"); } for (j = 0; j < eStackP; j++) { grcc_fprintf(GRCC_Stdout, "E:%4d ", j); eStack[j]->print("\n"); } } //************************************************************** // class Fraction //============================================================== Fraction::Fraction(BigInt n, BigInt d) { BigInt g; g = gcd(n, d); num = n/g; den = d/g; ratio = Real(n)/Real(d); } //-------------------------------------------------------------- void Fraction::print(const char *msg) { double err = Abs(Real(num)/Real(den) - ratio); if (err > GRCC_FRACERROR) { grcc_fprintf(GRCC_Stdout, "%ld/%ld(%g)(overflow)%s", num, den, ratio, msg); } else { grcc_fprintf(GRCC_Stdout, "%ld/%ld(%g)%s", num, den, ratio, msg); } } //-------------------------------------------------------------- void Fraction::setValue(BigInt n, BigInt d) { num = n; den = d; ratio = Real(n)/Real(d); } //-------------------------------------------------------------- void Fraction::setValue(Fraction &f) { num = f.num; den = f.den; ratio = f.ratio; } //-------------------------------------------------------------- BigInt Fraction::gcd(BigInt n0, BigInt n1) { BigInt nn[2], r; int nc; nn[0] = Abs(n0); nn[1] = Abs(n1); nc = 0; while (1) { r = nn[nc] % nn[1-nc]; if (r == 0) { return nn[1-nc]; } nn[nc] = r; nc = 1 - nc; } } //-------------------------------------------------------------- void Fraction::normal(void) { BigInt g; if (den == 0) { erEnd("Fraction: den==0"); } g = gcd(num, den); num /= g; den /= g; if (den < 0) { num = - num; den = - den; } } //-------------------------------------------------------------- void Fraction::add(BigInt n, BigInt d) { BigInt g, d1; if (d < 0) { n = -n; d = -d; } if (den < 0) { num = - num; den = - den; } g = gcd(den, d); d1 = d/g; num = num * d1 + n * (den/g); den = d1*den; g = gcd(num, den); num /= g; den /= g; ratio += Real(n)/Real(d); } //-------------------------------------------------------------- void Fraction::add(Fraction f) { double r = ratio + f.ratio; add(f.num, f.den); ratio = r; } //-------------------------------------------------------------- void Fraction::sub(Fraction f) { double r = ratio - f.ratio; add(-f.num, f.den); ratio = r; } //-------------------------------------------------------------- Bool Fraction::isEq(Fraction f) { return (num == f.num && den == f.den); } //************************************************************** // common.cc //============================================================== // Wrapper function for printing messages. This allows the use // of FORM MesPrint when compiled as part of FORM, and the // usual fprintf to GRCC_Stdout or GRCC_Stderr otherwise. static void grcc_fprintf(FILE* out, const char* fmt, ...) { va_list args; va_start(args, fmt); #ifndef NOFORM DUMMYUSE(out); // the second call of vsnprintf requires a copy of args va_list args_copy; va_copy(args_copy, args); // determine the required buffer size for the formatted string: const int len = vsnprintf(NULL, 0, fmt, args); char *buffer = new char[len+1]; vsnprintf(buffer, len+1, fmt, args_copy); MLOCK(ErrorMessageLock); MesPrint("%s%", buffer); MUNLOCK(ErrorMessageLock); delete[] buffer; va_end(args_copy); #else vfprintf(out, fmt, args); #endif va_end(args); return; } static void erEnd(const char *msg) { if (erExit != NULL) { (*erExit)(msg, erExitArg); } grcc_fprintf(GRCC_Stderr, "*** Error : %s\n\n", msg); GRCC_ABORT(); } #define MAXPART 100 //------------------------------------------------------------ static Bool nextPart(int nelem, int nclist, int *clist, int *nl, int *r) { // Generate configuration nl[] sequentially such that // sum_j^{nclist} nl[j]*clist[j] = nelem // 0 <= nl[j] (j = 0, ..., nclis-1) // For control // for the first call : *r < 0 // otherwise : *r >= 0, nl is the last configuration // Returns // True : succeeded // False : no more configuration int rem, pn, j, c; if (*r < 0) { *r = 0; rem = nelem; for (j = 0; j < nclist; j++) { nl[j] = rem/clist[j]; rem -= nl[j]*clist[j]; } if (rem == 0) { return True; } } else { rem = 0; } for (c = 0; c < MAXPART; c++) { rem += nl[nclist-1]*clist[nclist-1]; for (pn = nclist-2; pn >= 0 && nl[pn] == 0; pn--) { ; } if (pn < 0) { return False; } rem += clist[pn]; nl[pn]--; for (j = pn+1; j < nclist; j++) { nl[j] = rem/clist[j]; rem -= nl[j]*clist[j]; } if (rem == 0) { return True; } } erEnd("*** nextPart : illegal control : too many repetition"); return False; } //------------------------------------------------------------ static int *intdup(int n, int *a) { int *r, j; r = new int[n]; for (j = 0; j < n; j++) { r[j] = a[j]; } return r; } //------------------------------------------------------------ static int *delintdup(int *a) { if (a != NULL) { delete[] a; } return NULL; } //------------------------------------------------------------ static void prilist(int n, const int *a, const char *msg) { grcc_fprintf(GRCC_Stdout, "["); for (int j = 0; j < n; j++) { if (j!=0) grcc_fprintf(GRCC_Stdout, ", "); grcc_fprintf(GRCC_Stdout, "%d", a[j]); } grcc_fprintf(GRCC_Stdout, "]%s", msg); } //------------------------------------------------------------ static int nextPerm(int nelem, int nclass, int *cl, int *r, int *q, int *p, int count) { // Sequential generation of all permutations. int j, k, n, e, t; Bool b; for (j = 0; j < nelem; j++) { p[j] = j; } if (count < 1) { for (j = 0; j < nelem; j++) { q[j] = 0; r[j] = 0; } j = 0; for (k = 0; k < nclass; k++) { n = cl[k]; for (e = 0; e < n; e++) { r[j] = n - e - 1; j++; } } #ifdef CHECK if (j != nelem) { erEnd("inconsistent # elements"); } #endif return 1; } b = False; for (j = nelem-1; j >= 0; j--) { if (q[j] < r[j]) { for (k = j+1; k < nelem; k++) { q[k] = 0; } q[j]++; b = True; break; } } if (!b) { return (-count); } for (j = 0; j < nelem; j++) { k = j + q[j]; t = p[j]; p[j] = p[k]; p[k] = t; } return count + 1; } //------------------------------------------------------------ static BigInt factorial(int n) { // returns 1 for n < 1 int r, j; r = 1; for (j = 2; j <= n; j++) { r *= j; } return r; } //------------------------------------------------------------ static BigInt ipow(int n, int p) { int r, j; r = 1; for (j = 0; j < p; j++) { r *= n; } return r; } //------------------------------------------------------------ static int *newArray(int size, int val) { // memory allocation of an array int *a, j; a = new int[size]; for (j = 0; j < size; j++) { a[j] = val; } return a; } //------------------------------------------------------------ static int *deleteArray(int *a) { // memory allocation of an array delete[] a; return NULL; } //------------------------------------------------------------ static int **newMat(int n0, int n1, int val) { int **m, j, k; m = new int*[n0]; for (j = 0; j < n0; j++) { m[j] = new int[n1]; for (k = 0; k < n1; k++) { m[j][k] = val; } } return m; } //------------------------------------------------------------ static int **deleteMat(int **m, int n0) { int j; for (j = n0-1; j >= 0; j--) { delete[] m[j]; } delete[] m; return NULL; } //------------------------------------------------------------ static void bsort(int n, int *ord, int *a) { int i, j, t; for (j = n-1; j > 0; j--) { for (i = 0; i < j; i++) { if(a[ord[i+1]] < a[ord[i]]) { t = ord[i]; ord[i] = ord[i+1]; ord[i+1] = t; } } } } //-------------------------------------------------------------- static void prMomStr(int mom, const char *ms, int mn) { if (mom == 0) { return; } else if (mom == 1) { grcc_fprintf(GRCC_Stdout, " + %s%d", ms, mn); } else if (mom > 0) { grcc_fprintf(GRCC_Stdout, " + %d*%s%d", mom, ms, mn); } else if (mom == -1) { grcc_fprintf(GRCC_Stdout, " - %s%d", ms, mn); } else { grcc_fprintf(GRCC_Stdout, " - %d*%s%d", -mom, ms, mn); } } //-------------------------------------------------------------- static void prIntArray(int n, int *p, const char *msg) { int j; grcc_fprintf(GRCC_Stdout, "["); for (j = 0; j < n; j++) { if (j!=0) grcc_fprintf(GRCC_Stdout, ", "); grcc_fprintf(GRCC_Stdout, "%2d", p[j]); } grcc_fprintf(GRCC_Stdout, "]%s", msg); } //-------------------------------------------------------------- static void prIntArrayErr(int n, int *p, const char *msg) { int j; grcc_fprintf(GRCC_Stderr, "["); for (j = 0; j < n; j++) { if (j!=0) grcc_fprintf(GRCC_Stderr, ", "); grcc_fprintf(GRCC_Stderr, "%2d", p[j]); } grcc_fprintf(GRCC_Stderr, "]%s", msg); } //-------------------------------------------------------------- static void sortrec(int l, int r, int *a) { // quick sort : taken from N. Wirth int i,j, x, w; i = l; j = r; x = a[(l+r)/2]; do { while(a[i] < x) i++; while(x < a[j]) j--; if (i <= j) { w = a[i]; a[i] = a[j]; a[j] = w; i++; j--; } } while (i < j); if (l < j) sortrec(l, j, a); if (i < r) sortrec(i, r, a); } //-------------------------------------------------------------- static void sorti(int size, int *a) { sortrec(0, size-1, a); } //------------------------------------------------------------ static int sortb(int n, int *a) { int i, j, t, nswap; nswap = 0; for (j = n-1; j > 0; j--) { for (i = 0; i < j; i++) { if(a[i+1] < a[i]) { t = a[i]; a[i] = a[i+1]; a[i+1] = t; nswap++; } } } // the sign of the permutation is (-1)^{nswap} return nswap; } #ifdef CHECK //-------------------------------------------------------------- static Bool isIn(int n, int *a, int v) { int j; for (j = 0; j < n; j++) { if (a[j] == v) { return True; } } return False; } #endif //-------------------------------------------------------------- static int intSetAdd(int n, int *a, int v, const int size) { // Add 'v' into 'a'. // 'n' is the current # of element. // 'a' is assumed sorted without duplicated elements. // Size of 'a' should be large enough. int j, k; if (n >= size) { grcc_fprintf(GRCC_Stderr, "*** intSetAdd : array out of range (>%d)\n", size); erEnd("intSetAdd : array out of range (GRCC_MAXPSLIST)"); } for (j = 0; j < n; j++) { if (a[j] > v) { break; } else if (a[j] == v) { return n; } } // 'j' can be equal to 'n' for (k = n-1; k >= j; k--) { a[k+1] = a[k]; } a[j] = v; return n+1; } //-------------------------------------------------------------- static int intSListAdd(int n, int *a, int v, const int size) { // Add 'v' into 'a'. // 'n' is the current # of element. // 'a' is assumed sorted without duplicated elements. // Size of 'a' should be large enough. int j, k; if (n >= size) { grcc_fprintf(GRCC_Stderr, "*** intSListAdd : array out of range (>%d)\n", size); erEnd("intSListAdd : array out of range"); } for (j = 0; j < n; j++) { if (a[j] >= v) { break; } } // 'j' can be equal to 'n' for (k = n-1; k >= j; k--) { a[k+1] = a[k]; } a[j] = v; return n+1; } //-------------------------------------------------------------- static int cmpArray(int na, int *a, int nb, int *b) { int j, cmp; cmp = na - nb; if (cmp != 0) { return cmp; } for (j = 0; j < na; j++) { cmp = a[j] - b[j]; if (cmp != 0) { return cmp; } } return 0; } //-------------------------------------------------------------- static Bool leqArray(int n, int *a, int *b) { int j; for (j = 0; j < n; j++) { if (a[j] > b[j]) { return False; } } return True; } //-------------------------------------------------------------- // convert list to sorted list static int toSList(int n, int *a) { sorti(n, a); return n; } //-------------------------------------------------------------- // as set operation assuming a and b are sorted with duplication // p := a \ b; q := a \cap b; r := b \ a; // p, q, r are sorted without duplication static void listDiff(int na, int *a, int nb, int *b, int *np, int *p, int *nq, int *q, int *nr, int *r) { int ja, jb; *np = *nq = *nr = 0; ja = jb = 0; while (ja < na && jb < nb) { while (ja < na && a[ja] < b[jb]) { p[(*np)++] = a[ja++]; } while (jb < nb && b[jb] < a[ja]) { r[(*nr)++] = b[jb++]; } if (ja < na && jb < nb && a[ja] == b[jb]) { q[(*nq)++] = a[ja++]; jb++; } } for (; ja < na; ja++) { p[(*np)++] = a[ja]; } for (; jb < nb; jb++) { r[(*nr)++] = b[jb]; } } //-------------------------------------------------------------- static int isSubSList(int na, int *a, int nb, int *b) { int ja, jb; ja = jb = 0; while (ja < na && jb < nb) { for ( ; jb < nb && b[jb] < a[ja]; jb++) { ; } if (jb >= nb || b[jb] > a[ja]) { return False; } for ( ; jb < nb && ja < na && b[jb] == a[ja]; jb++, ja++) { ; } } return (ja >= na); } //-------------------------------------------------------------- static int subtrSet(int na, int *a, int nb, int *b, int *c, int size) { // set subtraction 'c' := 'a' - 'b'. // 'a' and 'b' are sorted lists (not always unique) // 'c' is the set (sorted and unique elements) int ja, jb, jc; jc = 0; ja = jb = 0; while (ja < na && jb < nb) { while (ja < na && a[ja] < b[jb]) { if (jc == 0 || c[jc-1] != a[ja]) { if (jc >= size) { erEnd("subsutSet: too small size of array (GRCC_MAXPSLIST)"); } c[jc++] = a[ja]; } ja++; } while (jb < nb && b[jb] < a[ja]) { ; } if (ja < na && jb < nb && a[ja] == b[jb]) { ja++; jb++; } } for (; ja < na; ja++) { if (jc == 0 || c[jc-1] != a[ja]) { c[jc++] = a[ja]; } } return jc; } // } ) ] form-5.0.1/sources/setfile.c0000644000175100017510000012424615217035721011441 /** @file setfile.c * * The routines that deal with the setup parameters. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : Routines that deal with settings and the setup file */ #include "form3.h" char curdirp[] = "."; char cursortdirp[] = "."; char commentchar[] = "*"; char dotchar[] = "_"; char highfirst[] = "highfirst"; char lowfirst[] = "lowfirst"; char procedureextension[] = "prc"; #define NUMERICALVALUE 0 #define STRINGVALUE 1 #define PATHVALUE 2 #define ONOFFVALUE 3 #define DEFINEVALUE 4 SETUPPARAMETERS setupparameters[] = { {(UBYTE *)"bracketindexsize", NUMERICALVALUE, 0, (LONG)MAXBRACKETBUFFERSIZE} ,{(UBYTE *)"commentchar", STRINGVALUE, 0, (LONG)commentchar} ,{(UBYTE *)"compresssize", NUMERICALVALUE, 0, (LONG)COMPRESSBUFFER} ,{(UBYTE *)"constindex", NUMERICALVALUE, 0, (LONG)NUMFIXED} ,{(UBYTE *)"continuationlines", NUMERICALVALUE, 0, (LONG)FORTRANCONTINUATIONLINES} #ifdef WITHFLOAT ,{(UBYTE *)"defaultprecision", NUMERICALVALUE, 0, (LONG)DEFAULTPRECISION} #endif ,{(UBYTE *)"define", DEFINEVALUE, 0, (LONG)0} ,{(UBYTE *)"dotchar", STRINGVALUE, 0, (LONG)dotchar} ,{(UBYTE *)"factorizationcache", NUMERICALVALUE, 0, (LONG)FBUFFERSIZE} ,{(UBYTE *)"filepatches", NUMERICALVALUE, 0, (LONG)MAXFPATCHES} ,{(UBYTE *)"functionlevels", NUMERICALVALUE, 0, (LONG)MAXFLEVELS} ,{(UBYTE *)"hidesize", NUMERICALVALUE, 0, (LONG)0} ,{(UBYTE *)"incdir", PATHVALUE, 0, (LONG)curdirp} ,{(UBYTE *)"indentspace", NUMERICALVALUE, 0, (LONG)INDENTSPACE} ,{(UBYTE *)"insidefirst", ONOFFVALUE, 0, (LONG)1} ,{(UBYTE *)"jumpratio", NUMERICALVALUE, 0, (LONG)JUMPRATIO} ,{(UBYTE *)"largepatches", NUMERICALVALUE, 0, (LONG)MAXPATCHES} ,{(UBYTE *)"largesize", NUMERICALVALUE, 0, (LONG)LARGEBUFFER} ,{(UBYTE *)"maxnumbersize", NUMERICALVALUE, 0, (LONG)0} /* ,{(UBYTE *)"maxnumbersize", NUMERICALVALUE, 0, (LONG)MAXNUMBERSIZE} */ ,{(UBYTE *)"maxtermsize", NUMERICALVALUE, 0, (LONG)MAXTER} #ifdef WITHFLOAT ,{(UBYTE *)"maxweight", NUMERICALVALUE, 0, (LONG)MAXWEIGHT} #endif ,{(UBYTE *)"maxwildcards", NUMERICALVALUE, 0, (LONG)MAXWILDC} ,{(UBYTE *)"nospacesinnumbers", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"numstorecaches", NUMERICALVALUE, 0, (LONG)NUMSTORECACHES} ,{(UBYTE *)"nwritefinalstatistics", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"nwriteprocessstatistics", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"nwritestatistics", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"nwritethreadstatistics", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"oldfactarg", ONOFFVALUE, 0, (LONG)NEWFACTARG} ,{(UBYTE *)"oldgcd", ONOFFVALUE, 0, (LONG)1} ,{(UBYTE *)"oldorder", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"oldparallelstatistics", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"oldprfsign", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"parentheses", NUMERICALVALUE, 0, (LONG)MAXPARLEVEL} ,{(UBYTE *)"path", PATHVALUE, 0, (LONG)curdirp} ,{(UBYTE *)"procedureextension", STRINGVALUE, 0, (LONG)procedureextension} ,{(UBYTE *)"processbucketsize", NUMERICALVALUE, 0, (LONG)DEFAULTPROCESSBUCKETSIZE} ,{(UBYTE *)"resettimeonclear", ONOFFVALUE, 0, (LONG)1} ,{(UBYTE *)"scratchsize", NUMERICALVALUE, 0, (LONG)SCRATCHSIZE} ,{(UBYTE *)"shmwinsize", NUMERICALVALUE, 0, (LONG)SHMWINSIZE} ,{(UBYTE *)"sizestorecache", NUMERICALVALUE, 0, (LONG)SIZESTORECACHE} ,{(UBYTE *)"smallextension", NUMERICALVALUE, 0, (LONG)SMALLOVERFLOW} ,{(UBYTE *)"smallsize", NUMERICALVALUE, 0, (LONG)SMALLBUFFER} ,{(UBYTE *)"sortiosize", NUMERICALVALUE, 0, (LONG)SORTIOSIZE} ,{(UBYTE *)"sorttype", STRINGVALUE, 0, (LONG)lowfirst} ,{(UBYTE *)"spectatorsize", NUMERICALVALUE, 0, (LONG)SPECTATORSIZE} ,{(UBYTE *)"subfilepatches", NUMERICALVALUE, 0, (LONG)SMAXFPATCHES} ,{(UBYTE *)"sublargepatches", NUMERICALVALUE, 0, (LONG)SMAXPATCHES} ,{(UBYTE *)"sublargesize", NUMERICALVALUE, 0, (LONG)SLARGEBUFFER} ,{(UBYTE *)"subsmallextension", NUMERICALVALUE, 0, (LONG)SSMALLOVERFLOW} ,{(UBYTE *)"subsmallsize", NUMERICALVALUE, 0, (LONG)SSMALLBUFFER} ,{(UBYTE *)"subsortiosize", NUMERICALVALUE, 0, (LONG)SSORTIOSIZE} ,{(UBYTE *)"subtermsinsmall", NUMERICALVALUE, 0, (LONG)STERMSSMALL} ,{(UBYTE *)"tempdir", STRINGVALUE, 0, (LONG)curdirp} ,{(UBYTE *)"tempsortdir", STRINGVALUE, 0, (LONG)cursortdirp} ,{(UBYTE *)"termsinsmall", NUMERICALVALUE, 0, (LONG)TERMSSMALL} ,{(UBYTE *)"threadbucketsize", NUMERICALVALUE, 0, (LONG)DEFAULTTHREADBUCKETSIZE} ,{(UBYTE *)"threadloadbalancing", ONOFFVALUE, 0, (LONG)DEFAULTTHREADLOADBALANCING} ,{(UBYTE *)"threads", NUMERICALVALUE, 0, (LONG)DEFAULTTHREADS} ,{(UBYTE *)"threadscratchoutsize", NUMERICALVALUE, 0, (LONG)THREADSCRATCHOUTSIZE} ,{(UBYTE *)"threadscratchsize", NUMERICALVALUE, 0, (LONG)THREADSCRATCHSIZE} ,{(UBYTE *)"threadsortfilesynch", ONOFFVALUE, 0, (LONG)0} ,{(UBYTE *)"totalsize", ONOFFVALUE, 0, (LONG)2} ,{(UBYTE *)"workspace", NUMERICALVALUE, 0, (LONG)WORKBUFFER} ,{(UBYTE *)"wtimestats", ONOFFVALUE, 0, (LONG)2} }; /* #] Includes : #[ Setups : #[ DoSetups : */ int DoSetups(void) { UBYTE *setbuffer, *s, *t, *u /*, c */; int errors = 0; setbuffer = LoadInputFile((UBYTE *)setupfilename,SETUPFILE); if ( setbuffer ) { /* The contents of the file are now in setbuffer. Each line is commentary or a single command. The buffer is terminated with a zero. */ s = setbuffer; while ( *s ) { if ( *s == ' ' || *s == '\t' || *s == '*' || *s == '#' || *s == '\n' ) { while ( *s && *s != '\n' ) s++; } else if ( tolower(*s) < 'a' || tolower(*s) > 'z' ) { t = s; while ( *s && *s != '\n' ) s++; /* c = *s; *s = 0; Error1("Setup file: Illegal statement: ",t); errors++; *s = c; */ } else { t = s; /* name of the option */ while ( tolower(*s) >= 'a' && tolower(*s) <= 'z' ) s++; *s++ = 0; while ( *s == ' ' || *s == '\t' ) s++; u = s; /* 'value' of the option */ while ( *s && *s != '\n' && *s != '\r' ) s++; if ( *s ) *s++ = 0; errors += ProcessOption(t,u,0); } while ( *s == '\n' || *s == '\r' ) s++; } M_free(setbuffer,"setup file buffer"); } if ( errors ) return(1); else return(0); } /* #] DoSetups : #[ ProcessOption : */ static char *proop1[3] = { "Setup file", "Setups in .frm file", "Setup in environment" }; int ProcessOption(UBYTE *s1, UBYTE *s2, int filetype) { SETUPPARAMETERS *sp; int n, giveback = 0, error = 0; UBYTE *s, *t, *s2ret; LONG x; sp = GetSetupPar(s1); if ( sp ) { /* We check now whether there are `' variables to be looked up in the environment. This is new (30-may-2008). This is only allowed in s2. */ restart:; { UBYTE *s3,*s4,*s5,*s6, c, *start; int n1,n2,n3; s = s2; while ( *s ) { if ( *s == '\\' ) s += 2; else if ( *s == '`' ) { start = s; s++; while ( *s && *s != '\'' ) { if ( *s == '\\' ) s++; s++; } if ( *s == 0 ) { MesPrint("%s: Illegal use of ` character for parameter %s" ,proop1[filetype],s1); return(1); } c = *s; *s = 0; s3 = (UBYTE *)getenv((char *)(start+1)); if ( s3 == 0 ) { MesPrint("%s: Cannot find environment variable %s for parameter %s" ,proop1[filetype],start+1,s1); return(1); } *s = c; s++; n1 = start - s2; s4 = s3; n2 = 0; while ( *s4 ) { if ( *s4 == '\\' ) { s4++; n2++; } s4++; n2++; } s4 = s; n3 = 0; while ( *s4 ) { if ( *s4 == '\\' ) { s4++; n3++; } s4++; n3++; } s4 = (UBYTE *)Malloc1((n1+n2+n3+1)*sizeof(UBYTE),"environment in setup"); s5 = s2; s6 = s4; while ( n1-- > 0 ) *s6++ = *s5++; s5 = s3; while ( n2-- > 0 ) *s6++ = *s5++; s5 = s; while ( n3-- > 0 ) *s6++ = *s5++; *s6 = 0; if ( giveback ) M_free(s2,"environment in setup"); s2 = s4; giveback = 1; goto restart; } else s++; } } n = sp->type; s2ret = s2; switch ( n ) { case NUMERICALVALUE: ParseNumber(x,s2); if ( *s2 == 'K' ) { x = x * 1000; s2++; } else if ( *s2 == 'M' ) { x = x * 1000000; s2++; } else if ( *s2 == 'G' ) { x = x * 1000000000; s2++; } else if ( *s2 == 'T' ) { x = x * 1000000000000; s2++; } if ( *s2 && *s2 != ' ' && *s2 != '\t' ) { MesPrint("%s: Numerical value expected for parameter %s" ,proop1[filetype],s1); error = 1; break; } sp->value = x; sp->flags = USEDFLAG; break; case STRINGVALUE: if ( StrICmp(s1,(UBYTE *)"tempsortdir") == 0 ) AM.havesortdir = 1; s = s2; t = s2; while ( *s ) { if ( *s == ' ' || *s == '\t' ) break; if ( *s == '\\' ) s++; *t++ = *s++; } *t = 0; if ( sp->flags == USEDFLAG && sp->value != 0 ) M_free((void *)(sp->value),"Process option"); sp->value = (LONG)strDup1(s2,"Process option"); sp->flags = USEDFLAG; break; case PATHVALUE: if ( StrICmp(s1,(UBYTE *)"incdir") == 0 ) { AM.IncDir = 0; } else if ( StrICmp(s1,(UBYTE *)"path") == 0 ) { if ( AM.Path ) M_free(AM.Path,"path"); AM.Path = 0; } else { MesPrint("Setups: %s not yet implemented",s1); error = 1; break; } if ( sp->flags == USEDFLAG && sp->value != 0 ) M_free((void *)(sp->value),"Process option"); sp->value = (LONG)strDup1(s2,"Process option"); sp->flags = USEDFLAG; break; case ONOFFVALUE: if ( tolower(*s2) == 'o' && tolower(s2[1]) == 'n' && ( s2[2] == 0 || s2[2] == ' ' || s2[2] == '\t' ) ) sp->value = 1; else if ( tolower(*s2) == 'o' && tolower(s2[1]) == 'f' && tolower(s2[2]) == 'f' && ( s2[3] == 0 || s2[3] == ' ' || s2[3] == '\t' ) ) sp->value = 0; else { MesPrint("%s: Unrecognized option for parameter %s: %s" ,proop1[filetype],s1,s2); error = 1; break; } sp->flags = USEDFLAG; break; case DEFINEVALUE: /* if ( sp->value ) M_free((UBYTE *)(sp->value),"Process option"); sp->value = (LONG)strDup1(s2,"Process option"); */ if ( TheDefine(s2,2) ) error = 1; break; default: Error1("Error in setupparameter table for:",s1); error = 1; break; } } else { MesPrint("%s: Keyword not recognized: %s",proop1[filetype],s1); error = 1; } if ( giveback ) M_free(s2ret,"environment in setup"); return(error); } /* #] ProcessOption : #[ GetSetupPar : */ SETUPPARAMETERS *GetSetupPar(UBYTE *s) { int hi, med, lo, i; lo = 0; // -1: remove possibility of out-of-bounds read in StrICmp hi = sizeof(setupparameters)/sizeof(SETUPPARAMETERS) - 1; do { med = ( hi + lo ) / 2; i = StrICmp(s,(UBYTE *)setupparameters[med].parameter); if ( i == 0 ) return(setupparameters+med); if ( i < 0 ) hi = med-1; else lo = med+1; } while ( hi >= lo ); return(0); } /* #] GetSetupPar : #[ RecalcSetups : */ int RecalcSetups(void) { SETUPPARAMETERS *sp, *sp1; sp1 = GetSetupPar((UBYTE *)"threads"); if ( AM.totalnumberofthreads > 1 ) sp1->value = AM.totalnumberofthreads - 1; else sp1->value = 0; /* if ( sp1->value > 0 ) AM.totalnumberofthreads = sp1->value+1; if ( AM.totalnumberofthreads == 0 ) AM.totalnumberofthreads = 1; */ sp = GetSetupPar((UBYTE *)"filepatches"); if ( sp->value < AM.totalnumberofthreads-1 ) sp->value = AM.totalnumberofthreads - 1; sp = GetSetupPar((UBYTE *)"smallsize"); sp1 = GetSetupPar((UBYTE *)"smallextension"); if ( 6*sp1->value < 7*sp->value ) sp1->value = (7*sp->value)/6; sp = GetSetupPar((UBYTE *)"termsinsmall"); sp->value = ( sp->value + 15 ) & (-16L); #ifdef WITHPTHREADS { SETUPPARAMETERS *sp2; LONG totalsize, minimumsize; sp = GetSetupPar((UBYTE *)"largesize"); totalsize = sp1->value+sp->value; sp2 = GetSetupPar((UBYTE *)"maxtermsize"); AM.MaxTer = sp2->value*sizeof(WORD); if ( AM.MaxTer < 200*(LONG)(sizeof(WORD)) ) AM.MaxTer = 200*(LONG)(sizeof(WORD)); if ( AM.MaxTer > MAXPOSITIVE - 200*(LONG)(sizeof(WORD)) ) AM.MaxTer = MAXPOSITIVE - 200*(LONG)(sizeof(WORD)); AM.MaxTer /= sizeof(WORD); AM.MaxTer *= sizeof(WORD); #ifdef WITHSORTBOTS if ( AM.totalnumberofthreads-1 > 2 ) { minimumsize = (2*(AM.totalnumberofthreads-1)-2)*(AM.MaxTer+ NUMBEROFBLOCKSINSORT*MINIMUMNUMBEROFTERMS/2*AM.MaxTer); } else #endif { minimumsize = (AM.totalnumberofthreads-1)*(AM.MaxTer+ NUMBEROFBLOCKSINSORT*MINIMUMNUMBEROFTERMS*AM.MaxTer); } if ( totalsize < minimumsize ) { sp->value = minimumsize - sp1->value; } } #endif return(0); } /* #] RecalcSetups : #[ AllocSetups : */ int AllocSetups(void) { SETUPPARAMETERS *sp; LONG LargeSize, SmallSize, SmallEsize, TermsInSmall, IOsize; int MaxPatches, MaxFpatches, error = 0, i, size; UBYTE *s; #ifndef WITHPTHREADS int j; #endif sp = GetSetupPar((UBYTE *)"threads"); if ( sp->value > 0 ) AM.totalnumberofthreads = sp->value+1; AM.OutBuffer = (UBYTE *)Malloc1(AM.OutBufSize+1,"OutputBuffer"); AP.PreAssignStack =(LONG *)Malloc1(AP.MaxPreAssignLevel*sizeof(LONG *),"PreAssignStack"); for ( i = 0; i < AP.MaxPreAssignLevel; i++ ) AP.PreAssignStack[i] = 0; AC.iBuffer = (UBYTE *)Malloc1(AC.iBufferSize+1,"statement buffer"); AC.iStop = AC.iBuffer + AC.iBufferSize-2; AP.preStart = (UBYTE *)Malloc1(AP.pSize,"instruction buffer"); AP.preStop = AP.preStart + AP.pSize - 3; /* AP.PreIfStack is already allocated in StartPrepro(), but to be sure we "if" the freeing */ if ( AP.PreIfStack ) M_free(AP.PreIfStack,"PreIfStack"); AP.PreIfStack = (int *)Malloc1(AP.MaxPreIfLevel*sizeof(int), "Preprocessor if stack"); AP.PreIfStack[0] = EXECUTINGIF; sp = GetSetupPar((UBYTE *)"insidefirst"); AM.ginsidefirst = AC.minsidefirst = AC.insidefirst = sp->value; /* We need to consider eliminating this variable */ sp = GetSetupPar((UBYTE *)"maxtermsize"); AM.MaxTer = sp->value*sizeof(WORD); if ( AM.MaxTer < 200*(LONG)(sizeof(WORD)) ) AM.MaxTer = 200*(LONG)(sizeof(WORD)); if ( AM.MaxTer > MAXPOSITIVE - 200*(LONG)(sizeof(WORD)) ) AM.MaxTer = MAXPOSITIVE - 200*(LONG)(sizeof(WORD)); AM.MaxTer /= (LONG)sizeof(WORD); AM.MaxTer *= (LONG)sizeof(WORD); /* Allocate workspace. */ sp = GetSetupPar((UBYTE *)"workspace"); AM.WorkSize = sp->value; #ifdef WITHPTHREADS #else AT.WorkSpace = (WORD *)Malloc1(AM.WorkSize*sizeof(WORD),(char *)(sp->parameter)); AT.WorkTop = AT.WorkSpace + AM.WorkSize; AT.WorkPointer = AT.WorkSpace; #endif /* Fixed indices */ sp = GetSetupPar((UBYTE *)"constindex"); if ( ( sp->value+100+5*WILDOFFSET ) > MAXPOSITIVE ) { MesPrint("Setting of %s in setupfile too large","constindex"); AM.OffsetIndex = MAXPOSITIVE - 5*WILDOFFSET - 100; MesPrint("value corrected to maximum allowed: %d",AM.OffsetIndex); } else AM.OffsetIndex = sp->value + 1; AC.FixIndices = (WORD *)Malloc1((AM.OffsetIndex)*sizeof(WORD),(char *)(sp->parameter)); AM.WilInd = AM.OffsetIndex + WILDOFFSET; AM.DumInd = AM.OffsetIndex + 2*WILDOFFSET; AM.IndDum = AM.DumInd + WILDOFFSET; #ifndef WITHPTHREADS AR.CurDum = AN.IndDum = AM.IndDum; #endif AM.mTraceDum = AM.IndDum + 2*WILDOFFSET; sp = GetSetupPar((UBYTE *)"parentheses"); AM.MaxParLevel = sp->value+1; AC.tokenarglevel = (WORD *)Malloc1((sp->value+1)*sizeof(WORD),(char *)(sp->parameter)); /* Space during calculations */ sp = GetSetupPar((UBYTE *)"maxnumbersize"); /* size = ( sp->value + 11 ) & (-4); AM.MaxTal = size - 2; if ( AM.MaxTal > (AM.MaxTer/sizeof(WORD)-2)/2 ) AM.MaxTal = (AM.MaxTer/sizeof(WORD)-2)/2; if ( AM.MaxTal < (AM.MaxTer/sizeof(WORD)-2)/4 ) AM.MaxTal = (AM.MaxTer/sizeof(WORD)-2)/4; */ /* There is too much confusion about MaxTal cq maxnumbersize. It seems better to fix it at its maximum value. This way we only worry about maxtermsize. This can be understood better by the 'innocent' user. */ if ( sp->value == 0 ) { AM.MaxTal = (AM.MaxTer/sizeof(WORD)-2)/2; } else { size = ( sp->value + 11 ) & (-4); AM.MaxTal = size - 2; if ( (size_t)AM.MaxTal > (size_t)((AM.MaxTer/sizeof(WORD)-2)/2) ) AM.MaxTal = (AM.MaxTer/sizeof(WORD)-2)/2; } AM.MaxTal &= -sizeof(WORD)*2; sp->value = AM.MaxTal; AC.cmod = (UWORD *)Malloc1(AM.MaxTal*4*sizeof(UWORD),(char *)(sp->parameter)); AM.gcmod = AC.cmod + AM.MaxTal; AC.powmod = AM.gcmod + AM.MaxTal; AM.gpowmod = AC.powmod + AM.MaxTal; /* The IO buffers for the input and output expressions. Fscr[2] will be assigned in a later stage for hiding expressions from the regular action. That will make the program faster. */ sp = GetSetupPar((UBYTE *)"scratchsize"); AM.ScratSize = sp->value/sizeof(WORD); if ( AM.ScratSize < 4*AM.MaxTer ) AM.ScratSize = 4*AM.MaxTer; AM.HideSize = AM.ScratSize; sp = GetSetupPar((UBYTE *)"hidesize"); if ( sp->value > 0 ) { AM.HideSize = sp->value/sizeof(WORD); if ( AM.HideSize < 4*AM.MaxTer ) AM.HideSize = 4*AM.MaxTer; } sp = GetSetupPar((UBYTE *)"factorizationcache"); AM.fbuffersize = sp->value; #ifdef WITHPTHREADS sp = GetSetupPar((UBYTE *)"threadscratchsize"); AM.ThreadScratSize = sp->value/sizeof(WORD); sp = GetSetupPar((UBYTE *)"threadscratchoutsize"); AM.ThreadScratOutSize = sp->value/sizeof(WORD); #endif #ifndef WITHPTHREADS for ( j = 0; j < 2; j++ ) { WORD *ScratchBuf; ScratchBuf = (WORD *)Malloc1(AM.ScratSize*sizeof(WORD),"scratchsize"); AR.Fscr[j].POsize = AM.ScratSize * sizeof(WORD); AR.Fscr[j].POfull = AR.Fscr[j].POfill = AR.Fscr[j].PObuffer = ScratchBuf; AR.Fscr[j].POstop = AR.Fscr[j].PObuffer + AM.ScratSize; PUTZERO(AR.Fscr[j].POposition); } AR.Fscr[2].PObuffer = 0; #endif sp = GetSetupPar((UBYTE *)"threadbucketsize"); AC.ThreadBucketSize = AM.gThreadBucketSize = AM.ggThreadBucketSize = sp->value; sp = GetSetupPar((UBYTE *)"threadloadbalancing"); AC.ThreadBalancing = AM.gThreadBalancing = AM.ggThreadBalancing = sp->value; sp = GetSetupPar((UBYTE *)"threadsortfilesynch"); AC.ThreadSortFileSynch = AM.gThreadSortFileSynch = AM.ggThreadSortFileSynch = sp->value; /* The size for shared memory window for oneside MPI2 communications (unused) */ sp = GetSetupPar((UBYTE *)"shmwinsize"); AM.shmWinSize = sp->value/sizeof(WORD); if ( AM.shmWinSize < 4*AM.MaxTer ) AM.shmWinSize = 4*AM.MaxTer; /* The sort buffer */ sp = GetSetupPar((UBYTE *)"smallsize"); SmallSize = sp->value; sp = GetSetupPar((UBYTE *)"smallextension"); SmallEsize = sp->value; sp = GetSetupPar((UBYTE *)"largesize"); LargeSize = sp->value; sp = GetSetupPar((UBYTE *)"termsinsmall"); TermsInSmall = sp->value; sp = GetSetupPar((UBYTE *)"largepatches"); MaxPatches = sp->value; sp = GetSetupPar((UBYTE *)"filepatches"); MaxFpatches = sp->value; sp = GetSetupPar((UBYTE *)"sortiosize"); IOsize = sp->value; if ( IOsize < AM.MaxTer ) { IOsize = AM.MaxTer; sp->value = IOsize; } #ifndef WITHPTHREADS #ifdef WITHZLIB for ( j = 0; j < 2; j++ ) { AR.Fscr[j].ziosize = IOsize; } #endif #endif AM.S0 = 0; AM.S0 = AllocSort(LargeSize,SmallSize,SmallEsize,TermsInSmall ,MaxPatches,MaxFpatches,IOsize,0); /* AM.S0->file.ziosize was already set to a (larger) value by AllocSort, here it is re-set. */ #ifdef WITHZLIB AM.S0->file.ziosize = IOsize; #ifndef WITHPTHREADS AR.FoStage4[0].ziosize = IOsize; AR.FoStage4[1].ziosize = IOsize; AT.S0 = AM.S0; #endif #else #ifndef WITHPTHREADS AT.S0 = AM.S0; #endif #endif #ifndef WITHPTHREADS AR.FoStage4[0].POsize = ((IOsize+sizeof(WORD)-1)/sizeof(WORD))*sizeof(WORD); AR.FoStage4[1].POsize = ((IOsize+sizeof(WORD)-1)/sizeof(WORD))*sizeof(WORD); #endif sp = GetSetupPar((UBYTE *)"subsmallsize"); AM.SSmallSize = sp->value; sp = GetSetupPar((UBYTE *)"subsmallextension"); AM.SSmallEsize = sp->value; sp = GetSetupPar((UBYTE *)"sublargesize"); AM.SLargeSize = sp->value; sp = GetSetupPar((UBYTE *)"subtermsinsmall"); AM.STermsInSmall = sp->value; sp = GetSetupPar((UBYTE *)"sublargepatches"); AM.SMaxPatches = sp->value; sp = GetSetupPar((UBYTE *)"subfilepatches"); AM.SMaxFpatches = sp->value; sp = GetSetupPar((UBYTE *)"subsortiosize"); AM.SIOsize = sp->value; /* As for IOsize, make sure SIOsize is at least as large as AM.MaxTer. */ if ( AM.SIOsize < AM.MaxTer ) { AM.SIOsize = AM.MaxTer; sp->value = AM.SIOsize; } sp = GetSetupPar((UBYTE *)"spectatorsize"); AM.SpectatorSize = sp->value; /* The next code is just for the moment (26-jan-1997) because we have the new parts combined with the old. Once the old parts are gone from the program, we can eliminate this code too. */ sp = GetSetupPar((UBYTE *)"functionlevels"); AM.maxFlevels = sp->value + 1; #ifdef WITHPTHREADS #else AT.Nest = (NESTING)Malloc1((LONG)sizeof(struct NeStInG)*AM.maxFlevels,"functionlevels"); AT.NestStop = AT.Nest + AM.maxFlevels; AT.NestPoin = AT.Nest; #endif sp = GetSetupPar((UBYTE *)"maxwildcards"); AM.MaxWildcards = sp->value; #ifdef WITHPTHREADS #else AT.WildMask = (WORD *)Malloc1((LONG)AM.MaxWildcards*sizeof(WORD),"maxwildcards"); #endif sp = GetSetupPar((UBYTE *)"compresssize"); if ( sp->value < 2*AM.MaxTer ) sp->value = 2*AM.MaxTer; AM.CompressSize = sp->value; #ifndef WITHPTHREADS AR.CompressBuffer = (WORD *)Malloc1((AM.CompressSize+10)*sizeof(WORD),"compresssize"); AR.CompressPointer = AR.CompressBuffer; AR.ComprTop = AR.CompressBuffer + AM.CompressSize; #endif sp = GetSetupPar((UBYTE *)"bracketindexsize"); if ( sp->value < 20*AM.MaxTer ) sp->value = 20*AM.MaxTer; AM.MaxBracketBufferSize = sp->value/sizeof(WORD); sp = GetSetupPar((UBYTE *)"dotchar"); AO.FortDotChar = ((UBYTE *)(sp->value))[0]; sp = GetSetupPar((UBYTE *)"commentchar"); AP.cComChar = AP.ComChar = ((UBYTE *)(sp->value))[0]; sp = GetSetupPar((UBYTE *)"procedureextension"); /* Check validity first. */ s = (UBYTE *)(sp->value); if ( FG.cTable[*s] != 0 ) { MesPrint(" Illegal string for procedure extension %s",(UBYTE *)sp->value); error = -2; } else { s++; while ( *s ) { if ( *s == ' ' || *s == '\t' || *s == '\n' ) { MesPrint(" Illegal string for procedure extension %s",(UBYTE *)sp->value); error = -2; break; } s++; } } AP.cprocedureExtension = strDup1((UBYTE *)(sp->value),"procedureExtension"); AP.procedureExtension = strDup1(AP.cprocedureExtension,"procedureExtension"); sp = GetSetupPar((UBYTE *)"totalsize"); if ( sp->value != 2 ) AM.PrintTotalSize = sp->value; sp = GetSetupPar((UBYTE *)"continuationlines"); AM.FortranCont = sp->value; sp = GetSetupPar((UBYTE *)"oldorder"); AM.OldOrderFlag = sp->value; sp = GetSetupPar((UBYTE *)"resettimeonclear"); AM.resetTimeOnClear = sp->value; sp = GetSetupPar((UBYTE *)"nospacesinnumbers"); AO.NoSpacesInNumbers = AM.gNoSpacesInNumbers = AM.ggNoSpacesInNumbers = sp->value; sp = GetSetupPar((UBYTE *)"indentspace"); AO.IndentSpace = AM.gIndentSpace = AM.ggIndentSpace = sp->value; sp = GetSetupPar((UBYTE *)"jumpratio"); AM.jumpratio = sp->value; sp = GetSetupPar((UBYTE *)"nwritestatistics"); AC.StatsFlag = AM.gStatsFlag = AM.ggStatsFlag = 1-sp->value; sp = GetSetupPar((UBYTE *)"nwritefinalstatistics"); AC.FinalStats = AM.gFinalStats = AM.ggFinalStats = 1-sp->value; sp = GetSetupPar((UBYTE *)"nwritethreadstatistics"); AC.ThreadStats = AM.gThreadStats = AM.ggThreadStats = 1-sp->value; sp = GetSetupPar((UBYTE *)"nwriteprocessstatistics"); AC.ProcessStats = AM.gProcessStats = AM.ggProcessStats = 1-sp->value; sp = GetSetupPar((UBYTE *)"oldparallelstatistics"); AC.OldParallelStats = AM.gOldParallelStats = AM.ggOldParallelStats = sp->value; sp = GetSetupPar((UBYTE *)"oldfactarg"); AC.OldFactArgFlag = AM.gOldFactArgFlag = AM.ggOldFactArgFlag = sp->value; sp = GetSetupPar((UBYTE *)"oldgcd"); AC.OldGCDflag = AM.gOldGCDflag = AM.ggOldGCDflag = sp->value; sp = GetSetupPar((UBYTE *)"oldprfsign"); AC.OldPRFSignFlag = sp->value; sp = GetSetupPar((UBYTE *)"wtimestats"); if ( sp->value == 2 ) sp->value = AM.ggWTimeStatsFlag; AC.WTimeStatsFlag = AM.gWTimeStatsFlag = AM.ggWTimeStatsFlag = sp->value; #ifdef WITHFLOAT sp = GetSetupPar((UBYTE *)"maxweight"); AC.MaxWeight = AM.gMaxWeight = AM.ggMaxWeight = sp->value; sp = GetSetupPar((UBYTE *)"defaultprecision"); AC.DefaultPrecision = AM.gDefaultPrecision = AM.ggDefaultPrecision = sp->value; #endif sp = GetSetupPar((UBYTE *)"sorttype"); if ( StrICmp((UBYTE *)"lowfirst",(UBYTE *)sp->value) == 0 ) { AC.lSortType = SORTLOWFIRST; } else if ( StrICmp((UBYTE *)"highfirst",(UBYTE *)sp->value) == 0 ) { AC.lSortType = SORTHIGHFIRST; } else { MesPrint(" Illegal SortType specification: %s",(UBYTE *)sp->value); error = -2; } sp = GetSetupPar((UBYTE *)"processbucketsize"); AM.hProcessBucketSize = AM.gProcessBucketSize = AC.ProcessBucketSize = AC.mProcessBucketSize = sp->value; /* The store caches (code installed 15-aug-2006 JV) */ sp = GetSetupPar((UBYTE *)"numstorecaches"); AM.NumStoreCaches = sp->value; sp = GetSetupPar((UBYTE *)"sizestorecache"); AM.SizeStoreCache = sp->value; /* Make sure this is a multiple of sizeof(WORD). */ AM.SizeStoreCache = ((AM.SizeStoreCache+sizeof(WORD)-1)/sizeof(WORD))*sizeof(WORD); #ifndef WITHPTHREADS /* Install the store caches (15-aug-2006 JV) Note that in the case of PTHREADS this is done in InitializeOneThread */ AT.StoreCache = AT.StoreCacheAlloc = 0; if ( AM.NumStoreCaches > 0 ) { STORECACHE sa, sb; size = sizeof(struct StOrEcAcHe)+AM.SizeStoreCache; size = ((size-1)/sizeof(size_t)+1)*sizeof(size_t); AT.StoreCacheAlloc = (STORECACHE)Malloc1(size*AM.NumStoreCaches,"StoreCaches"); AT.StoreCache = AT.StoreCacheAlloc; sa = AT.StoreCache; for ( j = 0; j < AM.NumStoreCaches; j++ ) { sb = (STORECACHE)(void *)((UBYTE *)sa+size); if ( j == AM.NumStoreCaches-1 ) { sa->next = 0; } else { sa->next = sb; } SETBASEPOSITION(sa->position,-1); SETBASEPOSITION(sa->toppos,-1); sa = sb; } } #endif /* And now some order sensitive things */ if ( AM.Path == 0 ) { sp = GetSetupPar((UBYTE *)"path"); AM.Path = strDup1((UBYTE *)(sp->value),"path"); } if ( AM.IncDir == 0 ) { sp = GetSetupPar((UBYTE *)"incdir"); AM.IncDir = strDup1((UBYTE *)(sp->value),"incdir"); } /* if ( AM.TempDir == 0 ) { sp = GetSetupPar((UBYTE *)"tempdir"); AM.TempDir = strDup1((UBYTE *)(sp->value),"tempdir"); } */ return(error); } /* #] AllocSetups : #[ WriteSetup : The routine writes the values of the setup parameters. We should do this better. (JV, 21-may-2008) The way it should be done is: a: write the raw values. b: give readjusted values. c: give derived values. Because this is a difficult subject, it would be nice to have a LaTeX document that explains this all exactly. There should then be a mechanism to poke the values of the setup into the LaTeX document. probably the easiest way is to make a file with lots of \def definitions and have that included into the LaTeX file. */ void WriteSetup(void) { int n = sizeof(setupparameters)/sizeof(SETUPPARAMETERS); SETUPPARAMETERS *sp; MesPrint(" The setup parameters are:"); for ( sp = setupparameters; n > 0; n--, sp++ ) { switch(sp->type){ case NUMERICALVALUE: MesPrint(" %s: %l",sp->parameter,sp->value); break; case PATHVALUE: if ( StrICmp(sp->parameter,(UBYTE *)"path") == 0 && AM.Path ) { MesPrint(" %s: '%s'",sp->parameter,(UBYTE *)(AM.Path)); break; } if ( StrICmp(sp->parameter,(UBYTE *)"incdir") == 0 && AM.IncDir ) { MesPrint(" %s: '%s'",sp->parameter,(UBYTE *)(AM.IncDir)); break; } /* fall through */ case STRINGVALUE: if ( StrICmp(sp->parameter,(UBYTE *)"tempdir") == 0 && AM.TempDir ) { MesPrint(" %s: '%s'",sp->parameter,(UBYTE *)(AM.TempDir)); } else if ( StrICmp(sp->parameter,(UBYTE *)"tempsortdir") == 0 && AM.TempSortDir ) { MesPrint(" %s: '%s'",sp->parameter,(UBYTE *)(AM.TempSortDir)); } else { MesPrint(" %s: '%s'",sp->parameter,(UBYTE *)(sp->value)); } break; case ONOFFVALUE: if ( sp->value == 0 ) MesPrint(" %s: OFF",sp->parameter); else if ( sp->value == 1 ) MesPrint(" %s: ON",sp->parameter); break; case DEFINEVALUE: /* MesPrint(" %s: '%s'",sp->parameter,(UBYTE *)(sp->value)); */ break; } } AC.SetupFlag = 0; } /* #] WriteSetup : #[ AllocSort : Routine allocates a complete struct for sorting. To be used for the main allocation of the sort buffers, and in a later stage for the function and subroutine sort buffers. The level arg denotes a main buffer allocation (0) or a sub-buffer allocation (1), used only for printing warning messages for buffer size adjustments in DEBUGGING mode. */ SORTING *AllocSort(LONG inLargeSize, LONG inSmallSize, LONG inSmallEsize, LONG inTermsInSmall, int inMaxPatches, int inMaxFpatches, LONG inIOsize, int level) { DUMMYUSE(level); /* This is only used in DEBUGGING mode */ LONG LargeSize = inLargeSize; LONG SmallSize = inSmallSize; LONG SmallEsize = inSmallEsize; LONG TermsInSmall = inTermsInSmall; int MaxPatches = inMaxPatches; int MaxFpatches = inMaxFpatches; LONG IOsize = inIOsize; LONG longer,terms2insmall,sortsize,longerp; LONG IObuffersize = IOsize; LONG IOtry; SORTING *sort; int fname2Size = 0, j = 0; char *s; if ( AM.S0 != 0 ) { s = FG.fname2; fname2Size = 0; while ( *s ) { s++; fname2Size++; } fname2Size += 16; } if ( MaxFpatches < 4 ) MaxFpatches = 4; longer = MaxPatches > MaxFpatches ? MaxPatches : MaxFpatches; longerp = longer; while ( (1 << j) < longerp ) j++; longerp = (1 << j) + 1; longerp += sizeof(WORD*) - (longerp%sizeof(WORD *)); longer++; longer += sizeof(WORD*) - (longer%sizeof(WORD *)); if ( SmallSize < 16*AM.MaxTer ) SmallSize = 16*AM.MaxTer+16; TermsInSmall = (TermsInSmall+15) & (-16L); terms2insmall = 2*TermsInSmall; /* Used to be just + 100 rather than *2 */ if ( SmallEsize < (SmallSize*3)/2 ) SmallEsize = (SmallSize*3)/2; if ( LargeSize > 0 && LargeSize < 2*SmallSize ) LargeSize = 2*SmallSize; SmallEsize = (SmallEsize+15) & (-16L); if ( LargeSize < 0 ) LargeSize = 0; sortsize = sizeof(SORTING); sortsize = (sortsize+15)&(-16L); IObuffersize = (IObuffersize+sizeof(WORD)-1)/sizeof(WORD); /* The next statement fixes a bug. In the rare case that we have a problem here, we expand the size of the large buffer or the small extension */ if ( (ULONG)( LargeSize+SmallEsize ) < MaxFpatches*((IObuffersize +COMPINC)*sizeof(WORD)+2*AM.MaxTer) ) { if ( LargeSize == 0 ) SmallEsize = MaxFpatches*((IObuffersize+COMPINC)*sizeof(WORD)+2*AM.MaxTer); else LargeSize = MaxFpatches*((IObuffersize+COMPINC)*sizeof(WORD)+2*AM.MaxTer) - SmallEsize; } IOtry = ((LargeSize+SmallEsize)/MaxFpatches-2*AM.MaxTer)/sizeof(WORD)-COMPINC; /* Here both IObuffersize and IOtry are in units of sizeof(WORD). */ if ( IObuffersize < IOtry ) { IObuffersize = IOtry; } #if DEBUGGING char *prefix; if ( level == 0 ) { prefix = ""; } else { prefix = "Sub"; } if ( LargeSize != inLargeSize ) { MesPrint("Warning: %sLargeSize adjusted: %l -> %l", prefix, inLargeSize, LargeSize); } if ( SmallSize != inSmallSize ) { MesPrint("Warning: %sSmallSize adjusted: %l -> %l", prefix, inSmallSize, SmallSize); } if ( SmallEsize != inSmallEsize ) {MesPrint("Warning: %sSmallEsize adjusted: %l -> %l", prefix, inSmallEsize, SmallEsize); } if ( TermsInSmall != inTermsInSmall ) { MesPrint("Warning: %sTermsInSmall adjusted: %l -> %l", prefix, inTermsInSmall, TermsInSmall); } if ( MaxPatches != inMaxPatches ) { MesPrint("Warning: MaxPatches adjusted: %d -> %d", inMaxPatches, MaxPatches); } if ( MaxFpatches != inMaxFpatches ) {MesPrint("Warning: MaxFPatches adjusted: %d -> %d", inMaxFpatches, MaxFpatches); } /* This one is always changed if the LargeSize has not been... */ /* if ( IObuffersize != inIOsize/(LONG)sizeof(WORD) ) { MesPrint("Warning: IOsize adjusted: %l -> %l", inIOsize/sizeof(WORD), IObuffersize); } */ #endif /* Allocate separate buffers for most struct members, for better testing and debugging with valgrind. */ sort = Malloc1(sizeof(*sort), "AllocSort: sorting struct"); sort->LargeSize = LargeSize/sizeof(WORD); sort->SmallSize = SmallSize/sizeof(WORD); sort->SmallEsize = SmallEsize/sizeof(WORD); sort->MaxPatches = MaxPatches; sort->MaxFpatches = MaxFpatches; sort->TermsInSmall = TermsInSmall; sort->Terms2InSmall = terms2insmall; sort->sPointer = Malloc1(sizeof(*(sort->sPointer ))*terms2insmall, "AllocSort: sPointer"); sort->Patches = Malloc1(sizeof(*(sort->Patches ))*longer, "AllocSort: Patches"); sort->pStop = Malloc1(sizeof(*(sort->pStop ))*longer, "AllocSort: pStop"); sort->poina = Malloc1(sizeof(*(sort->poina ))*longerp, "AllocSort: poina"); sort->poin2a = Malloc1(sizeof(*(sort->poin2a ))*longerp, "AllocSort: poin2a"); sort->fPatches = Malloc1(sizeof(*(sort->fPatches ))*longer, "AllocSort: fPatches"); sort->fPatchesStop = Malloc1(sizeof(*(sort->fPatchesStop))*longer, "AllocSort: fPatchesStop"); sort->inPatches = Malloc1(sizeof(*(sort->inPatches ))*longer, "AllocSort: inPatches"); sort->tree = Malloc1(sizeof(*(sort->tree ))*longerp, "AllocSort: tree"); sort->used = Malloc1(sizeof(*(sort->used ))*longerp, "AllocSort: used"); #ifdef WITHZLIB sort->fpcompressed = Malloc1(sizeof(*(sort->fpcompressed ))*(longerp+2), "AllocSort: fpcompressed"); sort->fpincompressed = Malloc1(sizeof(*(sort->fpincompressed))*(longerp+2), "AllocSort: fpincompressed"); sort->zsparray = 0; #endif sort->ktoi = Malloc1(sizeof(*(sort->ktoi))*(longerp+2), "AllocSort: ktoi"); // The combined Large buffer and Small buffer (+ extension) are used. // They must be allocated together. sort->lBuffer = Malloc1(sizeof(*(sort->lBuffer))*(sort->LargeSize+sort->SmallEsize), "AllocSort: lBuffer+sBuffer"); sort->lTop = sort->lBuffer+sort->LargeSize; sort->sBuffer = sort->lTop; if ( sort->LargeSize == 0 ) { sort->lBuffer = 0; sort->lTop = 0; } sort->sTop = sort->sBuffer + sort->SmallSize; sort->sTop2 = sort->sBuffer + sort->SmallEsize; sort->sHalf = sort->sBuffer + (LONG)((sort->SmallSize+sort->SmallEsize)>>1); sort->file.PObuffer = Malloc1(IObuffersize*sizeof(*(sort->file.PObuffer))+fname2Size+16, "AllocSort: PObuffer"); sort->file.POstop = sort->file.PObuffer+IObuffersize; sort->file.POsize = IObuffersize * sizeof(WORD); sort->file.POfill = sort->file.POfull = sort->file.PObuffer; sort->file.active = 0; sort->file.handle = -1; PUTZERO(sort->file.POposition); #ifdef WITHPTHREADS sort->file.pthreadslock = dummylock; #endif #ifdef WITHZLIB sort->file.ziosize = IObuffersize*sizeof(WORD); sort->file.ziobuffer = 0; #endif if ( AM.S0 != 0 ) { sort->file.name = (char *)(sort->file.PObuffer + IObuffersize); AllocSortFileName(sort); } else sort->file.name = 0; sort->cBuffer = 0; sort->cBufferSize = 0; sort->f = 0; sort->PolyWise = 0; return(sort); } /* #] AllocSort : #[ AllocSortFileName : */ void AllocSortFileName(SORTING *sort) { GETIDENTITY char *s, *t; /* This is not the allocation before the tempfiles are determined. Hence we can use the name in FG.fname2 and modify the tail */ s = FG.fname2; t = sort->file.name; while ( *s ) *t++ = *s++; #ifdef WITHPTHREADS t[-2] = 'F'; snprintf(t-1,FG.fname2size-(t-1-sort->file.name),"%d.%d",identity,AN.filenum); #else t[-2] = 'f'; snprintf(t-1,FG.fname2size-(t-1-sort->file.name),"%d",AN.filenum); #endif AN.filenum++; } /* #] AllocSortFileName : #[ AllocFileHandle : */ FILEHANDLE *AllocFileHandle(WORD par,char *name) { GETIDENTITY LONG allocation, Ssize; FILEHANDLE *fh; int i = 0; char *s, *t; s = FG.fname2; i = 0; while ( *s ) { s++; i++; } if ( par == 0 ) { i += 16; Ssize = AM.SIOsize; } else { s = name; while ( *s ) { i++; s++; } i+= 2; Ssize = AM.SpectatorSize; } allocation = sizeof(FILEHANDLE) + (Ssize+1)*sizeof(WORD) + i*sizeof(char) +FG.fname2size+20; fh = (FILEHANDLE *)Malloc1(allocation,"FileHandle"); fh->PObuffer = (WORD *)(fh+1); fh->POstop = fh->PObuffer+Ssize; fh->POsize = Ssize * sizeof(WORD); fh->active = 0; fh->handle = -1; PUTZERO(fh->POposition); #ifdef WITHPTHREADS fh->pthreadslock = dummylock; #endif if ( par == 0 ) { /* sort file */ if ( AM.S0 != 0 ) { fh->name = (char *)(fh->POstop + 1); s = FG.fname2; t = fh->name; while ( *s ) *t++ = *s++; #ifdef WITHPTHREADS t[-2] = 'F'; snprintf(t-1,FG.fname2size-(t-1-fh->name),"%d-%d",identity,AN.filenum); #else t[-2] = 'f'; snprintf(t-1,FG.fname2size-(t-1-fh->name),"%d",AN.filenum); #endif AN.filenum++; } else fh->name = 0; } else { /* Spectator file */ fh->name = (char *)(fh->POstop + 1); s = FG.fname; t = fh->name; for ( i = 0; i < FG.fnamebase; i++ ) *t++ = *s++; s = name; while ( *s ) *t++ = *s++; *t = 0; } fh->POfill = fh->POfull = fh->PObuffer; return(fh); } /* #] AllocFileHandle : #[ DeAllocFileHandle : Made to repair deallocation of AN.filenum. 21-sep-2000 */ void DeAllocFileHandle(FILEHANDLE *fh) { GETIDENTITY if ( fh->handle >= 0 ) { CloseFile(fh->handle); fh->handle = -1; remove(fh->name); } AN.filenum--; /* free namespace. was forgotten in first reading */ M_free(fh,"Temporary FileHandle"); } /* #] DeAllocFileHandle : #[ MakeSetupAllocs : */ int MakeSetupAllocs(void) { if ( RecalcSetups() || AllocSetups() ) return(1); else return(0); } /* #] MakeSetupAllocs : #[ AllocNormData : Allocate the arrays within the NORMDATA struct. These are dynamic, such that valgrind can detect buffer overruns in these arrays. */ NORMDATA* AllocNormData(void) { NORMDATA* tmp = Malloc1(sizeof(NORMDATA), "NormData struct"); tmp->psym = Malloc1(7*NORMSIZE*sizeof(*(tmp->psym)), "Normalize struct psym"); tmp->pvec = Malloc1(1*NORMSIZE*sizeof(*(tmp->pvec)), "Normalize struct pvec"); tmp->pdot = Malloc1(3*NORMSIZE*sizeof(*(tmp->pdot)), "Normalize struct pdot"); tmp->pdel = Malloc1(2*NORMSIZE*sizeof(*(tmp->pdel)), "Normalize struct pdel"); tmp->pind = Malloc1(1*NORMSIZE*sizeof(*(tmp->pind)), "Normalize struct pind"); tmp->peps = Malloc1(NORMSIZE/3*sizeof(*(tmp->peps)), "Normalize struct peps"); tmp->pden = Malloc1(NORMSIZE/3*sizeof(*(tmp->pden)), "Normalize struct pden"); tmp->pcom = Malloc1(1*NORMSIZE*sizeof(*(tmp->pcom)), "Normalize struct pcom"); tmp->pnco = Malloc1(1*NORMSIZE*sizeof(*(tmp->pnco)), "Normalize struct pnco"); tmp->pcon = Malloc1(2*NORMSIZE*sizeof(*(tmp->pcon)), "Normalize struct pcon"); return tmp; } /* #] AllocNormData : #[ TryFileSetups : Routine looks in the input file for a start of the type [#-] #: setupparameter value It keeps looking until the first line that does not start with #-, #+ or #: Then it rewinds the input. */ #define SETBUFSIZE 257 int TryFileSetups(void) { LONG oldstreamposition; int oldstream; int error = 0, eqnum; int oldNoShowInput = AC.NoShowInput; UBYTE buff[SETBUFSIZE+1], *s, *t, *u, *settop, c; LONG linenum, prevline; if ( AC.CurrentStream == 0 ) return(error); oldstream = AC.CurrentStream - AC.Streams; oldstreamposition = GetStreamPosition(AC.CurrentStream); linenum = AC.CurrentStream->linenumber; prevline = AC.CurrentStream->prevline; eqnum = AC.CurrentStream->eqnum; AC.NoShowInput = 1; settop = buff + SETBUFSIZE; if ( AC.CurrentStream->type == INPUTSTREAM && oldstreamposition == 0 ) AC.CurrentStream->fileposition = 0; for(;;) { c = GetInput(); if ( c == '*' || c == '\n' ) { while ( c != '\n' && c != ENDOFINPUT ) c = GetInput(); if ( c == ENDOFINPUT ) goto eoi; continue; } if ( c == ENDOFINPUT ) goto eoi; if ( c != '#' ) break; c = GetInput(); if ( c == ENDOFINPUT ) goto eoi; if ( c != '-' && c != '+' && c != ':' ) break; if ( c != ':' ) { while ( c != '\n' && c != ENDOFINPUT ) c = GetInput(); continue; } s = buff; while ( ( c = GetInput() ) == ' ' || c == '\t' || c == '\r' ) {} if ( c == ENDOFINPUT ) break; if ( c == LINEFEED ) continue; if ( c == 0 || c == ENDOFINPUT ) break; while ( c != LINEFEED && c != ENDOFINPUT ) { *s++ = c; c = GetInput(); if ( c != LINEFEED && c != '\r' ) continue; if ( s >= settop ) { while ( c != '\n' && c != ENDOFINPUT ) c = GetInput(); MesPrint("Setups in .frm file: Line too long. setup ignored"); error++; goto nextline; } } *s++ = '\n'; t = s = buff; /* name of the option */ while ( tolower(*s) >= 'a' && tolower(*s) <= 'z' ) s++; if ( *s != '\n' ) { *s++ = 0; while ( *s == ' ' || *s == '\t' ) s++; u = s; /* 'value' of the option */ while ( *s && *s != '\n' && *s != '\r' ) s++; if ( *s ) *s++ = 0; } else { /* The value is empty. */ u = s; *s++ = 0; } error += ProcessOption(t,u,1); nextline:; } AC.NoShowInput = oldNoShowInput; AC.CurrentStream = AC.Streams + oldstream; PositionStream(AC.CurrentStream,oldstreamposition); AC.CurrentStream->linenumber = linenum; AC.CurrentStream->prevline = prevline; AC.CurrentStream->eqnum = eqnum; ClearPushback(); if ( AC.CurrentStream->type == INPUTSTREAM ) AC.CurrentStream->fileposition = -1; return(error); eoi: MesPrint("Input file without a program."); return(-1); } /* #] TryFileSetups : #[ TryEnvironment : */ int TryEnvironment(void) { char *s, *t, *u, varname[100]; int i,imax = sizeof(setupparameters)/sizeof(SETUPPARAMETERS); int error = 0; varname[0] = 'F'; varname[1] = 'O'; varname[2] = 'R'; varname[3] = 'M'; varname[4] = '_'; varname[5] = 0; for ( i = 0; i < imax; i++ ) { t = s = (char *)(setupparameters[i].parameter); u = varname+5; while ( *s ) { *u++ = (char)(toupper((unsigned char)*s)); s++; } *u = 0; s = (char *)(getenv(varname)); if ( s ) { error += ProcessOption((UBYTE *)t,(UBYTE *)s,2); } } return(error); } /* #] TryEnvironment : #] Setups : */ form-5.0.1/sources/symmetr.c0000644000175100017510000017166215217035721011512 /** @file symmetr.c * * The routines that deal with the pattern matching of functions with * symmetric properties. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : function.c */ #include "form3.h" /* #] Includes : #[ MatchE : WORD MatchE(pattern,fun,inter,par) Matches symmetric and antisymmetric tensors. Pattern and fun point at a tensor. Problem is the wildcarding and all its possible permutations. This routine loops over all of them and calls for each possible wildcarding the recursion in ScanFunctions. Note that this can be very costly. Originally this routine did only Levi Civita tensors and hence it dealt only with commuting objects. Because of the backtracking we cannot fall back to the calling ScanFunctions routine and check the sequence of functions when non-commuting objects are involved. */ int MatchE(PHEAD WORD *pattern, WORD *fun, WORD *inter, WORD par) { GETBIDENTITY WORD *m, *t, *r, i; int retval; WORD *mstop, *tstop, j, newvalue, newfun; WORD fixvec[MAXMATCH],wcvec[MAXMATCH],fixind[MAXMATCH],wcind[MAXMATCH]; WORD tfixvec[MAXMATCH],tfixind[MAXMATCH]; WORD vwc,vfix,ifix,iwc,tvfix,tifix,nv,ni; WORD sign = 0, *rstop, first1, first2, first3, funwild; WORD *OldWork, nwstore, oRepFunNum; PERM perm1,perm2; DISTRIBUTE distr; WORD *newpat, /* *newter, *instart, */ offset; /* instart = fun; */ offset = WORDDIF(fun,AN.terstart); if ( pattern[1] != fun[1] ) return(0); if ( *pattern >= FUNCTION+WILDOFFSET ) { if ( CheckWild(BHEAD *pattern-WILDOFFSET,FUNTOFUN,*fun,&newfun) ) return(0); funwild = 1; } else funwild = 0; mstop = pattern + pattern[1]; tstop = fun + fun[1]; m = pattern + FUNHEAD; t = fun + FUNHEAD; while ( m < mstop ) { if ( *m != *t ) break; m++; t++; } if ( m >= mstop ) { AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; newpat = pattern + pattern[1]; if ( funwild ) { m = AN.WildValue; t = OldWork = AT.WorkPointer; nwstore = i = (m[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; r = AT.WildMask; if ( i > 0 ) { do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); } if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; AddWild(BHEAD *pattern-WILDOFFSET,FUNTOFUN,newfun); if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AN.UsedOtherFind = 1; return(1); } retval = 0; } else return(1); } else { /* newter = instart; */ retval = ScanFunctions(BHEAD newpat,inter,par); } if ( retval == 0 ) { m = AN.WildValue; t = OldWork; r = AT.WildMask; i = nwstore; if ( i > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --i > 0 ); } } AT.WorkPointer = OldWork; return(retval); } else { if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AN.UsedOtherFind = 1; return(1); } else return(0); } else return(1); } /* newter = instart; */ retval = ScanFunctions(BHEAD newpat,inter,par); return(retval); } /* Now the recursion */ } /* Strategy: 1: match the fixed arguments 2: match, permuting the wildcards if needed. 3: keep track of sign. */ vwc = 0; vfix = 0; ifix = 0; iwc = 0; r = pattern+FUNHEAD; while ( r < mstop ) { if ( *r < (AM.OffsetVector+WILDOFFSET) ) { fixvec[vfix++] = *r; /* Fixed vectors */ sign += vwc + ifix + iwc; } else if ( *r < MINSPEC ) { wcvec[vwc++] = *r; /* Wildcard vectors */ sign += ifix + iwc; } else if ( *r < (AM.OffsetIndex+WILDOFFSET) ) { fixind[ifix++] = *r; /* Fixed indices */ sign += iwc; } else if ( *r < (AM.OffsetIndex+(WILDOFFSET<<1)) ) { wcind[iwc++] = *r; /* Wildcard indices */ } else { fixind[ifix++] = *r; /* Generated indices ~ fixed */ sign += iwc; } r++; } if ( iwc == 0 && vwc == 0 ) return(0); tvfix = tifix = 0; t = fun + FUNHEAD; m = fixvec; mstop = m + vfix; r = fixind; rstop = r + ifix; nv = 0; ni = 0; while ( t < tstop ) { if ( *t < 0 ) { nv++; if ( m < mstop && *t == *m ) { m++; } else { sign += WORDDIF(mstop,m); tfixvec[tvfix++] = *t; } } else { ni++; if ( r < rstop && *r == *t ) { r++; } else { sign += WORDDIF(rstop,r); tfixind[tifix++] = *t; } } t++; } if ( m < mstop || r < rstop ) return(0); if ( tvfix < vwc || (tvfix+tifix) < (vwc+iwc) ) return(0); sign += ( nv - vfix - vwc ) & ni; /* Take now the wildcards that have an assignment already. See whether they match. */ { WORD *wv, *wm, n; wm = AT.WildMask; wv = AN.WildValue; n = AN.NumWild; do { if ( *wm ) { if ( *wv == VECTOVEC ) { for ( ni = 0; ni < vwc; ni++ ) { if ( wcvec[ni]-WILDOFFSET == wv[2] ) { /* Has been assigned */ sign += ni; vwc--; while ( ni < vwc ) { wcvec[ni] = wcvec[ni+1]; ni++; } /* TryVect: */ for ( ni = 0; ni < tvfix; ni++ ) { if ( tfixvec[ni] == wv[3] ) { sign += ni; tvfix--; while ( ni < tvfix ) { tfixvec[ni] = tfixvec[ni+1]; ni++; } goto NextWV; } } return(0); } } } else if ( *wv == INDTOIND ) { for ( ni = 0; ni < iwc; ni++ ) { if ( wcind[ni]-WILDOFFSET == wv[2] ) { /* Has been assigned */ sign += ni; iwc--; while ( ni < iwc ) { wcind[ni] = wcind[ni+1]; ni++; } for ( ni = 0; ni < tifix; ni++ ) { if ( tfixind[ni] == wv[3] ) { sign += ni; tifix--; while ( ni < tifix ) { tfixind[ni] = tfixind[ni+1]; ni++; } goto NextWV; } } /* goto TryVect; */ return(0); } } } else if ( *wv == VECTOSUB ) { for ( ni = 0; ni < vwc; ni++ ) { if ( wcvec[ni]-WILDOFFSET == wv[2] ) return(0); } } else if ( *wv == INDTOSUB ) { for ( ni = 0; ni < iwc; ni++ ) { if ( wcind[ni]-WILDOFFSET == wv[2] ) return(0); } } } NextWV: wm++; wv += wv[1]; n--; if ( n > 0 ) { while ( n > 0 && ( *wv == FROMSET || *wv == SETTONUM || *wv == LOADDOLLAR ) ) { wv += wv[1]; wm++; n--; } /* Freak problem: doesn't test for n and ran into a remaining code equal to SETTONUM followed by a big number and then ran out of the memory. while ( *wv == FROMSET || *wv == SETTONUM || ( *wv == LOADDOLLAR && n > 0 ) ) { wv += wv[1]; wm++; n--; } */ } } while ( n > 0 ); } /* Now there are only free wildcards left. Possibly the assigned values ate too many vectors. The rest has to be done the 'hard way' via permutations. This is too bad when there are 10 indices. This could cause 10! tries. We try to avoid the worst case by using a very special (somewhat slow) permutation routine that has as its worst cases some rather unlikely configurations, rather than some common ones (as would have been the case with the conventional permutation routine). assume: vvvvvvvvvvvviiiiiii (tvfix in tfixvec and tifix in tfixind) VVVVVVVVVIIIIIIIIII (vwc in wcvec and iwc in wcind) Note: all further assignments are possible at this point! Strategy: permute v permute i loop over the ordered distribution of the leftover v's through the i's. */ if ( tvfix < vwc ) { return(0); } perm1.n = tvfix; perm1.sign = 0; perm1.objects = tfixvec; perm2.n = tifix; perm2.sign = 0; perm2.objects = tfixind; distr.n1 = tvfix - vwc; distr.n2 = tifix; distr.obj1 = tfixvec + vwc; distr.obj2 = tfixind; distr.out = fixvec; /* For scratch */ first1 = 1; /* Store the current Wildcard assignments */ m = AN.WildValue; t = OldWork = AT.WorkPointer; nwstore = i = (m[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; r = AT.WildMask; if ( i > 0 ) { do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); } if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; while ( (first1 = Permute(&perm1,first1) ) == 0 ) { first2 = 1; while ( (first2 = Permute(&perm2,first2) ) == 0 ) { first3 = 1; while ( (first3 = Distribute(&distr,first3) ) == 0 ) { /* Make now the wildcard assignments */ for ( i = 0; i < vwc; i++ ) { j = wcvec[i] - WILDOFFSET; if ( CheckWild(BHEAD j,VECTOVEC,tfixvec[i],&newvalue) ) goto NoCaseB; AddWild(BHEAD j,VECTOVEC,newvalue); } for ( i = 0; i < iwc; i++ ) { j = wcind[i] - WILDOFFSET; if ( CheckWild(BHEAD j,INDTOIND,fixvec[i],&newvalue) ) goto NoCaseB; AddWild(BHEAD j,INDTOIND,newvalue); } /* Go into the recursion */ oRepFunNum = AN.RepFunNum; AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = ( perm1.sign + perm2.sign + distr.sign + sign ) & 1; newpat = pattern + pattern[1]; if ( funwild ) AddWild(BHEAD *pattern-WILDOFFSET,FUNTOFUN,newfun); if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AN.UsedOtherFind = 1; return(1); } } else return(1); } else { /* newter = instart; */ if ( ScanFunctions(BHEAD newpat,inter,par) ) { return(1); } } /* Restore the old Wildcard assignments */ AN.RepFunNum = oRepFunNum; NoCaseB: m = AN.WildValue; t = OldWork; r = AT.WildMask; i = nwstore; if ( i > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --i > 0 ); } AT.WorkPointer = t; } } } AT.WorkPointer = OldWork; return(0); } /* #] MatchE : #[ Permute : WORD Permute(perm,first) Special permutation function. Works recursively. The aim is to cycle through in as fast a way as possible, to take care that each object hits the various positions already early in the game. Start at two: -> cycle of two then three -> cycle of three etc; The innermost cycle is the longest. This is the opposite of the usual way of generating permutations and it is certainly not the fastest one. It allows for the fastest hit in the assignment of wildcards though. */ int Permute(PERM *perm, WORD first) { WORD *s, c, i, j; if ( first ) { perm->sign = ( perm->sign <= 1 ) ? 0: 1; for ( i = 0; i < perm->n; i++ ) perm->cycle[i] = 0; return(0); } i = perm->n; while ( --i > 0 ) { s = perm->objects; c = s[0]; j = i; while ( --j >= 0 ) { *s = s[1]; s++; } *s = c; if ( ( i & 1 ) != 0 ) perm->sign ^= 1; if ( perm->cycle[i] < i ) { (perm->cycle[i])++; return(0); } else { perm->cycle[i] = 0; } } return(1); } /* #] Permute : #[ PermuteP : WORD PermuteP(perm,first) Like Permute, but works on an array of pointers */ int PermuteP(PERMP *perm, WORD first) { WORD **s, *c, i, j; if ( first ) { perm->sign = ( perm->sign <= 1 ) ? 0: 1; for ( i = 0; i < perm->n; i++ ) perm->cycle[i] = 0; return(0); } i = perm->n; while ( --i > 0 ) { s = perm->objects; c = s[0]; j = i; while ( --j >= 0 ) { *s = s[1]; s++; } *s = c; if ( ( i & 1 ) != 0 ) perm->sign ^= 1; if ( perm->cycle[i] < i ) { (perm->cycle[i])++; return(0); } else { perm->cycle[i] = 0; } } return(1); } /* #] PermuteP : #[ Distribute : */ int Distribute(DISTRIBUTE *d, WORD first) { WORD *to, *from, *inc, *from2, i, j; if ( first ) { d->n = d->n1 + d->n2; to = d->out; from = d->obj2; for ( i = 0; i < d->n2; i++ ) { d->cycle[i] = 0; *to++ = *from++; } from = d->obj1; while ( i < d->n ) { d->cycle[i++] = 1; *to++ = *from++; } d->sign = 0; return(0); } if ( d->n1 == 0 || d->n2 == 0 ) return(1); j = 0; i = 0; inc = d->cycle; from = inc + d->n; while ( *inc ) { j++; inc++; } while ( inc < from && !*inc ) { i++; inc++; } if ( inc >= from ) return(1); d->sign ^= ((i&j)-j+1) & 1; *inc = 0; *--inc = 1; while ( --j >= 0 ) *--inc = 1; while ( --i > 0 ) *--inc = 0; to = d->out; from = d->obj1; from2 = d->obj2; for ( i = 0; i < d->n; i++ ) { if ( *inc++ ) { *to++ = *from++; } else { *to++ = *from2++; } } return(0); } /* #] Distribute : #[ MatchCy : Matching of (r)cyclic tensors. Parameters like in MatchE. The structure of the routine is much simpler, because the number of possibilities is much more limited. The major complication is the ?a-type wildcards We need a strategy for T(i1?,?a,i1?,?b). Which is the shorter match: ?a or ?b ? (if possible of course) This is also relevant in the case of the shortest match if there is more than one choice for i1. */ int MatchCy(PHEAD WORD *pattern, WORD *fun, WORD *inter, WORD par) { GETBIDENTITY WORD *t, *tstop, *p, *pstop, *m, *r, *oldworkpointer = AT.WorkPointer; WORD *thewildcards, *multiplicity, *renum, wc, newvalue, oldwilval = 0; WORD *params, *lowlevel = 0; int argcount = 0, funnycount = 0, tcount = fun[1] - FUNHEAD; int type = 0, pnum, i, j, k, nwstore, iraise, itop, sumeat; CBUF *C = cbuf+AT.ebufnum; int ntwa = 3*AN.NumTotWildArgs+1; LONG oldcpointer = C->Pointer - C->Buffer; WORD offset = fun-AN.terstart, *newpat; if ( (functions[fun[0]-FUNCTION].symmetric & ~REVERSEORDER) == RCYCLESYMMETRIC ) type = 1; pnum = pattern[0]; nwstore = (AN.WildValue[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; if ( pnum > FUNCTION + WILDOFFSET ) { pnum -= WILDOFFSET; if ( CheckWild(BHEAD pnum,FUNTOFUN,fun[0],&newvalue) ) return(0); oldwilval = 1; t = lowlevel = AT.WorkPointer; m = AN.WildValue; i = nwstore; r = AT.WildMask; if ( i > 0 ) { do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); } *t++ = C->numrhs; if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; AddWild(BHEAD pnum,FUNTOFUN,newvalue); } if ( (functions[pnum-FUNCTION].symmetric & ~REVERSEORDER) == RCYCLESYMMETRIC ) type = 1; /* First we have to make an inventory. Are there FUNNYWILD pointers? */ p = pattern + FUNHEAD; pstop = pattern + pattern[1]; while ( p < pstop ) { if ( *p == FUNNYWILD ) { p += 2; funnycount++; } else { p++; argcount++; } } if ( argcount > tcount ) goto NoSuccess; if ( argcount < tcount && funnycount == 0 ) goto NoSuccess; if ( argcount == 0 && tcount == 0 && funnycount == 0 ) { AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) return(j); goto NoSuccess; } tstop = fun + fun[1]; /* Store the wildcard assignments */ params = AT.WorkPointer; thewildcards = t = params + tcount; t += ntwa; if ( oldwilval ) lowlevel = oldworkpointer; else lowlevel = t; m = AN.WildValue; i = nwstore; if ( i > 0 ) { r = AT.WildMask; do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); *t++ = C->numrhs; } if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; /* #[ Case 1: no funnies or all funnies must be empty. We just cycle through. */ if ( argcount == tcount ) { if ( funnycount > 0 ) { /* Test all funnies first */ p = pattern + FUNHEAD; t = fun + FUNHEAD; while ( p < pstop ) { if ( *p != FUNNYWILD ) { p++; continue; } AN.argaddress = t; if ( CheckWild(BHEAD p[1],ARGTOARG,0,t) ) goto nomatch; AddWild(BHEAD p[1],ARGTOARG,0); p += 2; } oldwilval = 1; } for ( k = 0; k <= type; k++ ) { if ( k == 0 ) { p = params; t = fun + FUNHEAD; while ( t < tstop ) *p++ = *t++; } else { p = params+tcount; t = fun + FUNHEAD; while ( t < tstop ) *--p = *t++; } for ( i = 0; i < tcount; i++ ) { /* The various cycles */ p = pattern + FUNHEAD; wc = 0; for ( j = 0; j < tcount; j++, p++ ) { /* The arguments */ while ( *p == FUNNYWILD ) p += 2; t = params + (i+j)%tcount; if ( *t == *p ) continue; if ( *p >= AM.OffsetIndex + WILDOFFSET && *p < AM.OffsetIndex + 2*WILDOFFSET ) { /* Test wildcard index */ wc = *p - WILDOFFSET; if ( CheckWild(BHEAD wc,INDTOIND,*t,&newvalue) ) break; AddWild(BHEAD wc,INDTOIND,newvalue); } else if ( *t < MINSPEC && p[j] < MINSPEC && *p >= AM.OffsetVector + WILDOFFSET ) { /* Test wildcard vector */ wc = *p - WILDOFFSET; if ( CheckWild(BHEAD wc,VECTOVEC,*t,&newvalue) ) break; AddWild(BHEAD wc,VECTOVEC,newvalue); } else break; } if ( j >= tcount ) { /* Match! */ /* Continue with other functions. Make sure of the funnies */ AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; if ( funnycount > 0 ) { p = pattern + FUNHEAD; t = fun + FUNHEAD; while ( p < pstop ) { if ( *p != FUNNYWILD ) { p++; continue; } AN.argaddress = t; AddWild(BHEAD p[1],ARGTOARG,0); p += 2; } } newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { AT.WorkPointer = oldworkpointer; return(j); /* Full match. Return our success */ } AN.RepFunNum -= 2; } /* No (deeper) match. -> reset wildcards and continue */ if ( wc && nwstore > 0 ) { j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } } } goto NoSuccess; } /* #] Case 1: #[ Case 2: One FUNNYWILD. Fix its length. */ if ( funnycount == 1 ) { funnycount = tcount - argcount; /* Number or arguments to be eaten */ for ( k = 0; k <= type; k++ ) { if ( k == 0 ) { p = params; t = fun + FUNHEAD; while ( t < tstop ) *p++ = *t++; } else { p = params+tcount; t = fun + FUNHEAD; while ( t < tstop ) *--p = *t++; } for ( i = 0; i < tcount; i++ ) { /* The various cycles */ p = pattern + FUNHEAD; t = params; wc = 0; for ( j = 0; j < tcount; j++, p++, t++ ) { /* The arguments */ if ( *t == *p ) continue; if ( *p == FUNNYWILD ) { p++; wc = 1; AN.argaddress = t; if ( CheckWild(BHEAD *p,ARGTOARG|EATTENSOR,funnycount,t) ) break; AddWild(BHEAD *p,ARGTOARG|EATTENSOR,funnycount); j += funnycount-1; t += funnycount-1; } else if ( *p >= AM.OffsetIndex + WILDOFFSET && *p < AM.OffsetIndex + 2*WILDOFFSET ) { /* Test wildcard index */ wc = *p - WILDOFFSET; if ( CheckWild(BHEAD wc,INDTOIND,*t,&newvalue) ) break; AddWild(BHEAD wc,INDTOIND,newvalue); } else if ( *t < MINSPEC && *p < MINSPEC && *p >= AM.OffsetVector + WILDOFFSET ) { /* Test wildcard vector */ wc = *p - WILDOFFSET; if ( CheckWild(BHEAD wc,VECTOVEC,*t,&newvalue) ) break; AddWild(BHEAD wc,VECTOVEC,newvalue); } else break; } if ( j >= tcount ) { /* Match! */ /* Continue with other functions. Make sure of the funnies */ AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { AT.WorkPointer = oldworkpointer; return(j); /* Full match. Return our success */ } AN.RepFunNum -= 2; } /* No (deeper) match. -> reset wildcards and continue */ if ( wc ) { j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } t = params; wc = *t; for ( j = 1; j < tcount; j++ ) { *t = t[1]; t++; } *t = wc; } } goto NoSuccess; } /* #] Case 2: #[ Case 3: More than one FUNNYWILD. Complicated. */ sumeat = tcount - argcount; /* Total number to be eaten by Funnies */ /* In the first funnycount elements of 'thewildcards' we arrange for the summing over the various possibilities. The renumbering table is in thewildcards[2*funnycount] The multiplicity table is in thewildcards[funnycount] The number of arguments for each is in thewildcards[] */ p = pattern+FUNHEAD; for ( i = funnycount; i < ntwa; i++ ) thewildcards[i] = -1; multiplicity = thewildcards + funnycount; renum = multiplicity + funnycount; j = 0; while ( p < pstop ) { if ( *p != FUNNYWILD ) { p++; continue; } p++; if ( renum[*p] < 0 ) { renum[*p] = j; multiplicity[j] = 1; j++; } else multiplicity[renum[*p]]++; p++; } /* Strategy: First 'declared' has a tendency to be smaller */ for ( i = 1; i < AN.NumTotWildArgs; i++ ) { if ( renum[i] < 0 ) continue; for ( j = i+1; j <= AN.NumTotWildArgs; j++ ) { if ( renum[j] < 0 ) continue; if ( renum[i] < renum[j] ) continue; k = multiplicity[renum[i]]; multiplicity[renum[i]] = multiplicity[renum[j]]; multiplicity[renum[j]] = k; k = renum[i]; renum[i] = renum[j]; renum[j] = k; } } for ( i = 0; i < funnycount; i++ ) thewildcards[i] = 0; iraise = funnycount-1; for ( ;; ) { for ( i = 0, j = sumeat; i < iraise; i++ ) j -= thewildcards[i]*multiplicity[i]; if ( j < 0 || j % multiplicity[iraise] != 0 ) { if ( j > 0 ) { thewildcards[iraise-1]++; continue; } itop = iraise-1; while ( itop > 0 && j < 0 ) { j += thewildcards[itop]*multiplicity[itop]; thewildcards[itop] = 0; itop--; } if ( itop <= 0 && j <= 0 ) break; thewildcards[itop]++; continue; } thewildcards[iraise] = j / multiplicity[iraise]; for ( k = 0; k <= type; k++ ) { if ( k == 0 ) { p = params; t = fun + FUNHEAD; while ( t < tstop ) *p++ = *t++; } else { p = params+tcount; t = fun + FUNHEAD; while ( t < tstop ) *--p = *t++; } for ( i = 0; i < tcount; i++ ) { /* The various cycles */ p = pattern + FUNHEAD; t = params; wc = 0; for ( j = 0; j < tcount; j++, p++, t++ ) { /* The arguments */ if ( *t == *p ) continue; if ( *p == FUNNYWILD ) { p++; wc = thewildcards[renum[*p]]; AN.argaddress = t; if ( CheckWild(BHEAD *p,ARGTOARG|EATTENSOR,wc,t) ) break; AddWild(BHEAD *p,ARGTOARG|EATTENSOR,wc); j += wc-1; t += wc-1; wc = 1; } else if ( *p >= AM.OffsetIndex + WILDOFFSET && *p < AM.OffsetIndex + 2*WILDOFFSET ) { /* Test wildcard index */ wc = *p - WILDOFFSET; if ( CheckWild(BHEAD wc,INDTOIND,*t,&newvalue) ) break; AddWild(BHEAD wc,INDTOIND,newvalue); } else if ( *t < MINSPEC && *p < MINSPEC && *p >= AM.OffsetVector + WILDOFFSET ) { /* Test wildcard vector */ wc = *p - WILDOFFSET; if ( CheckWild(BHEAD wc,VECTOVEC,*t,&newvalue) ) break; AddWild(BHEAD wc,VECTOVEC,newvalue); } else break; } if ( j >= tcount ) { /* Match! */ /* Continue with other functions. Make sure of the funnies */ AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { AT.WorkPointer = oldworkpointer; return(j); /* Full match. Return our success */ } AN.RepFunNum -= 2; } /* No (deeper) match. -> reset wildcards and continue */ if ( wc ) { j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } t = params; wc = *t; for ( j = 1; j < tcount; j++ ) { *t = t[1]; t++; } *t = wc; } } (thewildcards[iraise-1])++; } /* #] Case 3: */ NoSuccess: if ( oldwilval > 0 ) { nomatch:; j = nwstore; if ( j > 0 ) { m = AN.WildValue; t = lowlevel; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } } AT.WorkPointer = oldworkpointer; return(0); } /* #] MatchCy : #[ FunMatchCy : Matching of (r)cyclic functions. Like MatchCy, but now for general functions. */ int FunMatchCy(PHEAD WORD *pattern, WORD *fun, WORD *inter, WORD par) { GETBIDENTITY WORD *t, *tstop, *p, *pstop, *m, *r, *oldworkpointer = AT.WorkPointer; WORD **a, *thewildcards, *multiplicity, *renum, wc, wcc, oldwilval = 0; LONG oww = AT.pWorkPointer; WORD newvalue, *lowlevel = 0; int argcount = 0, funnycount = 0, tcount = 0; int type = 0, pnum, i, j, k, nwstore, iraise, itop, sumeat; CBUF *C = cbuf+AT.ebufnum; int ntwa = 3*AN.NumTotWildArgs+1; LONG oldcpointer = C->Pointer - C->Buffer; WORD offset = fun-AN.terstart, *newpat; if ( (functions[fun[0]-FUNCTION].symmetric & ~REVERSEORDER) == RCYCLESYMMETRIC ) type = 1; pnum = pattern[0]; nwstore = (AN.WildValue[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; if ( pnum > FUNCTION + WILDOFFSET ) { pnum -= WILDOFFSET; if ( CheckWild(BHEAD pnum,FUNTOFUN,fun[0],&newvalue) ) return(0); oldwilval = 1; t = lowlevel = oldworkpointer; m = AN.WildValue; i = nwstore; r = AT.WildMask; if ( i > 0 ) { do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); } *t++ = C->numrhs; if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; AddWild(BHEAD pnum,FUNTOFUN,newvalue); } if ( (functions[pnum-FUNCTION].symmetric & ~REVERSEORDER) == RCYCLESYMMETRIC ) type = 1; /* First we have to make an inventory. Are there -ARGWILD pointers? */ p = pattern + FUNHEAD; pstop = pattern + pattern[1]; while ( p < pstop ) { if ( *p == -ARGWILD ) { p += 2; funnycount++; } else { NEXTARG(p); argcount++; } } t = fun + FUNHEAD; tstop = fun + fun[1]; while ( t < tstop ) { NEXTARG(t); tcount++; } if ( argcount > tcount ) return(0); if ( argcount < tcount && funnycount == 0 ) return(0); if ( argcount == 0 && tcount == 0 && funnycount == 0 ) { AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) return(j); goto NoSuccess; } /* Store the wildcard assignments */ WantAddPointers(tcount); AT.pWorkPointer += tcount; thewildcards = t = AT.WorkPointer; t += ntwa; if ( oldwilval ) lowlevel = oldworkpointer; else lowlevel = t; m = AN.WildValue; i = nwstore; if ( i > 0 ) { r = AT.WildMask; do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); *t++ = C->numrhs; } if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; /* #[ Case 1: no funnies or all funnies must be empty. We just cycle through. */ if ( argcount == tcount ) { if ( funnycount > 0 ) { /* Test all funnies first */ p = pattern + FUNHEAD; t = fun + FUNHEAD; while ( p < pstop ) { if ( *p != -ARGWILD ) { p++; continue; } AN.argaddress = t; if ( CheckWild(BHEAD p[1],ARGTOARG,0,t) ) goto nomatch; AddWild(BHEAD p[1],ARGTOARG,0); p += 2; } oldwilval = 1; } for ( k = 0; k <= type; k++ ) { if ( k == 0 ) { a = AT.pWorkSpace+oww; t = fun + FUNHEAD; while ( t < tstop ) { *a++ = t; NEXTARG(t); } } else { a = AT.pWorkSpace+oww+tcount; t = fun + FUNHEAD; while ( t < tstop ) { *--a = t; NEXTARG(t); } } for ( i = 0; i < tcount; i++ ) { /* The various cycles */ p = pattern + FUNHEAD; wc = 0; for ( j = 0; j < tcount; j++ ) { /* The arguments */ while ( *p == -ARGWILD ) p += 2; t = AT.pWorkSpace[oww+((i+j)%tcount)]; if ( ( wcc = MatchArgument(BHEAD t,p) ) == 0 ) break; if ( wcc > 1 ) wc = 1; NEXTARG(p); } if ( j >= tcount ) { /* Match! */ /* Continue with other functions. Make sure of the funnies */ AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; if ( funnycount > 0 ) { p = pattern + FUNHEAD; t = fun + FUNHEAD; while ( p < pstop ) { if ( *p != -ARGWILD ) { p++; continue; } AN.argaddress = t; AddWild(BHEAD p[1],ARGTOARG,0); p += 2; } } newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(j); /* Full match. Return our success */ } AN.RepFunNum -= 2; } /* No (deeper) match. -> reset wildcards and continue */ if ( wc && nwstore > 0 ) { j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } } } goto NoSuccess; } /* #] Case 1: #[ Case 2: One -ARGWILD. Fix its length. */ if ( funnycount == 1 ) { funnycount = tcount - argcount; /* Number or arguments to be eaten */ for ( k = 0; k <= type; k++ ) { if ( k == 0 ) { a = AT.pWorkSpace+oww; t = fun + FUNHEAD; while ( t < tstop ) { *a++ = t; NEXTARG(t); } } else { a = AT.pWorkSpace+oww+tcount; t = fun + FUNHEAD; while ( t < tstop ) { *--a = t; NEXTARG(t); } } for ( i = 0; i < tcount; i++ ) { /* The various cycles */ p = pattern + FUNHEAD; a = AT.pWorkSpace+oww; wc = 0; for ( j = 0; j < tcount; j++, a++ ) { /* The arguments */ t = *a; if ( *p == -ARGWILD ) { wc = 1; AN.argaddress = (WORD *)a; if ( CheckWild(BHEAD p[1],ARLTOARL,funnycount,(WORD *)a) ) break; AddWild(BHEAD p[1],ARLTOARL,funnycount); j += funnycount-1; a += funnycount-1; } else if ( MatchArgument(BHEAD t,p) == 0 ) break; NEXTARG(p); } if ( j >= tcount ) { /* Match! */ /* Continue with other functions. Make sure of the funnies */ AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(j); /* Full match. Return our success */ } AN.RepFunNum -= 2; } /* No (deeper) match. -> reset wildcards and continue */ if ( wc ) { j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } a = AT.pWorkSpace+oww; t = *a; for ( j = 1; j < tcount; j++ ) { *a = a[1]; a++; } *a = t; } } goto NoSuccess; } /* #] Case 2: #[ Case 3: More than one -ARGWILD. Complicated. */ sumeat = tcount - argcount; /* Total number to be eaten by Funnies */ /* In the first funnycount elements of 'thewildcards' we arrange for the summing over the various possibilities. The renumbering table is in thewildcards[2*funnycount] The multiplicity table is in thewildcards[funnycount] The number of arguments for each is in thewildcards[] */ p = pattern+FUNHEAD; for ( i = funnycount; i < ntwa; i++ ) thewildcards[i] = -1; multiplicity = thewildcards + funnycount; renum = multiplicity + funnycount; j = 0; while ( p < pstop ) { if ( *p != -ARGWILD ) { p++; continue; } p++; if ( renum[*p] < 0 ) { renum[*p] = j; multiplicity[j] = 1; j++; } else multiplicity[renum[*p]]++; p++; } /* Strategy: First 'declared' has a tendency to be smaller */ for ( i = 1; i < AN.NumTotWildArgs; i++ ) { if ( renum[i] < 0 ) continue; for ( j = i+1; j <= AN.NumTotWildArgs; j++ ) { if ( renum[j] < 0 ) continue; if ( renum[i] < renum[j] ) continue; k = multiplicity[renum[i]]; multiplicity[renum[i]] = multiplicity[renum[j]]; multiplicity[renum[j]] = k; k = renum[i]; renum[i] = renum[j]; renum[j] = k; } } for ( i = 0; i < funnycount; i++ ) thewildcards[i] = 0; iraise = funnycount-1; for ( ;; ) { for ( i = 0, j = sumeat; i < iraise; i++ ) j -= thewildcards[i]*multiplicity[i]; if ( j < 0 || j % multiplicity[iraise] != 0 ) { if ( j > 0 ) { thewildcards[iraise-1]++; continue; } itop = iraise-1; while ( itop > 0 && j < 0 ) { j += thewildcards[itop]*multiplicity[itop]; thewildcards[itop] = 0; itop--; } if ( itop <= 0 && j <= 0 ) break; thewildcards[itop]++; continue; } thewildcards[iraise] = j / multiplicity[iraise]; for ( k = 0; k <= type; k++ ) { if ( k == 0 ) { a = AT.pWorkSpace+oww; t = fun + FUNHEAD; while ( t < tstop ) { *a++ = t; NEXTARG(t); } } else { a = AT.pWorkSpace+oww+tcount; t = fun + FUNHEAD; while ( t < tstop ) { *--a = t; NEXTARG(t); } } for ( i = 0; i < tcount; i++ ) { /* The various cycles */ p = pattern + FUNHEAD; a = AT.pWorkSpace+oww; wc = 0; for ( j = 0; j < tcount; j++, a++ ) { /* The arguments */ t = *a; if ( *p == -ARGWILD ) { wc = thewildcards[renum[p[1]]]; AN.argaddress = (WORD *)a; if ( CheckWild(BHEAD p[1],ARLTOARL,wc,(WORD *)a) ) break; AddWild(BHEAD p[1],ARLTOARL,wc); j += wc-1; a += wc-1; wc = 1; } else if ( MatchArgument(BHEAD t,p) == 0 ) break; NEXTARG(p); } if ( j >= tcount ) { /* Match! */ /* Continue with other functions. Make sure of the funnies */ AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = 0; newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(j); /* Full match. Return our success */ } AN.RepFunNum -= 2; } /* No (deeper) match. -> reset wildcards and continue */ if ( wc ) { j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } a = AT.pWorkSpace+oww; t = *a; for ( j = 1; j < tcount; j++ ) { *a = a[1]; a++; } *a = t; } } (thewildcards[iraise-1])++; } /* #] Case 3: */ NoSuccess: if ( oldwilval > 0 ) { nomatch:; j = nwstore; m = AN.WildValue; t = lowlevel; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(0); } /* #] FunMatchCy : #[ FunMatchSy : Matching of (anti)symmetric functions. Like MatchE, but now for general functions. */ int FunMatchSy(PHEAD WORD *pattern, WORD *fun, WORD *inter, WORD par) { GETBIDENTITY WORD *t, *tstop, *p, *pstop, *m, *r, *oldworkpointer = AT.WorkPointer; WORD **a, *thewildcards, oldwilval = 0; WORD newvalue, *lowlevel = 0, num, assig; WORD *cycles; LONG oww = AT.pWorkPointer, lhpars, lhfunnies; int argcount = 0, funnycount = 0, tcount = 0, signs = 0, signfun = 0, signo; int type = 0, pnum, i, j, k, nwstore, iraise, cou2; CBUF *C = cbuf+AT.ebufnum; int ntwa = 3*AN.NumTotWildArgs+1; LONG oldcpointer = C->Pointer - C->Buffer; WORD offset = fun-AN.terstart, *newpat; if ( (functions[fun[0]-FUNCTION].symmetric & ~REVERSEORDER) == RCYCLESYMMETRIC ) type = 1; pnum = pattern[0]; nwstore = (AN.WildValue[-SUBEXPSIZE+1]-SUBEXPSIZE)/4; if ( pnum > FUNCTION + WILDOFFSET ) { pnum -= WILDOFFSET; if ( CheckWild(BHEAD pnum,FUNTOFUN,fun[0],&newvalue) ) return(0); oldwilval = 1; t = lowlevel = oldworkpointer; m = AN.WildValue; i = nwstore; r = AT.WildMask; if ( i > 0 ) { do { *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); } *t++ = C->numrhs; if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; AddWild(BHEAD pnum,FUNTOFUN,newvalue); } if ( (functions[pnum-FUNCTION].symmetric & ~REVERSEORDER) == RCYCLESYMMETRIC ) type = 1; /* Try for a straight match. After all, both have been normalized */ if ( fun[1] == pattern[1] ) { i = fun[1]-FUNHEAD; p = pattern+FUNHEAD; t = fun + FUNHEAD; while ( --i >= 0 ) { if ( *p++ != *t++ ) break; } if ( i < 0 ) goto quicky; } /* First we have to make an inventory. Are there -ARGWILD pointers? */ p = pattern + FUNHEAD; pstop = pattern + pattern[1]; while ( p < pstop ) { if ( *p == -ARGWILD ) { p += 2; funnycount++; } else { NEXTARG(p); argcount++; } } t = fun + FUNHEAD; tstop = fun + fun[1]; while ( t < tstop ) { NEXTARG(t); tcount++; } if ( argcount > tcount ) return(0); if ( argcount < tcount && funnycount == 0 ) return(0); if ( argcount == 0 && tcount == 0 && funnycount == 0 ) { quicky: if ( AN.SignCheck && signs != AN.ExpectedSign ) goto NoSuccess; AN.RepFunList[AN.RepFunNum++] = offset; AN.RepFunList[AN.RepFunNum++] = signs; newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AN.UsedOtherFind = 1; return(1); } j = 0; } else { AT.WorkPointer = oldworkpointer; return(1); } } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { AT.WorkPointer = oldworkpointer; return(j); } goto NoSuccess; } /* Store the wildcard assignments */ WantAddPointers(tcount+argcount+funnycount); AT.pWorkPointer += tcount+argcount+funnycount; thewildcards = t = AT.WorkPointer; t += ntwa; if ( oldwilval ) lowlevel = oldworkpointer; else lowlevel = t; m = AN.WildValue; i = nwstore; assig = 0; if ( i > 0 ) { r = AT.WildMask; do { assig += *r; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *m++; *t++ = *r++; } while ( --i > 0 ); *t++ = C->numrhs; } if ( t >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AT.WorkPointer = t; /* Store pointers to the arguments */ t = fun + FUNHEAD; a = AT.pWorkSpace+oww; while ( t < tstop ) { *a++ = t; NEXTARG(t) } lhpars = a-AT.pWorkSpace; t = pattern + FUNHEAD; while ( t < pstop ) { if ( *t != -ARGWILD ) *a++ = t; NEXTARG(t) } lhfunnies = a-AT.pWorkSpace; t = pattern + FUNHEAD; cou2 = 0; while ( t < pstop ) { cou2++; if ( *t == -ARGWILD ) { *a++ = t; /* signfun: last ?a: tcount-argcount: number of arguments in ?a (assume one ?a) argcount+funnycount-cou2: arguments after ?a. Together tells whether moving ?a to end of list is even or odd */ signfun = ((argcount+funnycount-cou2)*(tcount-argcount)) & 1; } NEXTARG(t) } signs += signfun; if ( funnycount > 0 ) { if ( ( (functions[fun[0]-FUNCTION].symmetric & ~REVERSEORDER) == SYMMETRIC ) || ( (functions[fun[0]-FUNCTION].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) || ( (functions[pnum-FUNCTION].symmetric & ~REVERSEORDER) == SYMMETRIC ) || ( (functions[pnum-FUNCTION].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; MLOCK(ErrorMessageLock); MesPrint("Sorry: no argument field wildcards yet in (anti)symmetric functions"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } /* Sort the regular arguments by 1: no wildcards, fast. 2: wildcards that have been assigned. 3: general arguments. 4: wildcards without an assignment. */ iraise = argcount; for ( i = 0; i < iraise; i++ ) { t = AT.pWorkSpace[i+lhpars]; if ( *t > 0 ) { /* Category 3: general argument */ continue; } else if ( *t <= -FUNCTION ) { if ( *t > -FUNCTION - WILDOFFSET ) goto cat1; type = FUNTOFUN; num = -*t - WILDOFFSET; } else if ( *t == -SYMBOL ) { if ( t[1] < 2*MAXPOWER ) goto cat1; type = SYMTOSYM; num = t[1] - 2*MAXPOWER; } else if ( *t == -INDEX ) { if ( t[1] < AM.OffsetIndex + WILDOFFSET ) goto cat1; type = INDTOIND; num = t[1] - WILDOFFSET; } else if ( *t == -VECTOR || *t == -MINVECTOR ) { if ( t[1] < AM.OffsetVector + WILDOFFSET ) goto cat1; type = VECTOVEC; num = t[1] - WILDOFFSET; } else goto cat1; /* Things like -SNUMBER etc. */ /* Now we have a wildcard and have to see whether it was assigned */ m = AN.WildValue; j = nwstore; r = AT.WildMask; while ( --j >= 0 ) { if ( m[2] == num && *r ) { if ( type == *m ) break; if ( type == SYMTOSYM ) { if ( *m == SYMTONUM || *m == SYMTOSUB ) break; } else if ( type == INDTOIND ) { if ( *m == INDTOSUB ) break; } else if ( type == VECTOVEC ) { if ( *m == VECTOMIN || *m == VECTOSUB ) break; } } m += 4; r++; } if ( j < 0 ) { /* Category 4: Wildcard that was not assigned */ a = AT.pWorkSpace+lhpars; iraise--; if ( iraise != i ) signs++; m = a[iraise]; a[iraise] = a[i]; a[i] = m; i--; } else { /* Category 2: Wildcard that was assigned */ for ( j = 0; j < tcount; j++ ) { if ( MatchArgument(BHEAD AT.pWorkSpace[oww+j],t) ) { k = nwstore; r = AT.WildMask; num = 0; while ( --k >= 0 ) num += *r++; if ( num == assig ) { /* no wildcards were changed */ goto oneless; } break; } } if ( j >= tcount ) goto NoSuccess; j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { /* undo assignment */ *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; } continue; cat1: for ( j = 0; j < tcount; j++ ) { m = AT.pWorkSpace[j+oww]; if ( *t != *m ) continue; if ( *t < 0 ) { if ( *t <= -FUNCTION ) break; if ( t[1] == m[1] ) break; } else { k = *t; r = t; while ( --k >= 0 && *m++ == *r++ ) {} if ( k < 0 ) break; } } if ( j >= tcount ) goto NoSuccess; /* Even the fixed ones don't match */ oneless: signs += j - i; /* The next statements replace the one that is commented out */ tcount--; while ( j < tcount ) { AT.pWorkSpace[oww+j] = AT.pWorkSpace[oww+j+1]; j++; } /* AT.pWorkSpace[oww+j] = AT.pWorkSpace[oww+(--tcount)]; */ argcount--; j = i; while ( j < argcount ) { AT.pWorkSpace[lhpars+j] = AT.pWorkSpace[lhpars+j+1]; j++; } iraise--; i--; } /* Now we see whether there are any ARGWILD objects that have been assigned already. In that case the work simplifies considerably. Currently (12-nov-2001) only in (R)CYCLIC functions; hence we do not test the sign! */ for ( i = 0; i < funnycount; i++ ) { k = AT.pWorkSpace[lhfunnies+i][1]; m = AN.WildValue; j = nwstore; r = AT.WildMask; while ( --j >= 0 ) { if ( *m == ARGTOARG && m[2] == k ) break; m += 4; r++; } if ( *r == 0 ) continue; /* not assigned yet */ m = cbuf[AT.ebufnum].rhs[m[3]]; if ( *m > 0 ) { /* Tensor arguments */ j = *m; if ( j > tcount - argcount ) goto NoSuccess; while ( --j >= 0 ) { m++; if ( *m < 0 ) type = -VECTOR; else if ( *m < AM.OffsetIndex ) type = -SNUMBER; else type = -INDEX; a = AT.pWorkSpace+oww; for ( k = 0; k < tcount; k++ ) { if ( a[k][0] != type || a[k][1] != *m ) continue; a[k] = a[--tcount]; goto nextjarg; } goto NoSuccess; nextjarg:; } } else { m++; while ( *m ) { for ( k = 0; k < tcount; k++ ) { t = AT.pWorkSpace[oww+k]; if ( *t != *m ) continue; r = m; if ( *r < 0 ) { if ( *r < -FUNCTION ) goto nextargw; else if ( r[1] == t[1] ) goto nextargw; } else { j = *r; while ( --j >= 0 && *r++ == *t++ ) {} if ( j < 0 ) goto nextargw; } } goto NoSuccess; nextargw:; AT.pWorkSpace[oww+k] = AT.pWorkSpace[oww+(--tcount)]; NEXTARG(m) } } AT.pWorkSpace[lhfunnies+i] = AT.pWorkSpace[lhfunnies+(--funnycount)]; } if ( tcount == 0 ) { if ( argcount > 0 ) goto NoSuccess; for ( i = 0; i < funnycount; i++ ) { AddWild(BHEAD AT.pWorkSpace[lhfunnies+i][1],ARGTOARG,0); } goto quicky; } /* We have now in lhpars first iraise elements with a dubious nature. Then argcount-iraise wildcards that have not been assigned. In lhfunnies we have funnycount ARGTOARG objects. ( (R)CyCLIC only ) First work our way through the 'dubious' objects We check whether assig changes. */ for ( i = 0; i < iraise; i++ ) { for ( j = 0; j < tcount; j++ ) { if ( MatchArgument(BHEAD AT.pWorkSpace[oww+j],AT.pWorkSpace[lhpars+i]) ) { k = nwstore; r = AT.WildMask; num = 0; while ( --k >= 0 ) num += *r++; if ( num == assig ) { /* no wildcards were changed */ signs += j-i; AT.pWorkSpace[oww+j] = AT.pWorkSpace[oww+(--tcount)]; if ( tcount > j ) signs += tcount-j-1; argcount--; a = AT.pWorkSpace + lhpars; for ( j = i; j < argcount; j++ ) a[j] = a[j+1]; iraise--; goto nextiraise; } else { /* We cannot use this yet */ j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { /* undo assignment */ *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; goto nextiraise; } } } goto NoSuccess; nextiraise:; } /* Now all leftover patterns have unassigned wildcards in them. From now on we are in potential factorial territory. Strategy: 1: cycle through the regular objects. 2: save wildcard settings 3: divide the ARGWILDs 4: make permutations of leftover arguments 5: try them all */ cycles = AT.WorkPointer; for ( i = 0; i < tcount; i++ ) cycles[i] = tcount-i; AT.WorkPointer += tcount; signo = 0; /*MesPrint("<1> signs = %d",signs);*/ for (;;) { WORD oRepFunNum = AN.RepFunNum; for ( j = 0; j < argcount; j++ ) { if ( MatchArgument(BHEAD AT.pWorkSpace[oww+j],AT.pWorkSpace[lhpars+j]) == 0 ) { break; } } if ( j >= argcount ) { /* Thus far we have a match. Now the funnies */ if ( funnycount ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; MLOCK(ErrorMessageLock); MesPrint("Sorry: no argument field wildcards yet in (anti)symmetric functions"); MUNLOCK(ErrorMessageLock); /* Bugfix 31-oct-2001, reported by Kasper Peeters We returned here with value -1 but that is not caught. Extra note (12-nov-2001): the sign becomes a bit problematic if we have funnies. No more than one allowed in antisymmetric functions, or we have serious problems. */ Terminate(-1); } AN.RepFunList[AN.RepFunNum++] = offset; if ( ( (functions[fun[0]-FUNCTION].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) || ( (functions[pnum-FUNCTION].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) ) { AN.RepFunList[AN.RepFunNum++] = ( signs + signo ) & 1; } else { AN.RepFunList[AN.RepFunNum++] = 0; } newpat = pattern + pattern[1]; if ( newpat >= AN.patstop ) { WORD countsgn, sgn = 0; for ( countsgn = oRepFunNum+1; countsgn < AN.RepFunNum; countsgn += 2 ) { if ( AN.RepFunList[countsgn] ) sgn ^= 1; } if ( AN.SignCheck == 0 || sgn == AN.ExpectedSign ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(1); } if ( AN.UseFindOnly == 0 ) { if ( FindOnce(BHEAD AN.findTerm,AN.findPattern) ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; AN.UsedOtherFind = 1; return(1); } } j = 0; } else j = ScanFunctions(BHEAD newpat,inter,par); if ( j ) { WORD countsgn, sgn = 0; for ( countsgn = oRepFunNum+1; countsgn < AN.RepFunNum; countsgn += 2 ) { if ( AN.RepFunList[countsgn] ) sgn ^= 1; } if ( AN.SignCheck == 0 || sgn == AN.ExpectedSign ) { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(j); } } AN.RepFunNum = oRepFunNum; i = argcount - 1; } else i = j; j = nwstore; m = AN.WildValue; t = thewildcards + ntwa; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; /* On to the next cycle */ a = AT.pWorkSpace + oww; for ( j = i+1, t = a[i]; j < tcount; j++ ) a[j-1] = a[j]; a[tcount-1] = t; cycles[i]--; signo += tcount - i - 1; while ( cycles[i] <= 0 ) { cycles[i] = tcount - i; i--; if ( i < 0 ) goto NoSuccess; /* MLOCK(ErrorMessageLock); MesPrint("Cycle i = %d",i); MUNLOCK(ErrorMessageLock); */ for ( j = i+1, t = a[i]; j < tcount; j++ ) a[j-1] = a[j]; a[tcount-1] = t; cycles[i]--; signo += tcount - i - 1; } } NoSuccess: if ( oldwilval > 0 ) { j = nwstore; m = AN.WildValue; t = lowlevel; r = AT.WildMask; if ( j > 0 ) { do { *m++ = *t++; *m++ = *t++; *m++ = *t++; *m++ = *t++; *r++ = *t++; } while ( --j > 0 ); } C->numrhs = *t++; C->Pointer = C->Buffer + oldcpointer; } AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oww; return(0); } /* #] FunMatchSy : #[ MatchArgument : */ int MatchArgument(PHEAD WORD *arg, WORD *pat) { GETBIDENTITY WORD *m = pat, *t = arg, i, j, newvalue; WORD *argmstop = pat, *argtstop = arg; WORD *cto, *cfrom, *csav, ci; WORD oRepFunNum, *oRepFunList; WORD *oterstart,*oterstop,*opatstop; WORD wildargs, wildeat; WORD *mtrmstop, *ttrmstop, *msubstop, msizcoef; WORD *wildargtaken; int wc = 1; NEXTARG(argmstop); NEXTARG(argtstop); /* #[ Both fast : */ if ( *m < 0 && *t < 0 ) { if ( *t <= -FUNCTION ) { if ( *t == *m ) {} else if ( *m <= -FUNCTION-WILDOFFSET && functions[-*t-FUNCTION].spec == functions[-*m-FUNCTION-WILDOFFSET].spec ) { i = -*m - WILDOFFSET; wc = 2; if ( CheckWild(BHEAD i,FUNTOFUN,-*t,&newvalue) ) { return(0); } AddWild(BHEAD i,FUNTOFUN,newvalue); } else if ( *m == -SYMBOL && m[1] >= 2*MAXPOWER ) { i = m[1] - 2*MAXPOWER; AN.argaddress = AT.FunArg; AT.FunArg[ARGHEAD+1] = -*t; if ( CheckWild(BHEAD i,SYMTOSUB,1,AN.argaddress) ) return(0); AddWild(BHEAD i,SYMTOSUB,0); } else return(0); } else if ( *t == *m ) { if ( t[1] == m[1] ) {} else if ( *t == -SYMBOL ) { j = SYMTOSYM; SymAll: if ( ( i = m[1] - 2*MAXPOWER ) < 0 ) return(0); wc = 2; if ( CheckWild(BHEAD i,j,t[1],&newvalue) ) return(0); AddWild(BHEAD i,j,newvalue); } else if ( *t == -INDEX ) { IndAll: i = m[1] - WILDOFFSET; if ( i < AM.OffsetIndex || i >= WILDOFFSET+AM.OffsetIndex ) return(0); /* We kill the summed over indices here */ wc = 2; if ( CheckWild(BHEAD i,INDTOIND,t[1],&newvalue) ) return(0); AddWild(BHEAD i,INDTOIND,newvalue); } else if ( *t == -VECTOR || *t == -MINVECTOR ) { i = m[1] - WILDOFFSET; if ( i < AM.OffsetVector ) return(0); wc = 2; if ( CheckWild(BHEAD i,VECTOVEC,t[1],&newvalue) ) return(0); AddWild(BHEAD i,VECTOVEC,newvalue); } else return(0); } else if ( *m == -INDEX && m[1] >= AM.OffsetIndex+WILDOFFSET && m[1] < AM.OffsetIndex+(WILDOFFSET<<1) ) { if ( *t == -VECTOR ) goto IndAll; if ( *t == -SNUMBER && t[1] >= 0 && t[1] < AM.OffsetIndex ) goto IndAll; if ( *t == -MINVECTOR ) { i = m[1] - WILDOFFSET; AN.argaddress = AT.MinVecArg; AT.MinVecArg[ARGHEAD+3] = t[1]; wc = 2; if ( CheckWild(BHEAD i,INDTOSUB,1,AN.argaddress) ) return(0); AddWild(BHEAD i,INDTOSUB,(WORD)0); } else return(0); } else if ( *m == -SYMBOL && m[1] >= 2*MAXPOWER && *t == -SNUMBER ) { j = SYMTONUM; goto SymAll; } else if ( *m == -VECTOR && *t == -MINVECTOR && ( i = m[1] - WILDOFFSET ) >= AM.OffsetVector ) { wc = 2; /* AN.argaddress = AT.MinVecArg; AT.MinVecArg[ARGHEAD+3] = t[1]; if ( CheckWild(BHEAD i,VECTOSUB,1,AN.argaddress) ) return(0); AddWild(BHEAD i,VECTOSUB,(WORD)0); */ if ( CheckWild(BHEAD i,VECTOMIN,t[1],&newvalue) ) return(0); AddWild(BHEAD i,VECTOMIN,newvalue); } else if ( *m == -MINVECTOR && *t == -VECTOR && ( i = m[1] - WILDOFFSET ) >= AM.OffsetVector ) { wc = 2; /* AN.argaddress = AT.MinVecArg; AT.MinVecArg[ARGHEAD+3] = t[1]; if ( CheckWild(BHEAD i,VECTOSUB,1,AN.argaddress) ) return(0); AddWild(BHEAD i,VECTOSUB,(WORD)0); */ if ( CheckWild(BHEAD i,VECTOMIN,t[1],&newvalue) ) return(0); AddWild(BHEAD i,VECTOMIN,newvalue); } else return(0); } /* #] Both fast : #[ Fast arg : */ else if ( *m > 0 && *t <= -FUNCTION ) { if ( ( m[ARGHEAD]+ARGHEAD == *m ) && m[*m-1] == 3 && m[*m-2] == 1 && m[*m-3] == 1 && m[ARGHEAD+1] >= FUNCTION && m[ARGHEAD+2] == *m-ARGHEAD-4 ) { /* Check for f(?a) etc */ WORD *mmmst, *mmm, mmmi; if ( m[ARGHEAD+1] >= FUNCTION+WILDOFFSET ) { mmmi = *m - WILDOFFSET; wc = 2; if ( CheckWild(BHEAD mmmi,FUNTOFUN,-*t,&newvalue) ) return(0); AddWild(BHEAD mmmi,FUNTOFUN,newvalue); } else if ( m[ARGHEAD+1] != -*t ) return(0); /* Only arguments allowed are ?a etc. */ mmmst = m+*m-3; mmm = m + ARGHEAD + FUNHEAD + 1; while ( mmm < mmmst ) { if ( *mmm != -ARGWILD ) return(0); mmmi = 0; AN.argaddress = t; wc = 2; if ( CheckWild(BHEAD mmm[1],ARGTOARG,mmmi,t) ) return(0); AddWild(BHEAD mmm[1],ARGTOARG,mmmi); mmm += 2; } } else return(0); } /* #] Fast arg : #[ Fast pat : */ else if ( *m < 0 && *t > 0 ) { if ( *m == -SYMBOL ) { /* SYMTOSUB */ if ( m[1] < 2*MAXPOWER ) return(0); i = m[1] - 2*MAXPOWER; AN.argaddress = t; wc = 2; if ( CheckWild(BHEAD i,SYMTOSUB,1,AN.argaddress) ) return(0); AddWild(BHEAD i,SYMTOSUB,0); } else if ( *m == -VECTOR ) { if ( ( i = m[1] - WILDOFFSET ) < AM.OffsetVector ) return(0); AN.argaddress = t; wc = 2; if ( CheckWild(BHEAD i,VECTOSUB,1,t) ) return(0); AddWild(BHEAD i,VECTOSUB,(WORD)0); } else if ( *m == -INDEX ) { if ( ( i = m[1] - WILDOFFSET ) < AM.OffsetIndex ) return(0); if ( i >= AM.OffsetIndex + WILDOFFSET ) return(0); AN.argaddress = t; wc = 2; if ( CheckWild(BHEAD i,INDTOSUB,1,AN.argaddress) ) return(0); AddWild(BHEAD i,INDTOSUB,(WORD)0); } else return(0); } /* #] Fast pat : #[ Both general : */ else if ( *m > 0 && *t > 0 ) { i = *m; do { if ( *m++ != *t++ ) break; } while ( --i > 0 ); if ( i > 0 ) { /* Not an exact match here. We have to hope that the pattern contains a composite wildcard. */ m = pat; t = arg; m += ARGHEAD; t += ARGHEAD; /* Point at (first?) term */ mtrmstop = m + *m; ttrmstop = t + *t; if ( mtrmstop < argmstop ) return(0);/* More than one term */ msizcoef = mtrmstop[-1]; if ( msizcoef < 0 ) msizcoef = -msizcoef; msubstop = mtrmstop - msizcoef; m++; if ( m >= msubstop ) return(0); /* Only coefficient */ /* Here we have a composite term. It can match provided it matches the entire argument. This argument must be a single term also and the coefficients should match (more or less). The matching takes: 1: Match the functions etc. Nothing can be left. 2: Match dotproducts and symbols. ONLY must match and nothing may be left. For safety it is best to take the term out and put it in workspace. */ if ( argtstop > ttrmstop ) return(0); m--; oterstart = AN.terstart; oterstop = AN.terstop; opatstop = AN.patstop; oRepFunList = AN.RepFunList; oRepFunNum = AN.RepFunNum; AN.RepFunNum = 0; wildargtaken = AT.WorkPointer; AN.RepFunList = wildargtaken + AN.NumTotWildArgs; AT.WorkPointer = (WORD *)(((UBYTE *)(AN.RepFunList)) + AM.MaxTer/2); csav = cto = AT.WorkPointer; cfrom = t; ci = *t; while ( --ci >= 0 ) *cto++ = *cfrom++; AT.WorkPointer = cto; ci = msizcoef; cfrom = mtrmstop; while ( --ci >= 0 ) { if ( *--cfrom != *--cto ) { AT.WorkPointer = wildargtaken; AN.RepFunList = oRepFunList; AN.RepFunNum = oRepFunNum; AN.terstart = oterstart; AN.terstop = oterstop; AN.patstop = opatstop; return(0); } } *m -= msizcoef; wildargs = AN.WildArgs; wildeat = AN.WildEat; for ( i = 0; i < wildargs; i++ ) wildargtaken[i] = AT.WildArgTaken[i]; AN.ForFindOnly = 0; AN.UseFindOnly = 1; AN.nogroundlevel++; if ( FindRest(BHEAD csav,m) && ( AN.UsedOtherFind || FindOnly(BHEAD csav,m) ) ) { } else { *m += msizcoef; AT.WorkPointer = wildargtaken; AN.RepFunList = oRepFunList; AN.RepFunNum = oRepFunNum; AN.terstart = oterstart; AN.terstop = oterstop; AN.patstop = opatstop; AN.WildArgs = wildargs; AN.WildEat = wildeat; AN.nogroundlevel--; for ( i = 0; i < wildargs; i++ ) AT.WildArgTaken[i] = wildargtaken[i]; return(0); } AN.nogroundlevel--; AN.WildArgs = wildargs; AN.WildEat = wildeat; for ( i = 0; i < wildargs; i++ ) AT.WildArgTaken[i] = wildargtaken[i]; Substitute(BHEAD csav,m,1); cto = csav; cfrom = cto + *cto - msizcoef; cto++; *m += msizcoef; AT.WorkPointer = wildargtaken; AN.RepFunList = oRepFunList; AN.RepFunNum = oRepFunNum; AN.terstart = oterstart; AN.terstop = oterstop; AN.patstop = opatstop; if ( *cto != SUBEXPRESSION ) return(0); cto += cto[1]; if ( cto < cfrom ) return(0); } } /* #] Both general : */ else return(0); /* And now the success: (wc = 2 means that there was a wildcard involved) */ return(wc); } /* #] MatchArgument : */ form-5.0.1/sources/argument.c0000644000175100017510000026434115217035721011631 /** @file argument.c * * Contains the routines that deal with the execution phase of the argument * and related statements (like term) */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ include : argument.c */ #include "form3.h" /* #] include : #[ execarg : Executes the subset of statements in an argument environment. The calling routine should be of the type if ( C->lhs[level][0] == TYPEARG ) { if ( execarg(term,level) ) goto GenCall; level = C->lhs[level][2]; goto SkipCount; } Note that there will be cases in which extra space is needed. In addition the compare with C->numlhs isn't very fine, because we need to insert a different value (C->lhs[level][2]). */ int execarg(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD *t, *r, *m, *v; WORD *start, *stop, *rstop, *r1, *r2 = 0, *r3 = 0, *r4, *r5, *r6, *r7, *r8, *r9; WORD *mm, *mstop, *rnext, *rr, *factor, type, ngcd, nq; CBUF *C = cbuf+AM.rbufnum, *CC = cbuf+AT.ebufnum; WORD i, j, k, oldnumlhs = AR.Cnumlhs, count, olddefer = AR.DeferFlag; int action = 0; WORD oldnumrhs = CC->numrhs, size, pow, jj; LONG oldcpointer = CC->Pointer - CC->Buffer, oldppointer = AT.pWorkPointer, lp; WORD *oldwork = AT.WorkPointer, *oldwork2, scale, renorm; WORD kLCM = 0, kGCD = 0, kGCD2, kkLCM = 0, jLCM = 0, jGCD, sign = 1; int ii, didpolyratfun; UWORD *EAscrat, *GCDbuffer = 0, *GCDbuffer2 = 0, *LCMbuffer = 0, *LCMb = 0, *LCMc = 0; AT.WorkPointer += *term; start = C->lhs[level]; AR.Cnumlhs = start[2]; stop = start + start[1]; type = *start; scale = start[4]; renorm = start[5]; start += TYPEARGHEADSIZE; /* #[ Dollars : */ if ( renorm && start[1] != 0 ) {/* We have to evaluate $ symbols inside () */ t = start+1; factor = oldwork2 = v = AT.WorkPointer; i = *t; t++; *v++ = i+3; i--; NCOPY(v,t,i); *v++ = 1; *v++ = 1; *v++ = 3; AT.WorkPointer = v; start = t; AR.Eside = LHSIDEX; NewSort(BHEAD0); if ( Generator(BHEAD factor,AR.Cnumlhs) ) { LowerSortLevel(); AT.WorkPointer = oldwork; return(-1); } AT.WorkPointer = v; if ( EndSort(BHEAD factor,0) < 0 ) {} if ( *factor && *(factor+*factor) != 0 ) { MLOCK(ErrorMessageLock); MesPrint("&$ in () does not evaluate into a single term"); MUNLOCK(ErrorMessageLock); return(-1); } AR.Eside = RHSIDE; if ( *factor > 0 ) { v = factor+*factor; v -= ABS(v[-1]); *factor = v-factor; } AT.WorkPointer = v; } else { if ( *start < 0 ) { factor = start + 1; start += -*start; } else factor = 0; } /* #] Dollars : */ t = term; r = t + *t; rstop = r - ABS(r[-1]); t++; /* #[ Argument detection : + argument statement */ /* Allocate Numbers for MakeInteger here, for re-use in case multiple functions are treated in the same term. */ if ( type == TYPENORM4 ) { GCDbuffer = NumberMalloc("execarg"); GCDbuffer2 = NumberMalloc("execarg"); LCMbuffer = NumberMalloc("execarg"); LCMb = NumberMalloc("execarg"); LCMc = NumberMalloc("execarg"); } didpolyratfun = 0; while ( t < rstop ) { if ( *t >= FUNCTION && functions[*t-FUNCTION].spec <= 0 ) { /* We have a function. First count the number of arguments. Tensors are excluded. */ count = 0; v = t; m = t + FUNHEAD; r = t + t[1]; while ( m < r ) { count++; NEXTARG(m) } if ( count <= 0 ) { t += t[1]; continue; } /* Now we take the arguments one by one and test for a match */ for ( i = 1; i <= count; i++ ) { m = start; while ( m < stop ) { r = m + m[1]; j = *r++; if ( j > 1 ) { while ( --j > 0 ) { if ( *r == i ) goto RightNum; r++; } m = r; continue; } RightNum: if ( m[1] == 2 ) { #ifdef WITHFLOAT if ( *t != FLOATFUN || TestFloat(t) == 0 ) #endif { m += 2; m += *m; goto HaveTodo; } #ifdef WITHFLOAT else { m += 2; } #endif } else { r = m + m[1]; m += 2; while ( m < r ) { if ( *m == CSET ) { r1 = SetElements + Sets[m[1]].first; r2 = SetElements + Sets[m[1]].last; while ( r1 < r2 ) { if ( *r1++ == *t ) goto HaveTodo; } } else if ( m[1] == *t ) goto HaveTodo; m += 2; } } m += *m; } continue; HaveTodo: /* If we come here we have to do the argument i (first is 1). */ sign = 1; action = 1; if ( *t == AR.PolyFun ) didpolyratfun = 1; v[2] |= DIRTYFLAG; r = t + FUNHEAD; j = i; while ( --j > 0 ) { NEXTARG(r) } if ( ( type == TYPESPLITARG ) || ( type == TYPESPLITFIRSTARG ) || ( type == TYPESPLITLASTARG ) ) { if ( *t > FUNCTION && *r > 0 ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; } continue; } else if ( type == TYPESPLITARG2 ) { if ( *t > FUNCTION && *r > 0 ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; } continue; } else if ( type == TYPEFACTARG || type == TYPEFACTARG2 ) { if ( *t > FUNCTION || *t == DENOMINATOR ) { if ( *r > 0 ) { mm = r + ARGHEAD; mstop = r + *r; if ( mm + *mm < mstop ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } if ( *mm == 1+ABS(mstop[-1]) ) continue; if ( mstop[-3] != 1 || mstop[-2] != 1 || mstop[-1] != 3 ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } GETSTOP(mm,mstop); mm++; if ( mm + mm[1] < mstop ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } if ( *mm == SYMBOL && ( mm[1] > 4 || ( mm[3] != 1 && mm[3] != -1 ) ) ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } else if ( *mm == DOTPRODUCT && ( mm[1] > 5 || ( mm[4] != 1 && mm[4] != -1 ) ) ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } else if ( ( *mm == DELTA || *mm == VECTOR ) && mm[1] > 4 ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } } else if ( factor && *factor == 4 && factor[2] == 1 ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } else if ( factor && *factor == 0 && ( *r == -SNUMBER && r[1] != 1 ) ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } else if ( *r == -MINVECTOR ) { WantAddPointers(2); AT.pWorkSpace[AT.pWorkPointer++] = t; AT.pWorkSpace[AT.pWorkPointer++] = r; continue; } } continue; } else if ( type == TYPENORM || type == TYPENORM2 || type == TYPENORM3 || type == TYPENORM4 ) { if ( *r < 0 ) { WORD rone; if ( *r == -MINVECTOR ) { rone = -1; *r = -INDEX; } else if ( *r != -SNUMBER || r[1] == 1 || r[1] == 0 ) continue; else { rone = r[1]; r[1] = 1; } /* Now we must multiply the general coefficient by r[1] */ if ( scale && ( factor == 0 || *factor ) ) { action = 1; v[2] |= DIRTYFLAG; if ( rone < 0 ) { if ( type == TYPENORM3 ) k = 1; else k = -1; rone = -rone; } else k = 1; r1 = term + *term; size = r1[-1]; size = REDLENG(size); if ( scale > 0 ) { for ( jj = 0; jj < scale; jj++ ) { if ( Mully(BHEAD (UWORD *)rstop,&size,(UWORD *)(&rone),k) ) goto execargerr; } } else { for ( jj = 0; jj > scale; jj-- ) { if ( Divvy(BHEAD (UWORD *)rstop,&size,(UWORD *)(&rone),k) ) goto execargerr; } } size = INCLENG(size); k = size < 0 ? -size: size; rstop[k-1] = size; *term = (WORD)(rstop - term) + k; } continue; } /* Now we have to find a reference term. If factor is defined and *factor != 0 we have to look for the first term that matches the pattern exactly Otherwise the first term plays this role If its coefficient is not one, we must set up a division of the whole argument by this coefficient, and a multiplication of the term when the type is not equal to TYPENORM2. We first multiply the coefficient of the term. Then we set up the division. First find the magic term */ if ( type == TYPENORM4 ) { /* For normalizing everything to integers we have to determine for all elements of this argument the LCM of the denominators and the GCD of the numerators. The buffers have been allocated already. */ r4 = r + *r; r1 = r + ARGHEAD; /* First take the first term to load up the LCM and the GCD */ r2 = r1 + *r1; j = r2[-1]; if ( j < 0 ) sign = -1; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kGCD = 0; kGCD < k; kGCD++ ) GCDbuffer[kGCD] = r3[kGCD]; k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; r1 = r2; /* Now go through the rest of the terms in this argument. */ while ( r1 < r4 ) { r2 = r1 + *r1; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( GCDbuffer[0] == 1 ) && ( kGCD == 1 ) ) ) { /* GCD is already 1 */ } else if ( ( ( k != 1 ) || ( r3[0] != 1 ) ) ) { if ( GcdLong(BHEAD GCDbuffer,kGCD,(UWORD *)r3,k,GCDbuffer2,&kGCD2) ) { NumberFree(GCDbuffer,"execarg"); NumberFree(GCDbuffer2,"execarg"); NumberFree(LCMbuffer,"execarg"); NumberFree(LCMb,"execarg"); NumberFree(LCMc,"execarg"); goto execargerr; } kGCD = kGCD2; for ( ii = 0; ii < kGCD; ii++ ) GCDbuffer[ii] = GCDbuffer2[ii]; } else { kGCD = 1; GCDbuffer[0] = 1; } k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( LCMbuffer[0] == 1 ) && ( kLCM == 1 ) ) ) { for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; } else if ( ( k != 1 ) || ( r3[0] != 1 ) ) { if ( GcdLong(BHEAD LCMbuffer,kLCM,(UWORD *)r3,k,LCMb,&kkLCM) ) { NumberFree(GCDbuffer,"execarg"); NumberFree(GCDbuffer2,"execarg"); NumberFree(LCMbuffer,"execarg"); NumberFree(LCMb,"execarg"); NumberFree(LCMc,"execarg"); goto execargerr; } DivLong((UWORD *)r3,k,LCMb,kkLCM,LCMb,&kkLCM,LCMc,&jLCM); MulLong(LCMbuffer,kLCM,LCMb,kkLCM,LCMc,&jLCM); for ( kLCM = 0; kLCM < jLCM; kLCM++ ) LCMbuffer[kLCM] = LCMc[kLCM]; } else {} /* LCM doesn't change */ r1 = r2; } /* Now put the factor together: GCD/LCM */ r3 = (WORD *)(GCDbuffer); if ( kGCD == kLCM ) { for ( jGCD = 0; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; k = kGCD; } else if ( kGCD > kLCM ) { for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; for ( jGCD = kLCM; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = 0; k = kGCD; } else { for ( jGCD = kGCD; jGCD < kLCM; jGCD++ ) r3[jGCD] = 0; for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kLCM] = LCMbuffer[jGCD]; k = kLCM; } j = 2*k+1; /* Now we have to correct the overall factor */ if ( scale && ( factor == 0 || *factor > 0 ) ) goto ScaledVariety; /* The if was added 28-nov-2012 to give MakeInteger also the (0) option. */ if ( scale && ( factor == 0 || *factor ) ) { size = term[*term-1]; size = REDLENG(size); if ( MulRat(BHEAD (UWORD *)rstop,size,(UWORD *)r3,k, (UWORD *)rstop,&size) ) goto execargerr; size = INCLENG(size); k = size < 0 ? -size: size; rstop[k-1] = size*sign; *term = (WORD)(rstop - term) + k; } } else { if ( factor && *factor >= 1 ) { r4 = r + *r; r1 = r + ARGHEAD; while ( r1 < r4 ) { r2 = r1 + *r1; r3 = r2 - ABS(r2[-1]); j = r3 - r1; r5 = factor; if ( j != *r5 ) { r1 = r2; continue; } r5++; r6 = r1+1; while ( --j > 0 ) { if ( *r5 != *r6 ) break; r5++; r6++; } if ( j > 0 ) { r1 = r2; continue; } break; } if ( r1 >= r4 ) continue; } else { r1 = r + ARGHEAD; r2 = r1 + *r1; r3 = r2 - ABS(r2[-1]); } if ( *r3 == 1 && r3[1] == 1 ) { if ( r2[-1] == 3 ) continue; if ( r2[-1] == -3 && type == TYPENORM3 ) continue; } action = 1; v[2] |= DIRTYFLAG; j = r2[-1]; k = REDLENG(j); if ( j < 0 ) j = -j; if ( type == TYPENORM && scale && ( factor == 0 || *factor ) ) { /* Now we correct the overall factor */ ScaledVariety:; size = term[*term-1]; size = REDLENG(size); if ( scale > 0 ) { for ( jj = 0; jj < scale; jj++ ) { if ( MulRat(BHEAD (UWORD *)rstop,size,(UWORD *)r3,k, (UWORD *)rstop,&size) ) goto execargerr; } } else { for ( jj = 0; jj > scale; jj-- ) { if ( DivRat(BHEAD (UWORD *)rstop,size,(UWORD *)r3,k, (UWORD *)rstop,&size) ) goto execargerr; } } size = INCLENG(size); k = size < 0 ? -size: size; rstop[k-1] = size*sign; *term = (WORD)(rstop - term) + k; } } /* We generate a statement for adapting all terms in the argument successively */ r4 = AddRHS(AT.ebufnum,1); while ( (r4+j+12) > CC->Top ) r4 = DoubleCbuffer(AT.ebufnum,r4,3); *r4++ = j+1; i = (j-1)/2; /* was (j-1)*2 ????? 17-oct-2017 */ for ( k = 0; k < i; k++ ) *r4++ = r3[i+k]; for ( k = 0; k < i; k++ ) *r4++ = r3[k]; if ( ( type == TYPENORM3 ) || ( type == TYPENORM4 ) ) *r4++ = j*sign; else *r4++ = r3[j-1]; *r4++ = 0; CC->rhs[CC->numrhs+1] = r4; CC->Pointer = r4; AT.mulpat[5] = CC->numrhs; AT.mulpat[7] = AT.ebufnum; } else if ( type == TYPEARGTOEXTRASYMBOL ) { WORD n; if ( r[0] < 0 ) { /* The argument is in the fast notation. */ WORD tmp[MaX(9,FUNHEAD+5)]; switch ( r[0] ) { case -SNUMBER: if ( r[1] == 0 ) { tmp[0] = 0; } else { tmp[0] = 4; tmp[1] = ABS(r[1]); tmp[2] = 1; tmp[3] = r[1] > 0 ? 3 : -3; tmp[4] = 0; } break; case -SYMBOL: tmp[0] = 8; tmp[1] = SYMBOL; tmp[2] = 4; tmp[3] = r[1]; tmp[4] = 1; tmp[5] = 1; tmp[6] = 1; tmp[7] = 3; tmp[8] = 0; break; case -INDEX: case -VECTOR: case -MINVECTOR: tmp[0] = 7; tmp[1] = INDEX; tmp[2] = 3; tmp[3] = r[1]; tmp[4] = 1; tmp[5] = 1; tmp[6] = r[0] != -MINVECTOR ? 3 : -3; tmp[7] = 0; break; default: if ( r[0] <= -FUNCTION ) { tmp[0] = FUNHEAD+4; tmp[1] = -r[0]; tmp[2] = FUNHEAD; ZeroFillRange(tmp,3,1+FUNHEAD); tmp[FUNHEAD+1] = 1; tmp[FUNHEAD+2] = 1; tmp[FUNHEAD+3] = 3; tmp[FUNHEAD+4] = 0; break; } else { MLOCK(ErrorMessageLock); MesPrint("Unknown fast notation found (TYPEARGTOEXTRASYMBOL)"); MUNLOCK(ErrorMessageLock); return(-1); } } n = FindSubexpression(tmp); } else { /* * NOTE: writing to r[r[0]] is legal. As long as we work * in a part of the term, at least the coefficient of * the term must follow. */ WORD old_rr0 = r[r[0]]; r[r[0]] = 0; /* zero-terminated */ n = FindSubexpression(r+ARGHEAD); r[r[0]] = old_rr0; } /* Put the new argument in the work space. */ if ( AT.WorkPointer+2 > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } r1 = AT.WorkPointer; if ( scale ) { /* means "tonumber" */ r1[0] = -SNUMBER; r1[1] = n; } else { r1[0] = -SYMBOL; r1[1] = MAXVARIABLES-n; } /* We need r2, r3, m and k to shift the data. */ r2 = r + (r[0] > 0 ? r[0] : r[0] <= -FUNCTION ? 1 : 2); r3 = r; m = r1+ARGHEAD+2; k = 2; goto do_shift; } r3 = r; AR.DeferFlag = 0; if ( *r > 0 ) { NewSort(BHEAD0); action = 1; r2 = r + *r; r += ARGHEAD; while ( r < r2 ) { /* Sum over the terms */ m = AT.WorkPointer; j = *r; while ( --j >= 0 ) *m++ = *r++; r1 = AT.WorkPointer; AT.WorkPointer = m; /* What to do with dummy indices? */ if ( type == TYPENORM || type == TYPENORM2 || type == TYPENORM3 || type == TYPENORM4 ) { if ( MultDo(BHEAD r1,AT.mulpat) ) goto execargerr; AT.WorkPointer = r1 + *r1; } if ( Generator(BHEAD r1,level) ) goto execargerr; AT.WorkPointer = r1; } } else { r2 = r + (( *r <= -FUNCTION ) ? 1:2); r1 = AT.WorkPointer; ToGeneral(r,r1,0); m = r1 + ARGHEAD; AT.WorkPointer = r1 + *r1; NewSort(BHEAD0); action = 1; /* What to do with dummy indices? */ if ( type == TYPENORM || type == TYPENORM2 || type == TYPENORM3 || type == TYPENORM4 ) { if ( MultDo(BHEAD m,AT.mulpat) ) goto execargerr; AT.WorkPointer = m + *m; } if ( (*m != 0 ) && Generator(BHEAD m,level) ) goto execargerr; AT.WorkPointer = r1; } if ( EndSort(BHEAD AT.WorkPointer+ARGHEAD,1) < 0 ) goto execargerr; AR.DeferFlag = olddefer; /* Now shift the sorted entity over the old argument. */ m = AT.WorkPointer+ARGHEAD; while ( *m ) m += *m; k = WORDDIF(m,AT.WorkPointer); *AT.WorkPointer = k; AT.WorkPointer[1] = 0; if ( ToFast(AT.WorkPointer,AT.WorkPointer) ) { if ( *AT.WorkPointer <= -FUNCTION ) k = 1; else k = 2; } do_shift: if ( *r3 > 0 ) j = k - *r3; else if ( *r3 <= -FUNCTION ) j = k - 1; else j = k - 2; t[1] += j; action = 1; v[2] |= DIRTYFLAG; if ( j > 0 ) { r = m + j; while ( m > AT.WorkPointer ) *--r = *--m; AT.WorkPointer = r; m = term + *term; r = m + j; while ( m > r2 ) *--r = *--m; } else if ( j < 0 ) { r = r2 + j; r1 = term + *term; while ( r2 < r1 ) *r++ = *r2++; } r = r3; m = AT.WorkPointer; NCOPY(r,m,k); *term += j; rstop += j; CC->numrhs = oldnumrhs; CC->Pointer = CC->Buffer + oldcpointer; } } t += t[1]; } /* If TYPENORM4, we allocated Number buffers before the above while loop. Free them. */ if ( type == TYPENORM4 ) { NumberFree(GCDbuffer,"execarg"); NumberFree(GCDbuffer2,"execarg"); NumberFree(LCMbuffer,"execarg"); NumberFree(LCMb,"execarg"); NumberFree(LCMc,"execarg"); } if ( didpolyratfun ) { PolyFunDirty(BHEAD term); didpolyratfun = 0; } /* #] Argument detection : #[ SplitArg : + varieties */ if ( ( type == TYPESPLITARG || type == TYPESPLITARG2 || type == TYPESPLITFIRSTARG || type == TYPESPLITLASTARG ) && AT.pWorkPointer > oldppointer ) { t = term+1; r1 = AT.WorkPointer + 1; lp = oldppointer; while ( t < rstop ) { if ( lp < AT.pWorkPointer && t == AT.pWorkSpace[lp] ) { v = t; m = t + FUNHEAD; r = t + t[1]; r2 = r1; while ( t < m ) *r1++ = *t++; while ( m < r ) { t = m; NEXTARG(m) if ( lp >= AT.pWorkPointer || t != AT.pWorkSpace[lp+1] ) { if ( *t > 0 ) t[1] = 0; while ( t < m ) *r1++ = *t++; continue; } /* Now we have a nontrivial argument that should be done. */ lp += 2; action = 1; v[2] |= DIRTYFLAG; r3 = t + *t; t += ARGHEAD; if ( type == TYPESPLITFIRSTARG ) { r4 = r1; r5 = t; r7 = oldwork; *r1++ = *t + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; j = 0; while ( t < r3 ) { i = *t; if ( j == 0 ) { NCOPY(r7,t,i) j++; } else { NCOPY(r1,t,i) } } *r4 = r1 - r4; if ( j ) { if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } r7 = oldwork; while ( --j >= 0 ) { r4 = r1; i = *r7; *r1++ = i+ARGHEAD; *r1++ = 0; FILLARG(r1); NCOPY(r1,r7,i) if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } } } t = r3; } else if ( type == TYPESPLITLASTARG ) { r4 = r1; r5 = t; r7 = oldwork; *r1++ = *t + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; j = 0; while ( t < r3 ) { i = *t; if ( t+i >= r3 ) { NCOPY(r7,t,i) j++; } else { NCOPY(r1,t,i) } } *r4 = r1 - r4; if ( j ) { if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } r7 = oldwork; while ( --j >= 0 ) { r4 = r1; i = *r7; *r1++ = i+ARGHEAD; *r1++ = 0; FILLARG(r1); NCOPY(r1,r7,i) if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } } } t = r3; } else if ( factor == 0 || ( type == TYPESPLITARG2 && *factor == 0 ) ) { while ( t < r3 ) { r4 = r1; *r1++ = *t + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; i = *t; while ( --i >= 0 ) *r1++ = *t++; if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } } } else if ( type == TYPESPLITARG2 ) { /* Here we better put the pattern matcher at work? Remember: there are no wildcards. */ WORD *oRepFunList = AN.RepFunList; WORD *oWildMask = AT.WildMask, *oWildValue = AN.WildValue; AN.WildValue = AT.locwildvalue; AT.WildMask = AT.locwildvalue+2; AN.NumWild = 0; r4 = r1; r5 = t; r7 = oldwork; *r1++ = *t + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; j = 0; while ( t < r3 ) { AN.UseFindOnly = 0; oldwork2 = AT.WorkPointer; AN.RepFunList = r1; AT.WorkPointer = r1+AN.RepFunNum+2; i = *t; if ( FindRest(BHEAD t,factor) && ( AN.UsedOtherFind || FindOnce(BHEAD t,factor) ) ) { NCOPY(r7,t,i) j++; } else if ( factor[0] == FUNHEAD+1 && factor[1] >= FUNCTION ) { WORD *rr1 = t+1, *rr2 = t+i; rr2 -= ABS(rr2[-1]); while ( rr1 < rr2 ) { if ( *rr1 == factor[1] ) break; rr1 += rr1[1]; } if ( rr1 < rr2 ) { NCOPY(r7,t,i) j++; } else { NCOPY(r1,t,i) } } else { NCOPY(r1,t,i) } AT.WorkPointer = oldwork2; } AN.RepFunList = oRepFunList; *r4 = r1 - r4; if ( j ) { if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } r7 = oldwork; while ( --j >= 0 ) { r4 = r1; i = *r7; *r1++ = i+ARGHEAD; *r1++ = 0; FILLARG(r1); NCOPY(r1,r7,i) if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } } } t = r3; AT.WildMask = oWildMask; AN.WildValue = oWildValue; } else { /* This code deals with splitting off a single term */ r4 = r1; r5 = t; *r1++ = *t + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; j = 0; while ( t < r3 ) { r6 = t + *t; r6 -= ABS(r6[-1]); if ( (r6 - t) == *factor ) { k = *factor - 1; for ( ; k > 0; k-- ) { if ( t[k] != factor[k] ) break; } if ( k <= 0 ) { j = r3 - t; t += *t; continue; } } else if ( (r6 - t) == 1 && *factor == 0 ) { j = r3 - t; t += *t; continue; } i = *t; NCOPY(r1,t,i) } *r4 = r1 - r4; if ( j ) { if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } t = r3 - j; r4 = r1; *r1++ = *t + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; i = *t; while ( --i >= 0 ) *r1++ = *t++; if ( ToFast(r4,r4) ) { r1 = r4; if ( *r1 > -FUNCTION ) r1++; r1++; } } t = r3; } } r2[1] = r1 - r2; } else { r = t + t[1]; while ( t < r ) *r1++ = *t++; } } r = term + *term; while ( t < r ) *r1++ = *t++; m = AT.WorkPointer; i = m[0] = r1 - m; t = term; while ( --i >= 0 ) *t++ = *m++; if ( AT.WorkPointer < m ) AT.WorkPointer = m; } /* #] SplitArg : #[ FACTARG : */ if ( ( type == TYPEFACTARG || type == TYPEFACTARG2 ) && AT.pWorkPointer > oldppointer ) { t = term+1; r1 = AT.WorkPointer + 1; lp = oldppointer; while ( t < rstop ) { if ( lp < AT.pWorkPointer && AT.pWorkSpace[lp] == t ) { v = t; m = t + FUNHEAD; r = t + t[1]; r2 = r1; while ( t < m ) *r1++ = *t++; while ( m < r ) { rr = t = m; NEXTARG(m) if ( lp >= AT.pWorkPointer || AT.pWorkSpace[lp+1] != t ) { if ( *t > 0 ) t[1] = 0; while ( t < m ) *r1++ = *t++; continue; } /* Now we have a nontrivial argument that should be studied. Try to find common factors. */ lp += 2; if ( *t < 0 ) { if ( factor && ( *factor == 0 && *t == -SNUMBER ) ) { *r1++ = *t++; if ( *t == 0 ) *r1++ = *t++; else { *r1++ = 1; t++; } continue; } else if ( factor && *factor == 4 && factor[2] == 1 ) { if ( *t == -SNUMBER ) { if ( factor[3] < 0 || t[1] >= 0 ) { while ( t < m ) *r1++ = *t++; } else { *r1++ = -SNUMBER; *r1++ = -1; *r1++ = *t++; *r1++ = -*t++; } } else { while ( t < m ) *r1++ = *t++; *r1++ = -SNUMBER; *r1++ = 1; } continue; } else if ( *t == -MINVECTOR ) { if ( AC.OldFactArgFlag == NEWFACTARG ) { *r1++ = -SNUMBER; *r1++ = -1; *r1++ = -VECTOR; t++; *r1++ = *t++; } else { *r1++ = -VECTOR; t++; *r1++ = *t++; *r1++ = -SNUMBER; *r1++ = -1; *r1++ = -SNUMBER; *r1++ = 1; } continue; } } /* Now we have a nontrivial argument */ r3 = t + *t; t += ARGHEAD; r5 = t; /* Store starting point */ /* We have terms from r5 to r3 */ if ( r5+*r5 == r3 && factor ) { /* One term only */ if ( *factor == 0 ) { GETSTOP(t,r6); r9 = r1; *r1++ = 0; *r1++ = 1; FILLARG(r1); *r1++ = (r6-t)+3; t++; while ( t < r6 ) *r1++ = *t++; *r1++ = 1; *r1++ = 1; *r1++ = 3; *r9 = r1-r9; if ( ToFast(r9,r9) ) { if ( *r9 <= -FUNCTION ) r1 = r9+1; else r1 = r9+2; } t = r3; continue; } if ( factor[0] == 4 && factor[2] == 1 ) { GETSTOP(t,r6); r7 = r1; *r1++ = (r6-t)+3+ARGHEAD; *r1++ = 0; FILLARG(r1); *r1++ = (r6-t)+3; t++; while ( t < r6 ) *r1++ = *t++; *r1++ = 1; *r1++ = 1; *r1++ = 3; if ( ToFast(r7,r7) ) { if ( *r7 <= -FUNCTION ) r1 = r7+1; else r1 = r7+2; } if ( r3[-1] < 0 && factor[3] > 0 ) { *r1++ = -SNUMBER; *r1++ = -1; if ( r3[-1] == -3 && r3[-2] == 1 && ( r3[-3] & MAXPOSITIVE ) == r3[-3] ) { *r1++ = -SNUMBER; *r1++ = r3[-3]; } else { *r1++ = (r3-r6)+1+ARGHEAD; *r1++ = 0; FILLARG(r1); *r1++ = (r3-r6+1); while ( t < r3 ) *r1++ = *t++; r1[-1] = -r1[-1]; } } else { if ( ( r3[-1] == -3 || r3[-1] == 3 ) && r3[-2] == 1 && ( r3[-3] & MAXPOSITIVE ) == r3[-3] ) { *r1++ = -SNUMBER; *r1++ = r3[-3]; if ( r3[-1] < 0 ) r1[-1] = - r1[-1]; } else { *r1++ = (r3-r6)+1+ARGHEAD; *r1++ = 0; FILLARG(r1); *r1++ = (r3-r6+1); while ( t < r3 ) *r1++ = *t++; } } t = r3; continue; } } /* Now we take the first term and look for its pieces inside the other terms. It is at this point that a more general factorization routine could take over (allowing for writing the output properly of course). */ if ( AC.OldFactArgFlag == NEWFACTARG ) { if ( factor == 0 ) { WORD *oldworkpointer2 = AT.WorkPointer; AT.WorkPointer = r1 + AM.MaxTer+FUNHEAD; if ( ArgFactorize(BHEAD t-ARGHEAD,r1) < 0 ) { MesCall("ExecArg"); return(-1); } AT.WorkPointer = oldworkpointer2; t = r3; while ( *r1 ) { NEXTARG(r1) } } else { rnext = t + *t; GETSTOP(t,r6); t++; t = r5; pow = 1; while ( t < r3 ) { t += *t; if ( t[-1] > 0 ) { pow = 0; break; } } /* We have to add here the code for computing the GCD and to divide it out. #[ Numerical factor : */ t = r5; EAscrat = (UWORD *)(TermMalloc("execarg")); if ( t + *t == r3 ) { if ( factor == 0 || *factor > 2 ) { if ( pow > 0 ) { *r1++ = -SNUMBER; *r1++ = -1; t = r5; while ( t < r3 ) { t += *t; t[-1] = -t[-1]; } } t = rr; *r1++ = *t++; *r1++ = 1; t++; COPYARG(r1,t); while ( t < m ) *r1++ = *t++; } } else { GETSTOP(t,r6); ngcd = t[t[0]-1]; i = abs(ngcd)-1; while ( --i >= 0 ) EAscrat[i] = r6[i]; t += *t; while ( t < r3 ) { GETSTOP(t,r6); i = t[t[0]-1]; if ( AccumGCD(BHEAD EAscrat,&ngcd,(UWORD *)r6,i) ) goto execargerr; if ( ngcd == 3 && EAscrat[0] == 1 && EAscrat[1] == 1 ) break; t += *t; } /* if ( ngcd != 3 || EAscrat[0] != 1 || EAscrat[1] != 1 ) */ { if ( pow ) ngcd = -ngcd; t = r5; r9 = r1; *r1++ = t[-ARGHEAD]; *r1++ = 1; FILLARG(r1); ngcd = REDLENG(ngcd); while ( t < r3 ) { GETSTOP(t,r6); r7 = t; r8 = r1; while ( r7 < r6) *r1++ = *r7++; t += *t; i = REDLENG(t[-1]); if ( DivRat(BHEAD (UWORD *)r6,i,EAscrat,ngcd,(UWORD *)r1,&nq) ) goto execargerr; nq = INCLENG(nq); i = ABS(nq)-1; r1 += i; *r1++ = nq; *r8 = r1-r8; } *r9 = r1-r9; ngcd = INCLENG(ngcd); i = ABS(ngcd)-1; if ( factor && *factor == 0 ) {} else if ( ( factor && factor[0] == 4 && factor[2] == 1 && factor[3] == -3 ) || pow == 0 ) { r9 = r1; *r1++ = ARGHEAD+2+i; *r1++ = 0; FILLARG(r1); *r1++ = i+2; for ( j = 0; j < i; j++ ) *r1++ = EAscrat[j]; *r1++ = ngcd; if ( ToFast(r9,r9) ) r1 = r9+2; } else if ( factor && factor[0] == 4 && factor[2] == 1 && factor[3] > 0 && pow ) { if ( ngcd < 0 ) ngcd = -ngcd; *r1++ = -SNUMBER; *r1++ = -1; r9 = r1; *r1++ = ARGHEAD+2+i; *r1++ = 0; FILLARG(r1); *r1++ = i+2; for ( j = 0; j < i; j++ ) *r1++ = EAscrat[j]; *r1++ = ngcd; if ( ToFast(r9,r9) ) r1 = r9+2; } else { if ( ngcd < 0 ) ngcd = -ngcd; if ( pow ) { *r1++ = -SNUMBER; *r1++ = -1; } if ( ngcd != 3 || EAscrat[0] != 1 || EAscrat[1] != 1 ) { r9 = r1; *r1++ = ARGHEAD+2+i; *r1++ = 0; FILLARG(r1); *r1++ = i+2; for ( j = 0; j < i; j++ ) *r1++ = EAscrat[j]; *r1++ = ngcd; if ( ToFast(r9,r9) ) r1 = r9+2; } } } /* #] Numerical factor : else { onetermnew:; if ( factor == 0 || *factor > 2 ) { if ( pow > 0 ) { *r1++ = -SNUMBER; *r1++ = -1; t = r5; while ( t < r3 ) { t += *t; t[-1] = -t[-1]; } } t = rr; *r1++ = *t++; *r1++ = 1; t++; COPYARG(r1,t); while ( t < m ) *r1++ = *t++; } } onetermnew:; */ } TermFree(EAscrat,"execarg"); } } else { /* AC.OldFactArgFlag is ON */ { WORD *mnext, ncom; rnext = t + *t; GETSTOP(t,r6); t++; if ( factor == 0 ) { while ( t < r6 ) { /* #[ SYMBOL : */ if ( *t == SYMBOL ) { r7 = t; r8 = t + t[1]; t += 2; while ( t < r8 ) { pow = t[1]; mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != SYMBOL ) mm += mm[1]; else break; } if ( *mm == SYMBOL ) { mstop = mm + mm[1]; mm += 2; while ( *mm != *t && mm < mstop ) mm += 2; if ( mm >= mstop ) pow = 0; else if ( pow > 0 && mm[1] > 0 ) { if ( mm[1] < pow ) pow = mm[1]; } else if ( pow < 0 && mm[1] < 0 ) { if ( mm[1] > pow ) pow = mm[1]; } else pow = 0; } else pow = 0; if ( pow == 0 ) break; mm = mnext; } if ( pow == 0 ) { t += 2; continue; } /* We have a factor */ action = 1; i = pow; if ( i > 0 ) { while ( --i >= 0 ) { *r1++ = -SYMBOL; *r1++ = *t; } } else { while ( i++ < 0 ) { *r1++ = 8 + ARGHEAD; for ( j = 1; j < ARGHEAD; j++ ) *r1++ = 0; *r1++ = 8; *r1++ = SYMBOL; *r1++ = 4; *r1++ = *t; *r1++ = -1; *r1++ = 1; *r1++ = 1; *r1++ = 3; } } /* Now we have to remove the symbols */ t[1] -= pow; mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != SYMBOL ) mm += mm[1]; else break; } mstop = mm + mm[1]; mm += 2; while ( mm < mstop && *mm != *t ) mm += 2; mm[1] -= pow; mm = mnext; } t += 2; } } /* #] SYMBOL : #[ DOTPRODUCT : */ else if ( *t == DOTPRODUCT ) { r7 = t; r8 = t + t[1]; t += 2; while ( t < r8 ) { pow = t[2]; mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != DOTPRODUCT ) mm += mm[1]; else break; } if ( *mm == DOTPRODUCT ) { mstop = mm + mm[1]; mm += 2; while ( ( *mm != *t || mm[1] != t[1] ) && mm < mstop ) mm += 3; if ( mm >= mstop ) pow = 0; else if ( pow > 0 && mm[2] > 0 ) { if ( mm[2] < pow ) pow = mm[2]; } else if ( pow < 0 && mm[2] < 0 ) { if ( mm[2] > pow ) pow = mm[2]; } else pow = 0; } else pow = 0; if ( pow == 0 ) break; mm = mnext; } if ( pow == 0 ) { t += 3; continue; } /* We have a factor */ action = 1; i = pow; if ( i > 0 ) { while ( --i >= 0 ) { *r1++ = 9 + ARGHEAD; for ( j = 1; j < ARGHEAD; j++ ) *r1++ = 0; *r1++ = 9; *r1++ = DOTPRODUCT; *r1++ = 5; *r1++ = *t; *r1++ = t[1]; *r1++ = 1; *r1++ = 1; *r1++ = 1; *r1++ = 3; } } else { while ( i++ < 0 ) { *r1++ = 9 + ARGHEAD; for ( j = 1; j < ARGHEAD; j++ ) *r1++ = 0; *r1++ = 9; *r1++ = DOTPRODUCT; *r1++ = 5; *r1++ = *t; *r1++ = t[1]; *r1++ = -1; *r1++ = 1; *r1++ = 1; *r1++ = 3; } } /* Now we have to remove the dotproducts */ t[2] -= pow; mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != DOTPRODUCT ) mm += mm[1]; else break; } mstop = mm + mm[1]; mm += 2; while ( mm < mstop && ( *mm != *t || mm[1] != t[1] ) ) mm += 3; mm[2] -= pow; mm = mnext; } t += 3; } } /* #] DOTPRODUCT : #[ DELTA/VECTOR : */ else if ( *t == DELTA || *t == VECTOR ) { r7 = t; r8 = t + t[1]; t += 2; while ( t < r8 ) { mm = rnext; pow = 1; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } if ( *mm == *r7 ) { mstop = mm + mm[1]; mm += 2; while ( ( *mm != *t || mm[1] != t[1] ) && mm < mstop ) mm += 2; if ( mm >= mstop ) pow = 0; } else pow = 0; if ( pow == 0 ) break; mm = mnext; } if ( pow == 0 ) { t += 2; continue; } /* We have a factor */ action = 1; *r1++ = 8 + ARGHEAD; for ( j = 1; j < ARGHEAD; j++ ) *r1++ = 0; *r1++ = 8; *r1++ = *r7; *r1++ = 4; *r1++ = *t; *r1++ = t[1]; *r1++ = 1; *r1++ = 1; *r1++ = 3; /* Now we have to remove the delta's/vectors */ mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } mstop = mm + mm[1]; mm += 2; while ( mm < mstop && ( *mm != *t || mm[1] != t[1] ) ) mm += 2; *mm = mm[1] = NOINDEX; mm = mnext; } *t = t[1] = NOINDEX; t += 2; } } /* #] DELTA/VECTOR : #[ INDEX : */ else if ( *t == INDEX ) { r7 = t; r8 = t + t[1]; t += 2; while ( t < r8 ) { mm = rnext; pow = 1; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } if ( *mm == *r7 ) { mstop = mm + mm[1]; mm += 2; while ( *mm != *t && mm < mstop ) mm++; if ( mm >= mstop ) pow = 0; } else pow = 0; if ( pow == 0 ) break; mm = mnext; } if ( pow == 0 ) { t++; continue; } /* We have a factor */ action = 1; /* The next looks like an error. We should have here a VECTOR or INDEX like object *r1++ = 7 + ARGHEAD; for ( j = 1; j < ARGHEAD; j++ ) *r1++ = 0; *r1++ = 7; *r1++ = *r7; *r1++ = 3; *r1++ = *t; *r1++ = 1; *r1++ = 1; *r1++ = 3; Replace this by: (11-apr-2007) */ if ( *t < 0 ) { *r1++ = -VECTOR; } else { *r1++ = -INDEX; } *r1++ = *t; /* Now we have to remove the index */ *t = NOINDEX; mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } mstop = mm + mm[1]; mm += 2; while ( mm < mstop && *mm != *t ) mm += 1; *mm = NOINDEX; mm = mnext; } t += 1; } } /* #] INDEX : #[ FUNCTION : */ else if ( *t >= FUNCTION ) { /* In the next code we should actually look inside the DENOMINATOR or EXPONENT for noncommuting objects */ if ( *t >= FUNCTION && functions[*t-FUNCTION].commute == 0 ) ncom = 0; else ncom = 1; if ( ncom ) { mm = r5 + 1; while ( mm < t && ( *mm == DUMMYFUN || *mm == DUMMYTEN ) ) mm += mm[1]; if ( mm < t ) { t += t[1]; continue; } } mm = rnext; pow = 1; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm == *t && mm[1] == t[1] ) { for ( i = 2; i < t[1]; i++ ) { if ( mm[i] != t[i] ) break; } if ( i >= t[1] ) { mm += mm[1]; goto nextmterm; } } if ( ncom && *mm != DUMMYFUN && *mm != DUMMYTEN ) { pow = 0; break; } mm += mm[1]; } if ( mm >= mstop ) pow = 0; if ( pow == 0 ) break; nextmterm: mm = mnext; } if ( pow == 0 ) { t += t[1]; continue; } /* Copy the function */ action = 1; *r1++ = t[1] + 4 + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; *r1++ = t[1] + 4; for ( i = 0; i < t[1]; i++ ) *r1++ = t[i]; *r1++ = 1; *r1++ = 1; *r1++ = 3; /* Now we have to take out the functions */ mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm == *t && mm[1] == t[1] ) { for ( i = 2; i < t[1]; i++ ) { if ( mm[i] != t[i] ) break; } if ( i >= t[1] ) { if ( functions[*t-FUNCTION].spec > 0 ) *mm = DUMMYTEN; else *mm = DUMMYFUN; mm += mm[1]; goto nextterm; } } mm += mm[1]; } nextterm: mm = mnext; } if ( functions[*t-FUNCTION].spec > 0 ) *t = DUMMYTEN; else *t = DUMMYFUN; action = 1; v[2] = DIRTYFLAG; t += t[1]; } /* #] FUNCTION : */ else { t += t[1]; } } } t = r5; pow = 1; while ( t < r3 ) { t += *t; if ( t[-1] > 0 ) { pow = 0; break; } } /* We have to add here the code for computing the GCD and to divide it out. */ /* #[ Numerical factor : */ t = r5; EAscrat = (UWORD *)(TermMalloc("execarg")); if ( t + *t == r3 ) goto oneterm; GETSTOP(t,r6); ngcd = t[t[0]-1]; i = abs(ngcd)-1; while ( --i >= 0 ) EAscrat[i] = r6[i]; t += *t; while ( t < r3 ) { GETSTOP(t,r6); i = t[t[0]-1]; if ( AccumGCD(BHEAD EAscrat,&ngcd,(UWORD *)r6,i) ) goto execargerr; if ( ngcd == 3 && EAscrat[0] == 1 && EAscrat[1] == 1 ) break; t += *t; } if ( ngcd != 3 || EAscrat[0] != 1 || EAscrat[1] != 1 ) { if ( pow ) ngcd = -ngcd; t = r5; r9 = r1; *r1++ = t[-ARGHEAD]; *r1++ = 1; FILLARG(r1); ngcd = REDLENG(ngcd); while ( t < r3 ) { GETSTOP(t,r6); r7 = t; r8 = r1; while ( r7 < r6) *r1++ = *r7++; t += *t; i = REDLENG(t[-1]); if ( DivRat(BHEAD (UWORD *)r6,i,EAscrat,ngcd,(UWORD *)r1,&nq) ) goto execargerr; nq = INCLENG(nq); i = ABS(nq)-1; r1 += i; *r1++ = nq; *r8 = r1-r8; } *r9 = r1-r9; ngcd = INCLENG(ngcd); i = ABS(ngcd)-1; if ( factor && *factor == 0 ) {} else if ( ( factor && factor[0] == 4 && factor[2] == 1 && factor[3] == -3 ) || pow == 0 ) { r9 = r1; *r1++ = ARGHEAD+2+i; *r1++ = 0; FILLARG(r1); *r1++ = i+2; for ( j = 0; j < i; j++ ) *r1++ = EAscrat[j]; *r1++ = ngcd; if ( ToFast(r9,r9) ) r1 = r9+2; } else if ( factor && factor[0] == 4 && factor[2] == 1 && factor[3] > 0 && pow ) { if ( ngcd < 0 ) ngcd = -ngcd; *r1++ = -SNUMBER; *r1++ = -1; r9 = r1; *r1++ = ARGHEAD+2+i; *r1++ = 0; FILLARG(r1); *r1++ = i+2; for ( j = 0; j < i; j++ ) *r1++ = EAscrat[j]; *r1++ = ngcd; if ( ToFast(r9,r9) ) r1 = r9+2; } else { if ( ngcd < 0 ) ngcd = -ngcd; if ( pow ) { *r1++ = -SNUMBER; *r1++ = -1; } if ( ngcd != 3 || EAscrat[0] != 1 || EAscrat[1] != 1 ) { r9 = r1; *r1++ = ARGHEAD+2+i; *r1++ = 0; FILLARG(r1); *r1++ = i+2; for ( j = 0; j < i; j++ ) *r1++ = EAscrat[j]; *r1++ = ngcd; if ( ToFast(r9,r9) ) r1 = r9+2; } } } /* #] Numerical factor : */ else { oneterm:; if ( factor == 0 || *factor > 2 ) { if ( pow > 0 ) { *r1++ = -SNUMBER; *r1++ = -1; t = r5; while ( t < r3 ) { t += *t; t[-1] = -t[-1]; } } t = rr; *r1++ = *t++; *r1++ = 1; t++; COPYARG(r1,t); while ( t < m ) *r1++ = *t++; } } TermFree(EAscrat,"execarg"); } } /* AC.OldFactArgFlag */ } /* r1 is fout in ons voorbeeld. */ r2[1] = r1 - r2; action = 1; v[2] = DIRTYFLAG; } else { r = t + t[1]; while ( t < r ) *r1++ = *t++; } } r = term + *term; while ( t < r ) *r1++ = *t++; m = AT.WorkPointer; i = m[0] = r1 - m; t = term; while ( --i >= 0 ) *t++ = *m++; if ( AT.WorkPointer < t ) AT.WorkPointer = t; } /* #] FACTARG : */ AR.Cnumlhs = oldnumlhs; if ( action && Normalize(BHEAD term) ) goto execargerr; AT.WorkPointer = oldwork; if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; AT.pWorkPointer = oldppointer; return(action); execargerr: AT.WorkPointer = oldwork; AT.pWorkPointer = oldppointer; MLOCK(ErrorMessageLock); MesCall("execarg"); MUNLOCK(ErrorMessageLock); return(-1); } /* #] execarg : #[ execterm : */ int execterm(PHEAD WORD *term, WORD level) { GETBIDENTITY CBUF *C = cbuf+AM.rbufnum; WORD oldnumlhs = AR.Cnumlhs; WORD maxisat = C->lhs[level][2]; WORD *buffer1 = 0; WORD *oldworkpointer = AT.WorkPointer; WORD *t1, i; WORD olddeferflag = AR.DeferFlag, tryterm = 0; AR.DeferFlag = 0; do { AR.Cnumlhs = C->lhs[level][3]; NewSort(BHEAD0); /* Normally for function arguments we do not use PolyFun/PolyRatFun. Hence NewSort sets the corresponding variables to zero. Here we overwrite that. */ AN.FunSorts[AR.sLevel]->PolyFlag = ( AR.PolyFun != 0 ) ? AR.PolyFunType: 0; if ( AR.PolyFun == 0 ) { AN.FunSorts[AR.sLevel]->PolyFlag = 0; } else if ( AR.PolyFunType == 1 ) { AN.FunSorts[AR.sLevel]->PolyFlag = 1; } else if ( AR.PolyFunType == 2 ) { if ( AR.PolyFunExp == 2 ) AN.FunSorts[AR.sLevel]->PolyFlag = 1; else AN.FunSorts[AR.sLevel]->PolyFlag = 2; } if ( buffer1 ) { term = buffer1; while ( *term ) { t1 = oldworkpointer; i = *term; while ( --i >= 0 ) *t1++ = *term++; AT.WorkPointer = t1; if ( Generator(BHEAD oldworkpointer,level) ) goto exectermerr; } } else { if ( Generator(BHEAD term,level) ) goto exectermerr; } if ( buffer1 ) { if ( tryterm ) { TermFree(buffer1,"buffer in sort statement"); tryterm = 0; } else { M_free((void *)buffer1,"buffer in sort statement"); } buffer1 = 0; } AN.tryterm = 1; if ( EndSort(BHEAD (WORD *)((void *)(&buffer1)),2) < 0 ) goto exectermerr; tryterm = AN.tryterm; AN.tryterm = 0; level = AR.Cnumlhs; } while ( AR.Cnumlhs < maxisat ); AR.Cnumlhs = oldnumlhs; AR.DeferFlag = olddeferflag; term = buffer1; while ( *term ) { t1 = oldworkpointer; i = *term; while ( --i >= 0 ) *t1++ = *term++; AT.WorkPointer = t1; if ( Generator(BHEAD oldworkpointer,level) ) goto exectermerr; } if ( tryterm ) { TermFree(buffer1,"buffer in term statement"); tryterm = 0; } else { M_free(buffer1,"buffer in term statement"); } buffer1 = 0; AT.WorkPointer = oldworkpointer; return(0); exectermerr: AT.WorkPointer = oldworkpointer; AR.DeferFlag = olddeferflag; MLOCK(ErrorMessageLock); MesCall("execterm"); MUNLOCK(ErrorMessageLock); return(-1); } /* #] execterm : #[ ArgumentImplode : */ int ArgumentImplode(PHEAD WORD *term, WORD *thelist) { GETBIDENTITY WORD *liststart, *liststop, *inlist; WORD *w, *t, *tend, *tstop, *tt, *ttstop, *ttt, ncount, i; int action = 0; liststop = thelist + thelist[1]; liststart = thelist + 2; t = term; tend = t + *t; tstop = tend - ABS(tend[-1]); t++; while ( t < tstop ) { if ( *t >= FUNCTION ) { inlist = liststart; while ( inlist < liststop && *inlist != *t ) inlist += inlist[1]; if ( inlist < liststop ) { tt = t; ttstop = t + t[1]; w = AT.WorkPointer; for ( i = 0; i < FUNHEAD; i++ ) *w++ = *tt++; while ( tt < ttstop ) { ncount = 0; if ( *tt == -SNUMBER && tt[1] == 0 ) { ncount = 1; ttt = tt; tt += 2; while ( tt < ttstop && *tt == -SNUMBER && tt[1] == 0 ) { ncount++; tt += 2; } } if ( ncount > 0 ) { if ( tt < ttstop && *tt == -SNUMBER && ( tt[1] == 1 || tt[1] == -1 ) ) { *w++ = -SNUMBER; *w++ = (ncount+1) * tt[1]; tt += 2; action = 1; } else if ( ( tt[0] == tt[ARGHEAD] + ARGHEAD ) && ( ABS(tt[tt[0]-1]) == 3 ) && ( tt[tt[0]-2] == 1 ) && ( tt[tt[0]-3] == 1 ) ) { /* Single term with coef +/- 1 */ i = *tt; NCOPY(w,tt,i) w[-3] = ncount+1; action = 1; } else if ( *tt == -SYMBOL ) { *w++ = ARGHEAD+8; *w++ = 0; FILLARG(w) *w++ = 8; *w++ = SYMBOL; *w++ = tt[1]; *w++ = 1; *w++ = ncount+1; *w++ = 1; *w++ = 3; tt += 2; action = 1; } else if ( *tt <= -FUNCTION ) { *w++ = ARGHEAD+FUNHEAD+4; *w++ = 0; FILLARG(w) *w++ = -*tt++; *w++ = FUNHEAD+4; FILLFUN(w) *w++ = ncount+1; *w++ = 1; *w++ = 3; action = 1; } else { while ( ttt < tt ) *w++ = *ttt++; if ( tt < ttstop && *tt == -SNUMBER ) { *w++ = *tt++; *w++ = *tt++; } } } else if ( *tt <= -FUNCTION ) { *w++ = *tt++; } else if ( *tt < 0 ) { *w++ = *tt++; *w++ = *tt++; } else { i = *tt; NCOPY(w,tt,i) } } AT.WorkPointer[1] = w - AT.WorkPointer; while ( tt < tend ) *w++ = *tt++; ttt = AT.WorkPointer; tt = t; while ( ttt < w ) *tt++ = *ttt++; term[0] = tt - term; AT.WorkPointer = tt; tend = tt; tstop = tt - ABS(tt[-1]); } } t += t[1]; } if ( action ) { if ( Normalize(BHEAD term) ) return(-1); } return(0); } /* #] ArgumentImplode : #[ ArgumentExplode : */ int ArgumentExplode(PHEAD WORD *term, WORD *thelist) { GETBIDENTITY WORD *liststart, *liststop, *inlist, *old; WORD *w, *t, *tend, *tstop, *tt, *ttstop, *ttt, ncount, i; int action = 0; LONG x; liststop = thelist + thelist[1]; liststart = thelist + 2; t = term; tend = t + *t; tstop = tend - ABS(tend[-1]); t++; while ( t < tstop ) { if ( *t >= FUNCTION ) { inlist = liststart; while ( inlist < liststop && *inlist != *t ) inlist += inlist[1]; if ( inlist < liststop ) { tt = t; ttstop = t + t[1]; w = AT.WorkPointer; for ( i = 0; i < FUNHEAD; i++ ) *w++ = *tt++; while ( tt < ttstop ) { if ( *tt == -SNUMBER && tt[1] != 0 ) { if ( tt[1] < AM.MaxTer/((WORD)sizeof(WORD)*4) && tt[1] > -(AM.MaxTer/((WORD)sizeof(WORD)*4)) && ( tt[1] > 1 || tt[1] < -1 ) ) { ncount = ABS(tt[1]); while ( ncount > 1 ) { *w++ = -SNUMBER; *w++ = 0; ncount--; } *w++ = -SNUMBER; if ( tt[1] < 0 ) *w++ = -1; else *w++ = 1; tt += 2; action = 1; } else { *w++ = *tt++; *w++ = *tt++; } } else if ( *tt <= -FUNCTION ) { *w++ = *tt++; } else if ( *tt < 0 ) { *w++ = *tt++; *w++ = *tt++; } else if ( tt[0] == tt[ARGHEAD]+ARGHEAD ) { ttt = tt + tt[0] - 1; i = (ABS(ttt[0])-1)/2; if ( i > 1 ) { TooMany: old = AN.currentTerm; AN.currentTerm = term; MesPrint("Too many arguments in output of ArgExplode"); MesPrint("Term = %t"); AN.currentTerm = old; return(-1); } if ( ttt[-1] != 1 ) goto NoExplode; x = ttt[-2]; if ( 2*x > (AT.WorkTop-w)-*term ) goto TooMany; ncount = x - 1; while ( ncount > 0 ) { *w++ = -SNUMBER; *w++ = 0; ncount--; } ttt[-2] = 1; i = *tt; NCOPY(w,tt,i) action = 1; } else { NoExplode: i = *tt; NCOPY(w,tt,i) } } AT.WorkPointer[1] = w - AT.WorkPointer; while ( tt < tend ) *w++ = *tt++; ttt = AT.WorkPointer; tt = t; while ( ttt < w ) *tt++ = *ttt++; term[0] = tt - term; AT.WorkPointer = tt; tend = tt; tstop = tt - ABS(tt[-1]); } } t += t[1]; } if ( action ) { if ( Normalize(BHEAD term) ) return(-1); } return(0); } /* #] ArgumentExplode : #[ ArgFactorize : */ /** * Factorizes an argument in general notation (meaning that the first * word of the argument is a positive size indicator) * Input (argin): pointer to the complete argument * Output (argout): Pointer to where the output should be written. * This is in the WorkSpace * Return value should be negative if anything goes wrong. * * The notation of the output should be a string of arguments terminated * by the number zero. * * Originally we sorted in a way that the constants came last. This gave * conflicts with the dollar and expression factorizations (in the expressions * we wanted the zero first and then followed by the constants). */ #define NEWORDER int ArgFactorize(PHEAD WORD *argin, WORD *argout) { /* #[ step 0 : Declarations and initializations */ WORD *argfree, *argextra, *argcopy, *t, *tstop, *a, *a1, *a2; #ifdef NEWORDER WORD *tt; #endif WORD startebuf = cbuf[AT.ebufnum].numrhs,oldword; WORD oldsorttype = AR.SortType, numargs; int error = 0, action = 0, i, ii, number, sign = 1; *argout = 0; /* #] step 0 : #[ step 1 : Take care of ordering */ AR.SortType = SORTHIGHFIRST; if ( oldsorttype != AR.SortType ) { NewSort(BHEAD0); oldword = argin[*argin]; argin[*argin] = 0; t = argin+ARGHEAD; while ( *t ) { tstop = t + *t; if ( AN.ncmod != 0 ) { if ( AN.ncmod != 1 || ( (WORD)AN.cmod[0] < 0 ) ) { MLOCK(ErrorMessageLock); MesPrint("Factorization modulus a number, greater than a WORD not implemented."); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( Modulus(t) ) { MLOCK(ErrorMessageLock); MesCall("ArgFactorize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( !*t) { t = tstop; continue; } } StoreTerm(BHEAD t); t = tstop; } /* par = 1, in case the arg has more than SubTermsInSmall terms */ EndSort(BHEAD argin+ARGHEAD,1); argin[*argin] = oldword; } /* #] step 1 : #[ step 2 : take out the 'content'. */ argfree = TakeArgContent(BHEAD argin,argout); { a1 = argout; while ( *a1 ) { if ( a1[0] == -SNUMBER && ( a1[1] == 1 || a1[1] == -1 ) ) { if ( a1[1] == -1 ) { sign = -sign; a1[1] = 1; } if ( a1[2] ) { a = t = a1+2; while ( *t ) NEXTARG(t); i = t - a1-2; t = a1; NCOPY(t,a,i); *t = 0; continue; } else { a1[0] = 0; } break; } else if ( a1[0] == FUNHEAD+ARGHEAD+4 && a1[ARGHEAD] == FUNHEAD+4 && a1[*a1-1] == 3 && a1[*a1-2] == 1 && a1[*a1-3] == 1 && a1[ARGHEAD+1] >= FUNCTION ) { a = t = a1+*a1; while ( *t ) NEXTARG(t); i = t - a; *a1 = -a1[ARGHEAD+1]; t = a1+1; NCOPY(t,a,i); *t = 0; } NEXTARG(a1); } } if ( argfree == 0 ) { argfree = argin; } else if ( argfree[0] == ( argfree[ARGHEAD]+ARGHEAD ) ) { Normalize(BHEAD argfree+ARGHEAD); argfree[0] = argfree[ARGHEAD]+ARGHEAD; argfree[1] = 0; if ( ( argfree[0] == ARGHEAD+4 ) && ( argfree[ARGHEAD+3] == 3 ) && ( argfree[ARGHEAD+1] == 1 ) && ( argfree[ARGHEAD+2] == 1 ) ) { goto return0; } } else { /* The way we took out objects is rather brutish. We have to normalize */ NewSort(BHEAD0); t = argfree+ARGHEAD; while ( *t ) { tstop = t + *t; Normalize(BHEAD t); StoreTerm(BHEAD t); t = tstop; } /* par = 1, in case the arg has more than SubTermsInSmall terms */ EndSort(BHEAD argfree+ARGHEAD,1); t = argfree+ARGHEAD; while ( *t ) t += *t; *argfree = t - argfree; } /* #] step 2 : #[ step 3 : look whether we have done this one already. */ if ( ( number = FindArg(BHEAD argfree) ) != 0 ) { if ( number > 0 ) t = cbuf[AT.fbufnum].rhs[number-1]; else t = cbuf[AC.ffbufnum].rhs[-number-1]; /* Now position on the result. Remember we have in the cache: inputarg,0,outputargs,0 t is currently at inputarg. *inputarg is always positive. in principle this holds also for the arguments in the output but we take no risks here (in case of future developments). */ t += *t; t++; tstop = t; ii = 0; while ( *tstop ) { if ( *tstop == -SNUMBER && tstop[1] == -1 ) { sign = -sign; ii += 2; } NEXTARG(tstop); } a = argout; while ( *a ) NEXTARG(a); #ifndef NEWORDER if ( sign == -1 ) { *a++ = -SNUMBER; *a++ = -1; *a = 0; sign = 1; } #endif i = tstop - t - ii; ii = a - argout; a2 = a; a1 = a + i; *a1 = 0; while ( ii > 0 ) { *--a1 = *--a2; ii--; } a = argout; while ( *t ) { if ( *t == -SNUMBER && t[1] == -1 ) { t += 2; } else { COPY1ARG(a,t) } } goto return0; } /* #] step 3 : #[ step 4 : invoke ConvertToPoly We make a copy first in case there are no factors */ argcopy = TermMalloc("argcopy"); for ( i = 0; i <= *argfree; i++ ) argcopy[i] = argfree[i]; tstop = argfree + *argfree; { WORD sumcommu = 0; t = argfree + ARGHEAD; while ( t < tstop ) { sumcommu += DoesCommu(t); t += *t; } if ( sumcommu > 1 ) { MesPrint("ERROR: Cannot factorize an argument with more than one noncommuting object"); Terminate(-1); } } t = argfree + ARGHEAD; while ( t < tstop ) { if ( ( t[1] != SYMBOL ) && ( *t != (ABS(t[*t-1])+1) ) ) { action = 1; break; } t += *t; } if ( action ) { t = argfree + ARGHEAD; argextra = AT.WorkPointer; NewSort(BHEAD0); while ( t < tstop ) { if ( LocalConvertToPoly(BHEAD t,argextra,startebuf,0) < 0 ) { error = -1; getout: AR.SortType = oldsorttype; TermFree(argcopy,"argcopy"); if ( argfree != argin ) TermFree(argfree,"argfree"); MesCall("ArgFactorize"); Terminate(-1); return(-1); } StoreTerm(BHEAD argextra); t += *t; argextra += *argextra; } /* par = 1, in case the arg has more than SubTermsInSmall terms */ if ( EndSort(BHEAD argfree+ARGHEAD,1) < 0 ) { error = -2; goto getout; } t = argfree + ARGHEAD; while ( *t > 0 ) t += *t; *argfree = t - argfree; } /* #] step 4 : #[ step 5 : If not in the tables, we have to do this by hard work. */ a = argout; while ( *a ) NEXTARG(a); if ( poly_factorize_argument(BHEAD argfree,a) < 0 ) { MesCall("ArgFactorize"); error = -1; } /* #] step 5 : #[ step 6 : use now ConvertFromPoly Be careful: there should be more than one argument now. */ if ( error == 0 && action ) { a1 = a; NEXTARG(a1); if ( *a1 != 0 ) { CBUF *C = cbuf+AC.cbufnum; CBUF *CC = cbuf+AT.ebufnum; WORD *oldworkpointer = AT.WorkPointer; WORD *argcopy2 = TermMalloc("argcopy2"), *a1, *a2; a1 = a; a2 = argcopy2; while ( *a1 ) { if ( *a1 < 0 ) { if ( *a1 > -FUNCTION ) *a2++ = *a1++; *a2++ = *a1++; *a2 = 0; continue; } t = a1 + ARGHEAD; tstop = a1 + *a1; argextra = AT.WorkPointer; NewSort(BHEAD0); while ( t < tstop ) { if ( ConvertFromPoly(BHEAD t,argextra,numxsymbol,CC->numrhs-startebuf+numxsymbol ,startebuf-numxsymbol,1) <= 0 ) { TermFree(argcopy2,"argcopy2"); LowerSortLevel(); error = -3; goto getout; } t += *t; AT.WorkPointer = argextra + *argextra; /* ConvertFromPoly leaves terms with subexpressions. Hence: */ if ( Generator(BHEAD argextra,C->numlhs) ) { TermFree(argcopy2,"argcopy2"); LowerSortLevel(); error = -4; goto getout; } } AT.WorkPointer = oldworkpointer; /* par = 1, in case the factor has more than SubTermsInSmall terms */ if ( EndSort(BHEAD a2+ARGHEAD,1) < 0 ) { error = -5; goto getout; } t = a2+ARGHEAD; while ( *t ) t += *t; *a2 = t - a2; a2[1] = 0; ZEROARG(a2); ToFast(a2,a2); NEXTARG(a2); a1 = tstop; } i = a2 - argcopy2; a2 = argcopy2; a1 = a; NCOPY(a1,a2,i); *a1 = 0; TermFree(argcopy2,"argcopy2"); /* Erase the entries we made temporarily in cbuf[AT.ebufnum] */ CC->numrhs = startebuf; } else { /* no factorization. recover the argument from before step 3. */ for ( i = 0; i <= *argcopy; i++ ) a[i] = argcopy[i]; } } /* #] step 6 : #[ step 7 : Add this one to the tables. Possibly drop some elements in the tables when they become too full. */ if ( error == 0 && AN.ncmod == 0 ) { if ( InsertArg(BHEAD argcopy,a,0) < 0 ) { error = -1; } } /* #] step 7 : #[ step 8 : Clean up and return. Change the order of the arguments in argout and a. Use argcopy as spare space. */ ii = a - argout; for ( i = 0; i < ii; i++ ) argcopy[i] = argout[i]; a1 = a; while ( *a1 ) { if ( *a1 == -SNUMBER && a1[1] < 0 ) { sign = -sign; a1[1] = -a1[1]; if ( a1[1] == 1 ) { a2 = a1+2; while ( *a2 ) NEXTARG(a2); i = a2-a1-2; a2 = a1+2; NCOPY(a1,a2,i); *a1 = 0; } while ( *a1 ) NEXTARG(a1); break; } else { if ( *a1 > 0 && *a1 == a1[ARGHEAD]+ARGHEAD && a1[*a1-1] < 0 ) { a1[*a1-1] = -a1[*a1-1]; sign = -sign; } if ( *a1 == ARGHEAD+4 && a1[ARGHEAD+1] == 1 && a1[ARGHEAD+2] == 1 ) { a2 = a1+ARGHEAD+4; while ( *a2 ) NEXTARG(a2); i = a2-a1-ARGHEAD-4; a2 = a1+ARGHEAD+4; NCOPY(a1,a2,i); *a1 = 0; break; } while ( *a1 ) NEXTARG(a1); break; } NEXTARG(a1); } i = a1 - a; a2 = argout; NCOPY(a2,a,i); for ( i = 0; i < ii; i++ ) *a2++ = argcopy[i]; #ifndef NEWORDER if ( sign == -1 ) { *a2++ = -SNUMBER; *a2++ = -1; sign = 1; } #endif *a2 = 0; TermFree(argcopy,"argcopy"); return0: if ( argfree != argin ) TermFree(argfree,"argfree"); if ( oldsorttype != AR.SortType ) { AR.SortType = oldsorttype; a = argout; while ( *a ) { if ( *a > 0 ) { NewSort(BHEAD0); oldword = a[*a]; a[*a] = 0; t = a+ARGHEAD; while ( *t ) { tstop = t + *t; StoreTerm(BHEAD t); t = tstop; } /* par = 1, in case the factor has more than SubTermsInSmall terms */ EndSort(BHEAD a+ARGHEAD,1); a[*a] = oldword; a += *a; } else { NEXTARG(a); } } } #ifdef NEWORDER t = argout; numargs = 0; while ( *t ) { tt = t; NEXTARG(t); if ( *tt == ABS(t[-1])+1+ARGHEAD && sign == -1 ) { t[-1] = -t[-1]; sign = 1; } else if ( *tt == -SNUMBER && sign == -1 ) { tt[1] = -tt[1]; sign = 1; } numargs++; } if ( sign == -1 ) { *t++ = -SNUMBER; *t++ = -1; *t = 0; sign = 1; numargs++; } #else /* Now we have to sort the arguments First have the number of 'nontrivial/nonnumerical' arguments Then make a piece of code like in FullSymmetrize with that number of arguments to be symmetrized. Put a function in front Call the Symmetrize routine */ t = argout; numargs = 0; while ( *t && *t != -SNUMBER && ( *t < 0 || ( ABS(t[*t-1]) != *t-1 ) ) ) { NEXTARG(t); numargs++; } #endif if ( numargs > 1 ) { WORD *Lijst; WORD x[3]; x[0] = argout[-FUNHEAD]; x[1] = argout[-FUNHEAD+1]; x[2] = argout[-FUNHEAD+2]; while ( *t ) { NEXTARG(t); } argout[-FUNHEAD] = SQRTFUNCTION; argout[-FUNHEAD+1] = t-argout+FUNHEAD; argout[-FUNHEAD+2] = 0; AT.WorkPointer = t+1; Lijst = AT.WorkPointer; for ( i = 0; i < numargs; i++ ) Lijst[i] = i; AT.WorkPointer += numargs; error = Symmetrize(BHEAD argout-FUNHEAD,Lijst,numargs,1,SYMMETRIC); AT.WorkPointer = Lijst; argout[-FUNHEAD] = x[0]; argout[-FUNHEAD+1] = x[1]; argout[-FUNHEAD+2] = x[2]; #ifdef NEWORDER /* Now we have to get a potential numerical argument to the first position */ tstop = argout; while ( *tstop ) { NEXTARG(tstop); } t = argout; number = 0; while ( *t ) { tt = t; NEXTARG(t); if ( *tt == -SNUMBER ) { if ( number == 0 ) break; x[0] = tt[1]; while ( tt > argout ) { *--t = *--tt; } argout[0] = -SNUMBER; argout[1] = x[0]; break; } else if ( *tt == ABS(t[-1])+1+ARGHEAD ) { if ( number == 0 ) break; ii = t - tt; for ( i = 0; i < ii; i++ ) tstop[i] = tt[i]; while ( tt > argout ) { *--t = *--tt; } for ( i = 0; i < ii; i++ ) argout[i] = tstop[i]; *tstop = 0; break; } number++; } #endif } /* #] step 8 : */ return(error); } /* #] ArgFactorize : #[ FindArg : */ /** * Looks the argument up in the (workers) table. * If it is found the number in the table is returned (plus one to make it positive). * If it is not found we look in the compiler provided table. * If it is found - the number in the table is returned (minus one to make it negative). * If in neither table we return zero. */ WORD FindArg(PHEAD WORD *a) { int number; if ( AN.ncmod != 0 ) return(0); /* no room for mod stuff */ number = FindTree(AT.fbufnum,a); if ( number >= 0 ) return(number+1); number = FindTree(AC.ffbufnum,a); if ( number >= 0 ) return(-number-1); return(0); } /* #] FindArg : #[ InsertArg : */ /** * Inserts the argument into the (workers) table. * If the table is too full we eliminate half of it. * The eliminated elements are the ones that have not been used * most recently, weighted by their total use and age(?). * If par == 0 it inserts in the regular factorization cache * If par == 1 it inserts in the cache defined with the FactorCache statement */ int InsertArg(PHEAD WORD *argin, WORD *argout,int par) { CBUF *C; WORD *a, i, bufnum; if ( par == 0 ) { bufnum = AT.fbufnum; C = cbuf+bufnum; if ( C->numrhs >= (C->maxrhs-2) ) CleanupArgCache(BHEAD AT.fbufnum); } else if ( par == 1 ) { bufnum = AC.ffbufnum; C = cbuf+bufnum; } else { return(-1); } AddRHS(bufnum,1); AddNtoC(bufnum,*argin,argin,1); AddToCB(C,0) a = argout; while ( *a ) NEXTARG(a); i = a - argout; AddNtoC(bufnum,i,argout,2); AddToCB(C,0) return(InsTree(bufnum,C->numrhs)); } /* #] InsertArg : #[ CleanupArgCache : */ /** * Cleans up the argument factorization cache. * We throw half the elements. * For a weight of what we want to keep we use the product of * usage and the number in the buffer. */ int CleanupArgCache(PHEAD WORD bufnum) { CBUF *C = cbuf + bufnum; COMPTREE *boomlijst = C->boomlijst; LONG *weights = (LONG *)Malloc1(2*(C->numrhs+1)*sizeof(LONG),"CleanupArgCache"); LONG w, whalf, *extraweights; WORD *a, *to, *from; int i,j,k; for ( i = 1; i <= C->numrhs; i++ ) { weights[i] = ((LONG)i) * (boomlijst[i].usage); } /* Now sort the weights and determine the halfway weight */ extraweights = weights+C->numrhs+1; SortWeights(weights+1,extraweights,C->numrhs); whalf = weights[C->numrhs/2+1]; /* We should drop everybody with a weight < whalf. */ to = C->Buffer; k = 1; for ( i = 1; i <= C->numrhs; i++ ) { from = C->rhs[i]; w = ((LONG)i) * (boomlijst[i].usage); if ( w >= whalf ) { if ( i < C->numrhs-1 ) { if ( to == from ) { to = C->rhs[i+1]; } else { j = C->rhs[i+1] - from; C->rhs[k] = to; NCOPY(to,from,j) } } else if ( to == from ) { to += *to + 1; while ( *to ) NEXTARG(to); to++; } else { a = from; a += *a+1; while ( *a ) NEXTARG(a); a++; j = a - from; C->rhs[k] = to; NCOPY(to,from,j) } weights[k++] = boomlijst[i].usage; } } C->numrhs = --k; C->Pointer = to; /* Next we need to rebuild the tree. Note that this can probably be done much faster by using the remains of the old tree !!!!!!!!!!!!!!!! */ ClearTree(AT.fbufnum); for ( i = 1; i <= k; i++ ) { InsTree(AT.fbufnum,i); boomlijst[i].usage = weights[i]; } /* And cleanup */ M_free(weights,"CleanupArgCache"); return(0); } /* #] CleanupArgCache : #[ ArgSymbolMerge : */ int ArgSymbolMerge(WORD *t1, WORD *t2) { WORD *t1e = t1+t1[1]; WORD *t2e = t2+t2[1]; WORD *t1a = t1+2; WORD *t2a = t2+2; WORD *t3; while ( t1a < t1e && t2a < t2e ) { if ( *t1a < *t2a ) { if ( t1a[1] >= 0 ) { t3 = t1a+2; while ( t3 < t1e ) { t3[-2] = *t3; t3[-1] = t3[1]; t3 += 2; } t1e -= 2; } else t1a += 2; } else if ( *t1a > *t2a ) { if ( t2a[1] >= 0 ) t2a += 2; else { t3 = t1e; while ( t3 > t1a ) { *t3 = t3[-2]; t3[1] = t3[-1]; t3 -= 2; } *t1a++ = *t2a++; *t1a++ = *t2a++; t1e += 2; } } else { if ( t2a[1] < t1a[1] ) t1a[1] = t2a[1]; t1a += 2; t2a += 2; } } while ( t2a < t2e ) { if ( t2a[1] < 0 ) { *t1a++ = *t2a++; *t1a++ = *t2a++; } else t2a += 2; } while ( t1a < t1e ) { if ( t1a[1] >= 0 ) { t3 = t1a+2; while ( t3 < t1e ) { t3[-2] = *t3; t3[-1] = t3[1]; t3 += 2; } t1e -= 2; } else t1a += 2; } t1[1] = t1a - t1; return(0); } /* #] ArgSymbolMerge : #[ ArgDotproductMerge : */ int ArgDotproductMerge(WORD *t1, WORD *t2) { WORD *t1e = t1+t1[1]; WORD *t2e = t2+t2[1]; WORD *t1a = t1+2; WORD *t2a = t2+2; WORD *t3; while ( t1a < t1e && t2a < t2e ) { if ( *t1a < *t2a || ( *t1a == *t2a && t1a[1] < t2a[1] ) ) { if ( t1a[2] >= 0 ) { t3 = t1a+3; while ( t3 < t1e ) { t3[-3] = *t3; t3[-2] = t3[1]; t3[-1] = t3[2]; t3 += 3; } t1e -= 3; } else t1a += 3; } else if ( *t1a > *t2a || ( *t1a == *t2a && t1a[1] > t2a[1] ) ) { if ( t2a[2] >= 0 ) t2a += 3; else { t3 = t1e; while ( t3 > t1a ) { *t3 = t3[-3]; t3[1] = t3[-2]; t3[2] = t3[-1]; t3 -= 3; } *t1a++ = *t2a++; *t1a++ = *t2a++; *t1a++ = *t2a++; t1e += 3; } } else { if ( t2a[2] < t1a[2] ) t1a[2] = t2a[2]; t1a += 3; t2a += 3; } } while ( t2a < t2e ) { if ( t2a[2] < 0 ) { *t1a++ = *t2a++; *t1a++ = *t2a++; *t1a++ = *t2a++; } else t2a += 3; } while ( t1a < t1e ) { if ( t1a[2] >= 0 ) { t3 = t1a+3; while ( t3 < t1e ) { t3[-3] = *t3; t3[-2] = t3[1]; t3[-1] = t3[2]; t3 += 3; } t1e -= 3; } else t1a += 2; } t1[1] = t1a - t1; return(0); } /* #] ArgDotproductMerge : #[ TakeArgContent : */ /** * Implements part of the old ExecArg in which we take common factors * from arguments with more than one term. * The common pieces are put in argout as a sequence of arguments. * The part with the multiple terms that are now relative prime is * put in argfree which is allocated via TermMalloc and is given as the * return value. * The difference with the old code is that negative powers are always * removed. Hence it is as in MakeInteger in which only numerators will * be left: now only zero or positive powers will be remaining. */ WORD *TakeArgContent(PHEAD WORD *argin, WORD *argout) { GETBIDENTITY WORD *t, *rnext, *r1, *r2, *r3, *r5, *r6, *r7, *r8, *r9; WORD pow, *mm, *mnext, *mstop, *argin2 = argin, *argin3 = argin, *argfree; WORD ncom; int j, i, act; r5 = t = argin + ARGHEAD; r3 = argin + *argin; rnext = t + *t; GETSTOP(t,r6); r1 = argout; t++; /* First pass: arrange everything but the symbols and dotproducts. They need separate treatment because we have to take out negative powers. */ while ( t < r6 ) { /* #[ DELTA/VECTOR : */ if ( *t == DELTA || *t == VECTOR ) { r7 = t; r8 = t + t[1]; t += 2; while ( t < r8 ) { mm = rnext; pow = 1; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } if ( *mm == *r7 ) { mstop = mm + mm[1]; mm += 2; while ( ( *mm != *t || mm[1] != t[1] ) && mm < mstop ) mm += 2; if ( mm >= mstop ) pow = 0; } else pow = 0; if ( pow == 0 ) break; mm = mnext; } if ( pow == 0 ) { t += 2; continue; } /* We have a factor */ *r1++ = 8 + ARGHEAD; for ( j = 1; j < ARGHEAD; j++ ) *r1++ = 0; *r1++ = 8; *r1++ = *r7; *r1++ = 4; *r1++ = *t; *r1++ = t[1]; *r1++ = 1; *r1++ = 1; *r1++ = 3; argout = r1; /* Now we have to remove the delta's/vectors */ mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } mstop = mm + mm[1]; mm += 2; while ( mm < mstop && ( *mm != *t || mm[1] != t[1] ) ) mm += 2; *mm = mm[1] = NOINDEX; mm = mnext; } *t = t[1] = NOINDEX; t += 2; } } /* #] DELTA/VECTOR : #[ INDEX : */ else if ( *t == INDEX ) { r7 = t; r8 = t + t[1]; t += 2; while ( t < r8 ) { mm = rnext; pow = 1; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } if ( *mm == *r7 ) { mstop = mm + mm[1]; mm += 2; while ( *mm != *t && mm < mstop ) mm++; if ( mm >= mstop ) pow = 0; } else pow = 0; if ( pow == 0 ) break; mm = mnext; } if ( pow == 0 ) { t++; continue; } /* We have a factor */ if ( *t < 0 ) { *r1++ = -VECTOR; } else { *r1++ = -INDEX; } *r1++ = *t; argout = r1; /* Now we have to remove the index */ *t = NOINDEX; mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm != *r7 ) mm += mm[1]; else break; } mstop = mm + mm[1]; mm += 2; while ( mm < mstop && *mm != *t ) mm += 1; *mm = NOINDEX; mm = mnext; } t += 1; } } /* #] INDEX : #[ FUNCTION : */ else if ( *t >= FUNCTION ) { /* In the next code we should actually look inside the DENOMINATOR or EXPONENT for noncommuting objects */ if ( *t >= FUNCTION && functions[*t-FUNCTION].commute == 0 ) ncom = 0; else ncom = 1; if ( ncom ) { mm = r5 + 1; while ( mm < t && ( *mm == DUMMYFUN || *mm == DUMMYTEN ) ) mm += mm[1]; if ( mm < t ) { t += t[1]; continue; } } mm = rnext; pow = 1; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm == *t && mm[1] == t[1] ) { for ( i = 2; i < t[1]; i++ ) { if ( mm[i] != t[i] ) break; } if ( i >= t[1] ) { mm += mm[1]; goto nextmterm; } } if ( ncom && *mm != DUMMYFUN && *mm != DUMMYTEN ) { pow = 0; break; } mm += mm[1]; } if ( mm >= mstop ) pow = 0; if ( pow == 0 ) break; nextmterm: mm = mnext; } if ( pow == 0 ) { t += t[1]; continue; } /* Copy the function */ *r1++ = t[1] + 4 + ARGHEAD; for ( i = 1; i < ARGHEAD; i++ ) *r1++ = 0; *r1++ = t[1] + 4; for ( i = 0; i < t[1]; i++ ) *r1++ = t[i]; *r1++ = 1; *r1++ = 1; *r1++ = 3; argout = r1; /* Now we have to take out the functions */ mm = rnext; while ( mm < r3 ) { mnext = mm + *mm; GETSTOP(mm,mstop); mm++; while ( mm < mstop ) { if ( *mm == *t && mm[1] == t[1] ) { for ( i = 2; i < t[1]; i++ ) { if ( mm[i] != t[i] ) break; } if ( i >= t[1] ) { if ( functions[*t-FUNCTION].spec > 0 ) *mm = DUMMYTEN; else *mm = DUMMYFUN; mm += mm[1]; goto nextterm; } } mm += mm[1]; } nextterm: mm = mnext; } if ( functions[*t-FUNCTION].spec > 0 ) *t = DUMMYTEN; else *t = DUMMYFUN; t += t[1]; } /* #] FUNCTION : */ else { t += t[1]; } } /* #[ SYMBOL : Now collect all symbols. We can use the space after r1 as storage */ t = argin+ARGHEAD; rnext = t + *t; r2 = r1; while ( t < r3 ) { GETSTOP(t,r6); t++; act = 0; while ( t < r6 ) { if ( *t == SYMBOL ) { act = 1; i = t[1]; NCOPY(r2,t,i) } else { t += t[1]; } } if ( act == 0 ) { *r2++ = SYMBOL; *r2++ = 2; } t = rnext; rnext = rnext + *rnext; } *r2 = 0; argin2 = argin; /* Now we have a list of all symbols as a sequence of SYMBOL subterms. Any symbol that is absent in a subterm has power zero. We now need a list of all minimum powers. This can be done by subsequent merges. */ r7 = r1; /* The first object into which we merge. */ r8 = r7 + r7[1]; /* The object that gets merged into r7. */ while ( *r8 ) { r2 = r8 + r8[1]; /* Next object */ ArgSymbolMerge(r7,r8); r8 = r2; } /* Now we have to divide by the object in r7 and take it apart as factors. The division can be simple if there are no negative powers. */ if ( r7[1] > 2 ) { r8 = r7+2; r2 = r7 + r7[1]; act = 0; pow = 0; while ( r8 < r2 ) { if ( r8[1] < 0 ) { act = 1; pow += -r8[1]*(ARGHEAD+8); } else { pow += 2*r8[1]; } r8 += 2; } /* The amount of space we need to move r7 is given in pow */ if ( act == 0 ) { /* this can be done 'in situ' */ t = argin + ARGHEAD; while ( t < r3 ) { rnext = t + *t; GETSTOP(t,r6); t++; while ( t < r6 ) { if ( *t != SYMBOL ) { t += t[1]; continue; } r8 = r7+2; r9 = t + t[1]; t += 2; while ( ( t < r9 ) && ( r8 < r2 ) ) { if ( *t == *r8 ) { t[1] -= r8[1]; t += 2; r8 += 2; } else { /* *t must be < than *r8 !!! */ t += 2; } } t = r9; } t = rnext; } /* And now the factors that go to argout. First we have to move r7 out of the way. */ r8 = r7+pow; i = r7[1]; while ( --i >= 0 ) r8[i] = r7[i]; r2 += pow; r8 += 2; while ( r8 < r2 ) { for ( i = 0; i < r8[1]; i++ ) { *r1++ = -SYMBOL; *r1++ = *r8; } r8 += 2; } } else { /* this needs a new location */ argin2 = TermMalloc("TakeArgContent2"); /* We have to multiply the inverse of r7 into argin The answer should go to argin2. */ r5 = argin2; *r5++ = 0; *r5++ = 0; FILLARG(r5); t = argin+ARGHEAD; while ( t < r3 ) { rnext = t + *t; GETSTOP(t,r6); r9 = r5; *r5++ = *t++ + r7[1]; while ( t < r6 ) *r5++ = *t++; i = r7[1] - 2; r8 = r7+2; *r5++ = r7[0]; *r5++ = r7[1]; while ( i > 0 ) { *r5++ = *r8++; *r5++ = -*r8++; i -= 2; } while ( t < rnext ) *r5++ = *t++; Normalize(BHEAD r9); r5 = r9 + *r9; } *r5 = 0; *argin2 = r5-argin2; /* We may have to sort the terms in argin2. */ NewSort(BHEAD0); t = argin2+ARGHEAD; while ( *t ) { StoreTerm(BHEAD t); t += *t; } t = argin2+ARGHEAD; if ( EndSort(BHEAD t,0) < 0 ) goto Irreg; while ( *t ) t += *t; *argin2 = t - argin2; r3 = t; /* And now the factors that go to argout. First we have to move r7 out of the way. */ r8 = r7+pow; i = r7[1]; while ( --i >= 0 ) r8[i] = r7[i]; r2 += pow; r8 += 2; while ( r8 < r2 ) { if ( r8[1] >= 0 ) { for ( i = 0; i < r8[1]; i++ ) { *r1++ = -SYMBOL; *r1++ = *r8; } } else { for ( i = 0; i < -r8[1]; i++ ) { *r1++ = ARGHEAD+8; *r1++ = 0; FILLARG(r1); *r1++ = 8; *r1++ = SYMBOL; *r1++ = 4; *r1++ = *r8; *r1++ = -1; *r1++ = 1; *r1++ = 1; *r1++ = 3; } } r8 += 2; } argout = r1; } } /* #] SYMBOL : #[ DOTPRODUCT : Now collect all dotproducts. We can use the space after r1 as storage */ t = argin2+ARGHEAD; rnext = t + *t; r2 = r1; while ( t < r3 ) { GETSTOP(t,r6); t++; act = 0; while ( t < r6 ) { if ( *t == DOTPRODUCT ) { act = 1; i = t[1]; NCOPY(r2,t,i) } else { t += t[1]; } } if ( act == 0 ) { *r2++ = DOTPRODUCT; *r2++ = 2; } t = rnext; rnext = rnext + *rnext; } *r2 = 0; argin3 = argin2; /* Now we have a list of all dotproducts as a sequence of DOTPRODUCT subterms. Any dotproduct that is absent in a subterm has power zero. We now need a list of all minimum powers. This can be done by subsequent merges. */ r7 = r1; /* The first object into which we merge. */ r8 = r7 + r7[1]; /* The object that gets merged into r7. */ while ( *r8 ) { r2 = r8 + r8[1]; /* Next object */ ArgDotproductMerge(r7,r8); r8 = r2; } /* Now we have to divide by the object in r7 and take it apart as factors. The division can be simple if there are no negative powers. */ if ( r7[1] > 2 ) { r8 = r7+2; r2 = r7 + r7[1]; act = 0; pow = 0; while ( r8 < r2 ) { if ( r8[2] < 0 ) { pow += -r8[2]*(ARGHEAD+9); } else { pow += r8[2]*(ARGHEAD+9); } r8 += 3; } /* The amount of space we need to move r7 is given in pow For dotproducts we always need a new location */ { argin3 = TermMalloc("TakeArgContent3"); /* We have to multiply the inverse of r7 into argin The answer should go to argin2. */ r5 = argin3; *r5++ = 0; *r5++ = 0; FILLARG(r5); t = argin2+ARGHEAD; while ( t < r3 ) { rnext = t + *t; GETSTOP(t,r6); r9 = r5; *r5++ = *t++ + r7[1]; while ( t < r6 ) *r5++ = *t++; i = r7[1] - 2; r8 = r7+2; *r5++ = r7[0]; *r5++ = r7[1]; while ( i > 0 ) { *r5++ = *r8++; *r5++ = *r8++; *r5++ = -*r8++; i -= 3; } while ( t < rnext ) *r5++ = *t++; Normalize(BHEAD r9); r5 = r9 + *r9; } *r5 = 0; *argin3 = r5-argin3; /* We may have to sort the terms in argin3. */ NewSort(BHEAD0); t = argin3+ARGHEAD; while ( *t ) { StoreTerm(BHEAD t); t += *t; } t = argin3+ARGHEAD; if ( EndSort(BHEAD t,0) < 0 ) goto Irreg; while ( *t ) t += *t; *argin3 = t - argin3; r3 = t; /* And now the factors that go to argout. First we have to move r7 out of the way. */ r8 = r7+pow; i = r7[1]; while ( --i >= 0 ) r8[i] = r7[i]; r2 += pow; r8 += 2; while ( r8 < r2 ) { for ( i = ABS(r8[2]); i > 0; i-- ) { *r1++ = ARGHEAD+9; *r1++ = 0; FILLARG(r1); *r1++ = 9; *r1++ = DOTPRODUCT; *r1++ = 5; *r1++ = *r8; *r1++ = r8[1]; *r1++ = r8[2] < 0 ? -1: 1; *r1++ = 1; *r1++ = 1; *r1++ = 3; } r8 += 3; } argout = r1; } } /* #] DOTPRODUCT : We have now in argin3 the argument stripped of negative powers and common factors. The only thing left to deal with is to make the coefficients integer. For that we have to find the LCM of the denominators and the GCD of the numerators. And to start with, the sign. We force the sign of the first term to be positive. */ t = argin3 + ARGHEAD; pow = 1; t += *t; if ( t[-1] < 0 ) { pow = 0; t[-1] = -t[-1]; while ( t < r3 ) { t += *t; t[-1] = -t[-1]; } } /* Now the GCD of the numerators and the LCM of the denominators: */ argfree = TermMalloc("TakeArgContent1"); if ( AN.cmod != 0 ) { r1 = MakeMod(BHEAD argin3,r1,argfree); } else { r1 = MakeInteger(BHEAD argin3,r1,argfree); } if ( pow == 0 ) { *r1++ = -SNUMBER; *r1++ = -1; } *r1 = 0; /* Cleanup */ if ( argin3 != argin2 ) TermFree(argin3,"TakeArgContent3"); if ( argin2 != argin ) TermFree(argin2,"TakeArgContent2"); return(argfree); Irreg: MesPrint("Irregularity while sorting argument in TakeArgContent"); if ( argin3 != argin2 ) TermFree(argin3,"TakeArgContent3"); if ( argin2 != argin ) TermFree(argin2,"TakeArgContent2"); Terminate(-1); return(0); } /* #] TakeArgContent : #[ MakeInteger : */ /** * For normalizing everything to integers we have to * determine for all elements of this argument the LCM of * the denominators and the GCD of the numerators. * The input argument is in argin. * The number that comes out should go to argout. * The new pointer in the argout buffer is the return value. * The normalized argument is in argfree. */ WORD *MakeInteger(PHEAD WORD *argin,WORD *argout,WORD *argfree) { UWORD *GCDbuffer, *GCDbuffer2, *LCMbuffer, *LCMb, *LCMc; WORD *r, *r1, *r2, *r3, *r4, *r5, *rnext, i, k, j; WORD kGCD, kLCM, kGCD2, kkLCM, jLCM, jGCD; GCDbuffer = NumberMalloc("MakeInteger"); GCDbuffer2 = NumberMalloc("MakeInteger"); LCMbuffer = NumberMalloc("MakeInteger"); LCMb = NumberMalloc("MakeInteger"); LCMc = NumberMalloc("MakeInteger"); r4 = argin + *argin; r = argin + ARGHEAD; /* First take the first term to load up the LCM and the GCD */ r2 = r + *r; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kGCD = 0; kGCD < k; kGCD++ ) GCDbuffer[kGCD] = r3[kGCD]; k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; r1 = r2; /* Now go through the rest of the terms in this argument. */ while ( r1 < r4 ) { r2 = r1 + *r1; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( GCDbuffer[0] == 1 ) && ( kGCD == 1 ) ) ) { /* GCD is already 1 */ } else if ( ( ( k != 1 ) || ( r3[0] != 1 ) ) ) { if ( GcdLong(BHEAD GCDbuffer,kGCD,(UWORD *)r3,k,GCDbuffer2,&kGCD2) ) { NumberFree(GCDbuffer,"MakeInteger"); NumberFree(GCDbuffer2,"MakeInteger"); NumberFree(LCMbuffer,"MakeInteger"); NumberFree(LCMb,"MakeInteger"); NumberFree(LCMc,"MakeInteger"); goto MakeIntegerErr; } kGCD = kGCD2; for ( i = 0; i < kGCD; i++ ) GCDbuffer[i] = GCDbuffer2[i]; } else { kGCD = 1; GCDbuffer[0] = 1; } k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( LCMbuffer[0] == 1 ) && ( kLCM == 1 ) ) ) { for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; } else if ( ( k != 1 ) || ( r3[0] != 1 ) ) { if ( GcdLong(BHEAD LCMbuffer,kLCM,(UWORD *)r3,k,LCMb,&kkLCM) ) { NumberFree(GCDbuffer,"MakeInteger"); NumberFree(GCDbuffer2,"MakeInteger"); NumberFree(LCMbuffer,"MakeInteger"); NumberFree(LCMb,"MakeInteger"); NumberFree(LCMc,"MakeInteger"); goto MakeIntegerErr; } DivLong((UWORD *)r3,k,LCMb,kkLCM,LCMb,&kkLCM,LCMc,&jLCM); MulLong(LCMbuffer,kLCM,LCMb,kkLCM,LCMc,&jLCM); for ( kLCM = 0; kLCM < jLCM; kLCM++ ) LCMbuffer[kLCM] = LCMc[kLCM]; } else {} /* LCM doesn't change */ r1 = r2; } /* Now put the factor together: GCD/LCM */ r3 = (WORD *)(GCDbuffer); if ( kGCD == kLCM ) { for ( jGCD = 0; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; k = kGCD; } else if ( kGCD > kLCM ) { for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; for ( jGCD = kLCM; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = 0; k = kGCD; } else { for ( jGCD = kGCD; jGCD < kLCM; jGCD++ ) r3[jGCD] = 0; for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kLCM] = LCMbuffer[jGCD]; k = kLCM; } j = 2*k+1; /* Now we have to write this to argout */ if ( ( j == 3 ) && ( r3[1] == 1 ) && ( (WORD)(r3[0]) > 0 ) ) { *argout = -SNUMBER; argout[1] = r3[0]; r1 = argout+2; } else { r1 = argout; *r1++ = j+1+ARGHEAD; *r1++ = 0; FILLARG(r1); *r1++ = j+1; r2 = r3; for ( i = 0; i < k; i++ ) { *r1++ = *r2++; *r1++ = *r2++; } *r1++ = j; } /* Next we have to take the factor out from the argument. This cannot be done in location, because the denominator stuff can make coefficients longer. */ r2 = argfree + 2; FILLARG(r2) while ( r < r4 ) { rnext = r + *r; j = ABS(rnext[-1]); r5 = rnext - j; r3 = r2; while ( r < r5 ) *r2++ = *r++; j = (j-1)/2; /* reduced length. Remember, k is the other red length */ if ( DivRat(BHEAD (UWORD *)r5,j,GCDbuffer,k,(UWORD *)r2,&i) ) { goto MakeIntegerErr; } i = 2*i+1; r2 = r2 + i; if ( rnext[-1] < 0 ) r2[-1] = -i; else r2[-1] = i; *r3 = r2-r3; r = rnext; } *r2 = 0; argfree[0] = r2-argfree; argfree[1] = 0; /* Cleanup */ NumberFree(LCMc,"MakeInteger"); NumberFree(LCMb,"MakeInteger"); NumberFree(LCMbuffer,"MakeInteger"); NumberFree(GCDbuffer2,"MakeInteger"); NumberFree(GCDbuffer,"MakeInteger"); return(r1); MakeIntegerErr: MesCall("MakeInteger"); Terminate(-1); return(0); } /* #] MakeInteger : #[ MakeMod : */ /** * Similar to MakeInteger but now with modulus arithmetic using only * a one WORD 'prime'. We make the coefficient of the first term in the * argument equal to one. * Already the coefficients are taken modulus AN.cmod and AN.ncmod == 1 */ WORD *MakeMod(PHEAD WORD *argin,WORD *argout,WORD *argfree) { WORD *r, *instop, *r1, *m, x, xx, ix, ip; int i; r = argin; instop = r + *r; r += ARGHEAD; x = r[*r-3]; if ( r[*r-1] < 0 ) x += AN.cmod[0]; if ( GetModInverses(x,(WORD)(AN.cmod[0]),&ix,&ip) ) { Terminate(-1); } argout[0] = -SNUMBER; argout[1] = x; argout[2] = 0; r1 = argout+2; /* Now we have to multiply all coefficients by ix. This does not make things longer, but we should keep to the conventions of MakeInteger. */ m = argfree + ARGHEAD; while ( r < instop ) { xx = r[*r-3]; if ( r[*r-1] < 0 ) xx += AN.cmod[0]; xx = (WORD)((((LONG)xx)*ix) % AN.cmod[0]); if ( xx != 0 ) { i = *r; NCOPY(m,r,i); m[-3] = xx; m[-1] = 3; } else { r += *r; } } *m = 0; *argfree = m - argfree; argfree[1] = 0; argfree += 2; FILLARG(argfree); return(r1); } /* #] MakeMod : #[ SortWeights : */ /** * Sorts an array of LONGS in the same way SplitMerge (in sort.c) works * We use gradual division in two. */ void SortWeights(LONG *weights,LONG *extraspace,WORD number) { LONG w, *fill, *from1, *from2; int n1,n2,i; if ( number >= 4 ) { n1 = number/2; n2 = number - n1; SortWeights(weights,extraspace,n1); SortWeights(weights+n1,extraspace,n2); /* We copy the first patch to the extra space. Then we merge Note that a potential remaining n2 objects are already in place. */ for ( i = 0; i < n1; i++ ) extraspace[i] = weights[i]; fill = weights; from1 = extraspace; from2 = weights+n1; while ( n1 > 0 && n2 > 0 ) { if ( *from1 <= *from2 ) { *fill++ = *from1++; n1--; } else { *fill++ = *from2++; n2--; } } while ( n1 > 0 ) { *fill++ = *from1++; n1--; } } /* Special cases */ else if ( number == 3 ) { /* 6 permutations of which one is trivial */ if ( weights[0] > weights[1] ) { if ( weights[1] > weights[2] ) { w = weights[0]; weights[0] = weights[2]; weights[2] = w; } else if ( weights[0] > weights[2] ) { w = weights[0]; weights[0] = weights[1]; weights[1] = weights[2]; weights[2] = w; } else { w = weights[0]; weights[0] = weights[1]; weights[1] = w; } } else if ( weights[0] > weights[2] ) { w = weights[0]; weights[0] = weights[2]; weights[2] = weights[1]; weights[1] = w; } else if ( weights[1] > weights[2] ) { w = weights[1]; weights[1] = weights[2]; weights[2] = w; } } else if ( number == 2 ) { if ( weights[0] > weights[1] ) { w = weights[0]; weights[0] = weights[1]; weights[1] = w; } } return; } /* #] SortWeights : */ form-5.0.1/sources/token.c0000644000175100017510000016604215217035721011126 /** @file token.c * * The tokenizer. This is a part of the compiler that does an intermediate * type of translation. It does look up the names etc and can do a number * of optimizations. The resulting output is a stream of bytes which can * be processed by the code generator (in the file compiler.c) */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include "form3.h" /* #] Includes : #[ Compiler : #[ tokenize : Takes the input in 'in' and translates it into tokens. The tokens are put in the token buffer which starts at 'AC.tokens' and runs till 'AC.toptokens' We may assume that the various types of brackets match properly. object = -1: after , or ( object = 0: name/variable/number etc is allowed object = 1: variable. object = 2: number object = 3: ) after subexpression */ #define CHECKPOLY {if(polyflag)MesPrint("&Illegal use of polynomial function"); polyflag = 0; } int tokenize(UBYTE *in, WORD leftright) { int error = 0, object, funlevel = 0, bracelevel = 0, explevel = 0, numexp; int polyflag = 0; WORD number, type; UBYTE *s = in, c; SBYTE *out, *outtop, num[MAXNUMSIZE], *t; LONG i; if ( AC.tokens == 0 ) { SBYTE **ppp = &(AC.tokens); /* to avoid a compiler warning */ SBYTE **pppp = &(AC.toptokens); DoubleBuffer((void **)ppp,(void **)pppp,sizeof(SBYTE),"start tokens"); } out = AC.tokens; outtop = AC.toptokens - MAXNUMSIZE; AC.dumnumflag = 0; object = 0; while ( *in ) { if ( out > outtop ) { LONG oldsize = (LONG)(out - AC.tokens); SBYTE **ppp = &(AC.tokens); /* to avoid a compiler warning */ SBYTE **pppp = &(AC.toptokens); DoubleBuffer((void **)ppp,(void **)pppp,sizeof(SBYTE),"expand tokens"); out = AC.tokens + oldsize; outtop = AC.toptokens - MAXNUMSIZE; } switch ( FG.cTable[*in] ) { case 0: /* a-zA-Z */ CHECKPOLY s = in++; while ( FG.cTable[*in] == 0 || FG.cTable[*in] == 1 || *in == '_' ) in++; dovariable: c = *in; *in = 0; if ( object > 0 ) { MesPrint("&Illegal position for %s",s); if ( !error ) error = 1; } if ( out > AC.tokens && ( out[-1] == TWILDCARD || out[-1] == TNOT ) ) { type = GetName(AC.varnames,s,&number,NOAUTO); } else { type = GetName(AC.varnames,s,&number,WITHAUTO); } if ( type < 0 ) type = GetName(AC.exprnames,s,&number,NOAUTO); switch ( type ) { case CSYMBOL: *out++ = TSYMBOL; break; case CINDEX: if ( number >= (AM.IndDum-AM.OffsetIndex) ) { if ( c != '?' ) { MesPrint("&Generated indices should be of the type Nnumber_?"); error = 1; } else { *in++ = c; c = *in; *in = 0; AC.dumnumflag = 1; } } *out++ = TINDEX; break; case CVECTOR: *out++ = TVECTOR; break; case CFUNCTION: #ifdef WITHMPI /* * In the preprocessor, random functions in #$var=... and #inside * may cause troubles, because the program flow on a slave may be * different from those on others. We set AC.RhsExprInModuleFlag in order * to make the change of $-variable be done on the master and thus keep the * consistency among the master and all slave processes. The previous value * of AC.RhsExprInModuleFlag will be restored after #$var=... and #inside. */ if ( AP.PreAssignFlag || AP.PreInsideLevel ) { switch ( number + FUNCTION ) { case RANDOMFUNCTION: case RANPERM: AC.RhsExprInModuleFlag = 1; } } #endif *out++ = TFUNCTION; break; case CSET: *out++ = TSET; break; case CEXPRESSION: *out++ = TEXPRESSION; if ( leftright == LHSIDE ) { if ( !error ) error = 1; MesPrint("&Expression not allowed in LH-side of substitution: %s",s); } /*[06nov2003 mt]:*/ #ifdef WITHMPI else { /*RHSide*/ /* NOTE: We always set AC.RhsExprInModuleFlag regardless of * AP.PreAssignFlag or AP.PreInsideLevel because we have to detect * RHS expressions even in those cases. */ AC.RhsExprInModuleFlag = 1; } if ( !AP.PreAssignFlag && !AP.PreInsideLevel ) Expressions[number].vflags |= ISINRHS; #endif /*:[06nov2003 mt]*/ if ( AC.exprfillwarning == 0 ) { AC.exprfillwarning = 1; } break; case CDELTA: *out++ = TDELTA; *in = c; object = 1; continue; case CDUBIOUS: *out++ = TDUBIOUS; break; default: *out++ = TDUBIOUS; if ( !error ) error = 1; MesPrint("&Undeclared variable %s",s); number = AddDubious(s); break; } object = 1; donumber: i = 0; do { num[i++] = (SBYTE)(number & 0x7F); number >>= 7; } while ( number ); while ( --i >= 0 ) *out++ = num[i]; *in = c; break; case 1: /* 0-9 */ { #ifdef WITHFLOAT int spec; UBYTE *in2; #endif CHECKPOLY s = in; while ( *s == '0' && FG.cTable[s[1]] == 1 ) s++; in = s+1; i = 1; while ( FG.cTable[*in] == 1 ) { in++; i++; } if ( object > 0 ) { c = *in; *in = 0; MesPrint("&Illegal position for %s",s); *in = c; if ( !error ) error = 1; } if ( i == 1 && *in == '_' && ( *s == '5' || *s == '6' || *s == '7' ) ) { in++; *out++ = TSGAMMA; *out++ = (SBYTE)(*s - '4'); object = 1; break; } #ifdef WITHFLOAT in2 = CheckFloat(in,&spec); if ( in2 > in ) { if ( spec == -1 ) { MesPrint("&The floating point system has not been started: %s",in); if ( !error ) error = 1; } else { in = in2; dofloat: while ( out + (in-s) >= AC.toptokens ) { LONG oldsize = (LONG)(out - AC.tokens); SBYTE **ppp = &(AC.tokens); /* to avoid a compiler warning */ SBYTE **pppp = &(AC.toptokens); DoubleBuffer((void **)ppp,(void **)pppp,sizeof(SBYTE),"more tokens"); out = AC.tokens + oldsize; outtop = AC.toptokens - MAXNUMSIZE; } *out++ = TFLOAT; while ( s < in ) *out++ = *s++; } } else #endif { *out++ = TNUMBER; if ( ( i & 1 ) != 0 ) *out++ = (SBYTE)(*s++ - '0'); while ( out + (in-s)/2 >= AC.toptokens ) { LONG oldsize = (LONG)(out - AC.tokens); SBYTE **ppp = &(AC.tokens); /* to avoid a compiler warning */ SBYTE **pppp = &(AC.toptokens); DoubleBuffer((void **)ppp,(void **)pppp,sizeof(SBYTE),"more tokens"); out = AC.tokens + oldsize; outtop = AC.toptokens - MAXNUMSIZE; } while ( s < in ) { /* We store in base 100 */ *out++ = (SBYTE)(( *s - '0' ) * 10 + ( s[1] - '0' )); s += 2; } } object = 2; } break; case 2: /* . $ _ ? # ' */ CHECKPOLY if ( *in == '?' ) { if ( leftright == LHSIDE ) { if ( object == 1 ) { /* follows a name */ in++; *out++ = TWILDCARD; if ( FG.cTable[in[0]] == 0 || in[0] == '[' || in[0] == '{' ) object = 0; } else if ( object == -1 ) { /* follows comma or ( */ in++; s = in; while ( FG.cTable[*in] == 0 || FG.cTable[*in] == 1 ) in++; c = *in; *in = 0; if ( FG.cTable[*s] != 0 ) { MesPrint("&Illegal name for argument list variable %s",s); error = 1; } else { i = AddWildcardName((UBYTE *)s); *in = c; *out++ = TWILDARG; *out++ = (SBYTE)i; } object = 1; } else { MesPrint("&Illegal position for ?"); error = 1; in++; } } else { if ( object != -1 ) goto IllPos; in++; if ( FG.cTable[*in] == 0 || FG.cTable[*in] == 1 ) { s = in; while ( FG.cTable[*in] == 0 || FG.cTable[*in] == 1 ) in++; c = *in; *in = 0; i = GetWildcardName((UBYTE *)s); if ( i <= 0 ) { MesPrint("&Undefined argument list variable %s",s); error = 1; } *in = c; *out++ = TWILDARG; *out++ = (SBYTE)i; } else { if ( AC.vectorlikeLHS == 0 ) { MesPrint("&Generated index ? only allowed in vector substitution",s); error = 1; } *out++ = TGENINDEX; } object = 1; } } else if ( *in == '.' ) { if ( object == 1 ) { /* follows a name */ *out++ = TDOT; object = 0; in++; } #ifdef WITHFLOAT else if ( object == 0 || object == -1 ) { /* Test for floating point number */ int spec; s = CheckFloat(in,&spec); if ( s > in ) { if ( spec == -1 ) { MesPrint("&The floating point system has not been started: %s",in); if ( !error ) error = 1; in++; } else { UBYTE *a = s; s = in; in = a; goto dofloat; } } else goto IllPos; } #endif else goto IllPos; } else if ( *in == '$' ) { /* $ variable */ in++; s = in; if ( FG.cTable[*in] == 0 ) { while ( FG.cTable[*in] == 0 || FG.cTable[*in] == 1 ) in++; if ( *in == '_' && AP.PreAssignFlag == 2 ) in++; c = *in; *in = 0; if ( object > 0 ) { if ( object != 1 || leftright == RHSIDE ) { MesPrint("&Illegal position for $%s",s); if ( !error ) error = 1; } /* else can be assignment in wildcard */ else { if ( ( number = GetDollar(s) ) < 0 ) { number = AddDollar(s,0,0,0); } } } else if ( ( number = GetDollar(s) ) < 0 ) { MesPrint("&Undefined variable $%s",s); if ( !error ) error = 1; number = AddDollar(s,0,0,0); } *out++ = TDOLLAR; object = 1; if ( ( AC.exprfillwarning == 0 ) && ( ( out > AC.tokens+1 ) && ( out[-2] != TWILDCARD ) ) ) { AC.exprfillwarning = 1; } goto donumber; } else { MesPrint("Illegal name for $ variable after %s",in); if ( !error ) error = 1; } } else if ( *in == '#' ) { in++; if ( object == 1 ) { /* follows a name */ *out++ = TCONJUGATE; } else { MesPrint("&Illegal position for %#"); error = 1; } } else goto IllPos; break; case 3: /* [ ] */ CHECKPOLY if ( *in == '[' ) { if ( object == 1 ) { /* after name */ t = out-1; if ( *t == RPARENTHESIS ) { *out++ = LBRACE; *out++ = LPARENTHESIS; bracelevel++; explevel = bracelevel; } else { while ( *t >= 0 && t > AC.tokens ) t--; if ( *t == TEXPRESSION ) { *out++ = LBRACE; *out++ = LPARENTHESIS; bracelevel++; explevel = bracelevel; } else {*out++ = LBRACE; bracelevel++; } } object = 0; } else { /* name. find matching ] */ s = in; in = SkipAName(in); goto dovariable; } } else { if ( explevel > 0 && explevel == bracelevel ) { *out++ = RPARENTHESIS; explevel = 0; } *out++ = RBRACE; object = 1; bracelevel--; } in++; break; case 4: /* ( ) = ; , */ if ( *in == '(' ) { if ( funlevel >= AM.MaxParLevel ) { MesPrint("&More than %d levels of parentheses",AM.MaxParLevel); return(-1); } if ( object == 1 ) { /* After name -> function,vector */ AC.tokenarglevel[funlevel++] = TYPEISFUN; *out++ = TFUNOPEN; if ( polyflag ) { if ( in[1] != ')' && in[1] != ',' ) { *out++ = TNUMBER; *out++ = (SBYTE)(polyflag); *out++ = TCOMMA; *out++ = LPARENTHESIS; } else { *out++ = LPARENTHESIS; *out++ = TNUMBER; *out++ = (SBYTE)(polyflag); } polyflag = 0; } else if ( in[1] != ')' && in[1] != ',' ) { *out++ = LPARENTHESIS; } } else if ( object <= 0 ) { CHECKPOLY AC.tokenarglevel[funlevel++] = TYPEISSUB; *out++ = LPARENTHESIS; } else { polyflag = 0; AC.tokenarglevel[funlevel++] = TYPEISMYSTERY; MesPrint("&Illegal position for (: %s",in); if ( error >= 0 ) error = -1; } object = -1; } else if ( *in == ')' ) { funlevel--; if ( funlevel < 0 ) { /* if ( funflag == 0 ) { */ MesPrint("&There is an unmatched parenthesis"); if ( error >= 0 ) error = -1; /* } */ } else if ( object <= 0 && ( AC.tokenarglevel[funlevel] != TYPEISFUN || out[-1] != TFUNOPEN ) ) { MesPrint("&Illegal position for closing parenthesis."); if ( error >= 0 ) error = -1; if ( AC.tokenarglevel[funlevel] == TYPEISFUN ) object = 1; else object = 3; } else { if ( AC.tokenarglevel[funlevel] == TYPEISFUN ) { if ( out[-1] == TFUNOPEN ) out--; else { if ( out[-1] != TCOMMA ) *out++ = RPARENTHESIS; *out++ = TFUNCLOSE; } object = 1; } else if ( AC.tokenarglevel[funlevel] == TYPEISSUB ) { *out++ = RPARENTHESIS; object = 3; } } } else if ( *in == ',' ) { if ( /* object > 0 && */ funlevel > 0 && AC.tokenarglevel[funlevel-1] == TYPEISFUN ) { if ( out[-1] != TFUNOPEN && out[-1] != TCOMMA ) *out++ = RPARENTHESIS; else { *out++ = TNUMBER; *out++ = 0; } *out++ = TCOMMA; if ( in[1] != ',' && in[1] != ')' ) *out++ = LPARENTHESIS; else if ( in[1] == ')' ) { *out++ = TNUMBER; *out++ = 0; } } /* else if ( object > 0 ) { } */ else { MesPrint("&Illegal position for comma: %s",in); MesPrint("&Forgotten ; ?"); if ( error >= 0 ) error = -1; } object = -1; } else goto IllPos; in++; break; case 5: /* + - * % / ^ : */ CHECKPOLY if ( *in == ':' || *in == '%' ) goto IllPos; if ( *in == '*' || *in == '/' || *in == '^' ) { if ( object <= 0 ) { MesPrint("&Illegal position for operator: %s",in); if ( error >= 0 ) error = -1; } else if ( *in == '*' ) *out++ = TMULTIPLY; else if ( *in == '/' ) *out++ = TDIVIDE; else *out++ = TPOWER; in++; } else { i = 1; while ( *in == '+' || *in == '-' ) { if ( *in == '-' ) i = -i; in++; } if ( i == 1 ) { if ( out > AC.tokens && out[-1] != TFUNOPEN && out[-1] != LPARENTHESIS && out[-1] != TCOMMA && out[-1] != LBRACE ) *out++ = TPLUS; } else *out++ = TMINUS; } object = 0; break; case 6: /* Whitespace */ in++; break; case 7: /* { | } */ CHECKPOLY if ( *in == '{' ) { if ( object > 0 ) { MesPrint("&Illegal position for %s",in); if ( !error ) error = 1; } s = in+1; SKIPBRA2(in) number = DoTempSet(s,in); in++; if ( number >= 0 ) { *out++ = TSET; i = 0; do { num[i++] = (SBYTE)(number & 0x7F); number >>= 7; } while ( number ); while ( --i >= 0 ) *out++ = num[i]; } else if ( error == 0 ) error = 1; object = 1; } else goto IllPos; break; case 8: /* ! & < > */ CHECKPOLY if ( *in != '!' || leftright == RHSIDE || object != 1 || out[-1] != TWILDCARD ) goto IllPos; *out++ = TNOT; if ( FG.cTable[in[1]] == 0 || in[1] == '[' || in[1] == '{' ) object = 0; in++; break; default: IllPos: MesPrint("&Illegal character at this position: %s",in); if ( error >= 0 ) error = -1; in++; polyflag = 0; break; } } *out++ = TENDOFIT; AC.endoftokens = out; if ( funlevel > 0 || bracelevel != 0 ) { if ( funlevel > 0 ) MesPrint("&Unmatched parentheses"); if ( bracelevel != 0 ) MesPrint("&Unmatched braces"); return(-1); } if ( AC.TokensWriteFlag ) WriteTokens(AC.tokens); /* Simplify fixed set elements */ if ( error == 0 && simp1token(AC.tokens) ) error = 1; /* Collect wildcards for the prototype. Simplify the leftover wildcards */ if ( error == 0 && leftright == LHSIDE && simpwtoken(AC.tokens) ) error = 1; /* Now prepare the set[n] objects in the RHS. */ if ( error == 0 && leftright == RHSIDE && simp4token(AC.tokens) ) error = 1; /* Simplify simple function arguments (and 1/fac_ and 1/invfac_) */ if ( error == 0 && simp2token(AC.tokens) ) error = 1; /* Next we try to remove composite denominators or exponents and replace them by their internal functions. This may involve expanding the buffer. The return code of 3a is negative if there is an error and positive if indeed we need to do some work. simp3btoken does the work */ numexp = 0; if ( error == 0 && ( numexp = simp3atoken(AC.tokens,leftright) ) < 0 ) error = 1; if ( numexp > 0 ) { // Make some space at the beginning of AC.tokens, filled with TEMPTY. SBYTE *tt; out = AC.tokens; while ( *out != TENDOFIT ) out++; while ( out+numexp*9 > outtop ) { LONG oldsize = (LONG)(out - AC.tokens); SBYTE **ppp = &(AC.tokens); /* to avoid a compiler warning */ SBYTE **pppp = &(AC.toptokens); DoubleBuffer((void **)ppp,(void **)pppp,sizeof(SBYTE),"out tokens"); out = AC.tokens + oldsize; outtop = AC.toptokens - MAXNUMSIZE; } tt = out + numexp*9; while ( out >= AC.tokens ) { *tt-- = *out--; } while ( tt >= AC.tokens ) { *tt-- = TEMPTY; } if ( error == 0 && simp3btoken(AC.tokens,leftright) ) error = 1; if ( error == 0 && simp2token(AC.tokens) ) error = 1; } /* In simp5token we test for special cases like sumvariables that are already wildcards, etc. */ if ( error == 0 && simp5token(AC.tokens,leftright) ) error = 1; /* In simp6token we test for special cases like factorized expressions that occur in the RHS in an improper way. */ if ( error == 0 && simp6token(AC.tokens,leftright) ) error = 1; return(error); } /* #] tokenize : #[ WriteTokens : */ char *ttypes[] = { "\n", "S", "I", "V", "F", "set", "E", "dotp", "#", "sub", "d_", "$", "dub", "(", ")", "?", "??", ".", "[", "]", ",", "((", "))", "*", "/", "^", "+", "-", "!", "end", "{{", "}}", "N_?", "conj", "()", "#d", "^d", "_", "snum" }; void WriteTokens(SBYTE *in) { int numinline = 0, x, n = sizeof(ttypes)/sizeof(char *); char outbuf[81], *s, *out, c; out = outbuf; while ( *in != TENDOFIT ) { if ( *in < 0 ) { if ( *in >= -n ) { s = ttypes[-*in]; while ( *s ) { *out++ = *s++; numinline++; } } else { *out++ = '-'; x = -*in; numinline++; goto writenumber; } } else { x = *in; writenumber: s = out; do { *out++ = (char)(( x % 10 ) + '0'); numinline++; x = x / 10; } while ( x ); c = out[-1]; out[-1] = *s; *s = c; } if ( numinline > 70 ) { *out = 0; MesPrint("%s",outbuf); out = outbuf; numinline = 0; } else { *out++ = ' '; numinline++; } in++; } if ( numinline > 0 ) { *out = 0; MesPrint("%s",outbuf); } } /* #] WriteTokens : #[ simp1token : Routine substitutes set elements if possible. This means sets with a fixed argument like setname[3]. */ int simp1token(SBYTE *s) { int error = 0, n, i, base; WORD numsub; SBYTE *fill = s, *start, *t, numtab[10]; SETS set; while ( *s != TENDOFIT ) { if ( *s == RBRACE ) { start = fill-1; while ( *start != LBRACE ) start--; t = start - 1; while ( *t >= 0 ) t--; if ( *t == TSET && ( start[1] == TNUMBER || start[1] == TNUMBER1 ) ) { base = start[1] == TNUMBER ? 100: 128; start += 2; numsub = *start++; while ( *start >= 0 && start < fill ) { numsub = base*numsub + *start++; } if ( start == fill ) { start = t; t++; n = *t++; while ( *t >= 0 ) { n = 128*n + *t++; } set = Sets+n; if ( ( set->type != CRANGE ) && ( numsub > 0 && numsub <= set->last-set->first ) ) { fill = start; n = SetElements[set->first+numsub-1]; switch (set->type) { case CSYMBOL: if ( n > MAXPOWER ) { n -= 2*MAXPOWER; if ( n < 0 ) { n = -n; *fill++ = TMINUS; } *fill++ = TNUMBER1; } else *fill++ = TSYMBOL; break; case CINDEX: if ( n < AM.OffsetIndex ) *fill++ = TNUMBER1; else { *fill++ = TINDEX; n -= AM.OffsetIndex; } break; case CVECTOR: *fill++ = TVECTOR; n -= AM.OffsetVector; break; case CFUNCTION: *fill++ = TFUNCTION; n -= FUNCTION; break; case CNUMBER: *fill++ = TNUMBER1; break; case CDUBIOUS: *fill++ = TDUBIOUS; n = 1; break; } i = 0; if ( n < 0 ) { MesPrint("Value of n = %d",n); } do { numtab[i++] = (SBYTE)(n & 0x7F); n >>= 7; } while ( n ); while ( --i >= 0 ) *fill++ = numtab[i]; } else { MesPrint("&Illegal element %d in set",numsub); error++; } s++; continue; } } *fill++ = *s++; } else *fill++ = *s++; } *fill++ = TENDOFIT; return(error); } /* #] simp1token : #[ simpwtoken : Only to be called in the LHS. Hunts down the wildcards and writes them to the wildcardbuffer. Next it causes the ProtoType to be constructed. All wildcards are simplified into the trailing TWILDCARD, because the specifics are stored in the prototype. These specifics also include the transfer of wildcard values to $variables. Types of wildcards: a?, a?set, a?!set, a?set[i], A?set1?set2, ?a After this we can strip the set information. We still need the ? because of the wildcarding offset in code generation */ int simpwtoken(SBYTE *s) { int error = 0, first = 1, notflag; WORD num, numto, numdollar, *w = AC.WildC, *wstart, *wtop; SBYTE *fill = s, *t, *v, *s0 = s; while ( *s != TENDOFIT ) { if ( *s == TWILDCARD ) { notflag = 0; t = fill; while ( t > s0 && t[-1] >= 0 ) t--; v = t; num = 0; *fill++ = *s++; while ( *v >= 0 ) num = 128*num + *v++; if ( t > s0 ) t--; AC.NwildC += 4; if ( AC.NwildC > 4*AM.MaxWildcards ) goto firsterr; switch ( *t ) { case TSYMBOL: case TDUBIOUS: *w++ = SYMTOSYM; *w++ = 4; *w++ = num; *w++ = num; break; case TINDEX: num += AM.OffsetIndex; *w++ = INDTOIND; *w++ = 4; *w++ = num; *w++ = num; break; case TVECTOR: num += AM.OffsetVector; *w++ = VECTOVEC; *w++ = 4; *w++ = num; *w++ = num; break; case TFUNCTION: num += FUNCTION; *w++ = FUNTOFUN; *w++ = 4; *w++ = num; *w++ = num; break; default: MesPrint("&Illegal type of wildcard in LHS"); error = -1; *w++ = SYMTOSYM; *w++ = 4; *w++ = num; *w++ = num; break; break; } /* Now the sets. The s pointer sits after the ? */ wstart = w; if ( *s == TNOT && s[1] == TSET ) { notflag = 1; s++; } if ( *s == TSET ) { s++; num = 0; while ( *s >= 0 ) num = 128*num + *s++; if ( notflag == 0 && *s == TWILDCARD && s[1] == TSET ) { s += 2; numto = 0; while ( *s >= 0 ) numto = 128*numto + *s++; if ( num < AM.NumFixedSets || numto < AM.NumFixedSets || Sets[num].type == CRANGE || Sets[numto].type == CRANGE ) { MesPrint("&This type of set not allowed in this wildcard construction"); error = 1; } else { AC.NwildC += 4; if ( AC.NwildC > 4*AM.MaxWildcards ) goto firsterr; *w++ = FROMSET; *w++ = 4; *w++ = num; *w++ = numto; wstart = w; } } else if ( notflag == 0 && *s == LBRACE && s[1] == TSYMBOL ) { if ( num < AM.NumFixedSets || Sets[num].type == CRANGE ) { MesPrint("&This type of set not allowed in this wildcard construction"); error = 1; } v = s; s += 2; numto = 0; while ( *s >= 0 ) numto = 128*numto + *s++; if ( *s == TWILDCARD ) s++; /* most common mistake */ if ( *s == RBRACE ) { s++; AC.NwildC += 8; if ( AC.NwildC > 4*AM.MaxWildcards ) goto firsterr; *w++ = SETTONUM; *w++ = 4; *w++ = num; *w++ = numto; wstart = w; *w++ = SYMTOSYM; *w++ = 4; *w++ = numto; *w++ = 0; } else if ( *s == TDOLLAR ) { s++; numdollar = 0; while ( *s >= 0 ) numdollar = 128*numdollar + *s++; if ( *s == RBRACE ) { s++; AC.NwildC += 12; if ( AC.NwildC > 4*AM.MaxWildcards ) goto firsterr; *w++ = SETTONUM; *w++ = 4; *w++ = num; *w++ = numto; wstart = w; *w++ = SYMTOSYM; *w++ = 4; *w++ = numto; *w++ = 0; *w++ = LOADDOLLAR; *w++ = 4; *w++ = numdollar; *w++ = numdollar; } else { s = v; goto singlewild; } } else { s = v; goto singlewild; } } else { singlewild: num += notflag * 2*WILDOFFSET; AC.NwildC += 4; if ( AC.NwildC > 4*AM.MaxWildcards ) goto firsterr; *w++ = FROMSET; *w++ = 4; *w++ = num; *w++ = -WILDOFFSET; wstart = w; } } else if ( *s != TDOLLAR && *s != TENDOFIT && *s != RPARENTHESIS && *s != RBRACE && *s != TCOMMA && *s != TFUNCLOSE && *s != TMULTIPLY && *s != TPOWER && *s != TDIVIDE && *s != TPLUS && *s != TMINUS && *s != TPOWER1 && *s != TEMPTY && *s != TFUNOPEN && *s != TDOT ) { MesPrint("&Illegal type of wildcard in LHS"); error = -1; } if ( *s == TDOLLAR ) { s++; numdollar = 0; while ( *s >= 0 ) numdollar = 128*numdollar + *s++; AC.NwildC += 4; if ( AC.NwildC > 4*AM.MaxWildcards ) goto firsterr; wtop = w + 4; if ( wstart < w ) { while ( w > wstart ) { w[4] = w[0]; w--; } } *w++ = LOADDOLLAR; *w++ = 4; *w++ = numdollar; *w++ = numdollar; w = wtop; } } else if ( *s == TWILDARG ) { *fill++ = *s++; num = 0; while ( *s >= 0 ) { num = 128*num + *s; *fill++ = *s++; } AC.NwildC += 4; if ( AC.NwildC > 4*AM.MaxWildcards ) { firsterr: if ( first ) { MesPrint("&More than %d wildcards",AM.MaxWildcards); error = -1; first = 0; } } else { *w++ = ARGTOARG; *w++ = 4; *w++ = num; *w++ = -1; } if ( *s == TDOLLAR ) { s++; num = 0; while ( *s >= 0 ) num = 128*num + *s++; AC.NwildC += 4; if ( AC.NwildC > 4*AM.MaxWildcards ) goto firsterr; *w++ = LOADDOLLAR; *w++ = 4; *w++ = num; *w++ = num; } } else *fill++ = *s++; } *fill++ = TENDOFIT; AC.WildC = w; return(error); } /* #] simpwtoken : #[ simp2token : Deals with function arguments. The tokenizer has given function arguments extra parentheses. We remove the double parentheses. Next we remove the parentheses around the simple arguments. It also replaces /fac_() by *invfac_() and /invfac_() by *fac_() */ int simp2token(SBYTE *s) { SBYTE *to, *fill, *t, *v, *w, *s0 = s, *vv; int error = 0, n; /* Set substitutions */ fill = to = s; while ( *s != TENDOFIT ) { if ( *s == LPARENTHESIS && s[1] == LPARENTHESIS ) { t = s+1; n = 0; while ( n >= 0 ) { t++; if ( *t == LPARENTHESIS ) n++; else if ( *t == RPARENTHESIS ) n--; } if ( t[1] == RPARENTHESIS ) { *t = TEMPTY; s++; } *fill++ = *s++; } else if ( *s == TEMPTY ) s++; else if ( *s == AM.facnum && ( fill > (s0+1) ) && fill[-2] == TDIVIDE && fill[-1] == TFUNCTION ) { fill[-2] = TMULTIPLY; *fill++ = (SBYTE)(AM.invfacnum); s++; } else if ( *s == AM.invfacnum && ( fill > (s0+1) ) && fill[-2] == TDIVIDE && fill[-1] == TFUNCTION ) { fill[-2] = TMULTIPLY; *fill++ = (SBYTE)(AM.facnum); s++; } else *fill++ = *s++; } *fill++ = TENDOFIT; /* Second round: try to locate 'simple' arguments and strip their brackets We add (9-feb-2010) to the simple arguments integers of any size */ fill = s = to; while ( *s != TENDOFIT ) { if ( *s == LPARENTHESIS ) { t = s; n = 0; while ( n >= 0 ) { t++; if ( *t == LPARENTHESIS ) n++; else if ( *t == RPARENTHESIS ) n--; } if ( t[1] == TFUNCLOSE && s[1] != TWILDARG ) { /* Check for last argument in sum */ v = fill - 1; n = 0; while ( n >= 0 && v >= to ) { if ( *v == TFUNOPEN ) n--; else if ( *v == TFUNCLOSE ) n++; v--; } if ( v > to ) { while ( *v >= 0 ) v--; if ( *v == TFUNCTION ) { v++; n = 0; while ( *v >= 0 && v < fill ) n = 128*n + *v++; if ( n == AM.sumnum || n == AM.sumpnum ) { *fill++ = *s++; continue; } else if ( ( n == (FIRSTBRACKET-FUNCTION) || n == (TERMSINEXPR-FUNCTION) || n == (SIZEOFFUNCTION-FUNCTION) || n == (NUMFACTORS-FUNCTION) || n == (GCDFUNCTION-FUNCTION) || n == (DIVFUNCTION-FUNCTION) || n == (REMFUNCTION-FUNCTION) || n == (INVERSEFUNCTION-FUNCTION) || n == (MULFUNCTION-FUNCTION) || n == (FACTORIN-FUNCTION) || n == (FIRSTTERM-FUNCTION) || n == (CONTENTTERM-FUNCTION) ) && fill[-1] == TFUNOPEN ) { v = s+1; if ( *v == TEXPRESSION ) { v++; n = 0; while ( *v >= 0 ) n = 128*n + *v++; if ( v == t ) { *t = TEMPTY; s++; } } } } } } if ( ( fill > to ) && ( ( fill[-1] == TFUNOPEN || fill[-1] == TCOMMA ) && ( t[1] == TFUNCLOSE || t[1] == TCOMMA ) ) ) { v = s + 1; switch ( *v ) { case TMINUS: v++; if ( *v == TVECTOR ) { w = v+1; while ( *w >= 0 ) w++; if ( w == t ) { *t = TEMPTY; s++; } } else { if ( *v == TNUMBER || *v == TNUMBER1 ) { if ( BITSINWORD == 16 ) { ULONG x; WORD base; base = ( *v == TNUMBER ) ? 100: 128; vv = v+1; x = 0; while ( *vv >= 0 ) { x = x*base + *vv++; } if ( ( vv != t ) || ( ( vv - v ) > 4 ) || ( x > (MAXPOSITIVE+1) ) ) *fill++ = *s++; else { *t = TEMPTY; s++; break; } } else if ( BITSINWORD == 32 ) { ULONG x; WORD base; base = ( *v == TNUMBER ) ? 100: 128; vv = v+1; x = 0; while ( *vv >= 0 ) { x = x*base + *vv++; } if ( ( vv != t ) || ( ( vv - v ) > 6 ) || ( x > (MAXPOSITIVE+1) ) ) *fill++ = *s++; else { *t = TEMPTY; s++; break; } } else { if ( ( v+2 == t ) || ( v+3 == t && v[2] >= 0 ) ) { *t = TEMPTY; s++; break; } else *fill++ = *s++; } } else if ( *v == LPARENTHESIS && t[-1] == RPARENTHESIS ) { w = v; n = 0; while ( n >= 0 ) { w++; if ( *w == LPARENTHESIS ) n++; else if ( *w == RPARENTHESIS ) n--; } if ( w == ( t-1 ) ) { *t = TEMPTY; s++; } else *fill++ = *s++; } else *fill++ = *s++; break; } /* fall through */ case TSETNUM: v++; while ( *v >= 0 ) v++; goto tcommon; case TSYMBOL: if ( ( v[1] == COEFFSYMBOL || v[1] == NUMERATORSYMBOL || v[1] == DENOMINATORSYMBOL ) && v[2] < 0 ) { *fill++ = *s++; break; } /* fall through */ case TSET: case TVECTOR: case TINDEX: case TFUNCTION: case TDOLLAR: case TDUBIOUS: case TSGAMMA: tcommon: v++; while ( *v >= 0 ) v++; if ( v == t || ( v[0] == TWILDCARD && v+1 == t ) ) { *t = TEMPTY; s++; } else *fill++ = *s++; break; case TGENINDEX: v++; if ( v == t ) { *t = TEMPTY; s++; } else *fill++ = *s++; break; case TNUMBER: case TNUMBER1: if ( BITSINWORD == 16 ) { ULONG x; WORD base; base = ( *v == TNUMBER ) ? 100: 128; vv = v+1; x = 0; while ( *vv >= 0 ) { x = x*base + *vv++; } if ( ( vv != t ) || ( ( vv - v ) > 4 ) || ( x > MAXPOSITIVE ) ) *fill++ = *s++; else { *t = TEMPTY; s++; break; } } else if ( BITSINWORD == 32 ) { ULONG x; WORD base; base = ( *v == TNUMBER ) ? 100: 128; vv = v+1; x = 0; while ( *vv >= 0 ) { x = x*base + *vv++; } if ( ( vv != t ) || ( ( vv - v ) > 6 ) || ( x > MAXPOSITIVE ) ) *fill++ = *s++; else { *t = TEMPTY; s++; break; } } else { if ( ( v+2 == t ) || ( v+3 == t && v[2] >= 0 ) ) { *t = TEMPTY; s++; break; } else *fill++ = *s++; } break; case TWILDARG: v++; while ( *v >= 0 ) v++; if ( v == t ) { *t = TEMPTY; s++; } else *fill++ = *s++; break; case TEXPRESSION: /* First establish that there is only the expression in this argument. */ vv = s+1; while ( vv < t ) { if ( *vv != TEXPRESSION ) break; vv++; while ( *vv >= 0 ) vv++; } if ( vv < t ) { *fill++ = *s++; break; } /* Find the function */ w = fill-1; n = 0; while ( n >= 0 && w >= to ) { if ( *w == TFUNOPEN ) n--; else if ( *w == TFUNCLOSE ) n++; w--; } w--; while ( w > to && *w >= 0 ) w--; if ( *w != TFUNCTION ) { *fill++ = *s++; break; } w++; n = 0; while ( *w >= 0 ) { n = 128*n + *w++; } if ( n == GCDFUNCTION-FUNCTION || n == DIVFUNCTION-FUNCTION || n == REMFUNCTION-FUNCTION || n == INVERSEFUNCTION-FUNCTION || n == MULFUNCTION-FUNCTION ) { *t = TEMPTY; s++; } else *fill++ = *s++; break; default: *fill++ = *s++; break; } } else *fill++ = *s++; } else if ( *s == TEMPTY ) s++; else *fill++ = *s++; } *fill++ = TENDOFIT; return(error); } /* #] simp2token : #[ simp3atoken : We hunt for denominators and exponents that seem hidden. For the denominators we have to recognize: /fun /fun() /fun^power /fun()^power /set[n] /set[n]() /set[n]^power /set[n]()^power /symbol^power (power no number or symbol wildcard) /dotpr^power (id) /#^power (id) /() /()^power /vect /index /vect(anything) /vect(anything)^power */ int simp3atoken(SBYTE *s, int mode) { int error = 0, n, numexp = 0, denom, base, numprot, i; SBYTE *t, c; LONG num; WORD *prot; if ( mode == RHSIDE ) { prot = AC.ProtoType; numprot = prot[1] - SUBEXPSIZE; prot += SUBEXPSIZE; } else { prot = 0; numprot = 0; } while ( *s != TENDOFIT ) { denom = 1; if ( *s == TDIVIDE ) { denom = -1; s++; } c = *s; switch(c) { case TSYMBOL: case TNUMBER: case TNUMBER1: s++; while ( *s >= 0 ) s++; /* skip the object */ if ( *s == TWILDCARD ) s++; /* and the possible wildcard */ dosymbol: if ( *s != TPOWER ) continue; /* No power -> done */ s++; /* Skip the power */ if ( *s == TMINUS ) s++; /* negative: no difference here */ if ( *s == TNUMBER || *s == TNUMBER1 ) { base = *s == TNUMBER ? 100: 128; /* NUMBER = base 100 */ s++; /* Now we compose the power */ num = *s++; /* If the number is way too large */ while ( *s >= 0 ) { /* it may look like not too big */ if ( num > MAXPOWER ) break; /* Hence... */ num = base*num + *s++; } while ( *s >= 0 ) s++; /* Finish the number if needed */ if ( *s == TPOWER ) goto doublepower; if ( num <= MAXPOWER ) continue; /* Simple case */ } else if ( *s == TSYMBOL && c != TNUMBER && c != TNUMBER1 ) { s++; n = 0; while ( *s >= 0 ) { n = 128*n + *s++; } if ( *s == TWILDCARD ) { s++; if ( *s == TPOWER ) goto doublepower; continue; } /* Now we have to test whether n happens to be a wildcard */ if ( mode == RHSIDE ) { n += 2*MAXPOWER; for ( i = 0; i < numprot; i += 4 ) { if ( prot[i+2] == n && prot[i] == SYMTOSYM ) break; } if ( i < numprot ) break; } if ( *s == TPOWER ) goto doublepower; } numexp++; break; case TINDEX: s++; while ( *s >= 0 ) s++; if ( *s == TWILDCARD ) s++; doindex: if ( denom < 0 || *s == TPOWER ) { MesPrint("&Index to a power or in denominator is illegal"); error = 1; } break; case TVECTOR: s++; while ( *s >= 0 ) s++; if ( *s == TWILDCARD ) s++; dovector: if ( *s == TFUNOPEN ) { s++; n = 1; for(;;) { if ( *s == TFUNOPEN ) { n++; MesPrint("&Illegal vector index"); error = 1; } else if ( *s == TFUNCLOSE ) { n--; if ( n <= 0 ) break; } s++; } s++; } else if ( *s == TDOT ) goto dodot; if ( denom < 0 || *s == TPOWER || *s == TPOWER1 ) numexp++; break; case TFUNCTION: s++; while ( *s >= 0 ) s++; if ( *s == TWILDCARD ) s++; dofunction: t = s; if ( *t == TFUNOPEN ) { t++; n = 1; for(;;) { if ( *t == TFUNOPEN ) n++; else if ( *t == TFUNCLOSE ) { if ( --n <= 0 ) break; } t++; } t++; s++; } if ( denom < 0 || *t == TPOWER || *t == TPOWER1 ) numexp++; break; #ifdef WITHFLOAT case TFLOAT: s++; while ( *s >= 0 ) s++; if ( denom < 0 || *s == TPOWER || *s == TPOWER1 ) numexp++; break; #endif case TEXPRESSION: s++; while ( *s >= 0 ) s++; t = s; if ( *t == TFUNOPEN ) { t++; n = 1; for(;;) { if ( *t == TFUNOPEN ) n++; else if ( *t == TFUNCLOSE ) { if ( --n <= 0 ) break; } t++; } t++; } if ( *t == LBRACE ) { t++; n = 1; for(;;) { if ( *t == LBRACE ) n++; else if ( *t == RBRACE ) { if ( --n <= 0 ) break; } t++; } t++; } if ( denom < 0 || ( ( *t == TPOWER || *t == TPOWER1 ) && t[1] == TMINUS ) ) numexp++; break; case TDOLLAR: s++; while ( *s >= 0 ) s++; if ( denom < 0 || ( ( *s == TPOWER || *s == TPOWER1 ) && s[1] == TMINUS ) ) numexp++; break; case LPARENTHESIS: s++; n = 1; t = s; for(;;) { if ( *t == LPARENTHESIS ) n++; else if ( *t == RPARENTHESIS ) { if ( --n <= 0 ) break; } t++; } t++; if ( denom > 0 && ( *t == TPOWER || *t == TPOWER1 ) ) { if ( ( t[1] == TNUMBER || t[1] == TNUMBER1 ) && t[2] >= 0 && t[3] < 0 ) break; numexp++; } else if ( denom < 0 && ( *t == TPOWER || *t == TPOWER1 ) ) { if ( t[1] == TMINUS && ( t[2] == TNUMBER || t[2] == TNUMBER1 ) && t[3] >= 0 && t[4] < 0 ) break; numexp++; } else if ( denom < 0 || ( ( *t == TPOWER || *t == TPOWER1 ) && ( t[1] == TMINUS || t[1] == LPARENTHESIS ) ) ) numexp++; break; case TSET: s++; n = *s++; while ( *s >= 0 ) { n = 128*n + *s++; } n = Sets[n].type; switch ( n ) { case CSYMBOL: goto dosymbol; case CINDEX: goto doindex; case CVECTOR: goto dovector; case CFUNCTION: goto dofunction; case CNUMBER: goto dosymbol; case CMODEL: if ( denom < 0 || *s == TPOWER ) { MesPrint("&A model to a power or in denominator is illegal"); error = 1; } break; case ANYTYPE: if ( denom < 0 || *s == TPOWER ) { MesPrint("&A set without type to a power or in denominator is illegal"); error = 1; } break; default: error = 1; break; } break; case TDOT: dodot: s++; if ( *s == TVECTOR ) { s++; while ( *s >= 0 ) s++; } else if ( *s == TSET ) { s++; n = *s++; while ( *s >= 0 ) { n = 128*n + *s++; } if ( Sets[n].type != CVECTOR ) { MesPrint("&Set in dotproduct is not a set of vectors"); error = 1; } if ( *s == LBRACE ) { s++; n = 1; for(;;) { if ( *s == LBRACE ) n++; else if ( *s == RBRACE ) { if ( --n <= 0 ) break; } s++; } s++; } else { MesPrint("&Set without argument in dotproduct"); error = 1; } } else if ( *s == TSETNUM ) { s++; n = *s++; while ( *s >= 0 ) { n = 128*n + *s++; } if ( *s != TVECTOR ) goto nodot; s++; n = *s++; while ( *s >= 0 ) { n = 128*n + *s++; } if ( Sets[n].type != CVECTOR ) { MesPrint("&Set in dotproduct is not a set of vectors"); error = 1; } } else { nodot: MesPrint("&Illegal second element in dotproduct"); error = 1; s++; while ( *s >= 0 ) s++; } goto dosymbol; default: s++; while ( *s >= 0 ) s++; break; } } if ( error ) return(-1); return(numexp); doublepower: MesPrint("&Dubious notation with object^power1^power2"); return(-1); } /* #] simp3atoken : #[ simp3btoken : */ int simp3btoken(SBYTE *s, int mode) { int error = 0, i, numprot, n, denom, base, inset = 0, dotp, sube = 0; SBYTE *t, c, *fill, *ff, *ss; LONG num; WORD *prot; // Work in a temporary buffer, to avoid clashes between input and output SBYTE *tmptokens = (SBYTE*)Malloc1((AC.toptokens-AC.tokens)*sizeof(SBYTE), "simp3btoken scratch"); SBYTE* tmptoptokens = tmptokens + (AC.toptokens-AC.tokens); fill = tmptokens; if ( mode == RHSIDE ) { prot = AC.ProtoType; numprot = prot[1] - SUBEXPSIZE; prot += SUBEXPSIZE; } else { prot = 0; numprot = 0; } while ( *s == TEMPTY ) s++; while ( *s != TENDOFIT ) { // If we are near the end of the output buffer, we'd better reallocate // both tmptokens and AC.tokens (which must fit the final result). // Experimentally, fill can move by at most 5 per loop iteration, but // this buffer of 20 of might not be enough for all cases! while ( tmptoptokens - fill < 20 ) { LONG tmppos; tmppos = s - AC.tokens; DoubleBuffer((void**)&(AC.tokens), (void**)&(AC.toptokens), sizeof(SBYTE), "simp3btoken double"); s = AC.tokens + tmppos; tmppos = fill - tmptokens; DoubleBuffer((void**)&tmptokens, (void**)&tmptoptokens, sizeof(SBYTE), "simp3btoken scratch double"); fill = tmptokens + tmppos; } if ( *s == TEMPTY ) { s++; continue; } denom = 1; if ( *s == TDIVIDE ) { denom = -1; *fill++ = *s++; } ff = fill; ss = s; c = *s; if ( c == TSETNUM ) { *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; c = *s; } dotp = 0; switch(c) { case TSYMBOL: case TNUMBER: case TNUMBER1: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; if ( *s == TWILDCARD ) *fill++ = *s++; dosymbol: t = s; if ( *s != TPOWER ) continue; *fill++ = *s++; if ( *s == TMINUS ) *fill++ = *s++; if ( *s == TPLUS ) s++; if ( *s == TSETNUM ) { *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; inset = 1; } else inset = 0; if ( *s == TNUMBER || *s == TNUMBER1 ) { base = *s == TNUMBER ? 100: 128; *fill++ = *s++; num = *s++; *fill++ = num; while ( *s >= 0 ) { if ( num > MAXPOWER ) break; *fill++ = *s; num = base*num + *s++; } while ( *s >= 0 ) *fill++ = *s++; if ( num <= MAXPOWER ) continue; goto putexp1; } else if ( *s == TSYMBOL && c != TNUMBER && c != TNUMBER1 ) { *fill++ = *s++; n = 0; while ( *s >= 0 ) { n = 128*n + *s; *fill++ = *s++; } if ( *s == TWILDCARD ) { *fill++ = *s++; if ( *s == TPOWER ) goto doublepower; break; } /* Now we have to test whether n happens to be a wildcard */ if ( mode == RHSIDE && inset == 0 ) { /* n += WILDOFFSET;*/ for ( i = 0; i < numprot; i += 4 ) { if ( prot[i+2] == n && prot[i] == SYMTOSYM ) break; } if ( i < numprot ) break; } putexp1: fill = ff; if ( denom < 0 ) fill[-1] = TMULTIPLY; *fill++ = TFUNCTION; *fill++ = (SBYTE)(AM.expnum); *fill++ = TFUNOPEN; if ( dotp ) *fill++ = LPARENTHESIS; while ( ss < t ) *fill++ = *ss++; if ( dotp ) *fill++ = RPARENTHESIS; *fill++ = TCOMMA; ss++; /* Skip TPOWER */ if ( *ss == TMINUS ) { denom = -denom; ss++; } if ( denom < 0 ) { *fill++ = LPARENTHESIS; *fill++ = TMINUS; while ( ss < s ) *fill++ = *ss++; *fill++ = RPARENTHESIS; } else { while ( ss < s ) *fill++ = *ss++; } *fill++ = TFUNCLOSE; if ( *ss == TPOWER ) goto doublepower; } else { /* other objects can be composite */ goto dofunpower; } break; case TINDEX: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; if ( *s == TWILDCARD ) *fill++ = *s++; break; case TVECTOR: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; if ( *s == TWILDCARD ) *fill++ = *s++; dovector: if ( *s == TFUNOPEN ) { while ( *s != TFUNCLOSE ) *fill++ = *s++; *fill++ = *s++; } else if ( *s == TDOT ) goto dodot; t = s; goto dofunpower; #ifdef WITHFLOAT case TFLOAT: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; t = s; sube = 0; goto dofunpower; #endif case TFUNCTION: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; if ( *s == TWILDCARD ) *fill++ = *s++; dofunction: t = s; if ( *t == TFUNOPEN ) { t++; n = 1; for(;;) { if ( *t == TFUNOPEN ) n++; else if ( *t == TFUNCLOSE ) { if ( --n <= 0 ) break; } t++; } t++; *fill++ = *s++; } sube = 0; dofunpower: if ( *t == TPOWER || *t == TPOWER1 ) { if ( sube ) { if ( ( t[1] == TNUMBER || t[1] == TNUMBER1 ) && denom > 0 ) { if ( t[2] >= 0 && t[3] < 0 ) { sube = 0; break; } } else if ( t[1] == TMINUS && denom < 0 && ( t[2] == TNUMBER || t[2] == TNUMBER1 ) ) { if ( t[2] >= 0 && t[3] < 0 ) { sube = 0; break; } } sube = 0; } fill = ff; *fill++ = TFUNCTION; *fill++ = (SBYTE)(AM.expnum); *fill++ = TFUNOPEN; *fill++ = LPARENTHESIS; while ( ss < t ) *fill++ = *ss++; t++; *fill++ = RPARENTHESIS; *fill++ = TCOMMA; if ( *t == TMINUS ) { t++; denom = -denom; } *fill++ = LPARENTHESIS; if ( denom < 0 ) *fill++ = TMINUS; if ( *t == LPARENTHESIS ) { *fill++ = *t++; n = 0; while ( n >= 0 ) { if ( *t == LPARENTHESIS ) n++; else if ( *t == RPARENTHESIS ) n--; *fill++ = *t++; } } else if ( *t == TFUNCTION || *t == TDUBIOUS ) { *fill++ = *t++; while ( *t >= 0 ) *fill++ = *t++; if ( *t == TWILDCARD ) *fill++ = *t++; if ( *t == TFUNOPEN ) { *fill++ = *t++; n = 0; while ( n >= 0 ) { if ( *t == TFUNOPEN ) n++; else if ( *t == TFUNCLOSE ) n--; *fill++ = *t++; } } } else if ( *t == TSET ) { *fill++ = *t++; n = 0; while ( *t >= 0 ) { n = 128*n + *t; *fill++ = *t++; } if ( *t == LBRACE ) { if ( n < AM.NumFixedSets || Sets[n].type == CRANGE ) { MesPrint("&This type of usage of sets is not allowed"); error = 1; } *fill++ = *t++; n = 0; while ( n >= 0 ) { if ( *t == LBRACE ) n++; else if ( *t == RBRACE ) n--; *fill++ = *t++; } } } else if ( *t == TEXPRESSION ) { *fill++ = *t++; while ( *t >= 0 ) *fill++ = *t++; if ( *t == TFUNOPEN ) { *fill++ = *t++; n = 0; while ( n >= 0 ) { if ( *t == TFUNOPEN ) n++; else if ( *t == TFUNCLOSE ) n--; *fill++ = *t++; } } if ( *t == LBRACE ) { *fill++ = *t++; n = 0; while ( n >= 0 ) { if ( *t == LBRACE ) n++; else if ( *t == RBRACE ) n--; *fill++ = *t++; } } } else if ( *t == TVECTOR ) { *fill++ = *t++; while ( *t >= 0 ) *fill++ = *t++; if ( *t == TFUNOPEN ) { *fill++ = *t++; n = 0; while ( n >= 0 ) { if ( *t == TFUNOPEN ) n++; else if ( *t == TFUNCLOSE ) n--; *fill++ = *t++; } } else if ( *t == TDOT ) { *fill++ = *t++; if ( *t == TVECTOR || *t == TDUBIOUS ) { *fill++ = *t++; while ( *t >= 0 ) *fill++ = *t++; } else if ( *t == TSET ) { *fill++ = *t++; num = 0; while ( *t >= 0 ) { num = 128*num + *t; *fill++ = *t++; } if ( Sets[num].type != CVECTOR ) { MesPrint("&Illegal set type in dotproduct"); error = 1; } if ( *t == LBRACE ) { *fill++ = *t++; n = 0; while ( n >= 0 ) { if ( *t == LBRACE ) n++; else if ( *t == RBRACE ) n--; *fill++ = *t++; } } } else if ( *t == TSETNUM ) { *fill++ = *t++; while ( *t >= 0 ) { *fill++ = *t++; } *fill++ = *t++; while ( *t >= 0 ) { *fill++ = *t++; } } } else { MesPrint("&Illegal second element in dotproduct"); error = 1; } } else { *fill++ = *t++; while ( *t >= 0 ) *fill++ = *t++; if ( *t == TWILDCARD ) *fill++ = *t++; } *fill++ = RPARENTHESIS; *fill++ = TFUNCLOSE; if ( *t == TPOWER ) goto doublepower; while ( fill > ff ) *--t = *--fill; s = t; } else if ( denom < 0 ) { fill = ff; ff[-1] = TMULTIPLY; *fill++ = TFUNCTION; *fill++ = (SBYTE)(AM.denomnum); *fill++ = TFUNOPEN; *fill++ = LPARENTHESIS; while ( ss < t ) *fill++ = *ss++; *fill++ = RPARENTHESIS; *fill++ = TFUNCLOSE; while ( fill > ff ) *--t = *--fill; s = t; denom = 1; sube = 0; break; } sube = 0; break; case TEXPRESSION: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; t = s; if ( *t == TFUNOPEN ) { t++; n = 1; for(;;) { if ( *t == TFUNOPEN ) n++; else if ( *t == TFUNCLOSE ) { if ( --n <= 0 ) break; } t++; } t++; } if ( *t == LBRACE ) { t++; n = 1; for(;;) { if ( *t == LBRACE ) n++; else if ( *t == RBRACE ) { if ( --n <= 0 ) break; } t++; } t++; } if ( t > s || denom < 0 || ( ( *t == TPOWER || *t == TPOWER1 ) && t[1] == TMINUS ) ) goto dofunpower; else goto dosymbol; case TDOLLAR: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; goto dosymbol; case LPARENTHESIS: *fill++ = *s++; n = 1; t = s; for(;;) { if ( *t == LPARENTHESIS ) n++; else if ( *t == RPARENTHESIS ) { if ( --n <= 0 ) break; } t++; } t++; sube = 1; goto dofunpower; case TSET: *fill++ = *s++; n = *s++; *fill++ = (SBYTE)n; while ( *s >= 0 ) { *fill++ = *s; n = 128*n + *s++; } n = Sets[n].type; switch ( n ) { case CSYMBOL: goto dosymbol; case CINDEX: break; case CVECTOR: goto dovector; case CFUNCTION: goto dofunction; case CNUMBER: goto dosymbol; case CMODEL: break; case ANYTYPE: break; default: error = 1; break; } break; case TDOT: dodot: *fill++ = *s++; if ( *s == TVECTOR ) { *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; } else if ( *s == TSET ) { *fill++ = *s++; n = *s++; *fill++ = (SBYTE)n; while ( *s >= 0 ) { *fill++ = *s; n = 128*n + *s++; } if ( *s == LBRACE ) { if ( n < AM.NumFixedSets || Sets[n].type == CRANGE ) { MesPrint("&This type of usage of sets is not allowed"); error = 1; } *fill++ = *s++; n = 1; for(;;) { if ( *s == LBRACE ) n++; else if ( *s == RBRACE ) { if ( --n <= 0 ) break; } *fill++ = *s++; } *fill++ = *s++; } else { MesPrint("&Set without argument in dotproduct"); error = 1; } } else if ( *s == TSETNUM ) { *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; if ( *s != TVECTOR ) goto nodot; *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; } else { nodot: MesPrint("&Illegal second element in dotproduct"); error = 1; *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; } dotp = 1; goto dosymbol; default: *fill++ = *s++; while ( *s >= 0 ) *fill++ = *s++; break; } } *fill = TENDOFIT; // Now copy the modified tokens back to the original buffer fill = tmptokens; s = AC.tokens; do { *s++ = *fill; } while ( *fill++ != TENDOFIT ); M_free(tmptokens, "simp3btoken scratch"); return(error); doublepower:; MesPrint("&Dubious notation with power of power"); M_free(tmptokens, "simp3btoken scratch"); return(-1); } /* #] simp3btoken : #[ simp4token : Deal with the set[n] objects in the RHS. */ int simp4token(SBYTE *s) { int error = 0, n, nsym, settype; WORD i, *w, *wstop, level; SBYTE *const s0 = s; SBYTE *fill = s, *s1, *s2, *s3, type, s1buf[10]; SBYTE *tbuf = s, *t, *t1; while ( *s != TENDOFIT ) { if ( *s != TSET ) { if ( *s == TEMPTY ) s++; else *fill++ = *s++; continue; } if ( fill >= (s0+1) && fill[-1] == TWILDCARD ) { *fill++ = *s++; continue; } if ( fill >= (s0+2) && fill[-1] == TNOT && fill[-2] == TWILDCARD ) { *fill++ = *s++; continue; } s1 = s++; n = 0; while ( *s >= 0 ) { n = 128*n + *s++; } i = Sets[n].type; if ( *s != LBRACE ) { while ( s1 < s ) *fill++ = *s1++; continue; } if ( n < AM.NumFixedSets || i == CRANGE ) { MesPrint("&It is not allowed to refer to individual elements of built in or ranged sets"); error = 1; } s++; if ( *s != TSYMBOL && *s != TDOLLAR ) { MesPrint("&Set index in RHS is not a wildcard symbol or $-variable"); error = 1; while ( s1 < s ) *fill++ = *s1++; continue; } settype = ( *s == TDOLLAR ); s++; nsym = 0; s2 = s; while ( *s >= 0 ) nsym = 128*nsym + *s++; if ( *s != RBRACE ) { MesPrint("&Improper set argument in RHS"); error = 1; while ( s1 < s ) *fill++ = *s1++; continue; } s++; /* Verify that nsym is a wildcard */ if ( !settype ) { w = AC.ProtoType; wstop = w + w[1]; w += SUBEXPSIZE; while ( w < wstop ) { if ( *w == SYMTOSYM && w[2] == nsym ) break; w += w[1]; } if ( w >= wstop ) { /* It could still be a summation parameter! */ t = fill - 1; while ( t >= tbuf ) { if ( *t == TFUNCLOSE ) { level = 1; t--; while ( t >= tbuf ) { if ( *t == TFUNCLOSE ) level++; else if ( *t == TFUNOPEN ) { level--; if ( level == 0 ) break; } t--; } } else if ( *t == RBRACE ) { level = 1; t--; while ( t >= tbuf ) { if ( *t == RBRACE ) level++; else if ( *t == LBRACE ) { level--; if ( level == 0 ) break; } t--; } } else if ( *t == RPARENTHESIS ) { level = 1; t--; while ( t >= tbuf ) { if ( *t == RPARENTHESIS ) level++; else if ( *t == LPARENTHESIS ) { level--; if ( level == 0 ) break; } t--; } } else if ( *t == TFUNOPEN ) { t1 = t-1; while ( *t1 > 0 && t1 > tbuf ) t1--; if ( *t1 == TFUNCTION ) { t1++; level = 0; while ( *t1 > 0 ) level = level*128+*t1++; if ( level == (SUMF1-FUNCTION) || level == (SUMF2-FUNCTION) ) { t1 = t + 1; if ( *t1 == LPARENTHESIS ) t1++; if ( *t1 == TSYMBOL ) { if ( ( t1[1] == COEFFSYMBOL || t1[1] == NUMERATORSYMBOL || t1[1] == DENOMINATORSYMBOL ) && t1[2] < 0 ) {} else { t1++; level = 0; while ( *t1 >= 0 && t1 < fill ) level = 128*level + *t1++; if ( level == nsym && t1 < fill ) { if ( t[1] == LPARENTHESIS && *t1 == RPARENTHESIS && t1[1] == TCOMMA ) break; if ( t[1] != LPARENTHESIS && *t1 == TCOMMA ) break; } } } } } } t--; } if ( t < tbuf ) { fill--; MesPrint("&Set index in RHS is not a wildcard symbol"); error = 1; while ( s1 < s ) *fill++ = *s1++; continue; } } } /* Now replace by a set marker: TSETNUM,nsym,TYPE,setnumber */ switch ( i ) { case CSYMBOL: type = TSYMBOL; break; case CINDEX: type = TINDEX; break; case CVECTOR: type = TVECTOR; break; case CFUNCTION: type = TFUNCTION; break; case CNUMBER: type = TNUMBER1; break; case CDUBIOUS: type = TDUBIOUS; break; default: MesPrint("&Unknown set type in simp4token"); error = 1; type = CDUBIOUS; break; } s3 = s1buf; s1++; while ( *s1 >= 0 ) *s3++ = *s1++; *s3 = -1; s1 = s1buf; if ( settype ) *fill++ = TSETDOL; else *fill++ = TSETNUM; while ( *s2 >= 0 ) *fill++ = *s2++; *fill++ = type; while ( *s1 >= 0 ) *fill++ = *s1++; } *fill++ = TENDOFIT; return(error); } /* #] simp4token : #[ simp5token : Making sure that first argument of sumfunction is not a wildcard already */ int simp5token(SBYTE *s, int mode) { int error = 0, n, type; WORD *w, *wstop; if ( mode == RHSIDE ) { while ( *s != TENDOFIT ) { if ( *s == TFUNCTION ) { s++; n = 0; while ( *s >= 0 ) n = 128*n + *s++; if ( n == AM.sumnum || n == AM.sumpnum ) { if ( *s != TFUNOPEN ) continue; s++; if ( *s != TSYMBOL && *s != TINDEX ) continue; type = *s++; n = 0; while ( *s >= 0 ) n = 128*n + *s++; if ( type == TINDEX ) n += AM.OffsetIndex; if ( *s != TCOMMA ) continue; w = AC.ProtoType; wstop = w + w[1]; w += SUBEXPSIZE; while ( w < wstop ) { if ( w[2] == n ) { if ( ( type == TSYMBOL && ( w[0] == SYMTOSYM || w[0] == SYMTONUM || w[0] == SYMTOSUB ) ) || ( type == TINDEX && ( w[0] == INDTOIND || w[0] == INDTOSUB ) ) ) { error = 1; MesPrint("&Parameter of sum function is already a wildcard"); } } w += w[1]; } } } else s++; } } return(error); } /* #] simp5token : #[ simp6token : Making sure that factorized expressions are used properly */ int simp6token(SBYTE *tokens, int mode) { /* EXPRESSIONS e = Expressions; */ int error = 0, n; int level = 0, haveone = 0; SBYTE *s = tokens, *ss; LONG numterms; WORD funnum = 0; GETIDENTITY if ( mode == RHSIDE ) { while ( *s == TPLUS || *s == TMINUS ) s++; numterms = 1; while ( *s != TENDOFIT ) { if ( *s == LPARENTHESIS ) level++; else if ( *s == RPARENTHESIS ) level--; else if ( *s == TFUNOPEN ) level++; else if ( *s == TFUNCLOSE ) level--; else if ( ( *s == TPLUS || *s == TMINUS ) && level == 0 ) { /* Special exception: x^-1 etc. */ if ( s[-1] != TPOWER && s[-1] != TPLUS && s[-1] != TMINUS ) { numterms++; } } else if ( *s == TEXPRESSION ) { ss = s; s++; n = 0; while ( *s >= 0 ) n = 128*n + *s++; if ( Expressions[n].status == STOREDEXPRESSION ) { POSITION position; /* #ifdef WITHPTHREADS RENUMBER renumber; #endif */ RENUMBER renumber; WORD TMproto[SUBEXPSIZE]; TMproto[0] = EXPRESSION; TMproto[1] = SUBEXPSIZE; TMproto[2] = n; TMproto[3] = 1; { int ie; for ( ie = 4; ie < SUBEXPSIZE; ie++ ) TMproto[ie] = 0; } AT.TMaddr = TMproto; PUTZERO(position); /* if ( ( #ifdef WITHPTHREADS renumber = #endif GetTable(n,&position,0) ) == 0 ) */ if ( ( renumber = GetTable(n,&position,0) ) == 0 ) { error = 1; MesPrint("&Problems getting information about stored expression %s(4)" ,EXPRNAME(n)); } /* #ifdef WITHPTHREADS */ if ( renumber->symb.lo != AN.dummyrenumlist ) M_free(renumber->symb.lo,"VarSpace"); M_free(renumber,"Renumber"); /* #endif */ } if ( ( ( AS.Oldvflags[n] & ISFACTORIZED ) != 0 ) && *s != LBRACE ) { if ( level == 0 ) { haveone = 1; } else if ( error == 0 ) { if ( ss[-1] != TFUNOPEN || funnum != NUMFACTORS-FUNCTION ) { MesPrint("&Illegal use of factorized expression(s) in RHS"); error = 1; } } } continue; } else if ( *s == TFUNCTION ) { s++; funnum = 0; while ( *s >= 0 ) funnum = 128*funnum + *s++; continue; } s++; } if ( haveone ) { if ( numterms > 1 ) { MesPrint("&Factorized expression in RHS in an expression of more than one term."); error = 1; } else if ( AC.ToBeInFactors == 0 ) { MesPrint("&Attempt to put a factorized expression inside an unfactorized expression."); error = 1; } } } return(error); } /* #] simp6token : #] Compiler : */ form-5.0.1/sources/diawrap.cc0000644000175100017510000007617415217035721011606 /** @file diawrap.cc * * Functions with interface FORM with grcc, to implement the diagrams_ function. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ // #[ Includes : diawrap.cc extern "C" { #include "form3.h" } #include "grccparam.h" #include "grcc.h" #include #define MAXPOINTS 120 typedef struct ToPoTyPe { WORD *vert; WORD *vertmax; Options *opt; int cldeg[MAXPOINTS], clnum[MAXPOINTS], clext[MAXPOINTS]; int cmind[MAXLEGS+1],cmaxd[MAXLEGS+1]; int ncl, nvert; } TOPOTYPE; static void ProcessDiagram(EGraph *eg, void *ti); static int processVertex(TOPOTYPE *TopoInf, int pointsremaining, int level); // #] Includes : // #[ LoadModel : int LoadModel(MODEL *m) { // // First check whether there was a model already. // In the Kaneko setup there can be only one at the same time. // Hence if there was one we need to remove it first. // Unless of course, it was already the model we want. // if ( m->grccmodel != NULL ) return(0); int i,j,k; // // First the information that goes into the Model struct. // Note that new Model takes over (does not copy) minp.cnamlist. // MInput minp; PInput pinp; IInput iinp; if ( m->ncouplings > GRCC_MAXNCPLG ) { MesPrint("Too many coupling constants in model. Current limit is %d.",(WORD)GRCC_MAXNCPLG); MesPrint("Suggestion: recompile Form with a larger value for GRCC_MAXNCPLG"); return(-1); } minp.defpart = GRCC_DEFBYCODE; minp.name = (char *)(m->name); minp.ncouple = m->ncouplings; for ( i = 0; i < GRCC_MAXNCPLG; i++ ) minp.cnamlist[i] = NULL; for ( i = 0; i < minp.ncouple; i++ ) minp.cnamlist[i] = (char *)(VARNAME(symbols,m->couplings[i])); Model *mdl = new Model(&minp); // // Now the particles // for ( i = 0; i < m->nparticles; i++ ) { if ( minp.defpart == GRCC_DEFBYCODE ) { pinp.name = NULL; pinp.aname = NULL; pinp.pcode = m->vertices[i]->particles[0].number; pinp.acode = m->vertices[i]->particles[1].number; switch ( m->vertices[i]->particles[0].spin ) { case 1: pinp.ptypec = GRCC_PT_Scalar; break; case -1: pinp.ptypec = GRCC_PT_Ghost; break; case 2: if ( m->vertices[i]->particles[0].type == 0 ) pinp.ptypec = GRCC_PT_Majorana; else pinp.ptypec = GRCC_PT_Undef; break; case -2: if ( m->vertices[i]->particles[0].type == 0 ) pinp.ptypec = GRCC_PT_Majorana; else pinp.ptypec = GRCC_PT_Dirac; break; case 3: pinp.ptypec = GRCC_PT_Vector; break; default: pinp.ptypec = GRCC_PT_Undef; break; } } else { pinp.name = (char *)(VARNAME(functions,m->vertices[i]->particles[0].number)); pinp.aname = (char *)(VARNAME(functions,m->vertices[i]->particles[1].number)); switch ( m->vertices[i]->particles[0].spin ) { case 1: pinp.ptypen = "scalar"; break; case -1: pinp.ptypen = "ghost"; break; case 2: if ( m->vertices[i]->particles[0].type == 0 ) pinp.ptypen = "majorana"; else pinp.ptypen = "undef"; break; case -2: if ( m->vertices[i]->particles[0].type == 0 ) pinp.ptypen = "majorana"; else pinp.ptypen = "dirac"; break; case 3: pinp.ptypen = "vector"; break; default: pinp.ptypen = "undef"; break; } } pinp.extonly = m->vertices[i]->externonly; mdl->addParticle(&pinp); } mdl->addParticleEnd(); // // Now the vertices // for ( i = m->nparticles; i < m->invertices; i++ ) { VERTEX *v = m->vertices[i]; if ( minp.defpart == GRCC_DEFBYCODE ) { iinp.icode = NODEFUNCTION+i; iinp.name = NULL; } else { iinp.name = "node_"; } iinp.nplistn = v->nparticles; for ( j = 0; j < iinp.nplistn; j++ ) { if ( minp.defpart == GRCC_DEFBYCODE ) { iinp.plistc[j] = v->particles[j].number; } else { iinp.plistn[j] = (char *)(VARNAME(functions,v->particles[j].number)); } } // // We need a properly ordered list of coupling constants // The ordered list is in m->couplings. // For each vertex they are in v->couplings. // // iinp.cvallist = (int *)Malloc1(m->ncouplings*sizeof(int),"couplings"); for ( j = 0; j < m->ncouplings; j++ ) { iinp.cvallist[j] = 0; for ( k = 0; k < v->ncouplings; k += 2 ) { if ( v->couplings[k] == m->couplings[j] ) { iinp.cvallist[j] = v->couplings[k+1]; break; } } } mdl->addInteraction(&iinp); } mdl->addInteractionEnd(); m->grccmodel = (void *)mdl; return(0); } // #] LoadModel : // #[ ConvertParticle : int ConvertParticle(Model *model,int formnum) { // // Returns the grcc number of the particle, because grcc does not convert // int i; for ( i = 0; i < model->nParticles; i++ ) { if ( model->particles[i]->pcode == formnum ) { return(i); } else if ( model->particles[i]->acode == formnum ) { return(-i); } } MesPrint("Particle %d not found in model %s",formnum,model->name); Terminate(-1); return(0); } // #] ConvertParticle : // #[ ReConvertParticle : int ReConvertParticle(Model *model,int grccnum) { // // Returns the grcc number of the particle, because grcc does not convert // if ( grccnum < 0 ) { return(model->particles[-grccnum]->acode); } else { return(model->particles[grccnum]->pcode); } } // #] ReConvertParticle : // #[ numParticle : int numParticle(MODEL *m,WORD n) { int i; for ( i = 0; i < m->nparticles; i++ ) { if ( m->vertices[i]->particles[0].number == n ) return(i); if ( m->vertices[i]->particles[1].number == n ) return(i); } MesPrint("numParticle: particle %d not found in model",n); Terminate(-1); return(-1); } // #] numParticle : // #[ ProcessDiagram : void ProcessDiagram(EGraph *eg, void *ti) { // // This is the routine that gets a complete diagram and passes it on // to Form (Generator) for further algebraic manipulations. // The term is picked up from AT.diaterm and a new term is constructed // in the workspace. // GETIDENTITY TERMINFO *info = (TERMINFO *)ti; if ( ( info->flags & TOPOLOGIESONLY ) == TOPOLOGIESONLY ) return; WORD *term = info->term, *newterm, *oldworkpointer = AT.WorkPointer; WORD *tdia = term + info->diaoffset; WORD *tail = tdia + tdia[1]; WORD *tend = term + *term; WORD *fill, *startfill, *cfill, *afill; int i, j, intr; Model *model = (Model *)info->currentModel; MODEL *m = (MODEL *)info->currentMODEL; int numlegs, vect, edge, maxmom = 0; newterm = term + *term; for ( i = 1; i < info->diaoffset; i++ ) newterm[i] = term[i]; fill = newterm + info->diaoffset; // // Now get the nodes // if ( ( info->flags & WITHOUTNODES ) == 0 ) { for ( i = 0; i < eg->nNodes; i++ ) { // // node_(number,coupling,particle_1(momentum_1),...,particle_n(momentum_n)) // numlegs = eg->nodes[i]->deg; startfill = fill; *fill++ = NODEFUNCTION; *fill++ = 0; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = i+1; // // Now we put the coupling constants. This is done inside the // function for when we want to work with counterterms. // if ( !eg->isExternal(i) ) { afill = fill; *fill++ = 0; *fill++ = 1; FILLARG(fill) cfill = fill; *fill++ = 0; intr = eg->nodes[i]->intrct; for ( j = 0; j < model->interacts[intr]->nclist; j++ ) { if ( model->interacts[intr]->clist[j] != 0 ) { *fill++ = SYMBOL; *fill++ = 4; *fill++ = m->couplings[j]; *fill++ = model->interacts[intr]->clist[j]; } } *fill++ = 1; *fill++ = 1; *fill++ = 3; *cfill = fill - cfill; *afill = fill - afill; } else { *fill++ = -SNUMBER; *fill++ = 1; } // // Now the particles and their momenta. // for ( j = 0; j < numlegs; j++ ) { *fill++ = ARGHEAD+FUNHEAD+6; *fill++ = 0; FILLARG(fill) edge = eg->nodes[i]->edges[j]; vect = ABS(edge)-1; *fill++ = 6+FUNHEAD; int a; if ( edge < 0 ) { a = ReConvertParticle(model,-eg->edges[vect]->ptcl); } else { a = ReConvertParticle(model,eg->edges[vect]->ptcl); } *fill++ = a; *fill++ = FUNHEAD+2; FILLFUN(fill) *fill++ = edge < 0 ? -MINVECTOR: -VECTOR; if ( numlegs == 1 || vect < info->numextern ) { // Look up in set of external momenta *fill++ = SetElements[Sets[info->externalset].first+vect]; } else { // Look up in set of internal momenta set *fill++ = SetElements[Sets[info->internalset].first+(vect-eg->nExtern)]; // determine the number of momenta required from internalset: maxmom = MaX(maxmom, vect-eg->nExtern); } *fill++ = 1; *fill++ = 1; *fill++ = 3; } startfill[1] = fill-startfill; } } if ( ( info->flags & WITHEDGES ) == WITHEDGES ) { for ( i = 0; i < eg->nEdges; i++ ) { int n1 = eg->edges[i]->nodes[0]; int n2 = eg->edges[i]->nodes[1]; // int l1 = eg->edges[i]->nlegs[0]; // int l2 = eg->edges[i]->nlegs[1]; startfill = fill; *fill++ = EDGE; *fill++ = 0; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = i+1; // number of the edge // *fill++ = ARGHEAD+FUNHEAD+6; *fill++ = 0; FILLARG(fill) *fill++ = 6+FUNHEAD; int a = ReConvertParticle(model,eg->edges[i]->ptcl); *fill++ = a; *fill++ = FUNHEAD+2; FILLFUN(fill) *fill++ = -VECTOR; // Look up in set of internal momenta set if ( i < info->numextern ) { // Look up in set of external momenta *fill++ = SetElements[Sets[info->externalset].first+i]; } else { // Look up in set of internal momenta set *fill++ = SetElements[Sets[info->internalset].first+(i-eg->nExtern)]; maxmom = MaX(maxmom, i-eg->nExtern); } *fill++ = 1; *fill++ = 1; *fill++ = 3; // *fill++ = -SNUMBER; *fill++ = n1+1; // number of the node from *fill++ = -SNUMBER; *fill++ = n2+1; // number of the node to startfill[1] = fill - startfill; } } if ( ( info->flags & WITHBLOCKS ) == WITHBLOCKS ) { for ( i = 0; i < eg->econn->nblocks; i++ ) { startfill = fill; *fill++ = BLOCK; *fill++ = 0; FILLFUN(fill); *fill++ = -SNUMBER; *fill++ = i+1; *fill++ = -SNUMBER; *fill++ = eg->econn->blocks[i].loop; // // Now we have to make a list of all nodes inside this block // int bnodes[GRCC_MAXNODES], k; WORD *argfill = fill, *funfill; *fill++ = 0; *fill++ = 0; FILLARG(fill) *fill++ = 0; for ( k = 0; k < GRCC_MAXNODES; k++ ) bnodes[k] = 0; for ( k = 0; k < eg->econn->blocks[i].nmedges; k++ ) { bnodes[eg->econn->blocks[i].edges[k][0]] = 1; bnodes[eg->econn->blocks[i].edges[k][1]] = 1; } for ( k = 0; k < GRCC_MAXNODES; k++ ) { if ( bnodes[k] == 0 ) continue; // // Now we put the node inside this argument. // funfill = fill; *fill++ = NODEFUNCTION; *fill++ = 0; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = k+1; numlegs = eg->nodes[k]->deg; for ( j = 0; j < numlegs; j++ ) { edge = eg->nodes[k]->edges[j]; vect = ABS(edge)-1; *fill++ = -VECTOR; if ( numlegs == 1 || vect < info->numextern ) { // Look up in set of external momenta *fill++ = SetElements[Sets[info->externalset].first+vect]; } else { // Look up in set of internal momenta set *fill++ = SetElements[Sets[info->internalset].first+(vect-info->numextern)]; maxmom = MaX(maxmom, vect-info->numextern); } } funfill[1] = fill-funfill; } *fill++ = 1; *fill++ = 1; *fill++ = 3; *argfill = fill - argfill; argfill[ARGHEAD] = argfill[0] - ARGHEAD; startfill[1] = fill-startfill; } } if ( ( info->flags & WITHONEPISETS ) == WITHONEPISETS ) { for ( i = 0; i < eg->econn->nopic; i++ ) { startfill = fill; *fill++ = ONEPI; *fill++ = 0; FILLFUN(fill); *fill++ = -SNUMBER; *fill++ = i+1; *fill++ = -ONEPI; for ( j = 0; j < eg->econn->opics[i].nnodes; j++ ) { *fill++ = -SNUMBER; *fill++ = eg->econn->opics[i].nodes[j]+1; } startfill[1] = fill-startfill; } } // // Topology counter. We have exaggerated a bit with the eye on the far future. // if ( info->numtopo-1 < MAXPOSITIVE ) { *fill++ = TOPO; *fill++ = FUNHEAD+2; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = (WORD)(info->numtopo-1); } else if ( info->numtopo-1 < FULLMAX-1 ) { *fill++ = TOPO; *fill++ = FUNHEAD+ARGHEAD+4; FILLFUN(fill) *fill++ = ARGHEAD+4; *fill++ = 0; FILLARG(fill) *fill++ = 4; *fill++ = (WORD)((info->numtopo-1) & WORDMASK); *fill++ = 1; *fill++ = 3; } else { // for now: science fiction *fill++ = TOPO; *fill++ = FUNHEAD+ARGHEAD+6; FILLFUN(fill) *fill++ = ARGHEAD+6; *fill++ = 0; FILLARG(fill) *fill++ = 6; *fill++ = (WORD)((info->numtopo-1) >> BITSINWORD); *fill++ = (WORD)((info->numtopo-1) & WORDMASK); *fill++ = 0; *fill++ = 1; *fill++ = 5; } // // Symmetry factors. We let Normalize do the multiplication. // if ( eg->nsym != 1 ) { *fill++ = SNUMBER; *fill++ = 4; *fill++ = (WORD)eg->nsym; *fill++ = -1; } if ( eg->esym != 1 ) { *fill++ = SNUMBER; *fill++ = 4; *fill++ = (WORD)eg->esym; *fill++ = -1; } if ( eg->extperm != 1 ) { *fill++ = SNUMBER; *fill++ = 4; *fill++ = (WORD)eg->extperm; *fill++ = 1; } // // verify internalset has sufficient momenta: // if ( maxmom >= Sets[info->internalset].last - Sets[info->internalset].first ) { MLOCK(ErrorMessageLock); MesPrint("&Insufficient internal momenta in diagrams_"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // // finish it off // while ( tail < tend ) *fill++ = *tail++; if ( eg->fsign < 0 ) fill[-1] = -fill[-1]; *newterm = fill - newterm; AT.WorkPointer = fill; Generator(BHEAD newterm,info->level); AT.WorkPointer = oldworkpointer; } // #] ProcessDiagram : // #[ fendMG : Bool fendMG(EGraph *eg, void *ti) { DUMMYUSE(eg); DUMMYUSE(ti); return True; } // #] fendMG : // #[ ProcessTopology : Bool ProcessTopology(EGraph *eg, void *ti) { // // This routine is called for each new topology. // New convention: return True; generate the corresponding diagrams if needed // return False; skip diagram generation (when asked for). // TERMINFO *info = (TERMINFO *)ti; // This seems to work properly. It was disabled before. #define WITHEARLYVETO #ifdef WITHEARLYVETO if ( ( ( info->flags & CHECKEXTERN ) == CHECKEXTERN ) && info->currentMODEL != NULL ) { int i, j; int numlegs, vect, edge; for ( i = 0; i < eg->nNodes; i++ ) { if ( eg->isExternal(i) ) continue; numlegs = eg->nodes[i]->deg; for ( j = 0; j < numlegs; j++ ) { edge = eg->nodes[i]->edges[j]; vect = ABS(edge)-1; if ( vect < info->numextern && info->legcouple[vect][numlegs] == 0 ) { // This cannot be. info->numtopo++; return False; } } } } #endif if ( ( info->flags & TOPOLOGIESONLY ) == 0 ) { info->numtopo++; return True; } // // Now we are just generating topologies. // GETIDENTITY WORD *term = info->term, *newterm, *oldworkpointer = AT.WorkPointer; WORD *tdia = term + info->diaoffset; WORD *tail = tdia + tdia[1]; WORD *tend = term + *term; WORD *fill, *startfill; Model *model = (Model *)info->currentModel; MODEL *m = (MODEL *)info->currentMODEL; int i, j; int numlegs, vect, edge, maxmom = 0; newterm = term + *term; for ( i = 1; i < info->diaoffset; i++ ) newterm[i] = term[i]; fill = newterm + info->diaoffset; // // Now get the nodes // for ( i = 0; i < eg->nNodes; i++ ) { // // node_(number,momentum_1,...,momentum_n) // numlegs = eg->nodes[i]->deg; startfill = fill; *fill++ = NODEFUNCTION; *fill++ = 0; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = i+1; if ( model != NULL && m != NULL ) { if ( !eg->isExternal(i) ) { WORD *afill = fill; *fill++ = 0; *fill++ = 1; FILLARG(fill) WORD *cfill = fill; *fill++ = 0; int cpl = 2*eg->nodes[i]->extloop+eg->nodes[i]->deg-2; *fill++ = SYMBOL; *fill++ = 4; *fill++ = m->couplings[0]; *fill++ = cpl; *fill++ = 1; *fill++ = 1; *fill++ = 3; *cfill = fill - cfill; *afill = fill - afill; if ( *afill == ARGHEAD+8 && afill[ARGHEAD+4] == 1 ) { fill = afill; *fill++ = -SYMBOL; *fill++ = afill[ARGHEAD+3]; } } else { *fill++ = -SNUMBER; *fill++ = 1; } } // // Now the momenta. // for ( j = 0; j < numlegs; j++ ) { edge = eg->nodes[i]->edges[j]; vect = ABS(edge)-1; *fill++ = edge < 0 ? -MINVECTOR: -VECTOR; if ( numlegs == 1 || vect < info->numextern ) { // Look up in set of external momenta *fill++ = SetElements[Sets[info->externalset].first+vect]; } else { // Look up in set of internal momenta set *fill++ = SetElements[Sets[info->internalset].first+(vect-info->numextern)]; // determine the number of momenta required from internalset: maxmom = MaX(maxmom, vect-info->numextern); } } startfill[1] = fill-startfill; } if ( ( info->flags & WITHEDGES ) == WITHEDGES ) { for ( i = 0; i < eg->nEdges; i++ ) { int n1 = eg->edges[i]->nodes[0]; int n2 = eg->edges[i]->nodes[1]; // int l1 = eg->edges[i]->nlegs[0]; // int l2 = eg->edges[i]->nlegs[1]; startfill = fill; *fill++ = EDGE; *fill++ = 0; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = i+1; // number of the edge // *fill++ = -VECTOR; if ( i < info->numextern ) { // Look up in set of external momenta *fill++ = SetElements[Sets[info->externalset].first+i]; } else { // Look up in set of internal momenta set *fill++ = SetElements[Sets[info->internalset].first+(i-eg->nExtern)]; maxmom = MaX(maxmom, i-eg->nExtern); } // *fill++ = -SNUMBER; *fill++ = n1+1; // number of the node from *fill++ = -SNUMBER; *fill++ = n2+1; // number of the node to startfill[1] = fill - startfill; } } // // Block information // if ( ( info->flags & WITHBLOCKS ) == WITHBLOCKS ) { for ( i = 0; i < eg->econn->nblocks; i++ ) { startfill = fill; *fill++ = BLOCK; *fill++ = 0; FILLFUN(fill); *fill++ = -SNUMBER; *fill++ = i+1; *fill++ = -SNUMBER; *fill++ = eg->econn->blocks[i].loop; // // Now we have to make a list of all nodes inside this block // int bnodes[GRCC_MAXNODES], k; WORD *argfill = fill, *funfill; *fill++ = 0; *fill++ = 0; FILLARG(fill) *fill++ = 0; for ( k = 0; k < GRCC_MAXNODES; k++ ) bnodes[k] = 0; for ( k = 0; k < eg->econn->blocks[i].nmedges; k++ ) { bnodes[eg->econn->blocks[i].edges[k][0]] = 1; bnodes[eg->econn->blocks[i].edges[k][1]] = 1; } for ( k = 0; k < GRCC_MAXNODES; k++ ) { if ( bnodes[k] == 0 ) continue; // // Now we put the node inside this argument. // funfill = fill; *fill++ = NODEFUNCTION; *fill++ = 0; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = k+1; numlegs = eg->nodes[k]->deg; for ( j = 0; j < numlegs; j++ ) { edge = eg->nodes[k]->edges[j]; vect = ABS(edge)-1; *fill++ = -VECTOR; if ( numlegs == 1 || vect < info->numextern ) { // Look up in set of external momenta *fill++ = SetElements[Sets[info->externalset].first+vect]; } else { // Look up in set of internal momenta set *fill++ = SetElements[Sets[info->internalset].first+(vect-info->numextern)]; maxmom = MaX(maxmom, vect-info->numextern); } } funfill[1] = fill-funfill; } *fill++ = 1; *fill++ = 1; *fill++ = 3; *argfill = fill - argfill; argfill[ARGHEAD] = argfill[0] - ARGHEAD; startfill[1] = fill-startfill; } // if ( eg->econn->narticuls > 0 ) { // startfill = fill; // *fill++ = BLOCK; // *fill++ = 0; // FILLFUN(fill); // for ( i = 0; i < eg->econn->snodes; i++ ) { // if ( eg->econn->articuls[i] != 0 ) { // *fill++ = -SNUMBER; // *fill++ = i+1; // } // } // startfill[1] = fill-startfill; // } } if ( ( info->flags & WITHONEPISETS ) == WITHONEPISETS ) { for ( i = 0; i < eg->econn->nopic; i++ ) { startfill = fill; *fill++ = ONEPI; *fill++ = 0; FILLFUN(fill); *fill++ = -SNUMBER; *fill++ = i+1; *fill++ = -ONEPI; for ( j = 0; j < eg->econn->opics[i].nnodes; j++ ) { *fill++ = -SNUMBER; *fill++ = eg->econn->opics[i].nodes[j]+1; } startfill[1] = fill-startfill; } } // // Topology counter. We have exaggerated a bit with the eye on the far future. // if ( info->numtopo < MAXPOSITIVE ) { *fill++ = TOPO; *fill++ = FUNHEAD+2; FILLFUN(fill) *fill++ = -SNUMBER; *fill++ = (WORD)(info->numtopo); } else if ( info->numtopo < FULLMAX-1 ) { *fill++ = TOPO; *fill++ = FUNHEAD+ARGHEAD+4; FILLFUN(fill) *fill++ = ARGHEAD+4; *fill++ = 0; FILLARG(fill) *fill++ = 4; *fill++ = (WORD)(info->numtopo & WORDMASK); *fill++ = 1; *fill++ = 3; } else { // for now: science fiction *fill++ = TOPO; *fill++ = FUNHEAD+ARGHEAD+6; FILLFUN(fill) *fill++ = ARGHEAD+6; *fill++ = 0; FILLARG(fill) *fill++ = 6; *fill++ = (WORD)(info->numtopo >> BITSINWORD); *fill++ = (WORD)(info->numtopo & WORDMASK); *fill++ = 0; *fill++ = 1; *fill++ = 5; } // // verify internalset has sufficient momenta: // if ( maxmom >= Sets[info->internalset].last - Sets[info->internalset].first ) { MLOCK(ErrorMessageLock); MesPrint("&Insufficient internal momenta in diagrams_"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // // finish it off // while ( tail < tend ) *fill++ = *tail++; if ( eg->fsign < 0 ) fill[-1] = -fill[-1]; *newterm = fill - newterm; AT.WorkPointer = fill; Generator(BHEAD newterm,info->level); AT.WorkPointer = oldworkpointer; info->numtopo++; return False; } // #] ProcessTopology : // #[ SetDualOpts : void SetDualOpts(int *opt, const WORD num, const int key, const char* key_name, const int dual, const char* dual_name, const int val, const int dval) { if ( ( num & key ) == key ) { if ( ( num & dual ) == dual ) { MLOCK(ErrorMessageLock); MesPrint("&Conflicting diagram filters: %s and %s.", key_name, dual_name); MUNLOCK(ErrorMessageLock); Terminate(-1); } else { *opt = val; } } else { if ( ( num & dual ) == dual ) { *opt = dval; } else { // The default value is always 0. *opt = 0; } } } // #] SetDualOpts : // #[ GenDiagrams : int GenDiagrams(PHEAD WORD *term, WORD level) { Model *model; MODEL *m; Options *opt; Process *proc; int pid = 1, x; int babble = AC.GrccVerbose ? 2 : 0; TERMINFO info; WORD inset,outset,*coupl,setnum,optionnumber = 0; int i, j, cpl[GRCC_MAXNCPLG]; int ninitl, initlPart[GRCC_MAXLEGS], nfinal, finalPart[GRCC_MAXLEGS]; for ( i = 0; i < GRCC_MAXNCPLG; i++ ) cpl[i] = 0; std::map momlist; // // Here we create an object of type Option and load it up. // Next we run the diagram generation on it. // info.term = term; info.level = level; info.diaoffset = AR.funoffset; info.externalset = term[info.diaoffset+FUNHEAD+7]; info.internalset = term[info.diaoffset+FUNHEAD+9]; info.flags = 0; inset = term[info.diaoffset+FUNHEAD+3]; outset = term[info.diaoffset+FUNHEAD+5]; coupl = term + info.diaoffset + FUNHEAD + 10; if ( *coupl < 0 ) { if ( term[info.diaoffset+1] > FUNHEAD + 12 ) { optionnumber = term[info.diaoffset+FUNHEAD+13]; } } else { if ( term[info.diaoffset+1] > *coupl+FUNHEAD+10 ) optionnumber = term[info.diaoffset+*coupl+FUNHEAD+11]; } setnum = term[info.diaoffset+FUNHEAD+1]; m = AC.models[SetElements[Sets[setnum].first]]; LoadModel(m); model = (Model *)m->grccmodel; info.currentModel = (void *)model; info.currentMODEL = (void *)m; info.numdia = 0; info.numtopo = 1; info.flags = optionnumber; opt = new Options(); opt->setOutAG(ProcessDiagram, &info); opt->setOutMG(ProcessTopology, &info); opt->values[GRCC_OPT_SymmInitial] = ( optionnumber & WITHSYMMETRIZEI ) == WITHSYMMETRIZEI; opt->values[GRCC_OPT_SymmFinal] = ( optionnumber & WITHSYMMETRIZEF ) == WITHSYMMETRIZEF; // WITHBLOCKS controls output formatting. We could introduce an extra filtering option // corresponding to GRCC_OPT_Block, which is somewhat like Qgraf "onevi" but not quite // the same currently. //opt->values[GRCC_OPT_Block] = ; // Now the "qgraf-compatible filtering options": int qgopt[GRCC_QGRAF_OPT_Size]; SetDualOpts(&qgopt[GRCC_QGRAF_OPT_ONEPI], optionnumber,ONEPARTI, "ONEPI_", ONEPARTR, "ONEPR_", 1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_ONSHELL], optionnumber,ONSHELL, "ONSHELL_", OFFSHELL, "OFFSHELL_", 1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_NOSIGMA], optionnumber,NOSIGMA, "NOSIGMA_", SIGMA, "SIGMA_", 1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_NOSNAIL], optionnumber,NOSNAIL, "NOSNAIL_", SNAIL, "SNAIL_", 1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_NOTADPOLE],optionnumber,NOTADPOLE,"NOTADPOLE_",TADPOLE , "TADPOLE_", 1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_SIMPLE], optionnumber,SIMPLE, "SIMPLE_", NOTSIMPLE,"NOTSIMPLE_",1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_BIPART], optionnumber,BIPART, "BIPART_", NONBIPART,"NONBIPART_",1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_CYCLI], optionnumber,CYCLI, "CYCLI_", CYCLR, "CYCLR_", 1,-1); SetDualOpts(&qgopt[GRCC_QGRAF_OPT_FLOOP], optionnumber,FLOOP, "FLOOP_", NOTFLOOP, "NOTFLOOP_", 1,-1); // Now set the options internally: opt->setQGrafOpt(qgopt); opt->setOutputF(False,""); opt->setOutputP(False,""); opt->printLevel(babble); // Load the various arrays. ninitl = Sets[inset].last - Sets[inset].first; for ( i = 0; i < ninitl; i++ ) { x = SetElements[Sets[inset].first+i]; initlPart[i] = ConvertParticle(model,x); info.legcouple[i] = m->vertices[numParticle(m,x)]->couplings; } nfinal = Sets[outset].last - Sets[outset].first; for ( i = 0; i < nfinal; i++ ) { x = SetElements[Sets[outset].first+i]; finalPart[i] = ConvertParticle(model,x); info.legcouple[i+ninitl] = m->vertices[numParticle(m,x)]->couplings; } info.numextern = ninitl + nfinal; for ( i = 2; i <= MAXLEGS; i++ ) { if ( m->legcouple[i] == 1 ) { for ( j = 0; j < info.numextern; j++ ) { if ( info.legcouple[j][i] == 0 ) { info.flags |= CHECKEXTERN; goto Go_on; } } } } // Check that we have sufficient external momenta in the set: if ( info.numextern > Sets[info.externalset].last - Sets[info.externalset].first ) { MLOCK(ErrorMessageLock); MesPrint("&Insufficient external momenta in diagrams_"); MUNLOCK(ErrorMessageLock); Terminate(-1); } // Check that none of the supplied momenta are negative or repeated: for ( i = 0; i < Sets[info.externalset].last - Sets[info.externalset].first; i++ ) { const int momcode = SetElements[Sets[info.externalset].first + i]; if ( momcode < AM.OffsetVector ) { MLOCK(ErrorMessageLock); MesPrint("&Invalid negative external momentum in diagrams_: -%s", VARNAME(vectors, momcode+WILDMASK-AM.OffsetVector)); MUNLOCK(ErrorMessageLock); Terminate(-1); } momlist[momcode]++; if ( momlist[momcode] != 1 ) { MLOCK(ErrorMessageLock); MesPrint("&Invalid repeated momentum in diagrams_: %s", VARNAME(vectors, momcode-AM.OffsetVector)); MUNLOCK(ErrorMessageLock); Terminate(-1); } } for ( i = 0; i < Sets[info.internalset].last - Sets[info.internalset].first; i++ ) { const int momcode = SetElements[Sets[info.internalset].first + i]; if ( momcode < AM.OffsetVector ) { MLOCK(ErrorMessageLock); MesPrint("&Invalid negative internal momentum in diagrams_: -%s", VARNAME(vectors, momcode+WILDMASK-AM.OffsetVector)); MUNLOCK(ErrorMessageLock); Terminate(-1); } momlist[momcode]++; if ( momlist[momcode] != 1 ) { MLOCK(ErrorMessageLock); MesPrint("&Invalid repeated momentum in diagrams_: %s", VARNAME(vectors, momcode-AM.OffsetVector)); MUNLOCK(ErrorMessageLock); Terminate(-1); } } Go_on:; // // Now we have to sort out the coupling constants. // The argument at coupl can be of type -SNUMBER, -SYMBOL or generic // It has however already be tested for syntax. // Note that one cannot have 1 for the coupling constants. // In that case one should select 0 loops or something equivalent. // if ( *coupl == -SNUMBER ) { // Number of loops // // This is the complicated case. // We have to compute the number of coupling constants and then // generate diagrams for all combinations with the proper power. // int nc = coupl[1]*2 + ninitl + nfinal - 2; int *scratch = (int *)Malloc1(nc*sizeof(int),"DistrN"); scratch[0] = -2; // indicating startup cq first call. if ( ( info.flags & TOPOLOGIESONLY ) == 0 ) { while ( DistrN(nc,cpl,m->ncouplings,scratch) ) { proc = new Process(pid, model, opt, ninitl, initlPart, nfinal, finalPart, cpl); delete proc; info.numtopo = 1; } } else { cpl[0] = nc; proc = new Process(pid, model, opt, ninitl, initlPart, nfinal, finalPart, cpl); delete proc; } M_free(scratch,"DistrN"); opt->end(); delete opt; return(0); } else if ( *coupl == -SYMBOL ) { // Just a single power of one constant for ( i = 0; i < m->ncouplings; i++ ) { if ( m->couplings[i] == coupl[1] ) { cpl[i] = 1; break; } } } else { // One term with powers of coupling constants WORD *t, *tstop; t = coupl + ARGHEAD+3; tstop = coupl+*coupl; tstop -= ABS(tstop[-1]); while ( t < tstop ) { for ( i = 0; i < m->ncouplings; i++ ) { if ( m->couplings[i] == *t ) { cpl[i] = t[1]; break; } } t += 2; } } /* And now the generation: */ proc = new Process(pid, model, opt, ninitl, initlPart, nfinal, finalPart, cpl); opt->end(); delete proc; delete opt; return(0); } // #] GenDiagrams : // #[ processVertex : // Routine is to be used recursively to work its way through a list // of possible vertices. The array of vertices is in TopoInf->vert // with TopoInf->nvert the number of possible vertices. // Currently we allow in TopoInf->vert only vertices with 3 or more edges. // // We work with a point system. Each n-point vertex contributes n-2 points. // When all points are assigned, we can call mgraph->generate(). // // The number of vertices of a given number of edges is stored in // TopoInf->clnum[..] but the loop that determines how many there are // may be limited by the corresponding element in TopoInf->vertmax[level] int processVertex(TOPOTYPE *TopoInf, int pointsremaining, int level) { int i, j; for ( i = pointsremaining, j = 0; i >= 0; i -= TopoInf->vert[level]-2, j++ ) { if ( TopoInf->vertmax && TopoInf->vertmax[level] >= 0 && j > TopoInf->vertmax[level] ) break; if ( i == 0 ) { // We got one! TopoInf->cldeg[TopoInf->ncl] = TopoInf->vert[level]; TopoInf->clnum[TopoInf->ncl] = j; TopoInf->clext[TopoInf->ncl] = 0; TopoInf->ncl++; MGraph *mgraph = new MGraph(1, TopoInf->ncl, TopoInf->cldeg, TopoInf->clnum, TopoInf->clext, TopoInf->cmind, TopoInf->cmaxd, TopoInf->opt); mgraph->generate(); delete mgraph; TopoInf->ncl--; break; } if ( level < TopoInf->nvert-1 ) { if ( j > 0 ) { TopoInf->cldeg[TopoInf->ncl] = TopoInf->vert[level]; TopoInf->clnum[TopoInf->ncl] = j; TopoInf->clext[TopoInf->ncl] = 0; TopoInf->ncl++; } if ( processVertex(TopoInf,i,level+1) < 0 ) return(-1); if ( j > 0 ) { TopoInf->ncl--; } } } return(0); } // #] processVertex : form-5.0.1/sources/mpi.c0000644000175100017510000015651115217035721010573 /** @file mpi.c * * MPI dependent functions of parform * * This file contains all the functions for the parallel version of form3 that * explicitly need to call mpi routines. This is the only file that really * needs to be linked to the mpi-library! */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes and variables : */ /* #define MPIDEBUGGING #define MPIDEBUGGING_DELAY_US 10000 */ #include #include "form3.h" #ifdef MPICH_PROFILING # include "mpe.h" #endif #ifdef MPIDEBUGGING #include "mpidbg.h" #endif /*[12oct2005 mt]:*/ /* Today there was some cleanup, some stuff is moved into another place in this file, and PF.packsize is removed and PF_packsize is used instead. It is rather difficult to proper comment it, so not all these changing are marked by "[12oct2005 mt]" */ #define PF_PACKSIZE 1600 /* Size in bytes, will be initialized soon as PF_packsize=PF_PACKSIZE/sizeof(int)*sizeof(int); for possible future developing we prefer to do this initialization not here, but in PF_LibInit: */ static int PF_packsize = 0; static MPI_Status PF_status; LONG PF_maxDollarChunkSize = 0; /*:[04oct2005 mt]*/ static int PF_ShortPackInit(void); static int PF_longPackInit(void); /*:[12oct2005 mt]*/ /** * A macro which exits the caller with a non-zero return value if \a err * is not MPI_SUCCESS. * * @param err The return value of a MPI function to be checked. * * @remark The MPI standard defines MPI_SUCCESS == 0. Then (_tmp_err == 0) appears * twice and we can expect the second evaluation will be eliminated by * the compiler optimization. */ #define MPI_ERRCODE_CHECK(err) \ do { \ int _tmp_err = (err); \ if ( _tmp_err != MPI_SUCCESS ) return _tmp_err != 0 ? _tmp_err : -1; \ } while (0) /* #] Includes and variables : #[ PF_RealTime : */ /** * Returns the realtime in 1/100 sec. as a LONG. * * @param i the timer will be reset if i == 0. * @return the real elapsed time in 1/100 second. */ LONG PF_RealTime(int i) { static double starttime; if ( i == PF_RESET ) { starttime = MPI_Wtime(); return((LONG)0); } return((LONG)( 100. * (MPI_Wtime() - starttime) ) ); } /* #] PF_RealTime : #[ PF_LibInit : */ /** * Performs all library dependent initializations. * * @param argcp pointer to the number of arguments. * @param argvp pointer to the arguments. * @return 0 if OK, nonzero on error. */ int PF_LibInit(int *argcp, char ***argvp) { int ret; ret = MPI_Init(argcp,argvp); if ( ret != MPI_SUCCESS ) return(ret); ret = MPI_Comm_rank(PF_COMM,&PF.me); if ( ret != MPI_SUCCESS ) return(ret); ret = MPI_Comm_size(PF_COMM,&PF.numtasks); if ( ret != MPI_SUCCESS ) return(ret); /* Initialization of packed communications. */ PF_packsize = PF_PACKSIZE/sizeof(int)*sizeof(int); if ( PF_ShortPackInit() ) return -1; if ( PF_longPackInit() ) return -1; {/*Block*/ int bytes, totalbytes=0; /* There is one problem with maximal possible packing: there is no API to convert bytes to the record number. So, here we calculate the buffer size needed for storing dollarvars: LONG PF_maxDollarChunkSize is the size for the portion of the dollar variable buffer suitable for broadcasting. This variable should be visible from parallel.c Evaluate PF_Pack(numterms,1,PF_INT): */ if ( ( ret = MPI_Pack_size(1,PF_INT,PF_COMM,&bytes) )!=MPI_SUCCESS ) return(ret); totalbytes+=bytes; /* Evaluate PF_Pack( newsize,1,PF_LONG): */ if ( ( ret = MPI_Pack_size(1,PF_LONG,PF_COMM,&bytes) )!=MPI_SUCCESS ) return(ret); totalbytes += bytes; /* Now available room is PF_packsize-totalbytes */ totalbytes = PF_packsize-totalbytes; /* Now totalbytes is the size of chunk in bytes. Evaluate this size in number of records: Rough estimate: */ PF_maxDollarChunkSize=totalbytes/sizeof(WORD); /* Go to the up limit: */ do { if ( ( ret = MPI_Pack_size( ++PF_maxDollarChunkSize,PF_WORD,PF_COMM,&bytes) )!=MPI_SUCCESS ) return(ret); } while ( bytestotalbytes ); /* Now PF_maxDollarChunkSize is the size of chunk of PF_WORD fitting the buffer <= (PF_packsize-PF_INT-PF_LONG) */ }/*Block*/ return(0); } /* #] PF_LibInit : #[ PF_LibTerminate : */ /** * Exits mpi, when there is an error either indicated or happening, * returnvalue is 1, else returnvalue is 0. * * @param error an error code. * @return 0 if OK, nonzero on error. */ int PF_LibTerminate(int error) { DUMMYUSE(error); return(MPI_Finalize()); } /* #] PF_LibTerminate : #[ PF_Probe : */ /** * Probes the next incoming message. * If src == PF_ANY_SOURCE this operation is blocking, * otherwise nonblocking. * * @param[in,out] src the source process number. In output, the process number of actual found source. * @return the tag value of the next incoming message if found, * 0 if a nonblocking probe (input src != PF_ANY_SOURCE) did not * find any messages. A negative returned value indicates an error. */ int PF_Probe(int *src) { int ret, flag; if ( *src == PF_ANY_SOURCE ) { /*Blocking call*/ ret = MPI_Probe(*src,MPI_ANY_TAG,PF_COMM,&PF_status); flag = 1; } else { /*Non-blocking call*/ ret = MPI_Iprobe(*src,MPI_ANY_TAG,PF_COMM,&flag,&PF_status); } *src = PF_status.MPI_SOURCE; if ( ret != MPI_SUCCESS ) { if ( ret > 0 ) ret *= -1; return(ret); } if ( !flag ) return(0); return(PF_status.MPI_TAG); } /* #] PF_Probe : #[ PF_ISendSbuf : */ /** * Nonblocking send operation. It sends everything from \c buff to \c fill of the * active buffer. * Depending on \a tag it also can do waiting for other sends to finish or * set the active buffer to the next one. * * @param to the destination process number. * @param tag the message tag. * @return 0 if OK, nonzero on error. */ int PF_ISendSbuf(int to, int tag) { PF_BUFFER *s = PF.sbuf; int a = s->active; int size = s->fill[a] - s->buff[a]; int r = 0; static int finished; s->fill[a] = s->buff[a]; if ( s->numbufs == 1 ) { r = MPI_Ssend(s->buff[a],size,PF_WORD,MASTER,tag,PF_COMM); if ( r != MPI_SUCCESS ) { fprintf(stderr,"[%d|%d] PF_ISendSbuf: MPI_Ssend returns: %d \n", PF.me,(int)AC.CModule,r); fflush(stderr); return(r); } return(0); } switch ( tag ) { /* things to do before sending */ case PF_TERM_MSGTAG: if ( PF.sbuf->request[to] != MPI_REQUEST_NULL) r = MPI_Wait(&PF.sbuf->request[to],&PF.sbuf->retstat[to]); if ( r != MPI_SUCCESS ) return(r); break; default: break; } r = MPI_Isend(s->buff[a],size,PF_WORD,to,tag,PF_COMM,&s->request[a]); if ( r != MPI_SUCCESS ) return(r); switch ( tag ) { /* things to do after initialising sending */ case PF_TERM_MSGTAG: finished = 0; break; case PF_ENDSORT_MSGTAG: if ( ++finished == PF.numtasks - 1 ) r = MPI_Waitall(s->numbufs,s->request,s->status); if ( r != MPI_SUCCESS ) return(r); break; case PF_BUFFER_MSGTAG: if ( ++s->active >= s->numbufs ) s->active = 0; while ( s->request[s->active] != MPI_REQUEST_NULL ) { r = MPI_Waitsome(s->numbufs,s->request,&size,s->index,s->retstat); if ( r != MPI_SUCCESS ) return(r); } break; case PF_ENDBUFFER_MSGTAG: if ( ++s->active >= s->numbufs ) s->active = 0; r = MPI_Waitall(s->numbufs,s->request,s->status); if ( r != MPI_SUCCESS ) return(r); break; default: return(-99); break; } return(0); } /* #] PF_ISendSbuf : #[ PF_RecvWbuf : */ /** * Blocking receive of a \c WORD buffer. * * @param[out] b the buffer to store the received data. * @param[in,out] s the size of the buffer. The output value is the actual size of the received data. * @param[in,out] src the source process number. The output value is the process number of actual source. * @return the received message tag. A negative value indicates an error. */ int PF_RecvWbuf(WORD *b, LONG *s, int *src) { int i, r = 0; for (;;) { r = MPI_Probe(*src,PF_ANY_MSGTAG,PF_COMM,&PF_status); if ( r != MPI_SUCCESS ) { if ( r > 0 ) r *= -1; return(r); } if ( PF_status.MPI_TAG != PF_RUNTIME_ERROR_MSGTAG ) break; PF_ReceiveRuntimeError(); } r = MPI_Recv(b,(int)*s,PF_WORD,PF_status.MPI_SOURCE,PF_status.MPI_TAG,PF_COMM,&PF_status); if ( r != MPI_SUCCESS ) { if ( r > 0 ) r *= -1; return(r); } r = MPI_Get_count(&PF_status,PF_WORD,&i); if ( r != MPI_SUCCESS ) { if ( r > 0 ) r *= -1; return(r); } *s = (LONG)i; *src = PF_status.MPI_SOURCE; return(PF_status.MPI_TAG); } /* #] PF_RecvWbuf : #[ PF_IRecvRbuf : */ /** * Posts nonblocking receive for the active receive buffer. * The buffer is filled from \c full to \c stop. * * @param r the \c PF_BUFFER struct for the nonblocking receive. * @param bn the index of the cyclic buffer. * @param from the source process number. * @return 0 if OK, nonzero on error. */ int PF_IRecvRbuf(PF_BUFFER *r, int bn, int from) { int ret; r->type[bn] = PF_WORD; if ( r->numbufs == 1 ) { r->tag[bn] = MPI_ANY_TAG; r->from[bn] = from; } else { ret = MPI_Irecv(r->full[bn],(int)(r->stop[bn] - r->full[bn]),PF_WORD,from, MPI_ANY_TAG,PF_COMM,&r->request[bn]); if (ret != MPI_SUCCESS) { if(ret > 0) ret *= -1; return(ret); } } return(0); } /* #] PF_IRecvRbuf : #[ PF_WaitRbuf : */ /** * Waits for the buffer \a bn to finish a pending nonblocking * receive. It returns the received tag and in *size the number of field * received. * If the receive is already finished, just return the flag and size, * else wait for it to finish, but also check for other pending receives. * * @param r the \c PF_BUFFER struct for the pending nonblocking receive. * @param bn the index of the cyclic buffer. * @param[out] size the actual size of received data. * @return the received message tag. A negative value indicates an error. */ int PF_WaitRbuf(PF_BUFFER *r, int bn, LONG *size) { int ret, rsize; if ( r->numbufs == 1 ) { *size = r->stop[bn] - r->full[bn]; ret = MPI_Recv(r->full[bn],(int)*size,r->type[bn],r->from[bn],r->tag[bn], PF_COMM,&(r->status[bn])); if ( ret != MPI_SUCCESS ) { if ( ret > 0 ) ret *= -1; return(ret); } ret = MPI_Get_count(&(r->status[bn]),r->type[bn],&rsize); if ( ret != MPI_SUCCESS ) { if ( ret > 0 ) ret *= -1; return(ret); } if ( rsize > *size ) return(-99); *size = (LONG)rsize; } else { while ( r->request[bn] != MPI_REQUEST_NULL ) { ret = MPI_Waitsome(r->numbufs,r->request,&rsize,r->index,r->retstat); if ( ret != MPI_SUCCESS ) { if ( ret > 0 ) ret *= -1; return(ret); } while ( --rsize >= 0 ) r->status[r->index[rsize]] = r->retstat[rsize]; } ret = MPI_Get_count(&(r->status[bn]),r->type[bn],&rsize); if ( ret != MPI_SUCCESS ) { if ( ret > 0 ) ret *= -1; return(ret); } *size = (LONG)rsize; } return(r->status[bn].MPI_TAG); } /* #] PF_WaitRbuf : #[ PF_Bcast : */ /** * Broadcasts a message from the master to slaves. * * @param[in,out] buffer the starting address of buffer. The contents in this buffer * on the master will be transferred to those on the slaves. * @param count the length of the buffer in bytes. * @return 0 if OK, nonzero on error. */ int PF_Bcast(void *buffer, int count) { if ( MPI_Bcast(buffer,count,MPI_BYTE,MASTER,PF_COMM) != MPI_SUCCESS ) return(-1); return(0); } /* #] PF_Bcast : #[ PF_Reduce : */ /** * Performs a reduce operation across all processes. * * @param[in] sendbuf the buffer containing the data to be reduced. * @param[out] recvbuf the buffer to store the reduced result (only for the root process). * @param count the number of elements in the buffers. * @param type the datatype of the elements. * @param op the operation to apply. * @param root the root process number. * @return 0 if OK, nonzero on error. */ int PF_Reduce(const void *sendbuf, void *recvbuf, int count, MPI_Datatype type, MPI_Op op, int root) { if ( MPI_Reduce(sendbuf,recvbuf,count,type,op,root,PF_COMM) != MPI_SUCCESS ) return(-1); return(0); } /* #] PF_Reduce : #[ PF_RawSend : */ /** * Sends \a l bytes from \a buf to \a dest. * Returns 0 on success, or -1. * * @param dest the destination process number. * @param buf the send buffer. * @param l the size of data in the send buffer in bytes. * @param tag the message tag. * @return 0 if OK, nonzero on error. */ int PF_RawSend(int dest, void *buf, LONG l, int tag) { int ret=MPI_Ssend(buf,(int)l,MPI_BYTE,dest,tag,PF_COMM); if ( ret != MPI_SUCCESS ) return(-1); return(0); } /* #] PF_RawSend : #[ PF_RawRecv : */ /** * Receives not more than \a thesize bytes from \a src, * returns the actual number of received bytes, or -1 on failure. * * @param[in,out] src the source process number. In output, that of the actual received message. * @param[out] buf the receive buffer. * @param thesize the size of the receive buffer in bytes. * @param[out] tag the message tag of the actual received message. * @return the actual sizeof received data in bytes, or -1 on failure. */ LONG PF_RawRecv(int *src,void *buf,LONG thesize,int *tag) { MPI_Status stat; int ret=MPI_Recv(buf,(int)thesize,MPI_BYTE,*src,MPI_ANY_TAG,PF_COMM,&stat); if ( ret != MPI_SUCCESS ) return(-1); if ( MPI_Get_count(&stat,MPI_BYTE,&ret) != MPI_SUCCESS ) return(-1); *tag = stat.MPI_TAG; *src = stat.MPI_SOURCE; return(ret); } /* #] PF_RawRecv : #[ PF_RawProbe : */ /** * Probes an incoming message. * * @param[in,out] src the source process number. In output, that of the actual received message. * @param[in,out] tag the message tag. In output, that of the actual received message. * @param[out] bytesize the size of incoming data in bytes. * @return 0 if OK, nonzero on error. */ int PF_RawProbe(int *src, int *tag, int *bytesize) { MPI_Status stat; int srcval = src != NULL ? *src : PF_ANY_SOURCE; int tagval = tag != NULL ? *tag : PF_ANY_MSGTAG; int ret = MPI_Probe(srcval, tagval, PF_COMM, &stat); if ( ret != MPI_SUCCESS ) return -1; if ( src != NULL ) *src = stat.MPI_SOURCE; if ( tag != NULL ) *tag = stat.MPI_TAG; if ( bytesize != NULL ) { ret = MPI_Get_count(&stat, MPI_BYTE, bytesize); if ( ret != MPI_SUCCESS ) return -1; } return 0; } /* #] PF_RawProbe : #[ PF_RawIsend : */ /** * Performs a nonblocking send. * * @param dest the destination process number. * @param[in] buf the send buffer. * @param count the number of elements in the send buffer. * @param type the datatype of the data in the send buffer. * @param tag the message tag. * @param[out] request the request handle for the nonblocking operation. * @return 0 if OK, nonzero on error. */ int PF_RawIsend(int dest, const void *buf, int count, MPI_Datatype type, int tag, MPI_Request *request) { int ret = MPI_Isend(buf, count, type, dest, tag, PF_COMM, request); if ( ret != MPI_SUCCESS ) return(-1); return(0); } /* #] PF_RawIsend : #[ PF_RawWaitAll : */ /** * Waits for all the given requests to complete. * * @param count the number of requests. * @param[in,out] request the array of request handles. * @param[out] status the array of status objects to store the status of each completed request. * @return 0 if OK, nonzero on error. */ int PF_RawWaitAll(int count, MPI_Request *request, MPI_Status *status) { int ret = MPI_Waitall(count, request, status); if ( ret != MPI_SUCCESS ) return(-1); return(0); } /* #] PF_RawWaitAll : #[ PF_Discard : */ /** * Discards an incoming message. * * @param[in,out] src the source process number. * On output, that of the actual received message. * @param[in,out] tag the message tag. * On output, that of the actual received message. * @return 0 if OK, nonzero on error. */ int PF_Discard(int *src, int *tag) { enum { DEFAULT_BUF_SIZE = 1024 }; MPI_Status stat; int count; void *buf; char default_buf[DEFAULT_BUF_SIZE]; int srcval = src != NULL ? *src : PF_ANY_SOURCE; int tagval = tag != NULL ? *tag : PF_ANY_MSGTAG; int ret = MPI_Probe(srcval, tagval, PF_COMM, &stat); if ( ret != MPI_SUCCESS ) return -1; if ( src != NULL ) *src = stat.MPI_SOURCE; if ( tag != NULL ) *tag = stat.MPI_TAG; ret = MPI_Get_count(&stat, MPI_BYTE, &count); if ( ret != MPI_SUCCESS ) return -1; buf = count <= DEFAULT_BUF_SIZE ? default_buf : Malloc1(count, "PF_Discard"); ret = MPI_Recv(buf, count, MPI_BYTE, stat.MPI_SOURCE, stat.MPI_TAG, PF_COMM, MPI_STATUS_IGNORE); if ( buf != default_buf ) M_free(buf, "PF_Discard"); if ( ret != MPI_SUCCESS ) return -1; return 0; } /* #] PF_Discard : #[ The pack buffer : #[ Variables : */ /* * The pack buffer with the fixed size (= PF_packsize). */ static UBYTE *PF_packbuf = NULL; static UBYTE *PF_packstop = NULL; static int PF_packpos = 0; /* #] Variables : #[ PF_ShortPackInit : */ /** * Initializes buffers for "short" packed communications. * PF_packsize must be set before calling this function. * * @return 0 if OK, nonzero on error. */ static int PF_ShortPackInit(void) { PF_packbuf = (UBYTE *)Malloc1(sizeof(UBYTE) * PF_packsize, "PF_ShortPackInit"); if ( PF_packbuf == NULL ) return -1; PF_packstop = PF_packbuf + PF_packsize; return 0; } /* #] PF_ShortPackInit : #[ PF_InitPackBuf : */ /** * Initializes the pack buffer for the next communication. * * @return 0 if OK, nonzero on error. */ static inline int PF_InitPackBuf(void) { /* This is definitely not the best place for allocating the buffer! Moved to PF_LibInit(): if ( PF_packbuf == 0 ) { PF_packbuf = (UBYTE *)Malloc1(sizeof(UBYTE)*PF.packsize,"PF_InitPackBuf"); if ( PF_packbuf == 0 ) return(-1); PF_packstop = PF_packbuf + PF.packsize; } */ PF_packpos = 0; return(0); } /* #] PF_InitPackBuf : #[ PF_PrintPackBuf : */ /** * Prints the contents in the pack buffer. * * @param s a message to be shown. * @param size the length of the buffer to be shown. * @return 0 if OK, nonzero on error. */ int PF_PrintPackBuf(char *s, int size) { #ifdef NOMESPRINTYET /* The use of printf should be discouraged. The results are flushed to the output at unpredictable moments. We should use printf only during startup when MesPrint doesn't have its buffers and output channels initialized. */ int i; printf("[%d] %s: ",PF.me,s); for(i=0;i INT_MAX ) return -99; err = MPI_Pack_size((int)count, type, PF_COMM, &bytes); MPI_ERRCODE_CHECK(err); if ( PF_packpos + bytes > PF_packstop - PF_packbuf ) return -99; err = MPI_Pack((void *)buffer, (int)count, type, PF_packbuf, PF_packsize, &PF_packpos, PF_COMM); MPI_ERRCODE_CHECK(err); return 0; } /* #] PF_Pack : #[ PF_Unpack : */ /** * Retrieves the next data in the pack buffer. * * @param[out] buffer the pointer to the buffer to store the unpacked data. * @param count the number of elements of data to be received. * @param type the data type of elements of data to be received. * @return 0 if OK, nonzero on error. */ int PF_Unpack(void *buffer, size_t count, MPI_Datatype type) { int err; if ( count > INT_MAX ) return -99; err = MPI_Unpack(PF_packbuf, PF_packsize, &PF_packpos, buffer, (int)count, type, PF_COMM); MPI_ERRCODE_CHECK(err); return 0; } /* #] PF_Unpack : #[ PF_PackString : */ /** * Packs a string \a str into the packed buffer PF_packbuf, including * the trailing zero. * * The first element (PF_INT) is the length of the packed portion of * the string. If the string does not fit to the buffer PF_packbuf, * the function packs only the initial portion. It returns * the number of packed bytes, so if (str[length-1]=='\0') then the whole * string fits to the buffer, if not, then the rest (str+length) must be * packed and send again. On error, the function returns the negative * error code. * * One exception: the string "\0!\0" is used as an image of the NULL, * so all 3 characters will be packed. * * @param str a string to be packed. * @return the number of packed bytes, or a negative value on failure. */ int PF_PackString(const UBYTE *str) { int ret,buflength,bytes,length; /* length will be packed in the beginning. Decrement buffer size by the length of the field "length": */ if ( ( ret = MPI_Pack_size(1,PF_INT,PF_COMM,&bytes) ) != MPI_SUCCESS ) return(ret); buflength = PF_packsize - bytes; /* Calculate the string length (INCLUDING the trailing zero!): */ for ( length = 0; length < buflength; length++ ) { if ( str[length] == '\0' ) { length++; /* since the trailing zero must be accounted */ break; } } /* The string "\0!\0" is used as an image of the NULL. */ if ( ( str[0] == '\0' ) /* empty string */ && ( str[1] == '!' ) /* Special case? */ && ( str[2] == '\0' ) /* Yes, pass 3 initial symbols */ ) length += 2; /* all 3 characters will be packed */ length++; /* Will be decremented in the following loop */ /* The problem: packed size of byte may be not equal 1! So first, suppose it is 1, and if this is not the case decrease the length of the string until it fits the buffer: */ do { if ( ( ret = MPI_Pack_size(--length,PF_BYTE,PF_COMM,&bytes) ) != MPI_SUCCESS ) return(ret); } while ( bytes > buflength ); /* Note, now if str[length-1] == '\0' then the string fits to the buffer (INCLUDING the trailing zero!);if not, the rest must be packed further! Pack the length to PF_packbuf: */ if ( ( ret = MPI_Pack(&length,1,PF_INT,PF_packbuf,PF_packsize, &PF_packpos,PF_COMM) ) != MPI_SUCCESS ) return(ret); /* Pack the string to PF_packbuf: */ if ( ( ret = MPI_Pack((UBYTE *)str,length,PF_BYTE,PF_packbuf,PF_packsize, &PF_packpos,PF_COMM) ) != MPI_SUCCESS ) return(ret); return(length); } /* #] PF_PackString : #[ PF_UnpackString : */ /** * Unpacks a string to \a str from the packed buffer PF_packbuf, including * the trailing zero. * * It returns the number of unpacked bytes, so if (str[length-1]=='\0') * then the whole string was unpacked, if not, then the rest must be appended * to (str+length). On error, the function returns the negative error code. * * @param[out] str the buffer to store the unpacked string * @return the number of unpacked bytes, or a negative value on failure. */ int PF_UnpackString(UBYTE *str) { int ret,length; /* Unpack the length: */ if( (ret = MPI_Unpack(PF_packbuf,PF_packsize,&PF_packpos, &length,1,PF_INT,PF_COMM))!= MPI_SUCCESS ) return(ret); /* Unpack the string: */ if ( ( ret = MPI_Unpack(PF_packbuf,PF_packsize,&PF_packpos, str,length,PF_BYTE,PF_COMM) ) != MPI_SUCCESS ) return(ret); /* Now if str[length-1]=='\0' then the whole string (INCLUDING the trailing zero!) was unpacked ;if not, the rest must be unpacked to str+length. */ return(length); } /* #] PF_UnpackString : #[ PF_Send : */ /** * Sends the contents in the pack buffer to the process specified by \a to. * * Example: * @code * if ( PF.me == SRC ) { * PF_PreparePack(); * // Packing operations here... * PF_Send(DEST, TAG); * } * else if ( PF.me == DEST ) { * PF_Receive(SRC, TAG, &actual_src, &actual_tag); * // Unpacking operations here... * } * @endcode * * @param to the destination process number. * @param tag the message tag. * @return 0 if OK, nonzero on error. */ int PF_Send(int to, int tag) { int err; err = MPI_Ssend(PF_packbuf, PF_packpos, MPI_PACKED, to, tag, PF_COMM); MPI_ERRCODE_CHECK(err); return 0; } /* #] PF_Send : #[ PF_Receive : */ /** * Receives data into the pack buffer from the process specified by \a src. * This function allows &src == psrc or &tag == ptag. * Either \a psrc or \a ptag can be NULL. * * See the example of PF_Send(). * * @param src the source process number (can be PF_ANY_SOURCE). * @param tag the source message tag (can be PF_ANY_TAG). * @param[out] psrc the actual source process number of received message. * @param[out] ptag the received message tag. * @return 0 if OK, nonzero on error. */ int PF_Receive(int src, int tag, int *psrc, int *ptag) { int err; MPI_Status status; PF_InitPackBuf(); err = MPI_Recv(PF_packbuf, PF_packsize, MPI_PACKED, src, tag, PF_COMM, &status); MPI_ERRCODE_CHECK(err); if ( psrc ) *psrc = status.MPI_SOURCE; if ( ptag ) *ptag = status.MPI_TAG; return 0; } /* #] PF_Receive : #[ PF_Broadcast : */ /** * Broadcasts the contents in the pack buffer on the master to those * on the slaves. * * Example: * @code * if ( PF.me == MASTER ) { * PF_PreparePack(); * // Packing operations here... * } * PF_Broadcast(); * if ( PF.me != MASTER ) { * // Unpacking operations here... * } * @endcode * * @return 0 if OK, nonzero on error. */ int PF_Broadcast(void) { int err; /* * If PF_SHORTBROADCAST is defined, then the broadcasting will be performed in * 2 steps. First, the size of the buffer will be broadcast, then the buffer of * exactly used size. This should be faster with slow connections, but slower on * SMP shmem MPI because of the latency. */ #ifdef PF_SHORTBROADCAST int pos = PF_packpos; #endif if ( PF.me != MASTER ) { err = PF_InitPackBuf(); if ( err ) return err; } #ifdef PF_SHORTBROADCAST err = MPI_Bcast(&pos, 1, MPI_INT, MASTER, PF_COMM); MPI_ERRCODE_CHECK(err); err = MPI_Bcast(PF_packbuf, pos, MPI_PACKED, MASTER, PF_COMM); #else err = MPI_Bcast(PF_packbuf, PF_packsize, MPI_PACKED, MASTER, PF_COMM); #endif MPI_ERRCODE_CHECK(err); return 0; } /* #] PF_Broadcast : #] The pack buffer : #[ Long pack stuff : #[ Explanations : The problems here are: 1. We need to send/receive long dollar variables. For preprocessor-defined dollarvars we used multiply packing/broadcasting (see parallel.c:PF_BroadcastPreDollar()) since each variable must be broadcast immediately. For run-time the changed dollar variables, collecting and broadcasting are performed at the end of the module and all modified dollarvars are transferred "at once", that is why the size of packed and transferred buffers may be really very large. 2. There is some strange feature of MPI_Bcast() on Altix MPI implementation, namely, sometimes it silently fails with big buffers. For better performance, it would be useful to send one big buffer instead of several small ones (since the latency is more important than the bandwidth). That is why we need two different sets of routines: for long point-to-point communication we collect big re-allocatable buffer, the corresponding routines have the prefix PF_longSingle, and for broadcasting we pack data into several smaller buffers, the corresponding routines have the prefix PF_longMulti. Note, from portability reasons we cannot split large packed buffer into small chunks, send them and collect back on the other side, see "Advice to users" on page 180 MPI--The Complete Reference Volume1, second edition. OPTIMIZING: We assume, for most communications, the single buffer of size PF_packsize is enough. How does it work: For point-to-point, there is one big re-allocatable buffer PF_longPackBuf with two integer positions: PF_longPackPos and PF_longPackTop (due to re-allocatable character of the buffer, it is better to use integers rather than pointers). Each time of re-allocation, the size of the buffer PF_longPackBuf is incremented by the same size of a "standard" chunk PF_packsize. For broadcasting there is one linked list (PF_longMultiRoot), which contains either positions of a chunk of PF_longPackBuf, or it's own buffer. This is done for better memory utilisation: longSingle and longMulti are never used simultaneously. When a new cell is needed for LongMulti packing, we increment the counter PF_longPackN and just follow the list. If it is not possible, we allocate the cell's own buffer and link it to the end of the list PF_longMultiRoot. When PF_longPackPos is reallocated, we link new chunks into existing PF_longMultiRoot list before the first longMulti allocated cell's own buffer. The pointer PF_longMultiLastChunk points to the last cell of PF_longMultiRoot containing the pointer to the chunk of PF_longPackBuf. Initialization PF_longPackBuf is made by the function PF_longSingleReset(). In the begin of the PF_longPackBuf it packs the size of the last sent buffer. Upon sending, the program checks, whether there was at list one re-allocation (PF_longPackN>1) . If so, the sender first packs and sends small buffer (PF_longPackSmallBuf) containing one integer number -- the _negative_ new size of the send buffer. Getting the buffer, a receiver unpacks one integer and checks whether it is <0 . If so, the receiver will repeat receiving, but first it checks whether it has enough buffer and increase it, if necessary. Initialization PF_longMultiRoot is made by the function PF_longMultiReset(). In the begin of the first chunk it packs one integer -- the number 1. Upon sending, the program checks, how many cells were packed (PF_longPackN). If more than 1, the sender packs to the next cell the integer PF_longPackN, than packs PF_longPackN pairs of integers -- the information about how many times chunk on each cell was accessed by the packing procedure, this information is contained by the nPacks field of the cell structure, and how many non-complete items was at the end of this chunk the structure field lastLen. Then the sender sends first this auxiliary chunk. The receiver unpacks the integer from obtained chunk and, if this integer is more than 1, it gets more chunks, unpacking information from the first auxiliary chunk into the corresponding nPacks fields. Unpacking information from multiple chunks, the receiver knows, when the chunk is expired and it must switch to the next cell, successively decrementing corresponding nPacks field. XXX: There are still some flaws: PF_LongSingleSend/PF_LongSingleReceive may fail, for example, for data transfers from the master to many slaves. Suppose that the master sends big data to slaves, which needs an increase of the buffer of the receivers. For the first data transfer, the master sends the new buffer size as the first message, and then sends the data as the second message, because PF_LongSinglePack records the increase of the buffer size on the master. For the next time, however, the master sends the data without sending the new buffer size, and then MPI_Recv fails due to the data overflow. In parallel.c, they are used for the communication from slaves to the master. In this case, this problem does not occur because the master always has enough buffer. The maximum size that PF_LongMultiBroadcast can broadcast is limited to around 320kB because the current implementation tries to pack all information of chained buffers into one buffer, whose size is PF_packsize = 1600B. #] Explanations : #[ Variables : */ typedef struct longMultiStruct { UBYTE *buffer; /* NULL if */ int bufpos; /* if >=0, PF_longPackBuf+bufpos is the chunk start */ int packpos; /* the current position */ int nPacks; /* How many times PF_longPack operates on this cell */ int lastLen; /* if > 0, the last packing didn't fit completely to this chunk, only lastLen items was packed, the rest is in the next cell. */ struct longMultiStruct *next; /* next linked cell, or NULL */ } PF_LONGMULTI; static UBYTE *PF_longPackBuf = NULL; static void *PF_longPackSmallBuf = NULL; static int PF_longPackPos = 0; static int PF_longPackTop = 0; static PF_LONGMULTI *PF_longMultiRoot = NULL; static PF_LONGMULTI *PF_longMultiTop = NULL; static PF_LONGMULTI *PF_longMultiLastChunk = NULL; static int PF_longPackN = 0; /* #] Variables : #[ Long pack private functions : #[ PF_longMultiNewCell : */ static inline int PF_longMultiNewCell(void) { /* Allocate a new cell: */ PF_longMultiTop->next = (PF_LONGMULTI *) Malloc1(sizeof(PF_LONGMULTI),"PF_longMultiCell"); if ( PF_longMultiTop->next == NULL ) return(-1); /* Allocate a private buffer: */ PF_longMultiTop->next->buffer=(UBYTE*) Malloc1(sizeof(UBYTE)*PF_packsize,"PF_longMultiChunk"); if ( PF_longMultiTop->next->buffer == NULL ) return(-1); /* For the private buffer position is -1: */ PF_longMultiTop->next->bufpos = -1; /* This is the last cell in the chain: */ PF_longMultiTop->next->next = NULL; /* packpos and nPacks are not initialized! */ return(0); } /* #] PF_longMultiNewCell : #[ PF_longMultiPack2NextCell : */ static inline int PF_longMultiPack2NextCell(void) { /* Is there a free cell in the chain? */ if ( PF_longMultiTop->next == NULL ) { /* No, allocate the new cell with a private buffer: */ if ( PF_longMultiNewCell() ) return(-1); } /* Move to the next cell in the chain: */ PF_longMultiTop = PF_longMultiTop->next; /* if >=0, the cell buffer is the chunk of PF_longPackBuf, initialize it: */ if ( PF_longMultiTop->bufpos > -1 ) PF_longMultiTop->buffer = PF_longPackBuf+PF_longMultiTop->bufpos; /* else -- the cell has it's own private buffer. Initialize the cell fields: */ PF_longMultiTop->nPacks = 0; PF_longMultiTop->lastLen = 0; PF_longMultiTop->packpos = 0; return(0); } /* #] PF_longMultiPack2NextCell : #[ PF_longMultiNewChunkAdded : */ static inline int PF_longMultiNewChunkAdded(int n) { /* Store the list tail: */ PF_LONGMULTI *MemCell = PF_longMultiLastChunk->next; int pos = PF_longPackTop; while ( n-- > 0 ) { /* Allocate a new cell: */ PF_longMultiLastChunk->next = (PF_LONGMULTI *) Malloc1(sizeof(PF_LONGMULTI),"PF_longMultiCell"); if ( PF_longMultiLastChunk->next == NULL ) return(-1); /* Update the Last Chunk Pointer: */ PF_longMultiLastChunk = PF_longMultiLastChunk->next; /* Initialize the new cell: */ PF_longMultiLastChunk->bufpos = pos; pos += PF_packsize; PF_longMultiLastChunk->buffer = NULL; PF_longMultiLastChunk->packpos = 0; PF_longMultiLastChunk->nPacks = 0; PF_longMultiLastChunk->lastLen = 0; } /* Hitch the tail: */ PF_longMultiLastChunk->next = MemCell; return(0); } /* #] PF_longMultiNewChunkAdded : #[ PF_longCopyChunk : */ static inline void PF_longCopyChunk(int *to, int *from, int n) { NCOPYI(to,from,n) /* for ( ; n > 0; n-- ) *to++ = *from++; */ } /* #] PF_longCopyChunk : #[ PF_longAddChunk : The chunk must be increased by n*PF_packsize. */ static int PF_longAddChunk(int n, int mustRealloc) { UBYTE *newbuf; if ( ( newbuf = (UBYTE*)Malloc1(sizeof(UBYTE)*(PF_longPackTop+n*PF_packsize), "PF_longPackBuf") ) == NULL ) return(-1); /* Allocate and chain a new cell for longMulti: */ if ( PF_longMultiNewChunkAdded(n) ) return(-1); /* Copy the content to the new buffer: */ if ( mustRealloc ) { PF_longCopyChunk((int*)newbuf,(int*)PF_longPackBuf,PF_longPackTop/sizeof(int)); } /* Note, PF_packsize is multiple by sizeof(int) by construction! */ PF_longPackTop += (n*PF_packsize); /* Free the old buffer and store the new one: */ M_free(PF_longPackBuf,"PF_longPackBuf"); PF_longPackBuf = newbuf; /* Count number of re-allocs: */ PF_longPackN += n; return(0); } /* #] PF_longAddChunk : #[ PF_longMultiHowSplit : "count" of "type" elements in an input buffer occupy "bytes" bytes. We know from the algorithm, that it is too many. How to split the buffer so that the head fits to rest of a storage buffer?*/ static inline int PF_longMultiHowSplit(int count, MPI_Datatype type, int bytes) { int ret, items, totalbytes; if ( count < 2 ) return(0); /* Nothing to split */ /* A rest of a storage buffer: */ totalbytes = PF_packsize - PF_longMultiTop->packpos; /* Rough estimate: */ items = (int)((double)totalbytes*count/bytes); /* Go to the up limit: */ do { if ( ( ret = MPI_Pack_size(++items,type,PF_COMM,&bytes) ) !=MPI_SUCCESS ) return(ret); } while ( bytes < totalbytes ); /* Now the value of "items" is too large And now evaluate the exact value: */ do { if ( ( ret = MPI_Pack_size(--items,type,PF_COMM,&bytes) ) !=MPI_SUCCESS ) return(ret); if ( items == 0 ) /* Nothing about MPI_Pack_size(0) == 0 in standards! */ return(0); } while ( bytes > totalbytes ); return(items); } /* #] PF_longMultiHowSplit : #[ PF_longPackInit : */ static int PF_longPackInit(void) { int ret; PF_longPackBuf = (UBYTE*)Malloc1(sizeof(UBYTE)*PF_packsize,"PF_longPackBuf"); if ( PF_longPackBuf == NULL ) return(-1); /* PF_longPackTop is not initialized yet, use in as a return value: */ ret = MPI_Pack_size(1,MPI_INT,PF_COMM,&PF_longPackTop); if ( ret != MPI_SUCCESS ) return(ret); PF_longPackSmallBuf = (void*)Malloc1(sizeof(UBYTE)*PF_longPackTop,"PF_longPackSmallBuf"); PF_longPackTop = PF_packsize; PF_longMultiRoot = (PF_LONGMULTI *)Malloc1(sizeof(PF_LONGMULTI),"PF_longMultiRoot"); if ( PF_longMultiRoot == NULL ) return(-1); PF_longMultiRoot->bufpos = 0; PF_longMultiRoot->buffer = NULL; PF_longMultiRoot->next = NULL; PF_longMultiLastChunk = PF_longMultiRoot; PF_longPackPos = 0; PF_longMultiRoot->packpos = 0; PF_longMultiTop = PF_longMultiRoot; PF_longPackN = 1; return(0); } /* #] PF_longPackInit : #[ PF_longMultiPreparePrefix : */ static inline int PF_longMultiPreparePrefix(void) { int ret; PF_LONGMULTI *thePrefix; int i = PF_longPackN; /* Here we have PF_longPackN>1! New cell (at the list end) to create the auxiliary chunk: */ if ( PF_longMultiPack2NextCell() ) return(-1); /* Store the pointer to the chunk we will proceed: */ thePrefix = PF_longMultiTop; /* Pack PF_longPackN: */ ret = MPI_Pack(&(PF_longPackN), 1, MPI_INT, thePrefix->buffer, PF_packsize, &(thePrefix->packpos), PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); /* And start from the beginning: */ for ( PF_longMultiTop = PF_longMultiRoot; i > 0; i-- ) { /* Pack number of Pack hits: */ ret = MPI_Pack(&(PF_longMultiTop->nPacks), 1, MPI_INT, thePrefix->buffer, PF_packsize, &(thePrefix->packpos), PF_COMM); /* Pack the length of the last fit portion: */ ret |= MPI_Pack(&(PF_longMultiTop->lastLen), 1, MPI_INT, thePrefix->buffer, PF_packsize, &(thePrefix->packpos), PF_COMM); /* Check the size -- not necessary, MPI_Pack did it. */ if ( ret != MPI_SUCCESS ) return(ret); /* Go to the next cell: */ PF_longMultiTop = PF_longMultiTop->next; } PF_longMultiTop = thePrefix; /* PF_longMultiTop is ready! */ return(0); } /* #] PF_longMultiPreparePrefix : #[ PF_longMultiProcessPrefix : */ static inline int PF_longMultiProcessPrefix(void) { int ret,i; /* We have PF_longPackN records packed in PF_longMultiRoot->buffer, pairs nPacks and lastLen. Loop through PF_longPackN cells, unpacking these integers into proper fields: */ for ( PF_longMultiTop = PF_longMultiRoot, i = 0; i < PF_longPackN; i++ ) { /* Go to th next cell, allocating, when necessary: */ if ( PF_longMultiPack2NextCell() ) return(-1); /* Unpack the number of Pack hits: */ ret = MPI_Unpack(PF_longMultiRoot->buffer, PF_packsize, &( PF_longMultiRoot->packpos), &(PF_longMultiTop->nPacks), 1, MPI_INT, PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); /* Unpack the length of the last fit portion: */ ret = MPI_Unpack(PF_longMultiRoot->buffer, PF_packsize, &( PF_longMultiRoot->packpos), &(PF_longMultiTop->lastLen), 1, MPI_INT, PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); } return(0); } /* #] PF_longMultiProcessPrefix : #[ PF_longSingleReset : */ /** * Resets the "long single" pack buffer. * * @param is_sender if the current process is the sender, it must be true. * Otherwise it must be false. * @return 0 if OK, nonzero on error. */ static inline int PF_longSingleReset(int is_sender) { int ret; PF_longPackPos=0; if ( is_sender ) { ret = MPI_Pack(&PF_longPackTop,1,MPI_INT, PF_longPackBuf,PF_longPackTop,&PF_longPackPos,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); PF_longPackN = 1; } else { PF_longPackN=0; } return(0); } /* #] PF_longSingleReset : #[ PF_longMultiReset : */ /** * Resets the "long multi" pack buffer. * * @param is_sender if the current process is the sender, it must be true. * Otherwise it must be false. * @return 0 if OK, nonzero on error. */ static inline int PF_longMultiReset(int is_sender) { int ret = 0, theone = 1; PF_longMultiRoot->packpos = 0; if ( is_sender ) { ret = MPI_Pack(&theone,1,MPI_INT, PF_longPackBuf,PF_longPackTop,&(PF_longMultiRoot->packpos),PF_COMM); PF_longPackN = 1; } else { PF_longPackN = 0; } PF_longMultiRoot->nPacks = 0; /* The auxiliary field is not counted */ PF_longMultiRoot->lastLen = 0; PF_longMultiTop = PF_longMultiRoot; PF_longMultiRoot->buffer = PF_longPackBuf; return ret; } /* #] PF_longMultiReset : #] Long pack private functions : #[ PF_PrepareLongSinglePack : */ /** * Prepares for the next long-single-pack operations on the sender. * * @return 0 if OK, nonzero on error. */ int PF_PrepareLongSinglePack(void) { return PF_longSingleReset(1); } /* #] PF_PrepareLongSinglePack : #[ PF_LongSinglePack : */ /** * Adds data into the "long single" pack buffer. * * @param buffer the pointer to the buffer storing the data to be packed. * @param count the number of elements in the buffer. * @param type the data type of elements in the buffer. * @return 0 if OK, nonzero on error. */ int PF_LongSinglePack(const void *buffer, size_t count, MPI_Datatype type) { int ret, bytes; /* XXX: Limited by int size. */ if ( count > INT_MAX ) return -99; ret = MPI_Pack_size((int)count,type,PF_COMM,&bytes); if ( ret != MPI_SUCCESS ) return(ret); while ( PF_longPackPos+bytes > PF_longPackTop ) { if ( PF_longAddChunk(1, 1) ) return(-1); } /* PF_longAddChunk(1, 1) means, the chunk must be increased by 1 and re-allocated */ ret = MPI_Pack((void *)buffer,(int)count,type, PF_longPackBuf,PF_longPackTop,&PF_longPackPos,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); return(0); } /* #] PF_LongSinglePack : #[ PF_LongSingleUnpack : */ /** * Retrieves the next data in the "long single" pack buffer. * * @param[out] buffer the pointer to the buffer to store the unpacked data. * @param count the number of elements of data to be received. * @param type the data type of elements of data to be received. * @return 0 if OK, nonzero on error. */ int PF_LongSingleUnpack(void *buffer, size_t count, MPI_Datatype type) { int ret; /* XXX: Limited by int size. */ if ( count > INT_MAX ) return -99; ret = MPI_Unpack(PF_longPackBuf,PF_longPackTop,&PF_longPackPos, buffer,(int)count,type,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); return(0); } /* #] PF_LongSingleUnpack : #[ PF_LongSingleSend : */ /** * Sends the contents in the "long single" pack buffer to the process * specified by \a to. * * Example: * @code * if ( PF.me == SRC ) { * PF_PrepareLongSinglePack(); * // Packing operations here... * PF_LongSingleSend(DEST, TAG); * } * else if ( PF.me == DEST ) { * PF_LongSingleReceive(SRC, TAG, &actual_src, &actual_tag); * // Unpacking operations here... * } * @endcode * * @param to the destination process number. * @param tag the message tag. * @return 0 if OK, nonzero on error. */ int PF_LongSingleSend(int to, int tag) { int ret, pos = 0; /* Note, here we assume that this function couldn't be used with to == PF_ANY_SOURCE! */ if ( PF_longPackN > 1 ) { /* The buffer was incremented, pack send the new size first: */ int tmp = -PF_longPackTop; /* Negative value means there will be the second buffer */ ret = MPI_Pack(&tmp, 1,PF_INT, PF_longPackSmallBuf,PF_longPackTop,&pos,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); ret = MPI_Ssend(PF_longPackSmallBuf,pos,MPI_PACKED,to,tag,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); } ret = MPI_Ssend(PF_longPackBuf,PF_longPackPos,MPI_PACKED,to,tag,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); return(0); } /* #] PF_LongSingleSend : #[ PF_LongSingleReceive : */ /** * Receives data into the "long single" pack buffer from the process * specified by \a src. * This function allows &src == psrc or &tag == ptag. * Either \a psrc or \a ptag can be NULL. * * See the example of PF_LongSingleSend(). * * @param src the source process number (can be PF_ANY_SOURCE). * @param tag the source message tag (can be PF_ANY_TAG). * @param[out] psrc the actual source process number of received message. * @param[out] ptag the received message tag. * @return 0 if OK, nonzero on error. */ int PF_LongSingleReceive(int src, int tag, int *psrc, int *ptag) { int ret, missed, oncemore; MPI_Status status; PF_longSingleReset(0); do { ret = MPI_Recv(PF_longPackBuf,PF_longPackTop,MPI_PACKED,src,tag, PF_COMM,&status); if ( ret != MPI_SUCCESS ) return(ret); /* The source and tag must be specified here for the case if MPI_Recv is performed more than once: */ src = status.MPI_SOURCE; tag = status.MPI_TAG; if ( psrc ) *psrc = status.MPI_SOURCE; if ( ptag ) *ptag = status.MPI_TAG; /* Now we got either small buffer with the new PF_longPackTop, or just a regular chunk. */ ret = MPI_Unpack(PF_longPackBuf,PF_longPackTop,&PF_longPackPos, &missed,1,MPI_INT,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); if ( missed < 0 ) { /* The small buffer was received. */ oncemore = 1; /* repeat receiving afterwards */ /* Reallocate the buffer and get the data */ missed = -missed; /* restore after unpacking small from buffer: */ PF_longPackPos = 0; } else { oncemore = 0; /* That's all, no repetition */ } if ( missed > PF_longPackTop ) { /* * The room must be increased. We need a re-allocation for the * case that there is no repetition. */ if ( PF_longAddChunk( (missed-PF_longPackTop)/PF_packsize, !oncemore ) ) return(-1); } } while ( oncemore ); return(0); } /* #] PF_LongSingleReceive : #[ PF_PrepareLongMultiPack : */ /** * Prepares for the next long-multi-pack operations on the sender. * * @return 0 if OK, nonzero on error. */ int PF_PrepareLongMultiPack(void) { return PF_longMultiReset(1); } /* #] PF_PrepareLongMultiPack : #[ PF_LongMultiPackImpl : */ /** * Adds data into the "long multi" pack buffer. * * @param buffer the pointer to the buffer storing the data to be packed. * @param count the number of elements in the buffer. * @param eSize the byte size of each element of data. * @param type the data type of elements in the buffer. * @return 0 if OK, nonzero on error. */ int PF_LongMultiPackImpl(const void*buffer, size_t count, size_t eSize, MPI_Datatype type) { int ret, items; /* XXX: Limited by int size. */ if ( count > INT_MAX ) return -99; ret = MPI_Pack_size((int)count,type,PF_COMM,&items); if ( ret != MPI_SUCCESS ) return(ret); if ( PF_longMultiTop->packpos + items <= PF_packsize ) { ret = MPI_Pack((void *)buffer,(int)count,type,PF_longMultiTop->buffer, PF_packsize,&(PF_longMultiTop->packpos),PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); PF_longMultiTop->nPacks++; return(0); } /* The data do not fit to the rest of the buffer. There are two possibilities here: go to the next cell immediately, or first try to pack some portion. The function PF_longMultiHowSplit() returns the number of items could be packed in the end of the current cell: */ if ( ( items = PF_longMultiHowSplit((int)count,type,items) ) < 0 ) return(items); if ( items > 0 ) { /* store the head */ ret = MPI_Pack((void *)buffer,items,type,PF_longMultiTop->buffer, PF_packsize,&(PF_longMultiTop->packpos),PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); PF_longMultiTop->nPacks++; PF_longMultiTop->lastLen = items; } /* Now the rest should be packed to the new cell. Slide to the new cell: */ if ( PF_longMultiPack2NextCell() ) return(-1); PF_longPackN++; /* Pack the rest to the next cell: */ return(PF_LongMultiPackImpl((char *)buffer+items*eSize,count-items,eSize,type)); } /* #] PF_LongMultiPackImpl : #[ PF_LongMultiUnpackImpl : */ /** * Retrieves the next data in the "long multi" pack buffer. * * @param[out] buffer the pointer to the buffer to store the unpacked data. * @param count the number of elements of data to be received. * @param eSize the byte size of each element of data. * @param type the data type of elements of data to be received. * @return 0 if OK, nonzero on error. */ int PF_LongMultiUnpackImpl(void *buffer, size_t count, size_t eSize, MPI_Datatype type) { int ret; /* XXX: Limited by int size. */ if ( count > INT_MAX ) return -99; if ( PF_longPackN < 2 ) { /* Just unpack the buffer from the single cell */ ret = MPI_Unpack( PF_longMultiTop->buffer, PF_packsize, &(PF_longMultiTop->packpos), buffer, count,type,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); return(0); } /* More than one cell is in use. */ if ( ( PF_longMultiTop->nPacks > 1 ) /* the cell is not expired */ || /* The last cell contains exactly required portion: */ ( ( PF_longMultiTop->nPacks == 1 ) && ( PF_longMultiTop->lastLen == 0 ) ) ) { /* Just unpack the buffer from the current cell */ ret = MPI_Unpack( PF_longMultiTop->buffer, PF_packsize, &(PF_longMultiTop->packpos), buffer, count,type,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); (PF_longMultiTop->nPacks)--; return(0); } if ( ( PF_longMultiTop->nPacks == 1 ) && ( PF_longMultiTop->lastLen != 0 ) ) { /* Unpack the head: */ ret = MPI_Unpack( PF_longMultiTop->buffer, PF_packsize, &(PF_longMultiTop->packpos), buffer, PF_longMultiTop->lastLen,type,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); /* Decrement the counter by read items: */ count -= PF_longMultiTop->lastLen; if ( count <= 0 ) return(-1); /*Something is wrong! */ /* Shift the output buffer position: */ buffer = (char *)buffer + PF_longMultiTop->lastLen * eSize; (PF_longMultiTop->nPacks)--; } /* Here PF_longMultiTop->nPacks == 0 */ if ( ( PF_longMultiTop = PF_longMultiTop->next ) == NULL ) return(-1); return(PF_LongMultiUnpackImpl(buffer,count,eSize,type)); } /* #] PF_LongMultiUnpackImpl : #[ PF_LongMultiBroadcast : */ /** * Broadcasts the contents in the "long multi" pack buffer on the master * to those on the slaves. * * Example: * @code * if ( PF.me == MASTER ) { * PF_PrepareLongMultiPack(); * // Packing operations here... * } * PF_LongMultiBroadcast(); * if ( PF.me != MASTER ) { * // Unpacking operations here... * } * @endcode * * @return 0 if OK, nonzero on error. */ int PF_LongMultiBroadcast(void) { int ret, i; if ( PF.me == MASTER ) { /* PF_longPackN is the number of packed chunks. If it is more than 1, we have to pack a new one and send it first */ if ( PF_longPackN > 1 ) { if ( PF_longMultiPreparePrefix() ) return(-1); ret = MPI_Bcast((void*)PF_longMultiTop->buffer, PF_packsize,MPI_PACKED,MASTER,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); /* PF_longPackN was not incremented by PF_longMultiPreparePrefix()! */ } /* Now we start from the beginning: */ PF_longMultiTop = PF_longMultiRoot; /* Just broadcast all the chunks: */ for ( i = 0; i < PF_longPackN; i++ ) { ret = MPI_Bcast((void*)PF_longMultiTop->buffer, PF_packsize,MPI_PACKED,MASTER,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); PF_longMultiTop = PF_longMultiTop->next; } return(0); } /* else - the slave */ PF_longMultiReset(0); /* Get the first chunk; it can be either the only data chunk, or an auxiliary chunk, if the data do not fit the single chunk: */ ret = MPI_Bcast((void*)PF_longMultiRoot->buffer, PF_packsize,MPI_PACKED,MASTER,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); ret = MPI_Unpack((void*)PF_longMultiRoot->buffer, PF_packsize, &(PF_longMultiRoot->packpos), &PF_longPackN,1,MPI_INT,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); /* Now in PF_longPackN we have the number of cells used for broadcasting. If it is >1, then we have to allocate enough cells, initialize them and receive all the chunks. */ if ( PF_longPackN < 2 ) /* That's all, the single chunk is received. */ return(0); /* Here we have to get PF_longPackN chunks. But, first, initialize cells by info from the received auxiliary chunk. */ if ( PF_longMultiProcessPrefix() ) return(-1); /* Now we have free PF_longPackN cells, starting from PF_longMultiRoot->next, with properly initialized nPacks and lastLen fields. Get chunks: */ for ( PF_longMultiTop = PF_longMultiRoot->next, i = 0; i < PF_longPackN; i++ ) { ret = MPI_Bcast((void*)PF_longMultiTop->buffer, PF_packsize,MPI_PACKED,MASTER,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); if ( i == 0 ) { /* The first chunk, it contains extra "1". */ int tmp; /* Extract this 1 into tmp and forget about it. */ ret = MPI_Unpack((void*)PF_longMultiTop->buffer, PF_packsize, &(PF_longMultiTop->packpos), &tmp,1,MPI_INT,PF_COMM); if ( ret != MPI_SUCCESS ) return(ret); } PF_longMultiTop = PF_longMultiTop->next; } /* multiUnPack starts with PF_longMultiTop, skip auxiliary chunk in PF_longMultiRoot: */ PF_longMultiTop = PF_longMultiRoot->next; return(0); } /* #] PF_LongMultiBroadcast : #] Long pack stuff : */ form-5.0.1/sources/smart.c0000644000175100017510000002744415217035721011136 /** @file smart.c * * The functions for smart pattern searches in combinations of functions. * When many wildcards are involved and the functions are (anti)symmetric * an exhaustive search for all possibilities may take very much time * (like factorial in the number of wildcards) while a human can often * see immediately that there cannot be a match. The routines here try * to make FORM a bit smarter in this respect. * * This is just the beginning. It still needs lots of work! */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : function.c */ #include "form3.h" /* #] Includes : #[ StudyPattern : Argument is a complete lhs of an id-statement Its last word is a zero (new convention(18-may-1997)) to indicate that no extra information is following. We can add there information about the pattern that will help during the actual pattern matching. Currently the WorkPointer points to just after this lhs. Task of this routine: To study the functions, their symmetry properties and their wildcards to determine in which order the functions can be matched best. If the order should be different we can change it here. Problem encountered 22-dec-2008 (JV): we don't take noncommuting functions into account. */ int StudyPattern(WORD *lhs) { GETIDENTITY WORD *fullproto, *pat, *p, *p1, *p2, *pstop, *info, f, nn; int numfun = 0, numsym = 0, allwilds = 0, i, j, k, nc; FUN_INFO *finf, *fmin, *f1, *f2, funscratch; fullproto = lhs + IDHEAD; /* if ( *lhs == TYPEIF ) fullproto--; */ pat = fullproto + fullproto[1]; info = pat + *pat; p = pat + 1; while ( p < info ) { if ( *p >= FUNCTION ) { numfun++; nn = *p - FUNCTION; if ( nn >= WILDOFFSET ) nn -= WILDOFFSET; /* We check here for cases that are not allowed like ?a inside symmetric functions or tensors. */ if ( ( functions[nn].symmetric == SYMMETRIC ) || ( functions[nn].symmetric == ANTISYMMETRIC ) ) { p2 = p+p[1]; p1 = p+FUNHEAD; if ( functions[nn].spec > 0 ) { while ( p1 < p2 ) { if ( *p1 == FUNNYWILD ) { MesPrint("&Argument field wildcards are not allowed inside (anti)symmetric functions or tensors"); return(1); } p1++; } } else { while ( p1 < p2 ) { if ( *p1 == -ARGWILD ) { MesPrint("&Argument field wildcards are not allowed inside (anti)symmetric functions or tensors"); return(1); } NEXTARG(p1); } } } } p += p[1]; } if ( numfun == 0 ) return(0); if ( ( lhs[2] & SUBMASK ) == SUBALL ) { p = pat + 1; while ( p < info ) { if ( *p == SYMBOL || *p == VECTOR || *p == DOTPRODUCT || *p == INDEX ) { MesPrint("&id,all can have only functions and/or tensors in the lhs."); return(1); } p += p[1]; } } /* We need now some room for the information about the functions */ if ( numfun > AN.numfuninfo ) { if ( AN.FunInfo ) M_free(AN.FunInfo,"funinfo"); AN.numfuninfo = numfun + 10; AN.FunInfo = (FUN_INFO *)Malloc1(AN.numfuninfo*sizeof(FUN_INFO),"funinfo"); } /* Now collect the information. First the locations. */ p = pat + 1; i = 0; while ( p < info ) { if ( *p >= FUNCTION ) AN.FunInfo[i++].location = p; p += p[1]; } for ( i = 0, finf = AN.FunInfo; i < numfun; i++, finf++ ) { p = finf->location; pstop = p + p[1]; f = *p; if ( f > FUNCTION+WILDOFFSET ) f -= WILDOFFSET; finf->numargs = finf->numfunnies = finf->numwildcards = 0; finf->symmet = functions[f-FUNCTION].symmetric; finf->tensor = functions[f-FUNCTION].spec; finf->commute = functions[f-FUNCTION].commute; if ( finf->tensor >= TENSORFUNCTION ) { p += FUNHEAD; while ( p < pstop ) { if ( *p == FUNNYWILD ) { finf->numfunnies++; p+= 2; continue; } else if ( *p < 0 ) { if ( *p >= AM.OffsetVector + WILDOFFSET && *p < MINSPEC ) { finf->numwildcards++; } } else { if ( *p >= AM.OffsetIndex + WILDOFFSET && *p <= AM.OffsetIndex + 2*WILDOFFSET ) finf->numwildcards++; } finf->numargs++; p++; } } else { p += FUNHEAD; while ( p < pstop ) { if ( *p > 0 ) { finf->numargs++; p += *p; continue; } if ( *p <= -FUNCTION ) { if ( *p <= -FUNCTION - WILDOFFSET ) finf->numwildcards++; p++; } else if ( *p == -SYMBOL ) { if ( p[1] >= 2*MAXPOWER ) finf->numwildcards++; p += 2; } else if ( *p == -INDEX ) { if ( p[1] >= AM.OffsetIndex + WILDOFFSET && p[1] <= AM.OffsetIndex + 2*WILDOFFSET ) finf->numwildcards++; p += 2; } else if ( *p == -VECTOR || *p == -MINVECTOR ) { if ( p[1] >= AM.OffsetVector + WILDOFFSET && p[1] < MINSPEC ) { finf->numwildcards++; } p += 2; } else if ( *p == -ARGWILD ) { finf->numfunnies++; p += 2; } else { p += 2; } finf->numargs++; } } if ( finf->symmet ) { numsym++; allwilds += finf->numwildcards + finf->numfunnies; } } if ( numsym == 0 ) return(0); if ( allwilds == 0 ) return(0); /* We have the information in the array AN.FunInfo. We sort things and then write the sorted pattern. Of course we may not play with the order of the noncommuting functions. Of course we have to become even smarter in the future and look during the sorting which wildcards are assigned when. But for now this should do. */ for ( nc = numfun-1; nc >= 0; nc-- ) { if ( AN.FunInfo[nc].commute ) break; } finf = AN.FunInfo; for ( i = nc+2; i < numfun; i++ ) { fmin = finf; finf++; if ( ( finf->symmet < fmin->symmet ) || ( ( finf->symmet == fmin->symmet ) && ( ( finf->numwildcards+finf->numfunnies < fmin->numwildcards+fmin->numfunnies ) || ( ( finf->numwildcards+finf->numfunnies == fmin->numwildcards+fmin->numfunnies ) && ( finf->numwildcards < fmin->numfunnies ) ) ) ) ) { funscratch = AN.FunInfo[i]; AN.FunInfo[i] = AN.FunInfo[i-1]; AN.FunInfo[i-1] = funscratch; for ( j = i-1; j > nc && j > 0; j-- ) { f1 = AN.FunInfo+j; f2 = f1-1; if ( ( f1->symmet < f2->symmet ) || ( ( f1->symmet == f2->symmet ) && ( ( f1->numwildcards+f1->numfunnies < f2->numwildcards+f2->numfunnies ) || ( ( f1->numwildcards+f1->numfunnies == f2->numwildcards+f2->numfunnies ) && ( f1->numwildcards < f2->numfunnies ) ) ) ) ) { funscratch = AN.FunInfo[j]; AN.FunInfo[j] = AN.FunInfo[j-1]; AN.FunInfo[j-1] = funscratch; } else break; } } } /* Now we rewrite the pattern. First into the space after it and then we copy it back. Be careful with the non-commutative functions. There the worst one should decide. */ p = pat + 1; p2 = info; for ( i = 0; i < numfun; i++ ) { if ( i == nc ) { for ( k = 0; k <= nc; k++ ) { if ( AN.FunInfo[k].commute ) { p1 = AN.FunInfo[k].location; j = p1[1]; NCOPY(p2,p1,j) } } } else if ( AN.FunInfo[i].commute == 0 ) { p1 = AN.FunInfo[i].location; j = p1[1]; NCOPY(p2,p1,j) } } p = pat + 1; p1 = info; while ( p1 < p2 ) *p++ = *p1++; /* And now we place the relevant information in the info part */ p2 = info+1; for ( i = 0; i < numfun; i++ ) { if ( i == nc ) { for ( k = 0; k <= nc; k++ ) { if ( AN.FunInfo[k].commute ) { finf = AN.FunInfo + k; *p2++ = finf->numargs; *p2++ = finf->numwildcards; *p2++ = finf->numfunnies; *p2++ = finf->symmet; } } } else if ( AN.FunInfo[i].commute == 0 ) { finf = AN.FunInfo + i; *p2++ = finf->numargs; *p2++ = finf->numwildcards; *p2++ = finf->numfunnies; *p2++ = finf->symmet; } } *info = p2-info; lhs[1] = p2-lhs; return(0); } /* #] StudyPattern : #[ MatchIsPossible : We come here when there are functions and there is nontrivial symmetry related wildcarding. */ int MatchIsPossible(WORD *pattern, WORD *term) { GETIDENTITY WORD *info = pattern + *pattern; WORD *t, *tstop, *tt, *inf, *p; int numfun = 0, inpat, i, j, numargs; FUN_INFO *finf; /* We need a list of functions and their number of arguments */ GETSTOP(term,tstop); t = term + 1; while ( t < tstop ) { if ( *t >= FUNCTION ) numfun++; t += t[1]; } if ( numfun == 0 ) goto NotPossible; if ( *info == SETSET ) info += info[1]; inpat = (*info-1)/4; if ( inpat > numfun ) goto NotPossible; /* We need now some room for the information about the functions */ if ( numfun > AN.numfuninfo ) { if ( AN.FunInfo ) M_free(AN.FunInfo,"funinfo"); AN.numfuninfo = numfun + 10; AN.FunInfo = (FUN_INFO *)Malloc1(AN.numfuninfo*sizeof(FUN_INFO),"funinfo"); } t = term + 1; finf = AN.FunInfo; while ( t < tstop ) { if ( *t >= FUNCTION ) { finf->location = t; if ( functions[*t-FUNCTION].spec >= TENSORFUNCTION ) { numargs = t[1]-FUNHEAD; t += t[1]; } else { numargs = 0; tt = t + t[1]; t += FUNHEAD; while ( t < tt ) { numargs++; NEXTARG(t) } } finf->numargs = numargs; finf++; } else t += t[1]; } /* Now we first find a partner for each function in the pattern with a fixed number of arguments */ for ( i = 0, inf = info+1, p = pattern+1; i < inpat; i++, inf += 4, p+=p[1] ) { if ( inf[2] ) continue; if ( *p >= (FUNCTION+WILDOFFSET) ) continue; for ( j = 0, finf = AN.FunInfo; j < numfun; j++, finf++ ) { if ( *p == *(finf->location) && *inf == finf->numargs ) { finf->numargs = -finf->numargs-1; break; } } if ( j >= numfun ) goto NotPossible; } for ( i = 0, inf = info+1, p = pattern+1; i < inpat; i++, inf += 4, p+=p[1] ) { if ( inf[2] ) continue; if ( *p < (FUNCTION+WILDOFFSET) ) continue; for ( j = 0, finf = AN.FunInfo; j < numfun; j++, finf++ ) { if ( *inf == finf->numargs ) { finf->numargs = -finf->numargs-1; break; } } if ( j >= numfun ) goto NotPossible; } for ( i = 0, inf = info+1, p = pattern+1; i < inpat; i++, inf += 4, p+=p[1] ) { if ( inf[2] == 0 ) continue; if ( *p >= (FUNCTION+WILDOFFSET) ) continue; for ( j = 0, finf = AN.FunInfo; j < numfun; j++, finf++ ) { if ( *p == *(finf->location) && (*inf-inf[2]) <= finf->numargs ) { finf->numargs = -finf->numargs-1; break; } } if ( j >= numfun ) goto NotPossible; } for ( i = 0, inf = info+1, p = pattern+1; i < inpat; i++, inf += 4, p+=p[1] ) { if ( inf[2] == 0 ) continue; if ( *p < (FUNCTION+WILDOFFSET) ) continue; for ( j = 0, finf = AN.FunInfo; j < numfun; j++, finf++ ) { if ( (*inf-inf[2]) <= finf->numargs ) { finf->numargs = -finf->numargs-1; break; } } if ( j >= numfun ) goto NotPossible; } /* Thus far we have determined that for each function in the pattern there is a potential partner with enough arguments. For now the rest is up to the real pattern matcher. To undo the disabling of the number of arguments we need this code for ( i = 0, finf = AN.FunInfo; i < numfun; i++, finf++ ) { if ( finf->numargs < 0 ) finf->numargs = -finf->numargs-1; } */ return(1); NotPossible: /* PrintTerm(pattern,"p"); PrintTerm(term,"t"); */ return(0); } /* #] MatchIsPossible : */ form-5.0.1/sources/normal.c0000644000175100017510000043422215217035721011274 /** @file normal.c * * Mainly the routine Normalize. This routine brings terms to standard * form. Its main buffers are in AT, but they have a fixed size controlled * by NORMSIZE, which limit the maximum complexity of terms which can be * normalized. * * Normalize is called recursively, currently via: * Normalize -> ExpandRat -> Normalize. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : normal.c */ #include "form3.h" #ifdef WITHFLOAT #include int PackFloat(WORD *,mpf_t); int UnpackFloat(mpf_t, WORD *); void RatToFloat(mpf_t result, UWORD *formrat, int ratsize); #endif /* #] Includes : #[ Normalize : #[ CompareFunctions : */ int CompareFunctions(WORD *fleft,WORD *fright) { WORD k, kk; if ( AC.properorderflag ) { if ( ( *fleft >= (FUNCTION+WILDOFFSET) && functions[*fleft-FUNCTION-WILDOFFSET].spec >= TENSORFUNCTION ) || ( *fleft >= FUNCTION && *fleft < (FUNCTION + WILDOFFSET) && functions[*fleft-FUNCTION].spec >= TENSORFUNCTION ) ) {} else { WORD *s1, *s2, *ss1, *ss2; s1 = fleft+FUNHEAD; s2 = fright+FUNHEAD; ss1 = fleft + fleft[1]; ss2 = fright + fright[1]; while ( s1 < ss1 && s2 < ss2 ) { k = CompArg(s1,s2); if ( k > 0 ) return(1); if ( k < 0 ) return(0); NEXTARG(s1) NEXTARG(s2) } if ( s1 < ss1 ) return(1); return(0); } k = fleft[1] - FUNHEAD; kk = fright[1] - FUNHEAD; fleft += FUNHEAD; fright += FUNHEAD; while ( k > 0 && kk > 0 ) { if ( *fleft < *fright ) return(0); else if ( *fleft++ > *fright++ ) return(1); k--; kk--; } if ( k > 0 ) return(1); return(0); } else { k = fleft[1] - FUNHEAD; kk = fright[1] - FUNHEAD; fleft += FUNHEAD; fright += FUNHEAD; while ( k > 0 && kk > 0 ) { if ( *fleft < *fright ) return(0); else if ( *fleft++ > *fright++ ) return(1); k--; kk--; } if ( k > 0 ) return(1); return(0); } } /* #] CompareFunctions : #[ Commute : This function gets two adjacent function pointers and decides whether these two functions should be exchanged to obtain a natural ordering. Currently there is only an ordering of gamma matrices belonging to different spin lines. Note that we skip for now the cases of (F)^(3/2) or 1/F and a few more of such funny functions. */ int Commute(WORD *fleft, WORD *fright) { WORD fun1, fun2; if ( *fleft == DOLLAREXPRESSION || *fright == DOLLAREXPRESSION ) return(0); fun1 = ABS(*fleft); fun2 = ABS(*fright); if ( *fleft >= GAMMA && *fleft <= GAMMASEVEN && *fright >= GAMMA && *fright <= GAMMASEVEN ) { if ( fleft[FUNHEAD] < AM.OffsetIndex && fleft[FUNHEAD] > fright[FUNHEAD] ) return(1); return(0); } if ( fun1 >= WILDOFFSET ) fun1 -= WILDOFFSET; if ( fun2 >= WILDOFFSET ) fun2 -= WILDOFFSET; if ( ( ( functions[fun1-FUNCTION].flags & COULDCOMMUTE ) == 0 ) || ( ( functions[fun2-FUNCTION].flags & COULDCOMMUTE ) == 0 ) ) return(0); /* if other conditions will come here, keep in mind that if *fleft < 0 or *fright < 0 they are arguments in the exponent function as in f^(3/2) */ if ( AC.CommuteInSet == 0 ) return(0); /* The code for CompareFunctions can be stolen from the commuting case. We need the syntax: Commute Fun1,Fun2,...,Fun`n'; For this Fun1,...,Fun`n' need to be noncommuting functions. These functions will commute with all members of the group. In the AC.paircommute buffer the representation is `n'+1,element1,...,element`n',`m'+1,element1,...,element`m',0 A function can belong to more than one group. If a function commutes with itself, it is most efficient to make a separate group of two elements for it as in Commute T,T; -> 3,T,T */ if ( fun1 >= fun2 ) { WORD *group = AC.CommuteInSet, *g1, *g2, *g3; while ( *group > 0 ) { g3 = group + *group; g1 = group+1; while ( g1 < g3 ) { if ( *g1 == fun1 || ( fun1 <= GAMMASEVEN && fun1 >= GAMMA && *g1 <= GAMMASEVEN && *g1 >= GAMMA ) ) { g2 = group+1; while ( g2 < g3 ) { if ( g1 != g2 && ( *g2 == fun2 || ( fun2 <= GAMMASEVEN && fun2 >= GAMMA && *g2 <= GAMMASEVEN && *g2 >= GAMMA ) ) ) { if ( fun1 != fun2 ) return(1); if ( *fleft < 0 ) return(0); if ( *fright < 0 ) return(1); return(CompareFunctions(fleft,fright)); } g2++; } break; } g1++; } group = g3; } } return(0); } /* #] Commute : #[ Normalize : This is the big normalization routine. It has a great need to be economical. The limit on the number of objects coming in is given by NORMSIZE. */ int Normalize(PHEAD WORD *term) { /* #[ Declarations : */ GETBIDENTITY WORD *t, *m, *r, i, j, k, l, nsym, *ss, *tt, *u; WORD shortnum, stype; WORD *stop, *to = 0, *from = 0; WORD *ppsym, *ppvec, *ppdot, *ppdel; WORD nvec, ndot, ndel, nind, neps, nden, ncom, nnco, ncon; AT.NormDepth++; #ifdef DEBUGGING if ( AT.NormDepth > 2 ) { // We don't expect this to happen in the current codebase. Terminate(-1); } #endif if ( AT.NormDepth > AT.NormDataSize ) { NORMDATA **top = AT.NormData + AT.NormDataSize; DoubleBuffer((void **)&(AT.NormData), (void **)&(top), sizeof(*AT.NormData), "double NormData pointers"); AT.NormDataSize *= 2; for ( LONG i = AT.NormDepth-1; i < AT.NormDataSize; i++ ) { AT.NormData[i] = NULL; } } if ( AT.NormData[AT.NormDepth-1] == NULL ) { AT.NormData[AT.NormDepth-1] = AllocNormData(); } WORD *psym = AT.NormData[AT.NormDepth-1]->psym; WORD *pvec = AT.NormData[AT.NormDepth-1]->pvec; WORD *pdot = AT.NormData[AT.NormDepth-1]->pdot; WORD *pdel = AT.NormData[AT.NormDepth-1]->pdel; WORD *pind = AT.NormData[AT.NormDepth-1]->pind; WORD **peps = AT.NormData[AT.NormDepth-1]->peps; WORD **pden = AT.NormData[AT.NormDepth-1]->pden; WORD **pcom = AT.NormData[AT.NormDepth-1]->pcom; WORD **pnco = AT.NormData[AT.NormDepth-1]->pnco; WORD **pcon = AT.NormData[AT.NormDepth-1]->pcon; WORD *n_coef, ncoef; /* Accumulator for the coefficient */ WORD *n_llnum, *lnum, nnum; WORD *termout, oldtoprhs = 0, subtype; WORD ReplaceType, ReplaceVeto = 0, didcontr; int regval = 0; WORD *ReplaceSub; WORD *fillsetexp; CBUF *C = cbuf+AT.ebufnum; WORD *ANsc = 0, *ANsm = 0, *ANsr = 0, PolyFunMode; #ifdef WITHFLOAT WORD withfloat = 0; WORD *firstfloat = 0; #endif LONG oldcpointer = 0, x; n_coef = TermMalloc("NormCoef"); n_llnum = TermMalloc("n_llnum"); lnum = n_llnum+1; /* int termflag; */ /* #] Declarations : #[ Setup : PrintTerm(term,"Normalize"); */ Restart: didcontr = 0; ReplaceType = -1; t = term; if ( !*t ) { AT.NormDepth--; TermFree(n_coef,"NormCoef"); TermFree(n_llnum,"n_llnum"); return(regval); } r = t + *t; ncoef = r[-1]; i = ABS(ncoef); r -= i; m = r; t = n_coef; NCOPY(t,r,i); termout = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); fillsetexp = termout+1; AN.PolyNormFlag = 0; PolyFunMode = AN.PolyFunTodo; /* termflag = 0; */ /* #] Setup : #[ First scan : */ nsym = nvec = ndot = ndel = neps = nden = nind = ncom = nnco = ncon = 0; ppsym = psym; ppvec = pvec; ppdot = pdot; ppdel = pdel; t = term + 1; conscan:; if ( t < m ) do { r = t + t[1]; switch ( *t ) { case SYMBOL : t += 2; from = m; do { if ( t[1] == 0 ) { /* if ( *t == 0 || *t == MAXPOWER ) goto NormZZ; */ t += 2; goto NextSymbol; } if ( *t <= DENOMINATORSYMBOL && *t >= COEFFSYMBOL ) { /* if ( AN.NoScrat2 == 0 ) { AN.NoScrat2 = (UWORD *)Malloc1((AM.MaxTal+2)*sizeof(UWORD),"Normalize"); } */ if ( AN.cTerm ) m = AN.cTerm; else m = term; m += *m; ncoef = REDLENG(ncoef); if ( *t == COEFFSYMBOL ) { i = t[1]; nnum = REDLENG(m[-1]); m -= ABS(m[-1]); if ( i > 0 ) { while ( i > 0 ) { if ( MulRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)m,nnum, (UWORD *)n_coef,&ncoef) ) goto FromNorm; i--; } } else if ( i < 0 ) { while ( i < 0 ) { if ( DivRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)m,nnum, (UWORD *)n_coef,&ncoef) ) goto FromNorm; i++; } } } else { i = m[-1]; nnum = (ABS(i)-1)/2; if ( *t == NUMERATORSYMBOL ) { m -= nnum + 1; } else { m--; } while ( *m == 0 && nnum > 1 ) { m--; nnum--; } m -= nnum; if ( i < 0 && *t == NUMERATORSYMBOL ) nnum = -nnum; i = t[1]; if ( i > 0 ) { while ( i > 0 ) { if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)m,nnum) ) goto FromNorm; i--; } } else if ( i < 0 ) { while ( i < 0 ) { if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)m,nnum) ) goto FromNorm; i++; } } } ncoef = INCLENG(ncoef); t += 2; goto NextSymbol; } else if ( *t == DIMENSIONSYMBOL ) { if ( AN.cTerm ) m = AN.cTerm; else m = term; k = DimensionTerm(m); if ( k == 0 ) goto NormZero; if ( k == MAXPOSITIVE ) { MLOCK(ErrorMessageLock); MesPrint("Dimension_ is undefined in term %t"); MUNLOCK(ErrorMessageLock); goto NormMin; } if ( k == -MAXPOSITIVE ) { MLOCK(ErrorMessageLock); MesPrint("Dimension_ out of range in term %t"); MUNLOCK(ErrorMessageLock); goto NormMin; } if ( k > 0 ) { *((UWORD *)lnum) = k; nnum = 1; } else { *((UWORD *)lnum) = -k; nnum = -1; } ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; ncoef = INCLENG(ncoef); t += 2; goto NextSymbol; } if ( ( *t >= MAXPOWER && *t < 2*MAXPOWER ) || ( *t < -MAXPOWER && *t > -2*MAXPOWER ) ) { /* #[ TO SNUMBER : */ if ( *t < 0 ) { *t += MAXPOWER; *t = -*t; if ( t[1] & 1 ) ncoef = -ncoef; } else if ( *t == MAXPOWER ) { if ( t[1] > 0 ) goto NormZero; goto NormInf; } else { *t -= MAXPOWER; } lnum[0] = *t; nnum = 1; if ( t[1] && RaisPow(BHEAD (UWORD *)lnum,&nnum,(UWORD)(ABS(t[1]))) ) goto FromNorm; ncoef = REDLENG(ncoef); if ( t[1] < 0 ) { if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; } else if ( t[1] > 0 ) { if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; } ncoef = INCLENG(ncoef); /* #] TO SNUMBER : */ t += 2; goto NextSymbol; } if ( ( *t <= NumSymbols && *t > -MAXPOWER ) && ( symbols[*t].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) { if ( t[1] <= 2*MAXPOWER && t[1] >= -2*MAXPOWER ) { t[1] %= symbols[*t].maxpower; if ( t[1] < 0 ) t[1] += symbols[*t].maxpower; if ( ( symbols[*t].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { if ( ( ( symbols[*t].maxpower & 1 ) == 0 ) && ( t[1] >= symbols[*t].maxpower/2 ) ) { t[1] -= symbols[*t].maxpower/2; ncoef = -ncoef; } } if ( t[1] == 0 ) { t += 2; goto NextSymbol; } } } i = nsym; m = ppsym; if ( i > 0 ) do { m -= 2; if ( *t == *m ) { t++; m++; if ( *t > 2*MAXPOWER || *t < -2*MAXPOWER || *m > 2*MAXPOWER || *m < -2*MAXPOWER ) { MLOCK(ErrorMessageLock); MesPrint("Illegal wildcard power combination."); MUNLOCK(ErrorMessageLock); goto NormMin; } *m += *t; if ( ( t[-1] <= NumSymbols && t[-1] > -MAXPOWER ) && ( symbols[t[-1]].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) { *m %= symbols[t[-1]].maxpower; if ( *m < 0 ) *m += symbols[t[-1]].maxpower; if ( ( symbols[t[-1]].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { if ( ( ( symbols[t[-1]].maxpower & 1 ) == 0 ) && ( *m >= symbols[t[-1]].maxpower/2 ) ) { *m -= symbols[t[-1]].maxpower/2; ncoef = -ncoef; } } } if ( *m >= 2*MAXPOWER || *m <= -2*MAXPOWER ) { MLOCK(ErrorMessageLock); MesPrint("Power overflow during normalization"); MUNLOCK(ErrorMessageLock); goto NormMin; } if ( !*m ) { m--; while ( i < nsym ) { *m = m[2]; m++; *m = m[2]; m++; i++; } ppsym -= 2; nsym--; } t++; goto NextSymbol; } } while ( *t < *m && --i > 0 ); m = ppsym; while ( i < nsym ) { m--; m[2] = *m; m--; m[2] = *m; i++; } *m++ = *t++; *m = *t++; ppsym += 2; nsym++; NextSymbol:; } while ( t < r ); m = from; break; case VECTOR : t += 2; do { if ( t[0] == AM.vectorzero ) goto NormZero; if ( t[1] == FUNNYVEC ) { pind[nind++] = *t; t += 2; } else if ( t[1] < 0 ) { if ( *t == NOINDEX && t[1] == NOINDEX ) t += 2; else { if ( t[1] == AM.vectorzero ) goto NormZero; *ppdot++ = *t++; *ppdot++ = *t++; *ppdot++ = 1; ndot++; } } else { *ppvec++ = *t++; *ppvec++ = *t++; nvec += 2; } } while ( t < r ); break; case DOTPRODUCT : t += 2; do { if ( t[2] == 0 ) t += 3; else if ( ndot > 0 && t[0] == ppdot[-3] && t[1] == ppdot[-2] ) { ppdot[-1] += t[2]; t += 3; if ( ppdot[-1] == 0 ) { ppdot -= 3; ndot--; } } else if ( t[0] == AM.vectorzero || t[1] == AM.vectorzero ) { if ( t[2] > 0 ) goto NormZero; goto NormInf; } else { *ppdot++ = *t++; *ppdot++ = *t++; *ppdot++ = *t++; ndot++; } } while ( t < r ); break; case HAAKJE : break; case SETSET: if ( WildFill(BHEAD termout,term,AT.dummysubexp) < 0 ) goto FromNorm; i = *termout; t = termout; m = term; NCOPY(m,t,i); goto Restart; case DOLLAREXPRESSION : /* We have DOLLAREXPRESSION,4,number,power Replace by SUBEXPRESSION and exit elegantly to let TestSub pick it up. Of course look for special cases first. Note that we have a special compiler buffer for the values. */ if ( AR.Eside != LHSIDE ) { DOLLARS d = Dollars + t[2]; #ifdef WITHPTHREADS int nummodopt, ptype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { ptype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(ptype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif if ( d->type == DOLZERO ) { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif if ( t[3] == 0 ) goto NormZZ; if ( t[3] < 0 ) goto NormInf; goto NormZero; } else if ( d->type == DOLNUMBER ) { nnum = d->where[0]; if ( nnum > 0 ) { nnum = d->where[nnum-1]; if ( nnum < 0 ) { ncoef = -ncoef; nnum = -nnum; } nnum = (nnum-1)/2; for ( i = 1; i <= nnum; i++ ) lnum[i-1] = d->where[i]; } if ( nnum == 0 || ( nnum == 1 && lnum[0] == 0 ) ) { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif if ( t[3] < 0 ) goto NormInf; else if ( t[3] == 0 ) goto NormZZ; goto NormZero; } if ( t[3] && RaisPow(BHEAD (UWORD *)lnum,&nnum,(UWORD)(ABS(t[3]))) ) goto FromNorm; ncoef = REDLENG(ncoef); if ( t[3] < 0 ) { if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif goto FromNorm; } } else if ( t[3] > 0 ) { if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif goto FromNorm; } } ncoef = INCLENG(ncoef); } else if ( d->type == DOLINDEX ) { if ( d->index == 0 ) { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif goto NormZero; } if ( d->index != NOINDEX ) pind[nind++] = d->index; } else if ( d->type == DOLTERMS ) { if ( t[3] >= MAXPOWER || t[3] <= -MAXPOWER ) { if ( d->where[0] == 0 ) goto NormZero; if ( d->where[d->where[0]] != 0 ) { IllDollarExp: MLOCK(ErrorMessageLock); MesPrint("!!!Illegal $ expansion with wildcard power!!!"); MUNLOCK(ErrorMessageLock); goto FromNorm; } /* At this point we should only admit symbols and dotproducts We expand the dollar directly and do not send it back. */ { WORD *td, *tdstop, dj; td = d->where+1; tdstop = d->where+d->where[0]; if ( tdstop[-1] != 3 || tdstop[-2] != 1 || tdstop[-3] != 1 ) goto IllDollarExp; tdstop -= 3; if ( td >= tdstop ) goto IllDollarExp; while ( td < tdstop ) { if ( *td == SYMBOL ) { for ( dj = 2; dj < td[1]; dj += 2 ) { if ( td[dj+1] == 1 ) { *ppsym++ = td[dj]; *ppsym++ = t[3]; nsym++; } else if ( td[dj+1] == -1 ) { *ppsym++ = td[dj]; *ppsym++ = -t[3]; nsym++; } else goto IllDollarExp; } } else if ( *td == DOTPRODUCT ) { for ( dj = 2; dj < td[1]; dj += 3 ) { if ( td[dj+2] == 1 ) { *ppdot++ = td[dj]; *ppdot++ = td[dj+1]; *ppdot++ = t[3]; ndot++; } else if ( td[dj+2] == -1 ) { *ppdot++ = td[dj]; *ppdot++ = td[dj+1]; *ppdot++ = -t[3]; ndot++; } else goto IllDollarExp; } } else goto IllDollarExp; td += td[1]; } regval = 2; break; } } t[0] = SUBEXPRESSION; t[4] = AM.dbufnum; if ( t[3] == 0 ) { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif break; } regval = 2; t = r; while ( t < m ) { if ( *t == DOLLAREXPRESSION ) { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif d = Dollars + t[2]; #ifdef WITHPTHREADS if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { ptype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(ptype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif if ( d->type == DOLTERMS ) { t[0] = SUBEXPRESSION; t[4] = AM.dbufnum; } } t += t[1]; } #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif goto RegEnd; } else { #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("!!!This $ variation has not been implemented yet!!!"); MUNLOCK(ErrorMessageLock); goto NormMin; } #ifdef WITHPTHREADS if ( ptype > 0 && ! DollarLocalCopy(ptype) ) { UNLOCK(d->pthreadslock); } #endif } else { pnco[nnco++] = t; /* The next statement should be safe as the value is used only by the compiler (ie the master). */ AC.lhdollarflag = 1; } break; case DELTA : t += 2; do { if ( *t < 0 ) { if ( *t == SUMMEDIND ) { if ( t[1] < -NMIN4SHIFT ) { k = -t[1]-NMIN4SHIFT; k = ExtraSymbol(k,1,nsym,ppsym,&ncoef); nsym += k; ppsym += (k * 2); } else if ( t[1] == 0 ) goto NormZero; else { if ( t[1] < 0 ) { lnum[0] = -t[1]; nnum = -1; } else { lnum[0] = t[1]; nnum = 1; } ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; ncoef = INCLENG(ncoef); } t += 2; } else if ( *t == NOINDEX && t[1] == NOINDEX ) t += 2; else if ( *t == EMPTYINDEX && t[1] == EMPTYINDEX ) { *ppdel++ = *t++; *ppdel++ = *t++; ndel += 2; } else if ( t[1] < 0 ) { *ppdot++ = *t++; *ppdot++ = *t++; *ppdot++ = 1; ndot++; } else { *ppvec++ = *t++; *ppvec++ = *t++; nvec += 2; } } else { if ( t[1] < 0 ) { *ppvec++ = t[1]; *ppvec++ = *t; t+=2; nvec += 2; } else { *ppdel++ = *t++; *ppdel++ = *t++; ndel += 2; } } } while ( t < r ); break; case FACTORIAL : /* (FACTORIAL,FUNHEAD+2,..,-SNUMBER,number) */ if ( t[FUNHEAD] == -SNUMBER && t[1] == FUNHEAD+2 && t[FUNHEAD+1] >= 0 ) { if ( Factorial(BHEAD t[FUNHEAD+1],(UWORD *)lnum,&nnum) ) goto FromNorm; MulIn: ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; ncoef = INCLENG(ncoef); } else pcom[ncom++] = t; break; case BERNOULLIFUNCTION : /* (BERNOULLIFUNCTION,FUNHEAD+2,..,-SNUMBER,number) */ if ( ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] >= 0 ) && ( t[1] == FUNHEAD+2 || ( t[1] == FUNHEAD+4 && t[FUNHEAD+2] == -SNUMBER && ABS(t[FUNHEAD+3]) == 1 ) ) ) { WORD inum, mnum; if ( Bernoulli(t[FUNHEAD+1],(UWORD *)lnum,&nnum) ) goto FromNorm; if ( nnum == 0 ) goto NormZero; inum = nnum; if ( inum < 0 ) inum = -inum; inum--; inum /= 2; mnum = inum; while ( lnum[mnum-1] == 0 ) mnum--; if ( nnum < 0 ) mnum = -mnum; ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,mnum) ) goto FromNorm; mnum = inum; while ( lnum[inum+mnum-1] == 0 ) mnum--; if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)(lnum+inum),mnum) ) goto FromNorm; ncoef = INCLENG(ncoef); if ( t[1] == FUNHEAD+4 && t[FUNHEAD+1] == 1 && t[FUNHEAD+3] == -1 ) ncoef = -ncoef; } else pcom[ncom++] = t; break; case NUMARGSFUN: /* Numerical function giving the number of arguments. */ k = 0; t += FUNHEAD; while ( t < r ) { k++; NEXTARG(t); } if ( k == 0 ) goto NormZero; *((UWORD *)lnum) = k; nnum = 1; goto MulIn; case NUMFACTORS: /* Numerical function giving the number of factors in an expression. */ t += FUNHEAD; if ( *t == -EXPRESSION ) { k = AS.OldNumFactors[t[1]]; } else if ( *t == -DOLLAREXPRESSION ) { k = Dollars[t[1]].nfactors; } else { pcom[ncom++] = t; break; } if ( k == 0 ) goto NormZero; *((UWORD *)lnum) = k; nnum = 1; goto MulIn; case NUMTERMSFUN: /* Numerical function giving the number of terms in the single argument. */ if ( t[FUNHEAD] < 0 ) { if ( t[FUNHEAD] <= -FUNCTION && t[1] == FUNHEAD+1 ) break; if ( t[FUNHEAD] > -FUNCTION && t[1] == FUNHEAD+2 ) { if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] == 0 ) goto NormZero; break; } pcom[ncom++] = t; break; } if ( t[FUNHEAD] > 0 && t[FUNHEAD] == t[1]-FUNHEAD ) { k = 0; t += FUNHEAD+ARGHEAD; while ( t < r ) { k++; t += *t; } if ( k == 0 ) goto NormZero; *((UWORD *)lnum) = k; nnum = 1; goto MulIn; } else pcom[ncom++] = t; break; case COUNTFUNCTION: if ( AN.cTerm ) { k = CountFun(AN.cTerm,t); } else { k = CountFun(term,t); } if ( k == 0 ) goto NormZero; if ( k > 0 ) { *((UWORD *)lnum) = k; nnum = 1; } else { *((UWORD *)lnum) = -k; nnum = -1; } goto MulIn; break; case MAKERATIONAL: if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+2] == -SNUMBER && t[1] == FUNHEAD+4 && t[FUNHEAD+3] > 1 ) { WORD x1[2], sgn; if ( t[FUNHEAD+1] == 0 ) goto NormZero; if ( t[FUNHEAD+1] < 0 ) { t[FUNHEAD+1] = -t[FUNHEAD+1]; sgn = -1; } else sgn = 1; if ( MakeRational(t[FUNHEAD+1],t[FUNHEAD+3],x1,x1+1) ) { static int warnflag = 1; if ( warnflag ) { MesPrint("%w Warning: fraction could not be reconstructed in MakeRational_"); warnflag = 0; } x1[0] = t[FUNHEAD+1]; x1[1] = 1; } if ( sgn < 0 ) { t[FUNHEAD+1] = -t[FUNHEAD+1]; x1[0] = -x1[0]; } if ( x1[0] < 0 ) { sgn = -1; x1[0] = -x1[0]; } else sgn = 1; ncoef = REDLENG(ncoef); if ( MulRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)x1,sgn, (UWORD *)n_coef,&ncoef) ) goto FromNorm; ncoef = INCLENG(ncoef); } else { WORD narg = 0, *tt, *ttstop, *arg1 = 0, *arg2 = 0; UWORD *x1, *x2, *xx; WORD nx1,nx2,nxx; ttstop = t + t[1]; tt = t+FUNHEAD; while ( tt < ttstop ) { narg++; if ( narg == 1 ) arg1 = tt; else arg2 = tt; NEXTARG(tt); } if ( narg != 2 ) goto defaultcase; if ( *arg2 == -SNUMBER && arg2[1] <= 1 ) goto defaultcase; else if ( *arg2 > 0 && ttstop[-1] < 0 ) goto defaultcase; x1 = NumberMalloc("Norm-MakeRational"); if ( *arg1 == -SNUMBER ) { if ( arg1[1] == 0 ) { NumberFree(x1,"Norm-MakeRational"); goto NormZero; } if ( arg1[1] < 0 ) { x1[0] = -arg1[1]; nx1 = -1; } else { x1[0] = arg1[1]; nx1 = 1; } } else if ( *arg1 > 0 ) { WORD *tc; nx1 = (ABS(arg2[-1])-1)/2; tc = arg1+ARGHEAD+1+nx1; if ( tc[0] != 1 ) { NumberFree(x1,"Norm-MakeRational"); goto defaultcase; } for ( i = 1; i < nx1; i++ ) if ( tc[i] != 0 ) { NumberFree(x1,"Norm-MakeRational"); goto defaultcase; } tc = arg1+ARGHEAD+1; for ( i = 0; i < nx1; i++ ) x1[i] = tc[i]; if ( arg2[-1] < 0 ) nx1 = -nx1; } else { NumberFree(x1,"Norm-MakeRational"); goto defaultcase; } x2 = NumberMalloc("Norm-MakeRational"); if ( *arg2 == -SNUMBER ) { if ( arg2[1] <= 1 ) { NumberFree(x2,"Norm-MakeRational"); NumberFree(x1,"Norm-MakeRational"); goto defaultcase; } else { x2[0] = arg2[1]; nx2 = 1; } } else if ( *arg2 > 0 ) { WORD *tc; nx2 = (ttstop[-1]-1)/2; tc = arg2+ARGHEAD+1+nx2; if ( tc[0] != 1 ) { NumberFree(x2,"Norm-MakeRational"); NumberFree(x1,"Norm-MakeRational"); goto defaultcase; } for ( i = 1; i < nx2; i++ ) if ( tc[i] != 0 ) { NumberFree(x2,"Norm-MakeRational"); NumberFree(x1,"Norm-MakeRational"); goto defaultcase; } tc = arg2+ARGHEAD+1; for ( i = 0; i < nx2; i++ ) x2[i] = tc[i]; } else { NumberFree(x2,"Norm-MakeRational"); NumberFree(x1,"Norm-MakeRational"); goto defaultcase; } if ( BigLong(x1,ABS(nx1),x2,nx2) >= 0 ) { UWORD *x3 = NumberMalloc("Norm-MakeRational"); UWORD *x4 = NumberMalloc("Norm-MakeRational"); WORD nx3, nx4; DivLong(x1,nx1,x2,nx2,x3,&nx3,x4,&nx4); for ( i = 0; i < ABS(nx4); i++ ) x1[i] = x4[i]; nx1 = nx4; NumberFree(x4,"Norm-MakeRational"); NumberFree(x3,"Norm-MakeRational"); } xx = (UWORD *)(TermMalloc("Norm-MakeRational")); if ( MakeLongRational(BHEAD x1,nx1,x2,nx2,xx,&nxx) ) { static int warnflag = 1; if ( warnflag ) { MesPrint("%w Warning: fraction could not be reconstructed in MakeRational_"); warnflag = 0; } ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,x1,nx1) ) goto FromNorm; } else { ncoef = REDLENG(ncoef); if ( MulRat(BHEAD (UWORD *)n_coef,ncoef,xx,nxx, (UWORD *)n_coef,&ncoef) ) goto FromNorm; } ncoef = INCLENG(ncoef); TermFree(xx,"Norm-MakeRational"); NumberFree(x2,"Norm-MakeRational"); NumberFree(x1,"Norm-MakeRational"); } break; case TERMFUNCTION: if ( t[1] == FUNHEAD && AN.cTerm ) { ANsr = r; ANsm = m; ANsc = AN.cTerm; AN.cTerm = 0; t = ANsc + 1; m = ANsc + *ANsc; ncoef = REDLENG(ncoef); nnum = REDLENG(m[-1]); m -= ABS(m[-1]); if ( MulRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)m,nnum, (UWORD *)n_coef,&ncoef) ) goto FromNorm; ncoef = INCLENG(ncoef); r = t; } break; case FIRSTBRACKET: if ( ( t[1] == FUNHEAD+2 ) && t[FUNHEAD] == -EXPRESSION ) { if ( GetFirstBracket(termout,t[FUNHEAD+1]) < 0 ) goto FromNorm; if ( *termout == 0 ) goto NormZero; if ( *termout > 4 ) { WORD *r1, *r2, *r3; while ( r < m ) *t++ = *r++; r1 = term + *term; r2 = termout + *termout; r2 -= ABS(r2[-1]); while ( r < r1 ) *r2++ = *r++; r3 = termout + 1; while ( r3 < r2 ) *t++ = *r3++; *term = t - term; if ( AT.WorkPointer > term && AT.WorkPointer < t ) AT.WorkPointer = t; goto Restart; } } break; case FIRSTTERM: case CONTENTTERM: if ( ( t[1] == FUNHEAD+2 ) && t[FUNHEAD] == -EXPRESSION ) { { EXPRESSIONS e = Expressions+t[FUNHEAD+1]; POSITION oldondisk = AS.OldOnFile[t[FUNHEAD+1]]; if ( e->replace == NEWLYDEFINEDEXPRESSION ) { AS.OldOnFile[t[FUNHEAD+1]] = e->onfile; } if ( *t == FIRSTTERM ) { if ( GetFirstTerm(termout,t[FUNHEAD+1],0) < 0 ) goto FromNorm; } else if ( *t == CONTENTTERM ) { if ( GetContent(termout,t[FUNHEAD+1]) < 0 ) goto FromNorm; } AS.OldOnFile[t[FUNHEAD+1]] = oldondisk; if ( *termout == 0 ) goto NormZero; } PasteIn:; { WORD *r1, *r2, *r3, *r4, *r5, nr1, *rterm; r2 = termout + *termout; lnum = r2 - ABS(r2[-1]); nnum = REDLENG(r2[-1]); r1 = term + *term; r3 = r1 - ABS(r1[-1]); nr1 = REDLENG(r1[-1]); if ( Mully(BHEAD (UWORD *)lnum,&nnum,(UWORD *)r3,nr1) ) goto FromNorm; nnum = INCLENG(nnum); nr1 = ABS(nnum); lnum[nr1-1] = nnum; rterm = TermMalloc("FirstTerm/ContentTerm"); r4 = rterm+1; r5 = term+1; while ( r5 < t ) *r4++ = *r5++; r5 = termout+1; while ( r5 < lnum ) *r4++ = *r5++; r5 = r; while ( r5 < r3 ) *r4++ = *r5++; r5 = lnum; NCOPY(r4,r5,nr1); *rterm = r4-rterm; nr1 = *rterm; r1 = term; r2 = rterm; NCOPY(r1,r2,nr1); TermFree(rterm,"FirstTerm/ContentTerm"); if ( AT.WorkPointer > term && AT.WorkPointer < r1 ) AT.WorkPointer = r1; goto Restart; } } else if ( ( t[1] == FUNHEAD+2 ) && t[FUNHEAD] == -DOLLAREXPRESSION ) { DOLLARS d = Dollars + t[FUNHEAD+1], newd = 0; int idol, ido; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[FUNHEAD+1] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } #endif if ( d->where && ( d->type == DOLTERMS || d->type == DOLNUMBER ) ) { newd = d; } else { if ( ( newd = DolToTerms(BHEAD t[FUNHEAD+1]) ) == 0 ) goto NormZero; } if ( newd->where[0] == 0 ) { M_free(newd,"Copy of dollar variable"); goto NormZero; } if ( *t == FIRSTTERM ) { idol = newd->where[0]; for ( ido = 0; ido < idol; ido++ ) termout[ido] = newd->where[ido]; } else if ( *t == CONTENTTERM ) { WORD *tterm; tterm = newd->where; idol = tterm[0]; for ( ido = 0; ido < idol; ido++ ) termout[ido] = tterm[ido]; tterm += *tterm; while ( *tterm ) { if ( ContentMerge(BHEAD termout,tterm) < 0 ) goto FromNorm; tterm += *tterm; } } if ( newd != d ) { if ( newd->factors ) M_free(newd->factors,"Dollar factors"); M_free(newd,"Copy of dollar variable"); newd = 0; } goto PasteIn; } break; case TERMSINEXPR: { if ( ( t[1] == FUNHEAD+2 ) && t[FUNHEAD] == -EXPRESSION ) { x = TermsInExpression(t[FUNHEAD+1]); multermnum: if ( x == 0 ) goto NormZero; if ( x < 0 ) { x = -x; if ( x > (LONG)WORDMASK ) { lnum[0] = x & WORDMASK; lnum[1] = x >> BITSINWORD; nnum = -2; } else { lnum[0] = x; nnum = -1; } } else if ( x > (LONG)WORDMASK ) { lnum[0] = x & WORDMASK; lnum[1] = x >> BITSINWORD; nnum = 2; } else { lnum[0] = x; nnum = 1; } ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; ncoef = INCLENG(ncoef); } else if ( ( t[1] == FUNHEAD+2 ) && t[FUNHEAD] == -DOLLAREXPRESSION ) { x = TermsInDollar(t[FUNHEAD+1]); goto multermnum; } else { pcom[ncom++] = t; } } break; case SIZEOFFUNCTION: { if ( ( t[1] == FUNHEAD+2 ) && t[FUNHEAD] == -EXPRESSION ) { x = SizeOfExpression(t[FUNHEAD+1]); goto multermnum; } else if ( ( t[1] == FUNHEAD+2 ) && t[FUNHEAD] == -DOLLAREXPRESSION ) { x = SizeOfDollar(t[FUNHEAD+1]); goto multermnum; } else { pcom[ncom++] = t; } } break; case MATCHFUNCTION: case PATTERNFUNCTION: break; case BINOMIAL: /* Binomial function for internal use for the moment. The routine in reken.c should be more efficient. */ if ( t[1] == FUNHEAD+4 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] >= 0 && t[FUNHEAD+2] == -SNUMBER && t[FUNHEAD+3] >= 0 && t[FUNHEAD+1] >= t[FUNHEAD+3] ) { if ( t[FUNHEAD+1] > t[FUNHEAD+3] ) { if ( GetBinom((UWORD *)lnum,&nnum, t[FUNHEAD+1],t[FUNHEAD+3]) ) goto FromNorm; if ( nnum == 0 ) goto NormZero; goto MulIn; } } else pcom[ncom++] = t; break; case SIGNFUN: /* Numerical function giving (-1)^arg */ if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER ) { if ( ( t[FUNHEAD+1] & 1 ) != 0 ) ncoef = -ncoef; } else if ( ( t[FUNHEAD] > 0 ) && ( t[1] == FUNHEAD+t[FUNHEAD] ) && ( t[FUNHEAD] == ARGHEAD+1+abs(t[t[1]-1]) ) ) { UWORD *numer1,*denom1; WORD nsize = abs(t[t[1]-1]), nnsize, isize; nnsize = (nsize-1)/2; numer1 = (UWORD *)(t + FUNHEAD+ARGHEAD+1); denom1 = numer1 + nnsize; for ( isize = 1; isize < nnsize; isize++ ) { if ( denom1[isize] ) break; } if ( ( denom1[0] != 1 ) || isize < nnsize ) { pcom[ncom++] = t; } else { if ( ( numer1[0] & 1 ) != 0 ) ncoef = -ncoef; } } else { goto doflags; /* pcom[ncom++] = t; */ } break; case SIGFUNCTION: /* Numerical function giving the sign of the numerical argument The sign of zero is 1. If there are roots of unity they are part of the sign. */ if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER ) { if ( t[FUNHEAD+1] < 0 ) ncoef = -ncoef; } else if ( ( t[1] == FUNHEAD+2 ) && ( t[FUNHEAD] == -SYMBOL ) && ( ( t[FUNHEAD+1] <= NumSymbols && t[FUNHEAD+1] > -MAXPOWER ) && ( symbols[t[FUNHEAD+1]].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) ) { k = t[FUNHEAD+1]; from = m; i = nsym; m = ppsym; if ( i > 0 ) do { m -= 2; if ( k == *m ) { m++; *m = *m + 1; *m %= symbols[k].maxpower; if ( ( symbols[k].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { if ( ( ( symbols[k].maxpower & 1 ) == 0 ) && ( *m >= symbols[k].maxpower/2 ) ) { *m -= symbols[k].maxpower/2; ncoef = -ncoef; } } if ( !*m ) { m--; while ( i < nsym ) { *m = m[2]; m++; *m = m[2]; m++; i++; } ppsym -= 2; nsym--; } goto sigDoneSymbol; } } while ( k < *m && --i > 0 ); m = ppsym; while ( i < nsym ) { m--; m[2] = *m; m--; m[2] = *m; i++; } *m++ = k; *m = 1; ppsym += 2; nsym++; sigDoneSymbol:; m = from; } else if ( ( t[FUNHEAD] > 0 ) && ( t[1] == FUNHEAD+t[FUNHEAD] ) ) { if ( t[FUNHEAD] == ARGHEAD+1+abs(t[t[1]-1]) ) { if ( t[t[1]-1] < 0 ) ncoef = -ncoef; } /* Now we should fish out the roots of unity */ else if ( ( t[FUNHEAD+ARGHEAD]+FUNHEAD+ARGHEAD == t[1] ) && ( t[FUNHEAD+ARGHEAD+1] == SYMBOL ) ) { WORD *ts = t + FUNHEAD+ARGHEAD+3; WORD its = ts[-1]-2; while ( its > 0 ) { if ( ( *ts != 0 ) && ( ( *ts > NumSymbols || *ts <= -MAXPOWER ) || ( symbols[*ts].complex & VARTYPEROOTOFUNITY ) != VARTYPEROOTOFUNITY ) ) { goto signogood; } ts += 2; its -= 2; } /* Now we have only roots of unity which should be registered in the list of symbols. */ if ( t[t[1]-1] < 0 ) ncoef = -ncoef; ts = t + FUNHEAD+ARGHEAD+3; its = ts[-1]-2; from = m; while ( its > 0 ) { i = nsym; m = ppsym; if ( i > 0 ) do { m -= 2; if ( *ts == *m ) { ts++; m++; *m += *ts; if ( ( ts[-1] <= NumSymbols && ts[-1] > -MAXPOWER ) && ( symbols[ts[-1]].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) { *m %= symbols[ts[-1]].maxpower; if ( *m < 0 ) *m += symbols[ts[-1]].maxpower; if ( ( symbols[ts[-1]].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { if ( ( ( symbols[ts[-1]].maxpower & 1 ) == 0 ) && ( *m >= symbols[ts[-1]].maxpower/2 ) ) { *m -= symbols[ts[-1]].maxpower/2; ncoef = -ncoef; } } } if ( !*m ) { m--; while ( i < nsym ) { *m = m[2]; m++; *m = m[2]; m++; i++; } ppsym -= 2; nsym--; } ts++; its -= 2; goto sigNextSymbol; } } while ( *ts < *m && --i > 0 ); m = ppsym; while ( i < nsym ) { m--; m[2] = *m; m--; m[2] = *m; i++; } *m++ = *ts++; *m = *ts++; ppsym += 2; nsym++; its -= 2; sigNextSymbol:; } m = from; } else { signogood: pcom[ncom++] = t; } } else pcom[ncom++] = t; break; case ABSFUNCTION: /* Numerical function giving the absolute value of the numerical argument. Or roots of unity. */ if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER ) { k = t[FUNHEAD+1]; if ( k < 0 ) k = -k; if ( k == 0 ) goto NormZero; *((UWORD *)lnum) = k; nnum = 1; goto MulIn; } else if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SYMBOL ) { k = t[FUNHEAD+1]; if ( ( k > NumSymbols || k <= -MAXPOWER ) || ( symbols[k].complex & VARTYPEROOTOFUNITY ) != VARTYPEROOTOFUNITY ) goto absnogood; } else if ( ( t[FUNHEAD] > 0 ) && ( t[1] == FUNHEAD+t[FUNHEAD] ) && ( t[1] == FUNHEAD+ARGHEAD+t[FUNHEAD+ARGHEAD] ) ) { if ( t[FUNHEAD] == ARGHEAD+1+abs(t[t[1]-1]) ) { WORD *ts; absnosymbols: ts = t + t[1] -1; ncoef = REDLENG(ncoef); nnum = REDLENG(*ts); if ( nnum < 0 ) nnum = -nnum; if ( MulRat(BHEAD (UWORD *)n_coef,ncoef, (UWORD *)(ts-ABS(*ts)+1),nnum, (UWORD *)n_coef,&ncoef) ) goto FromNorm; ncoef = INCLENG(ncoef); } /* Now get rid of the roots of unity. This includes i_ */ else if ( t[FUNHEAD+ARGHEAD+1] == SYMBOL ) { WORD *ts = t+FUNHEAD+ARGHEAD+1; WORD its = ts[1] - 2; ts += 2; while ( its > 0 ) { if ( *ts == 0 ) { } else if ( ( *ts > NumSymbols || *ts <= -MAXPOWER ) || ( symbols[*ts].complex & VARTYPEROOTOFUNITY ) != VARTYPEROOTOFUNITY ) goto absnogood; its -= 2; ts += 2; } goto absnosymbols; } else { absnogood: pcom[ncom++] = t; } } else pcom[ncom++] = t; break; case MODFUNCTION: case MOD2FUNCTION: /* Mod function. Does work if two arguments and the second argument is a positive short number */ if ( t[1] == FUNHEAD+4 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+2] == -SNUMBER && t[FUNHEAD+3] > 1 ) { WORD tmod; tmod = (t[FUNHEAD+1]%t[FUNHEAD+3]); if ( tmod < 0 ) tmod += t[FUNHEAD+3]; if ( *t == MOD2FUNCTION && tmod > t[FUNHEAD+3]/2 ) tmod -= t[FUNHEAD+3]; if ( tmod < 0 ) { *((UWORD *)lnum) = -tmod; nnum = -1; } else if ( tmod > 0 ) { *((UWORD *)lnum) = tmod; nnum = 1; } else goto NormZero; goto MulIn; } else if ( t[1] > t[FUNHEAD+2] && t[FUNHEAD] > 0 && t[FUNHEAD+t[FUNHEAD]] == -SNUMBER && t[FUNHEAD+t[FUNHEAD]+1] > 1 && t[1] == FUNHEAD+2+t[FUNHEAD] ) { WORD *ttt = t+FUNHEAD, iii; iii = ttt[*ttt-1]; if ( *ttt == ttt[ARGHEAD]+ARGHEAD && ttt[ARGHEAD] == ABS(iii)+1 ) { WORD ncmod = 1; WORD cmod = ttt[*ttt+1]; iii = REDLENG(iii); if ( *t == MODFUNCTION ) { if ( TakeModulus((UWORD *)(ttt+ARGHEAD+1) ,&iii,(UWORD *)(&cmod),ncmod,UNPACK|NOINVERSES) ) goto FromNorm; } else { if ( TakeModulus((UWORD *)(ttt+ARGHEAD+1) ,&iii,(UWORD *)(&cmod),ncmod,UNPACK|POSNEG|NOINVERSES) ) goto FromNorm; } if ( *t == MOD2FUNCTION && ttt[ARGHEAD+1] > cmod/2 && iii > 0 ) { ttt[ARGHEAD+1] -= cmod; } if ( ttt[ARGHEAD+1] < 0 ) { *((UWORD *)lnum) = -ttt[ARGHEAD+1]; nnum = -1; } else if ( ttt[ARGHEAD+1] > 0 ) { *((UWORD *)lnum) = ttt[ARGHEAD+1]; nnum = 1; } else goto NormZero; goto MulIn; } } else if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER ) { *((UWORD *)lnum) = t[FUNHEAD+1]; if ( *lnum == 0 ) goto NormZero; nnum = 1; goto MulIn; } else if ( ( ( t[FUNHEAD] < 0 ) && ( t[FUNHEAD] == -SNUMBER ) && ( t[1] >= ( FUNHEAD+6+ARGHEAD ) ) && ( t[FUNHEAD+2] >= 4+ARGHEAD ) && ( t[t[1]-1] == t[FUNHEAD+2+ARGHEAD]-1 ) ) || ( ( t[FUNHEAD] > 0 ) && ( t[FUNHEAD]-ARGHEAD-1 == ABS(t[FUNHEAD+t[FUNHEAD]-1]) ) && ( t[FUNHEAD+t[FUNHEAD]]-ARGHEAD-1 == t[t[1]-1] ) ) ) { /* Check that the last (long) number is integer */ WORD *ttt = t + t[1], iii, iii1; UWORD coefbuf[2], *coef2, ncoef2; iii = (ttt[-1]-1)/2; ttt -= iii; if ( ttt[-1] != 1 ) { exitfromhere: pcom[ncom++] = t; break; } iii--; for ( iii1 = 0; iii1 < iii; iii1++ ) { if ( ttt[iii1] != 0 ) goto exitfromhere; } /* Now we have a hit! The first argument will be put in lnum. It will be a rational. The second argument will be a long integer in coef2. */ ttt = t + FUNHEAD; if ( *ttt < 0 ) { if ( ttt[1] < 0 ) { nnum = -1; lnum[0] = -ttt[1]; lnum[1] = 1; } else { nnum = 1; lnum[0] = ttt[1]; lnum[1] = 1; } } else { nnum = ABS(ttt[ttt[0]-1] - 1); for ( iii = 0; iii < nnum; iii++ ) { lnum[iii] = ttt[ARGHEAD+1+iii]; } nnum = nnum/2; if ( ttt[ttt[0]-1] < 0 ) nnum = -nnum; } NEXTARG(ttt); if ( *ttt < 0 ) { coef2 = coefbuf; ncoef2 = 3; *coef2 = (UWORD)(ttt[1]); coef2[1] = 1; } else { coef2 = (UWORD *)(ttt+ARGHEAD+1); ncoef2 = (ttt[ttt[0]-1]-1)/2; } if ( TakeModulus((UWORD *)lnum,&nnum,(UWORD *)coef2,ncoef2, UNPACK|NOINVERSES|FROMFUNCTION) ) { goto FromNorm; } if ( *t == MOD2FUNCTION && nnum > 0 ) { UWORD *coef3 = NumberMalloc("Mod2Function"), two = 2; WORD ncoef3; if ( MulLong((UWORD *)lnum,nnum,&two,1,coef3,&ncoef3) ) goto FromNorm; if ( BigLong(coef3,ncoef3,(UWORD *)coef2,ncoef2) > 0 ) { nnum = -nnum; AddLong((UWORD *)lnum,nnum,(UWORD *)coef2,ncoef2 ,(UWORD *)lnum,&nnum); nnum = -nnum; } NumberFree(coef3,"Mod2Function"); } /* Do we have to pack? No, because the answer is not a fraction */ ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; ncoef = INCLENG(ncoef); } else pcom[ncom++] = t; break; case EXTEUCLIDEAN: { WORD argcount = 0, *tc, *ts, xc, xs, *tcc; UWORD *Num1, *Num2, *Num3, *Num4; WORD size1, size2, size3, size4, space; tc = t+FUNHEAD; ts = t + t[1]; while ( argcount < 3 && tc < ts ) { NEXTARG(tc); argcount++; } if ( argcount != 2 ) goto defaultcase; if ( t[FUNHEAD] == -SNUMBER ) { if ( t[FUNHEAD+1] <= 1 ) goto defaultcase; if ( t[FUNHEAD+2] == -SNUMBER ) { if ( t[FUNHEAD+3] <= 1 ) goto defaultcase; Num2 = NumberMalloc("modinverses"); *Num2 = t[FUNHEAD+3]; size2 = 1; } else { if ( ts[-1] < 0 ) goto defaultcase; if ( ts[-1] != t[FUNHEAD+2]-ARGHEAD-1 ) goto defaultcase; xs = (ts[-1]-1)/2; tcc = ts-xs-1; if ( *tcc != 1 ) goto defaultcase; for ( i = 1; i < xs; i++ ) { if ( tcc[i] != 0 ) goto defaultcase; } Num2 = NumberMalloc("modinverses"); size2 = xs; for ( i = 0; i < xs; i++ ) Num2[i] = t[FUNHEAD+ARGHEAD+3+i]; } Num1 = NumberMalloc("modinverses"); *Num1 = t[FUNHEAD+1]; size1 = 1; } else { tc = t + FUNHEAD + t[FUNHEAD]; if ( tc[-1] < 0 ) goto defaultcase; if ( tc[-1] != t[FUNHEAD]-ARGHEAD-1 ) goto defaultcase; xc = (tc[-1]-1)/2; tcc = tc-xc-1; if ( *tcc != 1 ) goto defaultcase; for ( i = 1; i < xc; i++ ) { if ( tcc[i] != 0 ) goto defaultcase; } if ( *tc == -SNUMBER ) { if ( tc[1] <= 1 ) goto defaultcase; Num2 = NumberMalloc("modinverses"); *Num2 = tc[1]; size2 = 1; } else { if ( ts[-1] < 0 ) goto defaultcase; if ( ts[-1] != t[FUNHEAD+2]-ARGHEAD-1 ) goto defaultcase; xs = (ts[-1]-1)/2; tcc = ts-xs-1; if ( *tcc != 1 ) goto defaultcase; for ( i = 1; i < xs; i++ ) { if ( tcc[i] != 0 ) goto defaultcase; } Num2 = NumberMalloc("modinverses"); size2 = xs; for ( i = 0; i < xs; i++ ) Num2[i] = tc[ARGHEAD+1+i]; } Num1 = NumberMalloc("modinverses"); size1 = xc; for ( i = 0; i < xc; i++ ) Num1[i] = t[FUNHEAD+ARGHEAD+1+i]; } Num3 = NumberMalloc("modinverses"); Num4 = NumberMalloc("modinverses"); GetLongModInverses(BHEAD Num1,size1,Num2,size2 ,Num3,&size3,Num4,&size4); /* Now we have to compose the answer. This needs more space and hence we have to put this inside the term. Compute first how much extra space we need. Then move the trailing part of the term upwards. Do not forget relevant pointers!!! (r, m, termout, AT.WorkPointer) */ space = 0; if ( ( size3 == 1 || size3 == -1 ) && (*Num3&TOPBITONLY) == 0 ) space += 2; else space += ARGHEAD + 2*ABS(size3) + 2; if ( ( size4 == 1 || size4 == -1 ) && (*Num4&TOPBITONLY) == 0 ) space += 2; else space += ARGHEAD + 2*ABS(size4) + 2; tt = term + *term; u = tt + space; while ( tt >= ts ) *--u = *--tt; m += space; r += space; *term += space; t[1] += space; if ( ( size3 == 1 || size3 == -1 ) && (*Num3&TOPBITONLY) == 0 ) { *ts++ = -SNUMBER; *ts = (WORD)(*Num3); if ( size3 < 0 ) *ts = -*ts; ts++; } else { *ts++ = 2*ABS(size3)+ARGHEAD+2; *ts++ = 0; FILLARG(ts) *ts++ = 2*ABS(size3)+1; for ( i = 0; i < ABS(size3); i++ ) *ts++ = Num3[i]; *ts++ = 1; for ( i = 1; i < ABS(size3); i++ ) *ts++ = 0; if ( size3 < 0 ) *ts++ = 2*size3-1; else *ts++ = 2*size3+1; } if ( ( size4 == 1 || size4 == -1 ) && (*Num4&TOPBITONLY) == 0 ) { *ts++ = -SNUMBER; *ts = *Num4; if ( size4 < 0 ) *ts = -*ts; ts++; } else { *ts++ = 2*ABS(size4)+ARGHEAD+2; *ts++ = 0; FILLARG(ts) *ts++ = 2*ABS(size4)+2; for ( i = 0; i < ABS(size4); i++ ) *ts++ = Num4[i]; *ts++ = 1; for ( i = 1; i < ABS(size4); i++ ) *ts++ = 0; if ( size4 < 0 ) *ts++ = 2*size4-1; else *ts++ = 2*size4+1; } NumberFree(Num4,"modinverses"); NumberFree(Num3,"modinverses"); NumberFree(Num1,"modinverses"); NumberFree(Num2,"modinverses"); t[2] = 0; /* mark function as clean. */ goto Restart; } break; case GCDFUNCTION: #ifdef EVALUATEGCD #ifdef NEWGCDFUNCTION { /* Has two integer arguments Four cases: S,S, S,L, L,S, L,L */ WORD *num1, *num2, size1, size2, stor1, stor2, *ttt, ti; if ( t[1] == FUNHEAD+4 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+2] == -SNUMBER && t[FUNHEAD+1] != 0 && t[FUNHEAD+3] != 0 ) { /* Short,Short */ stor1 = t[FUNHEAD+1]; stor2 = t[FUNHEAD+3]; if ( stor1 < 0 ) stor1 = -stor1; if ( stor2 < 0 ) stor2 = -stor2; num1 = &stor1; num2 = &stor2; size1 = size2 = 1; goto gcdcalc; } else if ( t[1] > FUNHEAD+4 ) { if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] != 0 && t[FUNHEAD+2] == t[1]-FUNHEAD-2 && ABS(t[t[1]-1]) == t[FUNHEAD+2]-1-ARGHEAD ) { /* Short,Long */ num2 = t + t[1]; size2 = ABS(num2[-1]); ttt = num2-1; num2 -= size2; size2 = (size2-1)/2; ti = size2; while ( ti > 1 && ttt[-1] == 0 ) { ttt--; ti--; } if ( ti == 1 && ttt[-1] == 1 ) { stor1 = t[FUNHEAD+1]; if ( stor1 < 0 ) stor1 = -stor1; num1 = &stor1; size1 = 1; goto gcdcalc; } else pcom[ncom++] = t; } else if ( t[FUNHEAD] > 0 && t[FUNHEAD]-1-ARGHEAD == ABS(t[t[FUNHEAD]+FUNHEAD-1]) ) { num1 = t + FUNHEAD + t[FUNHEAD]; size1 = ABS(num1[-1]); ttt = num1-1; num1 -= size1; size1 = (size1-1)/2; ti = size1; while ( ti > 1 && ttt[-1] == 0 ) { ttt--; ti--; } if ( ti == 1 && ttt[-1] == 1 ) { if ( t[1]-FUNHEAD == t[FUNHEAD]+2 && t[t[1]-2] == -SNUMBER && t[t[1]-1] != 0 ) { /* Long,Short */ stor2 = t[t[1]-1]; if ( stor2 < 0 ) stor2 = -stor2; num2 = &stor2; size2 = 1; goto gcdcalc; } else if ( t[1]-FUNHEAD == t[FUNHEAD]+t[FUNHEAD+t[FUNHEAD]] && ABS(t[t[1]-1]) == t[FUNHEAD+t[FUNHEAD]] - ARGHEAD-1 ) { num2 = t + t[1]; size2 = ABS(num2[-1]); ttt = num2-1; num2 -= size2; size2 = (size2-1)/2; ti = size2; while ( ti > 1 && ttt[-1] == 0 ) { ttt--; ti--; } if ( ti == 1 && ttt[-1] == 1 ) { gcdcalc: if ( GcdLong(BHEAD (UWORD *)num1,size1,(UWORD *)num2,size2 ,(UWORD *)lnum,&nnum) ) goto FromNorm; goto MulIn; } else pcom[ncom++] = t; } else pcom[ncom++] = t; } else pcom[ncom++] = t; } else pcom[ncom++] = t; } else pcom[ncom++] = t; } #else { WORD *gcd = AT.WorkPointer; if ( ( gcd = EvaluateGcd(BHEAD t) ) == 0 ) goto FromNorm; if ( *gcd == 4 && gcd[1] == 1 && gcd[2] == 1 && gcd[4] == 0 ) { AT.WorkPointer = gcd; } else if ( gcd[*gcd] == 0 ) { WORD *t1, iii, change, *num, *den, numsize, densize; if ( gcd[*gcd-1] < *gcd-1 ) { t1 = gcd+1; for ( iii = 2; iii < t1[1]; iii += 2 ) { change = ExtraSymbol(t1[iii],t1[iii+1],nsym,ppsym,&ncoef); nsym += change; ppsym += change * 2; } } t1 = gcd + *gcd; iii = t1[-1]; num = t1-iii; numsize = (iii-1)/2; den = num + numsize; densize = numsize; while ( numsize > 1 && num[numsize-1] == 0 ) numsize--; while ( densize > 1 && den[densize-1] == 0 ) densize--; if ( numsize > 1 || num[0] != 1 ) { ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)num,numsize) ) goto FromNorm; ncoef = INCLENG(ncoef); } if ( densize > 1 || den[0] != 1 ) { ncoef = REDLENG(ncoef); if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)den,densize) ) goto FromNorm; ncoef = INCLENG(ncoef); } AT.WorkPointer = gcd; } else { /* a whole expression */ /* Action: Put the expression in a compiler buffer. Insert a SUBEXPRESSION subterm Set the return value of the routine such that in Generator the term gets sent again to TestSub. 1: put in C (ebufnum) 2: after that the WorkSpace is free again. 3: insert the SUBEXPRESSION 4: copy the top part of the term down */ LONG size = AT.WorkPointer - gcd; ss = AddRHS(AT.ebufnum,1); while ( (ss + size + 10) > C->Top ) ss = DoubleCbuffer(AT.ebufnum,ss,13); tt = gcd; NCOPY(ss,tt,size); C->rhs[C->numrhs+1] = ss; C->Pointer = ss; t[0] = SUBEXPRESSION; t[1] = SUBEXPSIZE; t[2] = C->numrhs; t[3] = 1; t[4] = AT.ebufnum; t += 5; tt = term + *term; while ( r < tt ) *t++ = *r++; *term = t - term; regval = 1; goto RegEnd; } } #endif #else MesPrint(" Unexpected call to EvaluateGCD"); Terminate(-1); #endif break; case MINFUNCTION: case MAXFUNCTION: if ( t[1] == FUNHEAD ) break; { WORD *ttt = t + FUNHEAD; WORD *tttstop = t + t[1]; WORD tterm[4], iii; while ( ttt < tttstop ) { if ( *ttt > 0 ) { if ( ttt[ARGHEAD]-1 > ABS(ttt[*ttt-1]) ) goto nospec; ttt += *ttt; } else { if ( *ttt != -SNUMBER ) goto nospec; ttt += 2; } } /* Function has only numerical arguments Pick up the first argument. */ ttt = t + FUNHEAD; if ( *ttt > 0 ) { loadnew1: for ( iii = 0; iii < ttt[ARGHEAD]; iii++ ) n_llnum[iii] = ttt[ARGHEAD+iii]; ttt += *ttt; } else { loadnew2: if ( ttt[1] == 0 ) { n_llnum[0] = n_llnum[1] = n_llnum[2] = n_llnum[3] = 0; } else { n_llnum[0] = 4; if ( ttt[1] > 0 ) { n_llnum[1] = ttt[1]; n_llnum[3] = 3; } else { n_llnum[1] = -ttt[1]; n_llnum[3] = -3; } n_llnum[2] = 1; } ttt += 2; } /* Now loop over the other arguments */ while ( ttt < tttstop ) { if ( *ttt > 0 ) { if ( n_llnum[0] == 0 ) { if ( ( *t == MINFUNCTION && ttt[*ttt-1] < 0 ) || ( *t == MAXFUNCTION && ttt[*ttt-1] > 0 ) ) goto loadnew1; } else { ttt += ARGHEAD; iii = CompCoef(n_llnum,ttt); if ( ( iii > 0 && *t == MINFUNCTION ) || ( iii < 0 && *t == MAXFUNCTION ) ) { for ( iii = 0; iii < ttt[0]; iii++ ) n_llnum[iii] = ttt[iii]; } } ttt += *ttt; } else { if ( n_llnum[0] == 0 ) { if ( ( *t == MINFUNCTION && ttt[1] < 0 ) || ( *t == MAXFUNCTION && ttt[1] > 0 ) ) goto loadnew2; } else if ( ttt[1] == 0 ) { if ( ( *t == MINFUNCTION && n_llnum[*n_llnum-1] > 0 ) || ( *t == MAXFUNCTION && n_llnum[*n_llnum-1] < 0 ) ) { n_llnum[0] = 0; } } else { tterm[0] = 4; tterm[2] = 1; if ( ttt[1] < 0 ) { tterm[1] = -ttt[1]; tterm[3] = -3; } else { tterm[1] = ttt[1]; tterm[3] = 3; } iii = CompCoef(n_llnum,tterm); if ( ( iii > 0 && *t == MINFUNCTION ) || ( iii < 0 && *t == MAXFUNCTION ) ) { for ( iii = 0; iii < 4; iii++ ) n_llnum[iii] = tterm[iii]; } } ttt += 2; } } if ( n_llnum[0] == 0 ) goto NormZero; ncoef = REDLENG(ncoef); nnum = REDLENG(n_llnum[*n_llnum-1]); if ( MulRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)lnum,nnum, (UWORD *)n_coef,&ncoef) ) goto FromNorm; ncoef = INCLENG(ncoef); } break; case INVERSEFACTORIAL: if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] >= 0 ) { if ( Factorial(BHEAD t[FUNHEAD+1],(UWORD *)lnum,&nnum) ) goto FromNorm; ncoef = REDLENG(ncoef); if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; ncoef = INCLENG(ncoef); } else { nospec: pcom[ncom++] = t; } break; case MAXPOWEROF: if ( ( t[FUNHEAD] == -SYMBOL ) && ( t[FUNHEAD+1] > 0 ) && ( t[1] == FUNHEAD+2 ) ) { *((UWORD *)lnum) = symbols[t[FUNHEAD+1]].maxpower; nnum = 1; goto MulIn; } else { pcom[ncom++] = t; } break; case MINPOWEROF: if ( ( t[FUNHEAD] == -SYMBOL ) && ( t[FUNHEAD] > 0 ) && ( t[1] == FUNHEAD+2 ) ) { *((UWORD *)lnum) = symbols[t[FUNHEAD+1]].minpower; nnum = 1; goto MulIn; } else { pcom[ncom++] = t; } break; case PRIMENUMBER : if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] > 0 ) { UWORD xp = (UWORD)(NextPrime(BHEAD t[FUNHEAD+1])); ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,&xp,1) ) goto FromNorm; ncoef = INCLENG(ncoef); } else goto defaultcase; break; case MOEBIUS: /* Numerical function giving -1,0,1 or no evaluation */ if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] > 0 ) { WORD val = Moebius(BHEAD t[FUNHEAD+1]); if ( val == 0 ) goto NormZero; if ( val < 0 ) ncoef = -ncoef; } else { pcom[ncom++] = t; } break; case LNUMBER : ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)(t+3),t[2]) ) goto FromNorm; ncoef = INCLENG(ncoef); break; case SNUMBER : if ( t[2] < 0 ) { t[2] = -t[2]; if ( t[3] & 1 ) ncoef = -ncoef; } else if ( t[2] == 0 ) { if ( t[3] < 0 ) goto NormInf; goto NormZero; } lnum[0] = t[2]; nnum = 1; if ( t[3] && RaisPow(BHEAD (UWORD *)lnum,&nnum,(UWORD)(ABS(t[3]))) ) goto FromNorm; ncoef = REDLENG(ncoef); if ( t[3] < 0 ) { if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; } else if ( t[3] > 0 ) { if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; } ncoef = INCLENG(ncoef); break; case GAMMA : case GAMMAI : case GAMMAFIVE : case GAMMASIX : case GAMMASEVEN : if ( t[1] == FUNHEAD ) { MLOCK(ErrorMessageLock); MesPrint("Gamma matrix without spin line encountered."); MUNLOCK(ErrorMessageLock); goto NormMin; } pnco[nnco++] = t; t += FUNHEAD+1; goto ScanCont; case LEVICIVITA : peps[neps++] = t; if ( ( t[2] & DIRTYFLAG ) == DIRTYFLAG ) { t[2] &= ~DIRTYFLAG; t[2] |= DIRTYSYMFLAG; } t += FUNHEAD; ScanCont: while ( t < r ) { if ( *t >= AM.OffsetIndex && ( *t >= AM.DumInd || ( *t < AM.WilInd && indices[*t-AM.OffsetIndex].dimension ) ) ) pcon[ncon++] = t; t++; } break; case EXPONENT : { WORD *rr; k = 1; rr = t + FUNHEAD; if ( *rr == ARGHEAD || ( *rr == -SNUMBER && rr[1] == 0 ) ) k = 0; if ( *rr == -SNUMBER && rr[1] == 1 ) break; if ( *rr <= -FUNCTION ) k = *rr; NEXTARG(rr) if ( *rr == ARGHEAD || ( *rr == -SNUMBER && rr[1] == 0 ) ) { if ( k == 0 ) goto NormZZ; break; } if ( *rr == -SNUMBER && rr[1] > 0 && rr[1] < MAXPOWER && k < 0 ) { k = -k; if ( functions[k-FUNCTION].commute ) { for ( i = 0; i < rr[1]; i++ ) pnco[nnco++] = rr-1; } else { for ( i = 0; i < rr[1]; i++ ) pcom[ncom++] = rr-1; } break; } if ( k == 0 ) goto NormZero; if ( t[FUNHEAD] == -SYMBOL && *rr == -SNUMBER && t[1] == FUNHEAD+4 ) { if ( rr[1] < MAXPOWER ) { t[FUNHEAD+2] = t[FUNHEAD+1]; t += FUNHEAD+2; from = m; goto NextSymbol; } } /* if ( ( t[FUNHEAD] > 0 && t[FUNHEAD+1] != 0 ) || ( *rr > 0 && rr[1] != 0 ) ) {} else */ t[2] &= ~DIRTYSYMFLAG; pnco[nnco++] = t; } break; case DENOMINATOR : t[2] &= ~DIRTYSYMFLAG; pden[nden++] = t; pnco[nnco++] = t; break; case INDEX : t += 2; do { if ( *t == 0 || *t == AM.vectorzero ) goto NormZero; if ( *t > 0 && *t < AM.OffsetIndex ) { lnum[0] = *t++; nnum = 1; ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm; ncoef = INCLENG(ncoef); } else if ( *t == NOINDEX ) t++; else pind[nind++] = *t++; } while ( t < r ); break; case SUBEXPRESSION : if ( t[3] == 0 ) break; case EXPRESSION : goto RegEnd; case ROOTFUNCTION : /* Tries to take the n-th root inside the rationals If this is not possible, it clears all flags and hence tries no more. Notation: root_(power(=integer),(rational)number) */ { WORD nc; if ( t[2] == 0 ) goto defaultcase; if ( t[FUNHEAD] != -SNUMBER || t[FUNHEAD+1] < 0 ) goto defaultcase; if ( t[FUNHEAD+2] == -SNUMBER ) { if ( t[FUNHEAD+1] == 0 && t[FUNHEAD+3] == 0 ) goto NormZZ; if ( t[FUNHEAD+1] == 0 ) break; if ( t[FUNHEAD+3] < 0 ) { AT.WorkPointer[0] = -t[FUNHEAD+3]; nc = -1; } else { AT.WorkPointer[0] = t[FUNHEAD+3]; nc = 1; } AT.WorkPointer[1] = 1; } else if ( t[FUNHEAD+2] == t[1]-FUNHEAD-2 && t[FUNHEAD+2] == t[FUNHEAD+2+ARGHEAD]+ARGHEAD && ABS(t[t[1]-1]) == t[FUNHEAD+2+ARGHEAD] - 1 ) { WORD *r1, *r2; if ( t[FUNHEAD+1] == 0 ) break; i = t[t[1]-1]; r1 = t + FUNHEAD+ARGHEAD+3; nc = REDLENG(i); i = ABS(i) - 1; r2 = AT.WorkPointer; while ( --i >= 0 ) *r2++ = *r1++; } else goto defaultcase; if ( TakeRatRoot((UWORD *)AT.WorkPointer,&nc,t[FUNHEAD+1]) ) { t[2] = 0; goto defaultcase; } ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)AT.WorkPointer,nc) ) goto FromNorm; if ( nc < 0 ) nc = -nc; if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)(AT.WorkPointer+nc),nc) ) goto FromNorm; ncoef = INCLENG(ncoef); } break; case RANDOMFUNCTION : { WORD nnc, nc, nca, nr; UWORD xx; /* Needs one positive integer argument. returns (wranf()%argument)+1. We may call wranf several times to paste UWORDS together when we need long numbers. We make little errors when taking the % operator (not 100% uniform). We correct for that by redoing the calculation in the (unlikely) case that we are in leftover area */ if ( t[1] == FUNHEAD ) goto defaultcase; if ( t[1] == FUNHEAD+2 && t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] > 0 ) { if ( t[FUNHEAD+1] == 1 ) break; redoshort: ((UWORD *)AT.WorkPointer)[0] = wranf(BHEAD0); ((UWORD *)AT.WorkPointer)[1] = wranf(BHEAD0); nr = 2; if ( ((UWORD *)AT.WorkPointer)[1] == 0 ) { nr = 1; if ( ((UWORD *)AT.WorkPointer)[0] == 0 ) { nr = 0; } } xx = (UWORD)(t[FUNHEAD+1]); if ( nr ) { DivLong((UWORD *)AT.WorkPointer,nr ,&xx,1 ,((UWORD *)AT.WorkPointer)+4,&nnc ,((UWORD *)AT.WorkPointer)+2,&nc); ((UWORD *)AT.WorkPointer)[4] = 0; ((UWORD *)AT.WorkPointer)[5] = 0; ((UWORD *)AT.WorkPointer)[6] = 1; DivLong((UWORD *)AT.WorkPointer+4,3 ,&xx,1 ,((UWORD *)AT.WorkPointer)+9,&nnc ,((UWORD *)AT.WorkPointer)+7,&nca); AddLong((UWORD *)AT.WorkPointer+4,3 ,((UWORD *)AT.WorkPointer)+7,-nca ,((UWORD *)AT.WorkPointer)+9,&nnc); if ( BigLong((UWORD *)AT.WorkPointer,nr ,((UWORD *)AT.WorkPointer)+9,nnc) >= 0 ) goto redoshort; } else nc = 0; if ( nc == 0 ) { AT.WorkPointer[2] = (WORD)xx; nc = 1; } ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,((UWORD *)(AT.WorkPointer))+2,nc) ) goto FromNorm; ncoef = INCLENG(ncoef); } else if ( t[FUNHEAD] > 0 && t[1] == t[FUNHEAD]+FUNHEAD && ABS(t[t[1]-1]) == t[FUNHEAD]-1-ARGHEAD && t[t[1]-1] > 0 ) { WORD nna, nnb, nni, nnb2, nnb2a; UWORD *nnt; nna = t[t[1]-1]; nnb2 = nna-1; nnb = nnb2/2; nnt = (UWORD *)(t+t[1]-1-nnb); /* start of denominator */ if ( *nnt != 1 ) goto defaultcase; for ( nni = 1; nni < nnb; nni++ ) { if ( nnt[nni] != 0 ) goto defaultcase; } nnt = (UWORD *)(t + FUNHEAD + ARGHEAD + 1); for ( nni = 0; nni < nnb2; nni++ ) { ((UWORD *)AT.WorkPointer)[nni] = wranf(BHEAD0); } nnb2a = nnb2; while ( nnb2a > 0 && ((UWORD *)AT.WorkPointer)[nnb2a-1] == 0 ) nnb2a--; if ( nnb2a > 0 ) { DivLong((UWORD *)AT.WorkPointer,nnb2a ,nnt,nnb ,((UWORD *)AT.WorkPointer)+2*nnb2,&nnc ,((UWORD *)AT.WorkPointer)+nnb2,&nc); for ( nni = 0; nni < nnb2; nni++ ) { ((UWORD *)AT.WorkPointer)[nni+2*nnb2] = 0; } ((UWORD *)AT.WorkPointer)[3*nnb2] = 1; DivLong((UWORD *)AT.WorkPointer+2*nnb2,nnb2+1 ,nnt,nnb ,((UWORD *)AT.WorkPointer)+4*nnb2+1,&nnc ,((UWORD *)AT.WorkPointer)+3*nnb2+1,&nca); AddLong((UWORD *)AT.WorkPointer+2*nnb2,nnb2+1 ,((UWORD *)AT.WorkPointer)+3*nnb2+1,-nca ,((UWORD *)AT.WorkPointer)+4*nnb2+1,&nnc); if ( BigLong((UWORD *)AT.WorkPointer,nnb2a ,((UWORD *)AT.WorkPointer)+4*nnb2+1,nnc) >= 0 ) goto redoshort; } else nc = 0; if ( nc == 0 ) { for ( nni = 0; nni < nnb; nni++ ) { ((UWORD *)AT.WorkPointer)[nnb2+nni] = nnt[nni]; } nc = nnb; } ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,((UWORD *)(AT.WorkPointer))+nnb2,nc) ) goto FromNorm; ncoef = INCLENG(ncoef); } else goto defaultcase; } break; case RANPERM : if ( *t == RANPERM && t[1] > FUNHEAD && t[FUNHEAD] <= -FUNCTION ) { WORD **pwork; WORD *mm, *ww, *ow = AT.WorkPointer; WORD *Array, *targ, *argstop, narg = 0, itot; int ie; argstop = t+t[1]; targ = t+FUNHEAD+1; while ( targ < argstop ) { narg++; NEXTARG(targ); } WantAddPointers(narg); pwork = AT.pWorkSpace + AT.pWorkPointer; targ = t+FUNHEAD+1; narg = 0; while ( targ < argstop ) { pwork[narg++] = targ; NEXTARG(targ); } /* Make a random permutation of the numbers 0,...,narg-1 The following code works also for narg == 0 and narg == 1 */ ow = AT.WorkPointer; Array = AT.WorkPointer; AT.WorkPointer += narg; for ( i = 0; i < narg; i++ ) Array[i] = i; for ( i = 2; i <= narg; i++ ) { itot = (WORD)(iranf(BHEAD i)); for ( j = 0; j < itot; j++ ) CYCLE1(WORD,Array,i) } mm = AT.WorkPointer; *mm++ = -t[FUNHEAD]; *mm++ = t[1] - 1; for ( ie = 2; ie < FUNHEAD; ie++ ) *mm++ = t[ie]; for ( i = 0; i < narg; i++ ) { ww = pwork[Array[i]]; CopyArg(mm,ww); } mm = AT.WorkPointer; t++; ww = t; i = mm[1]; NCOPY(ww,mm,i) AT.WorkPointer = ow; goto TryAgain; } pnco[nnco++] = t; break; case PUTFIRST : /* First argument should be a function, second a number */ if ( ( t[2] & DIRTYFLAG ) != 0 && t[FUNHEAD] <= -FUNCTION && t[FUNHEAD+1] == -SNUMBER && t[FUNHEAD+2] > 0 ) { WORD *rr = t+t[1], *mm = t+FUNHEAD+3, *tt, *tt1, *tt2, num = 0; /* now count the arguments. If not enough: no action. */ while ( mm < rr ) { num++; NEXTARG(mm); } if ( num < t[FUNHEAD+2] ) { pnco[nnco++] = t; break; } /* Replace "putfirst_" with the resulting function code. mm goes to arg start. */ *t = -t[FUNHEAD]; mm = t+FUNHEAD+3; /* Set i to the arg number we are putting first, then move mm to its start. */ i = t[FUNHEAD+2]; while ( --i > 0 ) { NEXTARG(mm); } /* Keep a pointer to the arguments trailing the selected: */ WORD *argTail = mm; NEXTARG(argTail); tt = TermMalloc("Select_"); /* Move selected out of the way into tmp space */ tt1 = tt; /* Normal argument: */ if ( *mm > 0 ) { for ( i = 0; i < *mm; i++ ) *tt1++ = mm[i]; } /* Fast-notation function: single word */ else if ( *mm <= -FUNCTION ) { *tt1++ = *mm; } /* Fast-notation symbol, number etc: two words */ else { *tt1++ = mm[0]; *tt1++ = mm[1]; } /* Put tt2 at the start of the original arguments */ tt2 = t+FUNHEAD+3; /* Copy leading original arguments after the new first, in the tmp space. */ while ( tt2 < mm ) *tt1++ = *tt2++; /* i contains the size so far. tt1 goes to the start of the tmp space. tt2 to the final argument location (we overwrite "putfirst_") */ i = tt1-tt; tt1 = tt; tt2 = t+FUNHEAD; /* Copy everything so far to its final place */ NCOPY(tt2,tt1,i); /* We are finished with the tmp space */ TermFree(tt,"Select_"); /* Now copy the trailing args. Use the stored pointer, *mm has been edited during the copy to tt2 above! NEXTARG(mm) would produce nonsense. */ while ( argTail < rr ) *tt2++ = *argTail++; /* Set the size of all function args */ t[1] = tt2 - t; /* Now copy the rest of the term, and set the final term size */ rr = term + *term; while ( argTail < rr ) *tt2++ = *argTail++; *term = tt2-term; if ( functions[*t-FUNCTION].spec == TENSORFUNCTION ) { // If the output function is a tensor, we have one more job to do. // The args are formatted as single words, representing indices or vectors. // There is no ARGHEAD. WORD *dst = t + FUNHEAD; WORD *src = dst + 1; // Strip the type information from the args: while ( src < t + t[1] ) { *dst = *src; dst++; src++; src++; } t[1] = dst - t; // Now copy the rest of the term. We've advanced src one too many above. src--; while ( src < term + *term ) { *dst++ = *src++; } *term = dst - term; } goto Restart; } else pnco[nnco++] = t; break; #ifdef WITHFLOAT case FLOATFUN : /* If it is a proper float_ we give it special treatment. If it is not proper, we treat it as a regular commuting function. */ if ( withfloat == 0 ) { if ( TestFloat(t) == 0 ) goto defaultcase; firstfloat = t; withfloat = 1; } else { /* There are now at least two float_'s. Time for action. */ if ( TestFloat(t) == 0 ) goto defaultcase; if ( withfloat == 1 ) UnpackFloat(aux4,firstfloat); withfloat++; UnpackFloat(aux5,t); mpf_mul(aux4,aux4,aux5); } break; #endif case INTFUNCTION : /* Can be resolved if the first argument is a number and the second argument either doesn't exist or has the value +1, 0, -1 +1 : rounding up 0 : rounding towards zero -1 : rounding down (same as no argument) */ if ( t[1] <= FUNHEAD ) break; { WORD *rr, den, num; to = t + FUNHEAD; if ( *to > 0 ) { if ( *to == ARGHEAD ) goto NormZero; rr = to + *to; i = rr[-1]; j = ABS(i); if ( to[ARGHEAD] != j+1 ) goto NoInteg; if ( rr >= r ) k = -1; else if ( *rr == ARGHEAD ) { k = 0; rr += ARGHEAD; } else if ( *rr == -SNUMBER ) { k = rr[1]; rr += 2; } else goto NoInteg; if ( rr != r ) goto NoInteg; if ( k > 1 || k < -1 ) goto NoInteg; to += ARGHEAD+1; j = (j-1) >> 1; i = ( i < 0 ) ? -j: j; UnPack((UWORD *)to,i,&den,&num); /* Potentially the use of NoScrat2 is unsafe. It makes the routine not reentrant, but because it is used only locally and because we only call the low level routines DivLong and AddLong which never make calls involving Normalize, things are OK after all */ if ( AN.NoScrat2 == 0 ) { AN.NoScrat2 = (UWORD *)Malloc1((AM.MaxTal+2)*sizeof(UWORD),"Normalize"); } if ( DivLong((UWORD *)to,num,(UWORD *)(to+j),den ,(UWORD *)AT.WorkPointer,&num,AN.NoScrat2,&den) ) goto FromNorm; if ( k < 0 && den < 0 ) { *AN.NoScrat2 = 1; den = -1; if ( AddLong((UWORD *)AT.WorkPointer,num ,AN.NoScrat2,den,(UWORD *)AT.WorkPointer,&num) ) goto FromNorm; } else if ( k > 0 && den > 0 ) { *AN.NoScrat2 = 1; den = 1; if ( AddLong((UWORD *)AT.WorkPointer,num, AN.NoScrat2,den,(UWORD *)AT.WorkPointer,&num) ) goto FromNorm; } } else if ( *to == -SNUMBER ) { /* No rounding needed */ if ( to[1] < 0 ) { *AT.WorkPointer = -to[1]; num = -1; } else if ( to[1] == 0 ) goto NormZero; else { *AT.WorkPointer = to[1]; num = 1; } } else goto NoInteg; if ( num == 0 ) goto NormZero; ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)AT.WorkPointer,num) ) goto FromNorm; ncoef = INCLENG(ncoef); break; } NoInteg:; /* Fall through if it cannot be resolved */ default : defaultcase:; if ( *t < FUNCTION ) { MLOCK(ErrorMessageLock); MesPrint("Illegal code in Norm"); #ifdef DEBUGON { UBYTE OutBuf[140]; AO.OutFill = AO.OutputLine = OutBuf; t = term; AO.OutSkip = 3; FiniLine(); i = *t; while ( --i >= 0 ) { TalToLine((UWORD)(*t++)); TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); } #endif MUNLOCK(ErrorMessageLock); goto NormMin; } if ( *t == REPLACEMENT ) { if ( AR.Eside != LHSIDE ) ReplaceVeto--; pcom[ncom++] = t; break; } /* if ( *t == AM.termfunnum && t[1] == FUNHEAD+2 && t[FUNHEAD] == -DOLLAREXPRESSION ) termflag++; */ if ( *t == DUMMYFUN || *t == DUMMYTEN ) {} else { if ( *t < (FUNCTION + WILDOFFSET) ) { if ( ( ( functions[*t-FUNCTION].maxnumargs > 0 ) || ( functions[*t-FUNCTION].minnumargs > 0 ) ) && ( ( t[2] & DIRTYFLAG ) != 0 ) ) { /* Number of arguments is bounded. And we have not checked. */ WORD *ta = t + FUNHEAD, *tb = t + t[1]; int numarg = 0; while ( ta < tb ) { numarg++; NEXTARG(ta) } if ( ( functions[*t-FUNCTION].maxnumargs > 0 ) && ( numarg >= functions[*t-FUNCTION].maxnumargs ) ) goto NormZero; if ( ( functions[*t-FUNCTION].minnumargs > 0 ) && ( numarg < functions[*t-FUNCTION].minnumargs ) ) goto NormZero; } doflags: if ( ( ( t[2] & DIRTYFLAG ) != 0 ) && ( functions[*t-FUNCTION].tabl == 0 ) ) { t[2] &= ~DIRTYFLAG; t[2] |= DIRTYSYMFLAG; } if ( functions[*t-FUNCTION].commute ) { pnco[nnco++] = t; } else { pcom[ncom++] = t; } } else { if ( ( ( t[2] & DIRTYFLAG ) != 0 ) && ( functions[*t-FUNCTION-WILDOFFSET].tabl == 0 ) ) { t[2] &= ~DIRTYFLAG; t[2] |= DIRTYSYMFLAG; } if ( functions[*t-FUNCTION-WILDOFFSET].commute ) { pnco[nnco++] = t; } else { pcom[ncom++] = t; } } } /* Now hunt for contractible indices */ if ( ( *t < (FUNCTION + WILDOFFSET) && functions[*t-FUNCTION].spec >= TENSORFUNCTION ) || ( *t >= (FUNCTION + WILDOFFSET) && functions[*t-FUNCTION-WILDOFFSET].spec >= TENSORFUNCTION ) ) { if ( *t >= GAMMA && *t <= GAMMASEVEN ) t++; t += FUNHEAD; while ( t < r ) { if ( *t == AM.vectorzero ) goto NormZero; if ( *t >= AM.OffsetIndex && ( *t >= AM.DumInd || ( *t < AM.WilInd && indices[*t-AM.OffsetIndex].dimension ) ) ) { pcon[ncon++] = t; } else if ( *t == FUNNYWILD ) { t++; } t++; } } else { t += FUNHEAD; while ( t < r ) { if ( *t > 0 ) { /* Here we should worry about a recursion A problem is the possibility of a construct like f(mu+nu) */ t += *t; } else if ( *t <= -FUNCTION ) t++; else if ( *t == -INDEX ) { if ( t[1] >= AM.OffsetIndex && ( t[1] >= AM.DumInd || ( t[1] < AM.WilInd && indices[t[1]-AM.OffsetIndex].dimension ) ) ) pcon[ncon++] = t+1; t += 2; } else if ( *t == -SYMBOL ) { if ( t[1] >= MAXPOWER && t[1] < 2*MAXPOWER ) { *t = -SNUMBER; t[1] -= MAXPOWER; } else if ( t[1] < -MAXPOWER && t[1] > -2*MAXPOWER ) { *t = -SNUMBER; t[1] += MAXPOWER; } else t += 2; } else t += 2; } } break; } t = r; TryAgain:; } while ( t < m ); if ( ANsc ) { AN.cTerm = ANsc; r = t = ANsr; m = ANsm; ANsc = ANsm = ANsr = 0; goto conscan; } /* #] First scan : #[ Easy denominators : Easy denominators are denominators that can be replaced by negative powers of individual subterms. This may add to all our sublists. */ if ( nden ) { for ( k = 0, i = 0; i < nden; i++ ) { t = pden[i]; if ( ( t[2] & DIRTYFLAG ) == 0 ) continue; r = t + t[1]; m = t + FUNHEAD; if ( m >= r ) { for ( j = i+1; j < nden; j++ ) pden[j-1] = pden[j]; nden--; for ( j = 0; j < nnco; j++ ) if ( pnco[j] == t ) break; for ( j++; j < nnco; j++ ) pnco[j-1] = pnco[j]; nnco--; i--; } else { NEXTARG(m); if ( m >= r ) continue; /* We have more than one argument. Split the function. */ if ( k == 0 ) { k = 1; to = termout; from = term; } while ( from < t ) *to++ = *from++; m = t + FUNHEAD; while ( m < r ) { stop = to; *to++ = DENOMINATOR; for ( j = 1; j < FUNHEAD; j++ ) *to++ = 0; if ( *m < -FUNCTION ) *to++ = *m++; else if ( *m < 0 ) { *to++ = *m++; *to++ = *m++; } else { j = *m; while ( --j >= 0 ) *to++ = *m++; } stop[1] = WORDDIF(to,stop); } from = r; if ( i == nden - 1 ) { stop = term + *term; while ( from < stop ) *to++ = *from++; i = *termout = WORDDIF(to,termout); to = term; from = termout; while ( --i >= 0 ) *to++ = *from++; goto Restart; } } } for ( i = 0; i < nden; i++ ) { t = pden[i]; if ( ( t[2] & DIRTYFLAG ) == 0 ) continue; t[2] = 0; if ( t[FUNHEAD] == -SYMBOL ) { WORD change; t += FUNHEAD+1; change = ExtraSymbol(*t,-1,nsym,ppsym,&ncoef); nsym += change; ppsym += change * 2; goto DropDen; } else if ( t[FUNHEAD] == -SNUMBER ) { t += FUNHEAD+1; if ( *t == 0 ) goto NormInf; if ( *t < 0 ) { *AT.WorkPointer = -*t; j = -1; } else { *AT.WorkPointer = *t; j = 1; } ncoef = REDLENG(ncoef); if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)AT.WorkPointer,j) ) goto FromNorm; ncoef = INCLENG(ncoef); goto DropDen; } else if ( t[FUNHEAD] == ARGHEAD ) goto NormInf; else if ( t[FUNHEAD] > 0 && t[FUNHEAD+ARGHEAD] == t[FUNHEAD]-ARGHEAD ) { /* Only one term */ r = t + t[1] - 1; t += FUNHEAD + ARGHEAD + 1; j = *r; m = r - ABS(*r) + 1; if ( j != 3 || ( ( *m != 1 ) || ( m[1] != 1 ) ) ) { ncoef = REDLENG(ncoef); if ( DivRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)m,REDLENG(j),(UWORD *)n_coef,&ncoef) ) goto FromNorm; ncoef = INCLENG(ncoef); j = ABS(j) - 3; t[-FUNHEAD-ARGHEAD] -= j; t[-ARGHEAD-1] -= j; t[-1] -= j; m[0] = m[1] = 1; m[2] = 3; } while ( t < m ) { r = t + t[1]; if ( *t == SYMBOL || *t == DOTPRODUCT ) { k = t[1]; pden[i][1] -= k; pden[i][FUNHEAD] -= k; pden[i][FUNHEAD+ARGHEAD] -= k; m -= k; stop = m + 3; tt = to = t; from = r; if ( *t == SYMBOL ) { t += 2; while ( t < r ) { WORD change; change = ExtraSymbol(*t,-t[1],nsym,ppsym,&ncoef); nsym += change; ppsym += change * 2; t += 2; } } else { t += 2; while ( t < r ) { *ppdot++ = *t++; *ppdot++ = *t++; *ppdot++ = -*t++; ndot++; } } while ( to < stop ) *to++ = *from++; r = tt; } #ifdef WITHFLOAT else if ( *t == FLOATFUN && TestFloat(t) ) { k = t[1]; pden[i][1] -= k; pden[i][FUNHEAD] -= k; pden[i][FUNHEAD+ARGHEAD] -= k; UnpackFloat(aux5,t); if ( withfloat == 0 ) { mpf_ui_div(aux4,1,aux5); withfloat = 2; } else { if ( withfloat == 1 ) UnpackFloat(aux4,firstfloat); mpf_div(aux4,aux4,aux5); withfloat++; } tt = to = t; while ( r < m ) *to++ = *r++; *to++ = 1; *to++ = 1; *to++ = 3; if ( ncoef < 0 ) t[-1] = -t[-1]; m -= k; stop = m + 3; r = tt; } #endif t = r; } if ( pden[i][1] == 4+FUNHEAD+ARGHEAD ) { DropDen: for ( j = 0; j < nnco; j++ ) { if ( pden[i] == pnco[j] ) { --nnco; while ( j < nnco ) { pnco[j] = pnco[j+1]; j++; } break; } } pden[i--] = pden[--nden]; } } } } /* #] Easy denominators : #[ Index Contractions : */ if ( ndel ) { t = pdel; for ( i = 0; i < ndel; i += 2 ) { if ( t[0] == t[1] ) { if ( t[0] == EMPTYINDEX ) {} else if ( *t < AM.OffsetIndex ) { k = AC.FixIndices[*t]; if ( k < 0 ) { j = -1; k = -k; } else if ( k > 0 ) j = 1; else goto NormZero; goto WithFix; } else if ( *t >= AM.DumInd ) { k = AC.lDefDim; if ( k ) goto docontract; } else if ( *t >= AM.WilInd ) { k = indices[*t-AM.OffsetIndex-WILDOFFSET].dimension; if ( k ) goto docontract; } else if ( ( k = indices[*t-AM.OffsetIndex].dimension ) != 0 ) { docontract: if ( k > 0 ) { j = 1; WithFix: shortnum = k; ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)(&shortnum),j) ) goto FromNorm; ncoef = INCLENG(ncoef); } else { WORD change; change = ExtraSymbol((WORD)(-k),(WORD)1,nsym,ppsym,&ncoef); nsym += change; ppsym += change * 2; } t[1] = pdel[ndel-1]; t[0] = pdel[ndel-2]; HaveCon: ndel -= 2; i -= 2; } } else { if ( *t < AM.OffsetIndex && t[1] < AM.OffsetIndex ) goto NormZero; j = *t - AM.OffsetIndex; if ( j >= 0 && ( ( *t >= AM.DumInd && AC.lDefDim ) || ( *t < AM.WilInd && indices[j].dimension ) ) ) { for ( j = i + 2, m = pdel+j; j < ndel; j += 2, m += 2 ) { if ( *t == *m ) { *t = m[1]; *m++ = pdel[ndel-2]; *m = pdel[ndel-1]; goto HaveCon; } else if ( *t == m[1] ) { *t = *m; *m++ = pdel[ndel-2]; *m = pdel[ndel-1]; goto HaveCon; } } } j = t[1]-AM.OffsetIndex; if ( j >= 0 && ( ( t[1] >= AM.DumInd && AC.lDefDim ) || ( t[1] < AM.WilInd && indices[j].dimension ) ) ) { for ( j = i + 2, m = pdel+j; j < ndel; j += 2, m += 2 ) { if ( t[1] == *m ) { t[1] = m[1]; *m++ = pdel[ndel-2]; *m = pdel[ndel-1]; goto HaveCon; } else if ( t[1] == m[1] ) { t[1] = *m; *m++ = pdel[ndel-2]; *m = pdel[ndel-1]; goto HaveCon; } } } t += 2; } } if ( ndel > 0 ) { if ( nvec ) { t = pdel; for ( i = 0; i < ndel; i++ ) { if ( *t >= AM.OffsetIndex && ( ( *t >= AM.DumInd && AC.lDefDim ) || ( *t < AM.WilInd && indices[*t-AM.OffsetIndex].dimension ) ) ) { r = pvec + 1; for ( j = 1; j < nvec; j += 2 ) { if ( *r == *t ) { if ( i & 1 ) { *r = t[-1]; *t-- = pdel[--ndel]; i -= 2; } else { *r = t[1]; t[1] = pdel[--ndel]; i--; } *t-- = pdel[--ndel]; break; } r += 2; } } t++; } } if ( ndel > 0 && ncon ) { t = pdel; for ( i = 0; i < ndel; i++ ) { if ( *t >= AM.OffsetIndex && ( ( *t >= AM.DumInd && AC.lDefDim ) || ( *t < AM.WilInd && indices[*t-AM.OffsetIndex].dimension ) ) ) { for ( j = 0; j < ncon; j++ ) { if ( *pcon[j] == *t ) { if ( i & 1 ) { *pcon[j] = t[-1]; *t-- = pdel[--ndel]; i -= 2; } else { *pcon[j] = t[1]; t[1] = pdel[--ndel]; i--; } *t-- = pdel[--ndel]; didcontr++; r = pcon[j]; for ( j = 0; j < nnco; j++ ) { m = pnco[j]; if ( r > m && r < m+m[1] ) { m[2] |= DIRTYSYMFLAG; break; } } for ( j = 0; j < ncom; j++ ) { m = pcom[j]; if ( r > m && r < m+m[1] ) { m[2] |= DIRTYSYMFLAG; break; } } for ( j = 0; j < neps; j++ ) { m = peps[j]; if ( r > m && r < m+m[1] ) { m[2] |= DIRTYSYMFLAG; break; } } break; } } } t++; } } } } if ( nvec ) { t = pvec + 1; for ( i = 3; i < nvec; i += 2 ) { k = *t - AM.OffsetIndex; if ( k >= 0 && ( ( *t > AM.DumInd && AC.lDefDim ) || ( *t < AM.WilInd && indices[k].dimension ) ) ) { r = t + 2; for ( j = i; j < nvec; j += 2 ) { if ( *r == *t ) { /* Another dotproduct */ *ppdot++ = t[-1]; *ppdot++ = r[-1]; *ppdot++ = 1; ndot++; *r-- = pvec[--nvec]; *r = pvec[--nvec]; *t-- = pvec[--nvec]; *t-- = pvec[--nvec]; i -= 2; break; } r += 2; } } t += 2; } if ( nvec > 0 && ncon ) { t = pvec + 1; for ( i = 1; i < nvec; i += 2 ) { k = *t - AM.OffsetIndex; if ( k >= 0 && ( ( *t >= AM.DumInd && AC.lDefDim ) || ( *t < AM.WilInd && indices[k].dimension ) ) ) { for ( j = 0; j < ncon; j++ ) { if ( *pcon[j] == *t ) { *pcon[j] = t[-1]; *t-- = pvec[--nvec]; *t-- = pvec[--nvec]; r = pcon[j]; pcon[j] = pcon[--ncon]; i -= 2; for ( j = 0; j < nnco; j++ ) { m = pnco[j]; if ( r > m && r < m+m[1] ) { m[2] |= DIRTYSYMFLAG; break; } } for ( j = 0; j < ncom; j++ ) { m = pcom[j]; if ( r > m && r < m+m[1] ) { m[2] |= DIRTYSYMFLAG; break; } } for ( j = 0; j < neps; j++ ) { m = peps[j]; if ( r > m && r < m+m[1] ) { m[2] |= DIRTYSYMFLAG; break; } } break; } } } t += 2; } } } /* #] Index Contractions : #[ NonCommuting Functions : */ m = fillsetexp; if ( nnco ) { for ( i = 0; i < nnco; i++ ) { t = pnco[i]; if ( ( *t >= (FUNCTION+WILDOFFSET) && functions[*t-FUNCTION-WILDOFFSET].spec <= 0 ) || ( *t >= FUNCTION && *t < (FUNCTION + WILDOFFSET) && functions[*t-FUNCTION].spec <= 0 ) ) { DoRevert(t,m); if ( didcontr ) { r = t + FUNHEAD; t += t[1]; while ( r < t ) { if ( *r == -INDEX && r[1] >= 0 && r[1] < AM.OffsetIndex ) { *r = -SNUMBER; didcontr--; pnco[i][2] |= DIRTYSYMFLAG; } NEXTARG(r) } } } } /* First should come the code for function properties. */ /* First we test for symmetric properties and the DIRTYSYMFLAG */ for ( i = 0; i < nnco; i++ ) { t = pnco[i]; if ( *t > 0 && ( t[2] & DIRTYSYMFLAG ) && *t != DOLLAREXPRESSION ) { l = 0; /* to make the compiler happy */ if ( ( *t >= (FUNCTION+WILDOFFSET) && ( l = functions[*t-FUNCTION-WILDOFFSET].symmetric ) > 0 ) || ( *t >= FUNCTION && *t < (FUNCTION + WILDOFFSET) && ( l = functions[*t-FUNCTION].symmetric ) > 0 ) ) { if ( *t >= (FUNCTION+WILDOFFSET) ) { *t -= WILDOFFSET; j = FullSymmetrize(BHEAD t,l); *t += WILDOFFSET; } else j = FullSymmetrize(BHEAD t,l); if ( (l & ~REVERSEORDER) == ANTISYMMETRIC ) { if ( ( j & 2 ) != 0 ) goto NormZero; if ( ( j & 1 ) != 0 ) ncoef = -ncoef; } } else t[2] &= ~DIRTYSYMFLAG; } } /* Non commuting functions are then tested for commutation rules. If needed their order is exchanged. */ k = nnco - 1; for ( i = 0; i < k; i++ ) { j = i; while ( Commute(pnco[j],pnco[j+1]) ) { t = pnco[j]; pnco[j] = pnco[j+1]; pnco[j+1] = t; l = j-1; while ( l >= 0 && Commute(pnco[l],pnco[l+1]) ) { t = pnco[l]; pnco[l] = pnco[l+1]; pnco[l+1] = t; l--; } if ( ++j >= k ) break; } } /* Finally they are written to output. gamma matrices are bundled if possible */ for ( i = 0; i < nnco; i++ ) { t = pnco[i]; if ( *t == IDFUNCTION ) AN.idfunctionflag = 1; if ( *t >= GAMMA && *t <= GAMMASEVEN ) { WORD gtype; to = m; *m++ = GAMMA; m++; FILLFUN(m) *m++ = stype = t[FUNHEAD]; /* type of string */ j = 0; nnum = 0; do { r = t + t[1]; if ( *t == GAMMAFIVE ) { gtype = GAMMA5; t += FUNHEAD; goto onegammamatrix; } else if ( *t == GAMMASIX ) { gtype = GAMMA6; t += FUNHEAD; goto onegammamatrix; } else if ( *t == GAMMASEVEN ) { gtype = GAMMA7; t += FUNHEAD; goto onegammamatrix; } t += FUNHEAD+1; while ( t < r ) { gtype = *t; onegammamatrix: if ( gtype == GAMMA5 ) { if ( j == GAMMA1 ) j = GAMMA5; else if ( j == GAMMA5 ) j = GAMMA1; else if ( j == GAMMA7 ) ncoef = -ncoef; if ( nnum & 1 ) ncoef = -ncoef; } else if ( gtype == GAMMA6 || gtype == GAMMA7 ) { if ( nnum & 1 ) { if ( gtype == GAMMA6 ) gtype = GAMMA7; else gtype = GAMMA6; } if ( j == GAMMA1 ) j = gtype; else if ( j == GAMMA5 ) { j = gtype; if ( j == GAMMA7 ) ncoef = -ncoef; } else if ( j != gtype ) goto NormZero; else { shortnum = 2; ncoef = REDLENG(ncoef); if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)(&shortnum),1) ) goto FromNorm; ncoef = INCLENG(ncoef); } } else { *m++ = gtype; nnum++; } t++; } } while ( ( ++i < nnco ) && ( *(t = pnco[i]) >= GAMMA && *t <= GAMMASEVEN ) && ( t[FUNHEAD] == stype ) ); i--; if ( j ) { k = WORDDIF(m,to) - FUNHEAD-1; r = m; from = m++; while ( --k >= 0 ) *from-- = *--r; *from = j; } to[1] = WORDDIF(m,to); } else if ( *t < 0 ) { *m++ = -*t; *m++ = FUNHEAD; *m++ = 0; FILLFUN3(m) } else { if ( ( t[2] & DIRTYFLAG ) == DIRTYFLAG && *t != REPLACEMENT && *t != DOLLAREXPRESSION && TestFunFlag(BHEAD t) ) ReplaceVeto = 1; k = t[1]; NCOPY(m,t,k); } } } /* #] NonCommuting Functions : #[ Commuting Functions : */ if ( ncom ) { for ( i = 0; i < ncom; i++ ) { t = pcom[i]; if ( ( *t >= (FUNCTION+WILDOFFSET) && functions[*t-FUNCTION-WILDOFFSET].spec <= 0 ) || ( *t >= FUNCTION && *t < (FUNCTION + WILDOFFSET) && functions[*t-FUNCTION].spec <= 0 ) ) { DoRevert(t,m); if ( didcontr ) { r = t + FUNHEAD; t += t[1]; while ( r < t ) { if ( *r == -INDEX && r[1] >= 0 && r[1] < AM.OffsetIndex ) { *r = -SNUMBER; didcontr--; pcom[i][2] |= DIRTYSYMFLAG; } NEXTARG(r) } } } } /* Now we test for symmetric properties and the DIRTYSYMFLAG */ for ( i = 0; i < ncom; i++ ) { t = pcom[i]; if ( *t > 0 && ( t[2] & DIRTYSYMFLAG ) ) { l = 0; /* to make the compiler happy */ if ( ( *t >= (FUNCTION+WILDOFFSET) && ( l = functions[*t-FUNCTION-WILDOFFSET].symmetric ) > 0 ) || ( *t >= FUNCTION && *t < (FUNCTION + WILDOFFSET) && ( l = functions[*t-FUNCTION].symmetric ) > 0 ) ) { if ( *t >= (FUNCTION+WILDOFFSET) ) { *t -= WILDOFFSET; j = FullSymmetrize(BHEAD t,l); *t += WILDOFFSET; } else j = FullSymmetrize(BHEAD t,l); if ( (l & ~REVERSEORDER) == ANTISYMMETRIC ) { if ( ( j & 2 ) != 0 ) goto NormZero; if ( ( j & 1 ) != 0 ) ncoef = -ncoef; } } else t[2] &= ~DIRTYSYMFLAG; } } /* Sort the functions From a purists point of view this can be improved. There are slow and fast arguments and no conversions are taken into account here. */ for ( i = 1; i < ncom; i++ ) { for ( j = i; j > 0; j-- ) { WORD jj,kk; jj = j-1; t = pcom[jj]; r = pcom[j]; if ( *t < 0 ) { if ( *r < 0 ) { if ( *t >= *r ) goto NextI; } else { if ( -*t <= *r ) goto NextI; } goto jexch; } else if ( *r < 0 ) { if ( *t < -*r ) goto NextI; goto jexch; } else if ( *t != *r ) { if ( *t < *r ) goto NextI; jexch: t = pcom[j]; pcom[j] = pcom[jj]; pcom[jj] = t; continue; } if ( AC.properorderflag ) { if ( ( *t >= (FUNCTION+WILDOFFSET) && functions[*t-FUNCTION-WILDOFFSET].spec >= TENSORFUNCTION ) || ( *t >= FUNCTION && *t < (FUNCTION + WILDOFFSET) && functions[*t-FUNCTION].spec >= TENSORFUNCTION ) ) {} else { WORD *s1, *s2, *ss1, *ss2; s1 = t+FUNHEAD; s2 = r+FUNHEAD; ss1 = t + t[1]; ss2 = r + r[1]; while ( s1 < ss1 && s2 < ss2 ) { k = CompArg(s1,s2); if ( k > 0 ) goto jexch; if ( k < 0 ) goto NextI; NEXTARG(s1) NEXTARG(s2) } if ( s1 < ss1 ) goto jexch; goto NextI; } k = t[1] - FUNHEAD; kk = r[1] - FUNHEAD; t += FUNHEAD; r += FUNHEAD; while ( k > 0 && kk > 0 ) { if ( *t < *r ) goto NextI; else if ( *t++ > *r++ ) goto jexch; k--; kk--; } if ( k > 0 ) goto jexch; goto NextI; } else { k = t[1] - FUNHEAD; kk = r[1] - FUNHEAD; t += FUNHEAD; r += FUNHEAD; while ( k > 0 && kk > 0 ) { if ( *t < *r ) goto NextI; else if ( *t++ > *r++ ) goto jexch; k--; kk--; } if ( k > 0 ) goto jexch; goto NextI; } } NextI:; } for ( i = 0; i < ncom; i++ ) { t = pcom[i]; if ( *t == THETA || *t == THETA2 ) { if ( ( k = DoTheta(BHEAD t) ) == 0 ) goto NormZero; else if ( k < 0 ) { k = t[1]; NCOPY(m,t,k); } } else if ( *t == DELTA2 || *t == DELTAP ) { if ( ( k = DoDelta(t) ) == 0 ) goto NormZero; else if ( k < 0 ) { k = t[1]; NCOPY(m,t,k); } } else if ( *t == AR.PolyFunInv && AR.PolyFunType == 2 ) { /* If there are two arguments, exchange them, change the name of the function and go to dealing with PolyRatFun. */ WORD *mm, *tt = t, numt = 0; tt += FUNHEAD; while ( tt < t+t[1] ) { numt++; NEXTARG(tt) } if ( numt == 2 ) { tt = t; mm = m; k = t[1]; NCOPY(mm,tt,k) mm = m+FUNHEAD; NEXTARG(mm); tt = t+FUNHEAD; if ( *mm < 0 ) { if ( *mm <= -FUNCTION ) { *tt++ = *mm++; } else { *tt++ = *mm++; *tt++ = *mm++; } } else { k = *mm; NCOPY(tt,mm,k) } mm = m+FUNHEAD; if ( *mm < 0 ) { if ( *mm <= -FUNCTION ) { *tt++ = *mm++; } else { *tt++ = *mm++; *tt++ = *mm++; } } else { k = *mm; NCOPY(tt,mm,k) } *t = AR.PolyFun; t[2] |= MUSTCLEANPRF; goto regularratfun; } } else if ( *t == AR.PolyFun ) { if ( AR.PolyFunType == 1 ) { /* Regular PolyFun with one argument */ if ( t[FUNHEAD+1] == 0 && AR.Eside != LHSIDE && t[1] == FUNHEAD + 2 && t[FUNHEAD] == -SNUMBER ) goto NormZero; if ( i > 0 && pcom[i-1][0] == AR.PolyFun ) { if ( AN.PolyNormFlag == 0 ) { AN.PolyNormFlag = 1; AN.PolyFunTodo = 0; } } k = t[1]; NCOPY(m,t,k); } else if ( AR.PolyFunType == 2 ) { /* PolyRatFun. Regular type: Two arguments Power expanded: One argument. Here to be treated as AR.PolyFunType == 1, but with power cutoff. */ regularratfun:; /* First check for zeroes. */ if ( t[FUNHEAD+1] == 0 && AR.Eside != LHSIDE && t[1] > FUNHEAD + 2 && t[FUNHEAD] == -SNUMBER ) { u = t + FUNHEAD + 2; if ( *u < 0 ) { if ( *u <= -FUNCTION ) {} else if ( t[1] == FUNHEAD+4 && t[FUNHEAD+2] == -SNUMBER && t[FUNHEAD+3] == 0 ) goto NormPRF; else if ( t[1] == FUNHEAD+4 ) goto NormZero; } else if ( t[1] == *u+FUNHEAD+2 ) goto NormZero; } else { u = t+FUNHEAD; NEXTARG(u); if ( *u == -SNUMBER && u[1] == 0 ) goto NormInf; } if ( i > 0 && pcom[i-1][0] == AR.PolyFun ) AN.PolyNormFlag = 1; else if ( i < ncom-1 && pcom[i+1][0] == AR.PolyFun ) AN.PolyNormFlag = 1; k = t[1]; if ( AN.PolyNormFlag ) { if ( AR.PolyFunExp == 0 ) { AN.PolyFunTodo = 0; NCOPY(m,t,k); } else if ( AR.PolyFunExp == 1 ) { /* get highest divergence */ if ( PolyFunMode == 0 ) { NCOPY(m,t,k); AN.PolyFunTodo = 1; } else { WORD *mmm = m; NCOPY(m,t,k); if ( TreatPolyRatFun(BHEAD mmm) != 0 ) goto FromNorm; m = mmm+mmm[1]; } } else { if ( PolyFunMode == 0 ) { NCOPY(m,t,k); AN.PolyFunTodo = 1; } else { WORD *mmm = m; NCOPY(m,t,k); if ( ExpandRat(BHEAD mmm) != 0 ) goto FromNorm; m = mmm+mmm[1]; } } } else { if ( AR.PolyFunExp == 0 ) { AN.PolyFunTodo = 0; NCOPY(m,t,k); } else if ( AR.PolyFunExp == 1 ) { /* get highest divergence */ WORD *mmm = m; NCOPY(m,t,k); if ( TreatPolyRatFun(BHEAD mmm) != 0 ) goto FromNorm; m = mmm+mmm[1]; } else { WORD *mmm = m; NCOPY(m,t,k); if ( ExpandRat(BHEAD mmm) != 0 ) goto FromNorm; m = mmm+mmm[1]; } } } } else if ( *t > 0 ) { if ( ( t[2] & DIRTYFLAG ) == DIRTYFLAG && *t != REPLACEMENT && TestFunFlag(BHEAD t) ) ReplaceVeto = 1; k = t[1]; NCOPY(m,t,k); } else { *m++ = -*t; *m++ = FUNHEAD; *m++ = 0; FILLFUN3(m) } } } /* #] Commuting Functions : #[ Track Replace_ : */ if ( ReplaceVeto < 0 ) { /* We found one (or more) replace_ functions and all other functions are 'clean' (no dirty flag). Now we check whether one of these functions can be used. Thus far the functions go from fillsetexp to m. Somewhere in there there are -ReplaceVeto occurrences of REPLACEMENT. Hunt for the first one that fits the bill. Note that replace_ is a commuting function. */ WORD *ma = fillsetexp, *mb, *mc; while ( ma < m ) { mb = ma + ma[1]; if ( *ma != REPLACEMENT ) { ma = mb; continue; } if ( *ma == REPLACEMENT && ReplaceType == -1 ) { mc = ma; ReplaceType = 0; if ( AN.RSsize < 2*ma[1]+SUBEXPSIZE ) { if ( AN.ReplaceScrat ) M_free(AN.ReplaceScrat,"AN.ReplaceScrat"); AN.RSsize = 2*ma[1]+SUBEXPSIZE+40; AN.ReplaceScrat = (WORD *)Malloc1((AN.RSsize+1)*sizeof(WORD),"AN.ReplaceScrat"); } ma += FUNHEAD; ReplaceSub = AN.ReplaceScrat; ReplaceSub += SUBEXPSIZE; while ( ma < mb ) { if ( *ma > 0 ) goto NoRep; if ( *ma <= -FUNCTION ) { *ReplaceSub++ = FUNTOFUN; *ReplaceSub++ = 4; *ReplaceSub++ = -*ma++; if ( *ma > -FUNCTION ) goto NoRep; *ReplaceSub++ = -*ma++; } else if ( ma+4 > mb ) goto NoRep; else { if ( *ma == -SYMBOL ) { if ( ma[2] == -SYMBOL && ma+4 <= mb ) *ReplaceSub++ = SYMTOSYM; else if ( ma[2] == -SNUMBER && ma+4 <= mb ) { *ReplaceSub++ = SYMTONUM; if ( ReplaceType == 0 ) { oldtoprhs = C->numrhs; oldcpointer = C->Pointer - C->Buffer; } ReplaceType = 1; } else if ( ma[2] == ARGHEAD && ma+2+ARGHEAD <= mb ) { *ReplaceSub++ = SYMTONUM; *ReplaceSub++ = 4; *ReplaceSub++ = ma[1]; *ReplaceSub++ = 0; ma += 2+ARGHEAD; continue; } /* Next is the subexpression. We have to test that it isn't vector-like or index-like */ else if ( ma[2] > 0 ) { WORD *sstop, *ttstop, n; ss = ma+2; sstop = ss + *ss; ss += ARGHEAD; while ( ss < sstop ) { tt = ss + *ss; ttstop = tt - ABS(tt[-1]); ss++; while ( ss < ttstop ) { if ( *ss == INDEX ) goto NoRep; ss += ss[1]; } ss = tt; } subtype = SYMTOSUB; if ( ReplaceType == 0 ) { oldtoprhs = C->numrhs; oldcpointer = C->Pointer - C->Buffer; } ReplaceType = 1; ss = AddRHS(AT.ebufnum,1); tt = ma+2; n = *tt - ARGHEAD; tt += ARGHEAD; while ( (ss + n + 10) > C->Top ) ss = DoubleCbuffer(AT.ebufnum,ss,14); while ( --n >= 0 ) *ss++ = *tt++; *ss++ = 0; C->rhs[C->numrhs+1] = ss; C->Pointer = ss; *ReplaceSub++ = subtype; *ReplaceSub++ = 4; *ReplaceSub++ = ma[1]; *ReplaceSub++ = C->numrhs; ma += 2 + ma[2]; continue; } else goto NoRep; } else if ( ( *ma == -VECTOR || *ma == -MINVECTOR ) && ma+4 <= mb ) { if ( ma[2] == -VECTOR ) { if ( *ma == -VECTOR ) *ReplaceSub++ = VECTOVEC; else *ReplaceSub++ = VECTOMIN; } else if ( ma[2] == -MINVECTOR ) { if ( *ma == -VECTOR ) *ReplaceSub++ = VECTOMIN; else *ReplaceSub++ = VECTOVEC; } /* Next is a vector-like subexpression Search for vector nature first */ else if ( ma[2] > 0 ) { WORD *sstop, *ttstop, *w, *mm, n, count; WORD *v1, *v2 = 0; if ( *ma == -MINVECTOR ) { ss = ma+2; sstop = ss + *ss; ss += ARGHEAD; while ( ss < sstop ) { ss += *ss; ss[-1] = -ss[-1]; } *ma = -VECTOR; } ss = ma+2; sstop = ss + *ss; ss += ARGHEAD; while ( ss < sstop ) { tt = ss + *ss; ttstop = tt - ABS(tt[-1]); ss++; count = 0; while ( ss < ttstop ) { if ( *ss == INDEX ) { n = ss[1] - 2; ss += 2; while ( --n >= 0 ) { if ( *ss < MINSPEC ) count++; ss++; } } else ss += ss[1]; } if ( count != 1 ) goto NoRep; ss = tt; } subtype = VECTOSUB; if ( ReplaceType == 0 ) { oldtoprhs = C->numrhs; oldcpointer = C->Pointer - C->Buffer; } ReplaceType = 1; mm = AddRHS(AT.ebufnum,1); *ReplaceSub++ = subtype; *ReplaceSub++ = 4; *ReplaceSub++ = ma[1]; *ReplaceSub++ = C->numrhs; w = ma+2; n = *w - ARGHEAD; w += ARGHEAD; while ( (mm + n + 10) > C->Top ) mm = DoubleCbuffer(AT.ebufnum,mm,15); while ( --n >= 0 ) *mm++ = *w++; *mm++ = 0; C->rhs[C->numrhs+1] = mm; C->Pointer = mm; mm = AddRHS(AT.ebufnum,1); w = ma+2; n = *w - ARGHEAD; w += ARGHEAD; while ( (mm + n + 13) > C->Top ) mm = DoubleCbuffer(AT.ebufnum,mm,16); sstop = w + n; while ( w < sstop ) { tt = w + *w; ttstop = tt - ABS(tt[-1]); ss = mm; mm++; w++; while ( w < ttstop ) { /* Subterms */ if ( *w != INDEX ) { n = w[1]; NCOPY(mm,w,n); } else { v1 = mm; *mm++ = *w++; *mm++ = n = *w++; n -= 2; while ( --n >= 0 ) { if ( *w >= MINSPEC ) *mm++ = *w++; else v2 = w++; } n = WORDDIF(mm,v1); if ( n != v1[1] ) { if ( n <= 2 ) mm -= 2; else v1[1] = n; *mm++ = VECTOR; *mm++ = 4; *mm++ = *v2; *mm++ = FUNNYVEC; } } } while ( w < tt ) *mm++ = *w++; *ss = WORDDIF(mm,ss); } *mm++ = 0; C->rhs[C->numrhs+1] = mm; C->Pointer = mm; if ( mm > C->Top ) { MLOCK(ErrorMessageLock); MesPrint("Internal error in Normalize with extra compiler buffer"); MUNLOCK(ErrorMessageLock); Terminate(-1); } ma += 2 + ma[2]; continue; } else goto NoRep; } else if ( *ma == -INDEX ) { if ( ( ma[2] == -INDEX || ma[2] == -VECTOR ) && ma+4 <= mb ) *ReplaceSub++ = INDTOIND; else if ( ma[1] >= AM.OffsetIndex ) { if ( ma[2] == -SNUMBER && ma+4 <= mb && ma[3] >= 0 && ma[3] < AM.OffsetIndex ) *ReplaceSub++ = INDTOIND; else if ( ma[2] == ARGHEAD && ma+2+ARGHEAD <= mb ) { *ReplaceSub++ = INDTOIND; *ReplaceSub++ = 4; *ReplaceSub++ = ma[1]; *ReplaceSub++ = 0; ma += 2+ARGHEAD; continue; } else goto NoRep; } else goto NoRep; } else goto NoRep; *ReplaceSub++ = 4; *ReplaceSub++ = ma[1]; *ReplaceSub++ = ma[3]; ma += 4; } } AN.ReplaceScrat[1] = ReplaceSub-AN.ReplaceScrat; /* Success. This means that we have to remove the replace_ from the functions. It starts at mc and end at mb. */ while ( mb < m ) *mc++ = *mb++; m = mc; break; NoRep: if ( ReplaceType > 0 ) { C->numrhs = oldtoprhs; C->Pointer = C->Buffer + oldcpointer; } ReplaceType = -1; if ( ++ReplaceVeto >= 0 ) break; } ma = mb; } } /* #] Track Replace_ : #[ LeviCivita tensors : */ if ( neps ) { to = m; for ( i = 0; i < neps; i++ ) { /* Put the indices in order */ t = peps[i]; if ( ( t[2] & DIRTYSYMFLAG ) != DIRTYSYMFLAG ) continue; t[2] &= ~DIRTYSYMFLAG; if ( AR.Eside == LHSIDE || AR.Eside == LHSIDEX ) { /* Potential problems with FUNNYWILD */ /* First make sure all FUNNIES are at the end. Then sort separately */ r = t + FUNHEAD; m = tt = t + t[1]; while ( r < m ) { if ( *r != FUNNYWILD ) { r++; continue; } k = r[1]; u = r + 2; while ( u < tt ) { u[-2] = *u; if ( *u != FUNNYWILD ) ncoef = -ncoef; u++; } tt[-2] = FUNNYWILD; tt[-1] = k; m -= 2; } t += FUNHEAD; do { for ( r = t + 1; r < m; r++ ) { if ( *r < *t ) { k = *r; *r = *t; *t = k; ncoef = -ncoef; } else if ( *r == *t ) goto NormZero; } t++; } while ( t < m ); do { for ( r = t + 2; r < tt; r += 2 ) { if ( r[1] < t[1] ) { k = r[1]; r[1] = t[1]; t[1] = k; ncoef = -ncoef; } else if ( r[1] == t[1] ) goto NormZero; } t += 2; } while ( t < tt ); } else { m = t + t[1]; t += FUNHEAD; do { for ( r = t + 1; r < m; r++ ) { if ( *r < *t ) { k = *r; *r = *t; *t = k; ncoef = -ncoef; } else if ( *r == *t ) goto NormZero; } t++; } while ( t < m ); } } /* Sort the tensors */ for ( i = 0; i < (neps-1); i++ ) { t = peps[i]; for ( j = i+1; j < neps; j++ ) { r = peps[j]; if ( t[1] > r[1] ) { peps[i] = m = r; peps[j] = r = t; t = m; } else if ( t[1] == r[1] ) { k = t[1] - FUNHEAD; m = t + FUNHEAD; r += FUNHEAD; do { if ( *r < *m ) { m = peps[j]; peps[j] = t; peps[i] = t = m; break; } else if ( *r++ > *m++ ) break; } while ( --k > 0 ); } } } m = to; for ( i = 0; i < neps; i++ ) { t = peps[i]; k = t[1]; NCOPY(m,t,k); } } /* #] LeviCivita tensors : #[ Delta : */ if ( ndel ) { r = t = pdel; for ( i = 0; i < ndel; i += 2, r += 2 ) { if ( r[1] < r[0] ) { k = *r; *r = r[1]; r[1] = k; } } for ( i = 2; i < ndel; i += 2, t += 2 ) { r = t + 2; for ( j = i; j < ndel; j += 2 ) { if ( *r > *t ) { r += 2; } else if ( *r < *t ) { k = *r; *r++ = *t; *t++ = k; k = *r; *r++ = *t; *t-- = k; } else { if ( *++r < t[1] ) { k = *r; *r = t[1]; t[1] = k; } r++; } } } t = pdel; *m++ = DELTA; *m++ = ndel + 2; i = ndel; NCOPY(m,t,i); } /* #] Delta : #[ Loose Vectors/Indices : */ if ( nind ) { t = pind; for ( i = 0; i < nind; i++ ) { r = t + 1; for ( j = i+1; j < nind; j++ ) { if ( *r < *t ) { k = *r; *r = *t; *t = k; } r++; } t++; } t = pind; *m++ = INDEX; *m++ = nind + 2; i = nind; NCOPY(m,t,i); } /* #] Loose Vectors/Indices : #[ Vectors : */ if ( nvec ) { t = pvec; for ( i = 2; i < nvec; i += 2 ) { r = t + 2; for ( j = i; j < nvec; j += 2 ) { if ( *r == *t ) { if ( *++r < t[1] ) { k = *r; *r = t[1]; t[1] = k; } r++; } else if ( *r < *t ) { k = *r; *r++ = *t; *t++ = k; k = *r; *r++ = *t; *t-- = k; } else { r += 2; } } t += 2; } t = pvec; *m++ = VECTOR; *m++ = nvec + 2; i = nvec; NCOPY(m,t,i); } /* #] Vectors : #[ Dotproducts : */ if ( ndot ) { to = m; m = t = pdot; i = ndot; while ( --i >= 0 ) { if ( *t > t[1] ) { j = *t; *t = t[1]; t[1] = j; } t += 3; } t = m; ndot *= 3; m += ndot; while ( t < (m-3) ) { r = t + 3; do { if ( *r == *t ) { if ( *++r == *++t ) { r++; if ( ( *r < MAXPOWER && t[1] < MAXPOWER ) || ( *r > -MAXPOWER && t[1] > -MAXPOWER ) ) { t++; *t += *r; if ( *t > MAXPOWER || *t < -MAXPOWER ) { MLOCK(ErrorMessageLock); MesPrint("Exponent of dotproduct out of range: %d",*t); MUNLOCK(ErrorMessageLock); goto NormMin; } ndot -= 3; *r-- = *--m; *r-- = *--m; *r = *--m; if ( !*t ) { ndot -= 3; *t-- = *--m; *t-- = *--m; *t = *--m; t -= 3; break; } } else if ( *r < *++t ) { k = *r; *r++ = *t; *t = k; } else r++; t -= 2; } else if ( *r < *t ) { k = *r; *r++ = *t; *t++ = k; k = *r; *r++ = *t; *t = k; t -= 2; } else { r += 2; t--; } } else if ( *r < *t ) { k = *r; *r++ = *t; *t++ = k; k = *r; *r++ = *t; *t++ = k; k = *r; *r++ = *t; *t = k; t -= 2; } else { r += 3; } } while ( r < m ); t += 3; } m = to; t = pdot; if ( ( i = ndot ) > 0 ) { *m++ = DOTPRODUCT; *m++ = i + 2; NCOPY(m,t,i); } } /* #] Dotproducts : #[ Symbols : */ if ( nsym ) { nsym <<= 1; t = psym; *m++ = SYMBOL; r = m; *m++ = ( i = nsym ) + 2; if ( i ) { do { if ( !*t ) { if ( t[1] < (2*MAXPOWER) ) { /* powers of i */ if ( t[1] & 1 ) { *m++ = 0; *m++ = 1; } else *r -= 2; if ( *++t & 2 ) ncoef = -ncoef; t++; } } else if ( *t <= NumSymbols && *t > -2*MAXPOWER ) { /* Put powers in range */ if ( ( ( ( t[1] > symbols[*t].maxpower ) && ( symbols[*t].maxpower < MAXPOWER ) ) || ( ( t[1] < symbols[*t].minpower ) && ( symbols[*t].minpower > -MAXPOWER ) ) ) && ( t[1] < 2*MAXPOWER ) && ( t[1] > -2*MAXPOWER ) ) { if ( i <= 2 || t[2] != *t ) goto NormZero; } if ( AN.ncmod == 1 && ( AC.modmode & ALSOPOWERS ) != 0 ) { if ( AC.cmod[0] == 1 ) t[1] = 0; else if ( t[1] >= 0 ) t[1] = 1 + (t[1]-1)%(AC.cmod[0]-1); else { t[1] = -1 - (-t[1]-1)%(AC.cmod[0]-1); if ( t[1] < 0 ) t[1] += (AC.cmod[0]-1); } } if ( ( t[1] < (2*MAXPOWER) && t[1] >= MAXPOWER ) || ( t[1] > -(2*MAXPOWER) && t[1] <= -MAXPOWER ) ) { MLOCK(ErrorMessageLock); MesPrint("Exponent out of range: %d",t[1]); MUNLOCK(ErrorMessageLock); goto NormMin; } if ( AT.TrimPower && AR.PolyFunVar == *t && t[1] > AR.PolyFunPow ) { goto NormZero; } else if ( t[1] ) { *m++ = *t++; *m++ = *t++; } else { *r -= 2; t += 2; } } else { *m++ = *t++; *m++ = *t++; } } while ( (i-=2) > 0 ); } if ( *r <= 2 ) m = r-1; } /* #] Symbols : #[ float_ : Here we treat float_ functions and combined them with the regular coefficient. */ #ifdef WITHFLOAT if ( withfloat ) { WORD floatsign = 3; /* First check whether the coefficient is already 1/1 */ if ( ABS(ncoef) == 3 && n_coef[0] == 1 && n_coef[1] == 1 ) { if ( withfloat == 1 ) { t = firstfloat; /* We only interfere by making the sign positive. The float_ function has already been tested. */ if ( t[FUNHEAD+3] < 0 ) { t[FUNHEAD+3] = -t[FUNHEAD+3]; floatsign = -floatsign; } if ( ncoef < 0 ) floatsign = -floatsign; /* Copy to output; */ AT.FloatPos = m-termout; i = t[1]; NCOPY(m,t,i) } else { PackFloat(m,aux4); if ( m[FUNHEAD+3] < 0 ) { m[FUNHEAD+3] = -m[FUNHEAD+3]; floatsign = -floatsign; } if ( ncoef < 0 ) floatsign = -floatsign; AT.FloatPos = m-termout; m += m[1]; } } else { if ( withfloat == 1 ) UnpackFloat(aux4,firstfloat); RatToFloat(aux5,(UWORD *)n_coef,ncoef); mpf_mul(aux4,aux4,aux5); PackFloat(m,aux4); AT.FloatPos = m-termout; if ( m[FUNHEAD+3] < 0 ) { m[FUNHEAD+3] = -m[FUNHEAD+3]; floatsign = -floatsign; } m += m[1]; } n_coef[0] = 1; n_coef[1] = 1; ncoef = floatsign; } else AT.FloatPos = 0; #endif /* #] float_ : #[ Do Replace_ : */ stop = (WORD *)(((UBYTE *)(termout)) + AM.MaxTer); i = ABS(ncoef); if ( ( m + i ) > stop ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex during normalization"); MUNLOCK(ErrorMessageLock); goto NormMin; } if ( ReplaceType >= 0 ) { t = n_coef; i--; NCOPY(m,t,i); *m++ = ncoef; t = termout; *t = WORDDIF(m,t); if ( ReplaceType == 0 ) { AT.WorkPointer = termout+*termout; WildFill(BHEAD term,termout,AN.ReplaceScrat); termout = term + *term; } else { AT.WorkPointer = r = termout + *termout; WildFill(BHEAD r,termout,AN.ReplaceScrat); i = *r; m = term; NCOPY(m,r,i); termout = m; r = m = term; r += *term; r -= ABS(r[-1]); m++; while ( m < r ) { if ( *m >= FUNCTION && m[1] > FUNHEAD && functions[*m-FUNCTION].spec != TENSORFUNCTION ) m[2] |= DIRTYFLAG; m += m[1]; } } /* The next 'reset' cannot be done. We still need the expression in the buffer. Note though that this may cause a runaway pointer if we are not very careful. C->numrhs = oldtoprhs; C->Pointer = C->Buffer + oldcpointer; */ AT.NormDepth--; TermFree(n_llnum,"n_llnum"); TermFree(n_coef,"NormCoef"); return(1); } else { t = termout; k = WORDDIF(m,t); *t = k + i; m = term; NCOPY(m,t,k); i--; t = n_coef; NCOPY(m,t,i); *m++ = ncoef; } /* #] Do Replace_ : #[ Errors and Finish : */ RegEnd: if ( termout < term + *term && termout >= term ) AT.WorkPointer = term + *term; else AT.WorkPointer = termout; /* if ( termflag ) { We have to assign the term to $variable(s) TermAssign(term); } */ AT.NormDepth--; TermFree(n_llnum,"n_llnum"); TermFree(n_coef,"NormCoef"); return(regval); NormInf: MLOCK(ErrorMessageLock); MesPrint("Division by zero during normalization"); MUNLOCK(ErrorMessageLock); Terminate(-1); NormZZ: MLOCK(ErrorMessageLock); MesPrint("0^0 during normalization of term"); MUNLOCK(ErrorMessageLock); Terminate(-1); NormPRF: MLOCK(ErrorMessageLock); MesPrint("0/0 in polyratfun during normalization of term"); MUNLOCK(ErrorMessageLock); Terminate(-1); NormZero: *term = 0; AT.WorkPointer = termout; AT.NormDepth--; TermFree(n_llnum,"n_llnum"); TermFree(n_coef,"NormCoef"); return(regval); NormMin: AT.NormDepth--; TermFree(n_llnum,"n_llnum"); TermFree(n_coef,"NormCoef"); return(-1); FromNorm: MLOCK(ErrorMessageLock); MesCall("Norm"); MUNLOCK(ErrorMessageLock); AT.NormDepth--; TermFree(n_llnum,"n_llnum"); TermFree(n_coef,"NormCoef"); return(-1); /* #] Errors and Finish : */ } /* #] Normalize : #[ ExtraSymbol : */ int ExtraSymbol(WORD sym, WORD pow, WORD nsym, WORD *ppsym, WORD *ncoef) { WORD *m, i; i = nsym; m = ppsym - 2; while ( i > 0 ) { if ( sym == *m ) { m++; if ( pow > 2*MAXPOWER || pow < -2*MAXPOWER || *m > 2*MAXPOWER || *m < -2*MAXPOWER ) { MLOCK(ErrorMessageLock); MesPrint("Illegal wildcard power combination."); MUNLOCK(ErrorMessageLock); Terminate(-1); } *m += pow; if ( ( sym <= NumSymbols && sym > -MAXPOWER ) && ( symbols[sym].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) { *m %= symbols[sym].maxpower; if ( *m < 0 ) *m += symbols[sym].maxpower; if ( ( symbols[sym].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { if ( ( ( symbols[sym].maxpower & 1 ) == 0 ) && ( *m >= symbols[sym].maxpower/2 ) ) { *m -= symbols[sym].maxpower/2; *ncoef = -*ncoef; } } } if ( *m >= 2*MAXPOWER || *m <= -2*MAXPOWER ) { MLOCK(ErrorMessageLock); MesPrint("Power overflow during normalization"); MUNLOCK(ErrorMessageLock); return(-1); } if ( !*m ) { m--; while ( i < nsym ) { *m = m[2]; m++; *m = m[2]; m++; i++; } return(-1); } return(0); } else if ( sym < *m ) { m -= 2; i--; } else break; } m = ppsym; while ( i < nsym ) { m--; m[2] = *m; m--; m[2] = *m; i++; } *m++ = sym; *m = pow; return(1); } /* #] ExtraSymbol : #[ DoTheta : */ int DoTheta(PHEAD WORD *t) { GETBIDENTITY WORD k, *r1, *r2, *tstop, type; WORD ia, *ta, *tb, *stopa, *stopb; if ( AC.BracketNormalize ) return(-1); type = *t; k = t[1]; tstop = t + k; t += FUNHEAD; if ( k <= FUNHEAD ) return(1); r1 = t; NEXTARG(r1) if ( r1 == tstop ) { /* One argument */ if ( *t == ARGHEAD ) { if ( type == THETA ) return(1); else return(0); /* THETA2 */ } if ( *t < 0 ) { if ( *t == -SNUMBER ) { if ( t[1] < 0 ) return(0); else { if ( type == THETA2 && t[1] == 0 ) return(0); else return(1); } } return(-1); } k = t[*t-1]; if ( *t == ABS(k)+1+ARGHEAD ) { if ( k > 0 ) return(1); else return(0); } return(-1); } /* At least two arguments */ r2 = r1; NEXTARG(r2) if ( r2 < tstop ) return(-1); /* More than 2 arguments */ /* Note now that zero has to be treated specially We take the criteria from the symmetrize routine */ if ( *t == -SNUMBER && *r1 == -SNUMBER ) { if ( t[1] > r1[1] ) return(0); else if ( t[1] < r1[1] ) { return(1); } else if ( type == THETA ) return(1); else return(0); /* THETA2 */ } else if ( t[1] == 0 && *t == -SNUMBER ) { if ( *r1 > 0 ) { } else if ( *t < *r1 ) return(1); else if ( *t > *r1 ) return(0); } else if ( r1[1] == 0 && *r1 == -SNUMBER ) { if ( *t > 0 ) { } else if ( *t < *r1 ) return(1); else if ( *t > *r1 ) return(0); } r2 = AT.WorkPointer; if ( *t < 0 ) { ta = r2; ToGeneral(t,ta,0); r2 += *r2; } else ta = t; if ( *r1 < 0 ) { tb = r2; ToGeneral(r1,tb,0); } else tb = r1; stopa = ta + *ta; stopb = tb + *tb; ta += ARGHEAD; tb += ARGHEAD; while ( ta < stopa ) { if ( tb >= stopb ) return(0); if ( ( ia = CompareTerms(BHEAD ta,tb,(WORD)1) ) < 0 ) return(0); if ( ia > 0 ) return(1); ta += *ta; tb += *tb; } if ( type == THETA ) return(1); else return(0); /* THETA2 */ } /* #] DoTheta : #[ DoDelta : */ int DoDelta(WORD *t) { WORD k, *r1, *r2, *tstop, isnum, isnum2, type = *t; if ( AC.BracketNormalize ) return(-1); k = t[1]; if ( k <= FUNHEAD ) goto argzero; if ( k == FUNHEAD+ARGHEAD && t[FUNHEAD] == ARGHEAD ) goto argzero; tstop = t + k; t += FUNHEAD; r1 = t; NEXTARG(r1) if ( *t < 0 ) { k = 1; if ( *t == -SNUMBER ) { isnum = 1; k = t[1]; } else isnum = 0; } else { k = t[*t-1]; k = ABS(k); if ( k == *t-ARGHEAD-1 ) isnum = 1; else isnum = 0; k = 1; } if ( r1 >= tstop ) { /* Single argument */ if ( !isnum ) return(-1); if ( k == 0 ) goto argzero; goto argnonzero; } r2 = r1; NEXTARG(r2) if ( r2 < tstop ) return(-1); if ( *r1 < 0 ) { if ( *r1 == -SNUMBER ) { isnum2 = 1; } else isnum2 = 0; } else { k = r1[*r1-1]; k = ABS(k); if ( k == *r1-ARGHEAD-1 ) isnum2 = 1; else isnum2 = 0; } if ( isnum != isnum2 ) return(-1); tstop = r1; while ( t < tstop && r1 < r2 ) { if ( *t != *r1 ) { if ( !isnum ) return(-1); goto argnonzero; } t++; r1++; } if ( t != tstop || r1 != r2 ) { if ( !isnum ) return(-1); goto argnonzero; } argzero: if ( type == DELTA2 ) return(1); else return(0); argnonzero: if ( type == DELTA2 ) return(0); else return(1); } /* #] DoDelta : #[ DoRevert : */ void DoRevert(WORD *fun, WORD *tmp) { WORD *t, *r, *m, *to, *tt, *mm, i, j; to = fun + fun[1]; r = fun + FUNHEAD; while ( r < to ) { if ( *r <= 0 ) { if ( *r == -REVERSEFUNCTION ) { m = r; mm = m+1; while ( mm < to ) *m++ = *mm++; to--; (fun[1])--; fun[2] |= DIRTYSYMFLAG; } else if ( *r <= -FUNCTION ) r++; else { if ( *r == -INDEX && r[1] < MINSPEC ) *r = -VECTOR; r += 2; } } else { if ( ( *r > ARGHEAD ) && ( r[ARGHEAD+1] == REVERSEFUNCTION ) && ( *r == (r[ARGHEAD]+ARGHEAD) ) && ( r[ARGHEAD] == (r[ARGHEAD+2]+4) ) && ( *(r+*r-3) == 1 ) && ( *(r+*r-2) == 1 ) && ( *(r+*r-1) == 3 ) ) { mm = r; r += ARGHEAD + 1; tt = r + r[1]; r += FUNHEAD; m = tmp; t = r; j = 0; while ( t < tt ) { NEXTARG(t) j++; } while ( --j >= 0 ) { i = j; t = r; while ( --i >= 0 ) { NEXTARG(t) } if ( *t > 0 ) { i = *t; NCOPY(m,t,i); } else if ( *t <= -FUNCTION ) *m++ = *t++; else { *m++ = *t++; *m++ = *t++; } } i = WORDDIF(m,tmp); m = tmp; t = mm; r = t + *t; NCOPY(t,m,i); m = r; r = t; i = WORDDIF(to,m); NCOPY(t,m,i); fun[1] = WORDDIF(t,fun); to = t; fun[2] |= DIRTYSYMFLAG; } else r += *r; } } } /* #] DoRevert : #] Normalize : #[ DetCommu : Determines the number of terms in an expression that contain noncommuting objects. This can be used to see whether products of this expression can be evaluated with binomial coefficients. We don't try to be fancy. If a term contains noncommuting objects we are not looking whether they can commute with complete other terms. If the number gets too large we cut it off. */ #define MAXNUMBEROFNONCOMTERMS 2 WORD DetCommu(WORD *terms) { WORD *t, *tnext, *tstop; WORD num = 0; if ( *terms == 0 ) return(0); if ( terms[*terms] == 0 ) return(0); t = terms; while ( *t ) { tnext = t + *t; tstop = tnext - ABS(tnext[-1]); t++; while ( t < tstop ) { if ( *t >= FUNCTION ) { if ( functions[*t-FUNCTION].commute ) { num++; if ( num >= MAXNUMBEROFNONCOMTERMS ) return(num); break; } } else if ( *t == SUBEXPRESSION ) { if ( cbuf[t[4]].CanCommu[t[2]] ) { num++; if ( num >= MAXNUMBEROFNONCOMTERMS ) return(num); break; } } else if ( *t == EXPRESSION ) { num++; if ( num >= MAXNUMBEROFNONCOMTERMS ) return(num); break; } else if ( *t == DOLLAREXPRESSION ) { /* Technically this is not correct. We have to test first whether this is DollarLocalCopy (in TFORM) and if so, use the local version. Anyway, this should be rare to never occurring because dollars should be replaced. */ if ( cbuf[AM.dbufnum].CanCommu[t[2]] ) { num++; if ( num >= MAXNUMBEROFNONCOMTERMS ) return(num); break; } } t += t[1]; } t = tnext; } return(num); } /* #] DetCommu : #[ DoesCommu : Determines the number of noncommuting objects in a term. If the number gets too large we cut it off. */ WORD DoesCommu(WORD *term) { WORD *tstop; WORD num = 0; if ( *term == 0 ) return(0); tstop = term + *term; tstop = tstop - ABS(tstop[-1]); term++; while ( term < tstop ) { if ( ( *term >= FUNCTION ) && ( functions[*term-FUNCTION].commute ) ) { num++; if ( num >= MAXNUMBEROFNONCOMTERMS ) return(num); } term += term[1]; } return(num); } /* #] DoesCommu : #[ PolyNormPoly : Normalizes a polynomial */ #ifdef EVALUATEGCD WORD *PolyNormPoly (PHEAD WORD *Poly) { GETBIDENTITY; WORD *buffer = AT.WorkPointer; WORD *p; if ( NewSort(BHEAD0) ) { Terminate(-1); } AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); while ( *Poly ) { p = Poly + *Poly; if ( SymbolNormalize(Poly) < 0 ) return(0); if ( StoreTerm(BHEAD Poly) ) { AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); LowerSortLevel(); Terminate(-1); } Poly = p; } if ( EndSort(BHEAD buffer,1) < 0 ) { AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); Terminate(-1); } p = buffer; while ( *p ) p += *p; AR.CompareRoutine = (COMPAREDUMMY)(&Compare1); AT.WorkPointer = p + 1; return(buffer); } #endif /* #] PolyNormPoly : #[ EvaluateGcd : Try to evaluate the GCDFUNCTION gcd_. This function can have a number of arguments which can be numbers and/or polynomials. If there are objects that aren't SYMBOLS or numbers it cannot work currently. To make this work properly we have to intervene in proces.c proces.c: if ( Normalize(BHEAD m) ) { 1060 proces.c: if ( Normalize(BHEAD r) ) { 1126?proces.c: if ( Normalize(BHEAD term) ) { proces.c: if ( Normalize(BHEAD AT.WorkPointer) ) goto PasErr; 2308!proces.c: if ( ( retnorm = Normalize(BHEAD term) ) != 0 ) { proces.c: ReNumber(BHEAD term); Normalize(BHEAD term); proces.c: if ( Normalize(BHEAD v) ) Terminate(-1); proces.c: if ( Normalize(BHEAD w) ) { LowerSortLevel(); goto PolyCall; } proces.c: if ( Normalize(BHEAD term) ) goto PolyCall; */ #ifdef EVALUATEGCD WORD *EvaluateGcd(PHEAD WORD *subterm) { GETBIDENTITY WORD *oldworkpointer = AT.WorkPointer, *work1, *work2, *work3; WORD *t, *tt, *ttt, *t1, *t2, *t3, *t4, *tstop; WORD ct, nnum; UWORD gcdnum, stor; WORD *lnum=n_llnum+1; WORD *num1, *num2, *num3, *den1, *den2, *den3; WORD sizenum1, sizenum2, sizenum3, sizeden1, sizeden2, sizeden3; int i, isnumeric = 0, numarg = 0 /*, sizearg */; LONG size; /* Step 1: Look for -SNUMBER or -SYMBOL arguments. If encountered, treat everybody with it. */ tt = subterm + subterm[1]; t = subterm + FUNHEAD; while ( t < tt ) { numarg++; if ( *t == -SNUMBER ) { if ( t[1] == 0 ) { gcdzero:; MLOCK(ErrorMessageLock); MesPrint("Trying to take the GCD involving a zero term."); MUNLOCK(ErrorMessageLock); return(0); } gcdnum = ABS(t[1]); t1 = subterm + FUNHEAD; while ( gcdnum > 1 && t1 < tt ) { if ( *t1 == -SNUMBER ) { stor = ABS(t1[1]); if ( stor == 0 ) goto gcdzero; if ( GcdLong(BHEAD (UWORD *)&stor,1,(UWORD *)&gcdnum,1, (UWORD *)lnum,&nnum) ) goto FromGCD; gcdnum = lnum[0]; t1 += 2; continue; } else if ( *t1 == -SYMBOL ) goto gcdisone; else if ( *t1 < 0 ) goto gcdillegal; /* Now we have to go through all the terms in the argument. This includes long numbers. */ ttt = t1 + *t1; ct = *ttt; *ttt = 0; if ( t1[1] != 0 ) { /* First normalize the argument */ t1 = PolyNormPoly(BHEAD t1+ARGHEAD); } else t1 += ARGHEAD; while ( *t1 ) { t1 += *t1; i = ABS(t1[-1]); t2 = t1 - i; i = (i-1)/2; t3 = t2+i-1; while ( t3 > t2 && *t3 == 0 ) { t3--; i--; } if ( GcdLong(BHEAD (UWORD *)t2,(WORD)i,(UWORD *)&gcdnum,1, (UWORD *)lnum,&nnum) ) { *ttt = ct; goto FromGCD; } gcdnum = lnum[0]; if ( gcdnum == 1 ) { *ttt = ct; goto gcdisone; } } *ttt = ct; t1 = ttt; AT.WorkPointer = oldworkpointer; } if ( gcdnum == 1 ) goto gcdisone; oldworkpointer[0] = 4; oldworkpointer[1] = gcdnum; oldworkpointer[2] = 1; oldworkpointer[3] = 3; oldworkpointer[4] = 0; AT.WorkPointer = oldworkpointer + 5; return(oldworkpointer); } else if ( *t == -SYMBOL ) { t1 = subterm + FUNHEAD; i = t[1]; while ( t1 < tt ) { if ( *t1 == -SNUMBER ) goto gcdisone; if ( *t1 == -SYMBOL ) { if ( t1[1] != i ) goto gcdisone; t1 += 2; continue; } if ( *t1 < 0 ) goto gcdillegal; ttt = t1 + *t1; ct = *ttt; *ttt = 0; if ( t1[1] != 0 ) { /* First normalize the argument */ t2 = PolyNormPoly(BHEAD t1+ARGHEAD); } else t2 = t1 + ARGHEAD; while ( *t2 ) { t3 = t2+1; t2 = t2 + *t2; tstop = t2 - ABS(t2[-1]); while ( t3 < tstop ) { if ( *t3 != SYMBOL ) { *ttt = ct; goto gcdillegal; } t4 = t3 + 2; t3 += t3[1]; while ( t4 < t3 ) { if ( *t4 == i && t4[1] > 0 ) goto nextterminarg; t4 += 2; } } *ttt = ct; goto gcdisone; nextterminarg:; } *ttt = ct; t1 = ttt; AT.WorkPointer = oldworkpointer; } oldworkpointer[0] = 8; oldworkpointer[1] = SYMBOL; oldworkpointer[2] = 4; oldworkpointer[3] = t[1]; oldworkpointer[4] = 1; oldworkpointer[5] = 1; oldworkpointer[6] = 1; oldworkpointer[7] = 3; oldworkpointer[8] = 0; AT.WorkPointer = oldworkpointer+9; return(oldworkpointer); } else if ( *t < 0 ) { gcdillegal:; MLOCK(ErrorMessageLock); MesPrint("Illegal object in gcd_ function. Object not a number or a symbol."); MUNLOCK(ErrorMessageLock); goto FromGCD; } else if ( ABS(t[*t-1]) == *t-ARGHEAD-1 ) isnumeric = numarg; else if ( t[1] != 0 ) { ttt = t + *t; ct = *ttt; *ttt = 0; t = PolyNormPoly(BHEAD t+ARGHEAD); *ttt = ct; if ( t[*t] == 0 && ABS(t[*t-1]) == *t-ARGHEAD-1 ) isnumeric = numarg; AT.WorkPointer = oldworkpointer; t = ttt; } t += *t; } /* At this point there are only generic arguments. There are however still two cases: 1: There is an argument that is purely numerical In that case we have to take the gcd of all coefficients 2: All arguments are nontrivial polynomials. Here we don't worry so much about the factor. (???) We know whether case 1 occurs when isnumeric > 0. We can look up numarg to get a good starting value. */ AT.WorkPointer = oldworkpointer; if ( isnumeric ) { t = subterm + FUNHEAD; for ( i = 1; i < isnumeric; i++ ) { NEXTARG(t); } if ( t[1] != 0 ) { /* First normalize the argument */ ttt = t + *t; ct = *ttt; *ttt = 0; t = PolyNormPoly(BHEAD t+ARGHEAD); *ttt = ct; } t += *t; i = (ABS(t[-1])-1)/2; den1 = t - 1 - i; num1 = den1 - i; sizenum1 = sizeden1 = i; while ( sizenum1 > 1 && num1[sizenum1-1] == 0 ) sizenum1--; while ( sizeden1 > 1 && den1[sizeden1-1] == 0 ) sizeden1--; work1 = AT.WorkPointer+1; work2 = work1+sizenum1; for ( i = 0; i < sizenum1; i++ ) work1[i] = num1[i]; for ( i = 0; i < sizeden1; i++ ) work2[i] = den1[i]; num1 = work1; den1 = work2; AT.WorkPointer = work2 = work2 + sizeden1; t = subterm + FUNHEAD; while ( t < tt ) { ttt = t + *t; ct = *ttt; *ttt = 0; if ( t[1] != 0 ) { t = PolyNormPoly(BHEAD t+ARGHEAD); } else t += ARGHEAD; while ( *t ) { t += *t; i = (ABS(t[-1])-1)/2; den2 = t - 1 - i; num2 = den2 - i; sizenum2 = sizeden2 = i; while ( sizenum2 > 1 && num2[sizenum2-1] == 0 ) sizenum2--; while ( sizeden2 > 1 && den2[sizeden2-1] == 0 ) sizeden2--; num3 = AT.WorkPointer; if ( GcdLong(BHEAD (UWORD *)num2,sizenum2,(UWORD *)num1,sizenum1, (UWORD *)num3,&sizenum3) ) goto FromGCD; sizenum1 = sizenum3; for ( i = 0; i < sizenum1; i++ ) num1[i] = num3[i]; den3 = AT.WorkPointer; if ( GcdLong(BHEAD (UWORD *)den2,sizeden2,(UWORD *)den1,sizeden1, (UWORD *)den3,&sizeden3) ) goto FromGCD; sizeden1 = sizeden3; for ( i = 0; i < sizeden1; i++ ) den1[i] = den3[i]; if ( sizenum1 == 1 && num1[0] == 1 && sizeden1 == 1 && den1[1] == 1 ) goto gcdisone; } *ttt = ct; t = ttt; AT.WorkPointer = work2; } AT.WorkPointer = oldworkpointer; /* Now copy the GCD to the 'output' */ if ( sizenum1 > sizeden1 ) { while ( sizenum1 > sizeden1 ) den1[sizeden1++] = 0; } else if ( sizenum1 < sizeden1 ) { while ( sizenum1 < sizeden1 ) num1[sizenum1++] = 0; } t = oldworkpointer; i = 2*sizenum1+1; *t++ = i+1; if ( num1 != t ) { NCOPY(t,num1,sizenum1); } else t += sizenum1; if ( den1 != t ) { NCOPY(t,den1,sizeden1); } else t += sizeden1; *t++ = i; *t++ = 0; AT.WorkPointer = t; return(oldworkpointer); } /* Now the real stuff with only polynomials. Pick up the shortest term to start. We are a bit brutish about this. */ t = subterm + FUNHEAD; AT.WorkPointer += AM.MaxTer/sizeof(WORD); work2 = AT.WorkPointer; /* sizearg = subterm[1]; */ i = 0; work3 = 0; while ( t < tt ) { i++; work1 = AT.WorkPointer; ttt = t + *t; ct = *ttt; *ttt = 0; t = PolyNormPoly(BHEAD t+ARGHEAD); if ( *work1 < AT.WorkPointer-work1 ) { /* sizearg = AT.WorkPointer-work1; */ numarg = i; work3 = work1; } *ttt = ct; t = ttt; } *AT.WorkPointer++ = 0; /* We have properly normalized arguments and the shortest is indicated in work3 */ work1 = work3; while ( *work2 ) { if ( work2 != work3 ) { work1 = PolyGCD2(BHEAD work1,work2); } while ( *work2 ) work2 += *work2; work2++; } work2 = work1; while ( *work2 ) work2 += *work2; size = work2 - work1 + 1; t = oldworkpointer; NCOPY(t,work1,size); AT.WorkPointer = t; return(oldworkpointer); gcdisone:; oldworkpointer[0] = 4; oldworkpointer[1] = 1; oldworkpointer[2] = 1; oldworkpointer[3] = 3; oldworkpointer[4] = 0; AT.WorkPointer = oldworkpointer+5; return(oldworkpointer); FromGCD: MLOCK(ErrorMessageLock); MesCall("EvaluateGcd"); MUNLOCK(ErrorMessageLock); return(0); } #endif /* #] EvaluateGcd : #[ TreatPolyRatFun : if ( AR.PolyFunExp == 1 ) we have to trim the contents of the polyratfun down to its most divergent term and give it coefficient +1. This is done by taking the terms with the least power in the variable in the numerator and in the denominator and then combine them. Answer is either PolyRatFun(ep^n,1) or PolyRatFun(1,1) or PolyRatFun(1,ep^n) */ int TreatPolyRatFun(PHEAD WORD *prf) { WORD *t, *tstop, *r, *rstop, *m, *mstop; WORD exp1 = MAXPOWER, exp2 = MAXPOWER; t = prf+FUNHEAD; if ( *t < 0 ) { if ( *t == -SYMBOL && t[1] == AR.PolyFunVar ) { if ( exp1 > 1 ) exp1 = 1; t += 2; } else { if ( exp1 > 0 ) exp1 = 0; NEXTARG(t) } } else { tstop = t + *t; t += ARGHEAD; while ( t < tstop ) { /* Now look for the minimum power of AR.PolyFunVar */ r = t+1; t += *t; rstop = t - ABS(t[-1]); while ( r < rstop ) { if ( *r != SYMBOL ) { r += r[1]; continue; } m = r; mstop = m + m[1]; m += 2; while ( m < mstop ) { if ( *m == AR.PolyFunVar ) { if ( m[1] < exp1 ) exp1 = m[1]; break; } m += 2; } if ( m == mstop ) { if ( exp1 > 0 ) exp1 = 0; } break; } if ( r == rstop ) { if ( exp1 > 0 ) exp1 = 0; } } t = tstop; } if ( *t < 0 ) { if ( *t == -SYMBOL && t[1] == AR.PolyFunVar ) { if ( exp2 > 1 ) exp2 = 1; } else { if ( exp2 > 0 ) exp2 = 0; } } else { tstop = t + *t; t += ARGHEAD; while ( t < tstop ) { /* Now look for the minimum power of AR.PolyFunVar */ r = t+1; t += *t; rstop = t - ABS(t[-1]); while ( r < rstop ) { if ( *r != SYMBOL ) { r += r[1]; continue; } m = r; mstop = m + m[1]; m += 2; while ( m < mstop ) { if ( *m == AR.PolyFunVar ) { if ( m[1] < exp2 ) exp2 = m[1]; break; } m += 2; } if ( m == mstop ) { if ( exp2 > 0 ) exp2 = 0; } break; } if ( r == rstop ) { if ( exp2 > 0 ) exp2 = 0; } } } /* Now we can compose the output. Notice that the output can never be longer than the input provided we never can have arguments that consist of just a function. */ exp1 = exp1-exp2; /* if ( exp1 > 0 ) exp1 = 0; */ t = prf+FUNHEAD; if ( exp1 == 0 ) { *t++ = -SNUMBER; *t++ = 1; *t++ = -SNUMBER; *t++ = 1; } else if ( exp1 > 0 ) { if ( exp1 == 1 ) { *t++ = -SYMBOL; *t++ = AR.PolyFunVar; } else { *t++ = 8+ARGHEAD; *t++ = 0; FILLARG(t); *t++ = 8; *t++ = SYMBOL; *t++ = 4; *t++ = AR.PolyFunVar; *t++ = exp1; *t++ = 1; *t++ = 1; *t++ = 3; } *t++ = -SNUMBER; *t++ = 1; } else { *t++ = -SNUMBER; *t++ = 1; if ( exp1 == -1 ) { *t++ = -SYMBOL; *t++ = AR.PolyFunVar; } else { *t++ = 8+ARGHEAD; *t++ = 0; FILLARG(t); *t++ = 8; *t++ = SYMBOL; *t++ = 4; *t++ = AR.PolyFunVar; *t++ = -exp1; *t++ = 1; *t++ = 1; *t++ = 3; } } prf[2] = 0; /* Clean */ prf[1] = t - prf; return(0); } /* #] TreatPolyRatFun : #[ DropCoefficient : */ void DropCoefficient(PHEAD WORD *term) { GETBIDENTITY WORD *t = term + *term; WORD n, na; n = t[-1]; na = ABS(n); t -= na; if ( n == 3 && t[0] == 1 && t[1] == 1 ) return; *AN.RepPoint = 1; t[0] = 1; t[1] = 1; t[2] = 3; *term -= (na-3); } /* #] DropCoefficient : #[ DropSymbols : */ void DropSymbols(PHEAD WORD *term) { GETBIDENTITY WORD *tend = term + *term, *t1, *t2, *tstop; tstop = tend - ABS(tend[-1]); t1 = term+1; while ( t1 < tstop ) { if ( *t1 == SYMBOL ) { *AN.RepPoint = 1; t2 = t1+t1[1]; while ( t2 < tend ) *t1++ = *t2++; *term = t1 - term; break; } t1 += t1[1]; } } /* #] DropSymbols : #[ SymbolNormalize : */ /** * Routine normalizes terms that contain only symbols. * Regular minimum and maximum properties are ignored. * * We check whether there are negative powers in the output. * This is not allowed. */ int SymbolNormalize(WORD *term) { GETIDENTITY WORD *t, *b, *bb, *tt, *m, *tstop; // Here we use a stack-allocated array, since things are much smaller // compared to the full Normalize routine. WORD buffer[7*NORMSIZE]; int i; b = buffer; *b++ = SYMBOL; *b++ = 2; t = term + *term; tstop = t - ABS(t[-1]); t = term + 1; while ( t < tstop ) { /* Step 1: collect symbols */ if ( *t == SYMBOL && t < tstop ) { for ( i = 2; i < t[1]; i += 2 ) { const WORD sym = t[i]; const WORD pow = t[i+1]; bb = buffer+2; while ( bb < b ) { if ( bb[0] == sym ) { /* add powers */ bb[1] += pow; if ( bb[1] > MAXPOWER || bb[1] < -MAXPOWER ) { MLOCK(ErrorMessageLock); MesPrint("Power in SymbolNormalize out of range"); MUNLOCK(ErrorMessageLock); return(-1); } if ( bb[1] == 0 ) { b -= 2; while ( bb < b ) { bb[0] = bb[2]; bb[1] = bb[3]; bb += 2; } } goto Nexti; } else if ( bb[0] > sym ) { /* insert it */ m = b; while ( m > bb ) { m[1] = m[-1]; m[0] = m[-2]; m -= 2; } b += 2; bb[0] = sym; bb[1] = pow; goto Nexti; } bb += 2; } if ( bb >= b ) { /* add it to the end */ *b++ = sym; *b++ = pow; } Nexti:; } } else { MLOCK(ErrorMessageLock); MesPrint("Illegal term in SymbolNormalize"); MUNLOCK(ErrorMessageLock); return(-1); } t += t[1]; } buffer[1] = b - buffer; /* Veto negative powers */ if ( AT.LeaveNegative == 0 ) { b = buffer; bb = b + b[1]; b += 3; while ( b < bb ) { if ( *b < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Negative power in SymbolNormalize"); MUNLOCK(ErrorMessageLock); return(-1); } b += 2; } } /* Now we use the fact that the new term will not be longer than the old one Actually it should be shorter when there is more than one subterm! Copy back. */ i = buffer[1]; b = buffer; tt = term + 1; if ( i > 2 ) { NCOPY(tt,b,i) } if ( tt < tstop ) { i = term[*term-1]; if ( i < 0 ) i = -i; *term -= (tstop-tt); NCOPY(tt,tstop,i) } return(0); } /* #] SymbolNormalize : #[ TestFunFlag : Tests whether a function still has unsubstituted subexpressions This function has its dirtyflag on! */ int TestFunFlag(PHEAD WORD *tfun) { WORD *t, *tstop, *r, *rstop, *m, *mstop; if ( functions[*tfun-FUNCTION].spec <= 0 ) return(0); tstop = tfun + tfun[1]; t = tfun + FUNHEAD; while ( t < tstop ) { if ( *t < 0 ) { NEXTARG(t); continue; } rstop = t + *t; if ( t[1] == 0 ) { t = rstop; continue; } r = t + ARGHEAD; while ( r < rstop ) { /* Here we loop over terms */ m = r+1; mstop = r+*r; mstop -= ABS(mstop[-1]); while ( m < mstop ) { /* Loop over the subterms */ if ( *m == SUBEXPRESSION || *m == EXPRESSION || *m == DOLLAREXPRESSION ) return(1); if ( ( *m >= FUNCTION ) && ( ( m[2] & DIRTYFLAG ) == DIRTYFLAG ) && ( *m != REPLACEMENT ) && TestFunFlag(BHEAD m) ) return(1); m += m[1]; } r += *r; } t += *t; } return(0); } /* #] TestFunFlag : #[ BracketNormalize : */ int BracketNormalize(PHEAD WORD *term) { WORD *stop = term+*term-3, *t, *tt, *tstart, *r; WORD *oldwork = AT.WorkPointer; WORD *termout; WORD i, ii, j; termout = AT.WorkPointer = term+*term; /* First collect all functions and sort them */ tt = termout+1; t = term+1; while ( t < stop ) { if ( *t >= FUNCTION ) { i = t[1]; NCOPY(tt,t,i); } else t += t[1]; } if ( tt > termout+1 && tt-termout-1 > termout[2] ) { /* sorting */ r = termout+1; ii = tt-r; for ( i = 0; i < ii-FUNHEAD; i += FUNHEAD ) { /* Bubble sort */ for ( j = i+FUNHEAD; j > 0; j -= FUNHEAD ) { if ( functions[r[j-FUNHEAD]-FUNCTION].commute && functions[r[j]-FUNCTION].commute == 0 ) break; if ( r[j-FUNHEAD] > r[j] ) EXCH(r[j-FUNHEAD],r[j]) else break; } } } tstart = tt; t = term + 1; *tt++ = DELTA; *tt++ = 2; while ( t < stop ) { if ( *t == DELTA ) { i = t[1]-2; t += 2; tstart[1] += i; NCOPY(tt,t,i); } else t += t[1]; } if ( tstart[1] > 2 ) { for ( r = tstart+2; r < tstart+tstart[1]; r += 2 ) { if ( r[0] > r[1] ) EXCH(r[0],r[1]) } } if ( tstart[1] > 4 ) { /* sorting */ r = tstart+2; ii = tstart[1]-2; for ( i = 0; i < ii-2; i += 2 ) { /* Bubble sort */ for ( j = i+2; j > 0; j -= 2 ) { if ( r[j-2] > r[j] ) { EXCH(r[j-2],r[j]) EXCH(r[j-1],r[j+1]) } else if ( r[j-2] < r[j] ) break; else { if ( r[j-1] > r[j+1] ) EXCH(r[j-1],r[j+1]) else break; } } } tt = tstart+tstart[1]; } else if ( tstart[1] == 2 ) { tt = tstart; } else tt = tstart+4; tstart = tt; t = term + 1; *tt++ = INDEX; *tt++ = 2; while ( t < stop ) { if ( *t == INDEX ) { i = t[1]-2; t += 2; tstart[1] += i; NCOPY(tt,t,i); } else t += t[1]; } if ( tstart[1] >= 4 ) { /* sorting */ r = tstart+2; ii = tstart[1]-2; for ( i = 0; i < ii-1; i += 1 ) { /* Bubble sort */ for ( j = i+1; j > 0; j -= 1 ) { if ( r[j-1] > r[j] ) EXCH(r[j-1],r[j]) else break; } } tt = tstart+tstart[1]; } else if ( tstart[1] == 2 ) { tt = tstart; } else tt = tstart+3; tstart = tt; t = term + 1; *tt++ = DOTPRODUCT; *tt++ = 2; while ( t < stop ) { if ( *t == DOTPRODUCT ) { i = t[1]-2; t += 2; tstart[1] += i; NCOPY(tt,t,i); } else t += t[1]; } if ( tstart[1] > 5 ) { /* sorting */ r = tstart+2; ii = tstart[1]-2; for ( i = 0; i < ii; i += 3 ) { if ( r[i] > r[i+1] ) EXCH(r[i],r[i+1]) } for ( i = 0; i < ii-3; i += 3 ) { /* Bubble sort */ for ( j = i+3; j > 0; j -= 3 ) { if ( r[j-3] < r[j] ) break; if ( r[j-3] > r[j] ) { EXCH(r[j-3],r[j]) EXCH(r[j-2],r[j+1]) } else { if ( r[j-2] > r[j+1] ) EXCH(r[j-2],r[j+1]) else break; } } } tt = tstart+tstart[1]; } else if ( tstart[1] == 2 ) { tt = tstart; } else { if ( tstart[2] > tstart[3] ) EXCH(tstart[2],tstart[3]) tt = tstart+5; } tstart = tt; t = term + 1; *tt++ = SYMBOL; *tt++ = 2; while ( t < stop ) { if ( *t == SYMBOL ) { i = t[1]-2; t += 2; tstart[1] += i; NCOPY(tt,t,i); } else t += t[1]; } if ( tstart[1] > 4 ) { /* sorting */ r = tstart+2; ii = tstart[1]-2; for ( i = 0; i < ii-2; i += 2 ) { /* Bubble sort */ for ( j = i+2; j > 0; j -= 2 ) { if ( r[j-2] > r[j] ) EXCH(r[j-2],r[j]) else break; } } tt = tstart+tstart[1]; } else if ( tstart[1] == 2 ) { tt = tstart; } else tt = tstart+4; tstart = tt; t = term + 1; *tt++ = SETSET; *tt++ = 2; while ( t < stop ) { if ( *t == SETSET ) { i = t[1]-2; t += 2; tstart[1] += i; NCOPY(tt,t,i); } else t += t[1]; } if ( tstart[1] > 4 ) { /* sorting */ r = tstart+2; ii = tstart[1]-2; for ( i = 0; i < ii-2; i += 2 ) { /* Bubble sort */ for ( j = i+2; j > 0; j -= 2 ) { if ( r[j-2] > r[j] ) { EXCH(r[j-2],r[j]) EXCH(r[j-1],r[j+1]) } else break; } } tt = tstart+tstart[1]; } else if ( tstart[1] == 2 ) { tt = tstart; } else tt = tstart+4; *tt++ = 1; *tt++ = 1; *tt++ = 3; t = term; i = *termout = tt - termout; tt = termout; NCOPY(t,tt,i); AT.WorkPointer = oldwork; return(0); } /* #] BracketNormalize : */ form-5.0.1/sources/dollar.c0000644000175100017510000031731215217035721011261 /** @file dollar.c * * The routines that deal with the dollar variables. * The name administration is to be found in the file names.c */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include "form3.h" static UBYTE underscore[2] = {'_',0}; /* #] Includes : #[ CatchDollar : Works out a dollar expression during compile type. Steals it from the buffer and puts it in an assignment. At the moment we should keep this inside the small buffer. Later with more sort buffers we can do this better. Par == 0 : regular assignment par == -1: after error. Just make zero for now. */ int CatchDollar(int par) { GETIDENTITY CBUF *C = cbuf + AC.cbufnum; int error = 0, numterms = 0, numdollar, resetmods = 0; LONG newsize, retval; WORD *w, *t, n, nsize, *oldwork = AT.WorkPointer, *dbuffer; WORD oldncmod = AN.ncmod; DOLLARS d; if ( AN.ncmod && ( ( AC.modmode & ALSODOLLARS ) == 0 ) ) AN.ncmod = 0; if ( AN.ncmod && AN.cmod == 0 ) { SetMods(); resetmods = 1; } numdollar = C->lhs[C->numlhs][2]; d = Dollars+numdollar; if ( par == -1 ) { d->type = DOLUNDEFINED; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"$-buffer old"); d->size = 0; d->where = &(AM.dollarzero); cbuf[AM.dbufnum].rhs[numdollar] = d->where; AN.ncmod = oldncmod; if ( resetmods ) UnSetMods(); return(0); } #ifdef WITHMPI /* * The problem here is that only the master can make an assignment * like #$a=g; where g is an expression: only the master has an access to * the expression. So, in cases where the RHS contains expression names, * only the master invokes Generator() and then broadcasts the result to * the all slaves. * Broadcasting must be performed immediately; one cannot postpone it * to the end of the module because the dollar variable is visible * in the current module. For the same reason, this should be done * regardless of on/off parallel status. * If the RHS does not contain any expression names, it can be processed * in each slave. */ if ( PF.me == MASTER || !AC.RhsExprInModuleFlag ) { #endif EXCHINOUT if ( NewSort(BHEAD0) ) { if ( !error ) error = 1; goto onerror; } if ( NewSort(BHEAD0) ) { LowerSortLevel(); if ( !error ) error = 1; goto onerror; } AN.RepPoint = AT.RepCount + 1; w = C->rhs[C->lhs[C->numlhs][5]]; while ( *w ) { n = *w; t = oldwork; NCOPY(t,w,n) AT.WorkPointer = t; AR.Cnumlhs = C->numlhs; if ( Generator(BHEAD oldwork,C->numlhs) ) { error = 1; break; } } AT.WorkPointer = oldwork; AN.tryterm = 0; /* for now */ dbuffer = 0; if ( ( retval = EndSort(BHEAD (WORD *)((void *)(&dbuffer)),2) ) < 0 ) { error = 1; } LowerSortLevel(); if ( retval <= 1 || dbuffer == 0 ) { d->type = DOLZERO; if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"$-buffer old"); d->size = 0; d->where = &(AM.dollarzero); cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; goto docopy2; } w = dbuffer; if ( error == 0 ) while ( *w ) { w += *w; numterms++; } else goto onerror; newsize = (w-dbuffer)+1; #ifdef WITHMPI } if ( AC.RhsExprInModuleFlag ) /* PF_BroadcastPreDollar allocates dbuffer for slaves! */ if ( (error = PF_BroadcastPreDollar(&dbuffer, &newsize, &numterms)) != 0 ) goto onerror; #endif if ( newsize < MINALLOC ) newsize = MINALLOC; newsize = ((newsize+7)/8)*8; if ( numterms == 0 ) { d->type = DOLZERO; goto docopy; } else if ( numterms == 1 ) { t = dbuffer; n = *t; nsize = t[n-1]; if ( nsize < 0 ) { nsize = -nsize; } if ( nsize == (n-1) ) { /* numerical */ nsize = (nsize-1)/2; w = t + 1 + nsize; if ( *w != 1 ) goto doterms; w++; while ( w < ( t + n - 1 ) ) { if ( *w ) break; w++; } if ( w < ( t + n - 1 ) ) goto doterms; d->type = DOLNUMBER; goto docopy; } else if ( n == 7 && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[1] == INDEX && t[2] == 3 ) { d->type = DOLINDEX; d->index = t[3]; goto docopy; } else goto doterms; } else { doterms:; d->type = DOLTERMS; cbuf[AM.dbufnum].CanCommu[numdollar] = numcommute(dbuffer, &(cbuf[AM.dbufnum].NumTerms[numdollar])); docopy:; if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"$-buffer old"); d->size = newsize; d->where = dbuffer; docopy2:; cbuf[AM.dbufnum].rhs[numdollar] = d->where; } if ( C->Pointer > C->rhs[C->numrhs] ) C->Pointer = C->rhs[C->numrhs]; C->numlhs--; C->numrhs--; onerror: #ifdef WITHMPI if ( PF.me == MASTER || !AC.RhsExprInModuleFlag ) #endif BACKINOUT AN.ncmod = oldncmod; if ( resetmods ) UnSetMods(); return(error); } /* #] CatchDollar : #[ AssignDollar : To be called from Generator. Assigns an expression to a $ variable. This one is slightly different from CatchDollar. We have no easy buffer this time. We will have to hack our way using what we normally use for functions. Note that in the threaded case we trust the user. That means that we are not going to recheck whether there is a maximum, minimum or sum. If the user says it is like that, we treat it like that. We only check that in this centralized version MODLOCAL isn't used. In a later stage dtype could be used for actually checking MODMAX and MODMIN cases. */ int AssignDollar(PHEAD WORD *term, WORD level) { GETBIDENTITY CBUF *C = cbuf+AM.rbufnum; int numterms = 0, numdollar = C->lhs[level][2]; LONG newsize; DOLLARS d = Dollars + numdollar; WORD *w, *t, n, nsize, *rh = cbuf[C->lhs[level][7]].rhs[C->lhs[level][5]]; WORD *ss, *ww; WORD olddefer, oldcompress, oldncmod = AN.ncmod; #ifdef WITHPTHREADS int nummodopt, dtype = -1, dw; WORD numvalue; if ( AN.ncmod && ( ( AC.modmode & ALSODOLLARS ) == 0 ) ) AN.ncmod = 0; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { /* Here we come only when the module runs with more than one thread. This must be a variable with a special module option. For the multi-threaded version we only allow MODSUM, MODMAX and MODMIN. */ for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt >= NumModOptdollars ) { MLOCK(ErrorMessageLock); MesPrint("Illegal attempt to change $-variable in multi-threaded module %l",AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } #endif DUMMYUSE(term); w = rh; /* First some shortcuts */ if ( *w == 0 ) { /* #[ Thread version : Zero case */ #ifdef WITHPTHREADS if ( dtype > 0 ) { if ( ! DollarLocalCopy(dtype) ) { LOCK(d->pthreadslock); } NewValIsZero:; switch ( d->type ) { case DOLZERO: goto NoChangeZero; case DOLNUMBER: case DOLTERMS: if ( ( dw = d->where[0] ) > 0 && d->where[dw] != 0 ) { break; /* was not a single number. Trust the user */ } if ( dtype == MODMAX && d->where[dw-1] >= 0 ) goto NoChangeZero; if ( dtype == MODMIN && d->where[dw-1] <= 0 ) goto NoChangeZero; break; default: numvalue = DolToNumber(BHEAD numdollar); if ( AN.ErrorInDollar != 0 ) break; if ( dtype == MODMAX && numvalue >= 0 ) goto NoChangeZero; if ( dtype == MODMIN && numvalue <= 0 ) goto NoChangeZero; break; } d->type = DOLZERO; d->where[0] = 0; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; NoChangeZero:; CleanDollarFactors(d); if ( ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } AN.ncmod = oldncmod; return(0); } #endif /* #] Thread version : */ d->type = DOLZERO; d->where[0] = 0; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; CleanDollarFactors(d); AN.ncmod = oldncmod; return(0); } else if ( *w == 4 && w[4] == 0 && w[2] == 1 ) { /* #[ Thread version : New value is 'single precision' */ #ifdef WITHPTHREADS if ( dtype > 0 ) { if ( ! DollarLocalCopy(dtype) ) { LOCK(d->pthreadslock); } if ( d->size < MINALLOC ) { WORD oldsize, *oldwhere, i; oldsize = d->size; oldwhere = d->where; d->size = MINALLOC; d->where = (WORD *)Malloc1(d->size*sizeof(WORD),"dollar contents"); cbuf[AM.dbufnum].rhs[numdollar] = d->where; if ( oldsize > 0 ) { for ( i = 0; i < oldsize; i++ ) d->where[i] = oldwhere[i]; } else d->where[0] = 0; if ( oldwhere && oldwhere != &(AM.dollarzero) ) M_free(oldwhere,"dollar contents"); } switch ( d->type ) { case DOLZERO: HandleDolZero:; if ( dtype == MODMAX && w[3] <= 0 ) goto NoChangeOne; if ( dtype == MODMIN && w[3] >= 0 ) goto NoChangeOne; break; case DOLNUMBER: case DOLTERMS: if ( ( dw = d->where[0] ) > 0 && d->where[dw] != 0 ) { break; /* was not a single number. Trust the user */ } if ( dtype == MODMAX && CompCoef(d->where,w) >= 0 ) goto NoChangeOne; if ( dtype == MODMIN && CompCoef(d->where,w) <= 0 ) goto NoChangeOne; break; default: { /* Note that we convert the type for the next time around. */ WORD extraterm[4]; numvalue = DolToNumber(BHEAD numdollar); if ( AN.ErrorInDollar != 0 ) break; if ( numvalue == 0 ) { d->type = DOLZERO; d->where[0] = 0; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; goto HandleDolZero; } d->where[0] = extraterm[0] = 4; d->where[1] = extraterm[1] = ABS(numvalue); d->where[2] = extraterm[2] = 1; d->where[3] = extraterm[3] = numvalue > 0 ? 3 : -3; d->where[4] = 0; d->type = DOLNUMBER; if ( dtype == MODMAX && CompCoef(extraterm,w) >= 0 ) goto NoChangeOne; if ( dtype == MODMIN && CompCoef(extraterm,w) <= 0 ) goto NoChangeOne; break; } } d->where[0] = w[0]; d->where[1] = w[1]; d->where[2] = w[2]; d->where[3] = w[3]; d->where[4] = 0; d->type = DOLNUMBER; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 1; NoChangeOne:; CleanDollarFactors(d); if ( ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } AN.ncmod = oldncmod; return(0); } #endif /* #] Thread version : */ if ( d->size < MINALLOC ) { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollar contents"); d->size = MINALLOC; d->where = (WORD *)Malloc1(d->size*sizeof(WORD),"dollar contents"); cbuf[AM.dbufnum].rhs[numdollar] = d->where; } d->where[0] = w[0]; d->where[1] = w[1]; d->where[2] = w[2]; d->where[3] = w[3]; d->where[4] = 0; d->type = DOLNUMBER; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 1; CleanDollarFactors(d); AN.ncmod = oldncmod; return(0); } /* Now the real evaluation. We need to lock here before we work out the RHS, in case the RHS itself depends on the dollar variable. */ #ifdef WITHPTHREADS if ( ! DollarLocalCopy(dtype) ) { LOCK(d->pthreadslock); } #endif CleanDollarFactors(d); /* The following case cannot occur. We treated it already if ( *w == 0 ) { ss = 0; numterms = 0; newsize = 0; olddefer = AR.DeferFlag; AR.DeferFlag = 0; oldcompress = AR.NoCompress; AR.NoCompress = 1; } else */ { /* New value is an expression that has to be evaluated first This is all generic. It won't foliate due to the sort level */ if ( NewSort(BHEAD0) ) { AN.ncmod = oldncmod; return(1); } olddefer = AR.DeferFlag; AR.DeferFlag = 0; oldcompress = AR.NoCompress; AR.NoCompress = 1; while ( *w ) { n = *w; t = ww = AT.WorkPointer; NCOPY(t,w,n); AT.WorkPointer = t; if ( Generator(BHEAD ww,AR.Cnumlhs) ) { AT.WorkPointer = ww; LowerSortLevel(); AR.DeferFlag = olddefer; AN.ncmod = oldncmod; return(1); } AT.WorkPointer = ww; } AN.tryterm = 0; /* for now */ if ( ( newsize = EndSort(BHEAD (WORD *)((void *)(&ss)),2) ) < 0 ) { AN.ncmod = oldncmod; return(1); } numterms = 0; t = ss; while ( *t ) { numterms++; t += *t; } } if ( numterms == 0 ) { /* the new value evaluates to zero */ #ifdef WITHPTHREADS if ( dtype == MODMAX || dtype == MODMIN ) { if ( ss ) { M_free(ss,"Sort of $"); ss = 0; } AR.DeferFlag = olddefer; AR.NoCompress = oldcompress; goto NewValIsZero; } else #endif { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollar contents"); d->where = &(AM.dollarzero); d->size = 0; cbuf[AM.dbufnum].rhs[numdollar] = 0; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; d->type = DOLZERO; } if ( ss ) { M_free(ss,"Sort of $"); ss = 0; } } else { /* #[ Thread version : */ #ifdef WITHPTHREADS if ( dtype == MODMAX || dtype == MODMIN ) { if ( numterms == 1 && ( *ss-1 == ABS(ss[*ss-1]) ) ) { /* is number */ switch ( d->type ) { case DOLZERO: HandleDolZero1:; if ( dtype == MODMAX && ss[*ss-1] > 0 ) break; if ( dtype == MODMIN && ss[*ss-1] < 0 ) break; if ( ss ) { M_free(ss,"Sort of $"); ss = 0; } AR.DeferFlag = olddefer; AR.NoCompress = oldcompress; goto NoChange; case DOLTERMS: case DOLNUMBER: if ( ( dw = d->where[0] ) > 0 && d->where[dw] != 0 ) break; if ( dtype == MODMAX && CompCoef(ss,d->where) > 0 ) break; if ( dtype == MODMIN && CompCoef(ss,d->where) < 0 ) break; if ( ss ) { M_free(ss,"Sort of $"); ss = 0; } AR.DeferFlag = olddefer; AR.NoCompress = oldcompress; goto NoChange; default: { WORD extraterm[4]; numvalue = DolToNumber(BHEAD numdollar); if ( AN.ErrorInDollar != 0 ) break; if ( numvalue == 0 ) { d->type = DOLZERO; d->where[0] = 0; cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 0; goto HandleDolZero1; } d->where[0] = extraterm[0] = 4; d->where[1] = extraterm[1] = ABS(numvalue); d->where[2] = extraterm[2] = 1; d->where[3] = extraterm[3] = numvalue > 0 ? 3 : -3; d->where[4] = 0; d->type = DOLNUMBER; if ( dtype == MODMAX && CompCoef(ss,extraterm) > 0 ) break; if ( dtype == MODMIN && CompCoef(ss,extraterm) < 0 ) break; if ( ss ) { M_free(ss,"Sort of $"); ss = 0; } AR.DeferFlag = olddefer; AR.NoCompress = oldcompress; goto NoChange; } } } else { if ( ss ) { M_free(ss,"Sort of $"); ss = 0; } AR.DeferFlag = olddefer; AR.NoCompress = oldcompress; goto NoChange; } } #endif /* #] Thread version : */ d->type = DOLTERMS; if ( d->where && d->where != &(AM.dollarzero) ) { M_free(d->where,"dollar contents"); d->where = 0; } d->size = newsize + 1; d->where = ss; cbuf[AM.dbufnum].rhs[numdollar] = w = d->where; } AR.DeferFlag = olddefer; AR.NoCompress = oldcompress; /* Now find the special cases */ if ( numterms == 0 ) { d->type = DOLZERO; } else if ( numterms == 1 ) { t = d->where; n = *t; nsize = t[n-1]; if ( nsize < 0 ) { nsize = -nsize; } if ( nsize == (n-1) ) { nsize = (nsize-1)/2; w = t + 1 + nsize; if ( *w == 1 ) { w++; while ( w < ( t + n - 1 ) ) { if ( *w ) break; w++; } if ( w >= ( t + n - 1 ) ) d->type = DOLNUMBER; } } else if ( n == 7 && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[1] == INDEX && t[2] == 3 ) { d->type = DOLINDEX; d->index = t[3]; } } if ( d->type == DOLTERMS ) { cbuf[AM.dbufnum].CanCommu[numdollar] = numcommute(d->where, &(cbuf[AM.dbufnum].NumTerms[numdollar])); } else { cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 1; } #ifdef WITHPTHREADS NoChange:; if ( ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif AN.ncmod = oldncmod; return(0); } /* #] AssignDollar : #[ WriteDollarToBuffer : Takes the numbered dollar expression and writes it to output. We catch however the output in a buffer and return its address. This routine is needed when we need a text representation of a dollar expression like for the construction `$name' in the preprocessor. If par==0 we leave the current printing mode. If par==1 we insist on normal mode */ UBYTE *WriteDollarToBuffer(WORD numdollar, WORD par) { DOLLARS d = Dollars+numdollar; UBYTE *s, *oldcurbufwrt = AO.CurBufWrt; WORD *t, lbrac = 0, first = 0, arg[2], oldOutputMode = AC.OutputMode; WORD oldinfbrack = AO.InFbrack; int error = 0; int dict = AO.CurrentDictionary; AO.DollarOutSizeBuffer = 32; AO.DollarOutBuffer = (UBYTE *)Malloc1(AO.DollarOutSizeBuffer,"DollarOutBuffer"); AO.DollarInOutBuffer = 1; AO.PrintType = 1; AO.InFbrack = 0; s = AO.DollarOutBuffer; *s = 0; if ( par > 0 && AO.CurDictInDollars == 0 ) { AC.OutputMode = NORMALFORMAT; AO.CurrentDictionary = 0; } else { AO.CurBufWrt = (UBYTE *)underscore; } AO.OutInBuffer = 1; switch ( d->type ) { case DOLARGUMENT: WriteArgument(d->where); break; case DOLSUBTERM: WriteSubTerm(d->where,1); break; case DOLNUMBER: case DOLTERMS: t = d->where; while ( *t ) { if ( WriteTerm(t,&lbrac,first,PRINTON,0) ) { error = 1; break; } t += *t; } break; case DOLWILDARGS: t = d->where+1; while ( *t ) { WriteArgument(t); NEXTARG(t) if ( *t ) TokenToLine((UBYTE *)(",")); } break; case DOLINDEX: arg[0] = -INDEX; arg[1] = d->index; WriteArgument(arg); break; case DOLZERO: *s++ = '0'; *s = 0; AO.DollarInOutBuffer = 1; break; case DOLUNDEFINED: *s = 0; AO.DollarInOutBuffer = 1; break; } AC.OutputMode = oldOutputMode; AO.OutInBuffer = 0; AO.InFbrack = oldinfbrack; AO.CurBufWrt = oldcurbufwrt; AO.CurrentDictionary = dict; if ( error ) { MLOCK(ErrorMessageLock); MesPrint("&Illegal dollar object for writing"); MUNLOCK(ErrorMessageLock); M_free(AO.DollarOutBuffer,"DollarOutBuffer"); AO.DollarOutBuffer = 0; AO.DollarOutSizeBuffer = 0; return(0); } return(AO.DollarOutBuffer); } /* #] WriteDollarToBuffer : #[ WriteDollarFactorToBuffer : Takes the numbered dollar expression and writes it to output. We catch however the output in a buffer and return its address. This routine is needed when we need a text representation of a dollar expression like for the construction `$name' in the preprocessor. If par==0 we leave the current printing mode. If par==1 we insist on normal mode */ UBYTE *WriteDollarFactorToBuffer(WORD numdollar, WORD numfac, WORD par) { DOLLARS d = Dollars+numdollar; UBYTE *s, *oldcurbufwrt = AO.CurBufWrt; WORD *t, lbrac = 0, first = 0, n[5], oldOutputMode = AC.OutputMode; WORD oldinfbrack = AO.InFbrack; int error = 0; int dict = AO.CurrentDictionary; if ( numfac > d->nfactors || numfac < 0 ) { MLOCK(ErrorMessageLock); MesPrint("&Illegal factor number for this dollar variable: %d",numfac); MesPrint("&There are %d factors",d->nfactors); MUNLOCK(ErrorMessageLock); return(0); } AO.DollarOutSizeBuffer = 32; AO.DollarOutBuffer = (UBYTE *)Malloc1(AO.DollarOutSizeBuffer,"DollarOutBuffer"); AO.DollarInOutBuffer = 1; AO.PrintType = 1; AO.InFbrack = 0; s = AO.DollarOutBuffer; *s = 0; if ( par > 0 ) { AC.OutputMode = NORMALFORMAT; AO.CurrentDictionary = 0; } else { AO.CurBufWrt = (UBYTE *)underscore; } AO.OutInBuffer = 1; if ( numfac == 0 ) { /* write the number d->nfactors */ n[0] = 4; n[1] = d->nfactors; n[2] = 1; n[3] = 3; n[4] = 0; t = n; } else if ( numfac == 1 && d->factors == 0 ) { /* Here d->factors is zero and d->where is fine */ t = d->where; } else if ( d->factors[numfac-1].where == 0 ) { /* write the value */ if ( d->factors[numfac-1].value < 0 ) { n[0] = 4; n[1] = -d->factors[numfac-1].value; n[2] = 1; n[3] = -3; n[4] = 0; t = n; } else { n[0] = 4; n[1] = d->factors[numfac-1].value; n[2] = 1; n[3] = 3; n[4] = 0; t = n; } } else { t = d->factors[numfac-1].where; } while ( *t ) { if ( WriteTerm(t,&lbrac,first,PRINTON,0) ) { error = 1; break; } t += *t; } AC.OutputMode = oldOutputMode; AO.OutInBuffer = 0; AO.InFbrack = oldinfbrack; AO.CurBufWrt = oldcurbufwrt; AO.CurrentDictionary = dict; if ( error ) { MLOCK(ErrorMessageLock); MesPrint("&Illegal dollar object for writing"); MUNLOCK(ErrorMessageLock); M_free(AO.DollarOutBuffer,"DollarOutBuffer"); AO.DollarOutBuffer = 0; AO.DollarOutSizeBuffer = 0; return(0); } return(AO.DollarOutBuffer); } /* #] WriteDollarFactorToBuffer : #[ AddToDollarBuffer : */ void AddToDollarBuffer(UBYTE *s) { int i; UBYTE *t = s, *u, *newdob; LONG j; while ( *t ) { t++; } i = t - s; while ( i + AO.DollarInOutBuffer >= AO.DollarOutSizeBuffer ) { j = AO.DollarInOutBuffer; AO.DollarOutSizeBuffer *= 2; t = AO.DollarOutBuffer; newdob = (UBYTE *)Malloc1(AO.DollarOutSizeBuffer,"DollarOutBuffer"); u = newdob; while ( --j >= 0 ) *u++ = *t++; M_free(AO.DollarOutBuffer,"DollarOutBuffer"); AO.DollarOutBuffer = newdob; } t = AO.DollarOutBuffer + AO.DollarInOutBuffer-1; while ( t == AO.DollarOutBuffer && ( *s == '+' || *s == ' ' ) ) s++; i = 0; if ( AO.CurrentDictionary == 0 ) { while ( *s ) { if ( *s == ' ' ) { s++; continue; } *t++ = *s++; i++; } } else { while ( *s ) { *t++ = *s++; i++; } } *t = 0; AO.DollarInOutBuffer += i; } /* #] AddToDollarBuffer : #[ TermAssign : This routine is called from a piece of code in Normalize that has been commented out. */ void TermAssign(WORD *term) { DOLLARS d; WORD *t, *tstop, *astop, *w, *m; WORD i, newsize; for (;;) { astop = term + *term; tstop = astop - ABS(astop[-1]); t = term + 1; while ( t < tstop ) { if ( *t == AM.termfunnum && t[1] == FUNHEAD+2 && t[FUNHEAD] == -DOLLAREXPRESSION ) { d = Dollars + t[FUNHEAD+1]; newsize = *term - FUNHEAD - 1; if ( newsize < MINALLOC ) newsize = MINALLOC; newsize = ((newsize+7)/8)*8; if ( d->size > 2*newsize && d->size > 1000 ) { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollar contents"); d->size = 0; d->where = &(AM.dollarzero); } if ( d->size < newsize ) { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollar contents"); d->size = newsize; d->where = (WORD *)Malloc1(newsize*sizeof(WORD),"dollar contents"); } cbuf[AM.dbufnum].rhs[t[FUNHEAD+1]] = w = d->where; m = term; while ( m < t ) *w++ = *m++; m += t[1]; while ( m < tstop ) { if ( *m == AM.termfunnum && m[1] == FUNHEAD+2 && m[FUNHEAD] == -DOLLAREXPRESSION ) { m += m[1]; } else { i = m[1]; while ( --i >= 0 ) *w++ = *m++; } } while ( m < astop ) *w++ = *m++; *(d->where) = w - d->where; *w = 0; d->type = DOLTERMS; w = t; m = t + t[1]; while ( m < astop ) *w++ = *m++; *term = w - term; break; } t += t[1]; } if ( t >= tstop ) return; } } /* #] TermAssign : #[ PutTermInDollar : We assume here that the dollar is local. */ int PutTermInDollar(WORD *term, WORD numdollar) { DOLLARS d = Dollars+numdollar; WORD i; if ( term == 0 || *term == 0 ) { d->type = DOLZERO; return(0); } if ( d->size < *term || d->size > 2*term[0] || d->where == 0 ) { if ( d->size > 0 && d->where ) { M_free(d->where,"dollar contents"); } d->where = Malloc1((term[0]+1)*sizeof(WORD),"dollar contents"); d->size = term[0]+1; } d->type = DOLTERMS; for ( i = 0; i < term[0]; i++ ) d->where[i] = term[i]; d->where[i] = 0; return(0); } /* #] PutTermInDollar : #[ WildDollars : Note that we cannot upload wildcards into dollar variables when WITHPTHREADS. */ void WildDollars(PHEAD WORD *term) { GETBIDENTITY DOLLARS d; WORD *m, *t, *w, *ww, *orig = 0, *wildvalue, *wildstop; int numdollar; LONG weneed, i; #ifdef WITHPTHREADS int dtype = -1; #endif if ( term == 0 ) { m = wildvalue = AN.WildValue; wildstop = AN.WildStop; } else { ww = term + *term; ww -= ABS(ww[-1]); w = term+1; while ( w < ww && *w != SUBEXPRESSION ) w += w[1]; if ( w >= ww ) return; wildstop = w + w[1]; w += SUBEXPSIZE; wildvalue = m = w; } while ( m < wildstop ) { if ( *m != LOADDOLLAR ) { m += m[1]; continue; } t = m - 4; while ( *t == LOADDOLLAR || *t == FROMSET || *t == SETTONUM ) t -= 4; if ( t < wildvalue ) { MLOCK(ErrorMessageLock); MesPrint("&Serious bug in wildcard prototype. Found in WildDollars"); MUNLOCK(ErrorMessageLock); Terminate(-1); } numdollar = m[2]; d = Dollars + numdollar; #ifdef WITHPTHREADS { int nummodopt; dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { MLOCK(ErrorMessageLock); MesPrint("&Illegal attempt to use $-variable %s in module %l", DOLLARNAME(Dollars,numdollar),AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } } #endif /* The value of this wildcard goes into our $-variable First compute the space we need. */ switch ( *t ) { case SYMTONUM: weneed = 5; break; case SYMTOSYM: weneed = 9; break; case SYMTOSUB: case VECTOSUB: case INDTOSUB: orig = cbuf[AT.ebufnum].rhs[t[3]]; w = orig; while ( *w ) w += *w; weneed = w - orig + 1; break; case VECTOMIN: case VECTOVEC: case INDTOIND: weneed = 8; break; case FUNTOFUN: weneed = FUNHEAD+5; break; case ARGTOARG: orig = cbuf[AT.ebufnum].rhs[t[3]]; if ( *orig > 0 ) weneed = *orig+2; else { w = orig+1; while ( *w ) { NEXTARG(w) } weneed = w - orig + 1; } break; default: weneed = MINALLOC; break; } if ( weneed < MINALLOC ) weneed = MINALLOC; weneed = ((weneed+7)/8)*8; if ( d->size > 2*weneed && d->size > 1000 ) { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollarspace"); d->where = &(AM.dollarzero); d->size = 0; } if ( d->size < weneed ) { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollarspace"); d->where = (WORD *)Malloc1(weneed*sizeof(WORD),"dollarspace"); d->size = weneed; } /* It is not clear what the following code does for TFORM if ( dtype != MODLOCAL ) { */ cbuf[AM.dbufnum].CanCommu[numdollar] = 0; cbuf[AM.dbufnum].NumTerms[numdollar] = 1; /* cbuf[AM.dbufnum].rhs[numdollar] = d->where; */ cbuf[AM.dbufnum].rhs[numdollar] = (WORD *)(1); /* } Now load up the value of the wildcard in compiler buffer format */ w = d->where; d->type = DOLTERMS; switch ( *t ) { case SYMTONUM: d->where[0] = 4; d->where[2] = 1; if ( t[3] >= 0 ) { d->where[1] = t[3]; d->where[3] = 3; } else { d->where[1] = -t[3]; d->where[3] = -3; } if ( t[3] == 0 ) { d->type = DOLZERO; d->where[0] = 0; } else { d->type = DOLNUMBER; d->where[4] = 0; } break; case SYMTOSYM: *w++ = 8; *w++ = SYMBOL; *w++ = 4; *w++ = t[3]; *w++ = 1; *w++ = 1; *w++ = 1; *w++ = 3; *w = 0; break; case SYMTOSUB: case VECTOSUB: case INDTOSUB: while ( *orig ) { i = *orig; while ( --i >= 0 ) *w++ = *orig++; } *w = 0; /* And then we have to fix up CanCommu */ break; case VECTOMIN: *w++ = 7; *w++ = INDEX; *w++ = 3; *w++ = t[3]; *w++ = 1; *w++ = 1; *w++ = -3; *w = 0; break; case VECTOVEC: *w++ = 7; *w++ = INDEX; *w++ = 3; *w++ = t[3]; *w++ = 1; *w++ = 1; *w++ = 3; *w = 0; break; case INDTOIND: d->type = DOLINDEX; d->index = t[3]; *w = 0; break; case FUNTOFUN: *w++ = FUNHEAD+4; *w++ = t[3]; *w++ = FUNHEAD; FILLFUN(w) *w++ = 1; *w++ = 1; *w++ = 3; *w = 0; break; case ARGTOARG: if ( *orig > 0 ) ww = orig + *orig + 1; else { ww = orig+1; while ( *ww ) { NEXTARG(ww) } } while ( orig < ww ) *w++ = *orig++; *w = 0; d->type = DOLWILDARGS; break; default: d->type = DOLUNDEFINED; break; } m += m[1]; } } /* #] WildDollars : #[ DolToTensor : with LOCK */ WORD DolToTensor(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; WORD retval; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif AN.ErrorInDollar = 0; if ( d->type == DOLTERMS && d->where[0] == FUNHEAD+4 && d->where[FUNHEAD+4] == 0 && d->where[FUNHEAD+3] == 3 && d->where[FUNHEAD+2] == 1 && d->where[FUNHEAD+1] == 1 && d->where[1] >= FUNCTION && d->where[1] < FUNCTION+WILDOFFSET && functions[d->where[1]-FUNCTION].spec >= TENSORFUNCTION ) { retval = d->where[1]; } else if ( d->type == DOLARGUMENT && d->where[0] <= -FUNCTION && d->where[0] > -FUNCTION-WILDOFFSET && functions[-d->where[0]-FUNCTION].spec >= TENSORFUNCTION ) { retval = -d->where[0]; } else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] <= -FUNCTION && d->where[1] > -FUNCTION-WILDOFFSET && d->where[2] == 0 && functions[-d->where[1]-FUNCTION].spec >= TENSORFUNCTION ) { retval = -d->where[1]; } else if ( d->type == DOLSUBTERM && d->where[0] >= FUNCTION && d->where[0] < FUNCTION+WILDOFFSET && functions[d->where[0]-FUNCTION].spec >= TENSORFUNCTION ) { retval = d->where[0]; } else { AN.ErrorInDollar = 1; retval = 0; } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(retval); } /* #] DolToTensor : #[ DolToFunction : with LOCK */ WORD DolToFunction(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; WORD retval; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif AN.ErrorInDollar = 0; if ( d->type == DOLTERMS && d->where[0] == FUNHEAD+4 && d->where[FUNHEAD+4] == 0 && d->where[FUNHEAD+3] == 3 && d->where[FUNHEAD+2] == 1 && d->where[FUNHEAD+1] == 1 && d->where[1] >= FUNCTION && d->where[1] < FUNCTION+WILDOFFSET ) { retval = d->where[1]; } else if ( d->type == DOLARGUMENT && d->where[0] <= -FUNCTION && d->where[0] > -FUNCTION-WILDOFFSET ) { retval = -d->where[0]; } else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] <= -FUNCTION && d->where[1] > -FUNCTION-WILDOFFSET && d->where[2] == 0 ) { retval = -d->where[1]; } else if ( d->type == DOLSUBTERM && d->where[0] >= FUNCTION && d->where[0] < FUNCTION+WILDOFFSET ) { retval = d->where[0]; } else { AN.ErrorInDollar = 1; retval = 0; } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(retval); } /* #] DolToFunction : #[ DolToVector : with LOCK */ WORD DolToVector(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; WORD retval; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif AN.ErrorInDollar = 0; if ( d->type == DOLINDEX && d->index < 0 ) { retval = d->index; } else if ( d->type == DOLARGUMENT && ( d->where[0] == -VECTOR || d->where[0] == -MINVECTOR ) ) { retval = d->where[1]; } else if ( d->type == DOLSUBTERM && d->where[0] == INDEX && d->where[1] == 3 && d->where[2] < 0 ) { retval = d->where[2]; } else if ( d->type == DOLTERMS && d->where[0] == 7 && d->where[7] == 0 && d->where[6] == 3 && d->where[5] == 1 && d->where[4] == 1 && d->where[1] >= INDEX && d->where[3] < 0 ) { retval = d->where[3]; } else if ( d->type == DOLWILDARGS && d->where[0] == 0 && ( d->where[1] == -VECTOR || d->where[1] == -MINVECTOR ) && d->where[3] == 0 ) { retval = d->where[2]; } else if ( d->type == DOLWILDARGS && d->where[0] == 1 && d->where[1] < 0 ) { retval = d->where[1]; } else { AN.ErrorInDollar = 1; retval = 0; } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(retval); } /* #] DolToVector : #[ DolToNumber : */ WORD DolToNumber(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } #endif AN.ErrorInDollar = 0; if ( ( d->type == DOLTERMS || d->type == DOLNUMBER ) && d->where[0] == 4 && d->where[4] == 0 && ( d->where[3] == 3 || d->where[3] == -3 ) && d->where[2] == 1 && ( d->where[1] & TOPBITONLY ) == 0 ) { if ( d->where[3] > 0 ) return(d->where[1]); else return(-d->where[1]); } else if ( d->type == DOLARGUMENT && d->where[0] == -SNUMBER ) { return(d->where[1]); } else if ( d->type == DOLARGUMENT && d->where[0] == -INDEX && d->where[1] >= 0 && d->where[1] < AM.OffsetIndex ) { return(d->where[1]); } else if ( d->type == DOLZERO ) return(0); else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] == -SNUMBER && d->where[3] == 0 ) { return(d->where[2]); } else if ( d->type == DOLINDEX && d->index >= 0 && d->index < AM.OffsetIndex ) { return(d->index); } else if ( d->type == DOLWILDARGS && d->where[0] == 1 && d->where[1] >= 0 && d->where[1] < AM.OffsetIndex ) { return(d->where[1]); } else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] == -INDEX && d->where[3] == 0 && d->where[2] >= 0 && d->where[2] < AM.OffsetIndex ) { return(d->where[2]); } AN.ErrorInDollar = 1; return(0); } /* #] DolToNumber : #[ DolToSymbol : with LOCK */ WORD DolToSymbol(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; WORD retval; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif AN.ErrorInDollar = 0; if ( d->type == DOLTERMS && d->where[0] == 8 && d->where[8] == 0 && d->where[7] == 3 && d->where[6] == 1 && d->where[5] == 1 && d->where[4] == 1 && d->where[1] == SYMBOL ) { retval = d->where[3]; } else if ( d->type == DOLARGUMENT && d->where[0] == -SYMBOL ) { retval = d->where[1]; } else if ( d->type == DOLSUBTERM && d->where[0] == SYMBOL && d->where[1] == 4 && d->where[3] == 1 ) { retval = d->where[2]; } else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] == -SYMBOL && d->where[3] == 0 ) { retval = d->where[2]; } else { AN.ErrorInDollar = 1; retval = -1; } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(retval); } /* #] DolToSymbol : #[ DolToIndex : with LOCK */ WORD DolToIndex(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; WORD retval; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif AN.ErrorInDollar = 0; if ( d->type == DOLTERMS && d->where[0] == 7 && d->where[7] == 0 && d->where[6] == 3 && d->where[5] == 1 && d->where[4] == 1 && d->where[1] == INDEX && d->where[3] >= 0 ) { retval = d->where[3]; } else if ( d->type == DOLARGUMENT && d->where[0] == -SNUMBER && d->where[1] >= 0 && d->where[1] < AM.OffsetIndex ) { retval = d->where[1]; } else if ( d->type == DOLARGUMENT && d->where[0] == -INDEX && d->where[1] >= 0 ) { retval = d->where[1]; } else if ( d->type == DOLZERO ) return(0); else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] == -SNUMBER && d->where[3] == 0 && d->where[2] >= 0 && d->where[2] < AM.OffsetIndex ) { retval = d->where[2]; } else if ( d->type == DOLINDEX && d->index >= 0 ) { retval = d->index; } else if ( d->type == DOLNUMBER && d->where[0] == 4 && d->where[2] == 1 && d->where[3] == 3 && d->where[4] == 0 && d->where[1] < AM.OffsetIndex ) { retval = d->where[1]; } else if ( d->type == DOLWILDARGS && d->where[0] == 1 && d->where[1] >= 0 ) { retval = d->where[1]; } else if ( d->type == DOLSUBTERM && d->where[0] == INDEX && d->where[1] == 3 && d->where[2] >= 0 ) { retval = d->where[2]; } else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] == -INDEX && d->where[3] == 0 && d->where[2] >= 0 ) { retval = d->where[2]; } else { AN.ErrorInDollar = 1; retval = 0; } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(retval); } /* #] DolToIndex : #[ DolToTerms : Returns a struct of type DOLLARS which contains a copy of the original dollar variable, provided it can be expressed in terms of an expression (type = DOLTERMS). Otherwise it returns zero. The dollar is expressed in terms in the buffer "where" */ DOLLARS DolToTerms(PHEAD WORD numdollar) { GETBIDENTITY LONG size; DOLLARS d = Dollars + numdollar, newd; WORD *t, *w, i; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } #endif AN.ErrorInDollar = 0; switch ( d->type ) { case DOLARGUMENT: t = d->where; if ( t[0] < 0 ) { ShortArgument: w = AT.WorkPointer; if ( t[0] <= -FUNCTION ) { *w++ = FUNHEAD+4; *w++ = -t[0]; *w++ = FUNHEAD; FILLFUN(w) *w++ = 1; *w++ = 1; *w++ = 3; } else if ( t[0] == -SYMBOL ) { *w++ = 8; *w++ = SYMBOL; *w++ = 4; *w++ = t[1]; *w++ = 1; *w++ = 1; *w++ = 1; *w++ = 3; } else if ( t[0] == -VECTOR || t[0] == -INDEX ) { *w++ = 7; *w++ = INDEX; *w++ = 3; *w++ = t[1]; *w++ = 1; *w++ = 1; *w++ = 3; } else if ( t[0] == -MINVECTOR ) { *w++ = 7; *w++ = INDEX; *w++ = 3; *w++ = t[1]; *w++ = 1; *w++ = 1; *w++ = -3; } else if ( t[0] == -SNUMBER ) { *w++ = 4; if ( t[1] < 0 ) { *w++ = -t[1]; *w++ = 1; *w++ = -3; } else { *w++ = t[1]; *w++ = 1; *w++ = 3; } } *w = 0; size = w - AT.WorkPointer; w = AT.WorkPointer; break; } /* fall through */ case DOLNUMBER: case DOLTERMS: t = d->where; while ( *t ) t += *t; size = t - d->where; w = d->where; break; case DOLSUBTERM: w = AT.WorkPointer; size = d->where[1]; *w++ = size+4; t = d->where; NCOPY(w,t,size) *w++ = 1; *w++ = 1; *w++ = 3; w = AT.WorkPointer; size = d->where[1]+4; break; case DOLINDEX: w = AT.WorkPointer; *w++ = 7; *w++ = INDEX; *w++ = 3; *w++ = d->index; *w++ = 1; *w++ = 1; *w++ = 3; *w = 0; w = AT.WorkPointer; size = 7; break; case DOLWILDARGS: /* In some cases we can make a copy */ t = d->where+1; if ( *t == 0 ) return(0); NEXTARG(t); if ( *t ) { /* More than one argument in here */ MLOCK(ErrorMessageLock); MesPrint("Trying to convert a $ with an argument field into an expression"); MUNLOCK(ErrorMessageLock); Terminate(-1); } /* Now we have a single argument */ t = d->where+1; if ( *t < 0 ) goto ShortArgument; size = *t - ARGHEAD; w = t + ARGHEAD; break; case DOLUNDEFINED: MLOCK(ErrorMessageLock); MesPrint("Trying to use an undefined $ in an expression"); MUNLOCK(ErrorMessageLock); Terminate(-1); /* fall through */ case DOLZERO: if ( d->where ) { d->where[0] = 0; } else d->where = &(AM.dollarzero); size = 0; w = d->where; break; default: return(0); } newd = (DOLLARS)Malloc1(sizeof(struct DoLlArS)+(size+1)*sizeof(WORD), "Copy of dollar variable"); t = (WORD *)(newd+1); newd->where = t; newd->name = d->name; newd->node = d->node; newd->type = DOLTERMS; newd->size = size; newd->numdummies = d->numdummies; #ifdef WITHPTHREADS INIRECLOCK(newd->pthreadslock); #endif size++; NCOPY(t,w,size); newd->nfactors = d->nfactors; if ( d->nfactors > 1 ) { newd->factors = (FACDOLLAR *)Malloc1(d->nfactors*sizeof(FACDOLLAR),"Dollar factors"); for ( i = 0; i < d->nfactors; i++ ) { newd->factors[i].where = 0; newd->factors[i].size = 0; newd->factors[i].type = DOLUNDEFINED; newd->factors[i].value = d->factors[i].value; } } else { newd->factors = 0; } return(newd); } /* #] DolToTerms : #[ DolToLong : */ LONG DolToLong(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; LONG x; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } #endif AN.ErrorInDollar = 0; if ( ( d->type == DOLTERMS || d->type == DOLNUMBER ) && d->where[0] == 4 && d->where[4] == 0 && ( d->where[3] == 3 || d->where[3] == -3 ) && d->where[2] == 1 && ( d->where[1] & TOPBITONLY ) == 0 ) { x = d->where[1]; if ( d->where[3] > 0 ) return(x); else return(-x); } else if ( ( d->type == DOLTERMS || d->type == DOLNUMBER ) && d->where[0] == 6 && d->where[6] == 0 && ( d->where[5] == 5 || d->where[5] == -5 ) && d->where[3] == 1 && d->where[4] == 1 && ( d->where[2] & TOPBITONLY ) == 0 ) { x = d->where[1] + ( (LONG)(d->where[2]) << BITSINWORD ); if ( d->where[5] > 0 ) return(x); else return(-x); } else if ( d->type == DOLARGUMENT && d->where[0] == -SNUMBER ) { x = d->where[1]; return(x); } else if ( d->type == DOLARGUMENT && d->where[0] == -INDEX && d->where[1] >= 0 && d->where[1] < AM.OffsetIndex ) { x = d->where[1]; return(x); } else if ( d->type == DOLZERO ) return(0); else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] == -SNUMBER && d->where[3] == 0 ) { x = d->where[2]; return(x); } else if ( d->type == DOLINDEX && d->index >= 0 && d->index < AM.OffsetIndex ) { x = d->index; return(x); } else if ( d->type == DOLWILDARGS && d->where[0] == 1 && d->where[1] >= 0 && d->where[1] < AM.OffsetIndex ) { x = d->where[1]; return(x); } else if ( d->type == DOLWILDARGS && d->where[0] == 0 && d->where[1] == -INDEX && d->where[3] == 0 && d->where[2] >= 0 && d->where[2] < AM.OffsetIndex ) { x = d->where[2]; return(x); } AN.ErrorInDollar = 1; return(0); } /* #] DolToLong : #[ ExecInside : */ int ExecInside(UBYTE *s) { GETIDENTITY UBYTE *t, c; WORD *w, number; int error = 0; w = AT.WorkPointer; if ( AC.insidelevel >= MAXNEST ) { MLOCK(ErrorMessageLock); MesPrint("@Nesting of inside statements more than %d levels",(WORD)MAXNEST); MUNLOCK(ErrorMessageLock); return(-1); } AC.insidesumcheck[AC.insidelevel] = NestingChecksum(); AC.insidestack[AC.insidelevel] = cbuf[AC.cbufnum].Pointer - cbuf[AC.cbufnum].Buffer + 2; AC.insidelevel++; *w++ = TYPEINSIDE; w++; w++; for(;;) { /* Look for a (comma separated) list of dollar variables */ while ( *s == ',' ) s++; if ( *s == 0 ) break; if ( *s == '$' ) { s++; t = s; if ( FG.cTable[*s] != 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal name for $ variable: %s",s-1); MUNLOCK(ErrorMessageLock); goto skipdol; } while ( FG.cTable[*s] == 0 || FG.cTable[*s] == 1 ) s++; c = *s; *s = 0; if ( ( number = GetDollar(t) ) < 0 ) { number = AddDollar(t,0,0,0); } *s = c; *w++ = number; AddPotModdollar(number); } else { MLOCK(ErrorMessageLock); MesPrint("&Illegal object in Inside statement"); MUNLOCK(ErrorMessageLock); skipdol: error = 1; while ( *s && *s != ',' && s[1] != '$' ) s++; if ( *s == 0 ) break; } } AT.WorkPointer[1] = w - AT.WorkPointer; AddNtoL(AT.WorkPointer[1],AT.WorkPointer); return(error); } /* #] ExecInside : #[ InsideDollar : Execution part of Inside $a; We have to take the variables one by one and then convert them into proper terms and call Generator for the proper levels. The conversion copies the whole dollar into a new buffer, making us insensitive to redefinitions of $a inside the Inside. In the end we sort and redefine $a. */ int InsideDollar(PHEAD WORD *ll, WORD level) { GETBIDENTITY int numvar = (int)(ll[1]-3), j, error = 0; WORD numdol, *oldcterm, *oldwork = AT.WorkPointer, olddefer, *r, *m; WORD oldnumlhs, *dbuffer; DOLLARS d, newd; oldcterm = AN.cTerm; AN.cTerm = 0; oldnumlhs = AR.Cnumlhs; AR.Cnumlhs = ll[2]; ll += 3; olddefer = AR.DeferFlag; AR.DeferFlag = 0; while ( --numvar >= 0 ) { numdol = *ll++; d = Dollars + numdol; { #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdol == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif newd = DolToTerms(BHEAD numdol); if ( newd == 0 ) { continue; } if ( newd->where[0] == 0 ) { // DolToTerms potentially allocates memory. Free it. // The free below is inside the while loop. if ( newd->factors ) M_free(newd->factors,"Dollar factors"); M_free(newd,"Copy of dollar variable"); continue; } r = newd->where; NewSort(BHEAD0); while ( *r ) { /* Sum over the terms */ m = AT.WorkPointer; j = *r; while ( --j >= 0 ) *m++ = *r++; AT.WorkPointer = m; /* What to do with dummy indices? */ if ( Generator(BHEAD oldwork,level) ) { LowerSortLevel(); error = -1; goto idcall; } AT.WorkPointer = oldwork; } AN.tryterm = 0; /* for now */ if ( EndSort(BHEAD (WORD *)((void *)(&dbuffer)),2) < 0 ) { error = 1; break; } if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"old buffer of dollar"); d->where = dbuffer; if ( dbuffer == 0 || *dbuffer == 0 ) { d->type = DOLZERO; if ( dbuffer ) M_free(dbuffer,"buffer of dollar"); d->where = &(AM.dollarzero); d->size = 0; } else { d->type = DOLTERMS; r = d->where; while ( *r ) r += *r; d->size = (r-d->where)+1; } /* cbuf[AM.dbufnum].rhs[numdol] = d->where; */ cbuf[AM.dbufnum].rhs[numdol] = (WORD *)(1); /* Now we have a little cleaning up to do */ #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif if ( newd->factors ) M_free(newd->factors,"Dollar factors"); M_free(newd,"Copy of dollar variable"); } } idcall:; AR.Cnumlhs = oldnumlhs; AR.DeferFlag = olddefer; AN.cTerm = oldcterm; AT.WorkPointer = oldwork; return(error); } /* #] InsideDollar : #[ ExchangeDollars : */ void ExchangeDollars(int num1, int num2) { DOLLARS d1, d2; WORD node1, node2; LONG nam; d1 = Dollars + num1; node1 = d1->node; d2 = Dollars + num2; node2 = d2->node; nam = d1->name; d1->name = d2->name; d2->name = nam; d1->node = node2; d2->node = node1; AC.dollarnames->namenode[node1].number = num2; AC.dollarnames->namenode[node2].number = num1; } /* #] ExchangeDollars : #[ TermsInDollar : */ LONG TermsInDollar(WORD num) { GETIDENTITY DOLLARS d = Dollars + num; WORD *t; LONG n; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( num == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif if ( d->type == DOLTERMS ) { n = 0; t = d->where; while ( *t ) { t += *t; n++; } } else if ( d->type == DOLWILDARGS ) { n = 0; if ( d->where[0] == 0 ) { t = d->where+1; while ( *t != 0 ) { NEXTARG(t); n++; } } else if ( d->where[0] == 1 ) n = 1; } else if ( d->type == DOLZERO ) n = 0; else n = 1; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(n); } /* #] TermsInDollar : #[ SizeOfDollar : */ LONG SizeOfDollar(WORD num) { GETIDENTITY DOLLARS d = Dollars + num; WORD *t; LONG n; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( num == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif if ( d->type == DOLTERMS ) { t = d->where; while ( *t ) t += *t; t++; n = (LONG)(t - d->where); } else if ( d->type == DOLWILDARGS ) { n = 0; if ( d->where[0] == 0 ) { t = d->where+1; while ( *t != 0 ) { NEXTARG(t); n++; } t++; n = (LONG)(t - d->where); } else if ( d->where[0] == 1 ) n = 1; } else if ( d->type == DOLZERO ) n = 0; else n = 1; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(n); } /* #] SizeOfDollar : #[ PreIfDollarEval : Routine is invoked in #if etc after $( is encountered. $(expr1 operator expr2) makes compares between expressions, $(expr1 operator _keyword) makes compares between expressions, interpreted as expressions. We are here mainly looking at $variables. First we look for the operator: >, <, ==, >=, <=, != : < means that it comes before. _keywords can be: _set(setname) (does the expr belong to the set (only with == or !=)) _productof(expr) */ UBYTE *PreIfDollarEval(UBYTE *s, int *value) { GETIDENTITY UBYTE *s1,*s2,*s3,*s4,*s5,*t,c,c1,c2,c3; int oprtr, type; WORD *buf1 = 0, *buf2 = 0, numset, *oldwork = AT.WorkPointer; EXCHINOUT /* Find the three composing objects (epxression, operator, expression or keyw */ while ( *s == ' ' || *s == '\t' || *s == '\n' || *s == '\r' ) s++; s1 = t = s; while ( *t != '=' && *t != '!' && *t != '>' && *t != '<' ) { if ( *t == '[' ) { SKIPBRA1(t) } else if ( *t == '{' ) { SKIPBRA2(t) } else if ( *t == '(' ) { SKIPBRA3(t) } else if ( *t == ']' || *t == '}' || *t == ')' ) { MLOCK(ErrorMessageLock); MesPrint("@Improper bracketting in #if"); MUNLOCK(ErrorMessageLock); goto onerror; } t++; } s2 = t; while ( *t == '=' || *t == '!' || *t == '>' || *t == '<' ) t++; s3 = t; while ( *t && *t != ')' ) { if ( *t == '[' ) { SKIPBRA1(t) } else if ( *t == '{' ) { SKIPBRA2(t) } else if ( *t == '(' ) { SKIPBRA3(t) } else if ( *t == ']' || *t == '}' ) { MLOCK(ErrorMessageLock); MesPrint("@Improper brackets in #if"); MUNLOCK(ErrorMessageLock); goto onerror; } t++; } if ( *t == 0 ) { MLOCK(ErrorMessageLock); MesPrint("@Missing ) to match $( in #if"); MUNLOCK(ErrorMessageLock); goto onerror; } s4 = t; c2 = *s4; *s4 = 0; if ( s2+2 < s3 || s2 == s3 ) { IllOp:; MLOCK(ErrorMessageLock); MesPrint("@Illegal operator in $( option of #if"); MUNLOCK(ErrorMessageLock); goto onerror; } if ( s2+1 == s3 ) { if ( *s2 == '=' ) oprtr = EQUAL; else if ( *s2 == '>' ) oprtr = GREATER; else if ( *s2 == '<' ) oprtr = LESS; else goto IllOp; } else if ( *s2 == '!' && s2[1] == '=' ) oprtr = NOTEQUAL; else if ( *s2 == '=' && s2[1] == '=' ) oprtr = EQUAL; else if ( *s2 == '<' && s2[1] == '=' ) oprtr = LESSEQUAL; else if ( *s2 == '>' && s2[1] == '=' ) oprtr = GREATEREQUAL; else goto IllOp; c1 = *s2; *s2 = 0; /* The two expressions are now zero terminated Look for the special keywords */ while ( *s3 == ' ' || *s3 == '\t' || *s3 == '\n' || *s3 == '\r' ) s3++; t = s3; while ( chartype[*t] == 0 ) t++; if ( *t == '_' ) { t++; c = *t; *t = 0; if ( StrICmp(s3,(UBYTE *)"set_") == 0 ) { if ( oprtr != EQUAL && oprtr != NOTEQUAL ) { ImpOp:; MLOCK(ErrorMessageLock); MesPrint("@Improper operator for special keyword in $( ) option"); MUNLOCK(ErrorMessageLock); goto onerror; } type = 1; } else if ( StrICmp(s3,(UBYTE *)"multipleof_") == 0 ) { if ( oprtr != EQUAL && oprtr != NOTEQUAL ) goto ImpOp; type = 2; } /* else if ( StrICmp(s3,(UBYTE *)"productof_") == 0 ) { if ( oprtr != EQUAL && oprtr != NOTEQUAL ) goto ImpOp; type = 3; } */ else type = 0; } else { type = 0; c = *t; } if ( type > 0 ) { *t++ = c; s3 = t; s5 = s4-1; while ( *s5 != ')' ) { if ( *s5 == ' ' || *s5 == '\t' || *s5 == '\n' || *s5 == '\r' ) s5--; else { MLOCK(ErrorMessageLock); MesPrint("@Improper use of special keyword in $( ) option"); MUNLOCK(ErrorMessageLock); goto onerror; } } c3 = *s5; *s5 = 0; } else { c3 = c2; s5 = s4; } /* Expand the first expression. */ if ( ( buf1 = TranslateExpression(s1) ) == 0 ) { AT.WorkPointer = oldwork; goto onerror; } if ( type == 1 ) { /* determine the set */ if ( *s3 == '{' ) { t = s3+1; SKIPBRA2(s3) numset = DoTempSet(t,s3); s3++; if ( numset < 0 ) { noset:; MLOCK(ErrorMessageLock); MesPrint("@Argument of set_ is not a valid set"); MUNLOCK(ErrorMessageLock); goto onerror; } } else { t = s3; while ( FG.cTable[*s3] == 0 || FG.cTable[*s3] == 1 || *s3 == '_' ) s3++; c = *s3; *s3 = 0; if ( GetName(AC.varnames,t,&numset,NOAUTO) != CSET ) { *s3 = c; goto noset; } *s3 = c; } while ( *s3 == ' ' || *s3 == '\t' || *s3 == '\n' || *s3 == '\r' ) s3++; if ( s3 != s5 ) goto noset; *value = IsSetMember(buf1,numset); if ( oprtr == NOTEQUAL ) *value ^= 1; } else { if ( ( buf2 = TranslateExpression(s3) ) == 0 ) goto onerror; } if ( type == 0 ) { *value = TwoExprCompare(buf1,buf2,oprtr); } else if ( type == 2 ) { *value = IsMultipleOf(buf1,buf2); if ( oprtr == NOTEQUAL ) *value ^= 1; } /* else if ( type == 3 ) { *value = IsProductOf(buf1,buf2); if ( oprtr == NOTEQUAL ) *value ^= 1; } */ if ( buf1 ) M_free(buf1,"Buffer in $()"); if ( buf2 ) M_free(buf2,"Buffer in $()"); *s5 = c3; *s4++ = c2; *s2 = c1; AT.WorkPointer = oldwork; BACKINOUT return(s4); onerror: if ( buf1 ) M_free(buf1,"Buffer in $()"); if ( buf2 ) M_free(buf2,"Buffer in $()"); AT.WorkPointer = oldwork; BACKINOUT return(0); } /* #] PreIfDollarEval : #[ TranslateExpression : */ WORD *TranslateExpression(UBYTE *s) { GETIDENTITY CBUF *C = cbuf+AC.cbufnum; WORD oldnumrhs = C->numrhs; LONG oldcpointer = C->Pointer - C->Buffer; WORD *w = AT.WorkPointer; WORD retcode, oldEside; WORD *outbuffer; *w++ = SUBEXPSIZE + 4; AC.ProtoType = w; *w++ = SUBEXPRESSION; *w++ = SUBEXPSIZE; *w++ = C->numrhs+1; *w++ = 1; *w++ = AC.cbufnum; FILLSUB(w) *w++ = 1; *w++ = 1; *w++ = 3; *w++ = 0; AT.WorkPointer = w; if ( ( retcode = CompileAlgebra(s,RHSIDE,AC.ProtoType) ) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("@Error translating first expression in $( ) option"); MUNLOCK(ErrorMessageLock); return(0); } else { AC.ProtoType[2] = retcode; } /* Evaluate this expression */ if ( NewSort(BHEAD0) || NewSort(BHEAD0) ) { return(0); } AN.RepPoint = AT.RepCount + 1; oldEside = AR.Eside; AR.Eside = RHSIDE; AR.Cnumlhs = C->numlhs; if ( Generator(BHEAD AC.ProtoType-1,C->numlhs) ) { AR.Eside = oldEside; LowerSortLevel(); LowerSortLevel(); return(0); } AR.Eside = oldEside; AT.WorkPointer = w; AN.tryterm = 0; /* for now */ if ( EndSort(BHEAD (WORD *)((void *)(&outbuffer)),2) < 0 ) { LowerSortLevel(); return(0); } LowerSortLevel(); C->Pointer = C->Buffer + oldcpointer; C->numrhs = oldnumrhs; AT.WorkPointer = AC.ProtoType - 1; return(outbuffer); } /* #] TranslateExpression : #[ IsSetMember : Checks whether the expression in the buffer can be seen as an element of the given set. For the special sets: if more than one term: no match!!! */ int IsSetMember(WORD *buffer, WORD numset) { WORD *t = buffer, *tt, num, csize, num1; WORD bufterm[4]; int i, j, type; if ( numset < AM.NumFixedSets ) { if ( t[*t] != 0 ) return(0); /* More than one term */ if ( *t == 0 ) { if ( numset == POS0_ || numset == NEG0_ || numset == EVEN_ || numset == Z_ || numset == Q_ ) return(1); else return(0); } if ( numset == SYMBOL_ ) { if ( *t == 8 && t[1] == SYMBOL && t[7] == 3 && t[6] == 1 && t[5] == 1 && t[4] == 1 ) return(1); else return(0); } if ( numset == INDEX_ ) { if ( *t == 7 && t[1] == INDEX && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[3] > 0 ) return(1); if ( *t == 4 && t[3] == 3 && t[2] == 1 && t[1] < AM.OffsetIndex) return(1); return(0); } if ( numset == FIXED_ ) { if ( *t == 7 && t[1] == INDEX && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[3] > 0 && t[3] < AM.OffsetIndex ) return(1); if ( *t == 4 && t[3] == 3 && t[2] == 1 && t[1] < AM.OffsetIndex) return(1); return(0); } if ( numset == DUMMYINDEX_ ) { if ( *t == 7 && t[1] == INDEX && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[3] >= AM.IndDum && t[3] < AM.IndDum+MAXDUMMIES ) return(1); if ( *t == 4 && t[3] == 3 && t[2] == 1 && t[1] >= AM.IndDum && t[1] < AM.IndDum+MAXDUMMIES ) return(1); return(0); } if ( numset == VECTOR_ ) { if ( *t == 7 && t[1] == INDEX && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[3] < (AM.OffsetVector+WILDOFFSET) && t[3] >= AM.OffsetVector ) return(1); return(0); } tt = t + *t - 1; if ( ABS(tt[0]) != *t-1 ) return(0); if ( numset == Q_ ) return(1); if ( numset == POS_ || numset == POS0_ ) return(tt[0]>0); else if ( numset == NEG_ || numset == NEG0_ ) return(tt[0]<0); i = (ABS(tt[0])-1)/2; tt -= i; if ( tt[0] != 1 ) return(0); for ( j = 1; j < i; j++ ) { if ( tt[j] != 0 ) return(0); } if ( numset == Z_ ) return(1); if ( numset == ODD_ ) return(t[1]&1); if ( numset == EVEN_ ) return(1-(t[1]&1)); return(0); } if ( t[*t] != 0 ) return(0); /* More than one term */ type = Sets[numset].type; switch ( type ) { case CSYMBOL: if ( t[0] == 8 && t[1] == SYMBOL && t[7] == 3 && t[6] == 1 && t[5] == 1 && t[4] == 1 ) { num = t[3]; } else if ( t[0] == 4 && t[2] == 1 && t[1] <= MAXPOWER ) { num = t[1]; if ( t[3] < 0 ) num = -num; num += 2*MAXPOWER; } else return(0); break; case CVECTOR: if ( t[0] == 7 && t[1] == INDEX && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[3] < 0 ) { num = t[3]; } else return(0); break; case CINDEX: if ( t[0] == 7 && t[1] == INDEX && t[6] == 3 && t[5] == 1 && t[4] == 1 && t[3] > 0 ) { num = t[3]; } else if ( t[0] == 4 && t[3] == 3 && t[2] == 1 && t[1] < AM.OffsetIndex ) { num = t[1]; } else return(0); break; case CFUNCTION: if ( t[0] == 4+FUNHEAD && t[3+FUNHEAD] == 3 && t[2+FUNHEAD] == 1 && t[1+FUNHEAD] == 1 && t[1] >= FUNCTION ) { num = t[1]; } else return(0); break; case CNUMBER: if ( t[0] == 4 && t[2] == 1 && t[1] <= AM.OffsetIndex && t[3] == 3 ) { num = t[1]; } else return(0); break; case CRANGE: csize = t[t[0]-1]; csize = ABS(csize); if ( csize != t[0]-1 ) return(0); if ( Sets[numset].first < 3*MAXPOWER ) { num1 = num = Sets[numset].first; if ( num >= MAXPOWER ) num -= 2*MAXPOWER; if ( num == 0 ) { if ( num1 < MAXPOWER ) { if ( t[t[0]-1] >= 0 ) return(0); } else if ( t[t[0]-1] > 0 ) return(0); } else { bufterm[0] = 4; bufterm[1] = ABS(num); bufterm[2] = 1; if ( num < 0 ) bufterm[3] = -3; else bufterm[3] = 3; num = CompCoef(t,bufterm); if ( num1 < MAXPOWER ) { if ( num >= 0 ) return(0); } else if ( num > 0 ) return(0); } } if ( Sets[numset].last > -3*MAXPOWER ) { num1 = num = Sets[numset].last; if ( num <= -MAXPOWER ) num += 2*MAXPOWER; if ( num == 0 ) { if ( num1 > -MAXPOWER ) { if ( t[t[0]-1] <= 0 ) return(0); } else if ( t[t[0]-1] < 0 ) return(0); } else { bufterm[0] = 4; bufterm[1] = ABS(num); bufterm[2] = 1; if ( num < 0 ) bufterm[3] = -3; else bufterm[3] = 3; num = CompCoef(t,bufterm); if ( num1 > -MAXPOWER ) { if ( num <= 0 ) return(0); } else if ( num < 0 ) return(0); } } return(1); break; default: return(0); } t = SetElements + Sets[numset].first; tt = SetElements + Sets[numset].last; do { if ( num == *t ) return(1); t++; } while ( t < tt ); return(0); } /* #] IsSetMember : #[ IsProductOf : Checks whether the expression in buf1 is a single term multiple of the expression in buf2. int IsProductOf(WORD *buf1, WORD *buf2) { return(0); } #] IsProductOf : #[ IsMultipleOf : Checks whether the expression in buf1 is a numerical multiple of the expression in buf2. */ int IsMultipleOf(WORD *buf1, WORD *buf2) { GETIDENTITY LONG num1, num2; WORD *t1, *t2, *m1, *m2, *r1, *r2, nc1, nc2, ni1, ni2; UWORD *IfScrat1, *IfScrat2; int i, j; if ( *buf1 == 0 && *buf2 == 0 ) return(1); /* First count terms */ t1 = buf1; t2 = buf2; num1 = 0; num2 = 0; while ( *t1 ) { t1 += *t1; num1++; } while ( *t2 ) { t2 += *t2; num2++; } if ( num1 != num2 ) return(0); /* Test similarity of terms. Difference up to a number. */ t1 = buf1; t2 = buf2; while ( *t1 ) { m1 = t1+1; m2 = t2+1; t1 += *t1; t2 += *t2; r1 = t1 - ABS(t1[-1]); r2 = t2 - ABS(t2[-1]); if ( r1-m1 != r2-m2 ) return(0); while ( m1 < r1 ) { if ( *m1 != *m2 ) return(0); m1++; m2++; } } /* Now we have to test the constant factor */ IfScrat1 = (UWORD *)(TermMalloc("IsMultipleOf")); IfScrat2 = (UWORD *)(TermMalloc("IsMultipleOf")); t1 = buf1; t2 = buf2; t1 += *t1; t2 += *t2; if ( *t1 == 0 && *t2 == 0 ) return(1); r1 = t1 - ABS(t1[-1]); r2 = t2 - ABS(t2[-1]); nc1 = REDLENG(t1[-1]); nc2 = REDLENG(t2[-1]); if ( DivRat(BHEAD (UWORD *)r1,nc1,(UWORD *)r2,nc2,IfScrat1,&ni1) ) { MLOCK(ErrorMessageLock); MesPrint("@Called from MultipleOf in $( )"); MUNLOCK(ErrorMessageLock); TermFree(IfScrat1,"IsMultipleOf"); TermFree(IfScrat2,"IsMultipleOf"); Terminate(-1); } while ( *t1 ) { t1 += *t1; t2 += *t2; r1 = t1 - ABS(t1[-1]); r2 = t2 - ABS(t2[-1]); nc1 = REDLENG(t1[-1]); nc2 = REDLENG(t2[-1]); if ( DivRat(BHEAD (UWORD *)r1,nc1,(UWORD *)r2,nc2,IfScrat2,&ni2) ) { MLOCK(ErrorMessageLock); MesPrint("@Called from MultipleOf in $( )"); MUNLOCK(ErrorMessageLock); TermFree(IfScrat1,"IsMultipleOf"); TermFree(IfScrat2,"IsMultipleOf"); Terminate(-1); } if ( ni1 != ni2 ) return(0); i = 2*ABS(ni1); for ( j = 0; j < i; j++ ) { if ( IfScrat1[j] != IfScrat2[j] ) { TermFree(IfScrat1,"IsMultipleOf"); TermFree(IfScrat2,"IsMultipleOf"); return(0); } } } TermFree(IfScrat1,"IsMultipleOf"); TermFree(IfScrat2,"IsMultipleOf"); return(1); } /* #] IsMultipleOf : #[ TwoExprCompare : Compares the expressions in buf1 and buf2 according to oprtr */ int TwoExprCompare(WORD *buf1, WORD *buf2, int oprtr) { GETIDENTITY WORD *t1, *t2, cond; t1 = buf1; t2 = buf2; while ( *t1 && *t2 ) { cond = CompareTerms(BHEAD t1,t2,1); if ( cond != 0 ) { if ( cond > 0 ) { /* t1 comes first */ switch ( oprtr ) { /* t1 is less */ case EQUAL: return(0); case NOTEQUAL: return(1); case GREATEREQUAL: return(0); case GREATER: return(0); case LESS: return(1); case LESSEQUAL: return(1); } } else { switch ( oprtr ) { case EQUAL: return(0); case NOTEQUAL: return(1); case GREATEREQUAL: return(1); case GREATER: return(1); case LESS: return(0); case LESSEQUAL: return(0); } } } t1 += *t1; t2 += *t2; } if ( *t1 == *t2 ) { /* They are equal */ switch ( oprtr ) { case EQUAL: return(1); case NOTEQUAL: return(0); case GREATEREQUAL: return(1); case GREATER: return(0); case LESS: return(0); case LESSEQUAL: return(1); } } else if ( *t1 ) { /* t1 is greater */ switch ( oprtr ) { case EQUAL: return(0); case NOTEQUAL: return(1); case GREATEREQUAL: return(1); case GREATER: return(1); case LESS: return(0); case LESSEQUAL: return(0); } } else { switch ( oprtr ) { /* t1 is less */ case EQUAL: return(0); case NOTEQUAL: return(1); case GREATEREQUAL: return(0); case GREATER: return(0); case LESS: return(1); case LESSEQUAL: return(1); } } MLOCK(ErrorMessageLock); MesPrint("@Internal problems with operator in $( )"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } /* #] TwoExprCompare : #[ DollarRaiseLow : Raises or lowers the numerical value of a dollar variable Not to be used in parallel. */ static UWORD *dscrat = 0; static WORD ndscrat; int DollarRaiseLow(UBYTE *name, LONG value) { GETIDENTITY int num; DOLLARS d; int sgn = 1; WORD lnum[4], nnum, *t1, *t2, i; UBYTE *s, c; s = name; while ( *s ) s++; if ( s[-1] == '-' && s[-2] == '-' && s > name+2 ) s -= 2; else if ( s[-1] == '+' && s[-2] == '+' && s > name+2 ) s -= 2; c = *s; *s = 0; num = GetDollar(name); *s = c; d = Dollars + num; if ( value < 0 ) { value = -value; sgn = -1; } if ( d->type == DOLZERO ) { if ( d->where ) M_free(d->where,"DollarRaiseLow"); d->size = MINALLOC; d->where = (WORD *)Malloc1(d->size*sizeof(WORD),"DollarRaiseLow"); if ( ( value & AWORDMASK ) != 0 ) { d->where[0] = 6; d->where[1] = value >> BITSINWORD; d->where[2] = (WORD)value; d->where[3] = 1; d->where[4] = 0; d->where[5] = 5*sgn; d->where[6] = 0; d->type = DOLTERMS; } else { d->where[0] = 4; d->where[1] = (WORD)value; d->where[2] = 1; d->where[3] = 3*sgn; d->where[4] = 0; d->type = DOLNUMBER; } } else if ( d->type == DOLNUMBER || ( d->type == DOLTERMS && d->where[d->where[0]] == 0 && d->where[0] == ABS(d->where[d->where[0]-1])+1 ) ) { if ( ( value & AWORDMASK ) != 0 ) { lnum[0] = value >> BITSINWORD; lnum[1] = (WORD)value; lnum[2] = 1; lnum[3] = 0; nnum = 2*sgn; } else { lnum[0] = (WORD)value; lnum[1] = 1; nnum = sgn; } i = d->where[d->where[0]-1]; i = REDLENG(i); if ( dscrat == 0 ) { dscrat = (UWORD *)Malloc1((AM.MaxTal+2)*sizeof(UWORD),"DollarRaiseLow"); } if ( AddRat(BHEAD (UWORD *)(d->where+1),i, (UWORD *)lnum,nnum,dscrat,&ndscrat) ) { MLOCK(ErrorMessageLock); MesCall("DollarRaiseLow"); MUNLOCK(ErrorMessageLock); Terminate(-1); } ndscrat = INCLENG(ndscrat); i = ABS(ndscrat); if ( i == 0 ) { M_free(d->where,"DollarRaiseLow"); d->where = 0; d->type = DOLZERO; d->size = 0; return(0); } if ( i+2 > d->size ) { M_free(d->where,"DollarRaiseLow"); d->size = i+2; if ( d->size < MINALLOC ) d->size = MINALLOC; d->size = ((d->size+7)/8)*8; d->where = (WORD *)Malloc1(d->size*sizeof(WORD),"DollarRaiseLow"); } t1 = d->where; *t1++ = i+1; t2 = (WORD *)dscrat; while ( --i > 0 ) *t1++ = *t2++; *t1++ = ndscrat; *t1 = 0; d->type = DOLTERMS; } return(0); } /* #] DollarRaiseLow : #[ EvalDoLoopArg : */ /** * Evaluates one argument of a do loop. Such an argument is constructed * from SNUMBERs DOLLAREXPRESSIONs and possibly DOLLAREXPR2s which indicate * factors of the preceding dollar. Hence we have * SNUMBER,num * DOLLAREXPRESSION,numdollar * DOLLAREXPRESSION,numdollar,DOLLAREXPR2,numfactor * DOLLAREXPRESSION,numdollar,DOLLAREXPR2,numfactor,DOLLAREXPR2,numfactor * etc. * Because we have a do-loop at every stage we should have a number. * The notation in DOLLAREXPR2 is that >= 0 is number of yet another dollar * and < 0 is -n-1 with n the array element or zero. * The return value is the (short) number. * The routine works its way through the list in a recursive manner. */ WORD EvalDoLoopArg(PHEAD WORD *arg, WORD par) { WORD num, type, *td; DOLLARS d; if ( *arg == SNUMBER ) return(arg[1]); if ( *arg == DOLLAREXPR2 && arg[1] < 0 ) return(-arg[1]-1); d = Dollars + arg[1]; #ifdef WITHPTHREADS { int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( arg[1] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } } #endif if ( *arg == DOLLAREXPRESSION ) { if ( arg[2] != DOLLAREXPR2 ) { /* end of chain */ endofchain: type = d->type; if ( type == DOLZERO ) {} else if ( type == DOLNUMBER ) { td = d->where; if ( ( td[0] != 4 ) || ( (td[1]&SPECMASK) != 0 ) || ( td[2] != 1 ) ) { MLOCK(ErrorMessageLock); if ( par == -1 ) { MesPrint("$-variable is not a short number in print statement"); } else { MesPrint("$-variable is not a short number in do loop"); } MUNLOCK(ErrorMessageLock); Terminate(-1); } return( td[3] > 0 ? td[1]: -td[1] ); } else { MLOCK(ErrorMessageLock); if ( par == -1 ) { MesPrint("$-variable is not a number in print statement"); } else { MesPrint("$-variable is not a number in do loop"); } MUNLOCK(ErrorMessageLock); Terminate(-1); } return(0); } num = EvalDoLoopArg(BHEAD arg+2,par); } else if ( *arg == DOLLAREXPR2 ) { if ( arg[1] < 0 ) { num = -arg[1]-1; } else if ( arg[2] != DOLLAREXPR2 && par == -1 ) { goto endofchain; } else { num = EvalDoLoopArg(BHEAD arg+2,par); } } else { MLOCK(ErrorMessageLock); if ( par == -1 ) { MesPrint("Invalid $-variable in print statement"); } else { MesPrint("Invalid $-variable in do loop"); } MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } if ( num == 0 ) return(d->nfactors); if ( num > d->nfactors || num < 1 ) { MLOCK(ErrorMessageLock); if ( par == -1 ) { MesPrint("Not a valid factor number for $-variable in print statement"); } else { MesPrint("Not a valid factor number for $-variable in do loop"); } MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } if ( d->factors[num].type == DOLNUMBER ) return(d->factors[num].value); else { /* If correct, type can only be DOLNUMBER or DOLTERMS */ MLOCK(ErrorMessageLock); if ( par == -1 ) { MesPrint("$-variable in print statement is not a number"); } else { MesPrint("$-variable in do loop is not a number"); } MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } } /* #] EvalDoLoopArg : #[ TestDoLoop : */ WORD TestDoLoop(PHEAD WORD *lhsbuf, WORD level) { GETBIDENTITY WORD start,finish,incr; WORD *h; DOLLARS d; h = lhsbuf + 4; /* address of the start value */ start = EvalDoLoopArg(BHEAD h,0); while ( ( *h == DOLLAREXPRESSION || *h == DOLLAREXPR2 ) && ( h[2] == DOLLAREXPR2 ) ) h += 2; h += 2; finish = EvalDoLoopArg(BHEAD h,0); while ( ( *h == DOLLAREXPRESSION || *h == DOLLAREXPR2 ) && ( h[2] == DOLLAREXPR2 ) ) h += 2; h += 2; incr = EvalDoLoopArg(BHEAD h,0); if ( ( finish == start ) || ( finish > start && incr > 0 ) || ( finish < start && incr < 0 ) ) {} else { level = lhsbuf[3]; } /* skips the loop */ /* Put start in the dollar variable indicated by lhsbuf[2] */ d = Dollars + lhsbuf[2]; #ifdef WITHPTHREADS { int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( lhsbuf[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } } #endif if ( d->size < MINALLOC ) { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollar contents"); d->size = MINALLOC; d->where = (WORD *)Malloc1(d->size*sizeof(WORD),"dollar contents"); } if ( start > 0 ) { d->where[0] = 4; d->where[1] = start; d->where[2] = 1; d->where[3] = 3; d->where[4] = 0; d->type = DOLNUMBER; } else if ( start < 0 ) { d->where[0] = 4; d->where[1] = -start; d->where[2] = 1; d->where[3] = -3; d->where[4] = 0; d->type = DOLNUMBER; } else d->type = DOLZERO; if ( d == Dollars + lhsbuf[2] ) { cbuf[AM.dbufnum].CanCommu[lhsbuf[2]] = 0; cbuf[AM.dbufnum].NumTerms[lhsbuf[2]] = 1; cbuf[AM.dbufnum].rhs[lhsbuf[2]] = d->where; } return(level); } /* #] TestDoLoop : #[ TestEndDoLoop : */ WORD TestEndDoLoop(PHEAD WORD *lhsbuf, WORD level) { GETBIDENTITY WORD start,finish,incr,value; WORD *h; DOLLARS d; h = lhsbuf + 4; /* address of the start value */ start = EvalDoLoopArg(BHEAD h,0); while ( ( *h == DOLLAREXPRESSION || *h == DOLLAREXPR2 ) && ( h[2] == DOLLAREXPR2 ) ) h += 2; h += 2; finish = EvalDoLoopArg(BHEAD h,0); while ( ( *h == DOLLAREXPRESSION || *h == DOLLAREXPR2 ) && ( h[2] == DOLLAREXPR2 ) ) h += 2; h += 2; incr = EvalDoLoopArg(BHEAD h,0); if ( ( finish == start ) || ( finish > start && incr > 0 ) || ( finish < start && incr < 0 ) ) {} else { level = lhsbuf[3]; } /* skips the loop */ /* Put start in the dollar variable indicated by lhsbuf[2] */ d = Dollars + lhsbuf[2]; #ifdef WITHPTHREADS { int nummodopt, dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( lhsbuf[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } } #endif /* Get the value */ if ( d->type == DOLZERO ) { value = 0; } else if ( ( d->type == DOLNUMBER || d->type == DOLTERMS ) && ( d->where[4] == 0 ) && ( d->where[0] == 4 ) && ( d->where[1] > 0 ) && ( d->where[2] == 1 ) ) { value = ( d->where[3] < 0 ) ? -d->where[1]: d->where[1]; } else { MLOCK(ErrorMessageLock); MesPrint("Wrong type of object in do loop parameter"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(level); } value += incr; if ( ( finish > start && value <= finish ) || ( finish < start && value >= finish ) || ( finish == start && value == finish ) ) {} else level = lhsbuf[3]; if ( d->size < MINALLOC ) { if ( d->where && d->where != &(AM.dollarzero) ) M_free(d->where,"dollar contents"); d->size = MINALLOC; d->where = (WORD *)Malloc1(d->size*sizeof(WORD),"dollar contents"); } if ( value > 0 ) { d->where[0] = 4; d->where[1] = value; d->where[2] = 1; d->where[3] = 3; d->where[4] = 0; d->type = DOLNUMBER; } else if ( start < 0 ) { d->where[0] = 4; d->where[1] = -value; d->where[2] = 1; d->where[3] = -3; d->where[4] = 0; d->type = DOLNUMBER; } else d->type = DOLZERO; if ( d == Dollars + lhsbuf[2] ) { cbuf[AM.dbufnum].CanCommu[lhsbuf[2]] = 0; cbuf[AM.dbufnum].NumTerms[lhsbuf[2]] = 1; cbuf[AM.dbufnum].rhs[lhsbuf[2]] = d->where; } return(level); } /* #] TestEndDoLoop : #[ DollarFactorize : */ /** * Factors a dollar expression. * Notation: d->nfactors becomes nonzero. * if the number of factors is one, we leave d->factors zero. * Otherwise factors is an array of pointers to the factors. * These are pointers of the type FACDOLLAR. * fd->where pointer to contents in term notation * fd->size size of the buffer fd->where points to * fd->type DOLNUMBER or DOLTERMS * fd->value value if type is DOLNUMBER and it fits in a WORD. */ /* #define STEP2 */ #define STEP2 int DollarFactorize(PHEAD WORD numdollar) { GETBIDENTITY DOLLARS d = Dollars + numdollar; CBUF *C, *CC; WORD *oldworkpointer; WORD *buf1, *t, *term, *buf1content, *buf2, *termextra; WORD *buf3, *argextra; #ifdef STEP2 WORD *tstop, pow, *r; #endif int i, j, jj, action = 0, sign = 1; LONG insize, ii; WORD startebuf = cbuf[AT.ebufnum].numrhs; WORD nfactors, factorsincontent, extrafactor = 0; WORD oldsorttype = AR.SortType; #ifdef WITHPTHREADS int nummodopt, dtype; dtype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif CleanDollarFactors(d); #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif if ( d->type != DOLTERMS ) { /* only one term */ if ( d->type != DOLZERO ) d->nfactors = 1; return(0); } if ( d->where[d->where[0]] == 0 ) { /* only one term. easy */ } /* Here should come the code for the factorization We copied the routine ArgFactorize in argument.c and changed the memory management completely. For the actual factorization it calls WORD *DoFactorizeDollar(PHEAD WORD *expr) which allocates space for the answer. Notation: term,...,term,0,term,...,term,0,term,...,term,0,0 #[ Step 1: sort the terms properly and/or make copy --> buf1,insize */ term = d->where; AR.SortType = SORTHIGHFIRST; if ( oldsorttype != AR.SortType ) { NewSort(BHEAD0); while ( *term ) { t = term + *term; if ( AN.ncmod != 0 ) { if ( AN.ncmod != 1 || ( (WORD)AN.cmod[0] < 0 ) ) { AR.SortType = oldsorttype; MLOCK(ErrorMessageLock); MesPrint("Factorization modulus a number, greater than a WORD not implemented."); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( Modulus(term) ) { AR.SortType = oldsorttype; MLOCK(ErrorMessageLock); MesCall("DollarFactorize"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( !*term) { term = t; continue; } } StoreTerm(BHEAD term); term = t; } AN.tryterm = 0; /* for now */ EndSort(BHEAD (WORD *)((void *)(&buf1)),2); t = buf1; while ( *t ) t += *t; insize = t - buf1; } else { t = term; while ( *t ) t += *t; ii = insize = t - term; buf1 = (WORD *)Malloc1((insize+1)*sizeof(WORD),"DollarFactorize-1"); t = buf1; NCOPY(t,term,ii); *t++ = 0; } /* #] Step 1: #[ Step 2: take out the 'content'. */ #ifdef STEP2 buf1content = TermMalloc("DollarContent"); AN.tryterm = -1; if ( ( buf2 = TakeContent(BHEAD buf1,buf1content) ) == 0 ) { AN.tryterm = 0; TermFree(buf1content,"DollarContent"); M_free(buf1,"DollarFactorize-1"); AR.SortType = oldsorttype; MLOCK(ErrorMessageLock); MesCall("DollarFactorize"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(1); } else if ( ( buf1content[0] == 4 ) && ( buf1content[1] == 1 ) && ( buf1content[2] == 1 ) && ( buf1content[3] == 3 ) ) { /* Nothing happened */ AN.tryterm = 0; if ( buf2 != buf1 ) { M_free(buf2,"DollarFactorize-2"); buf2 = buf1; } factorsincontent = 0; } else { /* The way we took out objects is rather brutish. We have to normalize */ AN.tryterm = 0; if ( buf2 != buf1 ) M_free(buf1,"DollarFactorize-1"); buf1 = buf2; t = buf1; while ( *t ) t += *t; insize = t - buf1; /* Now analyse how many factors there are in the content */ factorsincontent = 0; term = buf1content; tstop = term + *term; if ( tstop[-1] < 0 ) factorsincontent++; if ( ABS(tstop[-1]) == 3 && tstop[-2] == 1 && tstop[-3] == 1 ) { tstop -= ABS(tstop[-1]); } else { factorsincontent++; tstop -= ABS(tstop[-1]); } term++; while ( term < tstop ) { switch ( *term ) { case SYMBOL: t = term+2; i = (term[1]-2)/2; while ( i > 0 ) { factorsincontent += ABS(t[1]); i--; t += 2; } break; case DOTPRODUCT: t = term+2; i = (term[1]-2)/3; while ( i > 0 ) { factorsincontent += ABS(t[2]); i--; t += 3; } break; case VECTOR: case DELTA: factorsincontent += (term[1]-2)/2; break; case INDEX: factorsincontent += term[1]-2; break; default: if ( *term >= FUNCTION ) factorsincontent++; break; } term += term[1]; } } #else factorsincontent = 0; buf1content = 0; #endif /* #] Step 2: take out the 'content'. #[ Step 3: ConvertToPoly if there are objects that are not SYMBOLs, invoke ConvertToPoly We keep the original in buf1 in case there are no factors */ t = buf1; while ( *t ) { if ( ( t[1] != SYMBOL ) && ( *t != (ABS(t[*t-1])+1) ) ) { action = 1; break; } t += *t; } if ( DetCommu(buf1) > 1 ) { MesPrint("Cannot factorize a $-expression with more than one noncommuting object"); AR.SortType = oldsorttype; M_free(buf1,"DollarFactorize-2"); if ( buf1content ) TermFree(buf1content,"DollarContent"); MesCall("DollarFactorize"); Terminate(-1); return(-1); } if ( action ) { t = buf1; termextra = AT.WorkPointer; NewSort(BHEAD0); NewSort(BHEAD0); while ( *t ) { if ( LocalConvertToPoly(BHEAD t,termextra,startebuf,0) < 0 ) { getout: AR.SortType = oldsorttype; M_free(buf1,"DollarFactorize-2"); if ( buf1content ) TermFree(buf1content,"DollarContent"); MesCall("DollarFactorize"); Terminate(-1); return(-1); } StoreTerm(BHEAD termextra); t += *t; } AN.tryterm = 0; /* for now */ if ( EndSort(BHEAD (WORD *)((void *)(&buf2)),2) < 0 ) { goto getout; } LowerSortLevel(); t = buf2; while ( *t > 0 ) t += *t; } else { buf2 = buf1; } /* #] Step 3: ConvertToPoly #[ Step 4: Now the hard work. */ if ( ( buf3 = poly_factorize_dollar(BHEAD buf2) ) == 0 ) { MesCall("DollarFactorize"); AR.SortType = oldsorttype; if ( buf2 != buf1 && buf2 ) M_free(buf2,"DollarFactorize-3"); M_free(buf1,"DollarFactorize-3"); if ( buf1content ) TermFree(buf1content,"DollarContent"); Terminate(-1); return(-1); } if ( buf2 != buf1 && buf2 ) { M_free(buf2,"DollarFactorize-3"); buf2 = 0; } term = buf3; AR.SortType = oldsorttype; /* Count the factors and strip a factor -1 */ nfactors = 0; while ( *term ) { #ifdef STEP2 if ( *term == 4 && term[4] == 0 && term[3] == -3 && term[2] == 1 && term[1] == 1 ) { WORD *tt1, *tt2, *ttstop; sign = -sign; tt1 = term; tt2 = term + *term + 1; ttstop = tt2; while ( *ttstop ) { while ( *ttstop ) ttstop += *ttstop; ttstop++; } while ( tt2 < ttstop ) *tt1++ = *tt2++; *tt1 = 0; factorsincontent++; extrafactor++; } else #endif { term += *term; while ( *term ) { term += *term; } nfactors++; term++; } } /* We have now: buf1: the original before ConvertToPoly for if only one factor buf3: the factored expression with nfactors factors #] Step 4: #[ Step 5: ConvertFromPoly If ConvertToPoly was used, use now ConvertFromPoly Be careful: there should be more than one factor now. */ #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { LOCK(d->pthreadslock); } #endif if ( nfactors == 1 && extrafactor == 0 ) { /* we can use the buf1 contents */ if ( factorsincontent == 0 ) { d->nfactors = 1; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif /* We used here (before 3-sep-2015) the original and did not make provisions for having a factors struct, figuring that all info is identical to the full dollar. This makes things too complicated at later stages. */ d->factors = (FACDOLLAR *)Malloc1(sizeof(FACDOLLAR),"factors in dollar"); term = buf1; while ( *term ) term += *term; d->factors[0].size = i = term - buf1; d->factors[0].where = t = (WORD *)Malloc1(sizeof(WORD)*(i+1),"DollarFactorize-5"); term = buf1; NCOPY(t,term,i); *t = 0; AR.SortType = oldsorttype; M_free(buf3,"DollarFactorize-4"); if ( buf2 != buf1 && buf2 ) M_free(buf2,"DollarFactorize-4"); M_free(buf1,"DollarFactorize-4"); if ( buf1content ) TermFree(buf1content,"DollarContent"); return(0); } else { d->factors = (FACDOLLAR *)Malloc1(sizeof(FACDOLLAR)*(nfactors+factorsincontent),"factors in dollar"); term = buf1; while ( *term ) term += *term; d->factors[0].size = i = term - buf1; d->factors[0].where = t = (WORD *)Malloc1(sizeof(WORD)*(i+1),"DollarFactorize-5"); term = buf1; NCOPY(t,term,i); *t = 0; M_free(buf3,"DollarFactorize-4"); buf3 = 0; if ( buf2 != buf1 && buf2 ) { M_free(buf2,"DollarFactorize-4"); buf2 = 0; } } } else if ( action ) { C = cbuf+AC.cbufnum; CC = cbuf+AT.ebufnum; oldworkpointer = AT.WorkPointer; d->factors = (FACDOLLAR *)Malloc1(sizeof(FACDOLLAR)*(nfactors+factorsincontent),"factors in dollar"); term = buf3; for ( i = 0; i < nfactors; i++ ) { argextra = AT.WorkPointer; NewSort(BHEAD0); NewSort(BHEAD0); while ( *term ) { if ( ConvertFromPoly(BHEAD term,argextra,numxsymbol,CC->numrhs-startebuf+numxsymbol ,startebuf-numxsymbol,1) <= 0 ) { LowerSortLevel(); getout2: AR.SortType = oldsorttype; M_free(d->factors,"factors in dollar"); d->factors = 0; #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif M_free(buf3,"DollarFactorize-4"); if ( buf2 != buf1 && buf2 ) M_free(buf2,"DollarFactorize-4"); M_free(buf1,"DollarFactorize-4"); if ( buf1content ) TermFree(buf1content,"DollarContent"); return(-3); } AT.WorkPointer = argextra + *argextra; /* ConvertFromPoly leaves terms with subexpressions. Hence: */ if ( Generator(BHEAD argextra,C->numlhs+1) ) { goto getout2; } term += *term; } term++; AT.WorkPointer = oldworkpointer; AN.tryterm = 0; /* for now */ EndSort(BHEAD (WORD *)((void *)(&(d->factors[i].where))),2); LowerSortLevel(); d->factors[i].type = DOLTERMS; t = d->factors[i].where; while ( *t ) t += *t; d->factors[i].size = t - d->factors[i].where; } CC->numrhs = startebuf; } else { C = cbuf+AC.cbufnum; oldworkpointer = AT.WorkPointer; d->factors = (FACDOLLAR *)Malloc1(sizeof(FACDOLLAR)*(nfactors+factorsincontent),"factors in dollar"); term = buf3; for ( i = 0; i < nfactors; i++ ) { NewSort(BHEAD0); while ( *term ) { argextra = oldworkpointer; j = *term; NCOPY(argextra,term,j) AT.WorkPointer = argextra; if ( Generator(BHEAD oldworkpointer,C->numlhs+1) ) { goto getout2; } } term++; AT.WorkPointer = oldworkpointer; AN.tryterm = 0; /* for now */ EndSort(BHEAD (WORD *)((void *)(&(d->factors[i].where))),2); d->factors[i].type = DOLTERMS; t = d->factors[i].where; while ( *t ) t += *t; d->factors[i].size = t - d->factors[i].where; } } d->nfactors = nfactors + factorsincontent; /* #] Step 5: ConvertFromPoly #[ Step 6: The factors of the content */ if ( buf3 ) M_free(buf3,"DollarFactorize-5"); if ( buf2 != buf1 && buf2 ) M_free(buf2,"DollarFactorize-5"); M_free(buf1,"DollarFactorize-5"); j = nfactors; #ifdef STEP2 term = buf1content; tstop = term + *term; if ( tstop[-1] < 0 ) { tstop[-1] = -tstop[-1]; sign = -sign; } tstop -= tstop[-1]; term++; while ( term < tstop ) { switch ( *term ) { case SYMBOL: t = term+2; i = (term[1]-2)/2; while ( i > 0 ) { if ( t[1] < 0 ) { t[1] = -t[1]; pow = -1; } else { pow = 1; } for ( jj = 0; jj < t[1]; jj++ ) { r = d->factors[j].where = (WORD *)Malloc1(9*sizeof(WORD),"factor"); r[0] = 8; r[1] = SYMBOL; r[2] = 4; r[3] = *t; r[4] = pow; r[5] = 1; r[6] = 1; r[7] = 3; r[8] = 0; d->factors[j].type = DOLTERMS; d->factors[j].size = 8; j++; } i--; t += 2; } break; case DOTPRODUCT: t = term+2; i = (term[1]-2)/3; while ( i > 0 ) { if ( t[2] < 0 ) { t[2] = -t[2]; pow = -1; } else { pow = 1; } for ( jj = 0; jj < t[2]; jj++ ) { r = d->factors[j].where = (WORD *)Malloc1(10*sizeof(WORD),"factor"); r[0] = 9; r[1] = DOTPRODUCT; r[2] = 5; r[3] = t[0]; r[4] = t[1]; r[5] = pow; r[6] = 1; r[7] = 1; r[8] = 3; r[9] = 0; d->factors[j].type = DOLTERMS; d->factors[j].size = 9; j++; } i--; t += 3; } break; case VECTOR: case DELTA: t = term+2; i = (term[1]-2)/2; while ( i > 0 ) { for ( jj = 0; jj < t[1]; jj++ ) { r = d->factors[j].where = (WORD *)Malloc1(9*sizeof(WORD),"factor"); r[0] = 8; r[1] = *term; r[2] = 4; r[3] = *t; r[4] = t[1]; r[5] = 1; r[6] = 1; r[7] = 3; r[8] = 0; d->factors[j].type = DOLTERMS; d->factors[j].size = 8; j++; } i--; t += 2; } break; case INDEX: t = term+2; i = term[1]-2; while ( i > 0 ) { for ( jj = 0; jj < t[1]; jj++ ) { r = d->factors[j].where = (WORD *)Malloc1(8*sizeof(WORD),"factor"); r[0] = 7; r[1] = *term; r[2] = 3; r[3] = *t; r[4] = 1; r[5] = 1; r[6] = 3; r[7] = 0; d->factors[j].type = DOLTERMS; d->factors[j].size = 7; j++; } i--; t++; } break; default: if ( *term >= FUNCTION ) { r = d->factors[j].where = (WORD *)Malloc1((term[1]+5)*sizeof(WORD),"factor"); *r++ = d->factors[j].size = term[1]+4; for ( jj = 0; jj < t[1]; jj++ ) *r++ = term[jj]; *r++ = 1; *r++ = 1; *r++ = 3; *r = 0; j++; } break; } term += term[1]; } #endif /* #] Step 6: #[ Step 7: Numerical factors */ #ifdef STEP2 term = buf1content; tstop = term + *term; if ( tstop[-1] == 3 && tstop[-2] == 1 && tstop[-3] == 1 ) {} else if ( tstop[-1] == 3 && tstop[-2] == 1 && (UWORD)(tstop[-3]) <= MAXPOSITIVE ) { d->factors[j].where = 0; d->factors[j].size = 0; d->factors[j].type = DOLNUMBER; d->factors[j].value = sign*tstop[-3]; sign = 1; j++; } else { d->factors[j].where = r = (WORD *)Malloc1((tstop[-1]+2)*sizeof(WORD),"numfactor"); d->factors[j].size = tstop[-1]+1; d->factors[j].type = DOLTERMS; d->factors[j].value = 0; i = tstop[-1]; t = tstop - i; *r++ = tstop[-1]+1; NCOPY(r,t,i); *r = 0; if ( sign < 0 ) { r = d->factors[j].where; while ( *r ) { r += *r; r[-1] = -r[-1]; } sign = 1; } j++; } #endif if ( sign < 0 ) { /* Note that this guy should come first */ for ( jj = j; jj > 0; jj-- ) { d->factors[jj] = d->factors[jj-1]; } d->factors[0].where = 0; d->factors[0].size = 0; d->factors[0].type = DOLNUMBER; d->factors[0].value = -1; j++; } d->nfactors = j; if ( buf1content ) TermFree(buf1content,"DollarContent"); /* #] Step 7: #[ Step 8: Sorting the factors There are d->nfactors factors. Look which ones have a 'where' Sort them by bubble sort */ if ( d->nfactors > 1 ) { WORD ***fac, j1, j2, k, ret, *s1, *s2, *s3; LONG **facsize, x; facsize = (LONG **)Malloc1((sizeof(WORD **)+sizeof(LONG *))*d->nfactors,"SortDollarFactors"); fac = (WORD ***)(facsize+d->nfactors); k = 0; for ( j = 0; j < d->nfactors; j++ ) { if ( d->factors[j].where ) { fac[k] = &(d->factors[j].where); facsize[k] = &(d->factors[j].size); k++; } } if ( k > 1 ) { for ( j = 1; j < k; j++ ) { /* bubble sort */ j1 = j; j2 = j1-1; nextj1:; s1 = *(fac[j1]); s2 = *(fac[j2]); while ( *s1 && *s2 ) { if ( ( ret = CompareTerms(BHEAD s2, s1, (WORD)2) ) == 0 ) { s1 += *s1; s2 += *s2; } else if ( ret > 0 ) goto nextj; else { exch: s3 = *(fac[j1]); *(fac[j1]) = *(fac[j2]); *(fac[j2]) = s3; x = *(facsize[j1]); *(facsize[j1]) = *(facsize[j2]); *(facsize[j2]) = x; j1--; j2--; if ( j1 > 0 ) goto nextj1; goto nextj; } } if ( *s1 ) goto nextj; if ( *s2 ) goto exch; nextj:; } } M_free(facsize,"SortDollarFactors"); } /* #] Step 8: */ #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif return(0); } /* #] DollarFactorize : #[ CleanDollarFactors : */ void CleanDollarFactors(DOLLARS d) { int i; if ( d->nfactors >= 1 ) { for ( i = 0; i < d->nfactors; i++ ) { if ( d->factors ) if ( d->factors[i].where ) M_free(d->factors[i].where,"dollar factors"); } } if ( d->factors ) { M_free(d->factors,"dollar factors"); d->factors = 0; } d->nfactors = 0; } /* #] CleanDollarFactors : #[ TakeDollarContent : */ WORD *TakeDollarContent(PHEAD WORD *dollarbuffer, WORD **factor) { WORD *remain, *t; int pow; /* We force the sign of the first term to be positive. */ t = dollarbuffer; pow = 1; t += *t; if ( t[-1] < 0 ) { pow = 0; t[-1] = -t[-1]; while ( *t ) { t += *t; t[-1] = -t[-1]; } } /* Now the GCD of the numerators and the LCM of the denominators: */ if ( AN.cmod != 0 ) { if ( ( *factor = MakeDollarMod(BHEAD dollarbuffer,&remain) ) == 0 ) { Terminate(-1); } if ( pow == 0 ) { (*factor)[**factor-1] = -(*factor)[**factor-1]; (*factor)[**factor-1] += AN.cmod[0]; } } else { if ( ( *factor = MakeDollarInteger(BHEAD dollarbuffer,&remain) ) == 0 ) { Terminate(-1); } if ( pow == 0 ) { (*factor)[**factor-1] = -(*factor)[**factor-1]; } } return(remain); } /* #] TakeDollarContent : #[ MakeDollarInteger : */ /** * For normalizing everything to integers we have to * determine for all elements of this argument the LCM of * the denominators and the GCD of the numerators. * The input argument is in bufin. * The number that comes out is the return value. * The normalized argument is in bufout. */ WORD *MakeDollarInteger(PHEAD WORD *bufin,WORD **bufout) { GETBIDENTITY UWORD *GCDbuffer, *GCDbuffer2, *LCMbuffer, *LCMb, *LCMc; WORD *r, *r1, *r2, *r3, *rnext, i, k, j, *oldworkpointer, *factor; WORD kGCD, kLCM, kGCD2, kkLCM, jLCM, jGCD; CBUF *C = cbuf+AC.cbufnum; GCDbuffer = NumberMalloc("MakeDollarInteger"); GCDbuffer2 = NumberMalloc("MakeDollarInteger"); LCMbuffer = NumberMalloc("MakeDollarInteger"); LCMb = NumberMalloc("MakeDollarInteger"); LCMc = NumberMalloc("MakeDollarInteger"); r = bufin; /* First take the first term to load up the LCM and the GCD */ r2 = r + *r; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kGCD = 0; kGCD < k; kGCD++ ) GCDbuffer[kGCD] = r3[kGCD]; k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; r1 = r2; /* Now go through the rest of the terms in this argument. */ while ( *r1 ) { r2 = r1 + *r1; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( GCDbuffer[0] == 1 ) && ( kGCD == 1 ) ) ) { /* GCD is already 1 */ } else if ( ( ( k != 1 ) || ( r3[0] != 1 ) ) ) { if ( GcdLong(BHEAD GCDbuffer,kGCD,(UWORD *)r3,k,GCDbuffer2,&kGCD2) ) { goto MakeDollarIntegerErr; } kGCD = kGCD2; for ( i = 0; i < kGCD; i++ ) GCDbuffer[i] = GCDbuffer2[i]; } else { kGCD = 1; GCDbuffer[0] = 1; } k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( LCMbuffer[0] == 1 ) && ( kLCM == 1 ) ) ) { for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; } else if ( ( k != 1 ) || ( r3[0] != 1 ) ) { if ( GcdLong(BHEAD LCMbuffer,kLCM,(UWORD *)r3,k,LCMb,&kkLCM) ) { goto MakeDollarIntegerErr; } DivLong((UWORD *)r3,k,LCMb,kkLCM,LCMb,&kkLCM,LCMc,&jLCM); MulLong(LCMbuffer,kLCM,LCMb,kkLCM,LCMc,&jLCM); for ( kLCM = 0; kLCM < jLCM; kLCM++ ) LCMbuffer[kLCM] = LCMc[kLCM]; } else {} /* LCM doesn't change */ r1 = r2; } /* Now put the factor together: GCD/LCM */ r3 = (WORD *)(GCDbuffer); if ( kGCD == kLCM ) { for ( jGCD = 0; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; k = kGCD; } else if ( kGCD > kLCM ) { for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; for ( jGCD = kLCM; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = 0; k = kGCD; } else { for ( jGCD = kGCD; jGCD < kLCM; jGCD++ ) r3[jGCD] = 0; for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kLCM] = LCMbuffer[jGCD]; k = kLCM; } j = 2*k+1; /* Now we have to write this to factor */ factor = r1 = (WORD *)Malloc1((j+2)*sizeof(WORD),"MakeDollarInteger"); *r1++ = j+1; r2 = r3; for ( i = 0; i < k; i++ ) { *r1++ = *r2++; *r1++ = *r2++; } *r1++ = j; *r1 = 0; /* Next we have to take the factor out from the argument. This cannot be done in location, because the denominator stuff can make coefficients longer. We do this via a sort because the things may be jumbled any way and we do not know in advance how much space we need. */ NewSort(BHEAD0); r = bufin; oldworkpointer = AT.WorkPointer; while ( *r ) { rnext = r + *r; j = ABS(rnext[-1]); r3 = rnext - j; r2 = oldworkpointer; while ( r < r3 ) *r2++ = *r++; j = (j-1)/2; /* reduced length. Remember, k is the other red length */ if ( DivRat(BHEAD (UWORD *)r3,j,GCDbuffer,k,(UWORD *)r2,&i) ) { goto MakeDollarIntegerErr; } i = 2*i+1; r2 = r2 + i; if ( rnext[-1] < 0 ) r2[-1] = -i; else r2[-1] = i; *oldworkpointer = r2-oldworkpointer; AT.WorkPointer = r2; if ( Generator(BHEAD oldworkpointer,C->numlhs) ) { goto MakeDollarIntegerErr; } r = rnext; } AT.WorkPointer = oldworkpointer; AN.tryterm = 0; /* for now */ EndSort(BHEAD (WORD *)bufout,2); /* Cleanup */ NumberFree(LCMc,"MakeDollarInteger"); NumberFree(LCMb,"MakeDollarInteger"); NumberFree(LCMbuffer,"MakeDollarInteger"); NumberFree(GCDbuffer2,"MakeDollarInteger"); NumberFree(GCDbuffer,"MakeDollarInteger"); return(factor); MakeDollarIntegerErr: NumberFree(LCMc,"MakeDollarInteger"); NumberFree(LCMb,"MakeDollarInteger"); NumberFree(LCMbuffer,"MakeDollarInteger"); NumberFree(GCDbuffer2,"MakeDollarInteger"); NumberFree(GCDbuffer,"MakeDollarInteger"); MesCall("MakeDollarInteger"); Terminate(-1); return(0); } /* #] MakeDollarInteger : #[ MakeDollarMod : */ /** * Similar to MakeDollarInteger but now with modulus arithmetic using only * a one WORD 'prime'. We make the coefficient of the first term in the * argument equal to one. * Already the coefficients are taken modulus AN.cmod and AN.ncmod == 1 */ WORD *MakeDollarMod(PHEAD WORD *buffer, WORD **bufout) { GETBIDENTITY WORD *r, *r1, x, xx, ix, ip; WORD *factor, *oldworkpointer; int i; CBUF *C = cbuf+AC.cbufnum; r = buffer; x = r[*r-3]; if ( r[*r-1] < 0 ) x += AN.cmod[0]; if ( GetModInverses(x,(WORD)(AN.cmod[0]),&ix,&ip) ) { Terminate(-1); } factor = (WORD *)Malloc1(5*sizeof(WORD),"MakeDollarMod"); factor[0] = 4; factor[1] = x; factor[2] = 1; factor[3] = 3; factor[4] = 0; /* Now we have to multiply all coefficients by ix. This does not make things longer, but we should keep to the conventions of MakeDollarInteger. */ NewSort(BHEAD0); r = buffer; oldworkpointer = AT.WorkPointer; while ( *r ) { r1 = oldworkpointer; i = *r; NCOPY(r1,r,i); xx = r1[-3]; if ( r1[-1] < 0 ) xx += AN.cmod[0]; r1[-1] = (WORD)((((LONG)xx)*ix) % AN.cmod[0]); *r1 = 0; AT.WorkPointer = r1; if ( Generator(BHEAD oldworkpointer,C->numlhs) ) { Terminate(-1); } } AT.WorkPointer = oldworkpointer; AN.tryterm = 0; /* for now */ EndSort(BHEAD (WORD *)bufout,2); return(factor); } /* #] MakeDollarMod : #[ GetDolNum : Evaluates a chain of DOLLAREXPR2 into a number */ int GetDolNum(PHEAD WORD *t, WORD *tstop) { DOLLARS d; WORD num, *w; if ( t+3 < tstop && t[3] == DOLLAREXPR2 ) { d = Dollars + t[2]; #ifdef WITHPTHREADS { int nummodopt, dtype; dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { MLOCK(ErrorMessageLock); MesPrint("&Illegal attempt to use $-variable %s in module %l", DOLLARNAME(Dollars,t[2]),AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } } #endif if ( d->factors == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Attempt to use a factor of an unfactored $-variable"); MUNLOCK(ErrorMessageLock); Terminate(-1); } num = GetDolNum(BHEAD t+t[1],tstop); if ( num == 0 ) return(d->nfactors); if ( num > d->nfactors ) { MLOCK(ErrorMessageLock); MesPrint("Attempt to use an nonexisting factor %d of a $-variable",num); MUNLOCK(ErrorMessageLock); Terminate(-1); } w = d->factors[num-1].where; if ( w == 0 ) return(d->factors[num-1].value); if ( w[0] == 4 && w[4] == 0 && w[3] == 3 && w[2] == 1 && w[1] > 0 && w[1] < MAXPOSITIVE ) return(w[1]); else { MLOCK(ErrorMessageLock); MesPrint("Illegal type of factor number of a $-variable"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } else if ( t[2] < 0 ) { return(-t[2]-1); } else { d = Dollars + t[2]; #ifdef WITHPTHREADS { int nummodopt, dtype; dtype = -1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { MLOCK(ErrorMessageLock); MesPrint("&Illegal attempt to use $-variable %s in module %l", DOLLARNAME(Dollars,t[2]),AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } } #endif if ( d->type == DOLZERO ) return(0); if ( d->type == DOLTERMS || d->type == DOLNUMBER ) { if ( d->where[0] == 4 && d->where[4] == 0 && d->where[3] == 3 && d->where[2] == 1 && d->where[1] > 0 && d->where[1] < MAXPOSITIVE ) return(d->where[1]); MLOCK(ErrorMessageLock); MesPrint("Attempt to use an nonexisting factor of a $-variable"); MUNLOCK(ErrorMessageLock); Terminate(-1); } MLOCK(ErrorMessageLock); MesPrint("Illegal type of factor number of a $-variable"); MUNLOCK(ErrorMessageLock); Terminate(-1); } return(0); } /* #] GetDolNum : #[ AddPotModdollar : */ /** * Adds a $-variable specified by \a numdollar to the list of potentially * modified $-variables unless it has already been included in the list. * * @param numdollar The index of the $-variable to be added. */ void AddPotModdollar(WORD numdollar) { int i, n = NumPotModdollars; for ( i = 0; i < n; i++ ) { if ( numdollar == PotModdollars[i] ) break; } if ( i >= n ) { *(WORD *)FromList(&AC.PotModDolList) = numdollar; } } /* #] AddPotModdollar : */ form-5.0.1/sources/factor.c0000644000175100017510000006047315217035721011265 /** @file factor.c * * The routines for finding (one term) factors in dollars and expressions. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : factor.c */ #include "form3.h" /* #] Includes : #[ FactorIn : This routine tests for a factor in a dollar expression. Note that unlike with regular active or hidden expressions we cannot add memory as easily as dollars are rather volatile. */ int FactorIn(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD *t, *tstop, *m, *mm, *oldwork, *mstop, *n1, *n2, *n3, *n4, *n1stop, *n2stop; WORD *r1, *r2, *r3, *r4, j, k, kGCD, kGCD2, kLCM, jGCD, kkLCM, jLCM, size; UWORD *GCDbuffer, *GCDbuffer2, *LCMbuffer, *LCMb, *LCMc; int fromwhere = 0, i; DOLLARS d; t = term; GETSTOP(t,tstop); t++; while ( ( t < tstop ) && ( *t != FACTORIN || ( ( *t == FACTORIN ) && ( t[FUNHEAD] != -DOLLAREXPRESSION || t[1] != FUNHEAD+2 ) ) ) ) t += t[1]; if ( t >= tstop ) { MLOCK(ErrorMessageLock); MesPrint("Internal error. Could not find proper factorin_ function."); MUNLOCK(ErrorMessageLock); return(-1); } oldwork = AT.WorkPointer; d = Dollars + t[FUNHEAD+1]; #ifdef WITHPTHREADS { int nummodopt, dtype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( t[FUNHEAD+1] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } } #endif if ( d->type == DOLTERMS ) { fromwhere = 1; } else if ( ( d = DolToTerms(BHEAD t[FUNHEAD+1]) ) == 0 ) { /* The variable cannot convert to an expression We replace the function by 1. */ m = oldwork; n1 = term; while ( n1 < t ) *m++ = *n1++; n1 = t + t[1]; tstop = term + *term; while ( n1 < tstop ) *m++ = *n1++; *oldwork = m - oldwork; AT.WorkPointer = m; if ( Generator(BHEAD oldwork,level) ) return(-1); AT.WorkPointer = oldwork; return(0); } if ( d->where[0] == 0 ) { if ( fromwhere == 0 ) { if ( d->factors ) M_free(d->factors,"Dollar factors"); M_free(d,"Dollar in FactorIn_"); } return(0); } /* Now we have an expression in d->where. Find the symbolic factor that divides the expression and the numerical factor that makes all coefficients integer. For the symbolic factor we make a copy of the first term, and then go through all terms, scratching in the copy the objects that do not occur in the terms. */ m = oldwork; mm = d->where; k = *mm - ABS((mm[*mm-1])); for ( j = 0; j < k; j++ ) *m++ = *mm++; mstop = m; *oldwork = k; /* The copy is in place. Now search through the terms. Start at the second term */ mm = d->where + d->where[0]; while ( *mm ) { m = oldwork+1; r2 = mm+*mm; r2 -= ABS(r2[-1]); r1 = mm+1; while ( m < mstop ) { while ( r1 < r2 ) { if ( *r1 != *m ) { r1 += r1[1]; continue; } /* Now the various cases #[ SYMBOL : */ if ( *m == SYMBOL ) { n1 = m+2; n1stop = m+m[1]; n2stop = r1+r1[1]; while ( n1 < n1stop ) { n2 = r1+2; while ( n2 < n2stop ) { if ( *n1 != *n2 ) { n2 += 2; continue; } if ( n1[1] > 0 ) { if ( n2[1] < 0 ) { n2 += 2; continue; } if ( n2[1] < n1[1] ) n1[1] = n2[1]; } else { if ( n2[1] > 0 ) { n2 += 2; continue; } if ( n2[1] > n1[1] ) n1[1] = n2[1]; } break; } if ( n2 >= n2stop ) { /* scratch symbol */ if ( m[1] == 4 ) goto scratch; m[1] -= 2; n3 = n1; n4 = n1+2; while ( n4 < mstop ) *n3++ = *n4++; *oldwork = n3 - oldwork; mstop -= 2; n1stop -= 2; continue; } n1 += 2; } break; } /* #] SYMBOL : #[ DOTPRODUCT : */ else if ( *m == DOTPRODUCT ) { n1 = m+2; n1stop = m+m[1]; n2stop = r1+r1[1]; while ( n1 < n1stop ) { n2 = r1+2; while ( n2 < n2stop ) { if ( *n1 != *n2 || n1[1] != n2[1] ) { n2 += 3; continue; } if ( n1[2] > 0 ) { if ( n2[2] < 0 ) { n2 += 3; continue; } if ( n2[2] < n1[2] ) n1[2] = n2[2]; } else { if ( n2[2] > 0 ) { n2 += 3; continue; } if ( n2[2] > n1[2] ) n1[2] = n2[2]; } break; } if ( n2 >= n2stop ) { /* scratch symbol */ if ( m[1] == 5 ) goto scratch; m[1] -= 3; n3 = n1; n4 = n1+3; while ( n4 < mstop ) *n3++ = *n4++; *oldwork = n3 - oldwork; mstop -= 3; n1stop -= 3; continue; } n1 += 3; } break; } /* #] DOTPRODUCT : #[ VECTOR : */ else if ( *m == VECTOR ) { /* Here we have to be careful if there is more than one of the same */ n1 = m+2; n1stop = m+m[1]; n2 = r1+2;n2stop = r1+r1[1]; while ( n1 < n1stop ) { while ( n2 < n2stop ) { if ( *n1 == *n2 && n1[1] == n2[1] ) { n2 += 2; goto nextn1; } n2 += 2; } if ( n2 >= n2stop ) { /* scratch symbol */ if ( m[1] == 4 ) goto scratch; m[1] -= 2; n3 = n1; n4 = n1+2; while ( n4 < mstop ) *n3++ = *n4++; *oldwork = n3 - oldwork; mstop -= 2; n1stop -= 2; continue; } n2 = r1+2; nextn1: n1 += 2; } break; } /* #] VECTOR : #[ REMAINDER : */ else { /* Again: watch for multiple occurrences of the same object */ if ( m[1] != r1[1] ) { r1 += r1[1]; continue; } for ( j = 2; j < m[1]; j++ ) { if ( m[j] != r1[j] ) break; } if ( j < m[1] ) { r1 += r1[1]; continue; } r1 += r1[1]; /* to restart at the next potential match */ goto nextm; /* match */ } /* #] REMAINDER : */ } if ( r1 >= r2 ) { /* no factor! */ scratch:; r3 = m + m[1]; r4 = m; while ( r3 < mstop ) *r4++ = *r3++; *oldwork = r4 - oldwork; if ( *oldwork == 1 ) goto nofactor; mstop = r4; r1 = mm + 1; continue; } r1 = mm + 1; nextm: m += m[1]; } mm = mm + *mm; } nofactor:; /* For the coefficient we have to determine the LCM of the denominators and the GCD of the numerators. */ GCDbuffer = NumberMalloc("FactorIn"); GCDbuffer2 = NumberMalloc("FactorIn"); LCMbuffer = NumberMalloc("FactorIn"); LCMb = NumberMalloc("FactorIn"); LCMc = NumberMalloc("FactorIn"); r1 = d->where; /* First take the first term to load up the LCM and the GCD */ r2 = r1 + *r1; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kGCD = 0; kGCD < k; kGCD++ ) GCDbuffer[kGCD] = r3[kGCD]; k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; r1 = r2; /* Now go through the rest of the terms in this dollar buffer. */ while ( *r1 ) { r2 = r1 + *r1; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( GCDbuffer[0] == 1 ) && ( kGCD == 1 ) ) ) { /* GCD is already 1 */ } else if ( ( ( k != 1 ) || ( r3[0] != 1 ) ) ) { if ( GcdLong(BHEAD GCDbuffer,kGCD,(UWORD *)r3,k,GCDbuffer2,&kGCD2) ) { goto onerror; } kGCD = kGCD2; for ( i = 0; i < kGCD; i++ ) GCDbuffer[i] = GCDbuffer2[i]; } else { kGCD = 1; GCDbuffer[0] = 1; } k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( LCMbuffer[0] == 1 ) && ( kLCM == 1 ) ) ) { for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; } else if ( ( k != 1 ) || ( r3[0] != 1 ) ) { if ( GcdLong(BHEAD LCMbuffer,kLCM,(UWORD *)r3,k,LCMb,&kkLCM) ) { goto onerror; } DivLong((UWORD *)r3,k,LCMb,kkLCM,LCMb,&kkLCM,LCMc,&jLCM); MulLong(LCMbuffer,kLCM,LCMb,kkLCM,LCMc,&jLCM); for ( kLCM = 0; kLCM < jLCM; kLCM++ ) LCMbuffer[kLCM] = LCMc[kLCM]; } else {} /* LCM doesn't change */ r1 = r2; } /* Now put the factor together: GCD/LCM */ r3 = (WORD *)(GCDbuffer); if ( kGCD == kLCM ) { for ( jGCD = 0; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; k = kGCD; } else if ( kGCD > kLCM ) { for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kGCD] = LCMbuffer[jGCD]; for ( jGCD = kLCM; jGCD < kGCD; jGCD++ ) r3[jGCD+kGCD] = 0; k = kGCD; } else { for ( jGCD = kGCD; jGCD < kLCM; jGCD++ ) r3[jGCD] = 0; for ( jGCD = 0; jGCD < kLCM; jGCD++ ) r3[jGCD+kLCM] = LCMbuffer[jGCD]; k = kLCM; } j = 2*k+1; mm = m = oldwork + oldwork[0]; /* Now compose the new term */ n1 = term; while ( n1 < t ) *m++ = *n1++; n1 += n1[1]; n2 = oldwork+1; while ( n2 < mm ) *m++ = *n2++; while ( n1 < tstop ) *m++ = *n1++; /* And the coefficient */ size = term[*term-1]; size = REDLENG(size); if ( MulRat(BHEAD (UWORD *)tstop,size,(UWORD *)r3,k, (UWORD *)m,&size) ) goto onerror; size = INCLENG(size); k = size < 0 ? -size: size; m[k-1] = size; m += k; *mm = (WORD)(m - mm); AT.WorkPointer = m; if ( Generator(BHEAD mm,level) ) goto onerror; AT.WorkPointer = oldwork; if ( fromwhere == 0 ) { if ( d->factors ) M_free(d->factors,"Dollar factors"); M_free(d,"Dollar in FactorIn"); } NumberFree(GCDbuffer,"FactorIn"); NumberFree(GCDbuffer2,"FactorIn"); NumberFree(LCMbuffer,"FactorIn"); NumberFree(LCMb,"FactorIn"); NumberFree(LCMc,"FactorIn"); return(0); onerror: AT.WorkPointer = oldwork; MLOCK(ErrorMessageLock); MesCall("FactorIn"); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"FactorIn"); NumberFree(GCDbuffer2,"FactorIn"); NumberFree(LCMbuffer,"FactorIn"); NumberFree(LCMb,"FactorIn"); NumberFree(LCMc,"FactorIn"); return(-1); } /* #] FactorIn : #[ FactorInExpr : This routine tests for a factor in an active or hidden expression. The factor from the last call is stored in a cache. Main problem here is whether the cache is global or private to each thread. A global cache gives most likely the same traffic jam for the computation as a local cache. The local cache may stay valid longer. In the future we may make it such that threads can look at the cache of the others, or even whether a certain factor is under construction. */ int FactorInExpr(PHEAD WORD *term, WORD level) { GETBIDENTITY WORD *t, *tstop, *m, *oldwork, *mstop, *n1, *n2, *n3, *n4, *n1stop, *n2stop; WORD *r1, *r2, *r3, *r4, j, k, kGCD, kGCD2, kLCM, jGCD, kkLCM, jLCM, size, sign; WORD *newterm, expr = 0; WORD olddeferflag = AR.DeferFlag, oldgetfile = AR.GetFile, oldhold = AR.KeptInHold; WORD newgetfile, newhold; int i; EXPRESSIONS e; FILEHANDLE *file = 0; POSITION position, oldposition, startposition; WORD *oldcpointer = AR.CompressPointer; UWORD *GCDbuffer, *GCDbuffer2, *LCMbuffer, *LCMb, *LCMc; GCDbuffer = NumberMalloc("FactorInExpr"); GCDbuffer2 = NumberMalloc("FactorInExpr"); LCMbuffer = NumberMalloc("FactorInExpr"); LCMb = NumberMalloc("FactorInExpr"); LCMc = NumberMalloc("FactorInExpr"); t = term; GETSTOP(t,tstop); t++; while ( t < tstop ) { if ( *t == FACTORIN && t[1] == FUNHEAD+2 && t[FUNHEAD] == -EXPRESSION ) { expr = t[FUNHEAD+1]; break; } t += t[1]; } if ( t >= tstop ) { MLOCK(ErrorMessageLock); MesPrint("Internal error. Could not find proper factorin_ function."); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); } oldwork = AT.WorkPointer; if ( AT.previousEfactor && ( expr == AT.previousEfactor[0] ) ) { /* We have a hit in the cache. Construct the new term. At the moment AT.previousEfactor[1] is reserved for future flags */ goto PutTheFactor; } /* No hit. We have to do the work. We start with constructing the factor in the WorkSpace. Later we will move it to the cache. Finally we will jump to PutTheFactor. */ e = Expressions + expr; switch ( e->status ) { case LOCALEXPRESSION: case SKIPLEXPRESSION: case DROPLEXPRESSION: case GLOBALEXPRESSION: case SKIPGEXPRESSION: case DROPGEXPRESSION: /* Expression is to be found in the input Scratch file. Set the file handle and the position. The rest is done by GetTerm. */ newhold = 0; newgetfile = 1; file = AR.infile; break; case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: case HIDELEXPRESSION: case HIDEGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: /* Expression is to be found in the hide Scratch file. Set the file handle and the position. The rest is done by GetTerm. */ newhold = 0; newgetfile = 2; file = AR.hidefile; break; case STOREDEXPRESSION: /* This is an 'illegal' case */ MLOCK(ErrorMessageLock); MesPrint("Error: factorin_ cannot determine factors in stored expressions."); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); case DROPPEDEXPRESSION: /* We replace the function by 1. */ m = oldwork; n1 = term; while ( n1 < t ) *m++ = *n1++; n1 = t + t[1]; tstop = term + *term; while ( n1 < tstop ) *m++ = *n1++; *oldwork = m - oldwork; AT.WorkPointer = m; if ( Generator(BHEAD oldwork,level) ) { NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); } AT.WorkPointer = oldwork; NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(0); default: MLOCK(ErrorMessageLock); MesPrint("Error: Illegal expression in factorinexpr."); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); } /* Before we start with the file we set the buffers for the coefficient For the coefficient we have to determine the LCM of the denominators and the GCD of the numerators. */ position = AS.OldOnFile[expr]; AR.DeferFlag = 0; AR.KeptInHold = newhold; AR.GetFile = newgetfile; SeekScratch(file,&oldposition); SetScratch(file,&position); if ( GetTerm(BHEAD oldwork) <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("(5) Expression %d has problems in scratchfile",expr); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); } SeekScratch(file,&startposition); SeekScratch(file,&position); /* Load the first term in the workspace */ if ( GetTerm(BHEAD oldwork) == 0 ) { SetScratch(file,&oldposition); /* We still need this until Processor is clean */ AR.DeferFlag = olddeferflag; oldwork[0] = 4; oldwork[1] = 1; oldwork[2] = 1; oldwork[3] = 3; goto Complete; } SeekScratch(file,&position); AR.DeferFlag = olddeferflag; AR.KeptInHold = oldhold; AR.GetFile = oldgetfile; r2 = m = oldwork + *oldwork; j = m[-1]; m -= ABS(j); *oldwork = (WORD)(m-oldwork); AT.WorkPointer = newterm = mstop = m; /* Now take the coefficient of the first term to load up the LCM and the GCD */ r3 = m; k = REDLENG(j); if ( k < 0 ) { k = -k; sign = -1; } else { sign = 1; } while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kGCD = 0; kGCD < k; kGCD++ ) GCDbuffer[kGCD] = r3[kGCD]; k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; /* The copy and the coefficient are in place. Now search through the terms. */ for (;;) { AR.DeferFlag = 0; AR.KeptInHold = newhold; AR.GetFile = newgetfile; SetScratch(file,&position); size = GetTerm(BHEAD newterm); SeekScratch(file,&position); AR.DeferFlag = olddeferflag; AR.KeptInHold = oldhold; AR.GetFile = oldgetfile; if ( size == 0 ) break; m = oldwork+1; r2 = newterm + *newterm; r2 -= ABS(r2[-1]); r1 = newterm+1; while ( m < mstop ) { while ( r1 < r2 ) { if ( *r1 != *m ) { r1 += r1[1]; continue; } /* Now the various cases #[ SYMBOL : */ if ( *m == SYMBOL ) { n1 = m+2; n1stop = m+m[1]; n2stop = r1+r1[1]; while ( n1 < n1stop ) { n2 = r1+2; while ( n2 < n2stop ) { if ( *n1 != *n2 ) { n2 += 2; continue; } if ( n1[1] > 0 ) { if ( n2[1] < 0 ) { n2 += 2; continue; } if ( n2[1] < n1[1] ) n1[1] = n2[1]; } else { if ( n2[1] > 0 ) { n2 += 2; continue; } if ( n2[1] > n1[1] ) n1[1] = n2[1]; } break; } if ( n2 >= n2stop ) { /* scratch symbol */ if ( m[1] == 4 ) goto scratch; m[1] -= 2; n3 = n1; n4 = n1+2; while ( n4 < mstop ) *n3++ = *n4++; *oldwork = n3 - oldwork; mstop -= 2; n1stop -= 2; continue; } n1 += 2; } break; } /* #] SYMBOL : #[ DOTPRODUCT : */ else if ( *m == DOTPRODUCT ) { n1 = m+2; n1stop = m+m[1]; n2stop = r1+r1[1]; while ( n1 < n1stop ) { n2 = r1+2; while ( n2 < n2stop ) { if ( *n1 != *n2 || n1[1] != n2[1] ) { n2 += 3; continue; } if ( n1[2] > 0 ) { if ( n2[2] < 0 ) { n2 += 3; continue; } if ( n2[2] < n1[2] ) n1[2] = n2[2]; } else { if ( n2[2] > 0 ) { n2 += 3; continue; } if ( n2[2] > n1[2] ) n1[2] = n2[2]; } break; } if ( n2 >= n2stop ) { /* scratch dotproduct */ if ( m[1] == 5 ) goto scratch; m[1] -= 3; n3 = n1; n4 = n1+3; while ( n4 < mstop ) *n3++ = *n4++; *oldwork = n3 - oldwork; mstop -= 3; n1stop -= 3; continue; } n1 += 3; } break; } /* #] DOTPRODUCT : #[ VECTOR : */ else if ( *m == VECTOR ) { /* Here we have to be careful if there is more than one of the same */ n1 = m+2; n1stop = m+m[1]; n2 = r1+2;n2stop = r1+r1[1]; while ( n1 < n1stop ) { while ( n2 < n2stop ) { if ( *n1 == *n2 && n1[1] == n2[1] ) { n2 += 2; goto nextn1; } n2 += 2; } if ( n2 >= n2stop ) { /* scratch vector */ if ( m[1] == 4 ) goto scratch; m[1] -= 2; n3 = n1; n4 = n1+2; while ( n4 < mstop ) *n3++ = *n4++; *oldwork = n3 - oldwork; mstop -= 2; n1stop -= 2; continue; } n2 = r1+2; nextn1: n1 += 2; } break; } /* #] VECTOR : #[ REMAINDER : */ else { /* Again: watch for multiple occurrences of the same object */ if ( m[1] != r1[1] ) { r1 += r1[1]; continue; } for ( j = 2; j < m[1]; j++ ) { if ( m[j] != r1[j] ) break; } if ( j < m[1] ) { r1 += r1[1]; continue; } r1 += r1[1]; /* to restart at the next potential match */ goto nextm; /* match */ } /* #] REMAINDER : */ } if ( r1 >= r2 ) { /* no factor! */ scratch:; r3 = m + m[1]; r4 = m; while ( r3 < mstop ) *r4++ = *r3++; *oldwork = r4 - oldwork; if ( *oldwork == 1 ) goto nofactor; mstop = r4; r1 = newterm + 1; continue; } r1 = newterm + 1; nextm: m += m[1]; } nofactor:; /* Now the coefficient */ r2 = newterm + *newterm; j = r2[-1]; r3 = r2 - ABS(j); k = REDLENG(j); if ( k < 0 ) k = -k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( GCDbuffer[0] == 1 ) && ( kGCD == 1 ) ) ) { /* GCD is already 1 */ } else if ( ( ( k != 1 ) || ( r3[0] != 1 ) ) ) { if ( GcdLong(BHEAD GCDbuffer,kGCD,(UWORD *)r3,k,GCDbuffer2,&kGCD2) ) { goto onerror; } kGCD = kGCD2; for ( i = 0; i < kGCD; i++ ) GCDbuffer[i] = GCDbuffer2[i]; } else { kGCD = 1; GCDbuffer[0] = 1; } k = REDLENG(j); if ( k < 0 ) k = -k; r3 += k; while ( ( k > 1 ) && ( r3[k-1] == 0 ) ) k--; if ( ( ( LCMbuffer[0] == 1 ) && ( kLCM == 1 ) ) ) { for ( kLCM = 0; kLCM < k; kLCM++ ) LCMbuffer[kLCM] = r3[kLCM]; } else if ( ( k != 1 ) || ( r3[0] != 1 ) ) { if ( GcdLong(BHEAD LCMbuffer,kLCM,(UWORD *)r3,k,LCMb,&kkLCM) ) { goto onerror; } DivLong((UWORD *)r3,k,LCMb,kkLCM,LCMb,&kkLCM,LCMc,&jLCM); MulLong(LCMbuffer,kLCM,LCMb,kkLCM,LCMc,&jLCM); for ( kLCM = 0; kLCM < jLCM; kLCM++ ) LCMbuffer[kLCM] = LCMc[kLCM]; } else {} /* LCM doesn't change */ } SetScratch(file,&oldposition); /* Needed until Processor is thread safe */ AR.DeferFlag = olddeferflag; /* Now put the term together in oldwork: GCD/LCM We have already the algebraic contents there. */ r3 = (WORD *)(GCDbuffer); r4 = (WORD *)(LCMbuffer); r1 = oldwork + *oldwork; if ( kGCD == kLCM ) { for ( jGCD = 0; jGCD < kGCD; jGCD++ ) *r1++ = *r3++; for ( jGCD = 0; jGCD < kGCD; jGCD++ ) *r1++ = *r4++; k = 2*kGCD+1; } else if ( kGCD > kLCM ) { for ( jGCD = 0; jGCD < kGCD; jGCD++ ) *r1++ = *r3++; for ( jGCD = 0; jGCD < kLCM; jGCD++ ) *r1++ = *r4++; for ( jGCD = kLCM; jGCD < kGCD; jGCD++ ) *r1++ = 0; k = 2*kGCD+1; } else { for ( jGCD = 0; jGCD < kGCD; jGCD++ ) *r1++ = *r3++; for ( jGCD = kGCD; jGCD < kLCM; jGCD++ ) *r1++ = 0; for ( jGCD = 0; jGCD < kLCM; jGCD++ ) *r1++ = *r4++; k = 2*kLCM+1; } if ( sign < 0 ) *r1++ = -k; else *r1++ = k; *oldwork = (WORD)(r1-oldwork); /* Now put the new term in the cache */ Complete:; if ( AT.previousEfactor ) M_free(AT.previousEfactor,"Efactor cache"); AT.previousEfactor = (WORD *)Malloc1((*oldwork+2)*sizeof(WORD),"Efactor cache"); AT.previousEfactor[0] = expr; r1 = oldwork; r2 = AT.previousEfactor + 2; k = *oldwork; NCOPY(r2,r1,k) AT.previousEfactor[1] = 0; /* Now we construct the new term in the workspace. */ PutTheFactor:; if ( AT.WorkPointer + AT.previousEfactor[2] >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MesPrint("Called from factorin_"); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); } n1 = oldwork; n2 = term; while ( n2 < t ) *n1++ = *n2++; n2 = AT.previousEfactor+2; GETSTOP(n2,n2stop); n3 = n2 + *n2; n2++; while ( n2 < n2stop ) *n1++ = *n2++; n2 = t + t[1]; while ( n2 < tstop ) *n1++ = *n2++; size = term[*term-1]; size = REDLENG(size); k = n3[-1]; k = REDLENG(k); if ( MulRat(BHEAD (UWORD *)tstop,size,(UWORD *)n2stop,k, (UWORD *)n1,&size) ) goto onerror; size = INCLENG(size); k = size < 0 ? -size: size; n1 += k; n1[-1] = size; *oldwork = n1 - oldwork; AT.WorkPointer = n1; if ( Generator(BHEAD oldwork,level) ) { NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); } AT.WorkPointer = oldwork; AR.CompressPointer = oldcpointer; NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(0); onerror: AT.WorkPointer = oldwork; AR.CompressPointer = oldcpointer; MLOCK(ErrorMessageLock); MesCall("FactorInExpr"); MUNLOCK(ErrorMessageLock); NumberFree(GCDbuffer,"FactorInExpr"); NumberFree(GCDbuffer2,"FactorInExpr"); NumberFree(LCMbuffer,"FactorInExpr"); NumberFree(LCMb,"FactorInExpr"); NumberFree(LCMc,"FactorInExpr"); return(-1); } /* #] FactorInExpr : */ form-5.0.1/sources/fsizes.h0000644000175100017510000001214015217035721011303 /** @file fsizes.h * * The definition the default values for certain buffer sizes etc. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* First the fixed variables */ #define MAXPRENAMESIZE 128 /* The following variables are default sizes. They can be changed into values read from the setup file Remark (21-dec-2008 JV): WILDOFFSET*3 should be larger than WILDMASK!!!! old value was WILDOFFSET 200000100 be careful with old .sav files!!! */ #if BITSINWORD == 32 #define MAXPOWER 500000000 #define MAXVARIABLES 200000050 #define MAXDOLLARVARIABLES 1000000000L #define WILDOFFSET 400000100 #define MAXINNAMETREE 2000000000 #define MAXDUMMIES 100000000 #define WORKBUFFER 40000000 #define MAXTER 40000 #define HALFMAX 0x10000 #define MAXSUBEXPRESSIONS 0x1FFFFFF #define MAXFILESTREAMSIZE 1024 #elif BITSINWORD == 16 #define MAXPOWER 10000 #define MAXVARIABLES 8050 #define MAXDOLLARVARIABLES 32000 #define WILDOFFSET 6100 #define MAXINNAMETREE 32768 #define MAXDUMMIES 1000 #define WORKBUFFER 10000000 #define MAXTER 10000 #define HALFMAX 0x100 #define MAXSUBEXPRESSIONS 0x3FFF #define MAXFILESTREAMSIZE 1048576 #else #error Only 64-bit and 32-bit platforms are supported. #endif #define MAXENAME 16 #define MAXSAVEFUNCTION 16384 #define MAXPARLEVEL 100 #define MAXNUMBERSIZE 200 #define MAXREPEAT 100 #define NORMSIZE 1000 #define INITNODESIZE 10 #define INITNAMESIZE 100 #define NUMFIXED 128 #define MAXNEST 100 #define MAXMATCH 30 #define MAXIF 20 #define SIZEFACS 640L #define NUMFACS 50 #define MAXLOOPS 30 #define MAXLABELS 20 #define COMMERCIALSIZE 24 #define MAXFLAGS 16 /* The next quantities should still be eliminated from the program This should be together with changes in setfile! */ #define COMPRESSBUFFER 90000 #define FORTRANCONTINUATIONLINES 15 #define MAXLEVELS 2000 #define MAXLHS 400 #define MAXWILDC 100 #define NUMTABLEENTRIES 1000 #define COMPILERBUFFER 20000 #if BITSINWORD == 32 #ifdef WITHPTHREADS #define SMALLBUFFER 300000000L #define SMALLOVERFLOW 600000000L #define TERMSSMALL 3000000L #define LARGEBUFFER 1500000000L #define SCRATCHSIZE 500000000L #else #define SMALLBUFFER 150000000L #define SMALLOVERFLOW 300000000L #define TERMSSMALL 2000000L #define LARGEBUFFER 800000000L #define SCRATCHSIZE 500000000L #endif #elif BITSINWORD == 16 #define SMALLBUFFER 10000000L #define SMALLOVERFLOW 20000000L #define TERMSSMALL 100000L #define LARGEBUFFER 50000000L #define SCRATCHSIZE 50000000L #else #error Only 64-bit and 32-bit platforms are supported. #endif #define MAXPATCHES 256 #define MAXFPATCHES 256 #define SORTIOSIZE 200000L #define SSMALLBUFFER 2560016L #define SSMALLOVERFLOW 3840032L #define STERMSSMALL 10000L #define SLARGEBUFFER 26880512L #define SMAXPATCHES 64 #define SMAXFPATCHES 64 #define SSORTIOSIZE 32768L #define SPECTATORSIZE 1048576L #define MAXFLEVELS 30 #define COMPINC 2 #define MAXNUMSIZE 10 #define MAXBRACKETBUFFERSIZE 200000 #define SFHSIZE 40 #define DEFAULTPROCESSBUCKETSIZE 1000 #define SHMWINSIZE 65536L #define TABLEEXTENSION 6 #define GZIPDEFAULT 6 #define DEFAULTTHREADS 0 #define DEFAULTTHREADBUCKETSIZE 500 #define DEFAULTTHREADLOADBALANCING 1 #define THREADSCRATCHSIZE 100000L #define THREADSCRATCHOUTSIZE 2500000L #if BITSINWORD == 32 #define MAXTABLECOMBUF 100000000000L #define MAXCOMBUFRHS 1000000000L #elif BITSINWORD == 16 #define MAXTABLECOMBUF 1000000L #define MAXCOMBUFRHS 32500L #else #error Only 64-bit and 32-bit platforms are supported. #endif #define NUMSTORECACHES 4 #define SIZESTORECACHE 32768 #define INDENTSPACE 3 #define MULTIINDENTSPACE 1 #define MAXMULTIBRACKETLEVELS 25 #define FBUFFERSIZE 1026 /* For the random number generator (see commentary there) */ #define NPAIR1 38 #define NPAIR2 89 #define MAXLINELENGTH 256 #define MINALLOC 32 #define JUMPRATIO 4 /* Note: MAXCOUPLINGS should be at least MAXPARTICLES/2+1 */ #define MAXPARTICLES 20 #define MAXCOUPLINGS 20 #define NUMOPTIONS 20 #define MAXLEGS 20 #ifdef WITHFLOAT #define MAXWEIGHT 0 #define DEFAULTPRECISION 1000 #endif form-5.0.1/sources/transform.c0000644000175100017510000027070115217035721012017 /** @file transform.c * * Routines that deal with the transform statement and its varieties. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : transform.c */ #include "form3.h" /* #] Includes : #[ Transform : #[ Intro : Here are the routines for the transform statement. This is a group of transformations on function arguments or groups of function arguments. The purpose of this command is that it avoids repetitive pattern matching. Syntax: Transform,SetOfFunctions,OneOrMoreTransformations; Each transformation is given by Replace(argfirst,arglast)=(,,,) Encode(argfirst,arglast):base=# Decode(argfirst,arglast):base=# Implode(argfirst,arglast) Explode(argfirst,arglast) Permute(cycle)(cycle)(cycle)...(cycle) Reverse(argfirst,arglast) Dedup(argfirst,arglast) Cycle(argfirst,arglast)=+/-num IsLyndon(argfirst,arglast)=(yes,no) ToLyndon(argfirst,arglast)=(yes,no) In replace the extra information is a replace_() without the name of the replace_ function. This can be as in (0,1,1,0) or (xarg_,1-xarg_) to indicate a symbolic argument or (x,y,y,x) to exchange x and y, etc. In Encode and Decode argfirst is the most significant 'word' and arglast is the least significant 'word'. Note that we need to introduce the generic symbolic arguments xarg_, parg_, iarg_ and farg_. Examples: Transform,{H,E} ,Replace(1:`WEIGHT')=(0,1,1,0) ,Encode(1:`WEIGHT')=base(2); Transform,{H,E} ,Decode(1:`WEIGHT')=base(3) ,Replace(1:`WEIGHT')=(2,-1,1,0,0,1); Others that can be added: symmetrize? 6-may-2016: Changed MAXPOSITIVE2 into MAXPOSITIVE4. This makes room for the use of dollar variables as arguments. #] Intro : #[ CoTransform : */ static WORD tranarray[10] = { SUBEXPRESSION, SUBEXPSIZE, 0, 1, 0, 0, 0, 0, 0, 0 }; int CoTransform(UBYTE *in) { GETIDENTITY UBYTE *s = in, c, *ss, *Tempbuf; WORD number, type, i, *work = AT.WorkPointer+2, *wp, range[2], one = 1; WORD numdol, *wstart; int error = 0, irhs; LONG x; while ( *in == ',' ) in++; wp = work + 1; /* #[ Sets : First the set specification(s). No sets means all functions (dangerous!) */ for(;;) { if ( *in == '{' ) { s = in+1; SKIPBRA2(in) number = DoTempSet(s,in); in++; if ( *in != ',' ) { c = in[1]; in[1] = 0; MesPrint("& %s: A set in a transform statement should be followed by a comma",s); in[1] = c; in++; if ( error == 0 ) error = 1; } } else if ( *in == '[' || FG.cTable[*in] == 0 ) { s = in; in = SkipAName(in); if ( *in != ',' ) break; c = *in; *in = 0; type = GetName(AC.varnames,s,&number,NOAUTO); if ( type == CFUNCTION ) { #ifdef WITHFLOAT if ( (number+FUNCTION) == FLOATFUN ) { MesPrint("&Illegal use of a transform statement and float_"); if ( error == 0 ) error = 1; } #endif number += MAXVARIABLES + FUNCTION; } else if ( type != CSET ) { MesPrint("& %s: A transform statement starts with sets of functions",s); if ( error == 0 ) error = 1; } *in++ = c; } else { MesPrint("&Illegal syntax in Transform statement",s); if ( error == 0 ) error = 1; return(error); } if ( number >= 0 ) { if ( number < MAXVARIABLES ) { /* Check that this is a set of functions */ if ( Sets[number].type != CFUNCTION ) { MesPrint("&A set in a transform statement should be a set of functions"); if ( error == 0 ) error = 1; } #ifdef WITHFLOAT WORD *r1, *r2; r1 = SetElements + Sets[number].first; r2 = SetElements + Sets[number].last; while ( r1 < r2 ) { if ( *r1++ == FLOATFUN ) { MesPrint("&Illegal use of a transform statement and float_"); if ( error == 0 ) error = 1; } } #endif } } else if ( error == 0 ) error = 1; /* Now write the number to the right place */ *wp++ = number; while ( *in == ',' ) in++; } *work = wp - work; work = wp; wp++; /* #] Sets : Now we should loop over the various transformations */ while ( *s ) { in = s; if ( FG.cTable[*in] != 0 ) { MesPrint("&Illegal character in Transform statement"); if ( error == 0 ) error = 1; return(error); } in = SkipAName(in); if ( *in == '>' || *in == '<' || *in == '+' || *in == '-' ) in++; ss = in; c = *ss; *ss = 0; if ( c != '(' ) { MesPrint("&Illegal syntax in specifying a transformation inside a Transform statement"); if ( error == 0 ) error = 1; return(error); } /* #[ replace : */ if ( StrICmp(s,(UBYTE *)"replace") == 0 ) { /* Subkeys: (,,,) as in replace_(,,,) The idea here is to read the subkeys as the argument of a replace_ function. We put the whole together as in the multiply statement (which could just be a replace_(....)) and compile it. Then we expand the tree with Generator and check the complete expression for legality. */ type = REPLACEARG; doreplace: *ss = c; if ( ( in = ReadRange(in,range,0) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } in++; /* We have replace(#,#)=(...), and we want dum_(...) (DUMFUN) to send to the compiler. The pointer is after the '='; */ s = in; if ( *s != '(' ) { MesPrint("&"); if ( error == 0 ) error = 1; return(error); } SKIPBRA3(in); if ( *in != ')' ) { MesPrint("&"); if ( error == 0 ) error = 1; return(error); } in++; if ( *in != ',' && *in != '\0' ) { MesPrint("&"); if ( error == 0 ) error = 1; return(error); } i = in - s; ss = Tempbuf = (UBYTE *)Malloc1(i+5,"CoTransform/replace"); *ss++ = 'd'; *ss++ = 'u'; *ss++ = 'm'; *ss++ = '_'; NCOPY(ss,s,i) *ss++ = 0; AC.ProtoType = tranarray; tranarray[4] = AC.cbufnum; irhs = CompileAlgebra(Tempbuf,RHSIDE,AC.ProtoType); M_free(Tempbuf,"CoTransform/replace"); if ( irhs < 0 ) { if ( error == 0 ) error = 1; return(error); } tranarray[2] = irhs; /* The result of the compilation goes through Generator during execution, because that takes care of $-variables. This is why we could not use replace_ and had to use dum_. */ *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *wp++ = SUBEXPSIZE+4; for ( i = 0; i < SUBEXPSIZE; i++ ) *wp++ = tranarray[i]; *wp++ = 1; *wp++ = 1; *wp++ = 3; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] replace : #[ encode/decode : */ else if ( StrICmp(s,(UBYTE *)"decode" ) == 0 ) { type = DECODEARG; goto doencode; } else if ( StrICmp(s,(UBYTE *)"encode" ) == 0 ) { type = ENCODEARG; doencode: *ss = c; if ( ( in = ReadRange(in,range,2) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } in++; s = in; while ( FG.cTable[*in] == 0 ) in++; c = *in; *in = 0; /* Subkeys: base=# or base=$var */ if ( StrICmp(s,(UBYTE *)"base") == 0 ) { *in = c; if ( *in != '=' ) { MesPrint("&Illegal base specification in encode/decode transformation"); if ( error == 0 ) error = 1; return(error); } in++; if ( *in == '$' ) { in++; ss = in; in = SkipAName(in); c = *in; *in = 0; if ( GetName(AC.dollarnames,ss,&numdol,NOAUTO) != CDOLLAR ) { MesPrint("&%s is undefined",ss-1); numdol = AddDollar(ss,DOLINDEX,&one,1); return(1); } *in = c; x = -numdol; } else { x = 0; while ( FG.cTable[*in] == 1 ) { x = 10*x + *in++ - '0'; if ( x > MAXPOSITIVE4 ) { illsize: MesPrint("&Illegal value for base in encode/decode transformation"); if ( error == 0 ) error = 1; return(error); } } if ( x <= 1 ) goto illsize; } if ( *in != ',' && *in != '\0' ) { MesPrint("&Illegal termination of transformation"); if ( error == 0 ) error = 1; return(error); } } else { MesPrint("&Illegal option in encode/decode transformation"); if ( error == 0 ) error = 1; return(error); } /* Now we can put the whole statement together We have the set(s) in work up to wp and the range in range. The base is in x and the type tells whether it is encode or decode. */ *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *wp++ = 4; *wp++ = BASECODE; *wp++ = (WORD)x; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] encode/decode : #[ implode : */ else if ( StrICmp(s,(UBYTE *)"implode") == 0 || StrICmp(s,(UBYTE *)"tosumnotation") == 0 ) { /* Subkeys: ? */ type = IMPLODEARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] implode : #[ explode : */ else if ( StrICmp(s,(UBYTE *)"explode") == 0 || StrICmp(s,(UBYTE *)"tointegralnotation") == 0 ) { /* Subkeys: ? */ type = EXPLODEARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] explode : #[ permute : */ else if ( StrICmp(s,(UBYTE *)"permute") == 0 ) { type = PERMUTEARG; *ss = c; *wp++ = ARGRANGE; *wp++ = 1; *wp++ = MAXPOSITIVE4; *wp++ = type; /* Now a sequence of cycles */ do { wstart = wp; wp++; do { in++; if ( *in == '$' ) { WORD number; UBYTE *t; in++; t = in; while ( FG.cTable[*in] < 2 ) in++; c = *in; *in = 0; if ( ( number = GetDollar(t) ) < 0 ) { MesPrint("&Undefined variable $%s",t); if ( !error ) error = 1; number = AddDollar(t,0,0,0); } *in = c; *wp++ = -number-1; } else { x = 0; while ( FG.cTable[*in] == 1 ) { x = 10*x + *in++ - '0'; if ( x > MAXPOSITIVE4 ) { MesPrint("&value in permute transformation too large"); if ( error == 0 ) error = 1; return(error); } } if ( x == 0 ) { MesPrint("&value 0 in permute transformation not allowed"); if ( error == 0 ) error = 1; return(error); } *wp++ = (WORD)x-1; } } while ( *in == ',' ); if ( *in != ')' ) { MesPrint("&Illegal syntax in permute transformation"); if ( error == 0 ) error = 1; return(error); } in++; if ( *in != ',' && *in != '(' && *in != '\0' ) { MesPrint("&Illegal ending in permute transformation"); if ( error == 0 ) error = 1; return(error); } *wstart = wp-wstart; if ( *wstart == 1 ) wstart--; } while ( *in == '(' ); *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] permute : #[ reverse : */ else if ( StrICmp(s,(UBYTE *)"reverse") == 0 ) { type = REVERSEARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] reverse : #[ dedup : */ else if ( StrICmp(s,(UBYTE *)"dedup") == 0 ) { type = DEDUPARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] dedup : #[ cycle : */ else if ( StrICmp(s,(UBYTE *)"cycle") == 0 ) { type = CYCLEARG; *ss = c; if ( ( in = ReadRange(in,range,0) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; /* Now a sequence of cycles */ in++; if ( *in == '+' ) { } else if ( *in == '-' ) { one = -1; } else { MesPrint("&Cycle in a Transform statement should be followed by =+/-number/$"); if ( error == 0 ) error = 1; return(error); } in++; x = 0; if ( *in == '$' ) { UBYTE *si = in; in++; si = in; while ( FG.cTable[*in] == 0 || FG.cTable[*in] == 1 ) in++; c = *in; *in = 0; if ( ( x = GetDollar(si) ) < 0 ) { MesPrint("&Undefined $-variable in transform,cycle statement."); error = 1; } *in = c; if ( one < 0 ) x += MAXPOSITIVE4; x += MAXPOSITIVE2; *wp++ = x; } else { while ( FG.cTable[*in] == 1 ) { x = 10*x + *in++ - '0'; if ( x > MAXPOSITIVE4 ) { MesPrint("&Number in cycle in a Transform statement too big"); if ( error == 0 ) error = 1; return(error); } } *wp++ = x*one; } *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] cycle : #[ islyndon/tolyndon : */ else if ( StrICmp(s,(UBYTE *)"islyndon" ) == 0 ) { type = ISLYNDON; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"islyndon<" ) == 0 ) { type = ISLYNDON; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"islyndon-" ) == 0 ) { type = ISLYNDON; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"islyndon>" ) == 0 ) { type = ISLYNDONR; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"islyndon+" ) == 0 ) { type = ISLYNDONR; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"tolyndon" ) == 0 ) { type = TOLYNDON; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"tolyndon<" ) == 0 ) { type = TOLYNDON; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"tolyndon-" ) == 0 ) { type = TOLYNDON; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"tolyndon>" ) == 0 ) { type = TOLYNDONR; goto doreplace; } else if ( StrICmp(s,(UBYTE *)"tolyndon+" ) == 0 ) { type = TOLYNDONR; goto doreplace; } /* #] islyndon/tolyndon : #[ addarg : */ else if ( StrICmp(s,(UBYTE *)"addargs" ) == 0 ) { type = ADDARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] addarg : #[ mularg : */ else if ( ( StrICmp(s,(UBYTE *)"mulargs" ) == 0 ) || ( StrICmp(s,(UBYTE *)"multiplyargs" ) == 0 ) ) { type = MULTIPLYARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] mularg : #[ droparg : */ else if ( StrICmp(s,(UBYTE *)"dropargs" ) == 0 ) { type = DROPARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] droparg : #[ selectarg : */ else if ( StrICmp(s,(UBYTE *)"selectargs" ) == 0 ) { type = SELECTARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] selectarg : #[ ZtoH : */ else if ( StrICmp(s,(UBYTE *)"ztoh") == 0 ) { /* Subkeys: ? */ type = ZTOHARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] ZtoH : #[ HtoZ : */ else if ( StrICmp(s,(UBYTE *)"htoz") == 0 ) { /* Subkeys: ? */ type = HTOZARG; *ss = c; if ( ( in = ReadRange(in,range,1) ) == 0 ) { if ( error == 0 ) error = 1; return(error); } *wp++ = ARGRANGE; *wp++ = range[0]; *wp++ = range[1]; *wp++ = type; *work = wp-work; work = wp; *wp++ = 0; s = in; } /* #] HtoZ : */ else { MesPrint("&Unknown transformation inside a Transform statement: %s",s); *ss = c; if ( error == 0 ) error = 1; return(error); } while ( *s == ',') s++; } AT.WorkPointer[0] = TYPETRANSFORM; AT.WorkPointer[1] = i = wp - AT.WorkPointer; AddNtoL(i,AT.WorkPointer); return(error); } /* #] CoTransform : #[ RunTransform : Executes the transform statement. This routine hunts down the functions and sends them to the various action routines. params: size,#set1,...,#setn, transformations */ int RunTransform(PHEAD WORD *term, WORD *params) { WORD *t, *tstop, *w, *m, *out, *in, *tt, retval; WORD *fun, *args, *info, *infoend, *onetransform, *funs, *endfun; WORD *thearg = 0, *iterm, *newterm, *nt, *oldwork = AT.WorkPointer, sign = 1; int i; out = tstop = term + *term; tstop -= ABS(tstop[-1]); in = term; t = term + 1; while ( t < tstop ) { endfun = onetransform = params + *params; funs = params + 1; if ( *t < FUNCTION ) {} else if ( funs == endfun ) { /* we do all functions */ hit:; #ifdef WITHFLOAT if ( *t == FLOATFUN ) goto next; #endif while ( in < t ) *out++ = *in++; tt = t + t[1]; fun = out; while ( in < tt ) *out++ = *in++; do { args = onetransform + 1; info = args; while ( *info <= MAXRANGEINDICATOR ) { if ( *info == ALLARGS ) info++; else if ( *info == NUMARG ) info += 2; else if ( *info == ARGRANGE ) info += 3; else if ( *info == MAKEARGS ) info += 3; } switch ( *info ) { case REPLACEARG: if ( RunReplace(BHEAD fun,args,info) ) goto abo; out = fun + fun[1]; break; case ENCODEARG: if ( RunEncode(BHEAD fun,args,info) ) goto abo; out = fun + fun[1]; break; case DECODEARG: if ( RunDecode(BHEAD fun,args,info) ) goto abo; out = fun + fun[1]; break; case IMPLODEARG: if ( RunImplode(fun,args) ) goto abo; out = fun + fun[1]; break; case EXPLODEARG: if ( RunExplode(BHEAD fun,args) ) goto abo; out = fun + fun[1]; break; case PERMUTEARG: if ( RunPermute(BHEAD fun,args,info) ) goto abo; out = fun + fun[1]; break; case REVERSEARG: if ( RunReverse(BHEAD fun,args) ) goto abo; out = fun + fun[1]; break; case DEDUPARG: if ( RunDedup(BHEAD fun,args) ) goto abo; out = fun + fun[1]; break; case CYCLEARG: if ( RunCycle(BHEAD fun,args,info) ) goto abo; out = fun + fun[1]; break; case ADDARG: if ( RunAddArg(BHEAD fun,args) ) goto abo; out = fun + fun[1]; break; case MULTIPLYARG: if ( RunMulArg(BHEAD fun,args) ) goto abo; out = fun + fun[1]; break; case ISLYNDON: if ( ( retval = RunIsLyndon(BHEAD fun,args,1) ) < -1 ) goto abo; goto returnvalues; break; case ISLYNDONR: if ( ( retval = RunIsLyndon(BHEAD fun,args,-1) ) < -1 ) goto abo; goto returnvalues; break; case TOLYNDON: if ( ( retval = RunToLyndon(BHEAD fun,args,1) ) < -1 ) goto abo; goto returnvalues; break; case TOLYNDONR: if ( ( retval = RunToLyndon(BHEAD fun,args,-1) ) < -1 ) goto abo; returnvalues:; out = fun + fun[1]; if ( retval == -1 ) break; /* Work out the yes/no stuff */ AT.WorkPointer += 2*AM.MaxTer; if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } iterm = AT.WorkPointer; info++; for ( i = 0; i < *info; i++ ) iterm[i] = info[i]; AT.WorkPointer = iterm + *iterm; AR.Eside = LHSIDEX; NewSort(BHEAD0); if ( Generator(BHEAD iterm,AR.Cnumlhs) ) { LowerSortLevel(); AT.WorkPointer = oldwork; return(-1); } newterm = AT.WorkPointer; if ( EndSort(BHEAD newterm,1) < 0 ) {} if ( ( *newterm && *(newterm+*newterm) != 0 ) || *newterm == 0 ) { MLOCK(ErrorMessageLock); MesPrint("&yes/no information in islyndon/tolyndon does not evaluate into a single term"); MUNLOCK(ErrorMessageLock); return(-1); } AR.Eside = RHSIDE; i = *newterm; tt = iterm; nt = newterm; NCOPY(tt,nt,i); AT.WorkPointer = iterm + *iterm; info = iterm + 1; infoend = info+info[1]; info += FUNHEAD; if ( retval == 0 ) { /* Need second argument (=no) */ if ( info >= infoend ) { abortlyndon:; MLOCK(ErrorMessageLock); MesPrint("There should be a yes and a no argument in islyndon/tolyndon"); MUNLOCK(ErrorMessageLock); Terminate(-1); } NEXTARG(info) if ( info >= infoend ) goto abortlyndon; thearg = info; } else if ( retval == 1 ) { /* Need first argument (=yes) */ if ( info >= infoend ) goto abortlyndon; thearg = info; NEXTARG(info) if ( info >= infoend ) goto abortlyndon; } NEXTARG(info) if ( info < infoend ) goto abortlyndon; /* The argument in thearg needs to be copied We did not pull it through generator to guarantee that it is a single argument. The easiest way is to let the routine Normalize do the job and put everything in an exponent function with the power one. */ if ( *thearg == -SNUMBER && thearg[1] == 0 ) { *term = 0; return(0); } if ( *thearg == -SNUMBER && thearg[1] == 1 ) { } else { fun = out; *out++ = EXPONENT; out++; *out++ = 1; FILLFUN3(out); COPY1ARG(out,thearg); *out++ = -SNUMBER; *out++ = 1; fun[1] = out-fun; } break; case DROPARG: if ( RunDropArg(BHEAD fun,args) ) goto abo; out = fun + fun[1]; break; case SELECTARG: if ( RunSelectArg(BHEAD fun,args) ) goto abo; out = fun + fun[1]; break; case ZTOHARG: { WORD s = RunZtoHArg(BHEAD fun,args); if ( s < 0 ) goto abo; if ( s == 1 ) sign = -sign; out = fun + fun[1]; } break; case HTOZARG: { WORD s = RunHtoZArg(BHEAD fun,args); if ( s < 0 ) goto abo; if ( s == 1 ) sign = -sign; out = fun + fun[1]; } break; default: MLOCK(ErrorMessageLock); MesPrint("Irregular code in execution of transform statement"); MUNLOCK(ErrorMessageLock); Terminate(-1); } onetransform += *onetransform; } while ( *onetransform ); } else { while ( funs < endfun ) { /* sum over sets */ if ( *funs > MAXVARIABLES ) { if ( *t == *funs-MAXVARIABLES ) goto hit; } else { w = SetElements + Sets[*funs].first; m = SetElements + Sets[*funs].last; while ( w < m ) { /* sum over set elements */ if ( *w == *t ) goto hit; w++; } } funs++; } } #ifdef WITHFLOAT next: #endif t += t[1]; } tt = term + *term; while ( in < tt ) *out++ = *in++; if ( sign == -1 ) out[-1] = -out[-1]; *tt = i = out - tt; /* Now copy the whole thing back */ NCOPY(term,tt,i) return(0); abo: MLOCK(ErrorMessageLock); MesCall("RunTransform"); MUNLOCK(ErrorMessageLock); return(-1); } /* #] RunTransform : #[ RunEncode : The info is given by ENCODEARG,size,BASECODE,num and possibly more codes to follow. Only one range is allowed and for now, it should be fully numerical If the range is in reverse order, we need to either revert it first or work with an array of pointers. */ int RunEncode(PHEAD WORD *fun, WORD *args, WORD *info) { WORD base, *f, *funstop, *fun1, *t, size1, size2, size3, *arg; int num, num1, num2, n, i, i1, i2; UWORD *scrat1, *scrat2, *scrat3; WORD *tt, *tstop, totarg, arg1, arg2; if ( functions[fun[0]-FUNCTION].spec != 0 ) return(0); if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunEncode"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg1 > totarg || arg2 > totarg ) return(0); if ( info[2] == BASECODE ) { base = info[3]; if ( base <= 0 ) { /* is a dollar variable */ i1 = -base; base = DolToNumber(BHEAD i1); if ( AN.ErrorInDollar || base < 2 ) { MLOCK(ErrorMessageLock); MesPrint("$%s does not have a number value > 1 in base/encode/transform statement in module %l", DOLLARNAME(Dollars,i1),AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } } /* Compute number of pointers needed and make sure there is space */ if ( arg1 > arg2 ) { num1 = arg2; num2 = arg1; } else { num1 = arg1; num2 = arg2; } num = num2-num1+1; WantAddPointers(num); /* Collect the pointers in pWorkSpace */ n = 1; funstop = fun+fun[1]; f = fun+FUNHEAD; while ( n < num1 ) { if ( f >= funstop ) return(0); NEXTARG(f); n++; } fun1 = f; i = 0; while ( n <= num2 ) { if ( f >= funstop ) return(0); if ( *f != -SNUMBER ) { if ( *f < 0 ) return(0); t = f + *f - 1; i1 = ABS(*t); if ( (*f-i1) != (ARGHEAD+1) ) return(0); /* Not numerical */ i1 = (i1-1)/2 - 1; t--; while ( i1 > 0 ) { if ( *t != 0 ) return(0); /* Not an integer */ t--; i1--; } } AT.pWorkSpace[AT.pWorkPointer+i] = f; i++; NEXTARG(f); n++; } /* f points now to after the arguments; fun1 at the first. Now check whether we need to revert the order */ if ( arg1 > arg2 ) { i1 = 0; i2 = i-1; while ( i1 < i2 ) { t = AT.pWorkSpace[AT.pWorkPointer+i1]; AT.pWorkSpace[AT.pWorkPointer+i1] = AT.pWorkSpace[AT.pWorkPointer+i2]; AT.pWorkSpace[AT.pWorkPointer+i2] = t; i1++; i2--; } } /* Now we can put the thing together. x = arg1; x = base*x+arg2 x = base*x+arg3 etc. We need three scratch arrays for long integers (see NumberMalloc in tools.c). */ scrat1 = NumberMalloc("RunEncode"); scrat2 = NumberMalloc("RunEncode"); scrat3 = NumberMalloc("RunEncode"); arg = AT.pWorkSpace[AT.pWorkPointer]; size1 = PutArgInScratch(arg,scrat1); i--; while ( i > 0 ) { if ( MulLong(scrat1,size1,(UWORD *)(&base),1,scrat2,&size2) ) { NumberFree(scrat3,"RunEncode"); NumberFree(scrat2,"RunEncode"); NumberFree(scrat1,"RunEncode"); goto CalledFrom; } NEXTARG(arg); size3 = PutArgInScratch(arg,scrat3); if ( AddLong(scrat2,size2,scrat3,size3,scrat1,&size1) ) { NumberFree(scrat3,"RunEncode"); NumberFree(scrat2,"RunEncode"); NumberFree(scrat1,"RunEncode"); goto CalledFrom; } i--; } /* Now put the output in place. There are two cases, one being much faster than the other. Hence we program both. Fast: it fits inside the old location. Slow: it does not. The total space is f-fun1 */ if ( size1 == 0 ) { /* Fits! */ *fun1++ = -SNUMBER; *fun1++ = 0; while ( f < funstop ) *fun1++ = *f++; fun[1] = funstop-fun; } else if ( size1 == 1 && scrat1[0] <= MAXPOSITIVE ) { /* Fits! */ *fun1++ = -SNUMBER; *fun1++ = scrat1[0]; while ( f < funstop ) *fun1++ = *f++; fun[1] = fun1-fun; } else if ( size1 == -1 && scrat1[0] <= MAXPOSITIVE+1 ) { /* Fits! */ *fun1++ = -SNUMBER; if ( scrat1[0] < MAXPOSITIVE ) *fun1++ = scrat1[0]; else *fun1++ = (WORD)(MAXPOSITIVE+1); while ( f < funstop ) *fun1++ = *f++; fun[1] = fun1-fun; } else if ( ABS(size1)*2+2+ARGHEAD <= f-fun1 ) { /* Fits! */ if ( size1 < 0 ) { size2 = size1*2-1; size1 = -size1; size3 = -size2; } else { size2 = 2*size1+1; size3 = size2; } *fun1++ = size3+ARGHEAD+1; *fun1++ = 0; FILLARG(fun1); *fun1++ = size3+1; for ( i = 0; i < size1; i++ ) *fun1++ = scrat1[i]; *fun1++ = 1; for ( i = 1; i < size1; i++ ) *fun1++ = 0; *fun1++ = size2; while ( f < funstop ) *fun1++ = *f++; fun[1] = fun1-fun; } else { /* Does not fit */ t = funstop; if ( size1 < 0 ) { size2 = size1*2-1; size1 = -size1; size3 = -size2; } else { size2 = 2*size1+1; size3 = size2; } *t++ = size3+ARGHEAD+1; *t++ = 0; FILLARG(t); *t++ = size3+1; for ( i = 0; i < size1; i++ ) *t++ = scrat1[i]; *t++ = 1; for ( i = 1; i < size1; i++ ) *t++ = 0; *t++ = size2; while ( f < funstop ) *t++ = *f++; f = funstop; while ( f < t ) *fun1++ = *f++; fun[1] = fun1-fun; } NumberFree(scrat3,"RunEncode"); NumberFree(scrat2,"RunEncode"); NumberFree(scrat1,"RunEncode"); } else { MLOCK(ErrorMessageLock); MesPrint("Unimplemented type of encoding encountered in RunEncode"); MUNLOCK(ErrorMessageLock); Terminate(-1); } return(0); CalledFrom: MLOCK(ErrorMessageLock); MesCall("RunEncode"); MUNLOCK(ErrorMessageLock); return(-1); } /* #] RunEncode : #[ RunDecode : */ int RunDecode(PHEAD WORD *fun, WORD *args, WORD *info) { WORD base, num, num1, num2, n, *f, *funstop, *fun1, size1, size2, size3, *t; WORD i1, i2, i, sig; UWORD *scrat1, *scrat2, *scrat3; WORD *tt, *tstop, totarg, arg1, arg2; if ( functions[fun[0]-FUNCTION].spec != 0 ) return(0); if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunDecode"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg1 > totarg && arg2 > totarg ) return(0); if ( info[2] == BASECODE ) { base = info[3]; if ( base <= 0 ) { /* is a dollar variable */ i1 = -base; base = DolToNumber(BHEAD i1); if ( AN.ErrorInDollar || base < 2 ) { MLOCK(ErrorMessageLock); MesPrint("$%s does not have a number value > 1 in base/decode/transform statement in module %l", DOLLARNAME(Dollars,i1),AC.CModule); MUNLOCK(ErrorMessageLock); Terminate(-1); } } /* Compute number of output arguments needed */ if ( arg1 > arg2 ) { num1 = arg2; num2 = arg1; } else { num1 = arg1; num2 = arg2; } num = num2-num1+1; if ( num <= 1 ) return(0); /* Find argument num1 */ funstop = fun + fun[1]; f = fun + FUNHEAD; n = 1; while ( f < funstop ) { if ( n == num1 ) break; NEXTARG(f); n++; } if ( f >= funstop ) return(0); /* not enough arguments */ /* Check that f is integer */ if ( *f == -SNUMBER ) {} else if ( *f < 0 ) return(0); else { t = f + *f - 1; i1 = ABS(*t); if ( (*f-i1) != (ARGHEAD+1) ) return(0); /* Not numerical */ i1 = (i1-1)/2 - 1; t--; while ( i1 > 0 ) { if ( *t != 0 ) return(0); /* Not an integer */ t--; i1--; } } fun1 = f; /* The argument that should be decoded is in fun1 We have to copy it to scratch */ scrat1 = NumberMalloc("RunEncode"); scrat2 = NumberMalloc("RunEncode"); scrat3 = NumberMalloc("RunEncode"); size1 = PutArgInScratch(fun1,scrat1); if ( size1 < 0 ) { sig = -1; size1 = -size1; } else sig = 1; /* We can check first whether this number can be decoded */ scrat2[0] = base; size2 = 1; if ( RaisPow(BHEAD scrat2,&size2,num) ) { NumberFree(scrat3,"RunEncode"); NumberFree(scrat2,"RunEncode"); NumberFree(scrat1,"RunEncode"); goto CalledFrom; } if ( BigLong(scrat1,size1,scrat2,size2) >= 0 ) { /* Number too big */ NumberFree(scrat3,"RunEncode"); NumberFree(scrat2,"RunEncode"); NumberFree(scrat1,"RunEncode"); return(0); } /* We need num*2 spaces */ if ( *fun1 > num*2 ) { /* shrink space */ t = fun1 + 2*num; f = fun1 + *fun1; while ( f < funstop ) *t++ = *f++; fun[1] = t - fun; } else if ( *fun1 < num*2 ) { /* case includes -SNUMBER */ if ( *fun1 < 0 ) { /* expand space from -SNUMBER */ fun[1] += (num-1)*2; t = funstop + (num-1)*2; } else { /* expand space from general argument */ fun[1] += 2*num - *fun1; t = funstop +2*num - *fun1; } f = funstop; while ( f > fun1 ) *--t = *--f; } /* Now there is space for num -SNUMBER arguments filled from the top. */ for ( i = num-1; i >= 0; i-- ) { DivLong(scrat1,size1,(UWORD *)(&base),1,scrat2,&size2,scrat3,&size3); fun1[2*i] = -SNUMBER; if ( size3 == 0 ) fun1[2*i+1] = 0; else fun1[2*i+1] = (WORD)(scrat3[0])*sig; for ( i1 = 0; i1 < size2; i1++ ) scrat1[i1] = scrat2[i1]; size1 = size2; } if ( size2 != 0 ) { MLOCK(ErrorMessageLock); MesPrint("RunDecode: number to be decoded is too big"); MUNLOCK(ErrorMessageLock); NumberFree(scrat3,"RunEncode"); NumberFree(scrat2,"RunEncode"); NumberFree(scrat1,"RunEncode"); goto CalledFrom; } /* Now check whether we should change the order of the arguments */ if ( arg1 > arg2 ) { i1 = 1; i2 = 2*num-1; while ( i2 > i1 ) { i = fun1[i1]; fun1[i1] = fun1[i2]; fun1[i2] = i; i1 += 2; i2 -= 2; } } NumberFree(scrat3,"RunEncode"); NumberFree(scrat2,"RunEncode"); NumberFree(scrat1,"RunEncode"); } else { MLOCK(ErrorMessageLock); MesPrint("Unimplemented type of encoding encountered in RunDecode"); MUNLOCK(ErrorMessageLock); Terminate(-1); } return(0); CalledFrom: MLOCK(ErrorMessageLock); MesCall("RunDecode"); MUNLOCK(ErrorMessageLock); return(-1); } /* #] RunDecode : #[ RunReplace : Gets the function, passes the arguments and looks whether they need to be treated. If so, the exact treatment is found in info. The info is given as if it is a function of type REPLACEMENT but its name is REPLACEARG (which is NOT a function). It is performed on the arguments. The output is at first written after fun and in the end overwrites fun. */ int RunReplace(PHEAD WORD *fun, WORD *args, WORD *info) { int n = 0, i, dirty = 0, totarg, nfix, nwild, ngeneral; WORD *t, *tt, *u, *tstop, *info1, *infoend, *oldwork = AT.WorkPointer; WORD *term, *newterm, *nt, *term1, *term2; WORD wild[4], mask, *term3, *term4, *oldmask = AT.WildMask; WORD n1, n2, doanyway; info++; t = fun; tstop = fun + fun[1]; u = tstop; for ( i = 0; i < FUNHEAD; i++ ) *u++ = *t++; tt = t; if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } } else { totarg = tstop - tt; } /* Now get the info through Generator to bring it to standard form. info points at a single term that should be sent to Generator. We want to put the information in the WorkSpace but fun etc lies there already. This means that we have to move the WorkPointer quite high up. */ AT.WorkPointer += 2*AM.MaxTer; if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } term = AT.WorkPointer; for ( i = 0; i < *info; i++ ) term[i] = info[i]; AT.WorkPointer = term + *term; AR.Eside = LHSIDEX; NewSort(BHEAD0); if ( Generator(BHEAD term,AR.Cnumlhs) ) { LowerSortLevel(); AT.WorkPointer = oldwork; return(-1); } newterm = AT.WorkPointer; if ( EndSort(BHEAD newterm,1) < 0 ) {} if ( ( *newterm && *(newterm+*newterm) != 0 ) || *newterm == 0 ) { MLOCK(ErrorMessageLock); MesPrint("&information in replace transformation does not evaluate into a single term"); MUNLOCK(ErrorMessageLock); return(-1); } AR.Eside = RHSIDE; i = *newterm; tt = term; nt = newterm; NCOPY(tt,nt,i); AT.WorkPointer = term + *term; info = term + 1; term1 = term + *term; term2 = term1+1; *term2++ = REPLACEMENT; term2++; FILLFUN(term2) /* First we count the different types of objects */ infoend = info + info[1]; info1 = info + FUNHEAD; nfix = nwild = ngeneral = 0; while ( info1 < infoend ) { if ( *info1 == -SNUMBER ) { nfix++; info1 += 2; NEXTARG(info1) } else if ( *info1 <= -FUNCTION ) { if ( *info1 == -WILDARGFUN ) { nwild++; info1++; NEXTARG(info1) } else { *term2++ = *info1++; COPY1ARG(term2,info1) ngeneral++; } } else if ( *info1 == -INDEX ) { if ( info1[1] == WILDARGINDEX + AM.OffsetIndex ) { nwild++; info1 += 2; NEXTARG(info1) } else { *term2++ = *info1++; *term2++ = *info1++; COPY1ARG(term2,info1) ngeneral++; } } else if ( *info1 == -SYMBOL ) { if ( info1[1] == WILDARGSYMBOL ) { nwild++; info1 += 2; NEXTARG(info1) } else { *term2++ = *info1++; *term2++ = *info1++; COPY1ARG(term2,info1) ngeneral++; } } else if ( *info1 == -MINVECTOR || *info1 == -VECTOR ) { if ( info1[1] == WILDARGVECTOR + AM.OffsetVector ) { nwild++; info1 += 2; NEXTARG(info1) } else { *term2++ = *info1++; *term2++ = *info1++; COPY1ARG(term2,info1) ngeneral++; } } else { MLOCK(ErrorMessageLock); MesPrint("&irregular code found in replace transformation (RunReplace)"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } AT.WorkPointer = term2; *term1 = term2 - term1; term1[2] = *term1 - 1; /* And now stepping through the arguments */ while ( t < tstop ) { n++; /* The number of the argument. Now check whether we need it */ if ( TestArgNum(n,totarg,args) == 0 ) { if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { if ( *t <= -FUNCTION ) { *u++ = *t++; } else if ( *t < 0 ) { *u++ = *t++; *u++ = *t++; } else { i = *t; NCOPY(u,t,i) } } else *u++ = *t++; continue; } /* Here we have in info effectively a replace_ function, but with additionally the possibility of integer arguments. We treat those first and for the rest we have to do some pattern matching. Note that the compilation routine should check that there is an even number of arguments in the replace function. First we go for number -> something */ doanyway = 0; if ( nfix > 0 ) { if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { if ( *t == -SNUMBER ) { info1 = info + FUNHEAD; while ( info1 < infoend ) { if ( *info1 == -SNUMBER ) { if ( info1[1] == t[1] ) { if ( info1[2] == -SNUMBER ) { *u++ = -SNUMBER; *u++ = info1[3]; info1 += 4; } else { info1 += 2; if ( info1[0] <= -FUNCTION ) i = 1; else if ( info1[0] < 0 ) i = 2; else i = *info1; NCOPY(u,info1,i) } t += 2; goto nextt; } info1 += 2; NEXTARG(info1); } else { NEXTARG(info1); NEXTARG(info1); } } /* Here we had no match in the style of 1->2. It could however be that xarg_ does something */ doanyway = 1; n2 = t[1]; } } else { /* Tensor */ if ( *t < AM.OffsetIndex && *t >= 0 ) { info1 = info + FUNHEAD; while ( info1 < infoend ) { if ( ( *info1 == -SNUMBER ) && ( info1[1] == *t ) && ( ( ( info1[2] == -SNUMBER ) && ( info1[3] >= 0 ) && ( info1[3] < AM.OffsetIndex ) ) || ( info1[2] == -INDEX || info1[2] == -VECTOR || info1[2] == -MINVECTOR ) ) ) { *u++ = info1[3]; info1 += 4; t++; goto nextt; } else { NEXTARG(info1); NEXTARG(info1); } } } } } else if ( *t == -SNUMBER ) { doanyway = 1; n2 = t[1]; } /* First we try to catch those elements that have an exact match in the traditional replace_ part. This means that *t should be less than zero and match an entry in the replace_ function that we prepared. */ if ( ngeneral > 0 ) { if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { if ( *t < 0 ) { term3 = term1 + *term1; term4 = term1 + FUNHEAD; while ( term4 < term3 ) { if ( *term4 == *t && ( *t <= -FUNCTION || ( t[1] == term4[1] ) ) ) break; NEXTARG(term4) } if ( term4 < term3 ) goto dothisnow; } } else { term3 = term1 + *term1; term4 = term1 + FUNHEAD; while ( term4 < term3 ) { if ( ( term4[1] == *t ) && ( ( *term4 == -INDEX || *term4 == -VECTOR || ( *term4 == -SYMBOL && term4[1] < AM.OffsetIndex && term4[1] >= 0 ) ) ) ) break; NEXTARG(term4) } if ( term4 < term3 ) goto dothisnow; } } /* First we eliminate the fixed arguments and make a 'new info' If there is anything left we can continue. Now we look for whole argument wildcards (arg_, parg_, iarg_ or farg_) */ if ( nwild > 0 ) { /* If we have f(a)*replace_(xarg_,b(xarg_)) this gives f(b(a)) In testing the wildcard we have CheckWild do the work. This means that we have to set op the special variables (AT.WildMask,AN.WildValue,AN.NumWild) */ wild[1] = 4; info1 = info + FUNHEAD; while ( info1 < infoend ) { if ( *info1 == -SYMBOL && info1[1] == WILDARGSYMBOL && ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) ) { wild[0] = SYMTOSUB; wild[2] = WILDARGSYMBOL; wild[3] = 0; AN.WildValue = wild; AT.WildMask = &mask; mask = 0; AN.NumWild = 1; if ( *t == -SYMBOL || ( *t > 0 && CheckWild(BHEAD WILDARGSYMBOL,SYMTOSUB,1,t) == 0 ) || doanyway ) { /* We put the part in replace in a function and make a replace_(xarg_,(t argument)). */ n1 = SYMBOL; n2 = WILDARGSYMBOL; info1 += 2; getthisone:; term3 = term2+1; if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { *term3++ = DUMFUN; term3++; FILLFUN(term3) COPY1ARG(term3,info1) } else { *term3++ = fun[0]; term3++; FILLFUN(term3) *term3++ = *info1; } term2[2] = term3 - term2 - 1; tt = term3; *term3++ = REPLACEMENT; term3++; FILLFUN(term3) *term3++ = -n1; if ( n1 < FUNCTION ) *term3++ = n2; if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { term4 = t; COPY1ARG(term3,term4) } else { *term3++ = *t; } tt[1] = term3 - tt; *term3++ = 1; *term3++ = 1; *term3++ = 3; *term2 = term3 - term2; AT.WorkPointer = term3; NewSort(BHEAD0); if ( Generator(BHEAD term2,AR.Cnumlhs) ) { LowerSortLevel(); AT.WorkPointer = oldwork; AT.WildMask = oldmask; return(-1); } term4 = AT.WorkPointer; if ( EndSort(BHEAD term4,1) < 0 ) {} if ( ( *term4 && *(term4+*term4) != 0 ) || *term4 == 0 ) { MLOCK(ErrorMessageLock); MesPrint("&information in replace transformation does not evaluate into a single term"); MUNLOCK(ErrorMessageLock); return(-1); } /* Now we can copy the new function argument to the output u */ i = term4[2]-FUNHEAD; term3 = term4+FUNHEAD+1; NCOPY(u,term3,i) if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { NEXTARG(t) } else t++; AT.WorkPointer = term2; goto nextt; } info1 += 2; NEXTARG(info1) } else if ( ( *info1 == -INDEX ) && ( info[1] == WILDARGINDEX + AM.OffsetIndex ) ) { wild[0] = INDTOSUB; wild[2] = WILDARGINDEX+AM.OffsetIndex; wild[3] = 0; AN.WildValue = wild; AT.WildMask = &mask; mask = 0; AN.NumWild = 1; if ( ( functions[fun[0]-FUNCTION].spec == TENSORFUNCTION ) || ( *t == -INDEX || ( *t > 0 && CheckWild(BHEAD WILDARGINDEX,INDTOSUB,1,t) == 0 ) ) ) { /* We put the part in replace in a function and make a replace_(xarg_,(t argument)). */ n1 = INDEX; n2 = WILDARGINDEX+AM.OffsetIndex; info1 += 2; goto getthisone; } info1 += 2; NEXTARG(info1) } else if ( ( *info1 == -VECTOR ) && ( info1[1] == WILDARGVECTOR + AM.OffsetVector ) ) { wild[0] = VECTOSUB; wild[2] = WILDARGVECTOR+AM.OffsetVector; wild[3] = 0; AN.WildValue = wild; AT.WildMask = &mask; mask = 0; AN.NumWild = 1; if ( functions[fun[0]-FUNCTION].spec == TENSORFUNCTION ) { if ( *t < MINSPEC ) { n1 = VECTOR; n2 = WILDARGVECTOR+AM.OffsetVector; info1 += 2; goto getthisone; } } else if ( *t == -VECTOR || *t == -MINVECTOR || ( *t > 0 && CheckWild(BHEAD WILDARGVECTOR,VECTOSUB,1,t) == 0 ) ) { /* We put the part in replace in a function and make a replace_(xarg_,(t argument)). */ n1 = VECTOR; n2 = WILDARGVECTOR+AM.OffsetVector; info1 += 2; goto getthisone; } info1 += 2; NEXTARG(info1) } else if ( *info1 == -WILDARGFUN ) { wild[0] = FUNTOFUN; wild[2] = WILDARGFUN; wild[3] = 0; AN.WildValue = wild; AT.WildMask = &mask; mask = 0; AN.NumWild = 1; if ( *t <= -FUNCTION || ( *t > 0 && CheckWild(BHEAD WILDARGFUN,FUNTOFUN,1,t) == 0 ) ) { /* We put the part in replace in a function and make a replace_(xarg_,(t argument)). */ n2 = n1 = -WILDARGFUN; /* n2 is to keep the compiler quiet */ info1++; goto getthisone; } info1++; NEXTARG(info1) } else { NEXTARG(info1) NEXTARG(info1) } } } if ( ngeneral > 0 ) { /* They are all in a replace_ function. Compose the whole thing into a term with replace_()*dum_(arg) which will be given to Generator. If we have f(a(x))*replace_(x,b) this gives f(a(b)) */ dothisnow:; term3 = term2; term4 = term1; i = *term1; NCOPY(term3,term4,i) term4 = term3; if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { *term3++ = DUMFUN; term3++; FILLFUN(term3); tt = t; COPY1ARG(term3,tt) } else { *term3++ = fun[0]; term3++; FILLFUN(term3); *term3++ = *t; } term4[1] = term3-term4; *term3++ = 1; *term3++ = 1; *term3++ = 3; *term2 = term3-term2; AT.WorkPointer = term3; NewSort(BHEAD0); if ( Generator(BHEAD term2,AR.Cnumlhs) ) { LowerSortLevel(); AT.WorkPointer = oldwork; AT.WildMask = oldmask; return(-1); } term4 = AT.WorkPointer; if ( EndSort(BHEAD term4,1) < 0 ) {} if ( ( *term4 && *(term4+*term4) != 0 ) || *term4 == 0 ) { MLOCK(ErrorMessageLock); MesPrint("&information in replace transformation does not evaluate into a single term"); MUNLOCK(ErrorMessageLock); return(-1); } /* Now we can copy the new function argument to the output u */ i = term4[2]-FUNHEAD; term3 = term4+FUNHEAD+1; NCOPY(u,term3,i) NEXTARG(t) AT.WorkPointer = term2; goto nextt; } /* No catch. Copy the argument and continue. */ if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { if ( *t <= -FUNCTION ) { *u++ = *t++; } else if ( *t < 0 ) { *u++ = *t++; *u++ = *t++; } else { i = *t; NCOPY(u,t,i) } } else { *u++ = *t++; } nextt:; } i = u - tstop; tstop[1] = i; tstop[2] = dirty; t = fun; u = tstop; NCOPY(t,u,i) AT.WorkPointer = oldwork; AT.WildMask = oldmask; return(0); } /* #] RunReplace : #[ RunImplode : Note that we restrict ourselves to short integers and/or single symbols */ int RunImplode(WORD *fun, WORD *args) { GETIDENTITY WORD *tt, *tstop, totarg, arg1, arg2, num1, num2, i1, n; WORD *f, *t, *ttt, *t4, *ff, *fff; WORD moveup, numzero, outspace; if ( functions[fun[0]-FUNCTION].spec != 0 ) return(0); if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunImplode"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); /* Get the proper range in forward direction and the number of arguments */ if ( arg1 > arg2 ) { num1 = arg2; num2 = arg1; } else { num1 = arg1; num2 = arg2; } if ( num1 > totarg || num2 > totarg ) return(0); /* We need, for the most general case 4 spots for each: x,pow,coef,sign Hence we put these in the workspace above the term after tstop */ n = 1; f = fun+FUNHEAD; while ( n < num1 ) { if ( f >= tstop ) return(0); NEXTARG(f); n++; } ff = f; /* We are now at the first argument to be done Go through the terms and test their validity. If one of them doesn't conform to the rules we don't do anything. The terms to be done are put in special notation after the function. Notation: numsymbol, power, |coef|, sign If numsymbol is negative there is no symbol. We do it this way because otherwise stepping backwards (as in range=(4,1)) would be very difficult. */ tt = tstop; while ( n <= num2 ) { if ( f >= tstop ) return(0); if ( *f == -SNUMBER ) { *tt++ = -1; *tt++ = 0; if ( f[1] < 0 ) { *tt++ = -f[1]; *tt++ = -1; } else { *tt++ = f[1]; *tt++ = 1; } f += 2; } else if ( *f == -SYMBOL ) { *tt++ = f[1]; *tt++ = 1; *tt++ = 1; *tt++ = 1; f += 2; } else if ( *f < 0 ) return(0); else { if ( *f != ( f[ARGHEAD]+ARGHEAD ) ) return(0); /* Not a single term */ t = f + *f - 1; i1 = ABS(*t); if ( ( i1 > 3 ) || ( t[-1] != 1 ) ) return(0); /* Not an integer or too big */ if ( (UWORD)(t[-2]) > MAXPOSITIVE4 ) return(0); /* number too big */ if ( f[ARGHEAD] == i1+1 ) { /* numerical which is fine */ *tt++ = -1; *tt++ = 0; *tt++ = t[-2]; if ( *t < 0 ) { *tt++ = -1; } else { *tt++ = 1; } } else if ( ( f[ARGHEAD+1] != SYMBOL ) || ( f[ARGHEAD+2] != 4 ) || ( ( f+ARGHEAD+1+f[ARGHEAD+2] ) < ( t-i1 ) ) ) return(0); /* not a single symbol with a coefficient */ else { *tt++ = f[ARGHEAD+3]; *tt++ = f[ARGHEAD+4]; *tt++ = t[-2]; if ( *t < 0 ) { *tt++ = -1; } else { *tt++ = 1; } } f += *f; } n++; } fff = f; /* At this point we can do the implosion. Requirement: no coefficient shall take more than one word. (a stricter requirement may be needed to keep the explosion contained) */ if ( arg1 > arg2 ) { /* Work backward. */ t = tt - 4; numzero = 0; while ( t >= tstop ) { if ( t[2] == 0 ) numzero++; else { if ( numzero > 0 ) { t[2] += numzero; t4 = t+4; ttt = t4 + 4*numzero; while ( ttt < tt ) *t4++ = *ttt++; tt -= 4*numzero; numzero = 0; } } t -= 4; } } else { t = tstop; numzero = 0; ttt = t; while ( t < tt ) { if ( t[2] == 0 ) numzero++; else { if ( numzero > 0 ) { t[2] += numzero; t4 = t; while ( t4 < tt ) *ttt++ = *t4++; tt -= 4*numzero; t -= 4*numzero; ttt = t + 4; numzero = 0; } else { ttt = t + 4; } } t += 4; } /* We may have numzero > 0 at the end. We leave them. Output space is currently from tstop to tt */ } /* Now we compute the real output space needed */ t = tstop; outspace = 0; while ( t < tt ) { if ( t[0] == -1 ) { if ( t[2] > MAXPOSITIVE4 ) { return(0); /* Number too big */ } outspace += 2; } else if ( t[1] == 1 && t[2] == 1 && t[3] == 1 ) { outspace += 2; } else { outspace += 8 + ARGHEAD; } t += 4; } if ( outspace < (fff-ff) ) { t = tstop; while ( t < tt ) { if ( t[0] == -1 ) { *ff++ = -SNUMBER; *ff++ = t[2]*t[3]; } else if ( t[1] == 1 && t[2] == 1 && t[3] == 1 ) { *ff++ = -SYMBOL; *ff++ = t[0]; } else { *ff++ = 8+ARGHEAD; *ff++ = 0; FILLARG(ff); *ff++ = 8; *ff++ = SYMBOL; *ff++ = 4; *ff++ = t[0]; *ff++ = t[1]; *ff++ = t[2]; *ff++ = 1; *ff++ = t[3] > 0 ? 3: -3; } t += 4; } while ( fff < tstop ) *ff++ = *fff++; fun[1] = ff - fun; } else if ( outspace > (fff-ff) ) { /* Move the answer up by the required amount. Move the tail to its new location Move in things as for outspace == (fff-ff) */ moveup = outspace-(fff-ff); ttt = tt + moveup; t = tt; while ( t > fff ) *--ttt = *--t; tt += moveup; tstop += moveup; fff += moveup; fun[1] += moveup; goto moveinto; } else { moveinto: t = tstop; while ( t < tt ) { if ( t[0] == -1 ) { *ff++ = -SNUMBER; *ff++ = t[2]*t[3]; } else if ( t[1] == 1 && t[2] == 1 && t[3] == 1 ) { *ff++ = -SYMBOL; *ff++ = t[0]; } else { *ff++ = 8+ARGHEAD; *ff++ = 0; FILLARG(ff); *ff++ = 8; *ff++ = SYMBOL; *ff++ = 4; *ff++ = t[0]; *ff++ = t[1]; *ff++ = t[2]; *ff++ = 1; *ff++ = t[3] > 0 ? 3: -3; } t += 4; } } return(0); } /* #] RunImplode : #[ RunExplode : */ int RunExplode(PHEAD WORD *fun, WORD *args) { WORD arg1, arg2, num1, num2, *tt, *tstop, totarg, *tonew, *newfun; WORD *ff, *f; int reverse = 0, iarg, i, numzero; if ( functions[fun[0]-FUNCTION].spec != 0 ) return(0); if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunExplode"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); /* Get the proper range in forward direction and the number of arguments */ if ( arg1 > arg2 ) { num1 = arg2; num2 = arg1; reverse = 1; } else { num1 = arg1; num2 = arg2; } if ( num1 > totarg || num2 > totarg ) return(0); if ( tstop + AM.MaxTer > AT.WorkTop ) goto OverWork; /* We will make the new function after the old one in the workspace Find the first argument */ tonew = newfun = tstop; ff = fun + FUNHEAD; iarg = 0; while ( ff < tstop ) { iarg++; if ( iarg == num1 ) { i = ff - fun; f = fun; NCOPY(tonew,f,i) break; } NEXTARG(ff) } /* We have reached the first argument to be done */ while ( iarg <= num2 ) { if ( *ff == -SYMBOL || ( *ff == -SNUMBER && ff[1] == 0 ) ) { *tonew++ = *ff++; *tonew++ = *ff++; } else if ( *ff == -SNUMBER ) { numzero = ABS(ff[1])-1; if ( reverse ) { *tonew++ = -SNUMBER; *tonew++ = ff[1] < 0 ? -1: 1; while ( numzero > 0 ) { *tonew++ = -SNUMBER; *tonew++ = 0; numzero--; } } else { while ( numzero > 0 ) { *tonew++ = -SNUMBER; *tonew++ = 0; numzero--; } *tonew++ = -SNUMBER; *tonew++ = ff[1] < 0 ? -1: 1; } ff += 2; } else if ( *ff < 0 ) { return(0); } else { if ( *ff != ARGHEAD+8 || ff[ARGHEAD] != 8 || ff[ARGHEAD+1] != SYMBOL || ABS(ff[ARGHEAD+7]) != 3 || ff[ARGHEAD+6] != 1 ) return(0); numzero = ff[ARGHEAD+5]; if ( numzero >= MAXPOSITIVE4 ) return(0); numzero--; if ( reverse ) { if ( ff[ARGHEAD+7] > 0 ) { *tonew++ = -SNUMBER; *tonew++ = 1; } else { *tonew++ = ARGHEAD+8; *tonew++ = 0; FILLARG(tonew) *tonew++ = 8; *tonew++ = SYMBOL; *tonew++ = ff[ARGHEAD+3]; *tonew++ = ff[ARGHEAD+4]; *tonew++ = 1; *tonew++ = 1; *tonew++ = -3; } while ( numzero > 0 ) { *tonew++ = -SNUMBER; *tonew++ = 0; numzero--; } } else { while ( numzero > 0 ) { *tonew++ = -SNUMBER; *tonew++ = 0; numzero--; } *tonew++ = ARGHEAD+8; *tonew++ = 0; FILLARG(tonew) *tonew++ = 8; *tonew++ = SYMBOL; *tonew++ = 4; *tonew++ = ff[ARGHEAD+3]; *tonew++ = ff[ARGHEAD+4]; *tonew++ = 1; *tonew++ = 1; if ( ff[ARGHEAD+7] > 0 ) *tonew++ = 3; else *tonew++ = -3; } ff += *ff; } if ( tonew > AT.WorkTop ) goto OverWork; iarg++; } /* Copy the tail, settle the size and copy the whole thing back. */ while ( ff < tstop ) *tonew++ = *ff++; i = newfun[1] = tonew-newfun; NCOPY(fun,newfun,i) return(0); OverWork:; MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* #] RunExplode : #[ RunPermute : */ int RunPermute(PHEAD WORD *fun, WORD *args, WORD *info) { WORD *tt, totarg, *tstop, arg1, arg2, n, num, i, *f, *f1, *f2, *infostop; WORD *in, *iw, withdollar; DOLLARS d; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunPermute"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } arg1 = 1; arg2 = totarg; /* We need to: 1: get pointers to the arguments 2: permute the pointers 3: copy the arguments to safe territory in the new order 4: copy this new order back in situ. */ num = arg2-arg1+1; WantAddPointers(num); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; NEXTARG(f) } f1 = f; while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; NEXTARG(f) } /* Now the permutations */ info++; while ( *info ) { infostop = info + *info; info++; if ( *info > totarg ) return(0); /* Now we have a look whether there are dollar variables to be expanded We also shift out all values that are out of range. */ withdollar = 0; in = info; while ( in < infostop ) { if ( *in < 0 ) { /* Dollar variable -(number+1) */ d = Dollars - *in - 1; #ifdef WITHPTHREADS { int nummodopt, dtype = -1, numdollar = -*in-1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } } #endif if ( ( d->type == DOLNUMBER || d->type == DOLTERMS ) && d->where[0] == 4 && d->where[4] == 0 ) { if ( d->where[3] < 0 || d->where[2] != 1 || d->where[1] > totarg ) return(0); } else if ( d->type == DOLWILDARGS ) { iw = d->where+1; while ( *iw ) { if ( *iw == -SNUMBER ) { if ( iw[1] <= 0 || iw[1] > totarg ) return(0); } else goto IllType; iw += 2; } } else { IllType: MLOCK(ErrorMessageLock); MesPrint("Illegal type of $-variable in RunPermute"); MUNLOCK(ErrorMessageLock); Terminate(-1); } withdollar++; } else if ( *in > totarg ) return(0); in++; } if ( withdollar ) { /* We need some space for a copy */ WORD *incopy, *tocopy; incopy = TermMalloc("RunPermute"); tocopy = incopy+1; in = info; while ( in < infostop ) { if ( *in < 0 ) { d = Dollars - *in - 1; #ifdef WITHPTHREADS { int nummodopt, dtype = -1, numdollar = -*in-1; if ( AS.MultiThreaded && ( AC.mparallelflag == PARALLELFLAG ) ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( numdollar == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } } #endif if ( d->type == DOLNUMBER || d->type == DOLTERMS ) { *tocopy++ = d->where[1] - 1; } else if ( d->type == DOLWILDARGS ) { iw = d->where+1; while ( *iw ) { *tocopy++ = iw[1] - 1; iw += 2; } } in++; } else *tocopy++ = *in++; } *tocopy = 0; *incopy = tocopy - incopy; in = incopy+1; tt = AT.pWorkSpace[AT.pWorkPointer+*in]; in++; while ( in < tocopy ) { if ( *in > totarg ) return(0); AT.pWorkSpace[AT.pWorkPointer+in[-1]] = AT.pWorkSpace[AT.pWorkPointer+*in]; in++; } AT.pWorkSpace[AT.pWorkPointer+in[-1]] = tt; TermFree(incopy,"RunPermute"); info = infostop; } else { tt = AT.pWorkSpace[AT.pWorkPointer+*info]; info++; while ( info < infostop ) { if ( *info > totarg ) return(0); AT.pWorkSpace[AT.pWorkPointer+info[-1]] = AT.pWorkSpace[AT.pWorkPointer+*info]; info++; } AT.pWorkSpace[AT.pWorkPointer+info[-1]] = tt; } } /* info++; while ( *info ) { infostop = info + *info; info++; if ( *info > totarg ) return(0); tt = AT.pWorkSpace[AT.pWorkPointer+*info]; info++; while ( info < infostop ) { if ( *info > totarg ) return(0); AT.pWorkSpace[AT.pWorkPointer+info[-1]] = AT.pWorkSpace[AT.pWorkPointer+*info]; info++; } AT.pWorkSpace[AT.pWorkPointer+info[-1]] = tt; } */ /* And the final cleanup */ if ( tstop+(f-f1) > AT.WorkTop ) goto OverWork; f2 = tstop; for ( i = 0; i < num; i++ ) { f = AT.pWorkSpace[AT.pWorkPointer+i]; COPY1ARG(f2,f) } i = f2 - tstop; NCOPY(f1,tstop,i) } else { /* tensors */ tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = tstop-tt; arg1 = 1; arg2 = totarg; num = arg2-arg1+1; WantAddPointers(num); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; f++; } f1 = f; while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; f++; } /* Now the permutations */ info++; while ( *info ) { infostop = info + *info; info++; if ( *info > totarg ) return(0); tt = AT.pWorkSpace[AT.pWorkPointer+*info]; info++; while ( info < infostop ) { if ( *info > totarg ) return(0); AT.pWorkSpace[AT.pWorkPointer+info[-1]] = AT.pWorkSpace[AT.pWorkPointer+*info]; info++; } AT.pWorkSpace[AT.pWorkPointer+info[-1]] = tt; } /* And the final cleanup */ if ( tstop+(f-f1) > AT.WorkTop ) goto OverWork; f2 = tstop; for ( i = 0; i < num; i++ ) { f = AT.pWorkSpace[AT.pWorkPointer+i]; *f2++= *f++; } i = f2 - tstop; NCOPY(f1,tstop,i) } return(0); OverWork:; MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* #] RunPermute : #[ RunReverse : */ int RunReverse(PHEAD WORD *fun, WORD *args) { WORD *tt, totarg, *tstop, arg1, arg2, n, num, i, *f, *f1, *f2, i1, i2; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunReverse"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); /* We need to: 1: get pointers to the arguments 2: reverse the order of the pointers 3: copy the arguments to safe territory in the new order 4: copy this new order back in situ. */ if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg2 > totarg ) return(0); num = arg2-arg1+1; WantAddPointers(num); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; NEXTARG(f) } f1 = f; while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; NEXTARG(f) } i1 = i-1; i2 = 0; while ( i1 > i2 ) { tt = AT.pWorkSpace[AT.pWorkPointer+i1]; AT.pWorkSpace[AT.pWorkPointer+i1] = AT.pWorkSpace[AT.pWorkPointer+i2]; AT.pWorkSpace[AT.pWorkPointer+i2] = tt; i1--; i2++; } if ( tstop+(f-f1) > AT.WorkTop ) goto OverWork; f2 = tstop; for ( i = 0; i < num; i++ ) { f = AT.pWorkSpace[AT.pWorkPointer+i]; COPY1ARG(f2,f) } i = f2 - tstop; NCOPY(f1,tstop,i) } else { /* Tensors */ tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = tstop - tt; if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); /* We need to: 1: get pointers to the arguments 2: reverse the order of the pointers 3: copy the arguments to safe territory in the new order 4: copy this new order back in situ. */ if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg2 > totarg ) return(0); num = arg2-arg1+1; WantAddPointers(num); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; f++; } f1 = f; while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; f++; } i1 = i-1; i2 = 0; while ( i1 > i2 ) { tt = AT.pWorkSpace[AT.pWorkPointer+i1]; AT.pWorkSpace[AT.pWorkPointer+i1] = AT.pWorkSpace[AT.pWorkPointer+i2]; AT.pWorkSpace[AT.pWorkPointer+i2] = tt; i1--; i2++; } if ( tstop+(f-f1) > AT.WorkTop ) goto OverWork; f2 = tstop; for ( i = 0; i < num; i++ ) { f = AT.pWorkSpace[AT.pWorkPointer+i]; *f2++ = *f++; } i = f2 - tstop; NCOPY(f1,tstop,i) } return(0); OverWork:; MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* #] RunReverse : #[ RunDedup : */ int RunDedup(PHEAD WORD *fun, WORD *args) { WORD *tt, totarg, *tstop, arg1, arg2, n, i, j,k, *f, *f1, *f2, *fd, *fstart; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunDedup"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg2 > totarg ) return(0); f = fun+FUNHEAD; n = 1; while ( n < arg1 ) { n++; NEXTARG(f) } f1 = f; // fast forward to first element in range i = 0; // new argument count fstart = f1; for (; n <= arg2; n++ ) { f2 = fstart; for ( j = 0; j < i; j++ ) { // check all previous terms fd = f2; NEXTARG(fd) for ( k = 0; k < fd-f2; k++ ) // byte comparison of args if ( f2[k] != f[k] ) break; if ( k == fd-f2 ) break; // duplicate arg f2 = fd; } if ( j == i ) { // unique factor, copy in situ COPY1ARG(f1,f) i++; } else { NEXTARG(f) } } // move the terms from after the range for (j = n; j <= totarg; j++) { COPY1ARG(f1,f) } fun[1] = f1 - fun; // resize function } else { /* Tensors */ tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = tstop - tt; if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg2 > totarg ) return(0); f = fun+FUNHEAD; i = arg1; // new argument count n = i; for (; n <= arg2; n++ ) { for ( j = arg1; j < i; j++ ) { // check all previous terms if ( f[n-1] == f[j-1] ) break; // duplicate arg } if ( j == i ) { // unique factor, copy in situ f[i-1] = f[n-1]; i++; } } // move the terms from after the range for (j = n; j <= totarg; j++, i++) { f[i-1] = f[j-1]; } fun[1] = f + i - 1 - fun; // resize function } return(0); } /* #] RunDedup : #[ RunCycle : */ int RunCycle(PHEAD WORD *fun, WORD *args, WORD *info) { WORD *tt, totarg, *tstop, arg1, arg2, n, num, i, j, *f, *f1, *f2, x, ncyc, cc; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunCycle"); MUNLOCK(ErrorMessageLock); Terminate(-1); } ncyc = info[1]; if ( ncyc >= MAXPOSITIVE2 ) { /* $ variable */ ncyc -= MAXPOSITIVE2; if ( ncyc >= MAXPOSITIVE4 ) { ncyc -= MAXPOSITIVE4; /* -$ */ cc = -1; } else cc = 1; ncyc = DolToNumber(BHEAD ncyc); if ( AN.ErrorInDollar ) { MesPrint(" Error in Dollar variable in transform,cycle()=$"); return(-1); } if ( ncyc >= MAXPOSITIVE4 || ncyc <= -MAXPOSITIVE4 ) { MesPrint(" Illegal value from Dollar variable in transform,cycle()=$"); return(-1); } ncyc *= cc; } if ( functions[fun[0]-FUNCTION].spec != TENSORFUNCTION ) { tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg1 > arg2 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg2 > totarg ) return(0); /* We need to: 1: get pointers to the arguments 2: cycle the pointers 3: copy the arguments to safe territory in the new order 4: copy this new order back in situ. */ num = arg2-arg1+1; WantAddPointers(num); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; NEXTARG(f) } f1 = f; while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; NEXTARG(f) } /* Now the cycle(s). First minimize the number of cycles. */ x = ncyc; if ( x >= i ) { x %= i; if ( x > i/2 ) x -= i; } else if ( x <= -i ) { x = -((-x) % i); if ( x <= -i/2 ) x += i; } while ( x ) { if ( x > 0 ) { tt = AT.pWorkSpace[AT.pWorkPointer+i-1]; for ( j = i-1; j > 0; j-- ) AT.pWorkSpace[AT.pWorkPointer+j] = AT.pWorkSpace[AT.pWorkPointer+j-1]; AT.pWorkSpace[AT.pWorkPointer] = tt; x--; } else { tt = AT.pWorkSpace[AT.pWorkPointer]; for ( j = 1; j < i; j++ ) AT.pWorkSpace[AT.pWorkPointer+j-1] = AT.pWorkSpace[AT.pWorkPointer+j]; AT.pWorkSpace[AT.pWorkPointer+j-1] = tt; x++; } } /* And the final cleanup */ if ( tstop+(f-f1) > AT.WorkTop ) goto OverWork; f2 = tstop; for ( i = 0; i < num; i++ ) { f = AT.pWorkSpace[AT.pWorkPointer+i]; COPY1ARG(f2,f) } i = f2 - tstop; NCOPY(f1,tstop,i) } else { /* Tensors */ tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = tstop - tt; if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg1 > arg2 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg2 > totarg ) return(0); /* We need to: 1: get pointers to the arguments 2: cycle the pointers 3: copy the arguments to safe territory in the new order 4: copy this new order back in situ. */ num = arg2-arg1+1; WantAddPointers(num); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; f++; } f1 = f; while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; f++; } /* Now the cycle(s). First minimize the number of cycles. */ x = ncyc; if ( x >= i ) { x %= i; if ( x > i/2 ) x -= i; } else if ( x <= -i ) { x = -((-x) % i); if ( x <= -i/2 ) x += i; } while ( x ) { if ( x > 0 ) { tt = AT.pWorkSpace[AT.pWorkPointer+i-1]; for ( j = i-1; j > 0; j-- ) AT.pWorkSpace[AT.pWorkPointer+j] = AT.pWorkSpace[AT.pWorkPointer+j-1]; AT.pWorkSpace[AT.pWorkPointer] = tt; x--; } else { tt = AT.pWorkSpace[AT.pWorkPointer]; for ( j = 1; j < i; j++ ) AT.pWorkSpace[AT.pWorkPointer+j-1] = AT.pWorkSpace[AT.pWorkPointer+j]; AT.pWorkSpace[AT.pWorkPointer+j-1] = tt; x++; } } /* And the final cleanup */ if ( tstop+(f-f1) > AT.WorkTop ) goto OverWork; f2 = tstop; for ( i = 0; i < num; i++ ) { f = AT.pWorkSpace[AT.pWorkPointer+i]; *f2++ = *f++; } i = f2 - tstop; NCOPY(f1,tstop,i) } return(0); OverWork:; MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* #] RunCycle : #[ RunAddArg : */ int RunAddArg(PHEAD WORD *fun, WORD *args) { WORD *tt, totarg, *tstop, arg1, arg2, n, num, *f, *f1, *f2; WORD scribble[10+ARGHEAD]; LONG space; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunAddArg"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( functions[fun[0]-FUNCTION].spec == TENSORFUNCTION ) { MLOCK(ErrorMessageLock); MesPrint("Illegal attempt to add arguments of a tensor in AddArg"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } /* ignore functions with no arguments */ if ( totarg == 0 ) return(0); if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); /* We need to: 1: establish that we actually need to add something 2: start a sort 3: if needed, convert arguments to long arguments 4: send (terms in) argument to StoreTerm 5: EndSort and copy the result back into the function Note that the function is in the workspace, above the term and no relevant information is trailing it. */ if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg2 > totarg ) return(0); num = arg2-arg1+1; if ( num == 1 ) return(0); f = fun+FUNHEAD; n = 1; while ( n < arg1 ) { n++; NEXTARG(f) } f1 = f; NewSort(BHEAD0); while ( n <= arg2 ) { if ( *f > 0 ) { f2 = f + *f; f += ARGHEAD; while ( f < f2 ) { StoreTerm(BHEAD f); f += *f; } } else if ( *f == -SNUMBER && f[1] == 0 ) { f+= 2; } else { ToGeneral(f,scribble,1); StoreTerm(BHEAD scribble); NEXTARG(f); } n++; } if ( EndSort(BHEAD tstop+ARGHEAD,1) < 0 ) return(-1); num = 0; f2 = tstop+ARGHEAD; while ( *f2 ) { f2 += *f2; num++; } *tstop = f2-tstop; for ( n = 1; n < ARGHEAD; n++ ) tstop[n] = 0; if ( num == 1 && ToFast(tstop,tstop) == 1 ) { f2 = tstop; NEXTARG(f2); } if ( *tstop == ARGHEAD ) { *tstop = -SNUMBER; tstop[1] = 0; f2 = tstop+2; } /* Copy the trailing arguments after the new argument, then copy the whole back. */ while ( f < tstop ) *f2++ = *f++; while ( f < f2 ) *f1++ = *f++; space = f1 - fun; if ( (space+8)*sizeof(WORD) > (UWORD)AM.MaxTer ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } fun[1] = (WORD)space; return(0); } /* #] RunAddArg : #[ RunMulArg : */ int RunMulArg(PHEAD WORD *fun, WORD *args) { WORD *t, totarg, *tstop, arg1, arg2, n, *f, nb, *m, i, *w; WORD *scratch, argbuf[20], argsize, *where, *newterm; LONG oldcpointer_pos; CBUF *C = cbuf + AT.ebufnum; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunMulArg"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( functions[fun[0]-FUNCTION].spec == TENSORFUNCTION ) { MLOCK(ErrorMessageLock); MesPrint("Illegal attempt to multiply arguments of a tensor in MulArg"); MUNLOCK(ErrorMessageLock); Terminate(-1); } t = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( t < tstop ) { totarg++; NEXTARG(t); } /* ignore functions with no arguments */ if ( totarg == 0 ) return(0); if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg1 > totarg ) return(0); if ( arg2 < 1 ) return(0); if ( arg1 < 1 ) arg1 = 1; if ( arg2 > totarg ) arg2 = totarg; if ( arg1 == arg2 ) return(0); /* Now we move the arguments to a compiler buffer Then we create a term in the workspace that is the product of subexpression pointers to the objects in the compiler buffer. Next we let Generator work out that term. Finally we pick up the results from EndSort and put it in the function. */ f = fun+FUNHEAD; n = 1; while ( n < arg1 ) { n++; NEXTARG(f) } t = f; if ( fun >= AT.WorkSpace && fun < AT.WorkTop ) { if ( AT.WorkPointer < fun+fun[1] ) AT.WorkPointer = fun+fun[1]; } scratch = AT.WorkPointer; w = scratch+1; oldcpointer_pos = C->Pointer-C->Buffer; nb = C->numrhs; while ( n <= arg2 ) { if ( *t > 0 ) { argsize = *t - ARGHEAD; where = t + ARGHEAD; t += *t; } else if ( *t <= -FUNCTION ) { argbuf[0] = FUNHEAD+4; argbuf[1] = -*t++; argbuf[2] = FUNHEAD; for ( i = 2; i < FUNHEAD; i++ ) argbuf[i+1] = 0; argbuf[FUNHEAD+1] = 1; argbuf[FUNHEAD+2] = 1; argbuf[FUNHEAD+3] = 3; argsize = argbuf[0]; where = argbuf; } else if ( *t == -SYMBOL ) { argbuf[0] = 8; argbuf[1] = SYMBOL; argbuf[2] = 4; argbuf[3] = t[1]; argbuf[4] = 1; argbuf[5] = 1; argbuf[6] = 1; argbuf[7] = 3; argsize = 8; t += 2; where = argbuf; } else if ( *t == -VECTOR || *t == -MINVECTOR ) { argbuf[0] = 7; argbuf[1] = INDEX; argbuf[2] = 3; argbuf[3] = t[1]; argbuf[4] = 1; argbuf[5] = 1; if ( *t == -MINVECTOR ) argbuf[6] = -3; else argbuf[6] = 3; argsize = 7; t += 2; where = argbuf; } else if ( *t == -INDEX ) { argbuf[0] = 7; argbuf[1] = INDEX; argbuf[2] = 3; argbuf[3] = t[1]; argbuf[4] = 1; argbuf[5] = 1; argbuf[6] = 3; argsize = 7; t += 2; where = argbuf; } else if ( *t == -SNUMBER ) { if ( t[1] < 0 ) { argbuf[0] = 4; argbuf[1] = -t[1]; argbuf[2] = 1; argbuf[3] = -3; } else { argbuf[0] = 4; argbuf[1] = t[1]; argbuf[2] = 1; argbuf[3] = 3; } argsize = 4; t += 2; where = argbuf; } else { /* unreachable */ return(1); } /* Now add the argbuf to AT.ebufnum */ m = AddRHS(AT.ebufnum,1); while ( (m + argsize + 10) > C->Top ) m = DoubleCbuffer(AT.ebufnum,m,17); for ( i = 0; i < argsize; i++ ) m[i] = where[i]; m[i] = 0; C->Pointer = m + i + 1; n++; *w++ = SUBEXPRESSION; *w++ = SUBEXPSIZE; *w++ = C->numrhs; *w++ = 1; *w++ = AT.ebufnum; FILLSUB(w); } *w++ = 1; *w++ = 1; *w++ = 3; *scratch = w-scratch; AT.WorkPointer = w; NewSort(BHEAD0); Generator(BHEAD scratch,AR.Cnumlhs); newterm = AT.WorkPointer; EndSort(BHEAD newterm+ARGHEAD,1); C->Pointer = C->Buffer+oldcpointer_pos; C->numrhs = nb; w = newterm+ARGHEAD; while ( *w ) w += *w; *newterm = w-newterm; newterm[1] = 0; if ( ToFast(newterm,newterm) ) { if ( *newterm <= -FUNCTION ) w = newterm+1; else w = newterm+2; } while ( t < tstop ) *w++ = *t++; i = w - newterm; t = newterm; NCOPY(f,t,i); fun[1] = f-fun; AT.WorkPointer = scratch; if ( AT.WorkPointer > AT.WorkSpace && AT.WorkPointer < f ) AT.WorkPointer = f; return(0); } /* #] RunMulArg : #[ RunIsLyndon : Determines whether the range constitutes a Lyndon word. The two cases of ordering are distinguished by the order of the numbers of the arguments in the range. */ int RunIsLyndon(PHEAD WORD *fun, WORD *args, int par) { WORD *tt, totarg, *tstop, arg1, arg2, arg, num, *f, n, i; /* WORD *f1; */ WORD sign, i1, i2, retval; if ( fun[0] <= GAMMASEVEN && fun[0] >= GAMMA ) return(0); if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunIsLyndon"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg1 > totarg || arg2 > totarg ) return(-1); /* Now make a list of the relevant arguments. */ if ( arg1 == arg2 ) return(1); if ( arg2 < arg1 ) { /* greater, rather than smaller */ arg = arg1; arg1 = arg2; arg2 = arg; sign = 1; } else sign = 0; num = arg2-arg1+1; WantAddPointers(num); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; NEXTARG(f) } /* f1 = f; */ while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; NEXTARG(f) } /* If sign == 1 we should alter the order of the pointers first */ if ( sign ) { i1 = i-1; i2 = 0; while ( i1 > i2 ) { tt = AT.pWorkSpace[AT.pWorkPointer+i1]; AT.pWorkSpace[AT.pWorkPointer+i1] = AT.pWorkSpace[AT.pWorkPointer+i2]; AT.pWorkSpace[AT.pWorkPointer+i2] = tt; i1--; i2++; } } /* The argument range is from f1 to f and the num pointers to the arguments are in AT.pWorkSpace[AT.pWorkPointer] to AT.pWorkSpace[AT.pWorkPointer+num-1] */ for ( i1 = 1; i1 < num; i1++ ) { retval = par * CompArg(AT.pWorkSpace[AT.pWorkPointer+i1], AT.pWorkSpace[AT.pWorkPointer]); if ( retval > 0 ) continue; if ( retval < 0 ) return(0); for ( i2 = 1; i2 < num; i2++ ) { retval = par * CompArg(AT.pWorkSpace[AT.pWorkPointer+(i1+i2)%num], AT.pWorkSpace[AT.pWorkPointer+i2]); if ( retval < 0 ) return(0); if ( retval > 0 ) goto nexti1; } /* If we come here the sequence is not unique. */ return(0); nexti1:; } return(1); } /* #] RunIsLyndon : #[ RunToLyndon : Determines whether the range constitutes a Lyndon word. If not, we rotate it to a Lyndon word. If this is not possible we return the noLyndon condition. The two cases of ordering are distinguished by the order of the numbers of the arguments in the range. */ WORD RunToLyndon(PHEAD WORD *fun, WORD *args, int par) { WORD *tt, totarg, *tstop, arg1, arg2, arg, num, *f, *f1, *f2, n, i; WORD sign, i1, i2, retval, unique; if ( fun[0] <= GAMMASEVEN && fun[0] >= GAMMA ) return(0); if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunToLyndon"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg1 > totarg || arg2 > totarg ) return(-1); /* Now make a list of the relevant arguments. */ if ( arg1 == arg2 ) return(1); if ( arg2 < arg1 ) { /* greater, rather than smaller */ arg = arg1; arg1 = arg2; arg2 = arg; sign = 1; } else sign = 0; num = arg2-arg1+1; WantAddPointers((2*num)); /* Guarantees the presence of enough pointers */ f = fun+FUNHEAD; n = 1; i = 0; while ( n < arg1 ) { n++; NEXTARG(f) } f1 = f; while ( n <= arg2 ) { AT.pWorkSpace[AT.pWorkPointer+i++] = f; n++; NEXTARG(f) } /* If sign == 1 we should alter the order of the pointers first */ if ( sign ) { i1 = i-1; i2 = 0; while ( i1 > i2 ) { tt = AT.pWorkSpace[AT.pWorkPointer+i1]; AT.pWorkSpace[AT.pWorkPointer+i1] = AT.pWorkSpace[AT.pWorkPointer+i2]; AT.pWorkSpace[AT.pWorkPointer+i2] = tt; i1--; i2++; } } /* The argument range is from f1 to f and the num pointers to the arguments are in AT.pWorkSpace[AT.pWorkPointer] to AT.pWorkSpace[AT.pWorkPointer+num-1] */ unique = 1; for ( i1 = 1; i1 < num; i1++ ) { retval = par * CompArg(AT.pWorkSpace[AT.pWorkPointer+i1], AT.pWorkSpace[AT.pWorkPointer]); if ( retval > 0 ) continue; if ( retval < 0 ) { Rotate:; /* Rotate so that i1 becomes the zero element. Then start again. */ for ( i2 = 0; i2 < num; i2++ ) { AT.pWorkSpace[AT.pWorkPointer+num+i2] = AT.pWorkSpace[AT.pWorkPointer+(i1+i2)%num]; } for ( i2 = 0; i2 < num; i2++ ) { AT.pWorkSpace[AT.pWorkPointer+i2] = AT.pWorkSpace[AT.pWorkPointer+i2+num]; } i1 = 0; goto nexti1; } for ( i2 = 1; i2 < num; i2++ ) { retval = par * CompArg(AT.pWorkSpace[AT.pWorkPointer+(i1+i2)%num], AT.pWorkSpace[AT.pWorkPointer+i2]); if ( retval < 0 ) goto Rotate; if ( retval > 0 ) goto nexti1; } /* If we come here the sequence is not unique. */ unique = 0; nexti1:; } if ( sign ) { i1 = i-1; i2 = 0; while ( i1 > i2 ) { tt = AT.pWorkSpace[AT.pWorkPointer+i1]; AT.pWorkSpace[AT.pWorkPointer+i1] = AT.pWorkSpace[AT.pWorkPointer+i2]; AT.pWorkSpace[AT.pWorkPointer+i2] = tt; i1--; i2++; } } /* Now rewrite the arguments into the proper order */ if ( tstop+(f-f1) > AT.WorkTop ) goto OverWork; f2 = tstop; for ( i = 0; i < num; i++ ) { f = AT.pWorkSpace[AT.pWorkPointer+i]; COPY1ARG(f2,f) } i = f2 - tstop; NCOPY(f1,tstop,i) /* The return value indicates whether we have a Lyndon word */ return(unique); OverWork:; MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-2); } /* #] RunToLyndon : #[ RunDropArg : */ int RunDropArg(PHEAD WORD *fun, WORD *args) { WORD *t, *tstop, *f, totarg, arg1, arg2, n; t = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( t < tstop ) { totarg++; NEXTARG(t); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg1 > totarg ) return(0); if ( arg2 < 1 ) return(0); if ( arg1 < 1 ) arg1 = 1; if ( arg2 > totarg ) arg2 = totarg; f = fun+FUNHEAD; n = 1; while ( n < arg1 ) { n++; NEXTARG(f) } t = f; while ( n <= arg2 ) { n++; NEXTARG(t) } while ( t < tstop ) *f++ = *t++; fun[1] = f-fun; return(0); } /* #] RunDropArg : #[ RunSelectArg : */ int RunSelectArg(PHEAD WORD *fun, WORD *args) { WORD *t, *tstop, *f, *tt, totarg, arg1, arg2, n; t = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( t < tstop ) { totarg++; NEXTARG(t); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); if ( arg2 < arg1 ) { n = arg1; arg1 = arg2; arg2 = n; } if ( arg1 > totarg ) return(0); if ( arg2 < 1 ) return(0); if ( arg1 < 1 ) arg1 = 1; if ( arg2 > totarg ) arg2 = totarg; f = fun+FUNHEAD; n = 1; t = f; while ( n < arg1 ) { n++; NEXTARG(t) } while ( n <= arg2 ) { tt = t; NEXTARG(tt) while ( t < tt ) *f++ = *t++; n++; } fun[1] = f-fun; return(0); } /* #] RunSelectArg : #[ RunZtoHArg : */ int RunZtoHArg(PHEAD WORD *fun, WORD *args) { WORD *tt, totarg, *tstop, arg1, arg2, n, i, *f, *f1; int sign = 0; WORD *t, *t1, *t2, *t3; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunZtoHArg."); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( functions[fun[0]-FUNCTION].spec != 0 ) { MLOCK(ErrorMessageLock); MesPrint("The ZtoH transformation can only be executed on regular functions with nonzero integer arguments."); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); /* Check the arguments. Should be -SNUMBER x!=0 */ f = fun+FUNHEAD; n = 1; while ( n < arg1 ) { n++; NEXTARG(f) } f1 = f; for ( i = arg1; i <= arg2; i++, f += 2 ) { if ( *f != -SNUMBER || f[1] == 0 ) return(-1); } /* Now we need a copy. */ t = f1; t1 = t2 = tt = TermMalloc("RunZtoHArg"); while ( t < f ) { *t1++ = *t++; *t1++ = *t++; } t = f1; while ( t2 < t1 ) { t += 2; if ( t2[1] < 0 ) { t3 = t; while ( t3 < f ) { t3[1] = -t3[1]; t3 += 2; } } t2 += 2; } TermFree(tt,"RunZtoHArg"); /* Now the overall sign. */ while ( f1 < f ) { if ( f1[1] < 0 ) sign = 1-sign; f1 += 2; } return(sign); } /* #] RunZtoHArg : #[ RunHtoZArg : */ int RunHtoZArg(PHEAD WORD *fun, WORD *args) { WORD *tt, totarg, *tstop, arg1, arg2, n, i, *f, *f1, *f2; int sign = 0; WORD *t, *t1, *t2; if ( *args != ARGRANGE ) { MLOCK(ErrorMessageLock); MesPrint("Illegal range encountered in RunZtoHArg."); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( functions[fun[0]-FUNCTION].spec != 0 ) { MLOCK(ErrorMessageLock); MesPrint("The HtoZ transformation can only be executed on regular functions with nonzero integer arguments."); MUNLOCK(ErrorMessageLock); Terminate(-1); } tt = fun+FUNHEAD; tstop = fun+fun[1]; totarg = 0; while ( tt < tstop ) { totarg++; NEXTARG(tt); } if ( FindRange(BHEAD args,&arg1,&arg2,totarg) ) return(-1); /* Check the arguments. Should be -SNUMBER x!=0 */ f = fun+FUNHEAD; n = 1; while ( n < arg1 ) { n++; NEXTARG(f) } f2 = f1 = f; for ( i = arg1; i <= arg2; i++, f += 2 ) { if ( *f != -SNUMBER || f[1] == 0 ) return(-1); } /* First the overall sign. */ while ( f2 < f ) { if ( f2[1] < 0 ) sign = 1-sign; f2 += 2; } /* Now we need a copy. */ t = f1; t1 = tt = TermMalloc("RunHtoZArg"); while ( t < f ) { *t1++ = *t++; *t1++ = *t++; } /* Now the transformation. */ t = f1; t2 = tt + 2; while ( t2 < t1 ) { t += 2; if ( t2[-1] < 0 ) t[1] = -t[1]; t2 += 2; } TermFree(tt,"RunHtoZArg"); return(sign); } /* #] RunHtoZArg : #[ TestArgNum : Looks whether argument n is contained in any of the ranges specified in args. Args contains objects of the types ALLARGS NUMARG,num ARGRANGE,num1,num2 The object MAKEARGS,num1,num2 is skipped Any other object terminates the range specifications. Currently only ARGRANGE is used (10-may-2016) */ int TestArgNum(int n, int totarg, WORD *args) { GETIDENTITY WORD x1, x2; for(;;) { switch ( *args ) { case ALLARGS: return(1); case NUMARG: if ( n == args[1] ) return(1); if ( args[1] >= MAXPOSITIVE4 ) { x1 = args[1]-MAXPOSITIVE4; if ( totarg-x1 == n ) return(1); } args += 2; break; case ARGRANGE: if ( args[1] >= MAXPOSITIVE2 ) { x1 = args[1] - MAXPOSITIVE2; if ( x1 > MAXPOSITIVE4 ) { x1 = x1 - MAXPOSITIVE4; x1 = DolToNumber(BHEAD x1); x1 = totarg - x1; } else { x1 = DolToNumber(BHEAD x1); } } else if ( args[1] >= MAXPOSITIVE4 ) { x1 = totarg-(args[1]-MAXPOSITIVE4); } else x1 = args[1]; if ( args[2] >= MAXPOSITIVE2 ) { x2 = args[2] - MAXPOSITIVE2; if ( x2 > MAXPOSITIVE4 ) { x2 = x2 - MAXPOSITIVE4; x2 = DolToNumber(BHEAD x2); x2 = totarg - x2; } else { x2 = DolToNumber(BHEAD x2); } } else if ( args[2] >= MAXPOSITIVE4 ) { x2 = totarg-(args[2]-MAXPOSITIVE4); } else x2 = args[2]; if ( x1 >= x2 ) { if ( n >= x2 && n <= x1 ) return(1); } else { if ( n >= x1 && n <= x2 ) return(1); } args += 3; break; case MAKEARGS: args += 3; break; default: return(0); } } } /* #] TestArgNum : #[ PutArgInScratch : */ WORD PutArgInScratch(WORD *arg,UWORD *scrat) { WORD size, *t, i; if ( *arg == -SNUMBER ) { scrat[0] = ABS(arg[1]); if ( arg[1] < 0 ) size = -1; else size = 1; } else { t = arg+*arg-1; if ( *t < 0 ) { i = ((-*t)-1)/2; size = -i; } else { i = ( *t -1)/2; size = i; } t = arg+ARGHEAD+1; NCOPY(scrat,t,i); } return(size); } /* #] PutArgInScratch : #[ ReadRange : Comes in at the bracket and leaves at the = sign Ranges can be: #1,#2 with # numbers. If the second is smaller than the first we work it backwards. first,#2 or #2,first #1,last or last,#1 first,last or last,first First is represented by 1. Last is represented by MAXPOSITIVE4. par = 0: we need the = after. par = 1: we need a , or '\0' after. par = 2: we need a : */ UBYTE *ReadRange(UBYTE *s, WORD *out, int par) { UBYTE *in = s, *ss, c; LONG x1, x2; SKIPBRA3(in) if ( par == 0 && in[1] != '=' ) { MesPrint("&A range in this type of transform statement should be followed by an = sign"); return(0); } else if ( par == 1 && in[1] != ',' && in[1] != '\0' ) { MesPrint("&A range in this type of transform statement should be followed by a comma or end-of-statement"); return(0); } else if ( par == 2 && in[1] != ':' ) { MesPrint("&A range in this type of transform statement should be followed by a :"); return(0); } s++; if ( FG.cTable[*s] == 0 ) { ss = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(ss,(UBYTE *)"first") == 0 ) { *s = c; x1 = 1; } else if ( StrICmp(ss,(UBYTE *)"last") == 0 ) { *s = c; if ( c == '-' ) { s++; if ( *s == '$' ) { s++; ss = s; while ( FG.cTable[*s] == 0 || FG.cTable[*s] == 1 ) s++; c = *s; *s = 0; if ( ( x1 = GetDollar(ss) ) < 0 ) goto Error; *s = c; x1 += MAXPOSITIVE2; } else { x1 = 0; while ( *s >= '0' && *s <= '9' ) { x1 = 10*x1 + *s++ - '0'; if ( x1 >= MAXPOSITIVE4 ) { MesPrint("&Fixed range indicator bigger than %l",(LONG)MAXPOSITIVE4); return(0); } } } x1 += MAXPOSITIVE4; } else x1 = MAXPOSITIVE4; } else { MesPrint("&Illegal keyword inside range specification"); return(0); } } else if ( FG.cTable[*s] == 1 ) { x1 = 0; while ( *s >= '0' && *s <= '9' ) { x1 = x1*10 + *s++ - '0'; if ( x1 >= MAXPOSITIVE4 ) { MesPrint("&Fixed range indicator bigger than %l",(LONG)MAXPOSITIVE4); return(0); } } } else if ( *s == '$' ) { s++; ss = s; while ( FG.cTable[*s] == 0 || FG.cTable[*s] == 1 ) s++; c = *s; *s = 0; if ( ( x1 = GetDollar(ss) ) < 0 ) goto Error; *s = c; x1 += MAXPOSITIVE2; } else { MesPrint("&Illegal character in range specification"); return(0); } if ( *s != ',' ) { MesPrint("&A range is two indicators, separated by a comma or blank"); return(0); } s++; if ( FG.cTable[*s] == 0 ) { ss = s; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICmp(ss,(UBYTE *)"first") == 0 ) { *s = c; x2 = 1; } else if ( StrICmp(ss,(UBYTE *)"last") == 0 ) { *s = c; if ( c == '-' ) { s++; if ( *s == '$' ) { s++; ss = s; while ( FG.cTable[*s] == 0 || FG.cTable[*s] == 1 ) s++; c = *s; *s = 0; if ( ( x2 = GetDollar(ss) ) < 0 ) goto Error; *s = c; x2 += MAXPOSITIVE2; } else { x2 = 0; while ( *s >= '0' && *s <= '9' ) { x2 = 10*x2 + *s++ - '0'; if ( x2 >= MAXPOSITIVE4 ) { MesPrint("&Fixed range indicator bigger than %l",(LONG)MAXPOSITIVE4); return(0); } } } x2 += MAXPOSITIVE4; } else x2 = MAXPOSITIVE4; } else { MesPrint("&Illegal keyword inside range specification"); return(0); } } else if ( FG.cTable[*s] == 1 ) { x2 = 0; while ( *s >= '0' && *s <= '9' ) { x2 = x2*10 + *s++ - '0'; if ( x2 >= MAXPOSITIVE4 ) { MesPrint("&Fixed range indicator bigger than %l",(LONG)MAXPOSITIVE4); return(0); } } } else if ( *s == '$' ) { s++; ss = s; while ( FG.cTable[*s] == 0 || FG.cTable[*s] == 1 ) s++; c = *s; *s = 0; if ( ( x2 = GetDollar(ss) ) < 0 ) goto Error; *s = c; x2 += MAXPOSITIVE2; } else { MesPrint("&Illegal character in range specification"); return(0); } if ( s < in ) { MesPrint("&A range is two indicators, separated by a comma or blank between parentheses"); return(0); } out[0] = x1; out[1] = x2; return(in+1); Error: MesPrint("&Undefined variable $%s in range",ss); return(0); } /* #] ReadRange : #[ FindRange : */ int FindRange(PHEAD WORD *args, WORD *arg1, WORD *arg2, WORD totarg) { WORD n[2], fromlast, i; for ( i = 0; i < 2; i++ ) { n[i] = args[i+1]; fromlast = 0; if ( n[i] >= MAXPOSITIVE2 ) { /* This is a dollar variable */ n[i] -= MAXPOSITIVE2; if ( n[i] >= MAXPOSITIVE4 ) { fromlast = 1; n[i] -= MAXPOSITIVE4; /* Now we have the number of the dollar variable */ } n[i] = DolToNumber(BHEAD n[i]); if ( AN.ErrorInDollar ) { MLOCK(ErrorMessageLock); MesPrint("Illegal $ value in range while executing transform statement."); MUNLOCK(ErrorMessageLock); return(-1); } if ( fromlast ) n[i] = totarg-n[i]; } else if ( n[i] >= MAXPOSITIVE4 ) { n[i] = totarg-(n[i]-MAXPOSITIVE4); } if ( n[i] <= 0 ) { MLOCK(ErrorMessageLock); MesPrint("Illegal non-positive value in range (%d) while executing transform statement.", i+1); MUNLOCK(ErrorMessageLock); return(-1); } } *arg1 = n[0]; *arg2 = n[1]; return(0); } /* #] FindRange : #] Transform : */ form-5.0.1/sources/sch.c0000644000175100017510000022140515217035721010556 /** @file sch.c * * Contains the functions that deal with the writing of expressions/terms * in a textual representation. (Dutch schrijven = to write) */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : sch.c */ #include "form3.h" static int startinline = 0; static char fcontchar = '&'; static int noextralinefeed = 0; static int lowestlevel = 1; /* #] Includes : #[ schryf-Utilities : #[ StrCopy : UBYTE *StrCopy(from,to) */ UBYTE *StrCopy(UBYTE *from, UBYTE *to) { while( ( *to++ = *from++ ) != 0 ); return(to-1); } /* #] StrCopy : #[ AddToLine : void AddToLine(s) Puts the characters of s in the outputline. If the line becomes filled it is written. */ void AddToLine(UBYTE *s) { UBYTE *Out; LONG num; int i; if ( AO.OutInBuffer ) { AddToDollarBuffer(s); return; } Out = AO.OutFill; while ( *s ) { if ( Out >= AO.OutStop ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { *Out++ = fcontchar; } #ifdef WITHRETURN *Out++ = CARRIAGERETURN; #endif *Out++ = LINEFEED; AO.FortFirst = 0; num = Out - AO.OutputLine; if ( AC.LogHandle >= 0 ) { if ( WriteFile(AC.LogHandle,AO.OutputLine+startinline ,num-startinline) != (num-startinline) ) { /* We cannot write to an otherwise open log file. The disk could be full of course. */ #ifdef DEBUGGER if ( BUG.logfileflag == 0 ) { fprintf(stderr,"Panic: Cannot write to log file! Disk full?\n"); BUG.logfileflag = 1; } BUG.eflag = 1; BUG.printflag = 1; #else Terminate(-1); #endif } } if ( ( AO.PrintType & PRINTLFILE ) == 0 ) { #ifdef WITHRETURN if ( num > 1 && AO.OutputLine[num-2] == CARRIAGERETURN ) { AO.OutputLine[num-2] = LINEFEED; num--; } #endif if ( WriteFile(AM.StdOut,AO.OutputLine+startinline ,num-startinline) != (num-startinline) ) { #ifdef DEBUGGER if ( BUG.stdoutflag == 0 ) { fprintf(stderr,"Panic: Cannot write to standard output!\n"); BUG.stdoutflag = 1; } BUG.eflag = 1; BUG.printflag = 1; #else Terminate(-1); #endif } } /* thomasr 23/04/09: A continuation line has been started. * In Fortran90 we do not want a space after the initial * '&' character otherwise we might end up with something * like: * ... 2.& * & 0 ... */ startinline = 0; for ( i = 0; i < AO.OutSkip; i++ ) AO.OutputLine[i] = ' '; Out = AO.OutputLine + AO.OutSkip; if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) && AO.OutSkip == 7 ) { /* thomasr 23/04/09: fix leading blank in fortran90 mode */ if(AC.IsFortran90 == ISFORTRAN90) { Out[-1] = fcontchar; } else { Out[-2] = fcontchar; Out[-1] = ' '; } } if ( AO.IsBracket ) { *Out++ = ' '; if ( AC.OutputSpaces == NORMALFORMAT ) { *Out++ = ' '; *Out++ = ' '; } } *Out = '\0'; if ( AC.OutputMode == FORTRANMODE || ( AC.OutputMode == CMODE && AO.FactorMode == 0 ) || AC.OutputMode == PFORTRANMODE ) AO.InFbrack++; } *Out++ = *s++; } *Out = '\0'; AO.OutFill = Out; } /* #] AddToLine : #[ FiniLine : void FiniLine() */ void FiniLine(void) { UBYTE *Out; WORD i; LONG num; if ( AO.OutInBuffer ) return; Out = AO.OutFill; while ( Out > AO.OutputLine ) { if ( Out[-1] == ' ' ) Out--; else break; } i = (WORD)(Out-AO.OutputLine); if ( noextralinefeed == 0 ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 && Out > AO.OutputLine ) { /* *Out++ = fcontchar; */ } #ifdef WITHRETURN *Out++ = CARRIAGERETURN; #endif *Out++ = LINEFEED; AO.FortFirst = 0; } num = Out - AO.OutputLine; if ( AC.LogHandle >= 0 ) { if ( WriteFile(AC.LogHandle,AO.OutputLine+startinline ,num-startinline) != (num-startinline) ) { #ifdef DEBUGGER if ( BUG.logfileflag == 0 ) { fprintf(stderr,"Panic: Cannot write to log file! Disk full?\n"); BUG.logfileflag = 1; } BUG.eflag = 1; BUG.printflag = 1; #else Terminate(-1); #endif } } if ( ( AO.PrintType & PRINTLFILE ) == 0 ) { #ifdef WITHRETURN if ( num > 1 && AO.OutputLine[num-2] == CARRIAGERETURN ) { AO.OutputLine[num-2] = LINEFEED; num--; } #endif if ( WriteFile(AM.StdOut,AO.OutputLine+startinline, num-startinline) != (num-startinline) ) { #ifdef DEBUGGER if ( BUG.stdoutflag == 0 ) { fprintf(stderr,"Panic: Cannot write to standard output!\n"); BUG.stdoutflag = 1; } BUG.eflag = 1; BUG.printflag = 1; #else Terminate(-1); #endif } } startinline = 0; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || ( AC.OutputMode == CMODE && AO.FactorMode == 0 ) ) AO.InFbrack++; Out = AO.OutputLine; AO.OutStop = Out + AC.LineLength; i = AO.OutSkip; while ( --i >= 0 ) *Out++ = ' '; if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) && AO.OutSkip == 7 ) { Out[-2] = fcontchar; Out[-1] = ' '; } AO.OutFill = Out; } /* #] FiniLine : #[ IniLine : void IniLine(extrablank) Initializes the output line for the type of output */ void IniLine(WORD extrablank) { UBYTE *Out; Out = AO.OutputLine; AO.OutStop = Out + AC.LineLength; *Out++ = ' '; *Out++ = ' '; *Out++ = ' '; *Out++ = ' '; *Out++ = ' '; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { *Out++ = fcontchar; AO.OutSkip = 7; } else AO.OutSkip = 6; *Out++ = ' '; while ( extrablank > 0 ) { *Out++ = ' '; extrablank--; } AO.OutFill = Out; } /* #] IniLine : #[ LongToLine : void LongToLine(a,na) Puts a Long integer in the output line. If it is only a single word long it is put in the line as a single token. The sign of a is ignored. */ static UBYTE *LLscratch = 0; void LongToLine(UWORD *a, WORD na) { UBYTE *OutScratch; if ( LLscratch == 0 ) { LLscratch = (UBYTE *)Malloc1(4*(AM.MaxTal*sizeof(WORD)+2)*sizeof(UBYTE),"LongToLine"); } OutScratch = LLscratch; if ( na < 0 ) na = -na; if ( na > 1 ) { PrtLong(a,na,OutScratch); if ( AO.NoSpacesInNumbers || AC.OutputMode == REDUCEMODE ) { AO.BlockSpaces = 1; TokenToLine(OutScratch); AO.BlockSpaces = 0; } else { TokenToLine(OutScratch); } } else if ( !na ) TokenToLine((UBYTE *)"0"); else TalToLine(*a); } /* #] LongToLine : #[ RatToLine : void RatToLine(a,na) Puts a rational number in the output line. The sign is ignored. */ static UBYTE *RLscratch = 0; static UWORD *RLscratE = 0; void RatToLine(UWORD *a, WORD na) { GETIDENTITY WORD adenom, anumer; ULONG maxInt; if ( AC.OutputMode == CMODE ) { // In C, integer literals over 2^32-1 are automatically promoted to longer types up to // unsigned long long, however FORM has always given integers over 2^32-1 a floating suffix // in C mode. Retain that behaviour here for now. In the future, maxInt could be a user- // configurable parameter. maxInt = 4294967295; } else { // In Fortran modes, literals over 2^31-1 should be printed with a float suffix maxInt = 2147483647; } if ( na < 0 ) na = -na; if ( AC.OutNumberType == RATIONALMODE ) { // Work out what is to be printed: WORD isOne = 0, isOneOver = 0, isIntegral = 0; WORD isLongNum = 0, isLongDen = 0; UnPack(a,na,&adenom,&anumer); if ( na == 1 && a[0] == 1 && a[1] == 1 ) { isOne = 1; isIntegral = 1; } else if ( adenom == 1 && a[na] == 1 ) { isIntegral = 1; } else if ( anumer == 1 && a[0] == 1 ) { isOneOver = 1; } if ( anumer > 1 || ( anumer == 1 && a[0] > maxInt ) ) { isLongNum = 1; }; if ( adenom > 1 || ( adenom == 1 && a[na] > maxInt ) ) { isLongDen = 1; }; // Now sort out the float suffix for the numerator: UBYTE* suffNum = (UBYTE*)""; UBYTE* suffDen = (UBYTE*)""; if ( isLongNum || !isIntegral || AC.Fortran90Kind || ( AO.DoubleFlag & 4 ) == 4 ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { if ( AC.Fortran90Kind ) { suffNum = AC.Fortran90Kind; } else { suffNum = (UBYTE*)"."; } } else if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == CMODE ) { if ( ( AO.DoubleFlag & 2 ) == 2 ) { suffNum = (UBYTE*)".Q0"; } else if ( ( AO.DoubleFlag & 1 ) == 1 ) { suffNum = (UBYTE*)".D0"; } else { suffNum = (UBYTE*)"."; } } } // The same again, for the denominator: if ( isLongDen || !isIntegral || AC.Fortran90Kind || ( AO.DoubleFlag & 4 ) == 4 ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { if ( AC.Fortran90Kind ) { suffDen = AC.Fortran90Kind; } else { suffDen = (UBYTE*)"."; } } else if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == CMODE ) { if ( ( AO.DoubleFlag & 2 ) == 2 ) { suffDen = (UBYTE*)".Q0"; } else if ( ( AO.DoubleFlag & 1 ) == 1 ) { suffDen = (UBYTE*)".D0"; } else { suffDen = (UBYTE*)"."; } } } // In PFORTRAN mode, rationals don't get a suffix if the integers are not long // Also the suffix is at least ".D0" (and never "."). if ( AC.OutputMode == PFORTRANMODE ) { if ( isLongNum ) { if ( ( AO.DoubleFlag & 2 ) == 2 ) { suffNum = (UBYTE*)".Q0"; } else { suffNum = (UBYTE*)".D0"; } } if ( isLongDen ) { if ( ( AO.DoubleFlag & 2 ) == 2 ) { suffDen = (UBYTE*)".Q0"; } else { suffDen = (UBYTE*)".D0"; } } } // Finally, print the number: // In PFORTRAN we use // one if denom = numerator = 1 // integer if denom = 1 // (one/integer) if numerator = 1 // ((one*integer)/integer) in the general case if ( AC.OutputMode == PFORTRANMODE ) { if ( isOne ) { AddToLine((UBYTE *)"one"); } else if ( isOneOver ) { AddToLine((UBYTE *)"(one/"); LongToLine(a+na,adenom); AddToLine(suffDen); AddToLine((UBYTE*)")"); } else if ( isIntegral ) { LongToLine(a,anumer); AddToLine(suffNum); } else { // rational AddToLine((UBYTE *)"((one*"); LongToLine(a,anumer); AddToLine(suffNum); AddToLine((UBYTE*)")/"); LongToLine(a+na,adenom); AddToLine(suffDen); AddToLine((UBYTE*)")"); } } // All other modes use the same printing code: else { // Numerator: LongToLine(a,anumer); AddToLine(suffNum); // Denominator, if it is not 1: if (!isIntegral) { AddToLine((UBYTE*)"/"); LongToLine(a+na,adenom); AddToLine(suffDen); } } } else { /* This is the float mode */ UBYTE *OutScratch; WORD exponent = 0, i, ndig, newl; UWORD *c, *den, b = 10, dig[10]; UBYTE *o, *out, cc; /* First we have to adjust the numerator and denominator */ if ( RLscratch == 0 ) { RLscratch = (UBYTE *)Malloc1(4*(AM.MaxTal+2)*sizeof(UBYTE),"RatToLine"); RLscratE = (UWORD *)Malloc1(2*(AM.MaxTal+2)*sizeof(UWORD),"RatToLine"); } out = OutScratch = RLscratch; c = RLscratE; for ( i = 0; i < 2*na; i++ ) c[i] = a[i]; UnPack(c,na,&adenom,&anumer); while ( BigLong(c,anumer,c+na,adenom) >= 0 ) { Divvy(BHEAD c,&na,&b,1); UnPack(c,na,&adenom,&anumer); exponent++; } while ( BigLong(c,anumer,c+na,adenom) < 0 ) { Mully(BHEAD c,&na,&b,1); UnPack(c,na,&adenom,&anumer); exponent--; } /* Now division will give a number between 1 and 9 */ den = c + na; i = 1; DivLong(c,anumer,den,adenom,dig,&ndig,c,&newl); *out++ = (UBYTE)(dig[0]+'0'); *out++ = '.'; while ( newl && i < AC.OutNumberType ) { Pack(c,&newl,den,adenom); Mully(BHEAD c,&newl,&b,1); na = newl; UnPack(c,na,&adenom,&anumer); den = c + na; DivLong(c,anumer,den,adenom,dig,&ndig,c,&newl); if ( ndig == 0 ) *out++ = '0'; else *out++ = (UBYTE)(dig[0]+'0'); i++; } *out++ = 'E'; if ( exponent < 0 ) { exponent = -exponent; *out++ = '-'; } else { *out++ = '+'; } o = out; do { *out++ = (UBYTE)((exponent % 10)+'0'); exponent /= 10; } while ( exponent ); *out = 0; out--; while ( o < out ) { cc = *o; *o = *out; *out = cc; o++; out--; } TokenToLine(OutScratch); } } /* #] RatToLine : #[ TalToLine : void TalToLine(x) Writes the unsigned number x to the output as a single token. Par indicates the number of leading blanks in the line. This parameter is needed here for the WriteLists routine. */ void TalToLine(UWORD x) { UBYTE t[BITSINWORD/3+1]; UBYTE *s; WORD i = 0, j; s = t; do { *s++ = (UBYTE)((x % 10)+'0'); i++; } while ( ( x /= 10 ) != 0 ); *s-- = '\0'; j = ( i - 1 ) >> 1; while ( j >= 0 ) { i = t[j]; t[j] = s[-j]; s[-j] = (UBYTE)i; j--; } TokenToLine(t); } /* #] TalToLine : #[ TokenToLine : void TokenToLine(s) Puts s in the output buffer. If it doesn't fit the buffer is flushed first. This routine keeps tokens as one unit. Par indicates the number of leading blanks in the line. This parameter is needed here for the WriteLists routine. Remark (27-oct-2007): i and j must be longer than WORD! It can happen that a number is so long that it has more than 2^15 or 2^31 digits! */ void TokenToLine(UBYTE *s) { UBYTE *t, *Out; LONG num, i = 0, j; if ( AO.OutInBuffer ) { AddToDollarBuffer(s); return; } t = s; Out = AO.OutFill; while ( *t++ ) i++; while ( i > 0 ) { if ( ( Out + i ) >= AO.OutStop && ( ( i < ((AC.LineLength-AO.OutSkip)>>1) ) || ( (AO.OutStop-Out) < (i>>2) ) ) ) { if ( AC.OutputMode == FORTRANMODE && AC.IsFortran90 == ISFORTRAN90 ) { *Out++ = fcontchar; } #ifdef WITHRETURN *Out++ = CARRIAGERETURN; #endif *Out++ = LINEFEED; AO.FortFirst = 0; num = Out - AO.OutputLine; if ( AC.LogHandle >= 0 ) { if ( WriteFile(AC.LogHandle,AO.OutputLine+startinline, num-startinline) != (num-startinline) ) { #ifdef DEBUGGER if ( BUG.logfileflag == 0 ) { fprintf(stderr,"Panic: Cannot write to log file! Disk full?\n"); BUG.logfileflag = 1; } BUG.eflag = 1; BUG.printflag = 1; #else Terminate(-1); #endif } } if ( ( AO.PrintType & PRINTLFILE ) == 0 ) { #ifdef WITHRETURN if ( num > 1 && AO.OutputLine[num-2] == CARRIAGERETURN ) { AO.OutputLine[num-2] = LINEFEED; num--; } #endif if ( WriteFile(AM.StdOut,AO.OutputLine+startinline, num-startinline) != (num-startinline) ) { #ifdef DEBUGGER if ( BUG.stdoutflag == 0 ) { fprintf(stderr,"Panic: Cannot write to standard output!\n"); BUG.stdoutflag = 1; } BUG.eflag = 1; BUG.printflag = 1; #else Terminate(-1); #endif } } startinline = 0; Out = AO.OutputLine; if ( AO.BlockSpaces == 0 ) { for ( j = 0; j < AO.OutSkip; j++ ) { *Out++ = ' '; } if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) ) { if ( AO.OutSkip == 7 ) { Out[-2] = fcontchar; Out[-1] = ' '; } } } /* Out = AO.OutputLine + AO.OutSkip; if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) && AO.OutSkip == 7 ) { Out[-2] = fcontchar; Out[-1] = ' '; } else { for ( j = 0; j < AO.OutSkip; j++ ) { AO.OutputLine[j] = ' '; } } */ if ( AO.IsBracket ) { *Out++ = ' '; *Out++ = ' '; *Out++ = ' '; } *Out = '\0'; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || ( AC.OutputMode == CMODE && AO.FactorMode == 0 ) ) AO.InFbrack++; } if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) { /* Very long numbers */ if ( i > (WORD)(AO.OutStop-Out) ) j = (WORD)(AO.OutStop - Out); else j = i; i -= j; NCOPYB(Out,s,j); } else { if ( i > (WORD)(AO.OutStop-Out) ) j = (WORD)(AO.OutStop - Out - 1); else j = i; i -= j; NCOPYB(Out,s,j); if ( i > 0 ) *Out++ = '\\'; } } *Out = '\0'; AO.OutFill = Out; } /* #] TokenToLine : #[ CodeToLine : void CodeToLine(name,number,mode) Writes a name and possibly its number to output as a single token. */ UBYTE *CodeToLine(WORD number, UBYTE *Out) { Out = StrCopy((UBYTE *)"(",Out); Out = NumCopy(number,Out); Out = StrCopy((UBYTE *)")",Out); return(Out); } /* #] CodeToLine : #[ MultiplyToLine : */ void MultiplyToLine(void) { int i; if ( AO.CurrentDictionary > 0 && AO.CurDictSpecials > 0 && AO.CurDictSpecials == DICT_DOSPECIALS ) { DICTIONARY *dict = AO.Dictionaries[AO.CurrentDictionary-1]; /* Find the star: */ for ( i = 0; i < dict->numelements; i++ ) { if ( dict->elements[i]->type != DICT_SPECIALCHARACTER ) continue; if ( (UBYTE)dict->elements[i]->lhs[0] == (UBYTE)('*') ) { TokenToLine((UBYTE *)(dict->elements[i]->rhs)); return; } } } TokenToLine((UBYTE *)"*"); } /* #] MultiplyToLine : #[ AddArrayIndex : */ UBYTE *AddArrayIndex(WORD num,UBYTE *out) { if ( AC.OutputMode == CMODE ) { out = StrCopy((UBYTE *)"[",out); out = NumCopy(num,out); out = StrCopy((UBYTE *)"]",out); } else { out = StrCopy((UBYTE *)"(",out); out = NumCopy(num,out); out = StrCopy((UBYTE *)")",out); } return(out); } /* #] AddArrayIndex : #[ PrtTerms : void PrtTerms() */ void PrtTerms(void) { UWORD a[2]; WORD na; a[0] = (UWORD)AO.NumInBrack; a[1] = (UWORD)(AO.NumInBrack >> BITSINWORD); if ( a[1] ) na = 2; else na = 1; TokenToLine((UBYTE *)" "); LongToLine(a,na); if ( a[0] == 1 && na == 1 ) { TokenToLine((UBYTE *)" term"); } else TokenToLine((UBYTE *)" terms"); AO.NumInBrack = 0; } /* #] PrtTerms : #[ WrtPower : */ UBYTE *WrtPower(UBYTE *Out, WORD Power) { if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || AC.OutputMode == REDUCEMODE ) { *Out++ = '*'; *Out++ = '*'; } else if ( AC.OutputMode == CMODE ) *Out++ = ','; else { UBYTE *Out1 = IsExponentSign(); if ( Out1 == 0 ) *Out++ = '^'; else { while ( *Out1 ) *Out++ = *Out1++; *Out = 0; } } if ( Power >= 0 ) { if ( Power < 2*MAXPOWER ) Out = NumCopy(Power,Out); else Out = StrCopy(FindSymbol((WORD)((LONG)Power-2*MAXPOWER)),Out); /* Out = StrCopy(VARNAME(symbols,(LONG)Power-2*MAXPOWER),Out); */ if ( AC.OutputMode == CMODE ) *Out++ = ')'; *Out = 0; } else { if ( ( AC.OutputMode >= FORTRANMODE || AC.OutputMode >= PFORTRANMODE || AC.OutputMode >= REDUCEMODE ) && AC.OutputMode != CMODE ) *Out++ = '('; *Out++ = '-'; if ( Power > -2*MAXPOWER ) Out = NumCopy(-Power,Out); else Out = StrCopy(FindSymbol((WORD)((LONG)Power-2*MAXPOWER)),Out); /* Out = StrCopy(VARNAME(symbols,(LONG)(-Power)-2*MAXPOWER),Out); */ if ( AC.OutputMode >= FORTRANMODE || AC.OutputMode >= PFORTRANMODE || AC.OutputMode >= REDUCEMODE) *Out++ = ')'; *Out = 0; } return(Out); } /* #] WrtPower : #[ PrintTime : */ void PrintTime(UBYTE *mess) { LONG millitime = TimeCPU(1); WORD timepart = (WORD)(millitime%1000); millitime /= 1000; timepart /= 10; MesPrint("At %s: Time = %7l.%2i sec",mess,millitime,timepart); } /* #] PrintTime : #] schryf-Utilities : #[ schryf-Writes : #[ WriteLists : void WriteLists() Writes the namelists. If mode > 0 also the internal codes are given. */ static UBYTE *symname[] = { (UBYTE *)"(cyclic)",(UBYTE *)"(reversecyclic)" ,(UBYTE *)"(symmetric)",(UBYTE *)"(antisymmetric)" }; static UBYTE *rsymname[] = { (UBYTE *)"(-cyclic)",(UBYTE *)"(-reversecyclic)" ,(UBYTE *)"(-symmetric)",(UBYTE *)"(-antisymmetric)" }; void WriteLists(void) { GETIDENTITY WORD i, j, k, *skip; int first, startvalue; UBYTE *OutScr, *Out; EXPRESSIONS e; CBUF *C = cbuf+AC.cbufnum; int olddict = AO.CurrentDictionary; skip = &AO.OutSkip; *skip = 0; AO.OutputLine = AO.OutFill = (UBYTE *)AT.WorkPointer; AO.CurrentDictionary = 0; FiniLine(); OutScr = (UBYTE *)AT.WorkPointer + ( TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer) ) /2; if ( AC.CodesFlag || AC.NamesFlag > 1 ) startvalue = 0; else startvalue = FIRSTUSERSYMBOL; /* #[ Symbols : */ if ( ( j = NumSymbols ) > startvalue ) { TokenToLine((UBYTE *)" Symbols"); *skip = 3; FiniLine(); for ( i = startvalue; i < j; i++ ) { if ( i >= BUILTINSYMBOLS && i < FIRSTUSERSYMBOL ) continue; Out = StrCopy(VARNAME(symbols,i),OutScr); if ( symbols[i].minpower > -MAXPOWER || symbols[i].maxpower < MAXPOWER ) { Out = StrCopy((UBYTE *)"(",Out); if ( symbols[i].minpower > -MAXPOWER ) Out = NumCopy(symbols[i].minpower,Out); Out = StrCopy((UBYTE *)":",Out); if ( symbols[i].maxpower < MAXPOWER ) Out = NumCopy(symbols[i].maxpower,Out); Out = StrCopy((UBYTE *)")",Out); } if ( ( symbols[i].complex & VARTYPEIMAGINARY ) == VARTYPEIMAGINARY ) { Out = StrCopy((UBYTE *)"#i",Out); } else if ( ( symbols[i].complex & VARTYPECOMPLEX ) == VARTYPECOMPLEX ) { Out = StrCopy((UBYTE *)"#c",Out); } else if ( ( symbols[i].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) { Out = StrCopy((UBYTE *)"#",Out); if ( ( symbols[i].complex & VARTYPEMINUS ) == VARTYPEMINUS ) { Out = StrCopy((UBYTE *)"-",Out); } else { Out = StrCopy((UBYTE *)"+",Out); } Out = NumCopy(symbols[i].maxpower,Out); } if ( AC.CodesFlag ) Out = CodeToLine(i,Out); if ( ( symbols[i].complex & VARTYPECOMPLEX ) == VARTYPECOMPLEX ) i++; StrCopy((UBYTE *)" ",Out); TokenToLine(OutScr); } *skip = 0; FiniLine(); } /* #] Symbols : #[ Indices : */ if ( AC.CodesFlag || AC.NamesFlag > 1 ) startvalue = 0; else startvalue = BUILTININDICES; if ( ( j = NumIndices ) > startvalue ) { TokenToLine((UBYTE *)" Indices"); *skip = 3; FiniLine(); for ( i = startvalue; i < j; i++ ) { Out = StrCopy(FindIndex(i+AM.OffsetIndex),OutScr); Out = StrCopy(VARNAME(indices,i),OutScr); if ( indices[i].dimension >= 0 ) { if ( indices[i].dimension != AC.lDefDim ) { Out = StrCopy((UBYTE *)"=",Out); Out = NumCopy(indices[i].dimension,Out); } } else if ( indices[i].dimension < 0 ) { Out = StrCopy((UBYTE *)"=",Out); Out = StrCopy(VARNAME(symbols,-indices[i].dimension),Out); if ( indices[i].nmin4 < -NMIN4SHIFT ) { Out = StrCopy((UBYTE *)":",Out); Out = StrCopy(VARNAME(symbols,-indices[i].nmin4-NMIN4SHIFT),Out); } } if ( AC.CodesFlag ) Out = CodeToLine(i+AM.OffsetIndex,Out); StrCopy((UBYTE *)" ",Out); TokenToLine(OutScr); } *skip = 0; FiniLine(); } /* #] Indices : #[ Vectors : */ if ( AC.CodesFlag || AC.NamesFlag > 1 ) startvalue = 0; else startvalue = BUILTINVECTORS; if ( ( j = NumVectors ) > startvalue ) { TokenToLine((UBYTE *)" Vectors"); *skip = 3; FiniLine(); for ( i = startvalue; i < j; i++ ) { Out = StrCopy(VARNAME(vectors,i),OutScr); if ( AC.CodesFlag ) Out = CodeToLine(i+AM.OffsetVector,Out); StrCopy((UBYTE *)" ",Out); TokenToLine(OutScr); } *skip = 0; FiniLine(); } /* #] Vectors : #[ Functions : */ if ( AC.CodesFlag || AC.NamesFlag > 1 ) startvalue = 0; else startvalue = AM.NumFixedFunctions; for ( k = 0; k < 2; k++ ) { first = 1; j = NumFunctions; for ( i = startvalue; i < j; i++ ) { if ( i > MAXBUILTINFUNCTION-FUNCTION && i < FIRSTUSERFUNCTION-FUNCTION ) continue; if ( ( k == 0 && functions[i].commute ) || ( k != 0 && !functions[i].commute ) ) { if ( first ) { TokenToLine((UBYTE *)(FG.FunNam[k])); *skip = 3; FiniLine(); first = 0; } Out = StrCopy(VARNAME(functions,i),OutScr); if ( ( functions[i].complex & VARTYPEIMAGINARY ) == VARTYPEIMAGINARY ) { Out = StrCopy((UBYTE *)"#i",Out); } else if ( ( functions[i].complex & VARTYPECOMPLEX ) == VARTYPECOMPLEX ) { Out = StrCopy((UBYTE *)"#c",Out); } if ( functions[i].spec == VERTEXFUNCTION ) { Out = StrCopy((UBYTE *)"(Particle)",Out); } else if ( functions[i].spec >= TENSORFUNCTION ) { Out = StrCopy((UBYTE *)"(Tensor)",Out); } if ( functions[i].symmetric > 0 ) { if ( ( functions[i].symmetric & REVERSEORDER ) != 0 ) { Out = StrCopy((UBYTE *)(rsymname[(functions[i].symmetric & ~REVERSEORDER)-1]),Out); } else { Out = StrCopy((UBYTE *)(symname[functions[i].symmetric-1]),Out); } } if ( AC.CodesFlag ) Out = CodeToLine(i+FUNCTION,Out); if ( ( functions[i].complex & VARTYPECOMPLEX ) == VARTYPECOMPLEX ) i++; StrCopy((UBYTE *)" ",Out); TokenToLine(OutScr); } } *skip = 0; if ( first == 0 ) FiniLine(); } /* #] Functions : #[ Sets : */ if ( AC.CodesFlag || AC.NamesFlag > 1 ) startvalue = 0; else startvalue = AM.NumFixedSets; if ( ( j = AC.SetList.num ) > startvalue ) { WORD element, LastElement, type, number; TokenToLine((UBYTE *)" Sets"); for ( i = startvalue; i < j; i++ ) { *skip = 3; FiniLine(); if ( Sets[i].name < 0 ) { Out = StrCopy((UBYTE *)"{}",OutScr); } else { Out = StrCopy(VARNAME(Sets,i),OutScr); } if ( AC.CodesFlag ) Out = CodeToLine(i,Out); StrCopy((UBYTE *)":",Out); TokenToLine(OutScr); if ( i < AM.NumFixedSets ) { TokenToLine((UBYTE *)" "); TokenToLine((UBYTE *)fixedsets[i].description); } else if ( Sets[i].type == CRANGE ) { int iflag = 0; if ( Sets[i].first == 3*MAXPOWER ) { } else if ( Sets[i].first >= MAXPOWER ) { TokenToLine((UBYTE *)"<="); NumCopy(Sets[i].first-2*MAXPOWER,OutScr); TokenToLine(OutScr); iflag = 1; } else { TokenToLine((UBYTE *)"<"); NumCopy(Sets[i].first,OutScr); TokenToLine(OutScr); iflag = 1; } if ( Sets[i].last == -3*MAXPOWER ) { } else if ( Sets[i].last <= -MAXPOWER ) { if ( iflag ) TokenToLine((UBYTE *)","); TokenToLine((UBYTE *)">="); NumCopy(Sets[i].last+2*MAXPOWER,OutScr); TokenToLine(OutScr); } else { if ( iflag ) TokenToLine((UBYTE *)","); TokenToLine((UBYTE *)">"); NumCopy(Sets[i].last,OutScr); TokenToLine(OutScr); } } else { element = Sets[i].first; LastElement = Sets[i].last; type = Sets[i].type; while ( element < LastElement ) { TokenToLine((UBYTE *)" "); number = SetElements[element++]; switch ( type ) { case CSYMBOL: if ( number < 0 ) { StrCopy(VARNAME(symbols,-number),OutScr); StrCopy((UBYTE *)"?",Out); TokenToLine(OutScr); } else if ( number < MAXPOWER ) TokenToLine(VARNAME(symbols,number)); else { NumCopy(number-2*MAXPOWER,OutScr); TokenToLine(OutScr); } break; case CINDEX: if ( number >= AM.IndDum ) { Out = StrCopy((UBYTE *)"N",OutScr); Out = NumCopy(number-(AM.IndDum),Out); StrCopy((UBYTE *)"_?",Out); TokenToLine(OutScr); } else if ( number >= AM.OffsetIndex + (WORD)WILDMASK ) { Out = StrCopy(VARNAME(indices,number -AM.OffsetIndex-WILDMASK),OutScr); StrCopy((UBYTE *)"?",Out); TokenToLine(OutScr); } else if ( number >= AM.OffsetIndex ) { TokenToLine(VARNAME(indices,number-AM.OffsetIndex)); } else { NumCopy(number,OutScr); TokenToLine(OutScr); } break; case CVECTOR: Out = OutScr; if ( number < AM.OffsetVector ) { number += WILDMASK; Out = StrCopy((UBYTE *)"-",Out); } if ( number >= AM.OffsetVector + WILDOFFSET ) { Out = StrCopy(VARNAME(vectors,number -AM.OffsetVector-WILDOFFSET),Out); StrCopy((UBYTE *)"?",Out); } else { Out = StrCopy(VARNAME(vectors,number-AM.OffsetVector),Out); } TokenToLine(OutScr); break; case CFUNCTION: if ( number >= FUNCTION + (WORD)WILDMASK ) { Out = StrCopy(VARNAME(functions,number -FUNCTION-WILDMASK),OutScr); StrCopy((UBYTE *)"?",Out); TokenToLine(OutScr); } TokenToLine(VARNAME(functions,number-FUNCTION)); break; default: NumCopy(number,OutScr); TokenToLine(OutScr); break; } } } } *skip = 0; FiniLine(); } /* #] Sets : #[ Expressions : */ if ( AS.ExecMode ) { e = Expressions; j = NumExpressions; first = 1; for ( i = 0; i < j; i++, e++ ) { if ( e->status >= 0 ) { if ( first ) { TokenToLine((UBYTE *)" Expressions"); *skip = 3; FiniLine(); first = 0; } Out = StrCopy(AC.exprnames->namebuffer+e->name,OutScr); Out = StrCopy((UBYTE *)(FG.ExprStat[e->status]),Out); if ( AC.CodesFlag ) Out = CodeToLine(i,Out); StrCopy((UBYTE *)" ",Out); TokenToLine(OutScr); } } if ( !first ) { *skip = 0; FiniLine(); } } e = Expressions; j = NumExpressions; first = 1; for ( i = 0; i < j; i++ ) { if ( e->printflag && ( e->status == LOCALEXPRESSION || e->status == GLOBALEXPRESSION || e->status == UNHIDELEXPRESSION || e->status == UNHIDEGEXPRESSION ) ) { if ( first ) { TokenToLine((UBYTE *)" Expressions to be printed"); *skip = 3; FiniLine(); first = 0; } Out = StrCopy(AC.exprnames->namebuffer+e->name,OutScr); StrCopy((UBYTE *)" ",Out); TokenToLine(OutScr); } e++; } if ( !first ) { *skip = 0; FiniLine(); } /* #] Expressions : #[ Dollars : */ if ( AC.CodesFlag || AC.NamesFlag > 1 ) startvalue = 0; else startvalue = BUILTINDOLLARS; if ( ( j = NumDollars ) > startvalue ) { TokenToLine((UBYTE *)" Dollar variables"); *skip = 3; FiniLine(); for ( i = startvalue; i < j; i++ ) { Out = StrCopy((UBYTE *)"$", OutScr); Out = StrCopy(DOLLARNAME(Dollars, i), Out); if ( AC.CodesFlag ) Out = CodeToLine(i, Out); StrCopy((UBYTE *)" ", Out); TokenToLine(OutScr); } *skip = 0; FiniLine(); } if ( ( j = NumPotModdollars ) > 0 ) { TokenToLine((UBYTE *)" Dollar variables to be modified"); *skip = 3; FiniLine(); for ( i = 0; i < j; i++ ) { Out = StrCopy((UBYTE *)"$", OutScr); Out = StrCopy(DOLLARNAME(Dollars, PotModdollars[i]), Out); for ( k = 0; k < NumModOptdollars; k++ ) if ( ModOptdollars[k].number == PotModdollars[i] ) break; if ( k < NumModOptdollars ) { switch ( ModOptdollars[k].type ) { case MODSUM: Out = StrCopy((UBYTE *)"(sum)", Out); break; case MODMAX: Out = StrCopy((UBYTE *)"(maximum)", Out); break; case MODMIN: Out = StrCopy((UBYTE *)"(minimum)", Out); break; case MODLOCAL: Out = StrCopy((UBYTE *)"(local)", Out); break; default: Out = StrCopy((UBYTE *)"(?)", Out); break; } } StrCopy((UBYTE *)" ", Out); TokenToLine(OutScr); } *skip = 0; FiniLine(); } /* #] Dollars : */ if ( AC.ncmod != 0 ) { TokenToLine((UBYTE *)"All arithmetic is modulus "); LongToLine((UWORD *)AC.cmod,ABS(AC.ncmod)); if ( AC.ncmod > 0 ) TokenToLine((UBYTE *)" with powerreduction"); else TokenToLine((UBYTE *)" without powerreduction"); if ( ( AC.modmode & POSNEG ) != 0 ) TokenToLine((UBYTE *)" centered around 0"); else TokenToLine((UBYTE *)" positive numbers only"); FiniLine(); } if ( AC.lDefDim != 4 ) { TokenToLine((UBYTE *)"The default dimension is "); if ( AC.lDefDim >= 0 ) { NumCopy(AC.lDefDim,OutScr); TokenToLine(OutScr); } else { TokenToLine(VARNAME(symbols,-AC.lDefDim)); if ( AC.lDefDim4 != -NMIN4SHIFT ) { TokenToLine((UBYTE *)":"); if ( AC.lDefDim4 >= -NMIN4SHIFT ) { NumCopy(AC.lDefDim4,OutScr); TokenToLine(OutScr); } else { TokenToLine(VARNAME(symbols,-AC.lDefDim4-NMIN4SHIFT)); } } } FiniLine(); } if ( AC.lUnitTrace != 4 ) { TokenToLine((UBYTE *)"The trace of the unit matrix is "); if ( AC.lUnitTrace >= 0 ) { NumCopy(AC.lUnitTrace,OutScr); TokenToLine(OutScr); } else { TokenToLine(VARNAME(symbols,-AC.lUnitTrace)); } FiniLine(); } if ( AO.NumDictionaries > 0 ) { for ( i = 0; i < AO.NumDictionaries; i++ ) { WriteDictionary(AO.Dictionaries[i]); } if ( olddict > 0 ) MesPrint("\nCurrently dictionary %s is active\n", AO.Dictionaries[olddict-1]->name); else MesPrint("\nCurrently there is no active dictionary\n"); } if ( AC.CodesFlag ) { if ( C->numlhs > 0 ) { TokenToLine((UBYTE *)" Left Hand Sides:"); AO.OutSkip = 3; for ( i = 1; i <= C->numlhs; i++ ) { FiniLine(); skip = C->lhs[i]; j = skip[1]; while ( --j >= 0 ) { TalToLine((UWORD)(*skip++)); TokenToLine((UBYTE *)" "); } } AO.OutSkip = 0; FiniLine(); } if ( C->numrhs > 0 ) { TokenToLine((UBYTE *)" Right Hand Sides:"); AO.OutSkip = 3; for ( i = 1; i <= C->numrhs; i++ ) { FiniLine(); skip = C->rhs[i]; while ( ( j = skip[0] ) != 0 ) { while ( --j >= 0 ) { TalToLine((UWORD)(*skip++)); TokenToLine((UBYTE *)" "); } } FiniLine(); } AO.OutSkip = 0; FiniLine(); } } AO.CurrentDictionary = olddict; } /* #] WriteLists : #[ WriteDictionary : This routine is part of WriteLists and should be called from there. */ void WriteDictionary(DICTIONARY *dict) { GETIDENTITY int i, first; WORD *skip, na, *a, spec, *t, *tstop, j; UBYTE str[2], *OutScr, *Out; WORD oldoutputmode = AC.OutputMode, oldoutputspaces = AC.OutputSpaces; WORD oldoutskip = AO.OutSkip; AC.OutputMode = NORMALFORMAT; AC.OutputSpaces = NOSPACEFORMAT; MesPrint("===Contents of dictionary %s===",dict->name); skip = &AO.OutSkip; *skip = 3; AO.OutputLine = AO.OutFill = (UBYTE *)AT.WorkPointer; for ( j = 0; j < *skip; j++ ) *(AO.OutFill)++ = ' '; OutScr = (UBYTE *)AT.WorkPointer + ( TOLONG(AT.WorkTop) - TOLONG(AT.WorkPointer) ) /2; for ( i = 0; i < dict->numelements; i++ ) { switch ( dict->elements[i]->type ) { case DICT_INTEGERNUMBER: LongToLine((UWORD *)(dict->elements[i]->lhs),dict->elements[i]->size); Out = OutScr; *Out = 0; break; case DICT_RATIONALNUMBER: a = dict->elements[i]->lhs; na = a[a[0]-1]; na = (ABS(na)-1)/2; RatToLine((UWORD *)(a+1),na); Out = OutScr; *Out = 0; break; case DICT_SYMBOL: na = dict->elements[i]->lhs[0]; Out = StrCopy(VARNAME(symbols,na),OutScr); break; case DICT_VECTOR: na = dict->elements[i]->lhs[0]-AM.OffsetVector; Out = StrCopy(VARNAME(vectors,na),OutScr); break; case DICT_INDEX: na = dict->elements[i]->lhs[0]-AM.OffsetIndex; Out = StrCopy(VARNAME(indices,na),OutScr); break; case DICT_FUNCTION: na = dict->elements[i]->lhs[0]-FUNCTION; Out = StrCopy(VARNAME(functions,na),OutScr); break; case DICT_FUNCTION_WITH_ARGUMENTS: t = dict->elements[i]->lhs; na = *t-FUNCTION; Out = StrCopy(VARNAME(functions,na),OutScr); spec = functions[*t - FUNCTION].spec; tstop = t + t[1]; first = 1; if ( t[1] <= FUNHEAD ) {} else if ( spec >= TENSORFUNCTION ) { t += FUNHEAD; *Out++ = (UBYTE)'('; while ( t < tstop ) { if ( first == 0 ) *Out++ = (UBYTE)(','); else first = 0; j = *t++; if ( j >= 0 ) { if ( j < AM.OffsetIndex ) { Out = NumCopy(j,Out); } else if ( j < AM.IndDum ) { Out = StrCopy(VARNAME(indices,j-AM.OffsetIndex),Out); } else { MesPrint("Currently wildcards are not allowed in dictionary elements"); Terminate(-1); } } else { Out = StrCopy(VARNAME(vectors,j-AM.OffsetVector),Out); } } *Out++ = (UBYTE)')'; *Out = 0; } else { t += FUNHEAD; *Out++ = (UBYTE)'('; *Out = 0; TokenToLine(OutScr); while ( t < tstop ) { if ( !first ) TokenToLine((UBYTE *)","); WriteArgument(t); NEXTARG(t) first = 0; } Out = OutScr; *Out++ = (UBYTE)')'; *Out = 0; } break; case DICT_SPECIALCHARACTER: str[0] = (UBYTE)(dict->elements[i]->lhs[0]); str[1] = 0; Out = StrCopy(str,OutScr); break; default: Out = OutScr; *Out = 0; break; } Out = StrCopy((UBYTE *)": \"",Out); Out = StrCopy((UBYTE *)(dict->elements[i]->rhs),Out); Out = StrCopy((UBYTE *)"\"",Out); TokenToLine(OutScr); FiniLine(); } MesPrint("========End of dictionary %s===",dict->name); AC.OutputMode = oldoutputmode; AC.OutputSpaces = oldoutputspaces; AO.OutSkip = oldoutskip; } /* #] WriteDictionary : #[ WriteArgument : void WriteArgument(WORD *t) Write a single argument field. The general field goes to WriteExpression and the fast field is dealt with here. */ void WriteArgument(WORD *t) { UBYTE buffer[180]; UBYTE *Out; WORD i; int oldoutsidefun, oldlowestlevel = lowestlevel; lowestlevel = 0; if ( *t > 0 ) { oldoutsidefun = AC.outsidefun; AC.outsidefun = 0; WriteExpression(t+ARGHEAD,(LONG)(*t-ARGHEAD)); AC.outsidefun = oldoutsidefun; goto CleanUp; } Out = buffer; if ( *t == -SNUMBER) { NumCopy(t[1],Out); } else if ( *t == -SYMBOL ) { if ( t[1] >= MAXVARIABLES-cbuf[AM.sbufnum].numrhs ) { Out = StrCopy(FindExtraSymbol(MAXVARIABLES-t[1]),Out); /* Out = StrCopy((UBYTE *)AC.extrasym,Out); if ( AC.extrasymbols == 0 ) { Out = NumCopy((MAXVARIABLES-t[1]),Out); Out = StrCopy((UBYTE *)"_",Out); } else if ( AC.extrasymbols == 1 ) { Out = AddArrayIndex((MAXVARIABLES-t[1]),Out); } */ /* else if ( AC.extrasymbols == 2 ) { Out = NumCopy((MAXVARIABLES-t[1]),Out); } */ } else { StrCopy(FindSymbol(t[1]),Out); /* StrCopy(VARNAME(symbols,t[1]),Out); */ } } else if ( *t == -VECTOR ) { if ( t[1] == FUNNYVEC ) { *Out++ = '?'; *Out = 0; } else StrCopy(FindVector(t[1]),Out); /* StrCopy(VARNAME(vectors,t[1] - AM.OffsetVector),Out); */ } else if ( *t == -MINVECTOR ) { *Out++ = '-'; StrCopy(FindVector(t[1]),Out); /* StrCopy(VARNAME(vectors,t[1] - AM.OffsetVector),Out); */ } else if ( *t == -INDEX ) { if ( t[1] >= 0 ) { if ( t[1] < AM.OffsetIndex ) { NumCopy(t[1],Out); } else { i = t[1]; if ( i >= AM.IndDum ) { i -= AM.IndDum; *Out++ = 'N'; Out = NumCopy(i,Out); *Out++ = '_'; *Out++ = '?'; *Out = 0; } else { i -= AM.OffsetIndex; Out = StrCopy(FindIndex(i%WILDOFFSET+AM.OffsetIndex),Out); /* Out = StrCopy(VARNAME(indices,i%WILDOFFSET),Out); */ if ( i >= WILDOFFSET ) { *Out++ = '?'; *Out = 0; } } } } else if ( t[1] == FUNNYVEC ) { *Out++ = '?'; *Out = 0; } else StrCopy(FindVector(t[1]),Out); /* StrCopy(VARNAME(vectors,t[1] - AM.OffsetVector),Out); */ } else if ( *t == -DOLLAREXPRESSION ) { DOLLARS d = Dollars + t[1]; *Out++ = '$'; StrCopy(AC.dollarnames->namebuffer+d->name,Out); } else if ( *t == -EXPRESSION ) { StrCopy(EXPRNAME(t[1]),Out); } else if ( *t == -SETSET ) { StrCopy(VARNAME(Sets,t[1]),Out); } else if ( *t <= -FUNCTION ) { StrCopy(FindFunction(-*t),Out); /* StrCopy(VARNAME(functions,-*t-FUNCTION),Out); */ } else { MesPrint("Illegal function argument while writing"); goto CleanUp; } TokenToLine(buffer); CleanUp: lowestlevel = oldlowestlevel; return; } /* #] WriteArgument : #[ WriteSubTerm : WORD WriteSubTerm(sterm,first) Writes a single subterm field to the output line. There is a recursion for functions. #define NUMSPECS 8 UBYTE *specfunnames[NUMSPECS] = { (UBYTE *)"fac" , (UBYTE *)"nargs", (UBYTE *)"binom" , (UBYTE *)"sign", (UBYTE *)"mod", (UBYTE *)"min", (UBYTE *)"max" , (UBYTE *)"invfac" }; */ int WriteSubTerm(WORD *sterm, WORD first) { UBYTE buffer[80]; UBYTE *Out, closepar[2] = { (UBYTE)')', 0}; WORD *stopper, *t, *tt, i, j, po = 0; int oldoutsidefun; stopper = sterm + sterm[1]; t = sterm + 2; switch ( *sterm ) { case SYMBOL : while ( t < stopper ) { if ( lowestlevel && ( ( AO.PrintType & PRINTALL ) != 0 ) ) { FiniLine(); if ( AC.OutputSpaces == NOSPACEFORMAT ) IniLine(1); else IniLine(3); if ( first ) TokenToLine((UBYTE *)" "); } if ( !first ) MultiplyToLine(); if ( AC.OutputMode == CMODE && t[1] != 1 ) { if ( AC.Cnumpows >= t[1] && t[1] > 0 ) { po = t[1]; Out = StrCopy((UBYTE *)"POW",buffer); Out = NumCopy(po,Out); Out = StrCopy((UBYTE *)"(",Out); TokenToLine(buffer); } else { TokenToLine((UBYTE *)"pow("); } } if ( *t < NumSymbols ) { Out = StrCopy(FindSymbol(*t),buffer); t++; /* Out = StrCopy(VARNAME(symbols,*t),buffer); t++; */ } else { /* see also routine PrintSubtermList. */ Out = StrCopy(FindExtraSymbol(MAXVARIABLES-*t),buffer); /* Out = StrCopy((UBYTE *)AC.extrasym,buffer); if ( AC.extrasymbols == 0 ) { Out = NumCopy((MAXVARIABLES-*t),Out); Out = StrCopy((UBYTE *)"_",Out); } else if ( AC.extrasymbols == 1 ) { Out = AddArrayIndex((MAXVARIABLES-*t),Out); } */ /* else if ( AC.extrasymbols == 2 ) { Out = NumCopy((MAXVARIABLES-*t),Out); } */ t++; } if ( AC.OutputMode == CMODE && po > 1 && AC.Cnumpows >= po ) { Out = StrCopy((UBYTE *)")",Out); po = 0; } else if ( *t != 1 ) WrtPower(Out,*t); TokenToLine(buffer); t++; first = 0; } break; case VECTOR : while ( t < stopper ) { if ( lowestlevel && ( ( AO.PrintType & PRINTALL ) != 0 ) ) { FiniLine(); if ( AC.OutputSpaces == NOSPACEFORMAT ) IniLine(1); else IniLine(3); if ( first ) TokenToLine((UBYTE *)" "); } if ( !first ) MultiplyToLine(); Out = StrCopy(FindVector(*t),buffer); /* Out = StrCopy(VARNAME(vectors,*t - AM.OffsetVector),buffer); */ t++; if ( AC.OutputMode == MATHEMATICAMODE ) *Out++ = '['; else *Out++ = '('; if ( *t >= AM.OffsetIndex ) { i = *t++; if ( i >= AM.IndDum ) { i -= AM.IndDum; *Out++ = 'N'; Out = NumCopy(i,Out); *Out++ = '_'; *Out++ = '?'; *Out = 0; } else Out = StrCopy(FindIndex(i),Out); /* Out = StrCopy(VARNAME(indices,i - AM.OffsetIndex),Out); */ } else if ( *t == FUNNYVEC ) { *Out++ = '?'; *Out = 0; } else { Out = NumCopy(*t++,Out); } if ( AC.OutputMode == MATHEMATICAMODE ) *Out++ = ']'; else *Out++ = ')'; *Out = 0; TokenToLine(buffer); first = 0; } break; case INDEX : while ( t < stopper ) { if ( lowestlevel && ( ( AO.PrintType & PRINTALL ) != 0 ) ) { FiniLine(); if ( AC.OutputSpaces == NOSPACEFORMAT ) IniLine(1); else IniLine(3); if ( first ) TokenToLine((UBYTE *)" "); } if ( !first ) MultiplyToLine(); if ( *t >= 0 ) { if ( *t < AM.OffsetIndex ) { TalToLine((UWORD)(*t++)); } else { i = *t++; if ( i >= AM.IndDum ) { i -= AM.IndDum; Out = buffer; *Out++ = 'N'; Out = NumCopy(i,Out); *Out++ = '_'; *Out++ = '?'; *Out = 0; } else { i -= AM.OffsetIndex; Out = StrCopy(FindIndex(i%WILDOFFSET+AM.OffsetIndex),buffer); /* Out = StrCopy(VARNAME(indices,i%WILDOFFSET),buffer); */ if ( i >= WILDOFFSET ) { *Out++ = '?'; *Out = 0; } } TokenToLine(buffer); } } else { TokenToLine(FindVector(*t)); t++; /* TokenToLine(VARNAME(vectors,*t - AM.OffsetVector)); t++; */ } first = 0; } break; case DOLLAREXPRESSION: { DOLLARS d = Dollars + sterm[2]; Out = StrCopy((UBYTE *)"$",buffer); Out = StrCopy(AC.dollarnames->namebuffer+d->name,Out); if ( sterm[3] != 1 ) WrtPower(Out,sterm[3]); TokenToLine(buffer); } first = 0; break; case DELTA : while ( t < stopper ) { if ( lowestlevel && ( ( AO.PrintType & PRINTALL ) != 0 ) ) { FiniLine(); if ( AC.OutputSpaces == NOSPACEFORMAT ) IniLine(1); else IniLine(3); if ( first ) TokenToLine((UBYTE *)" "); } if ( !first ) MultiplyToLine(); Out = StrCopy((UBYTE *)"d_(",buffer); if ( *t >= AM.OffsetIndex ) { if ( *t < AM.IndDum ) { Out = StrCopy(FindIndex(*t),Out); /* Out = StrCopy(VARNAME(indices,*t - AM.OffsetIndex),Out); */ t++; } else { *Out++ = 'N'; Out = NumCopy( *t++ - AM.IndDum, Out); *Out++ = '_'; *Out++ = '?'; *Out = 0; } } else if ( *t == FUNNYVEC ) { *Out++ = '?'; *Out = 0; } else { Out = NumCopy(*t++,Out); } *Out++ = ','; if ( *t >= AM.OffsetIndex ) { if ( *t < AM.IndDum ) { Out = StrCopy(FindIndex(*t),Out); /* Out = StrCopy(VARNAME(indices,*t - AM.OffsetIndex),Out); */ t++; } else { *Out++ = 'N'; Out = NumCopy(*t++ - AM.IndDum,Out); *Out++ = '_'; *Out++ = '?'; } } else { Out = NumCopy(*t++,Out); } *Out++ = ')'; *Out = 0; TokenToLine(buffer); first = 0; } break; case DOTPRODUCT : while ( t < stopper ) { if ( lowestlevel && ( ( AO.PrintType & PRINTALL ) != 0 ) ) { FiniLine(); if ( AC.OutputSpaces == NOSPACEFORMAT ) IniLine(1); else IniLine(3); if ( first ) TokenToLine((UBYTE *)" "); } if ( !first ) MultiplyToLine(); if ( AC.OutputMode == CMODE && t[2] != 1 ) TokenToLine((UBYTE *)"pow("); if ( AC.OutputMode == MATHEMATICAMODE ) TokenToLine((UBYTE *)"("); Out = StrCopy(FindVector(*t),buffer); /* Out = StrCopy(VARNAME(vectors,*t - AM.OffsetVector),buffer); */ t++; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || AC.OutputMode == CMODE ) *Out++ = AO.FortDotChar; else *Out++ = '.'; Out = StrCopy(FindVector(*t),Out); /* Out = StrCopy(VARNAME(vectors,*t - AM.OffsetVector),Out); */ if ( AC.OutputMode == MATHEMATICAMODE ) { *Out++ = ')'; *Out = 0; } t++; if ( *t != 1 ) WrtPower(Out,*t); t++; TokenToLine(buffer); first = 0; } break; case EXPONENT : #if FUNHEAD != 2 t += FUNHEAD - 2; #endif if ( !first ) MultiplyToLine(); if ( AC.OutputMode == CMODE ) TokenToLine((UBYTE *)"pow("); else TokenToLine((UBYTE *)"("); WriteArgument(t); if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || AC.OutputMode == REDUCEMODE ) TokenToLine((UBYTE *)")**("); else if ( AC.OutputMode == CMODE ) TokenToLine((UBYTE *)","); else { UBYTE *Out1 = IsExponentSign(); if ( Out1 ) { TokenToLine((UBYTE *)")"); TokenToLine(Out1); TokenToLine((UBYTE *)"("); } else TokenToLine((UBYTE *)")^("); } NEXTARG(t) WriteArgument(t); TokenToLine((UBYTE *)")"); break; case DENOMINATOR : #if FUNHEAD != 2 t += FUNHEAD - 2; #endif if ( first ) TokenToLine((UBYTE *)"1/("); else TokenToLine((UBYTE *)"/("); WriteArgument(t); TokenToLine((UBYTE *)")"); break; case SUBEXPRESSION: if ( !first ) MultiplyToLine(); TokenToLine((UBYTE *)"("); t = cbuf[sterm[4]].rhs[sterm[2]]; tt = t; while ( *tt ) tt += *tt; oldoutsidefun = AC.outsidefun; AC.outsidefun = 0; if ( *t ) { WriteExpression(t,(LONG)(tt-t)); } else { TokenToLine((UBYTE *)"0"); } AC.outsidefun = oldoutsidefun; TokenToLine((UBYTE *)")"); if ( sterm[3] != 1 ) { UBYTE *Out1 = IsExponentSign(); if ( Out1 ) TokenToLine(Out1); else TokenToLine((UBYTE *)"^"); Out = buffer; NumCopy(sterm[3],Out); TokenToLine(buffer); } break; default : if ( lowestlevel && ( ( AO.PrintType & PRINTALL ) != 0 ) ) { FiniLine(); if ( AC.OutputSpaces == NOSPACEFORMAT ) IniLine(1); else IniLine(3); if ( first ) TokenToLine((UBYTE *)" "); } if ( *sterm < FUNCTION ) { return(MesPrint("Illegal subterm while writing")); } if ( !first ) MultiplyToLine(); first = 1; { UBYTE *tmp; if ( ( tmp = FindFunWithArgs(sterm) ) != 0 ) { TokenToLine(tmp); break; } } t += FUNHEAD-2; if ( *sterm == GAMMA && t[-FUNHEAD+1] == FUNHEAD+1 ) { TokenToLine((UBYTE *)"gi_("); } else { if ( *sterm != DUMFUN ) { Out = StrCopy(FindFunction(*sterm),buffer); /* Out = StrCopy(VARNAME(functions,*sterm - FUNCTION),buffer); */ } else { Out = buffer; *Out = 0; } if ( t >= stopper ) { TokenToLine(buffer); break; } if ( AC.OutputMode == MATHEMATICAMODE ) { *Out++ = '['; closepar[0] = (UBYTE)']'; } else { *Out++ = '('; } *Out = 0; TokenToLine(buffer); } i = functions[*sterm - FUNCTION].spec; if ( i >= TENSORFUNCTION ) { int curdict = AO.CurrentDictionary; if ( AO.CurrentDictionary && AO.CurDictNotInFunctions > 0 ) AO.CurrentDictionary = 0; t = sterm + FUNHEAD; while ( t < stopper ) { if ( !first ) TokenToLine((UBYTE *)","); else first = 0; j = *t++; if ( j >= 0 ) { if ( j < AM.OffsetIndex ) TalToLine((UWORD)(j)); else if ( j < AM.IndDum ) { i = j - AM.OffsetIndex; Out = StrCopy(FindIndex(i%WILDOFFSET+AM.OffsetIndex),buffer); /* Out = StrCopy(VARNAME(indices,i%WILDOFFSET),buffer); */ if ( i >= WILDOFFSET ) { *Out++ = '?'; *Out = 0; } TokenToLine(buffer); } else { Out = buffer; *Out++ = 'N'; Out = NumCopy(j - AM.IndDum,Out); *Out++ = '_'; *Out++ = '?'; *Out = 0; TokenToLine(buffer); } } else if ( j == FUNNYVEC ) { TokenToLine((UBYTE *)"?"); } else if ( j > -WILDOFFSET ) { Out = buffer; Out = NumCopy((UWORD)(-j + 4),Out); *Out++ = '_'; *Out = 0; TokenToLine(buffer); } else { TokenToLine(FindVector(j)); /* TokenToLine(VARNAME(vectors,j - AM.OffsetVector)); */ } } AO.CurrentDictionary = curdict; } else { int curdict = AO.CurrentDictionary; if ( AO.CurrentDictionary && AO.CurDictNotInFunctions > 0 ) AO.CurrentDictionary = 0; while ( t < stopper ) { if ( !first ) TokenToLine((UBYTE *)","); WriteArgument(t); NEXTARG(t) first = 0; } AO.CurrentDictionary = curdict; } TokenToLine(closepar); closepar[0] = (UBYTE)')'; break; } return(0); } /* #] WriteSubTerm : #[ WriteInnerTerm : WORD WriteInnerTerm(term,first) Writes the contents of term to the output. Only the part that is inside parentheses is written. */ int WriteInnerTerm(WORD *term, WORD first) { WORD *t, *s, *s1, *s2, n, i, pow; #ifdef WITHFLOAT int FloatChars = 0; GETIDENTITY #endif t = term; s = t+1; GETCOEF(t,n); while ( s < t ) { if ( *s == HAAKJE ) break; s += s[1]; } if ( s < t ) { s += s[1]; } else { s = term+1; } if ( n < 0 || !first ) { if ( n > 0 ) { TOKENTOLINE(" + ","+") } else if ( n < 0 ) { n = -n; TOKENTOLINE(" - ","-") } } if ( AC.modpowers ) { if ( n == 1 && *t == 1 && t > s ) first = 1; else if ( ABS(AC.ncmod) == 1 ) { UBYTE *Out1 = IsExponentSign(); LongToLine((UWORD *)AC.powmod,AC.npowmod); if ( Out1 ) TokenToLine(Out1); else TokenToLine((UBYTE *)"^"); TalToLine(AC.modpowers[(LONG)((UWORD)*t)]); first = 0; } else { LONG jj; UBYTE *Out1 = IsExponentSign(); LongToLine((UWORD *)AC.powmod,AC.npowmod); if ( Out1 ) TokenToLine(Out1); else TokenToLine((UBYTE *)"^"); jj = (UWORD)*t; if ( n == 2 ) jj += ((LONG)t[1])< 0 ) TransformRational((UWORD *)t,n); else RatToLine((UWORD *)t,n); first = 0; } #ifdef WITHFLOAT /* Check whether there is a 'proper' float_ function and no raw mode. If so, print as float. Raw mode is indicated as AO.FloatPrec < 0. AO.FloatPrec == 0 indicated as many digits as the precision allows. */ else if ( AO.FloatPrec >= 0 && AT.aux_ != 0 ) { WORD *ss = s; while ( ss < t ) { if ( *ss == FLOATFUN ) { if ( ( FloatChars = PrintFloat(ss,AO.FloatPrec) ) != 0 ) { TokenToLine(AO.floatspace); if ( AC.IsFortran90 == ISFORTRAN90 && AC.Fortran90Kind ) { AddToLine(AC.Fortran90Kind); } first = 0; } break; } ss += ss[1]; } if ( ss >= t ) first = 1; } #endif else first = 1; while ( s < t ) { if ( lowestlevel && ( (AO.PrintType & (PRINTONEFUNCTION | PRINTALL)) == PRINTONEFUNCTION ) ) { FiniLine(); if ( AC.OutputSpaces == NOSPACEFORMAT ) IniLine(1); else IniLine(3); } /* #[ NEWGAMMA : */ #ifdef NEWGAMMA if ( *s == GAMMA ) { /* String them up */ WORD *tt,*ss; ss = AT.WorkPointer; *ss++ = GAMMA; *ss++ = s[1]; FILLFUN(ss) *ss++ = s[FUNHEAD]; tt = s + FUNHEAD + 1; n = s[1] - FUNHEAD-1; do { while ( --n >= 0 ) *ss++ = *tt++; tt = s + s[1]; while ( *tt == GAMMA && tt[FUNHEAD] == s[FUNHEAD] && tt < t ) { s = tt; tt += FUNHEAD + 1; n = s[1] - FUNHEAD-1; if ( n > 0 ) break; } } while ( n > 0 ); tt = AT.WorkPointer; AT.WorkPointer = ss; tt[1] = WORDDIF(ss,tt); if ( WriteSubTerm(tt,first) ) { MesCall("WriteInnerTerm"); SETERROR(-1) } AT.WorkPointer = tt; } else #endif /* #] NEWGAMMA : */ #ifdef WITHFLOAT if ( *s == FLOATFUN && AO.FloatPrec >= 0 && AT.aux_ != 0 ) { } else #endif { if ( *s >= FUNCTION && AC.funpowers > 0 && functions[*s-FUNCTION].spec == 0 && ( AC.funpowers == ALLFUNPOWERS || ( AC.funpowers == COMFUNPOWERS && functions[*s-FUNCTION].commute == 0 ) ) ) { pow = 1; for(;;) { s1 = s; s2 = s + s[1]; i = s[1]; if ( s2 < t ) { while ( --i >= 0 && *s1 == *s2 ) { s1++; s2++; } if ( i < 0 ) { pow++; s = s+s[1]; } else break; } else break; } if ( pow > 1 ) { if ( AC.OutputMode == CMODE ) { if ( !first ) MultiplyToLine(); TokenToLine((UBYTE *)"pow("); first = 1; } if ( WriteSubTerm(s,first) ) { MesCall("WriteInnerTerm"); SETERROR(-1) } if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE || AC.OutputMode == REDUCEMODE ) { TokenToLine((UBYTE *)"**"); } else if ( AC.OutputMode == CMODE ) { TokenToLine((UBYTE *)","); } else { UBYTE *Out1 = IsExponentSign(); if ( Out1 ) TokenToLine(Out1); else TokenToLine((UBYTE *)"^"); } TalToLine(pow); if ( AC.OutputMode == CMODE ) TokenToLine((UBYTE *)")"); } else if ( WriteSubTerm(s,first) ) { MesCall("WriteInnerTerm"); SETERROR(-1) } } else if ( WriteSubTerm(s,first) ) { MesCall("WriteInnerTerm"); SETERROR(-1) } } first = 0; s += s[1]; } return(0); } /* #] WriteInnerTerm : #[ WriteTerm : WORD WriteTerm(term,lbrac,first,prtf,br) Writes a term to output. It tests the bracket information first. If there are no brackets or the bracket is the same all is passed to WriteInnerTerm. If there are brackets and the bracket is not the same as for the predecessor the old bracket is closed and a new one is opened. br indicates whether we are in a subexpression, barring zeroing AO.IsBracket */ int WriteTerm(WORD *term, WORD *lbrac, WORD first, WORD prtf, WORD br) { WORD *t, *stopper, *b, n; int oldIsFortran90 = AC.IsFortran90, i; if ( *lbrac >= 0 ) { t = term + 1; stopper = (term + *term - 1); stopper -= ABS(*stopper) - 1; while ( t < stopper ) { if ( *t == HAAKJE ) { stopper = t; t = term+1; if ( *lbrac == ( n = WORDDIF(stopper,t) ) ) { b = AO.bracket + 1; t = term + 1; while ( n > 0 && ( *b++ == *t++ ) ) { n--; } if ( n <= 0 && ( ( AM.FortranCont <= 0 || AO.InFbrack < AM.FortranCont ) || ( lowestlevel == 0 ) ) ) { /* We continue inside a bracket. */ AO.IsBracket = 1; if ( ( prtf & PRINTCONTENTS ) != 0 ) { AO.NumInBrack++; } else { if ( WriteInnerTerm(term,0) ) goto WrtTmes; if ( ( AO.PrintType & PRINTONETERM ) != 0 ) { FiniLine(); TokenToLine((UBYTE *)" "); } } return(0); } t = term + 1; n = WORDDIF(stopper,t); } /* Close the bracket */ if ( *lbrac ) { if ( ( prtf & PRINTCONTENTS ) ) PrtTerms(); TOKENTOLINE(" )",")") if ( AC.OutputMode == CMODE && AO.FactorMode == 0 ) TokenToLine((UBYTE *)";"); else if ( AO.FactorMode && ( n == 0 ) ) { /* This should not happen. */ return(0); } AC.IsFortran90 = ISNOTFORTRAN90; FiniLine(); AC.IsFortran90 = oldIsFortran90; if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE && AC.OutputSpaces == NORMALFORMAT && AO.FactorMode == 0 ) FiniLine(); } else { if ( AC.OutputMode == CMODE && AO.FactorMode == 0 ) TokenToLine((UBYTE *)";"); if ( AO.FortFirst == 0 ) { if ( !first ) { AC.IsFortran90 = ISNOTFORTRAN90; FiniLine(); AC.IsFortran90 = oldIsFortran90; } } } if ( AO.FactorMode == 0 ) { if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) && !first ) { WORD oldmode = AC.OutputMode; AC.OutputMode = 0; IniLine(0); AC.OutputMode = oldmode; AO.OutSkip = 7; if ( AO.FortFirst == 0 ) { TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") TokenToLine(AO.CurBufWrt); } else { AO.FortFirst = 0; TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") } } else if ( AC.OutputMode == CMODE && !first ) { IniLine(0); if ( AO.FortFirst == 0 ) { TokenToLine(AO.CurBufWrt); TOKENTOLINE(" += ","+=") } else { AO.FortFirst = 0; TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") } } else if ( startinline == 0 ) { IniLine(0); } AO.InFbrack = 0; if ( ( *lbrac = n ) > 0 ) { b = AO.bracket; *b++ = n + 4; while ( --n >= 0 ) *b++ = *t++; *b++ = 1; *b++ = 1; *b = 3; AO.IsBracket = 0; if ( WriteInnerTerm(AO.bracket,0) ) { /* Error message */ WORD i; WrtTmes: t = term; AO.OutSkip = 3; FiniLine(); i = *t; while ( --i >= 0 ) { TalToLine((UWORD)(*t++)); if ( AC.OutputSpaces == NORMALFORMAT ) TokenToLine((UBYTE *)" "); } AO.OutSkip = 0; FiniLine(); MesCall("WriteTerm"); SETERROR(-1) } TOKENTOLINE(" * ( ","*(") AO.NumInBrack = 0; AO.IsBracket = 1; if ( ( prtf & PRINTONETERM ) != 0 ) { first = 0; FiniLine(); TokenToLine((UBYTE *)" "); } else first = 1; } else { AO.IsBracket = 0; first = 0; } } else { /* Here is the code that writes the glue between two factors. We should not forget factors that are zero! */ if ( ( *lbrac = n ) > 0 ) { b = AO.bracket; *b++ = n + 4; while ( --n >= 0 ) *b++ = *t++; *b++ = 1; *b++ = 1; *b = 3; for ( i = AO.FactorNum+1; i < AO.bracket[4]; i++ ) { if ( first ) { TOKENTOLINE(" ( 0 )"," (0)") first = 0; } else { TOKENTOLINE(" * ( 0 )","*(0)") } FiniLine(); IniLine(0); } AO.FactorNum = AO.bracket[4]; } else { AO.NumInBrack = 0; return(0); } if ( first == 0 ) { TOKENTOLINE(" * ( ","*(") } else { TOKENTOLINE(" ( "," (") } AO.NumInBrack = 0; first = 1; } if ( ( prtf & PRINTCONTENTS ) != 0 ) AO.NumInBrack++; else if ( WriteInnerTerm(term,first) ) goto WrtTmes; if ( ( AO.PrintType & PRINTONETERM ) != 0 ) { FiniLine(); TokenToLine((UBYTE *)" "); } return(0); } else t += t[1]; } if ( *lbrac > 0 ) { if ( ( prtf & PRINTCONTENTS ) != 0 ) PrtTerms(); TokenToLine((UBYTE *)" )"); if ( AC.OutputMode == CMODE ) TokenToLine((UBYTE *)";"); if ( AO.FortFirst == 0 ) { AC.IsFortran90 = ISNOTFORTRAN90; FiniLine(); AC.IsFortran90 = oldIsFortran90; } if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE && AC.OutputSpaces == NORMALFORMAT ) FiniLine(); if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) && !first ) { WORD oldmode = AC.OutputMode; AC.OutputMode = 0; IniLine(0); AC.OutputMode = oldmode; AO.OutSkip = 7; if ( AO.FortFirst == 0 ) { TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") TokenToLine(AO.CurBufWrt); } else { AO.FortFirst = 0; TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") } /* TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") if ( AO.FortFirst == 0 ) TokenToLine(AO.CurBufWrt); else AO.FortFirst = 0; */ } else if ( AC.OutputMode == CMODE && !first ) { IniLine(0); if ( AO.FortFirst == 0 ) { TokenToLine(AO.CurBufWrt); TOKENTOLINE(" += ","+=") } else { AO.FortFirst = 0; TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") } /* TokenToLine(AO.CurBufWrt); if ( AO.FortFirst == 0 ) { TOKENTOLINE(" += ","+=") } else { TOKENTOLINE(" = ","=") AO.FortFirst = 0; } */ } else IniLine(0); *lbrac = 0; first = 1; } } if ( !br ) AO.IsBracket = 0; if ( ( AM.FortranCont > 0 && AO.InFbrack >= AM.FortranCont ) && lowestlevel ) { if ( AC.OutputMode == CMODE ) TokenToLine((UBYTE *)";"); if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) && !first ) { WORD oldmode = AC.OutputMode; if ( AO.FortFirst == 0 ) { AC.IsFortran90 = ISNOTFORTRAN90; FiniLine(); AC.IsFortran90 = oldIsFortran90; AC.OutputMode = 0; IniLine(0); AC.OutputMode = oldmode; AO.OutSkip = 7; TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") TokenToLine(AO.CurBufWrt); } else { AO.FortFirst = 0; /* TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") */ } /* TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") if ( AO.FortFirst == 0 ) TokenToLine(AO.CurBufWrt); else AO.FortFirst = 0; */ } else if ( AC.OutputMode == CMODE && !first ) { FiniLine(); IniLine(0); if ( AO.FortFirst == 0 ) { TokenToLine(AO.CurBufWrt); TOKENTOLINE(" += ","+=") } else { AO.FortFirst = 0; TokenToLine(AO.CurBufWrt); TOKENTOLINE(" = ","=") } /* TokenToLine(AO.CurBufWrt); if ( AO.FortFirst == 0 ) { TOKENTOLINE(" += ","+=") } else { TOKENTOLINE(" = ","=") AO.FortFirst = 0; } */ } else { FiniLine(); IniLine(0); } AO.InFbrack = 0; } if ( WriteInnerTerm(term,first) ) goto WrtTmes; if ( ( AO.PrintType & PRINTONETERM ) != 0 ) { FiniLine(); IniLine(0); } return(0); } /* #] WriteTerm : #[ WriteExpression : WORD WriteExpression(terms,ltot) Writes a subexpression to output. The subexpression is in terms and contains ltot words. This is only used for function arguments. */ int WriteExpression(WORD *terms, LONG ltot) { WORD *stopper; WORD first, btot; WORD OldIsBracket = AO.IsBracket, OldPrintType = AO.PrintType; if ( !AC.outsidefun ) { AO.PrintType &= ~PRINTONETERM; first = 1; } else first = 0; stopper = terms + ltot; btot = -1; while ( terms < stopper ) { AO.IsBracket = OldIsBracket; if ( WriteTerm(terms,&btot,first,0,1) ) { MesCall("WriteExpression"); SETERROR(-1) } first = 0; terms += *terms; } /* AO.IsBracket = 0; */ AO.IsBracket = OldIsBracket; AO.PrintType = OldPrintType; return(0); } /* #] WriteExpression : #[ WriteAll : WORD WriteAll() Writes all expressions that should be written */ int WriteAll(void) { GETIDENTITY WORD lbrac, first; WORD *t, *stopper, n, prtf; int oldIsFortran90 = AC.IsFortran90, i; POSITION pos; FILEHANDLE *f; EXPRESSIONS e; if ( AM.exitflag ) return(0); #ifdef WITHMPI if ( PF.me != MASTER ) { /* * For the slaves, we need to call Optimize() the same number of times * as the master. The first argument doesn't have any important role. */ for ( n = 0; n < NumExpressions; n++ ) { e = &Expressions[n]; if ( (!e->printflag) & PRINTON ) continue; switch ( e->status ) { case LOCALEXPRESSION: case GLOBALEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: break; default: continue; } e->printflag = 0; PutPreVar(AM.oldnumextrasymbols, GetPreVar((UBYTE *)"EXTRASYMBOLS_", 0), 0, 1); if ( AO.OptimizationLevel > 0 ) { if ( Optimize(0, 1) ) return(-1); } } return(0); } #endif SeekScratch(AR.outfile,&pos); if ( ResetScratch() ) { MesCall("WriteAll"); SETERROR(-1) } AO.termbuf = AT.WorkPointer; AO.bracket = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer*2); AO.OutFill = AO.OutputLine = (UBYTE *)AT.WorkPointer; AT.WorkPointer += 2*AC.LineLength; *(AR.CompressBuffer) = 0; first = 0; for ( n = 0; n < NumExpressions; n++ ) { if ( ( Expressions[n].printflag & PRINTON ) != 0 ) { first = 1; break; } } if ( !first ) goto EndWrite; AO.IsBracket = 0; AO.OutSkip = 3; AR.DeferFlag = 0; while ( GetTerm(BHEAD AO.termbuf) ) { t = AO.termbuf + 1; e = Expressions + AO.termbuf[3]; n = e->status; if ( ( n == LOCALEXPRESSION || n == GLOBALEXPRESSION || n == UNHIDELEXPRESSION || n == UNHIDEGEXPRESSION ) && ( ( prtf = e->printflag ) & PRINTON ) != 0 ) { e->printflag = 0; AO.NumInBrack = 0; PutPreVar(AM.oldnumextrasymbols, GetPreVar((UBYTE *)"EXTRASYMBOLS_",0),0,1); if ( ( prtf & PRINTLFILE ) != 0 ) { if ( AC.LogHandle < 0 ) prtf &= ~PRINTLFILE; } AO.PrintType = prtf; /* if ( AC.OutputMode == VORTRANMODE ) { UBYTE *oldOutFill = AO.OutFill, *oldOutputLine = AO.OutputLine; AO.OutSkip = 6; if ( Optimize(AO.termbuf[3], 1) ) goto AboWrite; AO.OutSkip = 3; AO.OutFill = oldOutFill; AO.OutputLine = oldOutputLine; FiniLine(); continue; } else */ if ( AO.OptimizationLevel > 0 ) { UBYTE *oldOutFill = AO.OutFill, *oldOutputLine = AO.OutputLine; AO.OutSkip = 6; if ( Optimize(AO.termbuf[3], 1) ) goto AboWrite; AO.OutSkip = 3; AO.OutFill = oldOutFill; AO.OutputLine = oldOutputLine; FiniLine(); continue; } if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) AO.OutSkip = 6; FiniLine(); AO.CurBufWrt = EXPRNAME(AO.termbuf[3]); TokenToLine(AO.CurBufWrt); stopper = t + t[1]; t += SUBEXPSIZE; if ( t < stopper ) { TokenToLine((UBYTE *)"("); first = 1; while ( t < stopper ) { n = *t; if ( !first ) TokenToLine((UBYTE *)","); switch ( n ) { case SYMTOSYM : TokenToLine(FindSymbol(t[2])); /* TokenToLine(VARNAME(symbols,t[2])); */ break; case VECTOVEC : TokenToLine(FindVector(t[2])); /* TokenToLine(VARNAME(vectors,t[2] - AM.OffsetVector)); */ break; case INDTOIND : TokenToLine(FindIndex(t[2])); /* TokenToLine(VARNAME(indices,t[2] - AM.OffsetIndex)); */ break; default : TokenToLine(FindFunction(t[2])); /* TokenToLine(VARNAME(functions,t[2] - FUNCTION)); */ break; } t += t[1]; first = 0; } TokenToLine((UBYTE *)")"); } TOKENTOLINE(" =","="); if ( AC.OutputMode == MATHEMATICAMODE ) { TOKENTOLINE(" (","("); } lbrac = 0; AO.InFbrack = 0; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) AO.FortFirst = 1; else AO.FortFirst = 0; first = 1; if ( ( e->vflags & ISFACTORIZED ) != 0 ) { AO.FactorMode = 1+e->numfactors; AO.FactorNum = 0; /* Which factor are we doing. For factors that are zero */ } else { AO.FactorMode = 0; } while ( GetTerm(BHEAD AO.termbuf) ) { WORD *m; GETSTOP(AO.termbuf,m); if ( ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) && ( ( prtf & PRINTONETERM ) != 0 ) ) {} else { if ( first ) { FiniLine(); IniLine(0); } } if ( ( prtf & PRINTONETERM ) != 0 ) first = 0; if ( WriteTerm(AO.termbuf,&lbrac,first,prtf,0) ) goto AboWrite; first = 0; } if ( AO.FactorMode ) { if ( first ) { AO.FactorNum = 1; TOKENTOLINE(" ( 0 )"," (0)") } else TOKENTOLINE(" )",")"); for ( i = AO.FactorNum+1; i <= e->numfactors; i++ ) { FiniLine(); IniLine(0); TOKENTOLINE(" * ( 0 )","*(0)"); } AO.FactorNum = e->numfactors; if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE ) TokenToLine((UBYTE *)";"); } else if ( AO.FactorMode == 0 || first ) { if ( first ) { TOKENTOLINE(" 0","0") } else if ( lbrac ) { if ( ( prtf & PRINTCONTENTS ) != 0 ) PrtTerms(); TOKENTOLINE(" )",")") } else if ( ( prtf & PRINTCONTENTS ) != 0 ) { TOKENTOLINE(" + 1 * ( ","+1*(") PrtTerms(); TOKENTOLINE(" )",")") } if ( AC.OutputMode == MATHEMATICAMODE ) { TokenToLine((UBYTE *)")"); } if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE ) TokenToLine((UBYTE *)";"); } AO.OutSkip = 3; AC.IsFortran90 = ISNOTFORTRAN90; FiniLine(); AC.IsFortran90 = oldIsFortran90; AO.FactorMode = 0; } else { do { } while ( GetTerm(BHEAD AO.termbuf) ); } } if ( AC.OutputSpaces == NORMALFORMAT ) FiniLine(); EndWrite: if ( AR.infile->handle >= 0 ) { SeekFile(AR.infile->handle,&(AR.infile->filesize),SEEK_SET); } AO.IsBracket = 0; AT.WorkPointer = AO.termbuf; SetScratch(AR.infile,&pos); f = AR.outfile; AR.outfile = AR.infile; AR.infile = f; return(0); AboWrite: SetScratch(AR.infile,&pos); f = AR.outfile; AR.outfile = AR.infile; AR.infile = f; MesCall("WriteAll"); Terminate(-1); return(-1); } /* #] WriteAll : #[ WriteOne : WORD WriteOne(name,alreadyinline) Writes one expression from the preprocessor */ int WriteOne(UBYTE *name, int alreadyinline, int nosemi, WORD plus) { GETIDENTITY WORD number; WORD lbrac, first; POSITION pos; FILEHANDLE *f; WORD prf; if ( GetName(AC.exprnames,name,&number,NOAUTO) != CEXPRESSION ) { MesPrint("@%s is not an expression",name); return(-1); } switch ( Expressions[number].status ) { case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: case HIDELEXPRESSION: case HIDEGEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: /* case DROPHLEXPRESSION: case DROPHGEXPRESSION: */ AR.GetFile = 2; break; case LOCALEXPRESSION: case GLOBALEXPRESSION: case SKIPLEXPRESSION: case SKIPGEXPRESSION: /* case DROPLEXPRESSION: case DROPGEXPRESSION: */ AR.GetFile = 0; break; default: MesPrint("@expressions %s is not active. It cannot be written",name); return(-1); } SeekScratch(AR.outfile,&pos); f = AR.outfile; AR.outfile = AR.infile; AR.infile = f; /* if ( ResetScratch() ) { MesCall("WriteOne"); SETERROR(-1) } */ if ( AR.GetFile == 2 ) f = AR.hidefile; else f = AR.infile; prf = Expressions[number].printflag; if ( plus ) prf |= PRINTONETERM; /* Now position the file */ if ( f->handle >= 0 ) { SetScratch(f,&(Expressions[number].onfile)); } else { f->POfill = (WORD *)((UBYTE *)(f->PObuffer) + BASEPOSITION(Expressions[number].onfile)); } AO.termbuf = AT.WorkPointer; AO.bracket = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer*2); AO.OutFill = AO.OutputLine = (UBYTE *)AT.WorkPointer; AT.WorkPointer += 2*AC.LineLength; *(AR.CompressBuffer) = 0; AO.IsBracket = 0; AO.OutSkip = 3; AR.DeferFlag = 0; if ( AC.OutputMode == FORTRANMODE || AC.OutputMode == PFORTRANMODE ) AO.OutSkip = 6; if ( GetTerm(BHEAD AO.termbuf) <= 0 ) { MesPrint("@ReadError in expression %s",name); goto AboWrite; } /* PutPreVar(AM.oldnumextrasymbols, GetPreVar((UBYTE *)"EXTRASYMBOLS_",0),0,1); */ /* * Currently WriteOne() is called only from writeToChannel() with setting * AO.OptimizationLevel = 0, which means Optimize() is never called here. * So we don't need to think about how to ensure that the master and the * slaves call Optimize() at the same time. (TU 26 Jul 2013) */ if ( AO.OptimizationLevel > 0 ) { AO.OutSkip = 6; if ( Optimize(AO.termbuf[3], 1) ) goto AboWrite; AO.OutSkip = 3; FiniLine(); } else { lbrac = 0; AO.InFbrack = 0; AO.FortFirst = 0; first = 1; while ( GetTerm(BHEAD AO.termbuf) ) { WORD *m; GETSTOP(AO.termbuf,m); if ( first ) { IniLine(0); startinline = alreadyinline; AO.OutFill = AO.OutputLine + startinline; if ( WriteTerm(AO.termbuf,&lbrac,first,0,0) ) goto AboWrite; first = 0; } else { if ( ( prf & PRINTONETERM ) != 0 ) first = 1; if ( first ) { FiniLine(); IniLine(0); } first = 0; if ( WriteTerm(AO.termbuf,&lbrac,first,0,0) ) goto AboWrite; } } if ( first ) { IniLine(0); startinline = alreadyinline; AO.OutFill = AO.OutputLine + startinline; TOKENTOLINE(" 0","0"); } else if ( lbrac ) { TOKENTOLINE(" )",")"); } if ( AC.OutputMode != FORTRANMODE && AC.OutputMode != PFORTRANMODE && nosemi == 0 ) TokenToLine((UBYTE *)";"); AO.OutSkip = 3; if ( AC.OutputSpaces == NORMALFORMAT && nosemi == 0 ) { FiniLine(); } else { noextralinefeed = 1; FiniLine(); noextralinefeed = 0; } } AO.IsBracket = 0; AT.WorkPointer = AO.termbuf; SetScratch(f,&pos); f = AR.outfile; AR.outfile = AR.infile; AR.infile = f; AO.InFbrack = 0; return(0); AboWrite: SetScratch(AR.infile,&pos); f->POposition = pos; f = AR.outfile; AR.outfile = AR.infile; AR.infile = f; MesCall("WriteOne"); Terminate(-1); return(-1); } /* #] WriteOne : #] schryf-Writes : */ form-5.0.1/sources/lus.c0000644000175100017510000012174215217035721010607 /** @file lus.c * * Routines to find loops in index contractions. * These routines allow for a category of topological statements. * They were originally developed for the color library. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : lus.c */ #include "form3.h" /* #] Includes : #[ Lus : Routine to find loops. Mode: 0: Just tell whether there is such a loop. 1: Take out the functions and replace by outfun with the remaining arguments of the loop function > AM.OffsetIndex: This index must be included in the loop. < -AM.OffsetIndex: This index must be included in the loop. Replace. Return value: 0: no loop. 1: there is/was such a loop. funnum: the function(s) in which we look for a loop. numargs: the number of arguments admissible in the function. outfun: the output function in case of a substitution. loopsize: the size of the loop we are looking for. if < 0 we look for all loops. */ int Lus(WORD *term, WORD funnum, WORD loopsize, WORD numargs, WORD outfun, WORD mode) { GETIDENTITY WORD *w, *t, *tt, *m, *r, **loc, *tstop, minloopsize; int nfun, i, j, jj, k, n, sign = 0, action = 0, L, ten, ten2, totnum, sign2, *alist, *wi, mini, maxi, medi = 0; if ( numargs <= 1 ) return(0); GETSTOP(term,tstop); /* First count the number of functions with the proper number of arguments. */ t = term+1; nfun = 0; if ( ( ten = functions[funnum-FUNCTION].spec ) >= TENSORFUNCTION ) { while ( t < tstop ) { if ( *t == funnum && t[1] == FUNHEAD+numargs ) { nfun++; } t += t[1]; } } else { while ( t < tstop ) { if ( *t == funnum ) { i = 0; m = t+FUNHEAD; t += t[1]; while ( m < t ) { i++; NEXTARG(m) } if ( i == numargs ) nfun++; } else t += t[1]; } } if ( loopsize < 0 ) minloopsize = 2; else minloopsize = loopsize; if ( funnum < minloopsize ) return(0); /* quick abort */ if ( ((functions[funnum-FUNCTION].symmetric) & ~REVERSEORDER) == ANTISYMMETRIC ) sign = 1; if ( mode == 1 || mode < 0 ) { ten2 = functions[outfun-FUNCTION].spec >= TENSORFUNCTION; } else ten2 = -1; /* Allocations: */ if ( AN.numflocs < funnum ) { if ( AN.funlocs ) M_free(AN.funlocs,"Lus: AN.funlocs"); AN.numflocs = funnum; AN.funlocs = (WORD **)Malloc1(sizeof(WORD *)*AN.numflocs,"Lus: AN.funlocs"); } if ( AN.numfargs < funnum*numargs ) { if ( AN.funargs ) M_free(AN.funargs,"Lus: AN.funargs"); AN.numfargs = funnum*numargs; AN.funargs = (int *)Malloc1(sizeof(int *)*AN.numfargs,"Lus: AN.funargs"); } /* Make a list of relevant indices */ alist = AN.funargs; loc = AN.funlocs; t = term+1; if ( ten >= TENSORFUNCTION ) { while ( t < tstop ) { if ( *t == funnum && t[1] == FUNHEAD+numargs ) { *loc++ = t; t += FUNHEAD; j = i = numargs; while ( --i >= 0 ) { if ( *t >= AM.OffsetIndex && ( *t >= AM.OffsetIndex+WILDOFFSET || indices[*t-AM.OffsetIndex].dimension != 0 ) ) { *alist++ = *t++; j--; } else t++; } while ( --j >= 0 ) *alist++ = -1; } else t += t[1]; } } else { nfun = 0; while ( t < tstop ) { if ( *t == funnum ) { w = t; i = 0; m = t+FUNHEAD; t += t[1]; while ( m < t ) { i++; NEXTARG(m) } if ( i == numargs ) { m = w + FUNHEAD; while ( m < t ) { if ( *m == -INDEX && m[1] >= AM.OffsetIndex && ( m[1] >= AM.OffsetIndex+WILDOFFSET || indices[m[1]-AM.OffsetIndex].dimension != 0 ) ) { *alist++ = m[1]; m += 2; i--; } else if ( ten2 >= TENSORFUNCTION && *m != -INDEX && *m != -VECTOR && *m != -MINVECTOR && ( *m != -SNUMBER || *m < 0 || *m >= AM.OffsetIndex ) ) { i = numargs; break; } else { NEXTARG(m) } } if ( i < numargs ) { *loc++ = w; nfun++; while ( --i >= 0 ) *alist++ = -1; } } } else t += t[1]; } if ( nfun < minloopsize ) return(0); } /* We have now nfun objects. Not all indices may be usable though. If the list is not long, we use a quadratic algorithm to remove indices and vertices that cannot be used. If it becomes large we sort the list of available indices (and their multiplicity) and work with binary searches. */ alist = AN.funargs; totnum = numargs*nfun; if ( nfun > 7 ) { if ( AN.funisize < totnum ) { if ( AN.funinds ) M_free(AN.funinds,"AN.funinds"); AN.funisize = (totnum*3)/2; AN.funinds = (int *)Malloc1(AN.funisize*2*sizeof(int),"AN.funinds"); } i = totnum; n = 0; wi = AN.funinds; while ( --i >= 0 ) { if ( *alist >= 0 ) { n++; *wi++ = *alist; *wi++ = 1; } alist++; } n = SortTheList(AN.funinds,n); do { action = 0; for ( i = 0; i < nfun; i++ ) { alist = AN.funargs + i*numargs; jj = numargs; for ( j = 0; j < jj; j++ ) { if ( alist[j] < 0 ) break; mini = 0; maxi = n-1; while ( mini <= maxi ) { medi = (mini + maxi) / 2; k = AN.funinds[2*medi]; if ( alist[j] > k ) mini = medi + 1; else if ( alist[j] < k ) maxi = medi - 1; else break; } if ( AN.funinds[2*medi+1] <= 1 ) { (AN.funinds[2*medi+1])--; jj--; k = j; while ( k < jj ) { alist[k] = alist[k+1]; k++; } alist[jj] = -1; j--; } } if ( jj < 2 ) { if ( jj == 1 ) { mini = 0; maxi = n-1; while ( mini <= maxi ) { medi = (mini + maxi) / 2; k = AN.funinds[2*medi]; if ( alist[0] > k ) mini = medi + 1; else if ( alist[0] < k ) maxi = medi - 1; else break; } (AN.funinds[2*medi+1])--; if ( AN.funinds[2*medi+1] == 1 ) action++; } nfun--; totnum -= numargs; AN.funlocs[i] = AN.funlocs[nfun]; wi = AN.funargs + nfun*numargs; for ( j = 0; j < numargs; j++ ) alist[j] = *wi++; i--; } } } while ( action ); } else { for ( i = 0; i < totnum; i++ ) { if ( alist[i] == -1 ) continue; for ( j = 0; j < totnum; j++ ) { if ( alist[j] == alist[i] && j != i ) break; } if ( j >= totnum ) alist[i] = -1; } do { action = 0; for ( i = 0; i < nfun; i++ ) { alist = AN.funargs + i*numargs; n = numargs; for ( k = 0; k < n; k++ ) { if ( alist[k] < 0 ) { alist[k--] = alist[--n]; alist[n] = -1; } } if ( n <= 1 ) { if ( n == 1 ) { j = alist[0]; } else j = -1; nfun--; totnum -= numargs; AN.funlocs[i] = AN.funlocs[nfun]; wi = AN.funargs + nfun * numargs; for ( k = 0; k < numargs; k++ ) alist[k] = wi[k]; i--; if ( j >= 0 ) { for ( k = 0, jj = 0, wi = AN.funargs; k < totnum; k++, wi++ ) { if ( *wi == j ) { jj++; if ( jj > 1 ) break; } } if ( jj <= 1 ) { for ( k = 0, wi = AN.funargs; k < totnum; k++, wi++ ) { if ( *wi == j ) { *wi = -1; action = 1; } } } } } } } while ( action ); } if ( nfun < minloopsize ) return(0); /* Now we have nfun objects, each with at least 2 indices, each of which occurs at least twice in our list. There will be a loop! */ if ( mode != 0 && mode != 1 ) { if ( mode > 0 ) AN.tohunt = mode - 5; else AN.tohunt = -mode - 5; AN.nargs = numargs; AN.numoffuns = nfun; i = 0; if ( loopsize < 0 ) { if ( loopsize == -1 ) k = nfun; else { k = -loopsize-1; if ( k > nfun ) k = nfun; } for ( L = 2; L <= k; L++ ) { if ( FindLus(0,L,AN.tohunt) ) goto Success; } } else if ( FindLus(0,loopsize,AN.tohunt) ) { L = loopsize; goto Success; } } else { AN.nargs = numargs; AN.numoffuns = nfun; if ( loopsize < 0 ) { jj = 2; k = nfun; if ( loopsize < -1 ) { k = -loopsize-1; if ( k > nfun ) k = nfun; } } else { jj = k = loopsize; } for ( L = jj; L <= k; L++ ) { for ( i = 0; i <= nfun-L; i++ ) { alist = AN.funargs + i * numargs; for ( jj = 0; jj < numargs; jj++ ) { if ( alist[jj] < 0 ) continue; AN.tohunt = alist[jj]; for ( j = jj+1; j < numargs; j++ ) { if ( alist[j] < 0 ) continue; if ( FindLus(i+1,L-1,alist[j]) ) { alist[0] = alist[jj]; alist[1] = alist[j]; goto Success; } } } } } } return(0); Success:; if ( mode == 0 || mode > 1 ) return(1); /* Now we have to make the replacement and fix the potential sign */ sign2 = 1; wi = AN.funargs + i*numargs; loc = AN.funlocs + i; for ( k = 0; k < L; k++ ) *(loc[k]) = -1; if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; w = AT.WorkPointer + 1; m = t = term + 1; while ( t < tstop ) { if ( *t == -1 ) break; t += t[1]; } while ( m < t ) *w++ = *m++; r = w; *w++ = outfun; w++; *w++ = DIRTYFLAG; FILLFUN3(w) if ( functions[outfun-FUNCTION].spec >= TENSORFUNCTION ) { if ( ten >= TENSORFUNCTION ) { for ( i = 0; i < L; i++ ) { alist = wi + i*numargs; m = loc[i] + FUNHEAD; for ( k = 0; k < numargs; k++ ) { if ( m[k] == alist[0] ) { if ( k != 0 ) { jj = m[k]; m[k] = m[0]; m[0] = jj; sign = -sign; } break; } } for ( k = 1; k < numargs; k++ ) { if ( m[k] == alist[1] ) { if ( k != 1 ) { jj = m[k]; m[k] = m[1]; m[1] = jj; sign = -sign; } break; } } m += 2; for ( k = 2; k < numargs; k++ ) *w++ = *m++; } } else { WORD *t1, *t2, *t3; for ( i = 0; i < L; i++ ) { alist = wi + i*numargs; tt = loc[i]; m = tt + FUNHEAD; for ( k = 0; k < numargs; k++ ) { if ( *m == -INDEX && m[1] == alist[0] ) { if ( k != 0 ) { if ( ( k & 1 ) != 0 ) sign = -sign; /* now move to position 0 */ t2 = m+2; t1 = m; t3 = tt+FUNHEAD; while ( t1 > t3 ) { *--t2 = *--t1; } t3[0] = -INDEX; t3[1] = alist[0]; } break; } NEXTARG(m) } m = tt + FUNHEAD + 2; for ( k = 1; k < numargs; k++ ) { if ( *m == -INDEX && m[1] == alist[1] ) { if ( k != 1 ) { if ( ( k & 1 ) == 0 ) sign = -sign; /* now move to position 1 */ t2 = m+2; t1 = m; t3 = tt+FUNHEAD+2; while ( t1 > t3 ) { *--t2 = *--t1; } t3[0] = -INDEX; t3[1] = alist[1]; } break; } NEXTARG(m) } /* now copy the remaining arguments to w keep in mind that the output function is a tensor! */ t1 = tt + FUNHEAD + 4; t2 = tt + tt[1]; while ( t1 < t2 ) { if ( *t1 == -INDEX || *t1 == -VECTOR ) { *w++ = t1[1]; t1 += 2; } else if ( *t1 == -MINVECTOR ) { *w++ = t1[1]; t1 += 2; sign2 = -sign2; } else if ( ( *t1 == -SNUMBER ) && ( t1[1] >= 0 ) && ( t1[1] < AM.OffsetIndex ) ) { *w++ = t1[1]; t1 += 2; sign2 = -sign2; } else { MLOCK(ErrorMessageLock); MesPrint("Illegal attempt to use a non-index-like argument in a tensor in ReplaceLoop statement"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } } } } else { if ( ten >= TENSORFUNCTION ) { for ( i = 0; i < L; i++ ) { alist = wi + i*numargs; m = loc[i] + FUNHEAD; for ( k = 0; k < numargs; k++ ) { if ( m[k] == alist[0] ) { if ( k != 0 ) { jj = m[k]; m[k] = m[0]; m[0] = jj; sign = -sign; break; } } } for ( k = 1; k < numargs; k++ ) { if ( m[k] == alist[1] ) { if ( k != 1 ) { jj = m[k]; m[k] = m[1]; m[1] = jj; sign = -sign; break; } } } m += 2; for ( k = 2; k < numargs; k++ ) { if ( *m >= AM.OffsetIndex ) { *w++ = -INDEX; } else if ( *m < 0 ) { *w++ = -VECTOR; } else { *w = -SNUMBER; } *w++ = *m++; } } } else { WORD *t1, *t2, *t3; for ( i = 0; i < L; i++ ) { alist = wi + i*numargs; tt = loc[i]; m = tt + FUNHEAD; for ( k = 0; k < numargs; k++ ) { if ( *m == -INDEX && m[1] == alist[0] ) { if ( k != 0 ) { if ( ( k & 1 ) != 0 ) sign = -sign; /* now move to position 0 */ t2 = m+2; t1 = m; t3 = tt+FUNHEAD; while ( t1 > t3 ) { *--t2 = *--t1; } t3[0] = -INDEX; t3[1] = alist[0]; } break; } NEXTARG(m) } m = tt + FUNHEAD + 2; for ( k = 1; k < numargs; k++ ) { if ( *m == -INDEX && m[1] == alist[1] ) { if ( k != 1 ) { if ( ( k & 1 ) == 0 ) sign = -sign; /* now move to position 1 */ t2 = m+2; t1 = m; t3 = tt+FUNHEAD+2; while ( t1 > t3 ) { *--t2 = *--t1; } t3[0] = -INDEX; t3[1] = alist[1]; } break; } NEXTARG(m) } /* now copy the remaining arguments to w */ t1 = tt + FUNHEAD + 4; t2 = tt + tt[1]; while ( t1 < t2 ) *w++ = *t1++; } } } r[1] = w-r; while ( t < tstop ) { if ( *t == -1 ) { t += t[1]; continue; } i = t[1]; NCOPY(w,t,i) } tstop = term + *term; while ( t < tstop ) *w++ = *t++; if ( sign < 0 ) w[-1] = -w[-1]; i = w - AT.WorkPointer; *AT.WorkPointer = i; t = term; w = AT.WorkPointer; NCOPY(t,w,i) *AN.RepPoint = 1; /* For Repeat */ return(1); } /* #] Lus : #[ FindLus : */ int FindLus(int from, int level, int openindex) { GETIDENTITY int i, j, k, jj, *alist, *blist, *w, *m, partner; WORD **loc = AN.funlocs, *wor; if ( level == 1 ) { for ( i = from; i < AN.numoffuns; i++ ) { alist = AN.funargs + i*AN.nargs; for ( j = 0; j < AN.nargs; j++ ) { if ( alist[j] == openindex ) { for ( k = 0; k < AN.nargs; k++ ) { if ( k == j ) continue; if ( alist[k] == AN.tohunt ) { loc[from] = loc[i]; alist = AN.funargs + from*AN.nargs; alist[0] = openindex; alist[1] = AN.tohunt; return(1); } } } } } } else { for ( i = from; i < AN.numoffuns; i++ ) { alist = AN.funargs + i*AN.nargs; for ( j = 0; j < AN.nargs; j++ ) { if ( alist[j] == openindex ) { if ( from != i ) { wor = loc[i]; loc[i] = loc[from]; loc[from] = wor; blist = w = AN.funargs + from*AN.nargs; m = alist; k = AN.nargs; while ( --k >= 0 ) { jj = *m; *m++ = *w; *w++ = jj; } } else blist = alist; for ( k = 0; k < AN.nargs; k++ ) { if ( k == j || blist[k] < 0 ) continue; partner = blist[k]; if ( FindLus(from+1,level-1,partner) ) { blist[0] = openindex; blist[1] = partner; return(1); } } if ( from != i ) { wor = loc[i]; loc[i] = loc[from]; loc[from] = wor; w = AN.funargs + from*AN.nargs; m = alist; k = AN.nargs; while ( --k >= 0 ) { jj = *m; *m++ = *w; *w++ = jj; } } } } } } return(0); } /* #] FindLus : #[ SortTheList : */ int SortTheList(int *slist, int num) { GETIDENTITY int i, nleft, nright, *t1, *t2, *t3, *rlist; if ( num <= 2 ) { if ( num <= 1 ) return(num); if ( slist[0] < slist[2] ) return(2); if ( slist[0] > slist[2] ) { i = slist[0]; slist[0] = slist[2]; slist[2] = i; i = slist[1]; slist[1] = slist[3]; slist[3] = i; return(2); } slist[1] += slist[3]; return(1); } else { nleft = num/2; rlist = slist + 2*nleft; nright = SortTheList(rlist,num-nleft); nleft = SortTheList(slist,nleft); if ( AN.tlistsize < nleft ) { if ( AN.tlistbuf ) M_free(AN.tlistbuf,"AN.tlistbuf"); AN.tlistsize = (nleft*3)/2; AN.tlistbuf = (int *)Malloc1(AN.tlistsize*2*sizeof(int),"AN.tlistbuf"); } i = nleft; t1 = slist; t2 = AN.tlistbuf; while ( --i >= 0 ) { *t2++ = *t1++; *t2++ = *t1++; } i = nleft+nright; t1 = AN.tlistbuf; t2 = rlist; t3 = slist; while ( nleft > 0 && nright > 0 ) { if ( *t1 < *t2 ) { *t3++ = *t1++; *t3++ = *t1++; nleft--; } else if ( *t1 > *t2 ) { *t3++ = *t2++; *t3++ = *t2++; nright--; } else { *t3++ = *t1++; t2++; *t3++ = (*t1++) + (*t2++); i--; nleft--; nright--; } } while ( --nleft >= 0 ) { *t3++ = *t1++; *t3++ = *t1++; } while ( --nright >= 0 ) { *t3++ = *t2++; *t3++ = *t2++; } return(i); } } /* #] SortTheList : #[ AllLoops : Routine finds all possible loops that can be made in the arguments of the symmetric commuting vertex function v and creates for each loop a new term which is the original term times the loop. The occurrences of v can have different numbers of arguments. Each argument that occurs twice (and in different instances of v) in total will be considered. The input parameters are in C->lhs[level] and are C->lhs[level][0] TYPEALLLOOPS C->lhs[level][1] 6 C->lhs[level][2] Number of function v. C->lhs[level][3] Number of the output function loop. C->lhs[level][4] option1: the type of argument. C->lhs[level][5] option2: 0,1: what to do if no loop. Eligible arguments must be of the type SYMBOL, VECTOR, INDEX or SNUMBER. They must all be of the same type, indicated by option1. Extra restriction: In a loop, each v can be visited at most once. If there is no loop at all, option2 determines whether the term remains unmodified, or is replaced by zero. Function v can be either a regular function or a tensor. To facilitate this we copy the relevant arguments into the workspace. */ int AllLoops(PHEAD WORD *term,WORD level) { CBUF *C = cbuf+AM.rbufnum; WORD vcode = C->lhs[level][2]; /* The input function */ WORD option1 = C->lhs[level][4]; /* type of argument */ WORD option2 = C->lhs[level][5]; /* what to do when no loop */ WORD *tstop, *t, *tend, *tstart, *tfrom; WORD i, j, jj; WORD *arglist, nargs, *loop, nloop; WORD *oldworkpointer = AT.WorkPointer; LONG oldpworkpointer = AT.pWorkPointer; LONG numgenerated = 0, vert; WORD *a, *a1, *a2, *a3, *v, *vv, nvert, *to, *from, *tos, action; /* Search for the first occurrence of vcode. */ tstop = term+*term; tstop -= ABS(tstop[-1]); t = term + 1; while ( t < tstop && *t != vcode ) t += t[1]; if ( t == tstop ) { if ( option2 == 0 ) return(0); else return(Generator(BHEAD term,level)); } tstart = t; nvert = 0; do { t += t[1]; nvert++; } while ( t < tstop && *t == vcode ); tend = t; /* Make room for 2*nvert pointers */ WantAddPointers(2*nvert); vert = AT.pWorkPointer; AT.pWorkPointer += 2*nvert; nvert = 0; /* Next we copy these functions into the workspace, but only the arguments that agree with option1. Because of the difference between tensors and regular functions in the copy we strip the type of the argument. */ to = AT.WorkPointer; from = tstart; if ( functions[vcode-FUNCTION].spec == TENSORFUNCTION ) { from = tstart; while ( from < tend ) { tos = to++; tfrom = from+from[1]; from += FUNHEAD; while ( from < tfrom ) { if ( option1 == -INDEX && *from >= 0 ) { *to++ = *from++; } else if ( option1 == -VECTOR && *from < 0 ) { *to++ = *from++ - AM.OffsetVector; } else { from++; } } *tos = to-from; if ( *tos < 3 ) to = tos; else AT.pWorkSpace[vert+nvert++] = tos; } } else if ( functions[vcode-FUNCTION].spec == 0 ) { from = tstart; while ( from < tend ) { tos = to++; tfrom = from + from[1]; from += FUNHEAD; while ( from < tfrom ) { if ( option1 == -VECTOR && ( from[0] == -INDEX || from[0] == -VECTOR ) && from[1] < 0 ) { from++; *to++ = *from++ - AM.OffsetVector; } else if ( option1 == *from ) { from++; *to++ = *from++; } else { NEXTARG(from); } } *tos = to-tos; if ( *tos < 3 ) to = tos; else AT.pWorkSpace[vert+nvert++] = tos; } } else { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oldpworkpointer; if ( option2 == 0 ) return(0); return(Generator(BHEAD term,level)); } AT.WorkPointer = to; /* Now make a list of all relevant arguments. */ a = arglist = AT.WorkPointer; for ( i = 0; i < nvert; i++ ) { v = AT.pWorkSpace[vert+i]; j = *v-1; v++; NCOPY(a,v,j); } nargs = a-arglist; AT.WorkPointer = a; /* Now sort the list. Bubble type sort. */ a1 = arglist; a2 = a1+1; while ( a2 < a ) { a3 = a2; while ( a3 > a1 && a3[-1] > a3[0] ) { EXCH(*a3,a3[-1]); a3--; } a2++; } /* Now remove the elements from the list that do not occur exactly twice. */ a1 = arglist; a2 = a1; a3 = a1+nargs; while ( a2 < a3 ) { if ( a2+1 == a3 ) { break; } else if ( a2+2 == a3 ) { if ( a2[0] == a2[1] ) { *a1++ = a2[0]; } break; } else { if ( a2[0] != a2[1] ) { a2++; } else if ( a2[0] != a2[2] ) { *a1++ = a2[0]; a2 += 2; } else { a2++; while ( a2 < a3 && a2[-1] == a2[0] ) a2++; } } } nargs = a1-arglist; /* Now we need to redo the list of vertices and remove the elements that are not in our arglist. */ do { action = 0; for ( i = 0; i < nvert; i++ ) { vv = v = AT.pWorkSpace[vert+i]; v++; for ( j = 1; j < vv[0]; j++ ) { for ( jj = 0; jj < nargs; jj++ ) { if ( *v == arglist[jj] ) break; } if ( jj >= nargs ) { /* was not in the list */ vv[0] = vv[0]-1; for ( jj = j; jj < vv[0]; jj++ ) vv[jj] = vv[jj+1]; } v++; } } /* Next we need to remove vertices that have only one object remaining. Also, the object can be removed from arglist. After that we go back to clean up the list. */ for ( i = 0; i < nvert; i++ ) { vv = AT.pWorkSpace[vert+i]; if ( vv[0] == 1 ) { AT.pWorkSpace[vert+i] = AT.pWorkSpace[vert+nvert-1]; nvert--; i--; continue; } else if ( vv[0] == 2 ) { for ( j = 0; j < nargs; j++ ) { if ( arglist[j] == vv[1] ) break; } while ( j < nargs-1 ) arglist[j] = arglist[j+1]; nargs--; AT.pWorkSpace[vert+i] = AT.pWorkSpace[vert+nvert-1]; nvert--; i--; action = 1; } } } while ( action ); /* Because the user can remove tadpoles rather easily as in id v(?a,i?,?b,i?,?c) = v(?a,?b,?c) there is no need to avoid them as potential loops. At this point we are ready to look for loops. We have arglist,nargs list of eligible objects. vert,nvert position in pWorkSpace for vertices and their number. The vertices themselves are in the WorkSpace. loop,nloop The buildup of the loop. */ loop = AT.WorkPointer; AT.WorkPointer += nargs; nloop = 0; numgenerated += StartLoops(BHEAD term,level,vert,nvert,arglist,nargs,loop,nloop); AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oldpworkpointer; if ( numgenerated == 0 && option2 != 0 ) return(Generator(BHEAD term,level)); return(0); } /* #] AllLoops : #[ StartLoops : Algorithm. 1: have a list of vertices and objects that can be part of the loops. 2: starting with the first element of arglist, look for the two vertices that contain this object. The first is vstart. 3: At the second, look at all possible objects to continue from here. 4: For each, find the vertex with its partner. 5: if the partner vertex is vstart, we have a loop. --> 9. 6: The partner vertex is not allowed to be a vertex that we passed in the current build-up of the loop. 7: Put the object in loop and increase nloop. 8: Now sum over all allowed objects in the partner vertex. --> 4. 9: Create the function loop with the arguments from loop,nloop. 10: If a reverse cyclic permutation gives a smaller result, drop this solution and continue with the last summing over objects at a vertex. 11: If not, output the result by adding the function loop to the term and call Generator(term,level) 12: when all possibilities with the first element of arglist have been exhausted, raise arglist and lower nargs by one. --> 2 13: when nargs == 1, we can stop. The inclusion of a new object when we sum over the possibilities at a vertex can best be done in a recursion, because we have no idea how many nested loops we would otherwise need. Of course the recursion can be emulated, but that makes the algorithm rather messy. We have two routines: StartLoops and GenLoops. StartLoops takes care of the first argument (and the summing over who is the first argument), while GenLoops treats an additional vertex until a loop is closed. GenLoops also sends completed loops off toe Generator. */ LONG StartLoops(PHEAD WORD *term,WORD level,LONG vert,WORD nvert, WORD *arglist,WORD nargs,WORD *loop,WORD nloop) { LONG numgenerated = 0; WORD *v, *vv, *vstart, istart, *vpartner, ipartner, j; while ( nargs > 1 ) { /* Look for a vertex with arglist[0]. This is our starting vertex. Next we look for its partner and we put arglist[0] in loop. */ nloop = 0; loop[nloop++] = arglist[0]; for ( istart = 0; istart < nvert; istart++ ) { vstart = AT.pWorkSpace[vert+istart]; v = vstart+1; vv = vstart + *vstart; do { if ( *v == arglist[0] ) goto havestart; v++; } while ( v < vv ); } /* If we come here, we have a problem. */ MesPrint("Internal error in StartLoops. Object not found."); Terminate(-1); return(-1); havestart: AT.pWorkSpace[vert+nvert] = vstart; /* Check for tadpole. */ v++; while ( v < vv ) { if ( *v == arglist[0] ) { /* tadpole */ LoopOutput(BHEAD term,level,loop,nloop); numgenerated++; goto nextarg; } v++; } /* Now the partner vertex. */ for ( ipartner = istart+1; ipartner < nvert; ipartner++ ) { vpartner = AT.pWorkSpace[vert+ipartner]; vv = vpartner+*vpartner; v = vpartner+1; do { if ( *v == arglist[0] ) goto havepartner; v++; } while ( v < vv ); } return(numgenerated); havepartner: AT.pWorkSpace[vert+nvert+1] = vpartner; /* Now we run through all other possibilities at vpartner. vv is still OK. */ v = vpartner+1; while ( v < vv ) { if ( *v != arglist[0] ) { for ( j = 1; j < nargs; j++ ) { if ( *v == arglist[j] ) { loop[nloop++] = *v; numgenerated += GenLoops(BHEAD term,level,vert,nvert, arglist,nargs,loop,nloop); nloop--; break; } } } v++; } nextarg: arglist++; nargs--; } return(numgenerated); } /* #] StartLoops : #[ GenLoops : We enter with an open line in loop[nloop-1] */ LONG GenLoops(PHEAD WORD *term,WORD level,LONG vert,WORD nvert, WORD *arglist,WORD nargs,WORD *loop,WORD nloop) { LONG numgenerated = 0; WORD *vstart, *v, *vv, i, j, *vpartner; /* Start with checking whether the partner is in vstart (=vert[nvert]) */ vstart = AT.pWorkSpace[nvert]; vv = vstart + *vstart; v = vstart+1; while ( v < vv ) { if ( *v == loop[nloop-1] ) { /* This closes the loop. Now we can output it. */ LoopOutput(BHEAD term,level,loop,nloop); numgenerated++; return(numgenerated); } v++; } /* Start with finding the partner. */ for ( i = 0; i < nvert; i++ ) { vpartner = AT.pWorkSpace[vert+i]; if ( vpartner == vstart ) continue; for ( j = 0; j < nloop; j++ ) { if ( vpartner == AT.pWorkSpace[vert+nvert+j] ) break; } if ( j < nloop ) continue; v = vpartner+1; vv = vpartner + *vpartner; while ( v < vv ) { if ( *v == loop[nloop-1] ) { /* Found the partner. Now we can sum over the remaining permitted arguments of this vertex. */ v = vpartner + 1; while ( v < vv ) { /* *v should be in arglist. */ for ( j = 0; j < nargs; j++ ) { if ( *v == arglist[j] ) break; } if ( j >= nargs ) { v++; continue; } /* *v should not be in loops. */ for ( j = 0; j < nloop; j++ ) { if ( *v == loop[j] ) break; } if ( j >= nloop ) { AT.pWorkSpace[vert+nvert+nloop] = vpartner; loop[nloop++] = *v; numgenerated += GenLoops(BHEAD term,level,vert,nvert, arglist,nargs,loop,nloop); nloop--; } v++; } return(numgenerated); } v++; } } /* The partner is in a vertex we have finished before. */ return(numgenerated); } /* #] GenLoops : #[ LoopOutput : */ void LoopOutput(PHEAD WORD *term, WORD level, WORD *loop, WORD nloop) { CBUF *C = cbuf+AM.rbufnum; WORD loopfun = C->lhs[level][3]; /* The output function */ WORD option1 = C->lhs[level][4]; /* type of argument */ WORD *tstop, *tstop1, *t, *tt; WORD *outterm, *loop1; WORD i; tstop1 = term+*term; tstop = tstop1 - ABS(tstop1[-1]); /* Construct the rcycle symmetrized version of loop. */ if ( nloop > 2 ) { loop1 = AT.WorkPointer; loop1[0] = loop[0]; for ( i = 1; i < nloop; i++ ) { loop1[i] = loop[nloop-i]; } if ( loop1[1] < loop[1] ) { AT.WorkPointer += nloop; loop = loop1; } } outterm = AT.WorkPointer; tt = outterm; t = term; while ( t < tstop ) *tt++ = *t++; *tt++ = loopfun; if ( functions[loopfun-FUNCTION].spec == TENSORFUNCTION ) { *tt++ = FUNHEAD+nloop; FILLFUN(tt) if ( option1 == -VECTOR ) { for ( i = 0; i < nloop; i++ ) *tt++ = loop[i]+AM.OffsetVector; } else { for ( i = 0; i < nloop; i++ ) *tt++ = loop[i]; } } else { *tt++ = FUNHEAD+nloop*2; FILLFUN(tt) for ( i = 0; i< nloop; i++ ) { *tt++ = option1; if ( option1 == -VECTOR ) *tt++ = loop[i] + AM.OffsetVector; else *tt++ = loop[i]; } } while ( t < tstop1 ) *tt++ = *t++; *outterm = tt - outterm; AT.WorkPointer = tt; if ( Generator(BHEAD outterm,level) ) { MesCall("LoopOutput"); Terminate(-1); } AT.WorkPointer = outterm; } /* #] LoopOutput : #[ AllPaths : This routine has many similarities with AllLoops. In AllLoops we have startingpoint and endpoint at the same vertex. In AllPaths the startingpoint and the endpoints are different and given in advance. This endfun can occur only twice. */ int AllPaths(PHEAD WORD *term,WORD level) { CBUF *C = cbuf+AM.rbufnum; WORD endcode = C->lhs[level][2]; /* The endpoint function */ WORD vcode = C->lhs[level][3]; /* The intermediate function */ WORD option1 = C->lhs[level][5]; /* type of argument */ WORD option2 = C->lhs[level][6]; /* what to do when no loop */ WORD *t, *tstop, *tend1, *tend2, *tstart, *tend, numend, nvert, npass; WORD *tfrom, *to, *tos, *from; WORD *arglist, nargs, *path, npath, *a, *a1, *a2, *a3; WORD i, j, jj, *v, *vv, action; LONG vert,vert1; /* ,vert2; */ WORD numgenerated = 0; WORD *oldworkpointer = AT.WorkPointer; LONG oldpworkpointer = AT.pWorkPointer; /* Search for the two occurrences of endcode. */ tstop = term+*term; tstop -= ABS(tstop[-1]); t = term + 1; while ( t < tstop && *t != endcode ) t += t[1]; if ( t == tstop ) { /* no endpoints */ if ( option2 == 0 ) return(0); else return(Generator(BHEAD term,level)); } tend1 = t; numend = 0; while ( t < tstop && *t == endcode ) { tend2 = t; t += t[1]; numend++; } if ( numend != 2 ) { /* not 2 endpoints -> no path */ if ( option2 == 0 ) return(0); else return(Generator(BHEAD term,level)); } /* Search for the intermediate functions. */ t = term + 1; nvert = 0; while ( t < tstop && *t != vcode ) t += t[1]; tstart = t; while ( t < tstop && *t == vcode ) { t += t[1]; nvert++; } tend = t; /* Next we copy the relevant content of the various functions into the WorkSpace. We keep pointers to the functions in pWorkSpace. First the two endpoints and then the intermediate ones. */ WantAddPointers((2*nvert+8)); vert = AT.pWorkPointer+2; vert1 = AT.pWorkPointer; /* vert2 = AT.pWorkPointer+1; */ AT.pWorkPointer += 2*nvert+8; nvert = 0; /* Copy the endpoints. */ to = AT.WorkPointer; if ( functions[endcode-FUNCTION].spec == TENSORFUNCTION ) { from = tend1; npass = 0; redo1: tos = to++; tfrom = from+from[1]; from += FUNHEAD; while ( from < tfrom ) { if ( option1 == -INDEX && *from >= 0 ) { *to++ = *from++; } else if ( option1 == -VECTOR && *from < 0 ) { *to++ = *from++ - AM.OffsetVector; } else { from++; } } *tos = to-tos; if ( *tos < 2 ) to = tos; else AT.pWorkSpace[vert1+npass] = tos; npass++; if ( from == tend2 ) goto redo1; } else if ( functions[endcode-FUNCTION].spec == 0 ) { from = tend1; npass = 0; redo2: tos = to++; tfrom = from + from[1]; from += FUNHEAD; while ( from < tfrom ) { if ( option1 == -VECTOR && ( from[0] == -INDEX || from[0] == -VECTOR ) && from[1] < 0 ) { from++; *to++ = *from++ - AM.OffsetVector; } else if ( option1 == *from ) { from++; *to++ = *from++; } else { NEXTARG(from); } } *tos = to-tos; if ( *tos < 2 ) to = tos; else AT.pWorkSpace[vert1+npass] = tos; npass++; if ( from == tend2 ) goto redo2; } else { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oldpworkpointer; if ( option2 == 0 ) return(0); return(Generator(BHEAD term,level)); } /* And now the intermediate functions */ from = tstart; if ( functions[vcode-FUNCTION].spec == TENSORFUNCTION ) { from = tstart; while ( from < tend ) { tos = to++; tfrom = from+from[1]; from += FUNHEAD; while ( from < tfrom ) { if ( option1 == -INDEX && *from >= 0 ) { *to++ = *from++; } else if ( option1 == -VECTOR && *from < 0 ) { *to++ = *from++ - AM.OffsetVector; } else { from++; } } *tos = to-tos; if ( *tos < 3 ) to = tos; else AT.pWorkSpace[vert+nvert++] = tos; } } else if ( functions[vcode-FUNCTION].spec == 0 ) { from = tstart; while ( from < tend ) { tos = to++; tfrom = from + from[1]; from += FUNHEAD; while ( from < tfrom ) { if ( option1 == -VECTOR && ( from[0] == -INDEX || from[0] == -VECTOR ) && from[1] < 0 ) { from++; *to++ = *from++ - AM.OffsetVector; } else if ( option1 == *from ) { from++; *to++ = *from++; } else { NEXTARG(from); } } *tos = to-tos; if ( *tos < 3 ) to = tos; else AT.pWorkSpace[vert+nvert++] = tos; } } else { AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oldpworkpointer; if ( option2 == 0 ) return(0); return(Generator(BHEAD term,level)); } AT.WorkPointer = to; /* Now make a list of all relevant arguments. */ a = arglist = AT.WorkPointer; for ( i = -2; i < nvert; i++ ) { v = AT.pWorkSpace[vert+i]; j = *v-1; v++; NCOPY(a,v,j); } nargs = a-arglist; AT.WorkPointer = a; /* Now sort the list. Bubble type sort. */ a1 = arglist; a2 = a1+1; while ( a2 < a ) { a3 = a2; while ( a3 > a1 && a3[-1] > a3[0] ) { EXCH(*a3,a3[-1]); a3--; } a2++; } /* Now remove the elements from the list that do not occur exactly twice. */ a1 = arglist; a2 = a1; a3 = a1+nargs; while ( a2 < a3 ) { if ( a2+1 == a3 ) { break; } else if ( a2+2 == a3 ) { if ( a2[0] == a2[1] ) { *a1++ = a2[0]; } break; } else { if ( a2[0] != a2[1] ) { a2++; } else if ( a2[0] != a2[2] ) { *a1++ = a2[0]; a2 += 2; } else { a2++; while ( a2 < a3 && a2[-1] == a2[0] ) a2++; } } } nargs = a1-arglist; /* Now we need to redo the list of vertices and remove the elements that are not in our arglist. */ do { action = 0; for ( i = -2; i < nvert; i++ ) { vv = v = AT.pWorkSpace[vert+i]; v++; for ( j = 1; j < vv[0]; j++ ) { for ( jj = 0; jj < nargs; jj++ ) { if ( *v == arglist[jj] ) break; } if ( jj >= nargs ) { /* was not in the list */ vv[0] = vv[0]-1; for ( jj = j; jj < vv[0]; jj++ ) vv[jj] = vv[jj+1]; } v++; } } /* Next we need to remove vertices that have only one object remaining. Also, the object can be removed from arglist. After that we go back to clean up the list. */ for ( i = -2; i < nvert; i++ ) { vv = AT.pWorkSpace[vert+i]; if ( vv[0] == 1 ) { AT.pWorkSpace[vert+i] = AT.pWorkSpace[vert+nvert-1]; nvert--; i--; continue; } else if ( vv[0] == 2 && i >= 0 ) { for ( j = 0; j < nargs; j++ ) { if ( arglist[j] == vv[1] ) break; } while ( j < nargs-1 ) arglist[j] = arglist[j+1]; nargs--; AT.pWorkSpace[vert+i] = AT.pWorkSpace[vert+nvert-1]; nvert--; i--; action = 1; } } } while ( action ); /* Now we have a clean list of connections and we can start building the path. We start with summing over all objects in vert1. */ path = AT.WorkPointer; npath = 0; AT.WorkPointer += nvert+8; t = AT.pWorkSpace[vert1]; if ( *t >= 2 ) { for ( i = 1; i < *t; i++ ) { AT.pWorkSpace[vert+nvert] = t; path[npath++] = t[i]; numgenerated += GenPaths(BHEAD term,level,vert,nvert,arglist,nargs,path,npath); npath--; } } AT.WorkPointer = oldworkpointer; AT.pWorkPointer = oldpworkpointer; if ( numgenerated == 0 && option2 != 0 ) return(Generator(BHEAD term,level)); return(0); } /* #] AllPaths : #[ GenPaths : We enter with an open line in path[npath-1] We traverse though the vertices until we reach vert-1, the endpoint. */ LONG GenPaths(PHEAD WORD *term, WORD level, LONG vert, WORD nvert, WORD *arglist, WORD nargs, WORD *path, WORD npath) { LONG numgenerated = 0; WORD *t, *vpartner, *v, *vv; WORD i, j; /* Check whether path[npath-1] is part of the endpoint. */ t = AT.pWorkSpace[vert-1]; for ( i = 1; i < *t; i++ ) { if ( t[i] == path[npath-1] ) { /* Got a path! */ PathOutput(BHEAD term,level,path,npath); numgenerated++; return(numgenerated); } } /* Start with finding the partner. */ for ( i = 0; i < nvert; i++ ) { vpartner = AT.pWorkSpace[vert+i]; for ( j = 0; j < npath; j++ ) { if ( vpartner == AT.pWorkSpace[vert+nvert+j] ) break; } if ( j < npath ) continue; v = vpartner+1; vv = vpartner + *vpartner; while ( v < vv ) { if ( *v == path[npath-1] ) { /* Found the partner. Now we can sum over the remaining permitted arguments of this vertex. */ v = vpartner + 1; while ( v < vv ) { /* *v should be in arglist. */ for ( j = 0; j < nargs; j++ ) { if ( *v == arglist[j] ) break; } if ( j >= nargs ) { v++; continue; } /* *v should not be in path. */ for ( j = 0; j < npath; j++ ) { if ( *v == path[j] ) break; } if ( j >= npath ) { AT.pWorkSpace[vert+nvert+npath] = vpartner; path[npath++] = *v; numgenerated += GenPaths(BHEAD term,level,vert,nvert, arglist,nargs,path,npath); npath--; } v++; } return(numgenerated); } v++; } } /* The partner is in a vertex we have finished before. */ return(numgenerated); } /* #] GenPaths : #[ PathOutput : */ void PathOutput(PHEAD WORD *term, WORD level, WORD *path, WORD npath) { CBUF *C = cbuf+AM.rbufnum; WORD pathfun = C->lhs[level][4]; /* The output function */ WORD option1 = C->lhs[level][5]; /* type of argument */ WORD *tstop, *tstop1, *t, *tt; WORD *outterm; WORD i; tstop1 = term+*term; tstop = tstop1 - ABS(tstop1[-1]); outterm = AT.WorkPointer; tt = outterm; t = term; while ( t < tstop ) *tt++ = *t++; *tt++ = pathfun; if ( functions[pathfun-FUNCTION].spec == TENSORFUNCTION ) { *tt++ = FUNHEAD+npath; FILLFUN(tt) if ( option1 == -VECTOR ) { for ( i = 0; i < npath; i++ ) *tt++ = path[i]+AM.OffsetVector; } else { for ( i = 0; i < npath; i++ ) *tt++ = path[i]; } } else { *tt++ = FUNHEAD+npath*2; FILLFUN(tt) for ( i = 0; i< npath; i++ ) { *tt++ = option1; if ( option1 == -VECTOR ) *tt++ = path[i] + AM.OffsetVector; else *tt++ = path[i]; } } while ( t < tstop1 ) *tt++ = *t++; *outterm = tt - outterm; AT.WorkPointer = tt; if ( Generator(BHEAD outterm,level) ) { MesCall("PathOutput"); Terminate(-1); } AT.WorkPointer = outterm; } /* #] PathOutput : #[ AllOnePI : We assume a graph that has loops and is OnePI. This routine initializes the recursion that creates all onePI subgraphs. Algorithm: a: have a routine that removes all bridges: RemoveBridges b: output an empty diagram. c: output the diagram itself d: cut a line, followed by removing all bridges. e: if the diagram still has lines, go to c, else go to the next line in d. In order to avoid factorial blowup, we need to prune the tree as fast as possible. 1: list of lines to be cut. 2: once we have tried a line and removed its bridges, we do not have to try this line deeper in the tree, neither its bridges. 1 2 3 cut 1. x cut 2 -> bridge 3 x cut 2. x cut 3 -> bridge 1 ???? mag niet cut 3. x Hence 1,2,3,4,5,6,7 1 still to go 2,3,4,5,6,7 2 still to go 3,4,5,6,7 3 still to go 4,5,6,7 etc. bridges: if x is bridge, we take x from the list_to_go. If we have a bridge that is a number lower than the list_to_go we skip this possibility. We reach the end when the list_to_go is empty. */ WORD AllOnePI(WORD *term,WORD level) { CBUF *C = cbuf+AM.rbufnum; WORD vcode = C->lhs[level][2]; /* The vertex function */ WORD option1 = C->lhs[level][4]; /* type of argument */ /* First we have to collect all relevant information about the diagram. We should start with removing bridges to make the real starting point onePI. */ DUMMYUSE(term) DUMMYUSE(vcode) DUMMYUSE(option1) return(0); } /* #] AllOnePI : #[ RemoveBridges : */ int RemoveBridges(void) { return(0); } /* #] RemoveBridges : #[ TakeOneLine : */ int TakeOneLine(WORD*term,WORD level) { DUMMYUSE(term) DUMMYUSE(level) return(0); } /* #] TakeOneLine : #[ OutputOnePI : */ int OutputOnePI(PHEAD WORD *term,WORD level) { return(Generator(BHEAD term,level)); } /* #] OutputOnePI : */ form-5.0.1/sources/inivar.h0000644000175100017510000003150315217035721011274 /** @file inivar.h * * Contains the initialization of a number of structs at compile time * This file should only be included in the file startup.c !!! */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ FIXEDGLOBALS FG = { {Traces /* Dummy as zeroeth argument */ ,Traces ,EpfCon ,RatioGen ,SymGen ,TenVec ,DoSumF1 ,DoSumF2} ,{TraceFind /* Dummy as zeroeth argument */ ,TraceFind ,EpfFind ,RatioFind ,SymFind ,TenVecFind} ,{"symbol" ,"index" ,"vector" ,"function" ,"set" ,"expression" ,"dotproduct" ,"number" ,"subexp" ,"delta"} ,{"(local)" ,"(skip/local)" ,"(drop/local)" ,"(dropped)" ,"(global)" ,"(skip/global)" ,"(drop/global)" ,"(dropped)" ,"(stored)" ,"(local-hidden)" ,"(local-to be hidden)" ,"(local-hidden-dropped)" ,"(local-to be unhidden)" ,"(global-hidden)" ,"(global-to be hidden)" ,"(global-hidden-dropped)" ,"(global-to be unhidden)" ,"(into-hide-local)" ,"(into-hide-global)" ,"(spectator)" ,"(drop/spectator)"} ,{" Functions" ," Commuting Functions"} ,{"left " ,"active " ,"in output"} ,(char *)0 ,(char *)0 ,(UBYTE *)"1" ,(WORD)0 ,(WORD)0 ,(WORD)0 ,(WORD)0 /* ASCII table of character types. Note that on some computers this table may be different from the ASCII table. -1 Illegal character 0 Alphabetic character 1 Digit 2 . $ _ ? # or ' 3 [,] 4 ( ) = ; or , 5 + - * % / ^ : 6 blank, tab, linefeed 7 {,|,} 8 ! & < > 9 " 10 The ultimate end. */ ,{ 10,255,255,255,255,255,255,255,255, 6, 6,255,255, 6,255,255, 255,255,255,255,255,255,255,255,255,255, 10,255,255,255,255,255, 6, 8, 9, 2, 2, 5, 8, 2, 4, 4, 5, 5, 4, 5, 2, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 4, 8, 4, 8, 2, 255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,255, 3, 5, 2, 255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255, 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255 } }; ALLGLOBALS A; #ifdef WITHPTHREADS ALLPRIVATES **AB; #endif static struct fixedfun { char *name; int commu ,tensor ,complx ,symmetric; } fixedfunctions[] = { {"exp_" ,1 ,0 ,0 ,0} /* EXPONENT */ ,{"denom_" ,1 ,0 ,0 ,0} /* DENOMINATOR */ ,{"setfun_" ,1 ,0 ,0 ,0} /* SETFUNCTION */ ,{"g_" ,1 ,GAMMAFUNCTION ,VARTYPEIMAGINARY,0} /* GAMMA */ ,{"gi_" ,1 ,GAMMAFUNCTION ,VARTYPEIMAGINARY,0} /* GAMMAI */ ,{"g5_" ,1 ,GAMMAFUNCTION ,VARTYPEIMAGINARY,0} /* GAMMAFIVE */ ,{"g6_" ,1 ,GAMMAFUNCTION ,VARTYPEIMAGINARY,0} /* GAMMASIX */ ,{"g7_" ,1 ,GAMMAFUNCTION ,VARTYPEIMAGINARY,0} /* GAMMASEVEN */ ,{"sum_" ,1 ,0 ,0 ,0} /* SUMF1 */ ,{"sump_" ,1 ,0 ,0 ,0} /* SUMF2 */ ,{"dum_" ,1 ,0 ,0 ,0} /* DUMFUN */ ,{"replace_" ,0 ,0 ,0 ,0} /* REPLACEMENT */ ,{"reverse_" ,1 ,0 ,0 ,0} /* REVERSEFUNCTION */ ,{"distrib_" ,1 ,0 ,0 ,0} /* DISTRIBUTION */ ,{"dd_" ,0 ,TENSORFUNCTION ,0 ,0} /* DELTA3 */ ,{"dummy_" ,0 ,0 ,0 ,0} /* DUMMYFUN */ ,{"dummyten_",0 ,TENSORFUNCTION ,0 ,0} /* DUMMYTEN */ ,{"e_" ,0 ,TENSORFUNCTION|1 ,VARTYPEIMAGINARY,ANTISYMMETRIC} /* LEVICIVITA */ ,{"fac_" ,0 ,0 ,0 ,0} /* FACTORIAL */ ,{"invfac_" ,0 ,0 ,0 ,0} /* INVERSEFACTORIAL */ ,{"binom_" ,0 ,0 ,0 ,0} /* BINOMIAL */ ,{"nargs_" ,0 ,0 ,0 ,0} /* NUMARGSFUN */ ,{"sign_" ,0 ,0 ,0 ,0} /* SIGNFUN */ ,{"mod_" ,0 ,0 ,0 ,0} /* MODFUNCTION */ ,{"mod2_" ,0 ,0 ,0 ,0} /* MOD2FUNCTION */ ,{"min_" ,0 ,0 ,0 ,0} /* MINFUNCTION */ ,{"max_" ,0 ,0 ,0 ,0} /* MAXFUNCTION */ ,{"abs_" ,0 ,0 ,0 ,0} /* ABSFUNCTION */ ,{"sig_" ,0 ,0 ,0 ,0} /* SIGFUNCTION */ ,{"integer_" ,0 ,0 ,0 ,0} /* INTFUNCTION */ ,{"theta_" ,0 ,0 ,0 ,0} /* THETA */ ,{"thetap_" ,0 ,0 ,0 ,0} /* THETA2 */ ,{"delta_" ,0 ,0 ,0 ,0} /* DELTA2 */ ,{"deltap_" ,0 ,0 ,0 ,0} /* DELTAP */ ,{"bernoulli_",0,0 ,0 ,0} /* BERNOULLIFUNCTION */ ,{"count_" ,0 ,0 ,0 ,0} /* COUNTFUNCTION */ ,{"match_" ,0 ,0 ,0 ,0} /* MATCHFUNCTION */ ,{"pattern_" ,0 ,0 ,VARTYPECOMPLEX ,0} /* PATTERNFUNCTION */ ,{"term_" ,1 ,0 ,0 ,0} /* TERMFUNCTION */ ,{"conjg_" ,1 ,0 ,VARTYPECOMPLEX ,0} /* CONJUGATEFUNCTION */ ,{"root_" ,0 ,0 ,0 ,0} /* ROOTFUNCTION */ ,{"table_" ,1 ,0 ,0 ,0} /* TABLEFUNCTION */ ,{"firstbracket_",0 ,0 ,0 ,0} /* FIRSTBRACKET */ ,{"termsin_" ,0 ,0 ,0 ,0} /* TERMSINEXPR */ ,{"nterms_" ,0 ,0 ,0 ,0} /* NUMTERMSFUN */ ,{"gcd_" ,0 ,0 ,0 ,0} /* GCDFUNCTION */ ,{"div_" ,0 ,0 ,0 ,0} /* DIVFUNCTION */ ,{"rem_" ,0 ,0 ,0 ,0} /* REMFUNCTION */ ,{"maxpowerof_",0 ,0 ,0 ,0} /* MAXPOWEROF */ ,{"minpowerof_",0 ,0 ,0 ,0} /* MINPOWEROF */ ,{"tbl_" ,0 ,0 ,0 ,0} /* TABLESTUB */ ,{"factorin_",0 ,0 ,0 ,0} /* FACTORIN */ ,{"termsinbracket_",0 ,0 ,0 ,0} /* TERMSINBRACKET */ ,{"farg_" ,0 ,0 ,0 ,0} /* WILDARGFUN */ /* The following names are reserved for the floating point library. As long as we have no floating point numbers they do not do anything. */ ,{"sqrt_" ,0 ,0 ,0 ,0} /* SQRTFUNCTION */ ,{"ln_" ,0 ,0 ,0 ,0} /* LNFUNCTION */ ,{"sin_" ,0 ,0 ,0 ,0} /* SINFUNCTION */ ,{"cos_" ,0 ,0 ,0 ,0} /* COSFUNCTION */ ,{"tan_" ,0 ,0 ,0 ,0} /* TANFUNCTION */ ,{"asin_" ,0 ,0 ,0 ,0} /* ASINFUNCTION */ ,{"acos_" ,0 ,0 ,0 ,0} /* ACOSFUNCTION */ ,{"atan_" ,0 ,0 ,0 ,0} /* ATANFUNCTION */ ,{"atan2_" ,0 ,0 ,0 ,0} /* ATAN2FUNCTION */ ,{"sinh_" ,0 ,0 ,0 ,0} /* SINHFUNCTION */ ,{"cosh_" ,0 ,0 ,0 ,0} /* COSHFUNCTION */ ,{"tanh_" ,0 ,0 ,0 ,0} /* TANHFUNCTION */ ,{"asinh_" ,0 ,0 ,0 ,0} /* ASINHFUNCTION */ ,{"acosh_" ,0 ,0 ,0 ,0} /* ACOSHFUNCTION */ ,{"atanh_" ,0 ,0 ,0 ,0} /* ATANHFUNCTION */ ,{"li2_" ,0 ,0 ,0 ,0} /* LI2FUNCTION */ ,{"lin_" ,0 ,0 ,0 ,0} /* LINFUNCTION */ /* From here on we continue with new functions (26-sep-2010) */ ,{"extrasymbol_",0 ,0 ,0 ,0} /* EXTRASYMFUN */ ,{"random_" ,0 ,0 ,0 ,0} /* RANDOMFUNCTION */ ,{"ranperm_" ,1 ,0 ,0 ,0} /* RANPERM */ ,{"numfactors_" ,0 ,0 ,0 ,0} /* NUMFACTORS */ ,{"firstterm_" ,0 ,0 ,0 ,0} /* FIRSTTERM */ ,{"content_" ,0 ,0 ,0 ,0} /* CONTENTTERM */ ,{"prime_" ,0 ,0 ,0 ,0} /* PRIMENUMBER */ ,{"exteuclidean_",0 ,0 ,0 ,0} /* EXTEUCLIDEAN */ ,{"makerational_",0 ,0 ,0 ,0} /* MAKERATIONAL */ ,{"inverse_" ,0 ,0 ,0 ,0} /* INVERSEFUNCTION */ ,{"id_" ,1 ,0 ,0 ,0} /* IDFUNCTION */ ,{"putfirst_" ,1 ,0 ,0 ,0} /* PUTFIRST */ ,{"perm_" ,1 ,0 ,0 ,0} /* PERMUTATIONS */ ,{"partitions_" ,1 ,0 ,0 ,0} /* PARTITIONS */ ,{"mul_" ,0 ,0 ,0 ,0} /* MULFUNCTION */ ,{"moebius_" ,0 ,0 ,0 ,0} /* MOEBIUS */ ,{"topologies_" ,0 ,0 ,0 ,0} /* TOPOLOGIES */ ,{"diagrams_" ,0 ,0 ,0 ,0} /* DIAGRAMS */ ,{"topo_" ,0 ,0 ,0 ,0} /* TOPO */ ,{"node_" ,0 ,0 ,0 ,0} /* VERTEX */ ,{"edge_" ,0 ,0 ,0 ,0} /* EDGE */ ,{"sizeof_" ,0 ,0 ,0 ,0} /* SIZEOFFUNCTION */ ,{"block_" ,0 ,0 ,0 ,0} /* BLOCK */ ,{"onepi_" ,0 ,0 ,0 ,0} /* ONEPI */ ,{"phi_" ,0 ,VERTEXFUNCTION,0 ,0} /* PHI */ ,{"float_" ,0 ,0 ,0 ,0} /* FLOATFUN */ ,{"tofloat_" ,0 ,0 ,0 ,0} /* TOFLOAT */ ,{"torat_" ,0 ,0 ,0 ,0} /* TORAT */ ,{"mzv_" ,0 ,0 ,0 ,0} /* MZV */ ,{"euler_" ,0 ,0 ,0 ,0} /* EULER */ ,{"mzvhalf_" ,0 ,0 ,0 ,0} /* MZVHALF */ ,{"agm_" ,0 ,0 ,0 ,0} /* AGMFUNCTION */ ,{"gamma_" ,0 ,0 ,0 ,0} /* GAMMAFUN */ ,{"eexp_" ,0 ,0 ,0 ,0} /* EXPFUNCTION */ ,{"hpl_" ,0 ,0 ,0 ,0} /* HPLFUNCTION */ ,{"mpl_" ,0 ,0 ,0 ,0} /* MPLFUNCTION */ }; FIXEDSET fixedsets[] = { {"pos_", "integers > 0", CSYMBOL, 0} /* POS_ 0 */ ,{"pos0_", "integers >= 0", CSYMBOL, 0} /* POS0_ 1 */ ,{"neg_", "integers < 0", CSYMBOL, 0} /* NEG_ 2 */ ,{"neg0_", "integers <= 0", CSYMBOL, 0} /* NEG0_ 3 */ ,{"even_", "even integers", CSYMBOL, 0} /* EVEN_ 4 */ ,{"odd_", "odd integers", CSYMBOL, 0} /* ODD_ 5 */ ,{"int_", "all integers", CSYMBOL, 0} /* Z_ 6 */ ,{"symbol_","only symbols", CSYMBOL, MAXPOSITIVE} /* SYMBOL_ 7 */ ,{"fixed_", "fixed indices", CINDEX, 0} /* FIXED_ 8 */ ,{"index_", "all indices", CINDEX, 0} /* INDEX_ 9 */ ,{"number_","all rationals", CSYMBOL, 0} /* Q_ 10 */ ,{"dummyindices_", "dummy indices", CINDEX, 0} /* DUMMYINDEX_ 11 */ ,{"vector_","only vectors", CVECTOR, 0} /* VECTOR_ 12 */ }; UBYTE BufferForOutput[MAXLINELENGTH+14]; char *setupfilename = "form.set"; #ifdef WITHPTHREADS INILOCK(ErrorMessageLock) INILOCK(FileReadLock) #endif form-5.0.1/sources/vector.h0000644000175100017510000002200215217035721011300 #ifndef VECTOR_H_ #define VECTOR_H_ /** @file vector.h * * An implementation of dynamic array. * * Example: * @code * size_t i; * Vector(int, vec); * VectorPushBack(vec, 1); * VectorPushBack(vec, 2); * VectorPushBack(vec, 3); * for ( i = 0; i < VectorSize(vec); i++ ) * printf("%d\n", VectorPtr(vec)[i]); * VectorFree(vec); * @endcode */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include #include #include "declare.h" /* #] Includes : #[ Vector : #[ VectorStruct : */ /** * A struct for vector objects. * * @param T the type of elements. */ #define VectorStruct(T) \ struct { \ T *ptr; \ size_t size; \ size_t capacity; \ } /* #] VectorStruct : #[ Vector : */ /** * Defines and initialises a vector X of the type T. * The user must call VectorFree(X) after the use of X. * * @param T the type of elements. * @param X the name of vector object */ #define Vector(T, X) \ VectorStruct(T) X = { NULL, 0, 0 } /* #] Vector : #[ DeclareVector : */ /** * Declares a vector X of the type T. * The user must call VectorInit(X) before the use of X. * * @param T the type of elements. * @param X the name of vector object */ #define DeclareVector(T, X) \ VectorStruct(T) X /* #] DeclareVector : #[ VectorInit : */ /** * Initialises a vector X of the type T. * The user must call VectorFree(X) after the use of X. * * @param X the vector object. */ #define VectorInit(X) \ do { \ (X).ptr = NULL; \ (X).size = 0; \ (X).capacity = 0; \ } while (0) /* #] VectorInit : #[ VectorFree : */ /** * Frees the buffer allocated by the vector X. * * @param X the vector object. */ #define VectorFree(X) \ do { \ M_free((X).ptr, "VectorFree:" #X); \ (X).ptr = NULL; \ (X).size = 0; \ (X).capacity = 0; \ } while (0) /* #] VectorFree : #[ VectorPtr : */ /** * Returns the pointer to the buffer for the vector X. * NULL when VectorCapacity(X) == 0. * * @param X the vector object. * @return the pointer to the allocated buffer for the vector. */ #define VectorPtr(X) \ ((X).ptr) /* #] VectorPtr : #[ VectorFront : */ /** * Returns the first element of the vector X. * Undefined when VectorSize(X) == 0. * * @param X the vector object. * @return the first element of the vector. */ #define VectorFront(X) \ ((X).ptr[0]) /* #] VectorFront : #[ VectorBack : */ /** * Returns the last element of the vector X. * Undefined when VectorSize(X) == 0. * * @param X the vector object. * @return the last element of the vector. */ #define VectorBack(X) \ ((X).ptr[(X).size - 1]) /* #] VectorBack : #[ VectorSize : */ /** * Returns the size of the vector X. * * @param X the vector object. * @return the size of the vector. */ #define VectorSize(X) \ ((X).size) /* #] VectorSize : #[ VectorCapacity : */ /** * Returns the capacity (the number of the already allocated elements) of the vector X. * * @param X the vector object. * @return the capacity of the vector. */ #define VectorCapacity(X) \ ((X).capacity) /* #] VectorCapacity : #[ VectorEmpty : */ /** * Returns true the size of the vector X is zero. * * @param X the vector object. * @return true if the vector has no elements, false otherwise. */ #define VectorEmpty(X) \ ((X).size == 0) /* #] VectorEmpty : #[ VectorClear : */ /** * Sets the size of the vector X to zero. * * @param X the vector object. */ #define VectorClear(X) \ do { (X).size = 0; } while (0) /* #] VectorClear : #[ VectorReserve : */ /** * Requires that the capacity of the vector X is equal to or lager than newcapacity. * * @param X the vector object. * @param newcapacity the capacity to be reserved. */ #define VectorReserve(X, newcapacity) \ do { \ size_t v_tmp_newcapacity_ = (newcapacity); \ if ( (X).capacity < v_tmp_newcapacity_ ) { \ void *v_tmp_newptr_; \ v_tmp_newcapacity_ = (v_tmp_newcapacity_ * 3) / 2; \ if ( v_tmp_newcapacity_ < 4 ) v_tmp_newcapacity_ = 4; \ v_tmp_newptr_ = Malloc1(sizeof((X).ptr[0]) * v_tmp_newcapacity_, "VectorReserve:" #X); \ if ( (X).ptr != NULL ) { \ memcpy(v_tmp_newptr_, (X).ptr, (X).size * sizeof((X).ptr[0])); \ M_free((X).ptr, "VectorReserve:" #X); \ } \ (X).ptr = v_tmp_newptr_; \ (X).capacity = v_tmp_newcapacity_; \ } \ } while (0) /* #] VectorReserve : #[ VectorPushBack : */ /** * Adds an element x at the end of the vector X. * * @param X the vector object. * @param x the element to be added. */ #define VectorPushBack(X, x) \ do { \ VectorReserve((X), (X).size + 1); \ (X).ptr[(X).size++] = (x); \ } while (0) /* #] VectorPushBack : #[ VectorPushBacks : */ /** * Adds an n elements of src at the end of the vector X. * * @param X the vector object. * @param src the starting address of the buffer storing elements to be added. * @param n the number of elements to be added. */ #define VectorPushBacks(X, src, n) \ do { \ size_t v_tmp_n_ = (n); \ VectorReserve((X), (X).size + v_tmp_n_); \ memcpy((X).ptr + (X).size, (src), v_tmp_n_ * sizeof((X).ptr[0])); \ (X).size += v_tmp_n_; \ } while (0) /* #] VectorPushBacks : #[ VectorPopBack : */ /** * Removes the last element of the vector X. * VectorSize(X) must be > 0. * * @param X the vector object. */ #define VectorPopBack(X) \ do { (X).size --; } while (0) /* #] VectorPopBack : #[ VectorInsert : */ /** * Inserts an element x at the specified index of the vector X. * The index must be 0 <= index < VectorSize(X). * * @param X the vector object. * @param index the position at which the element will be inserted. * @param x the element to be inserted. */ #define VectorInsert(X, index, x) \ do { \ size_t v_tmp_index_ = (index); \ VectorReserve((X), (X).size + 1); \ memmove((X).ptr + v_tmp_index_ + 1, (X).ptr + v_tmp_index_, ((X).size - v_tmp_index_) * sizeof((X).ptr[0])); \ (X).ptr[v_tmp_index_] = (x); \ (X).size++; \ } while (0) /* #] VectorInsert : #[ VectorInserts : */ /** * Inserts an n elements of src at the specified index of the vector X. * The index must be 0 <= index < VectorSize(X). * * @param X the vector object. * @param index the position at which the elements will be inserted. * @param src the starting address of the buffer storing elements to be inserted. * @param n the number of elements to be inserted. */ #define VectorInserts(X, index, src, n) \ do { \ size_t v_tmp_index_ = (index), v_tmp_n_ = (n); \ VectorReserve((X), (X).size + v_tmp_n_); \ memmove((X).ptr + v_tmp_index_ + v_tmp_n_, (X).ptr + v_tmp_index_, ((X).size - v_tmp_index_) * sizeof((X).ptr[0])); \ memcpy((X).ptr + v_tmp_index_, (src), v_tmp_n_ * sizeof((X).ptr[0])); \ (X).size += v_tmp_n_; \ } while (0) /* #] VectorInserts : #[ VectorErase : */ /** * Removes an element at the specified index of the vector X. * The index must be 0 <= index < VectorSize(X). * * @param X the vector object. * @param index the position of the element to be removed. */ #define VectorErase(X, index) \ do { \ size_t v_tmp_index_ = (index); \ memmove((X).ptr + v_tmp_index_, (X).ptr + v_tmp_index_ + 1, ((X).size - v_tmp_index_ - 1) * sizeof((X).ptr[0])); \ (X).size--; \ } while (0) /* #] VectorErase : #[ VectorErases : */ /** * Removes an n elements at the specified index of the vector X. * The index must be 0 <= index < VectorSize(X) - n + 1. * * @param X the vector object. * @param index the starting position of the elements to be removed. * @param n the number of elements to be removed. */ #define VectorErases(X, index, n) \ do { \ size_t v_tmp_index_ = (index), v_tmp_n_ = (n); \ memmove((X).ptr + v_tmp_index_, (X).ptr + v_tmp_index_ + v_tmp_n_, ((X).size - v_tmp_index_ - 1) * sizeof((X).ptr[0])); \ (X).size -= v_tmp_n_; \ } while (0) /* #] VectorErases : #] Vector : */ #endif /* VECTOR_H_ */ form-5.0.1/sources/ratio.c0000644000175100017510000030463715217035721011130 /** @file ratio.c * * A variety of routines: * The ratio command for partial fractioning * (rather old. Schoonschip inheritance) * The sum routines. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : ratio.c */ #include "form3.h" /* #] Includes : #[ Ratio : These are the special operations regarding simple polynomials. The first and most needed is the partial fractioning expansion. Ratio,x1,x2,x3 The files belonging to the ratio command serve also as a good example of how to implement a new operation. #[ RatioFind : The routine that should locate the need for a ratio command. If located the corresponding symbols are removed and the operational parameters are loaded. A subexpression pointer is inserted and the code for success is returned. params points at the compiler output block defined in RatioComp. */ int RatioFind(PHEAD WORD *term, WORD *params) { GETBIDENTITY WORD *t, *m, *r; WORD x1, x2, i; WORD *y1, *y2, n1 = 0, n2 = 0; x1 = params[3]; x2 = params[4]; m = t = term; m += *m; m -= ABS(m[-1]); t++; if ( t < m ) do { if ( *t == SYMBOL ) { y1 = 0; y2 = 0; r = t + t[1]; m = t + 2; do { if ( *m == x1 ) { y1 = m; n1 = m[1]; } else if ( *m == x2 ) { y2 = m; n2 = m[1]; } m += 2; } while ( m < r ); if ( !y1 || !y2 || ( n1 > 0 && n2 > 0 ) ) return(0); m -= 2; if ( y1 > y2 ) { r = y1; y1 = y2; y2 = r; } *y2 = *m; y2[1] = m[1]; m -= 2; *y1 = *m; y1[1] = m[1]; i = WORDDIF(m,t); #if SUBEXPSIZE > 6 We have to revise the code for the second case. #endif if ( i > 2 ) { /* Subexpression fits exactly */ t[1] = i; y1 = term+*term; y2 = y1+SUBEXPSIZE-4; r = m+4; while ( y1 > r ) *--y2 = *--y1; *m++ = SUBEXPRESSION; *m++ = SUBEXPSIZE; *m++ = -1; *m++ = 1; *m++ = DUMMYBUFFER; FILLSUB(m) *term += SUBEXPSIZE-4; } else { /* All symbols are gone. Rest has to be moved */ m -= 2; *m++ = SUBEXPRESSION; *m++ = SUBEXPSIZE; *m++ = -1; *m++ = 1; *m++ = DUMMYBUFFER; FILLSUB(m) t = term; t += *t; *term += SUBEXPSIZE-6; r = m + 6-SUBEXPSIZE; do { *m++ = *r++; } while ( r < t ); } t = AT.TMout; /* Load up the TM out array for the generator */ *t++ = 7; *t++ = RATIO; *t++ = x1; *t++ = x2; *t++ = params[5]; *t++ = n1; *t++ = n2; return(1); } t += t[1]; } while ( t < m ); return(0); } /* #] RatioFind : #[ RatioGen : The algorithm: x1^-n1*x2^n2 ==> x2 --> x1 + x3 x1^n1*x2^-n2 ==> x1 --> x2 - x3 x1^-n1*x2^-n2 ==> +sum(i=0,n1-1){(-1)^i*binom(n2-1+i,n2-1) *x3^-(n2+i)*x1^-(n1-i)} +sum(i=0,n2-1){(-1)^(n1)*binom(n1-1+i,n1-1) *x3^-(n1+i)*x2^-(n2-i)} Actually there is an amount of arbitrariness in the first two formulae and the replacement x2 -> x1 + x3 could be made 'by hand'. It is better to use the nontrivial 'minimal change' formula: x1^-n1*x2^n2: if ( n1 >= n2 ) { +sum(i=0,n2){x3^i*x1^-(n1-n2+i)*binom(n2,i)} } else { sum(i=0,n2-n1){x2^(n2-n1-i)*x3^i*binom(n1-1+i,n1-1)} +sum(i=0,n1-1){x3^(n2-i)*x1^-(n1-i)*binom(n2,i)} } x1^n1*x2^-n2: Same but x3 -> -x3. The contents of the AT.TMout/params array are: length,type,x1,x2,x3,n1,n2 */ int RatioGen(PHEAD WORD *term, WORD *params, WORD num, WORD level) { GETBIDENTITY WORD *t, *m; WORD *tstops[3]; WORD n1, n2, i, j; WORD x1,x2,x3; UWORD *coef; WORD ncoef, sign = 0; coef = (UWORD *)AT.WorkPointer; t = term; tstops[2] = m = t + *t; m -= ABS(m[-1]); t++; do { if ( *t == SUBEXPRESSION && t[2] == num ) break; t += t[1]; } while ( t < m ); tstops[0] = t; tstops[1] = t + t[1]; /* Copying to termout will be from term to tstop1, then the induced part and finally from tstop2 to tstop3 Now separate the various cases: */ t = params + 2; x1 = *t++; x2 = *t++; x3 = *t++; n1 = *t++; n2 = *t++; if ( n1 > 0 ) { /* Flip the variables and indicate -x3 */ n2 = -n2; sign = 1; i = n1; n1 = n2; n2 = i; i = x1; x1 = x2; x2 = i; goto PosNeg; } else if ( n2 > 0 ) { n1 = -n1; PosNeg: if ( n2 <= n1 ) { /* x1 -> x2 + x3 */ *coef = 1; ncoef = 1; AT.WorkPointer = (WORD *)(coef + 1); j = n2; for ( i = 0; i <= n2; i++ ) { if ( BinomGen(BHEAD term,level,tstops,x1,x3,n2-n1-i,i,sign&i ,coef,ncoef) ) goto RatioCall; if ( i < n2 ) { if ( Product(coef,&ncoef,j) ) goto RatioCall; if ( Quotient(coef,&ncoef,i+1) ) goto RatioCall; j--; AT.WorkPointer = (WORD *)(coef + ABS(ncoef)); } } AT.WorkPointer = (WORD *)(coef); return(0); } else { /* sum(i=0,n2-n1){x2^(n2-n1-i)*x3^i*binom(n1-1+i,n1-1)} +sum(i=0,n1-1){x3^(n2-i)*x1^-(n1-i)*binom(n2,i)} */ *coef = 1; ncoef = 1; AT.WorkPointer = (WORD *)(coef + 1); j = n2 - n1; for ( i = 0; i <= j; i++ ) { if ( BinomGen(BHEAD term,level,tstops,x2,x3,n2-n1-i,i,sign&i ,coef,ncoef) ) goto RatioCall; if ( i < j ) { if ( Product(coef,&ncoef,n1+i) ) goto RatioCall; if ( Quotient(coef,&ncoef,i+1) ) goto RatioCall; AT.WorkPointer = (WORD *)(coef + ABS(ncoef)); } } *coef = 1; ncoef = 1; AT.WorkPointer = (WORD *)(coef + 1); j = n1-1; for ( i = 0; i <= j; i++ ) { if ( BinomGen(BHEAD term,level,tstops,x1,x3,i-n1,n2-i,sign&(n2-i) ,coef,ncoef) ) goto RatioCall; if ( i < j ) { if ( Product(coef,&ncoef,n2-i) ) goto RatioCall; if ( Quotient(coef,&ncoef,i+1) ) goto RatioCall; AT.WorkPointer = (WORD *)(coef + ABS(ncoef)); } } AT.WorkPointer = (WORD *)(coef); return(0); } } else { n2 = -n2; n1 = -n1; /* +sum(i=0,n1-1){(-1)^i*binom(n2-1+i,n2-1) *x3^-(n2+i)*x1^-(n1-i)} +sum(i=0,n2-1){(-1)^(n1)*binom(n1-1+i,n1-1) *x3^-(n1+i)*x2^-(n2-i)} */ *coef = 1; ncoef = 1; AT.WorkPointer = (WORD *)(coef + 1); j = n1-1; for ( i = 0; i <= j; i++ ) { if ( BinomGen(BHEAD term,level,tstops,x1,x3,i-n1,-n2-i,i&1 ,coef,ncoef) ) goto RatioCall; if ( i < j ) { if ( Product(coef,&ncoef,n2+i) ) goto RatioCall; if ( Quotient(coef,&ncoef,i+1) ) goto RatioCall; AT.WorkPointer = (WORD *)(coef + ABS(ncoef)); } } *coef = 1; ncoef = 1; AT.WorkPointer = (WORD *)(coef + 1); j = n2-1; for ( i = 0; i <= j; i++ ) { if ( BinomGen(BHEAD term,level,tstops,x2,x3,i-n2,-n1-i,n1&1 ,coef,ncoef) ) goto RatioCall; if ( i < j ) { if ( Product(coef,&ncoef,n1+i) ) goto RatioCall; if ( Quotient(coef,&ncoef,i+1) ) goto RatioCall; AT.WorkPointer = (WORD *)(coef + ABS(ncoef)); } } AT.WorkPointer = (WORD *)(coef); return(0); } RatioCall: MLOCK(ErrorMessageLock); MesCall("RatioGen"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] RatioGen : #[ BinomGen : Routine for the generation of terms in a binomialtype expansion. */ int BinomGen(PHEAD WORD *term, WORD level, WORD **tstops, WORD x1, WORD x2, WORD pow1, WORD pow2, WORD sign, UWORD *coef, WORD ncoef) { GETBIDENTITY WORD *t, *r; WORD *termout; WORD k; termout = AT.WorkPointer; t = termout; r = term; do { *t++ = *r++; } while ( r < tstops[0] ); *t++ = SYMBOL; if ( pow2 == 0 ) { if ( pow1 == 0 ) t--; else { *t++ = 4; *t++ = x1; *t++ = pow1; } } else if ( pow1 == 0 ) { *t++ = 4; *t++ = x2; *t++ = pow2; } else { *t++ = 6; *t++ = x1; *t++ = pow1; *t++ = x2; *t++ = pow2; } *t++ = LNUMBER; *t++ = ABS(ncoef) + 3; *t = ncoef; if ( sign ) *t = -*t; t++; ncoef = ABS(ncoef); for ( k = 0; k < ncoef; k++ ) *t++ = coef[k]; r = tstops[1]; do { *t++ = *r++; } while ( r < tstops[2] ); *termout = WORDDIF(t,termout); AT.WorkPointer = t; if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } *AN.RepPoint = 1; AR.expchanged = 1; if ( Generator(BHEAD termout,level) ) { MLOCK(ErrorMessageLock); MesCall("BinomGen"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } AT.WorkPointer = termout; return(0); } /* #] BinomGen : #] Ratio : #[ Sum : #[ DoSumF1 : Routine expands a sum_ function. Its arguments are: The term in which the function occurs. The parameter list: length of parameter field function number (SUMNUM1) number of the symbol that is loop parameter min value max value increment the number of the subexpression to be removed the level in the generation tree. Note that the insertion of the loop parameter in the argument is done via the regular wildcard substitution mechanism. */ int DoSumF1(PHEAD WORD *term, WORD *params, WORD replac, WORD level) { GETBIDENTITY WORD *termout, *t, extractbuff = AT.TMbuff; WORD isum, ival, iinc; LONG from; CBUF *C; ival = params[3]; iinc = params[5]; if ( ( iinc > 0 && params[4] >= ival ) || ( iinc < 0 && params[4] <= ival ) ) { isum = (params[4] - ival)/iinc + 1; } else return(0); termout = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } t = term + 1; while ( *t != SUBEXPRESSION || t[2] != replac || t[4] != extractbuff ) t += t[1]; C = cbuf+t[4]; t += SUBEXPSIZE; if ( params[2] < 0 ) { while ( *t != INDTOIND || t[2] != -params[2] ) t += t[1]; *t = INDTOIND; } else { while ( *t > SYMTOSUB || t[2] != params[2] ) t += t[1]; *t = SYMTONUM; } do { t[3] = ival; from = C->rhs[replac] - C->Buffer; while ( C->Buffer[from] ) { if ( InsertTerm(BHEAD term,replac,extractbuff,C->Buffer+from,termout,0) < 0 ) goto SumF1Call; AT.WorkPointer = termout + *termout; if ( Generator(BHEAD termout,level) < 0 ) goto SumF1Call; from += C->Buffer[from]; } ival += iinc; } while ( --isum > 0 ); AT.WorkPointer = termout; return(0); SumF1Call: MLOCK(ErrorMessageLock); MesCall("DoSumF1"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] DoSumF1 : #[ Glue : Routine multiplies two terms. The second term is subject to the wildcard substitutions in sub. Output in the first term. This routine is a variation on the routine InsertTerm. */ int Glue(PHEAD WORD *term1, WORD *term2, WORD *sub, WORD insert) { GETBIDENTITY UWORD *coef; WORD ncoef, *t, *t1, *t2, i, nc2, nc3, old, newer; coef = (UWORD *)(TermMalloc("Glue")); t = term1; t += *t; i = t[-1]; t -= ABS(i); old = WORDDIF(t,term1); ncoef = REDLENG(i); if ( i < 0 ) i = -i; i--; t1 = t; t2 = (WORD *)coef; while ( --i >= 0 ) *t2++ = *t1++; i = *--t; nc2 = WildFill(BHEAD t,term2,sub); *t = i; t += nc2; nc2 = t[-1]; t -= ABS(nc2); newer = WORDDIF(t,term1); if ( MulRat(BHEAD (UWORD *)t,REDLENG(nc2),coef,ncoef,(UWORD *)t,&nc3) ) { MLOCK(ErrorMessageLock); MesCall("Glue"); MUNLOCK(ErrorMessageLock); TermFree(coef,"Glue"); SETERROR(-1) } i = (ABS(nc3))*2; t += i++; *t++ = (nc3 >= 0)?i:-i; *term1 = WORDDIF(t,term1); /* Switch the new piece with the old tail, so that noncommuting variables get into their proper spot. */ i = old - insert; t1 = t; t2 = term1+insert; NCOPY(t1,t2,i); i = newer - old; t1 = term1+insert; t2 = term1+old; NCOPY(t1,t2,i); t2 = t; i = old - insert; NCOPY(t1,t2,i); TermFree(coef,"Glue"); return(0); } /* #] Glue : #[ DoSumF2 : */ int DoSumF2(PHEAD WORD *term, WORD *params, WORD replac, WORD level) { GETBIDENTITY WORD *termout, *t, *from, *sub, *to, extractbuff = AT.TMbuff; WORD isum, ival, iinc, insert, i; CBUF *C; ival = params[3]; iinc = params[5]; if ( ( iinc > 0 && params[4] >= ival ) || ( iinc < 0 && params[4] <= ival ) ) { isum = (params[4] - ival)/iinc + 1; } else return(0); termout = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } t = term + 1; while ( *t != SUBEXPRESSION || t[2] != replac || t[4] != extractbuff ) t += t[1]; insert = WORDDIF(t,term); from = term; to = termout; while ( from < t ) *to++ = *from++; from += t[1]; sub = term + *term; while ( from < sub ) *to++ = *from++; *termout -= t[1]; sub = t; C = cbuf+t[4]; t += SUBEXPSIZE; if ( params[2] < 0 ) { while ( *t != INDTOIND || t[2] != -params[2] ) t += t[1]; *t = INDTOIND; } else { while ( *t > SYMTOSUB || t[2] != params[2] ) t += t[1]; *t = SYMTONUM; } t[3] = ival; for(;;) { AT.WorkPointer = termout + *termout; to = AT.WorkPointer; if ( ( to + *termout ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } from = termout; i = *termout; NCOPY(to,from,i); from = AT.WorkPointer; AT.WorkPointer = to; if ( Generator(BHEAD from,level) < 0 ) goto SumF2Call; if ( --isum <= 0 ) break; ival += iinc; t[3] = ival; if ( Glue(BHEAD termout,C->rhs[replac],sub,insert) < 0 ) goto SumF2Call; } AT.WorkPointer = termout; return(0); SumF2Call: MLOCK(ErrorMessageLock); MesCall("DoSumF2"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] DoSumF2 : #] Sum : #[ GCDfunction : #[ GCDfunction : */ typedef struct { WORD *buffer; DOLLARS dollar; LONG size; int type; int dummy; } ARGBUFFER; int GCDfunction(PHEAD WORD *term,WORD level) { GETBIDENTITY WORD *t, *tstop, *tf, *termout, *tin, *tout, *m, *mnext, *mstop, *mm; int todo, i, ii, j, istart, sign = 1, action = 0; WORD firstshort = 0, firstvalue = 0, gcdisone = 0, mlength, tlength, newlength; WORD totargs = 0, numargs, argsdone = 0, *mh, oldval1, *g, *gcdout = 0; WORD *arg1, *arg2; UWORD x1,x2,x3; LONG args; #if ( FUNHEAD > 4 ) WORD sh[FUNHEAD+5]; #else WORD sh[9]; #endif DOLLARS d; ARGBUFFER *abuf = 0, ab; /* #[ Find Function. Count arguments : First find the proper function */ t = term + *term; tlength = t[-1]; tstop = t - ABS(tlength); t = term + 1; while ( t < tstop ) { if ( *t != GCDFUNCTION ) { t += t[1]; continue; } todo = 1; totargs = 0; tf = t + FUNHEAD; while ( tf < t + t[1] ) { totargs++; if ( *tf > 0 && tf[1] != 0 ) todo = 0; NEXTARG(tf); } if ( todo ) break; t += t[1]; } if ( t >= tstop ) { MLOCK(ErrorMessageLock); MesPrint("Internal error. Indicated gcd_ function not encountered."); MUNLOCK(ErrorMessageLock); Terminate(-1); } WantAddPointers(totargs); args = AT.pWorkPointer; AT.pWorkPointer += totargs; /* #] Find Function. Count arguments : #[ Do short arguments : The function we need, in agreement with TestSub, is now in t Make first a compilation of the short arguments (except $-s and expressions) to see whether we need to do much work. This means that after this scan we can ignore all short arguments with the exception of unevaluated $-s and expressions. */ numargs = 0; firstshort = 0; tf = t + FUNHEAD; while ( tf < t + t[1] ) { if ( *tf == -SNUMBER && tf[1] == 0 ) { NEXTARG(tf); continue; } if ( *tf > 0 || *tf == -DOLLAREXPRESSION || *tf == -EXPRESSION ) { AT.pWorkSpace[args+numargs++] = tf; NEXTARG(tf); continue; } if ( firstshort == 0 ) { firstshort = *tf; if ( *tf <= -FUNCTION ) { firstvalue = -(*tf); } else { firstvalue = tf[1]; } NEXTARG(tf); argsdone++; continue; } else if ( *tf != firstshort ) { if ( *tf != -INDEX && *tf != -VECTOR && *tf != -MINVECTOR ) { argsdone++; gcdisone = 1; break; } if ( firstshort != -INDEX && firstshort != -VECTOR && firstshort != -MINVECTOR ) { argsdone++; gcdisone = 1; break; } if ( tf[1] != firstvalue ) { argsdone++; gcdisone = 1; break; } if ( *t == -MINVECTOR ) { firstshort = -VECTOR; } if ( firstshort == -MINVECTOR ) { firstshort = -VECTOR; } } else if ( *tf > -FUNCTION && *tf != -SNUMBER && tf[1] != firstvalue ) { argsdone++; gcdisone = 1; break; } if ( *tf == -SNUMBER && firstvalue != tf[1] ) { /* make a new firstvalue which is gcd_(firstvalue,tf[1]) */ if ( firstvalue == 1 || tf[1] == 1 ) { gcdisone = 1; break; } if ( firstvalue < 0 && tf[1] < 0 ) { x1 = -firstvalue; x2 = -tf[1]; sign = -1; } else { x1 = ABS(firstvalue); x2 = ABS(tf[1]); sign = 1; } while ( ( x3 = x1%x2 ) != 0 ) { x1 = x2; x2 = x3; } firstvalue = ((WORD)x2)*sign; argsdone++; if ( firstvalue == 1 ) { gcdisone = 1; break; } } NEXTARG(tf); } termout = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); if ( AT.WorkPointer > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* #] Do short arguments : #[ Do trivial GCD : Copy head */ i = t - term; tin = term; tout = termout; NCOPY(tout,tin,i); if ( gcdisone || ( firstshort == -SNUMBER && firstvalue == 1 ) ) { sign = 1; gcdone: tin += t[1]; tstop = term + *term; while ( tin < tstop ) *tout++ = *tin++; *termout = tout - termout; if ( sign < 0 ) tout[-1] = -tout[-1]; AT.WorkPointer = tout; if ( argsdone && Generator(BHEAD termout,level) < 0 ) goto CalledFrom; AT.WorkPointer = termout; AT.pWorkPointer = args; return(0); } /* #] Do trivial GCD : #[ Do short argument GCD : */ if ( numargs == 0 ) { /* basically we are done */ doshort: sign = 1; if ( firstshort == 0 ) goto gcdone; if ( firstshort == -SNUMBER ) { *tout++ = SNUMBER; *tout++ = 4; *tout++ = firstvalue; *tout++ = 1; goto gcdone; } else if ( firstshort == -SYMBOL ) { *tout++ = SYMBOL; *tout++ = 4; *tout++ = firstvalue; *tout++ = 1; goto gcdone; } else if ( firstshort == -VECTOR || firstshort == -INDEX ) { *tout++ = INDEX; *tout++ = 3; *tout++ = firstvalue; goto gcdone; } else if ( firstshort == -MINVECTOR ) { sign = -1; *tout++ = INDEX; *tout++ = 3; *tout++ = firstvalue; goto gcdone; } else if ( firstshort <= -FUNCTION ) { *tout++ = firstvalue; *tout++ = FUNHEAD; FILLFUN(tout); goto gcdone; } else { MLOCK(ErrorMessageLock); MesPrint("Internal error. Illegal short argument in GCDfunction."); MUNLOCK(ErrorMessageLock); Terminate(-1); } } /* #] Do short argument GCD : #[ Convert short argument : Now we allocate space for the arguments in general notation. First the special one if there were short arguments */ if ( firstshort ) { switch ( firstshort ) { case -SNUMBER: sh[0] = 4; sh[1] = ABS(firstvalue); sh[2] = 1; if ( firstvalue < 0 ) sh[3] = -3; else sh[3] = 3; sh[4] = 0; break; case -MINVECTOR: case -VECTOR: case -INDEX: sh[0] = 8; sh[1] = INDEX; sh[2] = 3; sh[3] = firstvalue; sh[4] = 1; sh[5] = 1; if ( firstshort == -MINVECTOR ) sh[6] = -3; else sh[6] = 3; sh[7] = 0; break; case -SYMBOL: sh[0] = 8; sh[1] = SYMBOL; sh[2] = 4; sh[3] = firstvalue; sh[4] = 1; sh[5] = 1; sh[6] = 1; sh[7] = 3; sh[8] = 0; break; default: sh[0] = FUNHEAD+4; sh[1] = firstshort; sh[2] = FUNHEAD; for ( i = 2; i < FUNHEAD; i++ ) sh[i+1] = 0; sh[FUNHEAD+1] = 1; sh[FUNHEAD+2] = 1; sh[FUNHEAD+3] = 3; sh[FUNHEAD+4] = 0; break; } } /* #] Convert short argument : #[ Sort arguments : Now we should sort the arguments in a way that the dollars and the expressions come last. That way we may never need them. */ for ( i = 1; i < numargs; i++ ) { for ( ii = i; ii > 0; ii-- ) { arg1 = AT.pWorkSpace[args+ii]; arg2 = AT.pWorkSpace[args+ii-1]; if ( *arg1 < 0 ) { if ( *arg2 < 0 ) { if ( *arg1 == -EXPRESSION ) break; if ( *arg2 == -DOLLAREXPRESSION ) break; AT.pWorkSpace[args+ii] = arg2; AT.pWorkSpace[args+ii-1] = arg1; } else break; } else if ( *arg2 < 0 ) { AT.pWorkSpace[args+ii] = arg2; AT.pWorkSpace[args+ii-1] = arg1; } else { if ( *arg1 > *arg2 ) { AT.pWorkSpace[args+ii] = arg2; AT.pWorkSpace[args+ii-1] = arg1; } else break; } } } /* #] Sort arguments : #[ There is a single term argument : */ if ( firstshort ) { mh = sh; istart = 0; oneterm:; for ( i = istart; i < numargs; i++ ) { arg1 = AT.pWorkSpace[args+i]; if ( *arg1 > 0 ) { oldval1 = arg1[*arg1]; arg1[*arg1] = 0; m = arg1+ARGHEAD; while ( *m ) { GCDterms(BHEAD mh,m,mh); m += *m; if ( mh[0] == 4 && mh[1] == 1 && mh[2] == 1 && mh[3] == 3 ) { gcdisone = 1; sign = 1; arg1[*arg1] = oldval1; goto gcdone; } } arg1[*arg1] = oldval1; } else if ( *arg1 == -DOLLAREXPRESSION ) { if ( ( d = DolToTerms(BHEAD arg1[1]) ) != 0 ) { m = d->where; while ( *m ) { GCDterms(BHEAD mh,m,mh); m += *m; argsdone++; if ( mh[0] == 4 && mh[1] == 1 && mh[2] == 1 && mh[3] == 3 ) { gcdisone = 1; sign = 1; if ( d->factors ) M_free(d->factors,"Dollar factors"); M_free(d,"Copy of dollar variable"); goto gcdone; } } if ( d->factors ) M_free(d->factors,"Dollar factors"); M_free(d,"Copy of dollar variable"); } } else { mm = CreateExpression(BHEAD arg1[1]); m = mm; while ( *m ) { GCDterms(BHEAD mh,m,mh); m += *m; argsdone++; if ( mh[0] == 4 && mh[1] == 1 && mh[2] == 1 && mh[3] == 3 ) { gcdisone = 1; sign = 1; M_free(mm,"CreateExpression"); goto gcdone; } } M_free(mm,"CreateExpression"); } } if ( firstshort ) { if ( mh[0] == 4 ) { firstshort = -SNUMBER; firstvalue = mh[1] * (mh[3]/3); } else if ( mh[1] == SYMBOL ) { firstshort = -SYMBOL; firstvalue = mh[3]; } else if ( mh[1] == INDEX ) { firstshort = -INDEX; firstvalue = mh[3]; if ( mh[6] == -3 ) firstshort = -MINVECTOR; } else if ( mh[1] >= FUNCTION ) { firstshort = -mh[1]; firstvalue = mh[1]; } goto doshort; } else { /* We have a GCD that is only a single term. Paste it in and combine the coefficients. */ mh[mh[0]] = 0; mm = mh; ii = 0; goto multiterms; } } /* Now we have only regular arguments. But some have not yet been expanded. Check whether there are proper long arguments and if so if there is one with just a single term */ for ( i = 0; i < numargs; i++ ) { arg1 = AT.pWorkSpace[args+i]; if ( *arg1 > 0 && arg1[ARGHEAD]+ARGHEAD == *arg1 ) { /* We have an argument with a single term */ if ( i != 0 ) { arg2 = AT.pWorkSpace[args]; AT.pWorkSpace[args] = arg1; AT.pWorkSpace[args+1] = arg2; } m = mh = AT.WorkPointer; mm = arg1+ARGHEAD; i = *mm; NCOPY(m,mm,i); AT.WorkPointer = m; istart = 1; argsdone++; goto oneterm; } } /* #] There is a single term argument : #[ Expand $ and expr : We have: 1: regular multiterm arguments 2: dollars 3: expressions. The sum of them is numargs. Their addresses are in args. The problem is that expansion will lead to allocations that we have to return and all these allocations are different in nature. */ action = 1; abuf = (ARGBUFFER *)Malloc1(numargs*sizeof(ARGBUFFER),"argbuffer"); for ( i = 0; i < numargs; i++ ) { arg1 = AT.pWorkSpace[args+i]; if ( *arg1 > 0 ) { m = (WORD *)Malloc1(*arg1*sizeof(WORD),"argbuffer type 0"); abuf[i].buffer = m; abuf[i].type = 0; mm = arg1+ARGHEAD; j = *arg1-ARGHEAD; abuf[i].size = j; if ( j ) argsdone++; NCOPY(m,mm,j); *m = 0; } else if ( *arg1 == -DOLLAREXPRESSION ) { d = DolToTerms(BHEAD arg1[1]); abuf[i].buffer = d->where; abuf[i].type = 1; abuf[i].dollar = d; m = abuf[i].buffer; if ( *m ) argsdone++; while ( *m ) m+= *m; abuf[i].size = m-abuf[i].buffer; } else if ( *arg1 == -EXPRESSION ) { abuf[i].buffer = CreateExpression(BHEAD arg1[1]); abuf[i].type = 2; m = abuf[i].buffer; if ( *m ) argsdone++; while ( *m ) m+= *m; abuf[i].size = m-abuf[i].buffer; } else { MLOCK(ErrorMessageLock); MesPrint("What argument is this?"); MUNLOCK(ErrorMessageLock); goto CalledFrom; } } for ( i = 0; i < numargs; i++ ) { arg1 = abuf[i].buffer; if ( *arg1 == 0 ) {} else if ( arg1[*arg1] == 0 ) { /* After expansion there is an argument with a single term */ ab = abuf[i]; abuf[i] = abuf[0]; abuf[0] = ab; mh = abuf[0].buffer; for ( j = 1; j < numargs; j++ ) { m = abuf[j].buffer; while ( *m ) { GCDterms(BHEAD mh,m,mh); m += *m; argsdone++; if ( mh[0] == 4 && mh[1] == 1 && mh[2] == 1 && mh[3] == 3 ) { gcdisone = 1; sign = 1; break; } } if ( *m ) break; } mm = mh + *mh; if ( mm[-1] < 0 ) { sign = -1; mm[-1] = -mm[-1]; } mstop = mm - mm[-1]; m = mh+1; mlength = mm[-1]; while ( tin < t ) *tout++ = *tin++; while ( m < mstop ) *tout++ = *m++; tin += tin[1]; while ( tin < tstop ) *tout++ = *tin++; tlength = REDLENG(tlength); mlength = REDLENG(mlength); if ( MulRat(BHEAD (UWORD *)tstop,tlength,(UWORD *)mstop,mlength, (UWORD *)tout,&newlength) < 0 ) goto CalledFrom; mlength = INCLENG(newlength); tout += ABS(mlength); tout[-1] = mlength*sign; *termout = tout - termout; AT.WorkPointer = tout; if ( argsdone && Generator(BHEAD termout,level) < 0 ) goto CalledFrom; goto cleanup; } } /* There are only arguments with more than one term. We order them by size to make the computations as easy as possible. */ for ( i = 1; i < numargs; i++ ) { for ( ii = i; ii > 0; ii-- ) { if ( abuf[ii-1].size <= abuf[ii].size ) break; ab = abuf[ii-1]; abuf[ii-1] = abuf[ii]; abuf[ii] = ab; } } /* #] Expand $ and expr : #[ Multiterm subexpressions : */ ii = 0; gcdout = abuf[ii].buffer; for ( i = 0; i < numargs; i++ ) { if ( abuf[i].buffer[0] ) { gcdout = abuf[i].buffer; ii = i; i++; argsdone++; break; } } for ( ; i < numargs; i++ ) { if ( abuf[i].buffer[0] ) { g = GCDfunction3(BHEAD gcdout,abuf[i].buffer); argsdone++; if ( gcdout != abuf[ii].buffer ) M_free(gcdout,"gcdout"); gcdout = g; if ( gcdout[*gcdout] == 0 && gcdout[0] == 4 && gcdout[1] == 1 && gcdout[2] == 1 && gcdout[3] == 3 ) break; } } mm = gcdout; multiterms:; tlength = REDLENG(tlength); while ( *mm ) { tin = term; tout = termout; while ( tin < t ) *tout++ = *tin++; tin += t[1]; mnext = mm + *mm; mlength = mnext[-1]; mstop = mnext - ABS(mlength); mm++; while ( mm < mstop ) *tout++ = *mm++; while ( tin < tstop ) *tout++ = *tin++; mlength = REDLENG(mlength); if ( MulRat(BHEAD (UWORD *)tstop,tlength,(UWORD *)mm,mlength, (UWORD *)tout,&newlength) < 0 ) goto CalledFrom; mlength = INCLENG(newlength); tout += ABS(mlength); tout[-1] = mlength; *termout = tout - termout; AT.WorkPointer = tout; if ( argsdone && Generator(BHEAD termout,level) < 0 ) goto CalledFrom; mm = mnext; /* next term */ } if ( action && ( gcdout != abuf[ii].buffer ) ) M_free(gcdout,"gcdout"); /* #] Multiterm subexpressions : #[ Cleanup : */ cleanup:; if ( action ) { for ( i = 0; i < numargs; i++ ) { if ( abuf[i].type == 0 ) { M_free(abuf[i].buffer,"argbuffer type 0"); } else if ( abuf[i].type == 1 ) { d = abuf[i].dollar; if ( d->factors ) M_free(d->factors,"Dollar factors"); M_free(d,"Copy of dollar variable"); } else if ( abuf[i].type == 2 ) { M_free(abuf[i].buffer,"CreateExpression"); } } M_free(abuf,"argbuffer"); } /* #] Cleanup : */ AT.pWorkPointer = args; AT.WorkPointer = termout; return(0); CalledFrom: MLOCK(ErrorMessageLock); MesCall("GCDfunction"); MUNLOCK(ErrorMessageLock); SETERROR(-1) return(-1); } /* #] GCDfunction : #[ GCDfunction3 : Finds the GCD of the two arguments which are buffers with terms. In principle the first buffer can have only one term. If both buffers have more than one term, we need to replace all non-symbolic objects by generated symbols and substitute that back afterwards. The rest we leave to the powerful routines. Philosophical problem: What do we do with GCD_(x/z+y,x+y*z) ? Method: If we have only negative powers of z and no positive powers we let the EXTRASYMBOLS do their job. When mixed, multiply the arguments with the negative powers with enough powers of z to eliminate the negative powers. The DENOMINATOR function is always eliminated with the mechanism as we cannot tell whether there are positive powers of its contents. */ WORD *GCDfunction3(PHEAD WORD *in1, WORD *in2) { GETBIDENTITY WORD oldsorttype = AR.SortType, *ow = AT.WorkPointer;; WORD *t, *tt, *gcdout, *term1, *term2, *confree1, *confree2, *gcdout1, *proper1, *proper2; int i, actionflag1, actionflag2; WORD startebuf = cbuf[AT.ebufnum].numrhs; WORD tryterm1, tryterm2; if ( in2[*in2] == 0 ) { t = in1; in1 = in2; in2 = t; } if ( in1[*in1] == 0 ) { /* First input with only one term */ gcdout = (WORD *)Malloc1((*in1+1)*sizeof(WORD),"gcdout"); i = *in1; t = gcdout; tt = in1; NCOPY(t,tt,i); *t = 0; t = in2; while ( *t ) { GCDterms(BHEAD gcdout,t,gcdout); if ( gcdout[0] == 4 && gcdout[1] == 1 && gcdout[2] == 1 && gcdout[3] == 3 ) break; t += *t; } AT.WorkPointer = ow; return(gcdout); } /* We need to take out the content from the two expressions and determine their GCD. This plays with the negative powers! */ AR.SortType = SORTHIGHFIRST; term1 = TermMalloc("GCDfunction3-a"); term2 = TermMalloc("GCDfunction3-b"); confree1 = TakeContent(BHEAD in1,term1); tryterm1 = AN.tryterm; AN.tryterm = 0; confree2 = TakeContent(BHEAD in2,term2); tryterm2 = AN.tryterm; AN.tryterm = 0; /* confree1 = TakeSymbolContent(BHEAD in1,term1); confree2 = TakeSymbolContent(BHEAD in2,term2); */ GCDterms(BHEAD term1,term2,term1); TermFree(term2,"GCDfunction3-b"); /* Now we have to replace all non-symbols and symbols to a negative power by extra symbols. */ if ( ( proper1 = PutExtraSymbols(BHEAD confree1,startebuf,&actionflag1) ) == 0 ) goto CalledFrom; if ( confree1 != in1 ) { if ( tryterm1 ) { TermFree(confree1,"TakeContent"); } else { M_free(confree1,"TakeContent"); } } /* TermFree(confree1,"TakeSymbolContent"); */ if ( ( proper2 = PutExtraSymbols(BHEAD confree2,startebuf,&actionflag2) ) == 0 ) goto CalledFrom; if ( confree2 != in2 ) { if ( tryterm2 ) { TermFree(confree2,"TakeContent"); } else { M_free(confree2,"TakeContent"); } } /* TermFree(confree2,"TakeSymbolContent"); */ /* And now the real work: */ gcdout1 = poly_gcd(BHEAD proper1,proper2,0); M_free(proper1,"PutExtraSymbols"); M_free(proper2,"PutExtraSymbols"); AR.SortType = oldsorttype; if ( actionflag1 || actionflag2 ) { if ( ( gcdout = TakeExtraSymbols(BHEAD gcdout1,startebuf) ) == 0 ) goto CalledFrom; M_free(gcdout1,"gcdout"); } else { gcdout = gcdout1; } cbuf[AT.ebufnum].numrhs = startebuf; /* Now multiply gcdout by term1 */ if ( term1[0] != 4 || term1[3] != 3 || term1[1] != 1 || term1[2] != 1 ) { AN.tryterm = -1; if ( ( gcdout1 = MultiplyWithTerm(BHEAD gcdout,term1,2) ) == 0 ) goto CalledFrom; AN.tryterm = 0; M_free(gcdout,"gcdout"); gcdout = gcdout1; } TermFree(term1,"GCDfunction3-a"); AT.WorkPointer = ow; return(gcdout); CalledFrom: AN.tryterm = 0; MLOCK(ErrorMessageLock); MesCall("GCDfunction3"); MUNLOCK(ErrorMessageLock); return(0); } /* #] GCDfunction3 : #[ PutExtraSymbols : */ WORD *PutExtraSymbols(PHEAD WORD *in,WORD startebuf,int *actionflag) { WORD *termout = AT.WorkPointer; int action; *actionflag = 0; NewSort(BHEAD0); while ( *in ) { if ( ( action = LocalConvertToPoly(BHEAD in,termout,startebuf,0) ) < 0 ) { LowerSortLevel(); goto CalledFrom; } if ( action > 0 ) *actionflag = 1; StoreTerm(BHEAD termout); in += *in; } if ( EndSort(BHEAD (WORD *)((void *)(&termout)),2) < 0 ) goto CalledFrom; return(termout); CalledFrom: MLOCK(ErrorMessageLock); MesCall("PutExtraSymbols"); MUNLOCK(ErrorMessageLock); return(0); } /* #] PutExtraSymbols : #[ TakeExtraSymbols : */ WORD *TakeExtraSymbols(PHEAD WORD *in,WORD startebuf) { CBUF *C = cbuf+AC.cbufnum; CBUF *CC = cbuf+AT.ebufnum; WORD *oldworkpointer = AT.WorkPointer, *termout; termout = AT.WorkPointer; NewSort(BHEAD0); while ( *in ) { if ( ConvertFromPoly(BHEAD in,termout,numxsymbol,CC->numrhs-startebuf+numxsymbol,startebuf-numxsymbol,1) <= 0 ) { LowerSortLevel(); goto CalledFrom; } in += *in; AT.WorkPointer = termout + *termout; /* ConvertFromPoly leaves terms with subexpressions. Hence: */ if ( Generator(BHEAD termout,C->numlhs) ) { LowerSortLevel(); goto CalledFrom; } } AT.WorkPointer = oldworkpointer; if ( EndSort(BHEAD (WORD *)((void *)(&termout)),2) < 0 ) goto CalledFrom; return(termout); CalledFrom: MLOCK(ErrorMessageLock); MesCall("TakeExtraSymbols"); MUNLOCK(ErrorMessageLock); return(0); } /* #] TakeExtraSymbols : #[ MultiplyWithTerm : */ WORD *MultiplyWithTerm(PHEAD WORD *in, WORD *term, WORD par) { WORD *termout, *t, *tt, *tstop, *ttstop; WORD length, length1, length2; WORD oldsorttype = AR.SortType; COMPARE oldcompareroutine = (COMPARE)(AR.CompareRoutine); AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); if ( par == 0 || par == 2 ) AR.SortType = SORTHIGHFIRST; else AR.SortType = SORTLOWFIRST; termout = AT.WorkPointer; NewSort(BHEAD0); while ( *in ) { tt = termout + 1; tstop = in + *in; tstop -= ABS(tstop[-1]); t = in + 1; while ( t < tstop ) *tt++ = *t++; ttstop = term + *term; ttstop -= ABS(ttstop[-1]); t = term + 1; while ( t < ttstop ) *tt++ = *t++; length1 = REDLENG(in[*in-1]); length2 = REDLENG(term[*term-1]); if ( MulRat(BHEAD (UWORD *)tstop,length1, (UWORD *)ttstop,length2,(UWORD *)tt,&length) ) goto CalledFrom; length = INCLENG(length); tt += ABS(length); tt[-1] = length; *termout = tt - termout; SymbolNormalize(termout); StoreTerm(BHEAD termout); in += *in; } if ( par == 2 ) { /* if ( AN.tryterm == 0 ) AN.tryterm = 1; */ AN.tryterm = 0; /* For now */ if ( EndSort(BHEAD (WORD *)((void *)(&termout)),2) < 0 ) goto CalledFrom; } else { if ( EndSort(BHEAD termout,1) < 0 ) goto CalledFrom; } AR.CompareRoutine = (COMPAREDUMMY)oldcompareroutine; AR.SortType = oldsorttype; return(termout); CalledFrom: MLOCK(ErrorMessageLock); MesCall("MultiplyWithTerm"); MUNLOCK(ErrorMessageLock); return(0); } /* #] MultiplyWithTerm : #[ TakeContent : */ /** * Implements part of the old ExecArg in which we take common factors * from arguments with more than one term. * Here the input is a sequence of terms in 'in' and the answer is a * content-free sequence of terms. This sequence has been allocated by * the Malloc1 routine in a call to EndSort, unless the expression was * already content-free. In that case the input pointer is returned. * The content is returned in term. This is supposed to be a separate * allocation, made by TermMalloc in the calling routine. */ WORD *TakeContent(PHEAD WORD *in, WORD *term) { GETBIDENTITY WORD *t, *tstop, *tcom, *tout, *tstore, *r, *rstop, *m, *mm, *w, *ww, *wterm; WORD *tnext, *tt, *tterm, code[2]; WORD *inp, a, *den; int i, j, k, action = 0, sign; UWORD *GCDbuffer, *GCDbuffer2, *LCMbuffer, *LCMbuffer2, *ap; WORD GCDlen, GCDlen2, LCMlen, LCMlen2, length, redlength, len1, len2; tout = tstore = term+1; /* #[ INDEX : */ t = in; tnext = t + *t; tstop = tnext-ABS(tnext[-1]); t++; while ( t < tstop ) { if ( *t == INDEX ) { i = t[1]; NCOPY(tout,t,i); break; } else t += t[1]; } if ( tout > tstore ) { /* There are indices in the first term */ t = tnext; while ( *t ) { tnext = t + *t; rstop = tnext - ABS(tnext[-1]); r = t+1; if ( r == rstop ) goto noindices; while ( r < rstop ) { if ( *r != INDEX ) { r += r[1]; continue; } m = tstore+2; while ( m < tout ) { for ( i = 2; i < r[1]; i++ ) { if ( *m == r[i] ) break; if ( *m > r[i] ) continue; mm = m+1; while ( mm < tout ) { mm[-1] = mm[0]; mm++; } tout--; tstore[1]--; m--; break; } m++; } } if ( r >= rstop || tout <= tstore+2 ) { tout = tstore; break; } } if ( tout > tstore+2 ) { /* Now we have to take out what is in tstore */ t = in; w = in; while ( *t ) { wterm = w; tnext = t + *t; t++; w++; while ( *t != INDEX ) { i = t[1]; NCOPY(w,t,i); } tt = t + t[1]; t += 2; r = tstore+2; ww = w; *w++ = INDEX; w++; while ( r < tout && t < tt ) { if ( *r > *t ) { *w++ = *t++; } else if ( *r == *t ) { r++; t++; } else goto CalledFrom; } if ( r < tout ) goto CalledFrom; while ( t < tt ) *w++ = *t++; ww[1] = w - ww; if ( ww[1] == 2 ) w = ww; while ( t < tnext ) *w++ = *t++; *wterm = w - wterm; } *w = 0; } noindices: tstore = tout; } /* #] INDEX : #[ VECTOR/DELTA : */ code[0] = VECTOR; code[1] = DELTA; for ( k = 0; k < 2; k++ ) { t = in; tnext = t + *t; tstop = tnext-ABS(tnext[-1]); t++; while ( t < tstop ) { if ( *t == code[k] ) { i = t[1]; NCOPY(tout,t,i); break; } else t += t[1]; } if ( tout > tstore ) { /* There are vectors in the first term */ t = tnext; while ( *t ) { tnext = t + *t; rstop = tnext - ABS(tnext[-1]); r = t+1; if ( r == rstop ) { tstore = tout; goto novectors; } while ( r < rstop ) { if ( *r != code[k] ) { r += r[1]; continue; } m = tstore+2; while ( m < tout ) { for ( i = 2; i < r[1]; i += 2 ) { if ( *m == r[i] && m[1] == r[i+1] ) break; if ( *m > r[i] || ( *m == r[i] && m[1] > r[i+1] ) ) continue; mm = m+2; while ( mm < tout ) { mm[-2] = mm[0]; mm[-1] = mm[1]; mm += 2; } tout -= 2; tstore[1] -= 2; m -= 2; break; } m += 2; } } if ( r >= rstop || tout <= tstore+2 ) { tout = tstore; break; } } if ( tout > tstore+2 ) { /* Now we have to take out what is in tstore */ t = in; w = in; while ( *t ) { wterm = w; tnext = t + *t; t++; w++; while ( *t != code[k] ) { i = t[1]; NCOPY(w,t,i); } tt = t + t[1]; t += 2; r = tstore+2; ww = w; *w++ = code[k]; w++; while ( r < tout && t < tt ) { if ( ( *r > *t ) || ( *r == *t && r[1] > t[1] ) ) { *w++ = *t++; *w++ = *t++; } else if ( *r == *t && r[1] == t[1] ) { r += 2; t += 2; } else goto CalledFrom; } if ( r < tout ) goto CalledFrom; while ( t < tt ) *w++ = *t++; ww[1] = w - ww; if ( ww[1] == 2 ) w = ww; while ( t < tnext ) *w++ = *t++; *wterm = w - wterm; } *w = 0; } tstore = tout; } } novectors:; /* #] VECTOR/DELTA : #[ FUNCTIONS : */ t = in; tnext = t + *t; tstop = tnext-ABS(tnext[-1]); t++; tcom = 0; while ( t < tstop ) { if ( *t >= FUNCTION ) { if ( functions[*t-FUNCTION].commute ) { if ( tcom == 0 ) { tcom = tstore; } else { for ( i = 0; i < t[1]; i++ ) { if ( t[i] != tcom[i] ) { MLOCK(ErrorMessageLock); MesPrint("GCD or factorization of more than one noncommuting object not allowed"); MUNLOCK(ErrorMessageLock); goto CalledFrom; } } } } i = t[1]; NCOPY(tstore,t,i); } else t += t[1]; } if ( tout > tstore ) { t = tnext; while ( *t ) { tnext = t + *t; tstop = tnext - ABS(tnext[-1]); t++; if ( t == tstop ) goto nofunctions; r = tstore; while ( r < tout ) { tt = t; while ( tt < tstop ) { for ( i = 0; i < r[1]; i++ ) { if ( r[i] != tt[i] ) break; } if ( i == r[1] ) { r += r[1]; goto nextr1; } } /* Not encountered in this term. Scratch from list */ m = r; mm = r + r[1]; while ( mm < tout ) *m++ = *mm++; tout = m; nextr1:; } if ( tout <= tstore ) break; t += *t; } } if ( tout > tstore ) { /* Now we have one or more functions left that are common in all terms. Take them out. We do this one by one. */ r = tstore; while ( r < tout ) { t = in; ww = in; w = ww+1; while ( *t ) { tnext = t + *t; t++; for(;;) { for ( i = 0; i < r[1]; i++ ) { if ( t[i] != r[i] ) { j = t[1]; NCOPY(w,t,j); break; } } if ( i == r[1] ) { t += t[1]; while ( t < tnext ) *w++ = *t++; *ww = w - ww; break; } } } r += r[1]; *w = 0; } nofunctions: tstore = tout; } /* #] FUNCTIONS : #[ SYMBOL : We make a list of symbols and their minimal powers. This includes negative powers. In the end we have to multiply by the inverse of this list. That takes out all negative powers and leaves things ready for further processing. */ tterm = AT.WorkPointer; tt = tterm+1; tout[0] = SYMBOL; tout[1] = 2; t = in; tnext = t + *t; tstop = tnext - ABS(tnext[-1]); t++; while ( t < tstop ) { if ( *t == SYMBOL ) { for ( i = 0; i < t[1]; i++ ) tout[i] = t[i]; break; } t += t[1]; } t = tnext; while ( *t ) { tnext = t + *t; tstop = tnext - ABS(tnext[-1]); t++; if ( t == tstop ) { tout[1] = 2; break; } else { while ( t < tstop ) { if ( *t == SYMBOL ) { MergeSymbolLists(BHEAD tout,t,-1); break; } t += t[1]; } t = tnext; } } if ( tout[1] > 2 ) { t = tout; tt[0] = t[0]; tt[1] = t[1]; for ( i = 2; i < t[1]; i += 2 ) { tt[i] = t[i]; tt[i+1] = -t[i+1]; } tt += tt[1]; tout += tout[1]; action++; } /* #] SYMBOL : #[ DOTPRODUCT : We make a list of dotproducts and their minimal powers. This includes negative powers. In the end we have to multiply by the inverse of this list. That takes out all negative powers and leaves things ready for further processing. */ tout[0] = DOTPRODUCT; tout[1] = 2; t = in; while ( *t ) { tnext = t + *t; tstop = tnext - ABS(tnext[-1]); t++; if ( t == tstop ) { tout[1] = 2; break; } while ( t < tstop ) { if ( *t == DOTPRODUCT ) { MergeDotproductLists(BHEAD tout,t,-1); break; } t += t[1]; } t = tnext; } if ( tout[1] > 2 ) { t = tout; tt[0] = t[0]; tt[1] = t[1]; for ( i = 2; i < t[1]; i += 3 ) { tt[i] = t[i]; tt[i+1] = t[i+1]; tt[i+2] = -t[i+2]; } tt += tt[1]; tout += tout[1]; action++; } /* #] DOTPRODUCT : #[ Coefficient : Now we have to collect the GCD of the numerators and the LCM of the denominators. */ AT.WorkPointer = tt; if ( AN.cmod != 0 ) { WORD x, ix, ip; t = in; tnext = t + *t; tstop = tnext - ABS(tnext[-1]); x = tstop[0]; if ( tnext[-1] < 0 ) x += AC.cmod[0]; if ( GetModInverses(x,(WORD)(AN.cmod[0]),&ix,&ip) ) goto CalledFrom; *tout++ = x; *tout++ = 1; *tout++ = 3; *tt++ = ix; *tt++ = 1; *tt++ = 3; } else { GCDbuffer = NumberMalloc("MakeInteger"); GCDbuffer2 = NumberMalloc("MakeInteger"); LCMbuffer = NumberMalloc("MakeInteger"); LCMbuffer2 = NumberMalloc("MakeInteger"); t = in; tnext = t + *t; length = tnext[-1]; if ( length < 0 ) { sign = -1; length = -length; } else { sign = 1; } tstop = tnext - length; redlength = (length-1)/2; for ( i = 0; i < redlength; i++ ) { GCDbuffer[i] = (UWORD)(tstop[i]); LCMbuffer[i] = (UWORD)(tstop[redlength+i]); } GCDlen = LCMlen = redlength; while ( GCDbuffer[GCDlen-1] == 0 ) GCDlen--; while ( LCMbuffer[LCMlen-1] == 0 ) LCMlen--; t = tnext; while ( *t ) { tnext = t + *t; length = ABS(tnext[-1]); tstop = tnext - length; redlength = (length-1)/2; len1 = len2 = redlength; den = tstop + redlength; while ( tstop[len1-1] == 0 ) len1--; while ( den[len2-1] == 0 ) len2--; if ( GCDlen == 1 && GCDbuffer[0] == 1 ) {} else { GcdLong(BHEAD (UWORD *)tstop,len1,GCDbuffer,GCDlen,GCDbuffer2,&GCDlen2); ap = GCDbuffer; GCDbuffer = GCDbuffer2; GCDbuffer2 = ap; a = GCDlen; GCDlen = GCDlen2; GCDlen2 = a; } if ( len2 == 1 && den[0] == 1 ) {} else { GcdLong(BHEAD LCMbuffer,LCMlen,(UWORD *)den,len2,LCMbuffer2,&LCMlen2); DivLong((UWORD *)den,len2,LCMbuffer2,LCMlen2, GCDbuffer2,&GCDlen2,(UWORD *)AT.WorkPointer,&a); MulLong(LCMbuffer,LCMlen,GCDbuffer2,GCDlen2,LCMbuffer2,&LCMlen2); ap = LCMbuffer; LCMbuffer = LCMbuffer2; LCMbuffer2 = ap; a = LCMlen; LCMlen = LCMlen2; LCMlen2 = a; } t = tnext; } if ( GCDlen != 1 || GCDbuffer[0] != 1 || LCMlen != 1 || LCMbuffer[0] != 1 ) { redlength = GCDlen; if ( LCMlen > GCDlen ) redlength = LCMlen; for ( i = 0; i < GCDlen; i++ ) *tout++ = (WORD)(GCDbuffer[i]); for ( ; i < redlength; i++ ) *tout++ = 0; for ( i = 0; i < LCMlen; i++ ) *tout++ = (WORD)(LCMbuffer[i]); for ( ; i < redlength; i++ ) *tout++ = 0; *tout++ = (2*redlength+1)*sign; for ( i = 0; i < LCMlen; i++ ) *tt++ = (WORD)(LCMbuffer[i]); for ( ; i < redlength; i++ ) *tt++ = 0; for ( i = 0; i < GCDlen; i++ ) *tt++ = (WORD)(GCDbuffer[i]); for ( ; i < redlength; i++ ) *tt++ = 0; *tt++ = (2*redlength+1)*sign; action++; } else { *tout++ = 1; *tout++ = 1; *tout++ = 3*sign; *tt++ = 1; *tt++ = 1; *tt++ = 3*sign; if ( sign != 1 ) action++; } *tout = 0; NumberFree(LCMbuffer2,"MakeInteger"); NumberFree(LCMbuffer ,"MakeInteger"); NumberFree(GCDbuffer2,"MakeInteger"); NumberFree(GCDbuffer ,"MakeInteger"); } /* #] Coefficient : #[ Multiply by the inverse content : */ if ( action ) { *tterm = tt - tterm; AT.WorkPointer = tt; inp = MultiplyWithTerm(BHEAD in,tterm,2); AT.WorkPointer = tterm; in = inp; } /* #] Multiply by the inverse content : */ *term = tout - term; AT.WorkPointer = tterm; return(in); CalledFrom: MLOCK(ErrorMessageLock); MesCall("TakeContent"); MUNLOCK(ErrorMessageLock); return(0); } /* #] TakeContent : #[ MergeSymbolLists : Merges the extra list into the old. If par == -1 we take minimum powers If par == 1 we take maximum powers If par == 0 we take minimum of the absolute value of the powers if one is positive and the other negative we get zero. We assume that the symbols are in order in both lists */ int MergeSymbolLists(PHEAD WORD *old, WORD *extra, int par) { GETBIDENTITY WORD *new = TermMalloc("MergeSymbolLists"); WORD *t1, *t2, *fill; int i1,i2; fill = new + 2; *new = SYMBOL; i1 = old[1] - 2; i2 = extra[1] - 2; t1 = old + 2; t2 = extra + 2; switch ( par ) { case -1: while ( i1 > 0 && i2 > 0 ) { if ( *t1 > *t2 ) { if ( t2[1] < 0 ) { *fill++ = *t2++; *fill++ = *t2++; } else t2 += 2; i2 -= 2; } else if ( *t1 < *t2 ) { if ( t1[1] < 0 ) { *fill++ = *t1++; *fill++ = *t1++; } else t1 += 2; i1 -= 2; } else if ( t1[1] < t2[1] ) { *fill++ = *t1++; *fill++ = *t1++; t2 += 2; i1 -= 2; i2 -=2; } else { *fill++ = *t2++; *fill++ = *t2++; t1 += 2; i1 -= 2; i2 -=2; } } for ( ; i1 > 0; i1 -= 2 ) { if ( t1[1] < 0 ) { *fill++ = *t1++; *fill++ = *t1++; } else t1 += 2; } for ( ; i2 > 0; i2 -= 2 ) { if ( t2[1] < 0 ) { *fill++ = *t2++; *fill++ = *t2++; } else t2 += 2; } break; case 1: while ( i1 > 0 && i2 > 0 ) { if ( *t1 > *t2 ) { if ( t2[1] > 0 ) { *fill++ = *t2++; *fill++ = *t2++; } else t2 += 2; i2 -=2; } else if ( *t1 < *t2 ) { if ( t1[1] > 0 ) { *fill++ = *t1++; *fill++ = *t1++; } else t1 += 2; i1 -= 2; } else if ( t1[1] > t2[1] ) { *fill++ = *t1++; *fill++ = *t1++; t2 += 2; i1 -= 2; i2 -=2; } else { *fill++ = *t2++; *fill++ = *t2++; t1 += 2; i1 -= 2; i2 -=2; } } for ( ; i1 > 0; i1 -= 2 ) { if ( t1[1] > 0 ) { *fill++ = *t1++; *fill++ = *t1++; } else t1 += 2; } for ( ; i2 > 0; i2 -= 2 ) { if ( t2[1] > 0 ) { *fill++ = *t2++; *fill++ = *t2++; } else t2 += 2; } break; case 0: while ( i1 > 0 && i2 > 0 ) { if ( *t1 > *t2 ) { t2 += 2; i2 -= 2; } else if ( *t1 < *t2 ) { t1 += 2; i1 -= 2; } else if ( ( t1[1] > 0 ) && ( t2[1] < 0 ) ) { t1 += 2; t2 += 2; i1 -= 2; i2 -= 2; } else if ( ( t1[1] < 0 ) && ( t2[1] > 0 ) ) { t1 += 2; t2 += 2; i1 -= 2; i2 -= 2; } else if ( t1[1] > 0 ) { if ( t1[1] < t2[1] ) { *fill++ = *t1++; *fill++ = *t1++; t2 += 2; i2 -= 2; } else { *fill++ = *t2++; *fill++ = *t2++; t1 += 2; i1 -= 2; } } else { if ( t2[1] < t1[1] ) { *fill++ = *t2++; *fill++ = *t2++; t1 += 2; i1 -= 2; i2 -= 2; } else { *fill++ = *t1++; *fill++ = *t1++; t2 += 2; i1 -= 2; i2 -= 2; } } } for ( ; i1 > 0; i1-- ) *fill++ = *t1++; for ( ; i2 > 0; i2-- ) *fill++ = *t2++; break; } i1 = new[1] = fill - new; t2 = new; t1 = old; NCOPY(t1,t2,i1); TermFree(new,"MergeSymbolLists"); return(0); } /* #] MergeSymbolLists : #[ MergeDotproductLists : Merges the extra list into the old. If par == -1 we take minimum powers If par == 1 we take maximum powers If par == 0 we take minimum of the absolute value of the powers if one is positive and the other negative we get zero. We assume that the dotproducts are in order in both lists */ int MergeDotproductLists(PHEAD WORD *old, WORD *extra, int par) { GETBIDENTITY WORD *new = TermMalloc("MergeDotproductLists"); WORD *t1, *t2, *fill; int i1,i2; fill = new + 2; i1 = old[1] - 2; i2 = extra[1] - 2; t1 = old + 2; t2 = extra + 2; switch ( par ) { case -1: while ( i1 > 0 && i2 > 0 ) { if ( ( *t1 > *t2 ) || ( *t1 == *t2 && t1[1] > t2[1] ) ) { if ( t2[2] < 0 ) { *fill++ = *t2++; *fill++ = *t2++; *fill++ = *t2++; } else t2 += 3; } else if ( ( *t1 < *t2 ) || ( *t1 == *t2 && t1[1] < t2[1] ) ) { if ( t1[2] < 0 ) { *fill++ = *t1++; *fill++ = *t1++; *fill++ = *t1++; } else t1 += 3; } else if ( t1[2] < t2[2] ) { *fill++ = *t1++; *fill++ = *t1++; *fill++ = *t1++; t2 += 3; } else { *fill++ = *t2++; *fill++ = *t2++; *fill++ = *t2++; t1 += 3; } } break; case 1: while ( i1 > 0 && i2 > 0 ) { if ( ( *t1 > *t2 ) || ( *t1 == *t2 && t1[1] > t2[1] ) ) { if ( t2[2] > 0 ) { *fill++ = *t2++; *fill++ = *t2++; *fill++ = *t2++; } else t2 += 3; } else if ( ( *t1 < *t2 ) || ( *t1 == *t2 && t1[1] < t2[1] ) ) { if ( t1[2] > 0 ) { *fill++ = *t1++; *fill++ = *t1++; *fill++ = *t1++; } else t1 += 3; } else if ( t1[2] > t2[2] ) { *fill++ = *t1++; *fill++ = *t1++; *fill++ = *t1++; t2 += 3; } else { *fill++ = *t2++; *fill++ = *t2++; *fill++ = *t2++; t1 += 3; } } break; case 0: while ( i1 > 0 && i2 > 0 ) { if ( ( *t1 > *t2 ) || ( *t1 == *t2 && t1[1] > t2[1] ) ) { t2 += 3; } else if ( ( *t1 < *t2 ) || ( *t1 == *t2 && t1[1] < t2[1] ) ) { t1 += 3; } else if ( ( t1[2] > 0 ) && ( t2[2] < 0 ) ) { t1 += 3; t2 += 3; } else if ( ( t1[2] < 0 ) && ( t2[2] > 0 ) ) { t1 += 3; t2 += 3; } else if ( t1[2] > 0 ) { if ( t1[2] < t2[2] ) { *fill++ = *t1++; *fill++ = *t1++; *fill++ = *t1++; t2 += 3; } else { *fill++ = *t2++; *fill++ = *t2++; *fill++ = *t2++; t1 += 3; } } else { if ( t2[2] < t1[2] ) { *fill++ = *t2++; *fill++ = *t2++; *fill++ = *t2++; t1 += 3; } else { *fill++ = *t1++; *fill++ = *t1++; *fill++ = *t1++; t2 += 3; } } } break; } i1 = new[1] = fill - new; t2 = new; t1 = old; NCOPY(t1,t2,i1); TermFree(new,"MergeDotproductLists"); return(0); } /* #] MergeDotproductLists : #[ CreateExpression : Looks for the expression in the argument, reads it and puts it in a buffer. Returns the address of the buffer. We send the expression through the Generator system, because there may be unsubstituted (sub)expressions as in Local F = (a+b); Local G = gcd_(F,...); */ WORD *CreateExpression(PHEAD WORD nexp) { GETBIDENTITY CBUF *C = cbuf+AC.cbufnum; POSITION startposition, oldposition; FILEHANDLE *fi; WORD *term, *oldipointer = AR.CompressPointer; ; switch ( Expressions[nexp].status ) { case HIDDENLEXPRESSION: case HIDDENGEXPRESSION: case DROPHLEXPRESSION: case DROPHGEXPRESSION: case UNHIDELEXPRESSION: case UNHIDEGEXPRESSION: AR.GetOneFile = 2; fi = AR.hidefile; break; default: AR.GetOneFile = 0; fi = AR.infile; break; } SeekScratch(fi,&oldposition); startposition = AS.OldOnFile[nexp]; term = AT.WorkPointer; if ( GetOneTerm(BHEAD term,fi,&startposition,0) <= 0 ) goto CalledFrom; NewSort(BHEAD0); AR.CompressPointer = oldipointer; while ( GetOneTerm(BHEAD term,fi,&startposition,0) > 0 ) { AT.WorkPointer = term + *term; if ( Generator(BHEAD term,C->numlhs) ) { LowerSortLevel(); goto CalledFrom; } AR.CompressPointer = oldipointer; } AT.WorkPointer = term; if ( EndSort(BHEAD (WORD *)((void *)(&term)),2) < 0 ) goto CalledFrom; SetScratch(fi,&oldposition); return(term); CalledFrom: MLOCK(ErrorMessageLock); MesCall("CreateExpression"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } /* #] CreateExpression : #[ GCDterms : GCD of two terms Computes the GCD of two terms. Output in termout. termout may overlap with term1. */ int GCDterms(PHEAD WORD *term1, WORD *term2, WORD *termout) { GETBIDENTITY WORD *t1, *t1stop, *t1next, *t2, *t2stop, *t2next, *tout, *tt1, *tt2; int count1, count2, i, ii, x1, sign; WORD length1, length2; t1 = term1 + *term1; t1stop = t1 - ABS(t1[-1]); t1 = term1+1; t2 = term2 + *term2; t2stop = t2 - ABS(t2[-1]); t2 = term2+1; tout = termout+1; while ( t1 < t1stop ) { t1next = t1 + t1[1]; t2 = term2+1; if ( *t1 == SYMBOL ) { while ( t2 < t2stop && *t2 != SYMBOL ) t2 += t2[1]; if ( t2 < t2stop && *t2 == SYMBOL ) { t2next = t2+t2[1]; tt1 = t1+2; tt2 = t2+2; count1 = 0; while ( tt1 < t1next && tt2 < t2next ) { if ( *tt1 < *tt2 ) tt1 += 2; else if ( *tt1 > *tt2 ) tt2 += 2; else if ( ( tt1[1] > 0 && tt2[1] < 0 ) || ( tt2[1] > 0 && tt1[1] < 0 ) ) { tt1 += 2; tt2 += 2; } else { x1 = tt1[1]; if ( tt1[1] < 0 ) { if ( tt2[1] > x1 ) x1 = tt2[1]; } else { if ( tt2[1] < x1 ) x1 = tt2[1]; } tout[count1+2] = *tt1; tout[count1+3] = x1; tt1 += 2; tt2 += 2; count1 += 2; } } if ( count1 > 0 ) { *tout = SYMBOL; tout[1] = count1+2; tout += tout[1]; } } } else if ( *t1 == DOTPRODUCT ) { while ( t2 < t2stop && *t2 != DOTPRODUCT ) t2 += t2[1]; if ( t2 < t2stop && *t2 == DOTPRODUCT ) { t2next = t2+t2[1]; tt1 = t1+2; tt2 = t2+2; count1 = 0; while ( tt1 < t1next && tt2 < t2next ) { if ( *tt1 < *tt2 || ( *tt1 == *tt2 && tt1[1] < tt2[1] ) ) tt1 += 3; else if ( *tt1 > *tt2 || ( *tt1 == *tt2 && tt1[1] > tt2[1] ) ) tt2 += 3; else if ( ( tt1[2] > 0 && tt2[2] < 0 ) || ( tt2[2] > 0 && tt1[2] < 0 ) ) { tt1 += 3; tt2 += 3; } else { x1 = tt1[2]; if ( tt1[2] < 0 ) { if ( tt2[2] > x1 ) x1 = tt2[2]; } else { if ( tt2[2] < x1 ) x1 = tt2[2]; } tout[count1+2] = *tt1; tout[count1+3] = tt1[1]; tout[count1+4] = x1; tt1 += 3; tt2 += 3; count1 += 3; } } if ( count1 > 0 ) { *tout = DOTPRODUCT; tout[1] = count1+2; tout += tout[1]; } } } else if ( *t1 == VECTOR ) { while ( t2 < t2stop && *t2 != VECTOR ) t2 += t2[1]; if ( t2 < t2stop && *t2 == VECTOR ) { t2next = t2+t2[1]; tt1 = t1+2; tt2 = t2+2; count1 = 0; while ( tt1 < t1next && tt2 < t2next ) { if ( *tt1 < *tt2 || ( *tt1 == *tt2 && tt1[1] < tt2[1] ) ) tt1 += 2; else if ( *tt1 > *tt2 || ( *tt1 == *tt2 && tt1[1] > tt2[1] ) ) tt2 += 2; else { tout[count1+2] = *tt1; tout[count1+3] = tt1[1]; tt1 += 2; tt2 += 2; count1 += 2; } } if ( count1 > 0 ) { *tout = VECTOR; tout[1] = count1+2; tout += tout[1]; } } } else if ( *t1 == INDEX ) { while ( t2 < t2stop && *t2 != INDEX ) t2 += t2[1]; if ( t2 < t2stop && *t2 == INDEX ) { t2next = t2+t2[1]; tt1 = t1+2; tt2 = t2+2; count1 = 0; while ( tt1 < t1next && tt2 < t2next ) { if ( *tt1 < *tt2 ) tt1 += 1; else if ( *tt1 > *tt2 ) tt2 += 1; else { tout[count1+2] = *tt1; tt1 += 1; tt2 += 1; count1 += 1; } } if ( count1 > 0 ) { *tout = INDEX; tout[1] = count1+2; tout += tout[1]; } } } else if ( *t1 == DELTA ) { while ( t2 < t2stop && *t2 != DELTA ) t2 += t2[1]; if ( t2 < t2stop && *t2 == DELTA ) { t2next = t2+t2[1]; tt1 = t1+2; tt2 = t2+2; count1 = 0; while ( tt1 < t1next && tt2 < t2next ) { if ( *tt1 < *tt2 || ( *tt1 == *tt2 && tt1[1] < tt2[1] ) ) tt1 += 2; else if ( *tt1 > *tt2 || ( *tt1 == *tt2 && tt1[1] > tt2[1] ) ) tt2 += 2; else { tout[count1+2] = *tt1; tout[count1+3] = tt1[1]; tt1 += 2; tt2 += 2; count1 += 2; } } if ( count1 > 0 ) { *tout = DELTA; tout[1] = count1+2; tout += tout[1]; } } } else if ( *t1 >= FUNCTION ) { /* noncommuting functions? Forbidden! */ /* Count how many times this function occurs. Then count how many times it is in term2. */ count1 = 1; while ( t1next < t1stop && *t1 == *t1next && t1[1] == t1next[1] ) { for ( i = 2; i < t1[1]; i++ ) { if ( t1[i] != t1next[i] ) break; } if ( i < t1[1] ) break; count1++; t1next += t1next[1]; } count2 = 0; while ( t2 < t2stop ) { if ( *t2 == *t1 && t2[1] == t1[1] ) { for ( i = 2; i < t1[1]; i++ ) { if ( t2[i] != t1[i] ) break; } if ( i >= t1[1] ) count2++; } t2 += t2[1]; } if ( count1 < count2 ) count2 = count1; /* number of common occurrences */ if ( count2 > 0 ) { if ( tout == t1 ) { while ( count2 > 0 ) { tout += tout[1]; count2--; } } else { i = t1[1]*count2; NCOPY(tout,t1,i); } } } t1 = t1next; } /* Now the coefficients. They are in t1stop and t2stop. Should go to tout. */ sign = 1; length1 = term1[*term1-1]; ii = i = ABS(length1); t1 = t1stop; if ( t1 != tout ) { NCOPY(tout,t1,i); tout -= ii; } length2 = term2[*term2-1]; if ( length1 < 0 && length2 < 0 ) sign = -1; if ( AccumGCD(BHEAD (UWORD *)tout,&length1,(UWORD *)t2stop,length2) ) { MLOCK(ErrorMessageLock); MesCall("GCDterms"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( sign < 0 && length1 > 0 ) length1 = -length1; tout += ABS(length1); tout[-1] = length1; *termout = tout - termout; *tout = 0; return(0); } /* #] GCDterms : #[ ReadPolyRatFun : */ int ReadPolyRatFun(PHEAD WORD *term) { WORD *oldworkpointer = AT.WorkPointer; int flag, i; WORD *t, *fun, *nextt, *num, *den, *t1, *t2, size, numsize, densize; WORD *term1, *term2, *confree1, *confree2, *gcd, *num1, *den1, move, *newnum, *newden; WORD *tstop, *m1, *m2; WORD oldsorttype = AR.SortType; COMPARE oldcompareroutine = (COMPARE)(AR.CompareRoutine); AR.SortType = SORTHIGHFIRST; AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); tstop = term + *term; tstop -= ABS(tstop[-1]); if ( term + *term == AT.WorkPointer ) flag = 1; else flag = 0; t = term+1; while ( t < tstop ) { if ( *t != AR.PolyFun ) { t += t[1]; continue; } if ( ( t[2] & MUSTCLEANPRF ) == 0 ) { t += t[1]; continue; } fun = t; nextt = t + t[1]; if ( fun[1] > FUNHEAD && fun[FUNHEAD] == -SNUMBER && fun[FUNHEAD+1] == 0 ) { *term = 0; break; } if ( FromPolyRatFun(BHEAD fun, &num, &den) > 0 ) { t = nextt; continue; } if ( *num == ARGHEAD ) { *term = 0; break; } /* Now we have num and den. Both are in general argument notation, but can also be used as expressions as in num+ARGHEAD, den+ARGHEAD. We need the gcd. For this we have to take out the contents because PreGCD does not like contents. */ term1 = TermMalloc("ReadPolyRatFun"); term2 = TermMalloc("ReadPolyRatFun"); confree1 = TakeSymbolContent(BHEAD num+ARGHEAD,term1); confree2 = TakeSymbolContent(BHEAD den+ARGHEAD,term2); GCDclean(BHEAD term1,term2); /* gcd = PreGCD(BHEAD confree1,confree2,1); */ gcd = poly_gcd(BHEAD confree1,confree2,1); newnum = PolyDiv(BHEAD confree1,gcd,"ReadPolyRatFun"); newden = PolyDiv(BHEAD confree2,gcd,"ReadPolyRatFun"); TermFree(confree2,"ReadPolyRatFun"); TermFree(confree1,"ReadPolyRatFun"); num1 = MULfunc(BHEAD term1,newnum); den1 = MULfunc(BHEAD term2,newden); TermFree(newnum,"ReadPolyRatFun"); TermFree(newden,"ReadPolyRatFun"); /* M_free(gcd,"poly_gcd"); */ TermFree(gcd,"poly_gcd"); TermFree(term1,"ReadPolyRatFun"); TermFree(term2,"ReadPolyRatFun"); /* Now we can put the function back together. Notice that we cannot use ToFast, because there is no reservation for the header of the argument. Fortunately there are only two types of fast arguments. */ if ( num1[0] == 4 && num1[4] == 0 && num1[2] == 1 && num1[1] > 0 ) { numsize = 2; num1[0] = -SNUMBER; if ( num1[3] < 0 ) num1[1] = -num1[1]; } else if ( num1[0] == 8 && num1[8] == 0 && num1[7] == 3 && num1[6] == 1 && num1[5] == 1 && num1[1] == SYMBOL && num1[4] == 1 ) { numsize = 2; num1[0] = -SYMBOL; num1[1] = num1[3]; } else { m1 = num1; while ( *m1 ) m1 += *m1; numsize = (m1-num1)+ARGHEAD; } if ( den1[0] == 4 && den1[4] == 0 && den1[2] == 1 && den1[1] > 0 ) { densize = 2; den1[0] = -SNUMBER; if ( den1[3] < 0 ) den1[1] = -den1[1]; } else if ( den1[0] == 8 && den1[8] == 0 && den1[7] == 3 && den1[6] == 1 && den1[5] == 1 && den1[1] == SYMBOL && den1[4] == 1 ) { densize = 2; den1[0] = -SYMBOL; den1[1] = den1[3]; } else { m2 = den1; while ( *m2 ) m2 += *m2; densize = (m2-den1)+ARGHEAD; } size = FUNHEAD+numsize+densize; if ( size > fun[1] ) { move = size - fun[1]; t1 = term+*term; t2 = t1+move; while ( t1 > nextt ) *--t2 = *--t1; tstop += move; nextt += move; *term += move; } else if ( size < fun[1] ) { move = fun[1]-size; t2 = fun+size; t1 = nextt; tstop -= move; nextt -= move; t = term+*term; while ( t1 < t ) *t2++ = *t1++; *term -= move; } else { /* no need to move anything */ } fun[1] = size; fun[2] = 0; t2 = fun+FUNHEAD; t1 = num1; if ( *num1 < 0 ) { *t2++ = num1[0]; *t2++ = num1[1]; } else { *t2++ = numsize; *t2++ = 0; FILLARG(t2); i = numsize-ARGHEAD; NCOPY(t2,t1,i) } t1 = den1; if ( *den1 < 0 ) { *t2++ = den1[0]; *t2++ = den1[1]; } else { *t2++ = densize; *t2++ = 0; FILLARG(t2); i = densize-ARGHEAD; NCOPY(t2,t1,i) } TermFree(num1,"MULfunc"); TermFree(den1,"MULfunc"); t = nextt; } if ( flag ) AT.WorkPointer = term +*term; else AT.WorkPointer = oldworkpointer; AR.CompareRoutine = (COMPAREDUMMY)oldcompareroutine; AR.SortType = oldsorttype; return(0); } /* #] ReadPolyRatFun : #[ FromPolyRatFun : */ int FromPolyRatFun(PHEAD WORD *fun, WORD **numout, WORD **denout) { WORD *nextfun, *tt, *num, *den; int i; nextfun = fun + fun[1]; fun += FUNHEAD; num = AT.WorkPointer; if ( *fun < 0 ) { if ( *fun != -SNUMBER && *fun != -SYMBOL ) goto Improper; ToGeneral(fun,num,0); tt = num + *num; *tt++ = 0; fun += 2; } else { i = *fun; tt = num; NCOPY(tt,fun,i); *tt++ = 0; } den = tt; if ( *fun < 0 ) { if ( *fun != -SNUMBER && *fun != -SYMBOL ) goto Improper; ToGeneral(fun,den,0); tt = den + *den; *tt++ = 0; fun += 2; } else { i = *fun; tt = den; NCOPY(tt,fun,i); *tt++ = 0; } *numout = num; *denout = den; if ( fun != nextfun ) { return(1); } AT.WorkPointer = tt; return(0); Improper: MLOCK(ErrorMessageLock); MesPrint("Improper use of PolyRatFun"); MesCall("FromPolyRatFun"); MUNLOCK(ErrorMessageLock); SETERROR(-1); } /* #] FromPolyRatFun : #[ TakeSymbolContent : */ /** * Implements part of the old ExecArg in which we take common factors * from arguments with more than one term. * We allow only symbols as this code is used for the polyratfun only. * We have a special routine, because the generic TakeContent does too * much work and speed is at a premium here. * Input: in is the input expression as a sequence of terms. * Output: term: the content * return value: the contentfree expression. * it is in new allocation, made by TermMalloc. * (should be in a TermMalloc space?) */ WORD *TakeSymbolContent(PHEAD WORD *in, WORD *term) { GETBIDENTITY WORD *t, *tstop, *tout, *tstore; WORD *tnext, *tt, *tterm; WORD *inp, a, *den, *oldworkpointer = AT.WorkPointer; int i, action = 0, sign, first; UWORD *GCDbuffer, *GCDbuffer2, *LCMbuffer, *LCMbuffer2, *ap; WORD GCDlen, GCDlen2, LCMlen, LCMlen2, length, redlength, len1, len2; LONG j; tout = tstore = term+1; /* #[ SYMBOL : We make a list of symbols and their minimal powers. This includes negative powers. In the end we have to multiply by the inverse of this list. That takes out all negative powers and leaves things ready for further processing. */ tterm = AT.WorkPointer; tt = tterm+1; tout[0] = SYMBOL; tout[1] = 2; t = in; first = 1; while ( *t ) { tnext = t + *t; tstop = tnext - ABS(tnext[-1]); t++; while ( t < tstop ) { if ( first ) { if ( *t == SYMBOL ) { for ( i = 0; i < t[1]; i++ ) tout[i] = t[i]; goto didwork; } else { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: polynomials and polyratfuns must contain symbols only"); MUNLOCK(ErrorMessageLock); Terminate(1); } } else if ( *t == SYMBOL ) { MergeSymbolLists(BHEAD tout,t,-1); goto didwork; } else { t += t[1]; } } /* Here we come when there were no symbols. Only keep the negative ones. */ if ( first == 0 ) { int j = 2; for ( i = 2; i < tout[1]; i += 2 ) { if ( tout[i+1] < 0 ) { if ( i == j ) { j += 2; } else { tout[j] = tout[i]; tout[j+1] = tout[i+1]; j += 2; } } } tout[1] = j; } didwork:; first = 0; t = tnext; } if ( tout[1] > 2 ) { t = tout; tt[0] = t[0]; tt[1] = t[1]; for ( i = 2; i < t[1]; i += 2 ) { tt[i] = t[i]; tt[i+1] = -t[i+1]; } tt += tt[1]; tout += tout[1]; action++; } /* #] SYMBOL : #[ Coefficient : Now we have to collect the GCD of the numerators and the LCM of the denominators. */ AT.WorkPointer = tt; if ( AN.cmod != 0 ) { WORD x, ix, ip; t = in; tnext = t + *t; tstop = tnext - ABS(tnext[-1]); x = tstop[0]; if ( tnext[-1] < 0 ) x += AC.cmod[0]; if ( GetModInverses(x,(WORD)(AN.cmod[0]),&ix,&ip) ) goto CalledFrom; *tout++ = x; *tout++ = 1; *tout++ = 3; *tt++ = ix; *tt++ = 1; *tt++ = 3; } else { GCDbuffer = NumberMalloc("MakeInteger"); GCDbuffer2 = NumberMalloc("MakeInteger"); LCMbuffer = NumberMalloc("MakeInteger"); LCMbuffer2 = NumberMalloc("MakeInteger"); t = in; tnext = t + *t; length = tnext[-1]; if ( length < 0 ) { sign = -1; length = -length; } else { sign = 1; } tstop = tnext - length; redlength = (length-1)/2; for ( i = 0; i < redlength; i++ ) { GCDbuffer[i] = (UWORD)(tstop[i]); LCMbuffer[i] = (UWORD)(tstop[redlength+i]); } GCDlen = LCMlen = redlength; while ( GCDbuffer[GCDlen-1] == 0 ) GCDlen--; while ( LCMbuffer[LCMlen-1] == 0 ) LCMlen--; t = tnext; while ( *t ) { tnext = t + *t; length = ABS(tnext[-1]); tstop = tnext - length; redlength = (length-1)/2; len1 = len2 = redlength; den = tstop + redlength; while ( tstop[len1-1] == 0 ) len1--; while ( den[len2-1] == 0 ) len2--; if ( GCDlen == 1 && GCDbuffer[0] == 1 ) {} else { GcdLong(BHEAD (UWORD *)tstop,len1,GCDbuffer,GCDlen,GCDbuffer2,&GCDlen2); ap = GCDbuffer; GCDbuffer = GCDbuffer2; GCDbuffer2 = ap; a = GCDlen; GCDlen = GCDlen2; GCDlen2 = a; } if ( len2 == 1 && den[0] == 1 ) {} else { GcdLong(BHEAD LCMbuffer,LCMlen,(UWORD *)den,len2,LCMbuffer2,&LCMlen2); DivLong((UWORD *)den,len2,LCMbuffer2,LCMlen2, GCDbuffer2,&GCDlen2,(UWORD *)AT.WorkPointer,&a); MulLong(LCMbuffer,LCMlen,GCDbuffer2,GCDlen2,LCMbuffer2,&LCMlen2); ap = LCMbuffer; LCMbuffer = LCMbuffer2; LCMbuffer2 = ap; a = LCMlen; LCMlen = LCMlen2; LCMlen2 = a; } t = tnext; } if ( GCDlen != 1 || GCDbuffer[0] != 1 || LCMlen != 1 || LCMbuffer[0] != 1 ) { redlength = GCDlen; if ( LCMlen > GCDlen ) redlength = LCMlen; for ( i = 0; i < GCDlen; i++ ) *tout++ = (WORD)(GCDbuffer[i]); for ( ; i < redlength; i++ ) *tout++ = 0; for ( i = 0; i < LCMlen; i++ ) *tout++ = (WORD)(LCMbuffer[i]); for ( ; i < redlength; i++ ) *tout++ = 0; *tout++ = (2*redlength+1)*sign; for ( i = 0; i < LCMlen; i++ ) *tt++ = (WORD)(LCMbuffer[i]); for ( ; i < redlength; i++ ) *tt++ = 0; for ( i = 0; i < GCDlen; i++ ) *tt++ = (WORD)(GCDbuffer[i]); for ( ; i < redlength; i++ ) *tt++ = 0; *tt++ = (2*redlength+1)*sign; action++; } else { *tout++ = 1; *tout++ = 1; *tout++ = 3*sign; *tt++ = 1; *tt++ = 1; *tt++ = 3*sign; if ( sign != 1 ) action++; } NumberFree(LCMbuffer2,"MakeInteger"); NumberFree(LCMbuffer ,"MakeInteger"); NumberFree(GCDbuffer2,"MakeInteger"); NumberFree(GCDbuffer ,"MakeInteger"); } /* #] Coefficient : #[ Multiply by the inverse content : */ if ( action ) { *term = tout - term; *tout = 0; *tterm = tt - tterm; *tt = 0; AT.WorkPointer = tt; inp = MultiplyWithTerm(BHEAD in,tterm,2); AT.WorkPointer = tterm; t = inp; while ( *t ) t += *t; j = (t-inp); t = inp; if ( j*sizeof(WORD) > (size_t)(AM.MaxTer) ) goto OverWork; in = tout = TermMalloc("TakeSymbolContent"); NCOPY(tout,t,j); *tout = 0; if ( AN.tryterm > 0 ) { TermFree(inp,"MultiplyWithTerm"); AN.tryterm = 0; } else { M_free(inp,"MultiplyWithTerm"); } } else { t = in; while ( *t ) t += *t; j = (t-in); t = in; if ( j*sizeof(WORD) > (size_t)(AM.MaxTer) ) goto OverWork; in = tout = TermMalloc("TakeSymbolContent"); NCOPY(tout,t,j); *tout = 0; term[0] = 4; term[1] = 1; term[2] = 1; term[3] = 3; term[4] = 0; } /* #] Multiply by the inverse content : AT.WorkPointer = tterm + *tterm; */ AT.WorkPointer = oldworkpointer; return(in); OverWork: MLOCK(ErrorMessageLock); MesPrint("Term too complex. Maybe increasing MaxTermSize can help"); MUNLOCK(ErrorMessageLock); CalledFrom: MLOCK(ErrorMessageLock); MesCall("TakeSymbolContent"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } /* #] TakeSymbolContent : #[ GCDclean : Takes a numerator and a denominator that each consist of a single term with only a coefficient and symbols and makes them into a proper fraction. Output overwrites input. */ void GCDclean(PHEAD WORD *num, WORD *den) { WORD *out1 = TermMalloc("GCDclean"); WORD *out2 = TermMalloc("GCDclean"); WORD *t1, *t2, *r1, *r2, *t1stop, *t2stop, csize1, csize2, csize3, pow, sign; int i; t1stop = num+*num; sign = ( t1stop[-1] < 0 ) ? -1 : 1; csize1 = ABS(t1stop[-1]); t1stop -= csize1; t2stop = den+*den; if ( t2stop[-1] < 0 ) sign = -sign; csize2 = ABS(t2stop[-1]); t2stop -= csize2; t1 = num+1; t2 = den+1; r1 = out1+3; r2 = out2+3; if ( t1 == t1stop ) { if ( t2 < t2stop ) { for ( i = 2; i < t2[1]; i += 2 ) { if ( t2[i+1] < 0 ) { *r1++ = t2[i]; *r1++ = -t2[i+1]; } else { *r2++ = t2[i]; *r2++ = t2[i+1]; } } } } else if ( t2 == t2stop ) { for ( i = 2; i < t1[1]; i += 2 ) { if ( t1[i+1] < 0 ) { *r2++ = t1[i]; *r2++ = -t1[i+1]; } else { *r1++ = t1[i]; *r1++ = t1[i+1]; } } } else { t1 += 2; t2 += 2; while ( t1 < t1stop && t2 < t2stop ) { if ( *t1 < *t2 ) { if ( t1[1] > 0 ) { *r1++ = *t1; *r1++ = t1[1]; t1 += 2; } else if ( t1[1] < 0 ) { *r2++ = *t1; *r2++ = -t1[1]; t1 += 2; } } else if ( *t1 > *t2 ) { if ( t2[1] > 0 ) { *r2++ = *t2; *r2++ = t2[1]; t2 += 2; } else if ( t2[1] < 0 ) { *r1++ = *t2; *r1++ = -t2[1]; t2 += 2; } } else { pow = t1[1]-t2[1]; if ( pow > 0 ) { *r1++ = *t1; *r1++ = pow; } else if ( pow < 0 ) { *r2++ = *t1; *r2++ = -pow; } t1 += 2; t2 += 2; } } while ( t1 < t1stop ) { if ( t1[1] < 0 ) { *r2++ = *t1; *r2++ = -t1[1]; } else { *r1++ = *t1; *r1++ = t1[1]; } t1 += 2; } while ( t2 < t2stop ) { if ( t2[1] < 0 ) { *r1++ = *t2; *r1++ = -t2[1]; } else { *r2++ = *t2; *r2++ = t2[1]; } t2 += 2; } } if ( r1 > out1+3 ) { out1[1] = SYMBOL; out1[2] = r1 - out1 - 1; } else r1 = out1+1; if ( r2 > out2+3 ) { out2[1] = SYMBOL; out2[2] = r2 - out2 - 1; } else r2 = out2+1; /* Now the coefficients. */ csize1 = REDLENG(csize1); csize2 = REDLENG(csize2); if ( DivRat(BHEAD (UWORD *)t1stop,csize1,(UWORD *)t2stop,csize2,(UWORD *)r1,&csize3) ) { MLOCK(ErrorMessageLock); MesCall("GCDclean"); MUNLOCK(ErrorMessageLock); Terminate(-1); } UnPack((UWORD *)r1,csize3,&csize2,&csize1); t2 = r1+ABS(csize3); for ( i = 0; i < csize2; i++ ) r2[i] = t2[i]; r2 += csize2; *r2++ = 1; for ( i = 1; i < csize2; i++ ) *r2++ = 0; csize2 = INCLENG(csize2); *r2++ = csize2; *out2 = r2-out2; r1 += ABS(csize1); *r1++ = 1; for ( i = 1; i < ABS(csize1); i++ ) *r1++ = 0; csize1 = INCLENG(csize1); *r1++ = csize1; *out1 = r1-out1; t1 = num; t2 = out1; i = *out1; NCOPY(t1,t2,i); *t1 = 0; if ( sign < 0 ) t1[-1] = -t1[-1]; t1 = den; t2 = out2; i = *out2; NCOPY(t1,t2,i); *t1 = 0; TermFree(out2,"GCDclean"); TermFree(out1,"GCDclean"); } /* #] GCDclean : #[ PolyDiv : Special stub function for polynomials that should fit inside a term. We make sure that the space is allocated by TermMalloc. This makes things much easier on the calling routines. */ WORD *PolyDiv(PHEAD WORD *a,WORD *b,char *text) { /* Probably the following would work now */ DUMMYUSE(text); return(poly_div(BHEAD a,b,1)); /* WORD *quo, *qq; WORD *x, *xx; LONG i; quo = poly_div(BHEAD a,b,1); x = TermMalloc(text); qq = quo; while ( *qq ) qq += *qq; i = (qq-quo+1); if ( i*sizeof(WORD) > (size_t)(AM.MaxTer) ) { DUMMYUSE(text); MLOCK(ErrorMessageLock); MesPrint("PolyDiv: Term too complex. Maybe increasing MaxTermSize can help"); MUNLOCK(ErrorMessageLock); Terminate(-1); } xx = x; qq = quo; NCOPY(xx,qq,i) TermFree(quo,"poly_div"); return(x); */ } /* #] PolyDiv : #] GCDfunction : #[ DIVfunction : Input: a div_ function that has two arguments inside a term. Action: Calculates [arg1/arg2] using polynomial techniques if needed. Output: The output result is combined with the remainder of the term and sent to Generator for further processing. Note that the output can be just a number or many terms. In case par == 0 the output is [arg1/arg2] In case par == 1 the output is [arg1%arg2] In case par == 2 the output is [inverse of arg1 modulus arg2] In case par == 3 the output is [arg1*arg2] */ WORD divrem[4] = { DIVFUNCTION, REMFUNCTION, INVERSEFUNCTION, MULFUNCTION }; int DIVfunction(PHEAD WORD *term,WORD level,int par) { GETBIDENTITY WORD *t, *tt, *r, *arg1 = 0, *arg2 = 0, *arg3 = 0, *termout; WORD *tstop, *tend, *r3, *rr, *rstop, tlength, rlength, newlength; WORD *proper1, *proper2, *proper3 = 0, numdol = -1; int numargs = 0, type1, type2, actionflag1, actionflag2; WORD startebuf = cbuf[AT.ebufnum].numrhs; int division = ( par <= 2 ); /* false for mul_ */ if ( par < 0 || par > 3 ) { MLOCK(ErrorMessageLock); MesPrint("Internal error. Illegal parameter %d in DIVfunction.",par); MUNLOCK(ErrorMessageLock); Terminate(-1); } /* Find the function */ tend = term + *term; tstop = tend - ABS(tend[-1]); t = term+1; while ( t < tstop ) { if ( *t != divrem[par] ) { t += t[1]; continue; } r = t + FUNHEAD; tt = t + t[1]; numargs = 0; while ( r < tt ) { if ( numargs == 0 ) { arg1 = r; } if ( numargs == 1 ) { arg2 = r; } if ( numargs == 2 && *r == -DOLLAREXPRESSION ) { numdol = r[1]; } numargs++; NEXTARG(r); } if ( numargs == 2 ) break; if ( division && numargs == 3 ) break; t = tt; } if ( t >= tstop ) { MLOCK(ErrorMessageLock); MesPrint("Internal error. Indicated div_ or rem_ function not encountered."); MUNLOCK(ErrorMessageLock); Terminate(-1); } /* We have two arguments in arg1 and arg2. */ if ( division && *arg1 == -SNUMBER && arg1[1] == 0 ) { if ( *arg2 == -SNUMBER && arg2[1] == 0 ) { zerozero:; MLOCK(ErrorMessageLock); MesPrint("0/0 in either div_ or rem_ function."); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( numdol >= 0 ) PutTermInDollar(0,numdol); return(0); } if ( division && *arg2 == -SNUMBER && arg2[1] == 0 ) { divzero:; MLOCK(ErrorMessageLock); MesPrint("Division by zero in either div_ or rem_ function."); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( !division ) { if ( (*arg1 == -SNUMBER && arg1[1] == 0) || (*arg2 == -SNUMBER && arg2[1] == 0) ) { return(0); } } if ( ( arg1 = ConvertArgument(BHEAD arg1, &type1) ) == 0 ) goto CalledFrom; if ( ( arg2 = ConvertArgument(BHEAD arg2, &type2) ) == 0 ) goto CalledFrom; if ( division && *arg1 == 0 ) { if ( *arg2 == 0 ) { M_free(arg2,"DIVfunction"); M_free(arg1,"DIVfunction"); goto zerozero; } M_free(arg2,"DIVfunction"); M_free(arg1,"DIVfunction"); if ( numdol >= 0 ) PutTermInDollar(0,numdol); return(0); } if ( division && *arg2 == 0 ) { M_free(arg2,"DIVfunction"); M_free(arg1,"DIVfunction"); goto divzero; } if ( !division && (*arg1 == 0 || *arg2 == 0) ) { M_free(arg2,"DIVfunction"); M_free(arg1,"DIVfunction"); return(0); } if ( ( proper1 = PutExtraSymbols(BHEAD arg1,startebuf,&actionflag1) ) == 0 ) goto CalledFrom; if ( ( proper2 = PutExtraSymbols(BHEAD arg2,startebuf,&actionflag2) ) == 0 ) goto CalledFrom; /* if ( type2 == 0 ) M_free(arg2,"DIVfunction"); else { DOLLARS d = ((DOLLARS)arg2)-1; if ( d->factors ) M_free(d->factors,"Dollar factors"); M_free(d,"Copy of dollar variable"); } */ M_free(arg2,"DIVfunction"); /* if ( type1 == 0 ) M_free(arg1,"DIVfunction"); else { DOLLARS d = ((DOLLARS)arg1)-1; if ( d->factors ) M_free(d->factors,"Dollar factors"); M_free(d,"Copy of dollar variable"); } */ M_free(arg1,"DIVfunction"); if ( par == 0 ) proper3 = poly_div(BHEAD proper1, proper2,0); else if ( par == 1 ) proper3 = poly_rem(BHEAD proper1, proper2,0); else if ( par == 2 ) proper3 = poly_inverse(BHEAD proper1, proper2); else if ( par == 3 ) proper3 = poly_mul(BHEAD proper1, proper2); if ( proper3 == 0 ) goto CalledFrom; if ( actionflag1 || actionflag2 ) { if ( ( arg3 = TakeExtraSymbols(BHEAD proper3,startebuf) ) == 0 ) goto CalledFrom; M_free(proper3,"DIVfunction"); } else { arg3 = proper3; } M_free(proper2,"DIVfunction"); M_free(proper1,"DIVfunction"); cbuf[AT.ebufnum].numrhs = startebuf; if ( *arg3 ) { termout = AT.WorkPointer; tlength = tend[-1]; tlength = REDLENG(tlength); r3 = arg3; while ( *r3 ) { tt = term + 1; rr = termout + 1; while ( tt < t ) *rr++ = *tt++; r = r3 + 1; r3 = r3 + *r3; rstop = r3 - ABS(r3[-1]); while ( r < rstop ) *rr++ = *r++; tt += t[1]; while ( tt < tstop ) *rr++ = *tt++; rlength = r3[-1]; rlength = REDLENG(rlength); if ( MulRat(BHEAD (UWORD *)tstop,tlength,(UWORD *)rstop,rlength, (UWORD *)rr,&newlength) < 0 ) goto CalledFrom; rlength = INCLENG(newlength); rr += ABS(rlength); rr[-1] = rlength; *termout = rr - termout; AT.WorkPointer = rr; if ( Generator(BHEAD termout,level) ) goto CalledFrom; } AT.WorkPointer = termout; } M_free(arg3,"DIVfunction"); return(0); CalledFrom: MLOCK(ErrorMessageLock); MesCall("DIVfunction"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] DIVfunction : #[ MULfunc : Multiplies two polynomials and puts the results in TermMalloc space. */ WORD *MULfunc(PHEAD WORD *p1, WORD *p2) { WORD *prod,size1,size2,size3,*t,*tfill,*ps1,*ps2,sign1,sign2, error, *p3; UWORD *num1, *num2, *num3; int i; WORD oldsorttype = AR.SortType; COMPARE oldcompareroutine = (COMPARE)(AR.CompareRoutine); AR.SortType = SORTHIGHFIRST; AR.CompareRoutine = (COMPAREDUMMY)(&CompareSymbols); num3 = NumberMalloc("MULfunc"); prod = TermMalloc("MULfunc"); NewSort(BHEAD0); while ( *p1 ) { ps1 = p1+*p1; num1 = (UWORD *)(ps1 - ABS(ps1[-1])); size1 = ps1[-1]; if ( size1 < 0 ) { sign1 = -1; size1 = -size1; } else sign1 = 1; size1 = (size1-1)/2; p3 = p2; while ( *p3 ) { ps2 = p3+*p3; num2 = (UWORD *)(ps2 - ABS(ps2[-1])); size2 = ps2[-1]; if ( size2 < 0 ) { sign2 = -1; size2 = -size2; } else sign2 = 1; size2 = (size2-1)/2; if ( MulLong(num1,size1,num2,size2,num3,&size3) ) { error = 1; CalledFrom: MLOCK(ErrorMessageLock); MesPrint(" Error %d",error); MesCall("MulFunc"); MUNLOCK(ErrorMessageLock); Terminate(-1); } tfill = prod+1; t = p1+1; while ( t < (WORD *)num1 ) *tfill++ = *t++; t = p3+1; while ( t < (WORD *)num2 ) *tfill++ = *t++; t = (WORD *)num3; for ( i = 0; i < size3; i++ ) *tfill++ = *t++; *tfill++ = 1; for ( i = 1; i < size3; i++ ) *tfill++ = 0; *tfill++ = (2*size3+1)*sign1*sign2; prod[0] = tfill - prod; if ( SymbolNormalize(prod) ) { error = 2; goto CalledFrom; } if ( StoreTerm(BHEAD prod) ) { error = 3; goto CalledFrom; } p3 += *p3; } p1 += *p1; } NumberFree(num3,"MULfunc"); EndSort(BHEAD prod,1); AR.CompareRoutine = (COMPAREDUMMY)oldcompareroutine; AR.SortType = oldsorttype; return(prod); } /* #] MULfunc : #[ ConvertArgument : Converts an argument to a general notation in allocated space. */ WORD *ConvertArgument(PHEAD WORD *arg, int *type) { WORD *output, *t, *r; int i, size; if ( *arg > 0 ) { output = (WORD *)Malloc1((*arg)*sizeof(WORD),"ConvertArgument"); i = *arg - ARGHEAD; t = arg + ARGHEAD; r = output; NCOPY(r,t,i); *r = 0; *type = 0; return(output); } if ( *arg == -EXPRESSION ) { *type = 0; return(CreateExpression(BHEAD arg[1])); } if ( *arg == -DOLLAREXPRESSION ) { DOLLARS d; *type = 1; d = DolToTerms(BHEAD arg[1]); /* The problem is that DolToTerms creates a copy of the dollar variable. If we just return d->where we create a memory leak. Hence we have to copy the contents of d->where to a new buffer */ output = (WORD *)Malloc1((d->size+1)*sizeof(WORD),"Copy of dollar content"); WCOPY(output,d->where,d->size+1); if ( d->factors ) { M_free(d->factors,"Dollar factors"); d->factors = 0; } M_free(d,"Copy of dollar variable"); return(output); } #if ( FUNHEAD > 4 ) size = FUNHEAD+5; #else size = 9; #endif output = (WORD *)Malloc1(size*sizeof(WORD),"ConvertArgument"); switch(*arg) { case -SYMBOL: output[0] = 8; output[1] = SYMBOL; output[2] = 4; output[3] = arg[1]; output[4] = 1; output[5] = 1; output[6] = 1; output[7] = 3; output[8] = 0; break; case -INDEX: case -VECTOR: case -MINVECTOR: output[0] = 7; output[1] = INDEX; output[2] = 3; output[3] = arg[1]; output[4] = 1; output[5] = 1; if ( *arg == -MINVECTOR ) output[6] = -3; else output[6] = 3; output[7] = 0; break; case -SNUMBER: output[0] = 4; if ( arg[1] < 0 ) { output[1] = -arg[1]; output[2] = 1; output[3] = -3; } else { output[1] = arg[1]; output[2] = 1; output[3] = 3; } output[4] = 0; break; default: output[0] = FUNHEAD+4; output[1] = -*arg; output[2] = FUNHEAD; for ( i = 3; i <= FUNHEAD; i++ ) output[i] = 0; output[FUNHEAD+1] = 1; output[FUNHEAD+2] = 1; output[FUNHEAD+3] = 3; output[FUNHEAD+4] = 0; break; } *type = 0; return(output); } /* #] ConvertArgument : #[ ExpandRat : Expands the denominator of a PolyRatFun in the variable PolyFunVar. The output is a polyratfun with a single argument. In the case that there is a polyratfun with more than one argument or the dirtyflag is on, the argument(s) is/are normalized. The output overwrites the input. */ char *TheErrorMessage[] = { "PolyRatFun not of a type that FORM will expand: incorrect variable inside." ,"Division by zero in PolyRatFun encountered in ExpandRat." ,"Irregular code in PolyRatFun encountered in ExpandRat." ,"Called from ExpandRat." ,"WorkSpace overflow. Change parameter WorkSpace in setup file?" }; int ExpandRat(PHEAD WORD *fun) { WORD *r, *rr, *rrr, *tt, *tnext, *arg1, *arg2, *rmin = 0, *rmininv; WORD *rcoef, rsize, rcopy, *ow = AT.WorkPointer; WORD *numerator, *denominator, *rnext; WORD *thecopy, *rc, ncoef, newcoef, *m, *mm, nco, *outarg = 0; UWORD co[2], co1[2], co2[2]; WORD OldPolyFunPow = AR.PolyFunPow; int i, j, minpow = 0, eppow, first, error = 0, ipoly; if ( fun[1] == FUNHEAD ) { return(0); } tnext = fun + fun[1]; if ( fun[1] == fun[FUNHEAD]+FUNHEAD ) { /* Single argument */ if ( fun[2] == 0 ) { goto done; } /* We have to normalize the argument. This could make it shorter. */ NormArg:; if ( outarg == 0 ) outarg = TermMalloc("ExpandRat")+ARGHEAD; AT.TrimPower = 1; NewSort(BHEAD0); r = fun+FUNHEAD+ARGHEAD; if ( AR.PolyFunExp == 2 ) { /* Find minimum power */ WORD minpow2 = MAXPOWER, *rrm; rrm = r; while ( rrm < tnext ) { if ( *rrm == 4 ) { if ( minpow2 > 0 ) minpow2 = 0; } else if ( ABS(rrm[*rrm-1]) == (*rrm-1) ) { if ( minpow2 > 0 ) minpow2 = 0; } else { if ( rrm[1] == SYMBOL && rrm[2] == 4 && rrm[3] == AR.PolyFunVar ) { if ( rrm[4] < minpow2 ) minpow2 = rrm[4]; } else { MesPrint("Illegal term in expanded polyratfun."); goto onerror; } } rrm += *rrm; } AR.PolyFunPow += minpow2; } while ( r < tnext ) { rr = r + *r; i = *r; rrr = outarg; NCOPY(rrr,r,i); Normalize(BHEAD outarg); if ( *outarg > 0 ) StoreTerm(BHEAD outarg); } r = fun+FUNHEAD+ARGHEAD; EndSort(BHEAD r,1); AT.TrimPower = 0; if ( *r == 0 ) { fun[FUNHEAD] = -SNUMBER; fun[FUNHEAD+1] = 0; fun[1] = FUNHEAD+2; } else { rr = fun+FUNHEAD; if ( ToFast(rr,rr) ) { NEXTARG(rr); fun[1] = rr - fun; } else { while ( *r ) r += *r; *rr = r-rr; rr[1] = CLEANFLAG; fun[1] = r - fun; } } fun[2] = CLEANFLAG; goto done; } /* First test whether we have only AR.PolyFunVar in the denominator */ tt = fun + FUNHEAD; arg1 = arg2 = 0; if ( tt < tnext ) { arg1 = tt; NEXTARG(tt); if ( tt < tnext ) { arg2 = tt; NEXTARG(tt); if ( tt != tnext ) { arg1 = arg2 = 0; } /* more than two arguments */ } } if ( arg2 == 0 ) { if ( *arg1 < 0 ) { fun[2] = CLEANFLAG; goto done; } if ( fun[2] == CLEANFLAG ) goto done; goto NormArg; /* Note: should not come here */ } /* Produce the output argument in outarg */ if ( outarg == 0 ) outarg = TermMalloc("ExpandRat")+ARGHEAD; if ( *arg2 <= 0 ) { /* These cases are trivial. We try as much as possible to write the output directly into the function. We just have to be extremely careful not to overwrite relevant information before we are finished with it. */ if ( *arg2 == -SYMBOL && arg2[1] == AR.PolyFunVar ) { rr = r = fun+FUNHEAD+ARGHEAD; if ( *arg1 < 0 ) { if ( *arg1 == -SYMBOL ) { if ( arg1[1] == AR.PolyFunVar ) { *r++ = 4; *r++ = 1; *r++ = 1; *r++ = 3; *r = 0; } else { *r++ = 10; *r++ = SYMBOL; *r++ = 6; *r++ = arg1[1]; *r++ = 1; *r++ = AR.PolyFunVar; *r++ = -1; *r++ = 1; *r++ = 1; *r++ = 3; *r = 0; Normalize(BHEAD rr); } } else if ( *arg1 == -SNUMBER ) { nco = arg1[1]; if ( nco == 0 ) { *r++ = 0; } else { *r++ = 8; *r++ = SYMBOL; *r++ = 4; *r++ = AR.PolyFunVar; *r++ = -1; *r++ = ABS(nco); *r++ = 1; if ( nco < 0 ) *r++ = -3; else *r++ = 3; *r = 0; } } else { error = 2; goto onerror; } /* should not happen! */ } else { /* Multi-term numerator. */ m = arg1+ARGHEAD; NewSort(BHEAD0); /* Technically maybe not needed */ if ( AR.PolyFunExp == 2 ) { /* Find minimum power */ WORD minpow2 = MAXPOWER, *rrm; rrm = m; while ( rrm < arg2 ) { if ( *rrm == 4 ) { if ( minpow2 > 0 ) minpow2 = 0; } else if ( ABS(rrm[*rrm-1]) == (*rrm-1) ) { if ( minpow2 > 0 ) minpow2 = 0; } else { if ( rrm[1] == SYMBOL && rrm[2] == 4 && rrm[3] == AR.PolyFunVar ) { if ( rrm[4] < minpow2 ) minpow2 = rrm[4]; } else { MesPrint("Illegal term in expanded polyratfun."); goto onerror; } } rrm += *rrm; } AR.PolyFunPow += minpow2-1; } while ( m < arg2 ) { r = outarg; rrr = r++; mm = m + *m; *r++ = SYMBOL; *r++ = 4; *r++ = AR.PolyFunVar; *r++ = -1; m++; while ( m < mm ) *r++ = *m++; *rrr = r-rrr; Normalize(BHEAD rrr); StoreTerm(BHEAD rrr); } EndSort(BHEAD rr,1); r = rr; while ( *r ) r += *r; } if ( *rr == 0 ) { fun[FUNHEAD] = -SNUMBER; fun[FUNHEAD+1] = CLEANFLAG; fun[1] = FUNHEAD+2; } else { rr = fun+FUNHEAD; *rr = r-rr; rr[1] = CLEANFLAG; if ( ToFast(rr,rr) ) { NEXTARG(rr); fun[1] = rr - fun; } else { fun[1] = r - fun; } } fun[2] = CLEANFLAG; goto done; } else if ( *arg2 == -SNUMBER ) { rr = r = outarg; if ( arg2[1] == 0 ) { error = 1; goto onerror; } if ( *arg1 == -SNUMBER ) { /* Things may not be normalized */ if ( arg1[1] == 0 ) { *r++ = 0; } else { co1[0] = ABS(arg1[1]); co1[1] = 1; co2[0] = 1; co2[1] = ABS(arg2[1]); MulRat(BHEAD co1,1,co2,1,co,&nco); *r++ = 4; *r++ = (WORD)(co[0]); *r++ = (WORD)(co[1]); if ( ( arg1[1] < 0 && arg2[1] > 0 ) || ( arg1[1] > 0 && arg2[1] < 0 ) ) *r++ = -3; else *r++ = 3; *r = 0; } } else if ( *arg1 == -SYMBOL ) { *r++ = 8; *r++ = SYMBOL; *r++ = 4; *r++ = arg1[1]; *r++ = 1; *r++ = 1; *r++ = ABS(arg2[1]); if ( arg2[1] < 0 ) *r++ = -3; else *r++ = 3; *r = 0; } else if ( *arg1 < 0 ) { error = 2; goto onerror; } else { /* Multi-term numerator. */ m = arg1+ARGHEAD; NewSort(BHEAD0); /* Technically maybe not needed */ if ( AR.PolyFunExp == 2 ) { /* Find minimum power */ WORD minpow2 = MAXPOWER, *rrm; rrm = m; while ( rrm < arg2 ) { if ( *rrm == 4 ) { if ( minpow2 > 0 ) minpow2 = 0; } else if ( ABS(rrm[*rrm-1]) == (*rrm-1) ) { if ( minpow2 > 0 ) minpow2 = 0; } else { if ( rrm[1] == SYMBOL && rrm[2] == 4 && rrm[3] == AR.PolyFunVar ) { if ( rrm[4] < minpow2 ) minpow2 = rrm[4]; } else { MesPrint("Illegal term in expanded polyratfun."); goto onerror; } } rrm += *rrm; } AR.PolyFunPow += minpow2; } while ( m < arg2 ) { r = rr; rrr = r++; mm = m + *m; *r++ = DENOMINATOR; *r++ = FUNHEAD + 2; *r++ = DIRTYFLAG; FILLFUN3(r); *r++ = arg2[0]; *r++ = arg2[1]; m++; while ( m < mm ) *r++ = *m++; *rrr = r-rrr; if ( r < AT.WorkTop && r >= AT.WorkSpace ) AT.WorkPointer = r; Normalize(BHEAD rrr); if ( ABS(rrr[*rrr-1]) == *rrr-1 ) { if ( AR.PolyFunPow >= 0 ) { StoreTerm(BHEAD rrr); } } else if ( rrr[1] == SYMBOL && rrr[2] == 4 && rrr[3] == AR.PolyFunVar && rrr[4] <= AR.PolyFunPow ) { StoreTerm(BHEAD rrr); } } EndSort(BHEAD rr,1); } r = rr; while ( *r ) r += *r; i = r-rr; r = fun + FUNHEAD + ARGHEAD; NCOPY(r,rr,i); rr = fun + FUNHEAD; *rr = r - rr; rr[1] = CLEANFLAG; if ( ToFast(rr,rr) ) { NEXTARG(rr); fun[1] = rr - fun; } else { fun[1] = r - fun; } fun[2] = CLEANFLAG; goto done; } else { error = 0; goto onerror; } } else { r = arg2+ARGHEAD; /* The argument ends at tnext */ first = 1; while ( r < tnext ) { rr = r + *r; rr -= ABS(rr[-1]); if ( r+1 == rr ) { if ( first ) { minpow = 0; first = 0; rmin = r; } else if ( minpow > 0 ) { minpow = 0; rmin = r; } } else if ( r[1] != SYMBOL || r[2] != 4 || r[3] != AR.PolyFunVar || r[4] > MAXPOWER ) { error = 0; goto onerror; } else if ( first ) { minpow = r[4]; first = 0; rmin = r; } else if ( r[4] < minpow ) { minpow = r[4]; rmin = r; } r += *r; } /* We have now: 1: a numerator in arg1 which can contain several variables. 2: a denominator in arg2 with at most only AR.PolyFunVar (ep). 3: the minimum power in the denominator is minpow and the term with that minimum power is in rmin. Divide numerator and denominator by this minimum power. Determine the power range in the numerator. Call InvPoly. Multiply by the inverse in such a way that we never take more powers of ep than necessary. */ /* One: put 1/rmin in AT.WorkPointer -> rmininv */ AT.WorkPointer += AM.MaxTer/sizeof(WORD); if ( AT.WorkPointer + (AM.MaxTer/sizeof(WORD)) >= AT.WorkTop ) { error = 4; goto onerror; } rmininv = r = AT.WorkPointer; rr = rmin; i = *rmin; NCOPY(r,rr,i) if ( minpow != 0 ) { rmininv[4] = -rmininv[4]; } rsize = ABS(r[-1]); rcoef = r - rsize; rsize = (rsize-1)/2; rr = rcoef + rsize; for ( i = 0; i < rsize; i++ ) { rcopy = rcoef[i]; rcoef[i] = rr[i]; rr[i] = rcopy; } AT.WorkPointer = r; if ( *arg1 < 0 ) { ToGeneral(arg1,r,0); arg1 = r; r += *r; *r++ = 0; rcopy = 0; AT.WorkPointer = r; } else { r = arg1 + *arg1; rcopy = *r; *r++ = 0; } /* We can use MultiplyWithTerm. */ AT.LeaveNegative = 1; numerator = MultiplyWithTerm(BHEAD arg1+ARGHEAD,rmininv,0); AT.LeaveNegative = 0; r[-1] = rcopy; r = numerator; while ( *r ) r += *r; AT.WorkPointer = r+1; rcopy = arg2[*arg2]; arg2[*arg2] = 0; denominator = MultiplyWithTerm(BHEAD arg2+ARGHEAD,rmininv,1); arg2[*arg2] = rcopy; r = denominator; while ( *r ) r += *r; AT.WorkPointer = r+1; /* Now find the minimum power of ep in the numerator. */ r = numerator; first = 1; while ( *r ) { rr = r + *r; rr -= ABS(rr[-1]); if ( r+1 == rr ) { if ( first ) { minpow = 0; first = 0; } else if ( minpow > 0 ) { minpow = 0; } } else if ( r[1] != SYMBOL ) { error = 0; goto onerror; } else { for ( i = 3; i < r[2]; i += 2 ) { if ( r[i] == AR.PolyFunVar ) { if ( first ) { minpow = r[i+1]; first = 0; } else if ( r[i+1] < minpow ) minpow = r[i+1]; break; } } if ( i >= r[2] ) { if ( first ) { minpow = 0; first = 0; } else if ( minpow > 0 ) minpow = 0; } } r += *r; } /* We can invert the denominator. Note that the return value is an offset in AT.pWorkSpace. Hence there is no need to free memory afterwards. */ if ( AR.PolyFunExp == 3 ) { ipoly = InvPoly(BHEAD denominator,AR.PolyFunPow-minpow,AR.PolyFunVar); } else { ipoly = InvPoly(BHEAD denominator,AR.PolyFunPow,AR.PolyFunVar); } /* Now we start the multiplying */ NewSort(BHEAD0); r = numerator; while ( *r ) { /* 1: Find power of ep. */ rnext = r + *r; rrr = rnext - ABS(rnext[-1]); rr = r+1; eppow = 0; if ( rr < rrr ) { j = rr[1] - 2; rr += 2; while ( j > 0 ) { if ( *rr == AR.PolyFunVar ) { eppow = rr[1]; break; } j -= 2; rr += 2; } } /* 2: Multiply by the proper terms in ipoly */ for ( i = 0; i <= AR.PolyFunPow-eppow+minpow; i++ ) { if ( AT.pWorkSpace[ipoly+i] == 0 ) continue; /* Copy the term, add i to the power of ep and multiply coef. */ rc = r; rr = thecopy = AT.WorkPointer; while ( rc < rrr ) *rr++ = *rc++; if ( i != 0 ) { *rr++ = SYMBOL; *rr++ = 4; *rr++ = AR.PolyFunVar; *rr++ = i; } ncoef = REDLENG(rnext[-1]); MulRat(BHEAD (UWORD *)rrr,ncoef, (UWORD *)(AT.pWorkSpace[ipoly+i])+1,AT.pWorkSpace[ipoly+i][0] ,(UWORD *)rr,&newcoef); ncoef = ABS(newcoef); rr += 2*ncoef; newcoef = INCLENG(newcoef); *rr++ = newcoef; *thecopy = rr - thecopy; AT.WorkPointer = rr; Normalize(BHEAD thecopy); if ( *thecopy > 0 ) StoreTerm(BHEAD thecopy); AT.WorkPointer = thecopy; } r = rnext; } /* Now we have all. */ rr = fun + FUNHEAD; r = rr + ARGHEAD; EndSort(BHEAD r,1); if ( *r == 0 ) { fun[1] = FUNHEAD+2; fun[2] = CLEANFLAG; fun[FUNHEAD] = -SNUMBER; fun[FUNHEAD+1] = 0; } else { while ( *r ) r += *r; rr[0] = r-rr; rr[1] = CLEANFLAG; if ( ToFast(rr,rr) ) { NEXTARG(rr); fun[1] = rr-fun; } else { fun[1] = r-fun; } fun[2] = CLEANFLAG; } } done: if ( outarg ) TermFree(outarg-ARGHEAD,"ExpandRat"); AR.PolyFunPow = OldPolyFunPow; AT.WorkPointer = ow; AN.PolyNormFlag = 1; return(0); onerror: if ( outarg ) TermFree(outarg-ARGHEAD,"ExpandRat"); AR.PolyFunPow = OldPolyFunPow; AT.WorkPointer = ow; MLOCK(ErrorMessageLock); MesPrint(TheErrorMessage[error]); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); } /* #] ExpandRat : #[ InvPoly : The input polynomial is represented as a sequence of terms in ascending power. The first coefficient is 1. If we call this 1-a and a = sum_(j,1,n,x^j*a(j)), and b = 1/(1-a) we can find the coefficients of b with the recursion b(0) = 1, b(n) = sum_(j,1,n,a(j)*b(n-j)) The variable is the symbol sym and we need maxpow powers in the answer. The answer is an array of pointers to the coefficients of the various powers as rational numbers in the notation signedsize,numerator,denominator We put these powers in the workspace and the answer is in AT.pWorkSpace. Hence the return value is an offset in the pWorkSpace. A zero pointer indicates that this coefficient is zero. */ int InvPoly(PHEAD WORD *inpoly, WORD maxpow, WORD sym) { int needed, inpointers, outpointers, maxinput = 0, i, j; WORD *t, *tt, *ttt, *w, *c, *cc, *ccc, lenc, lenc1, lenc2, rc, *c1, *c2; /* Step 0: allocate the space */ needed = (maxpow+1)*2; WantAddPointers(needed); inpointers = AT.pWorkPointer; outpointers = AT.pWorkPointer+maxpow+1; for ( i = 0; i < needed; i++ ) AT.pWorkSpace[inpointers+i] = 0; /* Step 1: determine the coefficients in inpoly often there is a maximum power that is much smaller than maxpow. keeping track of this can speed up things. */ t = inpoly; w = AT.WorkPointer; while ( *t ) { if ( *t == 4 ) { if ( t[1] != 1 || t[2] != 1 || t[3] != 3 ) goto onerror; AT.pWorkSpace[inpointers] = 0; } else if ( t[1] != SYMBOL || t[2] != 4 || t[3] != sym || t[4] < 0 ) goto onerror; else if ( t[4] > maxpow ) {} /* power outside useful range */ else { if ( t[4] > maxinput ) maxinput = t[4]; AT.pWorkSpace[inpointers+t[4]] = w; tt = t + *t; rc = -*--tt; /* we need - the coefficient! */ rc = REDLENG(rc); *w++ = rc; ttt = t+5; while ( ttt < tt ) *w++ = *ttt++; } t += *t; } /* Step 2: compute the output. b(0) = 1. then the recursion starts. */ AT.pWorkSpace[outpointers] = w; *w++ = 1; *w++ = 1; *w++ = 1; c = TermMalloc("InvPoly"); c1 = TermMalloc("InvPoly"); c2 = TermMalloc("InvPoly"); for ( j = 1; j <= maxpow; j++ ) { /* Start at c = a(j)*b(0) = a(j) */ if ( ( cc = AT.pWorkSpace[inpointers+j] ) != 0 ) { lenc = *cc++; /* reduced length */ i = 2*ABS(lenc); ccc = c; NCOPY(ccc,cc,i); } else { lenc = 0; } for ( i = MiN(j-1,maxinput); i > 0; i-- ) { /* c -> c + a(i)*b(j-i) */ if ( AT.pWorkSpace[inpointers+i] == 0 || AT.pWorkSpace[outpointers+j-i] == 0 ) { } else { if ( MulRat(BHEAD (UWORD *)(AT.pWorkSpace[inpointers+i]+1),AT.pWorkSpace[inpointers+i][0], (UWORD *)(AT.pWorkSpace[outpointers+j-i]+1),AT.pWorkSpace[outpointers+j-i][0], (UWORD *)c1,&lenc1) ) goto calcerror; if ( lenc == 0 ) { cc = c; c = c1; c1 = cc; lenc = lenc1; } else { if ( AddRat(BHEAD (UWORD *)c,lenc,(UWORD *)c1,lenc1,(UWORD *)c2,&lenc2) ) goto calcerror; cc = c; c = c2; c2 = cc; lenc = lenc2; } } } /* Copy c to the proper location */ if ( lenc == 0 ) AT.pWorkSpace[outpointers+j] = 0; else { AT.pWorkSpace[outpointers+j] = w; *w++ = lenc; i = 2*ABS(lenc); ccc = c; NCOPY(w,ccc,i); } } AT.WorkPointer = w; TermFree(c2,"InvPoly"); TermFree(c1,"InvPoly"); TermFree(c ,"InvPoly"); return(outpointers); onerror: MLOCK(ErrorMessageLock); MesPrint("Incorrect symbol field in InvPoly."); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); calcerror: MLOCK(ErrorMessageLock); MesPrint("Called from InvPoly."); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); } /* #] InvPoly : */ form-5.0.1/sources/sort.c0000644000175100017510000037710015217035721010774 /** @file sort.c * * Contains the sort routines. * We distinguish levels of sorting. * The ground level is the sorting of terms in an expression. * When a term has functions, the arguments can contain terms that need * sorting, which this then done by raising the level. This can happen * recursively. NewSort and EndSort automatically raise and lower the * level. Because the ground level does some special things, sometimes * we have to raise immediately to the second level skipping the ground level. * * Special routines for the parallel sorting are in the file threads.c * Also the sorting of terms in polynomials is special but most of that is * controlled by changing the address of the compare routine. Other routines * relevant for adding rational polynomials are in the file polynito.c */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : sort.c Sort routines according to new conventions (25-jun-1997). This is more object oriented. The active sort is indicated by AT.SS which should agree with AN.FunSorts[AR.sLevel]; #define GZIPDEBUG */ #define NEWSPLITMERGE /* Comment to turn off Timsort in SplitMerge for debugging: */ #define NEWSPLITMERGETIMSORT /* During SplitMerge, print pointer array state on entry. Very spammy, for debugging. */ /* #define SPLITMERGEDEBUG */ /* Debug printing for GarbHand */ /* #define TESTGARB */ #include "form3.h" #ifdef WITHPTHREADS UBYTE THRbuf[100]; #endif #ifdef WITHSTATS extern LONG numwrites; extern LONG numreads; extern LONG numseeks; extern LONG nummallocs; extern LONG numfrees; #endif /* #] Includes : #[ SortUtilities : #[ WriteStats : void WriteStats(lspace,par,checkLogType) */ char *toterms[] = { " ", " >>", "-->" }; #define HUMANSTRLEN 12 #define HUMANSUFFLEN 4 const char humanTermsSuffix[HUMANSUFFLEN][4] = {"K ","M ","B ","T "}; const char humanBytesSuffix[HUMANSUFFLEN][4] = {"KiB","MiB","GiB","TiB"}; void HumanString(char* string, float input, const char suffix[HUMANSUFFLEN][4]) { int ind = -1; while (ind < 0 || (input >= 1000.0f && ind < HUMANSUFFLEN) ) { input /= 1000.0f; ind++; } if ( input <= 0.5f ) { snprintf(string, HUMANSTRLEN, " ( <1 %s)", suffix[ind]); } else { snprintf(string, HUMANSTRLEN, " (%3.f %s)", input, suffix[ind]); } } WORD DigitsIn(LONG x) { if ( x < 0 ) x = -x; WORD dig = 1; while ( x > 9 ) { dig++; x /= 10; } return dig; } /** * Writes the statistics. * * @param plspace The size in bytes currently occupied * @param par * par = 0 = STATSSPLITMERGE after a splitmerge. * par = 1 = STATSMERGETOFILE after merge to sortfile. * par = 2 = STATSPOSTSORT after the sort * @param checkLogType == CHECKLOGTYPE: The output should not * go to the log file if AM.LogType is 1. * * current expression is to be found in AR.CurExpr. * terms are in S->TermsLeft. * S->GenTerms. */ void WriteStats(POSITION *plspace, WORD par, WORD checkLogType) { GETIDENTITY char buf[120]; LONG millitime; WORD timepart; SORTING *S; int use_wtime; if ( AT.SS == AT.S0 && AC.StatsFlag ) { #ifdef WITHPTHREADS if ( AC.ThreadStats == 0 && identity > 0 ) return; #elif defined(WITHMPI) if ( AC.OldParallelStats ) return; if ( ! AC.ProcessStats && PF.me != MASTER ) return; #endif if ( Expressions == 0 ) return; if ( par == STATSSPLITMERGE ) { if ( AC.ShortStatsMax == 0 ) return; AR.ShortSortCount++; if ( AR.ShortSortCount < AC.ShortStatsMax ) return; } AR.ShortSortCount = 0; S = AT.SS; char humanGenTermsText[HUMANSTRLEN] = ""; char humanTermsLeftText[HUMANSTRLEN] = ""; char humanBytesText[HUMANSTRLEN] = ""; char humanUnsortedBytesText[HUMANSTRLEN] = ""; char humanComparisonsText[HUMANSTRLEN] = ""; if ( AC.HumanStatsFlag ) { HumanString(humanGenTermsText, (float)(S->GenTerms), humanTermsSuffix); HumanString(humanTermsLeftText, (float)(S->TermsLeft), humanTermsSuffix); HumanString(humanBytesText, (float)(BASEPOSITION(*plspace)), humanBytesSuffix); HumanString(humanUnsortedBytesText, (float)(S->verbUnsortedSize), humanBytesSuffix); HumanString(humanComparisonsText, (float)(S->verbComparisons), humanTermsSuffix); } MLOCK(ErrorMessageLock); /* If the statistics should not go to the log file, temporarily hide the * LogHandle. This must be done within the ErrorMessageLock region to * avoid a data race between threads. */ const WORD oldLogHandle = AC.LogHandle; if ( checkLogType && AM.LogType ) { AC.LogHandle = -1; } if ( AC.ShortStats ) {} else { #ifdef WITHPTHREADS if ( identity > 0 ) { MesPrint(" Thread %d reporting",identity); } else { MesPrint(""); } #elif defined(WITHMPI) if ( PF.me != MASTER ) { MesPrint(" Process %d reporting",PF.me); } else { MesPrint(""); } #else MesPrint(""); #endif } /* * We define WTimeStatsFlag as a flag to print the wall-clock time on * the *master*, not in workers. This can be confusing in thread * statistics when short statistics is used. Technically, * TimeWallClock() is not thread-safe in TFORM. */ use_wtime = AC.WTimeStatsFlag; #if defined(WITHPTHREADS) if ( use_wtime && identity > 0 ) use_wtime = 0; #elif defined(WITHMPI) if ( use_wtime && PF.me != MASTER ) use_wtime = 0; #endif char *wpref = use_wtime ? "W" : ""; char *wspac = use_wtime ? "" : " "; millitime = use_wtime ? TimeWallClock(1) * 10 : TimeCPU(1); timepart = (WORD)(millitime%1000); millitime /= 1000; timepart /= 10; if ( AC.ShortStats ) { #if defined(WITHPTHREADS) || defined(WITHMPI) #ifdef WITHPTHREADS if ( identity > 0 ) { #else if ( PF.me != MASTER ) { const int identity = PF.me; #endif if ( par == STATSSPLITMERGE || par == STATSPOSTSORT ) { snprintf(buf, sizeof(buf), "%d: %7ld.%02us %8ld>%10ld%3s%10ld:%10ld %s %s",identity, millitime,timepart,AN.ninterms,S->GenTerms,toterms[par], S->TermsLeft,BASEPOSITION(*plspace),EXPRNAME(AR.CurExpr), AC.Commercial); MesPrint("%s", buf); } else if ( par == STATSMERGETOFILE ) { snprintf(buf, sizeof(buf), "%d: %7ld.%02us %10ld:%10ld",identity,millitime,timepart, S->TermsLeft,BASEPOSITION(*plspace)); MesPrint("%s", buf); } } else #endif { if ( par == STATSSPLITMERGE || par == STATSPOSTSORT ) { snprintf(buf, sizeof(buf), "%7ld.%02us %8ld>%10ld%3s%10ld:%10ld %s %s", millitime,timepart,AN.ninterms,S->GenTerms,toterms[par], S->TermsLeft,BASEPOSITION(*plspace),EXPRNAME(AR.CurExpr), AC.Commercial); MesPrint("%s", buf); } else if ( par == STATSMERGETOFILE ) { snprintf(buf, sizeof(buf), "%7ld.%02us %10ld:%10ld",millitime,timepart, S->TermsLeft,BASEPOSITION(*plspace)); MesPrint("%s", buf); } } } else { if ( par == STATSMERGETOFILE ) { snprintf(buf, sizeof(buf), "%sTime = %7ld.%02u sec",wpref,millitime,timepart); MesPrint("%s", buf); } else { snprintf(buf, sizeof(buf), "%sTime = %7ld.%02u sec %sGenerated terms = %10ld%s", wpref,millitime,timepart,wspac,S->GenTerms,humanGenTermsText); MesPrint("%s", buf); } if ( par == STATSSPLITMERGE ) { snprintf(buf, sizeof(buf), "%16s%8ld Terms %s = %10ld%s", EXPRNAME(AR.CurExpr),AN.ninterms,FG.swmes[par],S->TermsLeft, humanTermsLeftText); MesPrint("%s", buf); } else { #ifdef WITHPTHREADS if ( identity > 0 && par == STATSPOSTSORT ) { snprintf(buf, sizeof(buf), "%16s Terms in thread = %10ld%s", EXPRNAME(AR.CurExpr),S->TermsLeft,humanTermsLeftText); MesPrint("%s", buf); } else #elif defined(WITHMPI) if ( PF.me != MASTER && par == STATSPOSTSORT ) { snprintf(buf, sizeof(buf), "%16s Terms in process= %10ld%s", EXPRNAME(AR.CurExpr),S->TermsLeft,humanTermsLeftText); MesPrint("%s", buf); } else #endif { snprintf(buf, sizeof(buf), "%16s Terms %s = %10ld%s", EXPRNAME(AR.CurExpr),FG.swmes[par],S->TermsLeft, humanTermsLeftText); MesPrint("%s", buf); } } const WORD dig = DigitsIn(BASEPOSITION(*plspace)); snprintf(buf, sizeof(buf), "%24s Bytes used%*s=%11ld%s", AC.Commercial,MiN(6,17-dig),"",BASEPOSITION(*plspace), humanBytesText); MesPrint("%s", buf); } if ( par == STATSPOSTSORT ) { if ( AC.SortVerbose ) { snprintf(buf, sizeof(buf), "%24s Unsorted bytes =%11ld%s", "",S->verbUnsortedSize,humanUnsortedBytesText); MesPrint("%s", buf); snprintf(buf, sizeof(buf), "%24s Small Buffer =%5ld,%5ld", "",S->verbSBsortTerms,S->verbSBsortCap); MesPrint("%s", buf); snprintf(buf, sizeof(buf), "%24s Large Buffer =%5ld,%5ld", "",S->verbLBsortPatches,S->verbLBsortCap); MesPrint("%s", buf); snprintf(buf, sizeof(buf), "%24s Comparisons =%11ld%s", "",S->verbComparisons,humanComparisonsText); MesPrint("%s", buf); } } #ifdef WITHSTATS MesPrint("Total number of writes: %l, reads: %l, seeks, %l" ,numwrites,numreads,numseeks); MesPrint("Total number of mallocs: %l, frees: %l" ,nummallocs,numfrees); #endif /* Put back the original LogHandle, it was changed if the statistics were * not printed in the log file. */ AC.LogHandle = oldLogHandle; MUNLOCK(ErrorMessageLock); } } /* #] WriteStats : #[ NewSort : WORD NewSort() */ /** * Starts a new sort. * At the lowest level this is a 'main sort' with the struct according * to the parameters in S0. At higher levels this is a sort for * functions, subroutines or dollars. * We prepare the arrays and structs. * * @return Regular convention (OK -> 0) */ int NewSort(PHEAD0) { GETBIDENTITY SORTING *S, **newFS; int i, newsize; if ( AN.SoScratC == 0 ) AN.SoScratC = (UWORD *)Malloc1(2*(AM.MaxTal+2)*sizeof(UWORD),"NewSort"); AR.sLevel++; if ( AR.sLevel >= AN.NumFunSorts ) { if ( AN.NumFunSorts == 0 ) newsize = 100; else newsize = 2*AN.NumFunSorts; newFS = (SORTING **)Malloc1((newsize+1)*sizeof(SORTING *),"FunSort pointers"); for ( i = 0; i < AN.NumFunSorts; i++ ) newFS[i] = AN.FunSorts[i]; for ( ; i <= newsize; i++ ) newFS[i] = 0; if ( AN.FunSorts ) M_free(AN.FunSorts,"FunSort pointers"); AN.FunSorts = newFS; AN.NumFunSorts = newsize; } if ( AR.sLevel == 0 ) { AN.FunSorts[0] = AT.S0; if ( AR.PolyFun == 0 ) { AT.S0->PolyFlag = 0; } else if ( AR.PolyFunType == 1 ) { AT.S0->PolyFlag = 1; } else if ( AR.PolyFunType == 2 ) { if ( AR.PolyFunExp == 2 || AR.PolyFunExp == 3 ) AT.S0->PolyFlag = 1; else AT.S0->PolyFlag = 2; } AR.ShortSortCount = 0; } else { if ( AN.FunSorts[AR.sLevel] == 0 ) { AN.FunSorts[AR.sLevel] = AllocSort( AM.SLargeSize,AM.SSmallSize,AM.SSmallEsize,AM.STermsInSmall ,AM.SMaxPatches,AM.SMaxFpatches,AM.SIOsize,1); } AN.FunSorts[AR.sLevel]->PolyFlag = 0; } AT.SS = S = AN.FunSorts[AR.sLevel]; S->sFill = S->sBuffer; S->lFill = S->lBuffer; S->lPatch = 0; S->fPatchN = 0; S->GenTerms = S->TermsLeft = S->GenSpace = S->SpaceLeft = 0; S->PoinFill = S->sPointer; *S->PoinFill = S->sFill; if ( AR.sLevel > 0 ) { S->PolyWise = 0; } PUTZERO(S->SizeInFile[0]); PUTZERO(S->SizeInFile[1]); PUTZERO(S->SizeInFile[2]); S->sTerms = 0; PUTZERO(S->file.POposition); S->stage4 = 0; if ( AR.sLevel > AN.MaxFunSorts ) AN.MaxFunSorts = AR.sLevel; // Zero the SortVerbose counters: S->verbComparisons = 0; S->verbSBsortTerms = 0; S->verbSBsortCap = 0; S->verbLBsortPatches = 0; S->verbLBsortCap = 0; S->verbUnsortedSize = 0; return(0); } /* #] NewSort : #[ EndSort : WORD EndSort(PHEAD buffer,par) */ /** * Finishes a sort. * At AR.sLevel == 0 the output is to the regular output stream. * When AR.sLevel > 0, the parameter par determines the actual output. * The AR.sLevel will be popped. * All ongoing stages are finished and if the sortfile is open * it is closed. * The statistics are printed when AR.sLevel == 0 * par == 0 Output to the buffer. * par == 1 Sort for function arguments. * The output will be copied into the buffer. * It is assumed that this is in the WorkSpace. * par == 2 Sort for $-variable. We return the address of the buffer * that contains the output in buffer (treated like WORD **). * We first catch the output in a file (unless we can * intercept things after the small buffer has been sorted) * Then we read from the file into a buffer. * Only when par == 0 data compression can be attempted at AT.SS==AT.S0. * * @param buffer buffer for output when needed * @param par See above * @return If negative: error. If positive: number of words in output. */ LONG EndSort(PHEAD WORD *buffer, int par) { GETBIDENTITY SORTING *S = AT.SS; WORD j, **ss, *to, *t; LONG sSpace, over, tover, spare, retval = 0; POSITION position, pp; off_t lSpace; FILEHANDLE *fout = 0, *oldoutfile = 0, *newout = 0; if ( AM.exitflag && AR.sLevel == 0 ) return(0); #ifdef WITHMPI if( (retval = PF_EndSort()) > 0){ oldoutfile = AR.outfile; retval = 0; goto RetRetval; } else if(retval < 0){ retval = -1; goto RetRetval; } /* PF_EndSort returned 0: for S != AM.S0 and slaves still do the regular sort */ #endif /* WITHMPI */ oldoutfile = AR.outfile; /* PolyFlag repair action if ( S == AT.S0 ) { if ( AR.PolyFun == 0 ) { S->PolyFlag = 0; } else if ( AR.PolyFunType == 1 ) { S->PolyFlag = 1; } else if ( AR.PolyFunType == 2 ) { if ( AR.PolyFunExp == 2 || AR.PolyFunExp == 3 ) S->PolyFlag = 1; else S->PolyFlag = 2; } S->PolyWise = 0; } else { S->PolyFlag = S->PolyWise = 0; } */ S->PolyWise = 0; *(S->PoinFill) = 0; #ifdef SPLITTIME PrintTime((UBYTE *)"EndSort, before SplitMerge"); #endif S->sPointer[SplitMerge(BHEAD S->sPointer,S->sTerms)] = 0; #ifdef SPLITTIME PrintTime((UBYTE *)"Endsort, after SplitMerge"); #endif sSpace = 0; tover = over = S->sTerms; ss = S->sPointer; if ( over >= 0 ) { if ( S->lPatch > 0 || S->file.handle >= 0 ) { ss[over] = 0; sSpace = ComPress(ss,&spare); S->TermsLeft -= over - spare; if ( par == 1 ) { AR.outfile = newout = AllocFileHandle(0,(char *)0); } } else if ( S != AT.S0 ) { ss[over] = 0; if ( par == 2 ) { sSpace = 3; while ( ( t = *ss++ ) != 0 ) { sSpace += *t; } if ( AN.tryterm > 0 && ( (sSpace+1)*sizeof(WORD) < (size_t)(AM.MaxTer) ) ) { to = TermMalloc("$-sort space"); } else { LONG allocsp = sSpace+1; if ( allocsp < MINALLOC ) allocsp = MINALLOC; allocsp = ((allocsp+7)/8)*8; to = (WORD *)Malloc1(allocsp*sizeof(WORD),"$-sort space"); if ( AN.tryterm > 0 ) AN.tryterm = 0; } *((WORD **)buffer) = to; ss = S->sPointer; while ( ( t = *ss++ ) != 0 ) { j = *t; while ( --j >= 0 ) *to++ = *t++; } *to = 0; retval = sSpace + 1; } else { to = buffer; sSpace = 0; while ( ( t = *ss++ ) != 0 ) { j = *t; if ( ( sSpace += j ) > AM.MaxTer/((LONG)sizeof(WORD)) ) { /* Too big! Get the total size for useful error message */ while ( ( t = *ss++ ) != 0 ) { sSpace += *t; } MLOCK(ErrorMessageLock); MesPrint("Sorted function argument too long (%d words). Increase MaxTermSize (%l words).", sSpace, AM.MaxTer/((LONG)sizeof(WORD))); MUNLOCK(ErrorMessageLock); retval = -1; goto RetRetval; } while ( --j >= 0 ) *to++ = *t++; } *to = 0; retval = to - buffer; } goto RetRetval; } else { POSITION oldpos; if ( S == AT.S0 ) { fout = AR.outfile; *AR.CompressPointer = 0; SeekScratch(AR.outfile,&position); } else { fout = &(S->file); PUTZERO(position); } oldpos = position; S->TermsLeft = 0; /* Here we can go directly to the output. */ #ifdef WITHZLIB { int oldgzipCompress = AR.gzipCompress; AR.gzipCompress = 0; #endif if ( tover > 0 ) { ss = S->sPointer; while ( ( t = *ss++ ) != 0 ) { if ( *t ) S->TermsLeft++; #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) ) { PutToMaster(BHEAD t); } else #endif if ( PutOut(BHEAD t,&position,fout,1) < 0 ) { retval = -1; goto RetRetval; } } } #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) ) { PutToMaster(BHEAD 0); } else #endif if ( FlushOut(&position,fout,1) ) { retval = -1; goto RetRetval; } #ifdef WITHZLIB AR.gzipCompress = oldgzipCompress; } #endif #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) ) goto RetRetval; #endif #ifdef WITHMPI if ( PF.me != MASTER && PF.exprtodo < 0 ) goto RetRetval; #endif DIFPOS(oldpos,position,oldpos); S->SpaceLeft = BASEPOSITION(oldpos); WriteStats(&oldpos,STATSPOSTSORT,NOCHECKLOGTYPE); pp = oldpos; goto RetRetval; } } else if ( par == 1 && newout == 0 ) { AR.outfile = newout = AllocFileHandle(0,(char *)0); } sSpace++; lSpace = sSpace + (S->lFill - S->lBuffer) - (LONG)S->lPatch*(AM.MaxTer/sizeof(WORD)); /* Note wrt MaxTer and lPatch: each patch starts with space for decompression */ /* Not needed if only large buffer, but needed when using files (?) */ SETBASEPOSITION(pp,lSpace); MULPOS(pp,sizeof(WORD)); if ( S->file.handle >= 0 ) { ADD2POS(pp,S->fPatches[S->fPatchN]); } if ( S == AT.S0 ) { if ( S->lPatch > 0 || S->file.handle >= 0 ) { WriteStats(&pp,STATSSPLITMERGE,CHECKLOGTYPE); } } if ( par == 2 ) { AR.outfile = newout = AllocFileHandle(0,(char *)0); } if ( S->lPatch > 0 ) { if ( ( S->lPatch >= S->MaxPatches ) || ( ( (WORD *)(((UBYTE *)(S->lFill + sSpace)) + 2*AM.MaxTer) ) >= S->lTop ) ) { /* The large buffer is too full. Merge and write it */ // Update SortVerbose counters if ( S->lPatch >= S->MaxPatches ) S->verbLBsortPatches++; else S->verbLBsortCap++; #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w EndSort: lPatch = %d, MaxPatches = %d,lFill = %x, sSpace = %ld, MaxTer = %d, lTop = %x" ,S->lPatch,S->MaxPatches,S->lFill,sSpace,AM.MaxTer/sizeof(WORD),S->lTop); MUNLOCK(ErrorMessageLock); #endif if ( MergePatches(1) ) { MLOCK(ErrorMessageLock); MesCall("EndSort"); MUNLOCK(ErrorMessageLock); retval = -1; goto RetRetval; } S->lPatch = 0; pp = S->SizeInFile[1]; MULPOS(pp,sizeof(WORD)); #ifndef WITHPTHREADS if ( S == AT.S0 ) #endif { POSITION pppp; SETBASEPOSITION(pppp,0); SeekFile(S->file.handle,&pppp,SEEK_CUR); SeekFile(S->file.handle,&pp,SEEK_END); SeekFile(S->file.handle,&pppp,SEEK_SET); WriteStats(&pp,STATSMERGETOFILE,CHECKLOGTYPE); UpdateMaxSize(); } } else { S->Patches[S->lPatch++] = S->lFill; to = (WORD *)(((UBYTE *)(S->lFill)) + AM.MaxTer); if ( tover > 0 ) { ss = S->sPointer; while ( ( t = *ss++ ) != 0 ) { j = *t; if ( j < 0 ) j = t[1] + 2; while ( --j >= 0 ) *to++ = *t++; } } *to++ = 0; S->lFill = to; if ( S->file.handle < 0 ) { if ( MergePatches(2) ) { MLOCK(ErrorMessageLock); MesCall("EndSort"); MUNLOCK(ErrorMessageLock); retval = -1; goto RetRetval; } if ( S == AT.S0 ) { pp = S->SizeInFile[2]; MULPOS(pp,sizeof(WORD)); #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) ) goto RetRetval; #endif WriteStats(&pp,STATSPOSTSORT,NOCHECKLOGTYPE); UpdateMaxSize(); } else { if ( par == 2 && newout->handle >= 0 ) { POSITION zeropos; PUTZERO(zeropos); #ifdef ALLLOCK LOCK(newout->pthreadslock); #endif SeekFile(newout->handle,&zeropos,SEEK_SET); to = (WORD *)Malloc1(BASEPOSITION(newout->filesize)+sizeof(WORD)*2 ,"$-buffer reading"); if ( AN.tryterm > 0 ) AN.tryterm = 0; if ( ( retval = ReadFile(newout->handle,(UBYTE *)to,BASEPOSITION(newout->filesize)) ) != BASEPOSITION(newout->filesize) ) { MLOCK(ErrorMessageLock); MesPrint("Error reading information for $ variable"); MUNLOCK(ErrorMessageLock); M_free(to,"$-buffer reading"); retval = -1; } else { *((WORD **)buffer) = to; retval /= sizeof(WORD); } #ifdef ALLLOCK UNLOCK(newout->pthreadslock); #endif } else if ( newout->handle >= 0 ) { /* We land here if par == 1 (function arg sort) and PutOut has created a file. This means that the term is larger than SIOsize, which we ensure is at least as large as MaxTermSize in setfile.c. Thus we know already that the term won't fit. */ TooLarge: MLOCK(ErrorMessageLock); MesPrint("(1)Output should fit inside a single term. Increase MaxTermSize?"); MesCall("EndSort"); MUNLOCK(ErrorMessageLock); retval = -1; goto RetRetval; } else { t = newout->PObuffer; // We deal with the par == 2 case after RetRetval. if ( par != 2 ) { j = newout->POfill - t; to = buffer; if ( to >= AT.WorkSpace && to < AT.WorkTop && to+j > AT.WorkTop ) goto WorkSpaceError; if ( j > AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("Encountered term of size: %d words.", j/(LONG)sizeof(WORD) ); MUNLOCK(ErrorMessageLock); goto TooLarge; } NCOPY(to,t,j); retval = to - buffer - 1; } } } goto RetRetval; } if ( MergePatches(1) ) { /* --> SortFile */ MLOCK(ErrorMessageLock); MesCall("EndSort"); MUNLOCK(ErrorMessageLock); retval = -1; goto RetRetval; } UpdateMaxSize(); pp = S->SizeInFile[1]; MULPOS(pp,sizeof(WORD)); #ifndef WITHPTHREADS if ( S == AT.S0 ) #endif { POSITION pppp; SETBASEPOSITION(pppp,0); SeekFile(S->file.handle,&pppp,SEEK_CUR); SeekFile(S->file.handle,&pp,SEEK_END); SeekFile(S->file.handle,&pppp,SEEK_SET); WriteStats(&pp,STATSMERGETOFILE,CHECKLOGTYPE); } #ifdef WITHERRORXXX if ( S != AT.S0 ) { /* This is wrong! We have sorted to the sort file. Things are not sitting in the output yet. */ if ( newout->handle >= 0 ) goto TooLarge; t = newout->PObuffer; j = newout->POfill - t; to = buffer; if ( to >= AT.WorkSpace && to < AT.WorkTop && to+j > AT.WorkTop ) goto WorkSpaceError; if ( j > AM.MaxTer ) goto TooLarge; NCOPY(to,t,j); goto RetRetval; } #endif } } if ( S->file.handle >= 0 ) { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w EndSort: fPatchN = %d, lPatch = %d, position = %12p" ,S->fPatchN,S->lPatch,&(S->fPatches[S->fPatchN])); MUNLOCK(ErrorMessageLock); #endif if ( S->lPatch <= 0 ) { StageSort(&(S->file)); position = S->fPatches[S->fPatchN]; ss = S->sPointer; if ( *ss ) { *AR.CompressPointer = 0; #ifdef WITHZLIB if ( S == AT.S0 && AR.NoCompress == 0 && AR.gzipCompress > 0 ) S->fpcompressed[S->fPatchN] = 1; else S->fpcompressed[S->fPatchN] = 0; SetupOutputGZIP(&(S->file)); #endif while ( ( t = *ss++ ) != 0 ) { if ( PutOut(BHEAD t,&position,&(S->file),1) < 0 ) { retval = -1; goto RetRetval; } } if ( FlushOut(&position,&(S->file),1) ) { retval = -1; goto RetRetval; } ++(S->fPatchN); S->fPatches[S->fPatchN] = position; UpdateMaxSize(); #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w EndSort+: fPatchN = %d, lPatch = %d, position = %12p" ,S->fPatchN,S->lPatch,&(S->fPatches[S->fPatchN])); MUNLOCK(ErrorMessageLock); #endif } } AR.Stage4Name = 0; #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch ) { if ( S->file.handle >= 0 ) { SynchFile(S->file.handle); } } #endif UpdateMaxSize(); if ( MergePatches(0) ) { MLOCK(ErrorMessageLock); MesCall("EndSort"); MUNLOCK(ErrorMessageLock); retval = -1; goto RetRetval; } S->stage4 = 0; #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) ) goto RetRetval; #endif pp = S->SizeInFile[0]; MULPOS(pp,sizeof(WORD)); WriteStats(&pp,STATSPOSTSORT,NOCHECKLOGTYPE); UpdateMaxSize(); } RetRetval: #ifdef WITHMPI /* NOTE: PF_EndSort has been changed such that it sets S->TermsLeft. (TU 30 Jun 2011) */ if ( AR.sLevel == 0 && (PF.me == MASTER || PF.exprtodo >= 0) ) { Expressions[AR.CurExpr].counter = S->TermsLeft; Expressions[AR.CurExpr].size = pp; } #else if ( AR.sLevel == 0 ) { Expressions[AR.CurExpr].counter = S->TermsLeft; Expressions[AR.CurExpr].size = pp; }/*if ( AR.sLevel == 0 )*/ #endif /*:[25nov2003 mt]*/ if ( S->file.handle >= 0 && ( par != 1 ) && ( par != 2 ) ) { /* sortfile is still open */ UpdateMaxSize(); #ifdef WITHZLIB ClearSortGZIP(&(S->file)); #endif CloseFile(S->file.handle); S->file.handle = -1; remove(S->file.name); #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%wEndSort: sortfile %s removed",S->file.name); MUNLOCK(ErrorMessageLock); #endif } AR.outfile = oldoutfile; AR.sLevel--; if ( AR.sLevel >= 0 ) AT.SS = AN.FunSorts[AR.sLevel]; if ( par == 1 ) { if ( retval < 0 ) { UpdateMaxSize(); if ( newout ) { DeAllocFileHandle(newout); newout = 0; } } else if ( newout ) { if ( newout->handle >= 0 ) { MLOCK(ErrorMessageLock); MesPrint("(2)Output should fit inside a single term. Increase MaxTermSize?"); MesCall("EndSort"); MUNLOCK(ErrorMessageLock); Terminate(-1); } else if ( newout->POfill > newout->PObuffer ) { /* Here we have to copy the contents of the 'file' into the buffer. We assume that this buffer lies in the WorkSpace. Hence */ j = newout->POfill-newout->PObuffer; if ( buffer >= AT.WorkSpace && buffer < AT.WorkTop && buffer+j > AT.WorkTop ) goto WorkSpaceError; else { to = buffer; t = newout->PObuffer; while ( j-- > 0 ) *to++ = *t++; } UpdateMaxSize(); } DeAllocFileHandle(newout); newout = 0; } } else if ( par == 2 ) { if ( newout ) { if ( retval == 0 ) { if ( newout->handle >= 0 ) { /* output resides at the moment in a file Find the size, make a buffer, copy into the buffer and clean up. */ POSITION zeropos; PUTZERO(position); #ifdef ALLLOCK LOCK(newout->pthreadslock); #endif SeekFile(newout->handle,&position,SEEK_END); PUTZERO(zeropos); SeekFile(newout->handle,&zeropos,SEEK_SET); to = (WORD *)Malloc1(BASEPOSITION(position)+sizeof(WORD)*3 ,"$-buffer reading"); if ( AN.tryterm > 0 ) AN.tryterm = 0; if ( ( retval = ReadFile(newout->handle,(UBYTE *)to,BASEPOSITION(position)) ) != BASEPOSITION(position) ) { MLOCK(ErrorMessageLock); MesPrint("Error reading information for $ variable"); MUNLOCK(ErrorMessageLock); M_free(to,"$-buffer reading"); retval = -1; } else { *((WORD **)buffer) = to; retval /= sizeof(WORD); } #ifdef ALLLOCK UNLOCK(newout->pthreadslock); #endif } else { /* output resides in the cache buffer and the file was never opened */ LONG wsiz = newout->POfill - newout->PObuffer; if ( AN.tryterm > 0 && ( (wsiz+2)*sizeof(WORD) < (size_t)(AM.MaxTer) ) ) { to = TermMalloc("$-sort space"); } else { LONG allocsp = wsiz+2; if ( allocsp < MINALLOC ) allocsp = MINALLOC; allocsp = ((allocsp+7)/8)*8; to = (WORD *)Malloc1(allocsp*sizeof(WORD),"$-buffer reading"); if ( AN.tryterm > 0 ) AN.tryterm = 0; } *((WORD **)buffer) = to; t = newout->PObuffer; retval = wsiz; NCOPY(to,t,wsiz); } } UpdateMaxSize(); DeAllocFileHandle(newout); newout = 0; } } else { if ( newout ) { DeAllocFileHandle(newout); newout = 0; } } return(retval); WorkSpaceError: MLOCK(ErrorMessageLock); MesWork(); MesCall("EndSort"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); } /* #] EndSort : #[ PutIn : LONG PutIn(handle,position,buffer,take,npat) */ /** * Reads a new patch from position in file handle. * It is put at buffer, anything after take is moved forward. * This would be part of a term that hasn't been used yet. * Because of this there should be some space before the start of the buffer * * @param file The file system from which to read * @param position The position from which to read * @param buffer The buffer into which to read * @param take The unused tail should be moved before the buffer * @param npat The number of the patch. Is needed if the information * was compressed with gzip, because each patch has its * own independent gzip encoding. */ LONG PutIn(FILEHANDLE *file, POSITION *position, WORD *buffer, WORD **take, int npat) { LONG i, RetCode; WORD *from, *to; #ifndef WITHZLIB DUMMYUSE(npat); #endif from = buffer + ( file->POsize * sizeof(UBYTE) )/sizeof(WORD); i = from - *take; if ( i*((LONG)(sizeof(WORD))) > AM.MaxTer ) { MLOCK(ErrorMessageLock); MesPrint("Problems in PutIn"); MUNLOCK(ErrorMessageLock); Terminate(-1); } to = buffer; while ( --i >= 0 ) *--to = *--from; *take = to; #ifdef WITHZLIB if ( ( RetCode = FillInputGZIP(file,position,(UBYTE *)buffer ,file->POsize,npat) ) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("PutIn: We have RetCode = %x while reading %x bytes", RetCode,file->POsize); MUNLOCK(ErrorMessageLock); Terminate(-1); } #else #ifdef ALLLOCK LOCK(file->pthreadslock); #endif SeekFile(file->handle,position,SEEK_SET); if ( ( RetCode = ReadFile(file->handle,(UBYTE *)buffer,file->POsize) ) < 0 ) { #ifdef ALLLOCK UNLOCK(file->pthreadslock); #endif MLOCK(ErrorMessageLock); MesPrint("PutIn: We have RetCode = %x while reading %x bytes", RetCode,file->POsize); MUNLOCK(ErrorMessageLock); Terminate(-1); } #ifdef ALLLOCK UNLOCK(file->pthreadslock); #endif #endif return(RetCode); } /* #] PutIn : #[ Sflush : WORD Sflush(file) */ /** * Puts the contents of a buffer to output * Only to be used when there is a single patch in the large buffer. * * @param fi The filesystem (or its cache) to which the patch should be written */ int Sflush(FILEHANDLE *fi) { LONG size, RetCode; #ifdef WITHZLIB GETIDENTITY int dobracketindex = 0; if ( AR.sLevel <= 0 && Expressions[AR.CurExpr].newbracketinfo && ( fi == AR.outfile || fi == AR.hidefile ) ) dobracketindex = 1; #endif if ( fi->handle < 0 ) { if ( ( RetCode = CreateFile(fi->name) ) >= 0 ) { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w Sflush created scratch file %s",fi->name); MUNLOCK(ErrorMessageLock); #endif fi->handle = (WORD)RetCode; PUTZERO(fi->filesize); PUTZERO(fi->POposition); } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create scratch file %s",fi->name); MUNLOCK(ErrorMessageLock); return(-1); } } #ifdef WITHZLIB if ( AT.SS == AT.S0 && !AR.NoCompress && AR.gzipCompress > 0 && dobracketindex == 0 ) { if ( FlushOutputGZIP(fi) ) return(-1); fi->POfill = fi->PObuffer; } else #endif { #ifdef ALLLOCK LOCK(fi->pthreadslock); #endif size = (fi->POfill-fi->PObuffer)*sizeof(WORD); SeekFile(fi->handle,&(fi->POposition),SEEK_SET); if ( WriteFile(fi->handle,(UBYTE *)(fi->PObuffer),size) != size ) { #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif MLOCK(ErrorMessageLock); MesPrint("Write error while finishing sort. Disk full?"); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(fi->filesize,size); ADDPOS(fi->POposition,size); fi->POfill = fi->PObuffer; #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif } return(0); } /* #] Sflush : #[ PutOut : WORD PutOut(term,position,file,ncomp) */ /** * Routine writes one term to file handle at position. It returns * the new value of the position. * * NOTE: * For 'final output' we may have to index the brackets. * See the struct BRACKETINDEX. * We should maintain: * 1: a list with brackets * array with the brackets * 2: a list of objects of type BRACKETINDEX. It contains * array with either pointers or offsets to the list of brackets. * starting positions in the file. * The index may be tied to a maximum size. In that case we may have to * prune the list occasionally. * * @param term The term to be written * @param position The position in the file. Afterwards it is updated * @param fi The file (or its cache) to which should be written * @param ncomp Information about what type of compression should be used */ WORD PutOut(PHEAD WORD *term, POSITION *position, FILEHANDLE *fi, WORD ncomp) { GETBIDENTITY WORD i, *p, ret, *r, *rr, j, k, first; int dobracketindex = 0; LONG RetCode; if ( AT.SS != AT.S0 ) { /* For this case no compression should be used */ if ( ( i = *term ) <= 0 ) return(0); ret = i; ADDPOS(*position,i*sizeof(WORD)); p = fi->POfill; do { if ( p >= fi->POstop ) { if ( fi->handle < 0 ) { if ( ( RetCode = CreateFile(fi->name) ) >= 0 ) { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w PutOut created sortfile %s",fi->name); MUNLOCK(ErrorMessageLock); #endif fi->handle = (WORD)RetCode; PUTZERO(fi->filesize); PUTZERO(fi->POposition); /* Should not be here anymore? #ifdef WITHZLIB fi->ziobuffer = 0; #endif */ } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create scratch file %s",fi->name); MUNLOCK(ErrorMessageLock); return(-1); } } #ifdef ALLLOCK LOCK(fi->pthreadslock); #endif if ( fi == AR.hidefile ) { LOCK(AS.inputslock); } SeekFile(fi->handle,&(fi->POposition),SEEK_SET); if ( ( RetCode = WriteFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize) ) != fi->POsize ) { if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif MLOCK(ErrorMessageLock); MesPrint("Write error during sort. Disk full?"); MesPrint("Attempt to write %l bytes on file %d at position %15p", fi->POsize,fi->handle,&(fi->POposition)); MesPrint("RetCode = %l, Buffer address = %l",RetCode,(LONG)(fi->PObuffer)); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(fi->filesize,fi->POsize); p = fi->PObuffer; ADDPOS(fi->POposition,fi->POsize); if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch ) { if ( fi->handle >= 0 ) SynchFile(fi->handle); } #endif } *p++ = *term++; } while ( --i > 0 ); fi->POfull = fi->POfill = p; return(ret); } if ( ( AP.PreDebug & DUMPOUTTERMS ) == DUMPOUTTERMS ) { MLOCK(ErrorMessageLock); #ifdef WITHPTHREADS snprintf((char *)(THRbuf),100,"PutOut(%d)",AT.identity); PrintTerm(term,(char *)(THRbuf)); #else PrintTerm(term,"PutOut"); #endif MesPrint("ncomp = %d, AR.NoCompress = %d, AR.sLevel = %d",ncomp,AR.NoCompress,AR.sLevel); MesPrint("File %s, position %p",fi->name,position); MUNLOCK(ErrorMessageLock); } if ( AR.sLevel <= 0 && Expressions[AR.CurExpr].newbracketinfo && ( fi == AR.outfile || fi == AR.hidefile ) ) dobracketindex = 1; r = rr = AR.CompressPointer; first = j = k = ret = 0; if ( ( i = *term ) != 0 ) { if ( i < 0 ) { /* Compressed term */ i = term[1] + 2; if ( fi == AR.outfile || fi == AR.hidefile ) { MLOCK(ErrorMessageLock); MesPrint("Ran into precompressed term"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); } } else if ( !AR.NoCompress && ( ncomp > 0 ) && AR.sLevel <= 0 ) { /* Must compress */ if ( dobracketindex ) { PutBracketInIndex(BHEAD term,position); } j = *r++ - 1; p = term + 1; i--; if ( AR.PolyFun ) { WORD *polystop, *sa; sa = p + i; sa -= ABS(sa[-1]); polystop = p; while ( polystop < sa && *polystop != AR.PolyFun ) { polystop += polystop[1]; } if ( polystop < sa ) { if ( AR.PolyFunType == 2 ) polystop[2] &= ~MUSTCLEANPRF; while ( i > 0 && j > 0 && *p == *r && p < polystop ) { i--; j--; k--; p++; r++; } } else { while ( i > 0 && j > 0 && *p == *r && p < sa ) { i--; j--; k--; p++; r++; } } } #ifdef WITHFLOAT else if ( AT.aux_ != 0 ) { WORD *floatstop, *sa; sa = p + i; sa -= ABS(sa[-1]); floatstop = p; while ( floatstop < sa && *floatstop != FLOATFUN ) { floatstop += floatstop[1]; } if ( floatstop < sa ) { while ( i > 0 && j > 0 && *p == *r && p < floatstop ) { i--; j--; k--; p++; r++; } } else { while ( i > 0 && j > 0 && *p == *r && p < sa ) { i--; j--; k--; p++; r++; } } } #endif else { WORD *sa; sa = p + i; sa -= ABS(sa[-1]); while ( i > 0 && j > 0 && *p == *r && p < sa ) { i--; j--; k--; p++; r++; } } if ( k > -2 ) { nocompress: j = i = *term; k = 0; p = term; r = rr; NCOPY(r,p,j); } else { *rr = *term; term = p; j = i; NCOPY(r,p,j); j = i; i += 2; first = 2; } /* Sabotage getting into the coefficient next time */ r[-(ABS(r[-1]))] = 0; if ( r >= AR.ComprTop ) { MLOCK(ErrorMessageLock); MesPrint("CompressSize of %10l is insufficient",AM.CompressSize); MUNLOCK(ErrorMessageLock); Terminate(-1); return(-1); } } else if ( !AR.NoCompress && ( ncomp < 0 ) && AR.sLevel <= 0 ) { /* No compress but put in compress buffer anyway */ if ( dobracketindex ) { PutBracketInIndex(BHEAD term,position); } j = *r++ - 1; p = term + 1; i--; if ( AR.PolyFun ) { WORD *polystop, *sa; sa = p + i; sa -= ABS(sa[-1]); polystop = p; while ( polystop < sa && *polystop != AR.PolyFun ) { polystop += polystop[1]; } if ( polystop < sa ) { if ( AR.PolyFunType == 2 ) polystop[2] &= ~MUSTCLEANPRF; while ( i > 0 && j > 0 && *p == *r && p < polystop ) { i--; j--; k--; p++; r++; } } else { while ( i > 0 && j > 0 && *p == *r ) { i--; j--; k--; p++; r++; } } } else { while ( i > 0 && j > 0 && *p == *r ) { i--; j--; k--; p++; r++; } } goto nocompress; } else { if ( AR.PolyFunType == 2 ) { WORD *t, *tstop; tstop = term + *term; tstop -= ABS(tstop[-1]); t = term+1; while ( t < tstop ) { if ( *t == AR.PolyFun ) { t[2] &= ~MUSTCLEANPRF; } t += t[1]; } } if ( dobracketindex ) { PutBracketInIndex(BHEAD term,position); } } ret = i; ADDPOS(*position,i*sizeof(WORD)); p = fi->POfill; do { if ( p >= fi->POstop ) { #ifdef WITHMPI /* [16mar1998 ar] */ if ( PF.me != MASTER && AR.sLevel <= 0 && (fi == AR.outfile || fi == AR.hidefile) && PF.parallel && PF.exprtodo < 0 ) { PF_BUFFER *sbuf = PF.sbuf; sbuf->fill[sbuf->active] = fi->POstop; PF_ISendSbuf(MASTER,PF_BUFFER_MSGTAG); p = fi->PObuffer = fi->POfill = fi->POfull = sbuf->buff[sbuf->active]; fi->POstop = sbuf->stop[sbuf->active]; } else #endif /* WITHMPI [16mar1998 ar] */ { if ( fi->handle < 0 ) { if ( ( RetCode = CreateFile(fi->name) ) >= 0 ) { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w PutOut created sortfile %s",fi->name); MUNLOCK(ErrorMessageLock); #endif fi->handle = (WORD)RetCode; PUTZERO(fi->filesize); PUTZERO(fi->POposition); /* Should not be here? #ifdef WITHZLIB fi->ziobuffer = 0; #endif */ } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create scratch file %s",fi->name); MUNLOCK(ErrorMessageLock); return(-1); } } #ifdef WITHZLIB if ( !AR.NoCompress && ncomp > 0 && AR.gzipCompress > 0 && dobracketindex == 0 && fi->zsp != 0 ) { fi->POfill = p; if ( PutOutputGZIP(fi) ) return(-1); p = fi->PObuffer; } else #endif { #ifdef ALLLOCK LOCK(fi->pthreadslock); #endif if ( fi == AR.hidefile ) { LOCK(AS.inputslock); } SeekFile(fi->handle,&(fi->POposition),SEEK_SET); if ( ( RetCode = WriteFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize) ) != fi->POsize ) { if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif MLOCK(ErrorMessageLock); MesPrint("Write error during sort. Disk full?"); MesPrint("Attempt to write %l bytes on file %d at position %15p", fi->POsize,fi->handle,&(fi->POposition)); MesPrint("RetCode = %l, Buffer address = %l",RetCode,(LONG)(fi->PObuffer)); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(fi->filesize,fi->POsize); p = fi->PObuffer; ADDPOS(fi->POposition,fi->POsize); if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch ) { if ( fi->handle >= 0 ) SynchFile(fi->handle); } #endif } } } if ( first ) { if ( first == 2 ) *p++ = k; else *p++ = j; first--; } else *p++ = *term++; /* if ( AP.DebugFlag ) { TalToLine((UWORD)(p[-1])); TokenToLine((UBYTE *)" "); } */ } while ( --i > 0 ); fi->POfull = fi->POfill = p; } /* if ( AP.DebugFlag ) { AO.OutSkip = 0; FiniLine(); } */ return(ret); } /* #] PutOut : #[ FlushOut : WORD FlushOut(position,file,compr) */ /** * Completes output to an output file and writes the trailing zero. * * @param position The position in the file after writing * @param fi The file (or its cache) * @param compr Indicates whether there should be compression with gzip. * @return Regular conventions (OK -> 0). */ int FlushOut(POSITION *position, FILEHANDLE *fi, int compr) { GETIDENTITY LONG size, RetCode; int dobracketindex = 0; #ifndef WITHZLIB DUMMYUSE(compr); #endif if ( AR.sLevel <= 0 && Expressions[AR.CurExpr].newbracketinfo && ( fi == AR.outfile || fi == AR.hidefile ) ) dobracketindex = 1; #ifdef WITHMPI /* [16mar1998 ar] */ if ( PF.me != MASTER && AR.sLevel <= 0 && (fi == AR.outfile || fi == AR.hidefile) && PF.parallel && PF.exprtodo < 0 ) { PF_BUFFER *sbuf = PF.sbuf; if ( fi->POfill >= fi->POstop ){ sbuf->fill[sbuf->active] = fi->POstop; PF_ISendSbuf(MASTER,PF_BUFFER_MSGTAG); fi->POfull = fi->POfill = fi->PObuffer = sbuf->buff[sbuf->active]; fi->POstop = sbuf->stop[sbuf->active]; } *(fi->POfill)++ = 0; sbuf->fill[sbuf->active] = fi->POfill; PF_ISendSbuf(MASTER,PF_ENDBUFFER_MSGTAG); fi->PObuffer = fi->POfill = fi->POfull = sbuf->buff[sbuf->active]; fi->POstop = sbuf->stop[sbuf->active]; return(0); } #endif /* WITHMPI [16mar1998 ar] */ if ( fi->POfill >= fi->POstop ) { if ( fi->handle < 0 ) { if ( ( RetCode = CreateFile(fi->name) ) >= 0 ) { #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w FlushOut created scratch file %s",fi->name); MUNLOCK(ErrorMessageLock); #endif PUTZERO(fi->filesize); PUTZERO(fi->POposition); fi->handle = (WORD)RetCode; /* Should not be here? #ifdef WITHZLIB fi->ziobuffer = 0; #endif */ } else { MLOCK(ErrorMessageLock); MesPrint("Cannot create scratch file %s",fi->name); MUNLOCK(ErrorMessageLock); return(-1); } } #ifdef WITHZLIB if ( AT.SS == AT.S0 && !AR.NoCompress && AR.gzipCompress > 0 && dobracketindex == 0 && ( compr > 0 ) && fi->zsp != 0 ) { if ( PutOutputGZIP(fi) ) return(-1); fi->POfill = fi->PObuffer; } else #endif { #ifdef ALLLOCK LOCK(fi->pthreadslock); #endif if ( fi == AR.hidefile ) { LOCK(AS.inputslock); } SeekFile(fi->handle,&(fi->POposition),SEEK_SET); if ( ( RetCode = WriteFile(fi->handle,(UBYTE *)(fi->PObuffer),fi->POsize) ) != fi->POsize ) { #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } MLOCK(ErrorMessageLock); MesPrint("Write error while sorting. Disk full?"); MesPrint("Attempt to write %l bytes on file %d at position %15p", fi->POsize,fi->handle,&(fi->POposition)); MesPrint("RetCode = %l, Buffer address = %l",RetCode,(LONG)(fi->PObuffer)); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(fi->filesize,fi->POsize); fi->POfill = fi->PObuffer; ADDPOS(fi->POposition,fi->POsize); if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch && fi != AR.hidefile ) { if ( fi->handle >= 0 ) SynchFile(fi->handle); } #endif } } *(fi->POfill)++ = 0; fi->POfull = fi->POfill; /* { UBYTE OutBuf[140]; if ( AP.DebugFlag ) { AO.OutFill = AO.OutputLine = OutBuf; AO.OutSkip = 3; FiniLine(); TokenToLine((UBYTE *)"End of expression written"); FiniLine(); } } */ size = (fi->POfill-fi->PObuffer)*sizeof(WORD); if ( fi->handle >= 0 ) { #ifdef WITHZLIB if ( AT.SS == AT.S0 && !AR.NoCompress && AR.gzipCompress > 0 && dobracketindex == 0 && ( compr > 0 ) && fi->zsp != 0 ) { if ( FlushOutputGZIP(fi) ) return(-1); fi->POfill = fi->PObuffer; } else #endif { #ifdef ALLLOCK LOCK(fi->pthreadslock); #endif if ( fi == AR.hidefile ) { LOCK(AS.inputslock); } SeekFile(fi->handle,&(fi->POposition),SEEK_SET); /* MesPrint("FlushOut: writing %l bytes to position %12p",size,&(fi->POposition)); */ if ( ( RetCode = WriteFile(fi->handle,(UBYTE *)(fi->PObuffer),size) ) != size ) { #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } MLOCK(ErrorMessageLock); MesPrint("Write error while finishing sorting. Disk full?"); MesPrint("Attempt to write %l bytes on file %d at position %15p", size,fi->handle,&(fi->POposition)); MesPrint("RetCode = %l, Buffer address = %l",RetCode,(LONG)(fi->PObuffer)); MUNLOCK(ErrorMessageLock); return(-1); } ADDPOS(fi->filesize,size); ADDPOS(fi->POposition,size); fi->POfill = fi->PObuffer; if ( fi == AR.hidefile ) { UNLOCK(AS.inputslock); } #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif #ifdef WITHPTHREADS if ( AS.MasterSort && AC.ThreadSortFileSynch ) { if ( fi->handle >= 0 ) SynchFile(fi->handle); } #endif } } if ( dobracketindex ) { BRACKETINFO *b = Expressions[AR.CurExpr].newbracketinfo; if ( b->indexfill > 0 ) { DIFPOS(b->indexbuffer[b->indexfill-1].next,*position,Expressions[AR.CurExpr].onfile); } } #ifdef WITHZLIB if ( AT.SS == AT.S0 && !AR.NoCompress && AR.gzipCompress > 0 && dobracketindex == 0 && ( compr > 0 ) && fi->zsp != 0 ) { PUTZERO(*position); if ( fi->handle >= 0 ) { #ifdef ALLLOCK LOCK(fi->pthreadslock); #endif SeekFile(fi->handle,position,SEEK_END); #ifdef ALLLOCK UNLOCK(fi->pthreadslock); #endif } else { ADDPOS(*position,((UBYTE *)fi->POfill-(UBYTE *)fi->PObuffer)); } } else #endif { ADDPOS(*position,sizeof(WORD)); } return(0); } /* #] FlushOut : #[ AddCoef : WORD AddCoef(pterm1,pterm2) */ /** * Adds the coefficients of the terms *ps1 and *ps2. * The problem comes when there is not enough space for a new * longer coefficient. First a local solution is tried. * If this is not successful we need to move terms around. * The possibility of a garbage collection should not be * ignored, as avoiding this costs very much extra space which * is nearly wasted otherwise. * * If the return value is zero the terms cancelled. * * The resulting term is left in *ps1. */ int AddCoef(PHEAD WORD **ps1, WORD **ps2) { GETBIDENTITY SORTING *S = AT.SS; WORD *s1, *s2; WORD l1, l2, i; WORD OutLen, *t, j; UWORD *OutCoef; #ifdef WITHFLOAT if ( AT.SortFloatMode ) return(AddWithFloat(BHEAD ps1,ps2)); #endif OutCoef = AN.SoScratC; s1 = *ps1; s2 = *ps2; GETCOEF(s1,l1); GETCOEF(s2,l2); if ( AddRat(BHEAD (UWORD *)s1,l1,(UWORD *)s2,l2,OutCoef,&OutLen) ) { MLOCK(ErrorMessageLock); MesCall("AddCoef"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( AN.ncmod != 0 ) { if ( ( AC.modmode & POSNEG ) != 0 ) { NormalModulus(OutCoef,&OutLen); /* We had forgotten that this can also become smaller but the denominator isn't there. Correct in the other case 17-may-2009 [JV] */ j = ABS(OutLen); OutCoef[j] = 1; for ( i = 1; i < j; i++ ) OutCoef[j+i] = 0; } else if ( BigLong(OutCoef,OutLen,(UWORD *)AC.cmod,ABS(AN.ncmod)) >= 0 ) { SubPLon(OutCoef,OutLen,(UWORD *)AC.cmod,ABS(AN.ncmod),OutCoef,&OutLen); OutCoef[OutLen] = 1; for ( i = 1; i < OutLen; i++ ) OutCoef[OutLen+i] = 0; } } if ( !OutLen ) { *ps1 = *ps2 = 0; return(0); } OutLen *= 2; if ( OutLen < 0 ) i = - ( --OutLen ); else i = ++OutLen; if ( l1 < 0 ) l1 = -l1; l1 *= 2; l1++; if ( i <= l1 ) { /* Fits in 1 */ l1 -= i; **ps1 -= l1; s2 = (WORD *)OutCoef; while ( --i > 0 ) *s1++ = *s2++; *s1++ = OutLen; while ( --l1 >= 0 ) *s1++ = 0; goto RegEnd; } if ( l2 < 0 ) l2 = -l2; l2 *= 2; l2++; if ( i <= l2 ) { /* Fits in 2 */ l2 -= i; **ps2 -= l2; s1 = (WORD *)OutCoef; while ( --i > 0 ) *s2++ = *s1++; *s2++ = OutLen; while ( --l2 >= 0 ) *s2++ = 0; *ps1 = *ps2; goto RegEnd; } /* Doesn't fit. Make a new term. */ t = s1; s1 = *ps1; j = *s1++ + i - l1; /* Space needed */ if ( (S->sFill + j) >= S->sTop2 ) { GarbHand(); s1 = *ps1; t = s1 + *s1 - 1; j = *s1++ + i - l1; /* Space needed */ l1 = *t; if ( l1 < 0 ) l1 = - l1; t -= l1-1; } s2 = S->sFill; *s2++ = j; while ( s1 < t ) *s2++ = *s1++; s1 = (WORD *)OutCoef; while ( --i > 0 ) *s2++ = *s1++; *s2++ = OutLen; *ps1 = S->sFill; S->sFill = s2; RegEnd: *ps2 = 0; if ( **ps1 > AM.MaxTer/((LONG)(sizeof(WORD))) ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex after addition in sort. MaxTermSize = %10l", AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } return(1); } /* #] AddCoef : #[ AddPoly : WORD AddPoly(pterm1,pterm2) */ /** * Routine should be called when S->PolyWise != 0. It points then * to the position of AR.PolyFun in both terms. * * We add the contents of the arguments of the two polynomials. * Special attention has to be given to special arguments. * We have to reserve a space equal to the size of one term + the * size of the argument of the other. The addition has to be done * in this routine because not all objects are reentrant. * * Newer addition (12-nov-2007). * The PolyFun can have two arguments. * In that case S->PolyFlag is 2 and we have to call the routine for * adding rational polynomials. * We have to be rather careful what happens with: * The location of the output * The order of the terms in the arguments * At first we allow only univariate polynomials in the PolyFun. * This restriction will be lifted a.s.a.p. * * @param ps1 A pointer to the position of the first term * @param ps2 A pointer to the position of the second term * @return If zero the terms cancel. Otherwise the new term is in *ps1. */ int AddPoly(PHEAD WORD **ps1, WORD **ps2) { GETBIDENTITY SORTING *S = AT.SS; WORD i; WORD *s1, *s2, *m, *w, *t, oldpw = S->PolyWise; s1 = *ps1 + S->PolyWise; s2 = *ps2 + S->PolyWise; w = AT.WorkPointer; /* Add here the two arguments. Is a straight merge. */ if ( S->PolyFlag == 2 && AR.PolyFunExp != 2 && AR.PolyFunExp != 3 ) { WORD **oldSplitScratch = AN.SplitScratch; LONG oldSplitScratchSize = AN.SplitScratchSize; LONG oldInScratch = AN.InScratch; WORD oldtype = AR.SortType; if ( (WORD *)((UBYTE *)w + AM.MaxTer) >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesPrint("Program was adding polyratfun arguments"); MesWork(); MUNLOCK(ErrorMessageLock); } AR.SortType = SORTHIGHFIRST; S->PolyWise = 0; AN.SplitScratch = AN.SplitScratch1; AN.SplitScratchSize = AN.SplitScratchSize1; AN.InScratch = AN.InScratch1; poly_ratfun_add(BHEAD s1,s2); S->PolyWise = oldpw; AN.SplitScratch1 = AN.SplitScratch; AN.SplitScratchSize1 = AN.SplitScratchSize; AN.InScratch1 = AN.InScratch; AN.SplitScratch = oldSplitScratch; AN.SplitScratchSize = oldSplitScratchSize; AN.InScratch = oldInScratch; AT.WorkPointer = w; AR.SortType = oldtype; if ( w[1] <= FUNHEAD || ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 ) ) { *ps1 = *ps2 = 0; return(0); } } else { if ( w + s1[1] + s2[1] + 12 + ARGHEAD >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesPrint("Program was adding polyfun arguments"); MesWork(); MUNLOCK(ErrorMessageLock); } AddArgs(BHEAD s1,s2,w); } /* Now we need to store the result in a convenient place. */ if ( w[1] <= FUNHEAD ) { *ps1 = *ps2 = 0; return(0); } if ( w[1] <= s1[1] || w[1] <= s2[1] ) { /* Fits in place. */ if ( w[1] > s1[1] ) { *ps1 = *ps2; s1 = s2; } t = s1 + s1[1]; m = *ps1 + **ps1; i = w[1]; NCOPY(s1,w,i); if ( s1 != t ) { while ( t < m ) *s1++ = *t++; **ps1 = WORDDIF(s1,(*ps1)); } *ps2 = 0; } else { /* Make new term */ #ifdef TESTGARB s2 = *ps2; #endif *ps2 = 0; if ( (S->sFill + (**ps1 + w[1] - s1[1])) >= S->sTop2 ) { #ifdef TESTGARB MesPrint("------Garbage collection-------"); #endif AT.WorkPointer += w[1]; GarbHand(); AT.WorkPointer = w; s1 = *ps1; if ( (S->sFill + (**ps1 + w[1] - s1[1])) >= S->sTop2 ) { #ifdef TESTGARB UBYTE OutBuf[140]; MLOCK(ErrorMessageLock); AO.OutFill = AO.OutputLine = OutBuf; AO.OutSkip = 3; FiniLine(); i = *s2; while ( --i >= 0 ) { TalToLine((UWORD)(*s2++)); TokenToLine((UBYTE *)" "); } FiniLine(); AO.OutFill = AO.OutputLine = OutBuf; AO.OutSkip = 3; FiniLine(); s2 = *ps1; i = *s2; while ( --i >= 0 ) { TalToLine((UWORD)(*s2++)); TokenToLine((UBYTE *)" "); } FiniLine(); AO.OutFill = AO.OutputLine = OutBuf; AO.OutSkip = 3; FiniLine(); s2 = w; i = w[1]; while ( --i >= 0 ) { TalToLine((UWORD)(*s2++)); TokenToLine((UBYTE *)" "); } FiniLine(); if ( AR.sLevel > 0 ) { MesPrint("Please increase SubSmallExtension setup parameter."); } else { MesPrint("Please increase SmallExtension setup parameter."); } MUNLOCK(ErrorMessageLock); #else MLOCK(ErrorMessageLock); if ( AR.sLevel > 0 ) { MesPrint("Please increase SubSmallExtension setup parameter."); } else { MesPrint("Please increase SmallExtension setup parameter."); } MUNLOCK(ErrorMessageLock); #endif Terminate(-1); } } t = *ps1; s2 = S->sFill; m = s2; i = S->PolyWise; NCOPY(s2,t,i); i = w[1]; NCOPY(s2,w,i); t = t + t[1]; w = *ps1 + **ps1; while ( t < w ) *s2++ = *t++; *m = WORDDIF(s2,m); *ps1 = m; S->sFill = s2; if ( *m > AM.MaxTer/((LONG)sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex after polynomial addition. MaxTermSize = %10l", AM.MaxTer/sizeof(WORD)); MUNLOCK(ErrorMessageLock); Terminate(-1); } } return(1); } /* #] AddPoly : #[ AddArgs : void AddArgs(arg1,arg2,to) */ #define INSLENGTH(x) w[1] = FUNHEAD+ARGHEAD+x; w[FUNHEAD] = ARGHEAD+x; /** * Adds the arguments of two occurrences of the PolyFun. * @param s1 Pointer to the first occurrence. * @param s2 Pointer to the second occurrence. * @param m Pointer to where the answer should be. */ void AddArgs(PHEAD WORD *s1, WORD *s2, WORD *m) { GETBIDENTITY WORD i1, i2; WORD *w = m, *mm, *t, *t1, *t2, *tstop1, *tstop2; WORD tempterm[8+FUNHEAD]; *m++ = AR.PolyFun; *m++ = 0; FILLFUN(m) *m++ = 0; *m++ = 0; FILLARG(m) if ( s1[FUNHEAD] < 0 || s2[FUNHEAD] < 0 ) { if ( s1[FUNHEAD] < 0 ) { if ( s2[FUNHEAD] < 0 ) { /* Both are special */ if ( s1[FUNHEAD] <= -FUNCTION ) { if ( s2[FUNHEAD] == s1[FUNHEAD] ) { *m++ = 4+FUNHEAD; *m++ = -s1[FUNHEAD]; *m++ = FUNHEAD; FILLFUN(m) *m++ = 2; *m++ = 1; *m++ = 3; INSLENGTH(4+FUNHEAD) } else if ( s2[FUNHEAD] <= -FUNCTION ) { i1 = functions[-FUNCTION-s1[FUNHEAD]].commute != 0; i2 = functions[-FUNCTION-s2[FUNHEAD]].commute != 0; if ( ( !i1 && i2 ) || ( i1 == i2 && i1 > i2 ) ) { i1 = s2[FUNHEAD]; s2[FUNHEAD] = s1[FUNHEAD]; s1[FUNHEAD] = i1; } *m++ = 4+FUNHEAD; *m++ = -s1[FUNHEAD]; *m++ = FUNHEAD; FILLFUN(m) *m++ = 1; *m++ = 1; *m++ = 3; *m++ = 4+FUNHEAD; *m++ = -s2[FUNHEAD]; *m++ = FUNHEAD; FILLFUN(m) *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(8+2*FUNHEAD) } else if ( s2[FUNHEAD] == -SYMBOL ) { *m++ = 8; *m++ = SYMBOL; *m++ = 4; *m++ = s2[FUNHEAD+1]; *m++ = 1; *m++ = 1; *m++ = 1; *m++ = 3; *m++ = 4+FUNHEAD; *m++ = -s1[FUNHEAD]; *m++ = FUNHEAD; FILLFUN(m) *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(12+FUNHEAD) } else { /* number */ *m++ = 4; *m++ = ABS(s2[FUNHEAD+1]); *m++ = 1; *m++ = s2[FUNHEAD+1] < 0 ? -3: 3; *m++ = 4+FUNHEAD; *m++ = -s1[FUNHEAD]; *m++ = FUNHEAD; FILLFUN(m) *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(8+FUNHEAD) } } else if ( s1[FUNHEAD] == -SYMBOL ) { if ( s2[FUNHEAD] == s1[FUNHEAD] ) { if ( s1[FUNHEAD+1] == s2[FUNHEAD+1] ) { *m++ = 8; *m++ = SYMBOL; *m++ = 4; *m++ = s1[FUNHEAD+1]; *m++ = 1; *m++ = 2; *m++ = 1; *m++ = 3; INSLENGTH(8) } else { if ( s1[FUNHEAD+1] > s2[FUNHEAD+1] ) { i1 = s2[FUNHEAD+1]; i2 = s1[FUNHEAD+1]; } else { i1 = s1[FUNHEAD+1]; i2 = s2[FUNHEAD+1]; } *m++ = 8; *m++ = SYMBOL; *m++ = 4; *m++ = i1; *m++ = 1; *m++ = 1; *m++ = 1; *m++ = 3; *m++ = 8; *m++ = SYMBOL; *m++ = 4; *m++ = i2; *m++ = 1; *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(16) } } else if ( s2[FUNHEAD] <= -FUNCTION ) { *m++ = 8; *m++ = SYMBOL; *m++ = 4; *m++ = s1[FUNHEAD+1]; *m++ = 1; *m++ = 1; *m++ = 1; *m++ = 3; *m++ = 4+FUNHEAD; *m++ = -s2[FUNHEAD]; *m++ = FUNHEAD; FILLFUN(m) *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(12+FUNHEAD) } else { *m++ = 4; *m++ = ABS(s2[FUNHEAD+1]); *m++ = 1; *m++ = s2[FUNHEAD+1] < 0 ? -3: 3; *m++ = 8; *m++ = SYMBOL; *m++ = 4; *m++ = s1[FUNHEAD+1]; *m++ = 1; *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(12) } } else { /* Must be -SNUMBER! */ if ( s2[FUNHEAD] <= -FUNCTION ) { *m++ = 4; *m++ = ABS(s1[FUNHEAD+1]); *m++ = 1; *m++ = s1[FUNHEAD+1] < 0 ? -3: 3; *m++ = 4+FUNHEAD; *m++ = -s2[FUNHEAD]; *m++ = FUNHEAD; FILLFUN(m) *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(8+FUNHEAD) } else if ( s2[FUNHEAD] == -SYMBOL ) { *m++ = 4; *m++ = ABS(s1[FUNHEAD+1]); *m++ = 1; *m++ = s1[FUNHEAD+1] < 0 ? -3: 3; *m++ = 8; *m++ = SYMBOL; *m++ = 4; *m++ = s2[FUNHEAD+1]; *m++ = 1; *m++ = 1; *m++ = 1; *m++ = 3; INSLENGTH(12) } else { /* Both are numbers. add. */ LONG x1; x1 = (LONG)s1[FUNHEAD+1] + (LONG)s2[FUNHEAD+1]; if ( x1 < 0 ) { i1 = (WORD)(-x1); i2 = -3; } else { i1 = (WORD)x1; i2 = 3; } if ( x1 && AN.ncmod != 0 ) { m[0] = 4; m[1] = i1; m[2] = 1; m[3] = i2; if ( Modulus(m) ) Terminate(-1); if ( *m == 0 ) w[1] = 0; else { if ( *m == 4 && ( m[1] & MAXPOSITIVE ) == m[1] && m[3] == 3 ) { i1 = m[1]; m -= ARGHEAD; *m++ = -SNUMBER; *m++ = i1; INSLENGTH(4) } else { INSLENGTH(*m) m += *m; } } } else { if ( x1 == 0 ) { w[1] = FUNHEAD; } else if ( ( i1 & MAXPOSITIVE ) == i1 ) { m -= ARGHEAD; *m++ = -SNUMBER; *m++ = (WORD)x1; w[1] = FUNHEAD+2; } else { *m++ = 4; *m++ = i1; *m++ = 1; *m++ = i2; INSLENGTH(4) } } } } } else { /* Only s1 is special */ s1only: /* Compose a term in `tempterm' */ t = tempterm; if ( s1[FUNHEAD] <= -FUNCTION ) { *t++ = 4+FUNHEAD; *t++ = -s1[FUNHEAD]; *t++ = FUNHEAD; FILLFUN(t) *t++ = 1; *t++ = 1; *t++ = 3; } else if ( s1[FUNHEAD] == -SYMBOL ) { *t++ = 8; *t++ = SYMBOL; *t++ = 4; *t++ = s1[FUNHEAD+1]; *t++ = 1; *t++ = 1; *t++ = 1; *t++ = 3; } else { *t++ = 4; *t++ = ABS(s1[FUNHEAD+1]); *t++ = 1; *t++ = s1[FUNHEAD+1] < 0 ? -3: 3; } tstop1 = t; s1 = tempterm; goto twogen; } } else { /* Only s2 is special */ t = s1; s1 = s2; s2 = t; goto s1only; } } else { int oldPolyFlag; tstop1 = s1 + s1[1]; s1 += FUNHEAD+ARGHEAD; twogen: tstop2 = s2 + s2[1]; s2 += FUNHEAD+ARGHEAD; /* Now we should merge the expressions in s1 and s2 into m. */ oldPolyFlag = AT.SS->PolyFlag; AT.SS->PolyFlag = 0; while ( s1 < tstop1 && s2 < tstop2 ) { i1 = CompareTerms(BHEAD s1,s2,(WORD)(-1)); if ( i1 > 0 ) { i2 = *s1; NCOPY(m,s1,i2); } else if ( i1 < 0 ) { i2 = *s2; NCOPY(m,s2,i2); } else { /* Coefficients should be added. */ WORD i; t = s1+*s1; i1 = t[-1]; i2 = *s1 - ABS(i1); t2 = s2 + i2; s2 += *s2; mm = m; NCOPY(m,s1,i2); t1 = s1; s1 = t; i2 = s2[-1]; /* t1,i1 is the first coefficient t2,i2 is the second coefficient It should be placed at m,i1 */ i1 = REDLENG(i1); i2 = REDLENG(i2); if ( AddRat(BHEAD (UWORD *)t1,i1,(UWORD *)t2,i2,(UWORD *)m,&i) ) { MLOCK(ErrorMessageLock); MesPrint("Addition of coefficients of PolyFun"); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( i == 0 ) { m = mm; } else { i1 = INCLENG(i); m += ABS(i1); m[-1] = i1; *mm = WORDDIF(m,mm); if ( AN.ncmod != 0 ) { if ( Modulus(mm) ) Terminate(-1); if ( !*mm ) m = mm; else m = mm + *mm; } } } } while ( s1 < tstop1 ) *m++ = *s1++; while ( s2 < tstop2 ) *m++ = *s2++; w[1] = WORDDIF(m,w); w[FUNHEAD] = w[1] - FUNHEAD; if ( ToFast(w+FUNHEAD,w+FUNHEAD) ) { if ( w[FUNHEAD] <= -FUNCTION ) w[1] = FUNHEAD+1; else w[1] = FUNHEAD+2; if ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 ) w[1] = FUNHEAD; } /* AT.SS->PolyFlag = AR.PolyFunType;*/ AT.SS->PolyFlag = oldPolyFlag; } } /* #] AddArgs : #[ Compare1 : WORD Compare1(term1,term2,level) */ /** * Compares two terms. The answer is: * 0 equal ( with exception of the coefficient if level == 0. ) * >0 term1 comes first. * <0 term2 comes first. * Some special precautions may be needed to keep the CompCoef routine * from generating overflows, although this is very unlikely in subterms. * This routine should not return an error condition. * * Originally this routine was called Compare. * With the treatment of special polynomials with terms that contain only * symbols and the need for extreme speed for the polynomial routines we * made a special compare routine and now we store the address of the * current compare routine in AR.CompareRoutine and have a macro Compare * which makes all existing code work properly and we can just replace the * routine on a thread by thread basis (each thread has its own AR struct). * * @param term1 First input term * @param term2 Second input term * @param level The sorting level (may influence on the result) * @return 0 equal ( with exception of the coefficient if level == 0. ) * >0 term1 comes first. * <0 term2 comes first. * * When there are floating point numbers active (float_ = FLOATFUN) * the presence of one or more float_ functions is returned in * AT.SortFloatMode: * 0: no float_ * 1: float_ in term1 only * 2: float_ in term2 only * 3: float_ in both terms */ WORD Compare1(PHEAD WORD *term1, WORD *term2, WORD level) { SORTING *S = AT.SS; WORD *stopper1, *stopper2, *t2; WORD *s1, *s2, *t1; WORD *stopex1, *stopex2; WORD c1, c2; WORD prevorder; WORD count = -1, localPoly, polyhit = -1; // Update SortVerbose counter S->verbComparisons++; if ( S->PolyFlag ) { /* if ( S->PolyWise != 0 ) { MLOCK(ErrorMessageLock); MesPrint("S->PolyWise is not zero!!!!!"); MUNLOCK(ErrorMessageLock); } */ count = 0; localPoly = 1; S->PolyWise = polyhit = 0; S->PolyFlag = AR.PolyFunType; if ( AR.PolyFunType == 2 && ( AR.PolyFunExp == 2 || AR.PolyFunExp == 3 ) ) S->PolyFlag = 1; } else { localPoly = 0; } #ifdef WITHFLOAT AT.SortFloatMode = 0; #endif prevorder = 0; GETSTOP(term1,s1); stopper1 = s1; GETSTOP(term2,stopper2); t1 = term1 + 1; t2 = term2 + 1; while ( t1 < stopper1 && t2 < stopper2 ) { if ( *t1 != *t2 ) { if ( *t1 == HAAKJE ) return(PREV(-1)); if ( *t2 == HAAKJE ) return(PREV(1)); if ( *t1 >= (FUNCTION-1) ) { if ( *t2 < (FUNCTION-1) ) return(PREV(-1)); if ( *t1 < FUNCTION && *t2 < FUNCTION ) return(PREV(*t2-*t1)); if ( *t1 < FUNCTION ) return(PREV(1)); if ( *t2 < FUNCTION ) return(PREV(-1)); c1 = functions[*t1-FUNCTION].commute; c2 = functions[*t2-FUNCTION].commute; if ( !c1 ) { if ( c2 ) return(PREV(1)); else return(PREV(*t2-*t1)); } else { if ( !c2 ) return(PREV(-1)); else return(PREV(*t2-*t1)); } } else return(PREV(*t2-*t1)); } s1 = t1 + 2; s2 = t2 + 2; c1 = *t1; t1 += t1[1]; t2 += t2[1]; if ( localPoly && c1 < FUNCTION ) { polyhit = 1; } if ( c1 <= (FUNCTION-1) || ( c1 >= FUNCTION && functions[c1-FUNCTION].spec > 0 ) ) { if ( c1 == SYMBOL ) { if ( *s1 == FACTORSYMBOL && *s2 == FACTORSYMBOL && s1[-1] == 4 && s2[-1] == 4 && ( ( t1 < stopper1 && *t1 == HAAKJE ) || ( t1 == stopper1 && AT.fromindex ) ) ) { /* We have to be very careful with the criteria here, because Compare1 is called both in the regular sorting and by the routine that makes the bracket index. In the last case there is no HAAKJE subterm. */ if ( s1[1] != s2[1] ) return(s2[1]-s1[1]); s1 += 2; s2 += 2; } else if ( AR.SortType >= SORTPOWERFIRST ) { WORD i1 = 0, *r1; r1 = s1; while ( s1 < t1 ) { i1 += s1[1]; s1 += 2; } s1 = r1; r1 = s2; while ( s2 < t2 ) { i1 -= s2[1]; s2 += 2; } s2 = r1; if ( i1 ) { if ( AR.SortType >= SORTANTIPOWER ) i1 = -i1; return(PREV(i1)); } } while ( s1 < t1 ) { if ( s2 >= t2 ) { /* return(PREV(1)); */ if ( AR.SortType==SORTLOWFIRST ) { return(PREV((s1[1]>0?-1:1))); } else { return(PREV((s1[1]<0?-1:1))); } } if ( *s1 != *s2 ) { /* return(PREV(*s2-*s1)); */ if ( AR.SortType==SORTLOWFIRST ) { if ( *s1 < *s2 ) { return(PREV((s1[1]<0?1:-1))); } else { return(PREV((s2[1]<0?-1:1))); } } else { if ( *s1 < *s2 ) { return(PREV((s1[1]<0?-1:1))); } else { return(PREV((s2[1]<0?1:-1))); } } } s1++; s2++; if ( *s1 != *s2 ) return( PREV((AR.SortType==SORTLOWFIRST?*s2-*s1:*s1-*s2))); s1++; s2++; } if ( s2 < t2 ) { /* return(PREV(-1)); */ if ( AR.SortType==SORTLOWFIRST ) { return(PREV((s2[1]<0?-1:1))); } else { return(PREV((s2[1]<0?1:-1))); } } } else if ( c1 == DOTPRODUCT ) { if ( AR.SortType >= SORTPOWERFIRST ) { WORD i1 = 0, *r1; r1 = s1; while ( s1 < t1 ) { i1 += s1[2]; s1 += 3; } s1 = r1; r1 = s2; while ( s2 < t2 ) { i1 -= s2[2]; s2 += 3; } s2 = r1; if ( i1 ) { if ( AR.SortType >= SORTANTIPOWER ) i1 = -i1; return(PREV(i1)); } } while ( s1 < t1 ) { if ( s2 >= t2 ) return(PREV(1)); if ( *s1 != *s2 ) return(PREV(*s2-*s1)); s1++; s2++; if ( *s1 != *s2 ) return(PREV(*s2-*s1)); s1++; s2++; if ( *s1 != *s2 ) return( PREV((AR.SortType==SORTLOWFIRST?*s2-*s1:*s1-*s2))); s1++; s2++; } if ( s2 < t2 ) return(PREV(-1)); } else { while ( s1 < t1 ) { if ( s2 >= t2 ) return(PREV(1)); if ( *s1 != *s2 ) return(PREV(*s2-*s1)); s1++; s2++; } if ( s2 < t2 ) return(PREV(-1)); } } else { #if FUNHEAD != 2 s1 += FUNHEAD-2; s2 += FUNHEAD-2; #endif if ( localPoly && c1 == AR.PolyFun ) { if ( count == 0 ) { if ( S->PolyFlag == 1 ) { WORD i1, i2; if ( *s1 > 0 ) i1 = *s1; else if ( *s1 <= -FUNCTION ) i1 = 1; else i1 = 2; if ( *s2 > 0 ) i2 = *s2; else if ( *s2 <= -FUNCTION ) i2 = 1; else i2 = 2; if ( s1+i1 == t1 && s2+i2 == t2 ) { /* This is the stuff */ /* Test for scalar nature */ if ( !polyhit ) { WORD *u1, *u2, *ustop; if ( *s1 < 0 ) { if ( *s1 != -SNUMBER && *s1 != -SYMBOL && *s1 > -FUNCTION ) goto NoPoly; } else { u1 = s1 + ARGHEAD; while ( u1 < t1 ) { u2 = u1 + *u1; ustop = u2 - ABS(u2[-1]); u1++; while ( u1 < ustop ) { if ( *u1 == INDEX ) goto NoPoly; u1 += u1[1]; } u1 = u2; } } if ( *s2 < 0 ) { if ( *s2 != -SNUMBER && *s2 != -SYMBOL && *s2 > -FUNCTION ) goto NoPoly; } else { u1 = s2 + ARGHEAD; while ( u1 < t2 ) { u2 = u1 + *u1; ustop = u2 - ABS(u2[-1]); u1++; while ( u1 < ustop ) { if ( *u1 == INDEX ) goto NoPoly; u1 += u1[1]; } u1 = u2; } } } S->PolyWise = WORDDIF(s1,term1); S->PolyWise -= FUNHEAD; count = 1; continue; } else { NoPoly: S->PolyWise = localPoly = 0; } } else if ( AR.PolyFunType == 2 ) { WORD i1, i2, i1a, i2a; if ( *s1 > 0 ) i1 = *s1; else if ( *s1 <= -FUNCTION ) i1 = 1; else i1 = 2; if ( *s2 > 0 ) i2 = *s2; else if ( *s2 <= -FUNCTION ) i2 = 1; else i2 = 2; if ( s1[i1] > 0 ) i1a = s1[i1]; else if ( s1[i1] <= -FUNCTION ) i1a = 1; else i1a = 2; if ( s2[i2] > 0 ) i2a = s2[i2]; else if ( s2[i2] <= -FUNCTION ) i2a = 1; else i2a = 2; if ( s1+i1+i1a == t1 && s2+i2+i2a == t2 ) { /* This is the stuff */ /* Test for scalar nature */ if ( !polyhit ) { WORD *u1, *u2, *ustop; if ( *s1 < 0 ) { if ( *s1 != -SNUMBER && *s1 != -SYMBOL && *s1 > -FUNCTION ) goto NoPoly; } else { u1 = s1 + ARGHEAD; while ( u1 < s1+i1 ) { u2 = u1 + *u1; ustop = u2 - ABS(u2[-1]); u1++; while ( u1 < ustop ) { if ( *u1 == INDEX ) goto NoPoly; u1 += u1[1]; } u1 = u2; } } if ( s1[i1] < 0 ) { if ( s1[i1] != -SNUMBER && s1[i1] != -SYMBOL && s1[i1] > -FUNCTION ) goto NoPoly; } else { u1 = s1 +i1 + ARGHEAD; while ( u1 < t1 ) { u2 = u1 + *u1; ustop = u2 - ABS(u2[-1]); u1++; while ( u1 < ustop ) { if ( *u1 == INDEX ) goto NoPoly; u1 += u1[1]; } u1 = u2; } } if ( *s2 < 0 ) { if ( *s2 != -SNUMBER && *s2 != -SYMBOL && *s2 > -FUNCTION ) goto NoPoly; } else { u1 = s2 + ARGHEAD; while ( u1 < s2+i2 ) { u2 = u1 + *u1; ustop = u2 - ABS(u2[-1]); u1++; while ( u1 < ustop ) { if ( *u1 == INDEX ) goto NoPoly; u1 += u1[1]; } u1 = u2; } } if ( s2[i2] < 0 ) { if ( s2[i2] != -SNUMBER && s2[i2] != -SYMBOL && s2[i2] > -FUNCTION ) goto NoPoly; } else { u1 = s2 + i2 + ARGHEAD; while ( u1 < t2 ) { u2 = u1 + *u1; ustop = u2 - ABS(u2[-1]); u1++; while ( u1 < ustop ) { if ( *u1 == INDEX ) goto NoPoly; u1 += u1[1]; } u1 = u2; } } } S->PolyWise = WORDDIF(s1,term1); S->PolyWise -= FUNHEAD; count = 1; continue; } else { S->PolyWise = localPoly = 0; } } else { S->PolyWise = localPoly = 0; } } else { t1 = term1 + S->PolyWise; t2 = term2 + S->PolyWise; S->PolyWise = 0; localPoly = 0; continue; } } #ifdef WITHFLOAT if ( level == 0 && c1 == FLOATFUN && t1 == stopper1 && t2 == stopper2 && AT.aux_ != 0 ) { /* We have two FLOATFUN's. Test whether they are 'legal' */ if ( TestFloat(s1-FUNHEAD) ) { if ( TestFloat(s2-FUNHEAD) ) { AT.SortFloatMode = 3; return(0); } else { return(1); } } else if ( TestFloat(s2-FUNHEAD) ) { return(-1); } } #endif while ( s1 < t1 ) { /* The next statement was added 9-nov-2001. It repaired a bad error */ if ( s2 >= t2 ) return(PREV(-1)); /* There is a little problem here with fast arguments We don't want to sacrifice speed, but we like to keep a rational ordering. This last one suffers in the solution that has been chosen here. */ if ( AC.properorderflag ) { WORD oldpolyflag; oldpolyflag = S->PolyFlag; S->PolyFlag = 0; if ( ( c2 = -CompArg(s1,s2) ) != 0 ) { S->PolyFlag = oldpolyflag; return(PREV(c2)); } S->PolyFlag = oldpolyflag; NEXTARG(s1) NEXTARG(s2) } else { if ( *s1 > 0 ) { if ( *s2 > 0 ) { WORD oldpolyflag; stopex1 = s1 + *s1; if ( s2 >= t2 ) return(PREV(-1)); stopex2 = s2 + *s2; s1 += ARGHEAD; s2 += ARGHEAD; oldpolyflag = S->PolyFlag; S->PolyFlag = 0; while ( s1 < stopex1 ) { if ( s2 >= stopex2 ) { S->PolyFlag = oldpolyflag; return(PREV(-1)); } if ( ( c2 = CompareTerms(BHEAD s1,s2,(WORD)1) ) != 0 ) { S->PolyFlag = oldpolyflag; return(PREV(c2)); } s1 += *s1; s2 += *s2; } S->PolyFlag = oldpolyflag; if ( s2 < stopex2 ) return(PREV(1)); } else return(PREV(1)); } else { if ( *s2 > 0 ) return(PREV(-1)); if ( *s1 != *s2 ) { return(PREV(*s1-*s2)); } if ( *s1 > -FUNCTION ) { if ( *++s1 != *++s2 ) { return(PREV(*s2-*s1)); } } s1++; s2++; } } } if ( s2 < t2 ) return(PREV(1)); } } #ifdef WITHFLOAT if ( level == 0 && t1 < stopper1 && *t1 == FLOATFUN && t1+t1[1] == stopper1 && TestFloat(t1) && AT.aux_ != 0 ) { AT.SortFloatMode = 1; return(0); } else if ( level == 0 && t2 < stopper2 && *t2 == FLOATFUN && t2+t2[1] == stopper2 && TestFloat(t2) && AT.aux_ != 0 ) { AT.SortFloatMode = 2; return(0); } #endif { if ( AR.SortType != SORTLOWFIRST ) { if ( t1 < stopper1 ) return(PREV(1)); if ( t2 < stopper2 ) return(PREV(-1)); } else { if ( t1 < stopper1 ) return(PREV(-1)); if ( t2 < stopper2 ) return(PREV(1)); } } if ( level == 3 ) return(CompCoef(term1,term2)); if ( level >= 1 ) return(CompCoef(term2,term1)); return(0); } /* #] Compare1 : #[ CompareSymbols : WORD CompareSymbols(term1,term2,par) */ /** * Compares the terms, based on the value of AN.polysortflag. * If term1 < term2 the return value is -1 * If term1 > term2 the return value is 1 * If term1 = term2 the return value is 0 * The coefficients may differ. * The terms contain only a single subterm of type SYMBOL. * If AN.polysortflag = 0 it is a 'regular' compare. * If AN.polysortflag = 1 the sum of the powers is more important * par is a dummy parameter to make the parameter field identical * to that of Compare1 which is the regular compare routine in sort.c */ WORD CompareSymbols(PHEAD WORD *term1, WORD *term2, WORD par) { WORD *t1, *t2, *tt1, *tt2; DUMMYUSE(par); const int low = AR.SortType == SORTLOWFIRST ? 1 : -1; const int high = - low; t1 = term1 + 3; tt1 = term1+*term1; tt1 -= ABS(tt1[-1]); t2 = term2 + 3; tt2 = term2+*term2; tt2 -= ABS(tt2[-1]); // Currently, FORM never sets polysortflag != 0, so disable this code. // if ( AN.polysortflag > 0 ) { // WORD sum1, sum2; // sum1 = 0; sum2 = 0; // while ( t1 < tt1 ) { sum1 += t1[1]; t1 += 2; } // while ( t2 < tt2 ) { sum2 += t2[1]; t2 += 2; } // if ( sum1 < sum2 ) return(low); // if ( sum1 > sum2 ) return(high); // t1 = term1+3; t2 = term2 + 3; // } while ( t1 < tt1 && t2 < tt2 ) { const WORD s1 = *t1; const WORD s2 = *t2; if ( s1 != s2 ) { return ( s1 > s2 ) ? low : high ; } const WORD p1 = t1[1]; const WORD p2 = t2[1]; if ( p1 != p2 ) { return ( p1 < p2 ) ? low : high ; } t1 += 2; t2 += 2; } if ( t1 < tt1 ) return(high); if ( t2 < tt2 ) return(low); return(0); } /* #] CompareSymbols : #[ CompareHSymbols : WORD CompareHSymbols(term1,term2,par) */ /** * Compares terms that can have only SYMBOL and HAAKJE subterms. * If term1 < term2 the return value is -1 * If term1 > term2 the return value is 1 * If term1 = term2 the return value is 0 * par is a dummy parameter to make the parameter field identical * to that of Compare1 which is the regular compare routine in sort.c */ WORD CompareHSymbols(PHEAD WORD *term1, WORD *term2, WORD par) { WORD *t1, *t2, *tt1, *tt2, *ttt1, *ttt2; DUMMYUSE(par); DUMMYUSE(AT.WorkPointer); t1 = term1 + 1; tt1 = term1+*term1; tt1 -= ABS(tt1[-1]); t1 += 2; t2 = term2 + 1; tt2 = term2+*term2; tt2 -= ABS(tt2[-1]); t2 += 2; while ( t1 < tt1 && t2 < tt2 ) { if ( *t1 != *t2 ) { if ( t1[0] < t2[0] ) return(-1); return(1); } else if ( *t1 == HAAKJE ) { t1 += 3; t2 += 3; continue; } ttt1 = t1+t1[1]; ttt2 = t2+t2[1]; while ( t1 < ttt1 && t2 < ttt2 ) { if ( *t1 > *t2 ) return(-1); if ( *t1 < *t2 ) return(1); if ( t1[1] < t2[1] ) return(-1); if ( t1[1] > t2[1] ) return(1); t1 += 2; t2 += 2; } if ( t1 < ttt1 ) return(1); if ( t2 < ttt2 ) return(-1); } if ( t1 < tt1 ) return(1); if ( t2 < tt2 ) return(-1); return(0); } /* #] CompareHSymbols : #[ ComPress : LONG ComPress(ss,n) */ /** * Gets a list of pointers to terms and compresses the terms. * In n it collects the number of terms and the return value * of the function is the space that is occupied. * * We have to pay some special attention to the compression of * terms with a PolyFun. This PolyFun should occur only straight * before the coefficient, so we can use the same trick as for * the coefficient to sabotage compression of this object * (Replace in the history the function pointer by zero. This * is safe, because terms that would be identical otherwise would * have been added). * * @param ss Array of pointers to terms to be compressed. * @param n Number of pointers in ss. * @return Total number of words needed for the compressed result. */ LONG ComPress(WORD **ss, LONG *n) { GETIDENTITY WORD *t, *s, j, k; LONG size = 0; int newsize, i; /* #[ debug : WORD **sss = ss; if ( AP.DebugFlag ) { UBYTE OutBuf[140]; MLOCK(ErrorMessageLock); MesPrint("ComPress:"); AO.OutFill = AO.OutputLine = OutBuf; AO.OutSkip = 3; FiniLine(); ss = sss; while ( *ss ) { s = *ss++; j = *s; if ( j < 0 ) { j = s[1] + 2; } while ( --j >= 0 ) { TalToLine((UWORD)(*s++)); TokenToLine((UBYTE *)" "); } FiniLine(); } AO.OutSkip = 0; FiniLine(); MUNLOCK(ErrorMessageLock); ss = sss; } #] debug : */ *n = 0; if ( AT.SS == AT.S0 && !AR.NoCompress ) { if ( AN.compressSize == 0 ) { if ( *ss ) { AN.compressSize = **ss + 64; } else { AN.compressSize = AM.MaxTer/sizeof(WORD) + 2; } AN.compressSpace = (WORD *)Malloc1(AN.compressSize*sizeof(WORD),"Compression"); } AN.compressSpace[0] = 0; while ( *ss ) { k = 0; s = *ss; j = *s++; if ( j > AN.compressSize ) { newsize = j + 64; t = (WORD *)Malloc1(newsize*sizeof(WORD),"Compression"); t[0] = 0; if ( AN.compressSpace ) { for ( i = 0; i < *AN.compressSpace; i++ ) t[i] = AN.compressSpace[i]; M_free(AN.compressSpace,"Compression"); } AN.compressSpace = t; AN.compressSize = newsize; } t = AN.compressSpace; i = *t - 1; *t++ = j; j--; if ( AR.PolyFun ) { WORD *polystop, *sa; sa = s + j; sa -= ABS(sa[-1]); polystop = s; while ( polystop < sa && *polystop != AR.PolyFun ) { polystop += polystop[1]; } while ( i > 0 && j > 0 && *s == *t && s < polystop ) { i--; j--; s++; t++; k--; } } else { WORD *sa; sa = s + j; sa -= ABS(sa[-1]); while ( i > 0 && j > 0 && *s == *t && s < sa ) { i--; j--; s++; t++; k--; } } if ( k < -1 ) { s[-1] = j; s[-2] = k; *ss = s-2; size += j + 2; } else { size += *AN.compressSpace; if ( k == -1 ) { t--; s--; j++; } } while ( --j >= 0 ) *t++ = *s++; /* Sabotage getting into the coefficient next time */ t = AN.compressSpace + *AN.compressSpace; t[-(ABS(t[-1]))] = 0; ss++; (*n)++; } } else { while ( *ss ) { size += *(*ss++); (*n)++; } } /* #[ debug : if ( AP.DebugFlag ) { UBYTE OutBuf[140]; AO.OutFill = AO.OutputLine = OutBuf; AO.OutSkip = 3; FiniLine(); ss = sss; while ( *ss ) { s = *ss++; j = *s; if ( j < 0 ) { j = s[1] + 2; } while ( --j >= 0 ) { TalToLine((UWORD)(*s++)); TokenToLine((UBYTE *)" "); } FiniLine(); } AO.OutSkip = 0; FiniLine(); } #] debug : */ return(size); } /* #] ComPress : #[ SplitMerge : void SplitMerge(Point,number) */ /** * Algorithm by J.A.M.Vermaseren (31-7-1988) * * Note that AN.SplitScratch and AN.InScratch are used also in GarbHand * * Merge sort in memory. The input is an array of pointers. * Sorting is done recursively by dividing the array in two equal parts * and calling SplitMerge for each. * When the parts are small enough we can do the compare and take the * appropriate action. * An addition is that we look for 'runs'. Sequences that are already * ordered. This happens a lot when there is very little action in a * module. This made FORM faster by a few percent. * * @param Pointer The array of pointers to the terms to be sorted. * @param number The number of pointers in Pointer. * * The terms are supposed to be sitting in the small buffer and there * is supposed to be an extension to this buffer for when there are * two terms that should be added and the result takes more space than * each of the original terms. The notation guarantees that the result * never needs more space than the sum of the spaces of the original * terms. */ #ifdef NEWSPLITMERGE LONG SplitMerge(PHEAD WORD **Pointer, LONG number) { GETBIDENTITY SORTING *S = AT.SS; WORD **pp3, **pp1, **pp2, **pptop; LONG i, newleft, newright, split; #ifdef SPLITMERGEDEBUG /* Print current array state on entry. */ printf("%4ld: ", number); for (int ii = 0; ii < S->sTerms; ii++) { if ( (S->sPointer)[ii] ) { printf("%4d ", (unsigned)(S->sPointer[ii]-S->sBuffer)); } else { printf(".... "); } } printf("\n"); fflush(stdout); #endif if ( number < 2 ) return(number); if ( number == 2 ) { pp1 = Pointer; pp2 = pp1 + 1; if ( ( i = CompareTerms(BHEAD *pp1,*pp2,(WORD)0) ) < 0 ) { pp3 = (WORD **)(*pp1); *pp1 = *pp2; *pp2 = (WORD *)pp3; } else if ( i == 0 ) { number--; if ( S->PolyWise ) { if ( AddPoly(BHEAD pp1,pp2) == 0 ) number = 0; } else { if ( AddCoef(BHEAD pp1,pp2) == 0 ) number = 0; } } return(number); } pptop = Pointer + number; split = number/2; newleft = SplitMerge(BHEAD Pointer,split); newright = SplitMerge(BHEAD Pointer+split,number-split); if ( newright == 0 ) return(newleft); /* We compare the last of the left with the first of the right If they are already in order, we will be done quickly. We may have to compactify the buffer because the recursion may have created holes. Also this compare may result in equal terms. Addition of 23-jul-1999. It makes things a bit faster. */ if ( newleft > 0 && newright > 0 && ( i = CompareTerms(BHEAD Pointer[newleft-1],Pointer[split],(WORD)0) ) >= 0 ) { pp2 = Pointer+split; pp1 = Pointer+newleft-1; if ( i == 0 ) { if ( S->PolyWise ) { if ( AddPoly(BHEAD pp1,pp2) > 0 ) pp1++; else newleft--; } else { if ( AddCoef(BHEAD pp1,pp2) > 0 ) pp1++; else newleft--; } *pp2++ = 0; newright--; } else pp1++; newleft += newright; if ( pp1 < pp2 ) { while ( --newright >= 0 ) *pp1++ = *pp2++; while ( pp1 < pptop ) *pp1++ = 0; } return(newleft); } if ( split >= AN.SplitScratchSize ) { AN.SplitScratchSize = (split*3)/2+100; if ( AN.SplitScratchSize > S->Terms2InSmall/2 ) AN.SplitScratchSize = S->Terms2InSmall/2; if ( AN.SplitScratch ) M_free(AN.SplitScratch,"AN.SplitScratch"); AN.SplitScratch = (WORD **)Malloc1(AN.SplitScratchSize*sizeof(WORD *),"AN.SplitScratch"); } pp3 = AN.SplitScratch; pp1 = Pointer; /* Move rather than copy, so GarbHand can't double-count. */ for ( i = 0; i < newleft; i++ ) { *pp3++ = *pp1; *pp1++ = 0; } AN.InScratch = newleft; pp1 = AN.SplitScratch; pp2 = Pointer + split; pp3 = Pointer; #ifdef NEWSPLITMERGETIMSORT /* An improvement in the style of Timsort */ while ( newleft > 8 ) { /* Check the middle of the LHS terms */ LONG nnleft = newleft/2; if ( ( i = CompareTerms(BHEAD pp1[nnleft],*pp2,(WORD)0) ) < 0 ) { /* The terms are not in order. Break out and continue as normal. */ break; } /* The terms merge or are in order. Copy pointers up to this point. */ /* In the copy, zero the skipped pointers so GarbHand can't double-count. */ for (int iii = 0; iii < nnleft; iii++) { *pp3++ = *pp1; *pp1++ = 0; } newleft -= nnleft; if ( i == 0 ) { if ( S->PolyWise ) { i = AddPoly(BHEAD pp1,pp2); } else { i = AddCoef(BHEAD pp1,pp2); } if ( i == 0 ) { /* The terms cancelled. The next term goes in *pp3. Don't move. */ } else { /* The terms added. Advance pp3. */ *pp3++ = *pp1; } /* We have taken a LHS (copy) and RHS term. */ *pp2++ = 0; newright--; *pp1++ = 0; newleft--; break; } } #endif while ( newleft > 0 && newright > 0 ) { if ( ( i = CompareTerms(BHEAD *pp1,*pp2,(WORD)0) ) < 0 ) { *pp3++ = *pp2; *pp2++ = 0; newright--; } else if ( i > 0 ) { *pp3++ = *pp1; *pp1++ = 0; newleft--; } else { if ( S->PolyWise ) { if ( AddPoly(BHEAD pp1,pp2) > 0 ) *pp3++ = *pp1; } else { if ( AddCoef(BHEAD pp1,pp2) > 0 ) *pp3++ = *pp1; } *pp1++ = 0; *pp2++ = 0; newleft--; newright--; } } for ( i = 0; i < newleft; i++ ) { *pp3++ = *pp1; *pp1++ = 0; } if ( pp3 == pp2 ) { pp3 += newright; } else { for ( i = 0; i < newright; i++ ) { *pp3++ = *pp2++; } } newleft = pp3 - Pointer; while ( pp3 < pptop ) *pp3++ = 0; AN.InScratch = 0; return(newleft); } #else LONG SplitMerge(PHEAD WORD **Pointer, LONG number) { GETBIDENTITY SORTING *S = AT.SS; WORD **pp3, **pp1, **pp2; LONG nleft, nright, i, newleft, newright; WORD **pptop; #ifdef SPLITMERGEDEBUG /* Print current array state on entry. */ printf("%4ld: ", number); for (int ii = 0; ii < S->sTerms; ii++) { if ( (S->sPointer)[ii] ) { printf("%4d ", (unsigned)(S->sPointer[ii]-S->sBuffer)); } else { printf(".... "); } } printf("\n"); fflush(stdout); #endif if ( number < 2 ) return(number); if ( number == 2 ) { pp1 = Pointer; pp2 = pp1 + 1; if ( ( i = CompareTerms(BHEAD *pp1,*pp2,(WORD)0) ) < 0 ) { pp3 = (WORD **)(*pp1); *pp1 = *pp2; *pp2 = (WORD *)pp3; } else if ( i == 0 ) { number--; if ( S->PolyWise ) { if ( AddPoly(BHEAD pp1,pp2) == 0 ) { number = 0; } } else { if ( AddCoef(BHEAD pp1,pp2) == 0 ) { number = 0; } } } return(number); } pptop = Pointer + number; nleft = number >> 1; nright = number - nleft; newleft = SplitMerge(BHEAD Pointer,nleft); newright = SplitMerge(BHEAD Pointer+nleft,nright); /* We compare the last of the left with the first of the right If they are already in order, we will be done quickly. We may have to compactify the buffer because the recursion may have created holes. Also this compare may result in equal terms. Addition of 23-jul-1999. It makes things a bit faster. */ if ( newleft > 0 && newright > 0 && ( i = CompareTerms(BHEAD Pointer[newleft-1],Pointer[nleft],(WORD)0) ) >= 0 ) { pp2 = Pointer+nleft; pp1 = Pointer+newleft-1; if ( i == 0 ) { if ( S->PolyWise ) { if ( AddPoly(BHEAD pp1,pp2) > 0 ) pp1++; else newleft--; } else { if ( AddCoef(BHEAD pp1,pp2) > 0 ) pp1++; else newleft--; } *pp2++ = 0; newright--; } else pp1++; newleft += newright; if ( pp1 < pp2 ) { while ( --newright >= 0 ) *pp1++ = *pp2++; while ( pp1 < pptop ) *pp1++ = 0; } return(newleft); } if ( nleft > AN.SplitScratchSize ) { AN.SplitScratchSize = (nleft*3)/2+100; if ( AN.SplitScratchSize > S->Terms2InSmall/2 ) AN.SplitScratchSize = S->Terms2InSmall/2; if ( AN.SplitScratch ) M_free(AN.SplitScratch,"AN.SplitScratch"); AN.SplitScratch = (WORD **)Malloc1(AN.SplitScratchSize*sizeof(WORD *),"AN.SplitScratch"); } pp3 = AN.SplitScratch; pp1 = Pointer; i = nleft; do { *pp3++ = *pp1; *pp1++ = 0; } while ( *pp1 && --i > 0 ); if ( i > 0 ) { *pp3 = 0; i--; } AN.InScratch = nleft - i; pp1 = AN.SplitScratch; pp2 = Pointer + nleft; pp3 = Pointer; while ( nleft > 0 && nright > 0 && *pp1 && *pp2 ) { if ( ( i = CompareTerms(BHEAD *pp1,*pp2,(WORD)0) ) < 0 ) { *pp3++ = *pp2; *pp2++ = 0; nright--; } else if ( i > 0 ) { *pp3++ = *pp1; *pp1++ = 0; nleft--; } else { if ( S->PolyWise ) { if ( AddPoly(BHEAD pp1,pp2) > 0 ) *pp3++ = *pp1; } else { if ( AddCoef(BHEAD pp1,pp2) > 0 ) *pp3++ = *pp1; } *pp1++ = 0; *pp2++ = 0; nleft--; nright--; } } while ( --nleft >= 0 && *pp1 ) { *pp3++ = *pp1; *pp1++ = 0; } while ( --nright >= 0 && *pp2 ) { *pp3++ = *pp2++; } nleft = pp3 - Pointer; while ( pp3 < pptop ) *pp3++ = 0; AN.InScratch = 0; return(nleft); } #endif /* #] SplitMerge : #[ GarbHand : void GarbHand() */ /** * Garbage collection that takes place when the small extension is full * and we need to place more terms there. * When this is the case there are many holes in the small buffer and * the whole can be compactified. * The major complication is the buffer for SplitMerge. * There are to options for temporary memory: * 1: find some buffer that has enough space (maybe in the large * buffer). * 2: allocate a buffer. Give it back afterwards of course. * If the small extension is properly dimensioned this routine should * be called very rarely. Most of the time it will be called when the * polyfun or polyratfun is active. */ void GarbHand(void) { GETIDENTITY SORTING *S = AT.SS; WORD **Point, *s2, *t, *garbuf, i; LONG k, total = 0; int tobereturned = 0; /* Compute the size needed. Put it in total. */ #ifdef TESTGARB MLOCK(ErrorMessageLock); MesPrint("in: S->sFill = %l, S->sTop2 = %l",S->sFill-S->sBuffer,S->sTop2-S->sBuffer); #endif Point = S->sPointer; k = S->sTerms; while ( --k >= 0 ) { if ( ( s2 = *Point++ ) != 0 ) { total += *s2; } } Point = AN.SplitScratch; k = AN.InScratch; while ( --k >= 0 ) { if ( ( s2 = *Point++ ) != 0 ) { total += *s2; } } #ifdef TESTGARB MesPrint("total = %l, nterms = %l",total,AN.InScratch); MUNLOCK(ErrorMessageLock); #endif /* Test now whether it fits. If so deal with the problem inside the memory at the tail of the large buffer. */ if ( S->lBuffer != 0 && S->lFill + total <= S->lTop ) { garbuf = S->lFill; } else { garbuf = (WORD *)Malloc1(total*sizeof(WORD),"Garbage buffer"); tobereturned = 1; } t = garbuf; Point = S->sPointer; k = S->sTerms; while ( --k >= 0 ) { if ( *Point ) { s2 = *Point++; i = *s2; NCOPY(t,s2,i); } else { Point++; } } Point = AN.SplitScratch; k = AN.InScratch; while ( --k >= 0 ) { if ( *Point ) { s2 = *Point++; i = *s2; NCOPY(t,s2,i); } else Point++; } s2 = S->sBuffer; t = garbuf; Point = S->sPointer; k = S->sTerms; while ( --k >= 0 ) { if ( *Point ) { *Point++ = s2; i = *t; NCOPY(s2,t,i); } else { Point++; } } Point = AN.SplitScratch; k = AN.InScratch; while ( --k >= 0 ) { if ( *Point ) { *Point++ = s2; i = *t; NCOPY(s2,t,i); } else Point++; } S->sFill = s2; #ifdef TESTGARB MLOCK(ErrorMessageLock); MesPrint("out: S->sFill = %l, S->sTop2 = %l",S->sFill-S->sBuffer,S->sTop2-S->sBuffer); if ( S->sFill >= S->sTop2 ) { MesPrint("We are in deep trouble"); } MUNLOCK(ErrorMessageLock); #endif if ( tobereturned ) M_free(garbuf,"Garbage buffer"); return; } /* #] GarbHand : #[ MergePatches : WORD MergePatches(par) */ /** * The general merge routine. Can be used for the large buffer * and the file merging. The array S->Patches tells where the patches * start S->pStop tells where they end (has to be computed first). * The end of a 'line to be merged' is indicated by a zero. If * the end is reached without running into a zero or a term * runs over the boundary of a patch it is a file merging operation * and a new piece from the file is read in. * * @param par * If par == 0 the sort is for file -> outputfile. * If par == 1 the sort is for large buffer -> sortfile. * If par == 2 the sort is for large buffer -> outputfile. * */ int MergePatches(WORD par) { GETIDENTITY SORTING *S = AT.SS; WORD **poin, **poin2, ul, k, i, im, *m1; WORD *p, lpat, mpat, level, l1, l2, r1, r2, r3, c; WORD *m2, *m3, r31, r33, ki, *rr; UWORD *coef; POSITION position; FILEHANDLE *fin, *fout; int fhandle; /* UBYTE *s; */ #ifdef WITHZLIB POSITION position2; int oldgzipCompress = AR.gzipCompress; if ( par == 2 ) { AR.gzipCompress = 0; } #endif fin = &S->file; fout = &(AR.FoStage4[0]); NewMerge: coef = AN.SoScratC; poin = S->poina; poin2 = S->poin2a; rr = AR.CompressPointer; *rr = 0; /* #[ Setup : */ if ( par == 1 ) { fout = &(S->file); if ( fout->handle < 0 ) { FileMake: PUTZERO(S->OldPosOut); if ( ( fhandle = CreateFile(fout->name) ) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Cannot create file %s",fout->name); MUNLOCK(ErrorMessageLock); goto ReturnError; } #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w MergePatches created output file %s",fout->name); MUNLOCK(ErrorMessageLock); #endif fout->handle = fhandle; PUTZERO(fout->filesize); PUTZERO(fout->POposition); /* Should not be here? #ifdef WITHZLIB fout->ziobuffer = 0; #endif */ #ifdef ALLLOCK LOCK(fout->pthreadslock); #endif SeekFile(fout->handle,&(fout->filesize),SEEK_SET); #ifdef ALLLOCK UNLOCK(fout->pthreadslock); #endif S->fPatchN = 0; PUTZERO(S->fPatches[0]); fout->POfill = fout->PObuffer; PUTZERO(fout->POposition); } ConMer: StageSort(fout); #ifdef WITHZLIB if ( S == AT.S0 && AR.NoCompress == 0 && AR.gzipCompress > 0 ) S->fpcompressed[S->fPatchN] = 1; else S->fpcompressed[S->fPatchN] = 0; SetupOutputGZIP(fout); #endif } else if ( par == 0 && S->stage4 > 0 ) { /* We will have to do our job more than once. Input is from S->file and output will go to AR.FoStage4. The file corresponding to this last one must be made now. */ AR.Stage4Name ^= 1; /* s = (UBYTE *)(fout->name); while ( *s ) s++; if ( AR.Stage4Name ) s[-1] += 1; else s[-1] -= 1; */ S->iPatches = S->fPatches; S->fPatches = S->inPatches; S->inPatches = S->iPatches; (S->inNum) = S->fPatchN; S->OldPosIn = S->OldPosOut; #ifdef WITHZLIB m1 = S->fpincompressed; S->fpincompressed = S->fpcompressed; S->fpcompressed = m1; for ( i = 0; i < S->inNum; i++ ) { S->fPatchesStop[i] = S->iPatches[i+1]; #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w fPatchesStop[%d] = %10p",i,&(S->fPatchesStop[i])); MUNLOCK(ErrorMessageLock); #endif } #endif S->stage4 = 0; goto FileMake; } else { #ifdef WITHZLIB /* The next statement is just for now */ AR.gzipCompress = 0; #endif if ( par == 0 ) { S->iPatches = S->fPatches; S->inNum = S->fPatchN; #ifdef WITHZLIB m1 = S->fpincompressed; S->fpincompressed = S->fpcompressed; S->fpcompressed = m1; for ( i = 0; i < S->inNum; i++ ) { S->fPatchesStop[i] = S->fPatches[i+1]; #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w fPatchesStop[%d] = %10p",i,&(S->fPatchesStop[i])); MUNLOCK(ErrorMessageLock); #endif } #endif } fout = AR.outfile; } if ( par ) { /* Mark end of patches */ S->Patches[S->lPatch] = S->lFill; for ( i = 0; i < S->lPatch; i++ ) { S->pStop[i] = S->Patches[i+1]-1; S->Patches[i] = (WORD *)(((UBYTE *)(S->Patches[i])) + AM.MaxTer); } } else { /* Load the patches */ S->lPatch = (S->inNum); #ifdef WITHMPI if ( S->lPatch > 1 || ( (PF.exprtodo <0) && (fout == AR.outfile || fout == AR.hidefile ) ) ) { #else if ( S->lPatch > 1 ) { #endif #ifdef WITHZLIB SetupAllInputGZIP(S); #endif p = S->lBuffer; for ( i = 0; i < S->lPatch; i++ ) { p = (WORD *)(((UBYTE *)p)+2*AM.MaxTer+COMPINC*sizeof(WORD)); S->Patches[i] = p; p = (WORD *)(((UBYTE *)p) + fin->POsize); S->pStop[i] = m2 = p; #ifdef WITHZLIB PutIn(fin,&(S->iPatches[i]),S->Patches[i],&m2,i); #else ADDPOS(S->iPatches[i],PutIn(fin,&(S->iPatches[i]),S->Patches[i],&m2,i)); #endif } } } if ( fout->handle >= 0 ) { PUTZERO(position); #ifdef ALLLOCK LOCK(fout->pthreadslock); #endif SeekFile(fout->handle,&position,SEEK_END); ADDPOS(position,((fout->POfill-fout->PObuffer)*sizeof(WORD))); #ifdef ALLLOCK UNLOCK(fout->pthreadslock); #endif } else { SETBASEPOSITION(position,(fout->POfill-fout->PObuffer)*sizeof(WORD)); } /* #] Setup : The old code had to be replaced because all output needs to go through PutOut. For this we have to go term by term and keep track of the compression. */ if ( S->lPatch == 1 ) { /* Single patch --> direct copy. Very rare. */ LONG length; if ( fout->handle < 0 ) if ( Sflush(fout) ) goto PatCall; if ( par ) { /* Memory to file */ #ifdef WITHZLIB /* We fix here the problem that the thing needs to go through PutOut */ m2 = m1 = *S->Patches; /* The m2 is to keep the compiler from complaining */ while ( *m1 ) { if ( *m1 < 0 ) { /* Need to uncompress */ i = -(*m1++); m2 += i; im = *m1+i+1; while ( i > 0 ) { *m1-- = *m2--; i--; } *m1 = im; } #ifdef WITHPTHREADS /* Check here (and in the following) that we are at ground level (so S == AT.S0) to use PutToMaster. Control can reach here, with AS.MasterSort, but with S != AT.S0, when the SortBots are adding PolyRatFun and the sorting of their arguments requires large buffer patches to be merged. In this case, terms escape the PolyRatFun argument and end up at ground level, if we use PutToMaster. */ if ( AS.MasterSort && ( fout == AR.outfile ) && S == AT.S0 ) { im = PutToMaster(BHEAD m1); } else #endif if ( ( im = PutOut(BHEAD m1,&position,fout,1) ) < 0 ) goto ReturnError; ADDPOS(S->SizeInFile[par],im); m2 = m1; m1 += *m1; } #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) && S == AT.S0 ) { PutToMaster(BHEAD 0); } else #endif if ( FlushOut(&position,fout,1) ) goto ReturnError; ADDPOS(S->SizeInFile[par],1); #else /* old code */ length = (LONG)(*S->pStop)-(LONG)(*S->Patches)+sizeof(WORD); if ( WriteFile(fout->handle,(UBYTE *)(*S->Patches),length) != length ) goto PatwCall; ADDPOS(position,length); ADDPOS(fout->POposition,length); ADDPOS(fout->filesize,length); ADDPOS(S->SizeInFile[par],length/sizeof(WORD)); #endif } else { /* File to file */ #ifdef WITHZLIB /* Note: if we change FRONTSIZE we need to make the minimum value of SmallEsize in AllocSort correspondingly larger or smaller. Theoretically we could get close to 2*AM.MaxTer! */ #define FRONTSIZE (2*AM.MaxTer) WORD *copybuf = (WORD *)(((UBYTE *)(S->sBuffer)) + FRONTSIZE); WORD *copytop; SetupAllInputGZIP(S); m1 = m2 = copybuf; position2 = S->iPatches[0]; while ( ( length = FillInputGZIP(fin,&position2, (UBYTE *)copybuf, (S->SmallEsize*sizeof(WORD)-FRONTSIZE),0) ) > 0 ) { copytop = (WORD *)(((UBYTE *)copybuf)+length); while ( *m1 && ( ( *m1 > 0 && m1+*m1 < copytop ) || ( *m1 < 0 && ( m1+1 < copytop ) && ( m1+m1[1]+1 < copytop ) ) ) ) /* 22-jun-2013 JV Extremely nasty bug that has been around for a while. What if the end is in the remaining part? We will loose terms! while ( *m1 && ( (WORD *)(((UBYTE *)(m1)) + AM.MaxTer ) < S->sTop2 ) ) */ { if ( *m1 < 0 ) { /* Need to uncompress */ i = -(*m1++); m2 += i; im = *m1+i+1; while ( i > 0 ) { *m1-- = *m2--; i--; } *m1 = im; } #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) && S == AT.S0 ) { im = PutToMaster(BHEAD m1); } else #endif if ( ( im = PutOut(BHEAD m1,&position,fout,1) ) < 0 ) goto ReturnError; ADDPOS(S->SizeInFile[par],im); m2 = m1; m1 += *m1; } if ( m1 < copytop && *m1 == 0 ) break; /* Now move the remaining part 'back' */ m3 = copybuf; m1 = copytop; while ( m1 > m2 ) *--m3 = *--m1; m2 = m3; m1 = m2 + *m2; } if ( length < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Readerror"); goto PatCall2; } #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) && S == AT.S0 ) { PutToMaster(BHEAD 0); } else #endif if ( FlushOut(&position,fout,1) ) goto ReturnError; ADDPOS(S->SizeInFile[par],1); #else /* old code */ SeekFile(fin->handle,&(S->iPatches[0]),SEEK_SET); /* needed for stage4 */ while ( ( length = ReadFile(fin->handle, (UBYTE *)(S->sBuffer),S->SmallEsize*sizeof(WORD)) ) > 0 ) { if ( WriteFile(fout->handle,(UBYTE *)(S->sBuffer),length) != length ) goto PatwCall; ADDPOS(position,length); ADDPOS(fout->POposition,length); ADDPOS(fout->filesize,length); ADDPOS(S->SizeInFile[par],length/sizeof(WORD)); } if ( length < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Readerror"); goto PatCall2; } #endif } goto EndOfAll; } else if ( S->lPatch > 0 ) { /* More than one patch. Construct the tree. */ lpat = 1; do { lpat *= 2; } while ( lpat < S->lPatch ); mpat = ( lpat >> 1 ) - 1; k = lpat - S->lPatch; /* k is the number of empty places in the tree. they will be at the even positions from 2 to 2*k */ for ( i = 1; i < lpat; i++ ) { S->tree[i] = -1; } for ( i = 1; i <= k; i++ ) { im = ( i * 2 ) - 1; poin[im] = S->Patches[i-1]; poin2[im] = poin[im] + *(poin[im]); S->used[i] = im; S->ktoi[im] = i-1; S->tree[mpat+i] = 0; poin[im-1] = poin2[im-1] = 0; } for ( i = (k*2)+1; i <= lpat; i++ ) { S->used[i-k] = i; S->ktoi[i] = i-k-1; poin[i] = S->Patches[i-k-1]; poin2[i] = poin[i] + *(poin[i]); } /* the array poin tells the position of the i-th element of the S->tree 'S->used' is a stack with the S->tree elements that need to be entered into the S->tree. at the beginning this is S->lPatch. during the sort there will be only very few elements. poin2 is the next value of poin. it has to be determined before the comparisons as the position or the size of the term indicated by poin may change. S->ktoi translates a S->tree element back to its stream number. start the sort */ level = S->lPatch; /* introduce one term */ OneTerm: k = S->used[level]; i = k + lpat - 1; if ( !*(poin[k]) ) { do { if ( !( i >>= 1 ) ) goto EndOfMerge; } while ( !S->tree[i] ); if ( S->tree[i] == -1 ) { S->tree[i] = 0; level--; goto OneTerm; } k = S->tree[i]; S->used[level] = k; S->tree[i] = 0; } /* move terms down the tree */ while ( i >>= 1 ) { if ( S->tree[i] > 0 ) { if ( ( c = CompareTerms(BHEAD poin[S->tree[i]],poin[k],(WORD)0) ) > 0 ) { /* S->tree[i] is the smaller. Exchange and go on. */ S->used[level] = S->tree[i]; S->tree[i] = k; k = S->used[level]; } else if ( !c ) { /* Terms are equal */ S->TermsLeft--; /* Here the terms are equal and their coefficients have to be added. */ l1 = *( m1 = poin[S->tree[i]] ); l2 = *( m2 = poin[k] ); if ( S->PolyWise ) { /* Here we work with PolyFun */ WORD *tt1, *w; tt1 = m1; m1 += S->PolyWise; m2 += S->PolyWise; if ( S->PolyFlag == 2 ) { w = poly_ratfun_add(BHEAD m1,m2); if ( *tt1 + w[1] - m1[1] > AM.MaxTer/((LONG)sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Term too complex in PolyRatFun addition. MaxTermSize of %10l is too small",AM.MaxTer); MUNLOCK(ErrorMessageLock); Terminate(-1); } AT.WorkPointer = w; } else { w = AT.WorkPointer; if ( w + m1[1] + m2[1] > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesPrint("A WorkSpace of %10l is too small",AM.WorkSize); MUNLOCK(ErrorMessageLock); Terminate(-1); } AddArgs(BHEAD m1,m2,w); } r1 = w[1]; if ( r1 <= FUNHEAD || ( w[FUNHEAD] == -SNUMBER && w[FUNHEAD+1] == 0 ) ) { goto cancelled; } if ( r1 == m1[1] ) { NCOPY(m1,w,r1); } else if ( r1 < m1[1] ) { r2 = m1[1] - r1; m2 = w + r1; m1 += m1[1]; while ( --r1 >= 0 ) *--m1 = *--m2; m2 = m1 - r2; r1 = S->PolyWise; while ( --r1 >= 0 ) *--m1 = *--m2; *m1 -= r2; poin[S->tree[i]] = m1; } else { r2 = r1 - m1[1]; m2 = tt1 - r2; r1 = S->PolyWise; m1 = tt1; *m1 += r2; poin[S->tree[i]] = m2; NCOPY(m2,m1,r1); r1 = w[1]; NCOPY(m2,w,r1); } } #ifdef WITHFLOAT else if ( AT.SortFloatMode ) { WORD *term1, *term2; term1 = poin[S->tree[i]]; term2 = poin[k]; if ( MergeWithFloat(BHEAD &term1,&term2) == 0 ) goto cancelled; poin[S->tree[i]] = term1; } #endif else { r1 = *( m1 += l1 - 1 ); m1 -= ABS(r1) - 1; r1 = ( ( r1 > 0 ) ? (r1-1) : (r1+1) ) >> 1; r2 = *( m2 += l2 - 1 ); m2 -= ABS(r2) - 1; r2 = ( ( r2 > 0 ) ? (r2-1) : (r2+1) ) >> 1; if ( AddRat(BHEAD (UWORD *)m1,r1,(UWORD *)m2,r2,coef,&r3) ) { MLOCK(ErrorMessageLock); MesCall("MergePatches"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } if ( AN.ncmod != 0 ) { if ( ( AC.modmode & POSNEG ) != 0 ) { NormalModulus(coef,&r3); } else if ( BigLong(coef,r3,(UWORD *)AC.cmod,ABS(AN.ncmod)) >= 0 ) { WORD ii; SubPLon(coef,r3,(UWORD *)AC.cmod,ABS(AN.ncmod),coef,&r3); coef[r3] = 1; for ( ii = 1; ii < r3; ii++ ) coef[r3+ii] = 0; } } r3 *= 2; r33 = ( r3 > 0 ) ? ( r3 + 1 ) : ( r3 - 1 ); if ( r3 < 0 ) r3 = -r3; if ( r1 < 0 ) r1 = -r1; r1 *= 2; r31 = r3 - r1; if ( !r3 ) { /* Terms cancel */ cancelled: ul = S->used[level] = S->tree[i]; S->tree[i] = -1; /* We skip to the next term in stream ul */ im = *poin2[ul]; if ( im < 0 ) { r1 = poin2[ul][1] - im + 1; m1 = poin2[ul] + 2; m2 = poin[ul] - im + 1; while ( ++im <= 0 ) *--m1 = *--m2; *--m1 = r1; poin2[ul] = m1; im = r1; } poin[ul] = poin2[ul]; ki = S->ktoi[ul]; if ( !par && (poin[ul] + im + COMPINC) >= S->pStop[ki] && im > 0 ) { #ifdef WITHZLIB PutIn(fin,&(S->iPatches[ki]),S->Patches[ki],&(poin[ul]),ki); #else ADDPOS(S->iPatches[ki],PutIn(fin,&(S->iPatches[ki]), S->Patches[ki],&(poin[ul]),ki)); #endif poin2[ul] = poin[ul] + im; } else { poin2[ul] += im; } S->used[++level] = k; S->TermsLeft--; } else if ( !r31 ) { /* copy coef into term1 */ goto CopCof2; } else if ( r31 < 0 ) { /* copy coef into term1 and adjust the length of term1 */ goto CopCoef; } else { /* this is the dreaded calamity. is there enough space? */ if( (poin[S->tree[i]]+l1+r31) >= poin2[S->tree[i]] ) { /* no space! now the special trick for which we left 2*maxlng spaces open at the beginning of each patch. */ if ( (l1 + r31) > AM.MaxTer/((LONG)sizeof(WORD)) ) { MLOCK(ErrorMessageLock); MesPrint("Coefficient overflow during sort"); MUNLOCK(ErrorMessageLock); goto ReturnError; } m2 = poin[S->tree[i]]; m3 = ( poin[S->tree[i]] -= r31 ); do { *m3++ = *m2++; } while ( m2 < m1 ); m1 = m3; } CopCoef: *(poin[S->tree[i]]) += r31; CopCof2: m2 = (WORD *)coef; im = r3; NCOPY(m1,m2,im); *m1 = r33; } } /* Now skip to the next term in stream k. */ NextTerm: im = poin2[k][0]; if ( im < 0 ) { r1 = poin2[k][1] - im + 1; m1 = poin2[k] + 2; m2 = poin[k] - im + 1; while ( ++im <= 0 ) *--m1 = *--m2; *--m1 = r1; poin2[k] = m1; im = r1; } poin[k] = poin2[k]; ki = S->ktoi[k]; if ( !par && ( (poin[k] + im + COMPINC) >= S->pStop[ki] ) && im > 0 ) { #ifdef WITHZLIB PutIn(fin,&(S->iPatches[ki]),S->Patches[ki],&(poin[k]),ki); #else ADDPOS(S->iPatches[ki],PutIn(fin,&(S->iPatches[ki]), S->Patches[ki],&(poin[k]),ki)); #endif poin2[k] = poin[k] + im; } else { poin2[k] += im; } goto OneTerm; } } else if ( S->tree[i] < 0 ) { S->tree[i] = k; level--; goto OneTerm; } } /* found the smallest in the set. indicated by k. write to its destination. */ #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) && S == AT.S0 ) { im = PutToMaster(BHEAD poin[k]); } else #endif if ( ( im = PutOut(BHEAD poin[k],&position,fout,1) ) < 0 ) { MLOCK(ErrorMessageLock); MesPrint("Called from MergePatches with k = %d (stream %d)",k,S->ktoi[k]); MUNLOCK(ErrorMessageLock); goto ReturnError; } ADDPOS(S->SizeInFile[par],im); goto NextTerm; } else { goto NormalReturn; } EndOfMerge: #ifdef WITHPTHREADS if ( AS.MasterSort && ( fout == AR.outfile ) && S == AT.S0 ) { PutToMaster(BHEAD 0); } else #endif if ( FlushOut(&position,fout,1) ) goto ReturnError; ADDPOS(S->SizeInFile[par],1); EndOfAll: if ( par == 1 ) { /* Set the fpatch pointers */ #ifdef WITHZLIB SeekFile(fout->handle,&position,SEEK_CUR); #endif (S->fPatchN)++; S->fPatches[S->fPatchN] = position; } if ( par == 0 && fout != AR.outfile ) { /* Output went to sortfile. We have two possibilities: 1: We are not finished with the current in-out cycle In that case we should pop to the next set of patches 2: We finished a cycle and should clean up the in file Then we restart the sort. */ (S->fPatchN)++; S->fPatches[S->fPatchN] = position; if ( ISNOTZEROPOS(S->OldPosIn) ) { /* We are not done */ SeekFile(fin->handle,&(S->OldPosIn),SEEK_SET); /* We don't need extra provisions for the zlib compression here. If part of an expression has been sorted, the whole has been so. This means that S->fpincompressed[] will remain the same */ if ( (ULONG)ReadFile(fin->handle,(UBYTE *)(&(S->inNum)),(LONG)sizeof(WORD)) != sizeof(WORD) || (ULONG)ReadFile(fin->handle,(UBYTE *)(&(S->OldPosIn)),(LONG)sizeof(POSITION)) != sizeof(POSITION) || (ULONG)ReadFile(fin->handle,(UBYTE *)S->iPatches,(LONG)((S->inNum)+1) *sizeof(POSITION)) != ((S->inNum)+1)*sizeof(POSITION) ) { MLOCK(ErrorMessageLock); MesPrint("Read error fourth stage sorting"); MUNLOCK(ErrorMessageLock); goto ReturnError; } *rr = 0; #ifdef WITHZLIB for ( i = 0; i < S->inNum; i++ ) { S->fPatchesStop[i] = S->iPatches[i+1]; #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w fPatchesStop[%d] = %10p",i,&(S->fPatchesStop[i])); MUNLOCK(ErrorMessageLock); #endif } #endif goto ConMer; } else { /* if ( fin == &(AR.FoStage4[0]) ) { s = (UBYTE *)(fin->name); while ( *s ) s++; if ( AR.Stage4Name == 1 ) s[-1] -= 1; else s[-1] += 1; } */ /* TruncateFile(fin->handle); */ UpdateMaxSize(); #ifdef WITHZLIB ClearSortGZIP(fin); #endif CloseFile(fin->handle); remove(fin->name); /* Gives diskspace free again. */ #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w MergePatches removed in file %s",fin->name); MUNLOCK(ErrorMessageLock); #endif /* if ( fin == &(AR.FoStage4[0]) ) { s = (UBYTE *)(fin->name); while ( *s ) s++; if ( AR.Stage4Name == 1 ) s[-1] += 1; else s[-1] -= 1; } */ fin->handle = -1; { FILEHANDLE *ff = fin; fin = fout; fout = ff; } PUTZERO(S->SizeInFile[0]); goto NewMerge; } } if ( par == 0 ) { /* TruncateFile(fin->handle); */ UpdateMaxSize(); #ifdef WITHZLIB ClearSortGZIP(fin); #endif CloseFile(fin->handle); remove(fin->name); fin->handle = -1; #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w MergePatches removed in file %s",fin->name); MUNLOCK(ErrorMessageLock); #endif } NormalReturn: #ifdef WITHZLIB AR.gzipCompress = oldgzipCompress; #endif return(0); ReturnError: #ifdef WITHZLIB AR.gzipCompress = oldgzipCompress; #endif return(-1); #ifndef WITHZLIB PatwCall: MLOCK(ErrorMessageLock); MesPrint("Error while writing to file."); goto PatCall2; #endif PatCall:; MLOCK(ErrorMessageLock); PatCall2:; MesCall("MergePatches"); MUNLOCK(ErrorMessageLock); #ifdef WITHZLIB AR.gzipCompress = oldgzipCompress; #endif SETERROR(-1) } /* #] MergePatches : #[ StoreTerm : WORD StoreTerm(term) */ /** * The central routine to accept terms, store them and keep things * at least partially sorted. A call to EndSort will then complete * storing and sorting. * * @param term The term to be stored * @return Regular return conventions (OK -> 0) */ int StoreTerm(PHEAD WORD *term) { GETBIDENTITY SORTING *S = AT.SS; WORD **ss, *lfill, j, *t; POSITION pp; LONG lSpace, sSpace, RetCode, over, tover; // Update SortVerbose counters S->verbUnsortedSize += *term * sizeof(*term); if ( ( ( AP.PreDebug & DUMPTOSORT ) == DUMPTOSORT ) && AR.sLevel == 0 ) { #ifdef WITHPTHREADS snprintf((char *)(THRbuf),100,"StoreTerm(%d)",AT.identity); PrintTerm(term,(char *)(THRbuf)); #else PrintTerm(term,"StoreTerm"); #endif } if ( AM.exitflag && AR.sLevel == 0 ) return(0); S->sFill = *(S->PoinFill); if ( S->sTerms >= S->TermsInSmall || ( S->sFill + *term ) >= S->sTop ) { /* The small buffer is full. It has to be sorted and written. */ // Update SortVerbose counters if ( S->sTerms >= S->TermsInSmall ) S->verbSBsortTerms++; else S->verbSBsortCap++; tover = over = S->sTerms; ss = S->sPointer; ss[over] = 0; #ifdef SPLITTIME PrintTime((UBYTE *)"Before SplitMerge"); #endif ss[SplitMerge(BHEAD ss,over)] = 0; #ifdef SPLITTIME PrintTime((UBYTE *)"After SplitMerge"); #endif sSpace = 0; if ( over > 0 ) { sSpace = ComPress(ss,&RetCode); S->TermsLeft -= over - RetCode; } sSpace++; lSpace = sSpace + (S->lFill - S->lBuffer) - (AM.MaxTer/sizeof(WORD))*((LONG)S->lPatch); SETBASEPOSITION(pp,lSpace); MULPOS(pp,sizeof(WORD)); if ( S->file.handle >= 0 ) { ADD2POS(pp,S->fPatches[S->fPatchN]); } if ( S == AT.S0 ) { /* Only statistics at ground level */ WriteStats(&pp,STATSSPLITMERGE,CHECKLOGTYPE); } if ( ( S->lPatch >= S->MaxPatches ) || ( ( (WORD *)(((UBYTE *)(S->lFill + sSpace)) + 2*AM.MaxTer ) ) >= S->lTop ) ) { /* The large buffer is too full. Merge and write it */ // Update SortVerbose counters if ( S->lPatch >= S->MaxPatches ) S->verbLBsortPatches++; else S->verbLBsortCap++; if ( MergePatches(1) ) goto StoreCall; /* pp = S->SizeInFile[1]; ADDPOS(pp,sSpace); MULPOS(pp,sizeof(WORD)); */ SETBASEPOSITION(pp,sSpace); MULPOS(pp,sizeof(WORD)); ADD2POS(pp,S->fPatches[S->fPatchN]); if ( S == AT.S0 ) { /* Only statistics at ground level */ WriteStats(&pp,STATSMERGETOFILE,CHECKLOGTYPE); } S->lPatch = 0; S->lFill = S->lBuffer; } S->Patches[S->lPatch++] = S->lFill; lfill = (WORD *)(((UBYTE *)(S->lFill)) + AM.MaxTer); if ( tover > 0 ) { ss = S->sPointer; while ( ( t = *ss++ ) != 0 ) { j = *t; if ( j < 0 ) j = t[1] + 2; while ( --j >= 0 ){ *lfill++ = *t++; } } } *lfill++ = 0; S->lFill = lfill; S->sTerms = 0; S->PoinFill = S->sPointer; *(S->PoinFill) = S->sFill = S->sBuffer; } j = *term; while ( --j >= 0 ) *S->sFill++ = *term++; S->sTerms++; S->GenTerms++; S->TermsLeft++; *++S->PoinFill = S->sFill; return(0); StoreCall: MLOCK(ErrorMessageLock); MesCall("StoreTerm"); MUNLOCK(ErrorMessageLock); SETERROR(-1) } /* #] StoreTerm : #[ StageSort : void StageSort(FILEHANDLE *fout) */ /** * Prepares a stage 4 or higher sort. * Stage 4 sorts occur when the sort file contains more patches than * can be merged in one pass. */ void StageSort(FILEHANDLE *fout) { GETIDENTITY SORTING *S = AT.SS; if ( S->fPatchN >= S->MaxFpatches ) { POSITION position; if ( S != AT.S0 ) { /* There are no proper provisions for stage 4 or higher sorts for function arguments and $ variables. The reason: The current code maps out the patches, based on the size of the buffers in the FoStage4 structs, while they are used inside the S->file struct that may have far smaller buffers. By itself that might still be repairable, but it goes completely wrong when during the sort polyRatFuns have to be added and they would go into stage4 (very rare but possible). The only really correct solution would be to put FoStage4 structs in all sort levels. Messy. (JV 8-oct-2018). */ MLOCK(ErrorMessageLock); MesPrint("Currently Stage 4 sorts are not allowed for function arguments or $ variables."); MesPrint("Please increase correspondingsorting parameters (sub-) in the setup."); MUNLOCK(ErrorMessageLock); Terminate(-1); } PUTZERO(position); MLOCK(ErrorMessageLock); #ifdef WITHPTHREADS MesPrint("StageSort in thread %d",identity); #elif defined(WITHMPI) MesPrint("StageSort in process %d",PF.me); #else MesPrint("StageSort"); #endif MUNLOCK(ErrorMessageLock); SeekFile(fout->handle,&position,SEEK_END); /* No extra compression data has to be written. S->fpincompressed should remain valid. */ if ( (ULONG)WriteFile(fout->handle,(UBYTE *)(&(S->fPatchN)),(LONG)sizeof(WORD)) != sizeof(WORD) || (ULONG)WriteFile(fout->handle,(UBYTE *)(&(S->OldPosOut)),(LONG)sizeof(POSITION)) != sizeof(POSITION) || (ULONG)WriteFile(fout->handle,(UBYTE *)(S->fPatches),(LONG)(S->fPatchN+1) *sizeof(POSITION)) != (S->fPatchN+1)*sizeof(POSITION) ) { MLOCK(ErrorMessageLock); MesPrint("Write error while staging sort. Disk full?"); MUNLOCK(ErrorMessageLock); Terminate(-1); } S->OldPosOut = position; fout->filesize = position; ADDPOS(fout->filesize,(S->fPatchN+2)*sizeof(POSITION) + sizeof(WORD)); fout->POposition = fout->filesize; S->fPatches[0] = fout->filesize; S->fPatchN = 0; if ( AR.FoStage4[0].PObuffer == 0 ) { AR.FoStage4[0].PObuffer = (WORD *)Malloc1(AR.FoStage4[0].POsize*sizeof(WORD) ,"Stage 4 buffer"); AR.FoStage4[0].POfill = AR.FoStage4[0].PObuffer; AR.FoStage4[0].POstop = AR.FoStage4[0].PObuffer + AR.FoStage4[0].POsize/sizeof(WORD); #ifdef WITHPTHREADS AR.FoStage4[0].pthreadslock = dummylock; #endif } if ( AR.FoStage4[1].PObuffer == 0 ) { AR.FoStage4[1].PObuffer = (WORD *)Malloc1(AR.FoStage4[1].POsize*sizeof(WORD) ,"Stage 4 buffer"); AR.FoStage4[1].POfill = AR.FoStage4[1].PObuffer; AR.FoStage4[1].POstop = AR.FoStage4[1].PObuffer + AR.FoStage4[1].POsize/sizeof(WORD); #ifdef WITHPTHREADS AR.FoStage4[1].pthreadslock = dummylock; #endif } S->stage4 = 1; } } /* #] StageSort : #[ SortWild : WORD SortWild(w,nw) */ /** * Sorts the wildcard entries in the parameter w. Double entries * are removed. Full space taken is nw words. * Routine serves for the reading of wildcards in the compiler. * The entries come in the format: * (type,4,number,0) in which the zero is reserved for the * future replacement of 'number'. * * @param w buffer with wildcard entries. * @param nw number of wildcard entries. * @return Normal conventions (OK -> 0) */ int SortWild(WORD *w, WORD nw) { GETIDENTITY WORD *v, *s, *m, k, i; WORD *pScrat, *stop, *sv; int error = 0; pScrat = AT.WorkPointer; if ( ( AT.WorkPointer + 8 * AM.MaxWildcards ) >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } stop = w + nw; i = 0; while ( i < nw ) { m = w + i; v = m + m[1]; while ( v < stop && ( *v == FROMSET || *v == SETTONUM || *v == LOADDOLLAR ) ) v += v[1]; while ( v < stop ) { if ( *v >= 0 ) { if ( AM.Ordering[*v] < AM.Ordering[*m] ) { m = v; } else if ( *v == *m ) { if ( v[2] < m[2] ) { m = v; } else if ( v[2] == m[2] ) { s = m + m[1]; sv = v + v[1]; if ( s < stop && ( *s == FROMSET || *s == SETTONUM || *s == LOADDOLLAR ) ) { if ( sv < stop && ( *sv == FROMSET || *sv == SETTONUM || *sv == LOADDOLLAR ) ) { if ( s[2] != sv[2] ) { error = -1; MLOCK(ErrorMessageLock); MesPrint("&Wildcard set conflict"); MUNLOCK(ErrorMessageLock); } } *v = -1; } else { if ( sv < stop && ( *sv == FROMSET || *sv == SETTONUM || *sv == LOADDOLLAR ) ) { *m = -1; m = v; } else { *v = -1; } } } } } v += v[1]; while ( v < stop && ( *v == FROMSET || *v == SETTONUM || *v == LOADDOLLAR ) ) v += v[1]; } s = pScrat; v = m; k = m[1]; NCOPY(s,m,k); while ( m < stop && ( *m == FROMSET || *m == SETTONUM || *m == LOADDOLLAR ) ) { k = m[1]; NCOPY(s,m,k); } *v = -1; pScrat = s; i = 0; while ( i < nw && ( w[i] < 0 || w[i] == FROMSET || w[i] == SETTONUM || w[i] == LOADDOLLAR ) ) i += w[i+1]; } AC.NwildC = k = WORDDIF(pScrat,AT.WorkPointer); s = AT.WorkPointer; m = w; NCOPY(m,s,k); AC.WildC = m; return(error); } /* #] SortWild : #[ CleanUpSort : void CleanUpSort(num) */ /** * Partially or completely frees function sort buffers. */ void CleanUpSort(int num) { GETIDENTITY SORTING *S; int minnum = num, i; if ( AN.FunSorts ) { if ( num == -1 ) { if ( AN.MaxFunSorts > 3 ) { minnum = (AN.MaxFunSorts+4)/2; } else minnum = 4; } else if ( minnum == 0 ) minnum = 1; for ( i = minnum; i < AN.NumFunSorts; i++ ) { S = AN.FunSorts[i]; if ( S ) { if ( S->file.handle >= 0 ) { /* TruncateFile(S->file.handle); */ UpdateMaxSize(); #ifdef WITHZLIB ClearSortGZIP(&(S->file)); #endif CloseFile(S->file.handle); S->file.handle = -1; remove(S->file.name); #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w CleanUpSort removed file %s",S->file.name); MUNLOCK(ErrorMessageLock); #endif } M_free(S->sPointer, "CleanUpSort: sPointer"); M_free(S->Patches, "CleanUpSort: Patches"); M_free(S->pStop, "CleanUpSort: pStop"); M_free(S->poina, "CleanUpSort: poina"); M_free(S->poin2a, "CleanUpSort: poin2a"); M_free(S->fPatches, "CleanUpSort: fPatches"); M_free(S->fPatchesStop, "CleanUpSort: fPatchesStop"); M_free(S->inPatches, "CleanUpSort: inPatches"); M_free(S->tree, "CleanUpSort: tree"); M_free(S->used, "CleanUpSort: used"); #ifdef WITHZLIB M_free(S->fpcompressed, "CleanUpSort: fpcompressed"); M_free(S->fpincompressed, "CleanUpSort: fpincompressed"); #endif M_free(S->ktoi, "CleanUpSort: ktoi"); M_free(S->lBuffer, "CleanUpSort: lBuffer+sBuffer"); M_free(S->file.PObuffer, "CleanUpSort: PObuffer"); M_free(S, "CleanUpSort: sorting struct"); } AN.FunSorts[i] = 0; } AN.MaxFunSorts = minnum; if ( num == 0 ) { S = AN.FunSorts[0]; if ( S ) { if ( S->file.handle >= 0 ) { /* TruncateFile(S->file.handle); */ UpdateMaxSize(); #ifdef WITHZLIB ClearSortGZIP(&(S->file)); #endif CloseFile(S->file.handle); S->file.handle = -1; remove(S->file.name); #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w CleanUpSort removed file %s",S->file.name); MUNLOCK(ErrorMessageLock); #endif } } } } for ( i = 0; i < 2; i++ ) { if ( AR.FoStage4[i].handle >= 0 ) { UpdateMaxSize(); #ifdef WITHZLIB ClearSortGZIP(&(AR.FoStage4[i])); #endif CloseFile(AR.FoStage4[i].handle); remove(AR.FoStage4[i].name); AR.FoStage4[i].handle = -1; #ifdef GZIPDEBUG MLOCK(ErrorMessageLock); MesPrint("%w CleanUpSort removed stage4 file %s",AR.FoStage4[i].name); MUNLOCK(ErrorMessageLock); #endif } } } /* #] CleanUpSort : #[ LowerSortLevel : void LowerSortLevel() */ /** * Lowers the level in the sort system. */ void LowerSortLevel(void) { GETIDENTITY if ( AR.sLevel >= 0 ) { AR.sLevel--; if ( AR.sLevel >= 0 ) AT.SS = AN.FunSorts[AR.sLevel]; } } /* #] LowerSortLevel : #[ PolyRatFunSpecial : Keeps only the most divergent term in AR.PolyFunVar We assume that the terms are already in that notation. */ WORD *PolyRatFunSpecial(PHEAD WORD *t1, WORD *t2) { WORD *oldworkpointer = AT.WorkPointer, *t, *r; WORD exp1, exp2; int i; t = t1+FUNHEAD; if ( *t == -SYMBOL ) { if ( t[1] != AR.PolyFunVar ) goto Illegal; exp1 = 1; if ( t[2] != -SNUMBER ) goto Illegal; t[3] = 1; } else if ( *t == -SNUMBER ) { t[1] = 1; t += 2; if ( *t == -SYMBOL ) { if ( t[1] != AR.PolyFunVar ) goto Illegal; exp1 = -1; } else if ( *t == -SNUMBER ) { t[1] = 1; exp1 = 0; } else if ( *t == ARGHEAD+8 && t[ARGHEAD] == 8 && t[ARGHEAD+1] == SYMBOL && t[ARGHEAD+3] == AR.PolyFunVar ) { t[ARGHEAD+5] = 1; t[ARGHEAD+6] = 1; t[ARGHEAD+7] = 3; exp1 = -t[ARGHEAD+4]; } else goto Illegal; } else if ( *t == ARGHEAD+8 && t[ARGHEAD] == 8 && t[ARGHEAD+1] == SYMBOL && t[ARGHEAD+3] == AR.PolyFunVar ) { t[ARGHEAD+5] = 1; t[ARGHEAD+6] = 1; t[ARGHEAD+7] = 3; exp1 = t[ARGHEAD+4]; t += *t; if ( *t != -SNUMBER ) goto Illegal; t[1] = 1; } else goto Illegal; t = t2+FUNHEAD; if ( *t == -SYMBOL ) { if ( t[1] != AR.PolyFunVar ) goto Illegal; exp2 = 1; if ( t[2] != -SNUMBER ) goto Illegal; t[3] = 1; } else if ( *t == -SNUMBER ) { t[1] = 1; t += 2; if ( *t == -SYMBOL ) { if ( t[1] != AR.PolyFunVar ) goto Illegal; exp2 = -1; } else if ( *t == -SNUMBER ) { t[1] = 1; exp2 = 0; } else if ( *t == ARGHEAD+8 && t[ARGHEAD] == 8 && t[ARGHEAD+1] == SYMBOL && t[ARGHEAD+3] == AR.PolyFunVar ) { t[ARGHEAD+5] = 1; t[ARGHEAD+6] = 1; t[ARGHEAD+7] = 3; exp2 = -t[ARGHEAD+4]; } else goto Illegal; } else if ( *t == ARGHEAD+8 && t[ARGHEAD] == 8 && t[ARGHEAD+1] == SYMBOL && t[ARGHEAD+3] == AR.PolyFunVar ) { t[ARGHEAD+5] = 1; t[ARGHEAD+6] = 1; t[ARGHEAD+7] = 3; exp2 = t[ARGHEAD+4]; t += *t; if ( *t != -SNUMBER ) goto Illegal; t[1] = 1; } else goto Illegal; if ( exp1 <= exp2 ) { i = t1[1]; r = t1; } else { i = t2[1]; r = t2; } t = oldworkpointer; NCOPY(t,r,i) return(oldworkpointer); Illegal: MesPrint("Illegal occurrence of PolyRatFun with divergent option"); Terminate(-1); return(0); } /* #] PolyRatFunSpecial : #[ SimpleSplitMerge : Sorts an array of WORDs. No adding of equal objects. */ void SimpleSplitMergeRec(WORD *array,WORD num,WORD *auxarray) { WORD n1,n2,i,j,k,*t1,*t2; if ( num < 2 ) return; if ( num == 2 ) { if ( array[0] > array[1] ) { EXCH(array[0],array[1]) } return; } n1 = num/2; n2 = num - n1; SimpleSplitMergeRec(array,n1,auxarray); SimpleSplitMergeRec(array+n1,n2,auxarray); if ( array[n1-1] <= array[n1] ) return; t1 = array; t2 = auxarray; i = n1; NCOPY(t2,t1,i); i = 0; j = n1; k = 0; while ( i < n1 && j < num ) { if ( auxarray[i] <= array[j] ) { array[k++] = auxarray[i++]; } else { array[k++] = array[j++]; } } while ( i < n1 ) array[k++] = auxarray[i++]; /* Remember: remnants of j are still in place! */ } void SimpleSplitMerge(WORD *array,WORD num) { WORD *auxarray = Malloc1(sizeof(WORD)*num/2,"SimpleSplitMerge"); SimpleSplitMergeRec(array,num,auxarray); M_free(auxarray,"SimpleSplitMerge"); } /* #] SimpleSplitMerge : #[ BinarySearch : Searches in the sorted array with length num for the object x. If x is in the list, it returns the number of the array element that matched. If it is not in the list, it returns -1. If there are identical objects in the list, which one will match is quasi random. */ WORD BinarySearch(WORD *array,WORD num,WORD x) { WORD i, bot, top, med; if ( num < 8 ) { for ( i = 0; i < num; i++ ) if ( array[i] == x ) return(i); return(-1); } if ( array[0] > x || array[num-1] < x ) return(-1); bot = 0; top = num-1; med = (top+bot)/2; do { if ( array[med] == x ) return(med); if ( array[med] < x ) { bot = med+1; } else { top = med-1; } med = (top+bot)/2; } while ( med >= bot && med <= top ); return(-1); } /* #] BinarySearch : #] SortUtilities : */ form-5.0.1/sources/if.c0000644000175100017510000007657615217035721010420 /** @file if.c * * Routines for the dealing with if statements. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : if.c */ #include "form3.h" /* #] Includes : #[ If statement : #[ Syntax : The `if' is a conglomerate of statements: if,else,endif The if consists in principle of: if ( number ); statements else; statements endif; The first set is taken when number != 0. The else is not mandatory. TRUE = 1 and FALSE = 0 The number can be built up via a logical expression: expr1 condition expr2 each expression can be a subexpression again. It has to be enclosed in parentheses in that case. Conditions are: >, >=, <, <=, ==, !=, ||, && When Expressions are chained evaluation is from left to right, independent of whether this indicates nonsense. if ( a || b || c || d ); is a perfectly normal statement. if ( a >= b || c == d ); would be messed up. This should be: if ( ( a >= b ) || ( c == d ) ); The building blocks of the Expressions are: Match(option,pattern) The number of times pattern fits in term_ Count(....) The count value of term_ Coeff[icient] The coefficient of term_ FindLoop(options) Are there loops (as in ReplaceLoop). Implementation for internal notation: TYPEIF,length,gotolevel(if fail),EXPRTYPE,length,...... EXPRTYPE can be: SHORTNUMBER ->,4,sign,size LONGNUMBER ->,|ncoef+2|,ncoef,numer,denom MATCH ->,patternsiz+3,keyword,pattern MULTIPLEOF ->,3,thenumber COUNT ->,countsiz+2,countinfo TYPEFINDLOOP ->,7 (findloop info) COEFFICIENT ->,2 IFDOLLAR ->,3,dollarnumber SUBEXPR ->,size,dummy,size1,EXPRTYPE,length,... ,2,condition1,size2,... This is like functions. Note that there must be a restriction to the number of nestings of parentheses in an if statement. It has been set to 10. The syntax of match corresponds to the syntax of the left side of an id statement. The only difference is the keyword MATCH vs TYPEIDNEW. #] Syntax : #[ GetIfDollarNum : */ WORD GetIfDollarNum(WORD *ifp, WORD *ifstop) { DOLLARS d; WORD num, *w; if ( ifp[2] < 0 ) { return(-ifp[2]-1); } d = Dollars+ifp[2]; if ( ifp+3 < ifstop && ifp[3] == IFDOLLAREXTRA ) { if ( d->nfactors == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Attempt to use a factor of an unfactored $-variable"); MUNLOCK(ErrorMessageLock); Terminate(-1); } num = GetIfDollarNum(ifp+3,ifstop); if ( num > d->nfactors ) { MLOCK(ErrorMessageLock); MesPrint("Dollar factor number %s out of range",num); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( num == 0 ) { return(d->nfactors); } w = d->factors[num-1].where; if ( w == 0 ) return(d->factors[num].value); getnumber:; if ( *w == 0 ) return(0); if ( *w == 4 && w[3] == 3 && w[2] == 1 && w[1] < MAXPOSITIVE && w[4] == 0 ) { return(w[1]); } if ( ( w[w[0]] != 0 ) || ( ABS(w[w[0]-1]) != w[0]-1 ) ) { MLOCK(ErrorMessageLock); MesPrint("Dollar factor number expected but found expression"); MUNLOCK(ErrorMessageLock); Terminate(-1); } else { MLOCK(ErrorMessageLock); MesPrint("Dollar factor number out of range"); MUNLOCK(ErrorMessageLock); Terminate(-1); } return(0); } /* Now we have just a dollar and should evaluate that into a short number */ if ( d->type == DOLZERO ) { return(0); } else if ( d->type == DOLNUMBER || d->type == DOLTERMS ) { w = d->where; goto getnumber; } else { MLOCK(ErrorMessageLock); MesPrint("Dollar factor number is wrong type"); MUNLOCK(ErrorMessageLock); Terminate(-1); return(0); } } /* #] GetIfDollarNum : #[ FindVar : */ int FindVar(WORD *v, WORD *term) { WORD *t, *tstop, *m, *mstop, *f, *fstop, *a, *astop; GETSTOP(term,tstop); t = term+1; while ( t < tstop ) { if ( *v == *t && *v < FUNCTION ) { /* VECTOR, INDEX, SYMBOL, DOTPRODUCT */ switch ( *v ) { case SYMBOL: m = t+2; mstop = t+t[1]; while ( m < mstop ) { if ( *m == v[1] ) return(1); m += 2; } break; case INDEX: case VECTOR: InVe: m = t+2; mstop = t+t[1]; while ( m < mstop ) { if ( *m == v[1] ) return(1); m++; } break; case DOTPRODUCT: m = t+2; mstop = t+t[1]; while ( m < mstop ) { if ( *m == v[1] && m[1] == v[2] ) return(1); if ( *m == v[2] && m[1] == v[1] ) return(1); m += 3; } break; } } else if ( *v == VECTOR && *t == INDEX ) goto InVe; else if ( *v == INDEX && *t == VECTOR ) goto InVe; else if ( ( *v == VECTOR || *v == INDEX ) && *t == DOTPRODUCT ) { m = t+2; mstop = t+t[1]; while ( m < mstop ) { if ( v[1] == m[0] || v[1] == m[1] ) return(1); m += 3; } } else if ( *t >= FUNCTION ) { if ( *v == FUNCTION && v[1] == *t ) return(1); if ( functions[*t-FUNCTION].spec > 0 ) { if ( *v == VECTOR || *v == INDEX ) { /* we need to check arguments */ int i; for ( i = FUNHEAD; i < t[1]; i++ ) { if ( v[1] == t[i] ) return(1); } } } else { fstop = t + t[1]; f = t + FUNHEAD; while ( f < fstop ) { /* Do the arguments one by one */ if ( *f <= 0 ) { switch ( *f ) { case -SYMBOL: if ( *v == SYMBOL && v[1] == f[1] ) return(1); f += 2; break; case -VECTOR: case -MINVECTOR: case -INDEX: if ( ( *v == VECTOR || *v == INDEX ) && ( v[1] == f[1] ) ) return(1); f += 2; break; case -SNUMBER: f += 2; break; default: if ( *v == FUNCTION && v[1] == -*f && *f <= -FUNCTION ) return(1); if ( *f <= -FUNCTION ) f++; else f += 2; break; } } else { a = f + ARGHEAD; astop = f + *f; while ( a < astop ) { if ( FindVar(v,a) == 1 ) return(1); a += *a; } f = astop; } } } } t += t[1]; } return(0); } /* #] FindVar : #[ DoIfStatement : WORD DoIfStatement(PHEAD ifcode,term) The execution time part of the if-statement. The arguments are a pointer to the TYPEIF and a pointer to the term. The answer is either 1 (success) or 0 (fail). The calling routine can figure out where to go in case of failure by picking up gotolevel. Note that the whole setup asks for recursions. */ int DoIfStatement(PHEAD WORD *ifcode, WORD *term) { GETBIDENTITY WORD *ifstop, *ifp; UWORD *coef1 = 0, *coef2, *coef3, *cc; WORD ncoef1, ncoef2, ncoef3, i = 0, first, *r, acoef, ismul1, ismul2, j; UWORD *Spac1, *Spac2; ifstop = ifcode + ifcode[1]; ifp = ifcode + 3; if ( ifp >= ifstop ) return(1); if ( ( ifp + ifp[1] ) >= ifstop ) { switch ( *ifp ) { case LONGNUMBER: if ( ifp[2] ) return(1); else return(0); case MATCH: case TYPEIF: if ( HowMany(BHEAD ifp,term) ) return(1); else return(0); case TYPEFINDLOOP: if ( Lus(term,ifp[3],ifp[4],ifp[5],ifp[6],ifp[2]) ) return(1); else return(0); case TYPECOUNT: if ( CountDo(term,ifp) ) return(1); else return(0); case COEFFI: case MULTIPLEOF: return(1); case IFDOLLAR: { DOLLARS d = Dollars + ifp[2]; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( ifp[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } } } dtype = d->type; #else int dtype = d->type; /* We use dtype to make the operation atomic */ #endif if ( dtype == DOLZERO ) return(0); if ( dtype == DOLUNDEFINED ) { if ( AC.UnsureDollarMode == 0 ) { MesPrint("$%s is undefined",AC.dollarnames->namebuffer+d->name); Terminate(-1); } } } return(1); case IFEXPRESSION: r = ifp+2; j = ifp[1] - 2; while ( --j >= 0 ) { if ( *r == AR.CurExpr ) return(1); r++; } return(0); case IFISFACTORIZED: r = ifp+2; j = ifp[1] - 2; if ( j == 0 ) { if ( ( Expressions[AR.CurExpr].vflags & ISFACTORIZED ) != 0 ) return(1); else return(0); } while ( --j >= 0 ) { if ( ( Expressions[*r].vflags & ISFACTORIZED ) == 0 ) return(0); r++; } return(1); case IFOCCURS: { WORD *OccStop = ifp + ifp[1]; ifp += 2; while ( ifp < OccStop ) { if ( FindVar(ifp,term) == 1 ) return(1); if ( *ifp == DOTPRODUCT ) ifp += 3; else ifp += 2; } } return(0); case IFUSERFLAG: if ( ( Expressions[AR.CurExpr].uflags & (1 << ifp[2]) ) != 0 ) return(1); return(0); default: /* Now we have a subexpression. Test first for one with a single item. */ if ( ifp[3] == ( ifp[1] + 3 ) ) return(DoIfStatement(BHEAD ifp,term)); ifstop = ifp + ifp[1]; ifp += 3; break; } } /* Here is the composite condition. */ coef3 = NumberMalloc("DoIfStatement"); Spac1 = NumberMalloc("DoIfStatement"); Spac2 = (UWORD *)(TermMalloc("DoIfStatement")); ncoef1 = 0; first = 1; ismul1 = 0; do { if ( !first ) { ifp += 2; if ( ifp[-2] == ORCOND && ncoef1 ) { coef1 = Spac1; ncoef1 = 1; coef1[0] = coef1[1] = 1; goto SkipCond; } if ( ifp[-2] == ANDCOND && !ncoef1 ) goto SkipCond; } coef2 = Spac2; ncoef2 = 1; ismul2 = 0; switch ( *ifp ) { case LONGNUMBER: ncoef2 = ifp[2]; j = 2*(ABS(ncoef2)); cc = (UWORD *)(ifp + 3); for ( i = 0; i < j; i++ ) coef2[i] = cc[i]; break; #ifdef WITHFLOAT case IFFLOATNUMBER: /* The sloppy solution is: Convert to rational. This way we can write it over coef2,ncoef2 */ ncoef2 = FloatFunToRat(BHEAD coef2,ifp); break; #endif case MATCH: case TYPEIF: coef2[0] = HowMany(BHEAD ifp,term); coef2[1] = 1; if ( coef2[0] == 0 ) ncoef2 = 0; break; case TYPECOUNT: acoef = CountDo(term,ifp); coef2[0] = ABS(acoef); coef2[1] = 1; if ( acoef == 0 ) ncoef2 = 0; else if ( acoef < 0 ) ncoef2 = -1; break; case TYPEFINDLOOP: acoef = Lus(term,ifp[3],ifp[4],ifp[5],ifp[6],ifp[2]); coef2[0] = ABS(acoef); coef2[1] = 1; if ( acoef == 0 ) ncoef2 = 0; else if ( acoef < 0 ) ncoef2 = -1; break; case COEFFI: r = term + *term; ncoef2 = r[-1]; i = ABS(ncoef2); cc = (UWORD *)(r - i); if ( ncoef2 < 0 ) ncoef2 = (ncoef2+1)>>1; else ncoef2 = (ncoef2-1)>>1; i--; for ( j = 0; j < i; j++ ) coef2[j] = cc[j]; break; case SUBEXPR: ncoef2 = coef2[0] = DoIfStatement(BHEAD ifp,term); coef2[1] = 1; break; case MULTIPLEOF: ncoef2 = 1; coef2[0] = ifp[2]; coef2[1] = 1; ismul2 = 1; break; case IFDOLLAREXTRA: break; case IFDOLLAR: { /* We need to abstract a long rational in coef2 with length ncoef2. What if that cannot be done? */ DOLLARS d = Dollars + ifp[2]; #ifdef WITHPTHREADS int nummodopt, dtype = -1; if ( AS.MultiThreaded ) { for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) { if ( ifp[2] == ModOptdollars[nummodopt].number ) break; } if ( nummodopt < NumModOptdollars ) { dtype = ModOptdollars[nummodopt].type; if ( DollarLocalCopy(dtype) ) { d = ModOptdollars[nummodopt].dstruct+AT.identity; } else { LOCK(d->pthreadslock); } } } #endif /* We have to pick up the IFDOLLAREXTRA pieces for [1], [$y] etc. */ if ( ifp+3 < ifstop && ifp[3] == IFDOLLAREXTRA ) { if ( d->nfactors == 0 ) { MLOCK(ErrorMessageLock); MesPrint("Attempt to use a factor of an unfactored $-variable"); MUNLOCK(ErrorMessageLock); Terminate(-1); } { WORD num = GetIfDollarNum(ifp+3,ifstop); WORD *w; while ( ifp+3 < ifstop && ifp[3] == IFDOLLAREXTRA ) ifp += 3; if ( num > d->nfactors ) { MLOCK(ErrorMessageLock); MesPrint("Dollar factor number %s out of range",num); MUNLOCK(ErrorMessageLock); Terminate(-1); } if ( num == 0 ) { ncoef2 = 1; coef2[0] = d->nfactors; coef2[1] = 1; break; } w = d->factors[num-1].where; if ( w == 0 ) { if ( d->factors[num-1].value < 0 ) { ncoef2 = -1; coef2[0] = -d->factors[num-1].value; coef2[1] = 1; } else { ncoef2 = 1; coef2[0] = d->factors[num-1].value; coef2[1] = 1; } break; } if ( w[*w] == 0 ) { r = w + *w - 1; i = ABS(*r); if ( i == ( *w-1 ) ) { ncoef2 = (i-1)/2; if ( *r < 0 ) ncoef2 = -ncoef2; i--; cc = coef2; r = w + 1; while ( --i >= 0 ) *cc++ = (UWORD)(*r++); break; } } goto generic; } } else { switch ( d->type ) { case DOLUNDEFINED: if ( AC.UnsureDollarMode == 0 ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s is undefined",AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } ncoef2 = 0; coef2[0] = 0; coef2[1] = 1; break; case DOLZERO: ncoef2 = coef2[0] = 0; coef2[1] = 1; break; case DOLSUBTERM: if ( d->where[0] != INDEX || d->where[1] != 3 || d->where[2] < 0 || d->where[2] >= AM.OffsetIndex ) { if ( AC.UnsureDollarMode == 0 ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s is of wrong type",AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } ncoef2 = 0; coef2[0] = 0; coef2[1] = 1; break; } d->index = d->where[2]; /* fall through */ case DOLINDEX: if ( d->index == 0 ) { ncoef2 = coef2[0] = 0; coef2[1] = 1; } else if ( d->index > 0 && d->index < AM.OffsetIndex ) { ncoef2 = 1; coef2[0] = d->index; coef2[1] = 1; } else if ( AC.UnsureDollarMode == 0 ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s is of wrong type",AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } ncoef2 = coef2[0] = 0; coef2[1] = 1; break; case DOLWILDARGS: if ( d->where[0] <= -FUNCTION || ( d->where[0] < 0 && d->where[2] != 0 ) || ( d->where[0] > 0 && d->where[d->where[0]] != 0 ) ) { if ( AC.UnsureDollarMode == 0 ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s is of wrong type",AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } ncoef2 = coef2[0] = 0; coef2[1] = 1; break; } /* fall through */ case DOLARGUMENT: if ( d->where[0] == -SNUMBER ) { if ( d->where[1] == 0 ) { ncoef2 = coef2[0] = 0; } else if ( d->where[1] < 0 ) { ncoef2 = -1; coef2[0] = -d->where[1]; } else { ncoef2 = 1; coef2[0] = d->where[1]; } coef2[1] = 1; } else if ( d->where[0] == -INDEX && d->where[1] >= 0 && d->where[1] < AM.OffsetIndex ) { if ( d->where[1] == 0 ) { ncoef2 = coef2[0] = 0; coef2[1] = 1; } else { ncoef2 = 1; coef2[0] = d->where[1]; coef2[1] = 1; } } else if ( d->where[0] > 0 && d->where[ARGHEAD] == (d->where[0]-ARGHEAD) && ABS(d->where[d->where[0]-1]) == (d->where[0] - ARGHEAD-1) ) { i = d->where[d->where[0]-1]; ncoef2 = (ABS(i)-1)/2; if ( i < 0 ) { ncoef2 = -ncoef2; i = -i; } i--; cc = coef2; r = d->where + ARGHEAD+1; while ( --i >= 0 ) *cc++ = (UWORD)(*r++); } else { if ( AC.UnsureDollarMode == 0 ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s is of wrong type",AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } ncoef2 = 0; coef2[0] = 0; coef2[1] = 1; } break; case DOLNUMBER: case DOLTERMS: if ( d->where[d->where[0]] == 0 ) { r = d->where + d->where[0]-1; i = ABS(*r); if ( i == ( d->where[0]-1 ) ) { ncoef2 = (i-1)/2; if ( *r < 0 ) ncoef2 = -ncoef2; i--; cc = coef2; r = d->where + 1; while ( --i >= 0 ) *cc++ = (UWORD)(*r++); break; } } generic:; if ( AC.UnsureDollarMode == 0 ) { #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif MLOCK(ErrorMessageLock); MesPrint("$%s is of wrong type",AC.dollarnames->namebuffer+d->name); MUNLOCK(ErrorMessageLock); Terminate(-1); } ncoef2 = 0; coef2[0] = 0; coef2[1] = 1; break; } } #ifdef WITHPTHREADS if ( dtype > 0 && ! DollarLocalCopy(dtype) ) { UNLOCK(d->pthreadslock); } #endif } break; case IFEXPRESSION: r = ifp+2; j = ifp[1] - 2; ncoef2 = 0; while ( --j >= 0 ) { if ( *r == AR.CurExpr ) { ncoef2 = 1; break; } r++; } coef2[0] = ncoef2; coef2[1] = 1; break; case IFISFACTORIZED: r = ifp+2; j = ifp[1] - 2; if ( j == 0 ) { ncoef2 = 0; if ( ( Expressions[AR.CurExpr].vflags & ISFACTORIZED ) != 0 ) { ncoef2 = 1; } } else { ncoef2 = 1; while ( --j >= 0 ) { if ( ( Expressions[*r].vflags & ISFACTORIZED ) == 0 ) { ncoef2 = 0; break; } r++; } } coef2[0] = ncoef2; coef2[1] = 1; break; case IFOCCURS: { WORD *OccStop = ifp + ifp[1], *ifpp = ifp+2; ncoef2 = 0; while ( ifpp < OccStop ) { if ( FindVar(ifpp,term) == 1 ) { ncoef2 = 1; break; } if ( *ifpp == DOTPRODUCT ) ifp += 3; else ifpp += 2; } coef2[0] = ncoef2; coef2[1] = 1; } break; case IFUSERFLAG: { ncoef2 = 0; if ( ( Expressions[AR.CurExpr].uflags & (1 << ifp[2]) ) != 0 ) ncoef2 = 1; coef2[0] = ncoef2; coef2[1] = 1; } break; default: break; } if ( !first ) { if ( ifp[-2] != ORCOND && ifp[-2] != ANDCOND ) { if ( ( ifp[-2] == EQUAL || ifp[-2] == NOTEQUAL ) && ( ismul2 || ismul1 ) ) { if ( ismul1 && ismul2 ) { if ( coef1[0] == coef2[0] ) i = 1; else i = 0; } else { if ( ismul1 ) { if ( ncoef2 ) Divvy(BHEAD coef2,&ncoef2,coef1,ncoef1); cc = coef2; ncoef3 = ncoef2; } else { if ( ncoef1 ) Divvy(BHEAD coef1,&ncoef1,coef2,ncoef2); cc = coef1; ncoef3 = ncoef1; } if ( ncoef3 < 0 ) ncoef3 = -ncoef3; if ( ncoef3 == 0 ) { if ( ifp[-2] == EQUAL ) i = 1; else i = 0; } else if ( cc[ncoef3] != 1 ) { if ( ifp[-2] == EQUAL ) i = 0; else i = 1; } else { for ( j = 1; j < ncoef3; j++ ) { if ( cc[ncoef3+j] != 0 ) break; } if ( j < ncoef3 ) { if ( ifp[-2] == EQUAL ) i = 0; else i = 1; } else if ( ifp[-2] == EQUAL ) i = 1; else i = 0; } } goto donemul; } else if ( AddRat(BHEAD coef1,ncoef1,coef2,-ncoef2,coef3,&ncoef3) ) { NumberFree(coef3,"DoIfStatement"); NumberFree(Spac1,"DoIfStatement"); TermFree(Spac2,"DoIfStatement"); MesCall("DoIfStatement"); return(-1); } switch ( ifp[-2] ) { case GREATER: if ( ncoef3 > 0 ) i = 1; else i = 0; break; case GREATEREQUAL: if ( ncoef3 >= 0 ) i = 1; else i = 0; break; case LESS: if ( ncoef3 < 0 ) i = 1; else i = 0; break; case LESSEQUAL: if ( ncoef3 <= 0 ) i = 1; else i = 0; break; case EQUAL: if ( ncoef3 == 0 ) i = 1; else i = 0; break; case NOTEQUAL: if ( ncoef3 != 0 ) i = 1; else i = 0; break; } donemul: if ( i ) { ncoef2 = 1; coef2 = Spac2; coef2[0] = coef2[1] = 1; } else ncoef2 = 0; ismul1 = ismul2 = 0; } } else { first = 0; } coef1 = Spac1; i = 2*ABS(ncoef2); for ( j = 0; j < i; j++ ) coef1[j] = coef2[j]; ncoef1 = ncoef2; SkipCond: ifp += ifp[1]; } while ( ifp < ifstop ); NumberFree(coef3,"DoIfStatement"); NumberFree(Spac1,"DoIfStatement"); TermFree(Spac2,"DoIfStatement"); if ( ncoef1 ) return(1); else return(0); } /* #] DoIfStatement : #[ HowMany : WORD HowMany(ifcode,term) Returns the number of times that the pattern in ifcode can be taken out from term. There is a subkey in ifcode[2]; The notation is identical to the lhs of an id statement. Most of the code comes from TestMatch. */ WORD HowMany(PHEAD WORD *ifcode, WORD *term) { GETBIDENTITY WORD *m, *t, *r, *w, power, RetVal, i, topje, *newterm; WORD *OldWork, *ww, *mm; int *RepSto, RepVal; int numdollars = 0; m = ifcode + IDHEAD; AN.FullProto = m; AN.WildValue = w = m + SUBEXPSIZE; m += m[1]; AN.WildStop = m; OldWork = AT.WorkPointer; if ( ( ifcode[4] & 1 ) != 0 ) { /* We have at least one dollar in the pattern */ AR.Eside = LHSIDEX; ww = AT.WorkPointer; i = m[0]; mm = m; NCOPY(ww,mm,i); *OldWork += 3; *ww++ = 1; *ww++ = 1; *ww++ = 3; AT.WorkPointer = ww; RepSto = AN.RepPoint; RepVal = *RepSto; NewSort(BHEAD0); if ( Generator(BHEAD OldWork,AR.Cnumlhs) ) { LowerSortLevel(); *RepSto = RepVal; AN.RepPoint = RepSto; AT.WorkPointer = OldWork; return(-1); } AT.WorkPointer = ww; if ( EndSort(BHEAD ww,0) < 0 ) {} *RepSto = RepVal; AN.RepPoint = RepSto; if ( *ww == 0 || *(ww+*ww) != 0 ) { if ( AP.lhdollarerror == 0 ) { MLOCK(ErrorMessageLock); MesPrint("&LHS must be one term"); MUNLOCK(ErrorMessageLock); AP.lhdollarerror = 1; } AT.WorkPointer = OldWork; return(-1); } m = ww; AT.WorkPointer = ww = m + *m; if ( m[*m-1] < 0 ) { m[*m-1] = -m[*m-1]; } *m -= m[*m-1]; AR.Eside = RHSIDE; } else { ww = term + *term; if ( AT.WorkPointer < ww ) AT.WorkPointer = ww; } ClearWild(BHEAD0); while ( w < AN.WildStop ) { if ( *w == LOADDOLLAR ) numdollars++; w += w[1]; } AN.RepFunNum = 0; AN.RepFunList = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer); topje = cbuf[AT.ebufnum].numrhs; if ( AT.WorkPointer >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AN.DisOrderFlag = ifcode[2] & SUBDISORDER; switch ( ifcode[2] & (~SUBDISORDER) ) { case SUBONLY : /* Must be an exact match */ AN.UseFindOnly = 1; AN.ForFindOnly = 0; /* Copy the term first to scratchterm. This is needed because of the Substitute. */ i = *term; t = term; newterm = r = AT.WorkPointer; NCOPY(r,t,i); AT.WorkPointer = r; RetVal = 0; if ( FindRest(BHEAD newterm,m) && ( AN.UsedOtherFind || FindOnly(BHEAD newterm,m) ) ) { Substitute(BHEAD newterm,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } ClearWild(BHEAD0); RetVal = 1; } else RetVal = 0; break; case SUBMANY : /* Copy the term first to scratchterm. This is needed because of the Substitute. */ i = *term; t = term; newterm = r = AT.WorkPointer; NCOPY(r,t,i); AT.WorkPointer = r; RetVal = 0; AN.UseFindOnly = 0; if ( ( power = FindRest(BHEAD newterm,m) ) > 0 ) { if ( ( power = FindOnce(BHEAD newterm,m) ) > 0 ) { AN.UseFindOnly = 0; do { Substitute(BHEAD newterm,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } ClearWild(BHEAD0); RetVal++; } while ( FindRest(BHEAD newterm,m) && ( AN.UsedOtherFind || FindOnce(BHEAD newterm,m) ) ); } else if ( power < 0 ) { do { Substitute(BHEAD newterm,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } ClearWild(BHEAD0); RetVal++; } while ( FindRest(BHEAD newterm,m) ); } } else if ( power < 0 ) { if ( FindOnce(BHEAD newterm,m) ) { do { Substitute(BHEAD newterm,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } ClearWild(BHEAD0); } while ( FindOnce(BHEAD newterm,m) ); RetVal = 1; } } break; case SUBONCE : /* Copy the term first to scratchterm. This is needed because of the Substitute. */ i = *term; t = term; newterm = r = AT.WorkPointer; NCOPY(r,t,i); AT.WorkPointer = r; RetVal = 0; AN.UseFindOnly = 0; if ( FindRest(BHEAD newterm,m) && ( AN.UsedOtherFind || FindOnce(BHEAD newterm,m) ) ) { Substitute(BHEAD newterm,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } ClearWild(BHEAD0); RetVal = 1; } else RetVal = 0; break; case SUBMULTI : RetVal = FindMulti(BHEAD term,m); break; case SUBVECTOR : RetVal = 0; for ( i = 0; i < *term; i++ ) ww[i] = term[i]; while ( ( power = FindAll(BHEAD ww,m,AR.Cnumlhs,ifcode) ) != 0 ) { RetVal += power; } break; case SUBSELECT : ifcode += IDHEAD; ifcode += ifcode[1]; ifcode += *ifcode; AN.UseFindOnly = 1; AN.ForFindOnly = ifcode; if ( FindRest(BHEAD term,m) && ( AN.UsedOtherFind || FindOnly(BHEAD term,m) ) ) RetVal = 1; else RetVal = 0; break; default : RetVal = 0; break; } AT.WorkPointer = AN.RepFunList; cbuf[AT.ebufnum].numrhs = topje; return(RetVal); } /* #] HowMany : #[ DoubleIfBuffers : */ void DoubleIfBuffers(void) { int newmax, i; WORD *newsumcheck; LONG *newheap, *newifcount; if ( AC.MaxIf == 0 ) newmax = 10; else newmax = 2*AC.MaxIf; newheap = (LONG *)Malloc1(sizeof(LONG)*(newmax+1),"IfHeap"); newsumcheck = (WORD *)Malloc1(sizeof(WORD)*(newmax+1),"IfSumCheck"); newifcount = (LONG *)Malloc1(sizeof(LONG)*(newmax+1),"IfCount"); if ( AC.MaxIf ) { for ( i = 0; i < AC.MaxIf; i++ ) { newheap[i] = AC.IfHeap[i]; newsumcheck[i] = AC.IfSumCheck[i]; newifcount[i] = AC.IfCount[i]; } AC.IfStack = (AC.IfStack-AC.IfHeap) + newheap; M_free(AC.IfHeap,"AC.IfHeap"); M_free(AC.IfCount,"AC.IfCount"); M_free(AC.IfSumCheck,"AC.IfSumCheck"); } else { AC.IfStack = newheap; } AC.IfHeap = newheap; AC.IfSumCheck = newsumcheck; AC.IfCount = newifcount; AC.MaxIf = newmax; } /* #] DoubleIfBuffers : #] If statement : #[ Switch statement : #[ DoSwitch : */ int DoSwitch(PHEAD WORD *term, WORD *lhs) { /* For the moment we ignore the compiler buffer problems. */ WORD numdollar = lhs[2]; WORD ncase = DolToNumber(BHEAD numdollar); SWITCHTABLE *swtab = FindCase(lhs[3],ncase); return(Generator(BHEAD term,swtab->value)); } /* #] DoSwitch : #[ DoEndSwitch : */ int DoEndSwitch(PHEAD WORD *term, WORD *lhs) { SWITCH *sw = AC.SwitchArray+lhs[2]; return(Generator(BHEAD term,sw->endswitch.value+1)); } /* #] DoEndSwitch : #[ FindCase : */ SWITCHTABLE *FindCase(WORD nswitch, WORD ncase) { /* First find the switch table and determine how we have to search. */ SWITCH *sw = AC.SwitchArray+nswitch; WORD hi, lo, med; if ( sw->typetable == DENSETABLE ) { med = ncase - sw->caseoffset; if ( med >= sw->numcases || med < 0 ) return(&sw->defaultcase); } else { /* We need a binary search in the table. */ if ( ncase > sw->maxcase || ncase < sw->mincase ) return(&sw->defaultcase); hi = sw->numcases-1; lo = 0; for(;;) { med = (hi+lo)/2; if ( ncase == sw->table[med].ncase ) break; else if ( ncase > sw->table[med].ncase ) { lo = med+1; if ( lo > hi ) return(&sw->defaultcase); } else { hi = med-1; if ( hi < lo ) return(&sw->defaultcase); } } } return(&sw->table[med]); } /* #] FindCase : #[ DoubleSwitchBuffers : */ int DoubleSwitchBuffers(void) { int newmax, i; SWITCH *newarray; WORD *newheap; if ( AC.MaxSwitch == 0 ) newmax = 10; else newmax = 2*AC.MaxSwitch; newarray = (SWITCH *)Malloc1(sizeof(SWITCH)*(newmax+1),"SwitchArray"); newheap = (WORD *)Malloc1(sizeof(WORD)*(newmax+1),"SwitchHeap"); if ( AC.MaxSwitch ) { for ( i = 0; i < AC.MaxSwitch; i++ ) { newarray[i] = AC.SwitchArray[i]; newheap[i] = AC.SwitchHeap[i]; } M_free(AC.SwitchHeap,"AC.SwitchHeap"); M_free(AC.SwitchArray,"AC.SwitchArray"); } for ( i = AC.MaxSwitch; i <= newmax; i++ ) { newarray[i].table = 0; newarray[i].tablesize = 0; newarray[i].defaultcase.ncase = 0; newarray[i].defaultcase.value = 0; newarray[i].defaultcase.compbuffer = 0; newarray[i].endswitch.ncase = 0; newarray[i].endswitch.value = 0; newarray[i].endswitch.compbuffer = 0; newarray[i].typetable = 0; newarray[i].mincase = 0; newarray[i].maxcase = 0; newarray[i].numcases = 0; newarray[i].caseoffset = 0; newarray[i].iflevel = 0; newarray[i].whilelevel = 0; newarray[i].nestingsum = 0; newheap[i] = 0; } AC.SwitchArray = newarray; AC.SwitchHeap = newheap; AC.MaxSwitch = newmax; return(0); } /* #] DoubleSwitchBuffers : #[ SwitchSplitMerge : Sorts an array of WORDs. No adding of equal objects. */ void SwitchSplitMergeRec(SWITCHTABLE *array,WORD num,SWITCHTABLE *auxarray) { WORD n1,n2,i,j,k; SWITCHTABLE *t1,*t2, t; if ( num < 2 ) return; if ( num == 2 ) { if ( array[0].ncase > array[1].ncase ) { t = array[0]; array[0] = array[1]; array[1] = t; } return; } n1 = num/2; n2 = num - n1; SwitchSplitMergeRec(array,n1,auxarray); SwitchSplitMergeRec(array+n1,n2,auxarray); if ( array[n1-1].ncase <= array[n1].ncase ) return; t1 = array; t2 = auxarray; i = n1; NCOPY(t2,t1,i); i = 0; j = n1; k = 0; while ( i < n1 && j < num ) { if ( auxarray[i].ncase <= array[j].ncase ) { array[k++] = auxarray[i++]; } else { array[k++] = array[j++]; } } while ( i < n1 ) array[k++] = auxarray[i++]; /* Remember: remnants of j are still in place! */ } void SwitchSplitMerge(SWITCHTABLE *array,WORD num) { SWITCHTABLE *auxarray = (SWITCHTABLE *)Malloc1(sizeof(SWITCHTABLE)*num/2,"SwitchSplitMerge"); SwitchSplitMergeRec(array,num,auxarray); M_free(auxarray,"SwitchSplitMerge"); } /* #] SwitchSplitMerge : #] Switch statement : */ form-5.0.1/sources/minos.h0000644000175100017510000001032715217035721011132 #ifndef __MANAGE_H__ #define __MANAGE_H__ /** @file minos.h * * Contains all needed declarations and definitions for the tablebase * low level file routines. These have been taken from the minos database * system and modified somewhat. * * !!!CAUTION!!! * Changes in this file will most likely have consequences for the recovery * mechanism (see checkpoint.c). You need to care for the code in checkpoint.c * as well and modify the code there accordingly! */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #include #include #include #include #include /* The following typedef has been moved to form3.h where all the sizes are defined for the various memory models. We want MLONG to have a more or less fixed size. In form3.h we try to fix it at 8 bytes. This should make files exchangeable between various 32-bits and 64-bits systems. At 4 bytes it might have problems with files of more than 2 Gbytes. typedef long MLONG; */ #if BITSINWORD == 32 #define NUMOBJECTS 1024 #define MAXINDEXSIZE 1000000000L #define NAMETABLESIZE 1008 #define ELEMENTSIZE 256 #elif BITSINWORD == 16 #define NUMOBJECTS 100 #define MAXINDEXSIZE 33000000L #define NAMETABLESIZE 1008 #define ELEMENTSIZE 128 #else #error Only 64-bit and 32-bit platforms are supported. #endif int minosread(FILE *f,char *buffer,MLONG size); int minoswrite(FILE *f,char *buffer,MLONG size); /* ELEMENTSIZE should make a nice number of sizeof(OBJECTS) Usually this will be much too much, but there are cases..... */ typedef struct iniinfo { /* should contains only MLONG variables or convertiniinfo should be modified */ MLONG entriesinindex; MLONG numberofindexblocks; MLONG firstindexblock; MLONG lastindexblock; MLONG numberoftables; MLONG numberofnamesblocks; MLONG firstnameblock; MLONG lastnameblock; } INIINFO; typedef struct objects { /* if any changes, convertblock should be adapted too!!!! */ MLONG position; /* position of RHS= */ MLONG size; /* size on disk (could be compressed) */ MLONG date; /* Time stamp */ MLONG tablenumber; /* Number of table. Refers to name in special index */ MLONG uncompressed; /* uncompressed size if compressed. If not: 0 */ MLONG spare1; MLONG spare2; MLONG spare3; char element[ELEMENTSIZE]; /* table element in character form */ } OBJECTS; typedef struct indexblock { MLONG flags; MLONG previousblock; MLONG position; OBJECTS objects[NUMOBJECTS]; } INDEXBLOCK; typedef struct nameblock { MLONG previousblock; MLONG position; char names[NAMETABLESIZE]; } NAMESBLOCK; typedef struct dbase { INIINFO info; MLONG mode; MLONG tablenamessize; MLONG topnumber; MLONG tablenamefill; MLONG rwmode; INDEXBLOCK **iblocks; NAMESBLOCK **nblocks; FILE *handle; char *name; char *fullname; char *tablenames; } DBASE; /* typedef int (*SFUN)(char *); typedef struct compile { char *keyword; SFUN func; } MCFUNCTION; */ #define TODISK 0 #define FROMDISK 1 #define MDIRTYFLAG 1 #define MCLEANFLAG (~MDIRTYFLAG) #define INANDOUT 0 #define INPUTONLY 1 #define OUTPUTONLY 2 #define NOCOMPRESS 4 extern int withoutflush; #endif form-5.0.1/sources/form3.h0000644000175100017510000002477015217035721011042 /** @file form3.h * * Contains critical defines for the compilation process * Also contains the inclusion of all necessary header files. * There are also some system dependencies concerning file functions. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #ifndef __FORM3H__ #define __FORM3H__ #ifdef HAVE_CONFIG_H #ifndef CONFIG_H_INCLUDED #define CONFIG_H_INCLUDED #include #endif #else /* HAVE_CONFIG_H */ #define MAJORVERSION 5 #define MINORVERSION 0 #define PATCHVERSION 1 #ifdef __DATE__ #define PRODUCTIONDATE __DATE__ #else #define PRODUCTIONDATE "24-jun-2026" #endif #undef BETAVERSION /*#define BETAVERSION*/ #ifdef LINUX32 #define UNIX #define LINUX #define _FILE_OFFSET_BITS 64 #define WITHZLIB #define WITHGMP #define WITHPOSIXCLOCK #endif #ifdef LINUX64 #define UNIX #define LINUX #define WITHZLIB #define WITHGMP #define WITHPOSIXCLOCK #define WITHFLOAT #endif #ifdef APPLE32 #define UNIX #define _FILE_OFFSET_BITS 64 #define WITHZLIB #endif #ifdef APPLE64 #define UNIX #define WITHZLIB #define WITHGMP #define WITHPOSIXCLOCK #define WITHFLOAT #define HAVE_UNORDERED_MAP #define HAVE_UNORDERED_SET #endif #ifdef CYGWIN32 #define UNIX #endif #ifdef _MSC_VER #define WINDOWS #define _CRT_SECURE_NO_WARNINGS #endif /* * We must not define WITHPOSIXCLOCK in compiling the sequential FORM or ParFORM. */ #if !defined(WITHPTHREADS) && defined(WITHPOSIXCLOCK) #undef WITHPOSIXCLOCK #endif #if !defined(__cplusplus) && !defined(inline) #if (defined(__STDC_VERSION__) && __STDC_VERSION__ >= 199901L) || (defined(__GNUC__) && !defined(__STRICT_ANSI__)) /* "inline" is available. */ #elif defined(__GNUC__) /* GNU C compiler has "__inline__". */ #define inline __inline__ #elif defined(_MSC_VER) /* Microsoft C compiler has "__inline". */ #define inline __inline #else /* Inline functions may be not supported. Define "inline" to be empty. */ #define inline #endif #endif #endif /* HAVE_CONFIG_H */ /* Workaround for MSVC. */ #if defined(_MSC_VER) /* * Old versions of MSVC didn't support C99 function `snprintf`, which is used * in poly.cc. On the other hand, macroizing `snprintf` gives a fatal error * with MSVC >= 2015. */ #if _MSC_VER < 1900 #define snprintf _snprintf #endif #endif /* * Translate our dialect "DEBUGGING" to the standard "NDEBUG". */ #ifdef DEBUGGING #ifdef NDEBUG #undef NDEBUG #endif #else #ifndef NDEBUG #define NDEBUG #endif #endif /* * STATIC_ASSERT(condition) will fail to be compiled if the given * condition is false. */ /* #define STATIC_ASSERT(condition) */ #define STATIC_ASSERT(condition) STATIC_ASSERT__1(condition,__LINE__) #define STATIC_ASSERT__1(X,L) STATIC_ASSERT__2(X,L) #define STATIC_ASSERT__2(X,L) STATIC_ASSERT__3(X,L) #define STATIC_ASSERT__3(X,L) \ typedef char static_assertion_failed_##L[(!!(X))*2-1] /* * UNIX or WINDOWS must be defined. */ #if defined(UNIX) #define mBSD #define ANSI #elif defined(WINDOWS) #define ANSI #define WIN32_LEAN_AND_MEAN #include #include #include /* Undefine/rename conflicted symbols. */ #undef MAXLONG /* WinNT.h */ #define WORD FORM_WORD /* WinDef.h */ #define LONG FORM_LONG /* WinNT.h */ #define ULONG FORM_ULONG /* WinDef.h */ #define BOOL FORM_BOOL /* WinDef.h */ #undef CreateFile /* WinBase.h */ #undef CopyFile /* WinBase.h */ #define OpenFile FORM_OpenFile /* WinBase.h */ #define ReOpenFile FORM_ReOpenFile /* WinBase.h */ #define ReadFile FORM_ReadFile /* WinBase.h */ #define WriteFile FORM_WriteFile /* WinBase.h */ #define DeleteObject FORM_DeleteObject /* WinGDI.h */ #else #error UNIX or WINDOWS must be defined! #endif #include #if UINTPTR_MAX == UINT64_MAX typedef int32_t WORD; typedef int64_t LONG; typedef uint32_t UWORD; typedef uint64_t ULONG; #define BITSINWORD 32 #define BITSINLONG 64 #define WORD_MIN_VALUE INT32_MIN #define WORD_MAX_VALUE INT32_MAX #define LONG_MIN_VALUE INT64_MIN #define LONG_MAX_VALUE INT64_MAX #elif UINTPTR_MAX == UINT32_MAX typedef int16_t WORD; typedef int32_t LONG; typedef uint16_t UWORD; typedef uint32_t ULONG; #define BITSINWORD 16 #define BITSINLONG 32 #define WORD_MIN_VALUE INT16_MIN #define WORD_MAX_VALUE INT16_MAX #define LONG_MIN_VALUE INT32_MIN #define LONG_MAX_VALUE INT32_MAX #else #error Can not detect if this is a 32-bit or 64-bit platform. #endif STATIC_ASSERT(sizeof(WORD) * 8 == BITSINWORD); STATIC_ASSERT(sizeof(LONG) * 8 == BITSINLONG); STATIC_ASSERT(sizeof(WORD) * 2 == sizeof(LONG)); STATIC_ASSERT(sizeof(LONG) >= sizeof(int *)); STATIC_ASSERT(sizeof(LONG) >= sizeof(int *)); STATIC_ASSERT(sizeof(int *) >= sizeof(int)); STATIC_ASSERT(sizeof(int) >= sizeof(WORD)); STATIC_ASSERT(sizeof(WORD) >= sizeof(char)); STATIC_ASSERT(sizeof(char) == 1); typedef signed char SBYTE; typedef unsigned char UBYTE; typedef unsigned int UINT; typedef ULONG RLONG; /* Used in reken.c. */ typedef int64_t MLONG; /* See commentary in minos.h. */ /* * NOTE: we don't use the standard _Bool (or C++ bool) because its size is * implementation-dependent. */ typedef char BOOL; /* E.g. in 32-bits */ #define TOPBITONLY ((ULONG)1 << (BITSINWORD - 1)) /* 0x00008000UL */ #define TOPLONGBITONLY ((ULONG)1 << (BITSINLONG - 1)) /* 0x80000000UL */ #define SPECMASK ((UWORD)1 << (BITSINWORD - 1)) /* 0x8000U */ #define WILDMASK ((UWORD)1 << (BITSINWORD - 2)) /* 0x4000U */ #define WORDMASK ((ULONG)FULLMAX - 1) /* 0x0000FFFFUL */ #define AWORDMASK (WORDMASK << BITSINWORD) /* 0xFFFF0000UL */ #define FULLMAX ((LONG)1 << BITSINWORD) /* 0x00010000L */ #define MAXPOSITIVE ((LONG)(TOPBITONLY - 1)) /* 0x00007FFFL */ #define MAXLONG ((LONG)(TOPLONGBITONLY - 1)) /* 0x7FFFFFFFL */ #define MAXPOSITIVE2 (MAXPOSITIVE / 2) /* 0x00003FFFL */ #define MAXPOSITIVE4 (MAXPOSITIVE / 4) /* 0x00001FFFL */ /* * form_alignof(type) returns the number of bytes used in the alignment of * the type. */ #if !defined(form_alignof) #if defined(__GNUC__) /* GNU C compiler has "__alignof__". */ #define form_alignof(type) __alignof__(type) #elif defined(_MSC_VER) /* Microsoft C compiler has "__alignof". */ #define form_alignof(type) __alignof(type) #elif !defined(__cplusplus) /* Generic case in C. */ #include #define form_alignof(type) offsetof(struct { char c_; type x_; }, x_) #else /* Generic case in C++, at least works with a POD struct. */ #include namespace alignof_impl_ { template struct calc { struct X { char c_; T x_; }; enum { value = offsetof(X, x_) }; }; } #define form_alignof(type) alignof_impl_::calc::value #endif #endif /* #define WITHPCOUNTER #define DEBUGGINGLOCKS #define WITHSTATS */ #define WITHSORTBOTS #include #include #include #include #include #include #include #ifdef WINDOWS #include "fwin.h" #endif #ifdef UNIX #include #include #include #include "unix.h" #endif #ifdef WITHZLIB #ifdef WITHZSTD #include #else #include #endif #endif #ifdef WITHPTHREADS #include #endif /* PARALLELCODE indicates code that is common for TFORM and ParFORM but should not be there for sequential FORM. */ #if defined(WITHMPI) || defined(WITHPTHREADS) #define PARALLELCODE #endif #include "ftypes.h" #include "fsizes.h" #include "minos.h" #include "structs.h" #include "declare.h" #include "variable.h" STATIC_ASSERT(sizeof(off_t) >= sizeof(LONG)); /* * The interface to file routines for UNIX or non-UNIX (Windows). */ #ifdef UNIX #define UFILES typedef struct FiLeS { int descriptor; } FILES; extern FILES *Uopen(char *,char *); extern int Uclose(FILES *); extern size_t Uread(char *,size_t,size_t,FILES *); extern size_t Uwrite(char *,size_t,size_t,FILES *); extern int Useek(FILES *,off_t,int); extern off_t Utell(FILES *); extern void Uflush(FILES *); extern int Ugetpos(FILES *,fpos_t *); extern int Usetpos(FILES *,fpos_t *); extern void Usetbuf(FILES *,char *); #define Usync(f) fsync(f->descriptor) #define Utruncate(f) { \ if ( ftruncate(f->descriptor, 0) ) { \ MLOCK(ErrorMessageLock); \ MesPrint("Utruncate failed"); \ MUNLOCK(ErrorMessageLock); \ /* Calling Terminate() here may cause an infinite loop due to CleanUpSort(). */ \ /* Terminate(-1); */ \ } \ } extern FILES *Ustdout; #define MAX_OPEN_FILES getdtablesize() #define GetPID() ((LONG)getpid()) #else /* UNIX */ #define FILES FILE #define Uopen(x,y) fopen(x,y) #define Uflush(x) fflush(x) #define Uclose(x) fclose(x) #define Uread(x,y,z,u) fread(x,y,z,u) #define Uwrite(x,y,z,u) fwrite(x,y,z,u) #define Usetbuf(x,y) setbuf(x,y) #define Useek(x,y,z) fseek(x,y,z) #define Utell(x) ftell(x) #define Ugetpos(x,y) fgetpos(x,y) #define Usetpos(x,y) fsetpos(x,y) #define Usync(x) fflush(x) #define Utruncate(x) _chsize(_fileno(x),0) #define Ustdout stdout #define MAX_OPEN_FILES FOPEN_MAX #define bzero(b,len) (memset((b), 0, (len)), (void)0) #define GetPID() ((LONG)GetCurrentProcessId()) #endif /* UNIX */ /* * Some system may implement the POSIX "environ" variable as a macro, e.g., * https://github.com/mingw-w64/mingw-w64/blob/v10.0.0/mingw-w64-headers/crt/stdlib.h#L704 * which breaks the definition of DoShattering() in diagrams.c that uses * "environ" as a formal parameter. Because FORM doesn't use the POSIX "environ" * or its variant anyway, we can just undefine it. */ #ifdef environ #undef environ #endif #ifdef WITHMPI #include "parallel.h" #endif #endif /* __FORM3H__ */ form-5.0.1/sources/structs.h0000644000175100017510000031421615217035721011520 /** @file structs.h * * Contains definitions for global structs. * * !!!CAUTION!!! * Changes in this file will most likely have consequences for the recovery * mechanism (see checkpoint.c). You need to care for the code in checkpoint.c * as well and modify the code there accordingly! * * The marker [D] is used in comments in this file to mark pointers to which * dynamically allocated memory is assigned by a call to malloc() during * runtime (in contrast to pointers that point into already allocated memory). * This information is especially helpful if one needs to know which pointers * need to be freed (cf. checkpoint.c). */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ #ifndef __STRUCTS__ #define __STRUCTS__ #ifdef _MSC_VER #include /* off_t */ #endif /* #[ sav&store : */ /** * */ typedef struct PoSiTiOn { off_t p1; } POSITION; /* Next are the index structs for stored and saved expressions */ /** * Defines the structure of the file header for store-files and save-files. * * The first 8 bytes serve as a unique mark to identity save-files that * contain such a header. Older versions of FORM don't have this header and * will write the POSITION of the next file index (struct FiLeInDeX) here, * which is always different from this pattern. * * It is always 512 bytes long. */ typedef struct { UBYTE headermark[8]; /**< Pattern for header identification. Old versions of FORM have a maximum sizeof(POSITION) of 8 */ UBYTE lenWORD; /**< Number of bytes for WORD */ UBYTE lenLONG; /**< Number of bytes for LONG */ UBYTE lenPOS; /**< Number of bytes for POSITION */ UBYTE lenPOINTER; /**< Number of bytes for void * */ UBYTE endianness[16]; /**< Used to determine endianness, sizeof(int) should be <= 16 */ UBYTE sSym; /**< sizeof(struct SyMbOl) */ UBYTE sInd; /**< sizeof(struct InDeX) */ UBYTE sVec; /**< sizeof(struct VeCtOr) */ UBYTE sFun; /**< sizeof(struct FuNcTiOn) */ UBYTE maxpower[16]; /**< Maximum power, see #MAXPOWER */ UBYTE wildoffset[16]; /**< #WILDOFFSET macro */ UBYTE revision; /**< Revision number of save-file system */ UBYTE reserved[512-8-4-16-4-16-16-1]; /**< Padding to 512 bytes */ } STOREHEADER; STATIC_ASSERT(sizeof(STOREHEADER) == 512); /** * Defines the structure of an entry in a file index (see struct FiLeInDeX). * * It represents one expression in the file. */ typedef struct InDeXeNtRy { POSITION position; /**< Position of the expression itself */ POSITION length; /**< Length of the expression itself */ POSITION variables; /**< Position of the list with variables */ LONG CompressSize; /**< Size of buffer before compress */ WORD nsymbols; /**< Number of symbols in the list */ WORD nindices; /**< Number of indices in the list */ WORD nvectors; /**< Number of vectors in the list */ WORD nfunctions; /**< Number of functions in the list */ WORD size; /**< Size of variables field */ SBYTE name[MAXENAME+1]; /**< Name of expression */ } INDEXENTRY; /** * Maximum number of entries (struct InDeXeNtRy) in a file index (struct * FiLeInDeX). Number is calculated such that the size of a file index is no * more than 512 bytes. */ #define INFILEINDEX ((512-2*sizeof(POSITION))/sizeof(INDEXENTRY)) /** * Number of empty filling bytes for a file index (struct FiLeInDeX). It is * calculated such that the size of a file index is always 512 bytes. */ #define EMPTYININDEX (512-2*sizeof(POSITION)-INFILEINDEX*sizeof(INDEXENTRY)) /** * Defines the structure of a file index in store-files and save-files. * * It contains several entries (see struct InDeXeNtRy) up to a maximum of * #INFILEINDEX. * * The variable number has been made of type POSITION to avoid padding * problems with some types of computers/OS and keep system independence * of the .sav files. * * This struct is always 512 bytes long. */ typedef struct FiLeInDeX { POSITION next; /**< Position of next FILEINDEX if any */ POSITION number; /**< Number of used entries in this index */ INDEXENTRY expression[INFILEINDEX]; /**< File index entries */ SBYTE empty[EMPTYININDEX]; /**< Padding to 512 bytes */ } FILEINDEX; STATIC_ASSERT(sizeof(FILEINDEX) == 512); /** * */ typedef struct FiLeDaTa { FILEINDEX Index; POSITION Fill; POSITION Position; WORD Handle; WORD dirtyflag; } FILEDATA; /** * * Contains the pointers to an array in which a binary search will be * performed. */ typedef struct VaRrEnUm { WORD *start; /**< Start point for search. Points inbetween lo and hi */ WORD *lo; /**< Start of memory area */ WORD *hi; /**< End of memory area */ } VARRENUM; /** * * Only symb.lo gets dynamically allocated. All other pointers points into this * memory. */ typedef struct ReNuMbEr { POSITION startposition; /* First stage renumbering */ VARRENUM symb; /**< Symbols */ VARRENUM indi; /**< Indices */ VARRENUM vect; /**< Vectors */ VARRENUM func; /**< Functions */ /* Second stage renumbering */ WORD *symnum; /**< Renumbered symbols */ WORD *indnum; /**< Renumbered indices */ WORD *vecnum; /**< Renumbered vectors */ WORD *funnum; /**< Renumbered functions */ } *RENUMBER; /* #] sav&store : #[ Variables : */ /** * Much information is stored in arrays of which we can double the size * if the array proves to be too small. Such arrays are controlled by * a variable of type #LIST. The routines that expand the lists are in the * file tools.c */ typedef struct { void *lijst; /**< [D] Holds space for "maxnum" elements of size "size" each */ char *message; /**< Text for Malloc1 when allocating lijst. Set to constant string. */ int num; /**< Number of elements in lijst. */ int maxnum; /**< Maximum number of elements in lijst. */ int size; /**< Size of one element in lijst. */ int numglobal; /**< Marker for position when .global is executed. */ int numtemp; /**< At the moment only needed for sets and setstore. */ int numclear; /**< Only for the clear instruction. */ } LIST; /** * The KEYWORD struct defines names of commands/statements and the routine * to be called when they are encountered by the compiler or preprocessor. */ typedef struct { char *name; TFUN func; int type; int flags; } KEYWORD; /** * The KEYWORDV struct defines names of commands/statements and the variable * to be affected when they are encountered by the compiler or preprocessor. */ typedef struct { char *name; int *var; int type; int flags; } KEYWORDV; /** * The names of variables are kept in an array. Elements of type #NAMENODE * define a tree (that is kept balanced) that make it easy and fast to look for * variables. See also #NAMETREE. */ typedef struct NaMeNode { LONG name; /**< Offset into NAMETREE::namebuffer. */ WORD parent; /**< =-1 if no parent. */ WORD left; /**< =-1 if no child. */ WORD right; /**< =-1 if no child. */ WORD balance; /**< Used for the balancing of the tree. */ WORD type; /**< Type associated with the name. See @ref CompilerTypes "compiler types". */ WORD number; /**< Number of variable in #LIST's like for example C_const::SymbolList. */ } NAMENODE; /** * A struct of type #NAMETREE controls a complete (balanced) tree of names * for the compiler. The compiler maintains several of such trees and the * system has been set up in such a way that one could define more of them * if we ever want to work with local name spaces. */ typedef struct NaMeTree { NAMENODE *namenode; /**< [D] Vector of #NAMENODE's. Number of elements is #nodesize. =0 if no memory has been allocated. */ UBYTE *namebuffer; /**< [D] Buffer that holds all the name strings referred to by the NAMENODE's. Allocation size is #namesize. =0 if no memory has been allocated. */ LONG nodesize; /**< Maximum number of elements in #namenode. */ LONG nodefill; /**< Number of currently used nodes in #namenode. */ LONG namesize; /**< Allocation size of #namebuffer in bytes. */ LONG namefill; /**< Number of bytes occupied. */ LONG oldnamefill; /**< UNUSED */ LONG oldnodefill; /**< UNUSED */ LONG globalnamefill; /**< Set by .global statement to the value of #namefill. When a .store command is processed, this value will be used to reset namefill.*/ LONG globalnodefill; /**< Same usage as #globalnamefill, but for nodefill. */ LONG clearnamefill; /**< Marks the reset point used by the .clear statement. */ LONG clearnodefill; /**< Marks the reset point used by the .clear statement. */ WORD headnode; /**< Offset in #namenode of head node. =-1 if tree is empty. */ } NAMETREE; /** * The subexpressions in the compiler are kept track of in a (balanced) tree * to reduce the need for subexpressions and hence save much space in * large rhs expressions (like when we have xxxxxxx occurrences of objects * like f(x+1,x+1) in which each x+1 becomes a subexpression. * The struct that controls this tree is COMPTREE. */ typedef struct tree { int parent; /**< Index of parent */ int left; /**< Left child (if not -1) */ int right; /**< Right child (if not -1) */ int value; /**< The object to be sorted and searched */ int blnce; /**< Balance factor */ int usage; /**< Number of uses in some types of trees */ } COMPTREE; /** * */ typedef struct MiNmAx { WORD mini; /**< Minimum value */ WORD maxi; /**< Maximum value */ WORD size; /**< Value of one unit in this position. */ } MINMAX; /** * */ typedef struct BrAcKeTiNdEx { /* For indexing brackets in local expressions */ POSITION start; /* Place where bracket starts - start of expr */ POSITION next; /* Place of next indexed bracket in expr */ LONG bracket; /* Offset of position in bracketbuffer */ LONG termsinbracket; } BRACKETINDEX; /** * */ typedef struct BrAcKeTiNfO { BRACKETINDEX *indexbuffer; /**< [D] */ WORD *bracketbuffer; /**< [D] */ LONG bracketbuffersize; LONG indexbuffersize; LONG bracketfill; LONG indexfill; WORD SortType; /**< The sorting criterium used (like POWERFIRST etc) */ } BRACKETINFO; /** * * buffers, mm, flags, and prototype are always dynamically allocated, * tablepointers only if needed (=0 if unallocated), * boomlijst and argtail only for sparse tables. * * Allocation is done for both the normal and the stub instance (spare), * except for prototype and argtail which share memory. */ typedef struct TaBlEs { WORD *tablepointers; /**< [D] Start in tablepointers table. */ #ifdef WITHPTHREADS WORD **prototype; /**< [D] The wildcard prototyping for arguments */ WORD **pattern; /**< The pattern with which to match the arguments */ #else WORD *prototype; /**< [D] The wildcard prototyping for arguments */ WORD *pattern; /**< The pattern with which to match the arguments */ #endif MINMAX *mm; /**< [D] Array bounds, dimension by dimension. # elements = numind. */ WORD *flags; /**< [D] Is element in use ? etc. # elements = numind. */ COMPTREE *boomlijst; /**< [D] Tree for searching in sparse tables */ UBYTE *argtail; /**< [D] The arguments in characters. Starts for tablebase with parenthesis to indicate tail */ struct TaBlEs *spare; /**< [D] For tablebase. Alternatingly stubs and real */ WORD *buffers; /**< [D] When we use more than one compiler buffer. */ LONG totind; /**< Total number requested */ LONG reserved; /**< Total reservation in tablepointers for sparse */ LONG defined; /**< Number of table elements that are defined */ LONG mdefined; /**< Same as defined but after .global */ int prototypeSize; /**< Size of allocated memory for prototype in bytes. */ int numind; /**< Number of array indices */ int bounds; /**< Array bounds check on/off. */ int strict; /**< >0: all must be defined. <0: undefined not substitute */ int sparse; /**< > 0 --> sparse table */ int numtree; /**< For the tree for sparse tables */ int rootnum; /**< For the tree for sparse tables */ int MaxTreeSize; /**< For the tree for sparse tables */ WORD bufnum; /**< Each table potentially its own buffer */ WORD bufferssize; /**< When we use more than one compiler buffer */ WORD buffersfill; /**< When we use more than one compiler buffer */ WORD tablenum; /**< For testing of tableuse */ WORD mode; /**< 0: normal, 1: stub */ WORD numdummies; /**< */ } *TABLES; /** * */ typedef struct ExPrEsSiOn { POSITION onfile; POSITION prototype; POSITION size; RENUMBER renum; /* For Renumbering of global stored expressions */ BRACKETINFO *bracketinfo; BRACKETINFO *newbracketinfo; WORD *renumlists; /**< Allocated only for threaded version if variables exist, else points to AN.dummyrenumlist */ WORD *inmem; /* If in memory like e.g. a polynomial */ LONG counter; LONG name; WORD hidelevel; WORD vflags; /* Various flags */ WORD printflag; WORD status; WORD replace; WORD node; WORD whichbuffer; WORD namesize; WORD compression; WORD numdummies; WORD numfactors; WORD sizeprototype; WORD uflags; /* User flags */ #ifdef PARALLELCODE WORD partodo; /* Whether to be done in parallel mode */ #endif } *EXPRESSIONS; /** * */ typedef struct SyMbOl { /* Don't change unless altering .sav too */ LONG name; /* Location in names buffer */ WORD minpower; /* Minimum power admissible */ WORD maxpower; /* Maximum power admissible */ WORD complex; /* Properties wrt complex conjugation */ WORD number; /* Number when stored in file */ WORD flags; /* Used to indicate usage when storing */ WORD node; WORD namesize; WORD dimension; /* For dimensionality checks */ #if BITSINWORD == 32 UBYTE d_u_m_m_y[8]; /* Padding for sav compatibility */ #elif BITSINWORD == 16 UBYTE d_u_m_m_y[4]; /* Padding for sav compatibility */ #endif } *SYMBOLS; #if BITSINWORD == 32 STATIC_ASSERT(sizeof(struct SyMbOl) == 48); #elif BITSINWORD == 16 STATIC_ASSERT(sizeof(struct SyMbOl) == 24); #endif /** * */ typedef struct InDeX { /* Don't change unless altering .sav too */ LONG name; /* Location in names buffer */ WORD type; /* Regular or dummy */ WORD dimension; /* Value of d_(n,n) or -number of symbol */ WORD number; /* Number when stored in file */ WORD flags; /* Used to indicate usage when storing */ WORD nmin4; /* Used for n-4 if dimension < 0 */ WORD node; WORD namesize; } *INDICES; #if BITSINWORD == 32 STATIC_ASSERT(sizeof(struct InDeX) == 40); #elif BITSINWORD == 16 STATIC_ASSERT(sizeof(struct InDeX) == 20); #endif /** * */ typedef struct VeCtOr { /* Don't change unless altering .sav too */ LONG name; /* Location in names buffer */ WORD complex; /* Properties under complex conjugation */ WORD number; /* Number when stored in file */ WORD flags; /* Used to indicate usage when storing */ WORD node; WORD namesize; WORD dimension; /* For dimensionality checks */ #if BITSINWORD == 32 UBYTE d_u_m_m_y[8]; /* Padding for sav compatibility */ #elif BITSINWORD == 16 UBYTE d_u_m_m_y[4]; /* Padding for sav compatibility */ #endif } *VECTORS; #if BITSINWORD == 32 STATIC_ASSERT(sizeof(struct VeCtOr) == 40); #elif BITSINWORD == 16 STATIC_ASSERT(sizeof(struct VeCtOr) == 20); #endif /** * Contains all information about a function. Also used for tables. * It is used in the #LIST elements of #AC. */ typedef struct FuNcTiOn { /* Don't change unless altering .sav too */ TABLES tabl; /**< Used if redefined as table. != 0 if function is a table */ LONG symminfo; /**< Info regarding symm properties offset in buffer */ LONG name; /**< Location in namebuffer of #NAMETREE */ WORD commute; /**< Commutation properties */ WORD complex; /**< Properties under complex conjugation */ WORD number; /**< Number when stored in file */ WORD flags; /**< Used to indicate usage when storing */ WORD spec; /**< Regular, Tensor, etc. See @ref FunSpecs. */ WORD symmetric; /**< > 0 if symmetric properties */ WORD node; /**< Location in namenode of #NAMETREE */ WORD namesize; /**< Length of the name */ WORD dimension; /* For dimensionality checks */ WORD maxnumargs; WORD minnumargs; } *FUNCTIONS; #if BITSINWORD == 32 STATIC_ASSERT(sizeof(struct FuNcTiOn) == 72); #elif BITSINWORD == 16 STATIC_ASSERT(sizeof(struct FuNcTiOn) == 36); #endif /** * */ typedef struct SeTs { LONG name; /* Location in names buffer */ WORD type; /* Symbol, vector, index or function */ WORD first; /* First element in setstore */ WORD last; /* Last element in setstore (excluding) */ WORD node; WORD namesize; WORD dimension; /* For dimensionality checks */ WORD flags; /* Like: ordered */ } *SETS; /** * */ typedef struct DuBiOuS { /* Undeclared objects. Just for compiler. */ LONG name; /* Location in names buffer */ WORD node; WORD dummy; } *DUBIOUSV; typedef struct FaCdOlLaR { WORD *where; /* A pointer(!) to the content */ LONG size; WORD type; /* Type can be DOLNUMBER or DOLTERMS */ WORD value; /* in case it is a (short) number */ } FACDOLLAR; typedef struct DoLlArS { WORD *where; /* A pointer(!) to the object */ FACDOLLAR *factors; /* an array of factors. nfactors elements */ #ifdef WITHPTHREADS pthread_mutex_t pthreadslock; #endif LONG size; /* The number of words */ LONG name; WORD type; WORD node; WORD index; WORD zero; WORD numdummies; WORD nfactors; } *DOLLARS; /** * */ typedef struct MoDoPtDoLlArS { #ifdef WITHPTHREADS DOLLARS dstruct; /* If local,min,max dollar: list of DOLLARS for each thread */ #endif WORD number; WORD type; } MODOPTDOLLAR; /** * */ typedef struct fixedset { char *name; char *description; int type; int dimension; } FIXEDSET; /** * */ typedef struct TaBlEbAsEsUbInDeX { POSITION where; LONG size; } TABLEBASESUBINDEX; /** * */ typedef struct TaBlEbAsE { POSITION fillpoint; POSITION current; UBYTE *name; int *tablenumbers; /* Number of each table */ TABLEBASESUBINDEX *subindex; /* For each table */ int numtables; } TABLEBASE; /** * The struct FUN_INFO is used for information about functions in the file * smart.c which is supposed to intelligently look for patterns in * complicated wildcard situations involving symmetric functions. */ typedef struct { WORD *location; int numargs; int numfunnies; int numwildcards; int symmet; int tensor; int commute; } FUN_INFO; typedef struct PaRtIcLe { WORD number; /* Number of the function */ WORD spin; /* +/- dimension of SU(2) representation */ WORD mass; /* Number of symbol or 0 */ WORD type; /* -1: anti particle, 1: particle, 0: own antiparticle */ } PARTICLE; typedef struct VeRtEx { PARTICLE particles[MAXPARTICLES]; WORD couplings[2*MAXCOUPLINGS]; WORD nparticles; WORD ncouplings; WORD type; WORD error; WORD externonly; WORD spare; } VERTEX; typedef struct MoDeL { VERTEX **vertices; WORD *couplings; UBYTE *name; void *grccmodel; WORD legcouple[MAXLEGS+2]; WORD nparticles; WORD nvertices; WORD invertices; WORD sizevertices; WORD sizecouplings; WORD ncouplings; WORD error; WORD dummy; } MODEL; /* * The struct NAMESPACE is used for the namespace info. It is a * doubly linked list of nested namespaces. */ typedef struct NaMeSpAcE { struct NaMeSpAcE *previous; struct NaMeSpAcE *next; NAMETREE *usenames; UBYTE *name; } NAMESPACE; /* #] Variables : #[ Files : */ /** * The type FILEHANDLE is the struct that controls all relevant information * of a file, whether it is open or not. The file may even not yet exist. * There is a system of caches (PObuffer) and as long as the information * to be written still fits inside the cache the file may never be * created. There are variables that can store information about different * types of files, like scratch files or sort files. * Depending on what is available in the system we may also have information * about gzip compression (currently sort file only) or locks (TFORM). */ typedef struct FiLe { POSITION POposition; /* File position */ POSITION filesize; /* Because SEEK_END is unsafe on IBM */ WORD *PObuffer; /* Address of the intermediate buffer */ WORD *POstop; /* End of the buffer */ WORD *POfill; /* Fill position of the buffer */ WORD *POfull; /* Full buffer when only cached */ #ifdef WITHPTHREADS WORD *wPObuffer; /* Address of the intermediate worker buffer */ WORD *wPOstop; /* End of the worker buffer */ WORD *wPOfill; /* Fill position of the worker buffer */ WORD *wPOfull; /* Full buffer when only worker cached */ #endif char *name; /* name of the file */ #ifdef WITHZLIB z_streamp zsp; /* The pointer to the stream struct for gzip */ Bytef *ziobuffer; /* The output buffer for compression */ #endif ULONG numblocks; /* Number of blocks in file */ ULONG inbuffer; /* Block in the buffer */ LONG POsize; /* size of the buffer */ #ifdef WITHZLIB LONG ziosize; /* size of the zoutbuffer */ #endif #ifdef WITHPTHREADS LONG wPOsize; /* size of the worker buffer */ pthread_mutex_t pthreadslock; #endif int handle; /**< Our own handle. Equal -1 if no file exists. */ int active; /* File is open or closed. Not used. */ } FILEHANDLE; /** * Input is read from 'streams' which are represented by objects of type * STREAM. A stream can be a file, a do-loop, a procedure, the string value * of a preprocessor variable ..... * When a new stream is opened we have to keep information about where * to fall back in the parent stream to allow this to happen even in the * middle of reading names etc as would be the case with a`i'b */ typedef struct StreaM { off_t fileposition; off_t linenumber; off_t prevline; UBYTE *buffer; /**< [D] Size in buffersize */ UBYTE *pointer; /**< pointer into buffer memory */ UBYTE *top; /**< pointer into buffer memory */ UBYTE *FoldName; /**< [D] */ UBYTE *name; /**< [D] */ UBYTE *pname; /**< for DOLLARSTREAM and PREVARSTREAM it points always to name, else it is undefined */ LONG buffersize; LONG bufferposition; LONG inbuffer; int previous; int handle; int type; int prevars; int previousNoShowInput; int eqnum; int afterwards; int olddelay; int oldnoshowinput; UBYTE isnextchar; UBYTE nextchar[2]; UBYTE reserved; } STREAM; typedef struct SpecTatoR { POSITION position; /* The place where we will be writing */ POSITION readpos; /* The place from which we read */ FILEHANDLE *fh; char *name; /* We identify the spectator by the name of the expression */ WORD exprnumber; /* During running we use the number. */ WORD flags; /* local, global? */ } SPECTATOR; /* #] Files : #[ Traces : */ /** * The struct TRACES keeps track of the progress during the expansion * of a 4-dimensional trace. Each time a term gets generated the expansion * tree continues in the next statement. When it returns it has to know * where to continue. The 4-dimensional traces are more complicated * than the n-dimensional traces (see TRACEN) because of the extra tricks * that can be used. They are responsible for the shorter final expressions. */ typedef struct TrAcEs { /* For computing 4 dimensional traces */ WORD *accu; /* NUMBER * 2 */ WORD *accup; WORD *termp; WORD *perm; /* number */ WORD *inlist; /* number */ WORD *nt3; /* number/2 */ WORD *nt4; /* number/2 */ WORD *j3; /* number*2 */ WORD *j4; /* number*2 */ WORD *e3; /* number*2 */ WORD *e4; /* number */ WORD *eers; /* number/2 */ WORD *mepf; /* number/2 */ WORD *mdel; /* number/2 */ WORD *pepf; /* number*2 */ WORD *pdel; /* number*3/2 */ WORD sgn; WORD stap; WORD step1,kstep,mdum; WORD gamm,ad,a3,a4,lc3,lc4; WORD sign1,sign2,gamma5,num,level,factor,allsign; WORD finalstep; } TRACES; /** * The struct TRACEN keeps track of the progress during the expansion * of a 4-dimensional trace. Each time a term gets generated the expansion * tree continues in the next statement. When it returns it has to know * where to continue. */ typedef struct TrAcEn { /* For computing n dimensional traces */ WORD *accu; /* NUMBER */ WORD *accup; WORD *termp; WORD *perm; /* number */ WORD *inlist; /* number */ WORD sgn,num,level,factor,allsign; } *TRACEN; /* #] Traces : #[ Preprocessor : */ /** * An element of the type PREVAR is needed for each preprocessor variable. */ typedef struct pReVaR { UBYTE *name; /**< allocated */ UBYTE *value; /**< points into memory of name */ UBYTE *argnames; /**< names of arguments, zero separated. points into memory of name */ int nargs; /**< 0 = regular, >= 1: number of macro arguments. total number */ int wildarg; /**< The number of a potential ?var. If none: 0. wildarg= 0 we have to get the value from a dollar */ WORD lastdollar; /* When >= 0 we have to get the value from a dollar */ WORD incdollar; /* When >= 0 we have to get the value from a dollar */ WORD NumPreTypes; WORD PreIfLevel; WORD PreSwitchLevel; } DOLOOP; /** * The struct bit_field is used by set_in, set_set, set_del and set_sub. * They in turn are used in pre.c to toggle bits that indicate whether * a character can be used as a separator of function arguments. * This facility is used in the communication with external channels. */ struct bit_field { /* Assume 8 bits per byte */ UBYTE bit_0 : 1; UBYTE bit_1 : 1; UBYTE bit_2 : 1; UBYTE bit_3 : 1; UBYTE bit_4 : 1; UBYTE bit_5 : 1; UBYTE bit_6 : 1; UBYTE bit_7 : 1; /* UINT bit_0 : 1; UINT bit_1 : 1; UINT bit_2 : 1; UINT bit_3 : 1; UINT bit_4 : 1; UINT bit_5 : 1; UINT bit_6 : 1; UINT bit_7 : 1; */ }; /** * Used in set_in, set_set, set_del and set_sub. */ typedef struct bit_field set_of_char[32]; /** * Used in set_in, set_set, set_del and set_sub. */ typedef struct bit_field *one_byte; /** * The struct HANDLERS is used in the communication with external channels. */ typedef struct { WORD newlogonly; WORD newhandle; WORD oldhandle; WORD oldlogonly; WORD oldprinttype; WORD oldsilent; } HANDLERS; /* #] Preprocessor : #[ Varia : */ typedef int (*FINISHUFFLE)(WORD *); typedef int (*DO_UFFLE)(WORD *,WORD,WORD,WORD); #ifdef WITHPTHREADS typedef WORD (*COMPAREDUMMY)(void *,WORD *,WORD *,WORD); #else typedef WORD (*COMPAREDUMMY)(WORD *,WORD *,WORD); #endif /** * The CBUF struct is used by the compiler. It is a compiler buffer of which * since version 3.0 there can be many. */ typedef struct CbUf { WORD *Buffer; /**< [D] Size in BufferSize */ WORD *Top; /**< pointer to the end of the Buffer memory */ WORD *Pointer; /**< pointer into the Buffer memory */ WORD **lhs; /**< [D] Size in maxlhs. list of pointers into Buffer. */ WORD **rhs; /**< [D] Size in maxrhs. list of pointers into Buffer. */ LONG *CanCommu; /**< points into rhs memory behind WORD* area. */ LONG *NumTerms; /**< points into rhs memory behind CanCommu area */ WORD *numdum; /**< points into rhs memory behind NumTerms */ WORD *dimension; /**< points into rhs memory behind numdum */ COMPTREE *boomlijst; /**< [D] Number elements in MaxTreeSize */ LONG BufferSize; /**< Number of allocated WORD's in Buffer */ int numlhs; int numrhs; int maxlhs; int maxrhs; int mnumlhs; int mnumrhs; int numtree; int rootnum; int MaxTreeSize; } CBUF; /** * When we read input from text files we have to remember not only their * handle but also their name. This is needed for error messages. * Hence we call such a file a channel and reserve a struct of type * #CHANNEL to allow to lay this link. */ typedef struct ChAnNeL { char *name; /**< [D] Name of the channel */ int handle; /**< File handle */ } CHANNEL; /** * Each setup parameter has one element of the struct SETUPPARAMETERS * assigned to it. By binary search in the array of them we can then * locate the proper element by name. * We have to assume that two ints make a long and either one or two longs * make a pointer. The long before the ints and padding gives a problem * in the initialization. */ typedef struct { UBYTE *parameter; int type; int flags; // This ordering is assumed by initializer lists in many places. In this // case the struct should anyway not have additional padding between the // two int and the LONG members. LONG value; } SETUPPARAMETERS; /** * The NESTING struct is used when we enter the argument of functions and * there is the possibility that we have to change something there. * Because functions can be nested we have to keep track of all levels * of functions in case we have to move the outer layers to make room * for a larger function argument. */ typedef struct NeStInG { WORD *termsize; WORD *funsize; WORD *argsize; } *NESTING; /** * The struct of type STORECACHE is used by a caching system for reading * terms from stored expressions. Each thread should have its own system * of caches. */ typedef struct StOrEcAcHe { POSITION position; POSITION toppos; struct StOrEcAcHe *next; WORD buffer[2]; } *STORECACHE; /** * The struct PERM is used to generate all permutations when the pattern * matcher has to try to match (anti)symmetric functions. */ typedef struct PeRmUtE { WORD *objects; WORD sign; WORD n; WORD cycle[MAXMATCH]; } PERM; /** * Like struct PERM but works with pointers. */ typedef struct PeRmUtEp { WORD **objects; WORD sign; WORD n; WORD cycle[MAXMATCH]; } PERMP; /** * The struct DISTRIBUTE is used to help the pattern * matcher when matching antisymmetric tensors. */ typedef struct DiStRiBuTe { WORD *obj1; WORD *obj2; WORD *out; WORD sign; WORD n1; WORD n2; WORD n; WORD cycle[MAXMATCH]; } DISTRIBUTE; /** * The struct PARTI is used to help determining whether a partition_ * function can be replaced. */ typedef struct PaRtI { WORD *psize; /* the sizes of the partitions */ WORD *args; /* the offsets of the arguments to be partitioned */ WORD *nargs; /* argument numbers (different number = different argument) */ WORD *nfun; /* the functions into which the partitions go */ WORD numargs; /* the number of arguments to be partitioned */ WORD numpart; /* the number of partitions */ WORD where; /* offset of the function in the term */ } PARTI; /** * The struct SORTING is used to control a sort operation. * It includes a small and a large buffer and arrays for keeping track * of various stages of the (merge) sorts. * Each sort level has its own struct and different levels can have * different sizes for its arrays. * Also different threads have their own set of SORTING structs. */ typedef struct sOrT { FILEHANDLE file; /* The own sort file */ POSITION SizeInFile[3]; /* Sizes in the various files */ POSITION OldPosIn; /* Sort file fill positions */ POSITION OldPosOut; WORD *lBuffer; /* The large buffer */ WORD *lTop; /* End of the large buffer */ WORD *lFill; /* The filling point of the large buffer */ WORD *used; /* auxiliary during actual sort */ WORD *sBuffer; /* The small buffer */ WORD *sTop; /* End of the small buffer */ WORD *sTop2; /* End of the extension of the small buffer */ WORD *sHalf; /* Halfway point in the extension */ WORD *sFill; /* Filling point in the small buffer */ WORD **sPointer; /* Pointers to terms in the small buffer */ WORD **PoinFill; /* Filling point for pointers to the sm.buf */ WORD *cBuffer; /* Compress buffer (if it exists) */ WORD **Patches; /* Positions of patches in large buffer */ WORD **pStop; /* Ends of patches in the large buffer */ WORD **poina; /* auxiliary during actual sort */ WORD **poin2a; /* auxiliary during actual sort */ WORD *ktoi; /* auxiliary during actual sort */ WORD *tree; /* auxiliary during actual sort */ #ifdef WITHZLIB WORD *fpcompressed; /* is output filepatch compressed? */ WORD *fpincompressed; /* is input filepatch compressed? */ z_streamp zsparray; /* the array of zstreams for decompression */ #endif POSITION *fPatches; /* Positions of output file patches */ POSITION *inPatches; /* Positions of input file patches */ POSITION *fPatchesStop; /* Positions of output file patches */ POSITION *iPatches; /* Input file patches, Points to fPatches or inPatches */ FILEHANDLE *f; /* The actual output file */ FILEHANDLE **ff; /* Handles for a staged sort */ LONG sTerms; /* Terms in small buffer */ LONG LargeSize; /* Size of large buffer (in words) */ LONG SmallSize; /* Size of small buffer (in words) */ LONG SmallEsize; /* Size of small + extension (in words) */ LONG TermsInSmall; /* Maximum number of terms in small buffer */ LONG Terms2InSmall; /* with extension for polyfuns etc. */ LONG GenTerms; /* Number of generated terms */ LONG TermsLeft; /* Number of terms still in existence */ LONG GenSpace; /* Amount of space of generated terms */ LONG SpaceLeft; /* Space needed for still existing terms */ LONG putinsize; /* Size of buffer in putin */ LONG ninterms; /* Which input term ? */ LONG verbComparisons; /* Counters for "On SortVerbose;" statistics */ LONG verbSBsortTerms; LONG verbSBsortCap; LONG verbLBsortPatches; LONG verbLBsortCap; LONG verbUnsortedSize; int MaxPatches; /* Maximum number of patches in large buffer */ int MaxFpatches; /* Maximum number of patches in one filesort */ int type; /* Main, function or sub(routine) */ int lPatch; /* Number of patches in the large buffer */ int fPatchN1; /* Number of patches in input file */ int PolyWise; /* Is there a polyfun and if so, where? */ int PolyFlag; /* */ int cBufferSize; /* Size of the compress buffer */ int maxtermsize; /* Keeps track for buffer allocations */ int newmaxtermsize; /* Auxiliary for maxtermsize */ int outputmode; /* Tells where the output is going */ int stagelevel; /* In case we have a 'staged' sort */ WORD fPatchN; /* Number of patches on file (output) */ WORD inNum; /* Number of patches on file (input) */ WORD stage4; /* Are we using stage4? */ } SORTING; #ifdef WITHPTHREADS /** * The SORTBLOCK's are used by TFORM when the master has to merge the sorted * results of each of the workers. */ typedef struct SoRtBlOcK { pthread_mutex_t *MasterBlockLock; WORD **MasterStart; WORD **MasterFill; WORD **MasterStop; LONG *BlockTerms; int MasterNumBlocks; int MasterBlock; int FillBlock; } SORTBLOCK; #endif #ifdef DEBUGGER typedef struct DeBuGgInG { int eflag; int printflag; int logfileflag; int stdoutflag; } DEBUGSTR; #endif #ifdef WITHPTHREADS /** * The THREADBUCKET struct defines one of the buckets used to pass terms * from the master to the workers in TFORM. */ typedef struct ThReAdBuCkEt { POSITION *deferbuffer; /* For Keep Brackets: remember position */ WORD *threadbuffer; /* Here are the (primary) terms */ WORD *compressbuffer; /* For keep brackets we need the compressbuffer */ LONG threadbuffersize; /* Number of words in threadbuffer */ LONG ddterms; /* Number of primary+secondary terms represented */ LONG firstterm; /* The number of the first term in the bucket */ LONG firstbracket; /* When doing complete brackets */ LONG lastbracket; /* When doing complete brackets */ pthread_mutex_t lock; /* For the load balancing phase */ int free; /* Status of the bucket */ int totnum; /* Total number of primary terms */ int usenum; /* Which is the term being used at the moment */ int busy; /* */ int type; /* Doing brackets? */ } THREADBUCKET; #endif /** * The POLYMOD struct controls one univariate polynomial of which the * coefficients have been taken modulus a (prime) number that fits inside * a variable of type WORD. The polynomial is stored as an array of * coefficients of size WORD. */ typedef struct { WORD *coefs; /* The array of coefficients */ WORD numsym; /* The number of the symbol in the polynomial */ WORD arraysize; /* The size of the allocation of coefs */ WORD polysize; /* The maximum power in the polynomial */ WORD modnum; /* The prime number of the modulus */ } POLYMOD; typedef struct { WORD *outterm; /* Used in DoShuffle/Merge/FinishShuffle system */ WORD *outfun; WORD *incoef; WORD *stop1; WORD *stop2; WORD *ststop1; WORD *ststop2; FINISHUFFLE finishuf; DO_UFFLE do_uffle; LONG combilast; WORD nincoef; WORD level; WORD thefunction; WORD option; } SHvariables; typedef struct { /* Used for computing calculational cost in optim.c */ LONG add; LONG mul; LONG div; LONG pow; } COST; typedef struct { UWORD *a; /* The number array */ UWORD *m; /* The modulus array */ WORD na; /* Size of the number */ WORD nm; /* size of the number in the modulus array */ } MODNUM; /* Struct for optimizing outputs. If changed, do not forget to change the padding information in the AO struct. */ typedef struct { union { /* we do this to allow padding */ float fval; int ival[2]; /* This should be enough */ } mctsconstant; int horner; int hornerdirection; int method; int mctstimelimit; int mctsnumexpand; int mctsnumkeep; int mctsnumrepeat; int greedytimelimit; int greedyminnum; int greedymaxperc; int printstats; int debugflags; int schemeflags; int mctsdecaymode; int saIter; /* Simulated annealing updates */ union { float fval; int ival[2]; } saMaxT; /* Maximum temperature of SA */ union { float fval; int ival[2]; } saMinT; /* Minimum temperature of SA */ int spare; } OPTIMIZE; typedef struct { WORD *code; UBYTE *nameofexpr; /* It is easier to remember an expression by name */ LONG codesize; /* We need this for the checkpoints */ WORD exprnr; /* Problem here is: we renumber them in execute.c */ WORD minvar; WORD maxvar; } OPTIMIZERESULT; typedef struct { WORD *lhs; /* Object to be replaced */ WORD *rhs; /* Depending on the type it will be UBYTE* or WORD* */ int type; int size; /* Size of the lhs */ } DICTIONARY_ELEMENT; typedef struct { DICTIONARY_ELEMENT **elements; UBYTE *name; int sizeelements; int numelements; int numbers; /* deal with numbers */ int variables; /* deal with single variables */ int characters; /* deal with special characters */ int funwith; /* deal with functions with arguments */ int gnumelements; /* if .global shrinks the dictionary */ int ranges; } DICTIONARY; typedef struct { WORD ncase; WORD value; WORD compbuffer; } SWITCHTABLE; typedef struct { SWITCHTABLE *table; SWITCHTABLE defaultcase; SWITCHTABLE endswitch; WORD typetable; WORD maxcase; WORD mincase; WORD numcases; WORD tablesize; WORD caseoffset; WORD iflevel; WORD whilelevel; WORD nestingsum; WORD padding; } SWITCH; typedef struct { WORD *term; void *currentModel; void *currentMODEL; WORD *legcouple[MAXLEGS+1]; LONG numtopo; LONG numdia; WORD diaoffset; WORD level; WORD externalset; WORD internalset; WORD numextern; WORD flags; } TERMINFO; /* Struct to hold temporary data in Normalize, so that it is not allocated on the stack each function call. The sizes of these arrays introduces a maximum complexity of terms which can be normalized. Each array is allocated dynamically, by AllocNormData, such that valgrind can detect errors if they are over-run. */ typedef struct NoRmDaTa { WORD *psym; WORD *pvec; WORD *pdot; WORD *pdel; WORD *pind; WORD **peps; WORD **pden; WORD **pcom; WORD **pnco; WORD **pcon; } NORMDATA; /* #] Varia : #[ A : #[ M : The M struct is for global settings at startup or .clear */ /** * The M_const struct is part of the global data and resides in the #ALLGLOBALS * struct #A under the name #M. * We see it used with the macro #AM as in AM.S0. * It contains global settings at startup or .clear. */ struct M_const { POSITION zeropos; /* (M) is zero */ SORTING *S0; /**< [D] The main sort buffer */ UWORD *gcmod; /**< Global setting of modulus. Uses AC.cmod's memory */ UWORD *gpowmod; /**< Global setting printing as powers. Uses AC.cmod's memory */ UBYTE *TempDir; /* (M) Path with where the temporary files go */ UBYTE *TempSortDir; /* (M) Path with where the sort files go */ UBYTE *IncDir; /* (M) Directory path for include files */ UBYTE *InputFileName; /* (M) */ UBYTE *LogFileName; /* (M) */ UBYTE *OutBuffer; /* (M) Output buffer in pre.c */ UBYTE *Path; /* (M) */ UBYTE *SetupDir; /* (M) Directory with setup file */ UBYTE *SetupFile; /* (M) Name of setup file */ UBYTE *gFortran90Kind; UBYTE *gextrasym; UBYTE *ggextrasym; UBYTE *oldnumextrasymbols; SPECTATOR *SpectatorFiles; #ifdef WITHPTHREADS pthread_rwlock_t handlelock; /* (M) */ pthread_mutex_t storefilelock; /* (M) */ pthread_mutex_t sbuflock; /* (M) Lock for writing in the AM.sbuffer */ LONG ThreadScratSize; /* (M) Size of Fscr[0/2] buffers of the workers */ LONG ThreadScratOutSize; /* (M) Size of Fscr[1] buffers of the workers */ #endif LONG MaxTer; /* (M) Maximum term size. Fixed at setup. In Bytes!!!*/ LONG CompressSize; /* (M) Size of Compress buffer */ LONG ScratSize; /* (M) Size of Fscr[] buffers */ LONG HideSize; /* (M) Size of Fscr[2] buffer */ LONG SizeStoreCache; /* (M) Size of the caches for reading global expr. */ LONG MaxStreamSize; /* (M) Maximum buffer size in reading streams */ LONG SIOsize; /* (M) Sort InputOutput buffer size */ LONG SLargeSize; /* (M) */ LONG SSmallEsize; /* (M) */ LONG SSmallSize; /* (M) */ LONG STermsInSmall; /* (M) */ LONG MaxBracketBufferSize; /* (M) Max Size for B+ or AB+ per expression */ LONG hProcessBucketSize; /* (M) */ LONG gProcessBucketSize; /* (M) */ LONG shmWinSize; /* (M) size for shared memory window used in communications */ LONG OldChildTime; /* (M) Zero time. Needed in timer. */ LONG OldSecTime; /* (M) Zero time for measuring wall clock time */ LONG OldMilliTime; /* (M) Same, but milli seconds */ LONG WorkSize; /* (M) Size of WorkSpace */ LONG gThreadBucketSize; /* (C) */ LONG ggThreadBucketSize; /* (C) */ LONG SumTime; /* Used in .clear */ LONG SpectatorSize; /* Size of the buffer in bytes */ LONG TimeLimit; /* Limit in sec to the total real time */ #ifdef WITHFLOAT LONG gDefaultPrecision; /* (M) Default precision in bits for float_ */ LONG gMaxWeight; /* (M) Maximum weight for MZV or Euler */ LONG ggDefaultPrecision; /* (M) Default precision in bits for float_ */ LONG ggMaxWeight; /* (M) Maximum weight for MZV or Euler */ #endif int FileOnlyFlag; /* (M) Writing only to file */ int Interact; /* (M) Interactive mode flag */ int MaxParLevel; /* (M) Maximum nesting of parentheses */ int OutBufSize; /* (M) size of OutBuffer */ int SMaxFpatches; /* (M) */ int SMaxPatches; /* (M) */ int StdOut; /* (M) Regular output channel */ int ginsidefirst; /* (M) Not used yet */ int gDefDim; /* (M) */ int gDefDim4; /* (M) */ int NumFixedSets; /* (M) Number of the predefined sets */ int NumFixedFunctions; /* (M) Number of built in functions */ int rbufnum; /* (M) startup compiler buffer */ int dbufnum; /* (M) dollar variables */ int sbufnum; /* (M) subterm variables */ int zbufnum; /* (M) special values */ int SkipClears; /* (M) Number of .clear to skip at start */ int gTokensWriteFlag; /* (M) */ int gfunpowers; /* (M) */ int gStatsFlag; /* (M) */ int gNamesFlag; /* (M) */ int gCodesFlag; /* (M) */ int gSortType; /* (M) */ int gproperorderflag; /* (M) */ int hparallelflag; /* (M) */ int gparallelflag; /* (M) */ int totalnumberofthreads; /* (M) */ int gSizeCommuteInSet; int gThreadStats; int ggThreadStats; int gFinalStats; int ggFinalStats; int gThreadsFlag; int ggThreadsFlag; int gThreadBalancing; int ggThreadBalancing; int gThreadSortFileSynch; int ggThreadSortFileSynch; int gProcessStats; int ggProcessStats; int gOldParallelStats; int ggOldParallelStats; int maxFlevels; /* () maximum function levels */ int resetTimeOnClear; /* (M) */ int gcNumDollars; /* () number of dollars for .clear */ int MultiRun; int gNoSpacesInNumbers; /* For very long numbers */ int ggNoSpacesInNumbers; /* For very long numbers */ int gIsFortran90; int PrintTotalSize; int fbuffersize; /* Size for the AT.fbufnum factorization caches */ int gOldFactArgFlag; int ggOldFactArgFlag; int gnumextrasym; int ggnumextrasym; int NumSpectatorFiles; /* Elements used in AM.spectatorfiles; */ int SizeForSpectatorFiles; /* Size in AM.spectatorfiles; */ int gOldGCDflag; int ggOldGCDflag; int gWTimeStatsFlag; int ggWTimeStatsFlag; int jumpratio; WORD MaxTal; /* (M) Maximum number of words in a number */ WORD IndDum; /* (M) Basis value for dummy indices */ WORD DumInd; /* (M) */ WORD WilInd; /* (M) Offset for wildcard indices */ WORD gncmod; /* (M) Global setting of modulus. size of gcmod */ WORD gnpowmod; /* (M) Global printing as powers. size gpowmod */ WORD gmodmode; /* (M) Global mode for modulus */ WORD gUnitTrace; /* (M) Global value of Tr[1] */ WORD gOutputMode; /* (M) */ WORD gOutputSpaces; /* (M) */ WORD gOutNumberType; /* (M) */ WORD gCnumpows; /* (M) */ WORD gUniTrace[4]; /* (M) */ WORD MaxWildcards; /* (M) Maximum number of wildcards */ WORD mTraceDum; /* (M) Position/Offset for generated dummies */ WORD OffsetIndex; /* (M) */ WORD OffsetVector; /* (M) */ WORD RepMax; /* (M) Max repeat levels */ WORD LogType; /* (M) Type of writing to log file */ WORD ggStatsFlag; /* (M) */ WORD gLineLength; /* (M) */ WORD qError; /* (M) Only error checking {-c option} */ WORD FortranCont; /* (M) Fortran Continuation character */ WORD HoldFlag; /* (M) Exit on termination? */ WORD Ordering[15]; /* (M) Auxiliary for ordering wildcards */ WORD silent; /* (M) Silent flag. Only results in output. */ WORD tracebackflag; /* (M) For tracing errors */ WORD expnum; /* (M) internal number of ^ function */ WORD denomnum; /* (M) internal number of / function */ WORD facnum; /* (M) internal number of fac_ function */ WORD invfacnum; /* (M) internal number of invfac_ function */ WORD sumnum; /* (M) internal number of sum_ function */ WORD sumpnum; /* (M) internal number of sump_ function */ WORD OldOrderFlag; /* (M) Flag for allowing old statement order */ WORD termfunnum; /* (M) internal number of term_ function */ WORD matchfunnum; /* (M) internal number of match_ function */ WORD countfunnum; /* (M) internal number of count_ function */ WORD gPolyFun; /* (M) global value of PolyFun */ WORD gPolyFunInv; /* (M) global value of Inverse of PolyFun */ WORD gPolyFunType; /* (M) global value of PolyFun */ WORD gPolyFunExp; WORD gPolyFunVar; WORD gPolyFunPow; WORD dollarzero; /* (M) for dollars with zero value */ WORD atstartup; /* To protect against DATE_ ending in \n */ WORD exitflag; /* (R) For the exit statement */ WORD NumStoreCaches; /* () Number of storage caches per processor */ WORD gIndentSpace; /* For indentation in output */ WORD ggIndentSpace; WORD gShortStatsMax; /**< For On FewerStatistics 10; */ WORD ggShortStatsMax; /**< For On FewerStatistics 10; */ WORD gextrasymbols; WORD ggextrasymbols; WORD zerorhs; WORD onerhs; WORD havesortdir; WORD vectorzero; /* p0_ */ WORD ClearStore; WORD BracketFactors[8]; BOOL FromStdin; /* read the input from STDIN */ BOOL IgnoreDeprecation; /* ignore deprecation warning */ }; /* #] M : #[ P : The P struct defines objects set by the preprocessor */ /** * The P_const struct is part of the global data and resides in the * ALLGLOBALS struct A under the name P * We see it used with the macro AP as in AP.InOutBuf * It contains objects that have dealings with the preprocessor. */ struct P_const { LIST DollarList; /* (R) Dollar variables. Contains pointers to contents of the variables.*/ LIST PreVarList; /* (R) List of preprocessor variables Points to contents. Can be changed */ LIST LoopList; /* (P) List of do loops */ LIST ProcList; /* (P) List of procedures */ INSIDEINFO inside; /* Information during #inside/#endinside */ NAMESPACE *firstnamespace; /* is zero when no namespace specified */ NAMESPACE *lastnamespace; /* is zero when no namespace specified */ UBYTE *fullname; /* buffer for namespace expanded names */ UBYTE **PreSwitchStrings; /* (P) The string in a switch */ UBYTE *preStart; /* (P) Preprocessor instruction buffer */ UBYTE *preStop; /* (P) end of preStart */ UBYTE *preFill; /* (P) Filling point in preStart */ UBYTE *procedureExtension; /* (P) Extension for procedure files (prc) */ UBYTE *cprocedureExtension; /* (P) Extension after .clear */ LONG *PreAssignStack; /* For nesting #$name assignments */ int *PreIfStack; /* (P) Tracks nesting of #if */ int *PreSwitchModes; /* (P) Stack of switch status */ int *PreTypes; /* (P) stack of #call, #do etc nesting */ #ifdef WITHPTHREADS pthread_mutex_t PreVarLock; /* (P) */ #endif LONG StopWatchZero; /* For `timer_' and #reset timer */ LONG InOutBuf; /* (P) Characters in the output buf in pre.c */ LONG pSize; /* (P) size of preStart */ int PreAssignFlag; /* (C) Indicates #assign -> catch dollar */ int PreContinuation; /* (C) Indicates whether the statement is new */ int PreproFlag; /* (P) Internal use to mark work on prepro instr. */ int iBufError; /* (P) Flag for errors with input buffer */ int PreOut; /* (P) Flag for #+ #- */ int PreSwitchLevel; /* (P) Nesting of #switch */ int NumPreSwitchStrings; /* (P) Size of PreSwitchStrings */ int MaxPreTypes; /* (P) Size of PreTypes */ int NumPreTypes; /* (P) Number of nesting objects in PreTypes */ int MaxPreIfLevel; /* (C) Maximum number of nested #if. Dynamic */ int PreIfLevel; /* (C) Current position if PreIfStack */ int PreInsideLevel; /* (C) #inside active? */ int DelayPrevar; /* (P) Delaying prevar substitution */ int AllowDelay; /* (P) Allow delayed prevar substitution */ int lhdollarerror; /* (R) */ int eat; /* () */ int gNumPre; /* (P) Number of preprocessor variables for .clear */ int PreDebug; /* (C) */ int OpenDictionary; int PreAssignLevel; /* For nesting #$name = ...; assignments */ int MaxPreAssignLevel; /* For nesting #$name = ...; assignments */ int fullnamesize; /* size of the fullname buffer */ WORD DebugFlag; /* (P) For debugging purposes */ WORD preError; /* (P) Blocks certain types of execution */ UBYTE ComChar; /* (P) Commentary character */ UBYTE cComChar; /* (P) Old commentary character for .clear */ }; /* #] P : #[ C : The C struct defines objects changed by the compiler */ /** * The C_const struct is part of the global data and resides in the #ALLGLOBALS * struct #A under the name #C. * We see it used with the macro #AC as in AC.exprnames. * It contains variables that involve the compiler and objects set during * compilation. */ struct C_const { set_of_char separators; /**< Separators in #call and #do */ POSITION StoreFileSize; /* () Size of store file */ NAMETREE *dollarnames; /**< [D] Names of dollar variables */ NAMETREE *exprnames; /**< [D] Names of expressions */ NAMETREE *varnames; /**< [D] Names of regular variables */ LIST ChannelList; /**< Used for the #write statement. Contains #CHANNEL */ /* Later also for write? */ LIST DubiousList; /**< List of dubious variables. Contains #DUBIOUSV. If not empty -> no execution */ LIST FunctionList; /**< List of functions and properties. Contains #FUNCTIONS */ LIST ExpressionList; /**< List of expressions, locations etc. */ LIST IndexList; /**< List of indices */ LIST SetElementList; /**< List of all elements of all sets */ LIST SetList; /**< List of the sets */ LIST SymbolList; /**< List of the symbols and their properties */ LIST VectorList; /**< List of the vectors */ LIST PotModDolList; /**< Potentially changed dollars */ LIST ModOptDolList; /**< Module Option Dollars list */ LIST TableBaseList; /**< TableBase list */ /* Compile buffer variables */ LIST cbufList; /**< List of compiler buffers */ /* Objects for auto declarations */ LIST AutoSymbolList; /* (C) */ LIST AutoIndexList; /* (C) */ LIST AutoVectorList; /* (C) */ LIST AutoFunctionList; /* (C) */ NAMETREE *autonames; /**< [D] Names in autodeclare */ LIST *Symbols; /* (C) Pointer for autodeclare. Which list is it searching. Later also for subroutines */ LIST *Indices; /* (C) id. */ LIST *Vectors; /* (C) id. */ LIST *Functions; /* (C) id. */ NAMETREE **activenames; /** (C) Pointer for AutoDeclare statement. Points either to varnames or autonames. */ STREAM *Streams; /**< [D] The input streams. */ STREAM *CurrentStream; /**< (C) The current input stream. Streams are: do loop, file, prevariable. points into Streams memory. */ SWITCH *SwitchArray; MODEL **models; WORD *SwitchHeap; LONG *termstack; /**< [D] Last term statement {offset} */ LONG *termsortstack; /**< [D] Last sort statement {offset} */ UWORD *cmod; /**< [D] Local setting of modulus. Pointer to value. */ UWORD *powmod; /**< Local setting printing as powers. Points into cmod memory */ UWORD *modpowers; /**< [D] The conversion table for mod-> powers. */ UWORD *halfmod; /* (C) half the modulus when not zero */ WORD *ProtoType; /* (C) The subexpression prototype {wildcards} */ WORD *WildC; /* (C) Filling point for wildcards. */ LONG *IfHeap; /**< [D] Keeps track of where to go in if */ LONG *IfCount; /**< [D] Keeps track of where to go in if */ LONG *IfStack; /**< Keeps track of where to go in if. Points into IfHeap-memory */ UBYTE *iBuffer; /**< [D] Compiler input buffer */ UBYTE *iPointer; /**< Running pointer in the compiler input buffer */ UBYTE *iStop; /**< Top of iBuffer */ UBYTE **LabelNames; /**< [D] List of names in label statements */ WORD *FixIndices; /**< [D] Buffer of fixed indices */ WORD *termsumcheck; /**< [D] Checking of nesting */ UBYTE *WildcardNames; /**< [D] Names of ?a variables */ int *Labels; /**< Label information for during run. Pointer into LabelNames memory. */ SBYTE *tokens; /**< [D] Array with tokens for tokenizer */ SBYTE *toptokens; /**< Top of tokens */ SBYTE *endoftokens; /**< End of the actual tokens */ WORD *tokenarglevel; /**< [D] Keeps track of function arguments */ UWORD *modinverses; /* Table for inverses of primes */ UBYTE *Fortran90Kind; /* The kind of number in Fortran 90 as in _ki */ WORD **MultiBracketBuf; /* Array of buffers for multi-level brackets */ UBYTE *extrasym; /* Array with the name for extra symbols in ToPolynomial */ WORD *doloopstack; /* To keep track of begin and end of doloops */ WORD *doloopnest; /* To keep track of nesting of doloops etc */ char *CheckpointRunAfter; /**< [D] Filename of script to be executed _before_ creating the snapshot. =0 if no script shall be executed. */ char *CheckpointRunBefore; /**< [D] Filename of script to be executed _after_ having created the snapshot. =0 if no script shall be executed.*/ WORD *IfSumCheck; /**< [D] Keeps track of if-nesting */ WORD *CommuteInSet; /* groups of noncommuting functions that can commute */ UBYTE *TestValue; /* For debugging */ #ifdef PARALLELCODE LONG *inputnumbers; /**< [D] For redefine */ WORD *pfirstnum; /**< For redefine. Points into inputnumbers memory */ #endif #ifdef WITHPTHREADS pthread_mutex_t halfmodlock; /* () Lock for adding buffer for halfmod */ #endif LONG argstack[MAXNEST]; /* (C) {contents} Stack for nesting of Argument */ LONG insidestack[MAXNEST]; /* (C) {contents} Stack for Argument or Inside. */ LONG inexprstack[MAXNEST]; /* (C) {contents} Stack for Argument or Inside. */ LONG iBufferSize; /* (C) Size of the input buffer */ LONG TransEname; /* (C) Used when a new definition overwrites an old expression. */ LONG ProcessBucketSize; /* (C) */ LONG mProcessBucketSize; /* (C) */ LONG CModule; /* (C) Counter of current module */ LONG ThreadBucketSize; /* (C) Roughly the maximum number of input terms */ LONG CheckpointStamp; /**< Timestamp of the last created snapshot (set to Timer(0)).*/ LONG CheckpointInterval; /**< Time interval in milliseconds for snapshots. =0 if snapshots shall be created at the end of _every_ module.*/ #ifdef WITHFLOAT LONG DefaultPrecision; /* (C) Default precision in bits for float_ */ LONG MaxWeight; /* (C) Maximum weight for MZV or Euler */ LONG tDefaultPrecision; /* (C) Default precision in bits for float_ */ LONG tMaxWeight; /* (C) Maximum weight for MZV or Euler */ #endif int cbufnum; /**< Current compiler buffer */ int AutoDeclareFlag; /** (C) Mode of looking for names. Set to NOAUTO (=0) or WITHAUTO (=2), cf. AutoDeclare statement */ int NoShowInput; /* (C) No listing of input as in .prc, #do */ int ShortStats; /* (C) */ int compiletype; /* (C) type of statement {DECLARATION etc} */ int firstconstindex; /* (C) flag for giving first error message */ int insidefirst; /* (C) Not used yet */ int minsidefirst; /* (?) Not used yet */ int wildflag; /* (C) Flag for marking use of wildcards */ int NumLabels; /* (C) Number of labels {in Labels} */ int MaxLabels; /* (C) Size of Labels array */ int lDefDim; /* (C) */ int lDefDim4; /* (C) */ int NumWildcardNames; /* (C) Number of ?a variables */ int WildcardBufferSize; /* (C) size of WildcardNames buffer */ int MaxIf; /* (C) size of IfHeap, IfSumCheck, IfCount */ int NumStreams; /* (C) */ int MaxNumStreams; /* (C) */ int firstctypemessage; /* (C) Flag for giving first st order error */ int tablecheck; /* (C) For table checking */ int idoption; /* (C) */ int BottomLevel; /* (C) For propercount. Not used!!! */ int CompileLevel; /* (C) Subexpression level */ int TokensWriteFlag; /* (C) */ int UnsureDollarMode; /* (C)?Controls error messages undefined $'s */ int outsidefun; /* (C) Used for writing Tables to file */ int funpowers; /* (C) */ int WarnFlag; /* (C) */ int StatsFlag; /* (C) */ int NamesFlag; /* (C) */ int CodesFlag; /* (C) */ int SetupFlag; /* (C) */ int SortType; /* (C) */ int lSortType; /* (C) */ int ThreadStats; /* (C) */ int FinalStats; /* (C) */ int OldParallelStats; /* (C) */ int ThreadsFlag; int ThreadBalancing; int ThreadSortFileSynch; int ProcessStats; /* (C) */ int BracketNormalize; /* (C) Indicates whether the bracket st is normalized */ int maxtermlevel; /* (C) Size of termstack */ int dumnumflag; /* (C) Where there dummy indices in tokenizer? */ int bracketindexflag; /* (C) Are brackets going to be indexed? */ int parallelflag; /* (C) parallel allowed? */ int mparallelflag; /* (C) parallel allowed in this module? */ int inparallelflag; /* (C) inparallel allowed? */ int partodoflag; /* (C) parallel allowed? */ int properorderflag; /* (C) clean normalizing. */ int vetofilling; /* (C) vetoes overwriting in tablebase stubs */ int tablefilling; /* (C) to notify AddRHS we are filling a table */ int vetotablebasefill; /* (C) For the load in tablebase */ int exprfillwarning; /* (C) Warning has been printed for expressions in fill statements */ int lhdollarflag; /* (R) left hand dollar present */ int NoCompress; /* (R) Controls native compression */ int IsFortran90; /* Tells whether the Fortran is Fortran90 */ int MultiBracketLevels; /* Number of elements in MultiBracketBuf */ int topolynomialflag; /* To avoid ToPolynomial and FactArg together */ int ffbufnum; /* Buffer number for user defined factorizations */ int OldFactArgFlag; int MemDebugFlag; /* Only used when MALLOCDEBUG in tools.c */ int OldGCDflag; int OldPRFSignFlag; int WTimeStatsFlag; int SortReallocateFlag; /* Controls reallocation of large+small buffer at module end. 0 : Off 1 : On, every module (set by On sortreallocate;) 2 : On, single module (set by #sortreallocate) */ int PrintBacktraceFlag; /* Print backtrace on terminate? */ int FlintPolyFlag; /* Use Flint for polynomial arithmetic */ int HumanStatsFlag; /* Print human-readable stats in the stats print? */ int GrccVerbose; /* Enable extra print statements in grcc? */ int SortVerbose; /* Enable extra sort stats information? */ int doloopstacksize; int dolooplevel; int CheckpointFlag; /**< Tells preprocessor whether checkpoint code must executed. -1 : do recovery from snapshot, set by command line option; 0 : do nothing; 1 : create snapshots, set by On checkpoint statement */ int SizeCommuteInSet; /* Size of the CommuteInSet buffer */ #ifdef PARALLELCODE int numpfirstnum; /* For redefine */ int sizepfirstnum; /* For redefine */ #endif int origin; /* Determines whether .sort or ModuleOption */ int vectorlikeLHS; int nummodels; int modelspace; int ModelLevel; int ShortStatsMax; /* For On FewerStatistics 10; */ int InnerTest; /* For debugging */ WORD argsumcheck[MAXNEST]; /* (C) Checking of nesting */ WORD insidesumcheck[MAXNEST];/* (C) Checking of nesting */ WORD inexprsumcheck[MAXNEST];/* (C) Checking of nesting */ WORD RepSumCheck[MAXREPEAT];/* (C) Checks nesting of repeat, if, argument */ WORD lUniTrace[4]; /* (C) */ WORD RepLevel; /* (C) Tracks nesting of repeat. */ WORD arglevel; /* (C) level of nested argument statements */ WORD insidelevel; /* (C) level of nested inside statements */ WORD inexprlevel; /* (C) level of nested inexpr statements */ WORD termlevel; /* (C) level of nested term statements */ WORD MustTestTable; /* (C) Indicates whether tables have been changed */ WORD DumNum; /* (C) */ WORD ncmod; /* (C) Local setting of modulus. size of cmod */ WORD npowmod; /* (C) Local printing as powers. size powmod */ WORD modmode; /* (C) Mode for modulus calculus */ WORD nhalfmod; /* relevant word size of halfmod when defined */ WORD DirtPow; /* (C) Flag for changes in printing mod powers */ WORD lUnitTrace; /* (C) Local value of Tr[1] */ WORD NwildC; /* (C) Wildcard counter */ WORD ComDefer; /* (C) defer brackets */ WORD CollectFun; /* (C) Collect function number */ WORD AltCollectFun; /* (C) Alternate Collect function number */ WORD OutputMode; /* (C) */ WORD Cnumpows; WORD OutputSpaces; /* (C) */ WORD OutNumberType; /* (C) Controls RATIONAL/FLOAT output */ WORD DidClean; /* (C) Test whether nametree needs cleaning */ WORD IfLevel; /* (C) */ WORD WhileLevel; /* (C) */ WORD SwitchLevel; WORD SwitchInArray; WORD MaxSwitch; WORD LogHandle; /* (C) The Log File */ WORD LineLength; /* (C) */ WORD StoreHandle; /* (C) Handle of .str file */ WORD HideLevel; /* (C) Hiding indicator */ WORD lPolyFun; /* (C) local value of PolyFun */ WORD lPolyFunInv; /* (C) local value of Inverse of PolyFun */ WORD lPolyFunType; /* (C) local value of PolyFunType */ WORD lPolyFunExp; WORD lPolyFunVar; WORD lPolyFunPow; WORD SymChangeFlag; /* (C) */ WORD CollectPercentage; /* (C) Collect function percentage */ WORD extrasymbols; /* Flag for the extra symbols output mode */ WORD PolyRatFunChanged; /* Keeps track whether we changed in the compiler */ WORD ToBeInFactors; #ifdef WITHMPI WORD RhsExprInModuleFlag; /* (C) Set by the compiler if RHS expressions exists. */ #endif UBYTE Commercial[COMMERCIALSIZE+2]; /* (C) Message to be printed in statistics */ UBYTE debugFlags[MAXFLAGS+2]; /* On/Off Flag number(s) */ }; /* #] C : #[ S : The S struct defines objects changed at the start of the run (Processor) Basically only set by the master. */ /** * The S_const struct is part of the global data and resides in the * ALLGLOBALS struct A under the name S * We see it used with the macro AS as in AS.ExecMode * It has some variables used by the master in multithreaded runs */ struct S_const { POSITION MaxExprSize; /* ( ) Maximum size of in/out/sort */ #ifdef WITHPTHREADS pthread_mutex_t inputslock; pthread_mutex_t outputslock; pthread_mutex_t MaxExprSizeLock; #endif POSITION *OldOnFile; /* (S) File positions of expressions */ WORD *OldNumFactors; /* ( ) NumFactors in (old) expression */ WORD *Oldvflags; /* ( ) vflags in (old) expression */ WORD *Olduflags; /* ( ) uflags in (old) expression */ #ifdef WITHFLOAT void *delta_1; #endif int NumOldOnFile; /* (S) Number of expressions in OldOnFile */ int NumOldNumFactors; /* (S) Number of expressions in OldNumFactors */ int MultiThreaded; /* (S) Are we running multi-threaded? */ #ifdef WITHPTHREADS int MasterSort; /* Final stage of sorting to the master */ #endif #ifdef WITHMPI int printflag; /* controls MesPrint() on each slave */ #endif int Balancing; /* For second stage loadbalancing */ WORD ExecMode; /* (S) */ WORD CollectOverFlag; /* (R) Indicates overflow at Collect */ #ifdef WITHPTHREADS WORD sLevel; /* Copy of AR0.sLevel because it can get messy */ #endif }; /* #] S : #[ R : The R struct defines objects changed at run time. They determine the environment that has to be transferred together with a term during multithreaded execution. */ /** * The R_const struct is part of the global data and resides either in the * ALLGLOBALS struct A, or the ALLPRIVATES struct B (TFORM) under the name R * We see it used with the macro AR as in AR.infile * It has the variables that define the running environment and that * should be transferred with a term in a multithreaded run. */ struct R_const { FILEDATA StoreData; /* (O) */ FILEHANDLE Fscr[3]; /* (R) Dollars etc play with it too */ FILEHANDLE FoStage4[2]; /* (R) In Sort. Stage 4. */ POSITION DefPosition; /* (R) Deferred position of keep brackets. */ FILEHANDLE *infile; /* (R) Points alternatingly to Fscr[0] or Fscr[1] */ FILEHANDLE *outfile; /* (R) Points alternatingly to Fscr[1] or Fscr[0] */ FILEHANDLE *hidefile; /* (R) Points to Fscr[2] */ WORD *CompressBuffer; /* (M) */ WORD *ComprTop; /* (M) */ WORD *CompressPointer; /* (R) */ COMPAREDUMMY CompareRoutine; ULONG *wranfia; SBYTE *moebiustable; LONG OldTime; /* (R) Zero time. Needed in timer. */ LONG InInBuf; /* (R) Characters in input buffer. Scratch files. */ LONG InHiBuf; /* (R) Characters in hide buffer. Scratch file. */ LONG pWorkSize; /* (R) Size of pWorkSpace */ LONG lWorkSize; /* (R) Size of lWorkSpace */ LONG posWorkSize; /* (R) Size of posWorkSpace */ ULONG wranfseed; int NoCompress; /* (R) Controls native compression */ int gzipCompress; /* (R) Controls gzip compression */ int Cnumlhs; /* Local copy of cbuf[rbufnum].numlhs */ int outtohide; /* Indicates that output is directly to hide */ #ifdef WITHPTHREADS int exprtodo; /* The expression to do in parallel mode */ #endif int wranfcall; int wranfnpair1; int wranfnpair2; #if ( BITSINWORD == 32 ) WORD PrimeList[5000]; WORD numinprimelist; WORD notfirstprime; #endif WORD GetFile; /* (R) Where to get the terms {like Hide} */ WORD KeptInHold; /* (R) */ WORD BracketOn; /* (R) Intensely used in poly_ */ WORD MaxBracket; /* (R) Size of BrackBuf. Changed by poly_ */ WORD CurDum; /* (R) Current maximum dummy number */ WORD DeferFlag; /* (R) For deferred brackets */ WORD TePos; /* (R) */ WORD sLevel; /* (R) Sorting level */ WORD Stage4Name; /* (R) Sorting only */ WORD GetOneFile; /* (R) Getting from hide or regular */ WORD PolyFun; /* (C) Number of the PolyFun function */ WORD PolyFunInv; /* (C) Number of the Inverse of the PolyFun function */ WORD PolyFunType; /* () value of PolyFunType */ WORD PolyFunExp; WORD PolyFunVar; WORD PolyFunPow; WORD Eside; /* () Tells which side of = sign */ WORD MaxDum; /* Maximum dummy value in an expression */ WORD level; /* Running level in Generator */ WORD expchanged; /* (R) Info about expression */ WORD expflags; /* (R) Info about expression */ WORD CurExpr; /* (S) Number of current expression */ WORD SortType; /* A copy of AC.SortType to play with */ WORD ShortSortCount; /* For On FewerStatistics 10; */ WORD modeloptions; WORD funoffset; WORD moebiustablesize; }; /* #] R : #[ T : These are variables that stay in each thread during multi threaded execution. */ /** * The T_const struct is part of the global data and resides either in the * ALLGLOBALS struct A, or the ALLPRIVATES struct B (TFORM) under the name T * We see it used with the macro AT as in AT.WorkPointer * It has variables that are private to each thread, most of which have * to be defined at startup. */ struct T_const { #ifdef WITHPTHREADS SORTBLOCK SB; #endif SORTING *S0; /* (-) The thread specific sort buffer */ SORTING *SS; /* (R) Current sort buffer */ NESTING Nest; /* (R) Nesting of function levels etc. */ NESTING NestStop; /* (R) */ NESTING NestPoin; /* (R) */ WORD *BrackBuf; /* (R) Bracket buffer. Used by poly_ at runtime. */ STORECACHE StoreCache; /* (R) Cache for picking up stored expr. */ STORECACHE StoreCacheAlloc; /* (R) Permanent address of StoreCache to keep valgrind happy */ WORD **pWorkSpace; /* (R) Workspace for pointers. Dynamic. */ LONG *lWorkSpace; /* (R) WorkSpace for LONG. Dynamic. */ POSITION *posWorkSpace; /* (R) WorkSpace for file positions */ WORD *WorkSpace; /* (M) */ WORD *WorkTop; /* (M) */ WORD *WorkPointer; /* (R) Pointer in the WorkSpace heap. */ int *RepCount; /* (M) Buffer for repeat nesting */ int *RepTop; /* (M) Top of RepCount buffer */ WORD *WildArgTaken; /* (N) Stack for wildcard pattern matching */ UWORD *factorials; /* (T) buffer of factorials. Dynamic. */ WORD *small_power_n; /* length of the number */ UWORD **small_power; /* the number*/ UWORD *bernoullis; /* (T) The buffer with Bernoulli numbers. Dynamic. */ WORD *primelist; LONG *pfac; /* (T) array of positions of factorials. Dynamic. */ LONG *pBer; /* (T) array of positions of Bernoulli's. Dynamic. */ WORD *TMaddr; /* (R) buffer for TestSub */ WORD *WildMask; /* (N) Wildcard info during pattern matching */ WORD *previousEfactor; /* () Cache for factors in expressions */ WORD **TermMemHeap; /* For TermMalloc. Set zero in Checkpoint */ UWORD **NumberMemHeap; /* For NumberMalloc. Set zero in Checkpoint */ UWORD **CacheNumberMemHeap; /* For CacheNumberMalloc. Set zero in Checkpoint */ BRACKETINFO *bracketinfo; WORD **ListPoly; WORD *ListSymbols; UWORD *NumMem; WORD *TopologiesTerm; WORD *TopologiesStart; #ifdef WITHFLOAT WORD *indi1; WORD *indi2; void *mpf_tab1; void *mpf_tab2; void *aux_; void *auxr_; #endif NORMDATA **NormData; LONG NormDataSize; LONG NormDepth; PARTI partitions; LONG sBer; /* (T) Size of the Bernoullis buffer */ LONG pWorkPointer; /* (R) Offset-pointer in pWorkSpace */ LONG lWorkPointer; /* (R) Offset-pointer in lWorkSpace */ LONG posWorkPointer; /* (R) Offset-pointer in posWorkSpace */ LONG InNumMem; int sfact; /* (T) size of the factorials buffer */ int mfac; /* (T) size of the pfac array. */ int ebufnum; /* (R) extra compiler buffer */ int fbufnum; /* extra compiler buffer for factorization cache */ int allbufnum; /* extra compiler buffer for id,all */ int aebufnum; /* extra compiler buffer for id,all */ int idallflag; /* indicates use of id,all buffers */ int idallnum; int idallmaxnum; int WildcardBufferSize; /* () local copy for updates */ #ifdef WITHPTHREADS int identity; /* () When we work with B->T */ int LoadBalancing; /* Needed for synchronization */ #ifdef WITHSORTBOTS int SortBotIn1; /* Input stream 1 for a SortBot */ int SortBotIn2; /* Input stream 2 for a SortBot */ #endif #endif int TermMemMax; /* For TermMalloc. Set zero in Checkpoint */ int TermMemTop; /* For TermMalloc. Set zero in Checkpoint */ int NumberMemMax; /* For NumberMalloc. Set zero in Checkpoint */ int NumberMemTop; /* For NumberMalloc. Set zero in Checkpoint */ int CacheNumberMemMax; /* For CacheNumberMalloc. Set zero in Checkpoint */ int CacheNumberMemTop; /* For CacheNumberMalloc. Set zero in Checkpoint */ int bracketindexflag; /* Are brackets going to be indexed? */ int optimtimes; /* Number of the evaluation of the MCTS tree */ int ListSymbolsSize; int NumListSymbols; int numpoly; int LeaveNegative; int TrimPower; /* Indicates trimming in polyratfun expansion */ WORD small_power_maxx; /* size of the cache for small powers */ WORD small_power_maxn; /* size of the cache for small powers */ WORD dummysubexp[SUBEXPSIZE+4]; /* () used in normal.c */ WORD comsym[8]; /* () Used in tools.c = {8,SYMBOL,4,0,1,1,1,3} */ WORD comnum[4]; /* () Used in tools.c = { 4,1,1,3 } */ WORD comfun[FUNHEAD+4]; /* () Used in tools.c = {7,FUNCTION,3,0,1,1,3} */ /* or { 8,FUNCTION,4,0,0,1,1,3 } */ WORD comind[7]; /* () Used in tools.c = {7,INDEX,3,0,1,1,3} */ WORD MinVecArg[7+ARGHEAD]; /* (N) but should be more local */ WORD FunArg[4+ARGHEAD+FUNHEAD]; /* (N) but can be more local */ WORD locwildvalue[SUBEXPSIZE]; /* () Used in argument.c = {SUBEXPRESSION,SUBEXPSIZE,0,0,0} */ WORD mulpat[SUBEXPSIZE+5]; /* () Used in argument.c = {TYPEMULT, SUBEXPSIZE+3, 0, */ /* SUBEXPRESSION, SUBEXPSIZE, 0, 1, 0, 0, 0 } */ WORD proexp[SUBEXPSIZE+5]; /* () Used in poly.c */ WORD TMout[40]; /* (R) Passing info */ WORD TMbuff; /* (R) Communication between TestSub and Genera */ WORD TMdolfac; /* factor number for dollar */ WORD nfac; /* (T) Number of highest stored factorial */ WORD nBer; /* (T) Number of highest Bernoulli number. */ WORD mBer; /* (T) Size of buffer pBer. */ WORD PolyAct; /* (R) Used for putting the PolyFun at end. ini at 0 */ WORD RecFlag; /* (R) Used in TestSub. ini at zero. */ WORD inprimelist; WORD sizeprimelist; WORD fromindex; /* Tells the compare routine whether call from index */ WORD setinterntopo; /* Set of internal momenta for topogen */ WORD setexterntopo; /* Set of external momenta for topogen */ WORD TopologiesLevel; WORD TopologiesOptions[2]; #ifdef WITHFLOAT WORD FloatPos; WORD SortFloatMode; #endif }; /* #] T : #[ N : The N struct contains variables used in running information that is inside blocks that should not be split, like pattern matching, traces etc. They are local for each thread. They don't need initializations. */ /** * The N_const struct is part of the global data and resides either in the * ALLGLOBALS struct A, or the ALLPRIVATES struct B (TFORM) under the name N * We see it used with the macro AN as in AN.RepFunNum * It has variables that are private to each thread and are used as * temporary storage during the expansion of the terms tree. */ struct N_const { POSITION theposition; /* () Used in index.c */ WORD *EndNest; /* (R) Nesting of function levels etc. */ WORD *Frozen; /* (R) Bracket info */ WORD *FullProto; /* (R) Prototype of a subexpression or table */ WORD *cTerm; /* (R) Current term for coef_ and term_ */ int *RepPoint; /* (R) Pointer in RepCount buffer. Tracks repeat */ WORD *WildValue; /* (N) Wildcard info during pattern matching */ WORD *WildStop; /* (N) Wildcard info during pattern matching */ WORD *argaddress; /* (N) Used in pattern matching of arguments */ WORD *RepFunList; /* (N) For pattern matching */ WORD *patstop; /* (N) Used in pattern matching */ WORD *terstop; /* (N) Used in pattern matching */ WORD *terstart; /* (N) Used in pattern matching */ WORD *terfirstcomm; /* (N) Used in pattern matching */ WORD *DumFound; /* (N) For renumbering indices {make local?} */ WORD **DumPlace; /* (N) For renumbering indices {make local?} */ WORD **DumFunPlace; /* (N) For renumbering indices {make local?} */ WORD *UsedSymbol; /* (N) When storing terms of a global expr. */ WORD *UsedVector; /* (N) When storing terms of a global expr. */ WORD *UsedIndex; /* (N) When storing terms of a global expr. */ WORD *UsedFunction; /* (N) When storing terms of a global expr. */ WORD *MaskPointer; /* (N) For wildcard pattern matching */ WORD *ForFindOnly; /* (N) For wildcard pattern matching */ WORD *findTerm; /* (N) For wildcard pattern matching */ WORD *findPattern; /* (N) For wildcard pattern matching */ #ifdef WITHZLIB Bytef **ziobufnum; /* () Used in compress.c */ Bytef *ziobuffers; /* () Used in compress.c */ #endif WORD *dummyrenumlist; /* () Used in execute.c and store.c */ int *funargs; /* () Used in lus.c */ WORD **funlocs; /* () Used in lus.c */ int *funinds; /* () Used in lus.c */ UWORD *NoScrat2; /* () Used in normal.c */ WORD *ReplaceScrat; /* () Used in normal.c */ TRACES *tracestack; /* () used in opera.c */ WORD *selecttermundo; /* () Used in pattern.c */ WORD *patternbuffer; /* () Used in pattern.c */ WORD *termbuffer; /* () Used in pattern.c */ WORD **PoinScratch; /* () used in reshuf.c */ WORD **FunScratch; /* () used in reshuf.c */ WORD *RenumScratch; /* () used in reshuf.c */ FUN_INFO *FunInfo; /* () Used in smart.c */ WORD **SplitScratch; /* () Used in sort.c */ WORD **SplitScratch1; /* () Used in sort.c */ SORTING **FunSorts; /* () Used in sort.c */ UWORD *SoScratC; /* () Used in sort.c */ WORD *listinprint; /* () Used in proces.c and message.c */ WORD *currentTerm; /* () Used in proces.c and message.c */ WORD **arglist; /* () Used in function.c */ int *tlistbuf; /* () used in lus.c */ #ifdef WHICHSUBEXPRESSION UWORD *BinoScrat; /* () Used in proces.c */ #endif WORD *compressSpace; /* () Used in sort.c */ #ifdef WITHPTHREADS THREADBUCKET *threadbuck; EXPRESSIONS expr; #endif UWORD *SHcombi; WORD *poly_vars; UWORD *cmod; /* Local setting of modulus. Pointer to value. */ SHvariables SHvar; LONG deferskipped; /* () Used in proces.c store.c and parallel.c */ LONG InScratch; /* () Used in sort.c */ LONG SplitScratchSize; /* () Used in sort.c */ LONG InScratch1; /* () Used in sort.c */ LONG SplitScratchSize1; /* () Used in sort.c */ LONG ninterms; /* () Used in proces.c and sort.c */ #ifdef WITHPTHREADS LONG inputnumber; /* () For use in redefine */ LONG lastinindex; #endif #ifdef WHICHSUBEXPRESSION LONG last2; /* () Used in proces.c */ LONG last3; /* () Used in proces.c */ #endif LONG SHcombisize; int NumTotWildArgs; /* (N) Used in pattern matching */ int UseFindOnly; /* (N) Controls pattern routines */ int UsedOtherFind; /* (N) Controls pattern routines */ int ErrorInDollar; /* (R) */ int numfargs; /* () Used in lus.c */ int numflocs; /* () Used in lus.c */ int nargs; /* () Used in lus.c */ int tohunt; /* () Used in lus.c */ int numoffuns; /* () Used in lus.c */ int funisize; /* () Used in lus.c */ int RSsize; /* () Used in normal.c */ int numtracesctack; /* () used in opera.c */ int intracestack; /* () used in opera.c */ int numfuninfo; /* () Used in smart.c */ int NumFunSorts; /* () Used in sort.c */ int MaxFunSorts; /* () Used in sort.c */ int arglistsize; /* () Used in function.c */ int tlistsize; /* () used in lus.c */ int filenum; /* () used in setfile.c */ int compressSize; /* () Used in sort.c */ int polysortflag; int nogroundlevel; /* () Used to see whether pattern matching at groundlevel */ int subsubveto; /* () Sabotage combining subexpressions in TestSub */ WORD MaxRenumScratch; /* () used in reshuf.c */ WORD oldtype; /* (N) WildCard info at pattern matching */ WORD oldvalue; /* (N) WildCard info at pattern matching */ WORD NumWild; /* (N) Used in Wildcard */ WORD RepFunNum; /* (N) Used in pattern matching */ WORD DisOrderFlag; /* (N) Disorder option? Used in pattern matching */ WORD WildDirt; /* (N) dirty in wildcard substitution. */ WORD NumFound; /* (N) in reshuf only. Local? */ WORD WildReserve; /* (N) Used in the wildcards */ WORD TeInFun; /* (R) Passing type of action */ WORD TeSuOut; /* (R) Passing info. Local? */ WORD WildArgs; /* (R) */ WORD WildEat; /* (R) */ WORD PolyNormFlag; /* (R) For polynomial arithmetic */ WORD PolyFunTodo; /* deals with expansions and multiplications */ WORD sizeselecttermundo; /* () Used in pattern.c */ WORD patternbuffersize; /* () Used in pattern.c */ WORD numlistinprint; /* () Used in process.c */ WORD ncmod; /* () used as some type of flag to disable */ WORD ExpectedSign; /** Used in pattern matching of antisymmetric functions */ WORD SignCheck; /** Used in pattern matching of antisymmetric functions */ WORD IndDum; /* Active dummy indices */ WORD poly_num_vars; WORD idfunctionflag; WORD poly_vars_type; /* type of allocation. For free. */ WORD tryterm; /* For EndSort(...,2) */ #ifdef WHICHSUBEXPRESSION WORD nbino; /* () Used in proces.c */ WORD last1; /* () Used in proces.c */ #endif }; /* #] N : #[ O : The O struct concerns output variables */ /** * The O_const struct is part of the global data and resides in the * ALLGLOBALS struct A under the name O * We see it used with the macro AO as in AO.OutputLine * It contains variables that involve the writing of text output and * save/store files. */ struct O_const { FILEDATA SaveData; /* (O) */ STOREHEADER SaveHeader; /* () System Independent save-Files */ OPTIMIZERESULT OptimizeResult; UBYTE *OutputLine; /* (O) Sits also in debug statements */ UBYTE *OutStop; /* (O) Top of OutputLine buffer */ UBYTE *OutFill; /* (O) Filling point in OutputLine buffer */ WORD *bracket; /* (O) For writing brackets */ WORD *termbuf; /* (O) For writing terms */ WORD *tabstring; UBYTE *wpos; /* (O) Only when storing file {local?} */ UBYTE *wpoin; /* (O) Only when storing file {local?} */ UBYTE *DollarOutBuffer; /* (O) Outputbuffer for Dollars */ UBYTE *CurBufWrt; /* (O) Name of currently written expr. */ void (*FlipWORD)(UBYTE *); /* () Function pointers for translations. Initialized by ReadSaveHeader() */ void (*FlipLONG)(UBYTE *); void (*FlipPOS)(UBYTE *); void (*FlipPOINTER)(UBYTE *); void (*ResizeData)(UBYTE *,int,UBYTE *,int); void (*ResizeWORD)(UBYTE *,UBYTE *); void (*ResizeNCWORD)(UBYTE *,UBYTE *); void (*ResizeLONG)(UBYTE *,UBYTE *); void (*ResizePOS)(UBYTE *,UBYTE *); void (*ResizePOINTER)(UBYTE *,UBYTE *); void (*CheckPower)(UBYTE *); void (*RenumberVec)(UBYTE *); DICTIONARY **Dictionaries; UBYTE *tensorList; /* Dynamically allocated list with functions that are tensorial. */ WORD *inscheme; /* for feeding a Horner scheme to Optimize */ #ifdef WITHFLOAT UBYTE *floatspace; LONG floatsize; #endif /*----Leave NumInBrack as first non-pointer. This is used by the checkpoints--*/ LONG NumInBrack; /* (O) For typing [] option in print */ LONG wlen; /* (O) Used to store files. */ LONG DollarOutSizeBuffer; /* (O) Size of DollarOutBuffer */ LONG DollarInOutBuffer; /* (O) Characters in DollarOutBuffer */ #if defined(mBSD) && defined(MICROTIME) LONG wrap; /* (O) For statistics time. wrap around */ LONG wrapnum; /* (O) For statistics time. wrap around */ #endif OPTIMIZE Optimize; int OutInBuffer; /* (O) Which routine does the writing */ int NoSpacesInNumbers; /* For very long numbers */ int BlockSpaces; /* For very long numbers */ int CurrentDictionary; int SizeDictionaries; int NumDictionaries; int CurDictNumbers; int CurDictVariables; int CurDictSpecials; int CurDictFunWithArgs; int CurDictNumberWarning; int CurDictNotInFunctions; int CurDictInDollars; int gNumDictionaries; int IndentSpace; /* For indentation in output */ #ifdef WITHFLOAT int FloatPrec; #endif WORD schemenum; /* for feeding a Horner scheme to Optimize */ WORD transFlag; /* () >0 indicates that translations have to be done */ WORD powerFlag; /* () >0 indicates that some exponents/powers had to be adjusted */ WORD mpower; /* For maxpower adjustment to larger value */ WORD resizeFlag; /* () >0 indicates that something went wrong when resizing words */ WORD bufferedInd; /* () Contains extra INDEXENTRIES, see ReadSaveIndex() for an explanation */ WORD OutSkip; /* (O) How many chars to skip in output line */ WORD IsBracket; /* (O) Controls brackets */ WORD InFbrack; /* (O) For writing only */ WORD PrintType; /* (O) */ WORD FortFirst; /* (O) Only in sch.c */ WORD DoubleFlag; /* (O) Output in double precision */ WORD FactorMode; /* When the output should be written as factors */ WORD FactorNum; /* Number of factor currently treated */ WORD ErrorBlock; WORD OptimizationLevel; /* Level of optimization in the output */ UBYTE FortDotChar; /* (O) */ /* For the padding, please count also the number of int's in the OPTIMIZE struct. */ }; /* #] O : #[ X : The X struct contains variables that deal with the external channel */ /** * The X_const struct is part of the global data and resides in the * ALLGLOBALS struct A under the name X * We see it used with the macro AX as in AX.timeout * It contains variables that involve communication with external programs */ struct X_const { UBYTE *currentPrompt; UBYTE *shellname; /* if !=NULL (default is "/bin/sh -c"), start in the specified subshell*/ UBYTE *stderrname; /* If !=NULL (default if "/dev/null"), stderr is redirected to the specified file*/ int timeout; /* timeout to initialize preset channels. If timeout<0, the preset channels are already initialized*/ int killSignal; /* signal number, SIGKILL by default*/ int killWholeGroup; /* if 0, the signal is sent only to a process, if !=0 (default) is sent to a whole process group*/ int daemonize; /* if !=0 (default), start in a daemon mode */ int currentExternalChannel; }; /* #] X : #[ Definitions : Note: we changed the definition from C to Cc in version 5. The reason is that everywhere the pointer to the compiler buffer was called C as well. Somehow that gave no problems but who knows what the future might bring. */ #ifdef WITHPTHREADS /** * With pthreads (TFORM) the ALLGLOBALS struct has all the variables of which * there is only a single copy. */ typedef struct AllGlobals { struct M_const M; struct C_const Cc; struct S_const S; struct O_const O; struct P_const P; struct X_const X; } ALLGLOBALS; /** * With pthreads (TFORM) the ALLPRIVATES struct has all the variables of which * each thread must have its own (private) copy. */ typedef struct AllPrivates { struct R_const R; struct N_const N; struct T_const T; } ALLPRIVATES; #else /** * Without pthreads (FORM) the ALLGLOBALS struct has all the global variables */ typedef struct AllGlobals { struct M_const M; struct C_const Cc; struct S_const S; struct R_const R; struct N_const N; struct O_const O; struct P_const P; struct T_const T; struct X_const X; } ALLGLOBALS; #endif /* #] Definitions : #] A : #[ FG : */ #ifdef WITHPTHREADS #define PHEAD ALLPRIVATES *B, #define PHEAD0 ALLPRIVATES *B #define BHEAD B, #define BHEAD0 B #else #define PHEAD #define PHEAD0 void #define BHEAD #define BHEAD0 #endif typedef int (*WCN)(PHEAD WORD *,WORD *,WORD,WORD); typedef int (*WCN2)(PHEAD WORD *,WORD *); typedef WORD (*COMPARE)(PHEAD WORD *,WORD *,WORD); /** * The FIXEDGLOBALS struct is an anachronism. It started as the struct * with global variables that needed initialization. * It contains the elements Operation and OperaFind which define a very early * way of automatically jumping to the proper operation. We find the results * of it in parts of the file opera.c * Later operations were treated differently in a more transparent way. * We never changed the existing code. The most important part is currently * the cTable which is used intensively in the compiler. */ typedef struct FixedGlobals { WCN Operation[8]; WCN2 OperaFind[6]; char *VarType[10]; char *ExprStat[21]; char *FunNam[2]; char *swmes[3]; char *fname; char *fname2; UBYTE *s_one; WORD fnamebase; WORD fname2base; WORD fnamesize; WORD fname2size; UINT cTable[256]; } FIXEDGLOBALS; /* #] FG : */ #endif form-5.0.1/sources/ftypes.h0000644000175100017510000006202115217035721011315 /** @file ftypes.h * * Contains the definitions of many internal codes * Rather than using numbers directly we do this by defines, making it * much easier to change things. Changing things is sometimes also * a good way of testing the code. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /** * The next macros were introduced when TFORM was programmed. In the case of * workers, each worker may need some private data. These can in principle be * accessed by some posix calls but that is unnecessarily slow. The passing of * a pointer to the complete data struct with private data will be much faster. * And anyway, there would have to be a macro that either makes the posix call * (TFORM) or doesn't (FORM). The solution by having macro's that either pass * the pointer (TFORM) or don't pass it (FORM) is seen as the best solution. * * In the declarations and the calling of the functions we have to use the * PHEAD or the BHEAD macro, respectively, if the pointer is to be passed. * These macro's contain the comma as well. Hence we need special macro's if * there are no other arguments. These are called PHEAD0 and BHEAD0. */ #define WITHOUTERROR 0 #define WITHERROR 1 /* The various streams. (look also in tools.c) */ #define FILESTREAM 0 #define PREVARSTREAM 1 #define PREREADSTREAM 2 #define PIPESTREAM 3 #define PRECALCSTREAM 4 #define DOLLARSTREAM 5 #define PREREADSTREAM2 6 #define EXTERNALCHANNELSTREAM 7 #define PREREADSTREAM3 8 #define REVERSEFILESTREAM 9 #define INPUTSTREAM 10 #define ENDOFSTREAM 0xFF #define ENDOFINPUT 0xFF /* Types of files */ #define SUBROUTINEFILE 0 #define PROCEDUREFILE 1 #define HEADERFILE 2 #define SETUPFILE 3 #define TABLEBASEFILE 4 /* Types of modules */ #define FIRSTMODULE -1 #define GLOBALMODULE 0 #define SORTMODULE 1 #define STOREMODULE 2 #define CLEARMODULE 3 #define ENDMODULE 4 #define POLYFUN 0 #define NOPARALLEL_DOLLAR 0x0001 #define NOPARALLEL_RHS 0x0002 #define NOPARALLEL_CONVPOLY 0x0004 #define NOPARALLEL_SPECTATOR 0x0008 #define NOPARALLEL_USER 0x0010 #define NOPARALLEL_TBLDOLLAR 0x0100 #define NOPARALLEL_NPROC 0x0200 #define PARALLELFLAG 0x0000 #define PRENOACTION 0 #define PRERAISEAFTER 1 #define PRELOWERAFTER 2 /* #define ELIUMOD 1 #define ELIZMOD 2 #define SKIUMOD 3 #define SKIZMOD 4 */ #define WITHSEMICOLON 0 #define WITHOUTSEMICOLON 1 #define MODULEINSTACK 8 #define EXECUTINGIF 0 #define LOOKINGFORELSE 1 #define LOOKINGFORENDIF 2 #define NEWSTATEMENT 1 #define OLDSTATEMENT 0 #define EXECUTINGPRESWITCH 0 #define SEARCHINGPRECASE 1 #define SEARCHINGPREENDSWITCH 2 #define PREPROONLY 1 #define DUMPTOCOMPILER 2 #define DUMPOUTTERMS 4 #define DUMPINTERMS 8 #define DUMPTOSORT 16 #define DUMPTOPARALLEL 32 #define THREADSDEBUG 64 #define ERROROUT 0 #define INPUTOUT 1 #define STATSOUT 2 #define EXPRSOUT 3 #define WRITEOUT 4 #define EXTERNALCHANNELOUT 5 #define NUMERICALLOOP 0 #define LISTEDLOOP 1 #define ONEEXPRESSION 2 #define PRETYPENONE 0 #define PRETYPEIF 1 #define PRETYPEDO 2 #define PRETYPEPROCEDURE 3 #define PRETYPESWITCH 4 #define PRETYPEINSIDE 5 /* Type of statement. Used to make sure that the statements are in proper order */ #define DECLARATION 1 #define SPECIFICATION 2 #define DEFINITION 3 #define STATEMENT 4 #define TOOUTPUT 5 #define ATENDOFMODULE 6 #define MIXED2 8 /* unused */ #define MIXED 9 /* The typedefs are to allow the compilers to do better error checking. */ typedef void (*PVFUNWP)(WORD *); typedef void (*PVFUNV)(void); typedef int (*CFUN)(void); typedef int (*TFUN)(UBYTE *); typedef int (*TFUN1)(UBYTE *,int); /* Flags used in the compiler's KEYWORD tables. */ #define NOAUTO 0 #define PARTEST 1 /* parentheses test */ #define WITHAUTO 2 /* auto-declaration */ #define ALLVARIABLES -1 #define SYMBOLONLY 1 #define INDEXONLY 2 #define VECTORONLY 4 #define FUNCTIONONLY 8 #define SETONLY 16 #define EXPRESSIONONLY 32 /** * @name Defines: compiler types * Type of variable found by the compiler. * @anchor CompilerTypes */ /*@{*/ #define CDELETE -1 #define ANYTYPE -1 #define CSYMBOL 0 #define CINDEX 1 #define CVECTOR 2 #define CFUNCTION 3 #define CSET 4 #define CEXPRESSION 5 #define CDOTPRODUCT 6 #define CNUMBER 7 #define CSUBEXP 8 #define CDELTA 9 #define CDOLLAR 10 #define CDUBIOUS 11 #define CRANGE 12 #define CMODEL 13 #define CVECTOR1 21 #define CDOUBLEDOT 22 /*@}*/ /* Types of tokens in the tokenizer. */ #define TSYMBOL -1 #define TINDEX -2 #define TVECTOR -3 #define TFUNCTION -4 #define TSET -5 #define TEXPRESSION -6 #define TDOTPRODUCT -7 #define TNUMBER -8 #define TSUBEXP -9 #define TDELTA -10 #define TDOLLAR -11 #define TDUBIOUS -12 #define LPARENTHESIS -13 #define RPARENTHESIS -14 #define TWILDCARD -15 #define TWILDARG -16 #define TDOT -17 #define LBRACE -18 #define RBRACE -19 #define TCOMMA -20 #define TFUNOPEN -21 #define TFUNCLOSE -22 #define TMULTIPLY -23 #define TDIVIDE -24 #define TPOWER -25 #define TPLUS -26 #define TMINUS -27 #define TNOT -28 #define TENDOFIT -29 #define TSETOPEN -30 #define TSETCLOSE -31 #define TGENINDEX -32 #define TCONJUGATE -33 #define LRPARENTHESES -34 #define TNUMBER1 -35 #define TPOWER1 -36 #define TEMPTY -37 #define TSETNUM -38 #define TSGAMMA -39 #define TSETDOL -40 #define TFLOAT -41 #define TYPEISFUN 0 #define TYPEISSUB 1 #define TYPEISMYSTERY -1 #define LHSIDEX 2 #define LHSIDE 1 #define RHSIDE 0 /* Output modes */ #define FORTRANMODE 1 #define REDUCEMODE 2 #define MAPLEMODE 3 #define MATHEMATICAMODE 4 #define CMODE 5 #define VORTRANMODE 6 #define PFORTRANMODE 7 #define DOUBLEFORTRANMODE 33 #define DOUBLEPRECISIONFLAG 32 #define NODOUBLEMASK 31 #define QUADRUPLEFORTRANMODE 65 #define QUADRUPLEPRECISIONFLAG 64 #define ALLINTEGERDOUBLE 128 #define NOQUADMASK 63 #define NORMALFORMAT 0 #define NOSPACEFORMAT 1 #define ISNOTFORTRAN90 0 #define ISFORTRAN90 1 #define ALSOREVERSE 1 #define CHISHOLM 2 #define NOTRICK 16 #define SORTLOWFIRST 0 #define SORTHIGHFIRST 1 #define SORTPOWERFIRST 2 #define SORTANTIPOWER 3 /* These control the output of WriteStats. The different sort * types have differently formatted stats. These variables should * not have arbitrary values since they are also used as array * indices by WriteStats. */ #define STATSSPLITMERGE 0 #define STATSMERGETOFILE 1 #define STATSPOSTSORT 2 /* CHECKLOGTYPE implies that statistics will not be printed in * the log file if AM.LogType = 1 (when running with -ll or -F). */ #define NOCHECKLOGTYPE 0 #define CHECKLOGTYPE 1 #define NMIN4SHIFT 4 /* The next are the main codes. Note: SETSET is not allowed to be 4*n+1 We use those codes in CoIdExpression for function information after the pattern. Because SETSET also stands there we have to be careful!! Don't forget MAXBUILTINFUNCTION when adding codes! The object FUNCTION is at the start of the functions that are in regular notation. Anything below it is in special notation. Remark: HAAKJE0 is for compression purposes and should only occur at moments that ARGWILD cannot occur. */ #define SYMBOL 1 #define DOTPRODUCT 2 #define VECTOR 3 #define INDEX 4 #define EXPRESSION 5 #define SUBEXPRESSION 6 #define DOLLAREXPRESSION 7 #define SETSET 8 #define ARGWILD 9 #define MINVECTOR 10 #define SETEXP 11 #define DOLLAREXPR2 12 #define HAAKJE0 9 #define FUNCTION 20 #define TMPPOLYFUN 14 #define ARGFIELD 15 #define SNUMBER 16 #define LNUMBER 17 #define HAAKJE 18 #define DELTA 19 #define EXPONENT 20 #define DENOMINATOR 21 #define SETFUNCTION 22 #define GAMMA 23 #define GAMMAI 24 #define GAMMAFIVE 25 #define GAMMASIX 26 #define GAMMASEVEN 27 #define SUMF1 28 #define SUMF2 29 #define DUMFUN 30 #define REPLACEMENT 31 #define REVERSEFUNCTION 32 #define DISTRIBUTION 33 #define DELTA3 34 #define DUMMYFUN 35 #define DUMMYTEN 36 #define LEVICIVITA 37 #define FACTORIAL 38 #define INVERSEFACTORIAL 39 #define BINOMIAL 40 #define NUMARGSFUN 41 #define SIGNFUN 42 #define MODFUNCTION 43 #define MOD2FUNCTION 44 #define MINFUNCTION 45 #define MAXFUNCTION 46 #define ABSFUNCTION 47 #define SIGFUNCTION 48 #define INTFUNCTION 49 #define THETA 50 #define THETA2 51 #define DELTA2 52 #define DELTAP 53 #define BERNOULLIFUNCTION 54 #define COUNTFUNCTION 55 #define MATCHFUNCTION 56 #define PATTERNFUNCTION 57 #define TERMFUNCTION 58 #define CONJUGATION 59 #define ROOTFUNCTION 60 #define TABLEFUNCTION 61 #define FIRSTBRACKET 62 #define TERMSINEXPR 63 #define NUMTERMSFUN 64 #define GCDFUNCTION 65 #define DIVFUNCTION 66 #define REMFUNCTION 67 #define MAXPOWEROF 68 #define MINPOWEROF 69 #define TABLESTUB 70 #define FACTORIN 71 #define TERMSINBRACKET 72 #define WILDARGFUN 73 /* In the past we would add new functions here and raise the numbers on the special reserved names. This is impractical in the light of the .sav files. The .sav files need a mechanism that contains the value of MAXBUILTINFUNCTION at the moment of writing. This allows form corrections if this value has changed in the mean time. */ #define SQRTFUNCTION 74 #define LNFUNCTION 75 #define SINFUNCTION 76 #define COSFUNCTION 77 #define TANFUNCTION 78 #define ASINFUNCTION 79 #define ACOSFUNCTION 80 #define ATANFUNCTION 81 #define ATAN2FUNCTION 82 #define SINHFUNCTION 83 #define COSHFUNCTION 84 #define TANHFUNCTION 85 #define ASINHFUNCTION 86 #define ACOSHFUNCTION 87 #define ATANHFUNCTION 88 #define LI2FUNCTION 89 #define LINFUNCTION 90 #define EXTRASYMFUN 91 #define RANDOMFUNCTION 92 #define RANPERM 93 #define NUMFACTORS 94 #define FIRSTTERM 95 #define CONTENTTERM 96 #define PRIMENUMBER 97 #define EXTEUCLIDEAN 98 #define MAKERATIONAL 99 #define INVERSEFUNCTION 100 #define IDFUNCTION 101 #define PUTFIRST 102 #define PERMUTATIONS 103 #define PARTITIONS 104 #define MULFUNCTION 105 #define MOEBIUS 106 #define TOPOLOGIES 107 #define DIAGRAMS 108 #define TOPO 109 #define NODEFUNCTION 110 #define EDGE 111 #define SIZEOFFUNCTION 112 #define BLOCK 113 #define ONEPI 114 #define PHI 115 #define FLOATFUN 116 #define TOFLOAT 117 #define TORAT 118 #define MZV 119 #define EULER 120 #define MZVHALF 121 #define AGMFUNCTION 122 #define GAMMAFUN 123 #define EXPFUNCTION 124 #define HPLFUNCTION 125 #define MPLFUNCTION 126 #define MAXBUILTINFUNCTION 126 #define FIRSTUSERFUNCTION 150 #define ALLFUNCTIONS -1 #define ALLMZVFUNCTIONS -2 /* Note: if we add a builtin table we have to look also inside names.c in the routine Globalize because there we assume there does not exist such an object */ #define ISYMBOL 0 #define PISYMBOL 1 #define COEFFSYMBOL 2 #define NUMERATORSYMBOL 3 #define DENOMINATORSYMBOL 4 #define WILDARGSYMBOL 5 #define DIMENSIONSYMBOL 6 #define FACTORSYMBOL 7 #define SEPARATESYMBOL 8 #define EESYMBOL 9 #define EMSYMBOL 10 #define BUILTINSYMBOLS 11 #define FIRSTUSERSYMBOL 20 #define BUILTININDICES 1 #define BUILTINVECTORS 1 #define BUILTINDOLLARS 1 #define WILDARGVECTOR 0 #define WILDARGINDEX 0 /* The objects that have a name that starts with TYPE are codes of statements made by the compiler. Each statement starts with such a code, followed by its size. For how most of these statements are used can be seen in the Generator function in the file proces.c TYPEOPERATION is an anachronism that remains used only for the statements that are executed in the file opera.c (like traces and contractions). */ #define TYPEEXPRESSION 0 #define TYPEIDNEW 1 #define TYPEIDOLD 2 #define TYPEOPERATION 3 #define TYPEREPEAT 4 #define TYPEENDREPEAT 5 /* The next counts must be higher than the ones before */ #define TYPECOUNT 20 #define TYPEMULT 21 #define TYPEGOTO 22 #define TYPEDISCARD 23 #define TYPEIF 24 #define TYPEELSE 25 #define TYPEELIF 26 #define TYPEENDIF 27 #define TYPESUM 28 #define TYPECHISHOLM 29 #define TYPEREVERSE 30 #define TYPEARG 31 #define TYPENORM 32 #define TYPENORM2 33 #define TYPENORM3 34 #define TYPEEXIT 35 #define TYPESETEXIT 36 #define TYPEPRINT 37 #define TYPEFPRINT 38 #define TYPEREDEFPRE 39 #define TYPESPLITARG 40 #define TYPESPLITARG2 41 #define TYPEFACTARG 42 #define TYPEFACTARG2 43 #define TYPETRY 44 #define TYPEASSIGN 45 #define TYPERENUMBER 46 #define TYPESUMFIX 47 #define TYPEFINDLOOP 48 #define TYPEUNRAVEL 49 #define TYPEADJUSTBOUNDS 50 #define TYPEINSIDE 51 #define TYPETERM 52 #define TYPESORT 53 #define TYPEDETCURDUM 54 #define TYPEINEXPRESSION 55 #define TYPESPLITFIRSTARG 56 #define TYPESPLITLASTARG 57 #define TYPEMERGE 58 #define TYPETESTUSE 59 #define TYPEAPPLY 60 #define TYPEAPPLYRESET 61 #define TYPECHAININ 62 #define TYPECHAINOUT 63 #define TYPENORM4 64 #define TYPEFACTOR 65 #define TYPEARGIMPLODE 66 #define TYPEARGEXPLODE 67 #define TYPEDENOMINATORS 68 #define TYPESTUFFLE 69 #define TYPEDROPCOEFFICIENT 70 #define TYPETRANSFORM 71 #define TYPETOPOLYNOMIAL 72 #define TYPEFROMPOLYNOMIAL 73 #define TYPEDOLOOP 74 #define TYPEENDDOLOOP 75 #define TYPEDROPSYMBOLS 76 #define TYPEPUTINSIDE 77 #define TYPETOSPECTATOR 78 #define TYPEARGTOEXTRASYMBOL 79 #define TYPECANONICALIZE 80 #define TYPESWITCH 81 #define TYPEENDSWITCH 82 #define TYPESETUSERFLAG 83 #define TYPECLEARUSERFLAG 84 #define TYPEALLLOOPS 85 #define TYPEALLPATHS 86 #ifdef WITHFLOAT #define TYPEEVALUATE 87 #define TYPEEXPAND 88 #define TYPETOFLOAT 89 #define TYPETORAT 90 #define TYPESTRICTROUNDING 91 #define TYPECHOP 92 #endif /* The codes for the 'operations' that are part of TYPEOPERATION. */ #define TAKETRACE 1 #define CONTRACT 2 #define RATIO 3 #define SYMMETRIZE 4 #define TENVEC 5 #define SUMNUM1 6 #define SUMNUM2 7 /* The various types of wildcards. */ #define WILDDUMMY 0 #define SYMTONUM 1 #define SYMTOSYM 2 #define SYMTOSUB 3 #define VECTOMIN 4 #define VECTOVEC 5 #define VECTOSUB 6 #define INDTOIND 7 #define INDTOSUB 8 #define FUNTOFUN 9 #define ARGTOARG 10 #define ARLTOARL 11 #define EXPTOEXP 12 #define FROMBRAC 13 #define FROMSET 14 #define SETTONUM 15 #define WILDCARDS 16 #define SETNUMBER 17 #define LOADDOLLAR 18 /* Some new types of wildcards that hold only for function arguments. */ #define NUMTONUM 20 #define NUMTOSYM 21 #define NUMTOIND 22 #define NUMTOSUB 23 /* Flag or-ed with ARGTOARG to give the number of arguments. */ #define EATTENSOR 0x2000 /* Dirty flags (introduced when functions got a field with a dirty flag) */ #define CLEANFLAG 0 #define DIRTYFLAG 1 #define DIRTYSYMFLAG 2 #define MUSTCLEANPRF 4 #define SUBTERMUSED1 8 #define SUBTERMUSED2 16 #define ALLDIRTY (DIRTYFLAG|DIRTYSYMFLAG) #define ARGHEAD 2 #define FUNHEAD 3 #define SUBEXPSIZE 5 #define EXPRHEAD 5 #define TYPEARGHEADSIZE 6 /* Actions to be taken with expressions. They are marked with these objects during compilation. */ #define SKIP 1 #define DROP 2 #define HIDE 3 #define UNHIDE 4 #define INTOHIDE 5 /* Types of expressions */ #define LOCALEXPRESSION 0 #define SKIPLEXPRESSION 1 #define DROPLEXPRESSION 2 #define DROPPEDEXPRESSION 3 #define GLOBALEXPRESSION 4 #define SKIPGEXPRESSION 5 #define DROPGEXPRESSION 6 #define STOREDEXPRESSION 8 #define HIDDENLEXPRESSION 9 #define HIDDENGEXPRESSION 13 #define INCEXPRESSION 9 #define HIDELEXPRESSION 10 #define HIDEGEXPRESSION 14 #define DROPHLEXPRESSION 11 #define DROPHGEXPRESSION 15 #define UNHIDELEXPRESSION 12 #define UNHIDEGEXPRESSION 16 #define INTOHIDELEXPRESSION 17 #define INTOHIDEGEXPRESSION 18 #define SPECTATOREXPRESSION 19 #define DROPSPECTATOREXPRESSION 20 #define SKIPUNHIDELEXPRESSION 21 #define SKIPUNHIDEGEXPRESSION 22 #define PRINTOFF 0 #define PRINTON 1 #define PRINTCONTENTS 2 #define PRINTCONTENT 3 #define PRINTLFILE 4 #define PRINTONETERM 8 #define PRINTONEFUNCTION 16 #define PRINTALL 32 /* Special codes for the replace variable in the EXPRESSIONS struct */ #define REGULAREXPRESSION -1 #define REDEFINEDEXPRESSION -2 #define NEWLYDEFINEDEXPRESSION -3 /** * @name Defines: function specs * Function specifications. * @anchor FunSpecs */ /*@{*/ #define VERTEXFUNCTION -1 #define GENERALFUNCTION 0 #define TENSORFUNCTION 2 #define GAMMAFUNCTION 4 /*@}*/ /* Special sets */ #define POS_ 0 /* integer > 0 */ #define POS0_ 1 /* integer >= 0 */ #define NEG_ 2 /* integer < 0 */ #define NEG0_ 3 /* integer <= 0 */ #define EVEN_ 4 /* integer (even) */ #define ODD_ 5 /* integer (odd) */ #define Z_ 6 /* integer */ #define SYMBOL_ 7 /* symbol only */ #define FIXED_ 8 /* fixed index */ #define INDEX_ 9 /* index only */ #define Q_ 10 /* rational */ #define DUMMYINDEX_ 11 /* dummy index only */ #define VECTOR_ 12 /* vector only */ /* Special indices. */ #define GAMMA1 0 #define GAMMA5 -1 #define GAMMA6 -2 #define GAMMA7 -3 #define FUNNYVEC -4 #define FUNNYWILD -5 #define SUMMEDIND -6 #define NOINDEX -7 #define FUNNYDOLLAR -8 #define EMPTYINDEX -9 /* The next one should be less than all of the above special indices. */ #define MINSPEC -10 #define USEDFLAG 2 #define DUMMYFLAG 1 #define MAINSORT 0 #define FUNCTIONSORT 1 #define SUBSORT 2 #define FLOATMODE 1 #define RATIONALMODE 0 #define NUMSPECSETS 10 #define ISZERO 1 #define ISUNMODIFIED 2 #define ISCOMPRESSED 4 #define ISINRHS 8 #define ISFACTORIZED 16 #define TOBEFACTORED 32 #define TOBEUNFACTORED 64 #define KEEPZERO 128 #define VARTYPENONE 0 #define VARTYPECOMPLEX 1 #define VARTYPEIMAGINARY 2 #define VARTYPEROOTOFUNITY 4 #define VARTYPEMINUS 8 #define CYCLESYMMETRIC 1 #define RCYCLESYMMETRIC 2 #define SYMMETRIC 3 #define ANTISYMMETRIC 4 #define REVERSEORDER 256 /* Types of id statements (substitutions) */ #define SUBMULTI 1 #define SUBONCE 2 #define SUBONLY 3 #define SUBMANY 4 #define SUBVECTOR 5 #define SUBSELECT 6 #define SUBALL 7 #define SUBMASK 15 #define SUBDISORDER 16 #define SUBAFTER 32 #define SUBAFTERNOT 64 #define IDHEAD 6 #define DOLLARFLAG 1 #define NORMALIZEFLAG 2 #define GIDENT 1 #define GFIVE 4 #define GPLUS 3 #define GMINUS 2 /* Types of objects inside an if clause. */ #define LONGNUMBER 1 #define MATCH 2 #define COEFFI 3 #define SUBEXPR 4 #define MULTIPLEOF 5 #define IFDOLLAR 6 #define IFEXPRESSION 7 #define IFDOLLAREXTRA 8 #define IFISFACTORIZED 9 #define IFOCCURS 10 #define IFUSERFLAG 11 #define IFFLOATNUMBER 12 #define GREATER 0 #define GREATEREQUAL 1 #define LESS 2 #define LESSEQUAL 3 #define EQUAL 4 #define NOTEQUAL 5 #define ORCOND 6 #define ANDCOND 7 #define DUMMY 1 #define SORT 1 #define STORE 2 #define END 3 #define GLOBAL 4 #define CLEAR 5 #define VECTBIT 1 #define DOTPBIT 2 #define FUNBIT 4 #define SETBIT 8 #define EXTRAPARAMETER 0x4000 #define GENCOMMUTE 0 #define GENNONCOMMUTE 0x2000 #define NAMENOTFOUND -9 /* Types of dollar expressions. */ #define DOLUNDEFINED 0 #define DOLNUMBER 1 #define DOLARGUMENT 2 #define DOLSUBTERM 3 #define DOLTERMS 4 #define DOLWILDARGS 5 #define DOLINDEX 6 #define DOLZERO 7 #define FINDLOOP 0 #define REPLACELOOP 1 #define NOFUNPOWERS 0 #define COMFUNPOWERS 1 #define ALLFUNPOWERS 2 #define PROPERORDERFLAG 0 #define REGULAR 0 #define FINISH 1 #define POLYADD 1 #define POLYSUB 2 #define POLYMUL 3 #define POLYDIV 4 #define POLYREM 5 #define POLYGCD 6 #define POLYINTFAC 7 #define POLYNORM 8 #define MODNONE 0 #define MODSUM 1 #define MODMAX 2 #define MODMIN 3 #define MODLOCAL 4 #define ELEMENTUSED 1 #define ELEMENTLOADED 2 /* Variables for the modulus statement, flags in AC.modmode For explanation, see CoModulus */ #define POSNEG 0x1 #define INVERSETABLE 0x2 #define COEFFICIENTSONLY 0x4 #define ALSOPOWERS 0x8 #define ALSOFUNARGS 0x10 #define ALSODOLLARS 0x20 #define NOINVERSES 0x40 #define POSITIVEONLY 0 #define UNPACK 0x80 #define NOUNPACK 0 #define FROMFUNCTION 0x100 #define VARNAMES 0 #define AUTONAMES 1 #define EXPRNAMES 2 #define DOLLARNAMES 3 #ifdef WITHPTHREADS /* Signals that the workers have to react to */ #define TERMINATETHREAD -1 #define STARTNEWEXPRESSION 1 #define LOWESTLEVELGENERATION 2 #define FINISHEXPRESSION 3 #define CLEANUPEXPRESSION 4 #define HIGHERLEVELGENERATION 5 #define STARTNEWMODULE 6 #define CLAIMOUTPUT 7 #define FINISHEXPRESSION2 8 #define INISORTBOT 7 #define RUNSORTBOT 8 #define DOONEEXPRESSION 9 #define DOBRACKETS 10 #define CLEARCLOCK 11 #define MCTSEXPANDTREE 12 #define OPTIMIZEEXPRESSION 13 #define MASTERBUFFERISFULL 1 /* Bucket states */ #define BUCKETFREE 1 #define BUCKETINUSE 0 #define BUCKETCOMINGFREE 2 #define BUCKETFILLED -1 #define BUCKETATEND -2 #define BUCKETTERMINATED 3 #define BUCKETRELEASED 4 #define BUCKETDOINGTERM 1 #define BUCKETASSIGNED -1 #define BUCKETTOBERELEASED -2 #define BUCKETPREPARINGTERM 0 #define BUCKETDOINGTERMS 0 #define BUCKETDOINGBRACKET 1 /* Sortblock config */ // The number of blocks in the ring-buffer for data transfer between // workers or sortbots and the master thread or other sortbots. With // sortbots, each thread has half of this number. // The merging algorithm requires at least 4 blocks, so this must be // at least 8, with sortbots. #define NUMBEROFBLOCKSINSORT 8 // The minimum number of terms which must fit in a block, i.e. they // must be at least this number times MaxTermSize. #define MINIMUMNUMBEROFTERMS 1 // The minimum number of terms which will be written in a block, // before potentially yielding the block to a waiting reading thread. #define MINWRITENUMBEROFTERMS 1 #endif /* The next variable is because there is some use of cbufnum that is probably irrelevant. We use here DUMMYBUFNUM instead of AC.cbufnum just in case we run into trouble later. */ #define DUMMYBUFFER 1 #define ALLARGS 1 #define NUMARG 2 #define ARGRANGE 3 #define MAKEARGS 4 #define MAXRANGEINDICATOR 4 #define REPLACEARG 5 #define ENCODEARG 6 #define DECODEARG 7 #define IMPLODEARG 8 #define EXPLODEARG 9 #define PERMUTEARG 10 #define REVERSEARG 11 #define CYCLEARG 12 #define ISLYNDON 13 #define ISLYNDONR 14 #define TOLYNDON 15 #define TOLYNDONR 16 #define ADDARG 17 #define MULTIPLYARG 18 #define DROPARG 19 #define SELECTARG 20 #define DEDUPARG 21 #define ZTOHARG 22 #define HTOZARG 23 /* #define ZTOSARG 24 #define STOZARG 25 #define HTOSARG 26 #define STOHARG 27 */ #define BASECODE 1 #define YESLYNDON 1 #define NOLYNDON 2 #define TOPOLYNOMIALFLAG 1 #define FACTARGFLAG 2 #define OLDFACTARG 1 #define NEWFACTARG 0 #define FROMMODULEOPTION 0 #define FROMPOINTINSTRUCTION 1 #define EXTRASYMBOL 0 #define REGULARSYMBOL 1 #define EXPRESSIONNUMBER 2 #define O_NONE 0 #define O_CSE 1 #define O_CSEGREEDY 2 #define O_GREEDY 3 #define O_OCCURRENCE 0 #define O_MCTS 1 #define O_SIMULATED_ANNEALING 2 #define O_FORWARD 0 #define O_BACKWARD 1 #define O_FORWARDORBACKWARD 2 #define O_FORWARDANDBACKWARD 3 #define OPTHEAD 3 #define DOALL 1 #define ONLYFUNCTIONS 2 #define INUSE 1 #define COULDCOMMUTE 2 #define DOESNOTCOMMUTE 4 #define DICT_NONUMBERS 0 #define DICT_INTEGERONLY 1 #define DICT_RATIONALONLY 2 #define DICT_ALLNUMBERS 3 #define DICT_NOVARIABLES 0 #define DICT_DOVARIABLES 1 #define DICT_NOSPECIALS 0 #define DICT_DOSPECIALS 1 #define DICT_NOFUNWITHARGS 0 #define DICT_DOFUNWITHARGS 1 #define DICT_NOTINDOLLARS 0 #define DICT_INDOLLARS 1 #define DICT_INTEGERNUMBER 1 #define DICT_RATIONALNUMBER 2 #define DICT_SYMBOL 3 #define DICT_VECTOR 4 #define DICT_INDEX 5 #define DICT_FUNCTION 6 #define DICT_FUNCTION_WITH_ARGUMENTS 7 #define DICT_SPECIALCHARACTER 8 #define DICT_RANGE 9 #define READSPECTATORFLAG 3 #define GLOBALSPECTATORFLAG 1 #define ORDEREDSET 1 #define DENSETABLE 1 #define SPARSETABLE 0 // Diagram generator flags. They should be powers of two, since they are added // to pass to diagrams and masked in diawrap.cc to check the flags. // We use a "stringified" version of these when defining the FORM preprocessor // variables, so can't neatly use "1<<10" etc here. #define TOPOLOGIESONLY 1 #define WITHOUTNODES 2 #define WITHEDGES 4 #define WITHBLOCKS 8 #define WITHONEPISETS 16 #define WITHSYMMETRIZEI 32 #define WITHSYMMETRIZEF 64 // This is not an "option" preprocessor var but is set by "external" particle definitions #define CHECKEXTERN 128 // The "qgraf compatible" filtering flags: #define ONEPARTI 256 #define ONEPARTR 512 #define ONSHELL 1024 #define OFFSHELL 2048 #define NOSIGMA 4096 #define SIGMA 8192 #define NOSNAIL 16384 #define SNAIL 32768 #define NOTADPOLE 65536 #define TADPOLE 131072 #define SIMPLE 262144 #define NOTSIMPLE 524288 #define BIPART 1048576 #define NONBIPART 2097152 #define CYCLI 4194304 #define CYCLR 8388608 #define FLOOP 16777216 #define NOTFLOOP 33554432 form-5.0.1/sources/pattern.c0000644000175100017510000017172615217035721011470 /** @file pattern.c * * Top level pattern matching routines. * More pattern matching is found in findpat.c, function.c, symmetr.c * and smart.c. The last three files contain the matching inside functions. * The file pattern.c contains also the very important routine Substitute. * All regular pattern matching is just the finding of the pattern and * indicating what are the wildcards etc. The routine Substitute does * the actual removal of the pattern and replaces it by a subterm of the * type SUBEXPRESSION. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* !!! Notice the change in OnePV in FindAll (7-may-2008 JV). #[ Includes : pattern.c */ #include "form3.h" /* #] Includes : #[ Patterns : #[ Rules : There are several rules governing the allowable replacements. 1: Multi with anything but symbols or dotproducts reverts to many. 2: Each symbol can have only one (wildcard) power, so x^2*x^n? is illegal. 3: when a single vector is used it replaces all occurrences of the vector. Therefore q*q(mu) or q*q(mu) cannot occur. Also q*q cannot be done. 4: Loose vector elements are replaced with p(mu), dotproducts with p?.q. 5: p?.q? is allowed. 6: x^n? can revert to n = 0 if there is no power of x. 7: x?^n? must match some x. There could be an ambiguity otherwise. #] Rules : #[ TestMatch : WORD TestMatch(term,level) */ /** This routine governs the pattern matching. If it decides that a substitution should be made, this can be either the insertion of a right hand side (C->rhs) or the automatic generation of terms as a result of an operation (like trace). The object to be replaced is removed from term and a subexpression pointer is inserted. If the substitution is made more than once there can be more subexpression pointers. Its number is positive as it corresponds to the level at which the C->rhs can be found in the compiler output. The subexpression pointer contains the wildcard substitution information. The power is found in *AT.TMout. For operations the subexpression pointer is negative and corresponds to an address in the array AT.TMout. In this array are then the instructions for the routine to be called and its number in the array 'Operations' The format is here: length,functionnumber,length-2 parameters There is a certain complexity wrt repeat levels. Another complication is the poking of the wildcard values in the subexpression prototype in the compiler buffer. This was how things were done in the past with sequential FORM, but with the advent of TFORM this cannot be maintained. Now, for TFORM we make a copy of it. 7-may-2008 (JV): We cannot yet guarantee that this has been done 100% correctly. There are errors that occur in TFORM only and that may indicate problems. */ int TestMatch(PHEAD WORD *term, WORD *level) { GETBIDENTITY WORD *ll, *m, *w, *llf, *OldWork, *StartWork, *ww, *mm, *t, *OldTermBuffer = 0; WORD power = 0, i, msign = 0, ll2; int match = 0; int numdollars = 0, protosize, oldallnumrhs; CBUF *C = cbuf+AM.rbufnum, *CC; AT.idallflag = 0; do { /* #[ Preliminaries : */ ll = C->lhs[*level]; if ( *ll == TYPEEXPRESSION ) { /* Expressions are not subject to anything. */ return(0); } else if ( *ll == TYPEREPEAT ) { *++AN.RepPoint = 0; return(0); /* Will force the next level */ } else if ( *ll == TYPEENDREPEAT ) { if ( *AN.RepPoint ) { AN.RepPoint[-1] = 1; /* Mark the higher level as dirty */ *AN.RepPoint = 0; *level = ll[2]; /* Level to jump back to */ } else { AN.RepPoint--; if ( AN.RepPoint < AT.RepCount ) { MLOCK(ErrorMessageLock); MesPrint("Internal problems with REPEAT count"); MUNLOCK(ErrorMessageLock); Terminate(-1); } } return(0); /* Force the next level */ } else if ( *ll == TYPEOPERATION ) { /* Operations have always their own level. */ if ( (*(FG.OperaFind[ll[2]]))(BHEAD term,ll) ) return(-1); else return(0); } /* #] Preliminaries : */ OldWork = AT.WorkPointer; if ( AT.WorkPointer < term + *term ) AT.WorkPointer = term + *term; ww = AT.WorkPointer; /* Here we need to make a copy of the subexpression object because we will be writing the values of the wildcards in it. Originally we copied it into the private version of the compiler buffer that is used for scratch space (ebufnum). This caused errors in the routines like ScanFunctions when the ebufnum Buffer was expanded and inpat was still pointing at the old Buffer. This expansion could be done in AddWild and hence cannot be fixed at > 100 places. The solution is to use AN.patternbuffer (JV 16-mar-2009). */ { WORD *ta = ll, *ma; int ja = ta[1]; /* New code (16-mar-2009) JV */ if ( ( ja + 2 ) > AN.patternbuffersize ) { if ( AN.patternbuffer ) M_free(AN.patternbuffer,"AN.patternbuffer"); AN.patternbuffersize = 2 * ja + 2; AN.patternbuffer = (WORD *)Malloc1(AN.patternbuffersize * sizeof(WORD), "AN.patternbuffer"); } ma = AN.patternbuffer; m = ma + IDHEAD; NCOPY(ma,ta,ja); *ma = 0; } AN.FullProto = m; AN.WildValue = w = m + SUBEXPSIZE; protosize = IDHEAD + m[1]; m += m[1]; AN.WildStop = m; StartWork = ww; ll2 = ll[2]; /* #[ Expand dollars : */ if ( ( ll[4] & DOLLARFLAG ) != 0 ) { /* We have at least one dollar in the pattern */ WORD oldRepPoint = *AN.RepPoint, olddefer = AR.DeferFlag; AR.Eside = LHSIDEX; /* Copy into WorkSpace. This means that AN.patternbuffer will be free. */ ww = AT.WorkPointer; i = m[0]; mm = m; NCOPY(ww,mm,i); *StartWork += 3; *ww++ = 1; *ww++ = 1; *ww++ = 3; AT.WorkPointer = ww; AR.DeferFlag = 0; NewSort(BHEAD0); if ( Generator(BHEAD StartWork,AR.Cnumlhs) ) { LowerSortLevel(); AT.WorkPointer = OldWork; AR.DeferFlag = olddefer; return(-1); } AT.WorkPointer = ww; if ( EndSort(BHEAD ww,0) < 0 ) {} AR.DeferFlag = olddefer; if ( *ww == 0 || *(ww+*ww) != 0 ) { if ( AP.lhdollarerror == 0 ) { /* If race condition we just get more error messages */ MLOCK(ErrorMessageLock); MesPrint("&LHS must be one term"); MUNLOCK(ErrorMessageLock); AP.lhdollarerror = 1; } AT.WorkPointer = OldWork; return(-1); } m = ww; ww = m + *m; if ( m[*m-1] < 0 ) { msign = 1; m[*m-1] = -m[*m-1]; } if ( *ww || m[*m-1] != 3 || m[*m-2] != 1 || m[*m-3] != 1 ) { MLOCK(ErrorMessageLock); MesPrint("Dollar variable develops into an illegal pattern in id-statement"); MUNLOCK(ErrorMessageLock); return(-1); } *m -= m[*m-1]; if ( ( *m + 1 + protosize ) > AN.patternbuffersize ) { if ( AN.patternbuffer ) M_free(AN.patternbuffer,"AN.patternbuffer"); AN.patternbuffersize = 2 * (*m) + 2 + protosize; AN.patternbuffer = (WORD *)Malloc1(AN.patternbuffersize * sizeof(WORD), "AN.patternbuffer"); mm = ll; ww = AN.patternbuffer; i = protosize; NCOPY(ww,mm,i); AN.FullProto = AN.patternbuffer + IDHEAD; AN.WildValue = w = AN.FullProto + SUBEXPSIZE; AN.WildStop = AN.patternbuffer + protosize; } mm = AN.patternbuffer + protosize; i = *m; NCOPY(mm,m,i); m = AN.patternbuffer + protosize; AR.Eside = RHSIDE; *mm = 0; /* Test the pattern. If only wildcard powers -> SUBONCE */ { WORD *mmm = m + *m, *m1 = m+1, jm, noveto = 0; while ( m1 < mmm ) { if ( *m1 == SYMBOL ) { for ( jm = 2; jm < m1[1]; jm+=2 ) { if ( m1[jm+1] < MAXPOWER && m1[jm+1] > -MAXPOWER ) break; } if ( jm < m1[1] ) { noveto = 1; break; } } else if ( *m1 == DOTPRODUCT ) { for ( jm = 2; jm < m1[1]; jm+=3 ) { if ( m1[jm+2] < MAXPOWER && m1[jm+2] > -MAXPOWER ) break; } if ( jm < m1[1] ) { noveto = 1; break; } } else { noveto = 1; break; } m1 += m1[1]; } if ( noveto == 0 ) { ll2 = ll2 & ~SUBMASK; ll2 |= SUBONCE; } } AT.WorkPointer = ww = StartWork; *AN.RepPoint = oldRepPoint; } /* #] Expand dollars : In case of id,all we have to check at this point that there are only functions in the pattern. */ if ( ( ll2 & SUBMASK ) == SUBALL ) { WORD *t = AN.patternbuffer+IDHEAD, *tt; WORD *tstop, *ttstop, ii; t += t[1]; tstop = t + *t; t++; while ( t < tstop ) { if ( *t < FUNCTION ) break; t += t[1]; } if ( t < tstop ) { MLOCK(ErrorMessageLock); MesPrint("Error: id,all can only be used with (products of) functions and/or tensors."); MUNLOCK(ErrorMessageLock); return(-1); } OldTermBuffer = AN.termbuffer; AN.termbuffer = TermMalloc("id,all"); /* Now make sure that only regular functions and tensors can take part. */ tt = term; ttstop = tt+*tt; ttstop -= ABS(ttstop[-1]); tt++; t = AN.termbuffer+1; while ( tt < ttstop ) { if ( *tt >= FUNCTION && *tt != AR.PolyFun && *tt != AR.PolyFunInv ) { ii = tt[1]; NCOPY(t,tt,ii); } else tt += tt[1]; } *t++ = 1; *t++ = 1; *t++ = 3; AN.termbuffer[0] = t-AN.termbuffer; } /* To be puristic, we need to check that all wildcards in the prototype are actually present. If the LHS contained a replace_ this may not be the case. */ ClearWild(BHEAD0); while ( w < AN.WildStop ) { if ( *w == LOADDOLLAR ) numdollars++; w += w[1]; } AN.RepFunNum = 0; /* rep = */ AN.RepFunList = AT.WorkPointer; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer/2); if ( AT.WorkPointer >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } AN.DisOrderFlag = ll2 & SUBDISORDER; AN.nogroundlevel = 0; switch ( ll2 & SUBMASK ) { case SUBONLY : /* Must be an exact match */ AN.UseFindOnly = 1; AN.ForFindOnly = 0; if ( FindRest(BHEAD term,m) && ( AN.UsedOtherFind || FindOnly(BHEAD term,m) ) ) { power = 1; if ( msign ) term[term[0]-1] = -term[term[0]-1]; } else power = 0; break; case SUBMANY : AN.UseFindOnly = -1; if ( ( power = FindRest(BHEAD term,m) ) > 0 ) { if ( ( power = FindOnce(BHEAD term,m) ) > 0 ) { AN.UseFindOnly = 0; do { if ( msign ) term[term[0]-1] = -term[term[0]-1]; Substitute(BHEAD term,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } if ( ww < term+term[0] ) ww = term+term[0]; ClearWild(BHEAD0); AT.WorkPointer = ww; /* if ( rep < ww ) {*/ AN.RepFunNum = 0; /* rep = */ AN.RepFunList = ww; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer/2); if ( AT.WorkPointer >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* } else { AN.RepFunList = rep; AN.RepFunNum = 0; } */ AN.nogroundlevel = 0; } while ( FindRest(BHEAD term,m) && ( AN.UsedOtherFind || FindOnce(BHEAD term,m) ) ); match = 1; } else if ( power < 0 ) { do { if ( msign ) term[term[0]-1] = -term[term[0]-1]; Substitute(BHEAD term,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } if ( ww < term+term[0] ) ww = term+term[0]; ClearWild(BHEAD0); AT.WorkPointer = ww; /* if ( rep < ww ) { */ AN.RepFunNum = 0; /* rep = */ AN.RepFunList = ww; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer/2); if ( AT.WorkPointer >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* } else { AN.RepFunList = rep; AN.RepFunNum = 0; } */ } while ( FindRest(BHEAD term,m) ); match = 1; } } else if ( power < 0 ) { if ( FindOnce(BHEAD term,m) ) { do { if ( msign ) term[term[0]-1] = -term[term[0]-1]; Substitute(BHEAD term,m,1); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } if ( ww < term+term[0] ) ww = term+term[0]; ClearWild(BHEAD0); AT.WorkPointer = ww; /* if ( rep < ww ) { */ AN.RepFunNum = 0; /* rep = */ AN.RepFunList = ww; AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer/2); if ( AT.WorkPointer >= AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); return(-1); } /* } else { AN.RepFunList = rep; AN.RepFunNum = 0; } */ } while ( FindOnce(BHEAD term,m) ); match = 1; } } if ( match ) { if ( ( ll2 & SUBAFTER ) != 0 ) *level = AC.Labels[ll[3]]; } else { if ( ( ll2 & SUBAFTERNOT ) != 0 ) *level = AC.Labels[ll[3]]; } goto nextlevel; case SUBONCE : AN.UseFindOnly = 0; if ( FindRest(BHEAD term,m) && ( AN.UsedOtherFind || FindOnce(BHEAD term,m) ) ) { power = 1; if ( msign ) term[term[0]-1] = -term[term[0]-1]; } else power = 0; break; case SUBMULTI : power = FindMulti(BHEAD term,m); if ( ( power & 1 ) != 0 && msign ) term[term[0]-1] = -term[term[0]-1]; break; case SUBVECTOR : while ( ( power = FindAll(BHEAD term,m,*level,(WORD *)0) ) != 0 ) { if ( ( power & 1 ) != 0 && msign ) term[term[0]-1] = -term[term[0]-1]; match = 1; } break; case SUBSELECT : llf = ll + IDHEAD; llf += llf[1]; llf += *llf; AN.UseFindOnly = 1; AN.ForFindOnly = llf; if ( FindRest(BHEAD term,m) && ( AN.UsedOtherFind || FindOnly(BHEAD term,m) ) ) { if ( msign ) term[term[0]-1] = -term[term[0]-1]; /* The following code needs to be hacked a bit to allow for all types of sets and for occurrence anywhere in the term The code at the end of FindOnly is a bit mysterious. */ if ( llf[1] > 2 ) { WORD *t1, *t2; if ( *term > AN.sizeselecttermundo ) { if ( AN.selecttermundo ) M_free(AN.selecttermundo,"AN.selecttermundo"); AN.sizeselecttermundo = *term +10; AN.selecttermundo = (WORD *)Malloc1( AN.sizeselecttermundo*sizeof(WORD),"AN.selecttermundo"); } t1 = term; t2 = AN.selecttermundo; i = *term; NCOPY(t2,t1,i); } power = 1; Substitute(BHEAD term,m,power); if ( llf[1] > 2 ) { if ( TestSelect(term,llf) ) { WORD *t1, *t2; power = 0; t1 = term; t2 = AN.selecttermundo; i = *t2; NCOPY(t1,t2,i); #if IDHEAD > 3 if ( ( ll2 & SUBAFTERNOT ) != 0 ) { *level = AC.Labels[ll[3]]; } #endif goto nextlevel; } } if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } match = 1; if ( ( ll2 & SUBAFTER ) != 0 ) { *level = AC.Labels[ll[3]]; } } else { if ( ( ll2 & SUBAFTERNOT ) != 0 ) { *level = AC.Labels[ll[3]]; } power = 0; } goto nextlevel; case SUBALL: AN.UseFindOnly = 0; CC = cbuf+AT.allbufnum; oldallnumrhs = CC->numrhs; t = AddRHS(AT.allbufnum,1); *t = 0; AT.idallflag = 1; AT.idallmaxnum = ll[5]; AT.idallnum = 0; if ( FindRest(BHEAD AN.termbuffer,m) || AT.idallflag > 1 ) { WORD *t, *tstop, *tt, first = 1, ii; power = 1; *CC->Pointer++ = 0; if ( msign ) term[term[0]-1] = -term[term[0]-1]; /* If we come here the matches are all already in the compiler buffer. All we need to do is take out all functions and replace them by a SUBEXPRESSION that points to this buffer. Note: the PolyFun/PolyRatFun should be excluded from this. This works because each match writes incrementally to the buffer using the routine SubsInAll. The call to WildDollars should be made in Generator..... */ t = term; tstop = t + *t; ii = ABS(tstop[-1]); tstop -= ii; tt = AT.WorkPointer+1; t++; while ( t < tstop ) { if ( *t >= FUNCTION && *t != AR.PolyFun && *t != AR.PolyFunInv ) { if ( first ) { /* SUBEXPRESSION */ *tt++ = SUBEXPRESSION; *tt++ = SUBEXPSIZE; *tt++ = CC->numrhs; *tt++ = 1; *tt++ = AT.allbufnum; FILLSUB(tt) first = 0; } t += t[1]; } else { i = t[1]; NCOPY(tt,t,i); } } if ( ( ll[4] & NORMALIZEFLAG ) != 0 ) { /* In case of the normalization option, we have to divide by AT.idallnum; */ WORD na = t[ii-1]; na = REDLENG(na); for ( i = 0; i < ii; i++ ) tt[i] = t[i]; Divvy(BHEAD (UWORD *)tt,&na,(UWORD *)(&(AT.idallnum)),1); na = INCLENG(na); ii = ABS(na); tt[ii-1] = na; tt += ii; } else { NCOPY(tt,t,ii); } ii = tt-AT.WorkPointer; *(AT.WorkPointer) = ii; tt = AT.WorkPointer; t = term; NCOPY(t,tt,ii); if ( ( ll2 & SUBAFTER ) != 0 ) { /* ifmatch -> */ *level = AC.Labels[ll[3]]; } TermFree(AN.termbuffer,"id,all"); AN.termbuffer = OldTermBuffer; AT.WorkPointer = AN.RepFunList; AT.idallflag = 0; CC->Pointer[0] = 0; TransferBuffer(AT.aebufnum,AT.ebufnum,AT.allbufnum); return(1); } AT.idallflag = 0; power = 0; CC->numrhs = oldallnumrhs; TermFree(AN.termbuffer,"id,all"); AN.termbuffer = OldTermBuffer; break; default : break; } if ( power ) { Substitute(BHEAD term,m,power); if ( numdollars ) { WildDollars(BHEAD (WORD *)0); numdollars = 0; } match = 1; if ( ( ll2 & SUBAFTER ) != 0 ) { /* ifmatch -> */ *level = AC.Labels[ll[3]]; } } else { AT.WorkPointer = AN.RepFunList; if ( ( ll2 & SUBAFTERNOT ) != 0 ) { /* ifnomatch -> */ *level = AC.Labels[ll[3]]; } } nextlevel:; } while ( (*level)++ < AR.Cnumlhs && C->lhs[*level][0] == TYPEIDOLD ); (*level)--; AT.WorkPointer = AN.RepFunList; return(match); } /* #] TestMatch : #[ Substitute : void Substitute(term,pattern,power) */ void Substitute(PHEAD WORD *term, WORD *pattern, WORD power) { GETBIDENTITY WORD *TemTerm; WORD *t, *m; WORD *tstop, *mstop; WORD *xstop, *ystop; WORD nt, *fill, nq, mt; WORD *q, *subterm, *tcoef, oldval1 = 0, newval3, i = 0; WORD PutExpr = 0, sign = 0; TemTerm = AT.WorkPointer; if ( ( (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer*2) ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); Terminate(-1); } m = pattern; mstop = m + *m; m++; t = term; t += *term - 1; tcoef = t; tstop = t - ABS(*t) + 1; t = term; t++; fill = TemTerm; fill++; if ( m < mstop ) { do { /* #[ SYMBOLS : */ if ( *m == SYMBOL ) { ystop = m + m[1]; m += 2; while ( *t != SYMBOL && t < tstop ) { nq = t[1]; NCOPY(fill,t,nq); } if ( t >= tstop ) goto SubCoef; *fill++ = SYMBOL; fill++; subterm = fill; xstop = t + t[1]; t += 2; do { if ( *m == *t && t < xstop ) { nt = t[1]; mt = m[1]; if ( mt >= 2*MAXPOWER ) { if ( CheckWild(BHEAD mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { nt -= AN.oldvalue; goto SubsL1; } } else if ( mt <= -2*MAXPOWER ) { if ( CheckWild(BHEAD -mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { nt += AN.oldvalue; goto SubsL1; } } else { nt -= mt * power; SubsL1: if ( nt ) { *fill++ = *t; *fill++ = nt; } } m += 2; t+= 2; } else if ( *m >= 2*MAXPOWER ) { while ( t < xstop ) { *fill++ = *t++; *fill++ = *t++; } nq = WORDDIF(fill,subterm); fill = subterm; while ( nq > 0 ) { if ( !CheckWild(BHEAD *m-2*MAXPOWER,SYMTOSYM,*fill,&newval3) ) { mt = m[1]; if ( mt >= 2*MAXPOWER ) { if ( CheckWild(BHEAD mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { if ( fill[1] -= AN.oldvalue ) goto SubsL2; } } else if ( mt <= -2*MAXPOWER ) { if ( CheckWild(BHEAD -mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { if ( fill[1] += AN.oldvalue ) goto SubsL2; } } else { if ( fill[1] -= mt * power ) { SubsL2: fill += nq; nq = 0; } } break; } nq -= 2; fill += 2; } if ( nq ) { nq -= 2; q = fill + 2; while ( --nq >= 0 ) *fill++ = *q++; } m += 2; } else if ( *m < *t || t >= xstop ) { m += 2; } else { *fill++ = *t++; *fill++ = *t++; } } while ( m < ystop ); while ( t < xstop ) *fill++ = *t++; nq = WORDDIF(fill,subterm); if ( nq > 0 ) { nq += 2; subterm[-1] = nq; } else { fill = subterm; fill -= 2; } } /* #] SYMBOLS : #[ DOTPRODUCTS : */ else if ( *m == DOTPRODUCT ) { ystop = m + m[1]; m += 2; while ( *t > DOTPRODUCT && t < tstop ) { nq = t[1]; NCOPY(fill,t,nq); } if ( t >= tstop ) goto SubCoef; if ( *t != DOTPRODUCT ) { m = ystop; goto EndLoop; } *fill++ = DOTPRODUCT; fill++; subterm = fill; xstop = t + t[1]; t += 2; do { if ( *m == *t && m[1] == t[1] && t < xstop ) { nt = t[2]; mt = m[2]; if ( mt >= 2*MAXPOWER ) { if ( CheckWild(BHEAD mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { nt -= AN.oldvalue; goto SubsL3; } } else if ( mt <= -2*MAXPOWER ) { if ( CheckWild(BHEAD -mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { nt += AN.oldvalue; goto SubsL3; } } else { nt -= mt * power; SubsL3: if ( nt ) { *fill++ = *t++; *fill++ = *t; *fill++ = nt; t += 2; } else t += 3; } m += 3; } else if ( *m >= (AM.OffsetVector+WILDOFFSET) ) { while ( t < xstop ) { *fill++ = *t++; *fill++ = *t++; *fill++ = *t++; } oldval1 = 1; goto SubsL4; } else if ( m[1] >= (AM.OffsetVector+WILDOFFSET) ) { while ( *m >= *t && t < xstop ) { *fill++ = *t++; *fill++ = *t++; *fill++ = *t++; } oldval1 = 0; SubsL4: nq = WORDDIF(fill,subterm); fill = subterm; while ( nq > 0 ) { if ( ( oldval1 && ( ( !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*fill,&newval3) && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,fill[1],&newval3) ) || ( !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,*fill,&newval3) && !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,fill[1],&newval3) ) ) ) || ( !oldval1 && ( ( *m == *fill && !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,fill[1],&newval3) ) || ( !CheckWild(BHEAD m[1]-WILDOFFSET,VECTOVEC,*fill,&newval3) && *m == fill[1] ) ) ) ) { mt = m[2]; if ( mt >= 2*MAXPOWER ) { if ( CheckWild(BHEAD mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { if ( fill[2] -= AN.oldvalue ) goto SubsL5; } } else if ( mt <= -2*MAXPOWER ) { if ( CheckWild(BHEAD -mt-2*MAXPOWER,SYMTONUM,-MAXPOWER,&newval3) ) { if ( fill[2] += AN.oldvalue ) goto SubsL5; } } else { if ( fill[2] -= mt * power ) { SubsL5: fill += nq; nq = 0; } } m += 3; break; } fill += 3; nq -= 3; } if ( nq ) { nq -= 3; q = fill + 3; while ( --nq >= 0 ) *fill++ = *q++; } } else if ( t >= xstop || *m < *t || ( *m == *t && m[1] < t[1] ) ) { m += 3; } else { *fill++ = *t++; *fill++ = *t++; *fill++ = *t++; } } while ( m < ystop ); while ( t < xstop ) *fill++ = *t++; nq = WORDDIF(fill,subterm); if ( nq > 0 ) { nq += 2; subterm[-1] = nq; } else { fill = subterm; fill -= 2; } } /* #] DOTPRODUCTS : #[ FUNCTIONS : */ else if ( *m >= FUNCTION ) { while ( *t >= FUNCTION || *t == SUBEXPRESSION ) { nt = WORDDIF(t,term); for ( mt = 0; mt < AN.RepFunNum; mt += 2 ) { if ( nt == AN.RepFunList[mt] ) break; } if ( mt >= AN.RepFunNum ) { nq = t[1]; NCOPY(fill,t,nq); } else { WORD *oldt = 0; if ( *m == GAMMA && m[1] != FUNHEAD+1 ) { oldt = t; if ( ( i = AN.RepFunList[mt+1] ) > 0 ) { *fill++ = GAMMA; *fill++ = i + FUNHEAD+1; FILLFUN(fill) nq = i + 1; t += FUNHEAD; NCOPY(fill,t,nq); } t = oldt; } else if ( ( *t == LEVICIVITA ) || ( *t >= FUNCTION && (functions[*t-FUNCTION].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) ) sign += AN.RepFunList[mt+1]; else if ( *m >= FUNCTION+WILDOFFSET && (functions[*m-FUNCTION-WILDOFFSET].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) sign += AN.RepFunList[mt+1]; if ( !PutExpr ) { xstop = t + t[1]; t = AN.FullProto; nq = t[1]; t[3] = power; NCOPY(fill,t,nq); t = xstop; PutExpr = 1; } else t += t[1]; if ( *m == GAMMA && m[1] != FUNHEAD+1 ) { i = oldt[1] - m[1] - i; if ( i > 0 ) { *fill++ = GAMMA; *fill++ = i + FUNHEAD+1; FILLFUN(fill) *fill++ = oldt[FUNHEAD]; t = t - i; NCOPY(fill,t,i); } } break; } } m += m[1]; } /* #] FUNCTIONS : #[ VECTORS : */ else if ( *m == VECTOR ) { while ( *t > VECTOR ) { nq = t[1]; NCOPY(fill,t,nq); } xstop = t + t[1]; ystop = m + m[1]; t += 2; m += 2; *fill++ = VECTOR; fill++; subterm = fill; do { if ( *m == *t && m[1] == t[1] ) { m += 2; t += 2; } else if ( *m >= (AM.OffsetVector+WILDOFFSET) ) { while ( t < xstop ) *fill++ = *t++; nq = WORDDIF(fill,subterm); fill = subterm; if ( m[1] < (AM.OffsetIndex+WILDOFFSET) ) { do { if ( m[1] == fill[1] && !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*fill,&newval3) ) break; fill += 2; nq -= 2; } while ( nq > 0 ); } else { /* Double wildcard */ do { if ( !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,fill[1],&newval3) && !CheckWild(BHEAD *m-WILDOFFSET,VECTOVEC,*fill,&newval3) ) break; if ( *fill == oldval1 && fill[1] == AN.oldvalue ) break; fill += 2; nq -= 2; } while ( nq > 0 ); } nq -= 2; q = fill + 2; if ( nq > 0 ) { NCOPY(fill,q,nq); } m += 2; } else if ( *m <= *t && m[1] >= (AM.OffsetIndex + WILDOFFSET) ) { while ( *m == *t && t < xstop ) { *fill++ = *t++; *fill++ = *t++; } nq = WORDDIF(fill,subterm); fill = subterm; do { if ( *m == *fill && !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,fill[1],&newval3) ) break; nq -= 2; fill += 2; } while ( nq > 0 ); nq -= 2; q = fill + 2; if ( nq > 0 ) { NCOPY(fill,q,nq); } m += 2; } else { *fill++ = *t++; *fill++ = *t++; } } while ( m < ystop ); while ( t < xstop ) *fill++ = *t++; nq = WORDDIF(fill,subterm); if ( nq > 0 ) { nq += 2; subterm[-1] = nq; } else { fill = subterm; fill -= 2; } } /* #] VECTORS : #[ INDICES : Currently without wildcards */ else if ( *m == INDEX ) { while ( *t > INDEX ) { nq = t[1]; NCOPY(fill,t,nq); } xstop = t + t[1]; ystop = m + m[1]; t += 2; m += 2; *fill++ = INDEX; fill++; subterm = fill; do { if ( *m == *t ) { m += 1; t += 1; } else if ( *m >= (AM.OffsetIndex+WILDOFFSET) ) { while ( t < xstop ) *fill++ = *t++; nq = WORDDIF(fill, subterm); fill = subterm; do { if ( !CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,*fill,&newval3) ) { break; } fill += 1; nq -= 1; } while ( nq > 0 ); nq -= 1; if ( nq > 0 ) { q = fill + 1; NCOPY(fill,q,nq); } m += 1; } else { *fill++ = *t++; } } while ( m < ystop ); while ( t < xstop ) *fill++ = *t++; nq = WORDDIF(fill,subterm); if ( nq > 0 ) { nq += 2; subterm[-1] = nq; } else { fill = subterm; fill -= 2; } } /* #] INDICES : #[ DELTAS : */ else if ( *m == DELTA ) { while ( *t > DELTA ) { nq = t[1]; NCOPY(fill,t,nq); } xstop = t + t[1]; ystop = m + m[1]; t += 2; m += 2; *fill++ = DELTA; fill++; subterm = fill; do { if ( *t == *m && t[1] == m[1] ) { m += 2; t += 2; } else if ( *m >= (AM.OffsetIndex+WILDOFFSET) ) { /* Two dummies */ while ( t < xstop ) *fill++ = *t++; /* fill = subterm; */ oldval1 = 1; goto SubsL6; } else if ( m[1] >= (AM.OffsetIndex+WILDOFFSET) ) { while ( (*m == *t || *m == t[1] ) && ( t < xstop ) ) { *fill++ = *t++; *fill++ = *t++; } oldval1 = 0; SubsL6: nq = WORDDIF(fill,subterm); fill = subterm; do { if ( ( oldval1 && ( ( !CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,*fill,&newval3) && !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,fill[1],&newval3) ) || ( !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,*fill,&newval3) && !CheckWild(BHEAD *m-WILDOFFSET,INDTOIND,fill[1],&newval3) ) ) ) || ( !oldval1 && ( ( *m == *fill && !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,fill[1],&newval3) ) || ( *m == fill[1] && !CheckWild(BHEAD m[1]-WILDOFFSET,INDTOIND,*fill,&newval3) ) ) ) ) break; fill += 2; nq -= 2; } while ( nq > 0 ); nq -= 2; if ( nq > 0 ) { q = fill + 2; NCOPY(fill,q,nq); } m += 2; } else { *fill++ = *t++; *fill++ = *t++; } } while ( m < ystop ); while ( t < xstop ) *fill++ = *t++; nq = WORDDIF(fill,subterm); if ( nq > 0 ) { nq += 2; subterm[-1] = nq; } else { fill = subterm; fill -= 2; } } /* #] DELTAS : */ EndLoop:; } while ( m < mstop ); } while ( t < tstop ) *fill++ = *t++; SubCoef: if ( !PutExpr ) { t = AN.FullProto; nq = t[1]; t[3] = power; NCOPY(fill,t,nq); } t = tcoef; nq = ABS(*t); t = tstop; NCOPY(fill,t,nq); nq = WORDDIF(fill,TemTerm); fill = term; t = TemTerm; *fill++ = nq--; t++; NCOPY(fill,t,nq); if ( sign ) { if ( ( sign & 1 ) != 0 ) fill[-1] = -fill[-1]; } if ( AT.WorkPointer < fill ) AT.WorkPointer = fill; AN.RepFunNum = 0; } /* #] Substitute : #[ FindSpecial : WORD FindSpecial(term) Routine to detect simplifications regarding the special functions exponent, denominator. void FindSpecial(WORD *term) { WORD *t; WORD *tstop; t = term; t += *t - 1; tstop = t - ABS(*t) + 1; t = term; t++; if ( t < tstop ) { do { if ( *t == EXPONENT ) { Exponents can become simpler when: a: the exponent of an expression becomes an integer. b: The expression becomes zero. } else if ( *t == DENOMINATOR ) { Denominators can become simpler when: a: The denominator is a single term without functions. b: An overall coefficient can be removed. c: An overall object can be removed. The task is here to bring the denominator in an unique form. } t += *t; } while ( t < tstop ); } } #] FindSpecial : #[ FindAll : WORD FindAll(term,pattern,level,par) */ int FindAll(PHEAD WORD *term, WORD *pattern, WORD level, WORD *par) { GETBIDENTITY WORD *t, *m, *r, *mm, rnum; WORD *tstop, *mstop, *TwoProto, *vwhere = 0, oldv, oldvv, vv, level2; WORD v, nq, OffNum = AM.OffsetVector + WILDOFFSET, i, ii = 0, jj; WORD fromindex, *intens, notflag1 = 0, notflag2 = 0; CBUF *C; C = cbuf+AM.rbufnum; v = pattern[3]; /* The vector to be found */ m = t = term; m += *m; m -= ABS(m[-1]); t++; if ( t < m ) do { tstop = t + t[1]; fromindex = 2; /* #[ VECTOR : */ if ( *t == VECTOR ) { r = t; r += 2; InVect: while ( r < tstop ) { oldv = *r; if ( v >= OffNum ) { vwhere = AN.FullProto + 3 + SUBEXPSIZE; if ( vwhere[1] == FROMSET || vwhere[1] == SETTONUM ) { WORD *afirst, *alast, j; j = vwhere[3]; if ( j > WILDOFFSET ) { j -= 2*WILDOFFSET; notflag1 = 1; } else { notflag1 = 0; } afirst = SetElements + Sets[j].first; alast = SetElements + Sets[j].last; ii = 1; if ( notflag1 == 0 ) { do { if ( *afirst == *r ) { if ( vwhere[1] == SETTONUM ) { AN.FullProto[8+SUBEXPSIZE] = SYMTONUM; AN.FullProto[11+SUBEXPSIZE] = ii; } else if ( vwhere[4] >= 0 ) { oldv = *(afirst - Sets[j].first + Sets[vwhere[4]].first); } goto DoVect; } ii++; } while ( ++afirst < alast ); } else { do { if ( *afirst == *r ) break; } while ( ++afirst < alast ); if ( afirst >= alast ) goto DoVect; } } else goto DoVect; } else if ( v == *r ) { DoVect: m = AT.WorkPointer; tstop = t; t = term; mstop = t + *t; do { *m++ = *t++; } while ( t < tstop ); vwhere = m; t = AN.FullProto; nq = t[1]; t[3] = 1; NCOPY(m,t,nq); t = tstop; if ( fromindex == 1 ) m[-1] = FUNNYVEC; else m[-1] = r[1]; /* The index is always here! */ if ( v >= OffNum ) vwhere[3+SUBEXPSIZE] = oldv; if ( vwhere[1] > 12+SUBEXPSIZE ) { vwhere[11+SUBEXPSIZE] = ii; vwhere[8+SUBEXPSIZE] = SYMTONUM; } if ( t[1] > fromindex+2 ) { *m++ = *t++; *m++ = *t++ - fromindex; while ( t < r ) *m++ = *t++; t += fromindex; } else t += t[1]; do { *m++ = *t++; } while ( t < mstop ); *AT.WorkPointer = nq = WORDDIF(m,AT.WorkPointer); m = AT.WorkPointer; t = term; NCOPY(t,m,nq); AT.WorkPointer = t; return(1); } r += fromindex; } } /* #] VECTOR : #[ DOTPRODUCT : */ else if ( *t == DOTPRODUCT ) { r = t; r += 2; do { if ( ( i = r[2] ) < 0 ) goto NextDot; if ( *r == r[1] ) { /* p.p */ oldv = *r; if ( v == *r ) { /* v.v */ TwoVec: m = AT.WorkPointer; tstop = t; t = term; mstop = t + *t; do { *m++ = *t++; } while ( t < tstop ); do { vwhere = m; t = AN.FullProto; nq = t[1]; t[3] = 2; NCOPY(m,t,nq); m[-1] = ++AR.CurDum; if ( v >= OffNum ) vwhere[3+SUBEXPSIZE] = oldv; } while ( --i > 0 ); CopRest: t = tstop; if ( t[1] > 5 ) { *m++ = *t++; *m++ = *t++ - 3; while ( t < r ) *m++ = *t++; t += 3; } else t += t[1]; do { *m++ = *t++; } while ( t < mstop ); *AT.WorkPointer = nq = WORDDIF(m,AT.WorkPointer); m = AT.WorkPointer; t = term; NCOPY(t,m,nq); AT.WorkPointer = t; return(1); } else if ( v >= OffNum ) { /* v?.v? */ vwhere = AN.FullProto + 3+SUBEXPSIZE; if ( vwhere[1] == FROMSET || vwhere[1] == SETTONUM ) { WORD *afirst, *alast, j; j = vwhere[3]; if ( j > WILDOFFSET ) { j -= 2*WILDOFFSET; notflag1 = 1; } else { notflag1 = 0; } afirst = SetElements + Sets[j].first; alast = SetElements + Sets[j].last; ii = 1; if ( notflag1 == 0 ) { do { if ( *afirst == *r ) { if ( vwhere[1] == SETTONUM ) { AN.FullProto[8+SUBEXPSIZE] = SYMTONUM; AN.FullProto[11+SUBEXPSIZE] = ii; } else if ( vwhere[4] >= 0 ) { oldv = *(afirst - Sets[j].first + Sets[vwhere[4]].first); } goto TwoVec; } ii++; } while ( ++afirst < alast ); } else { do { if ( *afirst == *r ) break; } while ( ++afirst < alast ); if ( afirst >= alast ) goto TwoVec; } } else goto TwoVec; } } else { if ( v == r[1] ) { r[1] = *r; *r = v; } oldv = *r; oldvv = r[1]; if ( v == *r ) { if ( !par ) { while ( ++level <= AR.Cnumlhs && C->lhs[level][0] == TYPEIDOLD ) { m = C->lhs[level]; m += IDHEAD; if ( m[-IDHEAD+2] == SUBVECTOR ) { if ( ( vv = m[m[1]+3] ) == r[1] ) { OnePV: TwoProto = AN.FullProto; TwoPV: m = AT.WorkPointer; tstop = t; t = term; mstop = t + *t; do { *m++ = *t++; } while ( t < tstop ); do { t = AN.FullProto; vwhere = m + 3 +SUBEXPSIZE; nq = t[1]; t[3] = 1; NCOPY(m,t,nq); m[-1] = ++AR.CurDum; if ( v >= OffNum ) *vwhere = oldv; if ( vwhere[-2-SUBEXPSIZE] > 12+SUBEXPSIZE ) { vwhere[8] = ii; vwhere[5] = SYMTONUM; } t = TwoProto; vwhere = m + 3+SUBEXPSIZE; mm = m; nq = t[1]; t[3] = 1; NCOPY(m,t,nq); /* The next two lines repair a bug. without them it takes twice the rhs of the first vector. */ mm[2] = C->lhs[level][IDHEAD+2]; mm[4] = C->lhs[level][IDHEAD+4]; m[-1] = AR.CurDum; if ( vv >= OffNum ) *vwhere = oldvv; } while ( --i > 0 ); goto CopRest; } else if ( vv > OffNum ) { vwhere = AN.FullProto + 3+SUBEXPSIZE; if ( vwhere[1] == FROMSET || vwhere[1] == SETTONUM ) { WORD *afirst, *alast, j; j = vwhere[3]; if ( j > WILDOFFSET ) { j -= 2*WILDOFFSET; notflag1 = 1; } else { notflag1 = 0; } afirst = SetElements + Sets[j].first; alast = SetElements + Sets[j].last; if ( notflag1 == 0 ) { ii = 1; do { if ( *afirst == r[1] ) { if ( vwhere[1] == SETTONUM ) { AN.FullProto[8+SUBEXPSIZE] = SYMTONUM; AN.FullProto[11+SUBEXPSIZE] = ii; } else if ( vwhere[4] >= 0 ) { oldvv = *(afirst - Sets[j].first + Sets[vwhere[4]].first); } goto OnePV; } ii++; } while ( ++afirst < alast ); } else { do { if ( *afirst == *r ) break; } while ( ++afirst < alast ); if ( afirst >= alast ) goto OnePV; } } else goto OnePV; } } }} /* v.q with v matching and no match for the q, also not in following idold statements. Notice that a following q.p? cannot match. */ rnum = r[1]; OneOnly: m = AT.WorkPointer; tstop = t; t = term; mstop = t + *t; do { *m++ = *t++; } while ( t < tstop ); vwhere = m; t = AN.FullProto; nq = t[1]; t[3] = i; NCOPY(m,t,nq); m[-4] = INDTOIND; m[-1] = rnum; if ( v >= OffNum ) vwhere[3+SUBEXPSIZE] = oldv; goto CopRest; } else if ( v >= OffNum ) { vwhere = AN.FullProto + 3+SUBEXPSIZE; if ( vwhere[1] == FROMSET || vwhere[1] == SETTONUM ) { WORD *afirst, *alast, *bfirst, *blast, j; j = vwhere[3]; if ( j > WILDOFFSET ) { j -= 2*WILDOFFSET; notflag1 = 1; } else { notflag1 = 0; } afirst = SetElements + Sets[j].first; alast = SetElements + Sets[j].last; ii = 1; if ( notflag1 == 0 ) { do { if ( *afirst == *r ) { if ( vwhere[1] == SETTONUM ) { AN.FullProto[8+SUBEXPSIZE] = SYMTONUM; AN.FullProto[11+SUBEXPSIZE] = ii; } else if ( vwhere[4] >= 0 ) { oldv = *(afirst - Sets[j].first + Sets[vwhere[4]].first); } Hitlevel1: level2 = level; do { if ( !par ) m = C->lhs[level2]; else m = par; m += IDHEAD; if ( m[-IDHEAD+2] == SUBVECTOR ) { if ( ( vv = m[m[1]+3] ) == r[1] ) goto OnePV; else if ( vv >= OffNum ) { if ( m[SUBEXPSIZE+4] != FROMSET && m[SUBEXPSIZE+4] != SETTONUM ) goto OnePV; j = m[SUBEXPSIZE+6]; if ( j > WILDOFFSET ) { j -= 2*WILDOFFSET; notflag2 = 1; } else { notflag2 = 0; } bfirst = SetElements + Sets[j].first; blast = SetElements + Sets[j].last; jj = 1; if ( notflag2 == 0 ) { do { if ( *bfirst == r[1] ) { if ( m[SUBEXPSIZE+4] == SETTONUM ) { m[SUBEXPSIZE+8] = SYMTONUM; m[SUBEXPSIZE+11] = jj; } else if ( m[SUBEXPSIZE+7] >= 0 ) { oldvv = *(bfirst - Sets[j].first + Sets[m[SUBEXPSIZE+7]].first); } goto OnePV; } jj++; } while ( ++bfirst < blast ); } else { do { if ( *bfirst == r[1] ) break; } while ( ++bfirst < blast ); if ( bfirst >= blast ) goto OnePV; } } } } while ( ++level2 < AR.Cnumlhs && C->lhs[level2][0] == TYPEIDOLD ); rnum = r[1]; goto OneOnly; } else if ( *afirst == r[1] ) { if ( vwhere[1] == SETTONUM ) { AN.FullProto[8+SUBEXPSIZE] = SYMTONUM; AN.FullProto[11+SUBEXPSIZE] = ii; } else if ( vwhere[4] >= 0 ) { oldv = *(afirst - Sets[j].first + Sets[vwhere[4]].first); } Hitlevel2: level2 = level; while ( ++level2 < AR.Cnumlhs && C->lhs[level2][0] == TYPEIDOLD ) { if ( !par ) m = C->lhs[level2]; else m = par; m += IDHEAD; if ( m[-IDHEAD+2] == SUBVECTOR ) { if ( ( vv = m[6] ) == *r ) goto OnePV; else if ( vv >= OffNum ) { if ( m[SUBEXPSIZE+4] != FROMSET && m[SUBEXPSIZE+4] != SETTONUM ) { j = *r; *r = r[1]; r[1] = j; goto OnePV; } j = m[SUBEXPSIZE+6]; bfirst = SetElements + Sets[j].first; blast = SetElements + Sets[j].last; jj = 1; do { if ( *bfirst == *r ) { if ( m[SUBEXPSIZE+4] == SETTONUM ) { m[SUBEXPSIZE+8] = SYMTONUM; m[SUBEXPSIZE+11] = jj; } else if ( m[SUBEXPSIZE+7] >= 0 ) { oldvv = *(bfirst - Sets[j].first + Sets[m[SUBEXPSIZE+7]].first); } j = *r; *r = r[1]; r[1] = j; j = oldv; oldv = oldvv; oldvv = j; goto OnePV; } jj++; } while ( ++bfirst < blast ); } } } jj = *r; *r = r[1]; r[1] = jj; jj = oldv; oldv = oldvv; oldvv = j; rnum = r[1]; goto OneOnly; } ii++; } while ( ++afirst < alast ); } else { do { if ( *afirst == *r ) break; } while ( ++afirst < alast ); if ( afirst >= alast ) goto Hitlevel1; do { if ( *afirst == r[1] ) break; } while ( ++afirst < alast ); if ( afirst >= alast ) goto Hitlevel2; } } else { /* Matches twice */ vv = v; TwoProto = AN.FullProto; goto TwoPV; } } } NextDot: r += 3; } while ( r < tstop ); } /* #] DOTPRODUCT : #[ LEVICIVITA : */ else if ( *t == LEVICIVITA ) { intens = 0; r = t; r += FUNHEAD; OneVect:; while ( r < tstop ) { oldv = *r; if ( v >= OffNum && *r < -10 ) { vwhere = AN.FullProto + 3+SUBEXPSIZE; if ( vwhere[1] == FROMSET || vwhere[1] == SETTONUM ) { WORD *afirst, *alast, j; j = vwhere[3]; if ( j > WILDOFFSET ) { j -= 2*WILDOFFSET; notflag1 = 1; } else { notflag1 = 0; } afirst = SetElements + Sets[j].first; alast = SetElements + Sets[j].last; ii = 1; if ( notflag1 == 0 ) { do { if ( *afirst == *r ) { if ( vwhere[1] == SETTONUM ) { AN.FullProto[8+SUBEXPSIZE] = SYMTONUM; AN.FullProto[11+SUBEXPSIZE] = ii; } else if ( vwhere[4] >= 0 ) { oldv = *(afirst - Sets[j].first + Sets[vwhere[4]].first); } goto DoVect; } ii++; } while ( ++afirst < alast ); } else { do { if ( *afirst == *r ) break; } while ( ++afirst < alast ); if ( afirst >= alast ) goto DoVect; } } else goto LeVect; } else if ( v == *r ) { LeVect: m = AT.WorkPointer; mstop = term + *term; t = term; *r = ++AR.CurDum; if ( intens ) *intens = DIRTYSYMFLAG; do { *m++ = *t++; } while ( t < tstop ); t = AN.FullProto; nq = t[1]; t[3] = 1; if ( v >= OffNum ) *vwhere = oldv; NCOPY(m,t,nq); m[-1] = AR.CurDum; t = tstop; do { *m++ = *t++; } while ( t < mstop ); *AT.WorkPointer = nq = WORDDIF(m,AT.WorkPointer); m = AT.WorkPointer; t = term; NCOPY(t,m,nq); AT.WorkPointer = t; return(1); } r++; } } /* #] LEVICIVITA : #[ GAMMA : */ else if ( *t == GAMMA ) { intens = 0; r = t; r += FUNHEAD+1; if ( r < tstop ) goto OneVect; } /* #] GAMMA : #[ INDEX : */ else if ( *t == INDEX ) { /* The 'forgotten' part */ r = t; r += 2; fromindex = 1; goto InVect; } /* #] INDEX : #[ FUNCTION : */ else if ( *t >= FUNCTION ) { if ( *t >= FUNCTION && functions[*t-FUNCTION].spec >= TENSORFUNCTION && t[1] > FUNHEAD ) { /* Tensors are linear in their vectors! */ r = t; r += FUNHEAD; intens = t+2; goto OneVect; } } /* #] FUNCTION : */ t += t[1]; } while ( t < m ); return(0); } /* #] FindAll : #[ TestSelect : Returns 1 if any of the objects in any of the sets in setp occur anywhere in the term */ int TestSelect(WORD *term, WORD *setp) { WORD *tstop, *t, *s, *el, *elstop, *termstop, *tt, n, ns; GETSTOP(term,tstop); term += 1; while ( term < tstop ) { switch ( *term ) { case SYMBOL: n = term[1] - 2; t = term + 2; while ( n > 0 ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CSYMBOL ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == *t ) return(1); } s++; } n -= 2; t += 2; } break; case VECTOR: n = term[1] - 2; t = term + 2; while ( n > 0 ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CVECTOR ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == *t ) return(1); } s++; } t++; ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CINDEX && Sets[*s].type != CNUMBER ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == *t ) return(1); } s++; } n -= 2; t++; } break; case INDEX: n = term[1] - 2; t = term + 2; goto dotensor; case DOTPRODUCT: n = term[1] - 2; t = term + 2; while ( n > 0 ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CVECTOR ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == *t ) return(1); } s++; } t++; ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CVECTOR ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == *t ) return(1); } s++; } n -= 3; t += 2; } break; case DELTA: n = term[1] - 2; t = term + 2; goto dotensor; default: if ( *term < FUNCTION ) break; ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CFUNCTION ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == *term ) return(1); } s++; } if ( functions[*term-FUNCTION].spec > 0 ) { n = term[1] - FUNHEAD; t = term + FUNHEAD; dotensor: while ( n > 0 ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( *t < MINSPEC ) { if ( Sets[*s].type != CVECTOR ) { s++; continue; } } else if ( *t >= 0 ) { if ( Sets[*s].type != CINDEX && Sets[*s].type != CNUMBER ) { s++; continue; } } else { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == *t ) return(1); } s++; } t++; n--; } } else { termstop = term + term[1]; tt = term + FUNHEAD; while ( tt < termstop ) { if ( *tt < 0 ) { if ( *tt == -SYMBOL ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CSYMBOL ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == tt[1] ) return(1); } s++; } tt += 2; } else if ( *tt == -VECTOR || *tt == -MINVECTOR ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CVECTOR ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == tt[1] ) return(1); } s++; } tt += 2; } else if ( *tt == -INDEX ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CINDEX && Sets[*s].type != CNUMBER ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == tt[1] ) return(1); } s++; } tt += 2; } else if ( *tt <= -FUNCTION ) { ns = setp[1] - 2; s = setp + 2; while ( --ns >= 0 ) { if ( Sets[*s].type != CFUNCTION ) { s++; continue; } el = SetElements + Sets[*s].first; elstop = SetElements + Sets[*s].last; while ( el < elstop ) { if ( *el++ == -(*tt) ) return(1); } s++; } tt++; } else tt += 2; } else { t = tt + ARGHEAD; tt += *tt; while ( t < tt ) { if ( TestSelect(t,setp) ) return(1); t += *t; } } } } break; } term += term[1]; } return(0); } /* #] TestSelect : #[ SubsInAll : void SubsInAll() This routine takes a match in id,all and stores it away in the AT.allbufnum 'compiler' buffer, after taking out the pattern. The main problem here is that id,all usually has (lots of) wildcards and their assignments are on stack and the difficult ones are in AT.ebufnum. Popping the stack while looking for more matches would loose those. Hence we have to copy them into yet another compiler buffer: AT.aebufnum. Because this may involve many matches and because the original term has only a limited number of arguments, it will pay to look for already existing ones in this buffer. (to be done later). */ void SubsInAll(PHEAD0) { GETBIDENTITY WORD *TemTerm; WORD *t, *m, *term; WORD *tstop, *mstop, *xstop; WORD nt, *fill, nq, mt; WORD *tcoef, i = 0; WORD PutExpr = 0, sign = 0; /* We start with building the term in the WorkSpace. Afterwards we will transfer it to AT.allbufnum. We have to make sure there is room in the WorkSpace. */ AT.idallflag = 2; TemTerm = AT.WorkPointer; if ( ( (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer*2) ) > AT.WorkTop ) { MLOCK(ErrorMessageLock); MesWork(); MUNLOCK(ErrorMessageLock); Terminate(-1); } m = AN.patternbuffer + IDHEAD; m += m[1]; mstop = m + *m; m++; term = AN.termbuffer; tstop = term + *term; tcoef = tstop-1; tstop -= ABS(tstop[-1]); t = term; t++; fill = TemTerm; fill++; while ( m < mstop ) { while ( t < tstop ) { nt = WORDDIF(t,term); for ( mt = 0; mt < AN.RepFunNum; mt += 2 ) { if ( nt == AN.RepFunList[mt] ) break; } if ( mt >= AN.RepFunNum ) { nq = t[1]; NCOPY(fill,t,nq); } else { WORD *oldt = 0; if ( *m == GAMMA && m[1] != FUNHEAD+1 ) { oldt = t; if ( ( i = AN.RepFunList[mt+1] ) > 0 ) { *fill++ = GAMMA; *fill++ = i + FUNHEAD+1; FILLFUN(fill) nq = i + 1; t += FUNHEAD; NCOPY(fill,t,nq); } t = oldt; } else if ( ( *t == LEVICIVITA ) || ( *t >= FUNCTION && (functions[*t-FUNCTION].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) ) sign += AN.RepFunList[mt+1]; else if ( *m >= FUNCTION+WILDOFFSET && (functions[*m-FUNCTION-WILDOFFSET].symmetric & ~REVERSEORDER) == ANTISYMMETRIC ) sign += AN.RepFunList[mt+1]; if ( !PutExpr ) { WORD *pstart = fill, *p, *w, *ww; xstop = t + t[1]; t = AN.FullProto; nq = t[1]; t[3] = 1; NCOPY(fill,t,nq); t = xstop; PutExpr = 1; /* Here we need provisions for keeping wildcard matches that reside in AT.ebufnum. We will move them to AT.aebufnum. Problem: the SUBEXPRESSION assumes automatically that the compiler buffer is AT.ebufnum. We have to correct that in TransferBuffer. */ p = pstart + SUBEXPSIZE; while ( p < fill ) { switch ( *p ) { case SYMTOSUB: case VECTOSUB: case INDTOSUB: case ARGTOARG: case ARLTOARL: w = cbuf[AT.ebufnum].rhs[p[3]]; ww = cbuf[AT.ebufnum].rhs[p[3]+1]; /* Here we could search for whether this object sits in the buffer already. To be done later. By the way: ww-w fits inside a WORD. */ AddRHS(AT.aebufnum,1); AddNtoC(AT.aebufnum,ww-w,w,11); p[3] = cbuf[AT.aebufnum].numrhs; cbuf[AT.aebufnum].rhs[p[3]+1] = cbuf[AT.aebufnum].Pointer; p += p[1]; break; case FROMSET: case SETTONUM: case LOADDOLLAR: p += p[1]; break; default: p += p[1]; break; } } } else t += t[1]; if ( *m == GAMMA && m[1] != FUNHEAD+1 ) { i = oldt[1] - m[1] - i; if ( i > 0 ) { *fill++ = GAMMA; *fill++ = i + FUNHEAD+1; FILLFUN(fill) *fill++ = oldt[FUNHEAD]; t = t - i; NCOPY(fill,t,i); } } break; } } m += m[1]; } while ( t < tstop ) *fill++ = *t++; if ( !PutExpr ) { t = AN.FullProto; nq = t[1]; t[3] = 1; NCOPY(fill,t,nq); } t = tcoef; nq = ABS(*t); t = tstop; NCOPY(fill,t,nq); if ( sign ) { if ( ( sign & 1 ) != 0 ) fill[-1] = -fill[-1]; } *TemTerm = fill-TemTerm; /* And now we copy this to AT.allbufnum */ AddNtoC(AT.allbufnum,TemTerm[0],TemTerm,12); cbuf[AT.allbufnum].Pointer[0] = 0; AN.RepFunNum = 0; } /* #] SubsInAll : #[ TransferBuffer : Adds the whole content of a (compiler)buffer to another buffer. In spectator we have an expression in the RHS that needs the wildcard resolutions adapted by an offset. */ void TransferBuffer(int from,int to,int spectator) { CBUF *C = cbuf + spectator; CBUF *Cf = cbuf + from; CBUF *Ct = cbuf + to; int offset = Ct->numrhs; LONG i; WORD *t, *tt, *ttt, *tstop, size; for ( i = 1; i <= Cf->numrhs; i++ ) { size = Cf->rhs[i+1]-Cf->rhs[i]; AddRHS(to,1); AddNtoC(to,size,Cf->rhs[i],13); } Ct->rhs[Ct->numrhs+1] = Ct->Pointer; Cf->numrhs = 0; /* Now we have to update the 'pointers' in the spectator. */ t = C->rhs[C->numrhs]; while ( *t ) { tt = t+1; t += *t; tstop = t-ABS(t[-1]); while ( tt < tstop ) { if ( *tt == SUBEXPRESSION ) { ttt = tt+SUBEXPSIZE; tt += tt[1]; while ( ttt < tt ) { switch ( *ttt ) { case SYMTOSUB: case VECTOSUB: case INDTOSUB: case ARGTOARG: case ARLTOARL: ttt[3] += offset; break; default: break; } ttt += 4; } } else tt += tt[1]; } } } /* #] TransferBuffer : #[ TakeIDfunction : */ #define PutInBuffers(pow) \ AddRHS(AT.ebufnum,1); \ *out++ = SUBEXPRESSION; \ *out++ = SUBEXPSIZE; \ *out++ = C->numrhs; \ *out++ = pow; \ *out++ = AT.ebufnum; \ FILLSUB(out) \ r = AT.pWorkSpace[rhs+i]; \ if ( *r > 0 ) { \ oldinr = r[*r]; r[*r] = 0; \ AddNtoC(AT.ebufnum,(*r+1-ARGHEAD),(r+ARGHEAD),14); \ r[*r] = oldinr; \ } \ else { \ ToGeneral(r,buffer,1); \ buffer[buffer[0]] = 0; \ AddNtoC(AT.ebufnum,buffer[0]+1,buffer,15); \ } int TakeIDfunction(PHEAD WORD *term) { WORD *tstop, *t, *r, *m, *f, *nextf, *funstop, *left, *l, *newterm; WORD *out, oldinr, pow; WORD buffer[20]; int i, ii, j, numsub, numfound = 0, first; LONG lhs,rhs; CBUF *C; GETSTOP(term,tstop); for ( t = term+1; t < tstop; t += t[1] ) { if ( *t == IDFUNCTION ) break; } if ( t >= tstop ) return(0); /* Step 1: test validity */ funstop = t + t[1]; f = t + FUNHEAD; left = term + *term; l = left+1; numsub = 0; while ( f < funstop ) { nextf = f; NEXTARG(nextf) if ( nextf >= funstop ) { return(0); } /* odd number of arguments */ if ( *f == -SYMBOL ) { *l++ = SYMBOL; *l++ = 4; *l++ = f[1]; *l++ = 1; } else if ( *f < -FUNCTION ) { *l++ = *f; *l++ = FUNHEAD; FILLFUN(l) } else if ( *f > 0 ) { if ( *f != f[ARGHEAD]+ARGHEAD ) goto noaction; if ( nextf[-1] != 3 || nextf[-2] != 1 || nextf[-3] != 1 ) goto noaction; if ( f[ARGHEAD] <= 4 ) goto noaction; if ( f[ARGHEAD] != f[ARGHEAD+2]+4 ) goto noaction; if ( f[ARGHEAD] == 8 && f[ARGHEAD+1] == SYMBOL ) { for ( i = 0; i < 4; i++ ) *l++ = f[ARGHEAD+1+i]; } else if ( f[ARGHEAD] == 9 && f[ARGHEAD+1] == DOTPRODUCT ) { for ( i = 0; i < 5; i++ ) *l++ = f[ARGHEAD+1+i]; } else if ( f[ARGHEAD+1] >= FUNCTION ) { for ( i = 0; i < f[ARGHEAD+1]-4; i++ ) *l++ = f[ARGHEAD+1+i]; } else goto noaction; } else goto noaction; numsub++; f = nextf; NEXTARG(f) } C = cbuf+AT.ebufnum; AT.WorkPointer = l; *left = l-left; /* Put the pointers to the lhs and the rhs in the pointer workspace */ WantAddPointers(2*numsub); lhs = AT.pWorkPointer; rhs = lhs+numsub; AT.pWorkPointer = rhs+numsub; f = t + FUNHEAD; l = left+1; for ( i = 0; i < numsub; i++ ) { AT.pWorkSpace[lhs+i] = l; l += l[1]; NEXTARG(f); AT.pWorkSpace[rhs+i] = f; NEXTARG(f); } /* Take out the patterns and replace them by SUBEXPRESSIONs pointing at the e buffer. We put the resulting term above the left sides. Note that we take out only the first id_ if there is more than one! */ first = 1; t = term+1; newterm = AT.WorkPointer; out = newterm+1; while ( t < tstop ) { if ( *t == IDFUNCTION && first ) { first = 0; t += t[1]; continue; } if ( *t >= FUNCTION ) { for ( i = 0; i < numsub; i++ ) { m = AT.pWorkSpace[lhs+i]; if ( *m != *t ) continue; for ( j = 1; j < t[1]; j++ ) { if ( m[j] != t[j] ) break; } if ( j != t[1] ) continue; numfound++; /* We have a match! Set up a SUBEXPRESSION subterm and put the corresponding rhs in the eBuffer. */ PutInBuffers(1) t += t[1]; } if ( i == numsub ) { /* no match. Just copy to output. */ j = t[1]; NCOPY(out,t,j) } } else if ( *t == SYMBOL ) { for ( i = 0; i < numsub; i++ ) { m = AT.pWorkSpace[lhs+i]; if ( *m != SYMBOL ) continue; for ( ii = 2; ii < t[1]; ii += 2 ) { if ( m[2] != t[ii] ) continue; pow = t[ii+1]/m[3]; if ( pow <= 0 ) continue; t[ii+1] = t[ii+1]%m[3]; numfound++; /* Create the proper rhs in the eBuffer and set up a SUBEXPRESSION subterm. */ PutInBuffers(pow) } } /* Now we copy whatever remains of the SYMBOL subterm to the output */ m = out; *out++ = t[0]; *out++ = t[1]; for ( ii = 2; ii < t[1]; ii += 2 ) { if ( t[ii+1] ) { *out++ = t[ii]; *out++ = t[ii+1]; } } m[1] = out-m; if ( m[1] == 2 ) out = m; t += t[1]; } else if ( *t == DOTPRODUCT ) { for ( i = 0; i < numsub; i++ ) { m = AT.pWorkSpace[lhs+i]; if ( *m != DOTPRODUCT ) continue; for ( ii = 2; ii < t[1]; ii += 3 ) { if ( m[2] != t[ii] || m[3] != t[ii+1] ) continue; pow = t[ii+2]/m[4]; if ( pow <= 0 ) continue; t[ii+2] = t[ii+2]%m[4]; numfound++; /* Create the proper rhs in the eBuffer and set up a SUBEXPRESSION subterm. */ PutInBuffers(pow) } } /* Now we copy whatever remains of the DOTPRODUCT subterm to the output */ m = out; *out++ = t[0]; *out++ = t[1]; for ( ii = 2; ii < t[1]; ii += 3 ) { if ( t[ii+2] ) { *out++ = t[ii]; *out++ = t[ii+1]; *out++ = t[ii+2]; } } m[1] = out-m; if ( m[1] == 2 ) out = m; t += t[1]; } else { j = t[1]; NCOPY(out,t,j) } } /* Copy the coefficient and set the size. */ t = tstop; r = term+*term; while ( t < r ) *out++ = *t++; *newterm = out-newterm; /* Finally we move the new term over the original term. */ i = *newterm; t = term; r = newterm; NCOPY(t,r,i) /* At this point we can return and if the calling Generator jumps back to its start, TestSub can take care of the expansions of SUBEXPRESSIONs. */ AT.pWorkPointer = lhs; AT.WorkPointer = t; return(numfound); noaction: return(0); } /* #] TakeIDfunction : #] Patterns : */ form-5.0.1/sources/poly.cc0000644000175100017510000021201715217035721011126 /* @file poly.cc * * Contains the class for representing sparse multivariate * polynomials with integer coefficients */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ includes : */ #include "poly.h" #include "polygcd.h" #include #include #include #include #include #include using namespace std; /* #] includes : #[ constructor (small constant polynomial) : */ // constructor for a small constant polynomial poly::poly (PHEAD int a, WORD modp, WORD modn): size_of_terms(AM.MaxTer/(LONG)sizeof(WORD)), modp(0), modn(1) { POLY_STOREIDENTITY; terms = TermMalloc("poly::poly(int)"); if (a == 0) { terms[0] = 1; // length } else { terms[0] = 4 + AN.poly_num_vars; // length terms[1] = 3 + AN.poly_num_vars; // length for (int i=0; i0 ? 1 : -1; // length coefficient } if (modp!=-1) setmod(modp,modn); } /* #] constructor (small constant polynomial) : #[ constructor (large constant polynomial) : */ // constructor for a large constant polynomial poly::poly (PHEAD const UWORD *a, WORD na, WORD modp, WORD modn): size_of_terms(AM.MaxTer/(LONG)sizeof(WORD)), modp(0), modn(1) { POLY_STOREIDENTITY; terms = TermMalloc("poly::poly(UWORD*,WORD)"); // remove leading zeros while (*(a+ABS(na)-1)==0) na -= SGN(na); terms[0] = 3 + AN.poly_num_vars + ABS(na); // length terms[1] = terms[0] - 1; // length for (int i=0; i MAXPOSITIVE) { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: polynomials too large (> WORDSIZE)"); MUNLOCK(ErrorMessageLock); Terminate(1); } WORD *newterms = (WORD *)Malloc1(new_size_of_terms * sizeof(WORD), "poly::expand_memory"); WCOPY(newterms, terms, size_of_terms); if (size_of_terms == AM.MaxTer/(LONG)sizeof(WORD)) TermFree(terms, "poly::expand_memory"); else M_free(terms, "poly::expand_memory"); terms = newterms; size_of_terms = new_size_of_terms; } /* #] expand_memory : #[ setmod : */ // sets the coefficient space to ZZ/p^n void poly::setmod(WORD _modp, WORD _modn) { POLY_GETIDENTITY(*this); if (_modp>0 && (_modp!=modp || _modn +(WORD)a[0]/2) terms[j+1+AN.poly_num_vars]-=a[0]; if (terms[j+1+AN.poly_num_vars] < -(WORD)a[0]/2) terms[j+1+AN.poly_num_vars]+=a[0]; n = SGN(terms[j+1+AN.poly_num_vars]); terms[j+1+AN.poly_num_vars] = ABS(terms[j+1+AN.poly_num_vars]); } } else TakeNormalModulus((UWORD *)&terms[j+1+AN.poly_num_vars], &n, a, na, NOUNPACK); if (n!=0) { terms[j] = 2+AN.poly_num_vars+ABS(n); terms[j+terms[j]-1] = n; j += terms[j]; } } terms[0] = j; } /* #] coefficients_modulo : #[ to_string : */ // converts an integer to a string const string int_to_string (WORD x) { char res[41]; snprintf (res, 41, "%i",x); return res; } // converts a polynomial to a string const string poly::to_string() const { POLY_GETIDENTITY(*this); string res; int printtimes; UBYTE *scoeff = (UBYTE *)NumberMalloc("poly::to_string"); if (terms[0]==1) // zero res = "0"; else { for (int i=1; i1) res += "+"; } if (ncoeff==1 && terms[i+terms[i]-1-ncoeff]==1) { // coeff=1, so don't print coefficient and '*' printtimes = 0; } else { // print coefficient PrtLong((UWORD*)&terms[i+terms[i]-1-ncoeff], ncoeff, scoeff); res += string((char *)scoeff); printtimes=1; } // print variables for (int j=0; j 0) { if (printtimes) res += "*"; res += string(1,'a'+j); if (terms[i+1+j] > 1) res += "^" + int_to_string(terms[i+1+j]); printtimes = 1; } } // iff coeff=1 and all power=0, print '1' after all if (!printtimes) res += "1"; } } // eventual modulo if (modp>0) { res += " (mod "; res += int_to_string(modp); if (modn>1) { res += "^"; res += int_to_string(modn); } res += ")"; } NumberFree(scoeff,"poly::to_string"); return res; } /* #] to_string : #[ ostream operator : */ // output stream operator ostream& operator<< (ostream &out, const poly &a) { return out << a.to_string(); } /* #] ostream operator : #[ monomial_compare : */ // compares two monomials (0:equal, <0:a smaller, >0:b smaller) int poly::monomial_compare (PHEAD const WORD *a, const WORD *b) { for (int i=0; i0 && monomial_compare(BHEAD &tmp[j], p[i])==0) { // duplicate term, so add coefficients WORD ncoeff = tmp[j+tmp[j]-1]; AddLong((UWORD *)&tmp[j+1+AN.poly_num_vars], ncoeff, (UWORD *)&p[i][1+AN.poly_num_vars], p[i][p[i][0]-1], (UWORD *)&tmp[j+1+AN.poly_num_vars], &ncoeff); tmp[j+1+AN.poly_num_vars+ABS(ncoeff)] = ncoeff; tmp[j] = 2+AN.poly_num_vars+ABS(ncoeff); } else { // new term prevj = j; j += tmp[j]; WCOPY(&tmp[j],p[i],p[i][0]); } if (modp!=0) { // bring coefficient to normal form mod p^n WORD ntmp = tmp[j+tmp[j]-1]; TakeNormalModulus((UWORD *)&tmp[j+1+AN.poly_num_vars], &ntmp, modq,nmodq, NOUNPACK); tmp[j] = 2+AN.poly_num_vars+ABS(ntmp); tmp[j+tmp[j]-1] = ntmp; } // add terms to polynomial if (tmp[j+tmp[j]-1]==0) { tmp[j]=0; j=prevj; } } j+=tmp[j]; tmp[0] = j; WCOPY(terms,tmp,tmp[0]); // M_free(p, "poly::normalize"); if (size_of_terms == AM.MaxTer/(LONG)sizeof(WORD)) TermFree(tmp, "poly::normalize"); else M_free(tmp, "poly::normalize"); AT.pWorkPointer = poffset; #undef p return *this; } /* #] normalize : #[ last_monomial_index : */ // index of the last monomial, i.e., the constant term WORD poly::last_monomial_index () const { POLY_GETIDENTITY(*this); return terms[0] - ABS(terms[terms[0]-1]) - AN.poly_num_vars - 2; } // pointer to the last monomial (the constant term) WORD * poly::last_monomial () const { return &terms[last_monomial_index()]; } /* #] last_monomial_index : #[ compare_degree_vector : */ int poly::compare_degree_vector(const poly & b) const { POLY_GETIDENTITY(*this); // special cases if one or both are 0 if (terms[0] == 1 && b[0] == 1) return 0; if (terms[0] == 1) return -1; if (b[0] == 1) return 1; for (int i = 0; i < AN.poly_num_vars; i++) { int d1 = degree(i); int d2 = b.degree(i); if (d1 != d2) return d1 - d2; } return 0; } /* #] compare_degree_vector : #[ degree_vector : */ std::vector poly::degree_vector() const { POLY_GETIDENTITY(*this); std::vector degrees(AN.poly_num_vars); for (int i = 0; i < AN.poly_num_vars; i++) { degrees[i] = degree(i); } return degrees; } /* #] degree_vector : #[ compare_degree_vector : */ int poly::compare_degree_vector(const vector & b) const { POLY_GETIDENTITY(*this); if (terms[0] == 1) return -1; for (int i = 0; i < AN.poly_num_vars; i++) { int d1 = degree(i); if (d1 != b[i]) return d1 - b[i]; } return 0; } /* #] compare_degree_vector : #[ add : */ // addition of polynomials by merging void poly::add (const poly &a, const poly &b, poly &c) { POLY_GETIDENTITY(a); c.modp = a.modp; c.modn = a.modn; WORD nmodq=0; UWORD *modq=NULL; bool both_mod_small=false; if (c.modp!=0) { if (c.modn == 1) { modq = (UWORD *)&c.modp; nmodq = 1; if (a.modp>0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD c.modp,c.modn,&modq,&nmodq); } } int ai=1,bi=1,ci=1; while (ai0) { // insert term from a c.termscopy(&a[ai],ci,a[ai]); ci+=a[ai]; ai+=a[ai]; } else if (ai==a[0] || cmp<0) { // insert term from b c.termscopy(&b[bi],ci,b[bi]); ci+=b[bi]; bi+=b[bi]; } else { // insert term from a+b c.termscopy(&a[ai],ci,MaX(a[ai],b[bi])); WORD nc=0; if (both_mod_small) { c[ci+1+AN.poly_num_vars] = ((LONG)a[ai+1+AN.poly_num_vars]*a[ai+a[ai]-1]+ (LONG)b[bi+1+AN.poly_num_vars]*b[bi+b[bi]-1]) % c.modp; if ((WORD)c[ci+1+AN.poly_num_vars] > +c.modp/2) c[ci+1+AN.poly_num_vars] -= c.modp; if ((WORD)c[ci+1+AN.poly_num_vars] < -c.modp/2) c[ci+1+AN.poly_num_vars] += c.modp; nc = (c[ci+1+AN.poly_num_vars]==0 ? 0 : SGN((WORD)c[ci+1+AN.poly_num_vars])); c[ci+1+AN.poly_num_vars] = ABS((WORD)c[ci+1+AN.poly_num_vars]); } else { AddLong((UWORD *)&a[ai+1+AN.poly_num_vars], a[ai+a[ai]-1], (UWORD *)&b[bi+1+AN.poly_num_vars], b[bi+b[bi]-1], (UWORD *)&c[ci+1+AN.poly_num_vars], &nc); if (c.modp!=0) TakeNormalModulus((UWORD *)&c[ci+1+AN.poly_num_vars], &nc, modq, nmodq, NOUNPACK); } if (nc!=0) { c[ci] = 2+AN.poly_num_vars+ABS(nc); c[ci+c[ci]-1] = nc; ci += c[ci]; } ai+=a[ai]; bi+=b[bi]; } } c[0]=ci; } /* #] add : #[ sub : */ // subtraction of polynomials by merging void poly::sub (const poly &a, const poly &b, poly &c) { POLY_GETIDENTITY(a); c.modp = a.modp; c.modn = a.modn; WORD nmodq=0; UWORD *modq=NULL; bool both_mod_small=false; if (c.modp!=0) { if (c.modn == 1) { modq = (UWORD *)&c.modp; nmodq = 1; if (a.modp>0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD c.modp,c.modn,&modq,&nmodq); } } int ai=1,bi=1,ci=1; while (ai0) { // insert term from a c.termscopy(&a[ai],ci,a[ai]); ci+=a[ai]; ai+=a[ai]; } else if (ai==a[0] || cmp<0) { // insert term from b c.termscopy(&b[bi],ci,b[bi]); ci+=b[bi]; bi+=b[bi]; c[ci-1]*=-1; } else { // insert term from a+b c.termscopy(&a[ai],ci,MaX(a[ai],b[bi])); WORD nc=0; if (both_mod_small) { c[ci+1+AN.poly_num_vars] = ((LONG)a[ai+1+AN.poly_num_vars]*a[ai+a[ai]-1]- (LONG)b[bi+1+AN.poly_num_vars]*b[bi+b[bi]-1]) % c.modp; if ((WORD)c[ci+1+AN.poly_num_vars] > +c.modp/2) c[ci+1+AN.poly_num_vars] -= c.modp; if ((WORD)c[ci+1+AN.poly_num_vars] < -c.modp/2) c[ci+1+AN.poly_num_vars] += c.modp; nc = (c[ci+1+AN.poly_num_vars]==0 ? 0 : SGN((WORD)c[ci+1+AN.poly_num_vars])); c[ci+1+AN.poly_num_vars] = ABS((WORD)c[ci+1+AN.poly_num_vars]); } else { AddLong((UWORD *)&a[ai+1+AN.poly_num_vars], a[ai+a[ai]-1], (UWORD *)&b[bi+1+AN.poly_num_vars],-b[bi+b[bi]-1], // -b[...] causes subtraction (UWORD *)&c[ci+1+AN.poly_num_vars], &nc); if (c.modp!=0) TakeNormalModulus((UWORD *)&c[ci+1+AN.poly_num_vars], &nc, modq, nmodq, NOUNPACK); } if (nc!=0) { c[ci] = 2+AN.poly_num_vars+ABS(nc); c[ci+c[ci]-1] = nc; ci += c[ci]; } ai+=a[ai]; bi+=b[bi]; } } c[0]=ci; } /* #] sub : #[ pop_heap : */ // pops the largest monomial from the heap and stores it in heap[n] void poly::pop_heap (PHEAD WORD **heap, int n) { WORD *old = heap[0]; heap[0] = heap[--n]; int i=0; while (2*i+20 || monomial_compare(BHEAD heap[2*i+2]+3, heap[i]+3)>0)) { if (monomial_compare(BHEAD heap[2*i+1]+3, heap[2*i+2]+3)>0) { swap(heap[i], heap[2*i+1]); i=2*i+1; } else { swap(heap[i], heap[2*i+2]); i=2*i+2; } } if (2*i+10) swap(heap[i], heap[2*i+1]); heap[n] = old; } /* #] pop_heap : #[ push_heap : */ // pushes the monomial in heap[n] onto the heap void poly::push_heap (PHEAD WORD **heap, int n) { int i=n-1; while (i>0 && monomial_compare(BHEAD heap[i]+3, heap[(i-1)/2]+3) > 0) { swap(heap[(i-1)/2], heap[i]); i=(i-1)/2; } } /* #] push_heap : #[ mul_one_term : */ // multiplies a polynomial with a monomial void poly::mul_one_term (const poly &a, const poly &b, poly &c) { POLY_GETIDENTITY(a); int ci=1; WORD nmodq=0; UWORD *modq=NULL; bool both_mod_small=false; if (c.modp!=0) { if (c.modn == 1) { modq = (UWORD *)&c.modp; nmodq = 1; if (a.modp>0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD c.modp,c.modn,&modq,&nmodq); } } for (int ai=1; ai +c.modp/2) c[ci-2] -= c.modp; if (c[ci-2] < -c.modp/2) c[ci-2] += c.modp; c[ci-1] = SGN(c[ci-2]); c[ci-2] = ABS(c[ci-2]); } else { c[ci-1] = nc; } } } c[0]=ci; } /* #] mul_one_term : #[ mul_univar : */ // dense univariate multiplication, i.e., for each power find all // pairs of monomials that result in that power void poly::mul_univar (const poly &a, const poly &b, poly &c, int var) { POLY_GETIDENTITY(a); WORD nmodq=0; UWORD *modq=NULL; bool both_mod_small=false; if (c.modp!=0) { if (c.modn == 1) { modq = (UWORD *)&c.modp; nmodq = 1; if (a.modp>0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD c.modp,c.modn,&modq,&nmodq); } } poly t(BHEAD 0); WORD nt; int ci=1; // bounds on the powers in a*b int minpow = AN.poly_num_vars==0 ? 0 : a.last_monomial()[1+var] + b.last_monomial()[1+var]; int maxpow = AN.poly_num_vars==0 ? 0 : a[2+var]+b[2+var]; int afirst=1, blast=1; for (int pow=maxpow; pow>=minpow; pow--) { c.check_memory(ci); WORD nc=0; // adjust range in a or b if (a[afirst+1+var] + b[blast+1+var] > pow) { if (blast+b[blast] < b[0]) blast+=b[blast]; else afirst+=a[afirst]; } // find terms that result in the correct power for (int ai=afirst, bi=blast; ai=1;) { int thispow = AN.poly_num_vars==0 ? 0 : a[ai+1+var] + b[bi+1+var]; if (thispow == pow) { // if both polynomials are modulo p^1, use integer calculus if (both_mod_small) { c[ci+1+AN.poly_num_vars] = ((nc==0 ? 0 : (LONG)c[ci+1+AN.poly_num_vars] * nc) + (LONG)a[ai+1+AN.poly_num_vars] * a[ai+2+AN.poly_num_vars] * b[bi+1+AN.poly_num_vars] * b[bi+2+AN.poly_num_vars]) % c.modp; nc = (c[ci+1+AN.poly_num_vars]==0 ? 0 : 1); } else { // otherwise, use form long calculus MulLong((UWORD *)&a[ai+1+AN.poly_num_vars], a[ai+a[ai]-1], (UWORD *)&b[bi+1+AN.poly_num_vars], b[bi+b[bi]-1], (UWORD *)&t[0], &nt); AddLong ((UWORD *)&t[0], nt, (UWORD *)&c[ci+1+AN.poly_num_vars], nc, (UWORD *)&c[ci+1+AN.poly_num_vars], &nc); if (c.modp!=0) TakeNormalModulus((UWORD *)&c[ci+1+AN.poly_num_vars], &nc, modq, nmodq, NOUNPACK); } ai += a[ai]; bi -= ABS(b[bi-1]) + 2 + AN.poly_num_vars; } else if (thispow > pow) ai += a[ai]; else bi -= ABS(b[bi-1]) + 2 + AN.poly_num_vars; } // add term to result if (nc != 0) { for (int j=0; j 0) c[ci+1+var] = pow; c[ci] = 2+AN.poly_num_vars+ABS(nc); ci += c[ci]; // if necessary, adjust to range [-p/2,p/2] if (both_mod_small) { if (c[ci-2] > +c.modp/2) c[ci-2] -= c.modp; if (c[ci-2] < -c.modp/2) c[ci-2] += c.modp; c[ci-1] = SGN(c[ci-2]); c[ci-2] = ABS(c[ci-2]); } else { c[ci-1] = nc; } } } c[0] = ci; } /* #] mul_univar : #[ mul_heap : */ /** Multiplication of polynomials with a heap * * Description * =========== * Multiplies two multivariate polynomials. The next element of the * product is efficiently determined by using a heap. If the product * of the maximum power in all variables is small, a hash table is * used to add equal terms for extra speed. * * A heap element h is formatted as follows: * - h[0] = index in a * - h[1] = index in b * - h[2] = hash code (-1 if no hash is used) * - h[3] = length of coefficient with sign * - h[4...4+AN.poly_num_vars-1] = powers * - h[4+AN.poly_num_vars...4+h[3]-1] = coefficient */ void poly::mul_heap (const poly &a, const poly &b, poly &c) { POLY_GETIDENTITY(a); WORD nmodq=0; UWORD *modq=NULL; bool both_mod_small=false; if (c.modp!=0) { if (c.modn == 1) { modq = (UWORD *)&c.modp; nmodq = 1; if (a.modp>0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD c.modp,c.modn,&modq,&nmodq); } } // find maximum powers in different variables WORD *maxpower = AT.WorkPointer; AT.WorkPointer += AN.poly_num_vars; WORD *maxpowera = AT.WorkPointer; AT.WorkPointer += AN.poly_num_vars; WORD *maxpowerb = AT.WorkPointer; AT.WorkPointer += AN.poly_num_vars; for (int i=0; i POLY_MAX_HASH_SIZE / (maxpower[i]+1)) { nhash = 1; use_hash = false; break; } nhash *= maxpower[i]+1; } // allocate heap and hash int nheap=a.number_of_terms(); WantAddPointers(nheap+nhash); WORD **heap = AT.pWorkSpace + AT.pWorkPointer; for (int ai=1, i=0; ai 0) { c.check_memory(ci); pop_heap(BHEAD heap, nheap--); WORD *p = heap[nheap]; // if non-zero if (p[3] != 0) { if (use_hash) hash[p[2]] = NULL; c[0] = ci; // append this term to the result if (use_hash || ci==1 || monomial_compare(BHEAD p+3, c.last_monomial())!=0) { p[4 + AN.poly_num_vars + ABS(p[3])] = p[3]; p[3] = 2 + AN.poly_num_vars + ABS(p[3]); c.termscopy(&p[3],ci,p[3]); ci += c[ci]; } else { // add this term to the last term of the result ci = c.last_monomial_index(); WORD nc = c[ci+c[ci]-1]; // if both polynomials are modulo p^1, use integer calculus if (both_mod_small) { c[ci+AN.poly_num_vars+1] = ((LONG)c[ci+AN.poly_num_vars+1]*nc + p[4+AN.poly_num_vars]*p[3]) % c.modp; if (c[ci+1+AN.poly_num_vars]==0) nc = 0; else { if (c[ci+1+AN.poly_num_vars] > +c.modp/2) c[ci+1+AN.poly_num_vars] -= c.modp; if (c[ci+1+AN.poly_num_vars] < -c.modp/2) c[ci+1+AN.poly_num_vars] += c.modp; nc = SGN(c[ci+1+AN.poly_num_vars]); c[ci+1+AN.poly_num_vars] = ABS(c[ci+1+AN.poly_num_vars]); } } else { // otherwise, use form long calculus AddLong ((UWORD *)&p[4+AN.poly_num_vars], p[3], (UWORD *)&c[ci+AN.poly_num_vars+1], nc, (UWORD *)&c[ci+AN.poly_num_vars+1],&nc); if (c.modp!=0) TakeNormalModulus((UWORD *)&c[ci+1+AN.poly_num_vars], &nc, modq, nmodq, NOUNPACK); } if (nc!=0) { c[ci] = 2 + AN.poly_num_vars + ABS(nc); ci += c[ci]; c[ci-1] = nc; } } } // add new term to the heap (ai, bi+1) while (p[1] < b[0]) { for (int j=0; j +c.modp/2) p[4+AN.poly_num_vars] -= c.modp; if (p[4+AN.poly_num_vars] < -c.modp/2) p[4+AN.poly_num_vars] += c.modp; p[3] = SGN(p[4+AN.poly_num_vars]); p[4+AN.poly_num_vars] = ABS(p[4+AN.poly_num_vars]); } } else { // otherwise, use form long calculus MulLong((UWORD *)&a[p[0]+1+AN.poly_num_vars], a[p[0]+a[p[0]]-1], (UWORD *)&b[p[1]+1+AN.poly_num_vars], b[p[1]+b[p[1]]-1], (UWORD *)&p[4+AN.poly_num_vars], &p[3]); if (c.modp!=0) TakeNormalModulus((UWORD *)&p[4+AN.poly_num_vars], &p[3], modq, nmodq, NOUNPACK); } p[1] += b[p[1]]; if (use_hash) { int ID = 0; for (int i=0; i +c.modp/2) h[4+AN.poly_num_vars] -= c.modp; if (h[4+AN.poly_num_vars] < -c.modp/2) h[4+AN.poly_num_vars] += c.modp; h[3] = SGN(h[4+AN.poly_num_vars]); h[4+AN.poly_num_vars] = ABS(h[4+AN.poly_num_vars]); } } else { // otherwise, use form long calculus AddLong ((UWORD *)&p[4+AN.poly_num_vars], p[3], (UWORD *)&h[4+AN.poly_num_vars], h[3], (UWORD *)&h[4+AN.poly_num_vars], &h[3]); if (c.modp!=0) TakeNormalModulus((UWORD *)&h[4+AN.poly_num_vars], &h[3], modq, nmodq, NOUNPACK); } } } else { // if no hash, push onto heap p[2] = -1; push_heap(BHEAD heap, ++nheap); break; } } } c[0] = ci; for (int ai=1, i=0; ai0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD q.modp,q.modn,&modq,&nmodq); } ltbinv = NumberMalloc("poly::div_one_term"); if (both_mod_small) { WORD ltb = b[b[1]]*b[2+AN.poly_num_vars]; GetModInverses(ltb + (ltb<0?q.modp:0), q.modp, (WORD*)ltbinv, NULL); nltbinv = 1; } else GetLongModInverses(BHEAD (UWORD *)&b[2+AN.poly_num_vars], b[b[1]], modq, nmodq, ltbinv, &nltbinv, NULL, NULL); } for (int ai=1; ai +q.modp/2) q[qi-2] -= q.modp; if (q[qi-2] < -q.modp/2) q[qi-2] += q.modp; q[qi-1] = SGN(q[qi-2]); q[qi-2] = ABS(q[qi-2]); } else { q[qi-1] = nq; } } if (nr != 0) { if (only_divides) { r = poly(BHEAD 1); ri=r[0]; break; } r[ri] = 2+AN.poly_num_vars+ABS(nr); ri += r[ri]; r[ri-1] = nr; } } q[0]=qi; r[0]=ri; if (q.modp!=0 || ltbinv != NULL) NumberFree(ltbinv,"poly::div_one_term"); } /* #] divmod_one_term : #[ divmod_univar : : */ /** Division of dense univariate polynomials. * * Description * =========== * Divides two dense univariate polynomials. For each power, the * method collects all terms that result in that power. * * Relevant formula [Q=A/B, P=SUM(p_i*x^i), n=deg(A), m=deg(B)]: * q_k = [ a_{m+k} - SUM(i=k+1...n-m, b_{m+k-i}*q_i) ] / b_m */ void poly::divmod_univar (const poly &a, const poly &b, poly &q, poly &r, int var, bool only_divides) { POLY_GETIDENTITY(a); WORD nmodq=0; UWORD *modq=NULL; WORD nltbinv=0; UWORD *ltbinv=NULL; bool both_mod_small=false; if (q.modp!=0) { if (q.modn == 1) { modq = (UWORD *)&q.modp; nmodq = 1; if (a.modp>0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD q.modp,q.modn,&modq,&nmodq); } ltbinv = NumberMalloc("poly::div_univar"); if (both_mod_small) { WORD ltb = b[b[1]]*b[2+AN.poly_num_vars]; GetModInverses(ltb + (ltb<0?q.modp:0), q.modp, (WORD*)ltbinv, NULL); nltbinv = 1; } else GetLongModInverses(BHEAD (UWORD *)&b[2+AN.poly_num_vars], b[b[1]], modq, nmodq, ltbinv, &nltbinv, NULL, NULL); } WORD ns=0; WORD nt; UWORD *s = NumberMalloc("poly::div_univar"); UWORD *t = NumberMalloc("poly::div_univar"); s[0]=0; int bpow = b[2+var]; int ai=1, qi=1, ri=1; for (int pow=a[2+var]; pow>=0; pow--) { q.check_memory(qi); r.check_memory(ri); // look for the correct power in a while (ai pow) ai+=a[ai]; // first term of the r.h.s. of the above equation if (ai1 && bi pow) bi += b[bi]; if (bi +q.modp/2) s[0] -= q.modp; if ((WORD)s[0] < -q.modp/2) s[0] += q.modp; ns = SGN((WORD)s[0]); s[0] = ABS((WORD)s[0]); } if (pow >= bpow) { // large power, so divide by b if (q.modp == 0) { DivLong(s, ns, (UWORD *)&b[2+AN.poly_num_vars], b[b[1]], (UWORD *)&q[qi+1+AN.poly_num_vars], &ns, t, &nt); } else { if (both_mod_small) { q[qi+1+AN.poly_num_vars] = ((LONG)s[0]*ns*ltbinv[0]*nltbinv) % q.modp; if ((WORD)q[qi+1+AN.poly_num_vars] > +q.modp/2) q[qi+1+AN.poly_num_vars] -= q.modp; if ((WORD)q[qi+1+AN.poly_num_vars] < -q.modp/2) q[qi+1+AN.poly_num_vars] += q.modp; ns = (q[qi+1+AN.poly_num_vars]==0 ? 0 : SGN((WORD)q[qi+1+AN.poly_num_vars])); q[qi+1+AN.poly_num_vars] = ABS((WORD)q[qi+1+AN.poly_num_vars]); } else { MulLong(s, ns, ltbinv, nltbinv, (UWORD *)&q[qi+1+AN.poly_num_vars], &ns); TakeNormalModulus((UWORD *)&q[qi+1+AN.poly_num_vars], &ns, modq,nmodq, NOUNPACK); } nt=0; } } else { // small power, so remainder WCOPY(t,s,ABS(ns)); nt = ns; ns = 0; } // add terms to quotient/remainder if (ns!=0) { for (int i=0; i0 && b.modp>0 && a.modn==1 && b.modn==1) both_mod_small=true; } else { RaisPowCached(BHEAD q.modp,q.modn,&modq,&nmodq); } ltbinv = NumberMalloc("poly::div_heap-a"); if (both_mod_small) { WORD ltb = b[b[1]]*b[2+AN.poly_num_vars]; GetModInverses(ltb + (ltb<0?q.modp:0), q.modp, (WORD*)ltbinv, NULL); nltbinv = 1; } else GetLongModInverses(BHEAD (UWORD *)&b[2+AN.poly_num_vars], b[b[1]], modq, nmodq, ltbinv, &nltbinv, NULL, NULL); } // allocate heap int nb=b.number_of_terms(); WantAddPointers(nb); WORD **heap = AT.pWorkSpace + AT.pWorkPointer; AT.pWorkPointer += nb; for (int i=0; i > insert; while (insert.size()>0 || nheap>0) { q.check_memory(qi); r.check_memory(ri); // collect a term t for the quotient/remainder t[0] = -1; do { WORD *p = heap[nheap]; bool this_insert; if (insert.empty()) { // extract element from the heap and prepare adding new ones this_insert = false; pop_heap(BHEAD heap, nheap--); p = heap[nheap]; if (t[0] == -1) { WCOPY(t, p, (5+ABS(p[3])+AN.poly_num_vars)); } else { // if both polynomials are modulo p^1, use integer calculus if (both_mod_small) { t[4+AN.poly_num_vars] = ((LONG)t[4+AN.poly_num_vars]*t[3] + p[4+AN.poly_num_vars]*p[3]) % q.modp; if (t[4+AN.poly_num_vars]==0) t[3]=0; else { if (t[4+AN.poly_num_vars] > +q.modp/2) t[4+AN.poly_num_vars] -= q.modp; if (t[4+AN.poly_num_vars] < -q.modp/2) t[4+AN.poly_num_vars] += q.modp; t[3] = SGN(t[4+AN.poly_num_vars]); t[4+AN.poly_num_vars] = ABS(t[4+AN.poly_num_vars]); } } else { // otherwise, use form long calculus AddLong ((UWORD *)&p[4+AN.poly_num_vars], p[3], (UWORD *)&t[4+AN.poly_num_vars], t[3], (UWORD *)&t[4+AN.poly_num_vars], &t[3]); if (q.modp!=0) TakeNormalModulus((UWORD *)&t[4+AN.poly_num_vars], &t[3], modq, nmodq, NOUNPACK); } } } else { // prepare adding an element of insert to the heap this_insert = true; p[0] = insert.back().first; p[1] = insert.back().second; insert.pop_back(); } // add elements to the heap while (true) { // prepare the element if (p[1]==0) { p[0] += a[p[0]]; if (p[0]==a[0]) break; WCOPY(&p[3], &a[p[0]], a[p[0]]); p[3] = p[2+p[3]]; } else { if (!this_insert) p[1] += q[p[1]]; this_insert = false; if (p[1]==qi) { s++; break; } for (int i=0; i +q.modp/2) p[4+AN.poly_num_vars] -= q.modp; if (p[4+AN.poly_num_vars] < -q.modp/2) p[4+AN.poly_num_vars] += q.modp; p[3] = SGN(p[4+AN.poly_num_vars]); p[4+AN.poly_num_vars] = ABS(p[4+AN.poly_num_vars]); } } else { // otherwise, use form long calculus MulLong((UWORD *)&b[p[0]+1+AN.poly_num_vars], b[p[0]+b[p[0]]-1], (UWORD *)&q[p[1]+1+AN.poly_num_vars], q[p[1]+q[p[1]]-1], (UWORD *)&p[4+AN.poly_num_vars], &p[3]); if (q.modp!=0) TakeNormalModulus((UWORD *)&p[4+AN.poly_num_vars], &p[3], modq, nmodq, NOUNPACK); } p[3] *= -1; } // no hashing p[2] = -1; // add it to a heap element swap (heap[nheap],p); push_heap(BHEAD heap, ++nheap); break; } } while (t[0]==-1 || (nheap>0 && monomial_compare(BHEAD heap[0]+3, t+3)==0)); if (t[3] == 0) continue; // check divisibility bool div = true; for (int i=0; i result not expressible in integers div_fail = true; break; } } else { // if both polynomials are modulo p^1, use integer calculus if (both_mod_small) { q[qi+1+AN.poly_num_vars] = ((LONG)t[4+AN.poly_num_vars]*t[3]*ltbinv[0]*nltbinv) % q.modp; if (q[qi+1+AN.poly_num_vars]==0) nq=0; else { if (q[qi+1+AN.poly_num_vars] > +q.modp/2) q[qi+1+AN.poly_num_vars] -= q.modp; if (q[qi+1+AN.poly_num_vars] < -q.modp/2) q[qi+1+AN.poly_num_vars] += q.modp; nq = SGN(q[qi+1+AN.poly_num_vars]); q[qi+1+AN.poly_num_vars] = ABS(q[qi+1+AN.poly_num_vars]); } } else { // otherwise, use form long calculus MulLong((UWORD *)&t[4+AN.poly_num_vars], t[3], ltbinv, nltbinv, (UWORD *)&q[qi+1+AN.poly_num_vars], &nq); TakeNormalModulus((UWORD *)&q[qi+1+AN.poly_num_vars], &nq, modq, nmodq, NOUNPACK); } nr=0; } // add terms to quotient and remainder if (nq != 0) { int bi = 1; for (int j=1; j0) return j; return var; } /* #] first_variable : #[ all_variables : */ // returns a list of all variables of a polynomial const vector poly::all_variables () const { POLY_GETIDENTITY(*this); vector used(AN.poly_num_vars, false); for (int i=1; i0) used[j] = true; vector vars; for (int i=0; i 0 ? 1 : -1; } /* #] sign : #[ degree : */ // returns the degree of x of a polynomial (deg=-1 iff a=0) int poly::degree (int x) const { int deg = -1; for (int i=1; i 0) { b.check_memory(bi); b.termscopy(&terms[i], bi, terms[i]); b[bi+1+x]--; WORD nb = b[bi+b[bi]-1]; Product((UWORD *)&b[bi+1+AN.poly_num_vars], &nb, power); b[bi] = 2 + AN.poly_num_vars + ABS(nb); b[bi+b[bi]-1] = nb; bi += b[bi]; } } b[0] = bi; b.setmod(modp, modn); return b; } /* #] derivative : #[ is_zero : */ // returns whether the polynomial is zero bool poly::is_zero () const { return terms[0] == 1; } /* #] is_zero : #[ is_one : */ // returns whether the polynomial is one bool poly::is_one () const { POLY_GETIDENTITY(*this); if (terms[0] != 4+AN.poly_num_vars) return false; if (terms[1] != 3+AN.poly_num_vars) return false; for (int i=0; i1 && terms[0]==terms[1]+1; } /* #] is_monomial : #[ is_dense_univariate : */ /** Dense univariate detection * * Description * =========== * This method returns whether the polynomial is dense and * univariate. The possible return values are: * * -2 is not dense univariate * -1 is no variables * n>=0 is univariate in n * * Notes * ===== * A univariate polynomial is considered dense iff more than half of * the coefficients a_0...a_deg are non-zero. */ int poly::is_dense_univariate () const { POLY_GETIDENTITY(*this); int num_terms=0, res=-1; // test univariate for (int i=1; i 0) { if (res == -1) res = j; if (res != j) return -2; } num_terms++; } // constant polynomial if (res == -1) return -1; // test density int deg = terms[2+res]; if (2*num_terms < deg+1) return -2; return res; } /* #] is_dense_univariate : #[ simple_poly (small) : */ // returns the polynomial (x-a)^b mod p^n with a small const poly poly::simple_poly (PHEAD int x, int a, int b, int p, int n) { poly tmp(BHEAD 0,p,n); int idx=1; tmp[idx++] = 3 + AN.poly_num_vars; // length for (int i=0; i>=1; } return res; } /* #] simple_poly (small) : #[ simple_poly (large) : */ // returns the polynomial (x-a)^b mod p^n with a large const poly poly::simple_poly (PHEAD int x, const poly &a, int b, int p, int n) { poly res(BHEAD 1,p,n); poly tmp(BHEAD 0,p,n); int idx=1; tmp[idx++] = 3 + AN.poly_num_vars; // length for (int i=0; i>=1; } return res; } /* #] simple_poly (large) : #[ get_variables : */ // gets all variables in the expressions and stores them in AN.poly_vars // (it is assumed that AN.poly_vars=NULL) void poly::get_variables (PHEAD const vector &es, bool with_arghead, bool sort_vars) { assert(AN.poly_vars == NULL); AN.poly_num_vars = 0; vector vars; vector degrees; map var_to_idx; // extract all variables for (int ei=0; ei<(int)es.size(); ei++) { const WORD *e = es[ei]; // fast notation if (*e == -SNUMBER) { } else if (*e == -SYMBOL) { if (!var_to_idx.count(e[1])) { vars.push_back(e[1]); var_to_idx[e[1]] = AN.poly_num_vars++; degrees.push_back(1); } } // JD: Here we need to check for non-symbol/number terms in fast notation. else if (*e < 0) { MLOCK(ErrorMessageLock); MesPrint ((char*)"ERROR: polynomials and polyratfuns must contain symbols only"); MUNLOCK(ErrorMessageLock); Terminate(1); } else { for (int i=with_arghead ? ARGHEAD : 0; with_arghead ? i (size_t)(AM.MaxTer) ) { // This can happen only in expressions with excessively many variables. AN.poly_vars = (WORD *)Malloc1((AN.poly_num_vars+1)*sizeof(WORD), "AN.poly_vars"); AN.poly_vars_type = 1; } else { AN.poly_vars = TermMalloc("AN.poly_vars"); AN.poly_vars_type = 0; } for (int i=0; i var_to_idx; for (int i=0; isecond] = 1; res[2+AN.poly_num_vars] = 1; res[3+AN.poly_num_vars] = 1; return res; } // find LCM of denominators of all terms WORD nden=1, npro=0, ngcd=0, ndum=0; UWORD *den = NumberMalloc("poly::argument_to_poly"); UWORD *pro = NumberMalloc("poly::argument_to_poly"); UWORD *gcd = NumberMalloc("poly::argument_to_poly"); UWORD *dum = NumberMalloc("poly::argument_to_poly"); den[0]=1; for (int i=with_arghead ? ARGHEAD : 0; with_arghead ? i0 && coe[ncoe-1]==0) ncoe--; MulLong(den,nden,coe,ncoe,pro,&npro); GcdLong(BHEAD den,nden,coe,ncoe,gcd,&ngcd); DivLong(pro,npro,gcd,ngcd,den,&nden,dum,&ndum); } if (denpoly!=NULL) *denpoly = poly(BHEAD den, nden); int ri=1; // ordinary notation for (int i=with_arghead ? ARGHEAD : 0; with_arghead ? isecond] = e[j+1]; // powers ri += res[ri]; // length } res[0] = ri; // JD: For univariate cases, check whether the ordering is correct or not. // There are various ways to arrive here, but with an incorrect ordering, such // as interactions with collect, moving a polyratfun out of another function // argument, etc. // If the ordering is not correct, make sure we normalize. In multivariate cases, // always normalize as before. if (sort_univar == false && AN.poly_num_vars == 1) { if (res.number_of_terms() >= 2) { if(res[2] < res.last_monomial()[2]) { sort_univar = true; } } } if (sort_univar || AN.poly_num_vars>1) { res.normalize(); } NumberFree(den,"poly::argument_to_poly"); NumberFree(pro,"poly::argument_to_poly"); NumberFree(gcd,"poly::argument_to_poly"); NumberFree(dum,"poly::argument_to_poly"); return res; } /* #] argument_to_poly : #[ poly_to_argument : */ // converts a polynomial class "poly" to a form expression void poly::poly_to_argument (const poly &a, WORD *res, bool with_arghead) { POLY_GETIDENTITY(a); // special case: a=0 if (a[0]==1) { if (with_arghead) { res[0] = -SNUMBER; res[1] = 0; } else { res[0] = 0; } return; } if (with_arghead) { res[1] = AN.poly_num_vars>1 ? DIRTYFLAG : 0; // dirty flag for (int i=2; i 0) { if (first) { first=false; res[L+1] = 1; // symbols res[L+2] = 2; // length } res[L+1+res[L+2]++] = AN.poly_vars[j]; // symbol res[L+1+res[L+2]++] = a[i+1+j]; // power } if (!first) res[L] += res[L+2]; // fix length WORD nc = a[i+a[i]-1]; WCOPY(&res[L+res[L]], &a[i+a[i]-1-ABS(nc)], ABS(nc)); // numerator res[L] += ABS(nc); // fix length memset(&res[L+res[L]], 0, ABS(nc)*sizeof(WORD)); // denominator one res[L+res[L]] = 1; // denominator one res[L] += ABS(nc); // fix length res[L+res[L]] = SGN(nc) * (2*ABS(nc)+1); // length of coefficient res[L]++; // fix length L += res[L]; // fix length } if (with_arghead) { res[0] = L; // convert to fast notation if possible ToFast(res,res); } else { res[L] = 0; } } /* #] poly_to_argument : #[ poly_to_argument_with_den : */ // converts a polynomial class "poly" divided by a number (nden, den) to a form expression // cf. poly::poly_to_argument() void poly::poly_to_argument_with_den (const poly &a, WORD nden, const UWORD *den, WORD *res, bool with_arghead) { POLY_GETIDENTITY(a); // special case: a=0 if (a[0]==1) { if (with_arghead) { res[0] = -SNUMBER; res[1] = 0; } else { res[0] = 0; } return; } if (with_arghead) { res[1] = AN.poly_num_vars>1 ? DIRTYFLAG : 0; // dirty flag for (int i=2; i 0) { if (first) { first=false; res[L+1] = 1; // symbols res[L+2] = 2; // length } res[L+1+res[L+2]++] = AN.poly_vars[j]; // symbol res[L+1+res[L+2]++] = a[i+1+j]; // power } if (!first) res[L] += res[L+2]; // fix length // numerator WORD nc = a[i+a[i]-1]; WCOPY(&res[L+res[L]], &a[i+a[i]-1-ABS(nc)], ABS(nc)); // denominator nden1 = nden; WCOPY(den1, den, ABS(nden)); if (nden != 1 || den[0] != 1) { // remove gcd(num,den) Simplify(BHEAD (UWORD *)&res[L+res[L]], &nc, den1, &nden1); } Pack((UWORD *)&res[L+res[L]], &nc, den1, nden1); // format res[L] += 2*ABS(nc)+1; // fix length res[L+res[L]-1] = SGN(nc)*(2*ABS(nc)+1); // length of coefficient L += res[L]; // fix length } NumberFree(den1, "poly_to_argument_with_den"); if (with_arghead) { res[0] = L; // convert to fast notation if possible ToFast(res,res); } else { res[L] = 0; } } /* #] poly_to_argument_with_den : #[ size_of_form_notation : */ // the size of the polynomial in form notation (without argheads and fast notation) int poly::size_of_form_notation () const { POLY_GETIDENTITY(*this); // special case: a=0 if (terms[0]==1) return 0; int len = 0; for (int i=1; i!=terms[0]; i+=terms[i]) { len++; int npow = 0; for (int j=0; j 0) npow++; if (npow > 0) len += 2*npow + 2; len += 2 * ABS(terms[i+terms[i]-1]) + 1; } return len; } /* #] size_of_form_notation : #[ size_of_form_notation_with_den : */ // the size of the polynomial divided by a number (its size is given by nden) // in form notation (without argheads and fast notation) // cf. poly::size_of_form_notation() int poly::size_of_form_notation_with_den (WORD nden) const { POLY_GETIDENTITY(*this); // special case: a=0 if (terms[0]==1) return 0; nden = ABS(nden); int len = 0; for (int i=1; i!=terms[0]; i+=terms[i]) { len++; int npow = 0; for (int j=0; j 0) npow++; if (npow > 0) len += 2*npow + 2; len += 2 * MaX(ABS(terms[i+terms[i]-1]), nden) + 1; } return len; } /* #] size_of_form_notation_with_den : #[ to_coefficient_list : */ // returns the coefficient list of a univariate polynomial const vector poly::to_coefficient_list (const poly &a) { POLY_GETIDENTITY(a); if (a.is_zero()) return vector(); int x = a.first_variable(); if (x == AN.poly_num_vars) x=0; vector res(1+a[2+x],0); for (int i=1; i poly::coefficient_list_divmod (const vector &a, const vector &b, WORD p, int divmod) { int bsize = (int)b.size(); while (b[bsize-1]==0) bsize--; WORD inv; GetModInverses(b[bsize-1] + (b[bsize-1]<0?p:0), p, &inv, NULL); vector q(a.size(),0); vector r(a); while ((int)r.size() >= bsize) { LONG mul = ((LONG)inv * r.back()) % p; int off = r.size()-bsize; q[off] = mul; for (int i=0; i0 && r.back()==0) r.pop_back(); } if (divmod==0) { while (q.size()>0 && q.back()==0) q.pop_back(); return q; } else { while (r.size()>0 && r.back()==0) r.pop_back(); return r; } } /* #] coefficient_list_divmod : #[ from_coefficient_list : */ // converts a coefficient list to a "poly" const poly poly::from_coefficient_list (PHEAD const vector &a, int x, WORD p) { poly res(BHEAD 0); int ri=1; for (int i=(int)a.size()-1; i>=0; i--) if (a[i] != 0) { res.check_memory(ri); res[ri] = AN.poly_num_vars+3; // length for (int j=0; j&2; \ exit 1;; \ esac; \ has_opt=no; \ sane_makeflags=$$MAKEFLAGS; \ if $(am__is_gnu_make); then \ sane_makeflags=$$MFLAGS; \ else \ case $$MAKEFLAGS in \ *\\[\ \ ]*) \ bs=\\; \ sane_makeflags=`printf '%s\n' "$$MAKEFLAGS" \ | sed "s/$$bs$$bs[$$bs $$bs ]*//g"`;; \ esac; \ fi; \ skip_next=no; \ strip_trailopt () \ { \ flg=`printf '%s\n' "$$flg" | sed "s/$$1.*$$//"`; \ }; \ for flg in $$sane_makeflags; do \ test $$skip_next = yes && { skip_next=no; continue; }; \ case $$flg in \ *=*|--*) continue;; \ -*I) strip_trailopt 'I'; skip_next=yes;; \ -*I?*) strip_trailopt 'I';; \ -*O) strip_trailopt 'O'; skip_next=yes;; \ -*O?*) strip_trailopt 'O';; \ -*l) strip_trailopt 'l'; skip_next=yes;; \ -*l?*) strip_trailopt 'l';; \ -[dEDm]) skip_next=yes;; \ -[JT]) skip_next=yes;; \ esac; \ case $$flg in \ 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maintainer-clean-am -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/form-gzclose.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/form-gzlib.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/form-gzread.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/form-gzwrite.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/form-zstd_zlibwrapper.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parform-gzclose.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parform-gzlib.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parform-gzread.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parform-gzwrite.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parform-zstd_zlibwrapper.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parvorm-gzclose.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parvorm-gzlib.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parvorm-gzread.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parvorm-gzwrite.Po -rm -f ../extern/zstd/zlibWrapper/$(DEPDIR)/parvorm-zstd_zlibwrapper.Po -rm -f 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mostlyclean-compile mostlyclean-generic pdf: pdf-am pdf-am: ps: ps-am ps-am: uninstall-am: uninstall-binPROGRAMS .MAKE: install-am install-strip .PHONY: CTAGS GTAGS TAGS all all-am am--depfiles check check-am clean \ clean-binPROGRAMS clean-generic cscopelist-am ctags ctags-am \ dist-hook distclean distclean-compile distclean-generic \ distclean-tags distdir dvi dvi-am html html-am info info-am \ install install-am install-binPROGRAMS install-data \ install-data-am install-dvi install-dvi-am install-exec \ install-exec-am install-html install-html-am install-info \ install-info-am install-man install-pdf install-pdf-am \ install-ps install-ps-am install-strip installcheck \ installcheck-am installdirs maintainer-clean \ maintainer-clean-generic mostlyclean mostlyclean-compile \ mostlyclean-generic pdf pdf-am ps ps-am tags tags-am uninstall \ uninstall-am uninstall-binPROGRAMS .PRECIOUS: Makefile form-startup.$(OBJEXT): version.h tform-startup.$(OBJEXT): version.h parform-startup.$(OBJEXT): version.h vorm-startup.$(OBJEXT): version.h tvorm-startup.$(OBJEXT): version.h parvorm-startup.$(OBJEXT): version.h .PHONY: update_version_h version.h: update_version_h $(UPDATE_VERSION_H) dist-hook: $(DISTHOOK_VERSION_H) # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: form-5.0.1/sources/parallel.h0000644000175100017510000002477615217035721011616 #ifndef __PARALLEL__ #define __PARALLEL__ /** @file parallel.h * * Header file with things relevant to ParForm. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ macros & definitions : */ /* * Rank of the master process. */ #define MASTER 0 /* * Selector constants for PF_RealTime(). */ #define PF_RESET 0 /* reset the timer */ #define PF_TIME 1 /* get the elapsed time */ /* * Message tags for communication during parallel execution. */ #define PF_TERM_MSGTAG 10 /* master -> slave: sending terms */ #define PF_ENDSORT_MSGTAG 11 /* master -> slave: no more terms to be distributed, slave -> master: after EndSort() */ #define PF_DOLLAR_MSGTAG 12 /* slave -> master: sending $-variables */ #define PF_BUFFER_MSGTAG 20 /* slave -> master: sending sorted terms, or in PF_SendFile()/PF_RecvFile() */ #define PF_ENDBUFFER_MSGTAG 21 /* same as PF_BUFFER_MSGTAG, but indicates the end of operation */ #define PF_READY_MSGTAG 30 /* slave -> master: slave is idle and can accept terms */ #define PF_DATA_MSGTAG 50 /* InParallel, DoCheckpoint() */ #define PF_EMPTY_MSGTAG 52 /* InParallel, DoCheckpoint(), PF_SendFile(), PF_RecvFile() */ #define PF_STDOUT_MSGTAG 60 /* slave -> master: sending text to the stdout */ #define PF_LOG_MSGTAG 61 /* slave -> master: sending text to the log file */ #define PF_OPT_MCTS_MSGTAG 70 /* master <-> slave: optimization */ #define PF_OPT_HORNER_MSGTAG 71 /* master <-> slave: optimization */ #define PF_OPT_COLLECT_MSGTAG 72 /* slave -> master: optimization */ #define PF_RUNTIME_ERROR_MSGTAG 80 /* slave <-> master: runtime error */ #define PF_RUNTIME_SYNC_MSGTAG 81 /* master <-> slave: sync after EndSort() */ #define PF_MISC_MSGTAG 100 /* * A macro for checking the version of gcc. */ #if defined(__GNUC__) && defined(__GNUC_MINOR__) && defined(__GNUC_PATCHLEVEL__) # define GNUC_PREREQ(major, minor, patchlevel) \ ((__GNUC__ << 16) + (__GNUC_MINOR__ << 8) + __GNUC_PATCHLEVEL__ >= \ ((major) << 16) + ((minor) << 8) + (patchlevel)) #else # define GNUC_PREREQ(major, minor, patchlevel) 0 #endif /* * The macro "indices" defined in variable.h collides with some function * argument names in the MPI-3.0 standard. */ #undef indices /* Avoid messy padding warnings which may appear in mpi.h. */ #if GNUC_PREREQ(4, 6, 0) # pragma GCC diagnostic push # pragma GCC diagnostic ignored "-Wpadded" # pragma GCC diagnostic ignored "-Wunused-parameter" #endif #if defined(__clang__) && defined(__has_warning) # pragma clang diagnostic push # if __has_warning("-Wpadded") # pragma clang diagnostic ignored "-Wpadded" # endif # if __has_warning("-Wunused-parameter") # pragma clang diagnostic ignored "-Wunused-parameter" # endif #endif # ifdef __cplusplus /* * form3.h (which includes parallel.h) is included from newpoly.h as * extern "C" { * #include "form3.h" * } * On the other hand, C++ interfaces to MPI are defined in mpi.h if it is * included from C++ sources. We first leave from the C-linkage, include * mpi.h, and then go back to the C-linkage. * (TU 7 Jun 2011) */ } # define OMPI_SKIP_MPICXX 1 # include extern "C" { # else # define OMPI_SKIP_MPICXX 1 # include # endif /* Now redefine "indices" in the same way as in variable.h. */ #define indices ((INDICES)(AC.IndexList.lijst)) /* Restore the warning settings. */ #if GNUC_PREREQ(4, 6, 0) # pragma GCC diagnostic pop #endif #if defined(__clang__) && defined(__has_warning) # pragma clang diagnostic pop #endif # define PF_ANY_SOURCE MPI_ANY_SOURCE # define PF_ANY_MSGTAG MPI_ANY_TAG # define PF_COMM MPI_COMM_WORLD # define PF_BYTE MPI_BYTE # define PF_INT MPI_INT #if BITSINWORD == 32 # define PF_WORD MPI_INT32_T # define PF_LONG MPI_INT64_T #elif BITSINWORD == 16 # define PF_WORD MPI_INT16_T # define PF_LONG MPI_INT32_T #else # error Can not detect if this is a 32-bit or 64-bit platform. #endif /* #] macros & definitions : #[ s/r-bufs : */ /** * A struct for nonblocking, unbuffered send of the sorted terms in the * PObuffers back to the master using several "rotating" PObuffers. */ typedef struct { WORD **buff; WORD **fill; WORD **full; WORD **stop; MPI_Status *status; MPI_Status *retstat; MPI_Request *request; MPI_Datatype *type; /* this is needed in PF_Wait for Get_count */ int *index; /* dummies for returnvalues */ int *tag; /* for the version with blocking send/receives */ int *from; int numbufs; /* number of cyclic buffers */ int active; /* flag telling which buffer is active */ } PF_BUFFER; /* #] s/r-bufs : #[ global variables used by the PF_functions : need to be known everywhere */ typedef struct ParallelVars { FILEHANDLE slavebuf; /* (slave) allocated if there are RHS expressions */ /* special buffers for nonblocking, unbuffered send/receives */ PF_BUFFER *sbuf; /* set of cyclic send buffers for master _and_ slave */ PF_BUFFER **rbufs; /* array of sets of cyclic receive buffers for master */ int me; /* Internal number of task: master is 0 */ int numtasks; /* total number of tasks */ int parallel; /* flags telling the master and slaves to do the sorting parallel */ /* [05nov2003 mt] This flag must be set to 0 in iniModule! */ int rhsInParallel; /* flag for parallel executing even if there are RHS expressions */ int mkSlaveInfile; /* flag tells that slavebuf is used on the slaves */ int exprbufsize; /* buffer size in WORDs to be used for transferring expressions */ int exprtodo; /* >= 0: the expression to do in InParallel, -1: otherwise */ int log; /* flag for logging mode */ int notMyFault; /* flag for termination due to another process's runtime error */ WORD numsbufs; /* number of cyclic send buffers (PF.sbuf->numbufs) */ WORD numrbufs; /* number of cyclic receive buffers (PF.rbufs[i]->numbufs, i=1,...numtasks-1) */ } PARALLELVARS; extern PARALLELVARS PF; /*[04oct2005 mt]:*/ /*for broadcasting dollarvars, see parallel.c:PF_BroadcastPreDollar():*/ extern LONG PF_maxDollarChunkSize; /*:[04oct2005 mt]*/ /* #] global variables used by the PF_functions : #[ Function prototypes : */ /* mpi.c */ extern int PF_ISendSbuf(int,int); extern int PF_Bcast(void *buffer, int count); extern int PF_Reduce(const void *sendbuf, void *recvbuf, int count, MPI_Datatype type, MPI_Op op, int root); extern int PF_RawSend(int,void *,LONG,int); extern LONG PF_RawRecv(int *,void *,LONG,int *); extern int PF_PreparePack(void); extern int PF_Pack(const void *buffer, size_t count, MPI_Datatype type); extern int PF_Unpack(void *buffer, size_t count, MPI_Datatype type); extern int PF_PackString(const UBYTE *str); extern int PF_UnpackString(UBYTE *str); extern int PF_Send(int to, int tag); extern int PF_Receive(int src, int tag, int *psrc, int *ptag); extern int PF_Broadcast(void); extern int PF_PrepareLongSinglePack(void); extern int PF_LongSinglePack(const void *buffer, size_t count, MPI_Datatype type); extern int PF_LongSingleUnpack(void *buffer, size_t count, MPI_Datatype type); extern int PF_LongSingleSend(int to, int tag); extern int PF_LongSingleReceive(int src, int tag, int *psrc, int *ptag); extern int PF_PrepareLongMultiPack(void); extern int PF_LongMultiPackImpl(const void *buffer, size_t count, size_t eSize, MPI_Datatype type); extern int PF_LongMultiUnpackImpl(void *buffer, size_t count, size_t eSize, MPI_Datatype type); extern int PF_LongMultiBroadcast(void); static inline size_t sizeof_datatype(MPI_Datatype type) { if ( type == PF_BYTE ) return sizeof(char); if ( type == PF_INT ) return sizeof(int); if ( type == PF_WORD ) return sizeof(WORD); if ( type == PF_LONG ) return sizeof(LONG); return(0); } #define PF_LongMultiPack(buffer, count, type) PF_LongMultiPackImpl(buffer, count, sizeof_datatype(type), type) #define PF_LongMultiUnpack(buffer, count, type) PF_LongMultiUnpackImpl(buffer, count, sizeof_datatype(type), type) /* parallel.c */ extern int PF_EndSort(void); extern WORD PF_Deferred(WORD *,WORD); extern int PF_Processor(EXPRESSIONS,WORD,WORD); extern int PF_Init(int*,char ***); extern void PF_PreTerminate(int errorcode); extern int PF_Terminate(int); extern LONG PF_GetSlaveTimes(void); extern LONG PF_BroadcastNumber(LONG); extern void PF_BroadcastBuffer(WORD **buffer, LONG *length); extern int PF_BroadcastString(UBYTE *); extern int PF_BroadcastPreDollar(WORD **, LONG *,int *); extern int PF_CollectModifiedDollars(void); extern int PF_BroadcastModifiedDollars(void); extern int PF_BroadcastRedefinedPreVars(void); extern int PF_BroadcastCBuf(int bufnum); extern int PF_BroadcastExpFlags(void); extern int PF_StoreInsideInfo(void); extern int PF_RestoreInsideInfo(void); extern int PF_BroadcastExpr(EXPRESSIONS e, FILEHANDLE *file); extern int PF_BroadcastRHS(void); extern int PF_InParallelProcessor(void); extern int PF_SendFile(int to, FILE *fd); extern int PF_RecvFile(int from, FILE *fd); extern void PF_MLock(void); extern void PF_MUnlock(void); extern LONG PF_WriteFileToFile(int,UBYTE *,LONG); extern void PF_FlushStdOutBuffer(void); extern void PF_ReceiveRuntimeError(void) NORETURN; /* #] Function prototypes : */ #endif form-5.0.1/sources/mpidbg.h0000644000175100017510000005707515217035721011262 #ifndef MPIDBG_H #define MPIDBG_H /** @file mpidbg.h * * MPI APIs with the logging feature. * NOTE: This file needs C99. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : */ #include #include #include #include #if defined(MPIDEBUGGING_DELAY_US) && MPIDEBUGGING_DELAY_US > 0 #include // for usleep() #endif #define MPIDBG_LINESIZE 1024 #define MPIDBG_BUFSIZE 128 /* #] Includes : #[ Utilities : #[ MPIDBG_RANK : */ static inline int MPIDBG_Get_rank(void) { return PF.me; /* Assume we are working with ParFORM. */ } #define MPIDBG_RANK MPIDBG_Get_rank() /* #] MPIDBG_RANK : #[ MPIDBG_Out : */ static inline void MPIDBG_Out(const char *file, int line, const char *func, const char *fmt, ...) { char buf[MPIDBG_LINESIZE]; va_list ap; va_start(ap, fmt); snprintf(buf,MPIDBG_LINESIZE, "*** [%d] %10s %4d @ %-16s: ", MPIDBG_RANK, file, line, func); vsnprintf(buf + strlen(buf),MPIDBG_LINESIZE-strlen(buf), fmt, ap); va_end(ap); /* Assume fprintf with a line will work well even in multi-processes. */ fprintf(stderr, "%s\n", buf); } #define MPIDBG_Out(...) MPIDBG_Out(file, line, func, __VA_ARGS__) /* #] MPIDBG_Out : #[ MPIDBG_insert_delay : */ static inline void MPIDBG_insert_delay(void) { #if defined(MPIDEBUGGING_DELAY_US) && MPIDEBUGGING_DELAY_US > 0 usleep(MPIDEBUGGING_DELAY_US); #endif } /* #] MPIDBG_insert_delay : #[ MPIDBG_sprint_requests : */ static inline void MPIDBG_sprint_requests(char *buf, int count, const MPI_Request *requests) { /* Assume sprintf never fail and returns >= 0... */ buf += sprintf(buf, "("); int i, first = 1; for ( i = 0; i < count; i++ ) { if ( first ) { first = 0; } else { buf += sprintf(buf, ","); } if ( requests[i] != MPI_REQUEST_NULL ) { buf += sprintf(buf, "%d", i); } else { buf += sprintf(buf, "*"); } } buf += sprintf(buf, ")"); } /* #] MPIDBG_sprint_requests : #[ MPIDBG_sprint_statuses : */ static inline void MPIDBG_sprint_statuses(char *buf, int count, const MPI_Request *old_requests, const MPI_Request *new_requests, const MPI_Status *statuses) { /* Assume sprintf never fail and returns >= 0... */ buf += sprintf(buf, "("); int i, first = 1; for ( i = 0; i < count; i++ ) { if ( first ) { first = 0; } else { buf += sprintf(buf, ","); } if ( old_requests[i] != MPI_REQUEST_NULL && new_requests[i] == MPI_REQUEST_NULL ) { int ret_size = 0; MPI_Get_count((MPI_Status *)&statuses[i], MPI_BYTE, &ret_size); buf += sprintf(buf, "(source=%d,tag=%d,size=%d)", statuses[i].MPI_SOURCE, statuses[i].MPI_TAG, ret_size); } else { buf += sprintf(buf, "*"); } } buf += sprintf(buf, ")"); } /* #] MPIDBG_sprint_statuses : #] Utilities : #[ MPI APIs : */ /* * The followings are the MPI APIs with the logging. */ #define MPIDBG_EXTARG const char *file, int line, const char *func /* #[ MPI_Init : */ static inline int MPIDBG_Init(int* argc, char*** argv, MPIDBG_EXTARG) { int ret = MPI_Init(argc, argv); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Init: OK"); } else { MPIDBG_Out("MPI_Init: Failed"); } return ret; } #define MPI_Init(...) MPIDBG_Init(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Init : #[ MPI_Finalize : */ static inline int MPIDBG_Finalize(MPIDBG_EXTARG) { MPIDBG_Out("MPI_Finalize"); int ret = MPI_Finalize(); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Finalize: OK"); } else { MPIDBG_Out("MPI_Finalize: Failed"); } return ret; } #define MPI_Finalize() MPIDBG_Finalize(__FILE__, __LINE__, __func__) /* #] MPI_Finalize : #[ MPI_Send : */ static inline int MPIDBG_Send(void *buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Send: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Send(buf, count, datatype, dest, tag, comm); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Send: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Send: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Send(...) MPIDBG_Send(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Send : #[ MPI_Recv : */ static inline int MPIDBG_Recv(void* buf, int count, MPI_Datatype datatype, int source, int tag, MPI_Comm comm, MPI_Status *status, MPIDBG_EXTARG) { MPI_Status st; if ( status == MPI_STATUS_IGNORE ) status = &st; MPIDBG_Out("MPI_Recv: src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); int ret = MPI_Recv(buf, count, datatype, source, tag, comm, status); if ( ret == MPI_SUCCESS ) { int ret_count = 0; MPI_Get_count(status, datatype, &ret_count); MPIDBG_Out("MPI_Recv: OK src=%d dest=%d tag=%d count=%d", status->MPI_SOURCE, MPIDBG_RANK, status->MPI_TAG, ret_count); } else { MPIDBG_Out("MPI_Recv: Failed src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); } return ret; } #define MPI_Recv(...) MPIDBG_Recv(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Recv : #[ MPI_Bsend : */ static inline int MPIDBG_Bsend(void* buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Bsend: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Bsend(buf, count, datatype, dest, tag, comm); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Bsend: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Bsend: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Bsend(...) MPIDBG_Bsend(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Bsend : #[ MPI_Ssend : */ static inline int MPIDBG_Ssend(void* buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Ssend: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Ssend(buf, count, datatype, dest, tag, comm); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Ssend: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Ssend: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Ssend(...) MPIDBG_Ssend(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Ssend : #[ MPI_Rsend : */ static inline int MPIDBG_Rsend(void* buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Rsend: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Rsend(buf, count, datatype, dest, tag, comm); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Rsend: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Rsend: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Rsend(...) MPIDBG_Rsend(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Rsend : #[ MPI_Isend : */ static inline int MPIDBG_Isend(const void* buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPI_Request *request, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Isend: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Isend(buf, count, datatype, dest, tag, comm, request); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Isend: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Isend: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Isend(...) MPIDBG_Isend(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Isend : #[ MPI_Ibsend : */ static inline int MPIDBG_Ibsend(void* buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPI_Request *request, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Ibsend: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Ibsend(buf, count, datatype, dest, tag, comm, request); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Ibsend: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Ibsend: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Ibsend(...) MPIDBG_Ibsend(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Ibsend : #[ MPI_Issend : */ static inline int MPIDBG_Issend(void* buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPI_Request *request, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Issend: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Issend(buf, count, datatype, dest, tag, comm, request); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Issend: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Issend: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Issend(...) MPIDBG_Issend(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Issend : #[ MPI_Irsend : */ static inline int MPIDBG_Irsend(void* buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm, MPI_Request *request, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Irsend: src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); int ret = MPI_Irsend(buf, count, datatype, dest, tag, comm, request); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Irsend: OK src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } else { MPIDBG_Out("MPI_Irsend: Failed src=%d dest=%d tag=%d count=%d", MPIDBG_RANK, dest, tag, count); } return ret; } #define MPI_Irsend(...) MPIDBG_Irsend(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Irsend : #[ MPI_Irecv : */ static inline int MPIDBG_Irecv(void* buf, int count, MPI_Datatype datatype, int source, int tag, MPI_Comm comm, MPI_Request *request, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Irecv: src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); int ret = MPI_Irecv(buf, count, datatype, source, tag, comm, request); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Irecv: OK src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); } else { MPIDBG_Out("MPI_Irecv: Failed src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); } return ret; } #define MPI_Irecv(...) MPIDBG_Irecv(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Irecv : #[ MPI_Wait : */ static inline int MPIDBG_Wait(MPI_Request *request, MPI_Status *status, MPIDBG_EXTARG) { MPI_Status st; if ( status == MPI_STATUS_IGNORE ) status = &st; char buf1[MPIDBG_BUFSIZE * 1], buf2[MPIDBG_BUFSIZE * 1]; MPI_Request old_request = *request; MPIDBG_sprint_requests(buf1, 1, request); MPIDBG_Out("MPI_Wait: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Wait(request, status); if ( ret == MPI_SUCCESS ) { MPIDBG_sprint_statuses(buf2, 1, request, &old_request, status); MPIDBG_Out("MPI_Wait: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Wait: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Wait(...) MPIDBG_Wait(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Wait : #[ MPI_Test : */ static inline int MPIDBG_Test(MPI_Request *request, int *flag, MPI_Status *status, MPIDBG_EXTARG) { MPI_Status st; if ( status == MPI_STATUS_IGNORE ) status = &st; char buf1[MPIDBG_BUFSIZE * 1], buf2[MPIDBG_BUFSIZE * 1]; MPI_Request old_request = *request; MPIDBG_sprint_requests(buf1, 1, request); MPIDBG_Out("MPI_Test: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Test(request, flag, status); if ( ret == MPI_SUCCESS ) { if ( *flag ) { MPIDBG_sprint_statuses(buf2, 1, request, &old_request, status); MPIDBG_Out("MPI_Test: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Test: OK rank=%d request=%s flag=false", MPIDBG_RANK, buf1); } } else { MPIDBG_Out("MPI_Test: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Test(...) MPIDBG_Test(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Test : #[ MPI_Waitany : */ static inline int MPIDBG_Waitany(int count, MPI_Request *array_of_requests, int *index, MPI_Status *status, MPIDBG_EXTARG) { MPI_Status st; if ( status == MPI_STATUS_IGNORE ) status = &st; char buf1[MPIDBG_BUFSIZE * 1], buf2[MPIDBG_BUFSIZE * 1]; MPI_Request old_requests[count]; memcpy(old_requests, array_of_requests, sizeof(MPI_Request) * count); MPIDBG_sprint_requests(buf1, count, array_of_requests); MPIDBG_Out("MPI_Waitany: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Waitany(count, array_of_requests, index, status); if ( ret == MPI_SUCCESS ) { MPI_Status statuses[count]; statuses[*index] = *status; MPIDBG_sprint_statuses(buf2, count, old_requests, array_of_requests, statuses); MPIDBG_Out("MPI_Waitany: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Waitany: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Waitany(...) MPIDBG_Waitany(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Waitany : #[ MPI_Testany : */ static inline int MPIDBG_Testany(int count, MPI_Request *array_of_requests, int *index, int *flag, MPI_Status *status, MPIDBG_EXTARG) { MPI_Status st; if ( status == MPI_STATUS_IGNORE ) status = &st; char buf1[MPIDBG_BUFSIZE * 1], buf2[MPIDBG_BUFSIZE * 1]; MPI_Request old_requests[count]; memcpy(old_requests, array_of_requests, sizeof(MPI_Request) * count); MPIDBG_sprint_requests(buf1, count, array_of_requests); MPIDBG_Out("MPI_Testany: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Testany(count, array_of_requests, index, flag, status); if ( ret == MPI_SUCCESS ) { if ( *flag ) { MPI_Status statuses[count]; statuses[*index] = *status; MPIDBG_sprint_statuses(buf2, count, old_requests, array_of_requests, statuses); MPIDBG_Out("MPI_Testany: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Testany: OK rank=%d request=%s flag=false", MPIDBG_RANK, buf1); } } else { MPIDBG_Out("MPI_Testany: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Testany(...) MPIDBG_Testany(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Testany : #[ MPI_Waitall : */ static inline int MPIDBG_Waitall(int count, MPI_Request *array_of_requests, MPI_Status *array_of_statuses, MPIDBG_EXTARG) { MPI_Status st[count]; if ( array_of_statuses == MPI_STATUSES_IGNORE ) array_of_statuses = st; char buf1[MPIDBG_BUFSIZE * count], buf2[MPIDBG_BUFSIZE * count]; MPI_Request old_requests[count]; memcpy(old_requests, array_of_requests, sizeof(MPI_Request) * count); MPIDBG_sprint_requests(buf1, count, array_of_requests); MPIDBG_Out("MPI_Waitall: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Waitall(count, array_of_requests, array_of_statuses); if ( ret == MPI_SUCCESS ) { MPIDBG_sprint_statuses(buf2, count, old_requests, array_of_requests, array_of_statuses); MPIDBG_Out("MPI_Waitall: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Waitall: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Waitall(...) MPIDBG_Waitall(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Waitall : #[ MPI_Testall : */ static inline int MPIDBG_Testall(int count, MPI_Request *array_of_requests, int *flag, MPI_Status *array_of_statuses, MPIDBG_EXTARG) { MPI_Status st[count]; if ( array_of_statuses == MPI_STATUSES_IGNORE ) array_of_statuses = st; char buf1[MPIDBG_BUFSIZE * count], buf2[MPIDBG_BUFSIZE * count]; MPI_Request old_requests[count]; memcpy(old_requests, array_of_requests, sizeof(MPI_Request) * count); MPIDBG_sprint_requests(buf1, count, array_of_requests); MPIDBG_Out("MPI_Testall: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Testall(count, array_of_requests, flag, array_of_statuses); if ( ret == MPI_SUCCESS ) { if ( *flag ) { MPIDBG_sprint_statuses(buf2, count, old_requests, array_of_requests, array_of_statuses); MPIDBG_Out("MPI_Testall: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Testall: OK rank=%d request=%s flag=false", MPIDBG_RANK, buf1); } } else { MPIDBG_Out("MPI_Testall: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Testall(...) MPIDBG_Testall(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Testall : #[ MPI_Waitsome : */ static inline int MPIDBG_Waitsome(int incount, MPI_Request *array_of_requests, int *outcount, int *array_of_indices, MPI_Status *array_of_statuses, MPIDBG_EXTARG) { MPI_Status st[incount]; if ( array_of_statuses == MPI_STATUSES_IGNORE ) array_of_statuses = st; char buf1[MPIDBG_BUFSIZE * incount], buf2[MPIDBG_BUFSIZE * incount]; MPI_Request old_requests[incount]; memcpy(old_requests, array_of_requests, sizeof(MPI_Request) * incount); MPIDBG_sprint_requests(buf1, incount, array_of_requests); MPIDBG_Out("MPI_Waitsome: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Waitsome(incount, array_of_requests, outcount, array_of_indices, array_of_statuses); if ( ret == MPI_SUCCESS ) { MPIDBG_sprint_statuses(buf2, incount, old_requests, array_of_requests, array_of_statuses); MPIDBG_Out("MPI_Waitsome: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Waitsome: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Waitsome(...) MPIDBG_Waitsome(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Waitsome : #[ MPI_Testsome : */ static inline int MPIDBG_Testsome(int incount, MPI_Request *array_of_requests, int *outcount, int *array_of_indices, MPI_Status *array_of_statuses, MPIDBG_EXTARG) { MPI_Status st[incount]; if ( array_of_statuses == MPI_STATUSES_IGNORE ) array_of_statuses = st; char buf1[MPIDBG_BUFSIZE * incount], buf2[MPIDBG_BUFSIZE * incount]; MPI_Request old_requests[incount]; memcpy(old_requests, array_of_requests, sizeof(MPI_Request) * incount); MPIDBG_sprint_requests(buf1, incount, array_of_requests); MPIDBG_Out("MPI_Testsome: rank=%d request=%s", MPIDBG_RANK, buf1); int ret = MPI_Testsome(incount, array_of_requests, outcount, array_of_indices, array_of_statuses); if ( ret == MPI_SUCCESS ) { MPIDBG_sprint_statuses(buf2, incount, old_requests, array_of_requests, array_of_statuses); MPIDBG_Out("MPI_Testsome: OK rank=%d request=%s result=%s", MPIDBG_RANK, buf1, buf2); } else { MPIDBG_Out("MPI_Testsome: Failed rank=%d request=%s", MPIDBG_RANK, buf1); } return ret; } #define MPI_Testsome(...) MPIDBG_Testsome(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Testsome : #[ MPI_Iprobe : */ static inline int MPIDBG_Iprobe(int source, int tag, MPI_Comm comm, int *flag, MPI_Status *status, MPIDBG_EXTARG) { MPI_Status st; if ( status == MPI_STATUS_IGNORE ) status = &st; MPIDBG_Out("MPI_Iprobe: src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); MPIDBG_insert_delay(); int ret = MPI_Iprobe(source, tag, comm, flag, status); if ( ret == MPI_SUCCESS ) { if ( *flag ) { int ret_size = 0; MPI_Get_count(status, MPI_BYTE, &ret_size); MPIDBG_Out("MPI_Iprobe: OK src=%d dest=%d tag=%d size=%d", status->MPI_SOURCE, MPIDBG_RANK, status->MPI_TAG, ret_size); } else { MPIDBG_Out("MPI_Iprobe: OK src=%d dest=%d tag=%d flag=false", source, MPIDBG_RANK, tag); } } else { MPIDBG_Out("MPI_Iprobe: Failed src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); } return ret; } #define MPI_Iprobe(...) MPIDBG_Iprobe(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Iprobe : #[ MPI_Probe : */ static inline int MPIDBG_Probe(int source, int tag, MPI_Comm comm, MPI_Status *status, MPIDBG_EXTARG) { MPI_Status st; if ( status == MPI_STATUS_IGNORE ) status = &st; MPIDBG_Out("MPI_Probe: src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); int ret = MPI_Probe(source, tag, comm, status); if ( ret == MPI_SUCCESS ) { int ret_size = 0; MPI_Get_count(status, MPI_BYTE, &ret_size); MPIDBG_Out("MPI_Probe: OK src=%d dest=%d tag=%d size=%d", status->MPI_SOURCE, MPIDBG_RANK, status->MPI_TAG, ret_size); } else { MPIDBG_Out("MPI_Probe: Failed src=%d dest=%d tag=%d", source, MPIDBG_RANK, tag); } return ret; } #define MPI_Probe(...) MPIDBG_Probe(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Probe : #[ MPI_Cancel : */ static inline int MPIDBG_Cancel(MPI_Request *request, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Cancel", MPIDBG_RANK); int ret = MPI_Cancel(request); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Cancel: OK"); } else { MPIDBG_Out("MPI_Cancel: Failed"); } return ret; } #define MPI_Cancel(...) MPIDBG_Cancel(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Cancel : #[ MPI_Test_cancelled : */ static inline int MPIDBG_Test_cancelled(MPI_Status *status, int *flag, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Test_cancelled", MPIDBG_RANK); int ret = MPI_Test_cancelled(status, flag); if ( ret == MPI_SUCCESS ) { if ( *flag ) { MPIDBG_Out("MPI_Test_cancelled: OK flag=true"); } else { MPIDBG_Out("MPI_Test_cancelled: OK flag=false"); } } else { MPIDBG_Out("MPI_Test_cancelled: Failed"); } return ret; } #define MPI_Test_cancelled(...) MPIDBG_Test_cancelled(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Test_cancelled : #[ MPI_Barrier : */ static inline int MPIDBG_Barrier(MPI_Comm comm, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Barrier"); int ret = MPI_Barrier(comm); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Barrier: OK"); } else { MPIDBG_Out("MPI_Barrier: Failed"); } return ret; } #define MPI_Barrier(...) MPIDBG_Barrier(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Barrier : #[ MPI_Bcast : */ static inline int MPIDBG_Bcast(void* buffer, int count, MPI_Datatype datatype, int root, MPI_Comm comm, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Bcast: root=%d count=%d", root, count); int ret = MPI_Bcast(buffer, count, datatype, root, comm); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Bcast: OK root=%d count=%d", root, count); } else { MPIDBG_Out("MPI_Bcast: Failed root=%d count=%d", root, count); } return ret; } #define MPI_Bcast(...) MPIDBG_Bcast(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Bcast : #[ MPI_Reduce : */ static inline int MPIDBG_Reduce(const void *sendbuf, void *recvbuf, int count, MPI_Datatype datatype, MPI_Op op, int root, MPI_Comm comm, MPIDBG_EXTARG) { MPIDBG_Out("MPI_Reduce: root=%d count=%d", root, count); int ret = MPI_Reduce(sendbuf, recvbuf, count, datatype, op, root, comm); if ( ret == MPI_SUCCESS ) { MPIDBG_Out("MPI_Reduce: OK root=%d count=%d", root, count); } else { MPIDBG_Out("MPI_Reduce: Failed root=%d count=%d", root, count); } return ret; } #define MPI_Reduce(...) MPIDBG_Reduce(__VA_ARGS__, __FILE__, __LINE__, __func__) /* #] MPI_Reduce : #] MPI APIs : */ #endif /* MPIDBG_H */ form-5.0.1/sources/variable.h0000644000175100017510000001160615217035721011573 #ifndef __VARIABLE__ #define __VARIABLE__ /** @file variable.h * * Contains a number of defines to make the coding easier. * Especially the defines for the use of the lists are very nice. * And of course the AC for A.Cc and AT for either A.T of B->T * are indispensable to keep FORM and TFORM in one set of sources. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /*See the file extcmd.c*/ #ifdef REMOVEDBY_MT extern int (*writeBufToExtChannel)(char *buf, size_t n); extern int (*getcFromExtChannel)(); extern int (*setTerminatorForExternalChannel)(char *newterminator); #endif extern WRITEBUFTOEXTCHANNEL writeBufToExtChannel; extern GETCFROMEXTCHANNEL getcFromExtChannel; extern SETTERMINATORFOREXTERNALCHANNEL setTerminatorForExternalChannel; extern SETKILLMODEFOREXTERNALCHANNEL setKillModeForExternalChannel; /* extern LONG (*WriteFile)(int handle, UBYTE *buffer, LONG number); */ extern WRITEFILE WriteFile; /*:[17nov2005 mt]*/ extern ALLGLOBALS A; #ifdef WITHPTHREADS extern ALLPRIVATES **AB; #endif extern FIXEDGLOBALS FG; extern FIXEDSET fixedsets[]; extern char *setupfilename; EXTERNLOCK(ErrorMessageLock) EXTERNLOCK(FileReadLock) EXTERNLOCK(dummylock) #ifdef VMS #include extern FILE **FileStructs; #endif #define chartype FG.cTable #define Procedures ((PROCEDURE *)(AP.ProcList.lijst)) #define NumProcedures AP.ProcList.num #define MaxProcedures AP.ProcList.maxnum #define DoLoops ((DOLOOP *)(AP.LoopList.lijst)) #define NumDoLoops AP.LoopList.num #define MaxDoLoops AP.LoopList.maxnum #define PreVar ((PREVAR *)(AP.PreVarList.lijst)) #define NumPre AP.PreVarList.num #define MaxNumPre AP.PreVarList.maxnum #define SetElements ((WORD *)(AC.SetElementList.lijst)) #define Sets ((SETS)(AC.SetList.lijst)) #define functions ((FUNCTIONS)(AC.FunctionList.lijst)) #define indices ((INDICES)(AC.IndexList.lijst)) #define symbols ((SYMBOLS)(AC.SymbolList.lijst)) #define vectors ((VECTORS)(AC.VectorList.lijst)) #define tablebases ((DBASE *)(AC.TableBaseList.lijst)) #define NumFunctions AC.FunctionList.num #define NumIndices AC.IndexList.num #define NumSymbols AC.SymbolList.num #define NumVectors AC.VectorList.num #define NumSets AC.SetList.num #define NumSetElements AC.SetElementList.num #define NumTableBases AC.TableBaseList.num #define GlobalFunctions AC.FunctionList.numglobal #define GlobalIndices AC.IndexList.numglobal #define GlobalSymbols AC.SymbolList.numglobal #define GlobalVectors AC.VectorList.numglobal #define GlobalSets AC.SetList.numglobal #define GlobalSetElements AC.SetElementList.numglobal #define cbuf ((CBUF *)(AC.cbufList.lijst)) #define channels ((CHANNEL *)(AC.ChannelList.lijst)) #define NumOutputChannels AC.ChannelList.num #define Dollars ((DOLLARS)(AP.DollarList.lijst)) #define NumDollars AP.DollarList.num #define Dubious ((DUBIOUSV)(AC.DubiousList.lijst)) #define NumDubious AC.DubiousList.num #define Expressions ((EXPRESSIONS)(AC.ExpressionList.lijst)) #define NumExpressions AC.ExpressionList.num #define autofunctions ((FUNCTIONS)(AC.AutoFunctionList.lijst)) #define autoindices ((INDICES)(AC.AutoIndexList.lijst)) #define autosymbols ((SYMBOLS)(AC.AutoSymbolList.lijst)) #define autovectors ((VECTORS)(AC.AutoVectorList.lijst)) #define xsymbol (cbuf[AM.sbufnum].rhs) #define numxsymbol (cbuf[AM.sbufnum].numrhs) #define PotModdollars ((WORD *)(AC.PotModDolList.lijst)) #define NumPotModdollars AC.PotModDolList.num #define ModOptdollars ((MODOPTDOLLAR *)(AC.ModOptDolList.lijst)) #define NumModOptdollars AC.ModOptDolList.num #define BUG A.bug; #ifdef WITHPTHREADS #define AC A.Cc #define AM A.M #define AO A.O #define AP A.P #define AS A.S #define AX A.X #define AN B->N #define AR B->R #define AT B->T #define AN0 B0->N #define AR0 B0->R #define AT0 B0->T #else #define AC A.Cc #define AM A.M #define AN A.N #define AO A.O #define AP A.P #define AR A.R #define AS A.S #define AT A.T #define AX A.X #endif #endif form-5.0.1/sources/unixfile.c0000644000175100017510000001151115217035721011617 /** @file unixfile.c * * The interface to a fast variety of file routines in the unix system. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Includes : File with direct interface to the UNIX functions. This makes a big difference in speed! */ #include "form3.h" /*[13jul2005 mt]:*/ #ifdef SAFESIGNAL /*[15oct2004 mt]:*/ /*To access errno variable and EINTR constant:*/ #include /*:[15oct2004 mt]*/ #endif /*:[13jul2005 mt]*/ #ifdef UFILES FILES TheStdout = { 1 }; FILES *Ustdout = &TheStdout; #ifdef GPP extern "C" open(); extern "C" close(); extern "C" read(); extern "C" write(); extern "C" lseek(); #endif /* #] Includes : #[ Uopen : */ FILES *Uopen(char *filename, char *mode) { FILES *f = (FILES *)Malloc1(sizeof(FILES),"Uopen"); int flags = 0, rights = 0644; while ( *mode ) { if ( *mode == 'r' ) { flags |= O_RDONLY; } else if ( *mode == 'w' ) { flags |= O_CREAT | O_TRUNC; } else if ( *mode == 'a' ) { flags |= O_APPEND; } else if ( *mode == 'b' ) { } else if ( *mode == '+' ) { flags |= O_RDWR; } mode++; } f->descriptor = open(filename,flags,rights); if ( f->descriptor >= 0 ) return(f); if ( ( flags & O_APPEND ) != 0 ) { flags |= O_CREAT; f->descriptor = open(filename,flags,rights); if ( f->descriptor >= 0 ) return(f); } M_free(f,"Uopen"); return(0); } /* #] Uopen : #[ Uclose : */ int Uclose(FILES *f) { int retval; if ( f ) { retval = close(f->descriptor); M_free(f,"Uclose"); return(retval); } return(EOF); } /* #] Uclose : #[ Uread : */ size_t Uread(char *ptr, size_t size, size_t nobj, FILES *f) { /*[13jul2005 mt]:*/ #ifdef SAFESIGNAL /*[15oct2004 mt]:*/ /*Operation read() can be interrupted by a signal. Note, this is rather unlikely, so we do not save size*nobj for future attempts*/ size_t ret; /*If the syscall is interrupted by a signal before it succeeded in getting any progress, it must be repeated:*/ while( ( (ret=read(f->descriptor,ptr,size*nobj))<1)&&(errno == EINTR) ); return(ret); #else #ifdef DEEPDEBUG { POSITION pos; SETBASEPOSITION(pos,lseek(f->descriptor,0L,SEEK_CUR)); MesPrint("handle %d: reading %ld bytes from position %p\n",f->descriptor,size*nobj,pos); } #endif return(read(f->descriptor,ptr,size*nobj)); #endif /*:[15oct2004 mt]*/ /*:[13jul2005 mt]*/ } /* #] Uread : #[ Uwrite : */ size_t Uwrite(char *ptr, size_t size, size_t nobj, FILES *f) { /*[13jul2005 mt]:*/ #ifdef SAFESIGNAL /*[15oct2004 mt]:*/ /*Operation write() can be interrupted by a signal. */ size_t ret; size_t thesize=size*nobj; /*If the syscall is interrupted by a signal before it succeeded in getting any progress, it must be repeated:*/ while( ( (ret=write(f->descriptor,ptr,thesize))<1 )&&(errno == EINTR) ); return(ret); #else #ifdef DEEPDEBUG { POSITION pos; SETBASEPOSITION(pos,lseek(f->descriptor,0L,SEEK_CUR)); MesPrint("handle %d: writing %ld bytes to position %p\n",f->descriptor,size*nobj,pos); } #endif return(write(f->descriptor,ptr,size*nobj)); /*:[15oct2004 mt]*/ #endif /*:[13jul2005 mt]*/ } /* #] Uwrite : #[ Useek : */ int Useek(FILES *f, off_t offset, int origin) { if ( f && ( lseek(f->descriptor,offset,origin) >= 0 ) ) return(0); return(-1); } /* #] Useek : #[ Utell : */ off_t Utell(FILES *f) { if ( f ) return((off_t)lseek(f->descriptor,0L,SEEK_CUR)); else return(-1); } /* #] Utell : #[ Uflush : */ void Uflush(FILES *f) { DUMMYUSE(f); } /* #] Uflush : #[ Ugetpos : */ int Ugetpos(FILES *f, fpos_t *ptr) { DUMMYUSE(f); DUMMYUSE(ptr); return(-1); } /* #] Ugetpos : #[ Usetpos : */ int Usetpos(FILES *f,fpos_t *ptr) { DUMMYUSE(f); DUMMYUSE(ptr); return(-1); } /* #] Usetpos : #[ Usetbuf : */ void Usetbuf(FILES *f, char *ptr) { DUMMYUSE(f); DUMMYUSE(ptr); } /* #] Usetbuf : */ #endif form-5.0.1/sources/model.c0000644000175100017510000003060415217035721011100 /** @file model.c * * Implementation of "Model", required by the diagrams_ function. */ /* #[ License : */ /* * Copyright (C) 1984-2026 J.A.M. Vermaseren * When using this file you are requested to refer to the publication * J.A.M.Vermaseren "New features of FORM" math-ph/0010025 * This is considered a matter of courtesy as the development was paid * for by FOM the Dutch physics granting agency and we would like to * be able to track its scientific use to convince FOM of its value * for the community. * * This file is part of FORM. * * FORM is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * FORM is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with FORM. If not, see . */ /* #] License : */ /* #[ Explanations : This is a second generation much simplified version of model.c Syntax: Model QED; Particle electron,positron,-2; Particle photon,+3; Vertex electron,positron,photon: g; EndModel; or: Model QCD; Particle quark,antiquark,-2; Particle ghost,antighost,-1; Particle gluon,+3; Vertex quark,antiquark,gluon: g; Vertex qhost,antighost,gluon: g; Vertex gluon,gluon,gluon: g; Vertex gluon,gluon,gluon,gluon: g^2; EndModel; Remarks: 1: if no second particle is given, a particle and its antiparticle are the same 2: Spin statistics is by dimension of SU(2) representation with a sign. 3: In a vertex we need to mention the coupling constants. 4: Internally a particle gives a vertex with only two lines. 5: All particles must have been declared before any vertex. The diagrams should be provided as a collection of nodes and edges with momenta with a direction substituted. The other parameters (like Lorentz indices, color indices etc.) can then be provided in a procedure that should go with this mode definition. In principle the edges are not needed if there are no 'insertions', but because we would like to have the insertions as well we need the edges. #] Explanations : #[ Includes : model.c */ #include "form3.h" /* #] Includes : #[ CreateVertex : */ VERTEX *CreateVertex(MODEL *m) { VERTEX *v, **new; WORD newsize; int i; if ( m->invertices >= m->sizevertices ) { if ( m->sizevertices == 0 ) newsize = 20; else newsize = 2*m->sizevertices; new = (VERTEX **)Malloc1(newsize*sizeof(VERTEX *),"m->vertices"); for ( i = 0; i < m->sizevertices; i++ ) new[i] = m->vertices[i]; if ( m->sizevertices > 0 ) M_free(m->vertices,"m->vertices"); m->vertices = new; m->sizevertices = newsize; } v = (VERTEX *)Malloc1(sizeof(VERTEX),"VERTEX"); m->vertices[m->invertices++] = v; v->nparticles = 0; v->ncouplings = 0; v->type = 0; v->error = 0; v->externonly = 0; v->spare = 0; return(v); } /* #] CreateVertex : #[ ReadParticle : */ UBYTE *ReadParticle(UBYTE *s, VERTEX *v, MODEL *m, int par) { UBYTE *name, c; PARTICLE *p = v->particles + v->nparticles++; WORD type, funnum; int i, j; SKIPBLANKS(s) name = s; s = SkipName(s); c = *s; *s = 0; if ( GetVar(name,&type,&funnum,CFUNCTION,NOAUTO) == NAMENOTFOUND ) { p->number = AddFunction(name,0,VERTEXFUNCTION,0,0,0,-1,-1) + FUNCTION; } else if ( par == 1 && type == CFUNCTION && functions[funnum].spec == VERTEXFUNCTION ) { p->number = funnum+FUNCTION; } else if ( par == 0 && type == CFUNCTION && functions[funnum].spec == VERTEXFUNCTION ) { /* We should check whether this particle exists already in this model. If so, this will be an error. */ for ( i = 0; i < m->nparticles-1; i++ ) { for ( j = 0; j < m->vertices[i]->nparticles; j++ ) { if ( m->vertices[i]->particles[j].number == funnum ) { MesPrint("&Illegal attempt to redefine a particle in the same model: %s",name); v->error = 1; } } } p->number = funnum+FUNCTION; } else { MesPrint("&Name of particle previously declared as another variable: %s",name); v->error = 1; } *s = c; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; return(s); } /* #] ReadParticle : #[ CoModel : */ int CoModel(UBYTE *s) { UBYTE *name, c; MODEL *m = (MODEL *)Malloc1(sizeof(MODEL),"Model"); WORD numberofset, *e; SETS set; SKIPBLANKS(s) AC.ModelLevel++; int i; /* We now have to add the model to the list of models. */ if ( AC.modelspace == 0 || AC.nummodels >= AC.modelspace ) { int newspace = 2*AC.modelspace+2, i; MODEL **models = (MODEL **)Malloc1((sizeof(MODEL *))*newspace,"AC.models"); for ( i = 0; i < AC.modelspace; i++ ) models[i] = AC.models[i]; if ( AC.models ) M_free(AC.models,"AC.models"); AC.modelspace = newspace; AC.models = models; } AC.models[AC.nummodels++] = m; m->vertices = 0; m->couplings = 0; m->nparticles = m->nvertices = m->sizevertices = m->invertices = 0; m->sizecouplings = 0; m->error = 0; m->grccmodel = NULL; name = s; if ( FG.cTable[*s] == 0 ) { while ( FG.cTable[*s] <= 1 ) s++; c = *s; *s = 0; m->name = strDup1(name,"Model name"); *s = c; SKIPBLANKS(s) if ( *s != 0 ) { MesPrint("&Illegal option in model statement: %s",s); return(1); } } else { m->name = strDup1((UBYTE *)"---","Model name"); m->error = 1; MesPrint("&Illegal name for model: %s",name); return(1); } /* Now make it a set with one element. The type of the set is rather special */ if ( GetName(AC.varnames,m->name,&numberofset,NOAUTO) != NAMENOTFOUND ) { MesPrint("&Name conflict with name %s of model",m->name); return(1); } numberofset = AddSet(name,0); set = Sets + numberofset; set->type = CMODEL; e = (WORD *)FromVarList(&AC.SetElementList); *e = AC.nummodels-1; set->last++; AC.SetList.numtemp = AC.SetList.num; AC.SetElementList.numtemp = AC.SetElementList.num; for ( i = 0; i <= MAXLEGS; i++ ) m->legcouple[i] = 0; m->legcouple[2] = 1; return(0); } /* #] CoModel : #[ CoParticle : */ int CoParticle(UBYTE *s) { MODEL *m; VERTEX *v; int i; if ( AC.nummodels <= 0 ) { MesPrint("&No open model for particle statement"); return(1); } m = AC.models[AC.nummodels-1]; if ( m->nvertices > 0 ) { MesPrint("&In a model description Particle statements should be before Vertex statements."); m->error = 1; return(1); } v = CreateVertex(m); m->nparticles++; s = ReadParticle(s,v,m,0); v->particles[0].type = 1; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; if ( v->error == 0 ) { if ( FG.cTable[*s] == 0 ) { s = ReadParticle(s,v,m,0); v->particles[1].type = -1; if ( v->particles[0].number == v->particles[1].number ) { v->particles[0].type = 0; v->particles[1].type = 0; } } else { /* Particle = antiparticle */ v->particles[1] = v->particles[0]; v->nparticles++; v->particles[0].type = 0; v->particles[1].type = 0; } } if ( v->error == 0 && ( *s == '+' || *s == '-' ) ) { int x = 0, sign = ( *s == '-' ) ? -1: 1; s++; while ( FG.cTable[*s] == 1 ) { x = 10*x + *s++ - '0'; } if ( x == 0 ) { v->error = 1; MesPrint("&Spin goes by dimension of SU(2) representation. Zero is not allowed."); } else { v->particles[0].spin = v->particles[1].spin = sign*x; } SKIPBLANKS(s) } else if ( v->error == 0 ) { v->particles[0].spin = v->particles[1].spin = 1; v->particles[0].type = 0; v->particles[1].type = 0; } /* Here will come future options */ while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; while ( v->error == 0 && *s != 0 && FG.cTable[*s] == 0 ) { UBYTE *opt = s, c; while ( FG.cTable[*s] == 0 ) s++; c = *s; *s = 0; if ( StrICont(opt,(UBYTE *)"external") == 0 ) { v->externonly = 1; } else { MesPrint("&Unrecognized option %s in particle statement.",opt); v->error = 1; } *s = c; while ( *s == ',' || *s == ' ' || *s == '\t' ) s++; } /* The couplings array will be used for registering in what kind of vertices the particle is involved. (example: in QCD the quarks only in 2 and 3-point vertices) */ for ( i = 0; i < MAXPARTICLES; i++ ) v->couplings[i] = 0; v->couplings[2] = 1; return(v->error); } /* #] CoParticle : #[ CoVertex : */ int CoVertex(UBYTE *s) { UBYTE *ss, *name, c; WORD type; MODEL *m; VERTEX *v; if ( AC.ModelLevel <= 0 ) { MesPrint("&No open model for vertex statement"); return(1); } m = AC.models[AC.nummodels-1]; /* Get an object of type VERTEX */ v = CreateVertex(m); m->nvertices++; SKIPBLANKS(s); while ( *s && *s != ':' ) { if ( v->error == 0 ) { s = ReadParticle(s,v,m,1); if ( v->error ) m->error = 1; } else { while ( *s && *s != ':' ) { if ( *s == '[' ) { SKIPBRA1(s) } else if ( *s == '(' ) { SKIPBRA3(s) } else if ( *s == 0 ) { v->error = 1; MesPrint("&No coupling constant in vertex statement."); break; } } break; } } if ( v->error == 0 ) { if ( *s == ':' ) { /* read symbols and powers */ s++; SKIPBLANKS(s); while ( *s ) { if ( v->ncouplings >= 2*MAXCOUPLINGS ) { MesPrint("&More than %d coupling constants in vertex.",(WORD)MAXCOUPLINGS); MesPrint(" Recompile with a larger value for MAXCOUPLINGS."); return(1); } ss = s; s = SkipName(s); c = *s; *s = 0; name = ConstructName(ss,0); // Forbid couplings which have no symbol or an overal numerical factor. if ( *name == 0 ) { v->error = 1; MesPrint("&Invalid coupling constant in vertex statement."); } if ( GetVar(name,&type,&v->couplings[v->ncouplings],CSYMBOL,WITHAUTO) == NAMENOTFOUND ) { WORD minpow = -MAXPOWER; WORD maxpow = MAXPOWER; WORD cplx = 0, dim = 0; v->couplings[v->ncouplings] = AddSymbol(name,minpow,maxpow,cplx,dim); } *s = c; v->ncouplings++; /* Now possibly a power */ if ( *s == '^' ) { /* we need an integer */ WORD x = 0; WORD sign = 1; s++; while ( *s == '-' || *s == '+' ) { if ( *s == '-' ) sign = -sign; s++; } if ( sign == -1 ) { v->error = 1; MesPrint("&Invalid negative power of coupling constant."); } while ( FG.cTable[*s] == 1 ) x = 10*x + *s++ - '0'; v->couplings[v->ncouplings++] = x; } else { v->couplings[v->ncouplings++] = 1; } SKIPBLANKS(s); if ( *s == '*' ) { s++; continue; } if ( *s != ',' ) break; s++; SKIPBLANKS(s); } } else { v->error = 1; MesPrint("&A vertex statement needs at least one coupling constant."); } } if ( v->error == 0 ) { /* Register which types of vertices are possible for each particle. */ int i, j; for ( i = 0; i < v->nparticles; i++ ) { for ( j = 0; j < m->nparticles; j++ ) { if ( m->vertices[j]->particles[0].number == v->particles[i].number ) break; if ( m->vertices[j]->particles[1].number == v->particles[i].number ) break; } m->vertices[j]->couplings[v->nparticles] = 1; } } return(v->error); } /* #] CoVertex : #[ CoEndModel : */ int CoEndModel(UBYTE *s) { int i, j, k, kk; WORD csize = 0, *newcouplings, newsize; MODEL *m; VERTEX *v; if ( AC.ModelLevel <= 0 ) { MesPrint("&EndModel statement without matching Model statement"); return(1); } m = AC.models[AC.nummodels-1]; /* Now create a list of all coupling constants. Note that we do not expect an astronomical number of them and hence we use a simple insertion algorithm. */ m->ncouplings = 0; for ( i = 0; i < m->nvertices; i++ ) { v = m->vertices[i+m->nparticles]; m->legcouple[v->nparticles] = 1; if ( m->ncouplings + v->ncouplings > csize ) { if ( csize == 0 ) newsize = v->ncouplings + 10; else newsize = 2*csize; newcouplings = (WORD *)Malloc1(newsize*sizeof(WORD),"m->couplings"); for ( k = 0; k < m->ncouplings; k++ ) newcouplings[k] = m->couplings[k]; if ( csize > 0 ) M_free(m->couplings,"m->couplings"); m->couplings = newcouplings; csize = newsize; } for ( j = 0; j < v->ncouplings; j += 2 ) { WORD sym = v->couplings[j]; for ( k = 0; k < m->ncouplings; k++ ) { if ( sym == m->couplings[k] ) break; if ( sym < m->couplings[k] ) { for ( kk = m->ncouplings; kk > k; k-- ) m->couplings[kk] = m->couplings[kk-1]; m->couplings[k] = sym; m->ncouplings++; break; } } if ( k >= m->ncouplings ) m->couplings[m->ncouplings++] = sym; } } AC.ModelLevel--; DUMMYUSE(s) return(LoadModel(m)); } /* #] CoEndModel : */ form-5.0.1/INSTALL0000644000175100017510000001634215217035721007205 Overview ======== FORM uses the GNU autoconf tools to configure and install. In principle, the three-step invocation ./configure make make install should be enough to configure, compile, and install FORM with default settings into the default path "/usr/bin". Nevertheless, you are strongly advised to carefully read the following sections in order to prevent common mistakes and to be able to choose the best configuration settings for your system. Prerequisites ============= In case you need to (re-)generate the script "configure" (see next section), you have to have the GNU autoconf/automake programs installed on your system. You should have at least autoconf version >= 2.69 and automake version >= 1.11. For generating the configure script from a GIT repository, you also need Git. To compile the sources you need reasonably modern C and C++ compilers, like for example the GNU compiler collection (GCC) or the Intel C compiler. The facilities in FORM for external communication need a POSIX compliant C library, like the GNU glibc. The threaded version of FORM needs a Posix compliant implementation of threads (pthreads). The parallel version ParFORM needs an MPI implementation. The automated test suite of FORM requires Ruby version >= 2.0 and the testing framework "test/unit". For the latter, you may need to install test-unit gem separately. The manual needs a LaTeX installation with the commands "latex" and "dvips" or "pdflatex" available. For the html format the command "htlatex" is needed. The source code documentation needs Doxygen, at least in version 1.3. As a default, FORM tries to use the GMP and MPFR libraries for fast numerics, the zlib and Zstandard (zstd) libraries for fast compression, and the FLINT library for fast polynomial arithmetic. If any of these libraries is not available, the corresponding feature will be deactivated. GMP should be at least version 4.2, zlib should be at least 1.2 and FLINT should be version 3.2 or higher. To use arbitrary precision floating-point arithmetic in FORM, both GMP and MPFR are required; if either is not available, this feature will not be enabled. Preparations ============ If you have acquired the FORM sources via GIT, several files will be missing, especially the script "configure". To generate these files you have to issue the command autoreconf -i If you have downloaded and extracted the tar-file distribution, these files are already there and the above step is not necessary. But in case you experience problems related to the GNU autoconf files, it can be a good idea to recreate all these files with the command "autoreconf", maybe with the option "-f" to force a recreation. Configuration ============= Running ./configure will check your system and activate the available default settings. The chosen configuration will be printed at the end of the running. To change the default installation path use the "--prefix" option: ./configure --prefix= The FORM executables will then be installed into the directory "/bin". As a default, the sequential version (form) and the threaded version (tform) of FORM will be selected for compilation. To prevent a flavor from being build, use one of the following options: ./configure --disable-scalar ./configure --disable-threaded If you want to build the parallel version ParFORM, then add the option: ./configure --enable-parform If you want to build the debugging versions of these flavors, then add the option: ./configure --enable-debug Use one of the following options ./configure --without-gmp ./configure --without-zlib ./configure --without-mpfr ./configure --without-zstd ./configure --without-flint to prevent FORM from using one of these libraries. The executable will not be linked against this library then and the functionality will be provided by internal code. Usually, you don't need to care about these options. If you want to build without arbitrary-precision floating-point arithmetic, configure with: ./configure --disable-float This disables the float feature. On Linux systems with "eu-addr2line" or "addr2line" available, it is strongly recommended to enable backtracing to help diagnose internal errors. To compile with backtrace support, configure with: ./configure --enable-backtrace Note that in some cases (but not most!) this may incur a potential small ~1% performance penalty. The option ./configure --disable-largefile forces FORM not to use large file support, i.e. to use _FILE_OFFSET_BITS==32 and thereby restrict files to be less than 4GB in size on 32bit machines. Usually, you don't need to care about this option. To choose a compiler that is different from the one "configure" automatically determines, you can set the environment variables "CC" and "CXX" on the command line: ./configure CC=icc CXX=icpc CFLAGS=-Werror CXXFLAGS=-Werror The above example shows also how to set additional compiler flags. The detailed compiler/linker options for the release versions and the debugging versions can be specified by the environment variables COMPILEFLAGS LINKFLAGS DEBUGCOMPILEFLAGS DEBUGLINKFLAGS If they are not set, they will be chosen for the local machine where you are compiling executables. If you would like to enable additional optimizations specific to the machine on which you are compiling FORM, use the following option. Note that the resulting binary may not run on CPUs with a different feature set. ./configure --enable-native The configure script creates a file "config.h" in which several options and settings are passed on to the source code files via preprocessor definitions. For short-term adjustments you can alter these settings manually, but beware that they will be overwritten the next time "configure" runs. Finally, the option "--help" shows the available options together with a short explanation: ./configure --help Compilation =========== Issue the command make to build all activated FORM flavors (form, tform, ...). The compilation will result in the executables sitting in the sources directory of the distribution. To compile only a specific flavor of FORM, name it as a parameter: make form make tform make vorm make tvorm make parform make parvorm Additional flags for the compiler or linker can be given at the command line, for example: make vorm CFLAGS=-O1 CXXFLAGS=-O1 To cleanup the distribution directory, the command make clean can be used. Testing ======= If Ruby version >= 2.0 and "test/unit" are installed on your system, the configure script enables the automated test suite. Then you can run it by make check Documentation ============= You need to change into the directory "doc" to build the documentation. There you can choose to run one of the commands make dvi make ps make pdf make html to build all documentation in the specified format. If you want to build only the manual or the source code documentation, you need to change directory into "doc/manual" or "doc/doxygen" before you issue the make commands. Installation ============ With the command make install the compiled executables will be copied into the configured path ("/usr/bin" as the default). Troubleshooting =============== No troubles to be shot, yet. form-5.0.1/config.h.in0000644000175100017510000001025515217035732010176 /* config.h.in. Generated from configure.ac by autoheader. */ /* Define to print a stack trace on Terminate. */ #undef ENABLE_BACKTRACE /* Define to 1 if you have the header file. */ #undef HAVE_BOOST_UNORDERED_MAP_HPP /* Define to 1 if you have the header file. */ #undef HAVE_BOOST_UNORDERED_SET_HPP /* Define to 1 if you have __builtin_popcount function. */ #undef HAVE_BUILTIN_POPCOUNT /* Define to 1 if you have clock_gettime. */ #undef HAVE_CLOCK_GETTIME /* Define to 1 if you have the header file. */ #undef HAVE_EXECINFO_H /* Define to 1 if you have the header file. */ #undef HAVE_FCNTL_H /* Define to 1 if you have ftime. */ #undef HAVE_FTIME /* Define to 1 if you have gettimeofday. */ #undef HAVE_GETTIMEOFDAY /* Define to 1 if you have the header file. */ #undef HAVE_INTTYPES_H /* Define to 1 if you have the header file. */ #undef HAVE_LIMITS_H /* Define to 1 if you have __popcnt function. */ #undef HAVE_POPCNT /* Define to 1 if you have the header file. */ #undef HAVE_STDINT_H /* Define to 1 if you have the header file. */ #undef HAVE_STDIO_H /* Define to 1 if you have the header file. */ #undef HAVE_STDLIB_H /* Define to 1 if you have the header file. */ #undef HAVE_STRINGS_H /* Define to 1 if you have the header file. */ #undef HAVE_STRING_H /* Define to 1 if you have the header file. */ #undef HAVE_SYS_FILE_H /* Define to 1 if you have the header file. */ #undef HAVE_SYS_STAT_H /* Define to 1 if you have the header file. */ #undef HAVE_SYS_TIME_H /* Define to 1 if you have the header file. */ #undef HAVE_SYS_TYPES_H /* Define to 1 if you have the header file. */ #undef HAVE_TR1_UNORDERED_MAP /* Define to 1 if you have the header file. */ #undef HAVE_TR1_UNORDERED_SET /* Define to 1 if you have the header file. */ #undef HAVE_UNISTD_H /* Define to 1 if you have the header file. */ #undef HAVE_UNORDERED_MAP /* Define to 1 if you have the header file. */ #undef HAVE_UNORDERED_SET /* Define to 1 if you have the header file. */ #undef HAVE_WINDOWS_H /* Compiling for a Linux system. */ #undef LINUX /* The "noreturn" function attribute. */ #undef NORETURN /* Name of package */ #undef PACKAGE /* Define to the address where bug reports for this package should be sent. */ #undef PACKAGE_BUGREPORT /* Define to the full name of this package. */ #undef PACKAGE_NAME /* Define to the full name and version of this package. */ #undef PACKAGE_STRING /* Define to the one symbol short name of this package. */ #undef PACKAGE_TARNAME /* Define to the home page for this package. */ #undef PACKAGE_URL /* Define to the version of this package. */ #undef PACKAGE_VERSION /* Define to 1 if all of the C90 standard headers exist (not just the ones required in a freestanding environment). 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